LMFDB - Embedded newform 770.2.o.b.549.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(439,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 3]))

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

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

chi := DirichletCharacter("770.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.o (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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			549.15
Character	$\chi$	$=$	770.549
Dual form			770.2.o.b.439.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.533793 - 0.924557i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.13643 - 1.92576i) q^{5} +1.06759 q^{6} +(-1.22107 + 2.34712i) q^{7} -1.00000 q^{8} +(0.930129 + 1.61103i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.533793 - 0.924557i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.13643 - 1.92576i) q^{5} +1.06759 q^{6} +(-1.22107 + 2.34712i) q^{7} -1.00000 q^{8} +(0.930129 + 1.61103i) q^{9} +(2.23597 + 0.0212957i) q^{10} +(2.97904 + 1.45786i) q^{11} +(0.533793 + 0.924557i) q^{12} +1.72838i q^{13} +(-2.64320 + 0.116087i) q^{14} +(-1.17386 - 2.07865i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.33846 + 0.772761i) q^{17} +(-0.930129 + 1.61103i) q^{18} +(-0.241835 - 0.418871i) q^{19} +(1.09954 + 1.94705i) q^{20} +(1.51825 + 2.38183i) q^{21} +(0.226978 + 3.30885i) q^{22} +(3.47535 - 2.00649i) q^{23} +(-0.533793 + 0.924557i) q^{24} +(-2.41707 - 4.37696i) q^{25} +(-1.49682 + 0.864188i) q^{26} +5.18875 q^{27} +(-1.42214 - 2.23104i) q^{28} -1.63137i q^{29} +(1.21323 - 2.05591i) q^{30} +(4.21221 + 2.43192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.93806 - 1.97610i) q^{33} +1.54552i q^{34} +(3.13234 + 5.01881i) q^{35} -1.86026 q^{36} +(-1.81722 + 1.04917i) q^{37} +(0.241835 - 0.418871i) q^{38} +(1.59798 + 0.922596i) q^{39} +(-1.13643 + 1.92576i) q^{40} +8.37376 q^{41} +(-1.30360 + 2.50576i) q^{42} -1.61281 q^{43} +(-2.75206 + 1.85099i) q^{44} +(4.15948 + 0.0396155i) q^{45} +(3.47535 + 2.00649i) q^{46} +(1.81833 + 3.14943i) q^{47} -1.06759 q^{48} +(-4.01799 - 5.73200i) q^{49} +(2.58202 - 4.28173i) q^{50} +(1.42892 - 0.824989i) q^{51} +(-1.49682 - 0.864188i) q^{52} +(-9.24141 - 5.33553i) q^{53} +(2.59437 + 4.49359i) q^{54} +(6.19293 - 4.08015i) q^{55} +(1.22107 - 2.34712i) q^{56} -0.516361 q^{57} +(1.41281 - 0.815686i) q^{58} +(3.56527 + 2.05841i) q^{59} +(2.38709 + 0.0227350i) q^{60} +(-0.573483 - 0.993302i) q^{61} +4.86384i q^{62} +(-4.91704 + 0.215952i) q^{63} +1.00000 q^{64} +(3.32843 + 1.96417i) q^{65} +(3.18038 + 1.55639i) q^{66} +(-4.81081 - 2.77752i) q^{67} +(-1.33846 + 0.772761i) q^{68} -4.28421i q^{69} +(-2.78025 + 5.22209i) q^{70} -6.87538 q^{71} +(-0.930129 - 1.61103i) q^{72} +(-6.69748 - 3.86679i) q^{73} +(-1.81722 - 1.04917i) q^{74} +(-5.33697 - 0.101669i) q^{75} +0.483671 q^{76} +(-7.05937 + 5.21203i) q^{77} +1.84519i q^{78} +(-8.64592 + 4.99172i) q^{79} +(-2.23597 - 0.0212957i) q^{80} +(-0.0206686 + 0.0357991i) q^{81} +(4.18688 + 7.25189i) q^{82} +3.34082i q^{83} +(-2.82185 + 0.123933i) q^{84} +(3.00921 - 1.69936i) q^{85} +(-0.806403 - 1.39673i) q^{86} +(-1.50830 - 0.870816i) q^{87} +(-2.97904 - 1.45786i) q^{88} +(6.49734 - 3.75124i) q^{89} +(2.04543 + 3.62202i) q^{90} +(-4.05672 - 2.11046i) q^{91} +4.01299i q^{92} +(4.49690 - 2.59629i) q^{93} +(-1.81833 + 3.14943i) q^{94} +(-1.08147 - 0.0103001i) q^{95} +(-0.533793 - 0.924557i) q^{96} -6.99351 q^{97} +(2.95506 - 6.34568i) q^{98} +(0.422237 + 6.15531i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	$ 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.533793	−	0.924557i	0.308186	−	0.533793i	−0.669780	−	0.742560i	$-0.733612\pi$
$3$	0.533793	−	0.924557i	0.308186	−	0.533793i	0.977966	+	0.208766i	$0.0669448\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.13643	−	1.92576i	0.508225	−	0.861224i
$5$	1.13643	−	1.92576i	0.508225	−	0.861224i
$6$	1.06759			0.435840
$7$	−1.22107	+	2.34712i	−0.461520	+	0.887130i
$7$	−1.22107	+	2.34712i	−0.461520	+	0.887130i
$8$	−1.00000			−0.353553
$9$	0.930129	+	1.61103i	0.310043	+	0.537010i
$10$	2.23597	+	0.0212957i	0.707075	+	0.00673428i
$11$	2.97904	+	1.45786i	0.898213	+	0.439560i
$11$	2.97904	+	1.45786i	0.898213	+	0.439560i
$12$	0.533793	+	0.924557i	0.154093	+	0.266897i
$13$			1.72838i			0.479365i	0.970851	+	0.239683i	$0.0770434\pi$
$13$			1.72838i			0.479365i	−0.970851	+	0.239683i	$0.922957\pi$
$14$	−2.64320	+	0.116087i	−0.706426	+	0.0310255i
$15$	−1.17386	−	2.07865i	−0.303088	−	0.536704i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.33846	+	0.772761i	0.324625	+	0.187422i	0.653452	−	0.756968i	$-0.273320\pi$
$17$	1.33846	+	0.772761i	0.324625	+	0.187422i	−0.328827	+	0.944390i	$0.606653\pi$
$18$	−0.930129	+	1.61103i	−0.219234	+	0.379724i
$19$	−0.241835	−	0.418871i	−0.0554809	−	0.0960957i	0.836951	−	0.547278i	$-0.184336\pi$
$19$	−0.241835	−	0.418871i	−0.0554809	−	0.0960957i	−0.892432	+	0.451182i	$0.851003\pi$
$20$	1.09954	+	1.94705i	0.245865	+	0.435374i
$21$	1.51825	+	2.38183i	0.331310	+	0.519757i
$22$	0.226978	+	3.30885i	0.0483918	+	0.705449i
$23$	3.47535	−	2.00649i	0.724660	−	0.418383i	−0.0918052	−	0.995777i	$-0.529264\pi$
$23$	3.47535	−	2.00649i	0.724660	−	0.418383i	0.816466	+	0.577394i	$0.195930\pi$
$24$	−0.533793	+	0.924557i	−0.108960	+	0.188724i
$25$	−2.41707	−	4.37696i	−0.483414	−	0.875392i
$26$	−1.49682	+	0.864188i	−0.293550	+	0.169481i
$27$	5.18875			0.998575
$28$	−1.42214	−	2.23104i	−0.268758	−	0.421627i
$29$		−	1.63137i		−	0.302938i	−0.988462	−	0.151469i	$-0.951600\pi$
$29$		−	1.63137i		−	0.302938i	0.988462	−	0.151469i	$-0.0484004\pi$
$30$	1.21323	−	2.05591i	0.221505	−	0.375356i
$31$	4.21221	+	2.43192i	0.756535	+	0.436786i	0.828050	−	0.560654i	$-0.189450\pi$
$31$	4.21221	+	2.43192i	0.756535	+	0.436786i	−0.0715154	+	0.997439i	$0.522783\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.93806	−	1.97610i	0.511451	−	0.343994i
$34$			1.54552i			0.265055i
$35$	3.13234	+	5.01881i	0.529462	+	0.848334i
$36$	−1.86026			−0.310043
$37$	−1.81722	+	1.04917i	−0.298749	+	0.172483i	−0.641881	−	0.766804i	$-0.721846\pi$
$37$	−1.81722	+	1.04917i	−0.298749	+	0.172483i	0.343132	+	0.939287i	$0.388512\pi$
$38$	0.241835	−	0.418871i	0.0392309	−	0.0679499i
$39$	1.59798	+	0.922596i	0.255882	+	0.147734i
$40$	−1.13643	+	1.92576i	−0.179685	+	0.304489i
$41$	8.37376			1.30776			0.653881	−	0.756597i	$-0.273140\pi$
$41$	8.37376			1.30776			0.653881	+	0.756597i	$0.273140\pi$
$42$	−1.30360	+	2.50576i	−0.201149	+	0.386647i
$43$	−1.61281			−0.245951			−0.122975	−	0.992410i	$-0.539244\pi$
$43$	−1.61281			−0.245951			−0.122975	+	0.992410i	$0.539244\pi$
$44$	−2.75206	+	1.85099i	−0.414888	+	0.279048i
$45$	4.15948	+	0.0396155i	0.620058	+	0.00590552i
$46$	3.47535	+	2.00649i	0.512412	+	0.295841i
$47$	1.81833	+	3.14943i	0.265230	+	0.459392i	0.967624	−	0.252397i	$-0.0812187\pi$
$47$	1.81833	+	3.14943i	0.265230	+	0.459392i	−0.702394	+	0.711789i	$0.747885\pi$
$48$	−1.06759			−0.154093
$49$	−4.01799	−	5.73200i	−0.573998	−	0.818856i
$50$	2.58202	−	4.28173i	0.365153	−	0.605527i
$51$	1.42892	−	0.824989i	0.200089	−	0.115522i
$52$	−1.49682	−	0.864188i	−0.207571	−	0.119841i
$53$	−9.24141	−	5.33553i	−1.26941	−	0.732892i	−0.294530	−	0.955642i	$-0.595163\pi$
$53$	−9.24141	−	5.33553i	−1.26941	−	0.732892i	−0.974875	+	0.222751i	$0.928496\pi$
$54$	2.59437	+	4.49359i	0.353050	+	0.611500i
$55$	6.19293	−	4.08015i	0.835054	−	0.550168i
$56$	1.22107	−	2.34712i	0.163172	−	0.313648i
$57$	−0.516361			−0.0683936
$58$	1.41281	−	0.815686i	0.185511	−	0.107105i
$59$	3.56527	+	2.05841i	0.464158	+	0.267982i	0.713791	−	0.700359i	$-0.246977\pi$
$59$	3.56527	+	2.05841i	0.464158	+	0.267982i	−0.249633	+	0.968341i	$0.580310\pi$
$60$	2.38709	+	0.0227350i	0.308172	+	0.00293507i
$61$	−0.573483	−	0.993302i	−0.0734270	−	0.127179i	0.826974	−	0.562240i	$-0.190060\pi$
$61$	−0.573483	−	0.993302i	−0.0734270	−	0.127179i	−0.900401	+	0.435061i	$0.856727\pi$
$62$			4.86384i			0.617708i
$63$	−4.91704	+	0.215952i	−0.619489	+	0.0272073i
$64$	1.00000			0.125000
$65$	3.32843	+	1.96417i	0.412841	+	0.243626i
$66$	3.18038	+	1.55639i	0.391478	+	0.191578i
$67$	−4.81081	−	2.77752i	−0.587735	−	0.339329i	0.176467	−	0.984307i	$-0.443533\pi$
$67$	−4.81081	−	2.77752i	−0.587735	−	0.339329i	−0.764201	+	0.644978i	$0.776867\pi$
$68$	−1.33846	+	0.772761i	−0.162312	+	0.0937110i
$69$		−	4.28421i		−	0.515758i
$70$	−2.78025	+	5.22209i	−0.332303	+	0.624159i
$71$	−6.87538			−0.815957			−0.407979	−	0.912991i	$-0.633766\pi$
$71$	−6.87538			−0.815957			−0.407979	+	0.912991i	$0.633766\pi$
$72$	−0.930129	−	1.61103i	−0.109617	−	0.189862i
$73$	−6.69748	−	3.86679i	−0.783881	−	0.452574i	0.0539227	−	0.998545i	$-0.482828\pi$
$73$	−6.69748	−	3.86679i	−0.783881	−	0.452574i	−0.837804	+	0.545971i	$0.816161\pi$
$74$	−1.81722	−	1.04917i	−0.211248	−	0.121964i
$75$	−5.33697	−	0.101669i	−0.616260	−	0.0117398i
$76$	0.483671			0.0554809
$77$	−7.05937	+	5.21203i	−0.804490	+	0.593966i
$78$			1.84519i			0.208927i
