LMFDB - Embedded newform 441.2.i.b.227.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(68,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 5]))

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

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

chi := DirichletCharacter("441.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.i (of order $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	10.0.288778218147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 4x^{7} + 34x^{6} - 19x^{5} + 64x^{4} - x^{3} + 64x^{2} - 21x + 9 $ x^10 - x^9 + 7x^8 - 4x^7 + 34x^6 - 19x^5 + 64x^4 - x^3 + 64x^2 - 21*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.3
Root			$-0.539982 - 0.935277i$ of defining polynomial
Character	$\chi$	$=$	441.227
Dual form			441.2.i.b.68.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.293869i q^{2} +(1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(0.152492 - 0.485617i) q^{6} -1.15010i q^{8} +(2.46146 + 1.71499i) q^{9} +O(q^{10})$	\(q-0.293869i q^{2} +(1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(0.152492 - 0.485617i) q^{6} -1.15010i q^{8} +(2.46146 + 1.71499i) q^{9} +(0.778834 + 0.449660i) q^{10} +(-3.37445 + 1.94824i) q^{11} +(3.16228 + 0.993010i) q^{12} +(2.02935 - 1.17164i) q^{13} +(-3.90379 + 3.58555i) q^{15} +3.48930 q^{16} +(1.68263 - 2.91440i) q^{17} +(0.503985 - 0.723348i) q^{18} +(-2.20696 + 1.27419i) q^{19} +(-2.92813 + 5.07167i) q^{20} +(0.572527 + 0.991647i) q^{22} +(2.58141 + 1.49038i) q^{23} +(0.596800 - 1.90053i) q^{24} +(-2.18263 - 3.78042i) q^{25} +(-0.344311 - 0.596363i) q^{26} +(3.17762 + 4.11130i) q^{27} +(-3.67241 - 2.12027i) q^{29} +(1.05368 + 1.14721i) q^{30} +0.472735i q^{31} -3.32560i q^{32} +(-6.58721 + 1.46841i) q^{33} +(-0.856452 - 0.494473i) q^{34} +(4.71035 + 3.28188i) q^{36} +(-3.89395 - 6.74451i) q^{37} +(0.374446 + 0.648559i) q^{38} +(3.96146 - 0.883081i) q^{39} +(3.04808 + 1.75981i) q^{40} +(-3.12737 - 5.41676i) q^{41} +(2.06191 - 3.57133i) q^{43} +(-6.45748 + 3.72823i) q^{44} +(-8.31157 + 3.89937i) q^{45} +(0.437976 - 0.758597i) q^{46} +4.05388 q^{47} +(5.76605 + 1.81064i) q^{48} +(-1.11095 + 0.641408i) q^{50} +(4.29284 - 3.94288i) q^{51} +(3.88344 - 2.24211i) q^{52} +(4.99439 + 2.88351i) q^{53} +(1.20818 - 0.933804i) q^{54} -11.9243i q^{55} +(-4.30818 + 0.960372i) q^{57} +(-0.623082 + 1.07921i) q^{58} +4.68705 q^{59} +(-7.47046 + 6.86145i) q^{60} -1.60018i q^{61} +0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +(0.431520 + 1.93578i) q^{66} +1.57566 q^{67} +(3.21994 - 5.57711i) q^{68} +(3.49238 + 3.80236i) q^{69} -13.6132i q^{71} +(1.97241 - 2.83093i) q^{72} +(0.856452 + 0.494473i) q^{73} +(-1.98201 + 1.14431i) q^{74} +(-1.64507 - 7.37971i) q^{75} +(-4.22333 + 2.43834i) q^{76} +(-0.259511 - 1.16415i) q^{78} -9.27815 q^{79} +(-5.33910 + 9.24760i) q^{80} +(3.11759 + 8.44279i) q^{81} +(-1.59182 + 0.919038i) q^{82} +(-5.49361 + 9.51520i) q^{83} +(5.14930 + 8.91884i) q^{85} +(-1.04950 - 0.605932i) q^{86} +(-4.96840 - 5.40938i) q^{87} +(2.24067 + 3.88095i) q^{88} +(2.15849 + 3.73861i) q^{89} +(1.14591 + 2.44252i) q^{90} +(4.93989 + 2.85205i) q^{92} +(-0.245308 + 0.781191i) q^{93} -1.19131i q^{94} -7.79874i q^{95} +(1.72569 - 5.49553i) q^{96} +(-4.98797 - 2.87980i) q^{97} +(-11.6473 - 0.991647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	$ 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) $ 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	0.293869i		−	0.207797i	−0.994588	−	0.103899i	$-0.966868\pi$
$2$		−	0.293869i		−	0.207797i	0.994588	−	0.103899i	$-0.0331317\pi$
$3$	1.65249	+	0.518912i	0.954067	+	0.299594i
$3$	1.65249	+	0.518912i	0.954067	+	0.299594i
$4$	1.91364			0.956820
$5$	−1.53014	+	2.65027i	−0.684297	+	1.18524i	0.289360	+	0.957220i	$0.406558\pi$
$5$	−1.53014	+	2.65027i	−0.684297	+	1.18524i	−0.973657	+	0.228017i	$0.926776\pi$
$6$	0.152492	−	0.485617i	0.0622547	−	0.198252i
$7$		0			0
$7$		0			0
$8$		−	1.15010i		−	0.406622i
$9$	2.46146	+	1.71499i	0.820487	+	0.571665i
$10$	0.778834	+	0.449660i	0.246289	+	0.142195i
$11$	−3.37445	+	1.94824i	−1.01743	+	0.587416i	−0.913360	−	0.407154i	$-0.866521\pi$
$11$	−3.37445	+	1.94824i	−1.01743	+	0.587416i	−0.104074	+	0.994570i	$0.533188\pi$
$12$	3.16228	+	0.993010i	0.912871	+	0.286657i
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	−0.191445	−	0.981503i	$-0.561317\pi$
$13$	2.02935	−	1.17164i	0.562840	−	0.324956i	0.754285	+	0.656548i	$0.227984\pi$
$14$		0			0
$15$	−3.90379	+	3.58555i	−1.00796	+	0.925785i
$16$	3.48930			0.872326
$17$	1.68263	−	2.91440i	0.408097	−	0.706845i	−0.586579	−	0.809892i	$-0.699526\pi$
$17$	1.68263	−	2.91440i	0.408097	−	0.706845i	0.994677	+	0.103047i	$0.0328591\pi$
$18$	0.503985	−	0.723348i	0.118790	−	0.170495i
$19$	−2.20696	+	1.27419i	−0.506312	+	0.292319i	−0.731316	−	0.682038i	$-0.761094\pi$
$19$	−2.20696	+	1.27419i	−0.506312	+	0.292319i	0.225004	+	0.974358i	$0.427760\pi$
$20$	−2.92813	+	5.07167i	−0.654750	+	1.13406i
$21$		0			0
$22$	0.572527	+	0.991647i	0.122063	+	0.211420i
$23$	2.58141	+	1.49038i	0.538261	+	0.310765i	0.744374	−	0.667763i	$-0.232748\pi$
$23$	2.58141	+	1.49038i	0.538261	+	0.310765i	−0.206113	+	0.978528i	$0.566081\pi$
$24$	0.596800	−	1.90053i	0.121821	−	0.387944i
$25$	−2.18263	−	3.78042i	−0.436525	−	0.756084i
$26$	−0.344311	−	0.596363i	−0.0675249	−	0.116956i
$27$	3.17762	+	4.11130i	0.611532	+	0.791219i
$28$		0			0
$29$	−3.67241	−	2.12027i	−0.681949	−	0.393724i	0.118640	−	0.992937i	$-0.462147\pi$
$29$	−3.67241	−	2.12027i	−0.681949	−	0.393724i	−0.800589	+	0.599214i	$0.795480\pi$
$30$	1.05368	+	1.14721i	0.192375	+	0.209450i
$31$			0.472735i			0.0849057i	0.999098	+	0.0424528i	$0.0135172\pi$
$31$			0.472735i			0.0849057i	−0.999098	+	0.0424528i	$0.986483\pi$
$32$		−	3.32560i		−	0.587888i
$33$	−6.58721	+	1.46841i	−1.14669	+	0.255617i
$34$	−0.856452	−	0.494473i	−0.146880	−	0.0848014i
$35$		0			0
$36$	4.71035	+	3.28188i	0.785059	+	0.546981i
$37$	−3.89395	−	6.74451i	−0.640161	−	1.10879i	−0.985397	−	0.170275i	$-0.945534\pi$
$37$	−3.89395	−	6.74451i	−0.640161	−	1.10879i	0.345236	−	0.938516i	$-0.387799\pi$
$38$	0.374446	+	0.648559i	0.0607431	+	0.105210i
$39$	3.96146	−	0.883081i	0.634342	−	0.141406i
$40$	3.04808	+	1.75981i	0.481943	+	0.278250i
$41$	−3.12737	−	5.41676i	−0.488413	−	0.845956i	0.511498	−	0.859284i	$-0.329091\pi$
$41$	−3.12737	−	5.41676i	−0.488413	−	0.845956i	−0.999911	+	0.0133282i	$0.995757\pi$
$42$		0			0
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	−0.664880	−	0.746950i	$-0.731517\pi$
$43$	2.06191	−	3.57133i	0.314438	−	0.544623i	0.979318	+	0.202328i	$0.0648506\pi$
$44$	−6.45748	+	3.72823i	−0.973501	+	0.562051i
$45$	−8.31157	+	3.89937i	−1.23902	+	0.581283i
$46$	0.437976	−	0.758597i	0.0645761	−	0.111849i
$47$	4.05388			0.591319			0.295659	−	0.955293i	$-0.404461\pi$
$47$	4.05388			0.591319			0.295659	+	0.955293i	$0.404461\pi$
$48$	5.76605	+	1.81064i	0.832257	+	0.261343i
$49$		0			0
$50$	−1.11095	+	0.641408i	−0.157112	+	0.0907087i
$51$	4.29284	−	3.94288i	0.601118	−	0.552114i
$52$	3.88344	−	2.24211i	0.538537	−	0.310924i
$53$	4.99439	+	2.88351i	0.686033	+	0.396081i	0.802124	−	0.597157i	$-0.203703\pi$
$53$	4.99439	+	2.88351i	0.686033	+	0.396081i	−0.116091	+	0.993239i	$0.537037\pi$
$54$	1.20818	−	0.933804i	0.164413	−	0.127075i
$55$		−	11.9243i		−	1.60787i
$56$		0			0
$57$	−4.30818	+	0.960372i	−0.570633	+	0.127204i
$58$	−0.623082	+	1.07921i	−0.0818146	+	0.141707i
$59$	4.68705			0.610201			0.305101	−	0.952320i	$-0.401310\pi$
$59$	4.68705			0.610201			0.305101	+	0.952320i	$0.401310\pi$
$60$	−7.47046	+	6.86145i	−0.964432	+	0.885810i
$61$		−	1.60018i		−	0.204883i	−0.994739	−	0.102441i	$-0.967335\pi$
$61$		−	1.60018i		−	0.204883i	0.994739	−	0.102441i	$-0.0326654\pi$
$62$	0.138922			0.0176432
$63$		0			0
$64$	6.00131			0.750164
$65$			7.17110i			0.889465i
$66$	0.431520	+	1.93578i	0.0531165	+	0.238278i
$67$	1.57566			0.192498			0.0962489	−	0.995357i	$-0.469316\pi$
$67$	1.57566			0.192498			0.0962489	+	0.995357i	$0.469316\pi$
$68$	3.21994	−	5.57711i	0.390476	−	0.676324i
$69$	3.49238	+	3.80236i	0.420434	+	0.457750i
$70$		0			0
$71$		−	13.6132i		−	1.61559i	−0.589462	−	0.807796i	$-0.700660\pi$
$71$		−	13.6132i		−	1.61559i	0.589462	−	0.807796i	$-0.299340\pi$
$72$	1.97241	−	2.83093i	0.232451	−	0.333628i
$73$	0.856452	+	0.494473i	0.100240	+	0.0578737i	0.549282	−	0.835637i	$-0.314901\pi$
$73$	0.856452	+	0.494473i	0.100240	+	0.0578737i	−0.449042	+	0.893511i	$0.648235\pi$
$74$	−1.98201	+	1.14431i	−0.230404	+	0.133024i
$75$	−1.64507	−	7.37971i	−0.189956	−	0.852135i
$76$	−4.22333	+	2.43834i	−0.484450	+	0.279697i
$77$		0			0
$78$	−0.259511	−	1.16415i	−0.0293838	−	0.131814i
