LMFDB - Embedded newform 322.2.g.b.45.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [322,2,Mod(45,322)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("322.45"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(322, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.g (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 12x^{14} + 73x^{12} + 312x^{10} + 1045x^{8} + 2808x^{6} + 5913x^{4} + 8748x^{2} + 6561 $ x^16 + 12x^14 + 73x^12 + 312x^10 + 1045x^8 + 2808x^6 + 5913x^4 + 8748*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			45.6
Root			$-1.36749 + 1.06300i$ of defining polynomial
Character	$\chi$	$=$	322.45
Dual form			322.2.g.b.229.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.0922753 + 0.0532752i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.78715 + 3.09543i) q^{5} +0.106550i q^{6} +(0.672033 + 2.55898i) q^{7} -1.00000 q^{8} +(-1.49432 - 2.58824i) q^{9} +(-1.78715 + 3.09543i) q^{10} +(-2.00891 - 1.15985i) q^{11} +(-0.0922753 + 0.0532752i) q^{12} -1.89279i q^{13} +(-1.88012 + 1.86149i) q^{14} +0.380843i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.602480 - 1.04353i) q^{17} +(1.49432 - 2.58824i) q^{18} +(1.42152 + 2.46214i) q^{19} -3.57430 q^{20} +(-0.0743180 + 0.271933i) q^{21} -2.31969i q^{22} +(2.14111 + 4.29134i) q^{23} +(-0.0922753 - 0.0532752i) q^{24} +(-3.88781 + 6.73388i) q^{25} +(1.63920 - 0.946394i) q^{26} -0.638093i q^{27} +(-2.55216 - 0.697491i) q^{28} +3.48008 q^{29} +(-0.329820 + 0.190421i) q^{30} +(2.40205 + 1.38682i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.123582 - 0.214050i) q^{33} +1.20496 q^{34} +(-6.72013 + 6.65351i) q^{35} +2.98865 q^{36} +(4.48318 - 2.58836i) q^{37} +(-1.42152 + 2.46214i) q^{38} +(0.100839 - 0.174658i) q^{39} +(-1.78715 - 3.09543i) q^{40} -11.1173i q^{41} +(-0.272660 + 0.0716054i) q^{42} +2.46789i q^{43} +(2.00891 - 1.15985i) q^{44} +(5.34116 - 9.25116i) q^{45} +(-2.64586 + 3.99993i) q^{46} +(10.1165 - 5.84076i) q^{47} -0.106550i q^{48} +(-6.09674 + 3.43944i) q^{49} -7.77562 q^{50} +(0.111188 - 0.0641944i) q^{51} +(1.63920 + 0.946394i) q^{52} +(-7.58334 - 4.37825i) q^{53} +(0.552604 - 0.319046i) q^{54} -8.29127i q^{55} +(-0.672033 - 2.55898i) q^{56} +0.302926i q^{57} +(1.74004 + 3.01384i) q^{58} +(-4.57525 - 2.64152i) q^{59} +(-0.329820 - 0.190421i) q^{60} +(-2.78587 - 4.82527i) q^{61} +2.77365i q^{62} +(5.61903 - 5.56333i) q^{63} +1.00000 q^{64} +(5.85900 - 3.38270i) q^{65} +(0.123582 - 0.214050i) q^{66} +(10.2210 + 5.90111i) q^{67} +(0.602480 + 1.04353i) q^{68} +(-0.0310501 + 0.510053i) q^{69} +(-9.12217 - 2.49304i) q^{70} +0.295533 q^{71} +(1.49432 + 2.58824i) q^{72} +(3.87636 + 2.23802i) q^{73} +(4.48318 + 2.58836i) q^{74} +(-0.717498 + 0.414247i) q^{75} -2.84303 q^{76} +(1.61797 - 5.92022i) q^{77} +0.201677 q^{78} +(-8.15403 + 4.70773i) q^{79} +(1.78715 - 3.09543i) q^{80} +(-4.44898 + 7.70585i) q^{81} +(9.62785 - 5.55864i) q^{82} -6.05170 q^{83} +(-0.198342 - 0.200328i) q^{84} +4.30689 q^{85} +(-2.13726 + 1.23395i) q^{86} +(0.321126 + 0.185402i) q^{87} +(2.00891 + 1.15985i) q^{88} +(-2.84347 - 4.92504i) q^{89} +10.6823 q^{90} +(4.84361 - 1.27202i) q^{91} +(-4.78697 - 0.291412i) q^{92} +(0.147767 + 0.255939i) q^{93} +(10.1165 + 5.84076i) q^{94} +(-5.08092 + 8.80042i) q^{95} +(0.0922753 - 0.0532752i) q^{96} +13.9847 q^{97} +(-6.02701 - 3.56022i) q^{98} +6.93274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46}+ \cdots - 6 q^{96}+O(q^{100}) $ 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9 + 6 * q^12 - 8 * q^16 - 10 * q^18 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.0922753	+	0.0532752i	0.0532752	+	0.0307584i	0.526401	−	0.850236i	$-0.323541\pi$
$3$	0.0922753	+	0.0532752i	0.0532752	+	0.0307584i	−0.473126	+	0.880995i	$0.656874\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.78715	+	3.09543i	0.799238	+	1.38432i	0.920113	+	0.391653i	$0.128096\pi$
$5$	1.78715	+	3.09543i	0.799238	+	1.38432i	−0.120876	+	0.992668i	$0.538570\pi$
$6$			0.106550i			0.0434990i
$7$	0.672033	+	2.55898i	0.254005	+	0.967203i
$7$	0.672033	+	2.55898i	0.254005	+	0.967203i
$8$	−1.00000			−0.353553
$9$	−1.49432	−	2.58824i	−0.498108	−	0.862748i
$10$	−1.78715	+	3.09543i	−0.565146	+	0.978862i
$11$	−2.00891	−	1.15985i	−0.605710	−	0.349707i	0.165575	−	0.986197i	$-0.447052\pi$
$11$	−2.00891	−	1.15985i	−0.605710	−	0.349707i	−0.771285	+	0.636490i	$0.780385\pi$
$12$	−0.0922753	+	0.0532752i	−0.0266376	+	0.0153792i
$13$		−	1.89279i		−	0.524965i	−0.964937	−	0.262483i	$-0.915459\pi$
$13$		−	1.89279i		−	0.524965i	0.964937	−	0.262483i	$-0.0845412\pi$
$14$	−1.88012	+	1.86149i	−0.502484	+	0.497503i
$15$			0.380843i			0.0983332i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.602480	−	1.04353i	0.146123	−	0.253092i	−0.783668	−	0.621179i	$-0.786654\pi$
$17$	0.602480	−	1.04353i	0.146123	−	0.253092i	0.929791	+	0.368087i	$0.119987\pi$
$18$	1.49432	−	2.58824i	0.352215	−	0.610055i
$19$	1.42152	+	2.46214i	0.326118	+	0.564853i	0.981738	−	0.190238i	$-0.0609260\pi$
$19$	1.42152	+	2.46214i	0.326118	+	0.564853i	−0.655620	+	0.755091i	$0.727593\pi$
$20$	−3.57430			−0.799238
$21$	−0.0743180	+	0.271933i	−0.0162175	+	0.0593407i
$22$		−	2.31969i		−	0.494560i
$23$	2.14111	+	4.29134i	0.446453	+	0.894807i
$23$	2.14111	+	4.29134i	0.446453	+	0.894807i
$24$	−0.0922753	−	0.0532752i	−0.0188356	−	0.0108748i
$25$	−3.88781	+	6.73388i	−0.777562	+	1.34678i
$26$	1.63920	−	0.946394i	0.321474	−	0.185603i
$27$		−	0.638093i		−	0.122801i
$28$	−2.55216	−	0.697491i	−0.482312	−	0.131813i
$29$	3.48008			0.646235			0.323118	−	0.946359i	$-0.395269\pi$
$29$	3.48008			0.646235			0.323118	+	0.946359i	$0.395269\pi$
$30$	−0.329820	+	0.190421i	−0.0602166	+	0.0347660i
$31$	2.40205	+	1.38682i	0.431421	+	0.249081i	0.699952	−	0.714190i	$-0.253205\pi$
$31$	2.40205	+	1.38682i	0.431421	+	0.249081i	−0.268531	+	0.963271i	$0.586538\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.123582	−	0.214050i	−0.0215129	−	0.0372614i
$34$	1.20496			0.206649
$35$	−6.72013	+	6.65351i	−1.13591	+	1.12465i
$36$	2.98865			0.498108
$37$	4.48318	−	2.58836i	0.737030	−	0.425524i	−0.0839585	−	0.996469i	$-0.526756\pi$
$37$	4.48318	−	2.58836i	0.737030	−	0.425524i	0.820988	+	0.570945i	$0.193423\pi$
$38$	−1.42152	+	2.46214i	−0.230600	+	0.399411i
$39$	0.100839	−	0.174658i	0.0161471	−	0.0279676i
$40$	−1.78715	−	3.09543i	−0.282573	−	0.489431i
$41$		−	11.1173i		−	1.73623i	−0.496365	−	0.868114i	$-0.665332\pi$
$41$		−	11.1173i		−	1.73623i	0.496365	−	0.868114i	$-0.334668\pi$
$42$	−0.272660	+	0.0716054i	−0.0420724	+	0.0110490i
$43$			2.46789i			0.376350i	0.982135	+	0.188175i	$0.0602573\pi$
$43$			2.46789i			0.376350i	−0.982135	+	0.188175i	$0.939743\pi$
$44$	2.00891	−	1.15985i	0.302855	−	0.174853i
$45$	5.34116	−	9.25116i	0.796213	−	1.37908i
$46$	−2.64586	+	3.99993i	−0.390110	+	0.589758i
$47$	10.1165	−	5.84076i	1.47564	−	0.851963i	0.476020	−	0.879434i	$-0.342079\pi$
$47$	10.1165	−	5.84076i	1.47564	−	0.851963i	0.999623	+	0.0274716i	$0.00874558\pi$
$48$		−	0.106550i		−	0.0153792i
$49$	−6.09674	+	3.43944i	−0.870963	+	0.491348i
$50$	−7.77562			−1.09964
$51$	0.111188	−	0.0641944i	0.0155694	−	0.00898902i
$52$	1.63920	+	0.946394i	0.227317	+	0.131241i
$53$	−7.58334	−	4.37825i	−1.04165	−	0.601398i	−0.121352	−	0.992610i	$-0.538723\pi$
$53$	−7.58334	−	4.37825i	−1.04165	−	0.601398i	−0.920301	+	0.391211i	$0.872056\pi$
$54$	0.552604	−	0.319046i	0.0751999	−	0.0434167i
$55$		−	8.29127i		−	1.11800i
$56$	−0.672033	−	2.55898i	−0.0898042	−	0.341958i
$57$			0.302926i			0.0401235i
$58$	1.74004	+	3.01384i	0.228479	+	0.395737i
$59$	−4.57525	−	2.64152i	−0.595646	−	0.343897i	0.171681	−	0.985153i	$-0.445080\pi$
$59$	−4.57525	−	2.64152i	−0.595646	−	0.343897i	−0.767327	+	0.641256i	$0.778414\pi$
$60$	−0.329820	−	0.190421i	−0.0425795	−	0.0245833i
$61$	−2.78587	−	4.82527i	−0.356694	−	0.617813i	0.630712	−	0.776017i	$-0.282763\pi$
$61$	−2.78587	−	4.82527i	−0.356694	−	0.617813i	−0.987406	+	0.158204i	$0.949430\pi$
$62$			2.77365i			0.352253i
$63$	5.61903	−	5.56333i	0.707931	−	0.700913i
$64$	1.00000			0.125000
$65$	5.85900	−	3.38270i	0.726720	−	0.419572i
$66$	0.123582	−	0.214050i	0.0152119	−	0.0263478i
$67$	10.2210	+	5.90111i	1.24870	+	0.720935i	0.970849	−	0.239690i	$-0.0770458\pi$
$67$	10.2210	+	5.90111i	1.24870	+	0.720935i	0.277847	+	0.960625i	$0.410379\pi$
$68$	0.602480	+	1.04353i	0.0730614	+	0.126546i
$69$	−0.0310501	+	0.510053i	−0.00373799	+	0.0614032i
$70$	−9.12217	−	2.49304i	−1.09031	−	0.297976i
$71$	0.295533			0.0350733			0.0175367	−	0.999846i	$-0.494418\pi$
$71$	0.295533			0.0350733			0.0175367	+	0.999846i	$0.494418\pi$
$72$	1.49432	+	2.58824i	0.176108	+	0.305028i
$73$	3.87636	+	2.23802i	0.453693	+	0.261940i	0.709389	−	0.704817i	$-0.248971\pi$