$79$	−8.64592	+	4.99172i	−0.972741	+	0.561613i	−0.900071	−	0.435743i	$-0.856485\pi$
$79$	−8.64592	+	4.99172i	−0.972741	+	0.561613i	−0.0726705	+	0.997356i	$0.523152\pi$
$80$	−2.23597	−	0.0212957i	−0.249989	−	0.00238093i
$81$	−0.0206686	+	0.0357991i	−0.00229651	+	0.00397767i
$82$	4.18688	+	7.25189i	0.462364	+	0.800837i
$83$			3.34082i			0.366703i	0.983047	+	0.183351i	$0.0586946\pi$
$83$			3.34082i			0.366703i	−0.983047	+	0.183351i	$0.941305\pi$
$84$	−2.82185	+	0.123933i	−0.307889	+	0.0135222i
$85$	3.00921	−	1.69936i	0.326395	−	0.184322i
$86$	−0.806403	−	1.39673i	−0.0869566	−	0.150613i
$87$	−1.50830	−	0.870816i	−0.161706	−	0.0933613i
$88$	−2.97904	−	1.45786i	−0.317566	−	0.155408i
$89$	6.49734	−	3.75124i	0.688716	−	0.397631i	−0.114415	−	0.993433i	$-0.536499\pi$
$89$	6.49734	−	3.75124i	0.688716	−	0.397631i	0.803131	+	0.595802i	$0.203166\pi$
$90$	2.04543	+	3.62202i	0.215607	+	0.381794i
$91$	−4.05672	−	2.11046i	−0.425259	−	0.221237i
$92$			4.01299i			0.418383i
$93$	4.49690	−	2.59629i	0.466307	−	0.269222i
$94$	−1.81833	+	3.14943i	−0.187546	+	0.324839i
$95$	−1.08147	−	0.0103001i	−0.110957	−	0.00105677i
$96$	−0.533793	−	0.924557i	−0.0544801	−	0.0943622i
$97$	−6.99351			−0.710084			−0.355042	−	0.934850i	$-0.615533\pi$
$97$	−6.99351			−0.710084			−0.355042	+	0.934850i	$0.615533\pi$
$98$	2.95506	−	6.34568i	0.298506	−	0.641010i
$99$	0.422237	+	6.15531i	0.0424364	+	0.618632i
$100$	4.99909	+	0.0952328i	0.499909	+	0.00952328i
$101$	1.06527	−	1.84510i	0.105998	−	0.183594i	−0.808148	−	0.588980i	$-0.799530\pi$
$101$	1.06527	−	1.84510i	0.105998	−	0.183594i	0.914146	+	0.405386i	$0.132863\pi$
$102$	1.42892	+	0.824989i	0.141484	+	0.0816861i
$103$	7.74347	+	13.4121i	0.762987	+	1.32153i	0.941305	+	0.337559i	$0.109601\pi$
$103$	7.74347	+	13.4121i	0.762987	+	1.32153i	−0.178318	+	0.983973i	$0.557066\pi$
$104$		−	1.72838i		−	0.169481i
$105$	6.31220	−	0.217016i	0.616008	−	0.0211786i
$106$		−	10.6711i		−	1.03647i
$107$	−0.324320	−	0.561739i	−0.0313532	−	0.0543054i	0.849923	−	0.526907i	$-0.176648\pi$
$107$	−0.324320	−	0.561739i	−0.0313532	−	0.0543054i	−0.881276	+	0.472602i	$0.843315\pi$
$108$	−2.59437	+	4.49359i	−0.249644	+	0.432396i
$109$	−17.4081	−	10.0506i	−1.66739	−	0.962669i	−0.969037	−	0.246916i	$-0.920583\pi$
$109$	−17.4081	−	10.0506i	−1.66739	−	0.962669i	−0.698354	−	0.715753i	$-0.746084\pi$
$110$	6.62998	+	3.32316i	0.632144	+	0.316851i
$111$			2.24017i			0.212627i
$112$	2.64320	−	0.116087i	0.249759	−	0.0109692i
$113$		−	2.42255i		−	0.227895i	−0.993487	−	0.113947i	$-0.963651\pi$
$113$		−	2.42255i		−	0.227895i	0.993487	−	0.113947i	$-0.0363495\pi$
$114$	−0.258180	−	0.447182i	−0.0241808	−	0.0418824i
$115$	0.0854592	−	8.97290i	0.00796912	−	0.836728i
$116$	1.41281	+	0.815686i	0.131176	+	0.0757346i
$117$	−2.78447	+	1.60761i	−0.257424	+	0.148624i
$118$			4.11682i			0.378984i
$119$	−3.44812	+	2.19794i	−0.316088	+	0.201485i
$120$	1.17386	+	2.07865i	0.107158	+	0.189754i
$121$	6.74931	+	8.68601i	0.613574	+	0.789637i
$122$	0.573483	−	0.993302i	0.0519207	−	0.0899293i
$123$	4.46986	−	7.74202i	0.403034	−	0.698075i
$124$	−4.21221	+	2.43192i	−0.378267	+	0.218393i
$125$	−11.1758	−	0.319396i	−0.999592	−	0.0285677i
$126$	−2.64554	−	4.15031i	−0.235683	−	0.369739i
$127$	16.9566			1.50465			0.752326	−	0.658791i	$-0.228932\pi$
$127$	16.9566			1.50465			0.752326	+	0.658791i	$0.228932\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−0.860905	+	1.49113i	−0.0757984	+	0.131287i
$130$	−0.0368069	+	3.86459i	−0.00322818	+	0.338947i
$131$	−3.04800	−	5.27929i	−0.266305	−	0.461254i	0.701600	−	0.712571i	$-0.252469\pi$
$131$	−3.04800	−	5.27929i	−0.266305	−	0.461254i	−0.967905	+	0.251318i	$0.919136\pi$
$132$	0.242318	+	3.53248i	0.0210911	+	0.307463i
$133$	1.27844	−	0.0561478i	0.110855	−	0.00486863i
$134$		−	5.55505i		−	0.479883i
$135$	5.89663	−	9.99226i	0.507501	−	0.859997i
$136$	−1.33846	−	0.772761i	−0.114772	−	0.0662637i
$137$	−8.99694	−	5.19438i	−0.768660	−	0.443786i	0.0637363	−	0.997967i	$-0.479698\pi$
$137$	−8.99694	−	5.19438i	−0.768660	−	0.443786i	−0.832396	+	0.554181i	$0.813032\pi$
$138$	3.71024	−	2.14211i	0.315836	−	0.182348i
$139$	−14.0908			−1.19517			−0.597584	−	0.801807i	$-0.703872\pi$
$139$	−14.0908			−1.19517			−0.597584	+	0.801807i	$0.703872\pi$
$140$	−5.91259	+	0.203278i	−0.499705	+	0.0171801i
$141$	3.88244			0.326961
$142$	−3.43769	−	5.95425i	−0.288484	−	0.499670i
$143$	−2.51972	+	5.14890i	−0.210710	+	0.430572i
$144$	0.930129	−	1.61103i	0.0775108	−	0.134253i
$145$	−3.14163	−	1.85393i	−0.260898	−	0.153961i
$146$		−	7.73359i		−	0.640036i
$147$	−7.44433	+	0.655159i	−0.613998	+	0.0540366i
$148$		−	2.09835i		−	0.172483i
$149$	−18.2929	+	10.5614i	−1.49861	+	0.865223i	−0.999999	−	0.00160170i	$-0.999490\pi$
$149$	−18.2929	+	10.5614i	−1.49861	+	0.865223i	−0.498612	+	0.866825i	$0.666157\pi$
$150$	−2.58043	−	4.67278i	−0.210692	−	0.381531i
$151$	−14.7836	−	8.53532i	−1.20307	−	0.694595i	−0.241836	−	0.970317i	$-0.577750\pi$
$151$	−14.7836	−	8.53532i	−1.20307	−	0.694595i	−0.961237	+	0.275723i	$0.911083\pi$
$152$	0.241835	+	0.418871i	0.0196154	+	0.0339750i
$153$			2.87507i			0.232436i
$154$	−8.04344	−	3.50758i	−0.648159	−	0.282649i
$155$	9.47015	−	5.34799i	0.760660	−	0.429561i
$156$	−1.59798	+	0.922596i	−0.127941	+	0.0738668i
$157$	5.57078	−	9.64888i	0.444597	−	0.770064i	−0.553427	−	0.832898i	$-0.686680\pi$
$157$	5.57078	−	9.64888i	0.444597	−	0.770064i	0.998024	+	0.0628331i	$0.0200136\pi$
$158$	−8.64592	−	4.99172i	−0.687832	−	0.397120i
$159$	−9.86601	+	5.69614i	−0.782425	+	0.451733i
$160$	−1.09954	−	1.94705i	−0.0869263	−	0.153928i
$161$	0.465855	+	10.6071i	0.0367145	+	0.835960i
$162$	−0.0413372			−0.00324776
$163$	16.7221	−	9.65452i	1.30978	−	0.756200i	0.327718	−	0.944776i	$-0.393720\pi$
$163$	16.7221	−	9.65452i	1.30978	−	0.756200i	0.982059	+	0.188575i	$0.0603870\pi$
$164$	−4.18688	+	7.25189i	−0.326940	+	0.566278i
$165$	−0.466589	−	7.90367i	−0.0363239	−	0.615300i
$166$	−2.89323	+	1.67041i	−0.224559	+	0.129649i
$167$		−	17.1797i		−	1.32940i	−0.747108	−	0.664702i	$-0.768558\pi$
$167$		−	17.1797i		−	1.32940i	0.747108	−	0.664702i	$-0.231442\pi$
$168$	−1.51825	−	2.38183i	−0.117136	−	0.183762i
$169$	10.0127			0.770209
$170$	2.97630	+	1.75637i	0.228272	+	0.134708i
$171$	0.449877	−	0.779209i	0.0344029	−	0.0595876i
$172$	0.806403	−	1.39673i	0.0614876	−	0.106500i
$173$	0.606406	−	0.350108i	0.0461042	−	0.0266182i	−0.476771	−	0.879028i	$-0.658193\pi$
$173$	0.606406	−	0.350108i	0.0461042	−	0.0266182i	0.522875	+	0.852409i	$0.324859\pi$
$174$		−	1.74163i		−	0.132033i
$175$	13.2247	−	0.328609i	0.999691	−	0.0248405i
$176$	−0.226978	−	3.30885i	−0.0171091	−	0.249414i
$177$	3.80623	−	2.19753i	0.286094	−	0.165176i
$178$	6.49734	+	3.75124i	0.486996	+	0.281167i
$179$	6.63861	−	11.4984i	0.496193	−	0.859431i	−0.503797	−	0.863822i	$-0.668064\pi$
$179$	6.63861	−	11.4984i	0.496193	−	0.859431i	0.999990	+	0.00439038i	$0.00139751\pi$
$180$	−2.11405	+	3.58240i	−0.157572	+	0.267017i
$181$		−	10.9605i		−	0.814687i	−0.913275	−	0.407344i	$-0.866455\pi$
$181$		−	10.9605i		−	0.814687i	0.913275	−	0.407344i	$-0.133545\pi$
$182$	−0.200642	−	4.56845i	−0.0148726	−	0.338636i
$183$	−1.22449			−0.0905166
$184$	−3.47535	+	2.00649i	−0.256206	+	0.147921i
$185$	−0.0446857	+	4.69183i	−0.00328536	+	0.344951i
$186$	4.49690	+	2.59629i	0.329729	+	0.190369i
$187$	2.86075	+	4.25337i	0.209199	+	0.311037i
$188$	−3.63665			−0.265230
$189$	−6.33581	+	12.1786i	−0.460862	+	0.885866i
$190$	−0.531816	−	0.941732i	−0.0385820	−	0.0683204i
$191$	7.21273	+	12.4928i	0.521894	+	0.903948i	0.999676	+	0.0254689i	$0.00810786\pi$
$191$	7.21273	+	12.4928i	0.521894	+	0.903948i	−0.477781	+	0.878479i	$0.658559\pi$
$192$	0.533793	−	0.924557i	0.0385232	−	0.0667242i
$193$	3.60370	−	6.24180i	0.259400	−	0.449294i	−0.706681	−	0.707532i	$-0.749808\pi$
$193$	3.60370	−	6.24180i	0.259400	−	0.449294i	0.966081	+	0.258238i	$0.0831418\pi$
$194$	−3.49676	−	6.05656i	−0.251053	−	0.434836i
$195$	3.59268	−	2.02886i	0.257277	−	0.145290i
$196$	6.97305	−	0.613682i	0.498075	−	0.0438344i
$197$	−15.3130			−1.09101			−0.545504	−	0.838108i	$-0.683662\pi$
$197$	−15.3130			−1.09101			−0.545504	+	0.838108i	$0.683662\pi$
$198$	−5.11954	+	3.44333i	−0.363830	+	0.244706i
$199$	14.6472	+	8.45658i	1.03831	+	0.599471i	0.919355	−	0.393428i	$-0.128711\pi$
$199$	14.6472	+	8.45658i	1.03831	+	0.599471i	0.118959	+	0.992899i	$0.462044\pi$
$200$	2.41707	+	4.37696i	0.170913	+	0.309498i
$201$	−5.13596	+	2.96525i	−0.362263	+	0.209153i
$202$	2.13053			0.149904
$203$	3.82904	+	1.99202i	0.268746	+	0.139812i
$204$			1.64998i			0.115522i
$205$	9.51616	−	16.1258i	0.664637	−	1.12628i
$206$	−7.74347	+	13.4121i	−0.539513	+	0.934464i
$207$	6.46505	+	3.73260i	0.449352	+	0.259433i
$208$	1.49682	−	0.864188i	0.103786	−	0.0599207i
$209$	−0.109783	−	1.60039i	−0.00759382	−	0.110702i
$210$	3.34404	+	5.35802i	0.230761	+	0.369738i
$211$		−	6.95564i		−	0.478846i	−0.970915	−	0.239423i	$-0.923042\pi$
$211$		−	6.95564i		−	0.478846i	0.970915	−	0.239423i	$-0.0769583\pi$
$212$	9.24141	−	5.33553i	0.634703	−	0.366446i
