LMFDB - Embedded newform 322.2.g.b.229.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(45,322)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$2.57118294509$
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			229.6
Root			$-1.36749 - 1.06300i$ of defining polynomial
Character	$\chi$	$=$	322.229
Dual form			322.2.g.b.45.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.0922753 - 0.0532752i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.78715 - 3.09543i) q^{5} -0.106550i q^{6} +(0.672033 - 2.55898i) q^{7} -1.00000 q^{8} +(-1.49432 + 2.58824i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.473126	−	0.880995i	$-0.656874\pi$
$3$	0.0922753	−	0.0532752i	0.0532752	−	0.0307584i	0.526401	+	0.850236i	$0.323541\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.78715	−	3.09543i	0.799238	−	1.38432i	−0.120876	−	0.992668i	$-0.538570\pi$
$5$	1.78715	−	3.09543i	0.799238	−	1.38432i	0.920113	−	0.391653i	$-0.128096\pi$
$6$		−	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	−0.771285	−	0.636490i	$-0.780385\pi$
$11$	−2.00891	+	1.15985i	−0.605710	+	0.349707i	0.165575	+	0.986197i	$0.447052\pi$
$12$	−0.0922753	−	0.0532752i	−0.0266376	−	0.0153792i
$13$			1.89279i			0.524965i	0.964937	+	0.262483i	$0.0845412\pi$
$13$			1.89279i			0.524965i	−0.964937	+	0.262483i	$0.915459\pi$
$14$	−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	0.929791	−	0.368087i	$-0.119987\pi$
$17$	0.602480	+	1.04353i	0.146123	+	0.253092i	−0.783668	+	0.621179i	$0.786654\pi$
$18$	1.49432	+	2.58824i	0.352215	+	0.610055i
$19$	1.42152	−	2.46214i	0.326118	−	0.564853i	−0.655620	−	0.755091i	$-0.727593\pi$
$19$	1.42152	−	2.46214i	0.326118	−	0.564853i	0.981738	+	0.190238i	$0.0609260\pi$
$20$	−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	−0.268531	−	0.963271i	$-0.586538\pi$
$31$	2.40205	−	1.38682i	0.431421	−	0.249081i	0.699952	+	0.714190i	$0.253205\pi$
$32$	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	0.820988	−	0.570945i	$-0.193423\pi$
$37$	4.48318	+	2.58836i	0.737030	+	0.425524i	−0.0839585	+	0.996469i	$0.526756\pi$
$38$	−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	$0.334668\pi$
$41$			11.1173i			1.73623i	−0.496365	+	0.868114i	$0.665332\pi$
$42$	−0.272660	−	0.0716054i	−0.0420724	−	0.0110490i
$43$		−	2.46789i		−	0.376350i	−0.982135	−	0.188175i	$-0.939743\pi$
$43$		−	2.46789i		−	0.376350i	0.982135	−	0.188175i	$-0.0602573\pi$
$44$	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	0.999623	−	0.0274716i	$-0.00874558\pi$
$47$	10.1165	+	5.84076i	1.47564	+	0.851963i	0.476020	+	0.879434i	$0.342079\pi$
$48$			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	−0.920301	−	0.391211i	$-0.872056\pi$
$53$	−7.58334	+	4.37825i	−1.04165	+	0.601398i	−0.121352	+	0.992610i	$0.538723\pi$
$54$	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	−0.767327	−	0.641256i	$-0.778414\pi$
$59$	−4.57525	+	2.64152i	−0.595646	+	0.343897i	0.171681	+	0.985153i	$0.445080\pi$
$60$	−0.329820	+	0.190421i	−0.0425795	+	0.0245833i
$61$	−2.78587	+	4.82527i	−0.356694	+	0.617813i	−0.987406	−	0.158204i	$-0.949430\pi$
$61$	−2.78587	+	4.82527i	−0.356694	+	0.617813i	0.630712	+	0.776017i	$0.282763\pi$
$62$		−	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	0.277847	−	0.960625i	$-0.410379\pi$
$67$	10.2210	−	5.90111i	1.24870	−	0.720935i	0.970849	+	0.239690i	$0.0770458\pi$
