LMFDB - Embedded newform 455.2.bq.a.36.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [455,2,Mod(36,455)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("455.36"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(455, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 455 = 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	455.bq (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$3.63319329197$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 24 x^{18} + 236 x^{16} + 1230 x^{14} + 3684 x^{12} + 6482 x^{10} + 6665 x^{8} + 3872 x^{6} + \cdots + 1 $ x^20 + 24x^18 + 236x^16 + 1230x^14 + 3684x^12 + 6482x^10 + 6665x^8 + 3872x^6 + 1162x^4 + 140*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			36.8
Root			$1.30628i$ of defining polynomial
Character	$\chi$	$=$	455.36
Dual form			455.2.bq.a.316.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.13127 - 0.653140i) q^{2} +(0.992163 + 1.71848i) q^{3} +(-0.146816 + 0.254293i) q^{4} -1.00000i q^{5} +(2.24481 + 1.29604i) q^{6} +(0.866025 + 0.500000i) q^{7} +2.99613i q^{8} +(-0.468774 + 0.811941i) q^{9} +(-0.653140 - 1.13127i) q^{10} +(-0.173399 + 0.100112i) q^{11} -0.582663 q^{12} +(2.42512 + 2.66810i) q^{13} +1.30628 q^{14} +(1.71848 - 0.992163i) q^{15} +(1.66326 + 2.88085i) q^{16} +(-0.153965 + 0.266675i) q^{17} +1.22470i q^{18} +(-2.49854 - 1.44253i) q^{19} +(0.254293 + 0.146816i) q^{20} +1.98433i q^{21} +(-0.130774 + 0.226508i) q^{22} +(-0.0132078 - 0.0228766i) q^{23} +(-5.14877 + 2.97265i) q^{24} -1.00000 q^{25} +(4.48612 + 1.43440i) q^{26} +4.09258 q^{27} +(-0.254293 + 0.146816i) q^{28} +(-1.66879 - 2.89043i) q^{29} +(1.29604 - 2.24481i) q^{30} -4.36047i q^{31} +(-1.42625 - 0.823447i) q^{32} +(-0.344080 - 0.198655i) q^{33} +0.402243i q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.137647 - 0.238412i) q^{36} +(-0.935201 + 0.539939i) q^{37} -3.76871 q^{38} +(-2.17895 + 6.81471i) q^{39} +2.99613 q^{40} +(4.14823 - 2.39498i) q^{41} +(1.29604 + 2.24481i) q^{42} +(-1.05264 + 1.82322i) q^{43} -0.0587923i q^{44} +(0.811941 + 0.468774i) q^{45} +(-0.0298832 - 0.0172531i) q^{46} -6.56495i q^{47} +(-3.30044 + 5.71654i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.13127 + 0.653140i) q^{50} -0.611034 q^{51} +(-1.03453 + 0.224972i) q^{52} +1.77119 q^{53} +(4.62981 - 2.67302i) q^{54} +(0.100112 + 0.173399i) q^{55} +(-1.49806 + 2.59472i) q^{56} -5.72492i q^{57} +(-3.77572 - 2.17991i) q^{58} +(-6.07534 - 3.50760i) q^{59} +0.582663i q^{60} +(4.28889 - 7.42858i) q^{61} +(-2.84800 - 4.93288i) q^{62} +(-0.811941 + 0.468774i) q^{63} -8.80433 q^{64} +(2.66810 - 2.42512i) q^{65} -0.518997 q^{66} +(-4.69371 + 2.70992i) q^{67} +(-0.0452092 - 0.0783046i) q^{68} +(0.0262086 - 0.0453946i) q^{69} -1.30628i q^{70} +(-8.72896 - 5.03966i) q^{71} +(-2.43268 - 1.40451i) q^{72} -8.13440i q^{73} +(-0.705311 + 1.22163i) q^{74} +(-0.992163 - 1.71848i) q^{75} +(0.733654 - 0.423575i) q^{76} -0.200224 q^{77} +(1.98597 + 9.13245i) q^{78} +4.64412 q^{79} +(2.88085 - 1.66326i) q^{80} +(5.46682 + 9.46882i) q^{81} +(3.12852 - 5.41875i) q^{82} -11.0233i q^{83} +(-0.504601 - 0.291331i) q^{84} +(0.266675 + 0.153965i) q^{85} +2.75007i q^{86} +(3.31143 - 5.73556i) q^{87} +(-0.299948 - 0.519525i) q^{88} +(6.23057 - 3.59722i) q^{89} +1.22470 q^{90} +(0.766168 + 3.52321i) q^{91} +0.00775648 q^{92} +(7.49336 - 4.32630i) q^{93} +(-4.28783 - 7.42674i) q^{94} +(-1.44253 + 2.49854i) q^{95} -3.26797i q^{96} +(12.2870 + 7.09388i) q^{97} +(1.13127 + 0.653140i) q^{98} -0.187720i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} + 4 q^{4} + 18 q^{6} - 6 q^{11} - 8 q^{12} + 6 q^{15} - 10 q^{17} + 26 q^{22} + 2 q^{23} + 12 q^{24} - 20 q^{25} - 2 q^{26} - 44 q^{27} + 12 q^{29} - 8 q^{30} - 6 q^{32} - 18 q^{33} + 10 q^{35}+ \cdots + 18 q^{97}+O(q^{100}) $ 20 * q + 4 * q^3 + 4 * q^4 + 18 * q^6 - 6 * q^11 - 8 * q^12 + 6 * q^15 - 10 * q^17 + 26 * q^22 + 2 * q^23 + 12 * q^24 - 20 * q^25 - 2 * q^26 - 44 * q^27 + 12 * q^29 - 8 * q^30 - 6 * q^32 - 18 * q^33 + 10 * q^35 - 22 * q^36 - 72 * q^38 + 8 * q^39 + 12 * q^41 - 8 * q^42 - 8 * q^43 + 10 * q^48 + 10 * q^49 - 60 * q^51 - 12 * q^52 - 24 * q^53 + 84 * q^54 + 12 * q^55 - 12 * q^58 - 12 * q^59 + 42 * q^61 - 40 * q^62 + 44 * q^64 + 4 * q^65 + 12 * q^66 + 6 * q^67 + 34 * q^68 - 44 * q^69 + 108 * q^71 - 24 * q^72 + 38 * q^74 - 4 * q^75 - 12 * q^76 - 24 * q^77 - 2 * q^78 - 44 * q^79 + 24 * q^80 + 2 * q^81 - 40 * q^82 - 18 * q^84 - 12 * q^85 + 4 * q^87 - 22 * q^88 + 6 * q^89 - 20 * q^90 - 14 * q^91 - 32 * q^92 + 108 * q^93 - 14 * q^94 + 16 * q^95 + 18 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/455\mathbb{Z}\right)^\times$.

$n$	$66$	$92$	$106$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.13127	−	0.653140i	0.799930	−	0.461840i	−0.0435168	−	0.999053i	$-0.513856\pi$
$2$	1.13127	−	0.653140i	0.799930	−	0.461840i	0.843447	+	0.537213i	$0.180523\pi$
$3$	0.992163	+	1.71848i	0.572825	+	0.992163i	0.996274	+	0.0862427i	$0.0274861\pi$
$3$	0.992163	+	1.71848i	0.572825	+	0.992163i	−0.423449	+	0.905920i	$0.639181\pi$
$4$	−0.146816	+	0.254293i	−0.0734082	+	0.127147i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.24481	+	1.29604i	0.916440	+	0.529107i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i
$8$			2.99613i			1.05929i
$9$	−0.468774	+	0.811941i	−0.156258	+	0.270647i
$10$	−0.653140	−	1.13127i	−0.206541	−	0.357739i
$11$	−0.173399	+	0.100112i	−0.0522818	+	0.0301849i	−0.525913	−	0.850538i	$-0.676276\pi$
$11$	−0.173399	+	0.100112i	−0.0522818	+	0.0301849i	0.473631	+	0.880723i	$0.342943\pi$
$12$	−0.582663			−0.168200
$13$	2.42512	+	2.66810i	0.672608	+	0.739999i
$13$	2.42512	+	2.66810i	0.672608	+	0.739999i
$14$	1.30628			0.349118
$15$	1.71848	−	0.992163i	0.443709	−	0.256175i
$16$	1.66326	+	2.88085i	0.415814	+	0.720212i
$17$	−0.153965	+	0.266675i	−0.0373420	+	0.0646783i	−0.884092	−	0.467312i	$-0.845222\pi$
$17$	−0.153965	+	0.266675i	−0.0373420	+	0.0646783i	0.846750	+	0.531990i	$0.178556\pi$
$18$			1.22470i			0.288665i
$19$	−2.49854	−	1.44253i	−0.573205	−	0.330940i	0.185223	−	0.982696i	$-0.440699\pi$
$19$	−2.49854	−	1.44253i	−0.573205	−	0.330940i	−0.758428	+	0.651756i	$0.774032\pi$
$20$	0.254293	+	0.146816i	0.0568617	+	0.0328291i
$21$			1.98433i			0.433015i
$22$	−0.130774	+	0.226508i	−0.0278812	+	0.0482916i
$23$	−0.0132078	−	0.0228766i	−0.00275401	−	0.00477009i	0.864645	−	0.502383i	$-0.167543\pi$
$23$	−0.0132078	−	0.0228766i	−0.00275401	−	0.00477009i	−0.867399	+	0.497613i	$0.834210\pi$
$24$	−5.14877	+	2.97265i	−1.05099	+	0.606789i
$25$	−1.00000			−0.200000
$26$	4.48612	+	1.43440i	0.879800	+	0.281310i
$27$	4.09258			0.787617
$28$	−0.254293	+	0.146816i	−0.0480569	+	0.0277457i
$29$	−1.66879	−	2.89043i	−0.309887	−	0.536740i	0.668450	−	0.743757i	$-0.266958\pi$
$29$	−1.66879	−	2.89043i	−0.309887	−	0.536740i	−0.978337	+	0.207017i	$0.933625\pi$
$30$	1.29604	−	2.24481i	0.236624	−	0.409845i
$31$		−	4.36047i		−	0.783164i	−0.920143	−	0.391582i	$-0.871928\pi$
$31$		−	4.36047i		−	0.783164i	0.920143	−	0.391582i	$-0.128072\pi$
$32$	−1.42625	−	0.823447i	−0.252128	−	0.145566i
$33$	−0.344080	−	0.198655i	−0.0598966	−	0.0345813i
$34$			0.402243i			0.0689841i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	−0.137647	−	0.238412i	−0.0229412	−	0.0397354i
$37$	−0.935201	+	0.539939i	−0.153746	+	0.0887653i	−0.574899	−	0.818224i	$-0.694959\pi$
$37$	−0.935201	+	0.539939i	−0.153746	+	0.0887653i	0.421153	+	0.906989i	$0.361625\pi$
$38$	−3.76871			−0.611365
$39$	−2.17895	+	6.81471i	−0.348912	+	1.09123i
$40$	2.99613			0.473729
$41$	4.14823	−	2.39498i	0.647845	−	0.374034i	−0.139785	−	0.990182i	$-0.544641\pi$
$41$	4.14823	−	2.39498i	0.647845	−	0.374034i	0.787630	+	0.616148i	$0.211308\pi$
$42$	1.29604	+	2.24481i	0.199984	+	0.346382i
$43$	−1.05264	+	1.82322i	−0.160525	+	0.278038i	−0.935057	−	0.354497i	$-0.884652\pi$
$43$	−1.05264	+	1.82322i	−0.160525	+	0.278038i	0.774532	+	0.632535i	$0.217986\pi$
$44$		−	0.0587923i		−	0.00886327i
$45$	0.811941	+	0.468774i	0.121037	+	0.0698807i
$46$	−0.0298832	−	0.0172531i	−0.00440604	−	0.00254383i
$47$		−	6.56495i		−	0.957596i	−0.877925	−	0.478798i	$-0.841073\pi$
$47$		−	6.56495i		−	0.957596i	0.877925	−	0.478798i	$-0.158927\pi$
$48$	−3.30044	+	5.71654i	−0.476378	+	0.825111i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−1.13127	+	0.653140i	−0.159986	+	0.0923679i
$51$	−0.611034			−0.0855618
$52$	−1.03453	+	0.224972i	−0.143463	+	0.0311980i
$53$	1.77119			0.243291			0.121646	−	0.992574i	$-0.461183\pi$
$53$	1.77119			0.243291			0.121646	+	0.992574i	$0.461183\pi$
$54$	4.62981	−	2.67302i	0.630038	−	0.363753i
$55$	0.100112	+	0.173399i	0.0134991	+	0.0233811i
$56$	−1.49806	+	2.59472i	−0.200187	+	0.346734i
$57$		−	5.72492i		−	0.758284i
$58$	−3.77572	−	2.17991i	−0.495776	−	0.286236i
$59$	−6.07534	−	3.50760i	−0.790942	−	0.456650i	0.0493522	−	0.998781i	$-0.484284\pi$