$213$	−3.67003	+	6.35668i	−0.251466	+	0.435553i
$214$	0.324320	−	0.561739i	0.0221701	−	0.0383997i
$215$	−1.83283	+	3.10587i	−0.124998	+	0.211819i
$216$	−5.18875			−0.353050
$217$	−10.8514	+	6.91704i	−0.736642	+	0.469559i
$218$		−	20.1011i		−	1.36142i
$219$	−7.15015	+	4.12814i	−0.483162	+	0.278954i
$220$	0.437051	+	7.40331i	0.0294659	+	0.499131i
$221$	−1.33562	+	2.31337i	−0.0898437	+	0.155614i
$222$	−1.94004	+	1.12008i	−0.130207	+	0.0751751i
$223$	12.4881			0.836264			0.418132	−	0.908386i	$-0.362685\pi$
$223$	12.4881			0.836264			0.418132	+	0.908386i	$0.362685\pi$
$224$	1.42214	+	2.23104i	0.0950204	+	0.149067i
$225$	4.80323	−	7.96512i	0.320215	−	0.531008i
$226$	2.09799	−	1.21128i	0.139556	−	0.0805729i
$227$	0.827974	+	0.478031i	0.0549546	+	0.0317280i	0.527226	−	0.849725i	$-0.323232\pi$
$227$	0.827974	+	0.478031i	0.0549546	+	0.0317280i	−0.472271	+	0.881453i	$0.656566\pi$
$228$	0.258180	−	0.447182i	0.0170984	−	0.0296153i
$229$	−19.5904	+	11.3105i	−1.29457	+	0.747421i	−0.979461	−	0.201634i	$-0.935375\pi$
$229$	−19.5904	+	11.3105i	−1.29457	+	0.747421i	−0.315110	+	0.949055i	$0.602041\pi$
$230$	7.81349	−	4.41244i	0.515206	−	0.290948i
$231$	1.05057	+	9.30894i	0.0691225	+	0.612483i
$232$			1.63137i			0.107105i
$233$	−2.76095	−	4.78210i	−0.180876	−	0.313286i	0.761303	−	0.648396i	$-0.224560\pi$
$233$	−2.76095	−	4.78210i	−0.180876	−	0.313286i	−0.942179	+	0.335110i	$0.891227\pi$
$234$	−2.78447	−	1.60761i	−0.182026	−	0.105093i
$235$	8.13143	+	0.0774449i	0.530436	+	0.00505195i
$236$	−3.56527	+	2.05841i	−0.232079	+	0.133991i
$237$			10.6582i			0.692324i
$238$	−3.62753	−	1.88719i	−0.235138	−	0.122328i
$239$			3.36046i			0.217370i	0.994076	+	0.108685i	$0.0346640\pi$
$239$			3.36046i			0.217370i	−0.994076	+	0.108685i	$0.965336\pi$
$240$	−1.21323	+	2.05591i	−0.0783139	+	0.132709i
$241$	5.95532	−	10.3149i	0.383616	−	0.664442i	−0.607960	−	0.793968i	$-0.708012\pi$
$241$	5.95532	−	10.3149i	0.383616	−	0.664442i	0.991576	+	0.129525i	$0.0413453\pi$
$242$	−4.14765	+	10.1881i	−0.266621	+	0.654915i
$243$	7.80519	+	13.5190i	0.500703	+	0.867243i
$244$	1.14697			0.0734270
$245$	−15.6046	+	1.22368i	−0.996939	+	0.0781779i
$246$	8.93972			0.569976
$247$	0.723967	−	0.417983i	0.0460649	−	0.0265956i
$248$	−4.21221	−	2.43192i	−0.267475	−	0.154427i
$249$	3.08878	+	1.78331i	0.195743	+	0.113013i
$250$	−5.31128	−	9.83820i	−0.335915	−	0.622223i
$251$		−	20.9460i		−	1.32210i	−0.750343	−	0.661049i	$-0.770112\pi$
$251$		−	20.9460i		−	1.32210i	0.750343	−	0.661049i	$-0.229888\pi$
$252$	2.27150	−	4.36626i	0.143091	−	0.275048i
$253$	13.2784	−	0.910859i	0.834804	−	0.0572652i
$254$	8.47828	+	14.6848i	0.531975	+	0.921408i
$255$	0.0351374	−	3.68930i	0.00220039	−	0.231033i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.95152	+	10.3083i	0.371245	+	0.643016i	0.989757	−	0.142759i	$-0.0455975\pi$
$257$	5.95152	+	10.3083i	0.371245	+	0.643016i	−0.618512	+	0.785775i	$0.712264\pi$
$258$	−1.72181			−0.107195
$259$	−0.243591	−	5.54636i	−0.0151360	−	0.344634i
$260$	−3.36524	+	1.90042i	−0.208703	+	0.117859i
$261$	2.62819	−	1.51739i	0.162681	−	0.0939239i
$262$	3.04800	−	5.27929i	0.188306	−	0.326156i
$263$	−12.0330	+	20.8417i	−0.741984	+	1.28515i	0.209606	+	0.977786i	$0.432782\pi$
$263$	−12.0330	+	20.8417i	−0.741984	+	1.28515i	−0.951591	+	0.307368i	$0.900552\pi$
$264$	−2.93806	+	1.97610i	−0.180825	+	0.121620i
$265$	−20.7771	+	11.7333i	−1.27633	+	0.720769i
$266$	0.687846	+	1.07909i	0.0421745	+	0.0661631i
$267$		−	8.00955i		−	0.490176i
$268$	4.81081	−	2.77752i	0.293867	−	0.169664i
$269$	−25.6188	−	14.7910i	−1.56200	−	0.901823i	−0.997054	−	0.0766981i	$-0.975562\pi$
$269$	−25.6188	−	14.7910i	−1.56200	−	0.901823i	−0.564950	−	0.825125i	$-0.691104\pi$
$270$	11.6019	+	0.110498i	0.706067	+	0.00672469i
$271$	−7.35747	−	12.7435i	−0.446934	−	0.774113i	0.551250	−	0.834340i	$-0.314151\pi$
$271$	−7.35747	−	12.7435i	−0.446934	−	0.774113i	−0.998185	+	0.0602268i	$0.980818\pi$
$272$		−	1.54552i		−	0.0937110i
$273$	−4.11669	+	2.62411i	−0.249154	+	0.158819i
$274$		−	10.3888i		−	0.627608i
$275$	−0.819572	−	16.5629i	−0.0494221	−	0.998778i
$276$	3.71024	+	2.14211i	0.223330	+	0.128940i
$277$	16.4309	−	28.4591i	0.987235	−	1.70994i	0.355686	−	0.934606i	$-0.384247\pi$
$277$	16.4309	−	28.4591i	0.987235	−	1.70994i	0.631549	−	0.775336i	$-0.282419\pi$
$278$	−7.04541	−	12.2030i	−0.422555	−	0.731887i
$279$			9.04800i			0.541689i
$280$	−3.13234	−	5.01881i	−0.187193	−	0.299931i
$281$			13.7160i			0.818227i	0.912484	+	0.409113i	$0.134162\pi$
$281$			13.7160i			0.818227i	−0.912484	+	0.409113i	$0.865838\pi$
$282$	1.94122	+	3.36229i	0.115598	+	0.200222i
$283$	11.1527	+	6.43900i	0.662958	+	0.382759i	0.793403	−	0.608697i	$-0.208307\pi$
$283$	11.1527	+	6.43900i	0.662958	+	0.382759i	−0.130445	+	0.991455i	$0.541641\pi$
$284$	3.43769	−	5.95425i	0.203989	−	0.353320i
$285$	−0.586806	+	0.994385i	−0.0347594	+	0.0589023i
$286$	−5.71894	+	0.392303i	−0.338168	+	0.0231974i
$287$	−10.2249	+	19.6543i	−0.603558	+	1.16015i
$288$	1.86026			0.109617
$289$	−7.30568	−	12.6538i	−0.429746	−	0.744342i
$290$	0.0347412	−	3.64770i	0.00204007	−	0.214200i
$291$	−3.73309	+	6.46591i	−0.218838	+	0.379038i
$292$	6.69748	−	3.86679i	0.391941	−	0.226287i
$293$			2.61732i			0.152905i	0.997073	+	0.0764527i	$0.0243594\pi$
$293$			2.61732i			0.152905i	−0.997073	+	0.0764527i	$0.975641\pi$
$294$	−4.28955	−	6.11940i	−0.250172	−	0.356891i
$295$	8.01566	−	4.52661i	0.466690	−	0.263549i
$296$	1.81722	−	1.04917i	0.105624	−	0.0609820i
$297$	15.4575	+	7.56445i	0.896933	+	0.438934i
$298$	−18.2929	−	10.5614i	−1.05968	−	0.611805i
$299$	3.46798	+	6.00671i	0.200558	+	0.347377i
$300$	2.75653	−	4.57111i	0.159148	−	0.263913i
$301$	1.96934	−	3.78546i	0.113511	−	0.218190i
$302$		−	17.0706i		−	0.982305i
$303$	−1.13726	−	1.96980i	−0.0653342	−	0.113162i
$304$	−0.241835	+	0.418871i	−0.0138702	+	0.0240239i
$305$	−2.56458	−	0.0244254i	−0.146847	−	0.00139860i
$306$	−2.48988	+	1.43754i	−0.142337	+	0.0821784i
$307$		−	11.4180i		−	0.651658i	−0.945429	−	0.325829i	$-0.894357\pi$
$307$		−	11.4180i		−	0.651658i	0.945429	−	0.325829i	$-0.105643\pi$
$308$	−0.984062	−	8.71961i	−0.0560721	−	0.496846i
$309$	16.5336			0.940566
$310$	9.36657	+	5.52739i	0.531985	+	0.313935i
$311$	−23.5119	−	13.5746i	−1.33324	−	0.769744i	−0.347442	−	0.937702i	$-0.612950\pi$
$311$	−23.5119	−	13.5746i	−1.33324	−	0.769744i	−0.985794	+	0.167957i	$0.946283\pi$
$312$	−1.59798	−	0.922596i	−0.0904680	−	0.0522317i
$313$	14.2815	+	24.7363i	0.807239	+	1.39818i	0.914769	+	0.403978i	$0.132373\pi$
$313$	14.2815	+	24.7363i	0.807239	+	1.39818i	−0.107530	+	0.994202i	$0.534294\pi$
$314$	11.1416			0.628755
$315$	−5.17198	+	9.71444i	−0.291408	+	0.547346i
$316$		−	9.98344i		−	0.561613i
$317$	11.7827	−	6.80274i	0.661782	−	0.382080i	−0.131174	−	0.991359i	$-0.541875\pi$
$317$	11.7827	−	6.80274i	0.661782	−	0.382080i	0.792956	+	0.609279i	$0.208541\pi$
$318$	−9.86601	−	5.69614i	−0.553258	−	0.319424i
$319$	2.37831	−	4.85992i	0.133160	−	0.272103i
$320$	1.13643	−	1.92576i	0.0635281	−	0.107653i
$321$	−0.692480			−0.0386505
$322$	−8.95313	+	5.70701i	−0.498938	+	0.318039i
$323$		−	0.747524i		−	0.0415933i
$324$	−0.0206686	−	0.0357991i	−0.00114826	−	0.00198884i
$325$	7.56503	−	4.17761i	0.419632	−	0.231732i
$326$	16.7221	+	9.65452i	0.926152	+	0.534714i
$327$	−18.5846	+	10.7298i	−1.02773	+	0.593361i
$328$	−8.37376			−0.462364
$329$	−9.61241	+	0.422167i	−0.529949	+	0.0232748i
$330$	6.61149	−	4.35592i	0.363950	−	0.239785i
$331$	9.39302	+	16.2692i	0.516287	+	0.894235i	0.999821	+	0.0189097i	$0.00601951\pi$
$331$	9.39302	+	16.2692i	0.516287	+	0.894235i	−0.483534	+	0.875325i	$0.660647\pi$
$332$	−2.89323	−	1.67041i	−0.158787	−	0.0916757i
$333$	−3.38050	−	1.95173i	−0.185250	−	0.106954i
$334$	14.8781	−	8.58985i	0.814091	−	0.470016i
$335$	−10.8160	+	6.10800i	−0.590940	+	0.333716i
$336$	1.30360	−	2.50576i	0.0711170	−	0.136700i
$337$	−1.86493			−0.101589			−0.0507946	−	0.998709i	$-0.516175\pi$
$337$	−1.86493			−0.101589			−0.0507946	+	0.998709i	$0.516175\pi$
$338$	5.00636	+	8.67126i	0.272310	+	0.471655i
$339$	−2.23979	−	1.29314i	−0.121649	−	0.0702339i
$340$	−0.0329129	+	3.45574i	−0.00178495	+	0.187414i
$341$	9.00293	+	13.3856i	0.487536	+	0.724869i
$342$	0.899753			0.0486531
$343$	18.3599	−	2.43157i	0.991344	−	0.131292i
$344$	1.61281			0.0869566
$345$	−8.25035	−	4.86869i	−0.444184	−	0.262121i
$346$	0.606406	+	0.350108i	0.0326006	+	0.0188219i
$347$	−5.05922	+	8.76283i	−0.271593	+	0.470414i	−0.969270	−	0.245999i	$-0.920884\pi$
$347$	−5.05922	+	8.76283i	−0.271593	+	0.470414i	0.697677	+	0.716413i	$0.254217\pi$
$348$	1.50830	−	0.870816i	0.0808532	−	0.0466806i
$349$	4.65704			0.249286			0.124643	−	0.992202i	$-0.460222\pi$
$349$	4.65704			0.249286			0.124643	+	0.992202i	$0.460222\pi$
$350$	6.89692	+	11.2886i	0.368656	+	0.603401i
$351$			8.96811i			0.478682i
$352$	2.75206	−	1.85099i	0.146685	−	0.0986583i
$353$	−15.9692	+	27.6595i	−0.849957	+	1.47217i	0.0312881	+	0.999510i	$0.490039\pi$
$353$	−15.9692	+	27.6595i	−0.849957	+	1.47217i	−0.881245	+	0.472659i	$0.843294\pi$
