LMFDB - Embedded newform 285.2.i.d.106.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.27573645761$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			106.2
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	285.106
Dual form			285.2.i.d.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} -2.82843 q^{11} +1.82843 q^{12} +(0.914214 + 1.58346i) q^{13} +(0.378680 - 0.655892i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.585786 - 1.01461i) q^{17} -0.414214 q^{18} +(4.00000 - 1.73205i) q^{19} +1.82843 q^{20} +(0.914214 - 1.58346i) q^{21} +(-0.585786 + 1.01461i) q^{22} +(0.414214 + 0.717439i) q^{23} +(0.792893 - 1.37333i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.757359 q^{26} -1.00000 q^{27} +(1.67157 + 2.89525i) q^{28} +(-4.82843 - 8.36308i) q^{29} -0.414214 q^{30} -5.00000 q^{31} +(2.20711 + 3.82282i) q^{32} +(-1.41421 + 2.44949i) q^{33} +(-0.242641 - 0.420266i) q^{34} +(0.914214 - 1.58346i) q^{35} +(0.914214 - 1.58346i) q^{36} -2.17157 q^{37} +(0.207107 - 1.79360i) q^{38} +1.82843 q^{39} +(0.792893 - 1.37333i) q^{40} +(-1.41421 + 2.44949i) q^{41} +(-0.378680 - 0.655892i) q^{42} +(-3.91421 + 6.77962i) q^{43} +(-2.58579 - 4.47871i) q^{44} -1.00000 q^{45} +0.343146 q^{46} +(1.58579 + 2.74666i) q^{47} +(1.50000 + 2.59808i) q^{48} -3.65685 q^{49} -0.414214 q^{50} +(-0.585786 - 1.01461i) q^{51} +(-1.67157 + 2.89525i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.207107 + 0.358719i) q^{54} +(-1.41421 + 2.44949i) q^{55} +2.89949 q^{56} +(0.500000 - 4.33013i) q^{57} -4.00000 q^{58} +(0.914214 - 1.58346i) q^{60} +(4.15685 + 7.19988i) q^{61} +(-1.03553 + 1.79360i) q^{62} +(-0.914214 - 1.58346i) q^{63} -4.17157 q^{64} +1.82843 q^{65} +(0.585786 + 1.01461i) q^{66} +(-2.74264 - 4.75039i) q^{67} +2.14214 q^{68} +0.828427 q^{69} +(-0.378680 - 0.655892i) q^{70} +(-5.00000 + 8.66025i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(-4.74264 + 8.21449i) q^{73} +(-0.449747 + 0.778985i) q^{74} -1.00000 q^{75} +(6.39949 + 4.75039i) q^{76} -5.17157 q^{77} +(0.378680 - 0.655892i) q^{78} +(1.67157 - 2.89525i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.585786 + 1.01461i) q^{82} -8.00000 q^{83} +3.34315 q^{84} +(-0.585786 - 1.01461i) q^{85} +(1.62132 + 2.80821i) q^{86} -9.65685 q^{87} -4.48528 q^{88} +(-6.24264 - 10.8126i) q^{89} +(-0.207107 + 0.358719i) q^{90} +(1.67157 + 2.89525i) q^{91} +(-0.757359 + 1.31178i) q^{92} +(-2.50000 + 4.33013i) q^{93} +1.31371 q^{94} +(0.500000 - 4.33013i) q^{95} +4.41421 q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.757359 + 1.31178i) q^{98} +(1.41421 + 2.44949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 + 16 * q^19 - 4 * q^20 - 2 * q^21 - 8 * q^22 - 4 * q^23 + 6 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 20 * q^31 + 6 * q^32 + 16 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 4 * q^39 + 6 * q^40 - 10 * q^42 - 10 * q^43 - 16 * q^44 - 4 * q^45 + 24 * q^46 + 12 * q^47 + 6 * q^48 + 8 * q^49 + 4 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 + 2 * q^54 - 28 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^60 - 6 * q^61 + 10 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 + 8 * q^66 + 6 * q^67 - 48 * q^68 - 8 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 - 2 * q^73 + 18 * q^74 - 4 * q^75 - 14 * q^76 - 32 * q^77 + 10 * q^78 + 18 * q^79 + 6 * q^80 - 2 * q^81 + 8 * q^82 - 32 * q^83 + 36 * q^84 - 8 * q^85 - 2 * q^86 - 16 * q^87 + 16 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 - 20 * q^92 - 10 * q^93 - 40 * q^94 + 2 * q^95 + 12 * q^96 + 12 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	−0.783465	−	0.621436i	$-0.786550\pi$
$2$	0.207107	−	0.358719i	0.146447	−	0.253653i	0.929912	+	0.367783i	$0.119883\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.207107	−	0.358719i	−0.0845510	−	0.146447i
$7$	1.82843			0.691080			0.345540	−	0.938404i	$-0.387696\pi$
$7$	1.82843			0.691080			0.345540	+	0.938404i	$0.387696\pi$
$8$	1.58579			0.560660
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.207107	−	0.358719i	−0.0654929	−	0.113437i
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$	1.82843			0.527821
$13$	0.914214	+	1.58346i	0.253557	+	0.439174i	0.964503	−	0.264073i	$-0.0850661\pi$
$13$	0.914214	+	1.58346i	0.253557	+	0.439174i	−0.710945	+	0.703247i	$0.751733\pi$
$14$	0.378680	−	0.655892i	0.101206	−	0.175295i
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	−0.786203	−	0.617968i	$-0.787956\pi$
$17$	0.585786	−	1.01461i	0.142074	−	0.246080i	0.928278	+	0.371888i	$0.121290\pi$
$18$	−0.414214			−0.0976311
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$19$	4.00000	−	1.73205i	0.917663	−	0.397360i
$20$	1.82843			0.408849
$21$	0.914214	−	1.58346i	0.199498	−	0.345540i
$22$	−0.585786	+	1.01461i	−0.124890	+	0.216316i
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	0.905974	−	0.423333i	$-0.139140\pi$
$23$	0.414214	+	0.717439i	0.0863695	+	0.149596i	−0.819604	+	0.572930i	$0.805807\pi$
$24$	0.792893	−	1.37333i	0.161849	−	0.280330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.757359			0.148530
$27$	−1.00000			−0.192450
$28$	1.67157	+	2.89525i	0.315898	+	0.547151i
$29$	−4.82843	−	8.36308i	−0.896616	−	1.55299i	−0.831791	−	0.555089i	$-0.812684\pi$
$29$	−4.82843	−	8.36308i	−0.896616	−	1.55299i	−0.0648251	−	0.997897i	$-0.520649\pi$
$30$	−0.414214			−0.0756247
$31$	−5.00000			−0.898027			−0.449013	−	0.893525i	$-0.648224\pi$
$31$	−5.00000			−0.898027			−0.449013	+	0.893525i	$0.648224\pi$
$32$	2.20711	+	3.82282i	0.390165	+	0.675786i
$33$	−1.41421	+	2.44949i	−0.246183	+	0.426401i
$34$	−0.242641	−	0.420266i	−0.0416125	−	0.0720750i
$35$	0.914214	−	1.58346i	0.154530	−	0.267654i
$36$	0.914214	−	1.58346i	0.152369	−	0.263911i
$37$	−2.17157			−0.357004			−0.178502	−	0.983940i	$-0.557125\pi$
$37$	−2.17157			−0.357004			−0.178502	+	0.983940i	$0.557125\pi$
$38$	0.207107	−	1.79360i	0.0335972	−	0.290960i
$39$	1.82843			0.292783
$40$	0.792893	−	1.37333i	0.125367	−	0.217143i
$41$	−1.41421	+	2.44949i	−0.220863	+	0.382546i	−0.955070	−	0.296379i	$-0.904221\pi$
$41$	−1.41421	+	2.44949i	−0.220863	+	0.382546i	0.734207	+	0.678925i	$0.237554\pi$
$42$	−0.378680	−	0.655892i	−0.0584315	−	0.101206i
$43$	−3.91421	+	6.77962i	−0.596912	+	1.03388i	0.396362	+	0.918094i	$0.370273\pi$
$43$	−3.91421	+	6.77962i	−0.596912	+	1.03388i	−0.993274	+	0.115788i	$0.963061\pi$
$44$	−2.58579	−	4.47871i	−0.389822	−	0.675191i
$45$	−1.00000			−0.149071
$46$	0.343146			0.0505941
$47$	1.58579	+	2.74666i	0.231311	+	0.400642i	0.958194	−	0.286119i	$-0.0923653\pi$
$47$	1.58579	+	2.74666i	0.231311	+	0.400642i	−0.726883	+	0.686761i	$0.759032\pi$
$48$	1.50000	+	2.59808i	0.216506	+	0.375000i