$59$	−6.07534	−	3.50760i	−0.790942	−	0.456650i	−0.840294	+	0.542131i	$0.817618\pi$
$60$			0.582663i			0.0752215i
$61$	4.28889	−	7.42858i	0.549137	−	0.951132i	−0.449197	−	0.893433i	$-0.648290\pi$
$61$	4.28889	−	7.42858i	0.549137	−	0.951132i	0.998334	−	0.0576999i	$-0.0183766\pi$
$62$	−2.84800	−	4.93288i	−0.361696	−	0.626476i
$63$	−0.811941	+	0.468774i	−0.102295	+	0.0590600i
$64$	−8.80433			−1.10054
$65$	2.66810	−	2.42512i	0.330937	−	0.300800i
$66$	−0.518997			−0.0638841
$67$	−4.69371	+	2.70992i	−0.573428	+	0.331069i	−0.758517	−	0.651653i	$-0.774076\pi$
$67$	−4.69371	+	2.70992i	−0.573428	+	0.331069i	0.185089	+	0.982722i	$0.440743\pi$
$68$	−0.0452092	−	0.0783046i	−0.00548242	−	0.00949583i
$69$	0.0262086	−	0.0453946i	0.00315514	−	0.00546486i
$70$		−	1.30628i		−	0.156130i
$71$	−8.72896	−	5.03966i	−1.03594	−	0.598098i	−0.117257	−	0.993102i	$-0.537410\pi$
$71$	−8.72896	−	5.03966i	−1.03594	−	0.598098i	−0.918680	+	0.395003i	$0.870743\pi$
$72$	−2.43268	−	1.40451i	−0.286694	−	0.165523i
$73$		−	8.13440i		−	0.952060i	−0.879429	−	0.476030i	$-0.842075\pi$
$73$		−	8.13440i		−	0.952060i	0.879429	−	0.476030i	$-0.157925\pi$
$74$	−0.705311	+	1.22163i	−0.0819907	+	0.142012i
$75$	−0.992163	−	1.71848i	−0.114565	−	0.198433i
$76$	0.733654	−	0.423575i	0.0841559	−	0.0485874i
$77$	−0.200224			−0.0228176
$78$	1.98597	+	9.13245i	0.224867	+	1.03405i
$79$	4.64412			0.522505			0.261252	−	0.965271i	$-0.415865\pi$
$79$	4.64412			0.522505			0.261252	+	0.965271i	$0.415865\pi$
$80$	2.88085	−	1.66326i	0.322088	−	0.185958i
$81$	5.46682	+	9.46882i	0.607425	+	1.05209i
$82$	3.12852	−	5.41875i	0.345487	−	0.598401i
$83$		−	11.0233i		−	1.20996i	−0.796240	−	0.604981i	$-0.793181\pi$
$83$		−	11.0233i		−	1.20996i	0.796240	−	0.604981i	$-0.206819\pi$
$84$	−0.504601	−	0.291331i	−0.0550565	−	0.0317869i
$85$	0.266675	+	0.153965i	0.0289250	+	0.0166999i
$86$			2.75007i			0.296548i
$87$	3.31143	−	5.73556i	0.355022	−	0.614917i
$88$	−0.299948	−	0.519525i	−0.0319746	−	0.0553816i
$89$	6.23057	−	3.59722i	0.660439	−	0.381305i	−0.132005	−	0.991249i	$-0.542142\pi$
$89$	6.23057	−	3.59722i	0.660439	−	0.381305i	0.792444	+	0.609944i	$0.208808\pi$
$90$	1.22470			0.129095
$91$	0.766168	+	3.52321i	0.0803162	+	0.369332i
$92$	0.00775648			0.000808669
$93$	7.49336	−	4.32630i	0.777026	−	0.448616i
$94$	−4.28783	−	7.42674i	−0.442256	−	0.766010i
$95$	−1.44253	+	2.49854i	−0.148001	+	0.256345i
$96$		−	3.26797i		−	0.333536i
$97$	12.2870	+	7.09388i	1.24755	+	0.720274i	0.970621	−	0.240615i	$-0.0773493\pi$
$97$	12.2870	+	7.09388i	1.24755	+	0.720274i	0.276931	+	0.960890i	$0.410683\pi$
$98$	1.13127	+	0.653140i	0.114276	+	0.0659771i
$99$		−	0.187720i		−	0.0188665i
$100$	0.146816	−	0.254293i	0.0146816	−	0.0254293i
$101$	−3.90663	−	6.76648i	−0.388724	−	0.673290i	0.603554	−	0.797322i	$-0.293751\pi$
$101$	−3.90663	−	6.76648i	−0.388724	−	0.673290i	−0.992278	+	0.124032i	$0.960417\pi$
$102$	−0.691245	+	0.399091i	−0.0684435	+	0.0395159i
$103$	−8.66126			−0.853419			−0.426710	−	0.904389i	$-0.640327\pi$
$103$	−8.66126			−0.853419			−0.426710	+	0.904389i	$0.640327\pi$
$104$	−7.99397	+	7.26598i	−0.783874	+	0.712488i
$105$	1.98433			0.193650
$106$	2.00369	−	1.15683i	0.194616	−	0.112362i
$107$	3.48460	+	6.03550i	0.336869	+	0.583474i	0.983842	−	0.179039i	$-0.0572988\pi$
$107$	3.48460	+	6.03550i	0.336869	+	0.583474i	−0.646973	+	0.762513i	$0.723966\pi$
$108$	−0.600857	+	1.04071i	−0.0578175	+	0.100143i
$109$			14.8633i			1.42364i	0.702361	+	0.711821i	$0.252129\pi$
$109$			14.8633i			1.42364i	−0.702361	+	0.711821i	$0.747871\pi$
$110$	0.226508	+	0.130774i	0.0215967	+	0.0124688i
$111$	−1.85574	−	1.07141i	−0.176139	−	0.101694i
$112$			3.32651i			0.314326i
$113$	−2.66162	+	4.61006i	−0.250384	+	0.433678i	−0.963632	−	0.267234i	$-0.913890\pi$
$113$	−2.66162	+	4.61006i	−0.250384	+	0.433678i	0.713247	+	0.700912i	$0.247224\pi$
$114$	−3.73917	−	6.47644i	−0.350206	−	0.606574i
$115$	−0.0228766	+	0.0132078i	−0.00213325	+	0.00123163i
$116$	0.980025			0.0909930
$117$	−3.30318	+	0.718319i	−0.305379	+	0.0664086i
$118$	−9.16381			−0.843597
$119$	−0.266675	+	0.153965i	−0.0244461	+	0.0141140i
$120$	2.97265	+	5.14877i	0.271364	+	0.470016i
$121$	−5.47996	+	9.49156i	−0.498178	+	0.862869i
$122$		−	11.2050i		−	1.01445i
$123$	8.23145	+	4.75243i	0.742204	+	0.428512i
$124$	1.10884	+	0.640188i	0.0995766	+	0.0574906i
$125$			1.00000i			0.0894427i
$126$	−0.612350	+	1.06062i	−0.0545525	+	0.0944877i
$127$	−1.27491	−	2.20822i	−0.113130	−	0.195948i	0.803900	−	0.594764i	$-0.202754\pi$
$127$	−1.27491	−	2.20822i	−0.113130	−	0.195948i	−0.917031	+	0.398816i	$0.869421\pi$
$128$	−7.10759	+	4.10357i	−0.628228	+	0.362708i
$129$	−4.17755			−0.367812
$130$	1.43440	−	4.48612i	0.125805	−	0.393459i
$131$	−7.01829			−0.613191			−0.306595	−	0.951840i	$-0.599190\pi$
$131$	−7.01829			−0.613191			−0.306595	+	0.951840i	$0.599190\pi$
$132$	0.101033	−	0.0583315i	0.00879381	−	0.00507711i
$133$	−1.44253	−	2.49854i	−0.125084	−	0.216651i
$134$	−3.53991	+	6.13130i	−0.305802	+	0.529664i
$135$		−	4.09258i		−	0.352233i
$136$	−0.798993	−	0.461299i	−0.0685131	−	0.0395561i
$137$	−5.12500	−	2.95892i	−0.437859	−	0.252798i	0.264830	−	0.964295i	$-0.414684\pi$
$137$	−5.12500	−	2.95892i	−0.437859	−	0.252798i	−0.702689	+	0.711497i	$0.748017\pi$
$138$		−	0.0684714i		−	0.00582867i
$139$	−11.6509	+	20.1800i	−0.988217	+	1.71164i	−0.361553	+	0.932352i	$0.617753\pi$
$139$	−11.6509	+	20.1800i	−0.988217	+	1.71164i	−0.626664	+	0.779290i	$0.715580\pi$
$140$	0.146816	+	0.254293i	0.0124082	+	0.0214917i
$141$	11.2817	−	6.51350i	0.950092	−	0.548536i
$142$	−13.1664			−1.10490
$143$	−0.687623	−	0.219862i	−0.0575019	−	0.0183858i
$144$	−3.11877			−0.259897
$145$	−2.89043	+	1.66879i	−0.240038	+	0.138586i
$146$	−5.31290	−	9.20222i	−0.439699	−	0.761581i
$147$	−0.992163	+	1.71848i	−0.0818322	+	0.141738i
$148$		−	0.317087i		−	0.0260644i
$149$	4.06826	+	2.34881i	0.333285	+	0.192422i	0.657298	−	0.753630i	$-0.271699\pi$
$149$	4.06826	+	2.34881i	0.333285	+	0.192422i	−0.324014	+	0.946052i	$0.605032\pi$
$150$	−2.24481	−	1.29604i	−0.183288	−	0.105821i
$151$			15.0451i			1.22435i	0.790722	+	0.612175i	$0.209705\pi$
$151$			15.0451i			1.22435i	−0.790722	+	0.612175i	$0.790295\pi$
$152$	4.32202	−	7.48595i	0.350562	−	0.607191i
$153$	−0.144350	−	0.250021i	−0.0116700	−	0.0202130i
$154$	−0.226508	+	0.130774i	−0.0182525	+	0.0105381i
$155$	−4.36047			−0.350241
$156$	−1.41303	−	1.55460i	−0.113133	−	0.124468i
$157$	13.8970			1.10910			0.554552	−	0.832149i	$-0.312890\pi$
$157$	13.8970			1.10910			0.554552	+	0.832149i	$0.312890\pi$
$158$	5.25376	−	3.03326i	0.417967	−	0.241313i
$159$	1.75731	+	3.04374i	0.139363	+	0.241384i
$160$	−0.823447	+	1.42625i	−0.0650992	+	0.112755i
$161$		−	0.0264156i		−	0.00208184i
$162$	12.3689	+	7.14120i	0.971795	+	0.561066i
$163$	−19.8668	−	11.4701i	−1.55608	−	0.898406i	−0.997625	−	0.0688744i	$-0.978059\pi$
$163$	−19.8668	−	11.4701i	−1.55608	−	0.898406i	−0.558460	−	0.829532i	$-0.688607\pi$
$164$			1.40649i			0.109828i
$165$	−0.198655	+	0.344080i	−0.0154652	+	0.0267866i
$166$	−7.19975	−	12.4703i	−0.558809	−	0.967885i
$167$	14.3031	−	8.25787i	1.10680	−	0.639014i	0.168804	−	0.985650i	$-0.446009\pi$
$167$	14.3031	−	8.25787i	1.10680	−	0.639014i	0.938000	+	0.346636i	$0.112676\pi$
$168$	−5.94529			−0.458689
$169$	−1.23754	+	12.9410i	−0.0951958	+	0.995459i
$170$	0.402243			0.0308506
$171$	2.34250	−	1.35245i	0.179136	−	0.103424i
$172$	−0.309088	−	0.535357i	−0.0235678	−	0.0408206i
$173$	−9.23532	+	15.9960i	−0.702149	+	1.21616i	0.265562	+	0.964094i	$0.414442\pi$
$173$	−9.23532	+	15.9960i	−0.702149	+	1.21616i	−0.967711	+	0.252063i	$0.918891\pi$
$174$		−	8.65131i		−	0.655854i
$175$	−0.866025	−	0.500000i	−0.0654654	−	0.0377964i
$176$	−0.576814	−	0.333024i	−0.0434790	−	0.0251026i
$177$		−	13.9204i		−	1.04632i
$178$	4.69898	−	8.13887i	0.352203	−	0.610034i
$179$	4.01478	+	6.95381i	0.300079	+	0.519752i	0.976154	−	0.217081i	$-0.0696536\pi$
$179$	4.01478	+	6.95381i	0.300079	+	0.519752i	−0.676075	+	0.736833i	$0.736320\pi$
$180$	−0.238412	+	0.137647i	−0.0177702	+	0.0102596i
$181$	−0.349155			−0.0259525			−0.0129763	−	0.999916i	$-0.504131\pi$
$181$	−0.349155			−0.0259525			−0.0129763	+	0.999916i	$0.504131\pi$
$182$	3.16789	+	3.48529i	0.234820	+	0.258347i
$183$	17.0211			1.25824
$184$	0.0685411	−	0.0395722i	0.00505292	−	0.00291730i
$185$	0.539939	+	0.935201i	0.0396971	+	0.0687573i
$186$	5.65135	−	9.78843i	0.414377	−	0.717723i
$187$		−	0.0616550i		−	0.00450866i
$188$	1.66942	+	0.963842i	0.121755	+	0.0702954i
$189$	3.54427	+	2.04629i	0.257808	+	0.148846i
$190$			3.76871i			0.273411i
$191$	−3.15923	+	5.47195i	−0.228594	+	0.395937i	−0.957392	−	0.288793i	$-0.906746\pi$
$191$	−3.15923	+	5.47195i	−0.228594	+	0.395937i	0.728798	+	0.684729i	$0.240080\pi$
$192$	−8.73533	−	15.1300i	−0.630418	−	1.09192i
$193$	16.3998	−	9.46842i	1.18048	−	0.681552i	0.224356	−	0.974507i	$-0.427972\pi$
$193$	16.3998	−	9.46842i	1.18048	−	0.681552i	0.956126	+	0.292956i	$0.0946388\pi$
