LMFDB - Embedded newform 1078.2.e.m.67.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(67,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1078.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.e (of order $3$, degree $2$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1078.67
Dual form			1078.2.e.m.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +(-1.70711 + 2.95680i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.207107 + 0.358719i) q^{12} -1.82843 q^{13} -1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.41421 - 2.44949i) q^{18} +(-1.70711 - 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(-1.12132 - 1.94218i) q^{23} +(0.207107 - 0.358719i) q^{24} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +2.41421 q^{27} -8.65685 q^{29} +(0.707107 + 1.22474i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.207107 + 0.358719i) q^{33} +7.65685 q^{34} -2.82843 q^{36} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(-0.378680 + 0.655892i) q^{39} +(-1.70711 - 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(-0.500000 - 0.866025i) q^{44} +(4.82843 - 8.36308i) q^{45} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} -0.414214 q^{48} +6.65685 q^{50} +(1.58579 + 2.74666i) q^{51} +(0.914214 - 1.58346i) q^{52} +(5.94975 - 10.3053i) q^{53} +(-1.20711 - 2.09077i) q^{54} +3.41421 q^{55} -1.41421 q^{57} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(0.707107 - 1.22474i) q^{60} +(3.08579 + 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(3.12132 + 5.40629i) q^{65} +(0.207107 - 0.358719i) q^{66} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} -0.928932 q^{69} +3.07107 q^{71} +(1.41421 + 2.44949i) q^{72} +(-3.29289 + 5.70346i) q^{73} +(3.29289 - 5.70346i) q^{74} +(1.37868 + 2.38794i) q^{75} +3.41421 q^{76} +0.757359 q^{78} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(-1.29289 - 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(-2.82843 - 4.89898i) q^{86} +(-1.79289 + 3.10538i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} -9.65685 q^{90} +2.24264 q^{92} +(0.828427 + 1.43488i) q^{93} +(3.24264 - 5.61642i) q^{94} +(-5.82843 + 10.0951i) q^{95} +(0.207107 + 0.358719i) q^{96} -1.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 16 q^{37} - 4 q^{38} - 10 q^{39} - 4 q^{40} + 16 q^{41} - 2 q^{44} + 8 q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} + 8 q^{55} + 6 q^{58} - 14 q^{59} + 18 q^{61} + 16 q^{62} + 4 q^{64} + 4 q^{65} - 2 q^{66} - 14 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{71} - 16 q^{73} + 16 q^{74} + 14 q^{75} + 8 q^{76} + 20 q^{78} + 18 q^{79} - 4 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 16 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} - 12 q^{95} - 2 q^{96} + 4 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 4 * q^27 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 16 * q^37 - 4 * q^38 - 10 * q^39 - 4 * q^40 + 16 * q^41 - 2 * q^44 + 8 * q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 2 * q^54 + 8 * q^55 + 6 * q^58 - 14 * q^59 + 18 * q^61 + 16 * q^62 + 4 * q^64 + 4 * q^65 - 2 * q^66 - 14 * q^67 - 4 * q^68 - 32 * q^69 - 16 * q^71 - 16 * q^73 + 16 * q^74 + 14 * q^75 + 8 * q^76 + 20 * q^78 + 18 * q^79 - 4 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 16 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 - 12 * q^95 - 2 * q^96 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	−0.800025	−	0.599966i	$-0.795181\pi$
$3$	0.207107	−	0.358719i	0.119573	−	0.207107i	0.919599	+	0.392859i	$0.128514\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	−0.941067	−	0.338221i	$-0.890175\pi$
$5$	−1.70711	−	2.95680i	−0.763441	−	1.32232i	0.177625	−	0.984098i	$-0.443158\pi$
$6$	−0.414214			−0.169102
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$	−1.70711	+	2.95680i	−0.539835	+	0.935021i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	0.207107	+	0.358719i	0.0597866	+	0.103553i
$13$	−1.82843			−0.507114			−0.253557	−	0.967320i	$-0.581601\pi$
$13$	−1.82843			−0.507114			−0.253557	+	0.967320i	$0.581601\pi$
$14$		0			0
$15$	−1.41421			−0.365148
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.142747	+	0.989759i	$0.545593\pi$
$17$	−3.82843	+	6.63103i	−0.928530	+	1.60826i	−0.785783	+	0.618502i	$0.787740\pi$
$18$	1.41421	−	2.44949i	0.333333	−	0.577350i
$19$	−1.70711	−	2.95680i	−0.391637	−	0.678335i	0.601028	−	0.799228i	$-0.294758\pi$
$19$	−1.70711	−	2.95680i	−0.391637	−	0.678335i	−0.992666	+	0.120892i	$0.961424\pi$
$20$	3.41421			0.763441
$21$		0			0
$22$	1.00000			0.213201
$23$	−1.12132	−	1.94218i	−0.233811	−	0.404973i	0.725115	−	0.688628i	$-0.241787\pi$
$23$	−1.12132	−	1.94218i	−0.233811	−	0.404973i	−0.958927	+	0.283654i	$0.908453\pi$
$24$	0.207107	−	0.358719i	0.0422755	−	0.0732233i
$25$	−3.32843	+	5.76500i	−0.665685	+	1.15300i
$26$	0.914214	+	1.58346i	0.179292	+	0.310543i
$27$	2.41421			0.464616
$28$		0			0
$29$	−8.65685			−1.60754			−0.803769	−	0.594942i	$-0.797175\pi$
$29$	−8.65685			−1.60754			−0.803769	+	0.594942i	$0.797175\pi$
$30$	0.707107	+	1.22474i	0.129099	+	0.223607i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.207107	+	0.358719i	0.0360527	+	0.0624450i
$34$	7.65685			1.31314
$35$		0			0
$36$	−2.82843			−0.471405
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	0.998827	+	0.0484222i	$0.0154193\pi$
$37$	3.29289	+	5.70346i	0.541348	+	0.937643i	−0.457479	+	0.889221i	$0.651247\pi$
$38$	−1.70711	+	2.95680i	−0.276929	+	0.479656i
$39$	−0.378680	+	0.655892i	−0.0606373	+	0.105027i
$40$	−1.70711	−	2.95680i	−0.269917	−	0.467510i
$41$	2.58579			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$41$	2.58579			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$42$		0			0
$43$	5.65685			0.862662			0.431331	−	0.902194i	$-0.358044\pi$
$43$	5.65685			0.862662			0.431331	+	0.902194i	$0.358044\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$	4.82843	−	8.36308i	0.719779	−	1.24669i
$46$	−1.12132	+	1.94218i	−0.165330	+	0.286359i
$47$	3.24264	+	5.61642i	0.472988	+	0.819239i	0.999522	−	0.0309151i	$-0.00984215\pi$
$47$	3.24264	+	5.61642i	0.472988	+	0.819239i	−0.526534	+	0.850154i	$0.676509\pi$
$48$	−0.414214			−0.0597866
$49$		0			0
$50$	6.65685			0.941421
$51$	1.58579	+	2.74666i	0.222055	+	0.384610i
$52$	0.914214	−	1.58346i	0.126779	−	0.219587i