$354$	3.80623	+	2.19753i	0.202299	+	0.116797i
$355$	−7.81336	+	13.2403i	−0.414690	+	0.702722i
$356$			7.50248i			0.397631i
$357$	0.191541	+	4.36123i	0.0101374	+	0.230821i
$358$	13.2772			0.701723
$359$	−15.3645	+	8.87070i	−0.810908	+	0.468178i	−0.847271	−	0.531161i	$-0.821756\pi$
$359$	−15.3645	+	8.87070i	−0.810908	+	0.468178i	0.0363633	+	0.999339i	$0.488423\pi$
$360$	−4.15948	−	0.0396155i	−0.219224	−	0.00208792i
$361$	9.38303	−	16.2519i	0.493844	−	0.855362i
$362$	9.49207	−	5.48025i	0.498892	−	0.288035i
$363$	11.6335	−	1.60359i	0.610598	−	0.0841667i
$364$	3.85607	−	2.45799i	0.202113	−	0.128833i
$365$	−15.0577	+	8.50340i	−0.788156	+	0.445088i
$366$	−0.612243	−	1.06044i	−0.0320025	−	0.0554299i
$367$	4.51064	−	7.81267i	0.235454	−	0.407818i	−0.723951	−	0.689852i	$-0.757676\pi$
$367$	4.51064	−	7.81267i	0.235454	−	0.407818i	0.959404	+	0.282034i	$0.0910091\pi$
$368$	−3.47535	−	2.00649i	−0.181165	−	0.104596i
$369$	7.78868	+	13.4904i	0.405463	+	0.702282i
$370$	−4.08559	+	2.30722i	−0.212400	+	0.119947i
$371$	23.8075	−	15.1757i	1.23603	−	0.787883i
$372$			5.19257i			0.269222i
$373$	11.6611	+	20.1977i	0.603791	+	1.04580i	0.992241	+	0.124327i	$0.0396771\pi$
$373$	11.6611	+	20.1977i	0.603791	+	1.04580i	−0.388451	+	0.921470i	$0.626990\pi$
$374$	−2.25315	+	4.60417i	−0.116508	+	0.238076i
$375$	−6.26086	+	10.1622i	−0.323309	+	0.524771i
$376$	−1.81833	−	3.14943i	−0.0937730	−	0.162420i
$377$	2.81963			0.145218
$378$	−13.7149	+	0.602345i	−0.705419	+	0.0309813i
$379$	−9.54007			−0.490040			−0.245020	−	0.969518i	$-0.578795\pi$
$379$	−9.54007			−0.490040			−0.245020	+	0.969518i	$0.578795\pi$
$380$	0.549656	−	0.931432i	0.0281968	−	0.0477815i
$381$	9.05130	−	15.6773i	0.463712	−	0.803173i
$382$	−7.21273	+	12.4928i	−0.369035	+	0.639188i
$383$	10.7286	+	18.5824i	0.548204	+	0.949517i	0.998398	+	0.0565859i	$0.0180215\pi$
$383$	10.7286	+	18.5824i	0.548204	+	0.949517i	−0.450194	+	0.892931i	$0.648645\pi$
$384$	1.06759			0.0544801
$385$	2.01464	+	19.5177i	0.102676	+	0.994715i
$386$	7.20741			0.366847
$387$	−1.50012	−	2.59828i	−0.0762553	−	0.132078i
$388$	3.49676	−	6.05656i	0.177521	−	0.307475i
$389$	1.52868	−	2.64775i	0.0775072	−	0.134246i	−0.824667	−	0.565619i	$-0.808637\pi$
$389$	1.52868	−	2.64775i	0.0775072	−	0.134246i	0.902174	+	0.431373i	$0.141971\pi$
$390$	3.55339	+	2.09692i	0.179933	+	0.106182i
$391$	6.20216			0.313657
$392$	4.01799	+	5.73200i	0.202939	+	0.289509i
$393$	−6.50801			−0.328286
$394$	−7.65651	−	13.2615i	−0.385729	−	0.668103i
$395$	−0.212604	+	22.3226i	−0.0106973	+	1.12317i
$396$	−5.54178	−	2.71199i	−0.278485	−	0.136283i
$397$	−8.08582	−	14.0051i	−0.405816	−	0.702893i	0.588600	−	0.808424i	$-0.299679\pi$
$397$	−8.08582	−	14.0051i	−0.405816	−	0.702893i	−0.994416	+	0.105531i	$0.966346\pi$
$398$			16.9132i			0.847780i
$399$	0.630511	−	1.21196i	0.0315650	−	0.0606740i
$400$	−2.58202	+	4.28173i	−0.129101	+	0.214086i
$401$	5.34633	+	9.26012i	0.266983	+	0.462428i	0.968081	−	0.250636i	$-0.0806399\pi$
$401$	5.34633	+	9.26012i	0.266983	+	0.462428i	−0.701098	+	0.713065i	$0.747307\pi$
$402$	−5.13596	−	2.96525i	−0.256158	−	0.147893i
$403$	−4.20327	+	7.28028i	−0.209380	+	0.362657i
$404$	1.06527	+	1.84510i	0.0529990	+	0.0917970i
$405$	0.0454519	+	0.0804856i	0.00225852	+	0.00399936i
$406$	0.189381	+	4.31205i	0.00939882	+	0.214003i
$407$	−6.94311	+	0.476278i	−0.344157	+	0.0236082i
$408$	−1.42892	+	0.824989i	−0.0707422	+	0.0408431i
$409$	15.5654	−	26.9600i	0.769659	−	1.33309i	−0.168089	−	0.985772i	$-0.553760\pi$
$409$	15.5654	−	26.9600i	0.769659	−	1.33309i	0.937748	−	0.347316i	$-0.112907\pi$
$410$	18.7235	+	0.178325i	0.924685	+	0.00880684i
$411$	−9.60501	+	5.54545i	−0.473780	+	0.273537i
$412$	−15.4869			−0.762987
$413$	−9.18478	+	5.85467i	−0.451953	+	0.288090i
$414$			7.46519i			0.366894i
$415$	6.43360	+	3.79659i	0.315813	+	0.186367i
$416$	1.49682	+	0.864188i	0.0733875	+	0.0423703i
$417$	−7.52158	+	13.0278i	−0.368334	+	0.637972i
$418$	1.33109	−	0.895272i	0.0651058	−	0.0437892i
$419$			31.1314i			1.52087i	0.649414	+	0.760435i	$0.275014\pi$
$419$			31.1314i			1.52087i	−0.649414	+	0.760435i	$0.724986\pi$
$420$	−2.96816	+	5.57503i	−0.144831	+	0.272034i
$421$	−40.0971			−1.95421			−0.977107	−	0.212748i	$-0.931759\pi$
$421$	−40.0971			−1.95421			−0.977107	+	0.212748i	$0.931759\pi$
$422$	6.02376	−	3.47782i	0.293232	−	0.169298i
$423$	−3.38256	+	5.85876i	−0.164466	+	0.284863i
$424$	9.24141	+	5.33553i	0.448803	+	0.259116i
$425$	0.147184	−	7.72621i	0.00713949	−	0.374776i
$426$	−7.34006			−0.355627
$427$	3.03166	−	0.133148i	0.146713	−	0.00644347i
$428$	0.648640			0.0313532
$429$	3.41544	+	5.07808i	0.164899	+	0.245172i
$430$	−3.60618	−	0.0343458i	−0.173905	−	0.00165630i
$431$	19.9486	+	11.5173i	0.960889	+	0.554769i	0.896446	−	0.443152i	$-0.146140\pi$
$431$	19.9486	+	11.5173i	0.960889	+	0.554769i	0.0644422	+	0.997921i	$0.479473\pi$
$432$	−2.59437	−	4.49359i	−0.124822	−	0.216198i
$433$	−1.89828			−0.0912254			−0.0456127	−	0.998959i	$-0.514524\pi$
$433$	−1.89828			−0.0912254			−0.0456127	+	0.998959i	$0.514524\pi$
$434$	−11.4160	−	5.93908i	−0.547987	−	0.285085i
$435$	−3.39105	+	1.91500i	−0.162588	+	0.0918170i
$436$	17.4081	−	10.0506i	0.833695	−	0.481334i
$437$	−1.68093	−	0.970483i	−0.0804096	−	0.0464245i
$438$	−7.15015	−	4.12814i	−0.341647	−	0.197250i
$439$	14.2518	+	24.6849i	0.680203	+	1.17815i	0.974919	+	0.222561i	$0.0714415\pi$
$439$	14.2518	+	24.6849i	0.680203	+	1.17815i	−0.294716	+	0.955585i	$0.595225\pi$
$440$	−6.19293	+	4.08015i	−0.295236	+	0.194514i
$441$	5.49717	−	11.8046i	0.261770	−	0.562124i
$442$	−2.67124			−0.127058
$443$	15.9939	−	9.23408i	0.759893	−	0.438724i	−0.0693646	−	0.997591i	$-0.522097\pi$
$443$	15.9939	−	9.23408i	0.759893	−	0.438724i	0.829257	+	0.558867i	$0.188764\pi$
$444$	−1.94004	−	1.12008i	−0.0920703	−	0.0531568i
$445$	0.159770	−	16.7753i	0.00757384	−	0.795225i
$446$	6.24404	+	10.8150i	0.295664	+	0.512105i
$447$			22.5504i			1.06660i
$448$	−1.22107	+	2.34712i	−0.0576900	+	0.110891i
$449$	−13.9134			−0.656615			−0.328308	−	0.944571i	$-0.606478\pi$
$449$	−13.9134			−0.656615			−0.328308	+	0.944571i	$0.606478\pi$
$450$	9.29961	+	0.177158i	0.438388	+	0.00835129i
$451$	24.9457	+	12.2077i	1.17465	+	0.574840i
$452$	2.09799	+	1.21128i	0.0986812	+	0.0569736i
$453$	−15.7828	+	9.11219i	−0.741540	+	0.428128i
$454$			0.956062i			0.0448702i
$455$	−8.67440	+	5.41386i	−0.406662	+	0.253806i
$456$	0.516361			0.0241808
$457$	6.86004	+	11.8819i	0.320899	+	0.555814i	0.980674	−	0.195650i	$-0.0626816\pi$
$457$	6.86004	+	11.8819i	0.320899	+	0.555814i	−0.659775	+	0.751464i	$0.729348\pi$
$458$	−19.5904	−	11.3105i	−0.915400	−	0.528506i
$459$	6.94494	+	4.00966i	0.324162	+	0.187155i
$460$	7.72803	+	4.56046i	0.360321	+	0.212633i
$461$	18.8586			0.878334			0.439167	−	0.898406i	$-0.355274\pi$
$461$	18.8586			0.878334			0.439167	+	0.898406i	$0.355274\pi$
$462$	−7.53649	+	5.56429i	−0.350629	+	0.258874i
$463$			28.2350i			1.31219i	0.754677	+	0.656096i	$0.227793\pi$
$463$			28.2350i			1.31219i	−0.754677	+	0.656096i	$0.772207\pi$
$464$	−1.41281	+	0.815686i	−0.0655881	+	0.0378673i
$465$	0.110579	−	11.6104i	0.00512799	−	0.538420i
$466$	2.76095	−	4.78210i	0.127898	−	0.221527i
$467$	−14.2257	−	24.6396i	−0.658287	−	1.14019i	−0.981059	−	0.193710i	$-0.937948\pi$
$467$	−14.2257	−	24.6396i	−0.658287	−	1.14019i	0.322772	−	0.946477i	$-0.395385\pi$
$468$		−	3.21523i		−	0.148624i
$469$	12.3935	−	7.90004i	0.572280	−	0.364790i
$470$	3.99865	+	7.08075i	0.184444	+	0.326611i
$471$	−5.94730	−	10.3010i	−0.274037	−	0.474646i
$472$	−3.56527	−	2.05841i	−0.164105	−	0.0947459i
$473$	−4.80461	−	2.35124i	−0.220916	−	0.108110i
$474$	−9.23026	+	5.32910i	−0.423960	+	0.244773i
$475$	−1.24885	+	2.07095i	−0.0573011	+	0.0950215i
$476$	−0.179415	−	4.08513i	−0.00822346	−	0.187242i
$477$		−	19.8509i		−	0.908912i
$478$	−2.91024	+	1.68023i	−0.133111	+	0.0768518i
$479$	17.7278	−	30.7054i	0.810002	−	1.40296i	−0.102860	−	0.994696i	$-0.532799\pi$
$479$	17.7278	−	30.7054i	0.810002	−	1.40296i	0.912862	−	0.408269i	$-0.133867\pi$
$480$	−2.38709	−	0.0227350i	−0.108955	−	0.00103770i
$481$	−1.81337	−	3.14084i	−0.0826824	−	0.143210i
$482$	11.9106			0.542515
$483$	10.0556	+	5.23131i	0.457545	+	0.238033i
$484$	−10.8970	+	1.50207i	−0.495316	+	0.0682759i
$485$	−7.94761	+	13.4678i	−0.360882	+	0.611541i
$486$	−7.80519	+	13.5190i	−0.354050	+	0.613233i
$487$	−9.99224	−	5.76902i	−0.452792	−	0.261419i	0.256217	−	0.966619i	$-0.417524\pi$
$487$	−9.99224	−	5.76902i	−0.452792	−	0.261419i	−0.709009	+	0.705200i	$0.750857\pi$
$488$	0.573483	+	0.993302i	0.0259604	+	0.0449647i
$489$		−	20.6141i		−	0.932200i
$490$	−8.86202	−	12.9021i	−0.400345	−	0.582858i
$491$			42.4086i			1.91387i	0.290299	+	0.956936i	$0.406245\pi$
$491$			42.4086i			1.91387i	−0.290299	+	0.956936i	$0.593755\pi$
$492$	4.46986	+	7.74202i	0.201517	+	0.349037i
$493$	1.26066	−	2.18353i	0.0567773	−	0.0983412i
$494$	0.723967	+	0.417983i	0.0325728	+	0.0188059i
$495$	12.3335	+	6.18193i	0.554348	+	0.277857i
$496$		−	4.86384i		−	0.218393i