$79$	−9.27815			−1.04387			−0.521937	−	0.852984i	$-0.674790\pi$
$79$	−9.27815			−1.04387			−0.521937	+	0.852984i	$0.674790\pi$
$80$	−5.33910	+	9.24760i	−0.596930	+	1.03391i
$81$	3.11759	+	8.44279i	0.346398	+	0.938088i
$82$	−1.59182	+	0.919038i	−0.175787	+	0.101491i
$83$	−5.49361	+	9.51520i	−0.603002	+	1.04443i	0.389362	+	0.921085i	$0.372695\pi$
$83$	−5.49361	+	9.51520i	−0.603002	+	1.04443i	−0.992364	+	0.123345i	$0.960638\pi$
$84$		0			0
$85$	5.14930	+	8.91884i	0.558519	+	0.967384i
$86$	−1.04950	−	0.605932i	−0.113171	−	0.0653393i
$87$	−4.96840	−	5.40938i	−0.532668	−	0.579946i
$88$	2.24067	+	3.88095i	0.238856	+	0.413710i
$89$	2.15849	+	3.73861i	0.228799	+	0.396292i	0.957452	−	0.288591i	$-0.0931868\pi$
$89$	2.15849	+	3.73861i	0.228799	+	0.396292i	−0.728653	+	0.684883i	$0.759853\pi$
$90$	1.14591	+	2.44252i	0.120789	+	0.257464i
$91$		0			0
$92$	4.93989	+	2.85205i	0.515019	+	0.297346i
$93$	−0.245308	+	0.781191i	−0.0254372	+	0.0810057i
$94$		−	1.19131i		−	0.122874i
$95$		−	7.79874i		−	0.800133i
$96$	1.72569	−	5.49553i	0.176128	−	0.560885i
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	0.224923	−	0.974377i	$-0.427787\pi$
$97$	−4.98797	−	2.87980i	−0.506451	−	0.292400i	−0.731374	+	0.681977i	$0.761120\pi$
$98$		0			0
$99$	−11.6473	−	0.991647i	−1.17060	−	0.0996642i
$100$	−4.17676	−	7.23437i	−0.417676	−	0.723437i
$101$	−8.57900	−	14.8593i	−0.853642	−	1.47855i	−0.877899	−	0.478846i	$-0.841055\pi$
$101$	−8.57900	−	14.8593i	−0.853642	−	1.47855i	0.0242566	−	0.999706i	$-0.492278\pi$
$102$	−1.15869	−	1.26154i	−0.114728	−	0.124911i
$103$	−8.50422	−	4.90992i	−0.837946	−	0.483788i	0.0186195	−	0.999827i	$-0.494073\pi$
$103$	−8.50422	−	4.90992i	−0.837946	−	0.483788i	−0.856566	+	0.516038i	$0.827406\pi$
$104$	−1.34751	−	2.33395i	−0.132134	−	0.228863i
$105$		0			0
$106$	0.847377	−	1.46770i	0.0823045	−	0.142556i
$107$	−3.00501	+	1.73494i	−0.290505	+	0.167723i	−0.638170	−	0.769896i	$-0.720308\pi$
$107$	−3.00501	+	1.73494i	−0.290505	+	0.167723i	0.347664	+	0.937619i	$0.386975\pi$
$108$	6.08081	+	7.86755i	0.585127	+	0.757055i
$109$	0.611066	−	1.05840i	0.0585295	−	0.101376i	−0.835276	−	0.549831i	$-0.814692\pi$
$109$	0.611066	−	1.05840i	0.0585295	−	0.101376i	0.893806	+	0.448455i	$0.148025\pi$
$110$	−3.50418			−0.334110
$111$	−2.93491	−	13.1659i	−0.278569	−	1.24965i
$112$		0			0
$113$	−1.87681	+	1.08358i	−0.176555	+	0.101934i	−0.585673	−	0.810547i	$-0.699170\pi$
$113$	−1.87681	+	1.08358i	−0.176555	+	0.101934i	0.409118	+	0.912482i	$0.365836\pi$
$114$	0.282224	+	1.26604i	0.0264327	+	0.118576i
$115$	−7.89981	+	4.56096i	−0.736661	+	0.425311i
$116$	−7.02767	−	4.05743i	−0.652503	−	0.376723i
$117$	7.00453	+	0.596363i	0.647569	+	0.0551338i
$118$		−	1.37738i		−	0.126798i
$119$		0			0
$120$	4.12374	+	4.48975i	0.376444	+	0.409856i
$121$	2.09126	−	3.62216i	0.190114	−	0.329287i
$122$	−0.470245			−0.0425740
$123$	−2.35713	−	10.5740i	−0.212535	−	0.953424i
$124$			0.904645i			0.0812395i
$125$	−1.94249			−0.173742
$126$		0			0
$127$	2.74889			0.243925			0.121962	−	0.992535i	$-0.461081\pi$
$127$	2.74889			0.243925			0.121962	+	0.992535i	$0.461081\pi$
$128$		−	8.41480i		−	0.743770i
$129$	5.26049	−	4.83165i	0.463160	−	0.425403i
$130$	2.10737			0.184828
$131$	3.73911	−	6.47632i	0.326687	−	0.565839i	−0.655165	−	0.755486i	$-0.727401\pi$
$131$	3.73911	−	6.47632i	0.326687	−	0.565839i	0.981852	+	0.189647i	$0.0607343\pi$
$132$	−12.6056	+	2.81000i	−1.09717	+	0.244580i
$133$		0			0
$134$		−	0.463039i		−	0.0400005i
$135$	−15.7582	+	2.13070i	−1.35625	+	0.183382i
$136$	−3.35185	−	1.93519i	−0.287418	−	0.165941i
$137$	−10.5731	+	6.10439i	−0.903321	+	0.521533i	−0.878276	−	0.478153i	$-0.841306\pi$
$137$	−10.5731	+	6.10439i	−0.903321	+	0.521533i	−0.0250451	+	0.999686i	$0.507973\pi$
$138$	1.11740	−	1.02631i	0.0951192	−	0.0873649i
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.0774943	−	0.996993i	$-0.475308\pi$
$139$	11.5501	−	6.66842i	0.979663	−	0.565608i	0.902168	+	0.431384i	$0.141975\pi$
$140$		0			0
$141$	6.69900	+	2.10360i	0.564157	+	0.177155i
$142$	−4.00051			−0.335715
$143$	−4.56528	+	7.90730i	−0.381768	+	0.661242i
$144$	8.58878	+	5.98414i	0.715732	+	0.498678i
$145$	11.2386	−	6.48859i	0.933312	−	0.538848i
$146$	0.145310	−	0.251685i	0.0120260	−	0.0208296i
$147$		0			0
$148$	−7.45161	−	12.9066i	−0.612519	−	1.06091i
$149$	−7.33827	−	4.23675i	−0.601174	−	0.347088i	0.168329	−	0.985731i	$-0.446163\pi$
$149$	−7.33827	−	4.23675i	−0.601174	−	0.347088i	−0.769503	+	0.638643i	$0.779496\pi$
$150$	−2.16867	+	0.483436i	−0.177071	+	0.0394724i
$151$	1.67827	+	2.90685i	0.136576	+	0.236556i	0.926198	−	0.377037i	$-0.123057\pi$
$151$	1.67827	+	2.90685i	0.136576	+	0.236556i	−0.789623	+	0.613593i	$0.789724\pi$
$152$	1.46545	+	2.53823i	0.118863	+	0.205877i
$153$	9.13990	−	4.28798i	0.738917	−	0.346662i
$154$		0			0
$155$	−1.25288	−	0.723348i	−0.100633	−	0.0581007i
$156$	7.58081	−	1.68990i	0.606951	−	0.135300i
$157$			16.7085i			1.33349i	0.745288	+	0.666743i	$0.232312\pi$
$157$			16.7085i			1.33349i	−0.745288	+	0.666743i	$0.767688\pi$
$158$			2.72657i			0.216914i
$159$	6.75691	+	7.35663i	0.535858	+	0.583419i
$160$	8.81374	+	5.08862i	0.696787	+	0.402290i
$161$		0			0
$162$	2.48108	−	0.916163i	0.194932	−	0.0719806i
$163$	12.6662	+	21.9385i	0.992094	+	1.71836i	0.604731	+	0.796430i	$0.293281\pi$
$163$	12.6662	+	21.9385i	0.992094	+	1.71836i	0.387363	+	0.921927i	$0.373386\pi$
$164$	−5.98466	−	10.3657i	−0.467324	−	0.809428i
$165$	6.18764	−	19.7048i	0.481707	−	1.53401i
$166$	2.79623	+	1.61440i	0.217029	+	0.125302i
$167$	−0.875828	−	1.51698i	−0.0677736	−	0.117387i	0.830147	−	0.557544i	$-0.188256\pi$
$167$	−0.875828	−	1.51698i	−0.0677736	−	0.117387i	−0.897921	+	0.440157i	$0.854923\pi$
$168$		0			0
$169$	−3.75450	+	6.50298i	−0.288808	+	0.500229i
$170$	2.62097	−	1.51322i	0.201020	−	0.116059i
$171$	−7.61759	−	0.648559i	−0.582531	−	0.0495965i
$172$	3.94575	−	6.83424i	0.300861	−	0.521106i
$173$	−23.9266			−1.81910			−0.909551	−	0.415592i	$-0.863574\pi$
$173$	−23.9266			−1.81910			−0.909551	+	0.415592i	$0.863574\pi$
$174$	−1.58965	+	1.46006i	−0.120511	+	0.110687i
$175$		0			0
$176$	−11.7745	+	6.79799i	−0.887533	+	0.512418i
$177$	7.74531	+	2.43216i	0.582173	+	0.182813i
$178$	1.09866	−	0.634313i	0.0823482	−	0.0475438i
$179$	21.9857	+	12.6935i	1.64329	+	0.948755i	0.979652	+	0.200702i	$0.0643223\pi$
$179$	21.9857	+	12.6935i	1.64329	+	0.948755i	0.663639	+	0.748053i	$0.269011\pi$
$180$	−15.9054	+	7.46199i	−1.18552	+	0.556184i
$181$			22.4032i			1.66522i	0.553859	+	0.832610i	$0.313155\pi$
$181$			22.4032i			1.66522i	−0.553859	+	0.832610i	$0.686845\pi$
$182$		0			0
$183$	0.830354	−	2.64429i	0.0613815	−	0.195472i
$184$	1.71408	−	2.96888i	0.126364	−	0.218869i
$185$	23.8331			1.75224
$186$	0.229568	+	0.0720884i	0.0168328	+	0.00528578i
$187$			13.1126i			0.958890i
$188$	7.75766			0.565786
$189$		0			0
$190$	−2.29181			−0.166265
$191$		−	4.28895i		−	0.310337i	−0.987888	−	0.155169i	$-0.950408\pi$
$191$		−	4.28895i		−	0.310337i	0.987888	−	0.155169i	$-0.0495921\pi$
$192$	9.91712	+	3.11415i	0.715707	+	0.224744i
$193$	−23.3449			−1.68041			−0.840203	−	0.542272i	$-0.817564\pi$
$193$	−23.3449			−1.68041			−0.840203	+	0.542272i	$0.817564\pi$
$194$	−0.846286	+	1.46581i	−0.0607598	+	0.105239i
$195$	−3.72117	+	11.8502i	−0.266478	+	0.848609i
$196$		0			0
$197$			18.7811i			1.33809i	0.743220	+	0.669047i	$0.233298\pi$
$197$			18.7811i			1.33809i	−0.743220	+	0.669047i	$0.766702\pi$
$198$	−0.291415	+	3.42278i	−0.0207099	+	0.243246i
$199$	3.92927	+	2.26856i	0.278539	+	0.160814i	0.632762	−	0.774347i	$-0.281921\pi$
$199$	3.92927	+	2.26856i	0.278539	+	0.160814i	−0.354223	+	0.935161i	$0.615255\pi$
$200$	−4.34786	+	2.51024i	−0.307440	+	0.177501i
$201$	2.60377	+	0.817629i	0.183656	+	0.0576711i
$202$	−4.36668	+	2.52111i	−0.307239	+	0.177384i
$203$		0			0
$204$	8.21496	−	7.54526i	0.575162	−	0.528274i
$205$	19.1412			1.33688
$206$	−1.44287	+	2.49913i	−0.100530	+	0.174123i
$207$	3.79805	+	8.09561i	0.263983	+	0.562684i
$208$	7.08101	−	4.08822i	0.490980	−	0.283467i
$209$	4.96485	−	8.59937i	0.343426	−	0.594831i
$210$		0			0
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	0.722908	−	0.690944i	$-0.242805\pi$
$211$	−3.44148	−	5.96082i	−0.236921	−	0.410360i	−0.959829	+	0.280584i	$0.909472\pi$
$212$	9.55747	+	5.51801i	0.656410	+	0.378978i
$213$	7.06406	−	22.4958i	0.484021	−	1.54138i
$214$	0.509847	+	0.883081i	0.0348524	+	0.0603662i
$215$	6.31000	+	10.9292i	0.430338	+	0.745368i
$216$	4.72840	−	3.65457i	0.321727	−	0.248662i
$217$		0			0
$218$	−0.311031	−	0.179574i	−0.0210657	−	0.0121623i
$219$	1.15869	+	1.26154i	0.0782972	+	0.0852467i
$220$		−	22.8188i		−	1.53844i