$53$	5.94975	−	10.3053i	0.817261	−	1.41554i	−0.0904325	−	0.995903i	$-0.528825\pi$
$53$	5.94975	−	10.3053i	0.817261	−	1.41554i	0.907693	−	0.419634i	$-0.137842\pi$
$54$	−1.20711	−	2.09077i	−0.164266	−	0.284518i
$55$	3.41421			0.460372
$56$		0			0
$57$	−1.41421			−0.187317
$58$	4.32843	+	7.49706i	0.568350	+	0.984412i
$59$	−4.20711	+	7.28692i	−0.547719	+	0.948677i	0.450712	+	0.892670i	$0.351170\pi$
$59$	−4.20711	+	7.28692i	−0.547719	+	0.948677i	−0.998430	+	0.0560070i	$0.982163\pi$
$60$	0.707107	−	1.22474i	0.0912871	−	0.158114i
$61$	3.08579	+	5.34474i	0.395094	+	0.684324i	0.993113	−	0.117158i	$-0.0373785\pi$
$61$	3.08579	+	5.34474i	0.395094	+	0.684324i	−0.598019	+	0.801482i	$0.704045\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	3.12132	+	5.40629i	0.387152	+	0.670567i
$66$	0.207107	−	0.358719i	0.0254931	−	0.0441553i
$67$	−5.62132	+	9.73641i	−0.686754	+	1.18949i	0.286129	+	0.958191i	$0.407632\pi$
$67$	−5.62132	+	9.73641i	−0.686754	+	1.18949i	−0.972882	+	0.231301i	$0.925702\pi$
$68$	−3.82843	−	6.63103i	−0.464265	−	0.804131i
$69$	−0.928932			−0.111830
$70$		0			0
$71$	3.07107			0.364469			0.182234	−	0.983255i	$-0.441667\pi$
$71$	3.07107			0.364469			0.182234	+	0.983255i	$0.441667\pi$
$72$	1.41421	+	2.44949i	0.166667	+	0.288675i
$73$	−3.29289	+	5.70346i	−0.385404	+	0.667539i	−0.991825	−	0.127604i	$-0.959271\pi$
$73$	−3.29289	+	5.70346i	−0.385404	+	0.667539i	0.606421	+	0.795144i	$0.292605\pi$
$74$	3.29289	−	5.70346i	0.382791	−	0.663014i
$75$	1.37868	+	2.38794i	0.159196	+	0.275736i
$76$	3.41421			0.391637
$77$		0			0
$78$	0.757359			0.0857541
$79$	2.37868	+	4.11999i	0.267622	+	0.463536i	0.968247	−	0.249994i	$-0.0804287\pi$
$79$	2.37868	+	4.11999i	0.267622	+	0.463536i	−0.700625	+	0.713530i	$0.747095\pi$
$80$	−1.70711	+	2.95680i	−0.190860	+	0.330580i
$81$	−3.74264	+	6.48244i	−0.415849	+	0.720272i
$82$	−1.29289	−	2.23936i	−0.142776	−	0.247296i
$83$	−16.1421			−1.77183			−0.885915	−	0.463848i	$-0.846468\pi$
$83$	−16.1421			−1.77183			−0.885915	+	0.463848i	$0.846468\pi$
$84$		0			0
$85$	26.1421			2.83551
$86$	−2.82843	−	4.89898i	−0.304997	−	0.528271i
$87$	−1.79289	+	3.10538i	−0.192218	+	0.332932i
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	−2.24264	−	3.88437i	−0.237719	−	0.411742i	0.722340	−	0.691538i	$-0.243067\pi$
$89$	−2.24264	−	3.88437i	−0.237719	−	0.411742i	−0.960060	+	0.279796i	$0.909733\pi$
$90$	−9.65685			−1.01792
$91$		0			0
$92$	2.24264			0.233811
$93$	0.828427	+	1.43488i	0.0859039	+	0.148790i
$94$	3.24264	−	5.61642i	0.334453	−	0.579289i
$95$	−5.82843	+	10.0951i	−0.597984	+	1.03574i
$96$	0.207107	+	0.358719i	0.0211377	+	0.0366117i
$97$	−1.82843			−0.185649			−0.0928243	−	0.995683i	$-0.529589\pi$
$97$	−1.82843			−0.185649			−0.0928243	+	0.995683i	$0.529589\pi$
$98$		0			0
$99$	−2.82843			−0.284268
$100$	−3.32843	−	5.76500i	−0.332843	−	0.576500i
$101$	5.91421	−	10.2437i	0.588486	−	1.01929i	−0.405945	−	0.913898i	$-0.633057\pi$
$101$	5.91421	−	10.2437i	0.588486	−	1.01929i	0.994431	−	0.105390i	$-0.0336092\pi$
$102$	1.58579	−	2.74666i	0.157016	−	0.271960i
$103$	5.29289	+	9.16756i	0.521524	+	0.903307i	0.999687	+	0.0250350i	$0.00796973\pi$
$103$	5.29289	+	9.16756i	0.521524	+	0.903307i	−0.478162	+	0.878271i	$0.658697\pi$
$104$	−1.82843			−0.179292
$105$		0			0
$106$	−11.8995			−1.15578
$107$	−5.53553	−	9.58783i	−0.535140	−	0.926890i	−0.999157	−	0.0410635i	$-0.986925\pi$
$107$	−5.53553	−	9.58783i	−0.535140	−	0.926890i	0.464016	−	0.885827i	$-0.346408\pi$
$108$	−1.20711	+	2.09077i	−0.116154	+	0.201184i
$109$	0.242641	−	0.420266i	0.0232408	−	0.0402542i	−0.854171	−	0.519992i	$-0.825935\pi$
$109$	0.242641	−	0.420266i	0.0232408	−	0.0402542i	0.877412	+	0.479738i	$0.159268\pi$
$110$	−1.70711	−	2.95680i	−0.162766	−	0.281919i
$111$	2.72792			0.258923
$112$		0			0
$113$	−13.8284			−1.30087			−0.650434	−	0.759562i	$-0.725413\pi$
$113$	−13.8284			−1.30087			−0.650434	+	0.759562i	$0.725413\pi$
$114$	0.707107	+	1.22474i	0.0662266	+	0.114708i
$115$	−3.82843	+	6.63103i	−0.357003	+	0.618347i
$116$	4.32843	−	7.49706i	0.401884	−	0.696084i
$117$	−2.58579	−	4.47871i	−0.239056	−	0.414057i
$118$	8.41421			0.774591
$119$		0			0
$120$	−1.41421			−0.129099
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	3.08579	−	5.34474i	0.279374	−	0.483890i
$123$	0.535534	−	0.927572i	0.0482875	−	0.0836363i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	5.65685			0.505964
$126$		0			0
$127$	−9.72792			−0.863213			−0.431607	−	0.902062i	$-0.642053\pi$
$127$	−9.72792			−0.863213			−0.431607	+	0.902062i	$0.642053\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	1.17157	−	2.02922i	0.103151	−	0.178663i
$130$	3.12132	−	5.40629i	0.273758	−	0.474163i
$131$	−1.70711	−	2.95680i	−0.149151	−	0.258336i	0.781763	−	0.623575i	$-0.214321\pi$
$131$	−1.70711	−	2.95680i	−0.149151	−	0.258336i	−0.930914	+	0.365239i	$0.880987\pi$
$132$	−0.414214			−0.0360527
$133$		0			0
$134$	11.2426			0.971216
$135$	−4.12132	−	7.13834i	−0.354707	−	0.614370i
$136$	−3.82843	+	6.63103i	−0.328285	+	0.568606i
$137$	2.67157	−	4.62730i	0.228248	−	0.395337i	−0.729041	−	0.684470i	$-0.760034\pi$
$137$	2.67157	−	4.62730i	0.228248	−	0.395337i	0.957289	+	0.289133i	$0.0933670\pi$
$138$	0.464466	+	0.804479i	0.0395380	+	0.0684818i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	2.68629			0.226227
$142$	−1.53553	−	2.65962i	−0.128859	−	0.223191i
$143$	0.914214	−	1.58346i	0.0764504	−	0.132416i
$144$	1.41421	−	2.44949i	0.117851	−	0.204124i
$145$	14.7782	+	25.5965i	1.22726	+	2.12568i
$146$	6.58579			0.545044
$147$		0			0
$148$	−6.58579			−0.541348
$149$	−3.17157	−	5.49333i	−0.259825	−	0.450031i	0.706370	−	0.707843i	$-0.250332\pi$
$149$	−3.17157	−	5.49333i	−0.259825	−	0.450031i	−0.966195	+	0.257812i	$0.916998\pi$
$150$	1.37868	−	2.38794i	0.112569	−	0.194975i
$151$	−4.86396	+	8.42463i	−0.395824	+	0.685586i	−0.993206	−	0.116370i	$-0.962874\pi$
$151$	−4.86396	+	8.42463i	−0.395824	+	0.685586i	0.597382	+	0.801957i	$0.296207\pi$
$152$	−1.70711	−	2.95680i	−0.138465	−	0.239828i
$153$	−21.6569			−1.75085
$154$		0			0
$155$	13.6569			1.09694
$156$	−0.378680	−	0.655892i	−0.0303186	−	0.0525134i
$157$	3.17157	−	5.49333i	0.253119	−	0.438415i	−0.711264	−	0.702925i	$-0.751877\pi$
$157$	3.17157	−	5.49333i	0.253119	−	0.438415i	0.964383	+	0.264510i	$0.0852102\pi$
$158$	2.37868	−	4.11999i	0.189238	−	0.327769i