$68$	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	−0.255695	−	0.966757i	$-0.582304\pi$
$73$	3.87636	−	2.23802i	0.453693	−	0.261940i	0.709389	+	0.704817i	$0.248971\pi$
$74$	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	−0.0345950	−	0.999401i	$-0.511014\pi$
$79$	−8.15403	−	4.70773i	−0.917399	−	0.529661i	−0.882805	+	0.469741i	$0.844347\pi$
$80$	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	−0.976455	−	0.215721i	$-0.930790\pi$
$89$	−2.84347	+	4.92504i	−0.301408	+	0.522053i	0.675047	+	0.737774i	$0.264123\pi$
$90$	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	0.0300201	−	0.999549i	$-0.490443\pi$
$101$	9.15207	−	5.28395i	0.910665	−	0.525773i	0.880645	+	0.473776i	$0.157110\pi$
$102$	0.111188	−	0.0641944i	0.0110093	−	0.00635620i
$103$	−5.92856	+	10.2686i	−0.584158	+	1.01179i	0.410822	+	0.911716i	$0.365242\pi$
$103$	−5.92856	+	10.2686i	−0.584158	+	1.01179i	−0.994980	+	0.100076i	$0.968091\pi$
$104$		−	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	−0.438235	−	0.898860i	$-0.644396\pi$
$107$	−14.8519	−	8.57475i	−1.43579	−	0.828953i	−0.997553	+	0.0699076i	$0.977730\pi$
$108$	0.552604	−	0.319046i	0.0531744	−	0.0307002i
$109$	9.34275	−	5.39404i	0.894873	−	0.516655i	0.0193399	−	0.999813i	$-0.493844\pi$
$109$	9.34275	−	5.39404i	0.894873	−	0.516655i	0.875533	+	0.483158i	$0.160510\pi$
$110$	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	$0.260339\pi$
$113$			15.5136i			1.45940i	−0.683770	+	0.729698i	$0.739661\pi$
$114$	−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	−0.0807127	−	0.996737i	$-0.525720\pi$
$131$	−11.2655	−	6.50412i	−0.984269	−	0.568268i	−0.903556	+	0.428469i	$0.859053\pi$
$132$	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	−0.942782	−	0.333411i	$-0.891800\pi$
$137$	−13.1728	+	7.60533i	−1.12543	+	0.649767i	−0.182648	+	0.983178i	$0.558467\pi$
$138$	−0.457244	−	0.228137i	−0.0389232	−	0.0194203i
$139$			17.4437i			1.47956i	0.672849	+	0.739779i	$0.265070\pi$
$139$			17.4437i			1.47956i	−0.672849	+	0.739779i	$0.734930\pi$
$140$	−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	0.255569	−	0.966791i	$-0.417737\pi$
$149$	−5.54069	−	3.19892i	−0.453911	−	0.262066i	−0.709481	+	0.704725i	$0.751070\pi$
$150$	−0.717498	+	0.414247i	−0.0585834	+	0.0338232i
$151$	3.81266	+	6.60372i	0.310270	+	0.537403i	0.978421	−	0.206623i	$-0.0662473\pi$
$151$	3.81266	+	6.60372i	0.310270	+	0.537403i	−0.668151	+	0.744026i	$0.732914\pi$
$152$	−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	0.752692	−	0.658373i	$-0.228755\pi$
$157$	−2.42858	−	4.20642i	−0.193821	−	0.335708i	−0.946514	+	0.322664i	$0.895422\pi$
$158$	−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	−0.993792	−	0.111252i	$-0.964514\pi$
$163$	−5.11387	+	8.85748i	−0.400549	+	0.693771i	0.593243	+	0.805023i	$0.297847\pi$
$164$	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	$-0.904018\pi$
$167$		−	7.67588i		−	0.593977i	0.954881	−	0.296989i	$-0.0959824\pi$
$168$	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	0.924142	−	0.382050i	$-0.124782\pi$
$173$	13.8809	+	8.01415i	1.05535	+	0.609305i	0.131205	+	0.991355i	$0.458115\pi$
$174$		−	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	−0.999085	−	0.0427604i	$-0.986385\pi$
$179$	−7.17887	−	12.4342i	−0.536574	−	0.929374i	0.462511	−	0.886613i	$-0.346949\pi$
$180$	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	−0.0656595	−	0.997842i	$-0.520915\pi$