$221$		−	7.88576i		−	0.530454i
$222$	−3.86905	+	0.862480i	−0.259673	+	0.0578859i
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	0.301705	−	0.953401i	$-0.402444\pi$
$223$	−5.57176	−	3.21686i	−0.373113	−	0.215417i	−0.674818	+	0.737985i	$0.735778\pi$
$224$		0			0
$225$	1.11095	−	13.0486i	0.0740634	−	0.869904i
$226$	0.318430	+	0.551537i	0.0211816	+	0.0366877i
$227$	9.86983	+	17.0951i	0.655084	+	1.13464i	0.981873	+	0.189541i	$0.0607000\pi$
$227$	9.86983	+	17.0951i	0.655084	+	1.13464i	−0.326789	+	0.945097i	$0.605967\pi$
$228$	−8.24431	+	1.83781i	−0.545993	+	0.121712i
$229$	−9.44564	−	5.45344i	−0.624185	−	0.360373i	0.154311	−	0.988022i	$-0.450684\pi$
$229$	−9.44564	−	5.45344i	−0.624185	−	0.360373i	−0.778497	+	0.627649i	$0.784017\pi$
$230$	1.34033	+	2.32151i	0.0883785	+	0.153076i
$231$		0			0
$232$	−2.43852	+	4.22364i	−0.160097	+	0.277295i
$233$	17.9944	−	10.3891i	1.17885	−	0.680611i	0.223104	−	0.974795i	$-0.428381\pi$
$233$	17.9944	−	10.3891i	1.17885	−	0.680611i	0.955749	+	0.294184i	$0.0950478\pi$
$234$	0.175253	−	2.05842i	0.0114566	−	0.134563i
$235$	−6.20298	+	10.7439i	−0.404638	+	0.700853i
$236$	8.96932			0.583853
$237$	−15.3321	−	4.81454i	−0.995925	−	0.312738i
$238$		0			0
$239$	23.6739	−	13.6681i	1.53134	−	0.884119i	0.532039	−	0.846720i	$-0.321426\pi$
$239$	23.6739	−	13.6681i	1.53134	−	0.884119i	0.999300	−	0.0373991i	$-0.0119073\pi$
$240$	−13.6215	+	12.5111i	−0.879265	+	0.807586i
$241$	18.4688	−	10.6630i	1.18968	−	0.686861i	0.231445	−	0.972848i	$-0.425655\pi$
$241$	18.4688	−	10.6630i	1.18968	−	0.686861i	0.958234	+	0.285987i	$0.0923213\pi$
$242$	−1.06444	−	0.614556i	−0.0684250	−	0.0395052i
$243$	0.770725	+	15.5694i	0.0494420	+	0.998777i
$244$		−	3.06218i		−	0.196036i
$245$		0			0
$246$	−3.10737	+	0.692689i	−0.198119	+	0.0441643i
$247$	−2.98580	+	5.17155i	−0.189982	+	0.329058i
$248$	0.543692			0.0345245
$249$	−14.0157	+	12.8731i	−0.888208	+	0.815800i
$250$			0.570839i			0.0361030i
$251$	26.7381			1.68769			0.843847	−	0.536584i	$-0.180286\pi$
$251$	26.7381			1.68769			0.843847	+	0.536584i	$0.180286\pi$
$252$		0			0
$253$	−11.6144			−0.730193
$254$		−	0.807815i		−	0.0506868i
$255$	3.88108	+	17.4103i	0.243043	+	1.09028i
$256$	9.52977			0.595611
$257$	1.52640	−	2.64380i	0.0952140	−	0.164916i	−0.814484	−	0.580186i	$-0.802980\pi$
$257$	1.52640	−	2.64380i	0.0952140	−	0.164916i	0.909698	+	0.415271i	$0.136313\pi$
$258$	−1.41987	−	1.54590i	−0.0883975	−	0.0962434i
$259$		0			0
$260$			13.7229i			0.851058i
$261$	−5.40325	−	11.5171i	−0.334453	−	0.712892i
$262$	−1.90319	−	1.09881i	−0.117580	−	0.0678847i
$263$	14.0447	−	8.10868i	0.866030	−	0.500003i	3.24009e−6	−	1.00000i	$-0.499999\pi$
$263$	14.0447	−	8.10868i	0.866030	−	0.500003i	0.866027	+	0.499997i	$0.166666\pi$
$264$	1.68881	+	7.57595i	0.103939	+	0.466267i
$265$	−15.2842	+	8.82433i	−0.938901	+	0.542074i
$266$		0			0
$267$	1.62687	+	7.29808i	0.0995631	+	0.446635i
$268$	3.01525			0.184186
$269$	−0.303255	+	0.525254i	−0.0184898	+	0.0320253i	−0.875122	−	0.483902i	$-0.839219\pi$
$269$	−0.303255	+	0.525254i	−0.0184898	+	0.0320253i	0.856632	+	0.515927i	$0.172552\pi$
$270$	0.626149	+	4.63086i	0.0381062	+	0.281825i
$271$	−19.8948	+	11.4863i	−1.20852	+	0.697742i	−0.962437	−	0.271505i	$-0.912479\pi$
$271$	−19.8948	+	11.4863i	−1.20852	+	0.697742i	−0.246088	+	0.969248i	$0.579145\pi$
$272$	5.87120	−	10.1692i	0.355994	−	0.616599i
$273$		0			0
$274$	1.79389	+	3.10711i	0.108373	+	0.187708i
$275$	14.7303	+	8.50455i	0.888271	+	0.512844i
$276$	6.68317	+	7.27635i	0.402279	+	0.437985i
$277$	−6.64173	−	11.5038i	−0.399063	−	0.691197i	0.594548	−	0.804060i	$-0.297331\pi$
$277$	−6.64173	−	11.5038i	−0.399063	−	0.691197i	−0.993611	+	0.112863i	$0.963998\pi$
$278$	−1.95965	−	3.39421i	−0.117532	−	0.203571i
$279$	−0.810738	+	1.16362i	−0.0485376	+	0.0696640i
$280$		0			0
$281$	5.68377	+	3.28153i	0.339065	+	0.195759i	0.659859	−	0.751390i	$-0.270616\pi$
$281$	5.68377	+	3.28153i	0.339065	+	0.195759i	−0.320793	+	0.947149i	$0.603950\pi$
$282$	0.618185	−	1.96863i	0.0368124	−	0.117230i
$283$		−	2.97234i		−	0.176687i	−0.996090	−	0.0883437i	$-0.971843\pi$
$283$		−	2.97234i		−	0.176687i	0.996090	−	0.0883437i	$-0.0281574\pi$
$284$		−	26.0508i		−	1.54583i
$285$	4.04685	−	12.8874i	0.239715	−	0.763381i
$286$	2.32371	+	1.34160i	0.137404	+	0.0793303i
$287$		0			0
$288$	5.70338	−	8.18583i	0.336075	−	0.482355i
$289$	2.83753	+	4.91475i	0.166914	+	0.289103i
$290$	−1.90680	−	3.30267i	−0.111971	−	0.193940i
$291$	−6.74821	−	7.34717i	−0.395587	−	0.430698i
$292$	1.63894	+	0.946243i	0.0959118	+	0.0553747i
$293$	−3.03087	−	5.24962i	−0.177065	−	0.306686i	0.763809	−	0.645443i	$-0.223327\pi$
$293$	−3.03087	−	5.24962i	−0.177065	−	0.306686i	−0.940874	+	0.338756i	$0.889994\pi$
$294$		0			0
$295$	−7.17181	+	12.4219i	−0.417559	+	0.723234i
$296$	−7.75686	+	4.47843i	−0.450858	+	0.260303i
$297$	−18.7325	−	7.68260i	−1.08697	−	0.445790i
$298$	−1.24505	+	2.15649i	−0.0721239	+	0.124922i
$299$	6.98477			0.403940
$300$	−3.14807	−	14.1221i	−0.181754	−	0.815340i
$301$		0			0
$302$	0.854235	−	0.493193i	0.0491557	−	0.0283801i
$303$	−6.46609	−	29.0066i	−0.371467	−	1.66638i
$304$	−7.70076	+	4.44604i	−0.441669	+	0.254998i
$305$	4.24092	+	2.44850i	0.242834	+	0.140201i
$306$	−1.26011	−	2.68594i	−0.0720354	−	0.153545i
$307$			21.6030i			1.23295i	0.787375	+	0.616474i	$0.211439\pi$
$307$			21.6030i			1.23295i	−0.787375	+	0.616474i	$0.788561\pi$
$308$		0			0
$309$	−11.5054	−	12.5265i	−0.654517	−	0.712610i
$310$	−0.212570	+	0.368182i	−0.0120732	+	0.0209113i
$311$	−11.0234			−0.625081			−0.312540	−	0.949905i	$-0.601180\pi$
$311$	−11.0234			−0.625081			−0.312540	+	0.949905i	$0.601180\pi$
$312$	−1.01563	−	4.55607i	−0.0574988	−	0.257937i
$313$		−	13.5542i		−	0.766129i	−0.923722	−	0.383064i	$-0.874869\pi$
$313$		−	13.5542i		−	0.766129i	0.923722	−	0.383064i	$-0.125131\pi$
$314$	4.91012			0.277094
$315$		0			0
$316$	−17.7551			−0.998800
$317$		−	11.1541i		−	0.626479i	−0.949674	−	0.313240i	$-0.898586\pi$
$317$		−	11.1541i		−	0.626479i	0.949674	−	0.313240i	$-0.101414\pi$
$318$	2.16189	−	1.98565i	0.121233	−	0.111350i
$319$	16.5231			0.925118
$320$	−9.18282	+	15.9051i	−0.513335	+	0.889123i
$321$	−5.86604	+	1.30765i	−0.327411	+	0.0729857i
$322$		0			0
$323$			8.57595i			0.477179i
$324$	5.96594	+	16.1565i	0.331441	+	0.897581i
$325$	−8.85862	−	5.11453i	−0.491388	−	0.283703i
$326$	6.44706	−	3.72221i	0.357070	−	0.206154i
$327$	1.55900	−	1.43190i	0.0862127	−	0.0791845i
$328$	−6.22982	+	3.59679i	−0.343984	+	0.198599i
$329$		0			0
$330$	−5.79063	−	1.81836i	−0.318763	−	0.100097i
$331$	−19.0202			−1.04544			−0.522722	−	0.852503i	$-0.675083\pi$
$331$	−19.0202			−1.04544			−0.522722	+	0.852503i	$0.675083\pi$
$332$	−10.5128	+	18.2087i	−0.576964	+	0.999331i
$333$	1.98201	−	23.2795i	0.108613	−	1.27571i
$334$	−0.445794	+	0.257379i	−0.0243927	+	0.0140832i
$335$	−2.41098	+	4.17593i	−0.131726	+	0.228156i
$336$		0			0
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	0.942289	−	0.334802i	$-0.108669\pi$
$337$	3.32635	+	5.76140i	0.181198	+	0.313843i	−0.761091	+	0.648645i	$0.775336\pi$
$338$	1.91103	+	1.10333i	0.103946	+	0.0600134i
$339$	−3.66369	+	0.816703i	−0.198984	+	0.0443572i
$340$	9.85390	+	17.0675i	0.534403	+	0.925613i
$341$	−0.921000	−	1.59522i	−0.0498749	−	0.0863859i
$342$	−0.190592	+	2.23858i	−0.0103060	+	0.121048i
$343$		0			0
$344$	−4.10738	−	2.37140i	−0.221455	−	0.127857i
$345$	−15.4211	+	3.43764i	−0.830244	+	0.185076i
$346$			7.03128i			0.378004i
$347$			26.6501i			1.43065i	0.698792	+	0.715325i	$0.253721\pi$
$347$			26.6501i			1.43065i	−0.698792	+	0.715325i	$0.746279\pi$
$348$	−9.50773	−	10.3516i	−0.509668	−	0.554904i
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.935711	−	0.352768i	$-0.114759\pi$
$349$	20.5135	+	11.8435i	1.09806	+	0.633966i	0.162350	+	0.986733i	$0.448093\pi$
$350$		0			0
$351$	11.2655	+	4.62022i	0.601306	+	0.246609i
$352$	6.47905	+	11.2221i	0.345335	+	0.598137i
$353$	−2.29422	−	3.97371i	−0.122109	−	0.211499i	0.798490	−	0.602008i	$-0.205632\pi$
$353$	−2.29422	−	3.97371i	−0.122109	−	0.211499i	−0.920599	+	0.390509i	$0.872299\pi$
$354$	0.714738	−	2.27611i	0.0379879	−	0.120974i
$355$	36.0788	+	20.8301i	1.91486	+	1.10555i
$356$	4.13057	+	7.15435i	0.218920	+	0.379180i
$357$		0			0
$358$	3.73022	−	6.46094i	0.197148	−	0.341471i
$359$	−5.30942	+	3.06540i	−0.280221	+	0.161785i	−0.633523	−	0.773724i	$-0.718392\pi$
$359$	−5.30942	+	3.06540i	−0.280221	+	0.161785i	0.353303	+	0.935509i	$0.385059\pi$
$360$	4.48466	+	9.55913i	0.236362	+	0.503811i
$361$	−6.25288	+	10.8303i	−0.329099	+	0.570016i
$362$	6.58363			0.346028
$363$	5.33537	−	4.90042i	0.280034	−	0.257205i
$364$		0			0
$365$	−2.62097	+	1.51322i	−0.137188	+	0.0792056i