$497$	8.39530	−	16.1374i	0.376581	−	0.723860i
$498$			3.56661i			0.159824i
$499$	15.5619	+	26.9540i	0.696648	+	1.20663i	0.969622	+	0.244608i	$0.0786592\pi$
$499$	15.5619	+	26.9540i	0.696648	+	1.20663i	−0.272975	+	0.962021i	$0.588007\pi$
$500$	5.86449	−	9.51881i	0.262268	−	0.425694i
$501$	−15.8836	−	9.17041i	−0.709628	−	0.409704i
$502$	18.1397	−	10.4730i	0.809616	−	0.467432i
$503$		−	35.6351i		−	1.58889i	−0.607335	−	0.794446i	$-0.707761\pi$
$503$		−	35.6351i		−	1.58889i	0.607335	−	0.794446i	$-0.292239\pi$
$504$	4.91704	−	0.215952i	0.219022	−	0.00961925i
$505$	−2.34261	−	4.14826i	−0.104245	−	0.184595i
$506$	7.42801	+	11.0440i	0.330215	+	0.490965i
$507$	5.34472	−	9.25733i	0.237367	−	0.411132i
$508$	−8.47828	+	14.6848i	−0.376163	+	0.651534i
$509$	7.10122	−	4.09989i	0.314756	−	0.181725i	−0.334297	−	0.942468i	$-0.608499\pi$
$509$	7.10122	−	4.09989i	0.314756	−	0.181725i	0.649053	+	0.760743i	$0.275165\pi$
$510$	3.21259	−	1.81422i	0.142256	−	0.0803350i
$511$	17.2539	−	10.9982i	0.763269	−	0.486532i
$512$	−1.00000			−0.0441942
$513$	−1.25482	−	2.17342i	−0.0554018	−	0.0959587i
$514$	−5.95152	+	10.3083i	−0.262510	+	0.454681i
$515$	34.6283	+	0.329805i	1.52590	+	0.0145329i
$516$	−0.860905	−	1.49113i	−0.0378992	−	0.0656434i
$517$	0.825439	+	12.0331i	0.0363028	+	0.529217i
$518$	4.68149	−	2.98413i	0.205693	−	0.131115i
$519$		−	0.747542i		−	0.0328135i
$520$	−3.32843	−	1.96417i	−0.145961	−	0.0861346i
$521$	9.95005	+	5.74466i	0.435919	+	0.251678i	0.701865	−	0.712310i	$-0.252351\pi$
$521$	9.95005	+	5.74466i	0.435919	+	0.251678i	−0.265946	+	0.963988i	$0.585684\pi$
$522$	2.62819	+	1.51739i	0.115033	+	0.0664143i
$523$	−18.0993	+	10.4496i	−0.791426	+	0.456930i	−0.840464	−	0.541867i	$-0.817718\pi$
$523$	−18.0993	+	10.4496i	−0.791426	+	0.456930i	0.0490385	+	0.998797i	$0.484384\pi$
$524$	6.09600			0.266305
$525$	6.75543	−	12.4024i	0.294831	−	0.541284i
$526$	−24.0659			−1.04932
$527$	3.75858	+	6.51006i	0.163727	+	0.283583i
$528$	−3.18038	−	1.55639i	−0.138408	−	0.0677331i
$529$	−3.44797	+	5.97205i	−0.149912	+	0.259655i
$530$	−20.5499	−	12.1269i	−0.892629	−	0.526758i
$531$			7.65834i			0.332344i
$532$	−0.590595	+	1.13524i	−0.0256055	+	0.0492187i
$533$			14.4730i			0.626896i
$534$	6.93647	−	4.00477i	0.300170	−	0.173304i
$535$	−1.45034	−	0.0138132i	−0.0627036	−	0.000597198i
$536$	4.81081	+	2.77752i	0.207796	+	0.119971i
$537$	−7.08729	−	12.2755i	−0.305839	−	0.529729i
$538$		−	29.5820i		−	1.27537i
$539$	−3.61331	−	22.9335i	−0.155636	−	0.987814i
$540$	5.70524	+	10.1028i	0.245514	+	0.434754i
$541$	−3.66159	+	2.11402i	−0.157424	+	0.0908887i	−0.576642	−	0.816997i	$-0.695637\pi$
$541$	−3.66159	+	2.11402i	−0.157424	+	0.0908887i	0.419219	+	0.907885i	$0.362304\pi$
$542$	7.35747	−	12.7435i	0.316030	−	0.547381i
$543$	−10.1336	−	5.85064i	−0.434875	−	0.251075i
$544$	1.33846	−	0.772761i	0.0573860	−	0.0331318i
$545$	−39.1379	+	22.1020i	−1.67648	+	0.946745i
$546$	−4.33090	−	2.25310i	−0.185345	−	0.0964240i
$547$	−2.46701			−0.105482			−0.0527409	−	0.998608i	$-0.516796\pi$
$547$	−2.46701			−0.105482			−0.0527409	+	0.998608i	$0.516796\pi$
$548$	8.99694	−	5.19438i	0.384330	−	0.221893i
$549$	1.06683	−	1.84780i	0.0455311	−	0.0788621i
$550$	13.9341	−	8.99120i	0.594151	−	0.383386i
$551$	−0.683335	+	0.394524i	−0.0291111	+	0.0168073i
$552$			4.28421i			0.182348i
$553$	−1.15895	−	26.3883i	−0.0492834	−	1.12214i
$554$	32.8617			1.39616
$555$	4.31402	+	2.54578i	0.183120	+	0.108063i
$556$	7.04541	−	12.2030i	0.298792	−	0.517523i
$557$	19.2421	−	33.3282i	0.815313	−	1.41216i	−0.0937905	−	0.995592i	$-0.529898\pi$
$557$	19.2421	−	33.3282i	0.815313	−	1.41216i	0.909103	−	0.416571i	$-0.136768\pi$
$558$	−7.83580	+	4.52400i	−0.331716	+	0.191516i
$559$		−	2.78754i		−	0.117900i
$560$	2.78025	−	5.22209i	0.117487	−	0.220674i
$561$	5.45953	−	0.374508i	0.230502	−	0.0158118i
$562$	−11.8784	+	6.85799i	−0.501060	+	0.289287i
$563$	4.29877	+	2.48190i	0.181171	+	0.104599i	0.587843	−	0.808975i	$-0.299977\pi$
$563$	4.29877	+	2.48190i	0.181171	+	0.104599i	−0.406671	+	0.913574i	$0.633311\pi$
$564$	−1.94122	+	3.36229i	−0.0817401	+	0.141578i
$565$	−4.66524	−	2.75305i	−0.196268	−	0.115822i
$566$			12.8780i			0.541303i
$567$	−0.0587871	−	0.0922248i	−0.00246883	−	0.00387308i
$568$	6.87538			0.288484
$569$	11.2085	−	6.47120i	0.469883	−	0.271287i	−0.246308	−	0.969192i	$-0.579217\pi$
$569$	11.2085	−	6.47120i	0.469883	−	0.271287i	0.716191	+	0.697905i	$0.245884\pi$
$570$	−1.15457	−	0.0109962i	−0.0483594	−	0.000460582i
$571$	−23.1404	−	13.3601i	−0.968396	−	0.559104i	−0.0696493	−	0.997572i	$-0.522188\pi$
$571$	−23.1404	−	13.3601i	−0.968396	−	0.559104i	−0.898747	+	0.438468i	$0.855521\pi$
$572$	−3.19921	−	4.75659i	−0.133766	−	0.198883i
$573$	15.4004			0.643362
$574$	−22.1336	+	0.972084i	−0.923837	+	0.0405740i
$575$	−17.1825	−	10.3616i	−0.716560	−	0.432109i
$576$	0.930129	+	1.61103i	0.0387554	+	0.0671263i
$577$	20.1579	−	34.9145i	0.839183	−	1.45351i	−0.0513953	−	0.998678i	$-0.516367\pi$
$577$	20.1579	−	34.9145i	0.839183	−	1.45351i	0.890578	−	0.454830i	$-0.150300\pi$
$578$	7.30568	−	12.6538i	0.303876	−	0.526329i
$579$	−3.84727	−	6.66366i	−0.159887	−	0.276932i
$580$	3.17637	−	1.79376i	0.131891	−	0.0744819i
$581$	−7.84132	−	4.07937i	−0.325313	−	0.169241i
$582$	−7.46618			−0.309483
$583$	−19.7521	−	29.3674i	−0.818047	−	1.21627i
$584$	6.69748	+	3.86679i	0.277144	+	0.160009i
$585$	−0.0684704	+	7.18914i	−0.00283090	+	0.297234i
$586$	−2.26667	+	1.30866i	−0.0936351	+	0.0540603i
$587$	−16.9602			−0.700021			−0.350011	−	0.936746i	$-0.613822\pi$
$587$	−16.9602			−0.700021			−0.350011	+	0.936746i	$0.613822\pi$
$588$	3.15478	−	6.77456i	0.130101	−	0.279378i
$589$		−	2.35250i		−	0.0969330i
$590$	7.92799	+	4.67846i	0.326390	+	0.192609i
$591$	−8.17399	+	14.1578i	−0.336233	+	0.582372i
$592$	1.81722	+	1.04917i	0.0746874	+	0.0431208i
$593$	15.0377	−	8.68202i	0.617524	−	0.356528i	−0.158380	−	0.987378i	$-0.550627\pi$
$593$	15.0377	−	8.68202i	0.617524	−	0.356528i	0.775905	+	0.630850i	$0.217294\pi$
$594$	1.17773	+	17.1688i	0.0483229	+	0.704444i
$595$	0.314170	+	9.13803i	0.0128797	+	0.374623i
$596$		−	21.1228i		−	0.865223i
$597$	15.6372	−	9.02813i	0.639987	−	0.369497i
$598$	−3.46798	+	6.00671i	−0.141816	+	0.245633i
$599$	−14.1370	+	24.4860i	−0.577621	+	1.00047i	0.418130	+	0.908387i	$0.362686\pi$
$599$	−14.1370	+	24.4860i	−0.577621	+	1.00047i	−0.995751	+	0.0920820i	$0.970648\pi$
$600$	5.33697	+	0.101669i	0.217881	+	0.00415063i
$601$	−33.5631			−1.36907			−0.684534	−	0.728981i	$-0.739994\pi$
$601$	−33.5631			−1.36907			−0.684534	+	0.728981i	$0.739994\pi$
$602$	4.26297	−	0.187225i	0.173746	−	0.00763074i
$603$		−	10.3338i		−	0.420826i
$604$	14.7836	−	8.53532i	0.601536	−	0.347297i
$605$	24.3972	−	3.12652i	0.991888	−	0.127111i
$606$	1.13726	−	1.96980i	0.0461982	−	0.0800177i
$607$	16.6958	−	9.63932i	0.677661	−	0.391248i	−0.121312	−	0.992614i	$-0.538710\pi$
$607$	16.6958	−	9.63932i	0.677661	−	0.391248i	0.798973	+	0.601367i	$0.205377\pi$
$608$	−0.483671			−0.0196154
$609$	3.88565	−	2.47684i	0.157454	−	0.100367i
$610$	−1.26114	−	2.23320i	−0.0510619	−	0.0904197i
$611$	−5.44341	+	3.14275i	−0.220217	+	0.127142i
$612$	−2.48988	−	1.43754i	−0.100648	−	0.0581089i
$613$	17.0669	−	29.5607i	0.689325	−	1.19395i	−0.282732	−	0.959199i	$-0.591241\pi$
$613$	17.0669	−	29.5607i	0.689325	−	1.19395i	0.972057	−	0.234746i	$-0.0754260\pi$
$614$	9.88826	−	5.70899i	0.399058	−	0.230396i
$615$	−9.82958	−	17.4061i	−0.396367	−	0.701881i
$616$	7.05937	−	5.21203i	0.284430	−	0.209999i
$617$			12.7295i			0.512469i	0.966615	+	0.256235i	$0.0824820\pi$
$617$			12.7295i			0.512469i	−0.966615	+	0.256235i	$0.917518\pi$
$618$	8.26682	+	14.3186i	0.332540	+	0.575977i
$619$	15.7044	+	9.06692i	0.631212	+	0.364430i	0.781221	−	0.624254i	$-0.214597\pi$
$619$	15.7044	+	9.06692i	0.631212	+	0.364430i	−0.150009	+	0.988685i	$0.547930\pi$
$620$	−0.103579	+	10.8754i	−0.00415982	+	0.436766i
$621$	18.0327	−	10.4112i	0.723628	−	0.417787i
$622$		−	27.1492i		−	1.08858i
$623$	0.870939	+	19.8306i	0.0348934	+	0.794495i
$624$		−	1.84519i		−	0.0738668i
$625$	−13.3155	+	21.1588i	−0.532621	+	0.846354i
$626$	−14.2815	+	24.7363i	−0.570804	+	0.988662i
$627$	−1.53826	−	0.752780i	−0.0614321	−	0.0300631i
$628$	5.57078	+	9.64888i	0.222298	+	0.385032i
$629$	−3.24304			−0.129309
$630$	−10.9989	+	0.378149i	−0.438208	+	0.0150658i
$631$	−9.75642			−0.388397			−0.194198	−	0.980962i	$-0.562211\pi$
$631$	−9.75642			−0.388397			−0.194198	+	0.980962i	$0.562211\pi$
$632$	8.64592	−	4.99172i	0.343916	−	0.198560i
$633$	−6.43089	−	3.71288i	−0.255605	−	0.147574i
$634$	11.7827	+	6.80274i	0.467950	+	0.270171i
$635$	19.2699	−	32.6542i	0.764702	−	1.29584i
$636$		−	11.3923i		−	0.451733i
$637$	9.90705	−	6.94460i	0.392531	−	0.275155i
$638$	5.39797	−	0.370285i	0.213708	−	0.0146597i
$639$	−6.39499	−	11.0764i	−0.252982	−	0.438177i
$640$	2.23597	+	0.0212957i	0.0883843	+	0.000841785i
$641$	5.88659	−	10.1959i	0.232506	−	0.402713i	−0.726039	−	0.687654i	$-0.758641\pi$
$641$	5.88659	−	10.1959i	0.232506	−	0.402713i	0.958545	+	0.284941i	$0.0919740\pi$