$194$	18.5332			1.33061
$195$	6.81471	+	2.17895i	0.488012	+	0.156038i
$196$	−0.293633			−0.0209738
$197$	13.1568	−	7.59606i	0.937380	−	0.541197i	0.0482419	−	0.998836i	$-0.484638\pi$
$197$	13.1568	−	7.59606i	0.937380	−	0.541197i	0.889138	+	0.457639i	$0.151305\pi$
$198$	−0.122607	−	0.212362i	−0.00871331	−	0.0150919i
$199$	−10.7673	+	18.6495i	−0.763275	+	1.32203i	0.177879	+	0.984052i	$0.443076\pi$
$199$	−10.7673	+	18.6495i	−0.763275	+	1.32203i	−0.941154	+	0.337978i	$0.890257\pi$
$200$		−	2.99613i		−	0.211858i
$201$	−9.31385	−	5.37735i	−0.656948	−	0.379289i
$202$	−8.83892	−	5.10315i	−0.621904	−	0.359057i
$203$		−	3.33759i		−	0.234253i
$204$	0.0897098	−	0.155382i	0.00628094	−	0.0108789i
$205$	−2.39498	−	4.14823i	−0.167273	−	0.289725i
$206$	−9.79824	+	5.65702i	−0.682676	+	0.394143i
$207$	0.0247659			0.00172135
$208$	−3.65279	+	11.4242i	−0.253275	+	0.792122i
$209$	0.577660			0.0399576
$210$	2.24481	−	1.29604i	0.154907	−	0.0894354i
$211$	2.52901	+	4.38037i	0.174104	+	0.301557i	0.939851	−	0.341585i	$-0.110964\pi$
$211$	2.52901	+	4.38037i	0.174104	+	0.301557i	−0.765747	+	0.643142i	$0.777630\pi$
$212$	−0.260039	+	0.450401i	−0.0178596	+	0.0309337i
$213$		−	20.0007i		−	1.37042i
$214$	7.88405	+	4.55186i	0.538943	+	0.311159i
$215$	1.82322	+	1.05264i	0.124343	+	0.0717892i
$216$			12.2619i			0.834315i
$217$	2.18024	−	3.77628i	0.148004	−	0.256350i
$218$	9.70779	+	16.8144i	0.657495	+	1.13881i
$219$	13.9788	−	8.07065i	0.944598	−	0.545364i
$220$	−0.0587923			−0.00396377
$221$	−1.08490	+	0.235926i	−0.0729784	+	0.0158701i
$222$	−2.79913			−0.187866
$223$	8.97504	−	5.18174i	0.601013	−	0.346995i	−0.168427	−	0.985714i	$-0.553869\pi$
$223$	8.97504	−	5.18174i	0.601013	−	0.346995i	0.769440	+	0.638719i	$0.220535\pi$
$224$	−0.823447	−	1.42625i	−0.0550189	−	0.0952955i
$225$	0.468774	−	0.811941i	0.0312516	−	0.0541294i
$226$			6.95365i			0.462550i
$227$	25.5240	+	14.7363i	1.69408	+	0.978080i	0.951156	+	0.308710i	$0.0998971\pi$
$227$	25.5240	+	14.7363i	1.69408	+	0.978080i	0.742929	+	0.669371i	$0.233436\pi$
$228$	1.45581	+	0.840511i	0.0964133	+	0.0556642i
$229$		−	4.96959i		−	0.328400i	−0.986427	−	0.164200i	$-0.947496\pi$
$229$		−	4.96959i		−	0.328400i	0.986427	−	0.164200i	$-0.0525042\pi$
$230$	−0.0172531	+	0.0298832i	−0.00113763	+	0.00197044i
$231$	−0.198655	−	0.344080i	−0.0130705	−	0.0226388i
$232$	8.66011	−	4.99992i	0.568564	−	0.328261i
$233$	0.263094			0.0172359			0.00861793	−	0.999963i	$-0.497257\pi$
$233$	0.263094			0.0172359			0.00861793	+	0.999963i	$0.497257\pi$
$234$	−3.26763	+	2.97005i	−0.213611	+	0.194158i
$235$	−6.56495			−0.428250
$236$	1.78392	−	1.02995i	0.116123	−	0.0670438i
$237$	4.60773	+	7.98081i	0.299304	+	0.518410i
$238$	−0.201122	+	0.348353i	−0.0130368	+	0.0225804i
$239$			12.6088i			0.815597i	0.913072	+	0.407798i	$0.133703\pi$
$239$			12.6088i			0.815597i	−0.913072	+	0.407798i	$0.866297\pi$
$240$	5.71654	+	3.30044i	0.369001	+	0.213043i
$241$	−12.9526	−	7.47817i	−0.834348	−	0.481711i	0.0209909	−	0.999780i	$-0.493318\pi$
$241$	−12.9526	−	7.47817i	−0.834348	−	0.481711i	−0.855339	+	0.518069i	$0.826651\pi$
$242$			14.3167i			0.920313i
$243$	−4.70910	+	8.15639i	−0.302089	+	0.523233i
$244$	1.25936	+	2.18127i	0.0806222	+	0.139642i
$245$	0.866025	−	0.500000i	0.0553283	−	0.0319438i
$246$	12.4160			0.791615
$247$	−2.21045	−	10.1647i	−0.140647	−	0.646764i
$248$	13.0645			0.829598
$249$	18.9432	−	10.9369i	1.20048	−	0.693097i
$250$	0.653140	+	1.13127i	0.0413082	+	0.0715479i
$251$	−4.62292	+	8.00714i	−0.291796	+	0.505406i	−0.974235	−	0.225537i	$-0.927586\pi$
$251$	−4.62292	+	8.00714i	−0.291796	+	0.505406i	0.682438	+	0.730943i	$0.260920\pi$
$252$		−	0.275295i		−	0.0173419i
$253$	0.00458043	+	0.00264452i	0.000287969	+	0.000166259i
$254$	−2.88455	−	1.66540i	−0.180993	−	0.104496i
$255$			0.611034i			0.0382644i
$256$	3.44392	−	5.96505i	0.215245	−	0.372816i
$257$	−9.15421	−	15.8556i	−0.571024	−	0.989042i	−0.996461	−	0.0840543i	$-0.973213\pi$
$257$	−9.15421	−	15.8556i	−0.571024	−	0.989042i	0.425437	−	0.904988i	$-0.360120\pi$
$258$	−4.72594	+	2.72852i	−0.294224	+	0.169870i
$259$	−1.07988			−0.0671003
$260$	0.224972	+	1.03453i	0.0139522	+	0.0641587i
$261$	3.12915			0.193689
$262$	−7.93959	+	4.58392i	−0.490510	+	0.283196i
$263$	−8.79491	−	15.2332i	−0.542318	−	0.939322i	−0.998770	−	0.0495740i	$-0.984214\pi$
$263$	−8.79491	−	15.2332i	−0.542318	−	0.939322i	0.456453	−	0.889748i	$-0.349120\pi$
$264$	0.595195	−	1.03091i	0.0366317	−	0.0634480i
$265$		−	1.77119i		−	0.108803i
$266$	−3.26380	−	1.88435i	−0.200116	−	0.115537i
$267$	12.3635	+	7.13806i	0.756632	+	0.436842i
$268$		−	1.59144i		−	0.0972126i
$269$	6.84686	−	11.8591i	0.417460	−	0.723063i	−0.578223	−	0.815879i	$-0.696254\pi$
$269$	6.84686	−	11.8591i	0.417460	−	0.723063i	0.995683	+	0.0928162i	$0.0295869\pi$
$270$	−2.67302	−	4.62981i	−0.162675	−	0.281762i
$271$	−8.20431	+	4.73676i	−0.498376	+	0.287738i	−0.728043	−	0.685532i	$-0.759570\pi$
$271$	−8.20431	+	4.73676i	−0.498376	+	0.287738i	0.229666	+	0.973269i	$0.426236\pi$
$272$	−1.02433			−0.0621094
$273$	−5.29438	+	4.81224i	−0.320431	+	0.291250i
$274$	−7.73036			−0.467008
$275$	0.173399	−	0.100112i	0.0104564	−	0.00603698i
$276$	0.00769569	+	0.0133293i	0.000463226	+	0.000802331i
$277$	1.90872	−	3.30601i	0.114684	−	0.198639i	−0.802969	−	0.596020i	$-0.796748\pi$
$277$	1.90872	−	3.30601i	0.114684	−	0.198639i	0.917653	+	0.397382i	$0.130081\pi$
$278$			30.4387i			1.82559i
$279$	3.54044	+	2.04408i	0.211961	+	0.122376i
$280$	2.59472	+	1.49806i	0.155064	+	0.0895264i
$281$		−	1.93927i		−	0.115687i	−0.998326	−	0.0578434i	$-0.981578\pi$
$281$		−	1.93927i		−	0.115687i	0.998326	−	0.0578434i	$-0.0184224\pi$
$282$	8.50845	−	14.7371i	0.506671	−	0.877580i
$283$	−8.17027	−	14.1513i	−0.485672	−	0.841209i	0.514192	−	0.857675i	$-0.328092\pi$
$283$	−8.17027	−	14.1513i	−0.485672	−	0.841209i	−0.999864	+	0.0164662i	$0.994758\pi$
$284$	2.56311	−	1.47981i	0.152092	−	0.0878106i
$285$	−5.72492			−0.339115
$286$	−0.921489	+	0.200390i	−0.0544888	+	0.0118493i
$287$	4.78997			0.282743
$288$	1.33718	−	0.772021i	0.0787941	−	0.0454918i
$289$	8.45259	+	14.6403i	0.497211	+	0.861195i
$290$	−2.17991	+	3.77572i	−0.128009	+	0.221718i
$291$			28.1531i			1.65037i
$292$	2.06852	+	1.19426i	0.121051	+	0.0698890i
$293$	−15.4368	−	8.91246i	−0.901829	−	0.520671i	−0.0240360	−	0.999711i	$-0.507652\pi$
$293$	−15.4368	−	8.91246i	−0.901829	−	0.520671i	−0.877793	+	0.479040i	$0.840985\pi$
$294$			2.59208i			0.151173i
$295$	−3.50760	+	6.07534i	−0.204220	+	0.353720i
$296$	−1.61772	−	2.80198i	−0.0940283	−	0.162862i
$297$	−0.709648	+	0.409716i	−0.0411780	+	0.0237741i
$298$	6.13641			0.355472
$299$	0.0290065	−	0.0907183i	0.00167749	−	0.00524637i
$300$	0.582663			0.0336401
$301$	−1.82322	+	1.05264i	−0.105089	+	0.0606729i
$302$	9.82654	+	17.0201i	0.565454	+	0.979394i
$303$	7.75203	−	13.4269i	0.445342	−	0.771355i
$304$		−	9.59722i		−	0.550439i
$305$	−7.42858	−	4.28889i	−0.425359	−	0.245581i
$306$	−0.326597	−	0.188561i	−0.0186703	−	0.0107793i
$307$			23.8244i			1.35973i	0.733337	+	0.679865i	$0.237962\pi$
$307$			23.8244i			1.35973i	−0.733337	+	0.679865i	$0.762038\pi$
$308$	0.0293961	−	0.0509156i	0.00167500	−	0.00290119i
$309$	−8.59338	−	14.8842i	−0.488860	−	0.846731i
$310$	−4.93288	+	2.84800i	−0.280169	+	0.161755i
$311$	32.9085			1.86607			0.933036	−	0.359782i	$-0.117149\pi$
$311$	32.9085			1.86607			0.933036	+	0.359782i	$0.117149\pi$
$312$	−20.4177	−	6.52842i	−1.15593	−	0.369599i
$313$	−16.1670			−0.913812			−0.456906	−	0.889515i	$-0.651042\pi$
$313$	−16.1670			−0.913812			−0.456906	+	0.889515i	$0.651042\pi$
$314$	15.7213	−	9.07670i	0.887205	−	0.512228i
$315$	0.468774	+	0.811941i	0.0264124	+	0.0457477i
$316$	−0.681833	+	1.18097i	−0.0383561	+	0.0664347i
$317$			28.7541i			1.61499i	0.589873	+	0.807496i	$0.299178\pi$
$317$			28.7541i			1.61499i	−0.589873	+	0.807496i	$0.700822\pi$
$318$	3.97598	+	2.29553i	0.222962	+	0.128727i
$319$	0.578734	+	0.334132i	0.0324029	+	0.0187078i
$320$			8.80433i			0.492177i
$321$	−6.91457	+	11.9764i	−0.385934	+	0.668457i
$322$	−0.0172531	−	0.0298832i	−0.000961476	−	0.00166533i
$323$	0.769377	−	0.444200i	0.0428093	−	0.0247159i
$324$	−3.21048			−0.178360
$325$	−2.42512	−	2.66810i	−0.134522	−	0.148000i
$326$	−29.9663			−1.65968
$327$	−25.5422	+	14.7468i	−1.41249	+	0.815499i
$328$	7.17567	+	12.4286i	0.396210	+	0.686256i
$329$	3.28248	−	5.68541i	0.180969	−	0.313447i
$330$			0.518997i			0.0285699i
$331$	−29.4468	−	17.0011i	−1.61855	−	0.934467i	−0.987297	−	0.158887i	$-0.949210\pi$
$331$	−29.4468	−	17.0011i	−1.61855	−	0.934467i	−0.631248	−	0.775581i	$-0.717457\pi$
$332$	2.80315	+	1.61840i	0.153843	+	0.0888211i
$333$		−	1.01244i		−	0.0554812i
$334$	10.7871	−	18.6838i	0.590244	−	1.02233i
$335$	2.70992	+	4.69371i	0.148059	+	0.256445i
$336$	−5.71654	+	3.30044i	−0.311863	+	0.180054i
$337$	−22.6372			−1.23312			−0.616562	−	0.787306i	$-0.711475\pi$