$49$	−3.65685			−0.522408
$50$	−0.414214			−0.0585786
$51$	−0.585786	−	1.01461i	−0.0820265	−	0.142074i
$52$	−1.67157	+	2.89525i	−0.231805	+	0.401499i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$	−0.207107	+	0.358719i	−0.0281837	+	0.0488155i
$55$	−1.41421	+	2.44949i	−0.190693	+	0.330289i
$56$	2.89949			0.387461
$57$	0.500000	−	4.33013i	0.0662266	−	0.573539i
$58$	−4.00000			−0.525226
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	0.914214	−	1.58346i	0.118024	−	0.204424i
$61$	4.15685	+	7.19988i	0.532231	+	0.921851i	0.999292	+	0.0376256i	$0.0119794\pi$
$61$	4.15685	+	7.19988i	0.532231	+	0.921851i	−0.467061	+	0.884225i	$0.654687\pi$
$62$	−1.03553	+	1.79360i	−0.131513	+	0.227787i
$63$	−0.914214	−	1.58346i	−0.115180	−	0.199498i
$64$	−4.17157			−0.521447
$65$	1.82843			0.226788
$66$	0.585786	+	1.01461i	0.0721053	+	0.124890i
$67$	−2.74264	−	4.75039i	−0.335067	−	0.580353i	0.648431	−	0.761274i	$-0.275426\pi$
$67$	−2.74264	−	4.75039i	−0.335067	−	0.580353i	−0.983498	+	0.180921i	$0.942092\pi$
$68$	2.14214			0.259772
$69$	0.828427			0.0997309
$70$	−0.378680	−	0.655892i	−0.0452609	−	0.0783941i
$71$	−5.00000	+	8.66025i	−0.593391	+	1.02778i	0.400381	+	0.916349i	$0.368878\pi$
$71$	−5.00000	+	8.66025i	−0.593391	+	1.02778i	−0.993772	+	0.111434i	$0.964456\pi$
$72$	−0.792893	−	1.37333i	−0.0934434	−	0.161849i
$73$	−4.74264	+	8.21449i	−0.555084	+	0.961434i	0.442813	+	0.896614i	$0.353981\pi$
$73$	−4.74264	+	8.21449i	−0.555084	+	0.961434i	−0.997897	+	0.0648198i	$0.979353\pi$
$74$	−0.449747	+	0.778985i	−0.0522821	+	0.0905552i
$75$	−1.00000			−0.115470
$76$	6.39949	+	4.75039i	0.734072	+	0.544907i
$77$	−5.17157			−0.589355
$78$	0.378680	−	0.655892i	0.0428770	−	0.0742652i
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	−0.756539	−	0.653949i	$-0.773111\pi$
$79$	1.67157	−	2.89525i	0.188067	−	0.325741i	0.944606	+	0.328208i	$0.106445\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.585786	+	1.01461i	0.0646893	+	0.112045i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	3.34315			0.364767
$85$	−0.585786	−	1.01461i	−0.0635375	−	0.110050i
$86$	1.62132	+	2.80821i	0.174831	+	0.302817i
$87$	−9.65685			−1.03532
$88$	−4.48528			−0.478133
$89$	−6.24264	−	10.8126i	−0.661719	−	1.14613i	−0.980164	−	0.198189i	$-0.936494\pi$
$89$	−6.24264	−	10.8126i	−0.661719	−	1.14613i	0.318445	−	0.947941i	$-0.396839\pi$
$90$	−0.207107	+	0.358719i	−0.0218310	+	0.0378124i
$91$	1.67157	+	2.89525i	0.175228	+	0.303505i
$92$	−0.757359	+	1.31178i	−0.0789602	+	0.136763i
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$	1.31371			0.135499
$95$	0.500000	−	4.33013i	0.0512989	−	0.444262i
$96$	4.41421			0.450524
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	−0.672569	−	0.740034i	$-0.734809\pi$
$97$	3.00000	−	5.19615i	0.304604	−	0.527589i	0.977173	+	0.212445i	$0.0681426\pi$
$98$	−0.757359	+	1.31178i	−0.0765048	+	0.132510i
$99$	1.41421	+	2.44949i	0.142134	+	0.246183i
$100$	0.914214	−	1.58346i	0.0914214	−	0.158346i
$101$	−6.07107	−	10.5154i	−0.604094	−	1.04632i	−0.992194	−	0.124704i	$-0.960202\pi$
$101$	−6.07107	−	10.5154i	−0.604094	−	1.04632i	0.388100	−	0.921617i	$-0.373131\pi$
$102$	−0.485281			−0.0480500
$103$	9.82843			0.968424			0.484212	−	0.874951i	$-0.339106\pi$
$103$	9.82843			0.968424			0.484212	+	0.874951i	$0.339106\pi$
$104$	1.44975	+	2.51104i	0.142159	+	0.246227i
$105$	−0.914214	−	1.58346i	−0.0892181	−	0.154530i
$106$	0.828427			0.0804640
$107$	14.0000			1.35343			0.676716	−	0.736245i	$-0.263403\pi$
$107$	14.0000			1.35343			0.676716	+	0.736245i	$0.263403\pi$
$108$	−0.914214	−	1.58346i	−0.0879702	−	0.152369i
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	−0.0695090	−	0.997581i	$-0.522143\pi$
$109$	8.65685	−	14.9941i	0.829176	−	1.43618i	0.898685	−	0.438594i	$-0.144523\pi$
$110$	0.585786	+	1.01461i	0.0558525	+	0.0967394i
$111$	−1.08579	+	1.88064i	−0.103058	+	0.178502i
$112$	−2.74264	+	4.75039i	−0.259155	+	0.448870i
$113$	4.00000			0.376288			0.188144	−	0.982141i	$-0.439753\pi$
$113$	4.00000			0.376288			0.188144	+	0.982141i	$0.439753\pi$
$114$	−1.44975	−	1.07616i	−0.135781	−	0.100791i
$115$	0.828427			0.0772512
$116$	8.82843	−	15.2913i	0.819699	−	1.41976i
$117$	0.914214	−	1.58346i	0.0845191	−	0.146391i
$118$		0			0
$119$	1.07107	−	1.85514i	0.0981846	−	0.170061i
$120$	−0.792893	−	1.37333i	−0.0723809	−	0.125367i
$121$	−3.00000			−0.272727
$122$	3.44365			0.311773
$123$	1.41421	+	2.44949i	0.127515	+	0.220863i
$124$	−4.57107	−	7.91732i	−0.410494	−	0.710996i
$125$	−1.00000			−0.0894427
$126$	−0.757359			−0.0674709
$127$	−6.48528	−	11.2328i	−0.575476	−	0.996753i	−0.995990	−	0.0894671i	$-0.971484\pi$
$127$	−6.48528	−	11.2328i	−0.575476	−	0.996753i	0.420514	−	0.907286i	$-0.361850\pi$
$128$	−5.27817	+	9.14207i	−0.466529	+	0.808052i
$129$	3.91421	+	6.77962i	0.344627	+	0.596912i
$130$	0.378680	−	0.655892i	0.0332124	−	0.0575256i
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	−0.972198	−	0.234160i	$-0.924766\pi$
$131$	−3.24264	+	5.61642i	−0.283311	+	0.490709i	0.688887	+	0.724868i	$0.258099\pi$
$132$	−5.17157			−0.450128
$133$	7.31371	−	3.16693i	0.634179	−	0.274608i
$134$	−2.27208			−0.196278
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	0.928932	−	1.60896i	0.0796553	−	0.137967i
$137$	5.24264	+	9.08052i	0.447909	+	0.775801i	0.998250	−	0.0591390i	$-0.0188355\pi$
$137$	5.24264	+	9.08052i	0.447909	+	0.775801i	−0.550341	+	0.834940i	$0.685502\pi$
$138$	0.171573	−	0.297173i	0.0146053	−	0.0252970i
$139$	8.15685	+	14.1281i	0.691855	+	1.19833i	0.971229	+	0.238146i	$0.0765398\pi$
$139$	8.15685	+	14.1281i	0.691855	+	1.19833i	−0.279374	+	0.960182i	$0.590127\pi$
$140$	3.34315			0.282547
$141$	3.17157			0.267095
$142$	2.07107	+	3.58719i	0.173800	+	0.301031i
$143$	−2.58579	−	4.47871i	−0.216234	−	0.374529i
$144$	3.00000			0.250000
$145$	−9.65685			−0.801958
$146$	1.96447	+	3.40256i	0.162580	+	0.281597i
$147$	−1.82843	+	3.16693i	−0.150806	+	0.261204i
$148$	−1.98528	−	3.43861i	−0.163189	−	0.282652i
$149$	0.585786	−	1.01461i	0.0479895	−	0.0831202i	−0.841033	−	0.540984i	$-0.818052\pi$
$149$	0.585786	−	1.01461i	0.0479895	−	0.0831202i	0.889022	+	0.457864i	$0.151385\pi$
$150$	−0.207107	+	0.358719i	−0.0169102	+	0.0292893i
$151$	10.3431			0.841713			0.420857	−	0.907127i	$-0.361730\pi$
$151$	10.3431			0.841713			0.420857	+	0.907127i	$0.361730\pi$
$152$	6.34315	−	2.74666i	0.514497	−	0.222784i
$153$	−1.17157			−0.0947161
$154$	−1.07107	+	1.85514i	−0.0863091	+	0.149492i
$155$	−2.50000	+	4.33013i	−0.200805	+	0.347804i
$156$	1.67157	+	2.89525i	0.133833	+	0.231805i
$157$	9.91421	−	17.1719i	0.791240	−	1.37047i	−0.133959	−	0.990987i	$-0.542769\pi$
