LMFDB - Embedded newform 363.2.e.j.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.89856959337$
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:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.j.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.190983 + 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.190983 + 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.61803 q^{10} -1.61803 q^{12} +(-0.545085 + 1.67760i) q^{13} +(1.50000 - 1.08981i) q^{14} +(2.11803 + 1.53884i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-0.500000 - 1.53884i) q^{17} +(-0.500000 - 0.363271i) q^{18} +(4.73607 - 3.44095i) q^{19} +(1.30902 - 4.02874i) q^{20} -3.00000 q^{21} +3.47214 q^{23} +(-0.690983 + 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(0.881966 + 0.640786i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(3.61803 + 2.62866i) q^{29} +(1.30902 - 0.951057i) q^{30} +(0.881966 - 2.71441i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(2.42705 - 7.46969i) q^{35} +(1.30902 - 0.951057i) q^{36} +(-0.190983 - 0.138757i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(-0.545085 - 1.67760i) q^{39} +(-4.73607 - 3.44095i) q^{40} +(-9.66312 + 7.02067i) q^{41} +(-0.572949 + 1.76336i) q^{42} -6.23607 q^{43} -2.61803 q^{45} +(0.663119 - 2.04087i) q^{46} +(-1.30902 + 0.951057i) q^{47} +(-1.50000 - 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(0.354102 + 1.08981i) q^{50} +(1.30902 + 0.951057i) q^{51} +(-2.30902 + 1.67760i) q^{52} +(-2.97214 + 9.14729i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(-1.80902 + 5.56758i) q^{57} +(2.23607 - 1.62460i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.30902 + 4.02874i) q^{60} +(-2.42705 - 7.46969i) q^{61} +(-1.42705 - 1.03681i) q^{62} +(2.42705 - 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(0.809017 - 2.48990i) q^{68} +(-2.80902 + 2.04087i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-2.61803 - 1.90211i) q^{73} +(-0.118034 + 0.0857567i) q^{74} +(0.572949 - 1.76336i) q^{75} +9.47214 q^{76} -1.09017 q^{78} +(-2.92705 + 9.00854i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.28115 + 7.02067i) q^{82} +(-0.218847 - 0.673542i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(-3.42705 + 2.48990i) q^{85} +(-1.19098 + 3.66547i) q^{86} -4.47214 q^{87} +0.527864 q^{89} +(-0.500000 + 1.53884i) q^{90} +(-4.28115 + 3.11044i) q^{91} +(4.54508 + 3.30220i) q^{92} +(0.881966 + 2.71441i) q^{93} +(0.309017 + 0.951057i) q^{94} +(-12.3992 - 9.00854i) q^{95} +(-4.54508 + 3.30220i) q^{96} +(-4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	$ 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} + 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} - 2 q^{17} - 2 q^{18} + 10 q^{19} + 3 q^{20} - 12 q^{21} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 8 q^{26} - q^{27} + 6 q^{28} + 10 q^{29} + 3 q^{30} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} + 3 q^{36} - 3 q^{37} + 9 q^{39} - 10 q^{40} - 23 q^{41} - 9 q^{42} - 16 q^{43} - 6 q^{45} - 13 q^{46} - 3 q^{47} - 6 q^{48} - 2 q^{49} - 12 q^{50} + 3 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} - 5 q^{57} - 20 q^{59} + 3 q^{60} - 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{69} - 9 q^{70} - 27 q^{71} - 5 q^{72} - 6 q^{73} + 4 q^{74} + 9 q^{75} + 20 q^{76} + 18 q^{78} - 5 q^{79} + 9 q^{80} - q^{81} - 11 q^{82} - 21 q^{83} - 9 q^{84} - 7 q^{85} - 7 q^{86} + 20 q^{89} - 2 q^{90} + 3 q^{91} + 7 q^{92} + 8 q^{93} - q^{94} - 25 q^{95} - 7 q^{96} - 33 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - 2 * q^10 - 2 * q^12 + 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 - 2 * q^17 - 2 * q^18 + 10 * q^19 + 3 * q^20 - 12 * q^21 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 + 6 * q^28 + 10 * q^29 + 3 * q^30 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 + 3 * q^36 - 3 * q^37 + 9 * q^39 - 10 * q^40 - 23 * q^41 - 9 * q^42 - 16 * q^43 - 6 * q^45 - 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 - 12 * q^50 + 3 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^60 - 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 - 5 * q^72 - 6 * q^73 + 4 * q^74 + 9 * q^75 + 20 * q^76 + 18 * q^78 - 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 - 21 * q^83 - 9 * q^84 - 7 * q^85 - 7 * q^86 + 20 * q^89 - 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 - q^94 - 25 * q^95 - 7 * q^96 - 33 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	−0.860552	−	0.509363i	$-0.829881\pi$
$2$	0.190983	−	0.587785i	0.135045	−	0.415627i	0.995597	+	0.0937362i	$0.0298810\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−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	$-0.299067\pi$
$6$	0.190983	+	0.587785i	0.0779685	+	0.239962i
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	0.942860	−	0.333188i	$-0.108125\pi$
$7$	2.42705	+	1.76336i	0.917339	+	0.666486i	−0.0255212	+	0.999674i	$0.508125\pi$
$8$	1.80902	−	1.31433i	0.639584	−	0.464685i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−1.61803			−0.511667
$11$		0			0
$11$		0			0
$12$	−1.61803			−0.467086
$13$	−0.545085	+	1.67760i	−0.151179	+	0.465282i	−0.997754	−	0.0669881i	$-0.978661\pi$
$13$	−0.545085	+	1.67760i	−0.151179	+	0.465282i	0.846574	+	0.532270i	$0.178661\pi$
$14$	1.50000	−	1.08981i	0.400892	−	0.291265i
$15$	2.11803	+	1.53884i	0.546874	+	0.397327i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	−0.500000	−	1.53884i	−0.121268	−	0.373224i	0.871935	−	0.489622i	$-0.162865\pi$
$17$	−0.500000	−	1.53884i	−0.121268	−	0.373224i	−0.993203	+	0.116398i	$0.962865\pi$
$18$	−0.500000	−	0.363271i	−0.117851	−	0.0856239i
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$	1.30902	−	4.02874i	0.292705	−	0.900854i
$21$	−3.00000			−0.654654
$22$		0			0
$23$	3.47214			0.723990			0.361995	−	0.932180i	$-0.382096\pi$
$23$	3.47214			0.723990			0.361995	+	0.932180i	$0.382096\pi$
$24$	−0.690983	+	2.12663i	−0.141046	+	0.434096i
$25$	−1.50000	+	1.08981i	−0.300000	+	0.217963i
$26$	0.881966	+	0.640786i	0.172968	+	0.125668i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	1.50000	+	4.61653i	0.283473	+	0.872441i
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	0.870645	−	0.491912i	$-0.163702\pi$
$29$	3.61803	+	2.62866i	0.671852	+	0.488129i	−0.198793	+	0.980042i	$0.563702\pi$
$30$	1.30902	−	0.951057i	0.238993	−	0.173638i
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	−0.840084	−	0.542456i	$-0.817495\pi$
$31$	0.881966	−	2.71441i	0.158406	−	0.487523i	0.998490	+	0.0549331i	$0.0174946\pi$
$32$	5.61803			0.993137
$33$		0			0
$34$	−1.00000			−0.171499
$35$	2.42705	−	7.46969i	0.410246	−	1.26261i
$36$	1.30902	−	0.951057i	0.218169	−	0.158509i
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	0.571976	−	0.820270i	$-0.306177\pi$
$37$	−0.190983	−	0.138757i	−0.0313974	−	0.0228116i	−0.603373	+	0.797459i	$0.706177\pi$
$38$	−1.11803	−	3.44095i	−0.181369	−	0.558197i
$39$	−0.545085	−	1.67760i	−0.0872835	−	0.268631i
$40$	−4.73607	−	3.44095i	−0.748838	−	0.544063i
$41$	−9.66312	+	7.02067i	−1.50913	+	1.09644i	−0.542562	+	0.840015i	$0.682546\pi$
$41$	−9.66312	+	7.02067i	−1.50913	+	1.09644i	−0.966563	+	0.256428i	$0.917454\pi$
$42$	−0.572949	+	1.76336i	−0.0884080	+	0.272092i
$43$	−6.23607			−0.950991			−0.475496	−	0.879718i	$-0.657731\pi$
$43$	−6.23607			−0.950991			−0.475496	+	0.879718i	$0.657731\pi$
$44$		0			0
$45$	−2.61803			−0.390273
$46$	0.663119	−	2.04087i	0.0977716	−	0.300910i
$47$	−1.30902	+	0.951057i	−0.190940	+	0.138726i	−0.679148	−	0.734001i	$-0.737651\pi$
$47$	−1.30902	+	0.951057i	−0.190940	+	0.138726i	0.488208	+	0.872727i	$0.337651\pi$
$48$	−1.50000	−	1.08981i	−0.216506	−	0.157301i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	0.354102	+	1.08981i	0.0500776	+	0.154123i
$51$	1.30902	+	0.951057i	0.183299	+	0.133175i
$52$	−2.30902	+	1.67760i	−0.320203	+	0.232641i
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	0.509893	+	0.860238i	$0.329685\pi$
$53$	−2.97214	+	9.14729i	−0.408254	+	1.25648i	−0.918147	+	0.396240i	$0.870315\pi$
$54$	0.618034			0.0841038
$55$		0			0
$56$	6.70820			0.896421
$57$	−1.80902	+	5.56758i	−0.239610	+	0.737444i
$58$	2.23607	−	1.62460i	0.293610	−	0.213320i
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.108617	−	0.994084i	$-0.534642\pi$
$59$	−8.35410	−	6.06961i	−1.08761	−	0.790196i	−0.978994	+	0.203888i	$0.934642\pi$
$60$	1.30902	+	4.02874i	0.168993	+	0.520108i
$61$	−2.42705	−	7.46969i	−0.310752	−	0.956396i	−0.977468	−	0.211084i	$-0.932301\pi$
$61$	−2.42705	−	7.46969i	−0.310752	−	0.956396i	0.666716	−	0.745312i	$-0.267699\pi$
$62$	−1.42705	−	1.03681i	−0.181236	−	0.131675i
$63$	2.42705	−	1.76336i	0.305780	−	0.222162i
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	4.61803			0.572797
$66$		0			0
$67$	−9.56231			−1.16822			−0.584111	−	0.811674i	$-0.698557\pi$
$67$	−9.56231			−1.16822			−0.584111	+	0.811674i	$0.698557\pi$
$68$	0.809017	−	2.48990i	0.0981077	−	0.301945i
$69$	−2.80902	+	2.04087i	−0.338166	+	0.245692i