$191$	−13.3040	−	7.68109i	−0.962646	−	0.555784i	−0.896986	+	0.442058i	$0.854248\pi$
$192$	0.0922753	−	0.0532752i	0.00665940	−	0.00384481i
$193$	−9.10226	−	15.7656i	−0.655195	−	1.13483i	−0.981845	−	0.189685i	$-0.939253\pi$
$193$	−9.10226	−	15.7656i	−0.655195	−	1.13483i	0.326650	−	0.945145i	$-0.394080\pi$
$194$	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	−0.968425	−	0.249307i	$-0.919797\pi$
$199$	−9.87639	−	17.1064i	−0.700118	−	1.21264i	0.268306	−	0.963334i	$-0.413536\pi$
$200$	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	$0.0513337\pi$
$223$			4.79568i			0.321143i	−0.987024	+	0.160571i	$0.948666\pi$
$224$	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	0.880092	−	0.474803i	$-0.157481\pi$
$227$	0.434746	+	0.753001i	0.0288551	+	0.0499785i	−0.851237	+	0.524781i	$0.824147\pi$
$228$	−0.262342	+	0.151463i	−0.0173740	+	0.0100309i
$229$	11.6322	−	20.1476i	0.768679	−	1.33139i	−0.169601	−	0.985513i	$-0.554248\pi$
$229$	11.6322	−	20.1476i	0.768679	−	1.33139i	0.938280	−	0.345878i	$-0.112419\pi$
$230$	−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	−0.997886	−	0.0649901i	$-0.979298\pi$
$233$	−6.75691	+	11.7033i	−0.442660	+	0.766709i	0.555226	+	0.831699i	$0.312632\pi$
$234$	−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	0.994821	−	0.101640i	$-0.0324090\pi$
$241$	6.35541	+	11.0079i	0.409388	+	0.709080i	−0.585434	+	0.810720i	$0.699076\pi$
$242$	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	0.0510362	−	0.998697i	$-0.483748\pi$
$257$	−12.6381	−	7.29661i	−0.788342	−	0.455150i	−0.839379	+	0.543547i	$0.817081\pi$
$258$	−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	−0.998952	−	0.0457619i	$-0.985428\pi$
$263$	−23.6577	+	13.6588i	−1.45880	+	0.842237i	−0.459845	+	0.887999i	$0.652095\pi$
$264$	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	−0.970939	−	0.239326i	$-0.923074\pi$
$269$	−20.4875	+	11.8285i	−1.24915	+	0.721195i	−0.278208	+	0.960521i	$0.589740\pi$
$270$	1.97517	−	1.14037i	0.120205	−	0.0694005i
$271$	−22.6067	−	13.0520i	−1.37326	−	0.792852i	−0.381924	−	0.924194i	$-0.624738\pi$
$271$	−22.6067	−	13.0520i	−1.37326	−	0.792852i	−0.991337	+	0.131341i	$0.958072\pi$
$272$	−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	−0.744309	−	0.667835i	$-0.767221\pi$
$277$	−15.8198	−	27.4006i	−0.950517	−	1.64634i	−0.206208	−	0.978508i	$-0.566112\pi$
$278$	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	$0.0916119\pi$
$281$			9.51640i			0.567701i	−0.958869	+	0.283850i	$0.908388\pi$
$282$	0.622335	−	1.07792i	0.0370595	−	0.0641890i
$283$	6.82667	+	11.8241i	0.405804	+	0.702873i	0.994415	−	0.105544i	$-0.0336583\pi$
$283$	6.82667	+	11.8241i	0.405804	+	0.702873i	−0.588611	+	0.808416i	$0.700325\pi$
$284$	−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	$-0.735384\pi$
$307$		−	25.8903i		−	1.47764i	0.673905	−	0.738818i	$-0.264616\pi$
$308$	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	−0.573264	−	0.819371i	$-0.694323\pi$
$311$	−2.65056	+	1.53030i	−0.150299	+	0.0867753i	0.422964	+	0.906146i	$0.360990\pi$
$312$	−0.100839	−	0.174658i	−0.00570887	−	0.00988804i
$313$	−2.69126	+	4.66141i	−0.152119	+	0.263478i	−0.932006	−	0.362442i	$-0.881943\pi$
$313$	−2.69126	+	4.66141i	−0.152119	+	0.263478i	0.779887	+	0.625920i	$0.215276\pi$
$314$	−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	−0.991483	−	0.130234i	$-0.958427\pi$
