LMFDB - Embedded newform 630.2.bt.a.443.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

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

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

chi := DirichletCharacter("630.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bt (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			443.26
Character	$\chi$	$=$	630.443
Dual form			630.2.bt.a.347.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 - 0.965926i) q^{2} +(-1.65767 + 0.502129i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.71852 - 1.43063i) q^{5} +(0.0559834 + 1.73115i) q^{6} +(-1.84712 - 1.89424i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.49573 - 1.66473i) q^{9} +O(q^{10})$	\(q+(0.258819 - 0.965926i) q^{2} +(-1.65767 + 0.502129i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.71852 - 1.43063i) q^{5} +(0.0559834 + 1.73115i) q^{6} +(-1.84712 - 1.89424i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.49573 - 1.66473i) q^{9} +(-1.82666 + 1.28969i) q^{10} -1.40006i q^{11} +(1.68665 + 0.393978i) q^{12} +(-0.862319 + 3.21822i) q^{13} +(-2.30777 + 1.29391i) q^{14} +(3.56710 + 1.50858i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.694879 + 2.59332i) q^{17} +(-0.962061 - 2.84156i) q^{18} +(0.845277 + 0.488021i) q^{19} +(0.772969 + 2.09822i) q^{20} +(4.01306 + 2.21254i) q^{21} +(-1.35235 - 0.362361i) q^{22} +(-0.628702 + 0.628702i) q^{23} +(0.817090 - 1.52721i) q^{24} +(0.906622 + 4.91712i) q^{25} +(2.88537 + 1.66587i) q^{26} +(-3.30119 + 4.01275i) q^{27} +(0.652527 + 2.56402i) q^{28} +(1.59174 - 2.75698i) q^{29} +(2.38041 - 3.05510i) q^{30} +(-3.12555 + 5.41362i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.703009 + 2.32083i) q^{33} +(2.32511 + 1.34240i) q^{34} +(0.464351 + 5.89783i) q^{35} +(-2.99373 + 0.193831i) q^{36} +(1.56810 + 5.85224i) q^{37} +(0.690166 - 0.690166i) q^{38} +(-0.186522 - 5.76773i) q^{39} +(2.22678 - 0.203572i) q^{40} +(-1.30462 + 0.753225i) q^{41} +(3.17581 - 3.30367i) q^{42} +(-3.55140 + 0.951596i) q^{43} +(-0.700028 + 1.21248i) q^{44} +(-6.67057 - 0.709589i) q^{45} +(0.444560 + 0.770000i) q^{46} +(-1.62966 + 6.08198i) q^{47} +(-1.26369 - 1.18452i) q^{48} +(-0.176325 + 6.99778i) q^{49} +(4.98422 + 0.396914i) q^{50} +(-0.150305 - 4.64779i) q^{51} +(2.35590 - 2.35590i) q^{52} +(-0.151267 - 0.0405318i) q^{53} +(3.02161 + 4.22728i) q^{54} +(-2.00296 + 2.40603i) q^{55} +(2.64554 + 0.0333249i) q^{56} +(-1.64624 - 0.384539i) q^{57} +(-2.25107 - 2.25107i) q^{58} +(6.30314 - 10.9174i) q^{59} +(-2.33490 - 3.09002i) q^{60} +(0.788770 + 1.36619i) q^{61} +(4.42020 + 4.42020i) q^{62} +(-7.76331 - 1.65258i) q^{63} -1.00000i q^{64} +(6.08597 - 4.29691i) q^{65} +(2.42370 - 0.0783800i) q^{66} +(-1.40294 - 5.23584i) q^{67} +(1.89845 - 1.89845i) q^{68} +(0.726491 - 1.35787i) q^{69} +(5.81705 + 1.07794i) q^{70} -4.15268i q^{71} +(-0.587608 + 2.94189i) q^{72} +(-2.49135 + 9.29786i) q^{73} +6.05868 q^{74} +(-3.97191 - 7.69571i) q^{75} +(-0.488021 - 0.845277i) q^{76} +(-2.65205 + 2.58607i) q^{77} +(-5.61948 - 1.31263i) q^{78} +(-3.35565 + 1.93738i) q^{79} +(0.379698 - 2.20359i) q^{80} +(3.45736 - 8.30943i) q^{81} +(0.389898 + 1.45512i) q^{82} +(-4.20762 - 15.7031i) q^{83} +(-2.36914 - 3.92265i) q^{84} +(4.90424 - 3.46257i) q^{85} +3.67669i q^{86} +(-1.25422 + 5.36943i) q^{87} +(0.989989 + 0.989989i) q^{88} +(-6.92869 + 12.0008i) q^{89} +(-2.41188 + 6.25962i) q^{90} +(7.68889 - 4.31098i) q^{91} +(0.858823 - 0.230121i) q^{92} +(2.46280 - 10.5434i) q^{93} +(5.45296 + 3.14827i) q^{94} +(-0.754451 - 2.04795i) q^{95} +(-1.47122 + 0.914056i) q^{96} +(3.30188 + 12.3228i) q^{97} +(6.71370 + 1.98147i) q^{98} +(-2.33071 - 3.49417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$2$	0.258819	−	0.965926i	0.183013	−	0.683013i
$3$	−1.65767	+	0.502129i	−0.957056	+	0.289905i
$3$	−1.65767	+	0.502129i	−0.957056	+	0.289905i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−1.71852	−	1.43063i	−0.768545	−	0.639795i
$5$	−1.71852	−	1.43063i	−0.768545	−	0.639795i
$6$	0.0559834	+	1.73115i	0.0228551	+	0.706737i
$7$	−1.84712	−	1.89424i	−0.698144	−	0.715957i
$7$	−1.84712	−	1.89424i	−0.698144	−	0.715957i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.49573	−	1.66473i	0.831911	−	0.554909i
$10$	−1.82666	+	1.28969i	−0.577642	+	0.407836i
$11$		−	1.40006i		−	0.422133i	−0.977472	−	0.211066i	$-0.932306\pi$
$11$		−	1.40006i		−	0.422133i	0.977472	−	0.211066i	$-0.0676936\pi$
$12$	1.68665	+	0.393978i	0.486893	+	0.113732i
$13$	−0.862319	+	3.21822i	−0.239164	+	0.892573i	0.737063	+	0.675824i	$0.236212\pi$
$13$	−0.862319	+	3.21822i	−0.239164	+	0.892573i	−0.976227	+	0.216749i	$0.930455\pi$
$14$	−2.30777	+	1.29391i	−0.616777	+	0.345812i
$15$	3.56710	+	1.50858i	0.921020	+	0.389515i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.694879	+	2.59332i	−0.168533	+	0.628974i	0.829030	+	0.559204i	$0.188893\pi$
$17$	−0.694879	+	2.59332i	−0.168533	+	0.628974i	−0.997563	+	0.0697697i	$0.977774\pi$
$18$	−0.962061	−	2.84156i	−0.226760	−	0.669761i
$19$	0.845277	+	0.488021i	0.193920	+	0.111960i	0.593816	−	0.804601i	$-0.297621\pi$
$19$	0.845277	+	0.488021i	0.193920	+	0.111960i	−0.399896	+	0.916560i	$0.630954\pi$
$20$	0.772969	+	2.09822i	0.172841	+	0.469176i
$21$	4.01306	+	2.21254i	0.875722	+	0.482816i
$22$	−1.35235	−	0.362361i	−0.288322	−	0.0772557i
$23$	−0.628702	+	0.628702i	−0.131094	+	0.131094i	−0.769609	−	0.638515i	$-0.779549\pi$
$23$	−0.628702	+	0.628702i	−0.131094	+	0.131094i	0.638515	+	0.769609i	$0.279549\pi$
$24$	0.817090	−	1.52721i	0.166788	−	0.311740i
$25$	0.906622	+	4.91712i	0.181324	+	0.983423i
$26$	2.88537	+	1.66587i	0.565868	+	0.326704i
$27$	−3.30119	+	4.01275i	−0.635314	+	0.772254i
$28$	0.652527	+	2.56402i	0.123316	+	0.484555i
$29$	1.59174	−	2.75698i	0.295580	−	0.511959i	−0.679540	−	0.733638i	$-0.737821\pi$
$29$	1.59174	−	2.75698i	0.295580	−	0.511959i	0.975120	+	0.221680i	$0.0711539\pi$
$30$	2.38041	−	3.05510i	0.434602	−	0.557782i
$31$	−3.12555	+	5.41362i	−0.561366	+	0.972315i	0.436012	+	0.899941i	$0.356391\pi$
$31$	−3.12555	+	5.41362i	−0.561366	+	0.972315i	−0.997378	+	0.0723734i	$0.976943\pi$
$32$	0.965926	−	0.258819i	0.170753	−	0.0457532i
$33$	0.703009	+	2.32083i	0.122378	+	0.404005i
$34$	2.32511	+	1.34240i	0.398753	+	0.230220i
$35$	0.464351	+	5.89783i	0.0784897	+	0.996915i
$36$	−2.99373	+	0.193831i	−0.498955	+	0.0323052i
$37$	1.56810	+	5.85224i	0.257794	+	0.962102i	0.966514	+	0.256612i	$0.0826063\pi$
$37$	1.56810	+	5.85224i	0.257794	+	0.962102i	−0.708720	+	0.705490i	$0.750727\pi$
$38$	0.690166	−	0.690166i	0.111960	−	0.111960i
$39$	−0.186522	−	5.76773i	−0.0298675	−	0.923577i
$40$	2.22678	−	0.203572i	0.352085	−	0.0321876i
$41$	−1.30462	+	0.753225i	−0.203748	+	0.117634i	−0.598403	−	0.801196i	$-0.704198\pi$
$41$	−1.30462	+	0.753225i	−0.203748	+	0.117634i	0.394655	+	0.918830i	$0.370864\pi$
$42$	3.17581	−	3.30367i	0.490037	−	0.509768i
$43$	−3.55140	+	0.951596i	−0.541584	+	0.145117i	−0.519232	−	0.854633i	$-0.673782\pi$
$43$	−3.55140	+	0.951596i	−0.541584	+	0.145117i	−0.0223518	+	0.999750i	$0.507115\pi$
$44$	−0.700028	+	1.21248i	−0.105533	+	0.182789i
$45$	−6.67057	−	0.709589i	−0.994390	−	0.105779i
$46$	0.444560	+	0.770000i	0.0655468	+	0.113530i
$47$	−1.62966	+	6.08198i	−0.237711	+	0.887149i	0.739197	+	0.673489i	$0.235205\pi$
$47$	−1.62966	+	6.08198i	−0.237711	+	0.887149i	−0.976908	+	0.213660i	$0.931462\pi$
$48$	−1.26369	−	1.18452i	−0.182398	−	0.170971i
$49$	−0.176325	+	6.99778i	−0.0251892	+	0.999683i
$50$	4.98422	+	0.396914i	0.704875	+	0.0561321i
$51$	−0.150305	−	4.64779i	−0.0210469	−	0.650821i
$52$	2.35590	−	2.35590i	0.326704	−	0.326704i
$53$	−0.151267	−	0.0405318i	−0.0207781	−	0.00556747i	0.248415	−	0.968654i	$-0.420090\pi$
$53$	−0.151267	−	0.0405318i	−0.0207781	−	0.00556747i	−0.269193	+	0.963086i	$0.586757\pi$
$54$	3.02161	+	4.22728i	0.411189	+	0.575260i
$55$	−2.00296	+	2.40603i	−0.270079	+	0.324428i
$56$	2.64554	+	0.0333249i	0.353525	+	0.00445322i
$57$	−1.64624	−	0.384539i	−0.218050	−	0.0509334i
$58$	−2.25107	−	2.25107i	−0.295580	−	0.295580i
$59$	6.30314	−	10.9174i	0.820599	−	1.42132i	−0.0846384	−	0.996412i	$-0.526974\pi$
$59$	6.30314	−	10.9174i	0.820599	−	1.42132i	0.905237	−	0.424907i	$-0.139693\pi$
$60$	−2.33490	−	3.09002i	−0.301435	−	0.398920i
$61$	0.788770	+	1.36619i	0.100992	+	0.174923i	0.912093	−	0.409982i	$-0.134465\pi$
$61$	0.788770	+	1.36619i	0.100992	+	0.174923i	−0.811102	+	0.584905i	$0.801132\pi$
$62$	4.42020	+	4.42020i	0.561366	+	0.561366i
$63$	−7.76331	−	1.65258i	−0.978085	−	0.208206i
$64$		−	1.00000i		−	0.125000i
$65$	6.08597	−	4.29691i	0.754872	−	0.532967i
$66$	2.42370	−	0.0783800i	0.298337	−	0.00964791i
$67$	−1.40294	−	5.23584i	−0.171396	−	0.639659i	−0.997137	−	0.0756101i	$-0.975910\pi$
$67$	−1.40294	−	5.23584i	−0.171396	−	0.639659i	0.825741	−	0.564049i	$-0.190757\pi$
$68$	1.89845	−	1.89845i	0.230220	−	0.230220i
$69$	0.726491	−	1.35787i	0.0874592	−	0.163468i
$70$	5.81705	+	1.07794i	0.695270	+	0.128839i
$71$		−	4.15268i		−	0.492833i	−0.969164	−	0.246416i	$-0.920747\pi$