$366$	−0.777076	−	0.244016i	−0.0406184	−	0.0127549i
$367$	−22.8860	+	13.2132i	−1.19464	+	0.689725i	−0.959355	−	0.282202i	$-0.908935\pi$
$367$	−22.8860	+	13.2132i	−1.19464	+	0.689725i	−0.235283	+	0.971927i	$0.575602\pi$
$368$	9.00732	+	5.20038i	0.469539	+	0.271088i
$369$	1.59182	−	18.6966i	0.0828669	−	0.973305i
$370$		−	7.00381i		−	0.364111i
$371$		0			0
$372$	−0.469431	+	1.49492i	−0.0243388	+	0.0775079i
$373$	−10.0581	+	17.4211i	−0.520789	+	0.902033i	0.478919	+	0.877859i	$0.341029\pi$
$373$	−10.0581	+	17.4211i	−0.520789	+	0.902033i	−0.999708	+	0.0241735i	$0.992305\pi$
$374$	3.85340			0.199255
$375$	−3.20995	−	1.00798i	−0.165761	−	0.0520519i
$376$		−	4.66236i		−	0.240443i
$377$	−9.93679			−0.511771
$378$		0			0
$379$	−17.4561			−0.896660			−0.448330	−	0.893868i	$-0.647981\pi$
$379$	−17.4561			−0.896660			−0.448330	+	0.893868i	$0.647981\pi$
$380$		−	14.9240i		−	0.765584i
$381$	4.54252	+	1.42643i	0.232720	+	0.0730783i
$382$	−1.26039			−0.0644872
$383$	14.0317	−	24.3036i	0.716985	−	1.24185i	−0.245204	−	0.969471i	$-0.578855\pi$
$383$	14.0317	−	24.3036i	0.716985	−	1.24185i	0.962189	−	0.272383i	$-0.0878117\pi$
$384$	4.36654	−	13.9054i	0.222829	−	0.709607i
$385$		0			0
$386$			6.86037i			0.349183i
$387$	11.2001	−	5.25453i	0.569334	−	0.267103i
$388$	−9.54517	−	5.51091i	−0.484583	−	0.279774i
$389$	−29.6520	+	17.1196i	−1.50342	+	0.867999i	−0.503426	+	0.864038i	$0.667928\pi$
$389$	−29.6520	+	17.1196i	−1.50342	+	0.867999i	−0.999992	+	0.00396103i	$0.998739\pi$
$390$	3.48241	+	1.09354i	0.176339	+	0.0553734i
$391$	8.68710	−	5.01550i	0.439325	−	0.253645i
$392$		0			0
$393$	9.53949	−	8.76181i	0.481203	−	0.441975i
$394$	5.51918			0.278052
$395$	14.1968	−	24.5896i	0.714320	−	1.23724i
$396$	−22.2887	−	1.89766i	−1.12005	−	0.0953608i
$397$	11.2926	−	6.51981i	0.566762	−	0.327220i	−0.189093	−	0.981959i	$-0.560555\pi$
$397$	11.2926	−	6.51981i	0.566762	−	0.327220i	0.755855	+	0.654739i	$0.227222\pi$
$398$	0.666662	−	1.15469i	0.0334167	−	0.0578795i
$399$		0			0
$400$	−7.61585	−	13.1910i	−0.380792	−	0.659552i
$401$	−15.8943	−	9.17659i	−0.793725	−	0.458257i	0.0475475	−	0.998869i	$-0.484859\pi$
$401$	−15.8943	−	9.17659i	−0.793725	−	0.458257i	−0.841272	+	0.540612i	$0.818193\pi$
$402$	0.240276	−	0.765168i	0.0119839	−	0.0381631i
$403$	0.553877	+	0.959344i	0.0275906	+	0.0477883i
$404$	−16.4171	−	28.4353i	−0.816782	−	1.41471i
$405$	−27.1460	−	4.65616i	−1.34890	−	0.231366i
$406$		0			0
$407$	26.2798	+	15.1727i	1.30264	+	0.752081i
$408$	−4.53471	−	4.93720i	−0.224501	−	0.244428i
$409$			6.46786i			0.319815i	0.987132	+	0.159907i	$0.0511196\pi$
$409$			6.46786i			0.319815i	−0.987132	+	0.159907i	$0.948880\pi$
$410$		−	5.62501i		−	0.277800i
$411$	−20.6396	+	4.60094i	−1.01808	+	0.226948i
$412$	−16.2740	−	9.39581i	−0.801764	−	0.462899i
$413$		0			0
$414$	2.37905	−	1.11613i	0.116924	−	0.0548548i
$415$	−16.8119	−	29.1191i	−0.825265	−	1.42940i
$416$	−3.89642	−	6.74880i	−0.191038	−	0.330887i
$417$	22.5467	−	5.02607i	1.10412	−	0.246127i
$418$	−2.52709	−	1.45902i	−0.123604	−	0.0713629i
$419$	−7.11542	−	12.3243i	−0.347611	−	0.602080i	0.638214	−	0.769859i	$-0.279674\pi$
$419$	−7.11542	−	12.3243i	−0.347611	−	0.602080i	−0.985825	+	0.167779i	$0.946340\pi$
$420$		0			0
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	−0.213324	−	0.976982i	$-0.568429\pi$
$421$	15.1718	−	26.2784i	0.739429	−	1.28073i	0.952753	−	0.303747i	$-0.0982378\pi$
$422$	−1.75170	+	1.01135i	−0.0852716	+	0.0492316i
$423$	9.97846	+	6.95238i	0.485169	+	0.338036i
$424$	3.31633	−	5.74405i	0.161055	−	0.278956i
$425$	−14.6902			−0.712579
$426$	−6.61081	−	2.07591i	−0.320295	−	0.100578i
$427$		0			0
$428$	−5.75051	+	3.32006i	−0.277962	+	0.160481i
$429$	−11.6473	+	10.6978i	−0.562336	+	0.516494i
$430$	3.21177	−	1.85432i	0.154885	−	0.0894230i
$431$	−2.12663	−	1.22781i	−0.102436	−	0.0591415i	0.447907	−	0.894080i	$-0.352170\pi$
$431$	−2.12663	−	1.22781i	−0.102436	−	0.0591415i	−0.550343	+	0.834939i	$0.685503\pi$
$432$	11.0877	+	14.3456i	0.533455	+	0.690201i
$433$		−	12.4545i		−	0.598525i	−0.954171	−	0.299262i	$-0.903259\pi$
$433$		−	12.4545i		−	0.598525i	0.954171	−	0.299262i	$-0.0967406\pi$
$434$		0			0
$435$	21.9386	−	4.89052i	1.05188	−	0.234483i
$436$	1.16936	−	2.02539i	0.0560022	−	0.0969987i
$437$	−7.59610			−0.363371
$438$	0.370727	−	0.340504i	0.0177140	−	0.0162699i
$439$		−	17.5300i		−	0.836663i	−0.908294	−	0.418331i	$-0.862615\pi$
$439$		−	17.5300i		−	0.836663i	0.908294	−	0.418331i	$-0.137385\pi$
$440$	−13.7141			−0.653794
$441$		0			0
$442$	−2.31739			−0.110227
$443$			9.00464i			0.427824i	0.976853	+	0.213912i	$0.0686205\pi$
$443$			9.00464i			0.427824i	−0.976853	+	0.213912i	$0.931379\pi$
$444$	−5.61636	−	25.1947i	−0.266541	−	1.19569i
$445$	−13.2111			−0.626266
$446$	−0.945337	+	1.63737i	−0.0447630	+	0.0775318i
$447$	−9.92793	−	10.8091i	−0.469575	−	0.511254i
$448$		0			0
$449$		−	30.8120i		−	1.45411i	−0.686581	−	0.727054i	$-0.740889\pi$
$449$		−	30.8120i		−	1.45411i	0.686581	−	0.727054i	$-0.259111\pi$
$450$	−3.83457	−	0.326474i	−0.180763	−	0.0153902i
$451$	21.1063	+	12.1857i	0.993856	+	0.573803i
$452$	−3.59154	+	2.07357i	−0.168932	+	0.0975327i
$453$	1.26493	+	5.67443i	0.0594317	+	0.266608i
$454$	5.02371	−	2.90044i	0.235775	−	0.136125i
$455$		0			0
$456$	1.10452	+	4.95484i	0.0517240	+	0.232032i
$457$	13.8286			0.646874			0.323437	−	0.946250i	$-0.395162\pi$
$457$	13.8286			0.646874			0.323437	+	0.946250i	$0.395162\pi$
$458$	−1.60260	+	2.77578i	−0.0748846	+	0.129704i
$459$	17.3287	−	2.34305i	0.808834	−	0.109364i
$460$	−15.1174	+	8.72803i	−0.704852	+	0.406947i
$461$	−6.16989	+	10.6866i	−0.287360	+	0.497723i	−0.973179	−	0.230050i	$-0.926111\pi$
$461$	−6.16989	+	10.6866i	−0.287360	+	0.497723i	0.685818	+	0.727773i	$0.259444\pi$
$462$		0			0
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	0.975312	−	0.220830i	$-0.0708765\pi$
$463$	6.37802	+	11.0471i	0.296412	+	0.513401i	−0.678900	+	0.734230i	$0.737543\pi$
$464$	−12.8141	−	7.39825i	−0.594882	−	0.343455i
$465$	−1.69501	−	1.84546i	−0.0786044	−	0.0855811i
$466$	−3.05303	−	5.28801i	−0.141429	−	0.244962i
$467$	5.48999	+	9.50894i	0.254046	+	0.440021i	0.964636	−	0.263585i	$-0.0849051\pi$
$467$	5.48999	+	9.50894i	0.254046	+	0.440021i	−0.710590	+	0.703607i	$0.751572\pi$
$468$	13.4041	+	1.14123i	0.619607	+	0.0527532i
$469$		0			0
$470$	3.15730	+	1.82287i	0.145635	+	0.0840825i
$471$	−8.67025	+	27.6107i	−0.399504	+	1.27223i
$472$		−	5.39057i		−	0.248121i
$473$			16.0683i			0.738823i
$474$	−1.41485	+	4.50563i	−0.0649861	+	0.206950i
$475$	9.63396	+	5.56217i	0.442036	+	0.255210i
$476$		0			0
$477$	7.34829	+	15.6630i	0.336455	+	0.717160i
$478$	−4.01665	−	6.95704i	−0.183717	−	0.318208i
$479$	5.59729	+	9.69478i	0.255747	+	0.442966i	0.965098	−	0.261889i	$-0.0843454\pi$
$479$	5.59729	+	9.69478i	0.255747	+	0.442966i	−0.709351	+	0.704855i	$0.751012\pi$
$480$	11.9241	+	12.9824i	0.544258	+	0.592565i
$481$	−15.8043	−	9.12464i	−0.720616	−	0.416048i
$482$	−3.13352	−	5.42741i	−0.142728	−	0.247212i
$483$		0			0
$484$	4.00191	−	6.93152i	0.181905	−	0.315069i
$485$	15.2645	−	8.81298i	0.693126	−	0.400177i
$486$	4.57537	−	0.226492i	0.207543	−	0.0102739i
$487$	−1.48332	+	2.56919i	−0.0672158	+	0.116421i	−0.897675	−	0.440659i	$-0.854745\pi$
$487$	−1.48332	+	2.56919i	−0.0672158	+	0.116421i	0.830459	+	0.557080i	$0.188078\pi$
$488$	−1.84037			−0.0833097
$489$	9.54666	+	42.8259i	0.431715	+	1.93665i
$490$		0			0
$491$	−20.1795	+	11.6507i	−0.910690	+	0.525787i	−0.880653	−	0.473762i	$-0.842896\pi$
$491$	−20.1795	+	11.6507i	−0.910690	+	0.525787i	−0.0300367	+	0.999549i	$0.509562\pi$
$492$	−4.51070	−	20.2348i	−0.203358	−	0.912256i
$493$	−12.3586	+	7.13524i	−0.556603	+	0.321355i
$494$	1.51976	+	0.877435i	0.0683773	+	0.0394776i
$495$	20.4501	−	29.3511i	0.919162	−	1.31923i
$496$			1.64952i			0.0740654i
$497$		0			0
$498$	3.78301	+	4.11878i	0.169521	+	0.184567i
$499$	2.29296	−	3.97152i	0.102647	−	0.177790i	−0.810127	−	0.586254i	$-0.800602\pi$
$499$	2.29296	−	3.97152i	0.102647	−	0.177790i	0.912774	+	0.408464i	$0.133935\pi$
$500$	−3.71723			−0.166240
$501$	−0.660121	−	2.96127i	−0.0294920	−	0.132300i
$502$		−	7.85751i		−	0.350698i
$503$	23.1383			1.03169			0.515844	−	0.856683i	$-0.327479\pi$
$503$	23.1383			1.03169			0.515844	+	0.856683i	$0.327479\pi$
$504$		0			0
$505$	52.5081			2.33658
$506$			3.41313i			0.151732i
$507$	−9.57875	+	8.79787i	−0.425407	+	0.390727i
$508$	5.26039			0.233392
$509$	−4.82853	+	8.36326i	−0.214021	+	0.370695i	−0.952969	−	0.303067i	$-0.901989\pi$
$509$	−4.82853	+	8.36326i	−0.214021	+	0.370695i	0.738948	+	0.673762i	$0.235323\pi$
$510$	5.11637	−	1.14053i	0.226557	−	0.0505036i
$511$		0			0