$317$	−6.81834	+	11.8097i	−0.382956	+	0.663299i	0.608527	+	0.793533i	$0.291761\pi$
$318$	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	−0.755013	−	0.655710i	$-0.772369\pi$
$331$	3.46322	−	5.99847i	0.190356	−	0.329706i	0.945368	+	0.326005i	$0.105703\pi$
$332$	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	$0.198005\pi$
$337$			21.3940i			1.16540i	−0.812686	+	0.582702i	$0.801995\pi$
$338$	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	0.960396	+	0.278637i	$0.0898828\pi$
$347$	13.4402	+	23.2790i	0.721505	+	1.24968i	−0.238891	+	0.971046i	$0.576784\pi$
$348$	−0.321126	−	0.185402i	−0.0172142	−	0.00993860i
$349$			16.2629i			0.870533i	0.900302	+	0.435266i	$0.143346\pi$
$349$			16.2629i			0.870533i	−0.900302	+	0.435266i	$0.856654\pi$
$350$	−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	−0.525069	−	0.851060i	$-0.675961\pi$
$353$	−0.950024	+	0.548496i	−0.0505647	+	0.0291935i	0.474505	+	0.880253i	$0.342627\pi$
$354$	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	0.497806	−	0.867289i	$-0.334139\pi$
$359$	−0.0830977	−	0.0479765i	−0.00438573	−	0.00253210i	−0.502191	+	0.864757i	$0.667473\pi$
$360$	−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	0.958433	+	0.285316i	$0.0920987\pi$
$367$	13.9141	+	24.0999i	0.726308	+	1.25800i	−0.232125	+	0.972686i	$0.574568\pi$
$368$	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	0.411416	−	0.911448i	$-0.365034\pi$
$373$	−3.32599	−	1.92026i	−0.172213	−	0.0994272i	−0.583629	+	0.812021i	$0.698368\pi$
$374$	−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	$-0.783937\pi$
$379$		−	24.4457i		−	1.25569i	0.778337	−	0.627846i	$-0.216063\pi$
$380$	−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	−0.0129283	+	0.999916i	$0.504115\pi$
$383$	−17.0735	+	29.5722i	−0.872417	+	1.51107i	−0.859489	+	0.511154i	$0.829218\pi$
$384$		−	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	0.590629	−	0.806943i	$-0.298880\pi$
$389$	31.2567	−	18.0461i	1.58478	−	0.914971i	0.994148	−	0.108028i	$-0.0344537\pi$
$390$	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	0.704106	−	0.710095i	$-0.251348\pi$
$397$	8.79081	+	5.07537i	0.441198	+	0.254726i	−0.262908	+	0.964821i	$0.584681\pi$
$398$	−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	−0.358192	−	0.933648i	$-0.616607\pi$
$401$	−26.9506	−	15.5600i	−1.34585	−	0.777027i	−0.987659	+	0.156621i	$0.949940\pi$
$402$	−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	−0.438998	−	0.898488i	$-0.644667\pi$
$409$	2.41908	−	1.39666i	0.119616	−	0.0690602i	0.558614	+	0.829428i	$0.311333\pi$
$410$	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	$-0.751759\pi$
$421$		−	28.8564i		−	1.40638i	0.711003	−	0.703189i	$-0.248241\pi$
$422$	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	−0.624101	−	0.781344i	$-0.714535\pi$
$431$	−5.38712	+	3.11026i	−0.259489	+	0.149816i	0.364613	+	0.931159i	$0.381201\pi$
$432$	−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	0.585583	−	0.810613i	$-0.300866\pi$
$439$	3.69521	+	2.13343i	0.176363	+	0.101823i	−0.409220	+	0.912436i	$0.634199\pi$
$440$		−	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	−0.208147	−	0.978097i	$-0.566743\pi$
$443$	15.6380	−	27.0858i	0.742984	−	1.28689i	0.951131	−	0.308788i	$-0.0999233\pi$
$444$	−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	−0.235980	−	0.971758i	$-0.575830\pi$
$457$	−25.5577	−	14.7557i	−1.19554	−	0.690243i	−0.959557	+	0.281515i	$0.909163\pi$