$70$	−3.92705	−	2.85317i	−0.469372	−	0.341019i
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	−0.999753	−	0.0222083i	$-0.992930\pi$
$71$	−1.71885	−	5.29007i	−0.203990	−	0.627815i	0.795764	−	0.605607i	$-0.207070\pi$
$72$	−0.690983	−	2.12663i	−0.0814331	−	0.250625i
$73$	−2.61803	−	1.90211i	−0.306418	−	0.222625i	0.423940	−	0.905690i	$-0.360647\pi$
$73$	−2.61803	−	1.90211i	−0.306418	−	0.222625i	−0.730358	+	0.683065i	$0.760647\pi$
$74$	−0.118034	+	0.0857567i	−0.0137212	+	0.00996902i
$75$	0.572949	−	1.76336i	0.0661585	−	0.203615i
$76$	9.47214			1.08653
$77$		0			0
$78$	−1.09017			−0.123437
$79$	−2.92705	+	9.00854i	−0.329319	+	1.01354i	0.640134	+	0.768263i	$0.278879\pi$
$79$	−2.92705	+	9.00854i	−0.329319	+	1.01354i	−0.969453	+	0.245276i	$0.921121\pi$
$80$	3.92705	−	2.85317i	0.439058	−	0.318994i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	2.28115	+	7.02067i	0.251911	+	0.775303i
$83$	−0.218847	−	0.673542i	−0.0240216	−	0.0739308i	0.938327	−	0.345749i	$-0.112375\pi$
$83$	−0.218847	−	0.673542i	−0.0240216	−	0.0739308i	−0.962349	+	0.271818i	$0.912375\pi$
$84$	−3.92705	−	2.85317i	−0.428476	−	0.311306i
$85$	−3.42705	+	2.48990i	−0.371716	+	0.270067i
$86$	−1.19098	+	3.66547i	−0.128427	+	0.395258i
$87$	−4.47214			−0.479463
$88$		0			0
$89$	0.527864			0.0559535			0.0279767	−	0.999609i	$-0.491094\pi$
$89$	0.527864			0.0559535			0.0279767	+	0.999609i	$0.491094\pi$
$90$	−0.500000	+	1.53884i	−0.0527046	+	0.162208i
$91$	−4.28115	+	3.11044i	−0.448787	+	0.326063i
$92$	4.54508	+	3.30220i	0.473858	+	0.344278i
$93$	0.881966	+	2.71441i	0.0914556	+	0.281471i
$94$	0.309017	+	0.951057i	0.0318727	+	0.0980940i
$95$	−12.3992	−	9.00854i	−1.27213	−	0.924256i
$96$	−4.54508	+	3.30220i	−0.463881	+	0.337029i
$97$	−4.33688	+	13.3475i	−0.440344	+	1.35524i	0.447167	+	0.894451i	$0.352433\pi$
$97$	−4.33688	+	13.3475i	−0.440344	+	1.35524i	−0.887510	+	0.460788i	$0.847567\pi$
$98$	1.23607			0.124862
$99$		0			0
$100$	−3.00000			−0.300000
$101$	0.927051	−	2.85317i	0.0922450	−	0.283901i	−0.894281	−	0.447506i	$-0.852312\pi$
$101$	0.927051	−	2.85317i	0.0922450	−	0.283901i	0.986526	+	0.163605i	$0.0523123\pi$
$102$	0.809017	−	0.587785i	0.0801046	−	0.0581994i
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	0.800663	−	0.599115i	$-0.204481\pi$
$103$	4.85410	+	3.52671i	0.478289	+	0.347497i	−0.322374	+	0.946612i	$0.604481\pi$
$104$	1.21885	+	3.75123i	0.119518	+	0.367838i
$105$	2.42705	+	7.46969i	0.236856	+	0.728968i
$106$	4.80902	+	3.49396i	0.467093	+	0.339363i
$107$	−3.42705	+	2.48990i	−0.331306	+	0.240708i	−0.740984	−	0.671522i	$-0.765641\pi$
$107$	−3.42705	+	2.48990i	−0.331306	+	0.240708i	0.409679	+	0.912230i	$0.365641\pi$
$108$	−0.500000	+	1.53884i	−0.0481125	+	0.148075i
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$		0			0
$111$	0.236068			0.0224066
$112$	−1.71885	+	5.29007i	−0.162416	+	0.499864i
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	−0.614408	−	0.788988i	$-0.710605\pi$
$113$	−0.572949	+	0.416272i	−0.0538985	+	0.0391596i	0.560510	+	0.828148i	$0.310605\pi$
$114$	2.92705	+	2.12663i	0.274143	+	0.199177i
$115$	−2.80902	−	8.64527i	−0.261942	−	0.806175i
$116$	2.23607	+	6.88191i	0.207614	+	0.638969i
$117$	1.42705	+	1.03681i	0.131931	+	0.0958534i
$118$	−5.16312	+	3.75123i	−0.475304	+	0.345328i
$119$	1.50000	−	4.61653i	0.137505	−	0.423196i
$120$	5.85410			0.534404
$121$		0			0
$122$	−4.85410			−0.439470
$123$	3.69098	−	11.3597i	0.332805	−	1.02427i
$124$	3.73607	−	2.71441i	0.335509	−	0.243761i
$125$	−6.66312	−	4.84104i	−0.595967	−	0.432996i
$126$	−0.572949	−	1.76336i	−0.0510424	−	0.157092i
$127$	1.14590	+	3.52671i	0.101682	+	0.312945i	0.988937	−	0.148333i	$-0.0473909\pi$
$127$	1.14590	+	3.52671i	0.101682	+	0.312945i	−0.887255	+	0.461279i	$0.847391\pi$
$128$	9.20820	+	6.69015i	0.813898	+	0.591331i
$129$	5.04508	−	3.66547i	0.444195	−	0.322727i
$130$	0.881966	−	2.71441i	0.0773535	−	0.238070i
$131$	7.14590			0.624340			0.312170	−	0.950026i	$-0.398944\pi$
$131$	7.14590			0.624340			0.312170	+	0.950026i	$0.398944\pi$
$132$		0			0
$133$	17.5623			1.52285
$134$	−1.82624	+	5.62058i	−0.157763	+	0.485544i
$135$	2.11803	−	1.53884i	0.182291	−	0.132442i
$136$	−2.92705	−	2.12663i	−0.250993	−	0.182357i
$137$	2.30902	+	7.10642i	0.197273	+	0.607143i	0.999943	+	0.0107192i	$0.00341210\pi$
$137$	2.30902	+	7.10642i	0.197273	+	0.607143i	−0.802670	+	0.596424i	$0.796588\pi$
$138$	0.663119	+	2.04087i	0.0564484	+	0.173730i
$139$	−0.690983	−	0.502029i	−0.0586084	−	0.0425815i	0.558095	−	0.829777i	$-0.311532\pi$
$139$	−0.690983	−	0.502029i	−0.0586084	−	0.0425815i	−0.616704	+	0.787195i	$0.711532\pi$
$140$	10.2812	−	7.46969i	0.868916	−	0.631304i
$141$	0.500000	−	1.53884i	0.0421076	−	0.129594i
$142$	−3.43769			−0.288485
$143$		0			0
$144$	1.85410			0.154508
$145$	3.61803	−	11.1352i	0.300461	−	0.924725i
$146$	−1.61803	+	1.17557i	−0.133909	+	0.0972909i
$147$	−1.61803	−	1.17557i	−0.133453	−	0.0969594i
$148$	−0.118034	−	0.363271i	−0.00970233	−	0.0298607i
$149$	−4.63525	−	14.2658i	−0.379735	−	1.16870i	−0.940228	−	0.340545i	$-0.889388\pi$
$149$	−4.63525	−	14.2658i	−0.379735	−	1.16870i	0.560493	−	0.828159i	$-0.310612\pi$
$150$	−0.927051	−	0.673542i	−0.0756934	−	0.0549945i
$151$	1.61803	−	1.17557i	0.131674	−	0.0956666i	−0.519999	−	0.854167i	$-0.674068\pi$
$151$	1.61803	−	1.17557i	0.131674	−	0.0956666i	0.651673	+	0.758500i	$0.274068\pi$
$152$	4.04508	−	12.4495i	0.328100	−	1.00979i
$153$	−1.61803			−0.130810
$154$		0			0
$155$	−7.47214			−0.600176
$156$	0.881966	−	2.71441i	0.0706138	−	0.217327i
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	−0.461601	−	0.887087i	$-0.652725\pi$
$157$	3.00000	−	2.17963i	0.239426	−	0.173953i	0.701028	+	0.713134i	$0.252725\pi$
$158$	4.73607	+	3.44095i	0.376781	+	0.273748i
$159$	−2.97214	−	9.14729i	−0.235706	−	0.725428i
$160$	−4.54508	−	13.9883i	−0.359321	−	1.10587i
$161$	8.42705	+	6.12261i	0.664145	+	0.482529i
$162$	−0.500000	+	0.363271i	−0.0392837	+	0.0285413i
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	−0.443282	−	0.896382i	$-0.646186\pi$
$163$	5.64590	−	17.3763i	0.442221	−	1.36102i	0.885503	−	0.464634i	$-0.153814\pi$
$164$	−19.3262			−1.50913
$165$		0			0
$166$	−0.437694			−0.0339717
$167$	−3.10081	+	9.54332i	−0.239948	+	0.738484i	0.756478	+	0.654019i	$0.226918\pi$
$167$	−3.10081	+	9.54332i	−0.239948	+	0.738484i	−0.996426	+	0.0844656i	$0.973082\pi$
$168$	−5.42705	+	3.94298i	−0.418706	+	0.304208i
$169$	8.00000	+	5.81234i	0.615385	+	0.447103i
$170$	0.809017	+	2.48990i	0.0620488	+	0.190966i
$171$	−1.80902	−	5.56758i	−0.138339	−	0.425764i
$172$	−8.16312	−	5.93085i	−0.622432	−	0.452223i
$173$	12.4443	−	9.04129i	0.946120	−	0.687397i	−0.00376565	−	0.999993i	$-0.501199\pi$
$173$	12.4443	−	9.04129i	0.946120	−	0.687397i	0.949886	+	0.312596i	$0.101199\pi$
$174$	−0.854102	+	2.62866i	−0.0647493	+	0.199278i
$175$	−5.56231			−0.420471
$176$		0			0
$177$	10.3262			0.776168
$178$	0.100813	−	0.310271i	0.00755626	−	0.0232558i
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	−0.518123	−	0.855306i	$-0.673369\pi$
$179$	1.80902	−	1.31433i	0.135212	−	0.0982375i	0.653335	+	0.757069i	$0.273369\pi$
$180$	−3.42705	−	2.48990i	−0.255437	−	0.185586i
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	−0.923930	−	0.382560i	$-0.875042\pi$
$181$	−5.39919	−	16.6170i	−0.401318	−	1.23513i	0.522612	−	0.852571i	$-0.324958\pi$
$182$	1.01064	+	3.11044i	0.0749139	+	0.230561i
$183$	6.35410	+	4.61653i	0.469709	+	0.341263i
$184$	6.28115	−	4.56352i	0.463053	−	0.336428i
$185$	−0.190983	+	0.587785i	−0.0140413	+	0.0432148i
$186$	1.76393			0.129338
$187$		0			0
$188$	−2.61803			−0.190940
$189$	−0.927051	+	2.85317i	−0.0674330	+	0.207538i
$190$	−7.66312	+	5.56758i	−0.555941	+	0.403915i
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	0.784604	−	0.619998i	$-0.212866\pi$
$191$	6.04508	+	4.39201i	0.437407	+	0.317795i	−0.347197	+	0.937792i	$0.612866\pi$
$192$	−0.0729490	−	0.224514i	−0.00526464	−	0.0162029i
$193$	5.73607	+	17.6538i	0.412891	+	1.27075i	0.914124	+	0.405436i	$0.132880\pi$
$193$	5.73607	+	17.6538i	0.412891	+	1.27075i	−0.501232	+	0.865313i	$0.667120\pi$
$194$	7.01722	+	5.09831i	0.503807	+	0.366037i
$195$	−3.73607	+	2.71441i	−0.267545	+	0.194383i
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	−24.3820			−1.73714			−0.868572	−	0.495564i	$-0.834961\pi$
$197$	−24.3820			−1.73714			−0.868572	+	0.495564i	$0.834961\pi$
$198$		0			0
$199$	−16.7082			−1.18441			−0.592207	−	0.805786i	$-0.701743\pi$
$199$	−16.7082			−1.18441			−0.592207	+	0.805786i	$0.701743\pi$
$200$	−1.28115	+	3.94298i	−0.0905912	+	0.278811i
$201$	7.73607	−	5.62058i	0.545660	−	0.396445i
$202$	−1.50000	−	1.08981i	−0.105540	−	0.0766790i
$203$	4.14590	+	12.7598i	0.290985	+	0.895560i
$204$	0.809017	+	2.48990i	0.0566425	+	0.174328i
$205$	25.2984	+	18.3803i	1.76692	+	1.28374i
$206$	3.00000	−	2.17963i	0.209020	−	0.151862i
$207$	1.07295	−	3.30220i	0.0745751	−	0.229519i
$208$	−3.27051			−0.226769
$209$		0			0
$210$	4.85410			0.334965