$71$		−	4.15268i		−	0.492833i	0.969164	−	0.246416i	$-0.0792531\pi$
$72$	−0.587608	+	2.94189i	−0.0692503	+	0.346705i
$73$	−2.49135	+	9.29786i	−0.291591	+	1.08823i	0.652296	+	0.757964i	$0.273806\pi$
$73$	−2.49135	+	9.29786i	−0.291591	+	1.08823i	−0.943887	+	0.330268i	$0.892861\pi$
$74$	6.05868			0.704308
$75$	−3.97191	−	7.69571i	−0.458636	−	0.888624i
$76$	−0.488021	−	0.845277i	−0.0559799	−	0.0969600i
$77$	−2.65205	+	2.58607i	−0.302229	+	0.294710i
$78$	−5.61948	−	1.31263i	−0.636281	−	0.148626i
$79$	−3.35565	+	1.93738i	−0.377540	+	0.217973i	−0.676747	−	0.736215i	$-0.736611\pi$
$79$	−3.35565	+	1.93738i	−0.377540	+	0.217973i	0.299207	+	0.954188i	$0.403278\pi$
$80$	0.379698	−	2.20359i	0.0424515	−	0.246369i
$81$	3.45736	−	8.30943i	0.384151	−	0.923270i
$82$	0.389898	+	1.45512i	0.0430570	+	0.160691i
$83$	−4.20762	−	15.7031i	−0.461847	−	1.72363i	−0.667138	−	0.744934i	$-0.732481\pi$
$83$	−4.20762	−	15.7031i	−0.461847	−	1.72363i	0.205292	−	0.978701i	$-0.434186\pi$
$84$	−2.36914	−	3.92265i	−0.258495	−	0.427996i
$85$	4.90424	−	3.46257i	0.531939	−	0.375568i
$86$			3.67669i			0.396467i
$87$	−1.25422	+	5.36943i	−0.134467	+	0.575663i
$88$	0.989989	+	0.989989i	0.105533	+	0.105533i
$89$	−6.92869	+	12.0008i	−0.734440	+	1.27209i	0.220529	+	0.975380i	$0.429222\pi$
$89$	−6.92869	+	12.0008i	−0.734440	+	1.27209i	−0.954969	+	0.296706i	$0.904112\pi$
$90$	−2.41188	+	6.25962i	−0.254235	+	0.659822i
$91$	7.68889	−	4.31098i	0.806015	−	0.451913i
$92$	0.858823	−	0.230121i	0.0895385	−	0.0239918i
$93$	2.46280	−	10.5434i	0.255380	−	1.09330i
$94$	5.45296	+	3.14827i	0.562430	+	0.324719i
$95$	−0.754451	−	2.04795i	−0.0774050	−	0.210115i
$96$	−1.47122	+	0.914056i	−0.150156	+	0.0932904i
$97$	3.30188	+	12.3228i	0.335255	+	1.25119i	0.903592	+	0.428394i	$0.140920\pi$
$97$	3.30188	+	12.3228i	0.335255	+	1.25119i	−0.568337	+	0.822796i	$0.692413\pi$
$98$	6.71370	+	1.98147i	0.678186	+	0.200159i
$99$	−2.33071	−	3.49417i	−0.234246	−	0.351177i
$100$	1.67340	−	4.71166i	0.167340	−	0.471166i
$101$		−	15.1630i		−	1.50877i	−0.656431	−	0.754386i	$-0.727935\pi$
$101$		−	15.1630i		−	1.50877i	0.656431	−	0.754386i	$-0.272065\pi$
$102$	−4.52832	−	1.05775i	−0.448371	−	0.104733i
$103$	−9.17481	−	9.17481i	−0.904021	−	0.904021i	0.0917599	−	0.995781i	$-0.470751\pi$
$103$	−9.17481	−	9.17481i	−0.904021	−	0.904021i	−0.995781	+	0.0917599i	$0.970751\pi$
$104$	−1.66587	−	2.88537i	−0.163352	−	0.282934i
$105$	−3.73121	−	9.54348i	−0.364129	−	0.931348i
$106$	−0.0783014	+	0.135622i	−0.00760530	+	0.0131728i
$107$	−15.7279	+	4.21428i	−1.52047	+	0.407410i	−0.919898	−	0.392158i	$-0.871729\pi$
$107$	−15.7279	+	4.21428i	−1.52047	+	0.407410i	−0.600576	+	0.799568i	$0.705062\pi$
$108$	4.86529	−	1.82455i	0.468163	−	0.175567i
$109$	−17.8085	+	10.2817i	−1.70574	+	0.984810i	−0.766053	+	0.642777i	$0.777782\pi$
$109$	−17.8085	+	10.2817i	−1.70574	+	0.984810i	−0.939688	+	0.342033i	$0.888885\pi$
$110$	1.80564	+	2.55743i	0.172161	+	0.243842i
$111$	−5.53798	−	8.91368i	−0.525641	−	0.846049i
$112$	0.716906	−	2.54677i	0.0677412	−	0.240647i
$113$	16.2428	+	4.35225i	1.52800	+	0.409425i	0.922365	−	0.386320i	$-0.126254\pi$
$113$	16.2428	+	4.35225i	1.52800	+	0.409425i	0.605632	+	0.795745i	$0.292921\pi$
$114$	−0.797514	+	1.49062i	−0.0746941	+	0.139609i
$115$	1.97988	−	0.181000i	0.184624	−	0.0168783i
$116$	−2.75698	+	1.59174i	−0.255979	+	0.147790i
$117$	3.20534	+	9.46733i	0.296334	+	0.875255i
$118$	−8.91398	−	8.91398i	−0.820599	−	0.820599i
$119$	6.19591	−	3.47390i	0.567978	−	0.318452i
$120$	−3.58905	+	1.45559i	−0.327634	+	0.132876i
$121$	9.03984			0.821804
$122$	1.52379	−	0.408297i	0.137957	−	0.0369655i
$123$	1.78442	−	1.90369i	0.160896	−	0.171650i
$124$	5.41362	−	3.12555i	0.486157	−	0.280683i
$125$	5.47650	−	9.74720i	0.489833	−	0.871816i
$126$	−3.60556	+	7.07106i	−0.321209	+	0.629940i
$127$	8.08485	−	8.08485i	0.717415	−	0.717415i	−0.250660	−	0.968075i	$-0.580648\pi$
$127$	8.08485	−	8.08485i	0.717415	−	0.717415i	0.968075	+	0.250660i	$0.0806477\pi$
$128$	−0.965926	−	0.258819i	−0.0853766	−	0.0228766i
$129$	5.40923	−	3.36070i	0.476256	−	0.295893i
$130$	−2.57533	−	6.99072i	−0.225872	−	0.613127i
$131$			19.8569i			1.73491i	0.497518	+	0.867454i	$0.334245\pi$
$131$			19.8569i			1.73491i	−0.497518	+	0.867454i	$0.665755\pi$
$132$	0.551591	−	2.36140i	0.0480098	−	0.205534i
$133$	−0.636894	−	2.50259i	−0.0552257	−	0.217002i
$134$	−5.42054			−0.468263
$135$	11.4139	−	2.17322i	0.982352	−	0.187041i
$136$	−1.34240	−	2.32511i	−0.115110	−	0.199377i
$137$	−6.26763	−	6.26763i	−0.535480	−	0.535480i	0.386718	−	0.922198i	$-0.373609\pi$
$137$	−6.26763	−	6.26763i	−0.535480	−	0.535480i	−0.922198	+	0.386718i	$0.873609\pi$
$138$	−1.12357	−	1.05318i	−0.0956448	−	0.0896525i
$139$	−11.4416	+	6.60583i	−0.970466	+	0.560299i	−0.899378	−	0.437171i	$-0.855980\pi$
$139$	−11.4416	+	6.60583i	−0.970466	+	0.560299i	−0.0710880	+	0.997470i	$0.522647\pi$
$140$	2.54677	−	5.33984i	0.215242	−	0.451299i
$141$	−0.352502	−	10.9002i	−0.0296860	−	0.917964i
$142$	−4.01118	−	1.07479i	−0.336611	−	0.0901947i
$143$	4.50569	+	1.20729i	0.376784	+	0.100959i
$144$	2.68956	+	1.32900i	0.224130	+	0.110750i
$145$	−6.67965	+	2.46074i	−0.554715	+	0.204353i
$146$	8.33623	+	4.81293i	0.689911	+	0.398321i
$147$	−3.22150	−	11.6885i	−0.265705	−	0.964054i
$148$	1.56810	−	5.85224i	0.128897	−	0.481051i
$149$	7.87935			0.645501			0.322751	−	0.946484i	$-0.395392\pi$
$149$	7.87935			0.645501			0.322751	+	0.946484i	$0.395392\pi$
$150$	−8.46149	+	1.84477i	−0.690878	+	0.150625i
$151$	−11.6792			−0.950438			−0.475219	−	0.879868i	$-0.657631\pi$
$151$	−11.6792			−0.950438			−0.475219	+	0.879868i	$0.657631\pi$
$152$	−0.942785	+	0.252618i	−0.0764699	+	0.0204901i
$153$	2.58295	+	7.62903i	0.208819	+	0.616770i
$154$	1.81155	+	3.23101i	0.145979	+	0.260362i
$155$	13.1162	−	4.83191i	1.05352	−	0.388109i
$156$	−2.72233	+	5.08826i	−0.217961	+	0.407387i
$157$	−1.94572	−	7.26153i	−0.155285	−	0.579533i	−0.999081	−	0.0428679i	$-0.986351\pi$
$157$	−1.94572	−	7.26153i	−0.155285	−	0.579533i	0.843795	−	0.536665i	$-0.180316\pi$
$158$	1.00286	+	3.74274i	0.0797836	+	0.297756i
$159$	0.271102	−	0.00876716i	0.0214998	−	0.000695281i
$160$	−2.03024	−	0.937092i	−0.160504	−	0.0740837i
$161$	2.35220	+	0.0296298i	0.185380	+	0.00233515i
$162$	−7.13147	−	5.49019i	−0.560301	−	0.431350i
$163$	−10.8476	+	2.90662i	−0.849653	+	0.227664i	−0.657269	−	0.753656i	$-0.728289\pi$
$163$	−10.8476	+	2.90662i	−0.849653	+	0.227664i	−0.192384	+	0.981320i	$0.561622\pi$
$164$	1.50645			0.117634
$165$	2.11210	−	4.99414i	0.164427	−	0.388793i
$166$	−16.2570			−1.26179
$167$	−6.65391	+	24.8327i	−0.514895	+	1.92161i	−0.158141	+	0.987416i	$0.550550\pi$
$167$	−6.65391	+	24.8327i	−0.514895	+	1.92161i	−0.356754	+	0.934198i	$0.616117\pi$
$168$	−4.40217	+	1.27316i	−0.339634	+	0.0982266i
$169$	1.64500	+	0.949743i	0.126539	+	0.0730572i
$170$	−2.07527	−	5.63331i	−0.159166	−	0.432055i
$171$	2.92201	−	0.189187i	0.223452	−	0.0144675i
$172$	3.55140	+	0.951596i	0.270792	+	0.0725585i
$173$	−25.0808	−	6.72039i	−1.90686	−	0.510942i	−0.994927	−	0.100604i	$-0.967923\pi$
$173$	−25.0808	−	6.72039i	−1.90686	−	0.510942i	−0.911934	−	0.410338i	$-0.865411\pi$
$174$	4.86185	+	2.60120i	0.368576	+	0.197196i
$175$	7.63959	−	10.7998i	0.577498	−	0.816392i
$176$	1.21248	−	0.700028i	0.0913945	−	0.0527666i
$177$	−4.96659	+	21.2624i	−0.373312	+	1.59818i
$178$	9.79865	+	9.79865i	0.734440	+	0.734440i
$179$	1.40001	+	2.42489i	0.104642	+	0.181245i	0.913592	−	0.406632i	$-0.133297\pi$
$179$	1.40001	+	2.42489i	0.104642	+	0.181245i	−0.808950	+	0.587878i	$0.799964\pi$
$180$	5.42209	+	3.94981i	0.404139	+	0.294401i
$181$	2.71266			0.201631			0.100815	−	0.994905i	$-0.467855\pi$
$181$	2.71266			0.201631			0.100815	+	0.994905i	$0.467855\pi$
$182$	−2.17405	−	8.54266i	−0.161152	−	0.633224i
$183$	−1.99352	−	1.86863i	−0.147366	−	0.138133i
$184$		−	0.889119i		−	0.0655468i
$185$	5.67755	−	12.3006i	0.417421	−	0.904355i
$186$	−9.54674	−	5.10772i	−0.700001	−	0.374516i
$187$	3.63080	+	0.972870i	0.265510	+	0.0711433i
$188$	4.45232	−	4.45232i	0.324719	−	0.324719i
$189$	13.6988	−	1.15875i	0.996442	−	0.0842870i
$190$	−2.17343	+	0.198695i	−0.157677	+	0.0144149i
$191$	7.21226	−	4.16400i	0.521861	−	0.301296i	−0.215835	−	0.976430i	$-0.569247\pi$
$191$	7.21226	−	4.16400i	0.521861	−	0.301296i	0.737696	+	0.675133i	$0.235914\pi$
$192$	0.502129	+	1.65767i	0.0362381	+	0.119632i
$193$	−8.17797	+	2.19128i	−0.588663	+	0.157732i	−0.540842	−	0.841124i	$-0.681894\pi$
$193$	−8.17797	+	2.19128i	−0.588663	+	0.157732i	−0.0478211	+	0.998856i	$0.515228\pi$
$194$	12.7575			0.915935
$195$	−7.93092	+	10.1788i	−0.567945	+	0.728920i
$196$	3.65159	−	5.97209i	0.260828	−	0.426578i
$197$	−2.30556	−	2.30556i	−0.164265	−	0.164265i	0.620188	−	0.784453i	$-0.287056\pi$
$197$	−2.30556	−	2.30556i	−0.164265	−	0.164265i	−0.784453	+	0.620188i	$0.787056\pi$
$198$	−3.97834	+	1.34694i	−0.282728	+	0.0957229i
$199$	−9.90016	+	5.71586i	−0.701803	+	0.405186i	−0.808019	−	0.589157i	$-0.799460\pi$