$512$		−	19.6301i		−	0.867536i
$513$	−12.2515	−	5.02459i	−0.540915	−	0.221841i
$514$	−0.776931	−	0.448561i	−0.0342690	−	0.0197852i
$515$	26.0252	−	15.0257i	1.14681	−	0.662110i
$516$	10.0667	−	9.24604i	0.443161	−	0.407034i
$517$	−13.6796	+	7.89791i	−0.601627	+	0.347350i
$518$		0			0
$519$	−39.5384	−	12.4158i	−1.73555	−	0.544992i
$520$	8.24748			0.361676
$521$	−5.00035	+	8.66086i	−0.219069	+	0.379439i	−0.954524	−	0.298135i	$-0.903635\pi$
$521$	−5.00035	+	8.66086i	−0.219069	+	0.379439i	0.735454	+	0.677574i	$0.236969\pi$
$522$	−3.38453	+	1.58785i	−0.148137	+	0.0694983i
$523$	10.7796	−	6.22361i	0.471359	−	0.272139i	−0.245449	−	0.969409i	$-0.578935\pi$
$523$	10.7796	−	6.22361i	0.471359	−	0.272139i	0.716809	+	0.697270i	$0.245602\pi$
$524$	7.15531	−	12.3934i	0.312581	−	0.541406i
$525$		0			0
$526$	−2.38289	−	4.12729i	−0.103899	−	0.179959i
$527$	1.37774	+	0.795437i	0.0600152	+	0.0346498i
$528$	−22.9848	+	5.12372i	−1.00028	+	0.222981i
$529$	−7.05755	−	12.2240i	−0.306850	−	0.531480i
$530$	2.59320	+	4.49156i	0.112641	+	0.195101i
$531$	11.5370	+	8.03826i	0.500662	+	0.348831i
$532$		0			0
$533$	−12.6930	−	7.32833i	−0.549797	−	0.317425i
$534$	2.14468	−	0.478089i	0.0928095	−	0.0206889i
$535$		−	10.6188i		−	0.459091i
$536$		−	1.81217i		−	0.0782737i
$537$	29.7445	+	32.3845i	1.28357	+	1.39750i
$538$	0.154356	+	0.0891175i	0.00665476	+	0.00384213i
$539$		0			0
$540$	−30.1556	+	4.07740i	−1.29769	+	0.175463i
$541$	6.96514	+	12.0640i	0.299455	+	0.518671i	0.976011	−	0.217720i	$-0.0698619\pi$
$541$	6.96514	+	12.0640i	0.299455	+	0.518671i	−0.676557	+	0.736391i	$0.736529\pi$
$542$	3.37547	+	5.84648i	0.144989	+	0.251128i
$543$	−11.6253	+	37.0212i	−0.498890	+	1.58873i
$544$	−9.69211	−	5.59574i	−0.415546	−	0.239916i
$545$	1.87003	+	3.23898i	0.0801032	+	0.138743i
$546$		0			0
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.138250	+	0.990397i	$0.544148\pi$
$547$	−21.6768	+	37.5454i	−0.926834	+	1.60532i	−0.788584	+	0.614926i	$0.789186\pi$
$548$	−20.2331	+	11.6816i	−0.864316	+	0.499013i
$549$	2.74431	−	3.93879i	0.117124	−	0.168103i
$550$	2.49923	−	4.32879i	0.106567	−	0.184580i
$551$	10.8065			0.460372
$552$	4.37309	−	4.01659i	0.186131	−	0.170957i
$553$		0			0
$554$	−3.38062	+	1.95180i	−0.143629	+	0.0829241i
$555$	39.3839	+	12.3673i	1.67176	+	0.524961i
$556$	22.1026	−	12.7610i	0.937361	−	0.541186i
$557$	−31.1339	−	17.9752i	−1.31919	−	0.761632i	−0.335588	−	0.942009i	$-0.608935\pi$
$557$	−31.1339	−	17.9752i	−1.31919	−	0.761632i	−0.983598	+	0.180377i	$0.942268\pi$
$558$	0.341952	+	0.238251i	0.0144760	+	0.0100860i
$559$		−	9.66329i		−	0.408714i
$560$		0			0
$561$	−6.80430	+	21.6685i	−0.287278	+	0.914846i
$562$	0.964340	−	1.67029i	0.0406782	−	0.0704568i
$563$	−6.11108			−0.257551			−0.128776	−	0.991674i	$-0.541105\pi$
$563$	−6.11108			−0.257551			−0.128776	+	0.991674i	$0.541105\pi$
$564$	12.8195	+	4.02554i	0.539797	+	0.169506i
$565$		−	6.63207i		−	0.279013i
$566$	−0.873481			−0.0367151
$567$		0			0
$568$	−15.6566			−0.656935
$569$			19.3045i			0.809285i	0.914475	+	0.404642i	$0.132604\pi$
$569$			19.3045i			0.809285i	−0.914475	+	0.404642i	$0.867396\pi$
$570$	−3.78720	−	1.18925i	−0.158628	−	0.0498121i
$571$	12.7224			0.532415			0.266207	−	0.963916i	$-0.414229\pi$
$571$	12.7224			0.532415			0.266207	+	0.963916i	$0.414229\pi$
$572$	−8.73631	+	15.1317i	−0.365284	+	0.632690i
$573$	2.22558	−	7.08745i	0.0929751	−	0.296083i
$574$		0			0
$575$		−	13.0118i		−	0.542628i
$576$	14.7720	+	10.2922i	0.615500	+	0.428843i
$577$	−7.05520	−	4.07332i	−0.293712	−	0.169575i	0.345903	−	0.938270i	$-0.387573\pi$
$577$	−7.05520	−	4.07332i	−0.293712	−	0.169575i	−0.639615	+	0.768696i	$0.720906\pi$
$578$	1.44429	−	0.833863i	0.0600747	−	0.0346841i
$579$	−38.5773	−	12.1140i	−1.60322	−	0.503439i
$580$	21.5066	−	12.4168i	0.893012	−	0.515581i
$581$		0			0
$582$	−2.15911	+	1.98309i	−0.0894979	+	0.0822019i
$583$	−22.4711			−0.930657
$584$	0.568693	−	0.985005i	0.0235327	−	0.0407598i
$585$	−12.2984	+	17.6514i	−0.508476	+	0.729795i
$586$	−1.54270	+	0.890680i	−0.0637285	+	0.0367937i
$587$	−12.3041	+	21.3113i	−0.507843	+	0.879610i	0.492116	+	0.870530i	$0.336224\pi$
$587$	−12.3041	+	21.3113i	−0.507843	+	0.879610i	−0.999959	+	0.00908019i	$0.997110\pi$
$588$		0			0
$589$	−0.602354	−	1.04331i	−0.0248196	−	0.0429888i
$590$	3.65043	+	2.10758i	0.150286	+	0.0867676i
$591$	−9.74571	+	31.0355i	−0.400885	+	1.27663i
$592$	−13.5872	−	23.5336i	−0.558429	−	0.967227i
$593$	18.9321	+	32.7913i	0.777447	+	1.34658i	0.933409	+	0.358814i	$0.116819\pi$
$593$	18.9321	+	32.7913i	0.777447	+	1.34658i	−0.155962	+	0.987763i	$0.549848\pi$
$594$	−2.25768	+	5.50490i	−0.0926338	+	0.225869i
$595$		0			0
$596$	−14.0428	−	8.10762i	−0.575216	−	0.332101i
$597$	5.31590	+	5.78773i	0.217565	+	0.236876i
$598$		−	2.05261i		−	0.0839375i
$599$		−	10.6529i		−	0.435268i	−0.976030	−	0.217634i	$-0.930166\pi$
$599$		−	10.6529i		−	0.435268i	0.976030	−	0.217634i	$-0.0698339\pi$
$600$	−8.48740	+	1.89199i	−0.346497	+	0.0772404i
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.985250	−	0.171122i	$-0.945261\pi$
$601$	−39.8636	−	23.0153i	−1.62607	−	0.938812i	−0.640821	−	0.767691i	$-0.721406\pi$
$602$		0			0
$603$	3.87843	+	2.70225i	0.157942	+	0.110044i
$604$	3.21161	+	5.56267i	0.130679	+	0.226342i
$605$	6.39981	+	11.0848i	0.260189	+	0.450661i
$606$	−8.52414	+	1.90019i	−0.346270	+	0.0771897i
$607$	−3.74063	−	2.15965i	−0.151827	−	0.0876576i	0.422162	−	0.906521i	$-0.361271\pi$
$607$	−3.74063	−	2.15965i	−0.151827	−	0.0876576i	−0.573989	+	0.818863i	$0.694605\pi$
$608$	4.23745	+	7.33947i	0.171851	+	0.297655i
$609$		0			0
$610$	0.719539	−	1.24628i	0.0291333	−	0.0504603i
$611$	8.22672	−	4.74970i	0.332818	−	0.192152i
$612$	17.4905	−	8.20565i	0.707011	−	0.331694i
$613$	14.3838	−	24.9135i	0.580956	−	1.00624i	−0.414411	−	0.910090i	$-0.636012\pi$
$613$	14.3838	−	24.9135i	0.580956	−	1.00624i	0.995366	−	0.0961549i	$-0.0306544\pi$
$614$	6.34846			0.256203
$615$	31.6307	+	9.93259i	1.27547	+	0.400521i
$616$		0			0
$617$	0.935498	−	0.540110i	0.0376617	−	0.0217440i	−0.481051	−	0.876693i	$-0.659745\pi$
$617$	0.935498	−	0.540110i	0.0376617	−	0.0217440i	0.518713	+	0.854949i	$0.326411\pi$
$618$	−3.68117	+	3.38107i	−0.148078	+	0.136007i
$619$	6.57128	−	3.79393i	0.264122	−	0.152491i	−0.362091	−	0.932143i	$-0.617937\pi$
$619$	6.57128	−	3.79393i	0.264122	−	0.152491i	0.626214	+	0.779652i	$0.284604\pi$
$620$	−2.39755	−	1.38423i	−0.0962881	−	0.0555920i
$621$	2.07534	+	15.3488i	0.0832806	+	0.615925i
$622$			3.23944i			0.129890i
$623$		0			0
$624$	13.8227	−	3.08134i	0.553352	−	0.123352i
$625$	13.8854	−	24.0502i	0.555416	−	0.962010i
$626$	−3.98316			−0.159199
$627$	12.6667	−	11.6341i	0.505859	−	0.464620i
$628$			31.9741i			1.27591i
$629$	−26.2082			−1.04499
$630$		0			0
$631$	35.0387			1.39487			0.697435	−	0.716648i	$-0.254325\pi$
$631$	35.0387			1.39487			0.697435	+	0.716648i	$0.254325\pi$
$632$			10.6708i			0.424462i
$633$	−2.59388	−	11.6360i	−0.103098	−	0.462491i
$634$	−3.27786			−0.130181
$635$	−4.20618	+	7.28531i	−0.166917	+	0.289109i
$636$	12.9303	+	14.0780i	0.512719	+	0.558227i
$637$		0			0
$638$		−	4.85564i		−	0.192237i
$639$	23.3466	−	33.5084i	0.923578	−	1.32557i
$640$	22.3015	+	12.8758i	0.881544	+	0.508960i
$641$	26.9229	−	15.5439i	1.06339	−	0.613949i	0.137023	−	0.990568i	$-0.456247\pi$
$641$	26.9229	−	15.5439i	1.06339	−	0.613949i	0.926368	+	0.376619i	$0.122913\pi$
$642$	0.384277	+	1.72385i	0.0151662	+	0.0680350i
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	−0.519159	−	0.854678i	$-0.673755\pi$
$643$	−0.977928	+	0.564607i	−0.0385657	+	0.0222659i	0.480593	+	0.876944i	$0.340421\pi$
$644$		0			0
$645$	4.75591	+	21.3348i	0.187264	+	0.840057i
$646$	2.52021			0.0991564
$647$	13.5992	−	23.5545i	0.534640	−	0.926023i	−0.464541	−	0.885552i	$-0.653781\pi$
$647$	13.5992	−	23.5545i	0.534640	−	0.926023i	0.999181	−	0.0404713i	$-0.0128859\pi$
$648$	9.71005	−	3.58553i	0.381447	−	0.140853i
$649$	−15.8162	+	9.13148i	−0.620839	+	0.358442i
$650$	−1.50300	+	2.60328i	−0.0589526	+	0.102109i
$651$		0			0
$652$	24.2386	+	41.9824i	0.949256	+	1.64416i
$653$	−19.3030	−	11.1446i	−0.755384	−	0.436121i	0.0722517	−	0.997386i	$-0.476981\pi$
$653$	−19.3030	−	11.1446i	−0.755384	−	0.436121i	−0.827636	+	0.561265i	$0.810315\pi$
$654$	−0.420793	−	0.458141i	−0.0164543	−	0.0179147i
$655$	11.4427	+	19.8193i	0.447102	+	0.774404i
$656$	−10.9123	−	18.9007i	−0.426055	−	0.737949i
$657$	1.26011	+	2.68594i	0.0491614	+	0.104788i
$658$		0			0
$659$	−7.69208	−	4.44103i	−0.299641	−	0.172998i	0.342641	−	0.939467i	$-0.388679\pi$
$659$	−7.69208	−	4.44103i	−0.299641	−	0.172998i	−0.642282	+	0.766469i	$0.722012\pi$
$660$	11.8409	−	37.7078i	0.460907	−	1.46778i