$337$	−22.6372			−1.23312			−0.616562	+	0.787306i	$0.711475\pi$
$338$	7.05226	+	15.4480i	0.383592	+	0.840262i
$339$	−10.5630			−0.573706
$340$	−0.0783046	+	0.0452092i	−0.00424666	+	0.00245181i
$341$	0.436535	+	0.756101i	0.0236397	+	0.0409452i
$342$	1.76667	−	3.05997i	0.0955307	−	0.165464i
$343$			1.00000i			0.0539949i
$344$	−5.46260	−	3.15383i	−0.294523	−	0.170043i
$345$	−0.0453946	−	0.0262086i	−0.00244396	−	0.00141102i
$346$			24.1278i			1.29712i
$347$	1.51920	−	2.63133i	0.0815549	−	0.141257i	−0.822363	−	0.568963i	$-0.807345\pi$
$347$	1.51920	−	2.63133i	0.0815549	−	0.141257i	0.903918	+	0.427706i	$0.140678\pi$
$348$	0.972344	+	1.68415i	0.0521231	+	0.0902799i
$349$	15.0905	−	8.71249i	0.807775	−	0.466369i	−0.0384078	−	0.999262i	$-0.512229\pi$
$349$	15.0905	−	8.71249i	0.807775	−	0.466369i	0.846183	+	0.532893i	$0.178895\pi$
$350$	−1.30628			−0.0698236
$351$	9.92501	+	10.9194i	0.529758	+	0.582835i
$352$	0.329747			0.0175756
$353$	16.5735	−	9.56874i	0.882121	−	0.509293i	0.0107637	−	0.999942i	$-0.496574\pi$
$353$	16.5735	−	9.56874i	0.882121	−	0.509293i	0.871357	+	0.490649i	$0.163240\pi$
$354$	−9.09199	−	15.7478i	−0.483234	−	0.836986i
$355$	−5.03966	+	8.72896i	−0.267478	+	0.463285i
$356$			2.11252i			0.111963i
$357$	−0.529171	−	0.305517i	−0.0280067	−	0.0161697i
$358$	9.08362	+	5.24443i	0.480084	+	0.277177i
$359$		−	26.4594i		−	1.39648i	−0.715866	−	0.698238i	$-0.753968\pi$
$359$		−	26.4594i		−	1.39648i	0.715866	−	0.698238i	$-0.246032\pi$
$360$	−1.40451	+	2.43268i	−0.0740240	+	0.128213i
$361$	−5.33819	−	9.24601i	−0.280957	−	0.486632i
$362$	−0.394990	+	0.228047i	−0.0207602	+	0.0119859i
$363$	−21.7480			−1.14148
$364$	−1.00841	−	0.322433i	−0.0528553	−	0.0169001i
$365$	−8.13440			−0.425774
$366$	19.2555	−	11.1172i	1.00650	−	0.581104i
$367$	15.6307	+	27.0732i	0.815917	+	1.41321i	0.908668	+	0.417520i	$0.137101\pi$
$367$	15.6307	+	27.0732i	0.815917	+	1.41321i	−0.0927509	+	0.995689i	$0.529566\pi$
$368$	0.0439359	−	0.0760992i	0.00229032	−	0.00396695i
$369$			4.49083i			0.233783i
$370$	1.22163	+	0.705311i	0.0635097	+	0.0366674i
$371$	1.53389	+	0.885593i	0.0796357	+	0.0459777i
$372$			2.54068i			0.131728i
$373$	4.56119	−	7.90022i	0.236170	−	0.409058i	−0.723442	−	0.690385i	$-0.757441\pi$
$373$	4.56119	−	7.90022i	0.236170	−	0.409058i	0.959612	+	0.281327i	$0.0907746\pi$
$374$	−0.0402693	−	0.0697485i	−0.00208228	−	0.00360661i
$375$	−1.71848	+	0.992163i	−0.0887417	+	0.0512351i
$376$	19.6694			1.01437
$377$	3.66495	−	11.4622i	0.188754	−	0.590332i
$378$	5.34605			0.274971
$379$	−29.1882	+	16.8518i	−1.49930	+	0.865619i	−1.00000		0.000812760i	$-0.999741\pi$
$379$	−29.1882	+	16.8518i	−1.49930	+	0.865619i	−0.499296	+	0.866431i	$0.666408\pi$
$380$	−0.423575	−	0.733654i	−0.0217290	−	0.0376357i
$381$	2.52985	−	4.38182i	0.129608	−	0.224487i
$382$			8.25369i			0.422295i
$383$	16.4956	+	9.52372i	0.842884	+	0.486639i	0.858243	−	0.513243i	$-0.171556\pi$
$383$	16.4956	+	9.52372i	0.842884	+	0.486639i	−0.0153596	+	0.999882i	$0.504889\pi$
$384$	−14.1038	−	8.14282i	−0.719730	−	0.415536i
$385$			0.200224i			0.0102044i
$386$	12.3684	−	21.4227i	0.629535	−	1.09039i
$387$	−0.986897	−	1.70936i	−0.0501668	−	0.0868914i
$388$	−3.60785	+	2.08299i	−0.183161	+	0.105748i
$389$	26.6480			1.35111			0.675554	−	0.737310i	$-0.263904\pi$
$389$	26.6480			1.35111			0.675554	+	0.737310i	$0.263904\pi$
$390$	9.13245	−	1.98597i	0.462440	−	0.100564i
$391$	0.00813416			0.000411362
$392$	−2.59472	+	1.49806i	−0.131053	+	0.0756636i
$393$	−6.96328	−	12.0608i	−0.351251	−	0.608385i
$394$	9.92258	−	17.1864i	0.499892	−	0.865839i
$395$		−	4.64412i		−	0.233671i
$396$	0.0477358	+	0.0275603i	0.00239882	+	0.00138496i
$397$	−5.73061	−	3.30857i	−0.287611	−	0.166052i	0.349253	−	0.937028i	$-0.386435\pi$
$397$	−5.73061	−	3.30857i	−0.287611	−	0.166052i	−0.636864	+	0.770976i	$0.719769\pi$
$398$			28.1303i			1.41004i
$399$	2.86246	−	4.95792i	0.143302	−	0.248207i
$400$	−1.66326	−	2.88085i	−0.0831629	−	0.144042i
$401$	0.278685	−	0.160899i	0.0139168	−	0.00803489i	−0.493025	−	0.870015i	$-0.664109\pi$
$401$	0.278685	−	0.160899i	0.0139168	−	0.00803489i	0.506942	+	0.861980i	$0.330776\pi$
$402$	−14.0487			−0.700684
$403$	11.6342	−	10.5747i	0.579540	−	0.526762i
$404$	2.29423			0.114142
$405$	9.46882	−	5.46682i	0.470509	−	0.271649i
$406$	−2.17991	−	3.77572i	−0.108187	−	0.187386i
$407$	0.108109	−	0.187250i	0.00535874	−	0.00928162i
$408$		−	1.83073i		−	0.0906349i
$409$	−21.1346	−	12.2021i	−1.04504	−	0.603353i	−0.123782	−	0.992309i	$-0.539502\pi$
$409$	−21.1346	−	12.2021i	−1.04504	−	0.603353i	−0.921256	+	0.388956i	$0.872836\pi$
$410$	−5.41875	−	3.12852i	−0.267613	−	0.154507i
$411$		−	11.7429i		−	0.579236i
$412$	1.27161	−	2.20250i	0.0626480	−	0.108509i
$413$	−3.50760	−	6.07534i	−0.172598	−	0.298948i
$414$	0.0280169	−	0.0161756i	0.00137696	−	0.000794987i
$415$	−11.0233			−0.541112
$416$	−1.26180	−	5.80235i	−0.0618647	−	0.284483i
$417$	−46.2384			−2.26430
$418$	0.653490	−	0.377293i	0.0319632	−	0.0184540i
$419$	−13.9559	−	24.1724i	−0.681793	−	1.18090i	−0.974433	−	0.224677i	$-0.927867\pi$
$419$	−13.9559	−	24.1724i	−0.681793	−	1.18090i	0.292641	−	0.956222i	$-0.405466\pi$
$420$	−0.291331	+	0.504601i	−0.0142155	+	0.0246220i
$421$			33.2765i			1.62180i	0.585186	+	0.810899i	$0.301021\pi$
$421$			33.2765i			1.62180i	−0.585186	+	0.810899i	$0.698979\pi$
$422$	5.72199	+	3.30359i	0.278542	+	0.160816i
$423$	5.33035	+	3.07748i	0.259170	+	0.149632i
$424$			5.30670i			0.257716i
$425$	0.153965	−	0.266675i	0.00746840	−	0.0129357i
$426$	−13.0632	−	22.6262i	−0.632916	−	1.09624i
$427$	7.42858	−	4.28889i	0.359494	−	0.207554i
$428$	−2.04638			−0.0989156
$429$	−0.304406	−	1.39980i	−0.0146968	−	0.0675831i
$430$	2.75007			0.132620
$431$	8.50494	−	4.91033i	0.409669	−	0.236522i	−0.280979	−	0.959714i	$-0.590659\pi$
$431$	8.50494	−	4.91033i	0.409669	−	0.236522i	0.690647	+	0.723192i	$0.257326\pi$
$432$	6.80701	+	11.7901i	0.327502	+	0.567251i
$433$	−5.76123	+	9.97874i	−0.276867	+	0.479548i	−0.970604	−	0.240680i	$-0.922629\pi$
$433$	−5.76123	+	9.97874i	−0.276867	+	0.479548i	0.693737	+	0.720228i	$0.255963\pi$
$434$		−	5.69599i		−	0.273416i
$435$	−5.73556	−	3.31143i	−0.274999	−	0.158771i
$436$	−3.77963	−	2.18217i	−0.181011	−	0.104507i
$437$			0.0762108i			0.00364566i
$438$	10.5425	−	18.2602i	0.503742	−	0.872506i
$439$	4.83402	+	8.37277i	0.230715	+	0.399611i	0.958019	−	0.286705i	$-0.0925601\pi$
$439$	4.83402	+	8.37277i	0.230715	+	0.399611i	−0.727303	+	0.686316i	$0.759227\pi$
$440$	−0.519525	+	0.299948i	−0.0247674	+	0.0142995i
$441$	−0.937548			−0.0446452
$442$	−1.07323	+	0.975489i	−0.0510481	+	0.0463993i
$443$	11.8698			0.563953			0.281977	−	0.959421i	$-0.409010\pi$
$443$	11.8698			0.563953			0.281977	+	0.959421i	$0.409010\pi$
$444$	0.544907	−	0.314602i	0.0258601	−	0.0149304i
$445$	−3.59722	−	6.23057i	−0.170525	−	0.295357i
$446$	6.76880	−	11.7239i	0.320512	−	0.555143i
$447$			9.32161i			0.440897i
$448$	−7.62478	−	4.40217i	−0.360237	−	0.207983i
$449$	−28.4486	−	16.4248i	−1.34257	−	0.775134i	−0.355387	−	0.934719i	$-0.615651\pi$
$449$	−28.4486	−	16.4248i	−1.34257	−	0.775134i	−0.987184	+	0.159585i	$0.948984\pi$
$450$		−	1.22470i		−	0.0577329i
$451$	−0.479533	+	0.830575i	−0.0225803	+	0.0391103i
$452$	−0.781539	−	1.35367i	−0.0367605	−	0.0636711i
$453$	−25.8546	+	14.9272i	−1.21475	+	0.701339i
$454$	38.4994			1.80687
$455$	3.52321	−	0.766168i	0.165170	−	0.0359185i
$456$	17.1526			0.803243
$457$	−25.8518	+	14.9256i	−1.20930	+	0.698188i	−0.962606	−	0.270906i	$-0.912677\pi$
$457$	−25.8518	+	14.9256i	−1.20930	+	0.698188i	−0.246691	+	0.969094i	$0.579343\pi$
$458$	−3.24584	−	5.62195i	−0.151668	−	0.262697i
$459$	−0.630114	+	1.09139i	−0.0294112	+	0.0509417i
$460$		−	0.00775648i		−	0.000361648i
$461$	−10.0672	−	5.81233i	−0.468878	−	0.270707i	0.246892	−	0.969043i	$-0.420591\pi$
$461$	−10.0672	−	5.81233i	−0.468878	−	0.270707i	−0.715770	+	0.698336i	$0.753924\pi$
$462$	−0.449465	−	0.259499i	−0.0209110	−	0.0120730i
$463$		−	41.2501i		−	1.91705i	−0.285001	−	0.958527i	$-0.591994\pi$
$463$		−	41.2501i		−	1.91705i	0.285001	−	0.958527i	$-0.408006\pi$
$464$	5.55127	−	9.61507i	0.257711	−	0.446369i
$465$	−4.32630	−	7.49336i	−0.200627	−	0.347496i
$466$	0.297631	−	0.171837i	0.0137875	−	0.00796020i
$467$	−14.8115			−0.685396			−0.342698	−	0.939446i	$-0.611341\pi$
$467$	−14.8115			−0.685396			−0.342698	+	0.939446i	$0.611341\pi$
$468$	0.302296	−	0.945437i	0.0139737	−	0.0437028i
$469$	−5.41983			−0.250265
$470$	−7.42674	+	4.28783i	−0.342570	+	0.197783i
$471$	13.7881	+	23.8817i	0.635323	+	1.10041i
$472$	10.5092	−	18.2025i	0.483726	−	0.837837i
$473$		−	0.421526i		−	0.0193818i
$474$	10.4252	+	6.01898i	0.478844	+	0.276461i
$475$	2.49854	+	1.44253i	0.114641	+	0.0661880i
$476$		−	0.0904184i		−	0.00414432i
$477$	−0.830286	+	1.43810i	−0.0380162	+	0.0658460i
$478$	8.23532	+	14.2640i	0.376675	+	0.652420i
$479$	−6.71433	+	3.87652i	−0.306785	+	0.177123i	−0.645487	−	0.763771i	$-0.723346\pi$