$199$	−9.90016	+	5.71586i	−0.701803	+	0.405186i	0.106215	+	0.994343i	$0.466127\pi$
$200$	−4.11800	−	2.83585i	−0.291187	−	0.200525i
$201$	4.95467	+	7.97483i	0.349476	+	0.562501i
$202$	−14.6463	−	3.92447i	−1.03051	−	0.276125i
$203$	−8.16254	+	2.07731i	−0.572898	+	0.145799i
$204$	−2.19373	+	4.10026i	−0.153592	+	0.287076i
$205$	3.31960	+	0.571996i	0.231851	+	0.0399499i
$206$	−11.2368	+	6.48757i	−0.782905	+	0.452011i
$207$	−0.522454	+	2.61569i	−0.0363131	+	0.181803i
$208$	−3.21822	+	0.862319i	−0.223143	+	0.0597910i
$209$	0.683257	−	1.18344i	0.0472619	−	0.0818600i
$210$	−10.1840	+	1.13404i	−0.702763	+	0.0782562i
$211$	5.02999	+	8.71220i	0.346279	+	0.599773i	0.985585	−	0.169179i	$-0.0541117\pi$
$211$	5.02999	+	8.71220i	0.346279	+	0.599773i	−0.639306	+	0.768952i	$0.720778\pi$
$212$	0.110735	+	0.110735i	0.00760530	+	0.00760530i
$213$	2.08518	+	6.88377i	0.142874	+	0.471668i
$214$			16.2827i			1.11306i
$215$	7.46454	+	3.44539i	0.509077	+	0.234974i
$216$	−0.503149	−	5.17173i	−0.0342350	−	0.351892i
$217$	16.0280	−	4.07902i	1.08805	−	0.276902i
$218$	5.32221	+	19.8628i	0.360466	+	1.34528i
$219$	−0.538888	−	16.6638i	−0.0364147	−	1.12603i
$220$	2.93762	−	1.08220i	0.198055	−	0.0729619i
$221$	−7.74667	−	4.47254i	−0.521098	−	0.300856i
$222$	−10.0433	+	3.04224i	−0.674062	+	0.204182i
$223$	−21.1382	+	5.66397i	−1.41552	+	0.379287i	−0.883892	−	0.467691i	$-0.845086\pi$
$223$	−21.1382	+	5.66397i	−1.41552	+	0.379287i	−0.531627	+	0.846978i	$0.678419\pi$
$224$	−2.27444	−	1.35163i	−0.151968	−	0.0903096i
$225$	10.4483	+	10.7625i	0.696557	+	0.717502i
$226$	8.40791	−	14.5629i	0.559286	−	0.968711i
$227$	−3.22042	−	3.22042i	−0.213747	−	0.213747i	0.592110	−	0.805857i	$-0.298295\pi$
$227$	−3.22042	−	3.22042i	−0.213747	−	0.213747i	−0.805857	+	0.592110i	$0.798295\pi$
$228$	1.23342	+	1.15614i	0.0816850	+	0.0765673i
$229$			12.4207i			0.820783i	0.911909	+	0.410391i	$0.134608\pi$
$229$			12.4207i			0.820783i	−0.911909	+	0.410391i	$0.865392\pi$
$230$	0.337597	−	1.95926i	0.0222605	−	0.129190i
$231$	3.09768	−	5.61851i	0.203812	−	0.369671i
$232$	0.823948	+	3.07501i	0.0540948	+	0.201885i
$233$	−0.782196	−	2.91920i	−0.0512434	−	0.191243i	0.935559	−	0.353169i	$-0.114896\pi$
$233$	−0.782196	−	2.91920i	−0.0512434	−	0.191243i	−0.986803	+	0.161926i	$0.948229\pi$
$234$	9.97435	−	0.645795i	0.652043	−	0.0422169i
$235$	11.5017	−	8.12057i	0.750285	−	0.529728i
$236$	−10.9174	+	6.30314i	−0.710659	+	0.410299i
$237$	4.58974	−	4.89651i	0.298135	−	0.318063i
$238$	−1.75191	−	6.88390i	−0.113559	−	0.446217i
$239$	−3.17214	−	5.49431i	−0.205189	−	0.355397i	0.745004	−	0.667060i	$-0.232447\pi$
$239$	−3.17214	−	5.49431i	−0.205189	−	0.355397i	−0.950193	+	0.311663i	$0.899114\pi$
$240$	0.477076	+	3.84349i	0.0307951	+	0.248096i
$241$	5.86832			0.378012			0.189006	−	0.981976i	$-0.439473\pi$
$241$	5.86832			0.378012			0.189006	+	0.981976i	$0.439473\pi$
$242$	2.33968	−	8.73182i	0.150401	−	0.561302i
$243$	−1.55875	+	15.5103i	−0.0999936	+	0.994988i
$244$		−	1.57754i		−	0.100992i
$245$	10.3142	−	11.7736i	0.658951	−	0.752186i
$246$	−1.37698	−	2.21633i	−0.0877930	−	0.141308i
$247$	−2.29946	+	2.29946i	−0.146311	+	0.146311i
$248$	−1.61791	−	6.03811i	−0.102737	−	0.383420i
$249$	14.8598	+	23.9177i	0.941702	+	1.51572i
$250$	−7.99765	−	7.81266i	−0.505816	−	0.494116i
$251$		−	1.52378i		−	0.0961804i	−0.998843	−	0.0480902i	$-0.984687\pi$
$251$		−	1.52378i		−	0.0961804i	0.998843	−	0.0480902i	$-0.0153135\pi$
$252$	5.89693	+	5.31283i	0.371472	+	0.334677i
$253$	0.880219	+	0.880219i	0.0553389	+	0.0553389i
$254$	−5.71685	−	9.90188i	−0.358707	−	0.621299i
$255$	−6.39095	+	8.20235i	−0.400217	+	0.513651i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.4548	+	14.4548i	0.901665	+	0.901665i	0.995580	−	0.0939149i	$-0.0299382\pi$
$257$	14.4548	+	14.4548i	0.901665	+	0.901665i	−0.0939149	+	0.995580i	$0.529938\pi$
$258$	−1.84617	−	6.09473i	−0.114938	−	0.379441i
$259$	8.18910	−	13.7801i	0.508846	−	0.856256i
$260$	−7.41907	+	0.678250i	−0.460111	+	0.0420633i
$261$	−0.617059	−	9.53051i	−0.0381950	−	0.589924i
$262$	19.1803	+	5.13935i	1.18496	+	0.317510i
$263$	−12.5963	+	12.5963i	−0.776721	+	0.776721i	−0.979272	−	0.202551i	$-0.935077\pi$
$263$	−12.5963	+	12.5963i	−0.776721	+	0.776721i	0.202551	+	0.979272i	$0.435077\pi$
$264$	−2.13818	−	1.14397i	−0.131596	−	0.0704066i
$265$	0.201969	+	0.286061i	0.0124069	+	0.0175726i
$266$	−2.58216	−	0.0325265i	−0.158322	−	0.00199433i
$267$	5.45950	−	23.3725i	0.334116	−	1.43038i
$268$	−1.40294	+	5.23584i	−0.0856981	+	0.319830i
$269$	−5.71601	−	9.90043i	−0.348512	−	0.603640i	0.637474	−	0.770472i	$-0.279979\pi$
$269$	−5.71601	−	9.90043i	−0.348512	−	0.603640i	−0.985985	+	0.166832i	$0.946646\pi$
$270$	0.854961	−	11.5875i	0.0520313	−	0.705190i
$271$	6.27563	−	10.8697i	0.381217	−	0.660288i	−0.610019	−	0.792387i	$-0.708838\pi$
$271$	6.27563	−	10.8697i	0.381217	−	0.660288i	0.991237	+	0.132099i	$0.0421716\pi$
$272$	−2.59332	+	0.694879i	−0.157243	+	0.0421332i
$273$	−10.5810	+	11.0070i	−0.640389	+	0.666173i
$274$	−7.67625	+	4.43189i	−0.463739	+	0.267740i
$275$	6.88424	−	1.26932i	0.415135	−	0.0765430i
$276$	−1.30809	+	0.812705i	−0.0787380	+	0.0489191i
$277$	−10.0338	+	10.0338i	−0.602872	+	0.602872i	−0.941074	−	0.338201i	$-0.890181\pi$
$277$	−10.0338	+	10.0338i	−0.602872	+	0.602872i	0.338201	+	0.941074i	$0.390181\pi$
$278$	3.41943	+	12.7615i	0.205084	+	0.765383i
$279$	1.21166	+	18.7141i	0.0725401	+	1.12039i
$280$	−4.49874	−	3.84205i	−0.268851	−	0.229606i
$281$	10.6559	+	6.15221i	0.635680	+	0.367010i	0.782948	−	0.622087i	$-0.213715\pi$
$281$	10.6559	+	6.15221i	0.635680	+	0.367010i	−0.147269	+	0.989097i	$0.547048\pi$
$282$	−10.6200	−	2.48069i	−0.632414	−	0.147723i
$283$	25.7854	−	6.90918i	1.53278	−	0.410708i	0.608858	−	0.793279i	$-0.291628\pi$
$283$	25.7854	−	6.90918i	1.53278	−	0.410708i	0.923926	+	0.382571i	$0.124961\pi$
$284$	−2.07634	+	3.59633i	−0.123208	+	0.213403i
$285$	2.27897	+	3.01599i	0.134994	+	0.178652i
$286$	2.33231	−	4.03969i	0.137913	−	0.238872i
$287$	3.83658	+	1.07998i	0.226466	+	0.0637494i
$288$	1.97983	−	2.25395i	0.116663	−	0.132815i
$289$	8.47996	+	4.89591i	0.498821	+	0.287994i
$290$	0.648070	+	7.08894i	0.0380560	+	0.416277i
$291$	−11.6611	−	18.7691i	−0.683584	−	1.10027i
$292$	6.80650	−	6.80650i	0.398321	−	0.398321i
$293$	7.93986	+	2.12748i	0.463851	+	0.124289i	0.483173	−	0.875525i	$-0.339484\pi$
$293$	7.93986	+	2.12748i	0.463851	+	0.124289i	−0.0193219	+	0.999813i	$0.506151\pi$
$294$	−12.1240	+	0.0865162i	−0.707089	+	0.00504572i
$295$	−26.4507	+	9.74426i	−1.54002	+	0.567333i
$296$	−5.24697	−	3.02934i	−0.304974	−	0.176077i
$297$	5.61808	+	4.62185i	0.325994	+	0.268187i
$298$	2.03932	−	7.61086i	0.118135	−	0.440886i
$299$	−1.48116	−	2.56544i	−0.0856576	−	0.148363i
$300$	−0.408083	+	8.65063i	−0.0235607	+	0.499445i
$301$	8.36241	+	4.96952i	0.482001	+	0.286438i
$302$	−3.02279	+	11.2812i	−0.173942	+	0.649161i
$303$	7.61378	+	25.1352i	0.437400	+	1.44398i
$304$			0.976042i			0.0559799i
$305$	0.598989	−	3.47626i	0.0342980	−	0.199050i
$306$	8.03759	−	0.520399i	0.459479	−	0.0297492i
$307$	16.8290	−	16.8290i	0.960480	−	0.960480i	−0.0387679	−	0.999248i	$-0.512343\pi$
$307$	16.8290	−	16.8290i	0.960480	−	0.960480i	0.999248	+	0.0387679i	$0.0123433\pi$
$308$	3.58978	−	0.913575i	0.204546	−	0.0520558i
$309$	19.8157	+	10.6019i	1.12728	+	0.603119i
$310$	−1.27255	−	13.9199i	−0.0722761	−	0.790595i
$311$	−4.47479	−	2.58352i	−0.253742	−	0.146498i	0.367734	−	0.929931i	$-0.380134\pi$
$311$	−4.47479	−	2.58352i	−0.253742	−	0.146498i	−0.621477	+	0.783433i	$0.713467\pi$
$312$	4.21029	+	3.94651i	0.238361	+	0.223427i
$313$	8.40593	−	31.3713i	0.475131	−	1.77321i	−0.145764	−	0.989319i	$-0.546564\pi$
$313$	8.40593	−	31.3713i	0.475131	−	1.77321i	0.620895	−	0.783894i	$-0.286769\pi$
$314$	−7.51769			−0.424248
$315$	10.9772	+	13.9464i	0.618494	+	0.785790i
$316$	3.87477			0.217973
$317$	1.09656	−	4.09240i	0.0615887	−	0.229852i	−0.928270	−	0.371907i	$-0.878704\pi$
$317$	1.09656	−	4.09240i	0.0615887	−	0.229852i	0.989859	+	0.142055i	$0.0453708\pi$
$318$	0.0616980	−	0.264134i	0.00345985	−	0.0148119i
$319$	−3.85993	−	2.22853i	−0.216115	−	0.124774i
$320$	−1.43063	+	1.71852i	−0.0799744	+	0.0960682i
$321$	23.9555	−	14.8833i	1.33707	−	0.830706i
$322$	0.637415	−	2.26438i	0.0355217	−	0.126189i
$323$	−1.85296	+	1.85296i	−0.103102	+	0.103102i
$324$	−7.14888	+	5.46750i	−0.397160	+	0.303750i
$325$	−16.6061	−	1.32242i	−0.921143	−	0.0733545i
$326$			11.2303i			0.621989i
$327$	24.3578	−	25.9858i	1.34699	−	1.43702i
$328$	0.389898	−	1.45512i	0.0215285	−	0.0803455i
$329$	14.5309	−	8.14715i	0.801117	−	0.449167i
$330$	−4.27731	−	3.33271i	−0.235458	−	0.183460i
$331$	11.9016	+	20.6141i	0.654169	+	1.13305i	0.982102	+	0.188352i	$0.0603147\pi$
$331$	11.9016	+	20.6141i	0.654169	+	1.13305i	−0.327933	+	0.944701i	$0.606352\pi$
$332$	−4.20762	+	15.7031i	−0.230923	+	0.861817i
$333$	13.6560	+	11.9952i	0.748342	+	0.657331i
$334$	22.2644	+	12.8544i	1.21826	+	0.703360i
$335$	−5.07954	+	11.0050i	−0.277525	+	0.601266i
$336$	0.0904163	+	4.58168i	0.00493261	+	0.249951i