$73$	3.87636	+	2.23802i	0.453693	+	0.261940i	−0.255695	+	0.966757i	$0.582304\pi$
$74$	4.48318	+	2.58836i	0.521159	+	0.300891i
$75$	−0.717498	+	0.414247i	−0.0828495	+	0.0478332i
$76$	−2.84303			−0.326118
$77$	1.61797	−	5.92022i	0.184384	−	0.674672i
$78$	0.201677			0.0228355
$79$	−8.15403	+	4.70773i	−0.917399	+	0.529661i	−0.882805	−	0.469741i	$-0.844347\pi$
$79$	−8.15403	+	4.70773i	−0.917399	+	0.529661i	−0.0345950	+	0.999401i	$0.511014\pi$
$80$	1.78715	−	3.09543i	0.199809	−	0.346080i
$81$	−4.44898	+	7.70585i	−0.494331	+	0.856206i
$82$	9.62785	−	5.55864i	1.06322	−	0.613849i
$83$	−6.05170			−0.664260			−0.332130	−	0.943234i	$-0.607767\pi$
$83$	−6.05170			−0.664260			−0.332130	+	0.943234i	$0.607767\pi$
$84$	−0.198342	−	0.200328i	−0.0216409	−	0.0218576i
$85$	4.30689			0.467147
$86$	−2.13726	+	1.23395i	−0.230467	+	0.133060i
$87$	0.321126	+	0.185402i	0.0344283	+	0.0198772i
$88$	2.00891	+	1.15985i	0.214151	+	0.123640i
$89$	−2.84347	−	4.92504i	−0.301408	−	0.522053i	0.675047	−	0.737774i	$-0.264123\pi$
$89$	−2.84347	−	4.92504i	−0.301408	−	0.522053i	−0.976455	+	0.215721i	$0.930790\pi$
$90$	10.6823			1.12602
$91$	4.84361	−	1.27202i	0.507748	−	0.133344i
$92$	−4.78697	−	0.291412i	−0.499076	−	0.0303819i
$93$	0.147767	+	0.255939i	0.0153227	+	0.0265396i
$94$	10.1165	+	5.84076i	1.04344	+	0.602429i
$95$	−5.08092	+	8.80042i	−0.521292	+	0.902904i
$96$	0.0922753	−	0.0532752i	0.00941781	−	0.00543738i
$97$	13.9847			1.41993			0.709964	−	0.704238i	$-0.248711\pi$
$97$	13.9847			1.41993			0.709964	+	0.704238i	$0.248711\pi$
$98$	−6.02701	−	3.56022i	−0.608820	−	0.359636i
$99$			6.93274i			0.696767i
$100$	−3.88781	−	6.73388i	−0.388781	−	0.673388i
$101$	9.15207	+	5.28395i	0.910665	+	0.525773i	0.880645	−	0.473776i	$-0.157110\pi$
$101$	9.15207	+	5.28395i	0.910665	+	0.525773i	0.0300201	+	0.999549i	$0.490443\pi$
$102$	0.111188	+	0.0641944i	0.0110093	+	0.00635620i
$103$	−5.92856	−	10.2686i	−0.584158	−	1.01179i	−0.994980	−	0.100076i	$-0.968091\pi$
$103$	−5.92856	−	10.2686i	−0.584158	−	1.01179i	0.410822	−	0.911716i	$-0.365242\pi$
$104$			1.89279i			0.185603i
$105$	−0.974569	+	0.255939i	−0.0951082	+	0.0249771i
$106$		−	8.75649i		−	0.850506i
$107$	−14.8519	+	8.57475i	−1.43579	+	0.828953i	−0.997553	−	0.0699076i	$-0.977730\pi$
$107$	−14.8519	+	8.57475i	−1.43579	+	0.828953i	−0.438235	+	0.898860i	$0.644396\pi$
$108$	0.552604	+	0.319046i	0.0531744	+	0.0307002i
$109$	9.34275	+	5.39404i	0.894873	+	0.516655i	0.875533	−	0.483158i	$-0.160510\pi$
$109$	9.34275	+	5.39404i	0.894873	+	0.516655i	0.0193399	+	0.999813i	$0.493844\pi$
$110$	7.18045	−	4.14564i	0.684629	−	0.395271i
$111$	0.551582			0.0523539
$112$	1.88012	−	1.86149i	0.177655	−	0.175894i
$113$		−	15.5136i		−	1.45940i	−0.683770	−	0.729698i	$-0.739661\pi$
$113$		−	15.5136i		−	1.45940i	0.683770	−	0.729698i	$-0.260339\pi$
$114$	−0.262342	+	0.151463i	−0.0245705	+	0.0141858i
$115$	−9.45708	+	14.2970i	−0.881877	+	1.33320i
$116$	−1.74004	+	3.01384i	−0.161559	+	0.279828i
$117$	−4.89900	+	2.82844i	−0.452913	+	0.261489i
$118$		−	5.28304i		−	0.486343i
$119$	3.07525	+	0.840449i	0.281907	+	0.0770438i
$120$		−	0.380843i		−	0.0347660i
$121$	−2.80951	−	4.86622i	−0.255410	−	0.442384i
$122$	2.78587	−	4.82527i	0.252221	−	0.436860i
$123$	0.592275	−	1.02585i	0.0534037	−	0.0924979i
$124$	−2.40205	+	1.38682i	−0.215710	+	0.124540i
$125$	−9.92089			−0.887351
$126$	7.62750	+	2.08456i	0.679511	+	0.185707i
$127$	5.46296			0.484759			0.242380	−	0.970182i	$-0.422072\pi$
$127$	5.46296			0.484759			0.242380	+	0.970182i	$0.422072\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.131478	+	0.227726i	−0.0115759	+	0.0200501i
$130$	5.85900	+	3.38270i	0.513869	+	0.296682i
$131$	−11.2655	+	6.50412i	−0.984269	+	0.568268i	−0.903556	−	0.428469i	$-0.859053\pi$
$131$	−11.2655	+	6.50412i	−0.984269	+	0.568268i	−0.0807127	+	0.996737i	$0.525720\pi$
$132$	0.247164			0.0215129
$133$	−5.34525	+	5.29227i	−0.463492	+	0.458898i
$134$			11.8022i			1.01956i
$135$	1.97517	−	1.14037i	0.169996	−	0.0981472i
$136$	−0.602480	+	1.04353i	−0.0516622	+	0.0894816i
$137$	−13.1728	−	7.60533i	−1.12543	−	0.649767i	−0.182648	−	0.983178i	$-0.558467\pi$
$137$	−13.1728	−	7.60533i	−1.12543	−	0.649767i	−0.942782	+	0.333411i	$0.891800\pi$
$138$	−0.457244	+	0.228137i	−0.0389232	+	0.0194203i
$139$		−	17.4437i		−	1.47956i	−0.672849	−	0.739779i	$-0.734930\pi$
$139$		−	17.4437i		−	1.47956i	0.672849	−	0.739779i	$-0.265070\pi$
$140$	−2.40205	−	9.14656i	−0.203010	−	0.773025i
$141$	1.24467			0.104820
$142$	0.147767	+	0.255939i	0.0124003	+	0.0214779i
$143$	−2.19534	+	3.80245i	−0.183584	+	0.317977i
$144$	−1.49432	+	2.58824i	−0.124527	+	0.215687i
$145$	6.21943	+	10.7724i	0.516496	+	0.894597i
$146$			4.47603i			0.370439i
$147$	−0.745816	−	0.00742987i	−0.0615138	−	0.000612805i
$148$			5.17673i			0.425524i
$149$	−5.54069	+	3.19892i	−0.453911	+	0.262066i	−0.709481	−	0.704725i	$-0.751070\pi$
$149$	−5.54069	+	3.19892i	−0.453911	+	0.262066i	0.255569	+	0.966791i	$0.417737\pi$
$150$	−0.717498	−	0.414247i	−0.0585834	−	0.0338232i
$151$	3.81266	−	6.60372i	0.310270	−	0.537403i	−0.668151	−	0.744026i	$-0.732914\pi$
$151$	3.81266	−	6.60372i	0.310270	−	0.537403i	0.978421	+	0.206623i	$0.0662473\pi$
$152$	−1.42152	−	2.46214i	−0.115300	−	0.199706i
$153$	−3.60120			−0.291140
$154$	5.93604	−	1.55891i	0.478340	−	0.125621i
$155$			9.91384i			0.796299i
$156$	0.100839	+	0.174658i	0.00807355	+	0.0139838i
$157$	−2.42858	+	4.20642i	−0.193821	+	0.335708i	−0.946514	−	0.322664i	$-0.895422\pi$
$157$	−2.42858	+	4.20642i	−0.193821	+	0.335708i	0.752692	+	0.658373i	$0.228755\pi$
$158$	−8.15403	−	4.70773i	−0.648699	−	0.374527i
$159$	−0.466504	−	0.808008i	−0.0369962	−	0.0640792i
$160$	3.57430			0.282573
$161$	−9.54256	+	8.36299i	−0.752059	+	0.659096i
$162$	−8.89795			−0.699089
$163$	−5.11387	−	8.85748i	−0.400549	−	0.693771i	0.593243	−	0.805023i	$-0.297847\pi$
$163$	−5.11387	−	8.85748i	−0.400549	−	0.693771i	−0.993792	+	0.111252i	$0.964514\pi$
$164$	9.62785	+	5.55864i	0.751809	+	0.434057i
$165$	0.441719	−	0.765080i	0.0343878	−	0.0595614i
$166$	−3.02585	−	5.24092i	−0.234851	−	0.406775i
$167$			7.67588i			0.593977i	0.954881	+	0.296989i	$0.0959824\pi$
$167$			7.67588i			0.593977i	−0.954881	+	0.296989i	$0.904018\pi$
$168$	0.0743180	−	0.271933i	0.00573376	−	0.0209801i
$169$	9.41735			0.724412
$170$	2.15344	+	3.72987i	0.165162	+	0.286068i
$171$	4.24841	−	7.35846i	0.324884	−	0.562715i
$172$	−2.13726	−	1.23395i	−0.162964	−	0.0940876i
$173$	13.8809	−	8.01415i	1.05535	−	0.609305i	0.131205	−	0.991355i	$-0.458115\pi$
$173$	13.8809	−	8.01415i	1.05535	−	0.609305i	0.924142	+	0.382050i	$0.124782\pi$
$174$			0.370804i			0.0281106i
$175$	−19.8446	−	5.42343i	−1.50011	−	0.409972i
$176$			2.31969i			0.174853i
$177$	−0.281455	−	0.487494i	−0.0211554	−	0.0366423i
$178$	2.84347	−	4.92504i	0.213127	−	0.369147i
$179$	−7.17887	+	12.4342i	−0.536574	+	0.929374i	0.462511	+	0.886613i	$0.346949\pi$
$179$	−7.17887	+	12.4342i	−0.536574	+	0.929374i	−0.999085	+	0.0427604i	$0.986385\pi$
$180$	5.34116	+	9.25116i	0.398107	+	0.689541i
$181$	−12.9851			−0.965172			−0.482586	−	0.875848i	$-0.660302\pi$
$181$	−12.9851			−0.965172			−0.482586	+	0.875848i	$0.660302\pi$
$182$	3.52340	+	3.55868i	0.261172	+	0.263787i
$183$		−	0.593671i		−	0.0438854i
$184$	−2.14111	−	4.29134i	−0.157845	−	0.316362i
$185$	16.0242	+	9.25159i	1.17812	+	0.680190i
$186$	−0.147767	+	0.255939i	−0.0108348	+	0.0187664i
$187$	−2.42066	+	1.39757i	−0.177016	+	0.102200i
$188$			11.6815i			0.851963i
$189$	1.63287	−	0.428819i	0.118773	−	0.0311920i
$190$	−10.1618			−0.737218
$191$	−13.3040	+	7.68109i	−0.962646	+	0.555784i	−0.896986	−	0.442058i	$-0.854248\pi$
$191$	−13.3040	+	7.68109i	−0.962646	+	0.555784i	−0.0656595	+	0.997842i	$0.520915\pi$
$192$	0.0922753	+	0.0532752i	0.00665940	+	0.00384481i
$193$	−9.10226	+	15.7656i	−0.655195	+	1.13483i	0.326650	+	0.945145i	$0.394080\pi$
$193$	−9.10226	+	15.7656i	−0.655195	+	1.13483i	−0.981845	+	0.189685i	$0.939253\pi$
$194$	6.99233	+	12.1111i	0.502020	+	0.869525i
$195$	0.720855			0.0516215
$196$	0.0697310	−	6.99965i	0.00498079	−	0.499975i
$197$	−21.3350			−1.52006			−0.760029	−	0.649889i	$-0.774816\pi$
$197$	−21.3350			−1.52006			−0.760029	+	0.649889i	$0.774816\pi$
$198$	−6.00393	+	3.46637i	−0.426681	+	0.246344i
$199$	−9.87639	+	17.1064i	−0.700118	+	1.21264i	0.268306	+	0.963334i	$0.413536\pi$
$199$	−9.87639	+	17.1064i	−0.700118	+	1.21264i	−0.968425	+	0.249307i	$0.919797\pi$
$200$	3.88781	−	6.73388i	0.274910	−	0.476157i
$201$	0.628765	+	1.08905i	0.0443497	+	0.0768159i
$202$			10.5679i			0.743555i
$203$	2.33873	+	8.90546i	0.164147	+	0.625041i
$204$			0.128389i			0.00898902i
$205$	34.4128	−	19.8683i	2.40350	−	1.38766i
$206$	5.92856	−	10.2686i	0.413062	−	0.715445i
$207$	7.90753	−	11.9544i	0.549611	−	0.830887i
$208$	−1.63920	+	0.946394i	−0.113658	+	0.0656206i