$479$	−6.71433	+	3.87652i	−0.306785	+	0.177123i	0.338702	+	0.940894i	$0.390012\pi$
$480$	−3.26797			−0.149162
$481$	−3.70859	−	1.18579i	−0.169097	−	0.0540676i
$482$	−19.5372			−0.889893
$483$	0.0453946	−	0.0262086i	0.00206552	−	0.00119253i
$484$	−1.60909	−	2.78703i	−0.0731406	−	0.126683i
$485$	7.09388	−	12.2870i	0.322116	−	0.557922i
$486$			12.3028i			0.558066i
$487$	4.07339	+	2.35177i	0.184583	+	0.106569i	0.589444	−	0.807809i	$-0.299347\pi$
$487$	4.07339	+	2.35177i	0.184583	+	0.106569i	−0.404861	+	0.914378i	$0.632680\pi$
$488$	22.2570	+	12.8501i	1.00753	+	0.581695i
$489$		−	45.5208i		−	2.05852i
$490$	0.653140	−	1.13127i	0.0295059	−	0.0511056i
$491$	−11.6548	−	20.1867i	−0.525975	−	0.911015i	−0.999542	−	0.0302572i	$-0.990367\pi$
$491$	−11.6548	−	20.1867i	−0.525975	−	0.911015i	0.473568	−	0.880757i	$-0.342966\pi$
$492$	−2.41702	+	1.39547i	−0.108968	+	0.0629126i
$493$	1.02774			0.0462872
$494$	−9.13959	−	10.0553i	−0.411209	−	0.452409i
$495$	−0.187720			−0.00843737
$496$	12.5618	−	7.25258i	0.564043	−	0.325651i
$497$	−5.03966	−	8.72896i	−0.226060	−	0.391547i
$498$	14.2866	−	24.7452i	0.640200	−	1.10886i
$499$			34.0556i			1.52454i	0.647262	+	0.762268i	$0.275914\pi$
$499$			34.0556i			1.52454i	−0.647262	+	0.762268i	$0.724086\pi$
$500$	−0.254293	−	0.146816i	−0.0113723	−	0.00656583i
$501$	28.3819	+	16.3863i	1.26801	+	0.732086i
$502$			12.0777i			0.539052i
$503$	−20.2284	+	35.0367i	−0.901941	+	1.56221i	−0.0769693	+	0.997033i	$0.524524\pi$
$503$	−20.2284	+	35.0367i	−0.901941	+	1.56221i	−0.824972	+	0.565174i	$0.808809\pi$
$504$	−1.40451	−	2.43268i	−0.0625617	−	0.108360i
$505$	−6.76648	+	3.90663i	−0.301105	+	0.173843i
$506$	0.00690895			0.000307140
$507$	−23.4666	+	10.7128i	−1.04219	+	0.475774i
$508$	0.748713			0.0332188
$509$	19.7880	−	11.4246i	0.877089	−	0.506387i	0.00739142	−	0.999973i	$-0.497647\pi$
$509$	19.7880	−	11.4246i	0.877089	−	0.506387i	0.869697	+	0.493585i	$0.164314\pi$
$510$	0.399091	+	0.691245i	0.0176720	+	0.0306089i
$511$	4.06720	−	7.04460i	0.179922	−	0.311635i
$512$		−	25.4117i		−	1.12305i
$513$	−10.2255	−	5.90368i	−0.451466	−	0.260654i
$514$	−20.7118	−	11.9580i	−0.913558	−	0.527443i
$515$			8.66126i			0.381661i
$516$	0.613332	−	1.06232i	0.0270004	−	0.0467661i
$517$	0.657230	+	1.13836i	0.0289049	+	0.0500648i
$518$	−1.22163	+	0.705311i	−0.0536755	+	0.0309896i
$519$	−36.6518			−1.60883
$520$	7.26598	+	7.99397i	0.318634	+	0.350559i
$521$	−4.49400			−0.196886			−0.0984428	−	0.995143i	$-0.531386\pi$
$521$	−4.49400			−0.196886			−0.0984428	+	0.995143i	$0.531386\pi$
$522$	3.53992	−	2.04377i	0.154938	−	0.0894535i
$523$	−4.19444	−	7.26498i	−0.183410	−	0.317675i	0.759630	−	0.650356i	$-0.225380\pi$
$523$	−4.19444	−	7.26498i	−0.183410	−	0.317675i	−0.943040	+	0.332681i	$0.892047\pi$
$524$	1.03040	−	1.78470i	0.0450132	−	0.0779652i
$525$		−	1.98433i		−	0.0866031i
$526$	−19.8989	−	11.4886i	−0.867632	−	0.500928i
$527$	1.16283	+	0.671360i	0.0506537	+	0.0292449i
$528$		−	1.32166i		−	0.0575177i
$529$	11.4997	−	19.9180i	0.499985	−	0.865999i
$530$	−1.15683	−	2.00369i	−0.0502496	−	0.0870349i
$531$	5.69592	−	3.28854i	0.247182	−	0.142711i
$532$	0.847151			0.0367286
$533$	16.4500	+	5.25978i	0.712530	+	0.227826i
$534$	18.6486			0.807004
$535$	6.03550	−	3.48460i	0.260937	−	0.150652i
$536$	−8.11925	−	14.0630i	−0.350698	−	0.607427i
$537$	−7.96664	+	13.7986i	−0.343786	+	0.595454i
$538$		−	17.8878i		−	0.771199i
$539$	−0.173399	−	0.100112i	−0.00746882	−	0.00431213i
$540$	1.04071	+	0.600857i	0.0447852	+	0.0258568i
$541$		−	6.79688i		−	0.292221i	−0.989268	−	0.146110i	$-0.953325\pi$
$541$		−	6.79688i		−	0.292221i	0.989268	−	0.146110i	$-0.0466754\pi$
$542$	−6.18754	+	10.7171i	−0.265777	+	0.460340i
$543$	−0.346419	−	0.600015i	−0.0148663	−	0.0257491i
$544$	0.439186	−	0.253564i	0.0188299	−	0.0108715i
$545$	14.8633			0.636672
$546$	−2.84632	+	8.90192i	−0.121811	+	0.380967i
$547$	−26.2774			−1.12354			−0.561770	−	0.827294i	$-0.689879\pi$
$547$	−26.2774			−1.12354			−0.561770	+	0.827294i	$0.689879\pi$
$548$	1.50487	−	0.868837i	0.0642848	−	0.0371149i
$549$	4.02104	+	6.96465i	0.171614	+	0.297244i
$550$	0.130774	−	0.226508i	0.00557623	−	0.00965832i
$551$			9.62917i			0.410216i
$552$	0.136008	+	0.0785242i	0.00578888	+	0.00334221i
$553$	4.02193	+	2.32206i	0.171030	+	0.0987441i
$554$		−	4.98666i		−	0.211863i
$555$	−1.07141	+	1.85574i	−0.0454790	+	0.0787719i
$556$	−3.42109	−	5.92549i	−0.145086	−	0.251297i
$557$	10.5442	−	6.08769i	0.446772	−	0.257944i	−0.259694	−	0.965691i	$-0.583622\pi$
$557$	10.5442	−	6.08769i	0.446772	−	0.257944i	0.706466	+	0.707747i	$0.250288\pi$
$558$	5.34027			0.226072
$559$	−7.41731	+	1.61299i	−0.313719	+	0.0682223i
$560$	3.32651			0.140571
$561$	0.105953	−	0.0611718i	0.00447332	−	0.00258267i
$562$	−1.26661	−	2.19384i	−0.0534288	−	0.0925414i
$563$	−19.7326	+	34.1779i	−0.831631	+	1.44043i	0.0651135	+	0.997878i	$0.479259\pi$
$563$	−19.7326	+	34.1779i	−0.831631	+	1.44043i	−0.896744	+	0.442549i	$0.854074\pi$
$564$			3.82515i			0.161068i
$565$	4.61006	+	2.66162i	0.193947	+	0.111975i
$566$	−18.4856	−	10.6727i	−0.777007	−	0.448605i
$567$			10.9336i			0.459170i
$568$	15.0995	−	26.1531i	0.633560	−	1.09736i
$569$	15.3717	+	26.6246i	0.644416	+	1.11616i	0.984436	+	0.175743i	$0.0562327\pi$
$569$	15.3717	+	26.6246i	0.644416	+	1.11616i	−0.340020	+	0.940418i	$0.610434\pi$
$570$	−6.47644	+	3.73917i	−0.271268	+	0.156617i
$571$	20.2688			0.848223			0.424112	−	0.905610i	$-0.360586\pi$
$571$	20.2688			0.848223			0.424112	+	0.905610i	$0.360586\pi$
$572$	0.156864	−	0.142579i	0.00655881	−	0.00596151i
$573$	−12.5379			−0.523778
$574$	5.41875	−	3.12852i	0.226174	−	0.130582i
$575$	0.0132078	+	0.0228766i	0.000550803	+	0.000954019i
$576$	4.12724	−	7.14860i	0.171968	−	0.297858i
$577$			10.3943i			0.432721i	0.976314	+	0.216360i	$0.0694186\pi$
$577$			10.3943i			0.432721i	−0.976314	+	0.216360i	$0.930581\pi$
$578$	19.1243	+	11.0414i	0.795468	+	0.459264i
$579$	32.5425	+	18.7884i	1.35242	+	0.780820i
$580$		−	0.980025i		−	0.0406933i
$581$	5.51164	−	9.54644i	0.228661	−	0.396053i
$582$	18.3879	+	31.8488i	0.762204	+	1.32018i
$583$	−0.307122	+	0.177317i	−0.0127197	+	0.00734372i
$584$	24.3717			1.00851
$585$	0.718319	+	3.30318i	0.0296988	+	0.136570i
$586$	−23.2843			−0.961867
$587$	−20.0823	+	11.5945i	−0.828884	+	0.478556i	−0.853470	−	0.521141i	$-0.825506\pi$
$587$	−20.0823	+	11.5945i	−0.828884	+	0.478556i	0.0245864	+	0.999698i	$0.492173\pi$
$588$	−0.291331	−	0.504601i	−0.0120143	−	0.0208094i
$589$	−6.29013	+	10.8948i	−0.259180	+	0.448913i
$590$			9.16381i			0.377268i
$591$	26.1073	+	15.0730i	1.07391	+	0.620022i
$592$	−3.11096	−	1.79611i	−0.127860	−	0.0738198i
$593$		−	28.3307i		−	1.16340i	−0.813403	−	0.581700i	$-0.802388\pi$
$593$		−	28.3307i		−	1.16340i	0.813403	−	0.581700i	$-0.197612\pi$
$594$	−0.535203	+	0.927000i	−0.0219597	+	0.0380353i
$595$	0.153965	+	0.266675i	0.00631195	+	0.0109326i
$596$	−1.19457	+	0.689687i	−0.0489316	+	0.0282507i
$597$	−42.7317			−1.74889
$598$	−0.0264375	−	0.121572i	−0.00108111	−	0.00497146i
$599$	−27.0557			−1.10547			−0.552733	−	0.833359i	$-0.686415\pi$
$599$	−27.0557			−1.10547			−0.552733	+	0.833359i	$0.686415\pi$
$600$	5.14877	−	2.97265i	0.210198	−	0.121358i
$601$	11.3577	+	19.6722i	0.463291	+	0.802444i	0.999123	−	0.0418811i	$-0.0133351\pi$
$601$	11.3577	+	19.6722i	0.463291	+	0.802444i	−0.535831	+	0.844325i	$0.680002\pi$
$602$	−1.37504	+	2.38163i	−0.0560423	+	0.0970682i
$603$		−	5.08135i		−	0.206929i
$604$	−3.82586	−	2.20886i	−0.155672	−	0.0898773i
$605$	9.49156	+	5.47996i	0.385887	+	0.222792i
$606$		−	20.2526i		−	0.822707i
$607$	19.6739	−	34.0762i	0.798539	−	1.38311i	−0.122029	−	0.992527i	$-0.538940\pi$
$607$	19.6739	−	34.0762i	0.798539	−	1.38311i	0.920568	−	0.390583i	$-0.127727\pi$
$608$	2.37570	+	4.11484i	0.0963474	+	0.166879i
$609$	5.73556	−	3.31143i	0.232417	−	0.134186i
$610$	−11.2050			−0.453677
$611$	17.5160	−	15.9208i	0.708620	−	0.644087i
$612$	0.0847716			0.00342669
$613$	2.54848	−	1.47136i	0.102932	−	0.0594278i	−0.447650	−	0.894209i	$-0.647739\pi$
$613$	2.54848	−	1.47136i	0.102932	−	0.0594278i	0.550582	+	0.834781i	$0.314406\pi$
$614$	15.5607	+	26.9519i	0.627978	+	1.08769i
$615$	4.75243	−	8.23145i	0.191636	−	0.331924i
$616$		−	0.599896i		−	0.0241705i
$617$	−28.0390	−	16.1883i	−1.12881	−	0.651718i	−0.185174	−	0.982706i	$-0.559285\pi$
$617$	−28.0390	−	16.1883i	−1.12881	−	0.651718i	−0.943635	+	0.330988i	$0.892618\pi$
$618$	−19.4429	−	11.2254i	−0.782108	−	0.451550i
$619$			11.9661i			0.480957i	0.970655	+	0.240478i	$0.0773043\pi$
$619$			11.9661i			0.480957i	−0.970655	+	0.240478i	$0.922696\pi$
$620$	0.640188	−	1.10884i	0.0257106	−	0.0445320i
$621$	−0.0540539	−	0.0936241i	−0.00216911	−	0.00375700i
$622$	37.2285	−	21.4939i	1.49273	−	0.861826i
$623$	7.19444			0.288239
$624$	−23.2563	+	5.05739i	−0.930997	+	0.202458i
$625$	1.00000			0.0400000