$337$	32.7514	+	8.77571i	1.78408	+	0.478044i	0.991318	−	0.131484i	$-0.0419742\pi$
$337$	32.7514	+	8.77571i	1.78408	+	0.478044i	0.792765	+	0.609528i	$0.208641\pi$
$338$	1.34314	−	1.34314i	0.0730572	−	0.0730572i
$339$	−29.1106	+	0.941407i	−1.58107	+	0.0511302i
$340$	−5.97848	+	0.546552i	−0.324229	+	0.0296409i
$341$	7.57937	+	4.37595i	0.410446	+	0.236971i
$342$	0.573531	−	2.87141i	0.0310130	−	0.155268i
$343$	13.5812	−	12.5917i	0.733316	−	0.679888i
$344$	1.83834	−	3.18410i	0.0991168	−	0.171675i
$345$	−3.19109	+	1.29419i	−0.171803	+	0.0696769i
$346$	−12.9828	+	22.4869i	−0.697959	+	1.20890i
$347$	−14.9033	+	3.99332i	−0.800051	+	0.214373i	−0.635606	−	0.772013i	$-0.719250\pi$
$347$	−14.9033	+	3.99332i	−0.800051	+	0.214373i	−0.164444	+	0.986386i	$0.552583\pi$
$348$	3.77090	−	4.02295i	0.202142	−	0.215653i
$349$	−10.9900	−	6.34509i	−0.588282	−	0.339645i	0.176136	−	0.984366i	$-0.443640\pi$
$349$	−10.9900	−	6.34509i	−0.588282	−	0.339645i	−0.764418	+	0.644721i	$0.776974\pi$
$350$	−8.45458	−	10.1745i	−0.451916	−	0.543849i
$351$	−10.0672	−	14.0842i	−0.537348	−	0.751759i
$352$	−0.362361	−	1.35235i	−0.0193139	−	0.0720805i
$353$	−16.8314	+	16.8314i	−0.895844	+	0.895844i	−0.995065	−	0.0992213i	$-0.968365\pi$
$353$	−16.8314	+	16.8314i	−0.895844	+	0.895844i	0.0992213	+	0.995065i	$0.468365\pi$
$354$	19.2524	+	10.3005i	1.02325	+	0.547463i
$355$	−5.94093	+	7.13647i	−0.315312	+	0.378764i
$356$	12.0008	−	6.92869i	0.636043	−	0.367220i
$357$	−8.52642	+	8.86973i	−0.451266	+	0.469436i
$358$	2.70462	−	0.724700i	0.142943	−	0.0383016i
$359$	−7.75620	+	13.4341i	−0.409356	+	0.709026i	−0.994818	−	0.101674i	$-0.967580\pi$
$359$	−7.75620	+	13.4341i	−0.409356	+	0.709026i	0.585461	+	0.810700i	$0.300913\pi$
$360$	5.21856	−	4.21505i	0.275042	−	0.222153i
$361$	−9.02367	−	15.6295i	−0.474930	−	0.822603i
$362$	0.702088	−	2.62023i	0.0369009	−	0.137716i
$363$	−14.9851	+	4.53917i	−0.786512	+	0.238245i
$364$	−8.81426	−	0.111030i	−0.461993	−	0.00581955i
$365$	17.5832	−	12.4144i	0.920346	−	0.649797i
$366$	−2.32092	+	1.44196i	−0.121316	+	0.0753725i
$367$	17.1757	−	17.1757i	0.896563	−	0.896563i	−0.0985674	−	0.995130i	$-0.531426\pi$
$367$	17.1757	−	17.1757i	0.896563	−	0.896563i	0.995130	+	0.0985674i	$0.0314260\pi$
$368$	−0.858823	−	0.230121i	−0.0447693	−	0.0119959i
$369$	−2.00208	+	4.05169i	−0.104224	+	0.210923i
$370$	−10.4120	−	8.66771i	−0.541292	−	0.450613i
$371$	0.202630	+	0.361403i	0.0105200	+	0.0187631i
$372$	−7.40455	+	7.89947i	−0.383908	+	0.409568i
$373$	3.30758	+	3.30758i	0.171260	+	0.171260i	0.787533	−	0.616273i	$-0.211358\pi$
$373$	3.30758	+	3.30758i	0.171260	+	0.171260i	−0.616273	+	0.787533i	$0.711358\pi$
$374$	1.87944	−	3.25529i	0.0971836	−	0.168327i
$375$	−4.18388	+	18.9075i	−0.216054	+	0.976381i
$376$	−3.14827	−	5.45296i	−0.162359	−	0.281215i
$377$	7.49998	+	7.49998i	0.386268	+	0.386268i
$378$	2.42624	−	13.5319i	0.124792	−	0.696008i
$379$			11.4905i			0.590226i	0.955462	+	0.295113i	$0.0953573\pi$
$379$			11.4905i			0.590226i	−0.955462	+	0.295113i	$0.904643\pi$
$380$	−0.370601	+	2.15080i	−0.0190114	+	0.110334i
$381$	−9.34237	+	17.4617i	−0.478624	+	0.894588i
$382$	−2.15544	−	8.04423i	−0.110282	−	0.411579i
$383$	5.99412	−	5.99412i	0.306285	−	0.306285i	−0.537181	−	0.843467i	$-0.680511\pi$
$383$	5.99412	−	5.99412i	0.306285	−	0.306285i	0.843467	+	0.537181i	$0.180511\pi$
$384$	1.73115	−	0.0559834i	0.0883422	−	0.00285689i
$385$	8.25729	−	0.650118i	0.420831	−	0.0331331i
$386$			8.46646i			0.430931i
$387$	−7.27921	+	8.28705i	−0.370023	+	0.421255i
$388$	3.30188	−	12.3228i	0.167628	−	0.625595i
$389$	−30.3634			−1.53949			−0.769744	−	0.638353i	$-0.779616\pi$
$389$	−30.3634			−1.53949			−0.769744	+	0.638353i	$0.779616\pi$
$390$	7.77930	+	10.2952i	0.393920	+	0.521315i
$391$	−1.19356	−	2.06730i	−0.0603608	−	0.104548i
$392$	−4.82350	−	5.07286i	−0.243623	−	0.256218i
$393$	−9.97074	−	32.9162i	−0.502957	−	1.66040i
$394$	−2.82373	+	1.63028i	−0.142257	+	0.0821323i
$395$	8.53842	+	1.47124i	0.429615	+	0.0740262i
$396$	0.271374	+	4.19139i	0.0136371	+	0.210625i
$397$	−1.06451	−	3.97279i	−0.0534260	−	0.199388i	0.934054	−	0.357131i	$-0.116245\pi$
$397$	−1.06451	−	3.97279i	−0.0534260	−	0.199388i	−0.987480	+	0.157743i	$0.949578\pi$
$398$	2.95875	+	11.0422i	0.148309	+	0.553495i
$399$	2.31239	+	3.82867i	0.115764	+	0.191673i
$400$	−3.80504	+	3.24372i	−0.190252	+	0.162186i
$401$			10.8119i			0.539918i	0.962872	+	0.269959i	$0.0870102\pi$
$401$			10.8119i			0.539918i	−0.962872	+	0.269959i	$0.912990\pi$
$402$	8.98545	−	2.72181i	0.448154	−	0.135752i
$403$	−14.7270	−	14.7270i	−0.733603	−	0.733603i
$404$	−7.58149	+	13.1315i	−0.377193	+	0.653318i
$405$	−17.8292	+	9.33374i	−0.885941	+	0.463797i
$406$	−0.106089	+	8.42205i	−0.00526512	+	0.417979i
$407$	8.19347	−	2.19543i	0.406135	−	0.108824i
$408$	3.39277	+	3.18020i	0.167967	+	0.157444i
$409$	−3.16814	−	1.82913i	−0.156655	−	0.0904446i	0.419623	−	0.907698i	$-0.362162\pi$
$409$	−3.16814	−	1.82913i	−0.156655	−	0.0904446i	−0.576278	+	0.817254i	$0.695495\pi$
$410$	1.41168	−	3.05845i	0.0697180	−	0.151046i
$411$	13.5368	+	7.24250i	0.667722	+	0.357246i
$412$	3.35821	+	12.5330i	0.165447	+	0.617458i
$413$	−32.3228	+	8.22594i	−1.59050	+	0.404772i
$414$	2.39134	+	1.18164i	0.117528	+	0.0580746i
$415$	−15.2343	+	33.0056i	−0.747823	+	1.62018i
$416$			3.33174i			0.163352i
$417$	15.6495	−	16.6955i	0.766357	−	0.817580i
$418$	−0.966272	−	0.966272i	−0.0472619	−	0.0472619i
$419$	−11.7629	−	20.3739i	−0.574655	−	0.995331i	−0.996079	−	0.0884676i	$-0.971803\pi$
$419$	−11.7629	−	20.3739i	−0.574655	−	0.995331i	0.421424	−	0.906864i	$-0.361530\pi$
$420$	−1.54042	+	10.1305i	−0.0751646	+	0.494318i
$421$	−4.56136	+	7.90050i	−0.222307	+	0.385047i	−0.955508	−	0.294965i	$-0.904692\pi$
$421$	−4.56136	+	7.90050i	−0.222307	+	0.385047i	0.733201	+	0.680012i	$0.238025\pi$
$422$	9.71720	−	2.60372i	0.473026	−	0.126747i
$423$	6.05765	+	17.8920i	0.294533	+	0.869936i
$424$	0.135622	−	0.0783014i	0.00658639	−	0.00380265i
$425$	−13.3817	−	1.06564i	−0.649106	−	0.0516910i
$426$	7.18890	−	0.232481i	0.348303	−	0.0112638i
$427$	1.13095	−	4.01763i	0.0547304	−	0.194427i
$428$	15.7279	+	4.21428i	0.760237	+	0.203705i
$429$	−8.07515	+	0.261142i	−0.389872	+	0.0126081i
$430$	5.25996	−	6.31846i	0.253658	−	0.304703i
$431$	−24.5878	+	14.1958i	−1.18435	+	0.683786i	−0.957017	−	0.290031i	$-0.906334\pi$
$431$	−24.5878	+	14.1958i	−1.18435	+	0.683786i	−0.227335	+	0.973817i	$0.573001\pi$
$432$	−5.12574	−	0.852539i	−0.246612	−	0.0410178i
$433$	−9.01561	−	9.01561i	−0.433262	−	0.433262i	0.456474	−	0.889737i	$-0.349112\pi$
$433$	−9.01561	−	9.01561i	−0.433262	−	0.433262i	−0.889737	+	0.456474i	$0.849112\pi$
$434$	0.208317	−	16.5376i	0.00999955	−	0.793828i
$435$	9.83705	−	7.43314i	0.471650	−	0.356392i
$436$	20.5634			0.984810
$437$	−0.838248	+	0.224608i	−0.0400988	+	0.0107445i
$438$	−16.2354	−	3.79237i	−0.775759	−	0.181206i
$439$	29.8999	−	17.2627i	1.42705	−	0.823906i	0.430160	−	0.902753i	$-0.358457\pi$
$439$	29.8999	−	17.2627i	1.42705	−	0.823906i	0.996887	+	0.0788471i	$0.0251239\pi$
$440$	−0.285013	−	3.11762i	−0.0135874	−	0.148627i
$441$	11.2093	+	17.7581i	0.533778	+	0.845625i
$442$	−6.32513	+	6.32513i	−0.300856	+	0.300856i
$443$	−2.41800	−	0.647901i	−0.114883	−	0.0307827i	0.200920	−	0.979608i	$-0.435607\pi$
$443$	−2.41800	−	0.647901i	−0.114883	−	0.0307827i	−0.315802	+	0.948825i	$0.602274\pi$
$444$	0.339186	+	10.4885i	0.0160970	+	0.497761i
$445$	29.0758	−	10.7113i	1.37833	−	0.507766i
$446$			21.8839i			1.03623i
$447$	−13.0613	+	3.95645i	−0.617781	+	0.187134i
$448$	−1.89424	+	1.84712i	−0.0894946	+	0.0872680i
$449$	−30.7956			−1.45334			−0.726668	−	0.686989i	$-0.758932\pi$
$449$	−30.7956			−1.45334			−0.726668	+	0.686989i	$0.758932\pi$
$450$	13.1000	−	7.30678i	0.617542	−	0.344445i
$451$	1.05456	+	1.82655i	0.0496572	+	0.0860087i
$452$	−11.8906	−	11.8906i	−0.559286	−	0.559286i
$453$	19.3602	−	5.86446i	0.909622	−	0.275536i
$454$	−3.94419	+	2.27718i	−0.185110	+	0.106873i
$455$	−19.3809	−	3.59142i	−0.908591	−	0.168369i
$456$	1.43598	−	0.892157i	0.0672458	−	0.0417791i
$457$	−25.0475	−	6.71146i	−1.17167	−	0.313949i	−0.380054	−	0.924964i	$-0.624095\pi$
$457$	−25.0475	−	6.71146i	−1.17167	−	0.313949i	−0.791619	+	0.611016i	$0.790761\pi$
$458$	11.9975	+	3.21471i	0.560605	+	0.150214i
$459$	−8.11243	−	11.3494i	−0.378656	−	0.529746i
$460$	−1.80512	−	0.833187i	−0.0841643	−	0.0388475i
$461$	−8.95950	−	5.17277i	−0.417286	−	0.240920i	0.276630	−	0.960977i	$-0.410782\pi$
$461$	−8.95950	−	5.17277i	−0.417286	−	0.240920i	−0.693915	+	0.720057i	$0.744116\pi$
$462$	−4.62533	−	4.44631i	−0.215190	−	0.206861i
$463$	0.590436	−	2.20354i	0.0274399	−	0.102407i	−0.950848	−	0.309659i	$-0.899785\pi$
$463$	0.590436	−	2.20354i	0.0274399	−	0.102407i	0.978288	+	0.207252i	$0.0664519\pi$
$464$	3.18349			0.147790
$465$	−19.3160	+	14.5957i	−0.895760	+	0.676861i
$466$	−3.02217			−0.140000
$467$	−4.89886	+	1.31265i	−0.226692	+	0.0607420i	−0.370377	−	0.928882i	$-0.620772\pi$
$467$	−4.89886	+	1.31265i	−0.226692	+	0.0607420i	0.143685	+	0.989623i	$0.454105\pi$