$458$	−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	$-0.711817\pi$
$461$		−	33.7799i		−	1.57329i	0.617408	−	0.786643i	$-0.288183\pi$
$462$	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	−0.626857	−	0.779135i	$-0.715659\pi$
$467$	7.80824	−	13.5243i	0.361322	−	0.625828i	0.988179	+	0.153306i	$0.0489921\pi$
$468$			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	0.986595	−	0.163187i	$-0.0521774\pi$
$479$	7.70331	+	13.3425i	0.351973	+	0.609636i	−0.634622	+	0.772823i	$0.718844\pi$
$480$	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	0.983579	−	0.180479i	$-0.0577646\pi$
$487$	7.40363	+	12.8235i	0.335490	+	0.581086i	−0.648088	+	0.761565i	$0.724431\pi$
$488$	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	−0.857150	−	0.515067i	$-0.827767\pi$
$499$	0.390598	−	0.676536i	0.0174856	−	0.0302859i	0.874636	+	0.484781i	$0.161101\pi$
$500$	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	0.902693	−	0.430286i	$-0.141587\pi$
$509$	22.1414	+	12.7833i	0.981401	+	0.566612i	0.0787080	+	0.996898i	$0.474921\pi$
$510$		−	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	−0.897208	−	0.441608i	$-0.854408\pi$
$521$	−18.9690	−	32.8553i	−0.831048	−	1.43942i	0.0661607	−	0.997809i	$-0.478925\pi$
$522$	5.20037	+	9.00731i	0.227614	+	0.394239i
$523$	5.52517	−	9.56987i	0.241599	−	0.418461i	−0.719571	−	0.694419i	$-0.755662\pi$
$523$	5.52517	−	9.56987i	0.241599	−	0.418461i	0.961170	+	0.275957i	$0.0889949\pi$
$524$			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	−0.877020	−	0.480454i	$-0.840472\pi$
$541$	−0.521594	+	0.903427i	−0.0224251	+	0.0388414i	0.854595	+	0.519295i	$0.173805\pi$
$542$	−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	−0.222229	−	0.974995i	$-0.571333\pi$
$557$	12.0607	−	6.96323i	0.511027	−	0.295041i	0.733256	+	0.679953i	$0.238000\pi$
$558$	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	0.910601	+	0.413286i	$0.135619\pi$
$563$	19.2957	+	33.4211i	0.813217	+	1.40853i	−0.0973844	+	0.995247i	$0.531048\pi$
$564$	−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	0.328185	−	0.944613i	$-0.393563\pi$
$569$	−7.77110	−	4.48665i	−0.325782	−	0.188090i	−0.653967	+	0.756523i	$0.726896\pi$
$570$	−0.937687	+	0.541374i	−0.0392754	+	0.0226757i
$571$	−34.9707	+	20.1903i	−1.46348	+	0.844939i	−0.999170	−	0.0407357i	$-0.987030\pi$
$571$	−34.9707	+	20.1903i	−1.46348	+	0.844939i	−0.464307	+	0.885674i	$0.653696\pi$
$572$	−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	−0.725550	−	0.688169i	$-0.758415\pi$
$577$	−11.8267	+	6.82817i	−0.492354	+	0.284260i	0.233197	+	0.972430i	$0.425081\pi$
$578$	−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	$-0.935558\pi$
$587$		−	9.74306i		−	0.402139i	0.979577	−	0.201070i	$-0.0644417\pi$
$588$	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	0.520309	−	0.853978i	$-0.325817\pi$
$593$	0.995904	+	0.574985i	0.0408969	+	0.0236118i	−0.479412	+	0.877590i	$0.659150\pi$
$594$	−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	0.999254	+	0.0386117i	$0.0122935\pi$
$599$	13.0465	+	22.5972i	0.533066	+	0.923297i	−0.466188	+	0.884685i	$0.654373\pi$
$600$	0.717498	+	0.414247i	0.0292917	+	0.0169116i
$601$		−	5.31574i		−	0.216833i	−0.994106	−	0.108417i	$-0.965422\pi$
$601$		−	5.31574i		−	0.216833i	0.994106	−	0.108417i	$-0.0345781\pi$
$602$	−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	0.394092	−	0.919071i	$-0.371059\pi$