$209$		−	6.59496i		−	0.456183i
$210$	−0.708934	−	0.716032i	−0.0489211	−	0.0494109i
$211$	14.9037			1.02601			0.513007	−	0.858384i	$-0.328531\pi$
$211$	14.9037			1.02601			0.513007	+	0.858384i	$0.328531\pi$
$212$	7.58334	−	4.37825i	0.520826	−	0.300699i
$213$	0.0272704	+	0.0157446i	0.00186854	+	0.00107880i
$214$	−14.8519	−	8.57475i	−1.01526	−	0.586158i
$215$	−7.63920	+	4.41050i	−0.520989	+	0.300793i
$216$			0.638093i			0.0434167i
$217$	−1.93459	+	7.07878i	−0.131329	+	0.480539i
$218$			10.7881i			0.730661i
$219$	0.238461	+	0.413027i	0.0161137	+	0.0279098i
$220$	7.18045	+	4.14564i	0.484106	+	0.279499i
$221$	−1.97517	−	1.14037i	−0.132865	−	0.0767094i
$222$	0.275791	+	0.477684i	0.0185099	+	0.0320601i
$223$		−	4.79568i		−	0.321143i	−0.987024	−	0.160571i	$-0.948666\pi$
$223$		−	4.79568i		−	0.321143i	0.987024	−	0.160571i	$-0.0513337\pi$
$224$	2.55216	+	0.697491i	0.170523	+	0.0466031i
$225$	23.2386			1.54924
$226$	13.4352	−	7.75679i	0.893694	−	0.515974i
$227$	0.434746	−	0.753001i	0.0288551	−	0.0499785i	−0.851237	−	0.524781i	$-0.824147\pi$
$227$	0.434746	−	0.753001i	0.0288551	−	0.0499785i	0.880092	+	0.474803i	$0.157481\pi$
$228$	−0.262342	−	0.151463i	−0.0173740	−	0.0100309i
$229$	11.6322	+	20.1476i	0.768679	+	1.33139i	0.938280	+	0.345878i	$0.112419\pi$
$229$	11.6322	+	20.1476i	0.768679	+	1.33139i	−0.169601	+	0.985513i	$0.554248\pi$
$230$	−17.1101	−	1.04160i	−1.12820	−	0.0686808i
$231$	0.464699	−	0.460093i	0.0305750	−	0.0302719i
$232$	−3.48008			−0.228479
$233$	−6.75691	−	11.7033i	−0.442660	−	0.766709i	0.555226	−	0.831699i	$-0.312632\pi$
$233$	−6.75691	−	11.7033i	−0.442660	−	0.766709i	−0.997886	+	0.0649901i	$0.979298\pi$
$234$	−4.89900	−	2.82844i	−0.320258	−	0.184901i
$235$	36.1594	+	20.8766i	2.35878	+	1.36184i
$236$	4.57525	−	2.64152i	0.297823	−	0.171948i
$237$	−1.00322			−0.0651662
$238$	0.809773	+	3.08347i	0.0524898	+	0.199871i
$239$	7.32401			0.473751			0.236875	−	0.971540i	$-0.423877\pi$
$239$	7.32401			0.473751			0.236875	+	0.971540i	$0.423877\pi$
$240$	0.329820	−	0.190421i	0.0212898	−	0.0122917i
$241$	6.35541	−	11.0079i	0.409388	−	0.709080i	−0.585434	−	0.810720i	$-0.699076\pi$
$241$	6.35541	−	11.0079i	0.409388	−	0.709080i	0.994821	+	0.101640i	$0.0324090\pi$
$242$	2.80951	−	4.86622i	0.180602	−	0.312813i
$243$	−2.47887	+	1.43118i	−0.159020	+	0.0918102i
$244$	5.57174			0.356694
$245$	−21.5423	−	12.7253i	−1.37629	−	0.812988i
$246$	1.18455			0.0755242
$247$	4.66031	−	2.69063i	0.296528	−	0.171201i
$248$	−2.40205	−	1.38682i	−0.152530	−	0.0880634i
$249$	−0.558422	−	0.322405i	−0.0353886	−	0.0204316i
$250$	−4.96044	−	8.59174i	−0.313726	−	0.543389i
$251$	9.86778			0.622849			0.311424	−	0.950271i	$-0.399194\pi$
$251$	9.86778			0.622849			0.311424	+	0.950271i	$0.399194\pi$
$252$	2.00847	+	7.64788i	0.126522	+	0.481771i
$253$	0.675987	−	11.1043i	0.0424990	−	0.698121i
$254$	2.73148	+	4.73106i	0.171388	+	0.296853i
$255$	0.397419	+	0.229450i	0.0248874	+	0.0143687i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.6381	+	7.29661i	−0.788342	+	0.455150i	−0.839379	−	0.543547i	$-0.817081\pi$
$257$	−12.6381	+	7.29661i	−0.788342	+	0.455150i	0.0510362	+	0.998697i	$0.483748\pi$
$258$	−0.262955			−0.0163709
$259$	9.63641	+	9.73289i	0.598778	+	0.604772i
$260$			6.76539i			0.419572i
$261$	−5.20037	−	9.00731i	−0.321895	−	0.557538i
$262$	−11.2655	−	6.50412i	−0.695983	−	0.401826i
$263$	−23.6577	−	13.6588i	−1.45880	−	0.842237i	−0.459845	−	0.887999i	$-0.652095\pi$
$263$	−23.6577	−	13.6588i	−1.45880	−	0.842237i	−0.998952	+	0.0457619i	$0.985428\pi$
$264$	0.123582	+	0.214050i	0.00760595	+	0.0131739i
$265$		−	31.2983i		−	1.92264i
$266$	−7.25586	−	1.98299i	−0.444885	−	0.121585i
$267$		−	0.605946i		−	0.0370833i
$268$	−10.2210	+	5.90111i	−0.624348	+	0.360468i
$269$	−20.4875	−	11.8285i	−1.24915	−	0.721195i	−0.278208	−	0.960521i	$-0.589740\pi$
$269$	−20.4875	−	11.8285i	−1.24915	−	0.721195i	−0.970939	+	0.239326i	$0.923074\pi$
$270$	1.97517	+	1.14037i	0.120205	+	0.0694005i
$271$	−22.6067	+	13.0520i	−1.37326	+	0.792852i	−0.991337	−	0.131341i	$-0.958072\pi$
$271$	−22.6067	+	13.0520i	−1.37326	+	0.792852i	−0.381924	+	0.924194i	$0.624738\pi$
$272$	−1.20496			−0.0730614
$273$	0.514712	+	0.140668i	0.0311518	+	0.00851363i
$274$		−	15.2107i		−	0.918910i
$275$	15.6205	−	9.01852i	0.941954	−	0.543837i
$276$	−0.426194	−	0.281917i	−0.0256539	−	0.0169694i
$277$	−15.8198	+	27.4006i	−0.950517	+	1.64634i	−0.206208	+	0.978508i	$0.566112\pi$
$277$	−15.8198	+	27.4006i	−0.950517	+	1.64634i	−0.744309	+	0.667835i	$0.767221\pi$
$278$	15.1067	−	8.72187i	0.906041	−	0.523103i
$279$		−	8.28945i		−	0.496276i
$280$	6.72013	−	6.65351i	0.401604	−	0.397623i
$281$		−	9.51640i		−	0.567701i	−0.958869	−	0.283850i	$-0.908388\pi$
$281$		−	9.51640i		−	0.567701i	0.958869	−	0.283850i	$-0.0916119\pi$
$282$	0.622335	+	1.07792i	0.0370595	+	0.0641890i
$283$	6.82667	−	11.8241i	0.405804	−	0.702873i	−0.588611	−	0.808416i	$-0.700325\pi$
$283$	6.82667	−	11.8241i	0.405804	−	0.702873i	0.994415	+	0.105544i	$0.0336583\pi$
$284$	−0.147767	+	0.255939i	−0.00876833	+	0.0151872i
$285$	−0.937687	+	0.541374i	−0.0555438	+	0.0320682i
$286$	−4.39069			−0.259627
$287$	28.4489	−	7.47118i	1.67928	−	0.441010i
$288$	−2.98865			−0.176108
$289$	7.77404	+	13.4650i	0.457296	+	0.792060i
$290$	−6.21943	+	10.7724i	−0.365218	+	0.632575i
$291$	1.29044	+	0.745036i	0.0756469	+	0.0436748i
$292$	−3.87636	+	2.23802i	−0.226847	+	0.130970i
$293$	20.4745			1.19613			0.598067	−	0.801446i	$-0.295936\pi$
$293$	20.4745			1.19613			0.598067	+	0.801446i	$0.295936\pi$
$294$	−0.366473	−	0.649610i	−0.0213732	−	0.0378860i
$295$		−	18.8832i		−	1.09942i
$296$	−4.48318	+	2.58836i	−0.260579	+	0.150446i
$297$	−0.740089	+	1.28187i	−0.0429443	+	0.0743818i
$298$	−5.54069	−	3.19892i	−0.320964	−	0.185308i
$299$	8.12261	−	4.05268i	0.469742	−	0.234372i
$300$		−	0.828495i		−	0.0478332i
$301$	−6.31529	+	1.65851i	−0.364007	+	0.0955947i
$302$	7.62532			0.438788
$303$	0.563007	+	0.975157i	0.0323439	+	0.0560213i
$304$	1.42152	−	2.46214i	0.0815295	−	0.141213i
$305$	9.95754	−	17.2470i	0.570167	−	0.987558i
$306$	−1.80060	−	3.11873i	−0.102933	−	0.178286i
$307$			25.8903i			1.47764i	0.673905	+	0.738818i	$0.264616\pi$
$307$			25.8903i			1.47764i	−0.673905	+	0.738818i	$0.735384\pi$
$308$	4.31808	+	4.36131i	0.246045	+	0.248509i
$309$		−	1.26338i		−	0.0718712i
$310$	−8.58564	+	4.95692i	−0.487632	+	0.281534i
$311$	−2.65056	−	1.53030i	−0.150299	−	0.0867753i	0.422964	−	0.906146i	$-0.360990\pi$
$311$	−2.65056	−	1.53030i	−0.150299	−	0.0867753i	−0.573264	+	0.819371i	$0.694323\pi$
$312$	−0.100839	+	0.174658i	−0.00570887	+	0.00988804i
$313$	−2.69126	−	4.66141i	−0.152119	−	0.263478i	0.779887	−	0.625920i	$-0.215276\pi$
$313$	−2.69126	−	4.66141i	−0.152119	−	0.263478i	−0.932006	+	0.362442i	$0.881943\pi$
$314$	−4.85715			−0.274105
$315$	27.2630	+	7.45083i	1.53609	+	0.419806i
$316$		−	9.41546i		−	0.529661i
$317$	−6.81834	−	11.8097i	−0.382956	−	0.663299i	0.608527	−	0.793533i	$-0.291761\pi$
$317$	−6.81834	−	11.8097i	−0.382956	−	0.663299i	−0.991483	+	0.130234i	$0.958427\pi$
$318$	0.466504	−	0.808008i	0.0261602	−	0.0453108i
$319$	−6.99118	−	4.03636i	−0.391431	−	0.225993i
$320$	1.78715	+	3.09543i	0.0999047	+	0.173040i
$321$	−1.82729			−0.101989
$322$	−12.0138	−	4.08260i	−0.669505	−	0.227514i
$323$	3.42574			0.190613
$324$	−4.44898	−	7.70585i	−0.247165	−	0.428103i
$325$	12.7458	+	7.35880i	0.707011	+	0.408193i
$326$	5.11387	−	8.85748i	0.283231	−	0.490571i
$327$	0.574737	+	0.995474i	0.0317830	+	0.0550498i
$328$			11.1173i			0.613849i
$329$	21.7450	+	21.9627i	1.19884	+	1.21084i
$330$	0.883438			0.0486317
$331$	3.46322	+	5.99847i	0.190356	+	0.329706i	0.945368	−	0.326005i	$-0.105703\pi$
$331$	3.46322	+	5.99847i	0.190356	+	0.329706i	−0.755013	+	0.655710i	$0.772369\pi$
$332$	3.02585	−	5.24092i	0.166065	−	0.287633i
$333$	−13.3986	−	7.73571i	−0.734241	−	0.423914i
$334$	−6.64751	+	3.83794i	−0.363735	+	0.210003i
$335$			42.1847i			2.30479i
$336$	0.272660	−	0.0716054i	0.0148748	−	0.00390639i
$337$		−	21.3940i		−	1.16540i	−0.812686	−	0.582702i	$-0.801995\pi$
$337$		−	21.3940i		−	1.16540i	0.812686	−	0.582702i	$-0.198005\pi$
$338$	4.70868	+	8.15566i	0.256118	+	0.443610i
$339$	0.826489	−	1.43152i	0.0448887	−	0.0777496i
$340$	−2.15344	+	3.72987i	−0.116787	+	0.202281i
$341$	−3.21700	−	5.57201i	−0.174210	−	0.301741i
$342$	8.49682			0.459455
$343$	−12.8987	−	13.2900i	−0.696462	−	0.717593i
$344$		−	2.46789i		−	0.133060i
$345$	−1.63433	+	0.815428i	−0.0879893	+	0.0439012i
$346$	13.8809	+	8.01415i	0.746243	+	0.430844i
$347$	13.4402	−	23.2790i	0.721505	−	1.24968i	−0.238891	−	0.971046i	$-0.576784\pi$
$347$	13.4402	−	23.2790i	0.721505	−	1.24968i	0.960396	−	0.278637i	$-0.0898828\pi$
$348$	−0.321126	+	0.185402i	−0.0172142	+	0.00993860i