$468$	1.95776	−	9.80162i	0.0904975	−	0.453080i
$469$	−7.32656	+	12.3287i	−0.338309	+	0.569287i
$470$	−4.86703	−	13.2115i	−0.224499	−	0.609401i
$471$	6.87159	+	11.0602i	0.316626	+	0.509627i
$472$	3.26274	+	12.1767i	0.150180	+	0.560479i
$473$	1.33229	+	4.97217i	0.0612587	+	0.228621i
$474$	−3.54176	−	5.70066i	−0.162678	−	0.261840i
$475$	−1.63331	+	4.59878i	−0.0749414	+	0.211006i
$476$	−7.10277	−	0.0894708i	−0.325555	−	0.00410089i
$477$	−0.444996	+	0.150661i	−0.0203749	+	0.00689832i
$478$	−6.12811	+	1.64202i	−0.280293	+	0.0751043i
$479$	−16.2407			−0.742057			−0.371028	−	0.928622i	$-0.620995\pi$
$479$	−16.2407			−0.742057			−0.371028	+	0.928622i	$0.620995\pi$
$480$	3.83600	+	0.533948i	0.175089	+	0.0243713i
$481$	−20.1860			−0.920401
$482$	1.51883	−	5.66837i	0.0691810	−	0.258187i
$483$	−3.91405	+	1.13199i	−0.178095	+	0.0515075i
$484$	−7.82873	−	4.51992i	−0.355851	−	0.205451i
$485$	11.9550	−	25.9007i	0.542846	−	1.17609i
$486$	14.5784	+	5.52000i	0.661289	+	0.250392i
$487$	20.8211	+	5.57899i	0.943494	+	0.252808i	0.697599	−	0.716488i	$-0.254252\pi$
$487$	20.8211	+	5.57899i	0.943494	+	0.252808i	0.245894	+	0.969297i	$0.420918\pi$
$488$	−1.52379	−	0.408297i	−0.0689786	−	0.0184828i
$489$	16.5223	−	10.2651i	0.747165	−	0.464205i
$490$	−8.70288	−	13.0100i	−0.393156	−	0.587732i
$491$	7.58826	−	4.38108i	0.342453	−	0.197716i	−0.318903	−	0.947787i	$-0.603314\pi$
$491$	7.58826	−	4.38108i	0.342453	−	0.197716i	0.661356	+	0.750072i	$0.269981\pi$
$492$	−2.49719	+	0.756433i	−0.112582	+	0.0341026i
$493$	6.04368	+	6.04368i	0.272194	+	0.272194i
$494$	1.62596	+	2.81625i	0.0731555	+	0.126709i
$495$	−0.993465	+	9.33917i	−0.0446529	+	0.419765i
$496$	−6.25111			−0.280683
$497$	−7.86620	+	7.67049i	−0.352847	+	0.344068i
$498$	26.9487	−	8.16312i	1.20760	−	0.365798i
$499$			18.1985i			0.814678i	0.913277	+	0.407339i	$0.133543\pi$
$499$			18.1985i			0.814678i	−0.913277	+	0.407339i	$0.866457\pi$
$500$	−9.61639	+	5.70307i	−0.430058	+	0.255049i
$501$	−1.43926	−	44.5056i	−0.0643016	−	1.98836i
$502$	−1.47186	−	0.394384i	−0.0656924	−	0.0176022i
$503$	4.37850	−	4.37850i	0.195228	−	0.195228i	−0.602723	−	0.797951i	$-0.705918\pi$
$503$	4.37850	−	4.37850i	0.195228	−	0.195228i	0.797951	+	0.602723i	$0.205918\pi$
$504$	6.65804	−	4.32094i	0.296573	−	0.192470i
$505$	−21.6925	+	26.0579i	−0.965306	+	1.15956i
$506$	1.07804	−	0.622409i	0.0479249	−	0.0276694i
$507$	−3.20377	−	0.748355i	−0.142284	−	0.0332356i
$508$	−11.0441	+	2.95926i	−0.490003	+	0.131296i
$509$	−38.0263			−1.68549			−0.842743	−	0.538316i	$-0.819061\pi$
$509$	−38.0263			−1.68549			−0.842743	+	0.538316i	$0.819061\pi$
$510$	6.26877	+	8.29611i	0.277586	+	0.367358i
$511$	22.2142	−	12.4550i	0.982700	−	0.550976i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−4.74873	+	1.78084i	−0.209661	+	0.0786258i
$514$	17.7034	−	10.2211i	0.780865	−	0.450833i
$515$	2.64138	+	28.8928i	0.116393	+	1.27317i
$516$	−6.36488	+	0.205833i	−0.280198	+	0.00906131i
$517$	8.51512	+	2.28162i	0.374495	+	0.100346i
$518$	−11.1911	−	11.4766i	−0.491708	−	0.504254i
$519$	44.9502	−	1.45364i	1.97310	−	0.0638078i
$520$	−1.26506	+	7.34181i	−0.0554764	+	0.321960i
$521$	9.69959	−	5.60006i	0.424947	−	0.245343i	−0.272245	−	0.962228i	$-0.587766\pi$
$521$	9.69959	−	5.60006i	0.424947	−	0.245343i	0.697191	+	0.716885i	$0.254433\pi$
$522$	−9.36548	−	1.87065i	−0.409916	−	0.0818759i
$523$	42.6224	−	11.4206i	1.86375	−	0.499389i	0.863756	−	0.503911i	$-0.168106\pi$
$523$	42.6224	−	11.4206i	1.86375	−	0.499389i	0.999990	+	0.00452171i	$0.00143931\pi$
$524$	9.92846	−	17.1966i	0.433727	−	0.751237i
$525$	−7.24098	+	21.7386i	−0.316022	+	0.948752i
$526$	8.90693	+	15.4273i	0.388360	+	0.672660i
$527$	−11.8674	−	11.8674i	−0.516951	−	0.516951i
$528$	−1.65839	+	1.76924i	−0.0721723	+	0.0769962i
$529$			22.2095i			0.965629i
$530$	0.328587	−	0.121049i	0.0142729	−	0.00525804i
$531$	−2.44349	−	37.7398i	−0.106038	−	1.63777i
$532$	−0.699730	+	2.48576i	−0.0303372	+	0.107771i
$533$	−1.29904	−	4.84808i	−0.0562677	−	0.209994i
$534$	−21.1631	−	11.3227i	−0.915817	−	0.489982i
$535$	33.0578	+	15.2584i	1.42921	+	0.659679i
$536$	4.69432	+	2.71027i	0.202764	+	0.117066i
$537$	−3.53837	−	3.31668i	−0.152692	−	0.143125i
$538$	−11.0425	+	2.95883i	−0.476076	+	0.127564i
$539$	9.79729	+	0.246864i	0.421999	+	0.0106332i
$540$	−10.9713	−	3.82488i	−0.472131	−	0.164597i
$541$	−10.1448	+	17.5713i	−0.436160	+	0.755451i	−0.997390	−	0.0722090i	$-0.976995\pi$
$541$	−10.1448	+	17.5713i	−0.436160	+	0.755451i	0.561230	+	0.827660i	$0.310328\pi$
$542$	−8.87508	−	8.87508i	−0.381217	−	0.381217i
$543$	−4.49669	+	1.36211i	−0.192972	+	0.0584536i
$544$			2.68481i			0.115110i
$545$	45.3135	+	7.80790i	1.94102	+	0.334454i
$546$	7.89338	+	13.0693i	0.337806	+	0.559312i
$547$	−7.97943	−	29.7796i	−0.341176	−	1.27329i	−0.897017	−	0.441997i	$-0.854270\pi$
$547$	−7.97943	−	29.7796i	−0.341176	−	1.27329i	0.555841	−	0.831289i	$-0.312396\pi$
$548$	2.29411	+	8.56175i	0.0979997	+	0.365740i
$549$	4.24289	+	2.09656i	0.181082	+	0.0894788i
$550$	0.555702	−	6.97819i	0.0236952	−	0.297551i
$551$	2.69093	−	1.55361i	0.114638	−	0.0661860i
$552$	0.446453	+	1.47387i	0.0190023	+	0.0627319i
$553$	9.86815	+	2.77784i	0.419637	+	0.118126i
$554$	7.09497	+	12.2888i	0.301436	+	0.522103i
$555$	−3.23502	+	23.2411i	−0.137319	+	0.986530i
$556$	13.2117			0.560299
$557$	5.38615	−	20.1014i	0.228219	−	0.851724i	−0.752871	−	0.658168i	$-0.771331\pi$
$557$	5.38615	−	20.1014i	0.228219	−	0.851724i	0.981089	−	0.193555i	$-0.0620018\pi$
$558$	18.3901	+	3.67320i	0.778514	+	0.155499i
$559$		−	12.2498i		−	0.518110i
$560$	−4.87549	+	3.35105i	−0.206027	+	0.141608i
$561$	−6.50717	+	0.210435i	−0.274733	+	0.00888458i
$562$	8.70054	−	8.70054i	0.367010	−	0.367010i
$563$	−0.313315	−	1.16931i	−0.0132047	−	0.0492804i	0.959009	−	0.283375i	$-0.0914541\pi$
$563$	−0.313315	−	1.16931i	−0.0132047	−	0.0492804i	−0.972214	+	0.234095i	$0.924787\pi$
$564$	−5.14483	+	9.61612i	−0.216637	+	0.404912i
$565$	−21.6872	−	30.7168i	−0.912386	−	1.29227i
$566$		−	26.6950i		−	1.12208i
$567$	−22.1262	+	8.79940i	−0.929215	+	0.369540i
$568$	2.93639	+	2.93639i	0.123208	+	0.123208i
$569$	−0.357819	−	0.619761i	−0.0150006	−	0.0259817i	0.858428	−	0.512935i	$-0.171442\pi$
$569$	−0.357819	−	0.619761i	−0.0150006	−	0.0259817i	−0.873428	+	0.486953i	$0.838108\pi$
$570$	3.50306	−	1.42072i	0.146727	−	0.0595072i
$571$	−21.6255	+	37.4565i	−0.905001	+	1.56751i	−0.0840845	+	0.996459i	$0.526797\pi$
$571$	−21.6255	+	37.4565i	−0.905001	+	1.56751i	−0.820916	+	0.571049i	$0.806537\pi$
$572$	−3.29839	−	3.29839i	−0.137913	−	0.137913i
$573$	−9.86467	+	10.5240i	−0.412102	+	0.439647i
$574$	2.03616	−	3.42634i	0.0849878	−	0.143012i
$575$	−3.66140	−	2.52141i	−0.152691	−	0.105150i
$576$	−1.66473	−	2.49573i	−0.0693637	−	0.103989i
$577$	−22.0276	−	5.90228i	−0.917021	−	0.245715i	−0.230710	−	0.973023i	$-0.574105\pi$
$577$	−22.0276	−	5.90228i	−0.917021	−	0.245715i	−0.686312	+	0.727308i	$0.740771\pi$
$578$	6.92386	−	6.92386i	0.287994	−	0.287994i
$579$	12.4561	−	7.73882i	0.517656	−	0.321614i
$580$	7.01512	+	1.20876i	0.291287	+	0.0501912i
$581$	−21.9735	+	36.9756i	−0.911613	+	1.53401i
$582$	−21.1477	+	6.40591i	−0.876601	+	0.265534i
$583$	−0.0567468	+	0.211782i	−0.00235021	+	0.00877111i
$584$	−4.81293	−	8.33623i	−0.199160	−	0.344956i
$585$	8.03577	−	20.8554i	0.332238	−	0.862266i
$586$	4.10997	−	7.11868i	0.169781	−	0.294070i
$587$	7.98463	−	2.13948i	0.329561	−	0.0883056i	−0.0902447	−	0.995920i	$-0.528765\pi$
$587$	7.98463	−	2.13948i	0.329561	−	0.0883056i	0.419806	+	0.907614i	$0.362098\pi$
$588$	−3.05437	+	11.7333i	−0.125960	+	0.483874i
$589$	−5.28392	+	3.05067i	−0.217720	+	0.125701i
$590$	2.56629	+	28.0714i	0.105652	+	1.15568i
$591$	4.97955	+	2.66417i	0.204831	+	0.109589i
$592$	−4.28414	+	4.28414i	−0.176077	+	0.176077i
$593$	−9.35349	−	34.9077i	−0.384102	−	1.43349i	−0.839578	−	0.543239i	$-0.817198\pi$
$593$	−9.35349	−	34.9077i	−0.384102	−	1.43349i	0.455476	−	0.890248i	$-0.349469\pi$
$594$	5.91843	−	4.23042i	0.242836	−	0.173576i
$595$	−15.6176	−	2.89406i	−0.640261	−	0.118645i
$596$	−6.82371	−	3.93967i	−0.279510	−	0.161375i
$597$	13.5411	−	14.4462i	0.554200	−	0.591242i
$598$	−2.86138	+	0.766704i	−0.117011	+	0.0313529i
$599$	13.5928	−	23.5434i	0.555386	−	0.961957i	−0.442487	−	0.896775i	$-0.645904\pi$
$599$	13.5928	−	23.5434i	0.555386	−	0.961957i	0.997873	−	0.0651822i	$-0.0207629\pi$
$600$	8.25025	+	2.63313i	0.336815	+	0.107497i
$601$	19.0237	−	32.9499i	0.775991	−	1.34406i	−0.158245	−	0.987400i	$-0.550584\pi$
$601$	19.0237	−	32.9499i	0.775991	−	1.34406i	0.934236	−	0.356656i	$-0.116083\pi$
$602$	6.96454	−	6.79126i	0.283853	−	0.276791i
$603$	−12.2176	−	10.7317i	−0.497539	−	0.437030i
$604$	10.1145	+	5.83959i	0.411552	+	0.237610i
$605$	−15.5351	−	12.9326i	−0.631594	−	0.525786i
$606$	26.2493	−	0.848876i	1.06631	−	0.0344832i
$607$	−11.6931	+	11.6931i	−0.474607	+	0.474607i	−0.903402	−	0.428795i	$-0.858938\pi$
$607$	−11.6931	+	11.6931i	−0.474607	+	0.474607i	0.428795	+	0.903402i	$0.358938\pi$
$608$	0.942785	+	0.252618i	0.0382350	+	0.0102450i