$661$		−	19.3670i		−	0.753291i	−0.926358	−	0.376645i	$-0.877078\pi$
$661$		−	19.3670i		−	0.753291i	0.926358	−	0.376645i	$-0.122922\pi$
$662$			5.58945i			0.217240i
$663$	4.09202	−	13.0312i	0.158921	−	0.506089i
$664$	10.9434	+	6.31819i	0.424687	+	0.245193i
$665$		0			0
$666$	−6.84112	−	0.582451i	−0.265088	−	0.0225695i
$667$	−6.31999	−	10.9465i	−0.244711	−	0.423852i
$668$	−1.67602	−	2.90295i	−0.0648472	−	0.112319i
$669$	−7.53803	−	8.20709i	−0.291437	−	0.317304i
$670$	1.22718	+	0.708512i	0.0474101	+	0.0273722i
$671$	3.11754	+	5.39973i	0.120351	+	0.208454i
$672$		0			0
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	−0.551670	−	0.834062i	$-0.686009\pi$
$673$	11.5828	−	20.0620i	0.446484	−	0.773333i	0.998154	+	0.0607292i	$0.0193426\pi$
$674$	1.69310	−	0.977511i	0.0652157	−	0.0376523i
$675$	8.60689	−	20.9862i	0.331279	−	0.807757i
$676$	−7.18476	+	12.4444i	−0.276337	+	0.478630i
$677$	−3.12693			−0.120177			−0.0600887	−	0.998193i	$-0.519138\pi$
$677$	−3.12693			−0.120177			−0.0600887	+	0.998193i	$0.519138\pi$
$678$	0.240004	+	1.07665i	0.00921730	+	0.0413484i
$679$		0			0
$680$	10.2576	−	5.92220i	0.393359	−	0.227106i
$681$	7.43900	+	33.3710i	0.285063	+	1.27878i
$682$	−0.468786	+	0.270654i	−0.0179507	+	0.0103639i
$683$	−27.1966	−	15.7020i	−1.04065	−	0.600819i	−0.120632	−	0.992697i	$-0.538492\pi$
$683$	−27.1966	−	15.7020i	−1.04065	−	0.600819i	−0.920017	+	0.391878i	$0.871825\pi$
$684$	−14.5773	−	1.24111i	−0.557378	−	0.0474550i
$685$		−	37.3621i		−	1.42753i
$686$		0			0
$687$	−12.7790	−	13.9132i	−0.487549	−	0.530822i
$688$	7.19462	−	12.4614i	0.274292	−	0.475088i
$689$	13.5138			0.514835
$690$	1.01022	+	4.53179i	0.0384584	+	0.172522i
$691$			44.1739i			1.68045i	0.542235	+	0.840227i	$0.317578\pi$
$691$			44.1739i			1.68045i	−0.542235	+	0.840227i	$0.682422\pi$
$692$	−45.7868			−1.74055
$693$		0			0
$694$	7.83164			0.297285
$695$			40.8144i			1.54818i
$696$	−6.22132	+	5.71415i	−0.235819	+	0.216594i
$697$	−21.0488			−0.797280
$698$	3.48043	−	6.02828i	0.131736	−	0.228174i
$699$	35.1266	−	7.83036i	1.32861	−	0.296171i
$700$		0			0
$701$			9.69906i			0.366328i	0.983082	+	0.183164i	$0.0586340\pi$
$701$			9.69906i			0.366328i	−0.983082	+	0.183164i	$0.941366\pi$
$702$	1.35774	−	3.31058i	0.0512446	−	0.124950i
$703$	17.1876	+	9.92326i	0.648242	+	0.374263i
$704$	−20.2511	+	11.6920i	−0.763242	+	0.440658i
$705$	−15.8255	+	14.5354i	−0.596023	+	0.547434i
$706$	−1.16775	+	0.674202i	−0.0439490	+	0.0253739i
$707$		0			0
$708$	14.8217	+	4.65429i	0.557035	+	0.174919i
$709$	−1.09786			−0.0412311			−0.0206156	−	0.999787i	$-0.506563\pi$
$709$	−1.09786			−0.0412311			−0.0206156	+	0.999787i	$0.506563\pi$
$710$	6.12132	−	10.6024i	0.229729	−	0.397903i
$711$	−22.8378	−	15.9120i	−0.856485	−	0.596746i
$712$	4.29977	−	2.48247i	0.161141	−	0.0930346i
$713$	−0.704553	+	1.22032i	−0.0263857	+	0.0457014i
$714$		0			0
$715$	−13.9710	−	24.1985i	−0.522486	−	0.904972i
$716$	42.0728	+	24.2908i	1.57233	+	0.907788i
$717$	46.2135	−	10.3018i	1.72588	−	0.384729i
$718$	0.900826	+	1.56028i	0.0336185	+	0.0582290i
$719$	−11.3648	−	19.6844i	−0.423835	−	0.734103i	0.572476	−	0.819921i	$-0.305983\pi$
$719$	−11.3648	−	19.6844i	−0.423835	−	0.734103i	−0.996311	+	0.0858183i	$0.972650\pi$
$720$	−29.0016	+	13.6061i	−1.08083	+	0.507068i
$721$		0			0
$722$	3.18269	+	1.83753i	0.118448	+	0.0683858i
$723$	36.0527	−	8.03679i	1.34081	−	0.298891i
$724$			42.8718i			1.59332i
$725$			18.5110i			0.687482i
$726$	−1.44008	−	1.56790i	−0.0534465	−	0.0581903i
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	0.563129	−	0.826369i	$-0.309598\pi$
$727$	3.47919	+	2.00871i	0.129036	+	0.0744990i	−0.434093	+	0.900868i	$0.642931\pi$
$728$		0			0
$729$	−6.80552	+	26.1282i	−0.252056	+	0.967713i
$730$	0.444689	+	0.770224i	0.0164587	+	0.0285073i
$731$	−6.93885	−	12.0184i	−0.256643	−	0.444518i
$732$	1.58900	−	5.06022i	0.0587311	−	0.187031i
$733$	7.20188	+	4.15801i	0.266008	+	0.153580i	0.627072	−	0.778961i	$-0.284253\pi$
$733$	7.20188	+	4.15801i	0.266008	+	0.153580i	−0.361064	+	0.932541i	$0.617587\pi$
$734$	3.88296	+	6.72549i	0.143323	+	0.248242i
$735$		0			0
$736$	4.95640	−	8.58473i	0.182695	−	0.316437i
$737$	−5.31698	+	3.06976i	−0.195854	+	0.113076i
$738$	−5.49435	−	0.467788i	−0.202250	−	0.0172195i
$739$	−2.28507	+	3.95785i	−0.0840576	+	0.145592i	−0.904989	−	0.425434i	$-0.860121\pi$
$739$	−2.28507	+	3.95785i	−0.0840576	+	0.145592i	0.820932	+	0.571026i	$0.193455\pi$
$740$	45.6079			1.67658
$741$	−7.61759	+	6.99659i	−0.279839	+	0.257026i
$742$		0			0
$743$	1.51258	−	0.873286i	0.0554910	−	0.0320378i	−0.471998	−	0.881600i	$-0.656467\pi$
$743$	1.51258	−	0.873286i	0.0554910	−	0.0320378i	0.527489	+	0.849562i	$0.323134\pi$
$744$	0.898447	+	0.282128i	0.0329387	+	0.0103433i
$745$	22.4571	−	12.9656i	0.822764	−	0.475023i
$746$	5.11954	+	2.95577i	0.187440	+	0.108218i
$747$	−29.8408	+	13.9998i	−1.09182	+	0.512226i
$748$			25.0929i			0.917486i
$749$		0			0
$750$	−0.296215	+	0.943307i	−0.0108162	+	0.0344447i
$751$	−2.91647	+	5.05147i	−0.106423	+	0.184331i	−0.914319	−	0.404995i	$-0.867273\pi$
$751$	−2.91647	+	5.05147i	−0.106423	+	0.184331i	0.807895	+	0.589326i	$0.200607\pi$
$752$	14.1452			0.515822
$753$	44.1845	+	13.8747i	1.61017	+	0.505622i
$754$			2.92012i			0.106345i
$755$	−10.2719			−0.373834
$756$		0			0
$757$	−42.0967			−1.53003			−0.765015	−	0.644013i	$-0.777268\pi$
$757$	−42.0967			−1.53003			−0.765015	+	0.644013i	$0.777268\pi$
$758$			5.12982i			0.186323i
$759$	−19.1928	−	6.02686i	−0.696653	−	0.218761i
$760$	−8.96932			−0.325352
$761$	−0.293431	+	0.508238i	−0.0106369	+	0.0184236i	−0.871295	−	0.490760i	$-0.836719\pi$
$761$	−0.293431	+	0.508238i	−0.0106369	+	0.0184236i	0.860658	+	0.509184i	$0.170053\pi$
$762$	0.419185	−	1.33491i	0.0151855	−	0.0483586i
$763$		0			0
$764$		−	8.20750i		−	0.296937i
$765$	−2.62097	+	30.7844i	−0.0947615	+	1.11301i
$766$	−7.14208	−	4.12348i	−0.258054	−	0.148987i
$767$	9.51165	−	5.49155i	0.343446	−	0.198288i
$768$	15.7479	+	4.94511i	0.568253	+	0.178441i
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.645403	−	0.763843i	$-0.276690\pi$
$769$	45.1905	−	26.0907i	1.62961	−	0.940856i	0.984208	−	0.177014i	$-0.0566437\pi$
$770$		0			0
$771$	3.89426	−	3.57679i	0.140248	−	0.128815i
$772$	−44.6738			−1.60785
$773$	16.3906	−	28.3894i	0.589530	−	1.02110i	−0.404764	−	0.914421i	$-0.632646\pi$
$773$	16.3906	−	28.3894i	0.589530	−	1.02110i	0.994294	−	0.106674i	$-0.0340202\pi$
$774$	−1.54415	−	3.29137i	−0.0555032	−	0.118306i
$775$	1.78714	−	1.03180i	0.0641959	−	0.0370635i
$776$	−3.31206	+	5.73666i	−0.118896	+	0.205934i
$777$		0			0
$778$	5.03093	+	8.71383i	0.180368	+	0.312406i
$779$	13.8040	+	7.96973i	0.494579	+	0.285545i
$780$	−7.12097	+	22.6770i	−0.254972	+	0.811967i
$781$	26.5218	+	45.9371i	0.949024	+	1.64376i
$782$	−1.47390	−	2.55287i	−0.0527066	−	0.0912906i
$783$	−2.95246	−	21.8358i	−0.105512	−	0.780346i
$784$		0			0
$785$	−44.2821	−	25.5663i	−1.58050	−	0.912500i
$786$	−2.57483	−	2.80336i	−0.0918411	−	0.0999927i
$787$			40.9934i			1.46126i	0.682775	+	0.730628i	$0.260773\pi$
$787$			40.9934i			1.46126i	−0.682775	+	0.730628i	$0.739227\pi$
$788$			35.9402i			1.28032i
$789$	27.4164	−	6.11160i	0.976048	−	0.217579i
$790$	−7.22614	−	4.17201i	−0.257095	−	0.148434i
$791$		0			0
$792$	−1.14049	+	13.3955i	−0.0405256	+	0.475990i
$793$	−1.87485	−	3.24733i	−0.0665778	−	0.115316i
$794$	−1.91597	−	3.31856i	−0.0679954	−	0.117771i
$795$	−29.8361	+	6.65100i	−1.05818	+	0.235887i
$796$	7.51921	+	4.34122i	0.266511	+	0.153870i
$797$	17.0441	+	29.5213i	0.603734	+	1.04570i	0.992250	+	0.124256i	$0.0396544\pi$
$797$	17.0441	+	29.5213i	0.603734	+	1.04570i	−0.388516	+	0.921442i	$0.627012\pi$
$798$		0			0
$799$	6.82116	−	11.8146i	0.241315	−	0.417971i
$800$	−12.5722	+	7.25854i	−0.444493	+	0.256628i
$801$	−1.09866	+	12.9042i	−0.0388193	+	0.455949i
$802$	−2.69672	+	4.67086i	−0.0952245	+	0.164934i
$803$	−3.85340			−0.135984
$804$	4.98268	+	1.56465i	0.175725	+	0.0551809i
$805$		0			0
$806$	0.281922	−	0.162768i	0.00993027	−	0.00573324i
$807$	−0.773687	+	0.710615i	−0.0272351	+	0.0250148i
$808$	−17.0896	+	9.86670i	−0.601211	+	0.347109i
$809$	−6.01547	−	3.47304i	−0.211493	−	0.122105i	0.390512	−	0.920598i	$-0.372298\pi$
$809$	−6.01547	−	3.47304i	−0.211493	−	0.122105i	−0.602005	+	0.798492i	$0.705631\pi$
$810$	−1.36830	+	7.97738i	−0.0480773	+	0.280297i
$811$		−	39.8573i		−	1.39958i	−0.714350	−	0.699789i	$-0.753277\pi$
$811$		−	39.8573i		−	1.39958i	0.714350	−	0.699789i	$-0.246723\pi$
$812$		0			0
$813$	−38.8364	+	8.65734i	−1.36205	+	0.303626i
$814$	4.45878	−	7.72284i	0.156280	−	0.270685i
$815$	−77.5240			−2.71555
$816$	14.9790	−	13.7579i	0.524371	−	0.481623i