$349$		−	16.2629i		−	0.870533i	−0.900302	−	0.435266i	$-0.856654\pi$
$349$		−	16.2629i		−	0.870533i	0.900302	−	0.435266i	$-0.143346\pi$
$350$	−5.22547	−	19.8976i	−0.279313	−	1.06357i
$351$	−1.20777			−0.0644662
$352$	−2.00891	+	1.15985i	−0.107075	+	0.0618200i
$353$	−0.950024	−	0.548496i	−0.0505647	−	0.0291935i	0.474505	−	0.880253i	$-0.342627\pi$
$353$	−0.950024	−	0.548496i	−0.0505647	−	0.0291935i	−0.525069	+	0.851060i	$0.675961\pi$
$354$	0.281455	−	0.487494i	0.0149592	−	0.0259100i
$355$	0.528162	+	0.914803i	0.0280319	+	0.0485527i
$356$	5.68695			0.301408
$357$	0.238994	+	0.241387i	0.0126489	+	0.0127756i
$358$	−14.3577			−0.758831
$359$	−0.0830977	+	0.0479765i	−0.00438573	+	0.00253210i	−0.502191	−	0.864757i	$-0.667473\pi$
$359$	−0.0830977	+	0.0479765i	−0.00438573	+	0.00253210i	0.497806	+	0.867289i	$0.334139\pi$
$360$	−5.34116	+	9.25116i	−0.281504	+	0.487579i
$361$	5.45859	−	9.45455i	0.287294	−	0.497608i
$362$	−6.49253	−	11.2454i	−0.341240	−	0.591045i
$363$		−	0.598709i		−	0.0314241i
$364$	−1.32020	+	4.83069i	−0.0691975	+	0.253197i
$365$			15.9987i			0.837409i
$366$	0.514134	−	0.296836i	0.0268742	−	0.0155158i
$367$	13.9141	−	24.0999i	0.726308	−	1.25800i	−0.232125	−	0.972686i	$-0.574568\pi$
$367$	13.9141	−	24.0999i	0.726308	−	1.25800i	0.958433	−	0.285316i	$-0.0920987\pi$
$368$	2.64586	−	3.99993i	0.137925	−	0.208511i
$369$	−28.7742	+	16.6128i	−1.49793	+	0.864829i
$370$			18.5032i			0.961934i
$371$	6.10758	−	22.3479i	0.317090	−	1.16025i
$372$	−0.295533			−0.0153227
$373$	−3.32599	+	1.92026i	−0.172213	+	0.0994272i	−0.583629	−	0.812021i	$-0.698368\pi$
$373$	−3.32599	+	1.92026i	−0.172213	+	0.0994272i	0.411416	+	0.911448i	$0.365034\pi$
$374$	−2.42066	−	1.39757i	−0.125169	−	0.0722665i
$375$	−0.915453	−	0.528537i	−0.0472738	−	0.0272935i
$376$	−10.1165	+	5.84076i	−0.521719	+	0.301214i
$377$		−	6.58706i		−	0.339251i
$378$	1.18780	+	1.19969i	0.0610939	+	0.0617055i
$379$			24.4457i			1.25569i	0.778337	+	0.627846i	$0.216063\pi$
$379$			24.4457i			1.25569i	−0.778337	+	0.627846i	$0.783937\pi$
$380$	−5.08092	−	8.80042i	−0.260646	−	0.451452i
$381$	0.504096	+	0.291040i	0.0258256	+	0.0149104i
$382$	−13.3040	−	7.68109i	−0.680693	−	0.392999i
$383$	−17.0735	−	29.5722i	−0.872417	−	1.51107i	−0.859489	−	0.511154i	$-0.829218\pi$
$383$	−17.0735	−	29.5722i	−0.872417	−	1.51107i	−0.0129283	−	0.999916i	$-0.504115\pi$
$384$			0.106550i			0.00543738i
$385$	21.2172	−	5.57201i	1.08133	−	0.283976i
$386$	−18.2045			−0.926585
$387$	6.38751	−	3.68783i	0.324695	−	0.187463i
$388$	−6.99233	+	12.1111i	−0.354982	+	0.614847i
$389$	31.2567	+	18.0461i	1.58478	+	0.914971i	0.994148	+	0.108028i	$0.0344537\pi$
$389$	31.2567	+	18.0461i	1.58478	+	0.914971i	0.590629	+	0.806943i	$0.298880\pi$
$390$	0.360428	+	0.624279i	0.0182510	+	0.0316116i
$391$	5.76810	+	0.351140i	0.291706	+	0.0177579i
$392$	6.09674	−	3.43944i	0.307932	−	0.173718i
$393$	−1.38603			−0.0699161
$394$	−10.6675	−	18.4767i	−0.537422	−	0.930842i
$395$	−29.1449	−	16.8268i	−1.46644	−	0.846650i
$396$	−6.00393	−	3.46637i	−0.301709	−	0.174192i
$397$	8.79081	−	5.07537i	0.441198	−	0.254726i	−0.262908	−	0.964821i	$-0.584681\pi$
$397$	8.79081	−	5.07537i	0.441198	−	0.254726i	0.704106	+	0.710095i	$0.251348\pi$
$398$	−19.7528			−0.990117
$399$	−0.775181	+	0.203576i	−0.0388076	+	0.0101916i
$400$	7.77562			0.388781
$401$	−26.9506	+	15.5600i	−1.34585	+	0.777027i	−0.987659	−	0.156621i	$-0.949940\pi$
$401$	−26.9506	+	15.5600i	−1.34585	+	0.777027i	−0.358192	+	0.933648i	$0.616607\pi$
$402$	−0.628765	+	1.08905i	−0.0313600	+	0.0543171i
$403$	2.62496	−	4.54657i	0.130759	−	0.226481i
$404$	−9.15207	+	5.28395i	−0.455333	+	0.262886i
$405$	−31.8039			−1.58035
$406$	−6.54299	+	6.47813i	−0.324723	+	0.321504i
$407$	−12.0084			−0.595235
$408$	−0.111188	+	0.0641944i	−0.00550463	+	0.00317810i
$409$	2.41908	+	1.39666i	0.119616	+	0.0690602i	0.558614	−	0.829428i	$-0.311333\pi$
$409$	2.41908	+	1.39666i	0.119616	+	0.0690602i	−0.438998	+	0.898488i	$0.644667\pi$
$410$	34.4128	+	19.8683i	1.69953	+	0.981223i
$411$	−0.810351	−	1.40357i	−0.0399717	−	0.0692329i
$412$	11.8571			0.584158
$413$	3.68487	−	13.4831i	0.181321	−	0.663462i
$414$	14.3066	+	0.870929i	0.703129	+	0.0428038i
$415$	−10.8153	−	18.7326i	−0.530902	−	0.919549i
$416$	−1.63920	−	0.946394i	−0.0803685	−	0.0464008i
$417$	0.929319	−	1.60963i	0.0455089	−	0.0788238i
$418$	5.71140	−	3.29748i	0.279354	−	0.161285i
$419$	31.7434			1.55077			0.775384	−	0.631490i	$-0.217556\pi$
$419$	31.7434			1.55077			0.775384	+	0.631490i	$0.217556\pi$
$420$	0.265635	−	0.971971i	0.0129616	−	0.0474273i
$421$			28.8564i			1.40638i	0.711003	+	0.703189i	$0.248241\pi$
$421$			28.8564i			1.40638i	−0.711003	+	0.703189i	$0.751759\pi$
$422$	7.45186	+	12.9070i	0.362751	+	0.628303i
$423$	−30.2346	−	17.4560i	−1.47006	−	0.848739i
$424$	7.58334	+	4.37825i	0.368280	+	0.212626i
$425$	4.68465	+	8.11405i	0.227239	+	0.393589i
$426$			0.0314892i			0.00152565i
$427$	10.4756	−	10.3717i	0.506948	−	0.501923i
$428$		−	17.1495i		−	0.828953i
$429$	−0.405152	+	0.233915i	−0.0195609	+	0.0112935i
$430$	−7.63920	−	4.41050i	−0.368395	−	0.212693i
$431$	−5.38712	−	3.11026i	−0.259489	−	0.149816i	0.364613	−	0.931159i	$-0.381201\pi$
$431$	−5.38712	−	3.11026i	−0.259489	−	0.149816i	−0.624101	+	0.781344i	$0.714535\pi$
$432$	−0.552604	+	0.319046i	−0.0265872	+	0.0153501i
$433$	24.5608			1.18032			0.590158	−	0.807288i	$-0.299065\pi$
$433$	24.5608			1.18032			0.590158	+	0.807288i	$0.299065\pi$
$434$	−7.09770	+	1.86398i	−0.340701	+	0.0894740i
$435$			1.32537i			0.0635464i
$436$	−9.34275	+	5.39404i	−0.447437	+	0.258328i
$437$	−7.52225	+	11.3719i	−0.359838	+	0.543993i
$438$	−0.238461	+	0.413027i	−0.0113941	+	0.0197352i
$439$	3.69521	−	2.13343i	0.176363	−	0.101823i	−0.409220	−	0.912436i	$-0.634199\pi$
$439$	3.69521	−	2.13343i	0.176363	−	0.101823i	0.585583	+	0.810613i	$0.300866\pi$
$440$			8.29127i			0.395271i
$441$	18.0126	+	10.6402i	0.857743	+	0.506677i
$442$		−	2.28073i		−	0.108483i
$443$	15.6380	+	27.0858i	0.742984	+	1.28689i	0.951131	+	0.308788i	$0.0999233\pi$
$443$	15.6380	+	27.0858i	0.742984	+	1.28689i	−0.208147	+	0.978097i	$0.566743\pi$
$444$	−0.275791	+	0.477684i	−0.0130885	+	0.0226699i
$445$	10.1634	−	17.6036i	0.481793	−	0.834489i
$446$	4.15318	−	2.39784i	0.196659	−	0.113541i
$447$	−0.681692			−0.0322429
$448$	0.672033	+	2.55898i	0.0317506	+	0.120900i
$449$	16.2525			0.767005			0.383502	−	0.923540i	$-0.374718\pi$
$449$	16.2525			0.767005			0.383502	+	0.923540i	$0.374718\pi$
$450$	11.6193	+	20.1252i	0.547738	+	0.948711i
$451$	−12.8943	+	22.3336i	−0.607171	+	1.05165i
$452$	13.4352	+	7.75679i	0.631937	+	0.364849i
$453$	0.703629	−	0.406240i	0.0330594	−	0.0190868i
$454$	0.869491			0.0408072
$455$	12.5937	+	12.7198i	0.590401	+	0.596312i
$456$		−	0.302926i		−	0.0141858i
$457$	−25.5577	+	14.7557i	−1.19554	+	0.690243i	−0.959557	−	0.281515i	$-0.909163\pi$
$457$	−25.5577	+	14.7557i	−1.19554	+	0.690243i	−0.235980	+	0.971758i	$0.575830\pi$
$458$	−11.6322	+	20.1476i	−0.543538	+	0.941435i
$459$	−0.665866	−	0.384438i	−0.0310800	−	0.0179440i
$460$	−7.65298	−	15.3385i	−0.356822	−	0.715163i
$461$			33.7799i			1.57329i	0.617408	+	0.786643i	$0.288183\pi$
$461$			33.7799i			1.57329i	−0.617408	+	0.786643i	$0.711817\pi$
$462$	0.630801	+	0.172395i	0.0293475	+	0.00802053i
$463$	−0.542299			−0.0252028			−0.0126014	−	0.999921i	$-0.504011\pi$
$463$	−0.542299			−0.0252028			−0.0126014	+	0.999921i	$0.504011\pi$
$464$	−1.74004	−	3.01384i	−0.0807794	−	0.139914i
$465$	−0.528162	+	0.914803i	−0.0244929	+	0.0424230i
$466$	6.75691	−	11.7033i	0.313008	−	0.542145i
$467$	7.80824	+	13.5243i	0.361322	+	0.625828i	0.988179	−	0.153306i	$-0.0489921\pi$
$467$	7.80824	+	13.5243i	0.361322	+	0.625828i	−0.626857	+	0.779135i	$0.715659\pi$
$468$		−	5.65688i		−	0.261489i
$469$	−8.23195	+	30.1211i	−0.380116	+	1.39086i
$470$			41.7533i			1.92593i
$471$	−0.448195	+	0.258766i	−0.0206517	+	0.0119233i
$472$	4.57525	+	2.64152i	0.210593	+	0.121586i
$473$	2.86238	−	4.95778i	0.131612	−	0.227959i
$474$	−0.501610	−	0.868814i	−0.0230397	−	0.0399060i
$475$	−22.1063			−1.01431
$476$	−2.26547	+	2.24302i	−0.103838	+	0.102808i
$477$			26.1701i			1.19824i
$478$	3.66201	+	6.34278i	0.167496	+	0.290112i
$479$	7.70331	−	13.3425i	0.351973	−	0.609636i	−0.634622	−	0.772823i	$-0.718844\pi$
$479$	7.70331	−	13.3425i	0.351973	−	0.609636i	0.986595	+	0.163187i	$0.0521774\pi$
$480$	0.329820	+	0.190421i	0.0150541	+	0.00869151i
$481$	−4.89923	−	8.48571i	−0.223386	−	0.386915i
$482$	12.7108			0.578962
$483$	−1.32608	+	0.263316i	−0.0603388	+	0.0119813i
$484$	5.61903			0.255410
$485$	24.9927	+	43.2886i	1.13486	+	1.96563i
$486$	−2.47887	−	1.43118i	−0.112444	−	0.0649196i
$487$	7.40363	−	12.8235i	0.335490	−	0.581086i	−0.648088	−	0.761565i	$-0.724431\pi$