$159$	−2.46447	−	4.26858i	−0.195445	−	0.338520i
$160$	3.41421			0.269917
$161$		0			0
$162$	7.48528			0.588099
$163$	7.86396	+	13.6208i	0.615953	+	1.06686i	0.990217	+	0.139539i	$0.0445622\pi$
$163$	7.86396	+	13.6208i	0.615953	+	1.06686i	−0.374264	+	0.927322i	$0.622104\pi$
$164$	−1.29289	+	2.23936i	−0.100958	+	0.174864i
$165$	0.707107	−	1.22474i	0.0550482	−	0.0953463i
$166$	8.07107	+	13.9795i	0.626436	+	1.08502i
$167$	11.7279			0.907534			0.453767	−	0.891120i	$-0.350080\pi$
$167$	11.7279			0.907534			0.453767	+	0.891120i	$0.350080\pi$
$168$		0			0
$169$	−9.65685			−0.742835
$170$	−13.0711	−	22.6398i	−1.00251	−	1.73639i
$171$	4.82843	−	8.36308i	0.369239	−	0.639541i
$172$	−2.82843	+	4.89898i	−0.215666	+	0.373544i
$173$	−2.08579	−	3.61269i	−0.158579	−	0.274668i	0.775777	−	0.631007i	$-0.217358\pi$
$173$	−2.08579	−	3.61269i	−0.158579	−	0.274668i	−0.934357	+	0.356339i	$0.884025\pi$
$174$	3.58579			0.271838
$175$		0			0
$176$	1.00000			0.0753778
$177$	1.74264	+	3.01834i	0.130985	+	0.226872i
$178$	−2.24264	+	3.88437i	−0.168093	+	0.291146i
$179$	9.44975	−	16.3674i	0.706307	−	1.22336i	−0.259910	−	0.965633i	$-0.583693\pi$
$179$	9.44975	−	16.3674i	0.706307	−	1.22336i	0.966218	−	0.257727i	$-0.0829736\pi$
$180$	4.82843	+	8.36308i	0.359890	+	0.623347i
$181$	−3.65685			−0.271812			−0.135906	−	0.990722i	$-0.543394\pi$
$181$	−3.65685			−0.271812			−0.135906	+	0.990722i	$0.543394\pi$
$182$		0			0
$183$	2.55635			0.188971
$184$	−1.12132	−	1.94218i	−0.0826648	−	0.143180i
$185$	11.2426	−	19.4728i	0.826575	−	1.43167i
$186$	0.828427	−	1.43488i	0.0607432	−	0.105210i
$187$	−3.82843	−	6.63103i	−0.279962	−	0.484909i
$188$	−6.48528			−0.472988
$189$		0			0
$190$	11.6569			0.845677
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	0.999161	−	0.0409507i	$-0.0130387\pi$
$191$	6.41421	+	11.1097i	0.464116	+	0.803873i	−0.535045	+	0.844824i	$0.679705\pi$
$192$	0.207107	−	0.358719i	0.0149466	−	0.0258883i
$193$	−1.05025	+	1.81909i	−0.0755988	+	0.130941i	−0.901347	−	0.433099i	$-0.857420\pi$
$193$	−1.05025	+	1.81909i	−0.0755988	+	0.130941i	0.825748	+	0.564040i	$0.190754\pi$
$194$	0.914214	+	1.58346i	0.0656367	+	0.113686i
$195$	2.58579			0.185172
$196$		0			0
$197$	−17.4853			−1.24577			−0.622887	−	0.782312i	$-0.714041\pi$
$197$	−17.4853			−1.24577			−0.622887	+	0.782312i	$0.714041\pi$
$198$	1.41421	+	2.44949i	0.100504	+	0.174078i
$199$	9.94975	−	17.2335i	0.705319	−	1.22165i	−0.261257	−	0.965269i	$-0.584137\pi$
$199$	9.94975	−	17.2335i	0.705319	−	1.22165i	0.966576	−	0.256379i	$-0.0825295\pi$
$200$	−3.32843	+	5.76500i	−0.235355	+	0.407647i
$201$	2.32843	+	4.03295i	0.164235	+	0.284463i
$202$	−11.8284			−0.832245
$203$		0			0
$204$	−3.17157			−0.222055
$205$	−4.41421	−	7.64564i	−0.308302	−	0.533995i
$206$	5.29289	−	9.16756i	0.368773	−	0.638734i
$207$	3.17157	−	5.49333i	0.220440	−	0.381813i
$208$	0.914214	+	1.58346i	0.0633893	+	0.109793i
$209$	3.41421			0.236166
$210$		0			0
$211$	4.58579			0.315699			0.157849	−	0.987463i	$-0.449544\pi$
$211$	4.58579			0.315699			0.157849	+	0.987463i	$0.449544\pi$
$212$	5.94975	+	10.3053i	0.408630	+	0.707768i
$213$	0.636039	−	1.10165i	0.0435807	−	0.0754839i
$214$	−5.53553	+	9.58783i	−0.378401	+	0.655410i
$215$	−9.65685	−	16.7262i	−0.658592	−	1.14071i
$216$	2.41421			0.164266
$217$		0			0
$218$	−0.485281			−0.0328674
$219$	1.36396	+	2.36245i	0.0921679	+	0.159640i
$220$	−1.70711	+	2.95680i	−0.115093	+	0.199347i
$221$	7.00000	−	12.1244i	0.470871	−	0.815572i
$222$	−1.36396	−	2.36245i	−0.0915431	−	0.158557i
$223$	−11.4142			−0.764352			−0.382176	−	0.924089i	$-0.624825\pi$
$223$	−11.4142			−0.764352			−0.382176	+	0.924089i	$0.624825\pi$
$224$		0			0
$225$	−18.8284			−1.25523
$226$	6.91421	+	11.9758i	0.459927	+	0.796616i
$227$	−11.5858	+	20.0672i	−0.768976	+	1.33190i	0.169143	+	0.985591i	$0.445900\pi$
$227$	−11.5858	+	20.0672i	−0.768976	+	1.33190i	−0.938119	+	0.346313i	$0.887433\pi$
$228$	0.707107	−	1.22474i	0.0468293	−	0.0811107i
$229$	0.343146	+	0.594346i	0.0226757	+	0.0392755i	0.877141	−	0.480234i	$-0.159448\pi$
$229$	0.343146	+	0.594346i	0.0226757	+	0.0392755i	−0.854465	+	0.519509i	$0.826115\pi$
$230$	7.65685			0.504878
$231$		0			0
$232$	−8.65685			−0.568350
$233$	0.707107	+	1.22474i	0.0463241	+	0.0802357i	0.888258	−	0.459345i	$-0.151916\pi$
$233$	0.707107	+	1.22474i	0.0463241	+	0.0802357i	−0.841934	+	0.539581i	$0.818583\pi$
$234$	−2.58579	+	4.47871i	−0.169038	+	0.292783i
$235$	11.0711	−	19.1757i	0.722197	−	1.25088i
$236$	−4.20711	−	7.28692i	−0.273859	−	0.474338i
$237$	1.97056			0.128002
$238$		0			0
$239$	−22.2132			−1.43685			−0.718426	−	0.695603i	$-0.755137\pi$
$239$	−22.2132			−1.43685			−0.718426	+	0.695603i	$0.755137\pi$
$240$	0.707107	+	1.22474i	0.0456435	+	0.0790569i
$241$	1.87868	−	3.25397i	0.121016	−	0.209607i	−0.799152	−	0.601129i	$-0.794718\pi$
$241$	1.87868	−	3.25397i	0.121016	−	0.209607i	0.920169	+	0.391522i	$0.128051\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	5.17157	+	8.95743i	0.331757	+	0.574619i
$244$	−6.17157			−0.395094
$245$		0			0
$246$	−1.07107			−0.0682888
$247$	3.12132	+	5.40629i	0.198605	+	0.343994i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	−3.34315	+	5.79050i	−0.211863	+	0.366958i
$250$	−2.82843	−	4.89898i	−0.178885	−	0.309839i
$251$	−2.14214			−0.135210			−0.0676052	−	0.997712i	$-0.521536\pi$
$251$	−2.14214			−0.135210			−0.0676052	+	0.997712i	$0.521536\pi$
$252$		0			0
$253$	2.24264			0.140994
$254$	4.86396	+	8.42463i	0.305192	+	0.528608i
$255$	5.41421	−	9.37769i	0.339051	−	0.587254i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.57107	+	2.72117i	0.0980005	+	0.169742i	0.910857	−	0.412722i	$-0.135422\pi$
$257$	1.57107	+	2.72117i	0.0980005	+	0.169742i	−0.812856	+	0.582464i	$0.802089\pi$
$258$	−2.34315			−0.145878
$259$		0			0
$260$	−6.24264			−0.387152
$261$	−12.2426	−	21.2049i	−0.757800	−	1.31255i
$262$	−1.70711	+	2.95680i	−0.105465	+	0.182671i
$263$	−15.5208	+	26.8828i	−0.957054	+	1.65767i	−0.227459	+	0.973788i	$0.573042\pi$
$263$	−15.5208	+	26.8828i	−0.957054	+	1.65767i	−0.729595	+	0.683879i	$0.760291\pi$
$264$	0.207107	+	0.358719i	0.0127465	+	0.0220777i
$265$	−40.6274			−2.49572
$266$		0			0
$267$	−1.85786			−0.113699
$268$	−5.62132	−	9.73641i	−0.343377	−	0.594746i
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	−0.579231	−	0.815163i	$-0.696647\pi$