$642$	−0.346240	−	0.599705i	−0.0136650	−	0.0236685i
$643$	44.3171			1.74769			0.873847	−	0.486200i	$-0.161618\pi$
$643$	44.3171			1.74769			0.873847	+	0.486200i	$0.161618\pi$
$644$	−9.41898	−	4.90013i	−0.371160	−	0.193092i
$645$	1.89320	+	3.35245i	0.0745447	+	0.132003i
$646$	0.647375	−	0.373762i	0.0254706	−	0.0147055i
$647$	−13.5518	+	23.4725i	−0.532778	+	0.922799i	0.466489	+	0.884527i	$0.345519\pi$
$647$	−13.5518	+	23.4725i	−0.532778	+	0.922799i	−0.999267	+	0.0382719i	$0.987815\pi$
$648$	0.0206686	−	0.0357991i	0.000811939	−	0.00140632i
$649$	7.62020	+	11.3297i	0.299119	+	0.444730i
$650$	7.40043	+	4.46270i	0.290269	+	0.175042i
$651$	0.602789	+	13.7250i	0.0236252	+	0.537926i
$652$			19.3090i			0.756200i
$653$	−1.27592	+	0.736655i	−0.0499308	+	0.0288275i	−0.524758	−	0.851252i	$-0.675844\pi$
$653$	−1.27592	+	0.736655i	−0.0499308	+	0.0288275i	0.474827	+	0.880079i	$0.342511\pi$
$654$	−18.5846	−	10.7298i	−0.726716	−	0.419570i
$655$	−13.6305	−	0.129818i	−0.532586	−	0.00507242i
$656$	−4.18688	−	7.25189i	−0.163470	−	0.283139i
$657$		−	14.3865i		−	0.561270i
$658$	−5.17181	−	8.11351i	−0.201618	−	0.316297i
$659$		−	22.0024i		−	0.857092i	−0.903520	−	0.428546i	$-0.859026\pi$
$659$		−	22.0024i		−	0.857092i	0.903520	−	0.428546i	$-0.140974\pi$
$660$	7.07808	+	3.54776i	0.275514	+	0.138096i
$661$	−8.51176	−	4.91427i	−0.331069	−	0.191143i	0.325247	−	0.945629i	$-0.394553\pi$
$661$	−8.51176	−	4.91427i	−0.331069	−	0.191143i	−0.656316	+	0.754486i	$0.727886\pi$
$662$	−9.39302	+	16.2692i	−0.365070	+	0.632320i
$663$	1.42589	+	2.46972i	0.0553771	+	0.0959159i
$664$		−	3.34082i		−	0.129649i
$665$	1.34473	−	2.52577i	0.0521462	−	0.0979453i
$666$		−	3.90347i		−	0.151256i
$667$	−3.27334	−	5.66959i	−0.126744	−	0.219527i
$668$	14.8781	+	8.58985i	0.575649	+	0.332351i
$669$	6.66606	−	11.5460i	0.257725	−	0.446392i
$670$	−10.6977	−	6.31290i	−0.413287	−	0.243889i
$671$	−0.260336	−	3.79514i	−0.0100502	−	0.146510i
$672$	2.82185	−	0.123933i	0.108855	−	0.00478081i
$673$	−38.5769			−1.48703			−0.743515	−	0.668719i	$-0.766843\pi$
$673$	−38.5769			−1.48703			−0.743515	+	0.668719i	$0.766843\pi$
$674$	−0.932466	−	1.61508i	−0.0359172	−	0.0622105i
$675$	−12.5416	−	22.7109i	−0.482726	−	0.874144i
$676$	−5.00636	+	8.67126i	−0.192552	+	0.333510i
$677$	−28.3508	+	16.3683i	−1.08961	+	0.629086i	−0.933472	−	0.358649i	$-0.883237\pi$
$677$	−28.3508	+	16.3683i	−1.08961	+	0.629086i	−0.156137	+	0.987735i	$0.549904\pi$
$678$		−	2.58628i		−	0.0993257i
$679$	8.53955	−	16.4147i	0.327718	−	0.629937i
$680$	−3.00921	+	1.69936i	−0.115398	+	0.0651676i
$681$	0.883934	−	0.510339i	0.0338724	−	0.0195563i
$682$	−7.09078	+	14.4896i	−0.271520	+	0.554834i
$683$	−10.5298	−	6.07940i	−0.402913	−	0.232622i	0.284827	−	0.958579i	$-0.408064\pi$
$683$	−10.5298	−	6.07940i	−0.402913	−	0.232622i	−0.687740	+	0.725957i	$0.741397\pi$
$684$	0.449877	+	0.779209i	0.0172015	+	0.0297938i
$685$	−20.2275	+	11.4229i	−0.772852	+	0.436445i
$686$	11.2858	+	14.6844i	0.430893	+	0.560653i
$687$			24.1499i			0.921378i
$688$	0.806403	+	1.39673i	0.0307438	+	0.0532499i
$689$	9.22181	−	15.9726i	0.351323	−	0.608509i
$690$	0.0912352	−	9.57935i	0.00347326	−	0.364680i
$691$	−16.7472	+	9.66903i	−0.637095	+	0.367827i	−0.783495	−	0.621398i	$-0.786565\pi$
$691$	−16.7472	+	9.66903i	−0.637095	+	0.367827i	0.146399	+	0.989226i	$0.453232\pi$
$692$			0.700217i			0.0266182i
$693$	−14.9629	−	6.52501i	−0.568392	−	0.247865i
$694$	−10.1184			−0.384091
$695$	−16.0132	+	27.1355i	−0.607414	+	1.02931i
$696$	1.50830	+	0.870816i	0.0571719	+	0.0330082i
$697$	11.2080	+	6.47092i	0.424532	+	0.245103i
$698$	2.32852	+	4.03312i	0.0881358	+	0.152656i
$699$	−5.89510			−0.222973
$700$	−6.32775	+	11.6172i	−0.239167	+	0.439089i
$701$			42.5093i			1.60556i	0.596279	+	0.802778i	$0.296645\pi$
$701$			42.5093i			1.60556i	−0.596279	+	0.802778i	$0.703355\pi$
$702$	−7.76661	+	4.48406i	−0.293132	+	0.169240i
$703$	0.878938	+	0.507455i	0.0331498	+	0.0191390i
$704$	2.97904	+	1.45786i	0.112277	+	0.0549450i
$705$	4.41211	−	7.47664i	0.166170	−	0.281586i
$706$	−31.9385			−1.20202
$707$	3.02991	+	4.75330i	0.113951	+	0.178766i
$708$			4.39506i			0.165176i
$709$	−16.0460	−	27.7925i	−0.602620	−	1.04377i	−0.992423	−	0.122870i	$-0.960790\pi$
$709$	−16.0460	−	27.7925i	−0.602620	−	1.04377i	0.389803	−	0.920898i	$-0.372543\pi$
$710$	−15.3731	−	0.146416i	−0.576943	−	0.00549489i
$711$	−16.0836	−	9.28589i	−0.603184	−	0.348248i
$712$	−6.49734	+	3.75124i	−0.243498	+	0.140584i
$713$	19.5185			0.730974
$714$	−3.68116	+	2.34649i	−0.137764	+	0.0878153i
$715$	7.05204	+	10.7037i	0.263731	+	0.400296i
$716$	6.63861	+	11.4984i	0.248096	+	0.429716i
$717$	3.10693	+	1.79379i	0.116031	+	0.0669903i
$718$	−15.3645	−	8.87070i	−0.573398	−	0.331052i
$719$	32.9162	−	19.0042i	1.22757	−	0.708736i	0.261046	−	0.965326i	$-0.415933\pi$
$719$	32.9162	−	19.0042i	1.22757	−	0.708736i	0.966520	+	0.256591i	$0.0825993\pi$
$720$	−2.04543	−	3.62202i	−0.0762287	−	0.134985i
$721$	−40.9351	+	1.79783i	−1.52450	+	0.0669547i
$722$	18.7661			0.698401
$723$	−6.35782	−	11.0121i	−0.236450	−	0.409543i
$724$	9.49207	+	5.48025i	0.352770	+	0.203672i
$725$	−7.14045	+	3.94315i	−0.265190	+	0.146445i
$726$	7.20548	+	9.27307i	0.267420	+	0.344156i
$727$	−34.4594			−1.27803			−0.639013	−	0.769196i	$-0.720657\pi$
$727$	−34.4594			−1.27803			−0.639013	+	0.769196i	$0.720657\pi$
$728$	4.05672	+	2.11046i	0.150352	+	0.0782190i
$729$	16.5414			0.612645
$730$	−14.8930	−	8.78865i	−0.551215	−	0.325283i
$731$	−2.15868	−	1.24631i	−0.0798416	−	0.0460966i
$732$	0.612243	−	1.06044i	0.0226292	−	0.0391948i
$733$	−2.49290	+	1.43927i	−0.0920772	+	0.0531608i	−0.545332	−	0.838220i	$-0.683596\pi$
$733$	−2.49290	+	1.43927i	−0.0920772	+	0.0531608i	0.453254	+	0.891381i	$0.350263\pi$
$734$	9.02129			0.332982
$735$	−7.19826	+	15.0805i	−0.265512	+	0.556253i
$736$		−	4.01299i		−	0.147921i
$737$	−10.2824	−	15.2878i	−0.378756	−	0.563134i
$738$	−7.78868	+	13.4904i	−0.286705	+	0.496588i
$739$	15.8781	+	9.16725i	0.584087	+	0.337223i	0.762756	−	0.646687i	$-0.223846\pi$
$739$	15.8781	+	9.16725i	0.584087	+	0.337223i	−0.178669	+	0.983909i	$0.557179\pi$
$740$	−4.04090	−	2.38462i	−0.148547	−	0.0876602i
$741$		−	0.892466i		−	0.0327856i
$742$	25.0463	+	13.0301i	0.919479	+	0.478350i
$743$	−11.1230			−0.408063			−0.204032	−	0.978964i	$-0.565405\pi$
$743$	−11.1230			−0.408063			−0.204032	+	0.978964i	$0.565405\pi$
$744$	−4.49690	+	2.59629i	−0.164864	+	0.0951844i
$745$	−0.449824	+	47.2299i	−0.0164803	+	1.73037i
$746$	−11.6611	+	20.1977i	−0.426945	+	0.739490i
$747$	−5.38216	+	3.10739i	−0.196923	+	0.113694i
$748$	−5.11390	+	0.350799i	−0.186983	+	0.0128265i
$749$	1.71449	−	0.0752986i	0.0626460	−	0.00275135i
$750$	−11.9311	−	0.340983i	−0.435663	−	0.0124510i
$751$	−21.0857	−	36.5215i	−0.769429	−	1.33269i	−0.937873	−	0.346979i	$-0.887208\pi$
$751$	−21.0857	−	36.5215i	−0.769429	−	1.33269i	0.168444	−	0.985711i	$-0.446126\pi$
$752$	1.81833	−	3.14943i	0.0663075	−	0.114848i
$753$	−19.3657	−	11.1808i	−0.705727	−	0.407452i
$754$	1.40981	+	2.44187i	0.0513424	+	0.0889276i
$755$	−33.2374	+	18.7699i	−1.20963	+	0.683105i
$756$	−7.37910	−	11.5763i	−0.268375	−	0.421026i
$757$		−	1.63573i		−	0.0594518i	−0.999558	−	0.0297259i	$-0.990537\pi$
$757$		−	1.63573i		−	0.0594518i	0.999558	−	0.0297259i	$-0.00946343\pi$
$758$	−4.77003	−	8.26194i	−0.173255	−	0.300087i
$759$	6.24576	−	12.7628i	0.226707	−	0.463261i
$760$	1.08147	+	0.0103001i	0.0392291	+	0.000373624i
$761$	−3.43564	−	5.95071i	−0.124542	−	0.215713i	0.797012	−	0.603964i	$-0.206413\pi$
$761$	−3.43564	−	5.95071i	−0.124542	−	0.215713i	−0.921554	+	0.388251i	$0.873079\pi$
$762$	18.1026			0.655788
$763$	44.8463	−	28.5865i	1.62355	−	1.03490i
$764$	−14.4255			−0.521894
$765$	5.53668	+	3.26730i	0.200179	+	0.118130i
$766$	−10.7286	+	18.5824i	−0.387639	+	0.671410i
$767$	−3.55771	+	6.16213i	−0.128461	+	0.222502i
$768$	0.533793	+	0.924557i	0.0192616	+	0.0333621i
$769$	13.3033			0.479731			0.239865	−	0.970806i	$-0.422897\pi$
$769$	13.3033			0.479731			0.239865	+	0.970806i	$0.422897\pi$
$770$	−15.8955	+	11.5036i	−0.572835	+	0.414561i
$771$	12.7075			0.457650
$772$	3.60370	+	6.24180i	0.129700	+	0.224647i
$773$	−20.3690	+	35.2802i	−0.732624	+	1.26894i	0.223135	+	0.974788i	$0.428371\pi$
$773$	−20.3690	+	35.2802i	−0.732624	+	1.26894i	−0.955758	+	0.294154i	$0.904962\pi$
$774$	1.50012	−	2.59828i	0.0539206	−	0.0933932i
$775$	0.463197	−	24.3148i	0.0166385	−	0.873413i
$776$	6.99351			0.251053
$777$	−5.25795	−	2.73540i	−0.188628	−	0.0981318i
$778$	3.05736			0.109612
$779$	−2.02507	−	3.50753i	−0.0725558	−	0.125670i
$780$	−0.0392946	+	4.12579i	−0.00140697	+	0.147727i
$781$	−20.4820	−	10.0233i	−0.732904	−	0.358662i
$782$	3.10108	+	5.37123i	0.110894	+	0.192075i
$783$		−	8.46478i		−	0.302507i
$784$	−2.95506	+	6.34568i	−0.105538	+	0.226631i
$785$	−12.2506	−	21.6932i	−0.437243	−	0.774264i
$786$	−3.25400	−	5.63610i	−0.116066	−	0.201033i
$787$	19.6167	+	11.3257i	0.699261	+	0.403718i	0.807072	−	0.590453i	$-0.201051\pi$