$487$	7.40363	−	12.8235i	0.335490	−	0.581086i	0.983579	+	0.180479i	$0.0577646\pi$
$488$	2.78587	+	4.82527i	0.126110	+	0.218430i
$489$		−	1.08977i		−	0.0492811i
$490$	0.249240	−	25.0189i	0.0112595	−	1.13024i
$491$	−23.9894			−1.08263			−0.541313	−	0.840821i	$-0.682073\pi$
$491$	−23.9894			−1.08263			−0.541313	+	0.840821i	$0.682073\pi$
$492$	0.592275	+	1.02585i	0.0267018	+	0.0462489i
$493$	2.09668	−	3.63156i	0.0944297	−	0.163557i
$494$	4.66031	+	2.69063i	0.209677	+	0.121057i
$495$	−21.4598	+	12.3898i	−0.964548	+	0.556882i
$496$		−	2.77365i		−	0.124540i
$497$	0.198608	+	0.756263i	0.00890879	+	0.0339230i
$498$		−	0.644810i		−	0.0288946i
$499$	0.390598	+	0.676536i	0.0174856	+	0.0302859i	0.874636	−	0.484781i	$-0.161101\pi$
$499$	0.390598	+	0.676536i	0.0174856	+	0.0302859i	−0.857150	+	0.515067i	$0.827767\pi$
$500$	4.96044	−	8.59174i	0.221838	−	0.384234i
$501$	−0.408934	+	0.708294i	−0.0182698	+	0.0316443i
$502$	4.93389	+	8.54575i	0.220210	+	0.381415i
$503$	−12.9522			−0.577512			−0.288756	−	0.957403i	$-0.593242\pi$
$503$	−12.9522			−0.577512			−0.288756	+	0.957403i	$0.593242\pi$
$504$	−5.61903	+	5.56333i	−0.250291	+	0.247810i
$505$			37.7728i			1.68087i
$506$	9.95460	−	4.96673i	0.442536	−	0.220798i
$507$	0.868989	+	0.501711i	0.0385932	+	0.0222818i
$508$	−2.73148	+	4.73106i	−0.121190	+	0.209907i
$509$	22.1414	−	12.7833i	0.981401	−	0.566612i	0.0787080	−	0.996898i	$-0.474921\pi$
$509$	22.1414	−	12.7833i	0.981401	−	0.566612i	0.902693	+	0.430286i	$0.141587\pi$
$510$			0.458900i			0.0203204i
$511$	−3.12199	+	11.4235i	−0.138109	+	0.505348i
$512$	−1.00000			−0.0441942
$513$	1.57107	−	0.907058i	0.0693645	−	0.0400476i
$514$	−12.6381	−	7.29661i	−0.557442	−	0.321839i
$515$	21.1904	−	36.7029i	0.933762	−	1.61732i
$516$	−0.131478	−	0.227726i	−0.00578797	−	0.0100251i
$517$	−27.0975			−1.19175
$518$	−3.61072	+	13.2118i	−0.158646	+	0.580494i
$519$	1.70782			0.0749651
$520$	−5.85900	+	3.38270i	−0.256934	+	0.148341i
$521$	−18.9690	+	32.8553i	−0.831048	+	1.43942i	0.0661607	+	0.997809i	$0.478925\pi$
$521$	−18.9690	+	32.8553i	−0.831048	+	1.43942i	−0.897208	+	0.441608i	$0.854408\pi$
$522$	5.20037	−	9.00731i	0.227614	−	0.394239i
$523$	5.52517	+	9.56987i	0.241599	+	0.418461i	0.961170	−	0.275957i	$-0.0889949\pi$
$523$	5.52517	+	9.56987i	0.241599	+	0.418461i	−0.719571	+	0.694419i	$0.755662\pi$
$524$		−	13.0082i		−	0.568268i
$525$	−1.54223	−	1.55767i	−0.0673085	−	0.0679824i
$526$		−	27.3176i		−	1.19110i
$527$	2.89437	−	1.67107i	0.126081	−	0.0727928i
$528$	−0.123582	+	0.214050i	−0.00537822	+	0.00931535i
$529$	−13.8313	+	18.3765i	−0.601359	+	0.798979i
$530$	27.1051	−	15.6492i	1.17737	−	0.679756i
$531$			15.7891i			0.685190i
$532$	−1.91061	−	7.27526i	−0.0828355	−	0.315422i
$533$	−21.0427			−0.911459
$534$	0.524765	−	0.302973i	0.0227088	−	0.0131109i
$535$	−53.0852	−	30.6487i	−2.29507	−	1.32506i
$536$	−10.2210	−	5.90111i	−0.441481	−	0.254889i
$537$	−1.32487	+	0.764912i	−0.0571722	+	0.0330084i
$538$		−	23.6570i		−	1.01992i
$539$	16.2370	+	0.161755i	0.699379	+	0.00696726i
$540$			2.28073i			0.0981472i
$541$	−0.521594	−	0.903427i	−0.0224251	−	0.0388414i	0.854595	−	0.519295i	$-0.173805\pi$
$541$	−0.521594	−	0.903427i	−0.0224251	−	0.0388414i	−0.877020	+	0.480454i	$0.840472\pi$
$542$	−22.6067	−	13.0520i	−0.971042	−	0.560631i
$543$	−1.19820	−	0.691782i	−0.0514197	−	0.0296872i
$544$	−0.602480	−	1.04353i	−0.0258311	−	0.0447408i
$545$			38.5598i			1.65172i
$546$	0.135534	+	0.516088i	0.00580031	+	0.0220865i
$547$	19.3013			0.825264			0.412632	−	0.910898i	$-0.364610\pi$
$547$	19.3013			0.825264			0.412632	+	0.910898i	$0.364610\pi$
$548$	13.1728	−	7.60533i	0.562715	−	0.324884i
$549$	−8.32599	+	14.4210i	−0.355344	+	0.615475i
$550$	15.6205	+	9.01852i	0.666062	+	0.384551i
$551$	4.94699	+	8.56844i	0.210749	+	0.365028i
$552$	0.0310501	−	0.510053i	0.00132158	−	0.0217093i
$553$	−17.5268	−	17.7022i	−0.745313	−	0.752775i
$554$	−31.6395			−1.34423
$555$	0.985760	+	1.70739i	0.0418432	+	0.0724745i
$556$	15.1067	+	8.72187i	0.640668	+	0.369890i
$557$	12.0607	+	6.96323i	0.511027	+	0.295041i	0.733256	−	0.679953i	$-0.238000\pi$
$557$	12.0607	+	6.96323i	0.511027	+	0.295041i	−0.222229	+	0.974995i	$0.571333\pi$
$558$	7.17887	−	4.14472i	0.303906	−	0.175460i
$559$	4.67120			0.197571
$560$	9.12217	+	2.49304i	0.385482	+	0.105350i
$561$	−0.297823			−0.0125741
$562$	8.24145	−	4.75820i	0.347644	−	0.200713i
$563$	19.2957	−	33.4211i	0.813217	−	1.40853i	−0.0973844	−	0.995247i	$-0.531048\pi$
$563$	19.2957	−	33.4211i	0.813217	−	1.40853i	0.910601	−	0.413286i	$-0.135619\pi$
$564$	−0.622335	+	1.07792i	−0.0262050	+	0.0453885i
$565$	48.0213	−	27.7251i	2.02027	−	1.16640i
$566$	13.6533			0.573893
$567$	−22.7090	−	6.20624i	−0.953687	−	0.260638i
$568$	−0.295533			−0.0124003
$569$	−7.77110	+	4.48665i	−0.325782	+	0.188090i	−0.653967	−	0.756523i	$-0.726896\pi$
$569$	−7.77110	+	4.48665i	−0.325782	+	0.188090i	0.328185	+	0.944613i	$0.393563\pi$
$570$	−0.937687	−	0.541374i	−0.0392754	−	0.0226757i
$571$	−34.9707	−	20.1903i	−1.46348	−	0.844939i	−0.464307	−	0.885674i	$-0.653696\pi$
$571$	−34.9707	−	20.1903i	−1.46348	−	0.844939i	−0.999170	+	0.0407357i	$0.987030\pi$
$572$	−2.19534	−	3.80245i	−0.0917919	−	0.158988i
$573$	−1.63684			−0.0683802
$574$	20.6947	+	20.9019i	0.863779	+	0.872427i
$575$	−37.2216	−	2.26591i	−1.55225	−	0.0944951i
$576$	−1.49432	−	2.58824i	−0.0622635	−	0.107844i
$577$	−11.8267	−	6.82817i	−0.492354	−	0.284260i	0.233197	−	0.972430i	$-0.425081\pi$
$577$	−11.8267	−	6.82817i	−0.492354	−	0.284260i	−0.725550	+	0.688169i	$0.758415\pi$
$578$	−7.77404	+	13.4650i	−0.323357	+	0.560071i
$579$	−1.67983	+	0.969849i	−0.0698112	+	0.0403055i
$580$	−12.4389			−0.516496
$581$	−4.06694	−	15.4862i	−0.168725	−	0.642474i
$582$			1.49007i			0.0617654i
$583$	10.1562	+	17.5910i	0.420626	+	0.728546i
$584$	−3.87636	−	2.23802i	−0.160405	−	0.0926098i
$585$	−17.5105	−	10.1097i	−0.723970	−	0.417984i
$586$	10.2373	+	17.7314i	0.422897	+	0.732479i
$587$			9.74306i			0.402139i	0.979577	+	0.201070i	$0.0644417\pi$
$587$			9.74306i			0.402139i	−0.979577	+	0.201070i	$0.935558\pi$
$588$	0.379342	−	0.642180i	0.0156438	−	0.0264831i
$589$			7.88556i			0.324919i
$590$	16.3533	−	9.44158i	0.673255	−	0.388704i
$591$	−1.96870	−	1.13663i	−0.0809814	−	0.0467546i
$592$	−4.48318	−	2.58836i	−0.184257	−	0.106381i
$593$	0.995904	−	0.574985i	0.0408969	−	0.0236118i	−0.479412	−	0.877590i	$-0.659150\pi$
$593$	0.995904	−	0.574985i	0.0408969	−	0.0236118i	0.520309	+	0.853978i	$0.325817\pi$
$594$	−1.48018			−0.0607325
$595$	2.89437	+	11.0212i	0.118658	+	0.451826i
$596$		−	6.39784i		−	0.262066i
$597$	−1.82269	+	1.05233i	−0.0745979	+	0.0430691i
$598$	7.57102	+	5.00805i	0.309602	+	0.204794i
$599$	13.0465	−	22.5972i	0.533066	−	0.923297i	−0.466188	−	0.884685i	$-0.654373\pi$
$599$	13.0465	−	22.5972i	0.533066	−	0.923297i	0.999254	−	0.0386117i	$-0.0122935\pi$
$600$	0.717498	−	0.414247i	0.0292917	−	0.0169116i
$601$			5.31574i			0.216833i	0.994106	+	0.108417i	$0.0345781\pi$
$601$			5.31574i			0.216833i	−0.994106	+	0.108417i	$0.965422\pi$
$602$	−4.59395	−	4.63995i	−0.187236	−	0.189110i
$603$		−	35.2727i		−	1.43641i
$604$	3.81266	+	6.60372i	0.155135	+	0.268702i
$605$	10.0420	−	17.3933i	0.408267	−	0.707139i
$606$	−0.563007	+	0.975157i	−0.0228706	+	0.0396130i
$607$	−5.04577	+	2.91318i	−0.204801	+	0.118242i	−0.598893	−	0.800829i	$-0.704393\pi$
$607$	−5.04577	+	2.91318i	−0.204801	+	0.118242i	0.394092	+	0.919071i	$0.371059\pi$
$608$	2.84303			0.115300
$609$	−0.258633	+	0.946351i	−0.0104803	+	0.0383481i
$610$	19.9151			0.806338
$611$	−11.0553	−	19.1484i	−0.447251	−	0.774661i
$612$	1.80060	−	3.11873i	0.0727849	−	0.126067i
$613$	−1.05598	−	0.609668i	−0.0426505	−	0.0246243i	0.478523	−	0.878075i	$-0.341172\pi$
$613$	−1.05598	−	0.609668i	−0.0426505	−	0.0246243i	−0.521174	+	0.853451i	$0.674506\pi$
$614$	−22.4216	+	12.9451i	−0.904864	+	0.522423i
$615$	4.23394			0.170729
$616$	−1.61797	+	5.92022i	−0.0651897	+	0.238532i
$617$		−	47.4233i		−	1.90919i	−0.297907	−	0.954595i	$-0.596288\pi$
$617$		−	47.4233i		−	1.90919i	0.297907	−	0.954595i	$-0.403712\pi$
$618$	1.09412	−	0.631690i	0.0440119	−	0.0254103i
$619$	−0.484010	+	0.838329i	−0.0194540	+	0.0336953i	−0.875589	−	0.483058i	$-0.839526\pi$
$619$	−0.484010	+	0.838329i	−0.0194540	+	0.0336953i	0.856135	+	0.516753i	$0.172859\pi$
$620$	−8.58564	−	4.95692i	−0.344808	−	0.199075i
$621$	2.73827	−	1.36623i	0.109883	−	0.0548249i
$622$		−	3.06060i		−	0.122719i
$623$	10.6922	−	10.5862i	0.428372	−	0.424126i
$624$	−0.201677			−0.00807355
$625$	1.70893	+	2.95996i	0.0683574	+	0.118398i
$626$	2.69126	−	4.66141i	0.107565	−	0.186307i
$627$	0.351348	−	0.608552i	0.0140315	−	0.0243032i
$628$	−2.42858	−	4.20642i	−0.0969107	−	0.167854i
$629$		−	6.23775i		−	0.248715i
$630$	7.17887	+	27.3358i	0.286013	+	1.08909i