$157$	9.91421	−	17.1719i	0.791240	−	1.37047i	0.925199	−	0.379482i	$-0.123898\pi$
$158$	−0.692388	−	1.19925i	−0.0550834	−	0.0954073i
$159$	2.00000			0.158610
$160$	4.41421			0.348974
$161$	0.757359	+	1.31178i	0.0596883	+	0.103383i
$162$	0.207107	+	0.358719i	0.0162718	+	0.0281837i
$163$	15.1421			1.18602			0.593012	−	0.805194i	$-0.297939\pi$
$163$	15.1421			1.18602			0.593012	+	0.805194i	$0.297939\pi$
$164$	−5.17157			−0.403832
$165$	1.41421	+	2.44949i	0.110096	+	0.190693i
$166$	−1.65685	+	2.86976i	−0.128597	+	0.222736i
$167$	12.4853	+	21.6251i	0.966140	+	1.67340i	0.706520	+	0.707693i	$0.250264\pi$
$167$	12.4853	+	21.6251i	0.966140	+	1.67340i	0.259620	+	0.965711i	$0.416403\pi$
$168$	1.44975	−	2.51104i	0.111850	−	0.193731i
$169$	4.82843	−	8.36308i	0.371417	−	0.643314i
$170$	−0.485281			−0.0372194
$171$	−3.50000	−	2.59808i	−0.267652	−	0.198680i
$172$	−14.3137			−1.09141
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	−0.970894	−	0.239510i	$-0.923013\pi$
$173$	−3.65685	+	6.33386i	−0.278025	+	0.481554i	0.692868	+	0.721064i	$0.256347\pi$
$174$	−2.00000	+	3.46410i	−0.151620	+	0.262613i
$175$	−0.914214	−	1.58346i	−0.0691080	−	0.119699i
$176$	4.24264	−	7.34847i	0.319801	−	0.553912i
$177$		0			0
$178$	−5.17157			−0.387626
$179$	16.1421			1.20652			0.603260	−	0.797545i	$-0.293868\pi$
$179$	16.1421			1.20652			0.603260	+	0.797545i	$0.293868\pi$
$180$	−0.914214	−	1.58346i	−0.0681415	−	0.118024i
$181$	−12.6569	−	21.9223i	−0.940777	−	1.62947i	−0.763994	−	0.645223i	$-0.776765\pi$
$181$	−12.6569	−	21.9223i	−0.940777	−	1.62947i	−0.176782	−	0.984250i	$-0.556569\pi$
$182$	1.38478			0.102646
$183$	8.31371			0.614567
$184$	0.656854	+	1.13770i	0.0484239	+	0.0838727i
$185$	−1.08579	+	1.88064i	−0.0798286	+	0.138267i
$186$	1.03553	+	1.79360i	0.0759290	+	0.131513i
$187$	−1.65685	+	2.86976i	−0.121161	+	0.209857i
$188$	−2.89949	+	5.02207i	−0.211467	+	0.366272i
$189$	−1.82843			−0.132999
$190$	−1.44975	−	1.07616i	−0.105176	−	0.0780727i
$191$	−16.8284			−1.21766			−0.608831	−	0.793300i	$-0.708361\pi$
$191$	−16.8284			−1.21766			−0.608831	+	0.793300i	$0.708361\pi$
$192$	−2.08579	+	3.61269i	−0.150529	+	0.260723i
$193$	12.3995	−	21.4766i	0.892535	−	1.54592i	0.0557094	−	0.998447i	$-0.482258\pi$
$193$	12.3995	−	21.4766i	0.892535	−	1.54592i	0.836826	−	0.547469i	$-0.184409\pi$
$194$	−1.24264	−	2.15232i	−0.0892164	−	0.154527i
$195$	0.914214	−	1.58346i	0.0654682	−	0.113394i
$196$	−3.34315	−	5.79050i	−0.238796	−	0.413607i
$197$	17.6569			1.25800			0.628999	−	0.777406i	$-0.283465\pi$
$197$	17.6569			1.25800			0.628999	+	0.777406i	$0.283465\pi$
$198$	1.17157			0.0832601
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	0.992434	+	0.122782i	$0.0391815\pi$
$199$	8.50000	+	14.7224i	0.602549	+	1.04365i	−0.389885	+	0.920864i	$0.627485\pi$
$200$	−0.792893	−	1.37333i	−0.0560660	−	0.0971092i
$201$	−5.48528			−0.386902
$202$	−5.02944			−0.353870
$203$	−8.82843	−	15.2913i	−0.619634	−	1.07324i
$204$	1.07107	−	1.85514i	0.0749897	−	0.129886i
$205$	1.41421	+	2.44949i	0.0987730	+	0.171080i
$206$	2.03553	−	3.52565i	0.141822	−	0.245644i
$207$	0.414214	−	0.717439i	0.0287898	−	0.0498655i
$208$	−5.48528			−0.380336
$209$	−11.3137	+	4.89898i	−0.782586	+	0.338869i
$210$	−0.757359			−0.0522628
$211$	0.156854	−	0.271680i	0.0107983	−	0.0187032i	−0.860576	−	0.509322i	$-0.829896\pi$
$211$	0.156854	−	0.271680i	0.0107983	−	0.0187032i	0.871374	+	0.490619i	$0.163229\pi$
$212$	−1.82843	+	3.16693i	−0.125577	+	0.217506i
$213$	5.00000	+	8.66025i	0.342594	+	0.593391i
$214$	2.89949	−	5.02207i	0.198205	−	0.343302i
$215$	3.91421	+	6.77962i	0.266947	+	0.462366i
$216$	−1.58579			−0.107899
$217$	−9.14214			−0.620609
$218$	−3.58579	−	6.21076i	−0.242860	−	0.420646i
$219$	4.74264	+	8.21449i	0.320478	+	0.555084i
$220$	−5.17157			−0.348667
$221$	2.14214			0.144096
$222$	0.449747	+	0.778985i	0.0301851	+	0.0522821i
$223$	−2.91421	+	5.04757i	−0.195150	+	0.338010i	−0.946950	−	0.321382i	$-0.895853\pi$
$223$	−2.91421	+	5.04757i	−0.195150	+	0.338010i	0.751800	+	0.659392i	$0.229186\pi$
$224$	4.03553	+	6.98975i	0.269635	+	0.467022i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	0.828427	−	1.43488i	0.0551062	−	0.0954467i
$227$	−18.9706			−1.25912			−0.629560	−	0.776952i	$-0.716765\pi$
$227$	−18.9706			−1.25912			−0.629560	+	0.776952i	$0.716765\pi$
$228$	7.31371	−	3.16693i	0.484362	−	0.209735i
$229$	−4.65685			−0.307734			−0.153867	−	0.988092i	$-0.549173\pi$
$229$	−4.65685			−0.307734			−0.153867	+	0.988092i	$0.549173\pi$
$230$	0.171573	−	0.297173i	0.0113132	−	0.0195950i
$231$	−2.58579	+	4.47871i	−0.170132	+	0.294678i
$232$	−7.65685	−	13.2621i	−0.502697	−	0.870697i
$233$	12.6569	−	21.9223i	0.829178	−	1.43618i	−0.0695057	−	0.997582i	$-0.522142\pi$
$233$	12.6569	−	21.9223i	0.829178	−	1.43618i	0.898684	−	0.438597i	$-0.144524\pi$
$234$	−0.378680	−	0.655892i	−0.0247551	−	0.0428770i
$235$	3.17157			0.206891
$236$		0			0
$237$	−1.67157	−	2.89525i	−0.108580	−	0.188067i
$238$	−0.443651	−	0.768426i	−0.0287576	−	0.0498096i
$239$	−24.6274			−1.59302			−0.796508	−	0.604629i	$-0.793322\pi$
$239$	−24.6274			−1.59302			−0.796508	+	0.604629i	$0.793322\pi$
$240$	3.00000			0.193649
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$	−0.621320	+	1.07616i	−0.0399400	+	0.0691781i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−7.60051	+	13.1645i	−0.486572	+	0.842768i
$245$	−1.82843	+	3.16693i	−0.116814	+	0.202328i
$246$	1.17157			0.0746968
$247$	6.39949	+	4.75039i	0.407190	+	0.302260i
$248$	−7.92893			−0.503488
$249$	−4.00000	+	6.92820i	−0.253490	+	0.439057i
$250$	−0.207107	+	0.358719i	−0.0130986	+	0.0226874i
$251$	8.17157	+	14.1536i	0.515785	+	0.893366i	0.999832	+	0.0183240i	$0.00583304\pi$
$251$	8.17157	+	14.1536i	0.515785	+	0.893366i	−0.484047	+	0.875042i	$0.660834\pi$
$252$	1.67157	−	2.89525i	0.105299	−	0.182384i
$253$	−1.17157	−	2.02922i	−0.0736562	−	0.127576i
$254$	−5.37258			−0.337106
$255$	−1.17157			−0.0733667
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	8.41421	+	14.5738i	0.524864	+	0.909091i	0.999581	+	0.0289528i	$0.00921724\pi$
$257$	8.41421	+	14.5738i	0.524864	+	0.909091i	−0.474717	+	0.880139i	$0.657449\pi$
$258$	3.24264			0.201878
$259$	−3.97056			−0.246719
$260$	1.67157	+	2.89525i	0.103667	+	0.179556i
$261$	−4.82843	+	8.36308i	−0.298872	+	0.517662i
$262$	1.34315	+	2.32640i	0.0829798	+	0.143725i
$263$	−12.8995	+	22.3426i	−0.795417	+	1.37770i	0.127157	+	0.991883i	$0.459415\pi$
$263$	−12.8995	+	22.3426i	−0.795417	+	1.37770i	−0.922574	+	0.385820i	$0.873919\pi$
$264$	−2.24264	+	3.88437i	−0.138025	+	0.239066i
$265$	2.00000			0.122859
$266$	0.378680	−	3.27946i	0.0232183	−	0.201077i
$267$	−12.4853			−0.764087
$268$	5.01472	−	8.68575i	0.306323	−	0.530566i