$626$	−18.2893	+	10.5593i	−0.730986	+	0.422035i
$627$	0.573133	+	0.992695i	0.0228887	+	0.0396444i
$628$	−2.04031	+	3.53392i	−0.0814173	+	0.141019i
$629$		−	0.332527i		−	0.0132587i
$630$	1.06062	+	0.612350i	0.0422562	+	0.0243966i
$631$	4.67579	+	2.69957i	0.186140	+	0.107468i	0.590174	−	0.807276i	$-0.299059\pi$
$631$	4.67579	+	2.69957i	0.186140	+	0.107468i	−0.404034	+	0.914744i	$0.632392\pi$
$632$			13.9144i			0.553484i
$633$	−5.01838	+	8.69209i	−0.199463	+	0.345479i
$634$	18.7805	+	32.5287i	0.745867	+	1.29188i
$635$	−2.20822	+	1.27491i	−0.0876304	+	0.0505934i
$636$	−1.03200			−0.0409217
$637$	−1.09808	+	3.43427i	−0.0435076	+	0.136071i
$638$	0.872941			0.0345600
$639$	8.18382	−	4.72493i	0.323747	−	0.186915i
$640$	4.10357	+	7.10759i	0.162208	+	0.280952i
$641$	9.66034	−	16.7322i	0.381560	−	0.660882i	−0.609725	−	0.792613i	$-0.708720\pi$
$641$	9.66034	−	16.7322i	0.381560	−	0.660882i	0.991285	+	0.131731i	$0.0420535\pi$
$642$			18.0647i			0.712958i
$643$	−3.89438	−	2.24842i	−0.153579	−	0.0886691i	0.421241	−	0.906949i	$-0.361595\pi$
$643$	−3.89438	−	2.24842i	−0.153579	−	0.0886691i	−0.574820	+	0.818280i	$0.694928\pi$
$644$	0.00671731	+	0.00387824i	0.000264699	+	0.000152824i
$645$			4.17755i			0.164491i
$646$	0.580250	−	1.00502i	0.0228296	−	0.0395420i
$647$	14.5332	+	25.1722i	0.571359	+	0.989622i	0.996427	+	0.0844607i	$0.0269168\pi$
$647$	14.5332	+	25.1722i	0.571359	+	0.989622i	−0.425068	+	0.905161i	$0.639750\pi$
$648$	−28.3698	+	16.3793i	−1.11447	+	0.643440i
$649$	1.40461			0.0551358
$650$	−4.48612	−	1.43440i	−0.175960	−	0.0562619i
$651$	8.65259			0.339122
$652$	5.83353	−	3.36799i	0.228459	−	0.131901i
$653$	13.0494	+	22.6022i	0.510662	+	0.884493i	0.999924	+	0.0123556i	$0.00393300\pi$
$653$	13.0494	+	22.6022i	0.510662	+	0.884493i	−0.489262	+	0.872137i	$0.662734\pi$
$654$	−19.2634	+	33.3652i	−0.753259	+	1.30468i
$655$			7.01829i			0.274227i
$656$	13.7992	+	7.96695i	0.538767	+	0.311057i
$657$	6.60465	+	3.81320i	0.257672	+	0.148767i
$658$		−	8.57566i		−	0.334314i
$659$	−11.7239	+	20.3064i	−0.456698	+	0.791024i	−0.998784	−	0.0492992i	$-0.984301\pi$
$659$	−11.7239	+	20.3064i	−0.456698	+	0.791024i	0.542086	+	0.840323i	$0.317635\pi$
$660$	−0.0583315	−	0.101033i	−0.00227055	−	0.00393271i
$661$	14.5986	−	8.42848i	0.567818	−	0.327830i	−0.188459	−	0.982081i	$-0.560349\pi$
$661$	14.5986	−	8.42848i	0.567818	−	0.327830i	0.756277	+	0.654251i	$0.227016\pi$
$662$	−44.4165			−1.72630
$663$	−1.48183	−	1.63030i	−0.0575496	−	0.0633156i
$664$	33.0271			1.28170
$665$	−2.49854	+	1.44253i	−0.0968894	+	0.0559391i
$666$	−0.661263	−	1.14534i	−0.0256234	−	0.0443811i
$667$	−0.0440821	+	0.0763525i	−0.00170687	+	0.00295638i
$668$			4.84956i			0.187635i
$669$	17.8094	+	10.2823i	0.688551	+	0.397535i
$670$	6.13130	+	3.53991i	0.236873	+	0.136759i
$671$			1.71748i			0.0663025i
$672$	1.63399	−	2.83015i	0.0630324	−	0.109175i
$673$	−8.57787	−	14.8573i	−0.330653	−	0.572707i	0.651987	−	0.758230i	$-0.273935\pi$
$673$	−8.57787	−	14.8573i	−0.330653	−	0.572707i	−0.982640	+	0.185523i	$0.940602\pi$
$674$	−25.6088	+	14.7852i	−0.986413	+	0.569506i
$675$	−4.09258			−0.157523
$676$	−3.10911	−	2.21464i	−0.119581	−	0.0851786i
$677$	−21.4458			−0.824231			−0.412115	−	0.911132i	$-0.635210\pi$
$677$	−21.4458			−0.824231			−0.412115	+	0.911132i	$0.635210\pi$
$678$	−11.9497	+	6.89915i	−0.458925	+	0.264960i
$679$	7.09388	+	12.2870i	0.272238	+	0.471530i
$680$	−0.461299	+	0.798993i	−0.0176900	+	0.0306400i
$681$			58.4831i			2.24108i
$682$	0.987680	+	0.570237i	0.0378202	+	0.0218355i
$683$	19.1865	+	11.0773i	0.734150	+	0.423862i	0.819938	−	0.572452i	$-0.194008\pi$
$683$	19.1865	+	11.0773i	0.734150	+	0.423862i	−0.0857885	+	0.996313i	$0.527341\pi$
$684$			0.794245i			0.0303687i
$685$	−2.95892	+	5.12500i	−0.113055	+	0.195816i
$686$	0.653140	+	1.13127i	0.0249370	+	0.0431922i
$687$	8.54012	−	4.93064i	0.325826	−	0.188116i
$688$	−7.00322			−0.266995
$689$	4.29535	+	4.72571i	0.163640	+	0.180035i
$690$	−0.0684714			−0.00260666
$691$	1.44939	−	0.836806i	0.0551374	−	0.0318336i	−0.472178	−	0.881503i	$-0.656532\pi$
$691$	1.44939	−	0.836806i	0.0551374	−	0.0318336i	0.527315	+	0.849670i	$0.323199\pi$
$692$	−2.71179	−	4.69696i	−0.103087	−	0.178552i
$693$	0.0938598	−	0.162570i	0.00356544	−	0.00617552i
$694$		−	3.96900i		−	0.150661i
$695$	20.1800	+	11.6509i	0.765469	+	0.441944i
$696$	17.1845	+	9.92146i	0.651376	+	0.376072i
$697$			1.47498i			0.0558687i
$698$	11.3810	−	19.7124i	0.430775	−	0.746125i
$699$	0.261032	+	0.452121i	0.00987313	+	0.0171008i
$700$	0.254293	−	0.146816i	0.00961139	−	0.00554914i
$701$	12.9755			0.490076			0.245038	−	0.969513i	$-0.421200\pi$
$701$	12.9755			0.490076			0.245038	+	0.969513i	$0.421200\pi$
$702$	18.3598	+	5.87040i	0.692945	+	0.221564i
$703$	3.11552			0.117504
$704$	1.52666	−	0.881419i	0.0575383	−	0.0332197i
$705$	−6.51350	−	11.2817i	−0.245313	−	0.424894i
$706$	12.4995	−	21.6497i	0.470423	−	0.814797i
$707$		−	7.81326i		−	0.293848i
$708$	3.53987	+	2.04375i	0.133037	+	0.0768087i
$709$	8.99203	+	5.19155i	0.337703	+	0.194973i	0.659256	−	0.751919i	$-0.270871\pi$
$709$	8.99203	+	5.19155i	0.337703	+	0.194973i	−0.321553	+	0.946892i	$0.604205\pi$
$710$			13.1664i			0.494127i
$711$	−2.17704	+	3.77075i	−0.0816455	+	0.141414i
$712$	10.7777	+	18.6676i	0.403912	+	0.699597i
$713$	−0.0997526	+	0.0575922i	−0.00373576	+	0.00215684i
$714$	−0.798181			−0.0298712
$715$	−0.219862	+	0.687623i	−0.00822239	+	0.0257156i
$716$	−2.35774			−0.0881130
$717$	−21.6680	+	12.5100i	−0.809205	+	0.467194i
$718$	−17.2817	−	29.9328i	−0.644948	−	1.11708i
$719$	8.73783	−	15.1344i	0.325866	−	0.564416i	−0.655821	−	0.754916i	$-0.727678\pi$
$719$	8.73783	−	15.1344i	0.325866	−	0.564416i	0.981687	+	0.190500i	$0.0610108\pi$
$720$			3.11877i			0.116230i
$721$	−7.50087	−	4.33063i	−0.279347	−	0.161281i
$722$	−12.0779	−	6.97317i	−0.449492	−	0.259514i
$723$		−	29.6782i		−	1.10375i
$724$	0.0512617	−	0.0887879i	0.00190513	−	0.00329978i
$725$	1.66879	+	2.89043i	0.0619774	+	0.107348i
$726$	−24.6029	+	14.2045i	−0.913100	+	0.527179i
$727$	21.1273			0.783568			0.391784	−	0.920057i	$-0.371858\pi$
$727$	21.1273			0.783568			0.391784	+	0.920057i	$0.371858\pi$
$728$	−10.5560	+	2.29554i	−0.391230	+	0.0850782i
$729$	14.1122			0.522674
$730$	−9.20222	+	5.31290i	−0.340589	+	0.196639i
$731$	−0.324138	−	0.561424i	−0.0119887	−	0.0207650i
$732$	−2.49898	+	4.32836i	−0.0923649	+	0.159981i
$733$		−	29.9120i		−	1.10482i	−0.833571	−	0.552412i	$-0.813708\pi$
$733$		−	29.9120i		−	1.10482i	0.833571	−	0.552412i	$-0.186292\pi$
$734$	35.3652	+	20.4181i	1.30535	+	0.753646i
$735$	1.71848	+	0.992163i	0.0633870	+	0.0365965i
$736$			0.0435037i			0.00160357i
$737$	0.542590	−	0.939793i	0.0199866	−	0.0346177i
$738$	2.93314	+	5.08034i	0.107970	+	0.187010i
$739$	−10.3578	+	5.98008i	−0.381018	+	0.219981i	−0.678261	−	0.734821i	$-0.737266\pi$
$739$	−10.3578	+	5.98008i	−0.381018	+	0.219981i	0.297243	+	0.954802i	$0.403933\pi$
$740$	−0.317087			−0.0116564
$741$	15.2747	−	13.8836i	0.561129	−	0.510028i
$742$	2.31367			0.0849373
$743$	35.5749	−	20.5392i	1.30512	−	0.753509i	0.323839	−	0.946112i	$-0.395026\pi$
$743$	35.5749	−	20.5392i	1.30512	−	0.753509i	0.981277	+	0.192603i	$0.0616931\pi$
$744$	12.9621	+	22.4511i	0.475215	+	0.823096i
$745$	2.34881	−	4.06826i	0.0860537	−	0.149049i
$746$		−	11.9164i		−	0.436290i
$747$	8.95025	+	5.16743i	0.327473	+	0.189066i
$748$	0.0156785	+	0.00905196i	0.000573261	+	0.000330972i
$749$			6.96919i			0.254649i
$750$	−1.29604	+	2.24481i	−0.0473248	+	0.0819689i
$751$	2.30782	+	3.99725i	0.0842134	+	0.145862i	0.905056	−	0.425293i	$-0.139829\pi$
$751$	2.30782	+	3.99725i	0.0842134	+	0.145862i	−0.820842	+	0.571155i	$0.806496\pi$
$752$	18.9126	−	10.9192i	0.689672	−	0.398182i
$753$	−18.3468			−0.668593
$754$	−3.34036	−	15.3606i	−0.121649	−	0.559398i
$755$	15.0451			0.547546
$756$	−1.04071	+	0.600857i	−0.0378504	+	0.0218530i
$757$	17.5848	+	30.4578i	0.639131	+	1.10701i	0.985624	+	0.168955i	$0.0540393\pi$
$757$	17.5848	+	30.4578i	0.639131	+	1.10701i	−0.346492	+	0.938053i	$0.612627\pi$
$758$	−22.0132	+	38.1279i	−0.799554	+	1.38487i
$759$			0.0104952i			0.000380950i
$760$	−7.48595	−	4.32202i	−0.271544	−	0.156776i
$761$	14.5863	+	8.42138i	0.528751	+	0.305275i	0.740508	−	0.672048i	$-0.234585\pi$
$761$	14.5863	+	8.42138i	0.528751	+	0.305275i	−0.211757	+	0.977322i	$0.567918\pi$
$762$		−	6.60937i		−	0.239432i
$763$	−7.43163	+	12.8720i	−0.269043	+	0.465996i
$764$	−0.927654	−	1.60674i	−0.0335614	−	0.0581300i
$765$	−0.250021	+	0.144350i	−0.00903953	+	0.00521897i
$766$	24.8813			0.898997
$767$	−5.37482	−	24.7160i	−0.194073	−	0.892443i
$768$	13.6677			0.493192
$769$	37.8459	−	21.8504i	1.36476	−	0.787944i	0.374506	−	0.927225i	$-0.377812\pi$
$769$	37.8459	−	21.8504i	1.36476	−	0.787944i	0.990253	+	0.139281i	$0.0444790\pi$
$770$	0.130774	+	0.226508i	0.00471278	+	0.00816277i
$771$	18.1649	−	31.4626i	0.654194	−	1.13310i
$772$			5.56047i			0.200126i