$211$	6.88197	−	21.1805i	0.473774	−	1.45813i	−0.373830	−	0.927497i	$-0.621956\pi$
$211$	6.88197	−	21.1805i	0.473774	−	1.45813i	0.847604	−	0.530629i	$-0.178044\pi$
$212$	−12.5902	+	9.14729i	−0.864696	+	0.628239i
$213$	4.50000	+	3.26944i	0.308335	+	0.224018i
$214$	0.809017	+	2.48990i	0.0553033	+	0.170206i
$215$	5.04508	+	15.5272i	0.344072	+	1.05894i
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	6.92705	−	5.03280i	0.470239	−	0.341649i
$218$		0			0
$219$	3.23607			0.218673
$220$		0			0
$221$	2.85410			0.191988
$222$	0.0450850	−	0.138757i	0.00302591	−	0.00931278i
$223$	−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	$0.307549\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$	0.572949	+	1.76336i	0.0381966	+	0.117557i
$226$	0.135255	+	0.416272i	0.00899702	+	0.0276900i
$227$	−20.1353	−	14.6291i	−1.33642	−	0.970969i	−0.999567	−	0.0294127i	$-0.990636\pi$
$227$	−20.1353	−	14.6291i	−1.33642	−	0.970969i	−0.336856	−	0.941556i	$-0.609364\pi$
$228$	−7.66312	+	5.56758i	−0.507502	+	0.368722i
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	−0.795541	−	0.605900i	$-0.792813\pi$
$229$	3.09017	−	9.51057i	0.204204	−	0.628476i	0.999745	−	0.0225760i	$-0.00718678\pi$
$230$	−5.61803			−0.370442
$231$		0			0
$232$	10.0000			0.656532
$233$	−7.51722	+	23.1356i	−0.492470	+	1.51567i	0.328394	+	0.944541i	$0.393493\pi$
$233$	−7.51722	+	23.1356i	−0.492470	+	1.51567i	−0.820863	+	0.571124i	$0.806507\pi$
$234$	0.881966	−	0.640786i	0.0576559	−	0.0418895i
$235$	3.42705	+	2.48990i	0.223556	+	0.162423i
$236$	−5.16312	−	15.8904i	−0.336090	−	1.03438i
$237$	−2.92705	−	9.00854i	−0.190132	−	0.585167i
$238$	−2.42705	−	1.76336i	−0.157322	−	0.114301i
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	−0.518719	−	0.854945i	$-0.673591\pi$
$239$	2.07295	−	1.50609i	0.134088	−	0.0974206i	0.652807	+	0.757524i	$0.273591\pi$
$240$	−1.50000	+	4.61653i	−0.0968246	+	0.297995i
$241$	23.1246			1.48959			0.744794	−	0.667295i	$-0.232548\pi$
$241$	23.1246			1.48959			0.744794	+	0.667295i	$0.232548\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$	3.92705	−	12.0862i	0.251404	−	0.773741i
$245$	4.23607	−	3.07768i	0.270632	−	0.196626i
$246$	−5.97214	−	4.33901i	−0.380769	−	0.276645i
$247$	3.19098	+	9.82084i	0.203037	+	0.624885i
$248$	−1.97214	−	6.06961i	−0.125231	−	0.385421i
$249$	0.572949	+	0.416272i	0.0363092	+	0.0263802i
$250$	−4.11803	+	2.99193i	−0.260447	+	0.189226i
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	−0.997856	−	0.0654431i	$-0.979154\pi$
$251$	−2.40983	+	7.41669i	−0.152107	+	0.468138i	0.845749	+	0.533581i	$0.179154\pi$
$252$	4.85410			0.305780
$253$		0			0
$254$	2.29180			0.143800
$255$	1.30902	−	4.02874i	0.0819738	−	0.252289i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	9.44427	+	6.86167i	0.589117	+	0.428019i	0.842000	−	0.539478i	$-0.181378\pi$
$257$	9.44427	+	6.86167i	0.589117	+	0.428019i	−0.252882	+	0.967497i	$0.581378\pi$
$258$	−1.19098	−	3.66547i	−0.0741474	−	0.228202i
$259$	−0.218847	−	0.673542i	−0.0135985	−	0.0418519i
$260$	6.04508	+	4.39201i	0.374900	+	0.272381i
$261$	3.61803	−	2.62866i	0.223951	−	0.162710i
$262$	1.36475	−	4.20025i	0.0843142	−	0.259493i
$263$	16.3262			1.00672			0.503359	−	0.864077i	$-0.332097\pi$
$263$	16.3262			1.00672			0.503359	+	0.864077i	$0.332097\pi$
$264$		0			0
$265$	25.1803			1.54682
$266$	3.35410	−	10.3229i	0.205653	−	0.632935i
$267$	−0.427051	+	0.310271i	−0.0261351	+	0.0189883i
$268$	−12.5172	−	9.09429i	−0.764611	−	0.555522i
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	0.984029	+	0.178006i	$0.0569645\pi$
$269$	4.79837	+	14.7679i	0.292562	+	0.900413i	−0.691467	+	0.722408i	$0.743035\pi$
$270$	−0.500000	−	1.53884i	−0.0304290	−	0.0936509i
$271$	−22.0623	−	16.0292i	−1.34019	−	0.973705i	−0.999437	−	0.0335518i	$-0.989318\pi$
$271$	−22.0623	−	16.0292i	−1.34019	−	0.973705i	−0.340753	−	0.940153i	$-0.610682\pi$
$272$	2.42705	−	1.76336i	0.147162	−	0.106919i
$273$	1.63525	−	5.03280i	0.0989701	−	0.304599i
$274$	4.61803			0.278986
$275$		0			0
$276$	−5.61803			−0.338166
$277$	−9.44427	+	29.0665i	−0.567451	+	1.74644i	0.0931022	+	0.995657i	$0.470322\pi$
$277$	−9.44427	+	29.0665i	−0.567451	+	1.74644i	−0.660554	+	0.750779i	$0.729678\pi$
$278$	−0.427051	+	0.310271i	−0.0256128	+	0.0186088i
$279$	−2.30902	−	1.67760i	−0.138237	−	0.100435i
$280$	−5.42705	−	16.7027i	−0.324328	−	0.998180i
$281$	0.236068	+	0.726543i	0.0140826	+	0.0433419i	0.957851	−	0.287266i	$-0.0927463\pi$
$281$	0.236068	+	0.726543i	0.0140826	+	0.0433419i	−0.943768	+	0.330608i	$0.892746\pi$
$282$	−0.809017	−	0.587785i	−0.0481763	−	0.0350021i
$283$	0.145898	−	0.106001i	0.00867274	−	0.00630111i	−0.583440	−	0.812156i	$-0.698294\pi$
$283$	0.145898	−	0.106001i	0.00867274	−	0.00630111i	0.592113	+	0.805855i	$0.298294\pi$
$284$	2.78115	−	8.55951i	0.165031	−	0.507913i
$285$	15.3262			0.907848
$286$		0			0
$287$	−35.8328			−2.11514
$288$	1.73607	−	5.34307i	0.102299	−	0.314843i
$289$	11.6353	−	8.45351i	0.684427	−	0.497265i
$290$	−5.85410	−	4.25325i	−0.343765	−	0.249760i
$291$	−4.33688	−	13.3475i	−0.254232	−	0.782447i
$292$	−1.61803	−	4.97980i	−0.0946883	−	0.291421i
$293$	0.0450850	+	0.0327561i	0.00263389	+	0.00191363i	0.589101	−	0.808059i	$-0.299482\pi$
$293$	0.0450850	+	0.0327561i	0.00263389	+	0.00191363i	−0.586468	+	0.809973i	$0.699482\pi$
$294$	−1.00000	+	0.726543i	−0.0583212	+	0.0423728i
$295$	−8.35410	+	25.7113i	−0.486395	+	1.49697i
$296$	−0.527864			−0.0306815
$297$		0			0
$298$	−9.27051			−0.537026
$299$	−1.89261	+	5.82485i	−0.109452	+	0.336860i
$300$	2.42705	−	1.76336i	0.140126	−	0.101807i
$301$	−15.1353	−	10.9964i	−0.872382	−	0.633822i
$302$	−0.381966	−	1.17557i	−0.0219797	−	0.0676465i
$303$	0.927051	+	2.85317i	0.0532577	+	0.163910i
$304$	8.78115	+	6.37988i	0.503634	+	0.365911i
$305$	−16.6353	+	12.0862i	−0.952532	+	0.692055i
$306$	−0.309017	+	0.951057i	−0.0176653	+	0.0543683i
$307$	−0.562306			−0.0320925			−0.0160462	−	0.999871i	$-0.505108\pi$
$307$	−0.562306			−0.0320925			−0.0160462	+	0.999871i	$0.505108\pi$
$308$		0			0
$309$	−6.00000			−0.341328
$310$	−1.42705	+	4.39201i	−0.0810510	+	0.249449i
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	−0.644257	−	0.764809i	$-0.722833\pi$
$311$	−2.04508	+	1.48584i	−0.115966	+	0.0842543i	0.528291	+	0.849064i	$0.322833\pi$
$312$	−3.19098	−	2.31838i	−0.180654	−	0.131253i
$313$	7.98278	+	24.5685i	0.451213	+	1.38869i	0.875524	+	0.483175i	$0.160517\pi$
$313$	7.98278	+	24.5685i	0.451213	+	1.38869i	−0.424310	+	0.905517i	$0.639483\pi$
$314$	−0.708204	−	2.17963i	−0.0399663	−	0.123004i
$315$	−6.35410	−	4.61653i	−0.358013	−	0.260112i
$316$	−12.3992	+	9.00854i	−0.697509	+	0.506770i
$317$	−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	$0.917022\pi$
$318$	−5.94427			−0.333338
$319$		0			0
$320$	0.618034			0.0345492
$321$	1.30902	−	4.02874i	0.0730622	−	0.224862i
$322$	5.20820	−	3.78398i	0.290242	−	0.210873i
$323$	−7.66312	−	5.56758i	−0.426387	−	0.309789i
$324$	−0.500000	−	1.53884i	−0.0277778	−	0.0854912i
$325$	−1.01064	−	3.11044i	−0.0560604	−	0.172536i
$326$	−9.13525	−	6.63715i	−0.505955	−	0.367598i
$327$		0			0
$328$	−8.25329	+	25.4010i	−0.455712	+	1.40254i
$329$	−4.85410			−0.267615
$330$		0			0
$331$	26.5967			1.46189			0.730945	−	0.682437i	$-0.239080\pi$
$331$	26.5967			1.46189			0.730945	+	0.682437i	$0.239080\pi$
$332$	0.354102	−	1.08981i	0.0194339	−	0.0598113i
$333$	−0.190983	+	0.138757i	−0.0104658	+	0.00760385i
$334$	5.01722	+	3.64522i	0.274530	+	0.199458i
$335$	7.73607	+	23.8092i	0.422667	+	1.30083i
$336$	−1.71885	−	5.29007i	−0.0937708	−	0.288597i
$337$	−0.236068	−	0.171513i	−0.0128594	−	0.00934293i	0.581337	−	0.813663i	$-0.302530\pi$
$337$	−0.236068	−	0.171513i	−0.0128594	−	0.00934293i	−0.594196	+	0.804320i	$0.702530\pi$
$338$	4.94427	−	3.59222i	0.268933	−	0.195391i
$339$	0.218847	−	0.673542i	0.0118861	−	0.0365818i
$340$	−6.85410			−0.371716
$341$		0			0
$342$	−3.61803			−0.195641
$343$	4.63525	−	14.2658i	0.250280	−	0.770283i
$344$	−11.2812	+	8.19624i	−0.608239	+	0.441912i
$345$	7.35410	+	5.34307i	0.395932	+	0.287661i
$346$	−2.93769	−	9.04129i	−0.157931	−	0.486063i
$347$	6.47214	+	19.9192i	0.347442	+	1.06932i	0.960263	+	0.279096i	$0.0900348\pi$
$347$	6.47214	+	19.9192i	0.347442	+	1.06932i	−0.612821	+	0.790222i	$0.709965\pi$
$348$	−5.85410	−	4.25325i	−0.313813	−	0.227998i
$349$	−8.19098	+	5.95110i	−0.438453	+	0.318555i	−0.785020	−	0.619470i	$-0.787347\pi$
$349$	−8.19098	+	5.95110i	−0.438453	+	0.318555i	0.346567	+	0.938025i	$0.387347\pi$
$350$	−1.06231	+	3.26944i	−0.0567826	+	0.174759i
$351$	−1.76393			−0.0941517
$352$		0			0
$353$	−10.4721			−0.557376			−0.278688	−	0.960382i	$-0.589899\pi$
$353$	−10.4721			−0.557376			−0.278688	+	0.960382i	$0.589899\pi$
$354$	1.97214	−	6.06961i	0.104818	−	0.322596i
$355$	−11.7812	+	8.55951i	−0.625279	+	0.454292i
$356$	0.690983	+	0.502029i	0.0366220	+	0.0266075i
$357$	1.50000	+	4.61653i	0.0793884	+	0.244332i
$358$	−0.427051	−	1.31433i	−0.0225703	−	0.0694644i