$269$	−0.828427	+	1.43488i	−0.0505101	+	0.0874860i	−0.890175	−	0.455619i	$-0.849418\pi$
$269$	−0.828427	+	1.43488i	−0.0505101	+	0.0874860i	0.839665	+	0.543105i	$0.182751\pi$
$270$	0.207107	+	0.358719i	0.0126041	+	0.0218310i
$271$	−6.82843	+	11.8272i	−0.414797	+	0.718450i	−0.995407	−	0.0957318i	$-0.969481\pi$
$271$	−6.82843	+	11.8272i	−0.414797	+	0.718450i	0.580610	+	0.814182i	$0.302814\pi$
$272$	1.75736	+	3.04384i	0.106556	+	0.184560i
$273$	3.34315			0.202336
$274$	4.34315			0.262379
$275$	1.41421	+	2.44949i	0.0852803	+	0.147710i
$276$	0.757359	+	1.31178i	0.0455877	+	0.0789602i
$277$	6.00000			0.360505			0.180253	−	0.983620i	$-0.442309\pi$
$277$	6.00000			0.360505			0.180253	+	0.983620i	$0.442309\pi$
$278$	6.75736			0.405279
$279$	2.50000	+	4.33013i	0.149671	+	0.259238i
$280$	1.44975	−	2.51104i	0.0866390	−	0.150063i
$281$	3.48528	+	6.03668i	0.207914	+	0.360118i	0.951057	−	0.309014i	$-0.0999991\pi$
$281$	3.48528	+	6.03668i	0.207914	+	0.360118i	−0.743143	+	0.669133i	$0.766666\pi$
$282$	0.656854	−	1.13770i	0.0391151	−	0.0677493i
$283$	10.4853	−	18.1610i	0.623285	−	1.07956i	−0.365584	−	0.930778i	$-0.619131\pi$
$283$	10.4853	−	18.1610i	0.623285	−	1.07956i	0.988870	−	0.148784i	$-0.0475358\pi$
$284$	−18.2843			−1.08497
$285$	−3.50000	−	2.59808i	−0.207322	−	0.153897i
$286$	−2.14214			−0.126667
$287$	−2.58579	+	4.47871i	−0.152634	+	0.264370i
$288$	2.20711	−	3.82282i	0.130055	−	0.225262i
$289$	7.81371	+	13.5337i	0.459630	+	0.796102i
$290$	−2.00000	+	3.46410i	−0.117444	+	0.203419i
$291$	−3.00000	−	5.19615i	−0.175863	−	0.304604i
$292$	−17.3431			−1.01493
$293$	−5.31371			−0.310430			−0.155215	−	0.987881i	$-0.549607\pi$
$293$	−5.31371			−0.310430			−0.155215	+	0.987881i	$0.549607\pi$
$294$	0.757359	+	1.31178i	0.0441701	+	0.0765048i
$295$		0			0
$296$	−3.44365			−0.200158
$297$	2.82843			0.164122
$298$	−0.242641	−	0.420266i	−0.0140558	−	0.0243454i
$299$	−0.757359	+	1.31178i	−0.0437992	+	0.0758625i
$300$	−0.914214	−	1.58346i	−0.0527821	−	0.0914214i
$301$	−7.15685	+	12.3960i	−0.412514	+	0.714496i
$302$	2.14214	−	3.71029i	0.123266	−	0.213503i
$303$	−12.1421			−0.697547
$304$	−1.50000	+	12.9904i	−0.0860309	+	0.745049i
$305$	8.31371			0.476042
$306$	−0.242641	+	0.420266i	−0.0138708	+	0.0240250i
$307$	8.82843	−	15.2913i	0.503865	−	0.872720i	−0.496125	−	0.868251i	$-0.665244\pi$
$307$	8.82843	−	15.2913i	0.503865	−	0.872720i	0.999990	−	0.00446862i	$-0.00142241\pi$
$308$	−4.72792	−	8.18900i	−0.269398	−	0.466612i
$309$	4.91421	−	8.51167i	0.279560	−	0.484212i
$310$	1.03553	+	1.79360i	0.0588144	+	0.101869i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$	2.89949			0.164152
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	0.938269	−	0.345907i	$-0.112429\pi$
$313$	3.00000	+	5.19615i	0.169570	+	0.293704i	−0.768699	+	0.639611i	$0.779095\pi$
$314$	−4.10660	−	7.11284i	−0.231749	−	0.401401i
$315$	−1.82843			−0.103020
$316$	6.11270			0.343866
$317$	−2.65685	−	4.60181i	−0.149224	−	0.258463i	0.781717	−	0.623633i	$-0.214344\pi$
$317$	−2.65685	−	4.60181i	−0.149224	−	0.258463i	−0.930941	+	0.365170i	$0.881011\pi$
$318$	0.414214	−	0.717439i	0.0232279	−	0.0402320i
$319$	13.6569	+	23.6544i	0.764637	+	1.32439i
$320$	−2.08579	+	3.61269i	−0.116599	+	0.201955i
$321$	7.00000	−	12.1244i	0.390702	−	0.676716i
$322$	0.627417			0.0349646
$323$	0.585786	−	5.07306i	0.0325940	−	0.282273i
$324$	−1.82843			−0.101579
$325$	0.914214	−	1.58346i	0.0507114	−	0.0878348i
$326$	3.13604	−	5.43178i	0.173689	−	0.300838i
$327$	−8.65685	−	14.9941i	−0.478725	−	0.829176i
$328$	−2.24264	+	3.88437i	−0.123829	+	0.214478i
$329$	2.89949	+	5.02207i	0.159854	+	0.276876i
$330$	1.17157			0.0644930
$331$	−5.34315			−0.293686			−0.146843	−	0.989160i	$-0.546911\pi$
$331$	−5.34315			−0.293686			−0.146843	+	0.989160i	$0.546911\pi$
$332$	−7.31371	−	12.6677i	−0.401392	−	0.695231i
$333$	1.08579	+	1.88064i	0.0595007	+	0.103058i
$334$	10.3431			0.565952
$335$	−5.48528			−0.299693
$336$	2.74264	+	4.75039i	0.149623	+	0.259155i
$337$	−8.74264	+	15.1427i	−0.476242	+	0.824875i	−0.999629	−	0.0272195i	$-0.991335\pi$
$337$	−8.74264	+	15.1427i	−0.476242	+	0.824875i	0.523387	+	0.852095i	$0.324668\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$	2.00000	−	3.46410i	0.108625	−	0.188144i
$340$	1.07107	−	1.85514i	0.0580868	−	0.100609i
$341$	14.1421			0.765840
$342$	−1.65685	+	0.717439i	−0.0895924	+	0.0387947i
$343$	−19.4853			−1.05211
$344$	−6.20711	+	10.7510i	−0.334665	+	0.579656i
$345$	0.414214	−	0.717439i	0.0223005	−	0.0386256i
$346$	1.51472	+	2.62357i	0.0814318	+	0.141044i
$347$	17.7279	−	30.7057i	0.951685	−	1.64837i	0.209906	−	0.977722i	$-0.432684\pi$
$347$	17.7279	−	30.7057i	0.951685	−	1.64837i	0.741779	−	0.670645i	$-0.233982\pi$
$348$	−8.82843	−	15.2913i	−0.473253	−	0.819699i
$349$	−31.6274			−1.69298			−0.846488	−	0.532407i	$-0.821288\pi$
$349$	−31.6274			−1.69298			−0.846488	+	0.532407i	$0.821288\pi$
$350$	−0.757359			−0.0404826
$351$	−0.914214	−	1.58346i	−0.0487971	−	0.0845191i
$352$	−6.24264	−	10.8126i	−0.332734	−	0.576312i
$353$	−1.31371			−0.0699216			−0.0349608	−	0.999389i	$-0.511131\pi$
$353$	−1.31371			−0.0699216			−0.0349608	+	0.999389i	$0.511131\pi$
$354$		0			0
$355$	5.00000	+	8.66025i	0.265372	+	0.459639i
$356$	11.4142	−	19.7700i	0.604952	−	1.04781i
$357$	−1.07107	−	1.85514i	−0.0566869	−	0.0981846i
$358$	3.34315	−	5.79050i	0.176691	−	0.306037i
$359$	−4.58579	+	7.94282i	−0.242029	+	0.419206i	−0.961292	−	0.275532i	$-0.911146\pi$
$359$	−4.58579	+	7.94282i	−0.242029	+	0.419206i	0.719263	+	0.694737i	$0.244479\pi$
$360$	−1.58579			−0.0835783
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−10.4853			−0.551094
$363$	−1.50000	+	2.59808i	−0.0787296	+	0.136364i
$364$	−3.05635	+	5.29375i	−0.160196	+	0.277468i
$365$	4.74264	+	8.21449i	0.248241	+	0.429966i
$366$	1.72183	−	2.98229i	0.0900013	−	0.155887i
$367$	17.0563	+	29.5425i	0.890334	+	1.54210i	0.839475	+	0.543398i	$0.182863\pi$
$367$	17.0563	+	29.5425i	0.890334	+	1.54210i	0.0508591	+	0.998706i	$0.483804\pi$
$368$	−2.48528			−0.129554
$369$	2.82843			0.147242
$370$	0.449747	+	0.778985i	0.0233813	+	0.0404975i
$371$	1.82843	+	3.16693i	0.0949272	+	0.164419i
$372$	−9.14214			−0.473998
$373$	−11.6569			−0.603569			−0.301785	−	0.953376i	$-0.597582\pi$
$373$	−11.6569			−0.603569			−0.301785	+	0.953376i	$0.597582\pi$
$374$	0.686292	+	1.18869i	0.0354873	+	0.0614658i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	2.51472	+	4.35562i	0.129687	+	0.224624i
$377$	8.82843	−	15.2913i	0.454687	−	0.787541i
$378$	−0.378680	+	0.655892i	−0.0194772	+	0.0337355i
$379$	1.68629			0.0866190			0.0433095	−	0.999062i	$-0.486210\pi$
$379$	1.68629			0.0866190			0.0433095	+	0.999062i	$0.486210\pi$