$609$	12.4877	−	7.54215i	0.506027	−	0.305623i
$610$	−3.20278	−	1.47830i	−0.129677	−	0.0598547i
$611$	−18.1679	−	10.4892i	−0.734993	−	0.424348i
$612$	1.57762	−	7.89841i	0.0637713	−	0.319274i
$613$	7.83235	−	29.2307i	0.316346	−	1.18062i	−0.606385	−	0.795171i	$-0.707381\pi$
$613$	7.83235	−	29.2307i	0.316346	−	1.18062i	0.922730	−	0.385446i	$-0.125952\pi$
$614$	−11.8999	−	20.6112i	−0.480240	−	0.831800i
$615$	−5.79002	+	0.718691i	−0.233476	+	0.0289804i
$616$	0.0466567	−	3.70391i	0.00187985	−	0.149235i
$617$	4.80213	−	17.9218i	0.193326	−	0.721504i	−0.799367	−	0.600843i	$-0.794832\pi$
$617$	4.80213	−	17.9218i	0.193326	−	0.721504i	0.992694	−	0.120661i	$-0.0385015\pi$
$618$	15.3693	−	16.3966i	0.618244	−	0.659567i
$619$		−	19.3098i		−	0.776126i	−0.921633	−	0.388063i	$-0.873144\pi$
$619$		−	19.3098i		−	0.776126i	0.921633	−	0.388063i	$-0.126856\pi$
$620$	−13.7749	−	2.37353i	−0.553214	−	0.0953234i
$621$	−0.447360	−	4.59829i	−0.0179519	−	0.184523i
$622$	−3.65365	+	3.65365i	−0.146498	+	0.146498i
$623$	35.5306	−	9.04232i	1.42350	−	0.362273i
$624$	4.90174	−	3.04540i	0.196227	−	0.121914i
$625$	−23.3561	+	8.91593i	−0.934243	+	0.356637i
$626$	−28.1268	−	16.2390i	−1.12417	−	0.649041i
$627$	−0.538376	+	2.30483i	−0.0215007	+	0.0920460i
$628$	−1.94572	+	7.26153i	−0.0776427	+	0.289766i
$629$	−16.2664			−0.648584
$630$	16.3123	−	6.99355i	0.649896	−	0.278630i
$631$	−43.1479			−1.71769			−0.858846	−	0.512234i	$-0.828818\pi$
$631$	−43.1479			−1.71769			−0.858846	+	0.512234i	$0.828818\pi$
$632$	1.00286	−	3.74274i	0.0398918	−	0.148878i
$633$	−12.7127	−	11.9162i	−0.505285	−	0.473628i
$634$	−3.66914	−	2.11838i	−0.145720	−	0.0841317i
$635$	−25.4604	+	2.32758i	−1.01036	+	0.0923674i
$636$	−0.239165	−	0.127959i	−0.00948351	−	0.00507389i
$637$	−22.3683	−	6.60177i	−0.886265	−	0.261571i
$638$	−3.15162	+	3.15162i	−0.124774	+	0.124774i
$639$	−6.91309	−	10.3640i	−0.273478	−	0.409993i
$640$	1.28969	+	1.82666i	0.0509795	+	0.0722052i
$641$			1.38585i			0.0547378i	0.999625	+	0.0273689i	$0.00871288\pi$
$641$			1.38585i			0.0547378i	−0.999625	+	0.0273689i	$0.991287\pi$
$642$	−8.17603	−	26.9914i	−0.322682	−	1.06526i
$643$	−0.560231	+	2.09081i	−0.0220933	+	0.0824535i	−0.976092	−	0.217356i	$-0.930257\pi$
$643$	−0.560231	+	2.09081i	−0.0220933	+	0.0824535i	0.953999	+	0.299810i	$0.0969233\pi$
$644$	−2.02225	−	1.20176i	−0.0796879	−	0.0473560i
$645$	−14.1038	−	1.96316i	−0.555335	−	0.0772993i
$646$	1.31024	+	2.26941i	0.0515508	+	0.0892886i
$647$	−3.66341	+	13.6720i	−0.144024	+	0.537503i	0.855773	+	0.517351i	$0.173082\pi$
$647$	−3.66341	+	13.6720i	−0.144024	+	0.537503i	−0.999797	+	0.0201523i	$0.993585\pi$
$648$	3.43093	+	8.32038i	0.134780	+	0.326855i
$649$	−15.2849	−	8.82475i	−0.599985	−	0.346402i
$650$	−5.57534	+	15.6980i	−0.218683	+	0.615728i
$651$	−24.5209	+	14.8098i	−0.961049	+	0.580441i
$652$	10.8476	+	2.90662i	0.424827	+	0.113832i
$653$	14.5028	−	14.5028i	0.567539	−	0.567539i	−0.363899	−	0.931438i	$-0.618555\pi$
$653$	14.5028	−	14.5028i	0.567539	−	0.567539i	0.931438	+	0.363899i	$0.118555\pi$
$654$	−18.7961	−	30.2534i	−0.734987	−	1.18300i
$655$	28.4078	−	34.1245i	1.10999	−	1.33336i
$656$	−1.30462	−	0.753225i	−0.0509370	−	0.0294085i
$657$	9.26066	+	27.3524i	0.361293	+	1.06712i
$658$	−4.10866	−	16.1445i	−0.160172	−	0.629376i
$659$	11.0170	−	19.0819i	0.429159	−	0.743326i	−0.567639	−	0.823277i	$-0.692143\pi$
$659$	11.0170	−	19.0819i	0.429159	−	0.743326i	0.996799	+	0.0799514i	$0.0254765\pi$
$660$	−4.32620	+	3.26900i	−0.168397	+	0.127246i
$661$	22.1733	−	38.4053i	0.862442	−	1.49379i	−0.00712311	−	0.999975i	$-0.502267\pi$
$661$	22.1733	−	38.4053i	0.862442	−	1.49379i	0.869565	−	0.493819i	$-0.164399\pi$
$662$	22.9920	−	6.16070i	0.893611	−	0.239442i
$663$	15.0872	+	3.52416i	0.585939	+	0.136867i
$664$	14.0790	+	8.12850i	0.546370	+	0.315447i
$665$	−2.48576	+	5.21191i	−0.0963936	+	0.202109i
$666$	15.1209	−	10.0861i	0.585921	−	0.390827i
$667$	0.732588	+	2.73406i	0.0283659	+	0.105863i
$668$	18.1788	−	18.1788i	0.703360	−	0.703360i
$669$	32.1961	−	20.0031i	1.24477	−	0.773365i
$670$	9.31530	+	7.75476i	0.359881	+	0.299592i
$671$	1.91274	−	1.10432i	0.0738406	−	0.0426319i
$672$	4.44897	+	1.09849i	0.171623	+	0.0423752i
$673$	0.676043	−	0.181145i	0.0260595	−	0.00698263i	−0.245766	−	0.969329i	$-0.579039\pi$
$673$	0.676043	−	0.181145i	0.0260595	−	0.00698263i	0.271825	+	0.962347i	$0.412373\pi$
$674$	16.9534	−	29.3641i	0.653020	−	1.13106i
$675$	−22.7241	−	12.5943i	−0.874650	−	0.484754i
$676$	−0.949743	−	1.64500i	−0.0365286	−	0.0632694i
$677$	−1.49336	+	5.57330i	−0.0573946	+	0.214199i	−0.988667	−	0.150123i	$-0.952033\pi$
$677$	−1.49336	+	5.57330i	−0.0573946	+	0.214199i	0.931273	+	0.364323i	$0.118700\pi$
$678$	−6.62505	+	28.3624i	−0.254434	+	1.08925i
$679$	17.2434	−	29.0162i	0.661742	−	1.11354i
$680$	−1.01942	+	5.91623i	−0.0390928	+	0.226877i
$681$	6.95545	+	3.72132i	0.266534	+	0.142601i
$682$	6.18853	−	6.18853i	0.236971	−	0.236971i
$683$	36.0556	+	9.66107i	1.37963	+	0.369671i	0.870987	−	0.491307i	$-0.163481\pi$
$683$	36.0556	+	9.66107i	1.37963	+	0.369671i	0.508643	+	0.860977i	$0.330147\pi$
$684$	−2.62513	−	1.29716i	−0.100374	−	0.0495983i
$685$	1.80442	+	19.7377i	0.0689432	+	0.754138i
$686$	−8.64758	−	16.3774i	−0.330166	−	0.625292i
$687$	−6.23680	−	20.5894i	−0.237949	−	0.785535i
$688$	−2.59981	−	2.59981i	−0.0991168	−	0.0991168i
$689$	0.260880	−	0.451858i	0.00993874	−	0.0172144i
$690$	0.424178	+	3.41732i	0.0161482	+	0.130095i
$691$	−6.18288	−	10.7091i	−0.235208	−	0.407392i	0.724125	−	0.689668i	$-0.242244\pi$
$691$	−6.18288	−	10.7091i	−0.235208	−	0.407392i	−0.959333	+	0.282277i	$0.908910\pi$
$692$	18.3604	+	18.3604i	0.697959	+	0.697959i
$693$	−2.31371	+	10.8691i	−0.0878904	+	0.412882i
$694$			15.4290i			0.585678i
$695$	29.1131	+	5.01644i	1.10432	+	0.190284i
$696$	−2.90989	−	4.68363i	−0.110299	−	0.177532i
$697$	−1.04680	−	3.90671i	−0.0396504	−	0.147977i
$698$	−8.97331	+	8.97331i	−0.339645	+	0.339645i
$699$	2.76244	+	4.44630i	0.104485	+	0.168174i
$700$	−12.0160	+	5.53315i	−0.454162	+	0.209133i
$701$			8.90880i			0.336481i	0.985746	+	0.168240i	$0.0538085\pi$
$701$			8.90880i			0.336481i	−0.985746	+	0.168240i	$0.946192\pi$
$702$	−16.2099	+	6.07893i	−0.611803	+	0.229434i
$703$	−1.53053	+	5.71203i	−0.0577252	+	0.215433i
$704$	−1.40006			−0.0527666
$705$	−14.9883	+	19.2365i	−0.564494	+	0.724490i
$706$	11.9016	+	20.6141i	0.447922	+	0.775824i
$707$	−28.7224	+	28.0078i	−1.08022	+	1.05334i
$708$	14.9324	−	15.9304i	0.561193	−	0.598703i
$709$	−23.2994	+	13.4519i	−0.875028	+	0.505198i	−0.869016	−	0.494784i	$-0.835247\pi$
$709$	−23.2994	+	13.4519i	−0.875028	+	0.505198i	−0.00601243	+	0.999982i	$0.501914\pi$
$710$	5.35567	+	7.58555i	0.200995	+	0.284681i
$711$	−5.14958	+	10.4214i	−0.193124	+	0.390834i
$712$	−3.58655	−	13.3852i	−0.134412	−	0.501632i
$713$	−1.43851	−	5.36860i	−0.0538727	−	0.201056i
$714$	6.36070	+	10.5315i	0.238043	+	0.394133i
$715$	−6.01592	−	8.52071i	−0.224983	−	0.318656i
$716$		−	2.80003i		−	0.104642i
$717$	8.01721	+	7.51492i	0.299408	+	0.280650i
$718$	10.9689	+	10.9689i	0.409356	+	0.409356i
$719$	−12.2314	+	21.1855i	−0.456156	+	0.790085i	−0.998754	−	0.0499071i	$-0.984107\pi$
$719$	−12.2314	+	21.1855i	−0.456156	+	0.790085i	0.542598	+	0.839993i	$0.317441\pi$
$720$	−2.72076	−	6.13168i	−0.101397	−	0.228514i
$721$	−0.432395	+	34.3263i	−0.0161032	+	1.27838i
$722$	−17.4324	+	4.67100i	−0.648766	+	0.173836i
$723$	−9.72774	+	2.94666i	−0.361778	+	0.109587i
$724$	−2.34923	−	1.35633i	−0.0873086	−	0.0504076i
$725$	14.9995	+	5.32725i	0.557068	+	0.197849i
$726$	0.506081	+	15.6493i	0.0187824	+	0.580799i
$727$	7.68656	+	28.6866i	0.285079	+	1.06393i	0.948782	+	0.315932i	$0.102317\pi$
$727$	7.68656	+	28.6866i	0.285079	+	1.06393i	−0.663703	+	0.747996i	$0.731016\pi$
$728$	−2.38855	+	8.48519i	−0.0885254	+	0.314482i
$729$	−5.20431	−	26.4937i	−0.192752	−	0.981247i
$730$	−7.44049	−	20.1971i	−0.275385	−	0.747529i
$731$		−	9.87119i		−	0.365099i
$732$	0.792129	+	2.61504i	0.0292779	+	0.0966546i
$733$	−1.37805	−	1.37805i	−0.0508996	−	0.0508996i	0.681199	−	0.732098i	$-0.261459\pi$
$733$	−1.37805	−	1.37805i	−0.0508996	−	0.0508996i	−0.732098	+	0.681199i	$0.761459\pi$
$734$	−12.1450	−	21.0358i	−0.448281	−	0.776446i
$735$	−11.1857	+	24.6957i	−0.412591	+	0.910916i
$736$	−0.444560	+	0.770000i	−0.0163867	+	0.0283826i
$737$	−7.33047	+	1.96419i	−0.270021	+	0.0723520i
$738$	3.39546	+	2.98251i	0.124989	+	0.109788i
$739$	−5.90884	+	3.41147i	−0.217360	+	0.125493i	−0.604727	−	0.796433i	$-0.706718\pi$
$739$	−5.90884	+	3.41147i	−0.217360	+	0.125493i	0.387367	+	0.921926i	$0.373385\pi$
$740$	−11.0672	+	7.81382i	−0.406838	+	0.287242i
$741$	2.65711	−	4.96636i	0.0976115	−	0.182444i
$742$	0.401533	−	0.102188i	0.0147407	−	0.00375142i
$743$	36.8739	+	9.88034i	1.35277	+	0.362474i	0.861158	−	0.508338i	$-0.169740\pi$
$743$	36.8739	+	9.88034i	1.35277	+	0.362474i	0.491615	+	0.870812i	$0.336407\pi$
$744$	5.71386	+	9.19678i	0.209480	+	0.337170i
$745$	−13.5408	−	11.2724i	−0.496097	−	0.412989i