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	0.280940	−	0.959725i	$-0.409354\pi$
$359$	−10.3262	−	7.50245i	−0.544998	−	0.395964i	−0.825938	+	0.563761i	$0.809354\pi$
$360$	−4.73607	+	3.44095i	−0.249613	+	0.181354i
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	−10.7984			−0.567550
$363$		0			0
$364$	−8.56231			−0.448787
$365$	−2.61803	+	8.05748i	−0.137034	+	0.421748i
$366$	3.92705	−	2.85317i	0.205270	−	0.149138i
$367$	−4.50000	−	3.26944i	−0.234898	−	0.170663i	0.464109	−	0.885778i	$-0.346375\pi$
$367$	−4.50000	−	3.26944i	−0.234898	−	0.170663i	−0.699007	+	0.715115i	$0.746375\pi$
$368$	1.98936	+	6.12261i	0.103702	+	0.319163i
$369$	3.69098	+	11.3597i	0.192145	+	0.591361i
$370$	0.309017	+	0.224514i	0.0160650	+	0.0116719i
$371$	−23.3435	+	16.9600i	−1.21193	+	0.880520i
$372$	−1.42705	+	4.39201i	−0.0739891	+	0.227715i
$373$	4.41641			0.228673			0.114336	−	0.993442i	$-0.463526\pi$
$373$	4.41641			0.228673			0.114336	+	0.993442i	$0.463526\pi$
$374$		0			0
$375$	8.23607			0.425309
$376$	−1.11803	+	3.44095i	−0.0576582	+	0.177454i
$377$	−6.38197	+	4.63677i	−0.328688	+	0.238806i
$378$	1.50000	+	1.08981i	0.0771517	+	0.0560540i
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	0.962838	−	0.270080i	$-0.0870502\pi$
$379$	0.489357	+	1.50609i	0.0251366	+	0.0773624i	−0.937701	+	0.347443i	$0.887050\pi$
$380$	−7.66312	−	23.5847i	−0.393110	−	1.20987i
$381$	−3.00000	−	2.17963i	−0.153695	−	0.111666i
$382$	3.73607	−	2.71441i	0.191154	−	0.138881i
$383$	8.30902	−	25.5725i	0.424571	−	1.30669i	−0.478834	−	0.877906i	$-0.658940\pi$
$383$	8.30902	−	25.5725i	0.424571	−	1.30669i	0.903405	−	0.428789i	$-0.141060\pi$
$384$	−11.3820			−0.580834
$385$		0			0
$386$	11.4721			0.583916
$387$	−1.92705	+	5.93085i	−0.0979575	+	0.301482i
$388$	−18.3713	+	13.3475i	−0.932663	+	0.677619i
$389$	−19.6353	−	14.2658i	−0.995547	−	0.723307i	−0.0344181	−	0.999408i	$-0.510958\pi$
$389$	−19.6353	−	14.2658i	−0.995547	−	0.723307i	−0.961129	+	0.276100i	$0.910958\pi$
$390$	0.881966	+	2.71441i	0.0446601	+	0.137450i
$391$	−1.73607	−	5.34307i	−0.0877967	−	0.270211i
$392$	3.61803	+	2.62866i	0.182738	+	0.132767i
$393$	−5.78115	+	4.20025i	−0.291621	+	0.211875i
$394$	−4.65654	+	14.3314i	−0.234593	+	0.722003i
$395$	24.7984			1.24774
$396$		0			0
$397$	−38.7082			−1.94271			−0.971355	−	0.237635i	$-0.923628\pi$
$397$	−38.7082			−1.94271			−0.971355	+	0.237635i	$0.923628\pi$
$398$	−3.19098	+	9.82084i	−0.159950	+	0.492274i
$399$	−14.2082	+	10.3229i	−0.711300	+	0.516790i
$400$	−2.78115	−	2.02063i	−0.139058	−	0.101031i
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	−0.922873	−	0.385106i	$-0.874165\pi$
$401$	−8.06231	−	24.8132i	−0.402612	−	1.23911i	0.520260	−	0.854008i	$-0.325835\pi$
$402$	−1.82624	−	5.62058i	−0.0910845	−	0.280329i
$403$	4.07295	+	2.95917i	0.202888	+	0.147407i
$404$	3.92705	−	2.85317i	0.195378	−	0.141950i
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	8.29180			0.411515
$407$		0			0
$408$	3.61803			0.179119
$409$	3.41641	−	10.5146i	0.168930	−	0.519915i	−0.830374	−	0.557207i	$-0.811873\pi$
$409$	3.41641	−	10.5146i	0.168930	−	0.519915i	0.999304	+	0.0372920i	$0.0118732\pi$
$410$	15.6353	−	11.3597i	0.772170	−	0.561014i
$411$	−6.04508	−	4.39201i	−0.298182	−	0.216642i
$412$	3.00000	+	9.23305i	0.147799	+	0.454880i
$413$	−9.57295	−	29.4625i	−0.471054	−	1.44976i
$414$	−1.73607	−	1.26133i	−0.0853231	−	0.0619909i
$415$	−1.50000	+	1.08981i	−0.0736321	+	0.0534969i
$416$	−3.06231	+	9.42481i	−0.150142	+	0.462089i
$417$	0.854102			0.0418256
$418$		0			0
$419$	16.5066			0.806399			0.403200	−	0.915112i	$-0.367898\pi$
$419$	16.5066			0.806399			0.403200	+	0.915112i	$0.367898\pi$
$420$	−3.92705	+	12.0862i	−0.191620	+	0.589747i
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.488795	−	0.872398i	$-0.337436\pi$
$421$	30.1525	−	21.9071i	1.46954	−	1.06768i	0.980746	−	0.195286i	$-0.0625636\pi$
$422$	−11.1353	−	8.09024i	−0.542056	−	0.393827i
$423$	0.500000	+	1.53884i	0.0243108	+	0.0748210i
$424$	6.64590	+	20.4540i	0.322753	+	0.993333i
$425$	2.42705	+	1.76336i	0.117729	+	0.0855353i
$426$	2.78115	−	2.02063i	0.134747	−	0.0978996i
$427$	7.28115	−	22.4091i	0.352360	−	1.08445i
$428$	−6.85410			−0.331306
$429$		0			0
$430$	10.0902			0.486591
$431$	12.2082	−	37.5730i	0.588048	−	1.80983i	0.00138127	−	0.999999i	$-0.499560\pi$
$431$	12.2082	−	37.5730i	0.588048	−	1.80983i	0.586667	−	0.809828i	$-0.300440\pi$
$432$	−1.50000	+	1.08981i	−0.0721688	+	0.0524337i
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	0.698281	−	0.715824i	$-0.253949\pi$
$433$	4.85410	+	3.52671i	0.233273	+	0.169483i	−0.465008	+	0.885307i	$0.653949\pi$
$434$	−1.63525	−	5.03280i	−0.0784947	−	0.241582i
$435$	3.61803	+	11.1352i	0.173471	+	0.533890i
$436$		0			0
$437$	16.4443	−	11.9475i	0.786636	−	0.571525i
$438$	0.618034	−	1.90211i	0.0295308	−	0.0908865i
$439$	−3.29180			−0.157109			−0.0785544	−	0.996910i	$-0.525030\pi$
$439$	−3.29180			−0.157109			−0.0785544	+	0.996910i	$0.525030\pi$
$440$		0			0
$441$	2.00000			0.0952381
$442$	0.545085	−	1.67760i	0.0259270	−	0.0797952i
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.664877	−	0.746953i	$-0.268484\pi$
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.915853	−	0.401514i	$-0.131516\pi$
$444$	0.309017	+	0.224514i	0.0146653	+	0.0106550i
$445$	−0.427051	−	1.31433i	−0.0202442	−	0.0623051i
$446$	0.135255	+	0.416272i	0.00640451	+	0.0197110i
$447$	12.1353	+	8.81678i	0.573978	+	0.417019i
$448$	−0.572949	+	0.416272i	−0.0270693	+	0.0196670i
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	0.598020	+	0.801481i	$0.295954\pi$
$449$	−7.56231	+	23.2744i	−0.356887	+	1.09839i	−0.954907	+	0.296905i	$0.904046\pi$
$450$	1.14590			0.0540182
$451$		0			0
$452$	−1.14590			−0.0538985
$453$	−0.618034	+	1.90211i	−0.0290378	+	0.0893691i
$454$	−12.4443	+	9.04129i	−0.584039	+	0.424329i
$455$	11.2082	+	8.14324i	0.525449	+	0.381761i
$456$	4.04508	+	12.4495i	0.189428	+	0.583001i
$457$	−2.53444	−	7.80021i	−0.118556	−	0.364878i	0.874116	−	0.485717i	$-0.161442\pi$
$457$	−2.53444	−	7.80021i	−0.118556	−	0.364878i	−0.992672	+	0.120839i	$0.961442\pi$
$458$	−5.00000	−	3.63271i	−0.233635	−	0.169746i
$459$	1.30902	−	0.951057i	0.0610997	−	0.0443915i
$460$	4.54508	−	13.9883i	0.211916	−	0.652209i
$461$	21.0902			0.982267			0.491134	−	0.871084i	$-0.336583\pi$
$461$	21.0902			0.982267			0.491134	+	0.871084i	$0.336583\pi$
$462$		0			0
$463$	−15.7984			−0.734213			−0.367106	−	0.930179i	$-0.619651\pi$
$463$	−15.7984			−0.734213			−0.367106	+	0.930179i	$0.619651\pi$
$464$	−2.56231	+	7.88597i	−0.118952	+	0.366097i
$465$	6.04508	−	4.39201i	0.280334	−	0.203675i
$466$	12.1631	+	8.83702i	0.563446	+	0.409367i
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	0.856660	−	0.515882i	$-0.172536\pi$
$467$	−3.01722	−	9.28605i	−0.139620	−	0.429707i	−0.996280	+	0.0861747i	$0.972536\pi$
$468$	0.881966	+	2.71441i	0.0407689	+	0.125474i
$469$	−23.2082	−	16.8617i	−1.07166	−	0.778603i
$470$	2.11803	−	1.53884i	0.0976976	−	0.0709815i
$471$	−1.14590	+	3.52671i	−0.0528002	+	0.162502i
$472$	−23.0902			−1.06281
$473$		0			0
$474$	−5.85410			−0.268888
$475$	−3.35410	+	10.3229i	−0.153897	+	0.473646i
$476$	6.35410	−	4.61653i	0.291240	−	0.211598i
$477$	7.78115	+	5.65334i	0.356275	+	0.258849i
$478$	−0.489357	−	1.50609i	−0.0223827	−	0.0688868i
$479$	8.68034	+	26.7153i	0.396615	+	1.22066i	0.927697	+	0.373335i	$0.121786\pi$
$479$	8.68034	+	26.7153i	0.396615	+	1.22066i	−0.531082	+	0.847320i	$0.678214\pi$
$480$	11.8992	+	8.64527i	0.543121	+	0.394601i
$481$	0.336881	−	0.244758i	0.0153605	−	0.0111600i
$482$	4.41641	−	13.5923i	0.201162	−	0.619113i
$483$	−10.4164			−0.473963
$484$		0			0
$485$	36.7426			1.66840
$486$	0.190983	−	0.587785i	0.00866317	−	0.0266625i
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	−0.851736	−	0.523972i	$-0.824450\pi$
$487$	−13.6074	+	9.88635i	−0.616610	+	0.447993i	0.235126	+	0.971965i	$0.424450\pi$
$488$	−14.2082	−	10.3229i	−0.643175	−	0.467294i
$489$	5.64590	+	17.3763i	0.255316	+	0.785783i
$490$	−1.00000	−	3.07768i	−0.0451754	−	0.139036i
$491$	20.3992	+	14.8209i	0.920602	+	0.668857i	0.943674	−	0.330877i	$-0.107345\pi$
$491$	20.3992	+	14.8209i	0.920602	+	0.668857i	−0.0230715	+	0.999734i	$0.507345\pi$
$492$	15.6353	−	11.3597i	0.704892	−	0.512134i
$493$	2.23607	−	6.88191i	0.100707	−	0.309946i
$494$	6.38197			0.287138
$495$		0			0
$496$	5.29180			0.237609
$497$	5.15654	−	15.8702i	0.231302	−	0.711876i
$498$	0.354102	−	0.257270i	0.0158677	−	0.0115286i
$499$	14.2082	+	10.3229i	0.636047	+	0.462115i	0.858490	−	0.512831i	$-0.171403\pi$
$499$	14.2082	+	10.3229i	0.636047	+	0.462115i	−0.222443	+	0.974946i	$0.571403\pi$
$500$	−4.11803	−	12.6740i	−0.184164	−	0.566799i
$501$	−3.10081	−	9.54332i	−0.138534	−	0.426364i
$502$	3.89919	+	2.83293i	0.174029	+	0.126440i
$503$	22.7082	−	16.4985i	1.01251	−	0.735631i	0.0477750	−	0.998858i	$-0.484787\pi$
$503$	22.7082	−	16.4985i	1.01251	−	0.735631i	0.964734	+	0.263227i	$0.0847870\pi$
$504$	2.07295	−	6.37988i	0.0923365	−	0.284182i
$505$	−7.85410			−0.349503