$380$	7.31371	−	3.16693i	0.375185	−	0.162460i
$381$	−12.9706			−0.664502
$382$	−3.48528	+	6.03668i	−0.178323	+	0.308864i
$383$	16.9706	−	29.3939i	0.867155	−	1.50196i	0.00226413	−	0.999997i	$-0.499279\pi$
$383$	16.9706	−	29.3939i	0.867155	−	1.50196i	0.864891	−	0.501960i	$-0.167387\pi$
$384$	5.27817	+	9.14207i	0.269351	+	0.466529i
$385$	−2.58579	+	4.47871i	−0.131784	+	0.228256i
$386$	−5.13604	−	8.89588i	−0.261418	−	0.452788i
$387$	7.82843			0.397941
$388$	10.9706			0.556946
$389$	7.72792	+	13.3852i	0.391821	+	0.678654i	0.992690	−	0.120694i	$-0.0385118\pi$
$389$	7.72792	+	13.3852i	0.391821	+	0.678654i	−0.600869	+	0.799348i	$0.705179\pi$
$390$	−0.378680	−	0.655892i	−0.0191752	−	0.0332124i
$391$	0.970563			0.0490835
$392$	−5.79899			−0.292893
$393$	3.24264	+	5.61642i	0.163570	+	0.283311i
$394$	3.65685	−	6.33386i	0.184230	−	0.319095i
$395$	−1.67157	−	2.89525i	−0.0841060	−	0.145676i
$396$	−2.58579	+	4.47871i	−0.129941	+	0.225064i
$397$	11.9142	−	20.6360i	0.597957	−	1.03569i	−0.395165	−	0.918610i	$-0.629313\pi$
$397$	11.9142	−	20.6360i	0.597957	−	1.03569i	0.993122	−	0.117082i	$-0.0373541\pi$
$398$	7.04163			0.352965
$399$	0.914214	−	7.91732i	0.0457679	−	0.396362i
$400$	3.00000			0.150000
$401$	11.3137	−	19.5959i	0.564980	−	0.978573i	−0.432072	−	0.901839i	$-0.642217\pi$
$401$	11.3137	−	19.5959i	0.564980	−	0.978573i	0.997052	−	0.0767343i	$-0.0244493\pi$
$402$	−1.13604	+	1.96768i	−0.0566605	+	0.0981388i
$403$	−4.57107	−	7.91732i	−0.227701	−	0.394390i
$404$	11.1005	−	19.2266i	0.552271	−	0.956561i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−7.31371			−0.362973
$407$	6.14214			0.304454
$408$	−0.928932	−	1.60896i	−0.0459890	−	0.0796553i
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	0.782274	−	0.622935i	$-0.214060\pi$
$409$	−3.00000	−	5.19615i	−0.148340	−	0.256933i	−0.930614	+	0.366002i	$0.880726\pi$
$410$	1.17157			0.0578599
$411$	10.4853			0.517201
$412$	8.98528	+	15.5630i	0.442673	+	0.766732i
$413$		0			0
$414$	−0.171573	−	0.297173i	−0.00843235	−	0.0146053i
$415$	−4.00000	+	6.92820i	−0.196352	+	0.340092i
$416$	−4.03553	+	6.98975i	−0.197858	+	0.342701i
$417$	16.3137			0.798886
$418$	−0.585786	+	5.07306i	−0.0286518	+	0.248131i
$419$	3.31371			0.161885			0.0809426	−	0.996719i	$-0.474207\pi$
$419$	3.31371			0.161885			0.0809426	+	0.996719i	$0.474207\pi$
$420$	1.67157	−	2.89525i	0.0815644	−	0.141274i
$421$	3.82843	−	6.63103i	0.186586	−	0.323177i	−0.757524	−	0.652808i	$-0.773591\pi$
$421$	3.82843	−	6.63103i	0.186586	−	0.323177i	0.944110	+	0.329631i	$0.106924\pi$
$422$	−0.0649712	−	0.112533i	−0.00316275	−	0.00547804i
$423$	1.58579	−	2.74666i	0.0771036	−	0.133547i
$424$	1.58579	+	2.74666i	0.0770126	+	0.133390i
$425$	−1.17157			−0.0568296
$426$	4.14214			0.200687
$427$	7.60051	+	13.1645i	0.367814	+	0.637073i
$428$	12.7990	+	22.1685i	0.618663	+	1.07155i
$429$	−5.17157			−0.249686
$430$	3.24264			0.156374
$431$	1.24264	+	2.15232i	0.0598559	+	0.103673i	0.894401	−	0.447267i	$-0.147603\pi$
$431$	1.24264	+	2.15232i	0.0598559	+	0.103673i	−0.834545	+	0.550940i	$0.814269\pi$
$432$	1.50000	−	2.59808i	0.0721688	−	0.125000i
$433$	19.9142	+	34.4924i	0.957016	+	1.65760i	0.729686	+	0.683783i	$0.239666\pi$
$433$	19.9142	+	34.4924i	0.957016	+	1.65760i	0.227330	+	0.973818i	$0.427000\pi$
$434$	−1.89340	+	3.27946i	−0.0908860	+	0.157419i
$435$	−4.82843	+	8.36308i	−0.231505	+	0.400979i
$436$	31.6569			1.51609
$437$	2.89949	+	2.15232i	0.138702	+	0.102959i
$438$	3.92893			0.187732
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	−0.994401	−	0.105675i	$-0.966300\pi$
$439$	−8.50000	+	14.7224i	−0.405683	+	0.702663i	0.588718	+	0.808339i	$0.299633\pi$
$440$	−2.24264	+	3.88437i	−0.106914	+	0.185180i
$441$	1.82843	+	3.16693i	0.0870680	+	0.150806i
$442$	0.443651	−	0.768426i	0.0211023	−	0.0365503i
$443$	−9.07107	−	15.7116i	−0.430979	−	0.746478i	0.565978	−	0.824420i	$-0.308499\pi$
$443$	−9.07107	−	15.7116i	−0.430979	−	0.746478i	−0.996958	+	0.0779417i	$0.975165\pi$
$444$	−3.97056			−0.188435
$445$	−12.4853			−0.591859
$446$	1.20711	+	2.09077i	0.0571582	+	0.0990008i
$447$	−0.585786	−	1.01461i	−0.0277067	−	0.0479895i
$448$	−7.62742			−0.360362
$449$	13.1716			0.621605			0.310802	−	0.950475i	$-0.399402\pi$
$449$	13.1716			0.621605			0.310802	+	0.950475i	$0.399402\pi$
$450$	0.207107	+	0.358719i	0.00976311	+	0.0169102i
$451$	4.00000	−	6.92820i	0.188353	−	0.326236i
$452$	3.65685	+	6.33386i	0.172004	+	0.297920i
$453$	5.17157	−	8.95743i	0.242982	−	0.420857i
$454$	−3.92893	+	6.80511i	−0.184394	+	0.319380i
$455$	3.34315			0.156729
$456$	0.792893	−	6.86666i	0.0371306	−	0.321561i
$457$	−4.17157			−0.195138			−0.0975690	−	0.995229i	$-0.531107\pi$
$457$	−4.17157			−0.195138			−0.0975690	+	0.995229i	$0.531107\pi$
$458$	−0.964466	+	1.67050i	−0.0450665	+	0.0780575i
$459$	−0.585786	+	1.01461i	−0.0273422	+	0.0473580i
$460$	0.757359	+	1.31178i	0.0353121	+	0.0611623i
$461$	−15.0711	+	26.1039i	−0.701930	+	1.21578i	0.265859	+	0.964012i	$0.414345\pi$
$461$	−15.0711	+	26.1039i	−0.701930	+	1.21578i	−0.967788	+	0.251766i	$0.918989\pi$
$462$	1.07107	+	1.85514i	0.0498306	+	0.0863091i
$463$	−22.7990			−1.05956			−0.529779	−	0.848135i	$-0.677725\pi$
$463$	−22.7990			−1.05956			−0.529779	+	0.848135i	$0.677725\pi$
$464$	28.9706			1.34492
$465$	2.50000	+	4.33013i	0.115935	+	0.200805i
$466$	−5.24264	−	9.08052i	−0.242861	−	0.420647i
$467$	23.7990			1.10129			0.550643	−	0.834741i	$-0.314383\pi$
$467$	23.7990			1.10129			0.550643	+	0.834741i	$0.314383\pi$
$468$	3.34315			0.154537
$469$	−5.01472	−	8.68575i	−0.231558	−	0.401071i
$470$	0.656854	−	1.13770i	0.0302984	−	0.0524784i
$471$	−9.91421	−	17.1719i	−0.456823	−	0.791240i
$472$		0			0
$473$	11.0711	−	19.1757i	0.509048	−	0.881697i
$474$	−1.38478			−0.0636049
$475$	−3.50000	−	2.59808i	−0.160591	−	0.119208i
$476$	3.91674			0.179523
$477$	1.00000	−	1.73205i	0.0457869	−	0.0793052i
$478$	−5.10051	+	8.83433i	−0.233292	+	0.404073i
$479$	−1.24264	−	2.15232i	−0.0567777	−	0.0983419i	0.836240	−	0.548364i	$-0.184749\pi$
$479$	−1.24264	−	2.15232i	−0.0567777	−	0.0983419i	−0.893017	+	0.450022i	$0.851416\pi$
$480$	2.20711	−	3.82282i	0.100740	−	0.174487i
$481$	−1.98528	−	3.43861i	−0.0905210	−	0.156787i
$482$	−2.07107			−0.0943346
$483$	1.51472			0.0689221
$484$	−2.74264	−	4.75039i	−0.124665	−	0.215927i
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$	0.414214			0.0187891
$487$	−6.34315			−0.287435			−0.143718	−	0.989619i	$-0.545906\pi$
$487$	−6.34315			−0.287435			−0.143718	+	0.989619i	$0.545906\pi$
$488$	6.59188	+	11.4175i	0.298401	+	0.516845i
$489$	7.57107	−	13.1135i	0.342376	−	0.593012i
$490$	0.757359	+	1.31178i	0.0342140	+	0.0592604i