$269$	6.82843	−	11.8272i	0.416337	−	0.721116i	0.995568	+	0.0940473i	$0.0299805\pi$
$270$	−4.12132	+	7.13834i	−0.250816	+	0.434425i
$271$	−13.2782	−	22.9985i	−0.806592	−	1.39706i	−0.915211	−	0.402974i	$-0.867976\pi$
$271$	−13.2782	−	22.9985i	−0.806592	−	1.39706i	0.108620	−	0.994083i	$-0.465357\pi$
$272$	7.65685			0.464265
$273$		0			0
$274$	−5.34315			−0.322791
$275$	−3.32843	−	5.76500i	−0.200712	−	0.347643i
$276$	0.464466	−	0.804479i	0.0279576	−	0.0484239i
$277$	1.91421	−	3.31552i	0.115014	−	0.199210i	−0.802771	−	0.596287i	$-0.796642\pi$
$277$	1.91421	−	3.31552i	0.115014	−	0.199210i	0.917785	+	0.397077i	$0.129975\pi$
$278$		0			0
$279$	−11.3137			−0.677334
$280$		0			0
$281$	−16.7279			−0.997904			−0.498952	−	0.866630i	$-0.666282\pi$
$281$	−16.7279			−0.997904			−0.498952	+	0.866630i	$0.666282\pi$
$282$	−1.34315	−	2.32640i	−0.0799832	−	0.138535i
$283$	−10.2929	+	17.8278i	−0.611849	+	1.05975i	0.379080	+	0.925364i	$0.376241\pi$
$283$	−10.2929	+	17.8278i	−0.611849	+	1.05975i	−0.990929	+	0.134389i	$0.957093\pi$
$284$	−1.53553	+	2.65962i	−0.0911172	+	0.157820i
$285$	2.41421	+	4.18154i	0.143006	+	0.247693i
$286$	−1.82843			−0.108117
$287$		0			0
$288$	−2.82843			−0.166667
$289$	−20.8137	−	36.0504i	−1.22434	−	2.12061i
$290$	14.7782	−	25.5965i	0.867804	−	1.50308i
$291$	−0.378680	+	0.655892i	−0.0221986	+	0.0384491i
$292$	−3.29289	−	5.70346i	−0.192702	−	0.333770i
$293$	5.17157			0.302127			0.151063	−	0.988524i	$-0.451730\pi$
$293$	5.17157			0.302127			0.151063	+	0.988524i	$0.451730\pi$
$294$		0			0
$295$	28.7279			1.67260
$296$	3.29289	+	5.70346i	0.191396	+	0.331507i
$297$	−1.20711	+	2.09077i	−0.0700434	+	0.121319i
$298$	−3.17157	+	5.49333i	−0.183724	+	0.318220i
$299$	2.05025	+	3.55114i	0.118569	+	0.205368i
$300$	−2.75736			−0.159196
$301$		0			0
$302$	9.72792			0.559779
$303$	−2.44975	−	4.24309i	−0.140734	−	0.243759i
$304$	−1.70711	+	2.95680i	−0.0979093	+	0.169584i
$305$	10.5355	−	18.2481i	0.603263	−	1.04488i
$306$	10.8284	+	18.7554i	0.619020	+	1.07217i
$307$	9.89949			0.564994			0.282497	−	0.959268i	$-0.408837\pi$
$307$	9.89949			0.564994			0.282497	+	0.959268i	$0.408837\pi$
$308$		0			0
$309$	4.38478			0.249441
$310$	−6.82843	−	11.8272i	−0.387829	−	0.671739i
$311$	−4.36396	+	7.55860i	−0.247458	+	0.428609i	−0.962820	−	0.270145i	$-0.912928\pi$
$311$	−4.36396	+	7.55860i	−0.247458	+	0.428609i	0.715362	+	0.698754i	$0.246262\pi$
$312$	−0.378680	+	0.655892i	−0.0214385	+	0.0371326i
$313$	−4.67157	−	8.09140i	−0.264053	−	0.457353i	0.703262	−	0.710931i	$-0.251726\pi$
$313$	−4.67157	−	8.09140i	−0.264053	−	0.457353i	−0.967315	+	0.253578i	$0.918393\pi$
$314$	−6.34315			−0.357964
$315$		0			0
$316$	−4.75736			−0.267622
$317$	−15.6569	−	27.1185i	−0.879377	−	1.52312i	−0.852026	−	0.523499i	$-0.824626\pi$
$317$	−15.6569	−	27.1185i	−0.879377	−	1.52312i	−0.0273502	−	0.999626i	$-0.508707\pi$
$318$	−2.46447	+	4.26858i	−0.138200	+	0.239370i
$319$	4.32843	−	7.49706i	0.242345	−	0.419755i
$320$	−1.70711	−	2.95680i	−0.0954302	−	0.165290i
$321$	−4.58579			−0.255954
$322$		0			0
$323$	26.1421			1.45459
$324$	−3.74264	−	6.48244i	−0.207924	−	0.360136i
$325$	6.08579	−	10.5409i	0.337579	−	0.584703i
$326$	7.86396	−	13.6208i	0.435545	−	0.754385i
$327$	−0.100505	−	0.174080i	−0.00555794	−	0.00962664i
$328$	2.58579			0.142776
$329$		0			0
$330$	−1.41421			−0.0778499
$331$	4.96447	+	8.59871i	0.272872	+	0.472628i	0.969596	−	0.244711i	$-0.0786932\pi$
$331$	4.96447	+	8.59871i	0.272872	+	0.472628i	−0.696724	+	0.717339i	$0.745360\pi$
$332$	8.07107	−	13.9795i	0.442957	−	0.767225i
$333$	−9.31371	+	16.1318i	−0.510388	+	0.884018i
$334$	−5.86396	−	10.1567i	−0.320862	−	0.555749i
$335$	38.3848			2.09718
$336$		0			0
$337$	−19.7574			−1.07625			−0.538126	−	0.842864i	$-0.680868\pi$
$337$	−19.7574			−1.07625			−0.538126	+	0.842864i	$0.680868\pi$
$338$	4.82843	+	8.36308i	0.262632	+	0.454892i
$339$	−2.86396	+	4.96053i	−0.155549	+	0.269419i
$340$	−13.0711	+	22.6398i	−0.708878	+	1.22781i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$	−9.65685			−0.522183
$343$		0			0
$344$	5.65685			0.304997
$345$	1.58579	+	2.74666i	0.0853759	+	0.147875i
$346$	−2.08579	+	3.61269i	−0.112133	+	0.194219i
$347$	−7.29289	+	12.6317i	−0.391503	+	0.678103i	−0.992648	−	0.121037i	$-0.961378\pi$
$347$	−7.29289	+	12.6317i	−0.391503	+	0.678103i	0.601145	+	0.799140i	$0.294711\pi$
$348$	−1.79289	−	3.10538i	−0.0961092	−	0.166466i
$349$		0			0			−	1.00000i	$-0.5\pi$
$349$		0			0				1.00000i	$0.5\pi$
$350$		0			0
$351$	−4.41421			−0.235613
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−12.6569	+	21.9223i	−0.673656	+	1.16681i	0.303203	+	0.952926i	$0.401944\pi$
$353$	−12.6569	+	21.9223i	−0.673656	+	1.16681i	−0.976860	+	0.213881i	$0.931389\pi$
$354$	1.74264	−	3.01834i	0.0926203	−	0.160423i
$355$	−5.24264	−	9.08052i	−0.278250	−	0.481944i
$356$	4.48528			0.237719
$357$		0			0
$358$	−18.8995			−0.998869
$359$	−5.37868	−	9.31615i	−0.283876	−	0.491687i	0.688460	−	0.725274i	$-0.258287\pi$
$359$	−5.37868	−	9.31615i	−0.283876	−	0.491687i	−0.972336	+	0.233587i	$0.924954\pi$
$360$	4.82843	−	8.36308i	0.254480	−	0.440773i
$361$	3.67157	−	6.35935i	0.193241	−	0.334703i
$362$	1.82843	+	3.16693i	0.0961000	+	0.166450i
$363$	−0.414214			−0.0217406
$364$		0			0
$365$	22.4853			1.17693
$366$	−1.27817	−	2.21386i	−0.0668113	−	0.115720i
$367$	7.36396	−	12.7548i	0.384396	−	0.665793i	−0.607290	−	0.794481i	$-0.707743\pi$
$367$	7.36396	−	12.7548i	0.384396	−	0.665793i	0.991685	+	0.128688i	$0.0410765\pi$
$368$	−1.12132	+	1.94218i	−0.0584529	+	0.101243i
$369$	3.65685	+	6.33386i	0.190368	+	0.329727i
$370$	−22.4853			−1.16895
$371$		0			0
$372$	−1.65685			−0.0859039
$373$	−6.98528	−	12.0989i	−0.361684	−	0.626455i	0.626554	−	0.779378i	$-0.284465\pi$
$373$	−6.98528	−	12.0989i	−0.361684	−	0.626455i	−0.988238	+	0.152923i	$0.951131\pi$
$374$	−3.82843	+	6.63103i	−0.197963	+	0.342882i
$375$	1.17157	−	2.02922i	0.0604998	−	0.104789i
$376$	3.24264	+	5.61642i	0.167226	+	0.289645i
$377$	15.8284			0.815205
$378$		0			0
$379$	−25.8701			−1.32886			−0.664428	−	0.747352i	$-0.731325\pi$
$379$	−25.8701			−1.32886			−0.664428	+	0.747352i	$0.731325\pi$
$380$	−5.82843	−	10.0951i	−0.298992	−	0.517869i
$381$	−2.01472	+	3.48960i	−0.103217	+	0.178777i
$382$	6.41421	−	11.1097i	0.328180	−	0.568424i
$383$	15.1924	+	26.3140i	0.776295	+	1.34458i	0.934064	+	0.357106i	$0.116236\pi$