$631$		−	15.4829i		−	0.616366i	−0.951327	−	0.308183i	$-0.900279\pi$
$631$		−	15.4829i		−	0.616366i	0.951327	−	0.308183i	$-0.0997208\pi$
$632$	8.15403	−	4.70773i	0.324350	−	0.187263i
$633$	1.37525	+	0.793999i	0.0546611	+	0.0315586i
$634$	6.81834	−	11.8097i	0.270791	−	0.469023i
$635$	9.76312	+	16.9102i	0.387438	+	0.671062i
$636$	0.933007			0.0369962
$637$	6.51013	+	11.5398i	0.257941	+	0.457225i
$638$		−	8.07272i		−	0.319602i
$639$	−0.441622	−	0.764912i	−0.0174703	−	0.0302594i
$640$	−1.78715	+	3.09543i	−0.0706433	+	0.122358i
$641$	11.0227	+	6.36397i	0.435371	+	0.251362i	0.701632	−	0.712539i	$-0.252455\pi$
$641$	11.0227	+	6.36397i	0.435371	+	0.251362i	−0.266261	+	0.963901i	$0.585788\pi$
$642$	−0.913643	−	1.58248i	−0.0360586	−	0.0624554i
$643$	−7.23372			−0.285270			−0.142635	−	0.989775i	$-0.545558\pi$
$643$	−7.23372			−0.285270			−0.142635	+	0.989775i	$0.545558\pi$
$644$	−2.47128	−	12.4456i	−0.0973823	−	0.490425i
$645$	−0.939880			−0.0370077
$646$	1.71287	+	2.96678i	0.0673919	+	0.116726i
$647$	27.1778	+	15.6911i	1.06847	+	0.616880i	0.927763	−	0.373171i	$-0.121730\pi$
$647$	27.1778	+	15.6911i	1.06847	+	0.616880i	0.140706	+	0.990051i	$0.455063\pi$
$648$	4.44898	−	7.70585i	0.174772	−	0.302714i
$649$	6.12751	+	10.6132i	0.240526	+	0.416603i
$650$			14.7176i			0.577272i
$651$	−0.555639	+	0.550131i	−0.0217772	+	0.0215613i
$652$	10.2277			0.400549
$653$	12.1383	+	21.0241i	0.475007	+	0.822735i	0.999590	−	0.0286234i	$-0.00911236\pi$
$653$	12.1383	+	21.0241i	0.475007	+	0.822735i	−0.524584	+	0.851359i	$0.675779\pi$
$654$	−0.574737	+	0.995474i	−0.0224740	+	0.0389261i
$655$	−40.2662	−	23.2477i	−1.57333	−	0.908362i
$656$	−9.62785	+	5.55864i	−0.375904	+	0.217029i
$657$		−	13.3773i		−	0.521897i
$658$	−8.14776	+	29.8131i	−0.317633	+	1.16224i
$659$		−	25.3820i		−	0.988744i	−0.869250	−	0.494372i	$-0.835398\pi$
$659$		−	25.3820i		−	0.988744i	0.869250	−	0.494372i	$-0.164602\pi$
$660$	0.441719	+	0.765080i	0.0171939	+	0.0297807i
$661$	13.7217	−	23.7667i	0.533713	−	0.924418i	−0.465512	−	0.885042i	$-0.654130\pi$
$661$	13.7217	−	23.7667i	0.533713	−	0.924418i	0.999224	−	0.0393759i	$-0.0125370\pi$
$662$	−3.46322	+	5.99847i	−0.134602	+	0.233137i
$663$	−0.121507	−	0.210455i	−0.00471892	−	0.00817341i
$664$	6.05170			0.234851
$665$	−25.9346	−	7.08780i	−1.00570	−	0.274853i
$666$		−	15.4714i		−	0.599505i
$667$	7.45126	+	14.9342i	0.288514	+	0.578256i
$668$	−6.64751	−	3.83794i	−0.257200	−	0.148494i
$669$	0.255491	−	0.442523i	0.00987785	−	0.0171089i
$670$	−36.5330	+	21.0923i	−1.41139	+	0.814868i
$671$			12.9247i			0.498954i
$672$	0.198342	+	0.200328i	0.00765121	+	0.00772782i
$673$	−31.3551			−1.20865			−0.604326	−	0.796737i	$-0.706557\pi$
$673$	−31.3551			−1.20865			−0.604326	+	0.796737i	$0.706557\pi$
$674$	18.5277	−	10.6970i	0.713662	−	0.412033i
$675$	4.29684	+	2.48078i	0.165385	+	0.0954853i
$676$	−4.70868	+	8.15566i	−0.181103	+	0.313679i
$677$	−25.7720	−	44.6383i	−0.990497	−	1.71559i	−0.614357	−	0.789028i	$-0.710585\pi$
$677$	−25.7720	−	44.6383i	−0.990497	−	1.71559i	−0.376140	−	0.926563i	$-0.622749\pi$
$678$	1.65298			0.0634822
$679$	9.39816	+	35.7865i	0.360668	+	1.37336i
$680$	−4.30689			−0.165162
$681$	0.0802326	−	0.0463223i	0.00307452	−	0.00177507i
$682$	3.21700	−	5.57201i	0.123185	−	0.213363i
$683$	13.9630	−	24.1846i	0.534278	−	0.925396i	−0.464920	−	0.885353i	$-0.653917\pi$
$683$	13.9630	−	24.1846i	0.534278	−	0.925396i	0.999198	−	0.0400436i	$-0.0127497\pi$
$684$	4.24841	+	7.35846i	0.162442	+	0.281358i
$685$		−	54.3675i		−	2.07727i
$686$	5.06016	−	17.8156i	0.193198	−	0.680202i
$687$			2.47883i			0.0945734i
$688$	2.13726	−	1.23395i	0.0814822	−	0.0470438i
$689$	−8.28709	+	14.3537i	−0.315713	+	0.546831i
$690$	−1.52335	−	1.00766i	−0.0579928	−	0.0383608i
$691$	8.61282	−	4.97261i	0.327647	−	0.189167i	−0.327149	−	0.944973i	$-0.606088\pi$
$691$	8.61282	−	4.97261i	0.327647	−	0.189167i	0.654796	+	0.755806i	$0.272755\pi$
$692$			16.0283i			0.609305i
$693$	−17.7407	+	4.65903i	−0.673915	+	0.176982i
$694$	26.8803			1.02036
$695$	53.9960	−	31.1746i	2.04818	−	1.18252i
$696$	−0.321126	−	0.185402i	−0.0121722	−	0.00702765i
$697$	−11.6012	−	6.69794i	−0.439426	−	0.253703i
$698$	14.0841	−	8.13145i	0.533090	−	0.307780i
$699$		−	1.43990i		−	0.0544621i
$700$	14.6191	−	14.4742i	0.552551	−	0.547074i
$701$			21.1920i			0.800411i	0.916425	+	0.400206i	$0.131061\pi$
$701$			21.1920i			0.800411i	−0.916425	+	0.400206i	$0.868939\pi$
$702$	−0.603887	−	1.04596i	−0.0227923	−	0.0394773i
$703$	12.7458	+	7.35880i	0.480718	+	0.277542i
$704$	−2.00891	−	1.15985i	−0.0757137	−	0.0437133i
$705$	2.22441	+	3.85280i	0.0837762	+	0.145105i
$706$		−	1.09699i		−	0.0412859i
$707$	−7.37102	+	26.9709i	−0.277216	+	1.01435i
$708$	0.562910			0.0211554
$709$	−9.25899	+	5.34568i	−0.347729	+	0.200761i	−0.663685	−	0.748013i	$-0.731008\pi$
$709$	−9.25899	+	5.34568i	−0.347729	+	0.200761i	0.315956	+	0.948774i	$0.397675\pi$
$710$	−0.528162	+	0.914803i	−0.0198216	+	0.0343319i
$711$	24.3695	+	14.0697i	0.913928	+	0.527656i
$712$	2.84347	+	4.92504i	0.106564	+	0.184574i
$713$	−0.808275	+	13.2774i	−0.0302701	+	0.497241i
$714$	−0.0895501	+	0.327669i	−0.00335133	+	0.0122627i
$715$	−15.6936			−0.586909
$716$	−7.17887	−	12.4342i	−0.268287	−	0.464687i
$717$	0.675826	+	0.390188i	0.0252392	+	0.0145718i
$718$	−0.0830977	−	0.0479765i	−0.00310118	−	0.00179047i
$719$	4.98103	−	2.87580i	0.185761	−	0.107249i	−0.404235	−	0.914655i	$-0.632462\pi$
$719$	4.98103	−	2.87580i	0.185761	−	0.107249i	0.589997	+	0.807406i	$0.299129\pi$
$720$	−10.6823			−0.398107
$721$	22.2928	−	22.0719i	0.830229	−	0.821999i
$722$	10.9172			0.406295
$723$	1.17289	−	0.677171i	0.0436204	−	0.0251843i
$724$	6.49253	−	11.2454i	0.241293	−	0.417932i
$725$	−13.5299	+	23.4345i	−0.502488	+	0.870334i
$726$	0.518498	−	0.299355i	0.0192433	−	0.0111101i
$727$	−19.5009			−0.723249			−0.361625	−	0.932324i	$-0.617778\pi$
$727$	−19.5009			−0.723249			−0.361625	+	0.932324i	$0.617778\pi$
$728$	−4.84361	+	1.27202i	−0.179516	+	0.0471441i
$729$	26.3889			0.977366
$730$	−13.8553	+	7.99934i	−0.512806	+	0.296069i
$731$	2.57531	+	1.48686i	0.0952513	+	0.0549934i
$732$	0.514134	+	0.296836i	0.0190030	+	0.0109714i
$733$	4.72907	+	8.19099i	0.174672	+	0.302541i	0.940048	−	0.341043i	$-0.110780\pi$
$733$	4.72907	+	8.19099i	0.174672	+	0.302541i	−0.765376	+	0.643584i	$0.777447\pi$
$734$	27.8281			1.02715
$735$	−1.30989	−	2.32190i	−0.0483159	−	0.0856446i
$736$	4.78697	+	0.291412i	0.176450	+	0.0107416i
$737$	−13.6888	−	23.7096i	−0.504232	−	0.873355i
$738$	−28.7742	−	16.6128i	−1.05919	−	0.611526i
$739$	−9.82769	+	17.0221i	−0.361517	+	0.626166i	−0.988211	−	0.153099i	$-0.951075\pi$
$739$	−9.82769	+	17.0221i	−0.361517	+	0.626166i	0.626693	+	0.779266i	$0.284408\pi$
$740$	−16.0242	+	9.25159i	−0.589062	+	0.340095i
$741$	0.573375			0.0210635
$742$	22.4077	−	5.88465i	0.822612	−	0.216032i
$743$		−	37.5029i		−	1.37585i	−0.725782	−	0.687925i	$-0.758522\pi$
$743$		−	37.5029i		−	1.37585i	0.725782	−	0.687925i	$-0.241478\pi$
$744$	−0.147767	−	0.255939i	−0.00541738	−	0.00938318i
$745$	−19.8041	−	11.4339i	−0.725566	−	0.418906i
$746$	−3.32599	−	1.92026i	−0.121773	−	0.0703057i
$747$	9.04319	+	15.6633i	0.330873	+	0.573089i
$748$		−	2.79514i		−	0.102200i
$749$	−31.9236	−	32.2432i	−1.16646	−	1.17814i
$750$		−	1.05707i		−	0.0385989i
$751$	15.3380	−	8.85537i	0.559690	−	0.323137i	−0.193331	−	0.981134i	$-0.561929\pi$
$751$	15.3380	−	8.85537i	0.559690	−	0.323137i	0.753021	+	0.657996i	$0.228596\pi$
$752$	−10.1165	−	5.84076i	−0.368911	−	0.212991i
$753$	0.910553	+	0.525708i	0.0331824	+	0.0191579i
$754$	5.70456	−	3.29353i	0.207748	−	0.119943i
$755$	27.2552			0.991917
$756$	−0.445064	+	1.62851i	−0.0161868	+	0.0592284i
$757$			10.9330i			0.397366i	0.980064	+	0.198683i	$0.0636664\pi$
$757$			10.9330i			0.397366i	−0.980064	+	0.198683i	$0.936334\pi$
$758$	−21.1706	+	12.2229i	−0.768952	+	0.443954i
$759$	0.653960	−	0.988639i	0.0237373	−	0.0358853i
$760$	5.08092	−	8.80042i	0.184304	−	0.319225i
$761$	14.8257	−	8.55962i	0.537431	−	0.310286i	−0.206606	−	0.978424i	$-0.566242\pi$
$761$	14.8257	−	8.55962i	0.537431	−	0.310286i	0.744037	+	0.668138i	$0.232909\pi$
$762$			0.582080i			0.0210865i
$763$	−7.52459	+	27.5329i	−0.272409	+	0.996757i
$764$		−	15.3622i		−	0.555784i
$765$	−6.43588	−	11.1473i	−0.232690	−	0.403031i
$766$	17.0735	−	29.5722i	0.616892	−	1.06849i
$767$	−4.99984	+	8.65997i	−0.180534	+	0.312694i
$768$	−0.0922753	+	0.0532752i	−0.00332970	+	0.00192240i
$769$	15.0496			0.542704			0.271352	−	0.962480i	$-0.412529\pi$
$769$	15.0496			0.542704			0.271352	+	0.962480i	$0.412529\pi$
$770$	15.4341	+	15.5886i	0.556206	+	0.561775i
$771$	−1.55491			−0.0559988
$772$	−9.10226	−	15.7656i	−0.327597	−	0.567415i
$773$	0.0920898	−	0.159504i	0.00331224	−	0.00573697i	−0.864365	−	0.502866i	$-0.832279\pi$