$491$	−11.8284	+	20.4874i	−0.533809	+	0.924585i	0.465411	+	0.885095i	$0.345907\pi$
$491$	−11.8284	+	20.4874i	−0.533809	+	0.924585i	−0.999220	+	0.0394901i	$0.987427\pi$
$492$	−2.58579	+	4.47871i	−0.116576	+	0.201916i
$493$	−11.3137			−0.509544
$494$	3.02944	−	1.31178i	0.136301	−	0.0590200i
$495$	2.82843			0.127128
$496$	7.50000	−	12.9904i	0.336760	−	0.583285i
$497$	−9.14214	+	15.8346i	−0.410081	+	0.710281i
$498$	1.65685	+	2.86976i	0.0742454	+	0.128597i
$499$	3.67157	−	6.35935i	0.164362	−	0.284684i	−0.772066	−	0.635542i	$-0.780777\pi$
$499$	3.67157	−	6.35935i	0.164362	−	0.284684i	0.936429	+	0.350858i	$0.114110\pi$
$500$	−0.914214	−	1.58346i	−0.0408849	−	0.0708147i
$501$	24.9706			1.11560
$502$	6.76955			0.302140
$503$	−6.92893	−	12.0013i	−0.308946	−	0.535110i	0.669186	−	0.743095i	$-0.266643\pi$
$503$	−6.92893	−	12.0013i	−0.308946	−	0.535110i	−0.978132	+	0.207985i	$0.933310\pi$
$504$	−1.44975	−	2.51104i	−0.0645769	−	0.111850i
$505$	−12.1421			−0.540318
$506$	−0.970563			−0.0431468
$507$	−4.82843	−	8.36308i	−0.214438	−	0.371417i
$508$	11.8579	−	20.5384i	0.526108	−	0.911245i
$509$	−16.5563	−	28.6764i	−0.733847	−	1.27106i	−0.955227	−	0.295873i	$-0.904389\pi$
$509$	−16.5563	−	28.6764i	−0.733847	−	1.27106i	0.221380	−	0.975188i	$-0.428944\pi$
$510$	−0.242641	+	0.420266i	−0.0107443	+	0.0186097i
$511$	−8.67157	+	15.0196i	−0.383608	+	0.664428i
$512$	−22.7574			−1.00574
$513$	−4.00000	+	1.73205i	−0.176604	+	0.0764719i
$514$	6.97056			0.307458
$515$	4.91421	−	8.51167i	0.216546	−	0.375069i
$516$	−7.15685	+	12.3960i	−0.315063	+	0.545705i
$517$	−4.48528	−	7.76874i	−0.197262	−	0.341669i
$518$	−0.822330	+	1.42432i	−0.0361311	+	0.0625809i
$519$	3.65685	+	6.33386i	0.160518	+	0.278025i
$520$	2.89949			0.127151
$521$	6.34315			0.277898			0.138949	−	0.990300i	$-0.455628\pi$
$521$	6.34315			0.277898			0.138949	+	0.990300i	$0.455628\pi$
$522$	2.00000	+	3.46410i	0.0875376	+	0.151620i
$523$	14.8848	+	25.7812i	0.650866	+	1.12733i	0.982913	+	0.184070i	$0.0589273\pi$
$523$	14.8848	+	25.7812i	0.650866	+	1.12733i	−0.332047	+	0.943263i	$0.607739\pi$
$524$	−11.8579			−0.518013
$525$	−1.82843			−0.0797991
$526$	5.34315	+	9.25460i	0.232972	+	0.403520i
$527$	−2.92893	+	5.07306i	−0.127586	+	0.220986i
$528$	−4.24264	−	7.34847i	−0.184637	−	0.319801i
$529$	11.1569	−	19.3242i	0.485081	−	0.840184i
$530$	0.414214	−	0.717439i	0.0179923	−	0.0311636i
$531$		0			0
$532$	11.7010	+	8.68575i	0.507303	+	0.376575i
$533$	−5.17157			−0.224006
$534$	−2.58579	+	4.47871i	−0.111898	+	0.193813i
$535$	7.00000	−	12.1244i	0.302636	−	0.524182i
$536$	−4.34924	−	7.53311i	−0.187859	−	0.325381i
$537$	8.07107	−	13.9795i	0.348292	−	0.603260i
$538$	0.343146	+	0.594346i	0.0147941	+	0.0256241i
$539$	10.3431			0.445511
$540$	−1.82843			−0.0786830
$541$	−8.15685	−	14.1281i	−0.350691	−	0.607414i	0.635680	−	0.771953i	$-0.280720\pi$
$541$	−8.15685	−	14.1281i	−0.350691	−	0.607414i	−0.986371	+	0.164539i	$0.947386\pi$
$542$	2.82843	+	4.89898i	0.121491	+	0.210429i
$543$	−25.3137			−1.08632
$544$	5.17157			0.221729
$545$	−8.65685	−	14.9941i	−0.370819	−	0.642277i
$546$	0.692388	−	1.19925i	0.0296315	−	0.0513232i
$547$	6.57107	+	11.3814i	0.280959	+	0.486635i	0.971621	−	0.236543i	$-0.0760143\pi$
$547$	6.57107	+	11.3814i	0.280959	+	0.486635i	−0.690663	+	0.723177i	$0.742681\pi$
$548$	−9.58579	+	16.6031i	−0.409485	+	0.709248i
$549$	4.15685	−	7.19988i	0.177410	−	0.307284i
$550$	1.17157			0.0499560
$551$	−33.7990	−	25.0892i	−1.43989	−	1.06884i
$552$	1.31371			0.0559151
$553$	3.05635	−	5.29375i	0.129969	−	0.225113i
$554$	1.24264	−	2.15232i	0.0527947	−	0.0914432i
$555$	1.08579	+	1.88064i	0.0460891	+	0.0798286i
$556$	−14.9142	+	25.8322i	−0.632504	+	1.09553i
$557$	4.51472	+	7.81972i	0.191295	+	0.331332i	0.945680	−	0.325100i	$-0.105398\pi$
$557$	4.51472	+	7.81972i	0.191295	+	0.331332i	−0.754385	+	0.656432i	$0.772065\pi$
$558$	2.07107			0.0876753
$559$	−14.3137			−0.605405
$560$	2.74264	+	4.75039i	0.115898	+	0.200741i
$561$	1.65685	+	2.86976i	0.0699524	+	0.121161i
$562$	2.88730			0.121793
$563$	−12.1421			−0.511730			−0.255865	−	0.966713i	$-0.582360\pi$
$563$	−12.1421			−0.511730			−0.255865	+	0.966713i	$0.582360\pi$
$564$	2.89949	+	5.02207i	0.122091	+	0.211467i
$565$	2.00000	−	3.46410i	0.0841406	−	0.145736i
$566$	−4.34315	−	7.52255i	−0.182556	−	0.316196i
$567$	−0.914214	+	1.58346i	−0.0383934	+	0.0664993i
$568$	−7.92893	+	13.7333i	−0.332691	+	0.576237i
$569$	4.97056			0.208377			0.104188	−	0.994558i	$-0.466776\pi$
$569$	4.97056			0.208377			0.104188	+	0.994558i	$0.466776\pi$
$570$	−1.65685	+	0.717439i	−0.0693980	+	0.0300502i
$571$	14.3137			0.599010			0.299505	−	0.954095i	$-0.403178\pi$
$571$	14.3137			0.599010			0.299505	+	0.954095i	$0.403178\pi$
$572$	4.72792	−	8.18900i	0.197684	−	0.342399i
$573$	−8.41421	+	14.5738i	−0.351509	+	0.608831i
$574$	1.07107	+	1.85514i	0.0447055	+	0.0774322i
$575$	0.414214	−	0.717439i	0.0172739	−	0.0299193i
$576$	2.08579	+	3.61269i	0.0869078	+	0.150529i
$577$	−36.3431			−1.51298			−0.756492	−	0.654002i	$-0.773089\pi$
$577$	−36.3431			−1.51298			−0.756492	+	0.654002i	$0.773089\pi$
$578$	6.47309			0.269245
$579$	−12.3995	−	21.4766i	−0.515305	−	0.892535i
$580$	−8.82843	−	15.2913i	−0.366580	−	0.634936i
$581$	−14.6274			−0.606848
$582$	−2.48528			−0.103018
$583$	−2.82843	−	4.89898i	−0.117141	−	0.202895i
$584$	−7.52082	+	13.0264i	−0.311214	+	0.539038i
$585$	−0.914214	−	1.58346i	−0.0377981	−	0.0654682i
$586$	−1.10051	+	1.90613i	−0.0454614	+	0.0787415i
$587$	−5.31371	+	9.20361i	−0.219320	+	0.379874i	−0.954600	−	0.297890i	$-0.903717\pi$
$587$	−5.31371	+	9.20361i	−0.219320	+	0.379874i	0.735280	+	0.677763i	$0.237051\pi$
$588$	−6.68629			−0.275738
$589$	−20.0000	+	8.66025i	−0.824086	+	0.356840i
$590$		0			0
$591$	8.82843	−	15.2913i	0.363153	−	0.628999i
$592$	3.25736	−	5.64191i	0.133877	−	0.231881i
$593$	4.92893	+	8.53716i	0.202407	+	0.350579i	0.949303	−	0.314361i	$-0.101790\pi$
$593$	4.92893	+	8.53716i	0.202407	+	0.350579i	−0.746896	+	0.664940i	$0.768457\pi$
$594$	0.585786	−	1.01461i	0.0240351	−	0.0416300i
$595$	−1.07107	−	1.85514i	−0.0439095	−	0.0760535i
$596$	2.14214			0.0877453
$597$	17.0000			0.695764
$598$	0.313708	+	0.543359i	0.0128285	+	0.0222196i
$599$	8.48528	+	14.6969i	0.346699	+	0.600501i	0.985661	−	0.168738i	$-0.0539691\pi$
$599$	8.48528	+	14.6969i	0.346699	+	0.600501i	−0.638962	+	0.769238i	$0.720636\pi$
$600$	−1.58579			−0.0647395
$601$	−35.3431			−1.44168			−0.720838	−	0.693103i	$-0.756243\pi$
$601$	−35.3431			−1.44168			−0.720838	+	0.693103i	$0.756243\pi$
$602$	2.96447	+	5.13461i	0.120823	+	0.209271i
$603$	−2.74264	+	4.75039i	−0.111689	+	0.193451i
$604$	9.45584	+	16.3780i	0.384753	+	0.666411i