$773$	38.7169	+	22.3532i	1.39255	+	0.803990i	0.993597	−	0.112982i	$-0.0360401\pi$
$773$	38.7169	+	22.3532i	1.39255	+	0.803990i	0.398954	+	0.916971i	$0.369373\pi$
$774$	−2.23290	−	1.28916i	−0.0802598	−	0.0463380i
$775$			4.36047i			0.156633i
$776$	−21.2542	+	36.8133i	−0.762980	+	1.32152i
$777$	−1.07141	−	1.85574i	−0.0384368	−	0.0665744i
$778$	30.1461	−	17.4049i	1.08079	−	0.623995i
$779$	−13.8194			−0.495131
$780$	−1.55460	+	1.41303i	−0.0556638	+	0.0505946i
$781$	2.01812			0.0722141
$782$	0.00920194	−	0.00531274i	0.000329061	−	0.000189983i
$783$	−6.82966	−	11.8293i	−0.244072	−	0.422746i
$784$	−1.66326	+	2.88085i	−0.0594020	+	0.102887i
$785$		−	13.8970i		−	0.496006i
$786$	−15.7547	−	9.09600i	−0.561953	−	0.324444i
$787$	36.4990	+	21.0727i	1.30105	+	0.751161i	0.980584	−	0.196099i	$-0.0628274\pi$
$787$	36.4990	+	21.0727i	1.30105	+	0.751161i	0.320465	+	0.947260i	$0.396161\pi$
$788$			4.46090i			0.158913i
$789$	17.4520	−	30.2277i	0.621307	−	1.07613i
$790$	−3.03326	−	5.25376i	−0.107919	−	0.186921i
$791$	−4.61006	+	2.66162i	−0.163915	+	0.0946364i
$792$	0.562432			0.0199851
$793$	30.2213	−	6.57202i	1.07319	−	0.233379i
$794$	−8.64383			−0.306758
$795$	3.04374	−	1.75731i	0.107950	−	0.0623252i
$796$	−3.16164	−	5.47611i	−0.112061	−	0.194096i
$797$	−12.7186	+	22.0292i	−0.450514	+	0.780314i	−0.998418	−	0.0562278i	$-0.982093\pi$
$797$	−12.7186	+	22.0292i	−0.450514	+	0.780314i	0.547904	+	0.836541i	$0.315426\pi$
$798$		−	7.47834i		−	0.264731i
$799$	1.75071	+	1.01077i	0.0619357	+	0.0357586i
$800$	1.42625	+	0.823447i	0.0504256	+	0.0291132i
$801$			6.74513i			0.238328i
$802$	0.210179	−	0.364040i	0.00742166	−	0.0128547i
$803$	0.814351	+	1.41050i	0.0287378	+	0.0497754i
$804$	2.73485	−	1.57897i	0.0964508	−	0.0556859i
$805$	−0.0264156			−0.000931027
$806$	6.25467	−	19.5616i	0.220311	−	0.689028i
$807$	27.1728			0.956528
$808$	20.2732	−	11.7048i	0.713210	−	0.411772i
$809$	−25.5196	−	44.2013i	−0.897222	−	1.55403i	−0.831030	−	0.556228i	$-0.812248\pi$
$809$	−25.5196	−	44.2013i	−0.897222	−	1.55403i	−0.0661927	−	0.997807i	$-0.521085\pi$
$810$	7.14120	−	12.3689i	0.250916	−	0.434600i
$811$			9.67358i			0.339685i	0.985471	+	0.169843i	$0.0543260\pi$
$811$			9.67358i			0.339685i	−0.985471	+	0.169843i	$0.945674\pi$
$812$	0.848726	+	0.490012i	0.0297844	+	0.0171961i
$813$	−16.2800	−	9.39928i	−0.570965	−	0.329647i
$814$		−	0.282440i		−	0.00989952i
$815$	−11.4701	+	19.8668i	−0.401779	+	0.695902i
$816$	−1.01631	−	1.76029i	−0.0355778	−	0.0616226i
$817$	5.26011	−	3.03693i	0.184028	−	0.106249i
$818$	−31.8786			−1.11461
$819$	−3.21979	−	1.02951i	−0.112509	−	0.0359738i
$820$	1.40649			0.0491168
$821$	−4.16223	+	2.40307i	−0.145263	+	0.0838676i	−0.570870	−	0.821041i	$-0.693394\pi$
$821$	−4.16223	+	2.40307i	−0.145263	+	0.0838676i	0.425607	+	0.904908i	$0.360061\pi$
$822$	−7.66978	−	13.2844i	−0.267514	−	0.463348i
$823$	−5.50917	+	9.54217i	−0.192038	+	0.332619i	−0.945925	−	0.324384i	$-0.894843\pi$
$823$	−5.50917	+	9.54217i	−0.192038	+	0.332619i	0.753888	+	0.657003i	$0.228176\pi$
$824$		−	25.9502i		−	0.904019i
$825$	0.344080	+	0.198655i	0.0119793	+	0.00691627i
$826$	−7.93609	−	4.58191i	−0.276132	−	0.159425i
$827$		−	18.7673i		−	0.652602i	−0.945266	−	0.326301i	$-0.894198\pi$
$827$		−	18.7673i		−	0.652602i	0.945266	−	0.326301i	$-0.105802\pi$
$828$	−0.00363604	+	0.00629780i	−0.000126361	+	0.000218864i
$829$	15.8574	+	27.4659i	0.550752	+	0.953930i	0.998221	+	0.0596307i	$0.0189923\pi$
$829$	15.8574	+	27.4659i	0.550752	+	0.953930i	−0.447469	+	0.894300i	$0.647674\pi$
$830$	−12.4703	+	7.19975i	−0.432851	+	0.249907i
$831$	7.57506			0.262776
$832$	−21.3516	−	23.4909i	−0.740234	−	0.814399i
$833$	−0.307930			−0.0106691
$834$	−52.3082	+	30.2001i	−1.81128	+	1.04574i
$835$	−8.25787	−	14.3031i	−0.285776	−	0.494978i
$836$	−0.0848099	+	0.146895i	−0.00293321	+	0.00508047i
$837$		−	17.8456i		−	0.616833i
$838$	−31.5759	−	18.2304i	−1.09077	−	0.629758i
$839$	−29.3713	−	16.9575i	−1.01401	−	0.585439i	−0.101647	−	0.994821i	$-0.532411\pi$
$839$	−29.3713	−	16.9575i	−1.01401	−	0.585439i	−0.912363	+	0.409382i	$0.865744\pi$
$840$			5.94529i			0.205132i
$841$	8.93026	−	15.4677i	0.307940	−	0.533368i
$842$	21.7342	+	37.6448i	0.749011	+	1.29732i
$843$	3.33258	−	1.92407i	0.114780	−	0.0662684i
$844$	−1.48520			−0.0511227
$845$	12.9410	+	1.23754i	0.445183	+	0.0425728i
$846$	8.04010			0.276424
$847$	−9.49156	+	5.47996i	−0.326134	+	0.188293i
$848$	2.94594	+	5.10252i	0.101164	+	0.175221i
$849$	16.2125	−	28.0808i	0.556411	−	0.963732i
$850$		−	0.402243i		−	0.0137968i
$851$	0.0247039	+	0.0142628i	0.000846838	+	0.000488922i
$852$	5.08604	+	2.93643i	0.174245	+	0.100600i
$853$			10.8950i			0.373038i	0.982451	+	0.186519i	$0.0597206\pi$
$853$			10.8950i			0.373038i	−0.982451	+	0.186519i	$0.940279\pi$
$854$	5.60250	−	9.70381i	0.191713	−	0.332057i
$855$	−1.35245	−	2.34250i	−0.0462527	−	0.0801120i
$856$	−18.0831	+	10.4403i	−0.618068	+	0.356842i
$857$	13.4585			0.459733			0.229867	−	0.973222i	$-0.426171\pi$
$857$	13.4585			0.459733			0.229867	+	0.973222i	$0.426171\pi$
$858$	−1.25863	−	1.38474i	−0.0429690	−	0.0472742i
$859$	−35.8119			−1.22189			−0.610943	−	0.791674i	$-0.709210\pi$
$859$	−35.8119			−1.22189			−0.610943	+	0.791674i	$0.709210\pi$
$860$	−0.535357	+	0.309088i	−0.0182555	+	0.0105398i
$861$	4.75243	+	8.23145i	0.161962	+	0.280527i
$862$	6.41427	−	11.1098i	0.218471	−	0.378403i
$863$		−	9.26997i		−	0.315553i	−0.987475	−	0.157777i	$-0.949567\pi$
$863$		−	9.26997i		−	0.315553i	0.987475	−	0.157777i	$-0.0504326\pi$
$864$	−5.83704	−	3.37002i	−0.198580	−	0.114650i
$865$	15.9960	+	9.23532i	0.543882	+	0.314010i
$866$			15.0516i			0.511473i
$867$	−16.7727	+	29.0512i	−0.569630	+	0.986629i
$868$	0.640188	+	1.10884i	0.0217294	+	0.0376364i
$869$	−0.805286	+	0.464932i	−0.0273175	+	0.0157717i
$870$	−8.65131			−0.293307
$871$	−18.6132	−	5.95142i	−0.630683	−	0.201656i
$872$	−44.5322			−1.50805
$873$	−11.5196	+	6.65085i	−0.389880	+	0.225097i
$874$	0.0497763	+	0.0862151i	0.00168371	+	0.00291627i
$875$	−0.500000	+	0.866025i	−0.0169031	+	0.0292770i
$876$			4.73961i			0.160137i
$877$	−15.1207	−	8.72994i	−0.510590	−	0.294789i	0.222486	−	0.974936i	$-0.428583\pi$
$877$	−15.1207	−	8.72994i	−0.510590	−	0.294789i	−0.733076	+	0.680147i	$0.761916\pi$
$878$	10.9372	+	6.31459i	0.369112	+	0.213107i
$879$		−	35.3704i		−	1.19302i
$880$	−0.333024	+	0.576814i	−0.0112262	+	0.0194444i
$881$	−28.0193	−	48.5308i	−0.943994	−	1.63505i	−0.757753	−	0.652542i	$-0.773703\pi$
$881$	−28.0193	−	48.5308i	−0.943994	−	1.63505i	−0.186241	−	0.982504i	$-0.559631\pi$
$882$	−1.06062	+	0.612350i	−0.0357130	+	0.0206189i
$883$	45.1973			1.52101			0.760504	−	0.649333i	$-0.224952\pi$
$883$	45.1973			1.52101			0.760504	+	0.649333i	$0.224952\pi$
$884$	0.0992868	−	0.310521i	0.00333938	−	0.0104440i
$885$	−13.9204			−0.467930
$886$	13.4280	−	7.75267i	0.451123	−	0.260456i
$887$	−28.9137	−	50.0799i	−0.970826	−	1.68152i	−0.693073	−	0.720868i	$-0.743744\pi$
$887$	−28.9137	−	50.0799i	−0.970826	−	1.68152i	−0.277753	−	0.960652i	$-0.589590\pi$
$888$	3.21009	−	5.56004i	0.107724	−	0.186583i
$889$		−	2.54983i		−	0.0855185i
$890$	−8.13887	−	4.69898i	−0.272815	−	0.157510i
$891$	−1.89588	−	1.09459i	−0.0635145	−	0.0366701i
$892$			3.04306i			0.101889i
$893$	−9.47017	+	16.4028i	−0.316907	+	0.548899i
$894$	6.08831	+	10.5453i	0.203624	+	0.352687i
$895$	6.95381	−	4.01478i	0.232440	−	0.134199i
$896$	−8.20714			−0.274181
$897$	0.184676	−	0.0401603i	0.00616616	−	0.00134091i
$898$	−42.9108			−1.43195
$899$	−12.6037	+	7.27672i	−0.420355	+	0.242692i
$900$	0.137647	+	0.238412i	0.00458825	+	0.00794708i
$901$	−0.272701	+	0.472332i	−0.00908499	+	0.0157357i
$902$			1.25281i			0.0417140i
$903$	−3.61786	−	2.08877i	−0.120395	−	0.0695100i
$904$	−13.8123	−	7.97456i	−0.459391	−	0.265230i
$905$			0.349155i			0.0116063i
$906$	−19.4990	+	33.7733i	−0.647813	+	1.12204i
$907$	6.24816	+	10.8221i	0.207467	+	0.359343i	0.950916	−	0.309450i	$-0.100145\pi$
$907$	6.24816	+	10.8221i	0.207467	+	0.359343i	−0.743449	+	0.668792i	$0.766811\pi$
$908$	−7.49467	+	4.32705i	−0.248719	+	0.143598i
$909$	7.32531			0.242965
$910$	3.48529	−	3.16789i	0.115536	−	0.105015i
$911$	9.63299			0.319155			0.159578	−	0.987185i	$-0.448987\pi$
$911$	9.63299			0.319155			0.159578	+	0.987185i	$0.448987\pi$
$912$	16.4926	−	9.52201i	0.546125	−	0.315305i
$913$	1.10356	+	1.91143i	0.0365226	+	0.0632590i
$914$	−19.4970	+	33.7697i	−0.644902	+	1.11700i
$915$		−	17.0211i		−	0.562701i
$916$	1.26373	+	0.729617i	0.0417549	+	0.0241072i
$917$	−6.07802	−	3.50914i	−0.200714	−	0.115882i
$918$			1.64621i			0.0543330i
$919$	−4.15538	+	7.19734i	−0.137073	+	0.237418i	−0.926388	−	0.376571i	$-0.877103\pi$
$919$	−4.15538	+	7.19734i	−0.137073	+	0.237418i	0.789314	+	0.613990i	$0.210436\pi$
$920$	−0.0395722	−	0.0685411i	−0.00130466	−	0.00225973i
$921$	−40.9417	+	23.6377i	−1.34907	+	0.778889i
$922$	−15.1851			−0.500093
$923$	−7.72246	−	35.5116i	−0.254188	−	1.16888i