$383$	15.1924	+	26.3140i	0.776295	+	1.34458i	−0.157769	+	0.987476i	$0.550430\pi$
$384$	−0.414214			−0.0211377
$385$		0			0
$386$	2.10051			0.106913
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	0.914214	−	1.58346i	0.0464122	−	0.0803882i
$389$	−1.36396	+	2.36245i	−0.0691556	+	0.119781i	−0.898530	−	0.438912i	$-0.855364\pi$
$389$	−1.36396	+	2.36245i	−0.0691556	+	0.119781i	0.829374	+	0.558693i	$0.188697\pi$
$390$	−1.29289	−	2.23936i	−0.0654682	−	0.113394i
$391$	17.1716			0.868404
$392$		0			0
$393$	−1.41421			−0.0713376
$394$	8.74264	+	15.1427i	0.440448	+	0.762878i
$395$	8.12132	−	14.0665i	0.408628	−	0.707764i
$396$	1.41421	−	2.44949i	0.0710669	−	0.123091i
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	−19.8995			−0.997472
$399$		0			0
$400$	6.65685			0.332843
$401$	2.15685	+	3.73578i	0.107708	+	0.186556i	0.914841	−	0.403813i	$-0.132315\pi$
$401$	2.15685	+	3.73578i	0.107708	+	0.186556i	−0.807133	+	0.590369i	$0.798982\pi$
$402$	2.32843	−	4.03295i	0.116131	−	0.201145i
$403$	3.65685	−	6.33386i	0.182161	−	0.315512i
$404$	5.91421	+	10.2437i	0.294243	+	0.509644i
$405$	25.5563			1.26991
$406$		0			0
$407$	−6.58579			−0.326445
$408$	1.58579	+	2.74666i	0.0785081	+	0.135980i
$409$	−11.3640	+	19.6830i	−0.561912	+	0.973260i	0.435418	+	0.900228i	$0.356601\pi$
$409$	−11.3640	+	19.6830i	−0.561912	+	0.973260i	−0.997330	+	0.0730312i	$0.976733\pi$
$410$	−4.41421	+	7.64564i	−0.218002	+	0.377591i
$411$	−1.10660	−	1.91669i	−0.0545846	−	0.0945434i
$412$	−10.5858			−0.521524
$413$		0			0
$414$	−6.34315			−0.311749
$415$	27.5563	+	47.7290i	1.35269	+	2.34292i
$416$	0.914214	−	1.58346i	0.0448230	−	0.0776357i
$417$		0			0
$418$	−1.70711	−	2.95680i	−0.0834973	−	0.144622i
$419$	−2.14214			−0.104650			−0.0523251	−	0.998630i	$-0.516663\pi$
$419$	−2.14214			−0.104650			−0.0523251	+	0.998630i	$0.516663\pi$
$420$		0			0
$421$	23.3137			1.13624			0.568120	−	0.822946i	$-0.307671\pi$
$421$	23.3137			1.13624			0.568120	+	0.822946i	$0.307671\pi$
$422$	−2.29289	−	3.97141i	−0.111616	−	0.193325i
$423$	−9.17157	+	15.8856i	−0.445937	+	0.772386i
$424$	5.94975	−	10.3053i	0.288945	−	0.500468i
$425$	−25.4853	−	44.1418i	−1.23622	−	2.14119i
$426$	−1.27208			−0.0616324
$427$		0			0
$428$	11.0711			0.535140
$429$	−0.378680	−	0.655892i	−0.0182828	−	0.0316668i
$430$	−9.65685	+	16.7262i	−0.465695	+	0.806607i
$431$	10.2071	−	17.6792i	0.491659	−	0.851578i	−0.508295	−	0.861183i	$-0.669724\pi$
$431$	10.2071	−	17.6792i	0.491659	−	0.851578i	0.999954	+	0.00960469i	$0.00305731\pi$
$432$	−1.20711	−	2.09077i	−0.0580770	−	0.100592i
$433$	2.14214			0.102944			0.0514722	−	0.998674i	$-0.483609\pi$
$433$	2.14214			0.102944			0.0514722	+	0.998674i	$0.483609\pi$
$434$		0			0
$435$	12.2426			0.586990
$436$	0.242641	+	0.420266i	0.0116204	+	0.0201271i
$437$	−3.82843	+	6.63103i	−0.183139	+	0.317205i
$438$	1.36396	−	2.36245i	0.0651726	−	0.112882i
$439$	4.69239	+	8.12745i	0.223955	+	0.387902i	0.956006	−	0.293349i	$-0.0947696\pi$
$439$	4.69239	+	8.12745i	0.223955	+	0.387902i	−0.732050	+	0.681251i	$0.761436\pi$
$440$	3.41421			0.162766
$441$		0			0
$442$	−14.0000			−0.665912
$443$	16.3137	+	28.2562i	0.775088	+	1.34249i	0.934745	+	0.355319i	$0.115628\pi$
$443$	16.3137	+	28.2562i	0.775088	+	1.34249i	−0.159658	+	0.987172i	$0.551039\pi$
$444$	−1.36396	+	2.36245i	−0.0647307	+	0.112117i
$445$	−7.65685	+	13.2621i	−0.362970	+	0.628682i
$446$	5.70711	+	9.88500i	0.270239	+	0.468068i
$447$	−2.62742			−0.124273
$448$		0			0
$449$	33.6569			1.58837			0.794183	−	0.607679i	$-0.207899\pi$
$449$	33.6569			1.58837			0.794183	+	0.607679i	$0.207899\pi$
$450$	9.41421	+	16.3059i	0.443790	+	0.768667i
$451$	−1.29289	+	2.23936i	−0.0608800	+	0.105447i
$452$	6.91421	−	11.9758i	0.325217	−	0.563293i
$453$	2.01472	+	3.48960i	0.0946597	+	0.163955i
$454$	23.1716			1.08750
$455$		0			0
$456$	−1.41421			−0.0662266
$457$	0.171573	+	0.297173i	0.00802584	+	0.0139012i	0.870010	−	0.493033i	$-0.164112\pi$
$457$	0.171573	+	0.297173i	0.00802584	+	0.0139012i	−0.861985	+	0.506934i	$0.830779\pi$
$458$	0.343146	−	0.594346i	0.0160341	−	0.0277720i
$459$	−9.24264	+	16.0087i	−0.431410	+	0.747223i
$460$	−3.82843	−	6.63103i	−0.178501	−	0.309173i
$461$	−14.3137			−0.666656			−0.333328	−	0.942811i	$-0.608172\pi$
$461$	−14.3137			−0.666656			−0.333328	+	0.942811i	$0.608172\pi$
$462$		0			0
$463$	7.17157			0.333291			0.166646	−	0.986017i	$-0.446706\pi$
$463$	7.17157			0.333291			0.166646	+	0.986017i	$0.446706\pi$
$464$	4.32843	+	7.49706i	0.200942	+	0.348042i
$465$	2.82843	−	4.89898i	0.131165	−	0.227185i
$466$	0.707107	−	1.22474i	0.0327561	−	0.0567352i
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	−0.927999	−	0.372584i	$-0.878472\pi$
$467$	−17.0000	−	29.4449i	−0.786666	−	1.36255i	0.141332	−	0.989962i	$-0.454861\pi$
$468$	5.17157			0.239056
$469$		0			0
$470$	−22.1421			−1.02134
$471$	−1.31371	−	2.27541i	−0.0605325	−	0.104845i
$472$	−4.20711	+	7.28692i	−0.193648	+	0.335408i
$473$	−2.82843	+	4.89898i	−0.130051	+	0.225255i
$474$	−0.985281	−	1.70656i	−0.0452555	−	0.0783848i
$475$	22.7279			1.04283
$476$		0			0
$477$	33.6569			1.54104
$478$	11.1066	+	19.2372i	0.508004	+	0.879889i
$479$	−13.0355	+	22.5782i	−0.595609	+	1.03162i	0.397852	+	0.917450i	$0.369756\pi$
$479$	−13.0355	+	22.5782i	−0.595609	+	1.03162i	−0.993461	+	0.114175i	$0.963578\pi$
$480$	0.707107	−	1.22474i	0.0322749	−	0.0559017i
$481$	−6.02082	−	10.4284i	−0.274526	−	0.475492i
$482$	−3.75736			−0.171143
$483$		0			0
$484$	1.00000			0.0454545
$485$	3.12132	+	5.40629i	0.141732	+	0.245487i
$486$	5.17157	−	8.95743i	0.234587	−	0.406317i
$487$	−0.828427	+	1.43488i	−0.0375396	+	0.0650205i	−0.884185	−	0.467137i	$-0.845285\pi$
$487$	−0.828427	+	1.43488i	−0.0375396	+	0.0650205i	0.846645	+	0.532158i	$0.178619\pi$
$488$	3.08579	+	5.34474i	0.139687	+	0.241945i
$489$	6.51472			0.294606
$490$		0			0
$491$	24.8284			1.12049			0.560246	−	0.828327i	$-0.310707\pi$
$491$	24.8284			1.12049			0.560246	+	0.828327i	$0.310707\pi$
$492$	0.535534	+	0.927572i	0.0241437	+	0.0418182i
$493$	33.1421	−	57.4039i	1.49265	−	2.58534i
$494$	3.12132	−	5.40629i	0.140435	−	0.243240i
$495$	4.82843	+	8.36308i	0.217022	+	0.375893i
$496$	4.00000			0.179605
$497$		0			0
$498$	6.68629			0.299620
$499$	3.07107	+	5.31925i	0.137480	+	0.238122i	0.926542	−	0.376191i	$-0.122766\pi$
$499$	3.07107	+	5.31925i	0.137480	+	0.238122i	−0.789062	+	0.614313i	$0.789433\pi$