$787$	19.6167	+	11.3257i	0.699261	+	0.403718i	−0.107811	+	0.994171i	$0.534384\pi$
$788$	7.65651	−	13.2615i	0.272752	−	0.472420i
$789$	12.8462	+	22.2503i	0.457338	+	0.792132i
$790$	−19.4383	+	10.9772i	−0.691583	+	0.390551i
$791$	5.68603	+	2.95810i	0.202172	+	0.105178i
$792$	−0.422237	−	6.15531i	−0.0150035	−	0.218720i
$793$	1.71680	−	0.991195i	0.0609654	−	0.0351984i
$794$	8.08582	−	14.0051i	0.286955	−	0.497021i
$795$	−0.242606	+	25.4728i	−0.00860436	+	0.903426i
$796$	−14.6472	+	8.45658i	−0.519157	+	0.299735i
$797$	16.3552			0.579332			0.289666	−	0.957128i	$-0.406456\pi$
$797$	16.3552			0.579332			0.289666	+	0.957128i	$0.406456\pi$
$798$	1.36485	−	0.0599427i	0.0483150	−	0.00212195i
$799$			5.62053i			0.198840i
$800$	−4.99909	−	0.0952328i	−0.176745	−	0.00336699i
$801$	12.0867	+	6.97828i	0.427064	+	0.246565i
$802$	−5.34633	+	9.26012i	−0.188786	+	0.326986i
$803$	−14.3148	−	21.2833i	−0.505159	−	0.751071i
$804$		−	5.93050i		−	0.209153i
$805$	20.9562	+	11.1571i	0.738608	+	0.393236i
$806$	−8.40655			−0.296108
$807$	−27.3503	+	15.7907i	−0.962775	+	0.555858i
$808$	−1.06527	+	1.84510i	−0.0374760	+	0.0649103i
$809$	3.23348	+	1.86685i	0.113683	+	0.0656351i	0.555763	−	0.831340i	$-0.312426\pi$
$809$	3.23348	+	1.86685i	0.113683	+	0.0656351i	−0.442080	+	0.896976i	$0.645759\pi$
$810$	−0.0469767	+	0.0796053i	−0.00165059	+	0.00279705i
$811$	−4.20210			−0.147556			−0.0737779	−	0.997275i	$-0.523506\pi$
$811$	−4.20210			−0.147556			−0.0737779	+	0.997275i	$0.523506\pi$
$812$	−3.63965	+	2.32003i	−0.127727	+	0.0814172i
$813$	−15.7095			−0.550955
$814$	−3.88403	−	5.77477i	−0.136135	−	0.202406i
$815$	0.411199	−	43.1744i	0.0144037	−	1.51233i
$816$	−1.42892	−	0.824989i	−0.0500223	−	0.0288804i
$817$	0.390034	+	0.675558i	0.0136455	+	0.0236348i
$818$	31.1308			1.08846
$819$	−0.373246	−	8.49850i	−0.0130423	−	0.296962i
$820$	9.20729	+	16.3041i	0.321533	+	0.569366i
$821$	24.6150	−	14.2115i	0.859070	−	0.495985i	−0.00463049	−	0.999989i	$-0.501474\pi$
$821$	24.6150	−	14.2115i	0.859070	−	0.495985i	0.863701	+	0.504005i	$0.168141\pi$
$822$	−9.60501	−	5.54545i	−0.335013	−	0.193420i
$823$	−34.4463	−	19.8876i	−1.20072	−	0.693237i	−0.240006	−	0.970771i	$-0.577150\pi$
$823$	−34.4463	−	19.8876i	−1.20072	−	0.693237i	−0.960716	+	0.277534i	$0.910483\pi$
$824$	−7.74347	−	13.4121i	−0.269756	−	0.467232i
$825$	−15.7508	−	8.08340i	−0.548372	−	0.281428i
$826$	−9.66268	−	5.02691i	−0.336208	−	0.174909i
$827$	6.76897			0.235380			0.117690	−	0.993050i	$-0.462451\pi$
$827$	6.76897			0.235380			0.117690	+	0.993050i	$0.462451\pi$
$828$	−6.46505	+	3.73260i	−0.224676	+	0.129717i
$829$	37.3030	+	21.5369i	1.29559	+	0.748008i	0.979639	−	0.200768i	$-0.0643437\pi$
$829$	37.3030	+	21.5369i	1.29559	+	0.748008i	0.315949	+	0.948776i	$0.397677\pi$
$830$	−0.0711450	+	7.46996i	−0.00246948	+	0.259286i
$831$	−17.5414	−	30.3826i	−0.608504	−	1.05396i
$832$			1.72838i			0.0599207i
$833$	−0.948459	−	10.7770i	−0.0328622	−	0.373401i
$834$	−15.0432			−0.520902
$835$	−33.0839	−	19.5235i	−1.14492	−	0.675637i
$836$	1.44087	+	0.705123i	0.0498336	+	0.0243872i
$837$	21.8561	+	12.6186i	0.755457	+	0.436163i
$838$	−26.9606	+	15.5657i	−0.931339	+	0.537709i
$839$		−	12.9299i		−	0.446389i	−0.974774	−	0.223194i	$-0.928352\pi$
$839$		−	12.9299i		−	0.446389i	0.974774	−	0.223194i	$-0.0716485\pi$
$840$	−6.31220	+	0.217016i	−0.217792	+	0.00748778i
$841$	26.3386			0.908228
$842$	−20.0486	−	34.7251i	−0.690919	−	1.19671i
$843$	12.6812	+	7.32150i	0.436764	+	0.252166i
$844$	6.02376	+	3.47782i	0.207346	+	0.119712i
$845$	11.3787	−	19.2820i	0.391439	−	0.663322i
$846$	−6.76511			−0.232589
$847$	−28.6285	+	5.23527i	−0.983687	+	0.179886i
$848$			10.6711i			0.366446i
$849$	11.9064	−	6.87419i	0.408628	−	0.235922i
$850$	6.76468	−	3.73564i	0.232027	−	0.128131i
$851$	−4.21032	+	7.29249i	−0.144328	+	0.249983i
$852$	−3.67003	−	6.35668i	−0.125733	−	0.217776i
$853$			23.3324i			0.798888i	0.916758	+	0.399444i	$0.130797\pi$
$853$			23.3324i			0.798888i	−0.916758	+	0.399444i	$0.869203\pi$
$854$	1.63114	+	2.55893i	0.0558165	+	0.0875646i
$855$	−0.989315	−	1.75187i	−0.0338339	−	0.0599125i
$856$	0.324320	+	0.561739i	0.0110850	+	0.0191998i
$857$	31.2079	+	18.0179i	1.06604	+	0.615478i	0.927097	−	0.374822i	$-0.122296\pi$
$857$	31.2079	+	18.0179i	1.06604	+	0.615478i	0.138943	+	0.990300i	$0.455629\pi$
$858$	−2.69002	+	5.49689i	−0.0918359	+	0.187661i
$859$	21.6813	−	12.5177i	0.739758	−	0.427099i	−0.0822233	−	0.996614i	$-0.526202\pi$
$859$	21.6813	−	12.5177i	0.739758	−	0.427099i	0.821981	+	0.569514i	$0.192869\pi$
$860$	−1.77335	−	3.14022i	−0.0604706	−	0.107080i
$861$	12.7135	+	19.9448i	0.433275	+	0.679719i
$862$			23.0346i			0.784562i
$863$	−7.88996	+	4.55527i	−0.268577	+	0.155063i	−0.628241	−	0.778019i	$-0.716225\pi$
$863$	−7.88996	+	4.55527i	−0.268577	+	0.155063i	0.359664	+	0.933082i	$0.382891\pi$
$864$	2.59437	−	4.49359i	0.0882624	−	0.152875i
$865$	0.0149116	−	1.56566i	0.000507009	−	0.0532341i
$866$	−0.949139	−	1.64396i	−0.0322531	−	0.0558639i
$867$	−15.5989			−0.529766
$868$	−0.564628	−	12.8561i	−0.0191647	−	0.436365i
$869$	−33.0337	+	2.26602i	−1.12059	+	0.0768694i
$870$	−3.35396	−	1.97924i	−0.113710	−	0.0671024i
$871$	4.80061	−	8.31490i	0.162662	−	0.281740i
$872$	17.4081	+	10.0506i	0.589512	+	0.340355i
$873$	−6.50487	−	11.2668i	−0.220157	−	0.381322i
$874$		−	1.94097i		−	0.0656541i
$875$	14.3960	−	25.8409i	0.486675	−	0.873583i
$876$		−	8.25628i		−	0.278954i
$877$	24.2128	+	41.9378i	0.817609	+	1.41614i	0.907440	+	0.420183i	$0.138034\pi$
$877$	24.2128	+	41.9378i	0.817609	+	1.41614i	−0.0898309	+	0.995957i	$0.528633\pi$
$878$	−14.2518	+	24.6849i	−0.480976	+	0.833075i
$879$	2.41986	+	1.39711i	0.0816199	+	0.0471233i
$880$	−6.62998	−	3.32316i	−0.223497	−	0.112024i
$881$		−	24.1928i		−	0.815077i	−0.913188	−	0.407538i	$-0.866387\pi$
$881$		−	24.1928i		−	0.815077i	0.913188	−	0.407538i	$-0.133613\pi$
$882$	12.9717	−	1.14161i	0.436779	−	0.0384399i
$883$		−	18.5791i		−	0.625236i	−0.949879	−	0.312618i	$-0.898794\pi$
$883$		−	18.5791i		−	0.625236i	0.949879	−	0.312618i	$-0.101206\pi$
$884$	−1.33562	−	2.31337i	−0.0449218	−	0.0778069i
$885$	0.0935957	−	9.82721i	0.00314619	−	0.330338i
$886$	15.9939	+	9.23408i	0.537325	+	0.310225i
$887$	39.3570	−	22.7228i	1.32148	−	0.762956i	0.337514	−	0.941320i	$-0.390414\pi$
$887$	39.3570	−	22.7228i	1.32148	−	0.762956i	0.983965	+	0.178364i	$0.0570805\pi$
$888$		−	2.24017i		−	0.0751751i
$889$	−20.7051	+	39.7992i	−0.694427	+	1.33482i
$890$	14.6077	−	8.24928i	0.489652	−	0.276517i
$891$	−0.113762	+	0.0765148i	−0.00381118	+	0.00256334i
$892$	−6.24404	+	10.8150i	−0.209066	+	0.362113i
$893$	0.879472	−	1.52329i	0.0294304	−	0.0509749i
$894$	−19.5292	+	11.2752i	−0.653155	+	0.377099i
$895$	−14.5988	−	25.8514i	−0.487986	−	0.864118i
$896$	−2.64320	+	0.116087i	−0.0883032	+	0.00387819i
$897$	7.40473			0.247237
$898$	−6.95671	−	12.0494i	−0.232149	−	0.402093i
$899$	3.96737	−	6.87168i	0.132319	−	0.229183i
$900$	4.49638	+	8.14227i	0.149879	+	0.271409i
$901$	−8.24618	−	14.2828i	−0.274720	−	0.475829i
$902$	1.90066	+	27.7075i	0.0632850	+	0.922559i
$903$	−2.44865	−	3.84142i	−0.0814859	−	0.127835i
$904$			2.42255i			0.0805729i
$905$	−21.1072	−	12.4558i	−0.701628	−	0.414044i
$906$	−15.7828	−	9.11219i	−0.524348	−	0.302732i
$907$	1.43738	+	0.829870i	0.0477273	+	0.0275554i	0.523674	−	0.851919i	$-0.324561\pi$
$907$	1.43738	+	0.829870i	0.0477273	+	0.0275554i	−0.475946	+	0.879474i	$0.657894\pi$
$908$	−0.827974	+	0.478031i	−0.0274773	+	0.0158640i
$909$	3.96334			0.131456
$910$	−9.02574	−	4.80532i	−0.299200	−	0.159295i
$911$	2.36767			0.0784443			0.0392221	−	0.999231i	$-0.487512\pi$
$911$	2.36767			0.0784443			0.0392221	+	0.999231i	$0.487512\pi$
$912$	0.258180	+	0.447182i	0.00854921	+	0.0148077i
$913$	−4.87043	+	9.95242i	−0.161188	+	0.329377i
$914$	−6.86004	+	11.8819i	−0.226910	+	0.393020i
$915$	−1.39154	+	2.35806i	−0.0460028	+	0.0779551i
$916$		−	22.6211i		−	0.747421i
$917$	16.1130	−	0.707665i	0.532097	−	0.0233692i
$918$			8.01932i			0.264677i
$919$	−19.9149	+	11.4979i	−0.656933	+	0.379281i	−0.791107	−	0.611677i	$-0.790495\pi$
$919$	−19.9149	+	11.4979i	−0.656933	+	0.379281i	0.134174	+	0.990958i	$0.457162\pi$
$920$	−0.0854592	+	8.97290i	−0.00281751	+	0.295828i
$921$	−10.5566	−	6.09484i	−0.347851	−	0.200832i
$922$	9.42931	+	16.3320i	0.310538	+	0.537867i
$923$		−	11.8832i		−	0.391142i
$924$	−8.58707	−	3.74465i	−0.282494	−	0.123190i
$925$	8.98455	+	5.41798i	0.295410	+	0.178142i
$926$	−24.4522	+	14.1175i	−0.803550	+	0.463930i
$927$	−14.4049	+	24.9499i	−0.473117	+	0.819463i
$928$	−1.41281	−	0.815686i	−0.0463778	−	0.0267762i
$929$	−38.7731	+	22.3856i	−1.27210	+	0.734449i	−0.975383	−	0.220516i	$-0.929226\pi$
$929$	−38.7731	+	22.3856i	−1.27210	+	0.734449i	−0.296720	+	0.954965i	$0.595893\pi$
$930$	10.1102	−	5.70944i	0.331527	−	0.187220i
$931$	−1.42928	+	3.06922i	−0.0468426	+	0.100590i
$932$	5.52190			0.180876
$933$	−25.1010	+	14.4920i	−0.821769	+	0.474448i
$934$	14.2257	−	24.6396i	0.465479	−	0.806234i
$935$	11.4420	−	0.675471i	0.374193	−	0.0220903i
$936$	2.78447	−	1.60761i	0.0910132	−	0.0525465i