$924$	0.116663			0.00383793
$925$	0.935201	−	0.539939i	0.0307492	−	0.0177531i
$926$	−26.9421	−	46.6651i	−0.885372	−	1.53351i
$927$	4.06017	−	7.03243i	0.133354	−	0.230975i
$928$			5.49665i			0.180436i
$929$	−18.9504	−	10.9410i	−0.621742	−	0.358963i	0.155805	−	0.987788i	$-0.450203\pi$
$929$	−18.9504	−	10.9410i	−0.621742	−	0.358963i	−0.777547	+	0.628825i	$0.783536\pi$
$930$	−9.78843	−	5.65135i	−0.320975	−	0.185315i
$931$		−	2.88507i		−	0.0945543i
$932$	−0.0386265	+	0.0669030i	−0.00126525	+	0.00219148i
$933$	32.6506	+	56.5526i	1.06893	+	1.85145i
$934$	−16.7559	+	9.67401i	−0.548269	+	0.316543i
$935$	−0.0616550			−0.00201633
$936$	−2.15218	−	9.89673i	−0.0703461	−	0.323485i
$937$	2.32476			0.0759467			0.0379733	−	0.999279i	$-0.487910\pi$
$937$	2.32476			0.0759467			0.0379733	+	0.999279i	$0.487910\pi$
$938$	−6.13130	+	3.53991i	−0.200194	+	0.115582i
$939$	−16.0403	−	27.7826i	−0.523455	−	0.906651i
$940$	0.963842	−	1.66942i	0.0314371	−	0.0544506i
$941$		−	28.6362i		−	0.933514i	−0.884386	−	0.466757i	$-0.845422\pi$
$941$		−	28.6362i		−	0.933514i	0.884386	−	0.466757i	$-0.154578\pi$
$942$	31.1962	+	18.0111i	1.01643	+	0.586834i
$943$	−0.109578	−	0.0632649i	−0.00356835	−	0.00206019i
$944$		−	23.3362i		−	0.759527i
$945$	2.04629	−	3.54427i	0.0665658	−	0.115295i
$946$	−0.275315	−	0.476860i	−0.00895127	−	0.0155041i
$947$	30.0572	−	17.3535i	0.976727	−	0.563913i	0.0754464	−	0.997150i	$-0.475962\pi$
$947$	30.0572	−	17.3535i	0.976727	−	0.563913i	0.901280	+	0.433236i	$0.142629\pi$
$948$	−2.70596			−0.0878854
$949$	21.7034	−	19.7269i	0.704523	−	0.640364i
$950$	3.76871			0.122273
$951$	−49.4133	+	28.5288i	−1.60233	+	0.925109i
$952$	−0.461299	−	0.798993i	−0.0149508	−	0.0258955i
$953$	−23.8877	+	41.3747i	−0.773797	+	1.34026i	0.161671	+	0.986845i	$0.448312\pi$
$953$	−23.8877	+	41.3747i	−0.773797	+	1.34026i	−0.935468	+	0.353412i	$0.885022\pi$
$954$			2.16917i			0.0702296i
$955$	5.47195	+	3.15923i	0.177068	+	0.102230i
$956$	−3.20634	−	1.85118i	−0.103700	−	0.0598715i
$957$			1.32605i			0.0428653i
$958$	−5.06382	+	8.77079i	−0.163605	+	0.283371i
$959$	−2.95892	−	5.12500i	−0.0955486	−	0.165495i
$960$	−15.1300	+	8.73533i	−0.488320	+	0.281932i
$961$	11.9863			0.386655
$962$	−4.96991	+	1.08077i	−0.160236	+	0.0348455i
$963$	−6.53395			−0.210554
$964$	3.80330	−	2.19583i	0.122496	−	0.0707231i
$965$	−9.46842	−	16.3998i	−0.304799	−	0.527928i
$966$	0.0342357	−	0.0592980i	0.00110152	−	0.00190788i
$967$		−	25.2911i		−	0.813307i	−0.913583	−	0.406653i	$-0.866696\pi$
$967$		−	25.2911i		−	0.813307i	0.913583	−	0.406653i	$-0.133304\pi$
$968$	−28.4379	−	16.4186i	−0.914029	−	0.527715i
$969$	1.52669	+	0.881437i	0.0490445	+	0.0283158i
$970$		−	18.5332i		−	0.595065i
$971$	−21.2696	+	36.8401i	−0.682574	+	1.18225i	0.291618	+	0.956535i	$0.405806\pi$
$971$	−21.2696	+	36.8401i	−0.682574	+	1.18225i	−0.974193	+	0.225719i	$0.927527\pi$
$972$	−1.38274	−	2.39498i	−0.0443515	−	0.0768191i
$973$	−20.1800	+	11.6509i	−0.646940	+	0.373511i
$974$	6.14415			0.196871
$975$	2.17895	−	6.81471i	0.0697824	−	0.218245i
$976$	28.5341			0.913355
$977$	45.2112	−	26.1027i	1.44643	−	0.835098i	0.448166	−	0.893950i	$-0.352077\pi$
$977$	45.2112	−	26.1027i	1.44643	−	0.835098i	0.998267	+	0.0588518i	$0.0187439\pi$
$978$	−29.7314	−	51.4963i	−0.950706	−	1.64667i
$979$	−0.720249	+	1.24751i	−0.0230193	+	0.0398705i
$980$			0.293633i			0.00937975i
$981$	−12.0681	−	6.96751i	−0.385304	−	0.222456i
$982$	−26.3695	−	15.2245i	−0.841486	−	0.485832i
$983$			42.2567i			1.34778i	0.738833	+	0.673889i	$0.235377\pi$
$983$			42.2567i			1.34778i	−0.738833	+	0.673889i	$0.764623\pi$
$984$	−14.2389	+	24.6624i	−0.453919	+	0.786210i
$985$	−7.59606	−	13.1568i	−0.242030	−	0.419209i
$986$	1.16266	−	0.671261i	0.0370266	−	0.0213773i
$987$	13.0270			0.414654
$988$	2.90934	+	0.930241i	0.0925586	+	0.0295949i
$989$	0.0556120			0.00176836
$990$	−0.212362	+	0.122607i	−0.00674930	+	0.00389671i
$991$	−2.53699	−	4.39419i	−0.0805901	−	0.139586i	0.822913	−	0.568167i	$-0.192347\pi$
$991$	−2.53699	−	4.39419i	−0.0805901	−	0.139586i	−0.903504	+	0.428581i	$0.859014\pi$
$992$	−3.59062	+	6.21913i	−0.114002	+	0.197458i
$993$		−	67.4716i		−	2.14115i
$994$	−11.4025	−	6.58321i	−0.361664	−	0.208807i
$995$	18.6495	+	10.7673i	0.591230	+	0.341347i
$996$			6.42286i			0.203516i
$997$	24.5510	−	42.5235i	0.777537	−	1.34673i	−0.155821	−	0.987785i	$-0.549802\pi$
$997$	24.5510	−	42.5235i	0.777537	−	1.34673i	0.933358	−	0.358948i	$-0.116864\pi$
$998$	22.2430	+	38.5261i	0.704091	+	1.21952i
$999$	−3.82738	+	2.20974i	−0.121093	+	0.0699131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	455.2.bq.a.36.8	✓	20
13.2	odd	12		5915.2.a.be.1.8		10
13.4	even	6	inner	455.2.bq.a.316.8	yes	20
13.11	odd	12		5915.2.a.bf.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
455.2.bq.a.36.8	✓	20	1.1	even	1	trivial
455.2.bq.a.316.8	yes	20	13.4	even	6	inner
5915.2.a.be.1.8		10	13.2	odd	12
5915.2.a.bf.1.3		10	13.11	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 455 = 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	455.bq (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.13127 - 0.653140i) q^{2} +(0.992163 + 1.71848i) q^{3} +(-0.146816 + 0.254293i) q^{4} -1.00000i q^{5} +(2.24481 + 1.29604i) q^{6} +(0.866025 + 0.500000i) q^{7} +2.99613i q^{8} +(-0.468774 + 0.811941i) q^{9} +(-0.653140 - 1.13127i) q^{10} +(-0.173399 + 0.100112i) q^{11} -0.582663 q^{12} +(2.42512 + 2.66810i) q^{13} +1.30628 q^{14} +(1.71848 - 0.992163i) q^{15} +(1.66326 + 2.88085i) q^{16} +(-0.153965 + 0.266675i) q^{17} +1.22470i q^{18} +(-2.49854 - 1.44253i) q^{19} +(0.254293 + 0.146816i) q^{20} +1.98433i q^{21} +(-0.130774 + 0.226508i) q^{22} +(-0.0132078 - 0.0228766i) q^{23} +(-5.14877 + 2.97265i) q^{24} -1.00000 q^{25} +(4.48612 + 1.43440i) q^{26} +4.09258 q^{27} +(-0.254293 + 0.146816i) q^{28} +(-1.66879 - 2.89043i) q^{29} +(1.29604 - 2.24481i) q^{30} -4.36047i q^{31} +(-1.42625 - 0.823447i) q^{32} +(-0.344080 - 0.198655i) q^{33} +0.402243i q^{34} +(0.500000 - 0.866025i) q^{35} +(-0.137647 - 0.238412i) q^{36} +(-0.935201 + 0.539939i) q^{37} -3.76871 q^{38} +(-2.17895 + 6.81471i) q^{39} +2.99613 q^{40} +(4.14823 - 2.39498i) q^{41} +(1.29604 + 2.24481i) q^{42} +(-1.05264 + 1.82322i) q^{43} -0.0587923i q^{44} +(0.811941 + 0.468774i) q^{45} +(-0.0298832 - 0.0172531i) q^{46} -6.56495i q^{47} +(-3.30044 + 5.71654i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-1.13127 + 0.653140i) q^{50} -0.611034 q^{51} +(-1.03453 + 0.224972i) q^{52} +1.77119 q^{53} +(4.62981 - 2.67302i) q^{54} +(0.100112 + 0.173399i) q^{55} +(-1.49806 + 2.59472i) q^{56} -5.72492i q^{57} +(-3.77572 - 2.17991i) q^{58} +(-6.07534 - 3.50760i) q^{59} +0.582663i q^{60} +(4.28889 - 7.42858i) q^{61} +(-2.84800 - 4.93288i) q^{62} +(-0.811941 + 0.468774i) q^{63} -8.80433 q^{64} +(2.66810 - 2.42512i) q^{65} -0.518997 q^{66} +(-4.69371 + 2.70992i) q^{67} +(-0.0452092 - 0.0783046i) q^{68} +(0.0262086 - 0.0453946i) q^{69} -1.30628i q^{70} +(-8.72896 - 5.03966i) q^{71} +(-2.43268 - 1.40451i) q^{72} -8.13440i q^{73} +(-0.705311 + 1.22163i) q^{74} +(-0.992163 - 1.71848i) q^{75} +(0.733654 - 0.423575i) q^{76} -0.200224 q^{77} +(1.98597 + 9.13245i) q^{78} +4.64412 q^{79} +(2.88085 - 1.66326i) q^{80} +(5.46682 + 9.46882i) q^{81} +(3.12852 - 5.41875i) q^{82} -11.0233i q^{83} +(-0.504601 - 0.291331i) q^{84} +(0.266675 + 0.153965i) q^{85} +2.75007i q^{86} +(3.31143 - 5.73556i) q^{87} +(-0.299948 - 0.519525i) q^{88} +(6.23057 - 3.59722i) q^{89} +1.22470 q^{90} +(0.766168 + 3.52321i) q^{91} +0.00775648 q^{92} +(7.49336 - 4.32630i) q^{93} +(-4.28783 - 7.42674i) q^{94} +(-1.44253 + 2.49854i) q^{95} -3.26797i q^{96} +(12.2870 + 7.09388i) q^{97} +(1.13127 + 0.653140i) q^{98} -0.187720i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} + 4 q^{4} + 18 q^{6} - 6 q^{11} - 8 q^{12} + 6 q^{15} - 10 q^{17} + 26 q^{22} + 2 q^{23} + 12 q^{24} - 20 q^{25} - 2 q^{26} - 44 q^{27} + 12 q^{29} - 8 q^{30} - 6 q^{32} - 18 q^{33} + 10 q^{35}+ \cdots + 18 q^{97}+O(q^{100}) \) 20 * q + 4 * q^3 + 4 * q^4 + 18 * q^6 - 6 * q^11 - 8 * q^12 + 6 * q^15 - 10 * q^17 + 26 * q^22 + 2 * q^23 + 12 * q^24 - 20 * q^25 - 2 * q^26 - 44 * q^27 + 12 * q^29 - 8 * q^30 - 6 * q^32 - 18 * q^33 + 10 * q^35 - 22 * q^36 - 72 * q^38 + 8 * q^39 + 12 * q^41 - 8 * q^42 - 8 * q^43 + 10 * q^48 + 10 * q^49 - 60 * q^51 - 12 * q^52 - 24 * q^53 + 84 * q^54 + 12 * q^55 - 12 * q^58 - 12 * q^59 + 42 * q^61 - 40 * q^62 + 44 * q^64 + 4 * q^65 + 12 * q^66 + 6 * q^67 + 34 * q^68 - 44 * q^69 + 108 * q^71 - 24 * q^72 + 38 * q^74 - 4 * q^75 - 12 * q^76 - 24 * q^77 - 2 * q^78 - 44 * q^79 + 24 * q^80 + 2 * q^81 - 40 * q^82 - 18 * q^84 - 12 * q^85 + 4 * q^87 - 22 * q^88 + 6 * q^89 - 20 * q^90 - 14 * q^91 - 32 * q^92 + 108 * q^93 - 14 * q^94 + 16 * q^95 + 18 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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