$500$	−2.82843	+	4.89898i	−0.126491	+	0.219089i
$501$	2.42893	−	4.20703i	0.108517	−	0.187956i
$502$	1.07107	+	1.85514i	0.0478041	+	0.0827991i
$503$	38.2132			1.70384			0.851921	−	0.523670i	$-0.175437\pi$
$503$	38.2132			1.70384			0.851921	+	0.523670i	$0.175437\pi$
$504$		0			0
$505$	−40.3848			−1.79710
$506$	−1.12132	−	1.94218i	−0.0498488	−	0.0863406i
$507$	−2.00000	+	3.46410i	−0.0888231	+	0.153846i
$508$	4.86396	−	8.42463i	0.215803	−	0.373782i
$509$	−6.65685	−	11.5300i	−0.295060	−	0.511059i	0.679939	−	0.733269i	$-0.262006\pi$
$509$	−6.65685	−	11.5300i	−0.295060	−	0.511059i	−0.974999	+	0.222210i	$0.928673\pi$
$510$	−10.8284			−0.479491
$511$		0			0
$512$	1.00000			0.0441942
$513$	−4.12132	−	7.13834i	−0.181961	−	0.315165i
$514$	1.57107	−	2.72117i	0.0692968	−	0.120026i
$515$	18.0711	−	31.3000i	0.796306	−	1.37924i
$516$	1.17157	+	2.02922i	0.0515756	+	0.0893316i
$517$	−6.48528			−0.285222
$518$		0			0
$519$	−1.72792			−0.0758474
$520$	3.12132	+	5.40629i	0.136879	+	0.237081i
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	−0.369984	−	0.929038i	$-0.620637\pi$
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	0.989563	−	0.144103i	$-0.0460297\pi$
$522$	−12.2426	+	21.2049i	−0.535846	+	0.928112i
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	0.970957	−	0.239256i	$-0.0769035\pi$
$523$	6.36396	+	11.0227i	0.278277	+	0.481989i	−0.692680	+	0.721245i	$0.743570\pi$
$524$	3.41421			0.149151
$525$		0			0
$526$	31.0416			1.35348
$527$	−15.3137	−	26.5241i	−0.667076	−	1.15541i
$528$	0.207107	−	0.358719i	0.00901317	−	0.0156113i
$529$	8.98528	−	15.5630i	0.390664	−	0.676651i
$530$	20.3137	+	35.1844i	0.882371	+	1.52831i
$531$	−23.7990			−1.03279
$532$		0			0
$533$	−4.72792			−0.204789
$534$	0.928932	+	1.60896i	0.0401988	+	0.0696264i
$535$	−18.8995	+	32.7349i	−0.817096	+	1.41525i
$536$	−5.62132	+	9.73641i	−0.242804	+	0.420549i
$537$	−3.91421	−	6.77962i	−0.168911	−	0.292562i
$538$	−13.6569			−0.588789
$539$		0			0
$540$	8.24264			0.354707
$541$	20.5711	+	35.6301i	0.884419	+	1.53186i	0.846378	+	0.532583i	$0.178779\pi$
$541$	20.5711	+	35.6301i	0.884419	+	1.53186i	0.0380415	+	0.999276i	$0.487888\pi$
$542$	−13.2782	+	22.9985i	−0.570346	+	0.987869i
$543$	−0.757359	+	1.31178i	−0.0325014	+	0.0562941i
$544$	−3.82843	−	6.63103i	−0.164142	−	0.284303i
$545$	−1.65685			−0.0709718
$546$		0			0
$547$	−18.8701			−0.806825			−0.403413	−	0.915018i	$-0.632176\pi$
$547$	−18.8701			−0.806825			−0.403413	+	0.915018i	$0.632176\pi$
$548$	2.67157	+	4.62730i	0.114124	+	0.197668i
$549$	−8.72792	+	15.1172i	−0.372499	+	0.645187i
$550$	−3.32843	+	5.76500i	−0.141925	+	0.245821i
$551$	14.7782	+	25.5965i	0.629571	+	1.09045i
$552$	−0.928932			−0.0395380
$553$		0			0
$554$	−3.82843			−0.162654
$555$	−4.65685	−	8.06591i	−0.197672	−	0.342379i
$556$		0			0
$557$	−12.2426	+	21.2049i	−0.518737	+	0.898479i	0.481026	+	0.876707i	$0.340264\pi$
$557$	−12.2426	+	21.2049i	−0.518737	+	0.898479i	−0.999763	+	0.0217729i	$0.993069\pi$
$558$	5.65685	+	9.79796i	0.239474	+	0.414781i
$559$	−10.3431			−0.437468
$560$		0			0
$561$	−3.17157			−0.133904
$562$	8.36396	+	14.4868i	0.352812	+	0.611089i
$563$	−2.53553	+	4.39167i	−0.106860	+	0.185087i	−0.914497	−	0.404594i	$-0.867413\pi$
$563$	−2.53553	+	4.39167i	−0.106860	+	0.185087i	0.807637	+	0.589681i	$0.200746\pi$
$564$	−1.34315	+	2.32640i	−0.0565566	+	0.0979590i
$565$	23.6066	+	40.8878i	0.993137	+	1.72016i
$566$	20.5858			0.865285
$567$		0			0
$568$	3.07107			0.128859
$569$	2.00000	+	3.46410i	0.0838444	+	0.145223i	0.904898	−	0.425628i	$-0.139947\pi$
$569$	2.00000	+	3.46410i	0.0838444	+	0.145223i	−0.821054	+	0.570851i	$0.806613\pi$
$570$	2.41421	−	4.18154i	0.101120	−	0.175145i
$571$	5.19239	−	8.99348i	0.217295	−	0.376365i	−0.736685	−	0.676236i	$-0.763610\pi$
$571$	5.19239	−	8.99348i	0.217295	−	0.376365i	0.953980	+	0.299870i	$0.0969434\pi$
$572$	0.914214	+	1.58346i	0.0382252	+	0.0662080i
$573$	5.31371			0.221983
$574$		0			0
$575$	14.9289			0.622580
$576$	1.41421	+	2.44949i	0.0589256	+	0.102062i
$577$	−16.1569	+	27.9845i	−0.672619	+	1.16501i	0.304540	+	0.952499i	$0.401497\pi$
$577$	−16.1569	+	27.9845i	−0.672619	+	1.16501i	−0.977159	+	0.212510i	$0.931836\pi$
$578$	−20.8137	+	36.0504i	−0.865736	+	1.49950i
$579$	0.435029	+	0.753492i	0.0180792	+	0.0313141i
$580$	−29.5563			−1.22726
$581$		0			0
$582$	0.757359			0.0313936
$583$	5.94975	+	10.3053i	0.246413	+	0.426800i
$584$	−3.29289	+	5.70346i	−0.136261	+	0.236011i
$585$	−8.82843	+	15.2913i	−0.365011	+	0.632217i
$586$	−2.58579	−	4.47871i	−0.106818	−	0.185014i
$587$	44.8995			1.85320			0.926600	−	0.376048i	$-0.122717\pi$
$587$	44.8995			1.85320			0.926600	+	0.376048i	$0.122717\pi$
$588$		0			0
$589$	13.6569			0.562721
$590$	−14.3640	−	24.8791i	−0.591355	−	1.02426i
$591$	−3.62132	+	6.27231i	−0.148961	+	0.258008i
$592$	3.29289	−	5.70346i	0.135337	−	0.234411i
$593$	−17.8492	−	30.9158i	−0.732981	−	1.26956i	−0.955604	−	0.294655i	$-0.904795\pi$
$593$	−17.8492	−	30.9158i	−0.732981	−	1.26956i	0.222623	−	0.974905i	$-0.428538\pi$
$594$	2.41421			0.0990564
$595$		0			0
$596$	6.34315			0.259825
$597$	−4.12132	−	7.13834i	−0.168674	−	0.292153i
$598$	2.05025	−	3.55114i	0.0838411	−	0.145217i
$599$	1.31371	−	2.27541i	0.0536767	−	0.0929707i	−0.837939	−	0.545765i	$-0.816239\pi$
$599$	1.31371	−	2.27541i	0.0536767	−	0.0929707i	0.891615	+	0.452794i	$0.149573\pi$
$600$	1.37868	+	2.38794i	0.0562844	+	0.0974874i
$601$	35.9411			1.46607			0.733035	−	0.680191i	$-0.238103\pi$
$601$	35.9411			1.46607			0.733035	+	0.680191i	$0.238103\pi$
$602$		0			0
$603$	−31.7990			−1.29495
$604$	−4.86396	−	8.42463i	−0.197912	−	0.342793i
$605$	−1.70711	+	2.95680i	−0.0694038	+	0.120211i
$606$	−2.44975	+	4.24309i	−0.0995142	+	0.172364i
$607$	−4.51472	−	7.81972i	−0.183247	−	0.317393i	0.759738	−	0.650230i	$-0.225327\pi$
$607$	−4.51472	−	7.81972i	−0.183247	−	0.317393i	−0.942984	+	0.332837i	$0.891994\pi$
$608$	3.41421			0.138465
$609$		0			0
$610$	−21.0711			−0.853143
$611$	−5.92893	−	10.2692i	−0.239859	−	0.415448i
$612$	10.8284	−	18.7554i	0.437713	−	0.758142i
$613$	8.31371	−	14.3998i	0.335788	−	0.581601i	−0.647848	−	0.761769i	$-0.724331\pi$
$613$	8.31371	−	14.3998i	0.335788	−	0.581601i	0.983636	+	0.180168i	$0.0576643\pi$
$614$	−4.94975	−	8.57321i	−0.199756	−	0.345987i
$615$	−3.65685			−0.147459
$616$		0			0