$773$	0.0920898	−	0.159504i	0.00331224	−	0.00573697i	0.867677	+	0.497129i	$0.165612\pi$
$774$	6.38751	+	3.68783i	0.229594	+	0.132556i
$775$	−18.6774	+	10.7834i	−0.670912	+	0.387351i
$776$	−13.9847			−0.502020
$777$	0.370682	+	1.41149i	0.0132981	+	0.0506368i
$778$			36.0921i			1.29396i
$779$	27.3723	−	15.8034i	0.980714	−	0.566215i
$780$	−0.360428	+	0.624279i	−0.0129054	+	0.0223528i
$781$	−0.593700	−	0.342773i	−0.0212443	−	0.0122654i
$782$	2.57996	+	5.17090i	0.0922590	+	0.184911i
$783$		−	2.22062i		−	0.0793583i
$784$	6.02701	+	3.56022i	0.215250	+	0.127151i
$785$	−17.3609			−0.619637
$786$	−0.693017	−	1.20034i	−0.0247191	−	0.0428147i
$787$	−24.8199	+	42.9892i	−0.884732	+	1.53240i	−0.0387121	+	0.999250i	$0.512326\pi$
$787$	−24.8199	+	42.9892i	−0.884732	+	1.53240i	−0.846020	+	0.533151i	$0.821008\pi$
$788$	10.6675	−	18.4767i	0.380015	−	0.658205i
$789$	−1.45535	−	2.52074i	−0.0518118	−	0.0897407i
$790$		−	33.6537i		−	1.19734i
$791$	39.6989	−	10.4256i	1.41153	−	0.370693i
$792$		−	6.93274i		−	0.246344i
$793$	−9.13322	+	5.27307i	−0.324330	+	0.187252i
$794$	8.79081	+	5.07537i	0.311974	+	0.180118i
$795$	1.66742	−	2.88806i	0.0591374	−	0.102429i
$796$	−9.87639	−	17.1064i	−0.350059	−	0.606320i
$797$	18.7530			0.664265			0.332132	−	0.943233i	$-0.392232\pi$
$797$	18.7530			0.664265			0.332132	+	0.943233i	$0.392232\pi$
$798$	−0.563893	−	0.569538i	−0.0199616	−	0.0201614i
$799$		−	14.0758i		−	0.497965i
$800$	3.88781	+	6.73388i	0.137455	+	0.238079i
$801$	−8.49814	+	14.7192i	−0.300267	+	0.520078i
$802$	−26.9506	−	15.5600i	−0.951660	−	0.549441i
$803$	−5.19151	−	8.99196i	−0.183204	−	0.317319i
$804$	−1.25753			−0.0443497
$805$	−42.9411	−	14.5924i	−1.51347	−	0.514316i
$806$	5.24993			0.184921
$807$	−1.26033	−	2.18295i	−0.0443657	−	0.0768436i
$808$	−9.15207	−	5.28395i	−0.321969	−	0.185889i
$809$	−17.5440	+	30.3871i	−0.616813	+	1.06835i	0.373250	+	0.927731i	$0.378243\pi$
$809$	−17.5440	+	30.3871i	−0.616813	+	1.06835i	−0.990063	+	0.140621i	$0.955090\pi$
$810$	−15.9020	−	27.5430i	−0.558738	−	0.967763i
$811$			53.0734i			1.86366i	0.362897	+	0.931829i	$0.381788\pi$
$811$			53.0734i			1.86366i	−0.362897	+	0.931829i	$0.618212\pi$
$812$	−8.88172	−	2.42733i	−0.311687	−	0.0851825i
$813$	−2.78139			−0.0975476
$814$	−6.00421	−	10.3996i	−0.210447	−	0.364506i
$815$	18.2785	−	31.6593i	0.640268	−	1.10898i
$816$	−0.111188	−	0.0641944i	−0.00389236	−	0.00224725i
$817$	−6.07629	+	3.50815i	−0.212583	+	0.122735i
$818$			2.79331i			0.0976658i
$819$	−10.5302	−	10.6356i	−0.367955	−	0.371639i
$820$			39.7365i			1.38766i
$821$	−11.7077	−	20.2784i	−0.408602	−	0.707720i	0.586131	−	0.810216i	$-0.300650\pi$
$821$	−11.7077	−	20.2784i	−0.408602	−	0.707720i	−0.994733	+	0.102496i	$0.967317\pi$
$822$	0.810351	−	1.40357i	0.0282642	−	0.0489551i
$823$	−0.372150	+	0.644582i	−0.0129723	+	0.0224687i	−0.872439	−	0.488724i	$-0.837463\pi$
$823$	−0.372150	+	0.644582i	−0.0129723	+	0.0224687i	0.859466	+	0.511192i	$0.170796\pi$
$824$	5.92856	+	10.2686i	0.206531	+	0.357722i
$825$	1.92185			0.0669103
$826$	13.5192	−	3.55038i	0.470393	−	0.123533i
$827$			42.7483i			1.48650i	0.669012	+	0.743251i	$0.266717\pi$
$827$			42.7483i			1.48650i	−0.669012	+	0.743251i	$0.733283\pi$
$828$	6.39903	+	12.8253i	0.222382	+	0.445710i
$829$	29.8873	+	17.2554i	1.03803	+	0.599306i	0.919274	−	0.393618i	$-0.128777\pi$
$829$	29.8873	+	17.2554i	1.03803	+	0.599306i	0.118754	+	0.992924i	$0.462110\pi$
$830$	10.8153	−	18.7326i	0.375404	−	0.650219i
$831$	−2.91955	+	1.68560i	−0.101278	+	0.0584728i
$832$		−	1.89279i		−	0.0656206i
$833$	−0.0840231	+	8.43430i	−0.00291123	+	0.292231i
$834$	1.85864			0.0643593
$835$	−23.7602	+	13.7179i	−0.822255	+	0.474729i
$836$	5.71140	+	3.29748i	0.197533	+	0.114046i
$837$	0.884921	−	1.53273i	0.0305874	−	0.0529789i
$838$	15.8717	+	27.4906i	0.548279	+	0.949647i
$839$	−8.64457			−0.298444			−0.149222	−	0.988804i	$-0.547677\pi$
$839$	−8.64457			−0.298444			−0.149222	+	0.988804i	$0.547677\pi$
$840$	0.974569	−	0.255939i	0.0336258	−	0.00883074i
$841$	−16.8890			−0.582380
$842$	−24.9904	+	14.4282i	−0.861227	+	0.497229i
$843$	0.506988	−	0.878129i	0.0174616	−	0.0302444i
$844$	−7.45186	+	12.9070i	−0.256504	+	0.444277i
$845$	16.8302	+	29.1508i	0.578977	+	1.00282i
$846$		−	34.9120i		−	1.20030i
$847$	10.5645	−	10.4597i	0.362999	−	0.359401i
$848$			8.75649i			0.300699i
$849$	1.25987	−	0.727385i	0.0432385	−	0.0249638i
$850$	−4.68465	+	8.11405i	−0.160682	+	0.278310i
$851$	20.7066	+	13.6969i	0.709812	+	0.469523i
$852$	−0.0272704	+	0.0157446i	−0.000934269	+	0.000539400i
$853$		−	2.37683i		−	0.0813810i	−0.999172	−	0.0406905i	$-0.987044\pi$
$853$		−	2.37683i		−	0.0813810i	0.999172	−	0.0406905i	$-0.0129558\pi$
$854$	14.2200	+	3.88624i	0.486597	+	0.132984i
$855$	30.3702			1.03864
$856$	14.8519	−	8.57475i	0.507628	−	0.293079i
$857$	38.3631	+	22.1489i	1.31046	+	0.756593i	0.982172	−	0.187985i	$-0.0601958\pi$
$857$	38.3631	+	22.1489i	1.31046	+	0.756593i	0.328286	+	0.944578i	$0.393529\pi$
$858$	−0.405152	−	0.233915i	−0.0138317	−	0.00798572i
$859$	−7.81247	+	4.51053i	−0.266558	+	0.153897i	−0.627322	−	0.778760i	$-0.715849\pi$
$859$	−7.81247	+	4.51053i	−0.266558	+	0.153897i	0.360764	+	0.932657i	$0.382516\pi$
$860$		−	8.82099i		−	0.300793i
$861$	3.02316	+	0.826214i	0.103029	+	0.0281573i
$862$		−	6.22051i		−	0.211871i
$863$	11.2424	+	19.4724i	0.382696	+	0.662849i	0.991447	−	0.130513i	$-0.0416623\pi$
$863$	11.2424	+	19.4724i	0.382696	+	0.662849i	−0.608751	+	0.793362i	$0.708329\pi$
$864$	−0.552604	−	0.319046i	−0.0188000	−	0.0108542i
$865$	49.6146	+	28.6450i	1.68695	+	0.973959i
$866$	12.2804	+	21.2703i	0.417305	+	0.722793i
$867$			1.65665i			0.0562629i
$868$	−5.16311	−	5.21480i	−0.175247	−	0.177002i
$869$	21.8410			0.740904
$870$	−1.14780	+	0.662683i	−0.0389141	+	0.0224670i
$871$	11.1696	−	19.3462i	0.378466	−	0.655522i
$872$	−9.34275	−	5.39404i	−0.316385	−	0.182665i
$873$	−20.8976	−	36.1957i	−0.707277	−	1.22504i
$874$	−13.6095	−	0.828495i	−0.460348	−	0.0280243i
$875$	−6.66717	−	25.3873i	−0.225391	−	0.858248i
$876$	−0.476923			−0.0161137
$877$	20.6397	+	35.7490i	0.696952	+	1.20716i	0.969518	+	0.245019i	$0.0787944\pi$
$877$	20.6397	+	35.7490i	0.696952	+	1.20716i	−0.272566	+	0.962137i	$0.587872\pi$
$878$	3.69521	+	2.13343i	0.124707	+	0.0719998i
$879$	1.88929	+	1.09078i	0.0637242	+	0.0367912i
$880$	−7.18045	+	4.14564i	−0.242053	+	0.139749i
$881$	51.9398			1.74990			0.874948	−	0.484217i	$-0.160895\pi$
$881$	51.9398			1.74990			0.874948	+	0.484217i	$0.160895\pi$
$882$	−0.208401	+	20.9195i	−0.00701724	+	0.704396i
$883$	14.5826			0.490745			0.245373	−	0.969429i	$-0.421090\pi$
$883$	14.5826			0.490745			0.245373	+	0.969429i	$0.421090\pi$
$884$	1.97517	−	1.14037i	0.0664323	−	0.0383547i
$885$	1.00600	−	1.74245i	0.0338165	−	0.0585718i
$886$	−15.6380	+	27.0858i	−0.525369	+	0.909965i
$887$	15.3778	−	8.87835i	0.516335	−	0.298106i	−0.219099	−	0.975703i	$-0.570312\pi$
$887$	15.3778	−	8.87835i	0.516335	−	0.298106i	0.735434	+	0.677597i	$0.236978\pi$
$888$	−0.551582			−0.0185099
$889$	3.67129	+	13.9796i	0.123131	+	0.468860i
$890$	20.3269			0.681358
$891$	17.8752	−	10.3203i	0.598842	−	0.345742i
$892$	4.15318	+	2.39784i	0.139059	+	0.0802857i
$893$	28.7615	+	16.6055i	0.962467	+	0.555681i
$894$	−0.340846	−	0.590363i	−0.0113996	−	0.0197447i
$895$	−51.3189			−1.71540
$896$	−1.88012	+	1.86149i	−0.0628105	+	0.0621879i
$897$	0.965423	+	0.0587713i	0.0322345	+	0.00196232i
$898$	8.12627	+	14.0751i	0.271177	+	0.469693i
$899$	8.35933	+	4.82626i	0.278799	+	0.160965i
$900$	−11.6193	+	20.1252i	−0.387310	+	0.670840i
$901$	−9.13762	+	5.27561i	−0.304418	+	0.175756i
$902$	−25.7887			−0.858669
$903$	−0.671102	−	0.183409i	−0.0223329	−	0.00610346i
$904$			15.5136i			0.515974i
$905$	−23.2063	−	40.1944i	−0.771402	−	1.33611i
$906$	0.703629	+	0.406240i	0.0233765	+	0.0134964i
$907$	−8.71677	−	5.03263i	−0.289436	−	0.167106i	0.348252	−	0.937401i	$-0.386775\pi$
$907$	−8.71677	−	5.03263i	−0.289436	−	0.167106i	−0.637687	+	0.770295i	$0.720109\pi$
$908$	0.434746	+	0.753001i	0.0144275	+	0.0249892i
$909$		−	31.5837i		−	1.04757i
$910$	−4.71880	+	17.2663i	−0.156427	+	0.572374i
$911$			27.1204i			0.898540i	0.893396	+	0.449270i	$0.148316\pi$
$911$			27.1204i			0.898540i	−0.893396	+	0.449270i	$0.851684\pi$
$912$	0.262342	−	0.151463i	0.00868700	−	0.00501544i
$913$	12.1573	+	7.01904i	0.402349	+	0.232296i
$914$	−25.5577	−	14.7557i	−0.845372	−	0.488076i
$915$	1.83767	−	1.06098i	0.0607515	−	0.0350749i
$916$	−23.2644			−0.768679
$917$	−24.2147	−	24.4571i	−0.799639	−	0.807645i
$918$		−	0.768876i		−	0.0253767i
$919$	−7.41041	+	4.27840i	−0.244447	+	0.141131i	−0.617219	−	0.786792i	$-0.711741\pi$
$919$	−7.41041	+	4.27840i	−0.244447	+	0.141131i	0.372772	+	0.927923i	$0.378407\pi$
$920$	9.45708	−	14.2970i	0.311791	−	0.471357i