$746$	4.05095	−	2.33882i	0.148316	−	0.0856301i
$747$	−36.6424	−	32.1861i	−1.34068	−	1.17763i
$748$	−2.65793	−	2.65793i	−0.0971836	−	0.0971836i
$749$	37.0341	+	22.0082i	1.35320	+	0.804163i
$750$	17.1804	+	8.93495i	0.627340	+	0.326258i
$751$	−7.58181			−0.276664			−0.138332	−	0.990386i	$-0.544174\pi$
$751$	−7.58181			−0.276664			−0.138332	+	0.990386i	$0.544174\pi$
$752$	−6.08198	+	1.62966i	−0.221787	+	0.0594277i
$753$	0.765137	+	2.52593i	0.0278831	+	0.0920500i
$754$	9.18556	−	5.30328i	0.334518	−	0.193134i
$755$	20.0709	+	16.7085i	0.730455	+	0.608086i
$756$	−12.4429	−	5.84589i	−0.452544	−	0.212613i
$757$	0.229660	−	0.229660i	0.00834713	−	0.00834713i	−0.702921	−	0.711268i	$-0.748121\pi$
$757$	0.229660	−	0.229660i	0.00834713	−	0.00834713i	0.711268	+	0.702921i	$0.248121\pi$
$758$	11.0989	+	2.97395i	0.403132	+	0.108019i
$759$	−1.90110	−	1.01713i	−0.0690054	−	0.0369194i
$760$	1.98160	+	0.914642i	0.0718801	+	0.0331775i
$761$			26.6430i			0.965808i	0.875673	+	0.482904i	$0.160418\pi$
$761$			26.6430i			0.965808i	−0.875673	+	0.482904i	$0.839582\pi$
$762$	14.4487	+	13.5434i	0.523420	+	0.490627i
$763$	52.3704	+	14.7420i	1.89594	+	0.533698i
$764$	−8.32800			−0.301296
$765$	6.47543	−	16.8059i	0.234120	−	0.607617i
$766$	−4.23849	−	7.34127i	−0.153143	−	0.265251i
$767$	29.6991	+	29.6991i	1.07237	+	1.07237i
$768$	0.393978	−	1.68665i	0.0142164	−	0.0608617i
$769$	25.3689	−	14.6467i	0.914824	−	0.528174i	0.0328440	−	0.999460i	$-0.489544\pi$
$769$	25.3689	−	14.6467i	0.914824	−	0.528174i	0.881980	+	0.471287i	$0.156210\pi$
$770$	1.50918	−	8.14420i	0.0543870	−	0.293496i
$771$	−31.2194	−	16.7031i	−1.12434	−	0.601547i
$772$	8.17797	+	2.19128i	0.294332	+	0.0788659i
$773$	38.0890	+	10.2059i	1.36997	+	0.367081i	0.867466	−	0.497496i	$-0.165747\pi$
$773$	38.0890	+	10.2059i	1.36997	+	0.367081i	0.502500	+	0.864577i	$0.332414\pi$
$774$	6.12068	+	9.17602i	0.220003	+	0.329825i
$775$	−29.4531	−	10.4606i	−1.05799	−	0.375756i
$776$	−11.0483	−	6.37875i	−0.396611	−	0.228984i
$777$	−6.65541	+	26.9549i	−0.238762	+	0.967001i
$778$	−7.85864	+	29.3288i	−0.281746	+	1.05149i
$779$	−1.47036			−0.0526811
$780$	11.9578	−	4.84965i	0.428157	−	0.173645i
$781$	−5.81399			−0.208041
$782$	−2.30578	+	0.617831i	−0.0824544	+	0.0220936i
$783$	5.80843	+	15.4886i	0.207576	+	0.553517i
$784$	−6.14842	+	3.34619i	−0.219586	+	0.119507i
$785$	−7.04477	+	15.2627i	−0.251438	+	0.544748i
$786$	−34.3752	+	1.11166i	−1.22612	+	0.0396515i
$787$	−11.1791	−	41.7210i	−0.398492	−	1.48719i	−0.815750	−	0.578405i	$-0.803675\pi$
$787$	−11.1791	−	41.7210i	−0.398492	−	1.48719i	0.417258	−	0.908788i	$-0.362991\pi$
$788$	0.843894	+	3.14946i	0.0300625	+	0.112195i
$789$	14.5555	−	27.2055i	0.518190	−	0.968540i
$790$	3.63102	−	7.86670i	0.129186	−	0.279884i
$791$	−21.7582	−	38.8070i	−0.773631	−	1.37982i
$792$	4.11881	+	0.822685i	0.146356	+	0.0292328i
$793$	−5.07687	+	1.36034i	−0.180285	+	0.0483072i
$794$	−4.11293			−0.145962
$795$	−0.478437	−	0.372779i	−0.0169684	−	0.0132211i
$796$	11.4317			0.405186
$797$	−3.28128	+	12.2459i	−0.116229	+	0.433772i	−0.999376	−	0.0353244i	$-0.988754\pi$
$797$	−3.28128	+	12.2459i	−0.116229	+	0.433772i	0.883147	+	0.469096i	$0.155420\pi$
$798$	4.29670	−	1.24266i	0.152102	−	0.0439897i
$799$	−14.6401	−	8.45249i	−0.517931	−	0.299028i
$800$	2.14837	+	4.51492i	0.0759564	+	0.159626i
$801$	2.68599	+	41.4853i	0.0949048	+	1.46581i
$802$	10.4435	+	2.79831i	0.368771	+	0.0988119i
$803$	13.0175	+	3.48804i	0.459379	+	0.123090i
$804$	−0.303460	−	9.38374i	−0.0107022	−	0.330939i
$805$	−3.99992	−	3.41604i	−0.140979	−	0.120400i
$806$	−18.0368	+	10.4135i	−0.635319	+	0.366801i
$807$	14.4466	+	13.5415i	0.508543	+	0.476682i
$808$	10.7218	+	10.7218i	0.377193	+	0.377193i
$809$	3.93638	+	6.81801i	0.138396	+	0.239708i	0.926890	−	0.375334i	$-0.122472\pi$
$809$	3.93638	+	6.81801i	0.138396	+	0.239708i	−0.788494	+	0.615043i	$0.789139\pi$
$810$	4.40116	+	19.6375i	0.154641	+	0.689990i
$811$	29.0830			1.02124			0.510621	−	0.859806i	$-0.329415\pi$
$811$	29.0830			1.02124			0.510621	+	0.859806i	$0.329415\pi$
$812$	8.10762	+	2.28226i	0.284522	+	0.0800917i
$813$	−4.94492	+	21.1696i	−0.173426	+	0.742449i
$814$		−	8.48250i		−	0.297311i
$815$	22.8002	+	10.5238i	0.798655	+	0.368634i
$816$	3.94995	−	2.45406i	0.138276	−	0.0859094i
$817$	−3.46632	−	0.928798i	−0.121271	−	0.0324945i
$818$	−2.58678	+	2.58678i	−0.0904446	+	0.0904446i
$819$	12.0128	−	23.5590i	0.419762	−	0.823217i
$820$	−2.58886	−	2.15517i	−0.0904071	−	0.0752616i
$821$	18.4176	−	10.6334i	0.642778	−	0.371108i	−0.142906	−	0.989736i	$-0.545645\pi$
$821$	18.4176	−	10.6334i	0.642778	−	0.371108i	0.785684	+	0.618628i	$0.212311\pi$
$822$	10.4993	−	11.2011i	0.366205	−	0.390682i
$823$	−20.2826	+	5.43470i	−0.707006	+	0.189442i	−0.594367	−	0.804194i	$-0.702597\pi$
$823$	−20.2826	+	5.43470i	−0.707006	+	0.189442i	−0.112639	+	0.993636i	$0.535931\pi$
$824$	12.9751			0.452011
$825$	−10.7744	+	5.56089i	−0.375117	+	0.193605i
$826$	−0.420102	+	33.3504i	−0.0146172	+	1.16041i
$827$	15.3137	+	15.3137i	0.532511	+	0.532511i	0.921319	−	0.388808i	$-0.127113\pi$
$827$	15.3137	+	15.3137i	0.532511	+	0.532511i	−0.388808	+	0.921319i	$0.627113\pi$
$828$	1.76030	−	2.00403i	0.0611748	−	0.0696448i
$829$	−47.3861	+	27.3584i	−1.64579	+	0.950196i	−0.667067	+	0.744998i	$0.732450\pi$
$829$	−47.3861	+	27.3584i	−1.64579	+	0.950196i	−0.978721	+	0.205198i	$0.934216\pi$
$830$	27.9380	+	23.2577i	0.969742	+	0.807286i
$831$	11.5944	−	21.6710i	0.402207	−	0.751758i
$832$	3.21822	+	0.862319i	0.111572	+	0.0298955i
$833$	−18.0250	−	5.31988i	−0.624529	−	0.184323i
$834$	−12.0762	−	19.4373i	−0.418164	−	0.673059i
$835$	46.9612	−	33.1563i	1.62516	−	1.14742i
$836$	−1.18344	+	0.683257i	−0.0409300	+	0.0236309i
$837$	−11.4054	−	30.4134i	−0.394230	−	1.05124i
$838$	−22.7242	+	6.08892i	−0.784993	+	0.210338i
$839$	−15.7307	+	27.2463i	−0.543083	+	0.940647i	0.455642	+	0.890163i	$0.349410\pi$
$839$	−15.7307	+	27.2463i	−0.543083	+	0.940647i	−0.998725	+	0.0504839i	$0.983924\pi$
$840$	9.38663	+	4.10989i	0.323869	+	0.141805i
$841$	9.43270	+	16.3379i	0.325265	+	0.563376i
$842$	6.45074	+	6.45074i	0.222307	+	0.222307i
$843$	−20.7532	−	4.84766i	−0.714779	−	0.166962i
$844$		−	10.0600i		−	0.346279i
$845$	−1.46824	−	3.98554i	−0.0505092	−	0.137107i
$846$	18.8501	−	1.22046i	0.648081	−	0.0419604i
$847$	−16.6976	−	17.1237i	−0.573738	−	0.588376i
$848$	−0.0405318	−	0.151267i	−0.00139187	−	0.00519452i
$849$	−39.2744	+	24.4008i	−1.34789	+	0.837432i
$850$	−4.49276	+	12.6499i	−0.154100	+	0.433888i
$851$	−4.66519	−	2.69345i	−0.159921	−	0.0923302i
$852$	1.63606	−	7.00411i	0.0560506	−	0.239957i
$853$	−16.5647	+	4.43850i	−0.567165	+	0.151971i	−0.530996	−	0.847374i	$-0.678182\pi$
$853$	−16.5647	+	4.43850i	−0.567165	+	0.151971i	−0.0361687	+	0.999346i	$0.511515\pi$
$854$	−3.58803	−	2.13225i	−0.122780	−	0.0729642i
$855$	−5.29219	−	3.85518i	−0.180989	−	0.131844i
$856$	8.14136	−	14.1012i	0.278266	−	0.481971i
$857$	17.3811	+	17.3811i	0.593728	+	0.593728i	0.938636	−	0.344909i	$-0.112090\pi$
$857$	17.3811	+	17.3811i	0.593728	+	0.593728i	−0.344909	+	0.938636i	$0.612090\pi$
$858$	−1.83776	+	7.86759i	−0.0627401	+	0.268595i
$859$		−	26.4716i		−	0.903201i	−0.892220	−	0.451600i	$-0.850853\pi$
$859$		−	26.4716i		−	0.903201i	0.892220	−	0.451600i	$-0.149147\pi$
$860$	−4.74178	−	6.71607i	−0.161693	−	0.229016i
$861$	−6.90208	+	0.136208i	−0.235222	+	0.00464194i
$862$	7.34827	+	27.4241i	0.250283	+	0.934069i
$863$	−5.10131	−	19.0383i	−0.173651	−	0.648073i	−0.996778	−	0.0802153i	$-0.974439\pi$
$863$	−5.10131	−	19.0383i	−0.173651	−	0.648073i	0.823127	−	0.567857i	$-0.192227\pi$
$864$	−2.15013	+	4.73043i	−0.0731488	+	0.160932i
$865$	33.4875	+	47.4304i	1.13861	+	1.61268i
$866$	−11.0418	+	6.37500i	−0.375216	+	0.216631i
$867$	−16.5153	−	3.85776i	−0.560890	−	0.131016i
$868$	−15.9201	−	4.48146i	−0.540365	−	0.152111i
$869$	2.71245	+	4.69810i	0.0920135	+	0.159372i
$870$	−4.63385	−	11.4257i	−0.157102	−	0.387367i
$871$	18.0598			0.611934
$872$	5.32221	−	19.8628i	0.180233	−	0.672638i
$873$	28.7547	+	25.2577i	0.973200	+	0.854842i
$874$			0.867818i			0.0293544i
$875$	−28.5793	+	7.63037i	−0.966157	+	0.257954i
$876$	−7.86519	+	14.7007i	−0.265740	+	0.496690i
$877$	38.6210	−	38.6210i	1.30414	−	1.30414i	0.378564	−	0.925575i	$-0.376418\pi$
$877$	38.6210	−	38.6210i	1.30414	−	1.30414i	0.925575	−	0.378564i	$-0.123582\pi$
$878$	−8.93585	−	33.3491i	−0.301570	−	1.12548i
$879$	−14.2299	+	0.460181i	−0.479963	+	0.0155215i
$880$	−3.08516	−	0.531599i	−0.104001	−	0.0179202i
$881$			38.5826i			1.29988i	0.759985	+	0.649940i	$0.225206\pi$
$881$			38.5826i			1.29988i	−0.759985	+	0.649940i	$0.774794\pi$
$882$	20.0542	−	6.23125i	0.675260	−	0.209817i
$883$	23.3647	+	23.3647i	0.786284	+	0.786284i	0.980883	−	0.194599i	$-0.0623404\pi$
$883$	23.3647	+	23.3647i	0.786284	+	0.786284i	−0.194599	+	0.980883i	$0.562340\pi$
$884$	4.47254	+	7.74667i	0.150428	+	0.260549i
$885$	38.9536	−	29.4344i	1.30941	−	0.989428i
$886$	−1.25165	+	2.16792i	−0.0420500	+	0.0728327i
$887$	2.28647	+	2.28647i	0.0767720	+	0.0767720i	0.744450	−	0.667678i	$-0.232712\pi$