$607$	−5.04577	−	2.91318i	−0.204801	−	0.118242i	−0.598893	+	0.800829i	$0.704393\pi$
$608$	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	−0.521174	−	0.853451i	$-0.674506\pi$
$613$	−1.05598	+	0.609668i	−0.0426505	+	0.0246243i	0.478523	+	0.878075i	$0.341172\pi$
$614$	−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	$0.403712\pi$
$617$			47.4233i			1.90919i	−0.297907	+	0.954595i	$0.596288\pi$
$618$	1.09412	+	0.631690i	0.0440119	+	0.0254103i
$619$	−0.484010	−	0.838329i	−0.0194540	−	0.0336953i	0.856135	−	0.516753i	$-0.172859\pi$
$619$	−0.484010	−	0.838329i	−0.0194540	−	0.0336953i	−0.875589	+	0.483058i	$0.839526\pi$
$620$	−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	$0.0997208\pi$
$631$			15.4829i			0.616366i	−0.951327	+	0.308183i	$0.900279\pi$
$632$	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	−0.266261	−	0.963901i	$-0.585788\pi$
$641$	11.0227	−	6.36397i	0.435371	−	0.251362i	0.701632	+	0.712539i	$0.252455\pi$
$642$	−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	0.140706	−	0.990051i	$-0.455063\pi$
$647$	27.1778	−	15.6911i	1.06847	−	0.616880i	0.927763	+	0.373171i	$0.121730\pi$
$648$	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	−0.524584	−	0.851359i	$-0.675779\pi$
$653$	12.1383	−	21.0241i	0.475007	−	0.822735i	0.999590	+	0.0286234i	$0.00911236\pi$
$654$	−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	$0.164602\pi$
$659$			25.3820i			0.988744i	−0.869250	+	0.494372i	$0.835398\pi$
$660$	0.441719	−	0.765080i	0.0171939	−	0.0297807i
$661$	13.7217	+	23.7667i	0.533713	+	0.924418i	0.999224	+	0.0393759i	$0.0125370\pi$
$661$	13.7217	+	23.7667i	0.533713	+	0.924418i	−0.465512	+	0.885042i	$0.654130\pi$
$662$	−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	−0.376140	+	0.926563i	$0.622749\pi$
$677$	−25.7720	+	44.6383i	−0.990497	+	1.71559i	−0.614357	+	0.789028i	$0.710585\pi$
$678$	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	0.999198	+	0.0400436i	$0.0127497\pi$
$683$	13.9630	+	24.1846i	0.534278	+	0.925396i	−0.464920	+	0.885353i	$0.653917\pi$
$684$	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	0.654796	−	0.755806i	$-0.272755\pi$
$691$	8.61282	+	4.97261i	0.327647	+	0.189167i	−0.327149	+	0.944973i	$0.606088\pi$
$692$		−	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	$-0.868939\pi$
$701$		−	21.1920i		−	0.800411i	0.916425	−	0.400206i	$-0.131061\pi$
$702$	−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	0.315956	−	0.948774i	$-0.397675\pi$
$709$	−9.25899	−	5.34568i	−0.347729	−	0.200761i	−0.663685	+	0.748013i	$0.731008\pi$
$710$	−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	0.589997	−	0.807406i	$-0.299129\pi$
$719$	4.98103	+	2.87580i	0.185761	+	0.107249i	−0.404235	+	0.914655i	$0.632462\pi$
$720$	−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	−0.765376	−	0.643584i	$-0.777447\pi$
$733$	4.72907	−	8.19099i	0.174672	−	0.302541i	0.940048	+	0.341043i	$0.110780\pi$
$734$	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	0.626693	−	0.779266i	$-0.284408\pi$
$739$	−9.82769	−	17.0221i	−0.361517	−	0.626166i	−0.988211	+	0.153099i	$0.951075\pi$
$740$	−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	$0.241478\pi$
$743$			37.5029i			1.37585i	−0.725782	+	0.687925i	$0.758522\pi$
$744$	−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	0.753021	−	0.657996i	$-0.228596\pi$