$506$		0			0
$507$	−9.88854			−0.439166
$508$	−1.85410	+	5.70634i	−0.0822625	+	0.253178i
$509$	−19.1074	+	13.8823i	−0.846920	+	0.615324i	−0.924295	−	0.381679i	$-0.875346\pi$
$509$	−19.1074	+	13.8823i	−0.846920	+	0.615324i	0.0773749	+	0.997002i	$0.475346\pi$
$510$	−2.11803	−	1.53884i	−0.0937881	−	0.0681411i
$511$	−3.00000	−	9.23305i	−0.132712	−	0.408446i
$512$	5.78115	+	17.7926i	0.255493	+	0.786327i
$513$	4.73607	+	3.44095i	0.209103	+	0.151922i
$514$	5.83688	−	4.24074i	0.257454	−	0.187051i
$515$	4.85410	−	14.9394i	0.213897	−	0.658308i
$516$	10.0902			0.444195
$517$		0			0
$518$	−0.437694			−0.0192312
$519$	−4.75329	+	14.6291i	−0.208646	+	0.642147i
$520$	8.35410	−	6.06961i	0.366352	−	0.266170i
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	0.818758	−	0.574139i	$-0.194663\pi$
$521$	12.0000	+	8.71851i	0.525730	+	0.381965i	−0.293028	+	0.956104i	$0.594663\pi$
$522$	−0.854102	−	2.62866i	−0.0373830	−	0.115053i
$523$	3.70163	+	11.3924i	0.161861	+	0.498156i	0.998791	−	0.0491529i	$-0.0156522\pi$
$523$	3.70163	+	11.3924i	0.161861	+	0.498156i	−0.836930	+	0.547309i	$0.815652\pi$
$524$	9.35410	+	6.79615i	0.408636	+	0.296891i
$525$	4.50000	−	3.26944i	0.196396	−	0.142690i
$526$	3.11803	−	9.59632i	0.135953	−	0.418420i
$527$	−4.61803			−0.201165
$528$		0			0
$529$	−10.9443			−0.475838
$530$	4.80902	−	14.8006i	0.208890	−	0.642898i
$531$	−8.35410	+	6.06961i	−0.362537	+	0.263399i
$532$	22.9894	+	16.7027i	0.996715	+	0.724156i
$533$	−6.51064	−	20.0377i	−0.282007	−	0.867929i
$534$	0.100813	+	0.310271i	0.00436261	+	0.0134267i
$535$	8.97214	+	6.51864i	0.387899	+	0.281825i
$536$	−17.2984	+	12.5680i	−0.747176	+	0.542855i
$537$	−0.690983	+	2.12663i	−0.0298181	+	0.0917707i
$538$	9.59675			0.413745
$539$		0			0
$540$	4.23607			0.182291
$541$	−6.04508	+	18.6049i	−0.259899	+	0.799885i	0.732926	+	0.680308i	$0.238154\pi$
$541$	−6.04508	+	18.6049i	−0.259899	+	0.799885i	−0.992825	+	0.119577i	$0.961846\pi$
$542$	−13.6353	+	9.90659i	−0.585684	+	0.425525i
$543$	14.1353	+	10.2699i	0.606602	+	0.440722i
$544$	−2.80902	−	8.64527i	−0.120436	−	0.370663i
$545$		0			0
$546$	−2.64590	−	1.92236i	−0.113234	−	0.0822693i
$547$	17.4894	−	12.7068i	0.747791	−	0.543302i	−0.147350	−	0.989084i	$-0.547075\pi$
$547$	17.4894	−	12.7068i	0.747791	−	0.543302i	0.895141	+	0.445782i	$0.147075\pi$
$548$	−3.73607	+	11.4984i	−0.159597	+	0.491189i
$549$	−7.85410			−0.335205
$550$		0			0
$551$	26.1803			1.11532
$552$	−2.39919	+	7.38394i	−0.102116	+	0.314281i
$553$	−22.9894	+	16.7027i	−0.977607	+	0.710273i
$554$	15.2812	+	11.1024i	0.649234	+	0.471696i
$555$	−0.190983	−	0.587785i	−0.00810678	−	0.0249501i
$556$	−0.427051	−	1.31433i	−0.0181110	−	0.0557399i
$557$	12.0623	+	8.76378i	0.511096	+	0.371333i	0.813239	−	0.581929i	$-0.197702\pi$
$557$	12.0623	+	8.76378i	0.511096	+	0.371333i	−0.302143	+	0.953263i	$0.597702\pi$
$558$	−1.42705	+	1.03681i	−0.0604119	+	0.0438918i
$559$	3.39919	−	10.4616i	0.143770	−	0.442479i
$560$	14.5623			0.615370
$561$		0			0
$562$	0.472136			0.0199159
$563$	2.74671	−	8.45351i	0.115760	−	0.356273i	−0.876345	−	0.481684i	$-0.840025\pi$
$563$	2.74671	−	8.45351i	0.115760	−	0.356273i	0.992105	+	0.125412i	$0.0400251\pi$
$564$	2.11803	−	1.53884i	0.0891853	−	0.0647969i
$565$	1.50000	+	1.08981i	0.0631055	+	0.0458488i
$566$	−0.0344419	−	0.106001i	−0.00144770	−	0.00445556i
$567$	−0.927051	−	2.85317i	−0.0389325	−	0.119822i
$568$	−10.0623	−	7.31069i	−0.422205	−	0.306750i
$569$	−19.4721	+	14.1473i	−0.816314	+	0.593087i	−0.915654	−	0.401966i	$-0.868327\pi$
$569$	−19.4721	+	14.1473i	−0.816314	+	0.593087i	0.0993400	+	0.995054i	$0.468327\pi$
$570$	2.92705	−	9.00854i	0.122601	−	0.377326i
$571$	−34.6869			−1.45160			−0.725801	−	0.687905i	$-0.758531\pi$
$571$	−34.6869			−1.45160			−0.725801	+	0.687905i	$0.758531\pi$
$572$		0			0
$573$	−7.47214			−0.312153
$574$	−6.84346	+	21.0620i	−0.285640	+	0.879111i
$575$	−5.20820	+	3.78398i	−0.217197	+	0.157803i
$576$	0.190983	+	0.138757i	0.00795763	+	0.00578155i
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	0.996114	−	0.0880726i	$-0.0280707\pi$
$577$	3.32624	+	10.2371i	0.138473	+	0.426176i	−0.857641	+	0.514249i	$0.828071\pi$
$578$	−2.74671	−	8.45351i	−0.114248	−	0.351620i
$579$	−15.0172	−	10.9106i	−0.624094	−	0.453431i
$580$	15.3262	−	11.1352i	0.636387	−	0.462363i
$581$	0.656541	−	2.02063i	0.0272379	−	0.0838297i
$582$	−8.67376			−0.359539
$583$		0			0
$584$	−7.23607			−0.299431
$585$	1.42705	−	4.39201i	0.0590013	−	0.181587i
$586$	0.0278640	−	0.0202444i	0.00115105	−	0.000836289i
$587$	30.9894	+	22.5151i	1.27907	+	0.929297i	0.999524	−	0.0308361i	$-0.00981699\pi$
$587$	30.9894	+	22.5151i	1.27907	+	0.929297i	0.279543	+	0.960133i	$0.409817\pi$
$588$	−1.00000	−	3.07768i	−0.0412393	−	0.126922i
$589$	−5.16312	−	15.8904i	−0.212743	−	0.654754i
$590$	13.5172	+	9.82084i	0.556495	+	0.404317i
$591$	19.7254	−	14.3314i	0.811396	−	0.589513i
$592$	0.135255	−	0.416272i	0.00555894	−	0.0171087i
$593$	−22.2148			−0.912252			−0.456126	−	0.889915i	$-0.650763\pi$
$593$	−22.2148			−0.912252			−0.456126	+	0.889915i	$0.650763\pi$
$594$		0			0
$595$	−12.7082			−0.520986
$596$	7.50000	−	23.0826i	0.307212	−	0.945501i
$597$	13.5172	−	9.82084i	0.553223	−	0.401940i
$598$	3.06231	+	2.22490i	0.125227	+	0.0909827i
$599$	−2.56231	−	7.88597i	−0.104693	−	0.322212i	0.884965	−	0.465657i	$-0.154182\pi$
$599$	−2.56231	−	7.88597i	−0.104693	−	0.322212i	−0.989658	+	0.143445i	$0.954182\pi$
$600$	−1.28115	−	3.94298i	−0.0523029	−	0.160972i
$601$	27.3713	+	19.8864i	1.11650	+	0.811184i	0.983675	−	0.179955i	$-0.0575953\pi$
$601$	27.3713	+	19.8864i	1.11650	+	0.811184i	0.132825	+	0.991140i	$0.457595\pi$
$602$	−9.35410	+	6.79615i	−0.381245	+	0.276991i
$603$	−2.95492	+	9.09429i	−0.120333	+	0.370348i
$604$	3.23607			0.131674
$605$		0			0
$606$	1.85410			0.0753177
$607$	−4.11803	+	12.6740i	−0.167146	+	0.514422i	−0.999188	−	0.0402904i	$-0.987172\pi$
$607$	−4.11803	+	12.6740i	−0.167146	+	0.514422i	0.832042	+	0.554712i	$0.187172\pi$
$608$	26.6074	−	19.3314i	1.07907	−	0.783992i
$609$	−10.8541	−	7.88597i	−0.439830	−	0.319555i
$610$	3.92705	+	12.0862i	0.159002	+	0.489357i
$611$	−0.881966	−	2.71441i	−0.0356805	−	0.109813i
$612$	−2.11803	−	1.53884i	−0.0856164	−	0.0622040i
$613$	28.0344	−	20.3682i	1.13230	−	0.822664i	0.146272	−	0.989244i	$-0.453272\pi$
$613$	28.0344	−	20.3682i	1.13230	−	0.822664i	0.986028	+	0.166580i	$0.0532724\pi$
$614$	−0.107391	+	0.330515i	−0.00433394	+	0.0133385i
$615$	−31.2705			−1.26095
$616$		0			0
$617$	19.5836			0.788406			0.394203	−	0.919023i	$-0.371021\pi$
$617$	19.5836			0.788406			0.394203	+	0.919023i	$0.371021\pi$
$618$	−1.14590	+	3.52671i	−0.0460948	+	0.141865i
$619$	7.13525	−	5.18407i	0.286790	−	0.208365i	−0.435084	−	0.900390i	$-0.643281\pi$
$619$	7.13525	−	5.18407i	0.286790	−	0.208365i	0.721874	+	0.692025i	$0.243281\pi$
$620$	−9.78115	−	7.10642i	−0.392821	−	0.285401i
$621$	1.07295	+	3.30220i	0.0430560	+	0.132513i
$622$	0.482779	+	1.48584i	0.0193577	+	0.0595768i
$623$	1.28115	+	0.930812i	0.0513283	+	0.0372922i
$624$	2.64590	−	1.92236i	0.105921	−	0.0769559i
$625$	−9.52786	+	29.3238i	−0.381115	+	1.17295i
$626$	15.9656			0.638112
$627$		0			0
$628$	6.00000			0.239426
$629$	−0.118034	+	0.363271i	−0.00470632	+	0.0144846i
$630$	−3.92705	+	2.85317i	−0.156457	+	0.113673i
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.974084	−	0.226187i	$-0.927374\pi$
$631$	−37.4336	−	27.1971i	−1.49021	−	1.08270i	−0.516125	−	0.856513i	$-0.672626\pi$
$632$	6.54508	+	20.1437i	0.260350	+	0.801273i
$633$	6.88197	+	21.1805i	0.273534	+	0.841850i
$634$	9.68034	+	7.03318i	0.384455	+	0.279323i
$635$	7.85410	−	5.70634i	0.311681	−	0.226449i
$636$	4.80902	−	14.8006i	0.190690	−	0.586883i
$637$	−3.52786			−0.139779
$638$		0			0
$639$	−5.56231			−0.220041
$640$	9.20820	−	28.3399i	0.363986	−	1.12023i
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.987415	−	0.158154i	$-0.949446\pi$
$641$	−28.9164	+	21.0090i	−1.14213	+	0.829806i	−0.154715	+	0.987959i	$0.549446\pi$
$642$	−2.11803	−	1.53884i	−0.0835921	−	0.0607332i
$643$	−11.9164	−	36.6749i	−0.469937	−	1.44632i	−0.852666	−	0.522457i	$-0.825015\pi$
$643$	−11.9164	−	36.6749i	−0.469937	−	1.44632i	0.382728	−	0.923861i	$-0.374985\pi$
$644$	5.20820	+	16.0292i	0.205232	+	0.631639i
$645$	−13.2082	−	9.59632i	−0.520073	−	0.377855i
$646$	−4.73607	+	3.44095i	−0.186338	+	0.135383i
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	−0.627655	−	0.778492i	$-0.715985\pi$
$647$	8.59017	−	26.4378i	0.337714	−	1.03938i	0.965369	−	0.260887i	$-0.0840149\pi$
$648$	−2.23607			−0.0878410
$649$		0			0
$650$	−2.02129			−0.0792814
$651$	−2.64590	+	8.14324i	−0.103701	+	0.319159i
$652$	23.9164	−	17.3763i	0.936639	−	0.680508i
$653$	−41.2877	−	29.9973i	−1.61571	−	1.17388i	−0.839323	−	0.543632i	$-0.817049\pi$
$653$	−41.2877	−	29.9973i	−1.61571	−	1.17388i	−0.776390	−	0.630252i	$-0.782951\pi$
$654$		0			0
$655$	−5.78115	−	17.7926i	−0.225888	−	0.695213i
$656$	−17.9164	−	13.0170i	−0.699518	−	0.508230i
$657$	−2.61803	+	1.90211i	−0.102139	+	0.0742085i