$605$	−1.50000	+	2.59808i	−0.0609837	+	0.105627i
$606$	−2.51472	+	4.35562i	−0.102153	+	0.176935i
$607$	−6.17157			−0.250496			−0.125248	−	0.992125i	$-0.539973\pi$
$607$	−6.17157			−0.250496			−0.125248	+	0.992125i	$0.539973\pi$
$608$	15.4497	+	11.4685i	0.626570	+	0.465108i
$609$	−17.6569			−0.715492
$610$	1.72183	−	2.98229i	0.0697147	−	0.120749i
$611$	−2.89949	+	5.02207i	−0.117301	+	0.203171i
$612$	−1.07107	−	1.85514i	−0.0432954	−	0.0749897i
$613$	−16.7990	+	29.0967i	−0.678505	+	1.17520i	0.296926	+	0.954900i	$0.404038\pi$
$613$	−16.7990	+	29.0967i	−0.678505	+	1.17520i	−0.975431	+	0.220304i	$0.929295\pi$
$614$	−3.65685	−	6.33386i	−0.147579	−	0.255614i
$615$	2.82843			0.114053
$616$	−8.20101			−0.330428
$617$	−12.8284	−	22.2195i	−0.516453	−	0.894523i	−0.999818	−	0.0191037i	$-0.993919\pi$
$617$	−12.8284	−	22.2195i	−0.516453	−	0.894523i	0.483364	−	0.875419i	$-0.339415\pi$
$618$	−2.03553	−	3.52565i	−0.0818812	−	0.141822i
$619$	15.6863			0.630485			0.315243	−	0.949011i	$-0.397914\pi$
$619$	15.6863			0.630485			0.315243	+	0.949011i	$0.397914\pi$
$620$	−9.14214			−0.367157
$621$	−0.414214	−	0.717439i	−0.0166218	−	0.0287898i
$622$	−0.828427	+	1.43488i	−0.0332169	+	0.0575334i
$623$	−11.4142	−	19.7700i	−0.457301	−	0.792068i
$624$	−2.74264	+	4.75039i	−0.109793	+	0.190168i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	2.48528			0.0993318
$627$	−1.41421	+	12.2474i	−0.0564782	+	0.489116i
$628$	36.2548			1.44673
$629$	−1.27208	+	2.20330i	−0.0507211	+	0.0878515i
$630$	−0.378680	+	0.655892i	−0.0150870	+	0.0261314i
$631$	6.64214	+	11.5045i	0.264419	+	0.457988i	0.967411	−	0.253210i	$-0.0814864\pi$
$631$	6.64214	+	11.5045i	0.264419	+	0.457988i	−0.702992	+	0.711198i	$0.748153\pi$
$632$	2.65076	−	4.59125i	0.105441	−	0.182630i
$633$	−0.156854	−	0.271680i	−0.00623440	−	0.0107983i
$634$	−2.20101			−0.0874133
$635$	−12.9706			−0.514721
$636$	1.82843	+	3.16693i	0.0725019	+	0.125577i
$637$	−3.34315	−	5.79050i	−0.132460	−	0.229428i
$638$	11.3137			0.447914
$639$	10.0000			0.395594
$640$	5.27817	+	9.14207i	0.208638	+	0.361372i
$641$	−14.0711	+	24.3718i	−0.555774	+	0.962628i	0.442069	+	0.896981i	$0.354245\pi$
$641$	−14.0711	+	24.3718i	−0.555774	+	0.962628i	−0.997843	+	0.0656474i	$0.979089\pi$
$642$	−2.89949	−	5.02207i	−0.114434	−	0.198205i
$643$	−2.91421	+	5.04757i	−0.114925	+	0.199057i	−0.917750	−	0.397159i	$-0.869996\pi$
$643$	−2.91421	+	5.04757i	−0.114925	+	0.199057i	0.802825	+	0.596215i	$0.203330\pi$
$644$	−1.38478	+	2.39850i	−0.0545678	+	0.0945143i
$645$	7.82843			0.308244
$646$	−1.69848	−	1.26080i	−0.0668260	−	0.0496054i
$647$	−32.2843			−1.26923			−0.634613	−	0.772830i	$-0.718840\pi$
$647$	−32.2843			−1.26923			−0.634613	+	0.772830i	$0.718840\pi$
$648$	−0.792893	+	1.37333i	−0.0311478	+	0.0539496i
$649$		0			0
$650$	−0.378680	−	0.655892i	−0.0148530	−	0.0257262i
$651$	−4.57107	+	7.91732i	−0.179154	+	0.310304i
$652$	13.8431	+	23.9770i	0.542139	+	0.939013i
$653$	39.9411			1.56302			0.781509	−	0.623895i	$-0.214451\pi$
$653$	39.9411			1.56302			0.781509	+	0.623895i	$0.214451\pi$
$654$	−7.17157			−0.280431
$655$	3.24264	+	5.61642i	0.126700	+	0.219452i
$656$	−4.24264	−	7.34847i	−0.165647	−	0.286910i
$657$	9.48528			0.370056
$658$	2.40202			0.0936405
$659$	−3.75736	−	6.50794i	−0.146366	−	0.253513i	0.783516	−	0.621372i	$-0.213424\pi$
$659$	−3.75736	−	6.50794i	−0.146366	−	0.253513i	−0.929882	+	0.367859i	$0.880091\pi$
$660$	−2.58579	+	4.47871i	−0.100652	+	0.174334i
$661$	3.48528	+	6.03668i	0.135562	+	0.234800i	0.925812	−	0.377985i	$-0.123383\pi$
$661$	3.48528	+	6.03668i	0.135562	+	0.234800i	−0.790250	+	0.612784i	$0.790049\pi$
$662$	−1.10660	+	1.91669i	−0.0430093	+	0.0744943i
$663$	1.07107	−	1.85514i	0.0415968	−	0.0720478i
$664$	−12.6863			−0.492324
$665$	0.914214	−	7.91732i	0.0354517	−	0.307021i
$666$	0.899495			0.0348547
$667$	4.00000	−	6.92820i	0.154881	−	0.268261i
$668$	−22.8284	+	39.5400i	−0.883258	+	1.52985i
$669$	2.91421	+	5.04757i	0.112670	+	0.195150i
$670$	−1.13604	+	1.96768i	−0.0438890	+	0.0760180i
$671$	−11.7574	−	20.3643i	−0.453888	−	0.786157i
$672$	8.07107			0.311348
$673$	−23.8284			−0.918518			−0.459259	−	0.888302i	$-0.651885\pi$
$673$	−23.8284			−0.918518			−0.459259	+	0.888302i	$0.651885\pi$
$674$	3.62132	+	6.27231i	0.139488	+	0.241600i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	17.6569			0.679110
$677$	−23.4558			−0.901481			−0.450741	−	0.892655i	$-0.648840\pi$
$677$	−23.4558			−0.901481			−0.450741	+	0.892655i	$0.648840\pi$
$678$	−0.828427	−	1.43488i	−0.0318156	−	0.0551062i
$679$	5.48528	−	9.50079i	0.210506	−	0.364607i
$680$	−0.928932	−	1.60896i	−0.0356229	−	0.0617007i
$681$	−9.48528	+	16.4290i	−0.363477	+	0.629560i
$682$	2.92893	−	5.07306i	0.112155	−	0.194257i
$683$	44.1421			1.68905			0.844526	−	0.535515i	$-0.179882\pi$
$683$	44.1421			1.68905			0.844526	+	0.535515i	$0.179882\pi$
$684$	0.914214	−	7.91732i	0.0349558	−	0.302726i
$685$	10.4853			0.400622
$686$	−4.03553	+	6.98975i	−0.154077	+	0.266870i
$687$	−2.32843	+	4.03295i	−0.0888350	+	0.153867i
$688$	−11.7426	−	20.3389i	−0.447684	−	0.775411i
$689$	−1.82843	+	3.16693i	−0.0696575	+	0.120650i
$690$	−0.171573	−	0.297173i	−0.00653167	−	0.0113132i
$691$	31.3137			1.19123			0.595615	−	0.803270i	$-0.296908\pi$
$691$	31.3137			1.19123			0.595615	+	0.803270i	$0.296908\pi$
$692$	−13.3726			−0.508349
$693$	2.58579	+	4.47871i	0.0982259	+	0.170132i
$694$	−7.34315	−	12.7187i	−0.278742	−	0.482795i
$695$	16.3137			0.618814
$696$	−15.3137			−0.580465
$697$	1.65685	+	2.86976i	0.0627578	+	0.108700i
$698$	−6.55025	+	11.3454i	−0.247931	+	0.429429i
$699$	−12.6569	−	21.9223i	−0.478726	−	0.829178i
$700$	1.67157	−	2.89525i	0.0631795	−	0.109430i
$701$	−16.0711	+	27.8359i	−0.606996	+	1.05135i	0.384737	+	0.923026i	$0.374292\pi$
$701$	−16.0711	+	27.8359i	−0.606996	+	1.05135i	−0.991733	+	0.128321i	$0.959041\pi$
$702$	−0.757359			−0.0285847
$703$	−8.68629	+	3.76127i	−0.327610	+	0.141859i
$704$	11.7990			0.444691
$705$	1.58579	−	2.74666i	0.0597242	−	0.103445i
$706$	−0.272078	+	0.471253i	−0.0102398	+	0.0177358i
$707$	−11.1005	−	19.2266i	−0.417477	−	0.723092i
$708$		0			0
$709$	−15.8137	−	27.3901i	−0.593896	−	1.02866i	−0.993702	−	0.112058i	$-0.964256\pi$
$709$	−15.8137	−	27.3901i	−0.593896	−	1.02866i	0.399805	−	0.916600i	$-0.369078\pi$
$710$	4.14214			0.155452
$711$	−3.34315			−0.125378
$712$	−9.89949	−	17.1464i	−0.370999	−	0.642590i
$713$	−2.07107	−	3.58719i	−0.0775621	−	0.134341i
$714$	−0.887302			−0.0332064
$715$	−5.17157			−0.193406
$716$	14.7574	+	25.5605i	0.551508	+	0.955241i
$717$	−12.3137	+	21.3280i	−0.459864	+	0.796508i
$718$	1.89949	+	3.29002i	0.0708885	+	0.122783i
$719$	11.5858	−	20.0672i	0.432077	−	0.748379i	−0.564975	−	0.825108i	$-0.691114\pi$