$751$	15.3380	+	8.85537i	0.559690	+	0.323137i	−0.193331	+	0.981134i	$0.561929\pi$
$752$	−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	$-0.936334\pi$
$757$		−	10.9330i		−	0.397366i	0.980064	−	0.198683i	$-0.0636664\pi$
$758$	−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	0.744037	−	0.668138i	$-0.232909\pi$
$761$	14.8257	+	8.55962i	0.537431	+	0.310286i	−0.206606	+	0.978424i	$0.566242\pi$
$762$		−	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	0.867677	−	0.497129i	$-0.165612\pi$
$773$	0.0920898	+	0.159504i	0.00331224	+	0.00573697i	−0.864365	+	0.502866i	$0.832279\pi$
$774$	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	−0.846020	−	0.533151i	$-0.821008\pi$
$787$	−24.8199	−	42.9892i	−0.884732	−	1.53240i	−0.0387121	−	0.999250i	$-0.512326\pi$
$788$	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	−0.990063	−	0.140621i	$-0.955090\pi$
$809$	−17.5440	−	30.3871i	−0.616813	−	1.06835i	0.373250	−	0.927731i	$-0.378243\pi$
$810$	−15.9020	+	27.5430i	−0.558738	+	0.967763i
$811$		−	53.0734i		−	1.86366i	−0.362897	−	0.931829i	$-0.618212\pi$
$811$		−	53.0734i		−	1.86366i	0.362897	−	0.931829i	$-0.381788\pi$
$812$	−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	−0.994733	−	0.102496i	$-0.967317\pi$
$821$	−11.7077	+	20.2784i	−0.408602	+	0.707720i	0.586131	+	0.810216i	$0.300650\pi$
$822$	0.810351	+	1.40357i	0.0282642	+	0.0489551i
$823$	−0.372150	−	0.644582i	−0.0129723	−	0.0224687i	0.859466	−	0.511192i	$-0.170796\pi$
$823$	−0.372150	−	0.644582i	−0.0129723	−	0.0224687i	−0.872439	+	0.488724i	$0.837463\pi$
$824$	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	$-0.733283\pi$
$827$		−	42.7483i		−	1.48650i	0.669012	−	0.743251i	$-0.266717\pi$
$828$	6.39903	−	12.8253i	0.222382	−	0.445710i
$829$	29.8873	−	17.2554i	1.03803	−	0.599306i	0.118754	−	0.992924i	$-0.462110\pi$
$829$	29.8873	−	17.2554i	1.03803	−	0.599306i	0.919274	+	0.393618i	$0.128777\pi$
$830$	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	$0.0129558\pi$
$853$			2.37683i			0.0813810i	−0.999172	+	0.0406905i	$0.987044\pi$
$854$	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	0.328286	−	0.944578i	$-0.393529\pi$
$857$	38.3631	−	22.1489i	1.31046	−	0.756593i	0.982172	+	0.187985i	$0.0601958\pi$
$858$	−0.405152	+	0.233915i	−0.0138317	+	0.00798572i
$859$	−7.81247	−	4.51053i	−0.266558	−	0.153897i	0.360764	−	0.932657i	$-0.382516\pi$
$859$	−7.81247	−	4.51053i	−0.266558	−	0.153897i	−0.627322	+	0.778760i	$0.715849\pi$
$860$			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	−0.608751	−	0.793362i	$-0.708329\pi$
$863$	11.2424	−	19.4724i	0.382696	−	0.662849i	0.991447	+	0.130513i	$0.0416623\pi$
$864$	−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	−0.272566	−	0.962137i	$-0.587872\pi$
$877$	20.6397	−	35.7490i	0.696952	−	1.20716i	0.969518	−	0.245019i	$-0.0787944\pi$
$878$	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	0.735434	−	0.677597i	$-0.236978\pi$
$887$	15.3778	+	8.87835i	0.516335	+	0.298106i	−0.219099	+	0.975703i	$0.570312\pi$
$888$	−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	−0.637687	−	0.770295i	$-0.720109\pi$
$907$	−8.71677	+	5.03263i	−0.289436	+	0.167106i	0.348252	+	0.937401i	$0.386775\pi$
$908$	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	$-0.851684\pi$
$911$		−	27.1204i		−	0.898540i	0.893396	−	0.449270i	$-0.148316\pi$
$912$	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	0.372772	−	0.927923i	$-0.378407\pi$