$658$	−0.927051	+	2.85317i	−0.0361402	+	0.111228i
$659$	10.6525			0.414962			0.207481	−	0.978239i	$-0.433474\pi$
$659$	10.6525			0.414962			0.207481	+	0.978239i	$0.433474\pi$
$660$		0			0
$661$	−9.90983			−0.385448			−0.192724	−	0.981253i	$-0.561732\pi$
$661$	−9.90983			−0.385448			−0.192724	+	0.981253i	$0.561732\pi$
$662$	5.07953	−	15.6332i	0.197421	−	0.607601i
$663$	−2.30902	+	1.67760i	−0.0896748	+	0.0651525i
$664$	−1.28115	−	0.930812i	−0.0497184	−	0.0361225i
$665$	−14.2082	−	43.7284i	−0.550971	−	1.69571i
$666$	0.0450850	+	0.138757i	0.00174701	+	0.00537674i
$667$	12.5623	+	9.12705i	0.486414	+	0.353401i
$668$	−13.1353	+	9.54332i	−0.508218	+	0.369242i
$669$	0.218847	−	0.673542i	0.00846112	−	0.0260406i
$670$	15.4721			0.597741
$671$		0			0
$672$	−16.8541			−0.650161
$673$	−3.83688	+	11.8087i	−0.147901	+	0.455192i	−0.997373	−	0.0724420i	$-0.976921\pi$
$673$	−3.83688	+	11.8087i	−0.147901	+	0.455192i	0.849472	+	0.527634i	$0.176921\pi$
$674$	−0.145898	+	0.106001i	−0.00561978	+	0.00408301i
$675$	−1.50000	−	1.08981i	−0.0577350	−	0.0419470i
$676$	4.94427	+	15.2169i	0.190164	+	0.585266i
$677$	−4.18034	−	12.8658i	−0.160664	−	0.494471i	0.838027	−	0.545629i	$-0.183709\pi$
$677$	−4.18034	−	12.8658i	−0.160664	−	0.494471i	−0.998691	+	0.0511572i	$0.983709\pi$
$678$	−0.354102	−	0.257270i	−0.0135992	−	0.00988040i
$679$	−34.0623	+	24.7477i	−1.30719	+	0.949730i
$680$	−2.92705	+	9.00854i	−0.112247	+	0.345462i
$681$	24.8885			0.953731
$682$		0			0
$683$	−3.11146			−0.119057			−0.0595283	−	0.998227i	$-0.518960\pi$
$683$	−3.11146			−0.119057			−0.0595283	+	0.998227i	$0.518960\pi$
$684$	2.92705	−	9.00854i	0.111919	−	0.344450i
$685$	15.8262	−	11.4984i	0.604689	−	0.439333i
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	3.09017	+	9.51057i	0.117897	+	0.362851i
$688$	−3.57295	−	10.9964i	−0.136217	−	0.419234i
$689$	−13.7254	−	9.97210i	−0.522897	−	0.379907i
$690$	4.54508	−	3.30220i	0.173028	−	0.125713i
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	0.669050	+	0.743217i	$0.266701\pi$
$691$	−8.12461	+	25.0050i	−0.309075	+	0.951234i	−0.978125	+	0.208017i	$0.933299\pi$
$692$	24.8885			0.946120
$693$		0			0
$694$	12.9443			0.491358
$695$	−0.690983	+	2.12663i	−0.0262105	+	0.0806676i
$696$	−8.09017	+	5.87785i	−0.306657	+	0.222799i
$697$	15.6353	+	11.3597i	0.592228	+	0.430278i
$698$	1.93363	+	5.95110i	0.0731889	+	0.225252i
$699$	−7.51722	−	23.1356i	−0.284327	−	0.875070i
$700$	−7.28115	−	5.29007i	−0.275202	−	0.199946i
$701$	−8.64590	+	6.28161i	−0.326551	+	0.237253i	−0.738966	−	0.673743i	$-0.764685\pi$
$701$	−8.64590	+	6.28161i	−0.326551	+	0.237253i	0.412415	+	0.910996i	$0.364685\pi$
$702$	−0.336881	+	1.03681i	−0.0127148	+	0.0391320i
$703$	−1.38197			−0.0521218
$704$		0			0
$705$	−4.23607			−0.159540
$706$	−2.00000	+	6.15537i	−0.0752710	+	0.231660i
$707$	7.28115	−	5.29007i	0.273836	−	0.198953i
$708$	13.5172	+	9.82084i	0.508008	+	0.369090i
$709$	15.0623	+	46.3570i	0.565677	+	1.74097i	0.665932	+	0.746012i	$0.268034\pi$
$709$	15.0623	+	46.3570i	0.565677	+	1.74097i	−0.100255	+	0.994962i	$0.531966\pi$
$710$	2.78115	+	8.55951i	0.104375	+	0.321233i
$711$	7.66312	+	5.56758i	0.287389	+	0.208801i
$712$	0.954915	−	0.693786i	0.0357870	−	0.0260007i
$713$	3.06231	−	9.42481i	0.114684	−	0.352962i
$714$	3.00000			0.112272
$715$		0			0
$716$	3.61803			0.135212
$717$	−0.791796	+	2.43690i	−0.0295702	+	0.0910076i
$718$	−6.38197	+	4.63677i	−0.238173	+	0.173043i
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	0.611418	−	0.791307i	$-0.290599\pi$
$719$	1.28115	+	0.930812i	0.0477789	+	0.0347134i	−0.563639	+	0.826021i	$0.690599\pi$
$720$	−1.50000	−	4.61653i	−0.0559017	−	0.172048i
$721$	5.56231	+	17.1190i	0.207151	+	0.637546i
$722$	−7.63525	−	5.54734i	−0.284155	−	0.206451i
$723$	−18.7082	+	13.5923i	−0.695766	+	0.505503i
$724$	8.73607	−	26.8869i	0.324673	−	0.999242i
$725$	−8.29180			−0.307950
$726$		0			0
$727$	38.8541			1.44102			0.720509	−	0.693445i	$-0.243908\pi$
$727$	38.8541			1.44102			0.720509	+	0.693445i	$0.243908\pi$
$728$	−3.65654	+	11.2537i	−0.135520	+	0.417089i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	4.23607	+	3.07768i	0.156784	+	0.113910i
$731$	3.11803	+	9.59632i	0.115325	+	0.354933i
$732$	3.92705	+	12.0862i	0.145148	+	0.446720i
$733$	−30.5066	−	22.1643i	−1.12679	−	0.818658i	−0.141562	−	0.989929i	$-0.545213\pi$
$733$	−30.5066	−	22.1643i	−1.12679	−	0.818658i	−0.985224	+	0.171271i	$0.945213\pi$
$734$	−2.78115	+	2.02063i	−0.102654	+	0.0745827i
$735$	−1.61803	+	4.97980i	−0.0596821	+	0.183683i
$736$	19.5066			0.719022
$737$		0			0
$738$	7.38197			0.271734
$739$	7.72542	−	23.7764i	0.284184	−	0.874629i	−0.702458	−	0.711726i	$-0.747914\pi$
$739$	7.72542	−	23.7764i	0.284184	−	0.874629i	0.986642	−	0.162904i	$-0.0520860\pi$
$740$	−0.809017	+	0.587785i	−0.0297401	+	0.0216074i
$741$	−8.35410	−	6.06961i	−0.306896	−	0.222973i
$742$	5.51064	+	16.9600i	0.202302	+	0.622622i
$743$	−10.8713	−	33.4585i	−0.398830	−	1.22747i	−0.925938	−	0.377675i	$-0.876724\pi$
$743$	−10.8713	−	33.4585i	−0.398830	−	1.22747i	0.527108	−	0.849798i	$-0.323276\pi$
$744$	5.16312	+	3.75123i	0.189289	+	0.137527i
$745$	−31.7705	+	23.0826i	−1.16398	+	0.845682i
$746$	0.843459	−	2.59590i	0.0308812	−	0.0950426i
$747$	−0.708204			−0.0259118
$748$		0			0
$749$	−12.7082			−0.464348
$750$	1.57295	−	4.84104i	0.0574360	−	0.176770i
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	−0.749701	−	0.661777i	$-0.769803\pi$
$751$	−9.64590	+	7.00816i	−0.351984	+	0.255731i	0.397717	+	0.917508i	$0.369803\pi$
$752$	−2.42705	−	1.76336i	−0.0885054	−	0.0643030i
$753$	−2.40983	−	7.41669i	−0.0878191	−	0.270279i
$754$	1.50658	+	4.63677i	0.0548663	+	0.168861i
$755$	−4.23607	−	3.07768i	−0.154166	−	0.112008i
$756$	−3.92705	+	2.85317i	−0.142825	+	0.103769i
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	−0.939544	−	0.342428i	$-0.888751\pi$
$757$	0.600813	−	1.84911i	0.0218369	−	0.0672071i	0.961381	+	0.275220i	$0.0887509\pi$
$758$	0.978714			0.0355485
$759$		0			0
$760$	−34.2705			−1.24312
$761$	9.54508	−	29.3768i	0.346009	−	1.06491i	−0.615032	−	0.788502i	$-0.710857\pi$
$761$	9.54508	−	29.3768i	0.346009	−	1.06491i	0.961041	−	0.276404i	$-0.0891429\pi$
$762$	−1.85410	+	1.34708i	−0.0671670	+	0.0487997i
$763$		0			0
$764$	3.73607	+	11.4984i	0.135166	+	0.415999i
$765$	1.30902	+	4.02874i	0.0473276	+	0.145659i
$766$	−13.4443	−	9.76784i	−0.485761	−	0.352926i
$767$	14.7361	−	10.7064i	0.532089	−	0.386585i
$768$	−2.02786	+	6.24112i	−0.0731742	+	0.225207i
$769$	−12.6869			−0.457502			−0.228751	−	0.973485i	$-0.573464\pi$
$769$	−12.6869			−0.457502			−0.228751	+	0.973485i	$0.573464\pi$
$770$		0			0
$771$	−11.6738			−0.420420
$772$	−9.28115	+	28.5645i	−0.334036	+	1.02806i
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	−0.0315378	−	0.999503i	$-0.510040\pi$
$773$	25.2812	−	18.3678i	0.909300	−	0.660645i	0.940838	+	0.338858i	$0.110040\pi$
$774$	3.11803	+	2.26538i	0.112075	+	0.0814276i
$775$	1.63525	+	5.03280i	0.0587401	+	0.180783i
$776$	9.69756	+	29.8460i	0.348122	+	1.07141i
$777$	0.572949	+	0.416272i	0.0205544	+	0.0149337i
$778$	−12.1353	+	8.81678i	−0.435070	+	0.316097i
$779$	−21.6074	+	66.5007i	−0.774165	+	2.38264i
$780$	−7.47214			−0.267545
$781$		0			0
$782$	−3.47214			−0.124163
$783$	−1.38197	+	4.25325i	−0.0493874	+	0.151999i
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$	−7.85410	−	5.70634i	−0.280325	−	0.203668i
$786$	1.36475	+	4.20025i	0.0486788	+	0.149818i
$787$	3.18034	+	9.78808i	0.113367	+	0.348907i	0.991603	−	0.129320i	$-0.0412795\pi$
$787$	3.18034	+	9.78808i	0.113367	+	0.348907i	−0.878236	+	0.478227i	$0.841279\pi$
$788$	−31.9164	−	23.1886i	−1.13697	−	0.826061i
$789$	−13.2082	+	9.59632i	−0.470225	+	0.341638i
$790$	4.73607	−	14.5761i	0.168502	−	0.518595i
$791$	−2.12461			−0.0755425
$792$		0			0
$793$	13.8541			0.491974
$794$	−7.39261	+	22.7521i	−0.262354	+	0.807442i
$795$	−20.3713	+	14.8006i	−0.722496	+	0.524924i
$796$	−21.8713	−	15.8904i	−0.775208	−	0.563222i
$797$	3.32624	+	10.2371i	0.117821	+	0.362617i	0.992525	−	0.122041i	$-0.0389440\pi$
$797$	3.32624	+	10.2371i	0.117821	+	0.362617i	−0.874704	+	0.484658i	$0.838944\pi$
$798$	3.35410	+	10.3229i	0.118734	+	0.365425i
$799$	2.11803	+	1.53884i	0.0749307	+	0.0544403i
$800$	−8.42705	+	6.12261i	−0.297941	+	0.216467i
$801$	0.163119	−	0.502029i	0.00576353	−	0.0177383i
$802$	−16.1246			−0.569380
$803$		0			0
$804$	15.4721			0.545660
$805$	8.42705	−	25.9358i	0.297015	−	0.914117i
$806$	2.51722	−	1.82887i	0.0886653	−	0.0644191i
$807$	−12.5623	−	9.12705i	−0.442214	−	0.321287i
$808$	−2.07295	−	6.37988i	−0.0729261	−	0.224443i
$809$	−2.98936	−	9.20029i	−0.105100	−	0.323465i	0.884654	−	0.466249i	$-0.154395\pi$
$809$	−2.98936	−	9.20029i	−0.105100	−	0.323465i	−0.989754	+	0.142783i	$0.954395\pi$
$810$	1.30902	+	0.951057i	0.0459942	+	0.0334167i
$811$	2.63525	−	1.91462i	0.0925363	−	0.0672316i	−0.540555	−	0.841309i	$-0.681786\pi$
$811$	2.63525	−	1.91462i	0.0925363	−	0.0672316i	0.633091	+	0.774077i	$0.281786\pi$