$817$			10.5091i			0.367665i
$818$	1.90071			0.0664566
$819$		0			0
$820$	36.6294			1.27915
$821$		−	42.1017i		−	1.46936i	−0.678414	−	0.734680i	$-0.737332\pi$
$821$		−	42.1017i		−	1.46936i	0.678414	−	0.734680i	$-0.262668\pi$
$822$	1.35208	+	6.06535i	0.0471591	+	0.211553i
$823$	32.6821			1.13923			0.569614	−	0.821913i	$-0.307093\pi$
$823$	32.6821			1.13923			0.569614	+	0.821913i	$0.307093\pi$
$824$	−5.64689	+	9.78070i	−0.196719	+	0.340727i
$825$	19.9286	+	21.6974i	0.693826	+	0.755408i
$826$		0			0
$827$			31.4399i			1.09327i	0.837370	+	0.546637i	$0.184092\pi$
$827$			31.4399i			1.09327i	−0.837370	+	0.546637i	$0.815908\pi$
$828$	7.26810	+	15.4921i	0.252584	+	0.538387i
$829$	−35.7122	−	20.6185i	−1.24034	−	0.716109i	−0.271174	−	0.962530i	$-0.587412\pi$
$829$	−35.7122	−	20.6185i	−1.24034	−	0.716109i	−0.969163	+	0.246421i	$0.920745\pi$
$830$	−8.55721	+	4.94051i	−0.297025	+	0.171488i
$831$	−5.00594	−	22.4564i	−0.173654	−	0.779005i
$832$	12.1788	−	7.03141i	0.422222	−	0.243770i
$833$		0			0
$834$	−1.47701	−	6.62578i	−0.0511446	−	0.229432i
$835$	5.36054			0.185509
$836$	9.50094	−	16.4561i	0.328597	−	0.569147i
$837$	−1.94355	+	1.50217i	−0.0671790	+	0.0519226i
$838$	−3.62173	+	2.09100i	−0.125110	+	0.0722326i
$839$	4.04385	−	7.00416i	0.139609	−	0.241810i	−0.787740	−	0.616009i	$-0.788749\pi$
$839$	4.04385	−	7.00416i	0.139609	−	0.241810i	0.927349	+	0.374198i	$0.122082\pi$
$840$		0			0
$841$	−5.50894	−	9.54177i	−0.189963	−	0.329026i
$842$	−7.72241	−	4.45853i	−0.266132	−	0.153651i
$843$	7.68956	+	8.37207i	0.264843	+	0.288349i
$844$	−6.58576	−	11.4069i	−0.226691	−	0.392641i
$845$	−11.4898	−	19.9009i	−0.395260	−	0.684611i
$846$	2.04309	−	2.93236i	0.0702429	−	0.100817i
$847$		0			0
$848$	17.4269	+	10.0615i	0.598444	+	0.345512i
$849$	1.54238	−	4.91177i	0.0529345	−	0.168572i
$850$			4.31700i			0.148072i
$851$		−	23.2138i		−	0.795759i
$852$	13.5181	−	43.0488i	0.463122	−	1.47483i
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	0.857910	−	0.513801i	$-0.171763\pi$
$853$	24.5887	+	14.1963i	0.841900	+	0.486071i	−0.0160098	+	0.999872i	$0.505096\pi$
$854$		0			0
$855$	13.3748	−	19.1963i	0.457408	−	0.656499i
$856$	1.99536	+	3.45606i	0.0682000	+	0.118126i
$857$	25.6587	+	44.4422i	0.876485	+	1.51812i	0.855172	+	0.518344i	$0.173451\pi$
$857$	25.6587	+	44.4422i	0.876485	+	1.51812i	0.0213132	+	0.999773i	$0.493215\pi$
$858$	3.14375	+	3.42278i	0.107326	+	0.116852i
$859$	−14.5234	−	8.38509i	−0.495532	−	0.286096i	0.231334	−	0.972874i	$-0.425691\pi$
$859$	−14.5234	−	8.38509i	−0.495532	−	0.286096i	−0.726867	+	0.686779i	$0.759024\pi$
$860$	12.0751	+	20.9146i	0.411756	+	0.713183i
$861$		0			0
$862$	−0.360816	+	0.624951i	−0.0122894	+	0.0212859i
$863$	−14.2380	+	8.22033i	−0.484668	+	0.279823i	−0.722360	−	0.691517i	$-0.756943\pi$
$863$	−14.2380	+	8.22033i	−0.484668	+	0.279823i	0.237692	+	0.971341i	$0.423609\pi$
$864$	13.6725	−	10.5675i	0.465149	−	0.359513i
$865$	36.6109	−	63.4119i	1.24481	−	2.15607i
$866$	−3.66000			−0.124372
$867$	2.13868	+	9.59401i	0.0726333	+	0.325830i
$868$		0			0
$869$	31.3086	−	18.0760i	1.06207	−	0.613188i
$870$	−1.43717	−	6.44710i	−0.0487248	−	0.218577i
$871$	3.19757	−	1.84612i	0.108345	−	0.0625532i
$872$	−1.21726	−	0.702787i	−0.0412217	−	0.0237994i
$873$	−7.33884	−	15.6429i	−0.248382	−	0.529431i
$874$			2.23226i			0.0755074i
$875$		0			0
$876$	2.21732	+	2.41413i	0.0749164	+	0.0815657i
$877$	−3.06175	+	5.30311i	−0.103388	+	0.179073i	−0.913078	−	0.407784i	$-0.866302\pi$
$877$	−3.06175	+	5.30311i	−0.103388	+	0.179073i	0.809690	+	0.586857i	$0.199635\pi$
$878$	−5.15154			−0.173856
$879$	−2.28440	−	10.2477i	−0.0770509	−	0.345647i
$880$		−	41.6074i		−	1.40258i
$881$	−41.3283			−1.39238			−0.696192	−	0.717855i	$-0.745124\pi$
$881$	−41.3283			−1.39238			−0.696192	+	0.717855i	$0.745124\pi$
$882$		0			0
$883$	24.2918			0.817483			0.408741	−	0.912650i	$-0.365968\pi$
$883$	24.2918			0.817483			0.408741	+	0.912650i	$0.365968\pi$
$884$		−	15.0905i		−	0.507549i
$885$	−18.2973	+	16.8056i	−0.615056	+	0.564915i
$886$	2.64619			0.0889005
$887$	−3.35036	+	5.80299i	−0.112494	+	0.194845i	−0.916775	−	0.399404i	$-0.869217\pi$
$887$	−3.35036	+	5.80299i	−0.112494	+	0.194845i	0.804281	+	0.594249i	$0.202551\pi$
$888$	−15.1421	+	3.37544i	−0.508134	+	0.113272i
$889$		0			0
$890$			3.88234i			0.130136i
$891$	−26.9687	−	22.4159i	−0.903485	−	0.750962i
$892$	−10.6624	−	6.15591i	−0.357002	−	0.206115i
$893$	−8.94675	+	5.16541i	−0.299392	+	0.172854i
$894$	−3.17647	+	2.91752i	−0.106237	+	0.0975764i
$895$	−67.2823	+	38.8455i	−2.24900	+	1.29846i
$896$		0			0
$897$	11.5423	+	3.62448i	0.385385	+	0.121018i
$898$	−9.05470			−0.302159
$899$	1.00232	−	1.73608i	0.0334294	−	0.0579014i
$900$	2.12596	−	24.9703i	0.0708653	−	0.832342i
$901$	16.8074	−	9.70376i	0.559936	−	0.323279i
$902$	3.58101	−	6.20249i	0.119235	−	0.206520i
$903$		0			0
$904$	1.24622	+	2.15852i	0.0414487	+	0.0717912i
$905$	−59.3747	−	34.2800i	−1.97368	−	1.13951i
$906$	1.66754	−	0.371725i	0.0554003	−	0.0123497i
$907$	−10.1494	−	17.5793i	−0.337005	−	0.583710i	0.646863	−	0.762606i	$-0.276081\pi$
$907$	−10.1494	−	17.5793i	−0.337005	−	0.583710i	−0.983868	+	0.178897i	$0.942747\pi$
$908$	18.8873	+	32.7138i	0.626798	+	1.08565i
$909$	4.36668	−	51.2884i	0.144834	−	1.70113i
$910$		0			0
$911$	−30.3982	−	17.5504i	−1.00714	−	0.581472i	−0.0967861	−	0.995305i	$-0.530856\pi$
$911$	−30.3982	−	17.5504i	−1.00714	−	0.581472i	−0.910353	+	0.413833i	$0.864190\pi$
$912$	−15.0325	+	3.35103i	−0.497777	+	0.110964i
$913$		−	42.8114i		−	1.41685i
$914$		−	4.06380i		−	0.134419i
$915$	5.73754	+	6.24679i	0.189677	+	0.206512i
$916$	−18.0756	−	10.4359i	−0.597233	−	0.344813i
$917$		0			0
$918$	−0.688551	−	5.09237i	−0.0227256	−	0.168073i
$919$	−16.9132	−	29.2946i	−0.557916	−	0.966339i	−0.997670	−	0.0682206i	$-0.978268\pi$
$919$	−16.9132	−	29.2946i	−0.557916	−	0.966339i	0.439754	−	0.898118i	$-0.355066\pi$
$920$	5.24555	+	9.08557i	0.172941	+	0.299542i
$921$	−11.2100	+	35.6988i	−0.369384	+	1.17631i
$922$	3.14046	+	1.81314i	0.103425	+	0.0597127i
$923$	−15.9499	−	27.6260i	−0.524996	−	0.909320i
$924$		0			0
$925$	−16.9981	+	29.4415i	−0.558893	+	0.968031i
$926$	3.24639	−	1.87431i	0.106683	−	0.0615935i
$927$	−12.5123	−	26.6703i	−0.410959	−	0.875967i
$928$	−7.05115	+	12.2130i	−0.231465	+	0.400910i
$929$	−32.1171			−1.05373			−0.526864	−	0.849950i	$-0.676632\pi$
$929$	−32.1171			−1.05373			−0.526864	+	0.849950i	$0.676632\pi$
$930$	−0.542324	+	0.498113i	−0.0177835	+	0.0163338i
$931$		0			0
$932$	34.4348	−	19.8810i	1.12795	−	0.651222i
$933$	−18.2161	−	5.72018i	−0.596369	−	0.187270i
$934$	2.79439	−	1.61334i	0.0914351	−	0.0527901i
$935$	−34.7520	−	20.0641i	−1.13651	−	0.656166i
$936$	0.685877	−	8.05590i	0.0224186	−	0.263315i
$937$			13.9224i			0.454824i	0.973799	+	0.227412i	$0.0730263\pi$
$937$			13.9224i			0.454824i	−0.973799	+	0.227412i	$0.926974\pi$
$938$		0			0
$939$	7.03343	−	22.3982i	0.229527	−	0.730938i
$940$	−11.8703	+	20.5599i	−0.387166	+	0.670590i
$941$	−57.2094			−1.86497			−0.932487	−	0.361203i	$-0.882366\pi$
$941$	−57.2094			−1.86497			−0.932487	+	0.361203i	$0.882366\pi$
$942$	8.11394	+	2.54792i	0.264367	+	0.0830157i
$943$		−	18.6438i		−	0.607127i
$944$	16.3545			0.532294
$945$		0			0
$946$	4.72200			0.153525
$947$			34.4861i			1.12065i	0.828274	+	0.560324i	$0.189323\pi$
$947$			34.4861i			1.12065i	−0.828274	+	0.560324i	$0.810677\pi$
$948$	−29.3401	−	9.21330i	−0.952922	−	0.299234i
$949$	2.31739			0.0752255
$950$	1.63455	−	2.83113i	0.0530318	−	0.0918538i
$951$	5.78802	−	18.4321i	0.187689	−	0.597703i
$952$		0			0
$953$		−	2.58761i		−	0.0838209i	−0.999121	−	0.0419104i	$-0.986656\pi$
$953$		−	2.58761i		−	0.0838209i	0.999121	−	0.0419104i	$-0.0133444\pi$
$954$	4.60288	−	2.15944i	0.149024	−	0.0699144i
$955$	11.3669	+	6.56267i	0.367824	+	0.212363i
$956$	45.3034	−	26.1559i	1.46522	−	0.845943i
$957$	27.3043	+	8.57404i	0.882624	+	0.277159i
$958$	2.84900	−	1.64487i	0.0920470	−	0.0531434i
$959$		0			0
$960$	−23.4279	+	21.5180i	−0.756132	+	0.694491i
$961$	30.7765			0.992791
$962$	−2.68145	+	4.64441i	−0.0864535	+	0.149742i
$963$	−10.3721	−	0.883081i	−0.334238	−	0.0284569i
$964$	35.3426	−	20.4051i	1.13831	−	0.657203i
$965$	35.7209	−	61.8704i	1.14990	−	1.99168i
$966$		0			0
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	0.907457	−	0.420145i	$-0.138021\pi$
$967$	2.79472	+	4.84059i	0.0898721	+	0.155663i	−0.817585	+	0.575808i	$0.804688\pi$
$968$	−4.16585	−	2.40515i	−0.133895	−	0.0773045i
$969$	−4.45016	+	14.1717i	−0.142960	+	0.455260i
$970$	−2.58986	−	4.48578i	−0.0831555	−	0.144030i
$971$	−8.01661	−	13.8852i	−0.257265	−	0.445597i	0.708243	−	0.705969i	$-0.249488\pi$