$617$	−8.02944			−0.323253			−0.161626	−	0.986852i	$-0.551674\pi$
$617$	−8.02944			−0.323253			−0.161626	+	0.986852i	$0.551674\pi$
$618$	−2.19239	−	3.79733i	−0.0881908	−	0.152751i
$619$	22.9706	−	39.7862i	0.923265	−	1.59914i	0.128937	−	0.991653i	$-0.458844\pi$
$619$	22.9706	−	39.7862i	0.923265	−	1.59914i	0.794328	−	0.607489i	$-0.207823\pi$
$620$	−6.82843	+	11.8272i	−0.274236	+	0.474991i
$621$	−2.70711	−	4.68885i	−0.108632	−	0.188157i
$622$	8.72792			0.349958
$623$		0			0
$624$	0.757359			0.0303186
$625$	6.98528	+	12.0989i	0.279411	+	0.483954i
$626$	−4.67157	+	8.09140i	−0.186714	+	0.323397i
$627$	0.707107	−	1.22474i	0.0282391	−	0.0489116i
$628$	3.17157	+	5.49333i	0.126560	+	0.219208i
$629$	−50.4264			−2.01063
$630$		0			0
$631$	48.7279			1.93983			0.969914	−	0.243448i	$-0.0782785\pi$
$631$	48.7279			1.93983			0.969914	+	0.243448i	$0.0782785\pi$
$632$	2.37868	+	4.11999i	0.0946188	+	0.163885i
$633$	0.949747	−	1.64501i	0.0377491	−	0.0653833i
$634$	−15.6569	+	27.1185i	−0.621813	+	1.07701i
$635$	16.6066	+	28.7635i	0.659013	+	1.14144i
$636$	4.92893			0.195445
$637$		0			0
$638$	−8.65685			−0.342728
$639$	4.34315	+	7.52255i	0.171812	+	0.297587i
$640$	−1.70711	+	2.95680i	−0.0674793	+	0.116878i
$641$	20.6421	−	35.7532i	0.815315	−	1.41217i	−0.0937859	−	0.995592i	$-0.529897\pi$
$641$	20.6421	−	35.7532i	0.815315	−	1.41217i	0.909101	−	0.416575i	$-0.136770\pi$
$642$	2.29289	+	3.97141i	0.0904933	+	0.156739i
$643$	−4.41421			−0.174080			−0.0870398	−	0.996205i	$-0.527741\pi$
$643$	−4.41421			−0.174080			−0.0870398	+	0.996205i	$0.527741\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$	−13.0711	−	22.6398i	−0.514274	−	0.890749i
$647$	−23.0919	+	39.9963i	−0.907836	+	1.57242i	−0.0907706	+	0.995872i	$0.528933\pi$
$647$	−23.0919	+	39.9963i	−0.907836	+	1.57242i	−0.817065	+	0.576546i	$0.804400\pi$
$648$	−3.74264	+	6.48244i	−0.147025	+	0.254654i
$649$	−4.20711	−	7.28692i	−0.165143	−	0.286037i
$650$	−12.1716			−0.477408
$651$		0			0
$652$	−15.7279			−0.615953
$653$	−9.19239	−	15.9217i	−0.359726	−	0.623064i	0.628189	−	0.778061i	$-0.283796\pi$
$653$	−9.19239	−	15.9217i	−0.359726	−	0.623064i	−0.987915	+	0.154997i	$0.950463\pi$
$654$	−0.100505	+	0.174080i	−0.00393006	+	0.00680706i
$655$	−5.82843	+	10.0951i	−0.227735	+	0.394449i
$656$	−1.29289	−	2.23936i	−0.0504790	−	0.0874322i
$657$	−18.6274			−0.726725
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$	0.707107	+	1.22474i	0.0275241	+	0.0476731i
$661$	−7.48528	+	12.9649i	−0.291144	+	0.504276i	−0.974080	−	0.226202i	$-0.927369\pi$
$661$	−7.48528	+	12.9649i	−0.291144	+	0.504276i	0.682937	+	0.730478i	$0.260702\pi$
$662$	4.96447	−	8.59871i	0.192949	−	0.334198i
$663$	−2.89949	−	5.02207i	−0.112607	−	0.195041i
$664$	−16.1421			−0.626436
$665$		0			0
$666$	18.6274			0.721798
$667$	9.70711	+	16.8132i	0.375861	+	0.651010i
$668$	−5.86396	+	10.1567i	−0.226883	+	0.392974i
$669$	−2.36396	+	4.09450i	−0.0913960	+	0.158303i
$670$	−19.1924	−	33.2422i	−0.741467	−	1.28426i
$671$	−6.17157			−0.238251
$672$		0			0
$673$	−25.5563			−0.985125			−0.492562	−	0.870277i	$-0.663940\pi$
$673$	−25.5563			−0.985125			−0.492562	+	0.870277i	$0.663940\pi$
$674$	9.87868	+	17.1104i	0.380513	+	0.659067i
$675$	−8.03553	+	13.9180i	−0.309288	+	0.535702i
$676$	4.82843	−	8.36308i	0.185709	−	0.321657i
$677$	−6.34315	−	10.9867i	−0.243787	−	0.422251i	0.718003	−	0.696040i	$-0.245056\pi$
$677$	−6.34315	−	10.9867i	−0.243787	−	0.422251i	−0.961790	+	0.273789i	$0.911723\pi$
$678$	5.72792			0.219980
$679$		0			0
$680$	26.1421			1.00251
$681$	4.79899	+	8.31209i	0.183898	+	0.318520i
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	−8.20711	+	14.2151i	−0.314036	+	0.543927i	−0.979232	−	0.202742i	$-0.935015\pi$
$683$	−8.20711	+	14.2151i	−0.314036	+	0.543927i	0.665196	+	0.746669i	$0.268348\pi$
$684$	4.82843	+	8.36308i	0.184620	+	0.319770i
$685$	−18.2426			−0.697015
$686$		0			0
$687$	0.284271			0.0108456
$688$	−2.82843	−	4.89898i	−0.107833	−	0.186772i
$689$	−10.8787	+	18.8424i	−0.414445	+	0.717839i
$690$	1.58579	−	2.74666i	0.0603699	−	0.104564i
$691$	6.96447	+	12.0628i	0.264941	+	0.458891i	0.967548	−	0.252687i	$-0.0813143\pi$
$691$	6.96447	+	12.0628i	0.264941	+	0.458891i	−0.702607	+	0.711578i	$0.747981\pi$
$692$	4.17157			0.158579
$693$		0			0
$694$	14.5858			0.553669
$695$		0			0
$696$	−1.79289	+	3.10538i	−0.0679594	+	0.117709i
$697$	−9.89949	+	17.1464i	−0.374970	+	0.649467i
$698$		0			0
$699$	0.585786			0.0221565
$700$		0			0
$701$	36.1127			1.36396			0.681979	−	0.731372i	$-0.261120\pi$
$701$	36.1127			1.36396			0.681979	+	0.731372i	$0.261120\pi$
$702$	2.20711	+	3.82282i	0.0833019	+	0.144283i
$703$	11.2426	−	19.4728i	0.424024	−	0.734432i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$	−4.58579	−	7.94282i	−0.172711	−	0.299144i
$706$	25.3137			0.952694
$707$		0			0
$708$	−3.48528			−0.130985
$709$	−18.0208	−	31.2130i	−0.676786	−	1.17223i	−0.975943	−	0.218024i	$-0.930039\pi$
$709$	−18.0208	−	31.2130i	−0.676786	−	1.17223i	0.299158	−	0.954204i	$-0.403294\pi$
$710$	−5.24264	+	9.08052i	−0.196753	+	0.340786i
$711$	−6.72792	+	11.6531i	−0.252317	+	0.437026i
$712$	−2.24264	−	3.88437i	−0.0840465	−	0.145573i
$713$	8.97056			0.335950
$714$		0			0
$715$	−6.24264			−0.233462
$716$	9.44975	+	16.3674i	0.353154	+	0.611680i
$717$	−4.60051	+	7.96831i	−0.171809	+	0.297582i
$718$	−5.37868	+	9.31615i	−0.200731	+	0.347675i
$719$	−9.24264	−	16.0087i	−0.344692	−	0.597025i	0.640605	−	0.767870i	$-0.278683\pi$
$719$	−9.24264	−	16.0087i	−0.344692	−	0.597025i	−0.985298	+	0.170846i	$0.945350\pi$
$720$	−9.65685			−0.359890
$721$		0			0
$722$	−7.34315			−0.273284
$723$	−0.778175	−	1.34784i	−0.0289406	−	0.0501266i
$724$	1.82843	−	3.16693i	0.0679530	−	0.117698i
$725$	28.8137	−	49.9068i	1.07011	−	1.85349i
$726$	0.207107	+	0.358719i	0.00768645	+	0.0133133i
$727$	48.4264			1.79604			0.898018	−	0.439959i	$-0.145007\pi$
$727$	48.4264			1.79604			0.898018	+	0.439959i	$0.145007\pi$
$728$		0			0
$729$	−18.1716			−0.673021
$730$	−11.2426	−	19.4728i	−0.416109	−	0.720722i
$731$	−21.6569	+	37.5108i	−0.801008	+	1.38739i
$732$	−1.27817	+	2.21386i	−0.0472427	+	0.0818267i
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	0.720655	−	0.693294i	$-0.243841\pi$
$733$	−6.50000	−	11.2583i	−0.240083	−	0.415836i	−0.960738	+	0.277458i	$0.910508\pi$
$734$	−14.7279			−0.543618
$735$		0			0