$812$	−6.70820	+	20.6457i	−0.235412	+	0.724523i
$813$	27.2705			0.956419
$814$		0			0
$815$	−47.8328			−1.67551
$816$	−0.927051	+	2.85317i	−0.0324533	+	0.0998809i
$817$	−29.5344	+	21.4580i	−1.03328	+	0.750721i
$818$	−5.52786	−	4.01623i	−0.193277	−	0.140424i
$819$	1.63525	+	5.03280i	0.0571404	+	0.175860i
$820$	15.6353	+	48.1204i	0.546007	+	1.68044i
$821$	32.6976	+	23.7562i	1.14115	+	0.829096i	0.987279	−	0.158995i	$-0.0508252\pi$
$821$	32.6976	+	23.7562i	1.14115	+	0.829096i	0.153873	+	0.988091i	$0.450825\pi$
$822$	−3.73607	+	2.71441i	−0.130310	+	0.0946760i
$823$	−10.9615	+	33.7360i	−0.382094	+	1.17596i	0.556473	+	0.830866i	$0.312154\pi$
$823$	−10.9615	+	33.7360i	−0.382094	+	1.17596i	−0.938567	+	0.345098i	$0.887846\pi$
$824$	13.4164			0.467383
$825$		0			0
$826$	−19.1459			−0.666171
$827$	−16.4164	+	50.5245i	−0.570854	+	1.75691i	0.0790257	+	0.996873i	$0.474819\pi$
$827$	−16.4164	+	50.5245i	−0.570854	+	1.75691i	−0.649880	+	0.760037i	$0.725181\pi$
$828$	4.54508	−	3.30220i	0.157953	−	0.114759i
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	0.310887	−	0.950447i	$-0.399374\pi$
$829$	−14.3090	−	10.3961i	−0.496973	−	0.361072i	−0.807859	+	0.589375i	$0.799374\pi$
$830$	0.354102	+	1.08981i	0.0122911	+	0.0378280i
$831$	−9.44427	−	29.0665i	−0.327618	−	1.00831i
$832$	−0.336881	−	0.244758i	−0.0116792	−	0.00848547i
$833$	2.61803	−	1.90211i	0.0907095	−	0.0659043i
$834$	0.163119	−	0.502029i	0.00564835	−	0.0173838i
$835$	26.2705			0.909128
$836$		0			0
$837$	2.85410			0.0986522
$838$	3.15248	−	9.70232i	0.108900	−	0.335161i
$839$	29.6976	−	21.5765i	1.02527	−	0.744905i	0.0579164	−	0.998321i	$-0.481554\pi$
$839$	29.6976	−	21.5765i	1.02527	−	0.744905i	0.967357	+	0.253417i	$0.0815543\pi$
$840$	14.2082	+	10.3229i	0.490230	+	0.356173i
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	−7.11803	−	21.9071i	−0.245304	−	0.754967i
$843$	−0.618034	−	0.449028i	−0.0212862	−	0.0154653i
$844$	29.1525	−	21.1805i	1.00347	−	0.729063i
$845$	8.00000	−	24.6215i	0.275208	−	0.847004i
$846$	1.00000			0.0343807
$847$		0			0
$848$	−17.8328			−0.612381
$849$	−0.0557281	+	0.171513i	−0.00191258	+	0.00588633i
$850$	1.50000	−	1.08981i	0.0514496	−	0.0373803i
$851$	−0.663119	−	0.481784i	−0.0227314	−	0.0165153i
$852$	2.78115	+	8.55951i	0.0952807	+	0.293244i
$853$	3.07295	+	9.45756i	0.105216	+	0.323821i	0.989781	−	0.142596i	$-0.0455448\pi$
$853$	3.07295	+	9.45756i	0.105216	+	0.323821i	−0.884565	+	0.466416i	$0.845545\pi$
$854$	−11.7812	−	8.55951i	−0.403143	−	0.292900i
$855$	−12.3992	+	9.00854i	−0.424043	+	0.308085i
$856$	−2.92705	+	9.00854i	−0.100045	+	0.307905i
$857$	−47.7214			−1.63013			−0.815065	−	0.579369i	$-0.803299\pi$
$857$	−47.7214			−1.63013			−0.815065	+	0.579369i	$0.803299\pi$
$858$		0			0
$859$	7.11146			0.242640			0.121320	−	0.992613i	$-0.461287\pi$
$859$	7.11146			0.242640			0.121320	+	0.992613i	$0.461287\pi$
$860$	−8.16312	+	25.1235i	−0.278360	+	0.856704i
$861$	28.9894	−	21.0620i	0.987955	−	0.717791i
$862$	−19.7533	−	14.3516i	−0.672800	−	0.488818i
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	0.993911	−	0.110183i	$-0.0351436\pi$
$863$	3.67376	+	11.3067i	0.125056	+	0.384884i	−0.868855	+	0.495067i	$0.835144\pi$
$864$	1.73607	+	5.34307i	0.0590622	+	0.181775i
$865$	−32.5795	−	23.6704i	−1.10774	−	0.804818i
$866$	3.00000	−	2.17963i	0.101944	−	0.0740668i
$867$	−4.44427	+	13.6781i	−0.150935	+	0.464531i
$868$	13.8541			0.470239
$869$		0			0
$870$	7.23607			0.245326
$871$	5.21227	−	16.0417i	0.176611	−	0.543553i
$872$		0			0
$873$	11.3541	+	8.24924i	0.384278	+	0.279194i
$874$	−3.88197	−	11.9475i	−0.131309	−	0.404129i
$875$	−7.63525	−	23.4989i	−0.258119	−	0.794408i
$876$	4.23607	+	3.07768i	0.143123	+	0.103985i
$877$	5.19098	−	3.77147i	0.175287	−	0.127353i	−0.496682	−	0.867932i	$-0.665449\pi$
$877$	5.19098	−	3.77147i	0.175287	−	0.127353i	0.671969	+	0.740579i	$0.265449\pi$
$878$	−0.628677	+	1.93487i	−0.0212168	+	0.0652987i
$879$	−0.0557281			−0.00187966
$880$		0			0
$881$	13.9098			0.468634			0.234317	−	0.972160i	$-0.424715\pi$
$881$	13.9098			0.468634			0.234317	+	0.972160i	$0.424715\pi$
$882$	0.381966	−	1.17557i	0.0128615	−	0.0395835i
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	−0.722462	−	0.691411i	$-0.756990\pi$
$883$	−8.56231	+	6.22088i	−0.288145	+	0.209349i	0.434318	+	0.900760i	$0.356990\pi$
$884$	3.73607	+	2.71441i	0.125658	+	0.0912956i
$885$	−8.35410	−	25.7113i	−0.280820	−	0.864275i
$886$	−7.85410	−	24.1724i	−0.263864	−	0.812089i
$887$	2.42705	+	1.76336i	0.0814924	+	0.0592077i	0.627785	−	0.778386i	$-0.283962\pi$
$887$	2.42705	+	1.76336i	0.0814924	+	0.0592077i	−0.546293	+	0.837594i	$0.683962\pi$
$888$	0.427051	−	0.310271i	0.0143309	−	0.0104120i
$889$	−3.43769	+	10.5801i	−0.115297	+	0.354846i
$890$	−0.854102			−0.0286296
$891$		0			0
$892$	−1.14590			−0.0383675
$893$	−2.92705	+	9.00854i	−0.0979500	+	0.301459i
$894$	7.50000	−	5.44907i	0.250838	−	0.182244i
$895$	−4.73607	−	3.44095i	−0.158309	−	0.115018i
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	−1.89261	−	5.82485i	−0.0631924	−	0.194486i
$898$	12.2361	+	8.89002i	0.408323	+	0.296664i
$899$	10.3262	−	7.50245i	0.344399	−	0.250221i
$900$	−0.927051	+	2.85317i	−0.0309017	+	0.0951057i
$901$	15.5623			0.518456
$902$		0			0
$903$	18.7082			0.622570
$904$	−0.489357	+	1.50609i	−0.0162758	+	0.0500917i
$905$	−37.0066	+	26.8869i	−1.23014	+	0.893749i
$906$	1.00000	+	0.726543i	0.0332228	+	0.0241378i
$907$	−13.2812	−	40.8752i	−0.440993	−	1.35724i	−0.886818	−	0.462118i	$-0.847090\pi$
$907$	−13.2812	−	40.8752i	−0.440993	−	1.35724i	0.445825	−	0.895120i	$-0.352910\pi$
$908$	−12.4443	−	38.2995i	−0.412978	−	1.27101i
$909$	−2.42705	−	1.76336i	−0.0805002	−	0.0584868i
$910$	6.92705	−	5.03280i	0.229630	−	0.166836i
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	−0.815088	−	0.579337i	$-0.803311\pi$
$911$	5.57953	−	17.1720i	0.184858	−	0.568934i	0.999946	+	0.0104029i	$0.00331142\pi$
$912$	−10.8541			−0.359415
$913$		0			0
$914$	−5.06888			−0.167664
$915$	6.35410	−	19.5559i	0.210060	−	0.646499i
$916$	13.0902	−	9.51057i	0.432511	−	0.314238i
$917$	17.3435	+	12.6008i	0.572731	+	0.416114i
$918$	−0.309017	−	0.951057i	−0.0101991	−	0.0313895i
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	−0.840955	−	0.541106i	$-0.818006\pi$
$919$	−14.5106	−	44.6592i	−0.478662	−	1.47317i	0.362293	−	0.932064i	$-0.381994\pi$
$920$	−16.4443	−	11.9475i	−0.542152	−	0.393896i
$921$	0.454915	−	0.330515i	0.0149900	−	0.0108908i
$922$	4.02786	−	12.3965i	0.132651	−	0.408257i
$923$	9.81153			0.322950
$924$		0			0
$925$	0.437694			0.0143913
$926$	−3.01722	+	9.28605i	−0.0991520	+	0.305159i
$927$	4.85410	−	3.52671i	0.159430	−	0.115832i
$928$	20.3262	+	14.7679i	0.667241	+	0.484779i
$929$	−10.1631	−	31.2789i	−0.333441	−	1.02623i	−0.967485	−	0.252929i	$-0.918606\pi$
$929$	−10.1631	−	31.2789i	−0.333441	−	1.02623i	0.634044	−	0.773297i	$-0.281394\pi$
$930$	−1.42705	−	4.39201i	−0.0467948	−	0.144020i
$931$	9.47214	+	6.88191i	0.310437	+	0.225545i
$932$	−31.8435	+	23.1356i	−1.04307	+	0.757833i
$933$	0.781153	−	2.40414i	0.0255738	−	0.0787081i
$934$	−6.03444			−0.197453
$935$		0			0
$936$	3.94427			0.128923
$937$	5.12868	−	15.7844i	0.167547	−	0.515655i	−0.831668	−	0.555273i	$-0.812614\pi$
$937$	5.12868	−	15.7844i	0.167547	−	0.515655i	0.999215	+	0.0396173i	$0.0126139\pi$
$938$	−14.3435	+	10.4211i	−0.468331	+	0.340262i
$939$	−20.8992	−	15.1841i	−0.682019	−	0.495516i
$940$	2.11803	+	6.51864i	0.0690827	+	0.212615i
$941$	13.7918	+	42.4468i	0.449600	+	1.38373i	0.877360	+	0.479833i	$0.159303\pi$
$941$	13.7918	+	42.4468i	0.449600	+	1.38373i	−0.427760	+	0.903892i	$0.640697\pi$
$942$	1.85410	+	1.34708i	0.0604099	+	0.0438904i
$943$	−33.5517	+	24.3767i	−1.09259	+	0.793815i
$944$	5.91641	−	18.2088i	0.192563	−	0.592647i
$945$	7.85410			0.255494
$946$		0			0
$947$	18.3262			0.595523			0.297761	−	0.954640i	$-0.403760\pi$
$947$	18.3262			0.595523			0.297761	+	0.954640i	$0.403760\pi$
$948$	4.73607	−	14.5761i	0.153820	−	0.473410i
$949$	4.61803	−	3.35520i	0.149908	−	0.108914i
$950$	5.42705	+	3.94298i	0.176077	+	0.127927i
$951$	−5.98278	−	18.4131i	−0.194005	−	0.597086i
$952$	−3.35410	−	10.3229i	−0.108707	−	0.334566i
$953$	30.5967	+	22.2298i	0.991126	+	0.720095i	0.960167	−	0.279426i	$-0.0901440\pi$
$953$	30.5967	+	22.2298i	0.991126	+	0.720095i	0.0309585	+	0.999521i	$0.490144\pi$
$954$	4.80902	−	3.49396i	0.155698	−	0.113121i
$955$	6.04508	−	18.6049i	0.195614	−	0.602039i
$956$	4.14590			0.134088
$957$		0			0
$958$	17.3607			0.560898
$959$	−6.92705	+	21.3193i	−0.223686	+	0.688435i
$960$	−0.500000	+	0.363271i	−0.0161374	+	0.0117245i
$961$	18.4894	+	13.4333i	0.596431	+	0.433332i
$962$	−0.0795268	−	0.244758i	−0.00256405	−	0.00789133i
$963$	1.30902	+	4.02874i	0.0421825	+	0.129824i
$964$	30.2705	+	21.9928i	0.974947	+	0.708341i
$965$	39.3156	−	28.5645i	1.26561	−	0.919522i
$966$	−1.98936	+	6.12261i	−0.0640065	+	0.196992i
$967$	34.6869			1.11546			0.557728	−	0.830024i	$-0.311673\pi$