$971$	−8.01661	−	13.8852i	−0.257265	−	0.445597i	−0.965508	+	0.260372i	$0.916155\pi$
$972$	1.47489	+	29.7942i	0.0473071	+	0.955650i
$973$		0			0
$974$	0.755007	+	0.435904i	0.0241920	+	0.0139673i
$975$	−11.9848	−	13.0486i	−0.383821	−	0.417888i
$976$		−	5.58353i		−	0.178724i
$977$			43.9026i			1.40457i	0.711896	+	0.702285i	$0.247837\pi$
$977$			43.9026i			1.40457i	−0.711896	+	0.702285i	$0.752163\pi$
$978$	12.5852	−	2.80547i	0.402431	−	0.0897091i
$979$	−14.5674	−	8.41048i	−0.465576	−	0.268800i
$980$		0			0
$981$	3.31926	−	1.55723i	0.105976	−	0.0497185i
$982$	3.42377	+	5.93015i	0.109257	+	0.189239i
$983$	9.08808	+	15.7410i	0.289865	+	0.502061i	0.973777	−	0.227503i	$-0.0730563\pi$
$983$	9.08808	+	15.7410i	0.289865	+	0.502061i	−0.683912	+	0.729564i	$0.739723\pi$
$984$	−12.1611	+	2.71094i	−0.387683	+	0.0864215i
$985$	−49.7749	−	28.7376i	−1.58596	−	0.915655i
$986$	2.09683	+	3.63181i	0.0667766	+	0.115660i
$987$		0			0
$988$	−5.71374	+	9.89649i	−0.181778	+	0.314849i
$989$	10.6453	−	6.14604i	0.338499	−	0.195433i
$990$	−8.62540	−	6.00965i	−0.274133	−	0.190999i
$991$	−23.8146	+	41.2481i	−0.756496	+	1.31029i	0.188131	+	0.982144i	$0.439757\pi$
$991$	−23.8146	+	41.2481i	−0.756496	+	1.31029i	−0.944627	+	0.328145i	$0.893576\pi$
$992$	1.57213			0.0499151
$993$	−31.4307	−	9.86979i	−0.997423	−	0.313208i
$994$		0			0
$995$	−12.0246	+	6.94242i	−0.381206	+	0.220090i
$996$	−26.8210	+	24.6345i	−0.849856	+	0.780574i
$997$	−28.4838	+	16.4451i	−0.902090	+	0.520822i	−0.877878	−	0.478885i	$-0.841041\pi$
$997$	−28.4838	+	16.4451i	−0.902090	+	0.520822i	−0.0242120	+	0.999707i	$0.507708\pi$
$998$	−1.16711	−	0.673830i	−0.0369442	−	0.0213297i
$999$	15.3552	−	37.4406i	0.485818	−	1.18457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.i.b.227.3		10
3.2	odd	2		1323.2.i.b.521.3		10
7.2	even	3		63.2.s.b.47.3	yes	10
7.3	odd	6		441.2.o.d.146.3		10
7.4	even	3		441.2.o.c.146.3		10
7.5	odd	6		441.2.s.b.362.3		10
7.6	odd	2		63.2.i.b.38.3	yes	10
9.4	even	3		1323.2.s.b.962.3		10
9.5	odd	6		441.2.s.b.374.3		10
21.2	odd	6		189.2.s.b.89.3		10
21.5	even	6		1323.2.s.b.656.3		10
21.11	odd	6		1323.2.o.d.440.3		10
21.17	even	6		1323.2.o.c.440.3		10
21.20	even	2		189.2.i.b.143.3		10
28.23	odd	6		1008.2.df.b.929.5		10
28.27	even	2		1008.2.ca.b.353.4		10
63.2	odd	6		567.2.p.d.404.3		10
63.4	even	3		1323.2.o.c.881.3		10
63.5	even	6	inner	441.2.i.b.68.3		10
63.13	odd	6		189.2.s.b.17.3		10
63.16	even	3		567.2.p.c.404.3		10
63.20	even	6		567.2.p.c.80.3		10
63.23	odd	6		63.2.i.b.5.3	✓	10
63.31	odd	6		1323.2.o.d.881.3		10
63.32	odd	6		441.2.o.d.293.3		10
63.34	odd	6		567.2.p.d.80.3		10
63.40	odd	6		1323.2.i.b.1097.3		10
63.41	even	6		63.2.s.b.59.3	yes	10
63.58	even	3		189.2.i.b.152.3		10
63.59	even	6		441.2.o.c.293.3		10
84.23	even	6		3024.2.df.b.1601.1		10
84.83	odd	2		3024.2.ca.b.2033.1		10
252.23	even	6		1008.2.ca.b.257.4		10
252.139	even	6		3024.2.df.b.17.1		10
252.167	odd	6		1008.2.df.b.689.5		10
252.247	odd	6		3024.2.ca.b.2609.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.i.b.5.3	✓	10	63.23	odd	6
63.2.i.b.38.3	yes	10	7.6	odd	2
63.2.s.b.47.3	yes	10	7.2	even	3
63.2.s.b.59.3	yes	10	63.41	even	6
189.2.i.b.143.3		10	21.20	even	2
189.2.i.b.152.3		10	63.58	even	3
189.2.s.b.17.3		10	63.13	odd	6
189.2.s.b.89.3		10	21.2	odd	6
441.2.i.b.68.3		10	63.5	even	6	inner
441.2.i.b.227.3		10	1.1	even	1	trivial
441.2.o.c.146.3		10	7.4	even	3
441.2.o.c.293.3		10	63.59	even	6
441.2.o.d.146.3		10	7.3	odd	6
441.2.o.d.293.3		10	63.32	odd	6
441.2.s.b.362.3		10	7.5	odd	6
441.2.s.b.374.3		10	9.5	odd	6
567.2.p.c.80.3		10	63.20	even	6
567.2.p.c.404.3		10	63.16	even	3
567.2.p.d.80.3		10	63.34	odd	6
567.2.p.d.404.3		10	63.2	odd	6
1008.2.ca.b.257.4		10	252.23	even	6
1008.2.ca.b.353.4		10	28.27	even	2
1008.2.df.b.689.5		10	252.167	odd	6
1008.2.df.b.929.5		10	28.23	odd	6
1323.2.i.b.521.3		10	3.2	odd	2
1323.2.i.b.1097.3		10	63.40	odd	6
1323.2.o.c.440.3		10	21.17	even	6
1323.2.o.c.881.3		10	63.4	even	3
1323.2.o.d.440.3		10	21.11	odd	6
1323.2.o.d.881.3		10	63.31	odd	6
1323.2.s.b.656.3		10	21.5	even	6
1323.2.s.b.962.3		10	9.4	even	3
3024.2.ca.b.2033.1		10	84.83	odd	2
3024.2.ca.b.2609.1		10	252.247	odd	6
3024.2.df.b.17.1		10	252.139	even	6
3024.2.df.b.1601.1		10	84.23	even	6

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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.293869i q^{2} +(1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(0.152492 - 0.485617i) q^{6} -1.15010i q^{8} +(2.46146 + 1.71499i) q^{9} +O(q^{10})\)	\(q-0.293869i q^{2} +(1.65249 + 0.518912i) q^{3} +1.91364 q^{4} +(-1.53014 + 2.65027i) q^{5} +(0.152492 - 0.485617i) q^{6} -1.15010i q^{8} +(2.46146 + 1.71499i) q^{9} +(0.778834 + 0.449660i) q^{10} +(-3.37445 + 1.94824i) q^{11} +(3.16228 + 0.993010i) q^{12} +(2.02935 - 1.17164i) q^{13} +(-3.90379 + 3.58555i) q^{15} +3.48930 q^{16} +(1.68263 - 2.91440i) q^{17} +(0.503985 - 0.723348i) q^{18} +(-2.20696 + 1.27419i) q^{19} +(-2.92813 + 5.07167i) q^{20} +(0.572527 + 0.991647i) q^{22} +(2.58141 + 1.49038i) q^{23} +(0.596800 - 1.90053i) q^{24} +(-2.18263 - 3.78042i) q^{25} +(-0.344311 - 0.596363i) q^{26} +(3.17762 + 4.11130i) q^{27} +(-3.67241 - 2.12027i) q^{29} +(1.05368 + 1.14721i) q^{30} +0.472735i q^{31} -3.32560i q^{32} +(-6.58721 + 1.46841i) q^{33} +(-0.856452 - 0.494473i) q^{34} +(4.71035 + 3.28188i) q^{36} +(-3.89395 - 6.74451i) q^{37} +(0.374446 + 0.648559i) q^{38} +(3.96146 - 0.883081i) q^{39} +(3.04808 + 1.75981i) q^{40} +(-3.12737 - 5.41676i) q^{41} +(2.06191 - 3.57133i) q^{43} +(-6.45748 + 3.72823i) q^{44} +(-8.31157 + 3.89937i) q^{45} +(0.437976 - 0.758597i) q^{46} +4.05388 q^{47} +(5.76605 + 1.81064i) q^{48} +(-1.11095 + 0.641408i) q^{50} +(4.29284 - 3.94288i) q^{51} +(3.88344 - 2.24211i) q^{52} +(4.99439 + 2.88351i) q^{53} +(1.20818 - 0.933804i) q^{54} -11.9243i q^{55} +(-4.30818 + 0.960372i) q^{57} +(-0.623082 + 1.07921i) q^{58} +4.68705 q^{59} +(-7.47046 + 6.86145i) q^{60} -1.60018i q^{61} +0.138922 q^{62} +6.00131 q^{64} +7.17110i q^{65} +(0.431520 + 1.93578i) q^{66} +1.57566 q^{67} +(3.21994 - 5.57711i) q^{68} +(3.49238 + 3.80236i) q^{69} -13.6132i q^{71} +(1.97241 - 2.83093i) q^{72} +(0.856452 + 0.494473i) q^{73} +(-1.98201 + 1.14431i) q^{74} +(-1.64507 - 7.37971i) q^{75} +(-4.22333 + 2.43834i) q^{76} +(-0.259511 - 1.16415i) q^{78} -9.27815 q^{79} +(-5.33910 + 9.24760i) q^{80} +(3.11759 + 8.44279i) q^{81} +(-1.59182 + 0.919038i) q^{82} +(-5.49361 + 9.51520i) q^{83} +(5.14930 + 8.91884i) q^{85} +(-1.04950 - 0.605932i) q^{86} +(-4.96840 - 5.40938i) q^{87} +(2.24067 + 3.88095i) q^{88} +(2.15849 + 3.73861i) q^{89} +(1.14591 + 2.44252i) q^{90} +(4.93989 + 2.85205i) q^{92} +(-0.245308 + 0.781191i) q^{93} -1.19131i q^{94} -7.79874i q^{95} +(1.72569 - 5.49553i) q^{96} +(-4.98797 - 2.87980i) q^{97} +(-11.6473 - 0.991647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9}+O(q^{10}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9	\( 10 q + 3 q^{3} - 8 q^{4} - 12 q^{6} + 3 q^{9} + 15 q^{10} - 12 q^{11} + 12 q^{12} + 6 q^{13} - 3 q^{15} + 12 q^{16} - 12 q^{17} + 24 q^{18} - 3 q^{19} - 3 q^{20} + 5 q^{22} - 15 q^{23} + 7 q^{25} + 3 q^{26} + 27 q^{27} - 15 q^{29} + 6 q^{30} + 3 q^{34} - 18 q^{36} + 6 q^{37} - 18 q^{38} + 18 q^{39} - 15 q^{40} - 9 q^{41} + 3 q^{43} - 24 q^{44} - 30 q^{45} - 13 q^{46} - 30 q^{47} - 15 q^{48} + 3 q^{50} + 21 q^{51} + 12 q^{52} + 9 q^{53} - 9 q^{54} - 36 q^{57} + 8 q^{58} + 36 q^{59} - 48 q^{60} + 12 q^{62} + 6 q^{64} + 39 q^{66} + 20 q^{67} + 27 q^{68} - 3 q^{69} - 30 q^{72} - 3 q^{73} - 30 q^{74} - 6 q^{75} + 9 q^{76} + 24 q^{78} - 40 q^{79} - 30 q^{80} + 15 q^{81} - 9 q^{82} - 15 q^{83} + 18 q^{85} + 54 q^{86} - 6 q^{87} - 8 q^{88} + 24 q^{89} + 24 q^{90} + 39 q^{92} + 36 q^{93} - 33 q^{96} + 6 q^{97} + 21 q^{99}+O(q^{100}) \) 10 * q + 3 * q^3 - 8 * q^4 - 12 * q^6 + 3 * q^9 + 15 * q^10 - 12 * q^11 + 12 * q^12 + 6 * q^13 - 3 * q^15 + 12 * q^16 - 12 * q^17 + 24 * q^18 - 3 * q^19 - 3 * q^20 + 5 * q^22 - 15 * q^23 + 7 * q^25 + 3 * q^26 + 27 * q^27 - 15 * q^29 + 6 * q^30 + 3 * q^34 - 18 * q^36 + 6 * q^37 - 18 * q^38 + 18 * q^39 - 15 * q^40 - 9 * q^41 + 3 * q^43 - 24 * q^44 - 30 * q^45 - 13 * q^46 - 30 * q^47 - 15 * q^48 + 3 * q^50 + 21 * q^51 + 12 * q^52 + 9 * q^53 - 9 * q^54 - 36 * q^57 + 8 * q^58 + 36 * q^59 - 48 * q^60 + 12 * q^62 + 6 * q^64 + 39 * q^66 + 20 * q^67 + 27 * q^68 - 3 * q^69 - 30 * q^72 - 3 * q^73 - 30 * q^74 - 6 * q^75 + 9 * q^76 + 24 * q^78 - 40 * q^79 - 30 * q^80 + 15 * q^81 - 9 * q^82 - 15 * q^83 + 18 * q^85 + 54 * q^86 - 6 * q^87 - 8 * q^88 + 24 * q^89 + 24 * q^90 + 39 * q^92 + 36 * q^93 - 33 * q^96 + 6 * q^97 + 21 * q^99

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