$921$	−1.37931	+	2.38903i	−0.0454498	+	0.0787213i
$922$	−29.2542	+	16.8899i	−0.963437	+	0.556241i
$923$		−	0.559382i		−	0.0184123i
$924$	0.166102	+	0.632488i	0.00546437	+	0.0208073i
$925$			40.2523i			1.32349i
$926$	−0.271149	−	0.469645i	−0.00891052	−	0.0154335i
$927$	−17.7184	+	30.6891i	−0.581947	+	1.00796i
$928$	1.74004	−	3.01384i	0.0571197	−	0.0989342i
$929$	−18.2134	+	10.5155i	−0.597562	+	0.345003i	−0.768082	−	0.640352i	$-0.778789\pi$
$929$	−18.2134	+	10.5155i	−0.597562	+	0.345003i	0.170520	+	0.985354i	$0.445455\pi$
$930$	−1.05632			−0.0346382
$931$	−17.1350	−	10.1218i	−0.561576	−	0.331729i
$932$	13.5138			0.442660
$933$	−0.163054	−	0.282418i	−0.00533815	−	0.00924594i
$934$	−7.80824	+	13.5243i	−0.255493	+	0.442527i
$935$	−8.65216	−	4.99533i	−0.282956	−	0.163365i
$936$	4.89900	−	2.82844i	0.160129	−	0.0924504i
$937$	2.26428			0.0739708			0.0369854	−	0.999316i	$-0.488225\pi$
$937$	2.26428			0.0739708			0.0369854	+	0.999316i	$0.488225\pi$
$938$	−30.2016	+	7.93148i	−0.986118	+	0.258972i
$939$		−	0.573510i		−	0.0187158i
$940$	−36.1594	+	20.8766i	−1.17939	+	0.680921i
$941$	−14.9699	+	25.9287i	−0.488006	+	0.845251i	−0.999905	−	0.0137945i	$-0.995609\pi$
$941$	−14.9699	+	25.9287i	−0.488006	+	0.845251i	0.511899	+	0.859046i	$0.328942\pi$
$942$	−0.448195	−	0.258766i	−0.0146030	−	0.00843104i
$943$	47.7081	−	23.8034i	1.55359	−	0.775145i
$944$			5.28304i			0.171948i
$945$	4.24556	+	4.28806i	0.138108	+	0.139491i
$946$	5.72475			0.186128
$947$	−6.92591	−	11.9960i	−0.225062	−	0.389819i	0.731276	−	0.682082i	$-0.238925\pi$
$947$	−6.92591	−	11.9960i	−0.225062	−	0.389819i	−0.956338	+	0.292263i	$0.905592\pi$
$948$	0.501610	−	0.868814i	0.0162915	−	0.0282178i
$949$	4.23609	−	7.33713i	0.137509	−	0.238173i
$950$	−11.0532	−	19.1446i	−0.358612	−	0.621134i
$951$		−	1.45299i		−	0.0471165i
$952$	−3.07525	−	0.840449i	−0.0996693	−	0.0272391i
$953$		−	23.0621i		−	0.747055i	−0.927619	−	0.373527i	$-0.878148\pi$
$953$		−	23.0621i		−	0.747055i	0.927619	−	0.373527i	$-0.121852\pi$
$954$	−22.6639	+	13.0850i	−0.733772	+	0.423644i
$955$	−47.5526	−	27.4545i	−1.53877	−	0.888407i
$956$	−3.66201	+	6.34278i	−0.118438	+	0.205140i
$957$	−0.430076	−	0.744913i	−0.0139024	−	0.0240796i
$958$	15.4066			0.497765
$959$	10.6093	−	38.8200i	0.342592	−	1.25356i
$960$			0.380843i			0.0122917i
$961$	−11.6534	−	20.1844i	−0.375918	−	0.651108i
$962$	4.89923	−	8.48571i	0.157957	−	0.273590i
$963$	44.3871	+	25.6269i	1.43035	+	0.825816i
$964$	6.35541	+	11.0079i	0.204694	+	0.354540i
$965$	−65.0684			−2.09463
$966$	−0.891080	−	1.01676i	−0.0286700	−	0.0327138i
$967$	−17.9343			−0.576728			−0.288364	−	0.957521i	$-0.593111\pi$
$967$	−17.9343			−0.576728			−0.288364	+	0.957521i	$0.593111\pi$
$968$	2.80951	+	4.86622i	0.0903012	+	0.156406i
$969$	0.316111	+	0.182507i	0.0101549	+	0.00586296i
$970$	−24.9927	+	43.2886i	−0.802467	+	1.38991i
$971$	−4.81459	−	8.33912i	−0.154508	−	0.267615i	0.778372	−	0.627803i	$-0.216046\pi$
$971$	−4.81459	−	8.33912i	−0.154508	−	0.267615i	−0.932880	+	0.360188i	$0.882712\pi$
$972$		−	2.86236i		−	0.0918102i
$973$	44.6382	−	11.7228i	1.43103	−	0.375815i
$974$	14.8073			0.474455
$975$	0.784083	+	1.35807i	0.0251107	+	0.0434931i
$976$	−2.78587	+	4.82527i	−0.0891736	+	0.154453i
$977$	12.0300	+	6.94552i	0.384874	+	0.222207i	0.679937	−	0.733271i	$-0.262007\pi$
$977$	12.0300	+	6.94552i	0.384874	+	0.222207i	−0.295063	+	0.955478i	$0.595341\pi$
$978$	0.943768	−	0.544885i	0.0301784	−	0.0174235i
$979$			13.1920i			0.421617i
$980$	21.7916	−	12.2936i	0.696107	−	0.392704i
$981$		−	32.2418i		−	1.02940i
$982$	−11.9947	−	20.7754i	−0.382766	−	0.662970i
$983$	−24.8749	+	43.0845i	−0.793385	+	1.37418i	0.130475	+	0.991452i	$0.458350\pi$
$983$	−24.8749	+	43.0845i	−0.793385	+	1.37418i	−0.923860	+	0.382731i	$0.874984\pi$
$984$	−0.592275	+	1.02585i	−0.0188810	+	0.0327029i
$985$	−38.1289	−	66.0412i	−1.21489	−	2.10425i
$986$	4.19336			0.133544
$987$	0.836460	+	3.18509i	0.0266248	+	0.101382i
$988$			5.38126i			0.171201i
$989$	−10.5906	+	5.28404i	−0.336761	+	0.168023i
$990$	−21.4598	−	12.3898i	−0.682039	−	0.393775i
$991$	9.85207	−	17.0643i	0.312961	−	0.542065i	−0.666041	−	0.745915i	$-0.732012\pi$
$991$	9.85207	−	17.0643i	0.312961	−	0.542065i	0.979002	+	0.203850i	$0.0653456\pi$
$992$	2.40205	−	1.38682i	0.0762651	−	0.0440317i
$993$			0.738014i			0.0234202i
$994$	−0.555639	+	0.550131i	−0.0176238	+	0.0174491i
$995$	−70.6023			−2.23824
$996$	0.558422	−	0.322405i	0.0176943	−	0.0102158i
$997$	11.6042	+	6.69967i	0.367507	+	0.212181i	0.672369	−	0.740216i	$-0.265277\pi$
$997$	11.6042	+	6.69967i	0.367507	+	0.212181i	−0.304862	+	0.952397i	$0.598610\pi$
$998$	−0.390598	+	0.676536i	−0.0123642	+	0.0214154i
$999$	−1.65162	−	2.86068i	−0.0522548	−	0.0905080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.g.b.45.6	yes	16
7.3	odd	6		2254.2.c.b.2253.10		16
7.4	even	3		2254.2.c.b.2253.7		16
7.5	odd	6	inner	322.2.g.b.229.5	yes	16
23.22	odd	2	inner	322.2.g.b.45.5	✓	16
161.45	even	6		2254.2.c.b.2253.9		16
161.68	even	6	inner	322.2.g.b.229.6	yes	16
161.137	odd	6		2254.2.c.b.2253.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.b.45.5	✓	16	23.22	odd	2	inner
322.2.g.b.45.6	yes	16	1.1	even	1	trivial
322.2.g.b.229.5	yes	16	7.5	odd	6	inner
322.2.g.b.229.6	yes	16	161.68	even	6	inner
2254.2.c.b.2253.7		16	7.4	even	3
2254.2.c.b.2253.8		16	161.137	odd	6
2254.2.c.b.2253.9		16	161.45	even	6
2254.2.c.b.2253.10		16	7.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.0922753 + 0.0532752i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.78715 + 3.09543i) q^{5} +0.106550i q^{6} +(0.672033 + 2.55898i) q^{7} -1.00000 q^{8} +(-1.49432 - 2.58824i) q^{9} +(-1.78715 + 3.09543i) q^{10} +(-2.00891 - 1.15985i) q^{11} +(-0.0922753 + 0.0532752i) q^{12} -1.89279i q^{13} +(-1.88012 + 1.86149i) q^{14} +0.380843i q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.602480 - 1.04353i) q^{17} +(1.49432 - 2.58824i) q^{18} +(1.42152 + 2.46214i) q^{19} -3.57430 q^{20} +(-0.0743180 + 0.271933i) q^{21} -2.31969i q^{22} +(2.14111 + 4.29134i) q^{23} +(-0.0922753 - 0.0532752i) q^{24} +(-3.88781 + 6.73388i) q^{25} +(1.63920 - 0.946394i) q^{26} -0.638093i q^{27} +(-2.55216 - 0.697491i) q^{28} +3.48008 q^{29} +(-0.329820 + 0.190421i) q^{30} +(2.40205 + 1.38682i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.123582 - 0.214050i) q^{33} +1.20496 q^{34} +(-6.72013 + 6.65351i) q^{35} +2.98865 q^{36} +(4.48318 - 2.58836i) q^{37} +(-1.42152 + 2.46214i) q^{38} +(0.100839 - 0.174658i) q^{39} +(-1.78715 - 3.09543i) q^{40} -11.1173i q^{41} +(-0.272660 + 0.0716054i) q^{42} +2.46789i q^{43} +(2.00891 - 1.15985i) q^{44} +(5.34116 - 9.25116i) q^{45} +(-2.64586 + 3.99993i) q^{46} +(10.1165 - 5.84076i) q^{47} -0.106550i q^{48} +(-6.09674 + 3.43944i) q^{49} -7.77562 q^{50} +(0.111188 - 0.0641944i) q^{51} +(1.63920 + 0.946394i) q^{52} +(-7.58334 - 4.37825i) q^{53} +(0.552604 - 0.319046i) q^{54} -8.29127i q^{55} +(-0.672033 - 2.55898i) q^{56} +0.302926i q^{57} +(1.74004 + 3.01384i) q^{58} +(-4.57525 - 2.64152i) q^{59} +(-0.329820 - 0.190421i) q^{60} +(-2.78587 - 4.82527i) q^{61} +2.77365i q^{62} +(5.61903 - 5.56333i) q^{63} +1.00000 q^{64} +(5.85900 - 3.38270i) q^{65} +(0.123582 - 0.214050i) q^{66} +(10.2210 + 5.90111i) q^{67} +(0.602480 + 1.04353i) q^{68} +(-0.0310501 + 0.510053i) q^{69} +(-9.12217 - 2.49304i) q^{70} +0.295533 q^{71} +(1.49432 + 2.58824i) q^{72} +(3.87636 + 2.23802i) q^{73} +(4.48318 + 2.58836i) q^{74} +(-0.717498 + 0.414247i) q^{75} -2.84303 q^{76} +(1.61797 - 5.92022i) q^{77} +0.201677 q^{78} +(-8.15403 + 4.70773i) q^{79} +(1.78715 - 3.09543i) q^{80} +(-4.44898 + 7.70585i) q^{81} +(9.62785 - 5.55864i) q^{82} -6.05170 q^{83} +(-0.198342 - 0.200328i) q^{84} +4.30689 q^{85} +(-2.13726 + 1.23395i) q^{86} +(0.321126 + 0.185402i) q^{87} +(2.00891 + 1.15985i) q^{88} +(-2.84347 - 4.92504i) q^{89} +10.6823 q^{90} +(4.84361 - 1.27202i) q^{91} +(-4.78697 - 0.291412i) q^{92} +(0.147767 + 0.255939i) q^{93} +(10.1165 + 5.84076i) q^{94} +(-5.08092 + 8.80042i) q^{95} +(0.0922753 - 0.0532752i) q^{96} +13.9847 q^{97} +(-6.02701 - 3.56022i) q^{98} +6.93274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46}+ \cdots - 6 q^{96}+O(q^{100}) \) 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9 + 6 * q^12 - 8 * q^16 - 10 * q^18 + 8 * q^23 + 6 * q^24 + 2 * q^25 - 6 * q^26 - 16 * q^29 + 12 * q^31 + 8 * q^32 - 20 * q^36 - 2 * q^39 - 8 * q^46 - 6 * q^47 - 18 * q^49 + 4 * q^50 - 6 * q^52 + 18 * q^54 - 8 * q^58 + 36 * q^59 + 16 * q^64 - 12 * q^70 - 52 * q^71 - 10 * q^72 + 24 * q^73 + 30 * q^77 - 4 * q^78 - 20 * q^81 + 54 * q^82 + 80 * q^85 + 54 * q^87 - 16 * q^92 - 26 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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