$937$		−	49.6646i		−	1.62247i	−0.584718	−	0.811236i	$-0.698795\pi$
$937$		−	49.6646i		−	1.62247i	0.584718	−	0.811236i	$-0.301205\pi$
$938$	13.0384	+	6.78309i	0.425719	+	0.221476i
$939$	30.4935			0.995119
$940$	−4.13279	+	7.00330i	−0.134797	+	0.228423i
$941$	3.48321	−	6.03310i	0.113549	−	0.196673i	−0.803650	−	0.595103i	$-0.797111\pi$
$941$	3.48321	−	6.03310i	0.113549	−	0.196673i	0.917199	+	0.398429i	$0.130445\pi$
$942$	5.94730	−	10.3010i	0.193773	−	0.335625i
$943$	29.1017	−	16.8019i	0.947683	−	0.547145i
$944$		−	4.11682i		−	0.133991i
$945$	16.2529	+	26.0413i	0.528707	+	0.847125i
$946$	−0.366071	−	5.33653i	−0.0119020	−	0.173506i
$947$	−19.0548	+	11.0013i	−0.619198	+	0.357494i	−0.776557	−	0.630047i	$-0.783036\pi$
$947$	−19.0548	+	11.0013i	−0.619198	+	0.357494i	0.157359	+	0.987542i	$0.449702\pi$
$948$	−9.23026	−	5.32910i	−0.299785	−	0.173081i
$949$	6.68328	−	11.5758i	0.216948	−	0.375766i
$950$	−2.41792	−	0.0460613i	−0.0784476	−	0.00149443i
$951$		−	14.5250i		−	0.471006i
$952$	3.44812	−	2.19794i	0.111754	−	0.0712357i
$953$	36.6699			1.18785			0.593927	−	0.804519i	$-0.297577\pi$
$953$	36.6699			1.18785			0.593927	+	0.804519i	$0.297577\pi$
$954$	17.1914	−	9.92547i	0.556593	−	0.321349i
$955$	32.2548	+	0.307200i	1.04374	+	0.00994075i
$956$	−2.91024	−	1.68023i	−0.0941239	−	0.0543424i
$957$	−3.22375	−	4.79307i	−0.104209	−	0.154938i
$958$	35.4555			1.14552
$959$	23.1777	−	14.7742i	0.748448	−	0.477085i
$960$	−1.17386	−	2.07865i	−0.0378860	−	0.0670880i
$961$	−3.67153	−	6.35929i	−0.118437	−	0.205138i
$962$	1.81337	−	3.14084i	0.0584653	−	0.101265i
$963$	0.603319	−	1.04498i	0.0194417	−	0.0336740i
$964$	5.95532	+	10.3149i	0.191808	+	0.332221i
$965$	−7.92484	−	14.0332i	−0.255110	−	0.451744i
$966$	0.497341	+	11.3240i	0.0160017	+	0.364345i
$967$	−58.1623			−1.87037			−0.935186	−	0.354157i	$-0.884768\pi$
$967$	−58.1623			−1.87037			−0.935186	+	0.354157i	$0.884768\pi$
$968$	−6.74931	−	8.68601i	−0.216931	−	0.279179i
$969$	−0.691129	−	0.399023i	−0.0222023	−	0.0128185i
$970$	−15.6373	−	0.148932i	−0.502082	−	0.00478190i
$971$	37.6008	−	21.7088i	1.20667	−	0.696669i	0.244637	−	0.969615i	$-0.421331\pi$
$971$	37.6008	−	21.7088i	1.20667	−	0.696669i	0.962029	+	0.272946i	$0.0879979\pi$
$972$	−15.6104			−0.500703
$973$	17.2058	−	33.0729i	0.551594	−	1.06027i
$974$		−	11.5380i		−	0.369703i
$975$	0.175723	−	9.22429i	0.00562763	−	0.295414i
$976$	−0.573483	+	0.993302i	−0.0183567	+	0.0317948i
$977$	44.2882	+	25.5698i	1.41690	+	0.818050i	0.996026	−	0.0890675i	$-0.0283887\pi$
$977$	44.2882	+	25.5698i	1.41690	+	0.818050i	0.420878	+	0.907117i	$0.361722\pi$
$978$	17.8523	−	10.3070i	0.570854	−	0.329583i
$979$	24.8246	−	1.70290i	0.793397	−	0.0544248i
$980$	6.74255	−	14.1258i	0.215383	−	0.451232i
$981$		−	37.3933i		−	1.19387i
$982$	−36.7269	+	21.2043i	−1.17200	+	0.676656i
$983$	−22.8638	+	39.6013i	−0.729243	+	1.26309i	0.227960	+	0.973670i	$0.426794\pi$
$983$	−22.8638	+	39.6013i	−0.729243	+	1.26309i	−0.957203	+	0.289416i	$0.906539\pi$
$984$	−4.46986	+	7.74202i	−0.142494	+	0.246807i
$985$	−17.4021	+	29.4891i	−0.554477	+	0.939602i
$986$	2.52132			0.0802953
$987$	−4.74072	+	9.11257i	−0.150899	+	0.290056i
$988$			0.835966i			0.0265956i
$989$	−5.60506	+	3.23608i	−0.178231	+	0.102901i
$990$	0.813027	+	13.7721i	0.0258397	+	0.437705i
$991$	−2.30721	+	3.99621i	−0.0732910	+	0.126944i	−0.900342	−	0.435183i	$-0.856684\pi$
$991$	−2.30721	+	3.99621i	−0.0732910	+	0.126944i	0.827051	+	0.562127i	$0.190017\pi$
$992$	4.21221	−	2.43192i	0.133738	−	0.0772135i
$993$	20.0557			0.636449
$994$	18.1730	−	0.798141i	0.576413	−	0.0253155i
$995$	32.9308	−	18.5967i	1.04398	−	0.589555i
$996$	−3.08878	+	1.78331i	−0.0978717	+	0.0565063i
$997$	−45.4090	−	26.2169i	−1.43812	−	0.830298i	−0.440400	−	0.897802i	$-0.645163\pi$
$997$	−45.4090	−	26.2169i	−1.43812	−	0.830298i	−0.997719	+	0.0675035i	$0.978497\pi$
$998$	−15.5619	+	26.9540i	−0.492604	+	0.853216i
$999$	−9.42911	+	5.44390i	−0.298324	+	0.172237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.o.b.549.15	yes	48
5.4	even	2		770.2.o.a.549.10	yes	48
7.5	odd	6	inner	770.2.o.b.439.10	yes	48
11.10	odd	2		770.2.o.a.549.15	yes	48
35.19	odd	6		770.2.o.a.439.15	yes	48
55.54	odd	2	inner	770.2.o.b.549.10	yes	48
77.54	even	6		770.2.o.a.439.10	✓	48
385.54	even	6	inner	770.2.o.b.439.15	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.o.a.439.10	✓	48	77.54	even	6
770.2.o.a.439.15	yes	48	35.19	odd	6
770.2.o.a.549.10	yes	48	5.4	even	2
770.2.o.a.549.15	yes	48	11.10	odd	2
770.2.o.b.439.10	yes	48	7.5	odd	6	inner
770.2.o.b.439.15	yes	48	385.54	even	6	inner
770.2.o.b.549.10	yes	48	55.54	odd	2	inner
770.2.o.b.549.15	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.533793 - 0.924557i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.13643 - 1.92576i) q^{5} +1.06759 q^{6} +(-1.22107 + 2.34712i) q^{7} -1.00000 q^{8} +(0.930129 + 1.61103i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.533793 - 0.924557i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.13643 - 1.92576i) q^{5} +1.06759 q^{6} +(-1.22107 + 2.34712i) q^{7} -1.00000 q^{8} +(0.930129 + 1.61103i) q^{9} +(2.23597 + 0.0212957i) q^{10} +(2.97904 + 1.45786i) q^{11} +(0.533793 + 0.924557i) q^{12} +1.72838i q^{13} +(-2.64320 + 0.116087i) q^{14} +(-1.17386 - 2.07865i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.33846 + 0.772761i) q^{17} +(-0.930129 + 1.61103i) q^{18} +(-0.241835 - 0.418871i) q^{19} +(1.09954 + 1.94705i) q^{20} +(1.51825 + 2.38183i) q^{21} +(0.226978 + 3.30885i) q^{22} +(3.47535 - 2.00649i) q^{23} +(-0.533793 + 0.924557i) q^{24} +(-2.41707 - 4.37696i) q^{25} +(-1.49682 + 0.864188i) q^{26} +5.18875 q^{27} +(-1.42214 - 2.23104i) q^{28} -1.63137i q^{29} +(1.21323 - 2.05591i) q^{30} +(4.21221 + 2.43192i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.93806 - 1.97610i) q^{33} +1.54552i q^{34} +(3.13234 + 5.01881i) q^{35} -1.86026 q^{36} +(-1.81722 + 1.04917i) q^{37} +(0.241835 - 0.418871i) q^{38} +(1.59798 + 0.922596i) q^{39} +(-1.13643 + 1.92576i) q^{40} +8.37376 q^{41} +(-1.30360 + 2.50576i) q^{42} -1.61281 q^{43} +(-2.75206 + 1.85099i) q^{44} +(4.15948 + 0.0396155i) q^{45} +(3.47535 + 2.00649i) q^{46} +(1.81833 + 3.14943i) q^{47} -1.06759 q^{48} +(-4.01799 - 5.73200i) q^{49} +(2.58202 - 4.28173i) q^{50} +(1.42892 - 0.824989i) q^{51} +(-1.49682 - 0.864188i) q^{52} +(-9.24141 - 5.33553i) q^{53} +(2.59437 + 4.49359i) q^{54} +(6.19293 - 4.08015i) q^{55} +(1.22107 - 2.34712i) q^{56} -0.516361 q^{57} +(1.41281 - 0.815686i) q^{58} +(3.56527 + 2.05841i) q^{59} +(2.38709 + 0.0227350i) q^{60} +(-0.573483 - 0.993302i) q^{61} +4.86384i q^{62} +(-4.91704 + 0.215952i) q^{63} +1.00000 q^{64} +(3.32843 + 1.96417i) q^{65} +(3.18038 + 1.55639i) q^{66} +(-4.81081 - 2.77752i) q^{67} +(-1.33846 + 0.772761i) q^{68} -4.28421i q^{69} +(-2.78025 + 5.22209i) q^{70} -6.87538 q^{71} +(-0.930129 - 1.61103i) q^{72} +(-6.69748 - 3.86679i) q^{73} +(-1.81722 - 1.04917i) q^{74} +(-5.33697 - 0.101669i) q^{75} +0.483671 q^{76} +(-7.05937 + 5.21203i) q^{77} +1.84519i q^{78} +(-8.64592 + 4.99172i) q^{79} +(-2.23597 - 0.0212957i) q^{80} +(-0.0206686 + 0.0357991i) q^{81} +(4.18688 + 7.25189i) q^{82} +3.34082i q^{83} +(-2.82185 + 0.123933i) q^{84} +(3.00921 - 1.69936i) q^{85} +(-0.806403 - 1.39673i) q^{86} +(-1.50830 - 0.870816i) q^{87} +(-2.97904 - 1.45786i) q^{88} +(6.49734 - 3.75124i) q^{89} +(2.04543 + 3.62202i) q^{90} +(-4.05672 - 2.11046i) q^{91} +4.01299i q^{92} +(4.49690 - 2.59629i) q^{93} +(-1.81833 + 3.14943i) q^{94} +(-1.08147 - 0.0103001i) q^{95} +(-0.533793 - 0.924557i) q^{96} -6.99351 q^{97} +(2.95506 - 6.34568i) q^{98} +(0.422237 + 6.15531i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9}+O(q^{10}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9	\( 48 q + 24 q^{2} - 24 q^{4} - 6 q^{5} + 4 q^{7} - 48 q^{8} - 28 q^{9} - 6 q^{10} + q^{11} + 2 q^{14} + 4 q^{15} - 24 q^{16} + 28 q^{18} + 2 q^{22} - 6 q^{26} - 2 q^{28} + 2 q^{30} + 12 q^{31} + 24 q^{32} - 24 q^{33} + 8 q^{35} + 56 q^{36} + 6 q^{40} - 24 q^{43} + q^{44} + 6 q^{45} - 36 q^{49} - 6 q^{52} - 4 q^{56} + 4 q^{57} - 2 q^{60} + 52 q^{63} + 48 q^{64} - 24 q^{66} - 2 q^{70} - 40 q^{71} + 28 q^{72} - 42 q^{73} + 90 q^{75} - 19 q^{77} + 6 q^{80} - 72 q^{81} + 40 q^{85} - 12 q^{86} - 18 q^{87} - q^{88} + 60 q^{89} - 56 q^{91} - 24 q^{95} - 42 q^{98} - 58 q^{99}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 6 * q^5 + 4 * q^7 - 48 * q^8 - 28 * q^9 - 6 * q^10 + q^11 + 2 * q^14 + 4 * q^15 - 24 * q^16 + 28 * q^18 + 2 * q^22 - 6 * q^26 - 2 * q^28 + 2 * q^30 + 12 * q^31 + 24 * q^32 - 24 * q^33 + 8 * q^35 + 56 * q^36 + 6 * q^40 - 24 * q^43 + q^44 + 6 * q^45 - 36 * q^49 - 6 * q^52 - 4 * q^56 + 4 * q^57 - 2 * q^60 + 52 * q^63 + 48 * q^64 - 24 * q^66 - 2 * q^70 - 40 * q^71 + 28 * q^72 - 42 * q^73 + 90 * q^75 - 19 * q^77 + 6 * q^80 - 72 * q^81 + 40 * q^85 - 12 * q^86 - 18 * q^87 - q^88 + 60 * q^89 - 56 * q^91 - 24 * q^95 - 42 * q^98 - 58 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more