$736$	2.24264			0.0826648
$737$	−5.62132	−	9.73641i	−0.207064	−	0.358645i
$738$	3.65685	−	6.33386i	0.134611	−	0.233153i
$739$	−16.2132	+	28.0821i	−0.596412	+	1.03302i	0.396934	+	0.917847i	$0.370074\pi$
$739$	−16.2132	+	28.0821i	−0.596412	+	1.03302i	−0.993346	+	0.115169i	$0.963259\pi$
$740$	11.2426	+	19.4728i	0.413288	+	0.715835i
$741$	2.58579			0.0949912
$742$		0			0
$743$	9.31371			0.341687			0.170843	−	0.985298i	$-0.445351\pi$
$743$	9.31371			0.341687			0.170843	+	0.985298i	$0.445351\pi$
$744$	0.828427	+	1.43488i	0.0303716	+	0.0526052i
$745$	−10.8284	+	18.7554i	−0.396723	+	0.687144i
$746$	−6.98528	+	12.0989i	−0.255749	+	0.442971i
$747$	−22.8284	−	39.5400i	−0.835248	−	1.44669i
$748$	7.65685			0.279962
$749$		0			0
$750$	−2.34315			−0.0855596
$751$	−17.1716	−	29.7420i	−0.626600	−	1.08530i	−0.988229	−	0.152980i	$-0.951113\pi$
$751$	−17.1716	−	29.7420i	−0.626600	−	1.08530i	0.361630	−	0.932322i	$-0.382220\pi$
$752$	3.24264	−	5.61642i	0.118247	−	0.204810i
$753$	−0.443651	+	0.768426i	−0.0161675	+	0.0280030i
$754$	−7.91421	−	13.7078i	−0.288219	−	0.499209i
$755$	33.2132			1.20875
$756$		0			0
$757$	19.6569			0.714441			0.357220	−	0.934020i	$-0.383725\pi$
$757$	19.6569			0.714441			0.357220	+	0.934020i	$0.383725\pi$
$758$	12.9350	+	22.4041i	0.469821	+	0.813755i
$759$	0.464466	−	0.804479i	0.0168591	−	0.0292007i
$760$	−5.82843	+	10.0951i	−0.211419	+	0.366189i
$761$	−1.48528	−	2.57258i	−0.0538414	−	0.0932561i	0.837849	−	0.545903i	$-0.183813\pi$
$761$	−1.48528	−	2.57258i	−0.0538414	−	0.0932561i	−0.891690	+	0.452647i	$0.850480\pi$
$762$	4.02944			0.145971
$763$		0			0
$764$	−12.8284			−0.464116
$765$	36.9706	+	64.0349i	1.33667	+	2.31519i
$766$	15.1924	−	26.3140i	0.548923	−	0.950763i
$767$	7.69239	−	13.3236i	0.277756	−	0.481088i
$768$	0.207107	+	0.358719i	0.00747332	+	0.0129442i
$769$	10.9706			0.395609			0.197804	−	0.980242i	$-0.436619\pi$
$769$	10.9706			0.395609			0.197804	+	0.980242i	$0.436619\pi$
$770$		0			0
$771$	1.30152			0.0468729
$772$	−1.05025	−	1.81909i	−0.0377994	−	0.0654705i
$773$	22.9706	−	39.7862i	0.826194	−	1.43101i	−0.0748099	−	0.997198i	$-0.523835\pi$
$773$	22.9706	−	39.7862i	0.826194	−	1.43101i	0.901004	−	0.433812i	$-0.142832\pi$
$774$	8.00000	−	13.8564i	0.287554	−	0.498058i
$775$	−13.3137	−	23.0600i	−0.478243	−	0.828340i
$776$	−1.82843			−0.0656367
$777$		0			0
$778$	2.72792

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:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.207107 - 0.358719i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.70711 - 2.95680i) q^{5} -0.414214 q^{6} +1.00000 q^{8} +(1.41421 + 2.44949i) q^{9} +(-1.70711 + 2.95680i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(0.207107 + 0.358719i) q^{12} -1.82843 q^{13} -1.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.82843 + 6.63103i) q^{17} +(1.41421 - 2.44949i) q^{18} +(-1.70711 - 2.95680i) q^{19} +3.41421 q^{20} +1.00000 q^{22} +(-1.12132 - 1.94218i) q^{23} +(0.207107 - 0.358719i) q^{24} +(-3.32843 + 5.76500i) q^{25} +(0.914214 + 1.58346i) q^{26} +2.41421 q^{27} -8.65685 q^{29} +(0.707107 + 1.22474i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.207107 + 0.358719i) q^{33} +7.65685 q^{34} -2.82843 q^{36} +(3.29289 + 5.70346i) q^{37} +(-1.70711 + 2.95680i) q^{38} +(-0.378680 + 0.655892i) q^{39} +(-1.70711 - 2.95680i) q^{40} +2.58579 q^{41} +5.65685 q^{43} +(-0.500000 - 0.866025i) q^{44} +(4.82843 - 8.36308i) q^{45} +(-1.12132 + 1.94218i) q^{46} +(3.24264 + 5.61642i) q^{47} -0.414214 q^{48} +6.65685 q^{50} +(1.58579 + 2.74666i) q^{51} +(0.914214 - 1.58346i) q^{52} +(5.94975 - 10.3053i) q^{53} +(-1.20711 - 2.09077i) q^{54} +3.41421 q^{55} -1.41421 q^{57} +(4.32843 + 7.49706i) q^{58} +(-4.20711 + 7.28692i) q^{59} +(0.707107 - 1.22474i) q^{60} +(3.08579 + 5.34474i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(3.12132 + 5.40629i) q^{65} +(0.207107 - 0.358719i) q^{66} +(-5.62132 + 9.73641i) q^{67} +(-3.82843 - 6.63103i) q^{68} -0.928932 q^{69} +3.07107 q^{71} +(1.41421 + 2.44949i) q^{72} +(-3.29289 + 5.70346i) q^{73} +(3.29289 - 5.70346i) q^{74} +(1.37868 + 2.38794i) q^{75} +3.41421 q^{76} +0.757359 q^{78} +(2.37868 + 4.11999i) q^{79} +(-1.70711 + 2.95680i) q^{80} +(-3.74264 + 6.48244i) q^{81} +(-1.29289 - 2.23936i) q^{82} -16.1421 q^{83} +26.1421 q^{85} +(-2.82843 - 4.89898i) q^{86} +(-1.79289 + 3.10538i) q^{87} +(-0.500000 + 0.866025i) q^{88} +(-2.24264 - 3.88437i) q^{89} -9.65685 q^{90} +2.24264 q^{92} +(0.828427 + 1.43488i) q^{93} +(3.24264 - 5.61642i) q^{94} +(-5.82843 + 10.0951i) q^{95} +(0.207107 + 0.358719i) q^{96} -1.82843 q^{97} -2.82843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} - 4 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} - 4 q^{17} - 4 q^{19} + 8 q^{20} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{26} + 4 q^{27} - 12 q^{29} - 8 q^{31} - 2 q^{32} - 2 q^{33} + 8 q^{34} + 16 q^{37} - 4 q^{38} - 10 q^{39} - 4 q^{40} + 16 q^{41} - 2 q^{44} + 8 q^{45} + 4 q^{46} - 4 q^{47} + 4 q^{48} + 4 q^{50} + 12 q^{51} - 2 q^{52} + 4 q^{53} - 2 q^{54} + 8 q^{55} + 6 q^{58} - 14 q^{59} + 18 q^{61} + 16 q^{62} + 4 q^{64} + 4 q^{65} - 2 q^{66} - 14 q^{67} - 4 q^{68} - 32 q^{69} - 16 q^{71} - 16 q^{73} + 16 q^{74} + 14 q^{75} + 8 q^{76} + 20 q^{78} + 18 q^{79} - 4 q^{80} + 2 q^{81} - 8 q^{82} - 8 q^{83} + 48 q^{85} - 10 q^{87} - 2 q^{88} + 8 q^{89} - 16 q^{90} - 8 q^{92} - 8 q^{93} - 4 q^{94} - 12 q^{95} - 2 q^{96} + 4 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 - 4 * q^10 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 - 4 * q^17 - 4 * q^19 + 8 * q^20 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^26 + 4 * q^27 - 12 * q^29 - 8 * q^31 - 2 * q^32 - 2 * q^33 + 8 * q^34 + 16 * q^37 - 4 * q^38 - 10 * q^39 - 4 * q^40 + 16 * q^41 - 2 * q^44 + 8 * q^45 + 4 * q^46 - 4 * q^47 + 4 * q^48 + 4 * q^50 + 12 * q^51 - 2 * q^52 + 4 * q^53 - 2 * q^54 + 8 * q^55 + 6 * q^58 - 14 * q^59 + 18 * q^61 + 16 * q^62 + 4 * q^64 + 4 * q^65 - 2 * q^66 - 14 * q^67 - 4 * q^68 - 32 * q^69 - 16 * q^71 - 16 * q^73 + 16 * q^74 + 14 * q^75 + 8 * q^76 + 20 * q^78 + 18 * q^79 - 4 * q^80 + 2 * q^81 - 8 * q^82 - 8 * q^83 + 48 * q^85 - 10 * q^87 - 2 * q^88 + 8 * q^89 - 16 * q^90 - 8 * q^92 - 8 * q^93 - 4 * q^94 - 12 * q^95 - 2 * q^96 + 4 * q^97

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