$719$	11.5858	−	20.0672i	0.432077	−	0.748379i	0.997052	+	0.0767288i	$0.0244476\pi$
$720$	1.50000	−	2.59808i	0.0559017	−	0.0968246i
$721$	17.9706			0.669259
$722$	−2.27817	−	7.53311i	−0.0847849	−	0.280353i
$723$	−5.00000			−0.185952
$724$	23.1421	−	40.0834i	0.860071	−	1.48969i
$725$	−4.82843	+	8.36308i	−0.179323	+	0.310597i
$726$	0.621320	+	1.07616i	0.0230594	+	0.0399400i
$727$	−18.0858	+	31.3255i	−0.670765	+	1.16180i	0.306923	+	0.951734i	$0.400701\pi$
$727$	−18.0858	+	31.3255i	−0.670765	+	1.16180i	−0.977688	+	0.210064i	$0.932633\pi$
$728$	2.65076	+	4.59125i	0.0982436	+	0.170163i
$729$	1.00000			0.0370370
$730$	3.92893			0.145416
$731$	4.58579	+	7.94282i	0.169611	+	0.293776i
$732$	7.60051	+	13.1645i	0.280923	+	0.486572i
$733$	3.65685			0.135069			0.0675345	−	0.997717i	$-0.478487\pi$
$733$	3.65685			0.135069			0.0675345	+	0.997717i	$0.478487\pi$
$734$	14.1299			0.521546
$735$	1.82843	+	3.16693i	0.0674426	+	0.116814i
$736$	−1.82843	+	3.16693i	−0.0673967	+	0.116735i
$737$	7.75736	+	13.4361i	0.285746	+	0.494927i
$738$	0.585786	−	1.01461i	0.0215631	−	0.0373484i
$739$	20.8137	−	36.0504i	0.765645	−	1.32614i	−0.174260	−	0.984700i	$-0.555753\pi$
$739$	20.8137	−	36.0504i	0.765645	−	1.32614i	0.939905	−	0.341436i	$-0.110913\pi$
$740$	−3.97056			−0.145961
$741$	7.31371	−	3.16693i	0.268676	−	0.116340i
$742$	1.51472			0.0556071
$743$	−17.0711	+	29.5680i	−0.626277	+	1.08474i	0.362016	+	0.932172i	$0.382089\pi$
$743$	−17.0711	+	29.5680i	−0.626277	+	1.08474i	−0.988292	+	0.152571i	$0.951245\pi$
$744$	−3.96447	+	6.86666i	−0.145344	+	0.251744i
$745$	−0.585786	−	1.01461i	−0.0214616	−	0.0371725i
$746$	−2.41421	+	4.18154i	−0.0883906	+	0.153097i
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$	−6.05887			−0.221534
$749$	25.5980			0.935330
$750$	0.207107	+	0.358719i	0.00756247	+	0.0130986i
$751$	−13.1569	−	22.7883i	−0.480100	−	0.831558i	0.519639	−	0.854386i	$-0.326066\pi$
$751$	−13.1569	−	22.7883i	−0.480100	−	0.831558i	−0.999739	+	0.0228276i	$0.992733\pi$
$752$	−9.51472			−0.346966
$753$	16.3431			0.595577
$754$	−3.65685	−	6.33386i	−0.133175	−	0.230665i
$755$	5.17157	−	8.95743i	0.188213	−	0.325994i
$756$	−1.67157	−	2.89525i	−0.0607945	−	0.105299i
$757$	16.5711	−	28.7019i	0.602286	−	1.04319i	−0.390188	−	0.920735i	$-0.627590\pi$
$757$	16.5711	−	28.7019i	0.602286	−	1.04319i	0.992474	−	0.122454i	$-0.0390765\pi$
$758$	0.349242	−	0.604906i	0.0126851	−	0.0219712i
$759$	−2.34315			−0.0850508
$760$	0.792893	−	6.86666i	0.0287613	−	0.249080i
$761$	51.5980			1.87043			0.935213	−	0.354087i	$-0.115208\pi$
$761$	51.5980			1.87043			0.935213	+	0.354087i	$0.115208\pi$
$762$	−2.68629	+	4.65279i	−0.0973141	+	0.168553i
$763$	15.8284	−	27.4156i	0.573028	−	0.992513i
$764$	−15.3848	−	26.6472i	−0.556602	−	0.964062i
$765$	−0.585786	+	1.01461i	−0.0211792	+	0.0366834i
$766$	−7.02944	−	12.1753i	−0.253984	−	0.439913i
$767$		0			0
$768$	−3.97056			−0.143275
$769$	−7.15685	−	12.3960i	−0.258083	−	0.447012i	0.707646	−	0.706568i	$-0.249757\pi$
$769$	−7.15685	−	12.3960i	−0.258083	−	0.447012i	−0.965728	+	0.259555i	$0.916424\pi$
$770$	1.07107	+	1.85514i	0.0385986	+	0.0668547i
$771$

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} -2.82843 q^{11} +1.82843 q^{12} +(0.914214 + 1.58346i) q^{13} +(0.378680 - 0.655892i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.585786 - 1.01461i) q^{17} -0.414214 q^{18} +(4.00000 - 1.73205i) q^{19} +1.82843 q^{20} +(0.914214 - 1.58346i) q^{21} +(-0.585786 + 1.01461i) q^{22} +(0.414214 + 0.717439i) q^{23} +(0.792893 - 1.37333i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.757359 q^{26} -1.00000 q^{27} +(1.67157 + 2.89525i) q^{28} +(-4.82843 - 8.36308i) q^{29} -0.414214 q^{30} -5.00000 q^{31} +(2.20711 + 3.82282i) q^{32} +(-1.41421 + 2.44949i) q^{33} +(-0.242641 - 0.420266i) q^{34} +(0.914214 - 1.58346i) q^{35} +(0.914214 - 1.58346i) q^{36} -2.17157 q^{37} +(0.207107 - 1.79360i) q^{38} +1.82843 q^{39} +(0.792893 - 1.37333i) q^{40} +(-1.41421 + 2.44949i) q^{41} +(-0.378680 - 0.655892i) q^{42} +(-3.91421 + 6.77962i) q^{43} +(-2.58579 - 4.47871i) q^{44} -1.00000 q^{45} +0.343146 q^{46} +(1.58579 + 2.74666i) q^{47} +(1.50000 + 2.59808i) q^{48} -3.65685 q^{49} -0.414214 q^{50} +(-0.585786 - 1.01461i) q^{51} +(-1.67157 + 2.89525i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.207107 + 0.358719i) q^{54} +(-1.41421 + 2.44949i) q^{55} +2.89949 q^{56} +(0.500000 - 4.33013i) q^{57} -4.00000 q^{58} +(0.914214 - 1.58346i) q^{60} +(4.15685 + 7.19988i) q^{61} +(-1.03553 + 1.79360i) q^{62} +(-0.914214 - 1.58346i) q^{63} -4.17157 q^{64} +1.82843 q^{65} +(0.585786 + 1.01461i) q^{66} +(-2.74264 - 4.75039i) q^{67} +2.14214 q^{68} +0.828427 q^{69} +(-0.378680 - 0.655892i) q^{70} +(-5.00000 + 8.66025i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(-4.74264 + 8.21449i) q^{73} +(-0.449747 + 0.778985i) q^{74} -1.00000 q^{75} +(6.39949 + 4.75039i) q^{76} -5.17157 q^{77} +(0.378680 - 0.655892i) q^{78} +(1.67157 - 2.89525i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.585786 + 1.01461i) q^{82} -8.00000 q^{83} +3.34315 q^{84} +(-0.585786 - 1.01461i) q^{85} +(1.62132 + 2.80821i) q^{86} -9.65685 q^{87} -4.48528 q^{88} +(-6.24264 - 10.8126i) q^{89} +(-0.207107 + 0.358719i) q^{90} +(1.67157 + 2.89525i) q^{91} +(-0.757359 + 1.31178i) q^{92} +(-2.50000 + 4.33013i) q^{93} +1.31371 q^{94} +(0.500000 - 4.33013i) q^{95} +4.41421 q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.757359 + 1.31178i) q^{98} +(1.41421 + 2.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 + 2 * q^6 - 4 * q^7 + 12 * q^8 - 2 * q^9 + 2 * q^10 - 4 * q^12 - 2 * q^13 + 10 * q^14 - 2 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 + 16 * q^19 - 4 * q^20 - 2 * q^21 - 8 * q^22 - 4 * q^23 + 6 * q^24 - 2 * q^25 + 20 * q^26 - 4 * q^27 + 18 * q^28 - 8 * q^29 + 4 * q^30 - 20 * q^31 + 6 * q^32 + 16 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 - 2 * q^38 - 4 * q^39 + 6 * q^40 - 10 * q^42 - 10 * q^43 - 16 * q^44 - 4 * q^45 + 24 * q^46 + 12 * q^47 + 6 * q^48 + 8 * q^49 + 4 * q^50 - 8 * q^51 - 18 * q^52 + 4 * q^53 + 2 * q^54 - 28 * q^56 + 2 * q^57 - 16 * q^58 - 2 * q^60 - 6 * q^61 + 10 * q^62 + 2 * q^63 - 28 * q^64 - 4 * q^65 + 8 * q^66 + 6 * q^67 - 48 * q^68 - 8 * q^69 - 10 * q^70 - 20 * q^71 - 6 * q^72 - 2 * q^73 + 18 * q^74 - 4 * q^75 - 14 * q^76 - 32 * q^77 + 10 * q^78 + 18 * q^79 + 6 * q^80 - 2 * q^81 + 8 * q^82 - 32 * q^83 + 36 * q^84 - 8 * q^85 - 2 * q^86 - 16 * q^87 + 16 * q^88 - 8 * q^89 + 2 * q^90 + 18 * q^91 - 20 * q^92 - 10 * q^93 - 40 * q^94 + 2 * q^95 + 12 * q^96 + 12 * q^97 - 20 * q^98

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