$967$	34.6869			1.11546			0.557728	+	0.830024i	$0.311673\pi$
$968$		0			0
$969$	9.47214			0.304289
$970$	7.01722	−	21.5968i	0.225309	−	0.693431i
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.957885	−	0.287151i	$-0.907292\pi$
$971$	−30.5623	+	22.2048i	−0.980791	+	0.712586i	−0.0229058	+	0.999738i	$0.507292\pi$
$972$	1.30902	+	0.951057i	0.0419867	+	0.0305052i
$973$	−0.791796	−	2.43690i	−0.0253838	−	0.0781234i
$974$	3.21227	+	9.88635i	0.102928	+	0.316779i
$975$	2.64590	+	1.92236i	0.0847366	+	0.0615647i
$976$	11.7812	−	8.55951i	0.377106	−	0.273983i
$977$	−1.43363	+	4.41226i	−0.0458658	+	0.141161i	−0.971367	−	0.237585i	$-0.923644\pi$
$977$	−1.43363	+	4.41226i	−0.0458658	+	0.141161i	0.925501	+	0.378745i	$0.123644\pi$
$978$	11.2918			0.361072
$979$		0			0
$980$	8.47214			0.270632
$981$		0			0
$982$	12.6074	−	9.15981i	0.402318	−	0.292301i
$983$	22.0902	+	16.0494i	0.704567	+	0.511898i	0.881416	−	0.472340i	$-0.156591\pi$
$983$	22.0902	+	16.0494i	0.704567	+	0.511898i	−0.176849	+	0.984238i	$0.556591\pi$
$984$	−8.25329	−	25.4010i	−0.263105	−	0.809755i
$985$	19.7254	+	60.7086i	0.628504	+	1.93434i
$986$	−3.61803	−	2.62866i	−0.115222	−	0.0837134i
$987$	3.92705	−	2.85317i	0.124999	−	0.0908174i
$988$	−5.16312	+	15.8904i	−0.164261	+	0.505542i
$989$	−21.6525			−0.688509
$990$		0			0
$991$	21.2705			0.675680			0.337840	−	0.941204i	$-0.390304\pi$
$991$	21.2705			0.675680			0.337840	+	0.941204i	$0.390304\pi$
$992$	4.95492	−	15.2497i	0.157319	−	0.484177i
$993$	−21.5172	+	15.6332i	−0.682828	+	0.496104i
$994$	−8.34346	−	6.06188i	−0.264638	−	0.192271i
$995$	13.5172	+	41.6017i	0.428525	+	1.31886i
$996$	0.354102	+	1.08981i	0.0112202	+	0.0345321i
$997$	−10.5000	−	7.62870i	−0.332538	−	0.241603i	0.408969	−	0.912548i	$-0.365889\pi$
$997$	−10.5000	−	7.62870i	−0.332538	−	0.241603i	−0.741507	+	0.670945i	$0.765889\pi$
$998$	8.78115	−	6.37988i	0.277963	−	0.201952i
$999$	0.0729490	−	0.224514i	0.00230800	−	0.00710331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.j.130.1		4
11.2	odd	10		363.2.e.h.124.1		4
11.3	even	5		363.2.e.c.202.1		4
11.4	even	5		363.2.a.e.1.2		2
11.5	even	5	inner	363.2.e.j.148.1		4
11.6	odd	10		33.2.e.a.16.1	✓	4
11.7	odd	10		363.2.a.h.1.1		2
11.8	odd	10		363.2.e.h.202.1		4
11.9	even	5		363.2.e.c.124.1		4
11.10	odd	2		33.2.e.a.31.1	yes	4
33.17	even	10		99.2.f.b.82.1		4
33.26	odd	10		1089.2.a.s.1.1		2
33.29	even	10		1089.2.a.m.1.2		2
33.32	even	2		99.2.f.b.64.1		4
44.7	even	10		5808.2.a.bl.1.1		2
44.15	odd	10		5808.2.a.bm.1.1		2
44.39	even	10		528.2.y.f.49.1		4
44.43	even	2		528.2.y.f.97.1		4
55.4	even	10		9075.2.a.bv.1.1		2
55.17	even	20		825.2.bx.b.49.2		8
55.28	even	20		825.2.bx.b.49.1		8
55.29	odd	10		9075.2.a.x.1.2		2
55.32	even	4		825.2.bx.b.724.1		8
55.39	odd	10		825.2.n.f.676.1		4
55.43	even	4		825.2.bx.b.724.2		8
55.54	odd	2		825.2.n.f.526.1		4
99.32	even	6		891.2.n.a.460.1		8
99.43	odd	6		891.2.n.d.757.1		8
99.50	even	30		891.2.n.a.379.1		8
99.61	odd	30		891.2.n.d.676.1		8
99.65	even	6		891.2.n.a.757.1		8
99.76	odd	6		891.2.n.d.460.1		8
99.83	even	30		891.2.n.a.676.1		8
99.94	odd	30		891.2.n.d.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.16.1	✓	4	11.6	odd	10
33.2.e.a.31.1	yes	4	11.10	odd	2
99.2.f.b.64.1		4	33.32	even	2
99.2.f.b.82.1		4	33.17	even	10
363.2.a.e.1.2		2	11.4	even	5
363.2.a.h.1.1		2	11.7	odd	10
363.2.e.c.124.1		4	11.9	even	5
363.2.e.c.202.1		4	11.3	even	5
363.2.e.h.124.1		4	11.2	odd	10
363.2.e.h.202.1		4	11.8	odd	10
363.2.e.j.130.1		4	1.1	even	1	trivial
363.2.e.j.148.1		4	11.5	even	5	inner
528.2.y.f.49.1		4	44.39	even	10
528.2.y.f.97.1		4	44.43	even	2
825.2.n.f.526.1		4	55.54	odd	2
825.2.n.f.676.1		4	55.39	odd	10
825.2.bx.b.49.1		8	55.28	even	20
825.2.bx.b.49.2		8	55.17	even	20
825.2.bx.b.724.1		8	55.32	even	4
825.2.bx.b.724.2		8	55.43	even	4
891.2.n.a.379.1		8	99.50	even	30
891.2.n.a.460.1		8	99.32	even	6
891.2.n.a.676.1		8	99.83	even	30
891.2.n.a.757.1		8	99.65	even	6
891.2.n.d.379.1		8	99.94	odd	30
891.2.n.d.460.1		8	99.76	odd	6
891.2.n.d.676.1		8	99.61	odd	30
891.2.n.d.757.1		8	99.43	odd	6
1089.2.a.m.1.2		2	33.29	even	10
1089.2.a.s.1.1		2	33.26	odd	10
5808.2.a.bl.1.1		2	44.7	even	10
5808.2.a.bm.1.1		2	44.15	odd	10
9075.2.a.x.1.2		2	55.29	odd	10
9075.2.a.bv.1.1		2	55.4	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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.190983 + 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.190983 - 0.587785i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(1.30902 + 0.951057i) q^{4} +(-0.809017 - 2.48990i) q^{5} +(0.190983 + 0.587785i) q^{6} +(2.42705 + 1.76336i) q^{7} +(1.80902 - 1.31433i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.61803 q^{10} -1.61803 q^{12} +(-0.545085 + 1.67760i) q^{13} +(1.50000 - 1.08981i) q^{14} +(2.11803 + 1.53884i) q^{15} +(0.572949 + 1.76336i) q^{16} +(-0.500000 - 1.53884i) q^{17} +(-0.500000 - 0.363271i) q^{18} +(4.73607 - 3.44095i) q^{19} +(1.30902 - 4.02874i) q^{20} -3.00000 q^{21} +3.47214 q^{23} +(-0.690983 + 2.12663i) q^{24} +(-1.50000 + 1.08981i) q^{25} +(0.881966 + 0.640786i) q^{26} +(0.309017 + 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(3.61803 + 2.62866i) q^{29} +(1.30902 - 0.951057i) q^{30} +(0.881966 - 2.71441i) q^{31} +5.61803 q^{32} -1.00000 q^{34} +(2.42705 - 7.46969i) q^{35} +(1.30902 - 0.951057i) q^{36} +(-0.190983 - 0.138757i) q^{37} +(-1.11803 - 3.44095i) q^{38} +(-0.545085 - 1.67760i) q^{39} +(-4.73607 - 3.44095i) q^{40} +(-9.66312 + 7.02067i) q^{41} +(-0.572949 + 1.76336i) q^{42} -6.23607 q^{43} -2.61803 q^{45} +(0.663119 - 2.04087i) q^{46} +(-1.30902 + 0.951057i) q^{47} +(-1.50000 - 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(0.354102 + 1.08981i) q^{50} +(1.30902 + 0.951057i) q^{51} +(-2.30902 + 1.67760i) q^{52} +(-2.97214 + 9.14729i) q^{53} +0.618034 q^{54} +6.70820 q^{56} +(-1.80902 + 5.56758i) q^{57} +(2.23607 - 1.62460i) q^{58} +(-8.35410 - 6.06961i) q^{59} +(1.30902 + 4.02874i) q^{60} +(-2.42705 - 7.46969i) q^{61} +(-1.42705 - 1.03681i) q^{62} +(2.42705 - 1.76336i) q^{63} +(-0.0729490 + 0.224514i) q^{64} +4.61803 q^{65} -9.56231 q^{67} +(0.809017 - 2.48990i) q^{68} +(-2.80902 + 2.04087i) q^{69} +(-3.92705 - 2.85317i) q^{70} +(-1.71885 - 5.29007i) q^{71} +(-0.690983 - 2.12663i) q^{72} +(-2.61803 - 1.90211i) q^{73} +(-0.118034 + 0.0857567i) q^{74} +(0.572949 - 1.76336i) q^{75} +9.47214 q^{76} -1.09017 q^{78} +(-2.92705 + 9.00854i) q^{79} +(3.92705 - 2.85317i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(2.28115 + 7.02067i) q^{82} +(-0.218847 - 0.673542i) q^{83} +(-3.92705 - 2.85317i) q^{84} +(-3.42705 + 2.48990i) q^{85} +(-1.19098 + 3.66547i) q^{86} -4.47214 q^{87} +0.527864 q^{89} +(-0.500000 + 1.53884i) q^{90} +(-4.28115 + 3.11044i) q^{91} +(4.54508 + 3.30220i) q^{92} +(0.881966 + 2.71441i) q^{93} +(0.309017 + 0.951057i) q^{94} +(-12.3992 - 9.00854i) q^{95} +(-4.54508 + 3.30220i) q^{96} +(-4.33688 + 13.3475i) q^{97} +1.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9	\( 4 q + 3 q^{2} - q^{3} + 3 q^{4} - q^{5} + 3 q^{6} + 3 q^{7} + 5 q^{8} - q^{9} - 2 q^{10} - 2 q^{12} + 9 q^{13} + 6 q^{14} + 4 q^{15} + 9 q^{16} - 2 q^{17} - 2 q^{18} + 10 q^{19} + 3 q^{20} - 12 q^{21} - 4 q^{23} - 5 q^{24} - 6 q^{25} + 8 q^{26} - q^{27} + 6 q^{28} + 10 q^{29} + 3 q^{30} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} + 3 q^{36} - 3 q^{37} + 9 q^{39} - 10 q^{40} - 23 q^{41} - 9 q^{42} - 16 q^{43} - 6 q^{45} - 13 q^{46} - 3 q^{47} - 6 q^{48} - 2 q^{49} - 12 q^{50} + 3 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} - 5 q^{57} - 20 q^{59} + 3 q^{60} - 3 q^{61} + q^{62} + 3 q^{63} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{69} - 9 q^{70} - 27 q^{71} - 5 q^{72} - 6 q^{73} + 4 q^{74} + 9 q^{75} + 20 q^{76} + 18 q^{78} - 5 q^{79} + 9 q^{80} - q^{81} - 11 q^{82} - 21 q^{83} - 9 q^{84} - 7 q^{85} - 7 q^{86} + 20 q^{89} - 2 q^{90} + 3 q^{91} + 7 q^{92} + 8 q^{93} - q^{94} - 25 q^{95} - 7 q^{96} - 33 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - q^3 + 3 * q^4 - q^5 + 3 * q^6 + 3 * q^7 + 5 * q^8 - q^9 - 2 * q^10 - 2 * q^12 + 9 * q^13 + 6 * q^14 + 4 * q^15 + 9 * q^16 - 2 * q^17 - 2 * q^18 + 10 * q^19 + 3 * q^20 - 12 * q^21 - 4 * q^23 - 5 * q^24 - 6 * q^25 + 8 * q^26 - q^27 + 6 * q^28 + 10 * q^29 + 3 * q^30 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 + 3 * q^36 - 3 * q^37 + 9 * q^39 - 10 * q^40 - 23 * q^41 - 9 * q^42 - 16 * q^43 - 6 * q^45 - 13 * q^46 - 3 * q^47 - 6 * q^48 - 2 * q^49 - 12 * q^50 + 3 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 - 5 * q^57 - 20 * q^59 + 3 * q^60 - 3 * q^61 + q^62 + 3 * q^63 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^69 - 9 * q^70 - 27 * q^71 - 5 * q^72 - 6 * q^73 + 4 * q^74 + 9 * q^75 + 20 * q^76 + 18 * q^78 - 5 * q^79 + 9 * q^80 - q^81 - 11 * q^82 - 21 * q^83 - 9 * q^84 - 7 * q^85 - 7 * q^86 + 20 * q^89 - 2 * q^90 + 3 * q^91 + 7 * q^92 + 8 * q^93 - q^94 - 25 * q^95 - 7 * q^96 - 33 * q^97 - 4 * q^98

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