$919$	−7.41041	−	4.27840i	−0.244447	−	0.141131i	−0.617219	+	0.786792i	$0.711741\pi$
$920$	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	0.170520	−	0.985354i	$-0.445455\pi$
$929$	−18.2134	−	10.5155i	−0.597562	−	0.345003i	−0.768082	+	0.640352i	$0.778789\pi$
$930$	−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	0.511899	−	0.859046i	$-0.328942\pi$
$941$	−14.9699	−	25.9287i	−0.488006	−	0.845251i	−0.999905	+	0.0137945i	$0.995609\pi$
$942$	−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	−0.956338	−	0.292263i	$-0.905592\pi$
$947$	−6.92591	+	11.9960i	−0.225062	+	0.389819i	0.731276	+	0.682082i	$0.238925\pi$
$948$	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	$0.121852\pi$
$953$			23.0621i			0.747055i	−0.927619	+	0.373527i	$0.878148\pi$
$954$	−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	−0.932880	−	0.360188i	$-0.882712\pi$
$971$	−4.81459	+	8.33912i	−0.154508	+	0.267615i	0.778372	+	0.627803i	$0.216046\pi$
$972$			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	−0.295063	−	0.955478i	$-0.595341\pi$
$977$	12.0300	−	6.94552i	0.384874	−	0.222207i	0.679937	+	0.733271i	$0.262007\pi$
$978$	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	−0.923860	−	0.382731i	$-0.874984\pi$
$983$	−24.8749	−	43.0845i	−0.793385	−	1.37418i	0.130475	−	0.991452i	$-0.458350\pi$
$984$	−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	0.979002	−	0.203850i	$-0.0653456\pi$
$991$	9.85207	+	17.0643i	0.312961	+	0.542065i	−0.666041	+	0.745915i	$0.732012\pi$
$992$	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	−0.304862	−	0.952397i	$-0.598610\pi$
$997$	11.6042	−	6.69967i	0.367507	−	0.212181i	0.672369	+	0.740216i	$0.265277\pi$
$998$	−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.229.6	yes	16
7.2	even	3		2254.2.c.b.2253.9		16
7.3	odd	6	inner	322.2.g.b.45.5	✓	16
7.5	odd	6		2254.2.c.b.2253.8		16
23.22	odd	2	inner	322.2.g.b.229.5	yes	16
161.45	even	6	inner	322.2.g.b.45.6	yes	16
161.68	even	6		2254.2.c.b.2253.7		16
161.114	odd	6		2254.2.c.b.2253.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.b.45.5	✓	16	7.3	odd	6	inner
322.2.g.b.45.6	yes	16	161.45	even	6	inner
322.2.g.b.229.5	yes	16	23.22	odd	2	inner
322.2.g.b.229.6	yes	16	1.1	even	1	trivial
2254.2.c.b.2253.7		16	161.68	even	6
2254.2.c.b.2253.8		16	7.5	odd	6
2254.2.c.b.2253.9		16	7.2	even	3
2254.2.c.b.2253.10		16	161.114	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.0922753 - 0.0532752i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.78715 - 3.09543i) q^{5} -0.106550i q^{6} +(0.672033 - 2.55898i) q^{7} -1.00000 q^{8} +(-1.49432 + 2.58824i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9}+O(q^{10}) \) 16 * q + 8 * q^2 - 6 * q^3 - 8 * q^4 - 16 * q^8 + 10 * q^9	\( 16 q + 8 q^{2} - 6 q^{3} - 8 q^{4} - 16 q^{8} + 10 q^{9} + 6 q^{12} - 8 q^{16} - 10 q^{18} + 8 q^{23} + 6 q^{24} + 2 q^{25} - 6 q^{26} - 16 q^{29} + 12 q^{31} + 8 q^{32} - 20 q^{36} - 2 q^{39} - 8 q^{46} - 6 q^{47} - 18 q^{49} + 4 q^{50} - 6 q^{52} + 18 q^{54} - 8 q^{58} + 36 q^{59} + 16 q^{64} - 12 q^{70} - 52 q^{71} - 10 q^{72} + 24 q^{73} + 30 q^{77} - 4 q^{78} - 20 q^{81} + 54 q^{82} + 80 q^{85} + 54 q^{87} - 16 q^{92} - 26 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96}+O(q^{100}) \) 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

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