$887$	2.28647	+	2.28647i	0.0767720	+	0.0767720i	−0.667678	+	0.744450i	$0.732712\pi$
$888$	10.2189	+	2.38699i	0.342923	+	0.0801020i
$889$	−30.2484	−	0.381027i	−1.01450	−	0.0127792i
$890$	−2.82098	−	30.8574i	−0.0945594	−	1.03434i
$891$	−11.6337	−	4.84050i	−0.389743	−	0.162163i
$892$	21.1382	+	5.66397i	0.707760	+	0.189644i
$893$	−4.34565	+	4.34565i	−0.145422	+	0.145422i
$894$	0.441113	+	13.6403i	0.0147530	+	0.456200i
$895$	1.06316	−	6.17012i	0.0355377	−	0.206244i
$896$	1.29391	+	2.30777i	0.0432265	+	0.0770971i
$897$	3.74346	+	3.50892i	0.124990	+	0.117159i
$898$	−7.97050	+	29.7463i	−0.265979	+	0.992647i
$899$	9.95017	+	17.2342i	0.331857	+	0.574793i
$900$	−3.66727	−	14.5448i	−0.122242	−	0.484827i
$901$	0.210224	−	0.364119i	0.00700358	−	0.0121306i
$902$	2.03725	−	0.545879i	0.0678330	−	0.0181758i
$903$	−16.3575	−	4.03881i	−0.544342	−	0.134403i
$904$	−14.5629	+	8.40791i	−0.484355	+	0.279643i
$905$	−4.66176	−	3.88080i	−0.154962	−	0.129002i
$906$	−0.653840	−	20.2184i	−0.0217224	−	0.671710i
$907$	−31.8893	+	31.8893i	−1.05887	+	1.05887i	−0.0607118	+	0.998155i	$0.519337\pi$
$907$	−31.8893	+	31.8893i	−1.05887	+	1.05887i	−0.998155	+	0.0607118i	$0.980663\pi$
$908$	1.17875	+	4.39917i	0.0391184	+	0.145992i
$909$	−25.2422	−	37.8427i	−0.837232	−	1.25516i
$910$	−8.48520	+	17.7910i	−0.281282	+	0.589766i
$911$	23.2044	+	13.3971i	0.768797	+	0.443865i	0.832445	−	0.554107i	$-0.186940\pi$
$911$	23.2044	+	13.3971i	0.768797	+	0.443865i	−0.0636484	+	0.997972i	$0.520274\pi$
$912$	−0.490100	−	1.61796i	−0.0162288	−	0.0535758i
$913$	−21.9852	+	5.89091i	−0.727603	+	0.194961i
$914$	−12.9655	+	22.4570i	−0.428862	+	0.742811i
$915$	0.752607	+	6.06326i	0.0248804	+	0.200445i
$916$	6.21035	−	10.7566i	0.205196	−	0.355409i
$917$	37.6139	−	36.6780i	1.24212	−	1.21122i
$918$	−13.0624	+	4.89856i	−0.431122	+	0.161677i
$919$	−13.6927	−	7.90548i	−0.451680	−	0.260778i	0.256859	−	0.966449i	$-0.417312\pi$
$919$	−13.6927	−	7.90548i	−0.451680	−	0.260778i	−0.708539	+	0.705671i	$0.750646\pi$
$920$	−1.27200	+	1.52797i	−0.0419365	+	0.0503757i
$921$	−19.4465	+	36.3472i	−0.640785	+	1.19768i
$922$	−7.31540	+	7.31540i	−0.240920	+	0.240920i
$923$	13.3642	+	3.58094i	0.439889	+	0.117868i
$924$	−5.49193	+	3.31694i	−0.180671	+	0.109119i
$925$	−27.3545	+	13.0163i	−0.899409	+	0.427974i
$926$	−1.97564	−	1.14063i	−0.0649235	−	0.0374836i
$927$	−38.1714	−	7.62431i	−1.25371	−	0.250415i
$928$	0.823948	−	3.07501i	0.0270474	−	0.100942i
$929$	−4.74623	−	8.22070i	−0.155719	−	0.269713i	0.777602	−	0.628757i	$-0.216436\pi$
$929$	−4.74623	−	8.22070i	−0.155719	−	0.269713i	−0.933320	+	0.359044i	$0.883103\pi$
$930$	9.09904	+	22.4355i	0.298369	+	0.735690i
$931$	−3.56411	+	5.82901i	−0.116809	+	0.191038i
$932$	−0.782196	+	2.91920i	−0.0256217	+	0.0956215i
$933$	8.71499	+	2.03570i	0.285316	+	0.0666458i
$934$			5.07167i			0.165950i
$935$	−4.84779	−	6.86621i	−0.158540	−	0.224549i
$936$	−8.96093	−	4.42790i	−0.292897	−	0.144730i
$937$	9.11713	−	9.11713i	0.297844	−	0.297844i	−0.542325	−	0.840169i	$-0.682456\pi$
$937$	9.11713	−	9.11713i	0.297844	−	0.297844i	0.840169	+	0.542325i	$0.182456\pi$
$938$	10.0124	+	10.2678i	0.326915	+	0.335256i
$939$	1.81823	+	56.2242i	0.0593357	+	1.83481i
$940$	−14.0210	+	1.28180i	−0.457315	+	0.0418077i
$941$	−38.1958	−	22.0523i	−1.24515	−	0.718886i	−0.275010	−	0.961441i	$-0.588681\pi$
$941$	−38.1958	−	22.0523i	−1.24515	−	0.718886i	−0.970138	+	0.242555i	$0.922014\pi$
$942$	12.4618	−	3.77485i	0.406028	−	0.122991i
$943$	0.346666	−	1.29377i	0.0112890	−	0.0421311i
$944$	12.6063			0.410299
$945$	−25.1994	−	17.6065i	−0.819737	−	0.572740i
$946$	5.14757			0.167362
$947$	−3.59896	+	13.4315i	−0.116950	+	0.436465i	−0.999425	−	0.0338945i	$-0.989209\pi$
$947$	−3.59896	+	13.4315i	−0.116950	+	0.436465i	0.882475	+	0.470359i	$0.155876\pi$
$948$	−6.42308	+	1.94564i	−0.208612	+	0.0631913i
$949$	−27.7742	−	16.0354i	−0.901588	−	0.520532i
$950$	4.01935	+	2.76791i	0.130405	+	0.0898028i
$951$	0.237189	+	7.33446i	0.00769137	+	0.237836i
$952$	−1.92475	+	6.83759i	−0.0623816	+	0.221608i
$953$	−38.6288	+	38.6288i	−1.25131	+	1.25131i	−0.296177	+	0.955133i	$0.595712\pi$
$953$	−38.6288	+	38.6288i	−1.25131	+	1.25131i	−0.955133	+	0.296177i	$0.904288\pi$
$954$	0.0303545	+	0.468827i	0.000982762	+	0.0151788i
$955$	−18.3515	−	3.16212i	−0.593842	−	0.102324i
$956$			6.34428i			0.205189i
$957$	7.51750	+	1.75598i	0.243006	+	0.0567629i
$958$	−4.20340	+	15.6873i	−0.135806	+	0.506834i
$959$	−0.295384	+	23.4495i	−0.00953844	+	0.757223i
$960$	1.50858	−	3.56710i	0.0486893	−	0.115128i
$961$	−4.03817	−	6.99432i	−0.130264	−	0.225623i
$962$	−5.22452	+	19.4982i	−0.168445	+	0.628646i
$963$	−32.2370	+	36.7004i	−1.03882	+	1.18265i
$964$	−5.08212	−	2.93416i	−0.163684	−	0.0945030i
$965$	17.1889	+	7.93385i	0.553331	+	0.255400i
$966$	0.0803909	+	4.07366i	0.00258653	+	0.131068i
$967$	−37.3334	−	10.0035i	−1.20056	−	0.321690i	−0.397509	−	0.917598i	$-0.630125\pi$
$967$	−37.3334	−	10.0035i	−1.20056	−	0.321690i	−0.803052	+	0.595909i	$0.796792\pi$
$968$	−6.39213	+	6.39213i	−0.205451	+	0.205451i
$969$	2.14117	−	4.00203i	0.0687844	−	0.128564i
$970$	−21.9240	−	18.2512i	−0.703938	−	0.586011i
$971$	45.4479	+	26.2393i	1.45849	+	0.842060i	0.998937	−	0.0460897i	$-0.0146760\pi$
$971$	45.4479	+	26.2393i	1.45849	+	0.842060i	0.459554	+	0.888150i	$0.348009\pi$
$972$	9.10508	−	12.6530i	0.292046	−	0.405844i
$973$	33.6471	+	9.47151i	1.07868	+	0.303643i
$974$	10.7778	−	18.6677i	0.345343	−	0.598151i
$975$	28.1915	−	6.14630i	0.902851	−	0.196839i
$976$	−0.788770	+	1.36619i	−0.0252479	+	0.0437307i
$977$	53.6221	−	14.3680i	1.71552	−	0.459673i	0.738756	−	0.673972i	$-0.235413\pi$
$977$	53.6221	−	14.3680i	1.71552	−	0.459673i	0.976768	+	0.214299i	$0.0687467\pi$
$978$	−5.63907	−	18.6161i	−0.180317	−	0.595278i
$979$	16.8019	+	9.70056i	0.536990	+	0.310031i
$980$	−14.8192	+	5.03910i	−0.473381	+	0.160968i
$981$	−27.3289	+	55.3067i	−0.872544	+	1.76581i
$982$	−2.26782	−	8.46361i	−0.0723689	−	0.270084i
$983$	−7.12361	+	7.12361i	−0.227208	+	0.227208i	−0.811525	−	0.584317i	$-0.801362\pi$
$983$	−7.12361	+	7.12361i	−0.227208	+	0.227208i	0.584317	+	0.811525i	$0.301362\pi$
$984$	0.0843362	+	2.60788i	0.00268854	+	0.0831363i
$985$	0.663759	+	7.26055i	0.0211491	+	0.231340i
$986$	7.40197	−	4.27353i	0.235727	−	0.136097i
$987$	−19.9966	+	20.8017i	−0.636498	+	0.662125i
$988$	3.14112	−	0.841659i	0.0999322	−	0.0267768i
$989$	1.63451	−	2.83105i	0.0519743	−	0.0900221i
$990$	8.76382	+	3.37677i	0.278533	+	0.107321i
$991$	14.8773	+	25.7683i	0.472594	+	0.818556i	0.999508	−	0.0313623i	$-0.00998456\pi$
$991$	14.8773	+	25.7683i	0.472594	+	0.818556i	−0.526915	+	0.849918i	$0.676651\pi$
$992$	−1.61791	+	6.03811i	−0.0513686	+	0.191710i
$993$	−30.0798	−	28.1952i	−0.954553	−	0.894749i
$994$	5.37320	+	9.58343i	0.170428	+	0.303968i
$995$	25.1909	+	4.34060i	0.798604	+	0.137606i
$996$	−0.910123	−	28.1432i	−0.0288383	−	0.891753i
$997$	−28.8474	+	28.8474i	−0.913607	+	0.913607i	−0.996554	−	0.0829470i	$-0.973567\pi$
$997$	−28.8474	+	28.8474i	−0.913607	+	0.913607i	0.0829470	+	0.996554i	$0.473567\pi$
$998$	17.5784	+	4.71013i	0.556436	+	0.149096i
$999$	−28.6602	−	13.0269i	−0.906768	−	0.412154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.443.26	yes	192
5.2	odd	4	inner	630.2.bt.a.317.38	✓	192
7.4	even	3		630.2.cd.a.263.41	yes	192
9.5	odd	6		630.2.cd.a.23.18	yes	192
35.32	odd	12		630.2.cd.a.137.18	yes	192
45.32	even	12		630.2.cd.a.527.41	yes	192
63.32	odd	6	inner	630.2.bt.a.473.38	yes	192
315.32	even	12	inner	630.2.bt.a.347.26	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.38	✓	192	5.2	odd	4	inner
630.2.bt.a.347.26	yes	192	315.32	even	12	inner
630.2.bt.a.443.26	yes	192	1.1	even	1	trivial
630.2.bt.a.473.38	yes	192	63.32	odd	6	inner
630.2.cd.a.23.18	yes	192	9.5	odd	6
630.2.cd.a.137.18	yes	192	35.32	odd	12
630.2.cd.a.263.41	yes	192	7.4	even	3
630.2.cd.a.527.41	yes	192	45.32	even	12

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.65767 + 0.502129i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.71852 - 1.43063i) q^{5} +(0.0559834 + 1.73115i) q^{6} +(-1.84712 - 1.89424i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.49573 - 1.66473i) q^{9} +O(q^{10})\)	\(q+(0.258819 - 0.965926i) q^{2} +(-1.65767 + 0.502129i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.71852 - 1.43063i) q^{5} +(0.0559834 + 1.73115i) q^{6} +(-1.84712 - 1.89424i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.49573 - 1.66473i) q^{9} +(-1.82666 + 1.28969i) q^{10} -1.40006i q^{11} +(1.68665 + 0.393978i) q^{12} +(-0.862319 + 3.21822i) q^{13} +(-2.30777 + 1.29391i) q^{14} +(3.56710 + 1.50858i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.694879 + 2.59332i) q^{17} +(-0.962061 - 2.84156i) q^{18} +(0.845277 + 0.488021i) q^{19} +(0.772969 + 2.09822i) q^{20} +(4.01306 + 2.21254i) q^{21} +(-1.35235 - 0.362361i) q^{22} +(-0.628702 + 0.628702i) q^{23} +(0.817090 - 1.52721i) q^{24} +(0.906622 + 4.91712i) q^{25} +(2.88537 + 1.66587i) q^{26} +(-3.30119 + 4.01275i) q^{27} +(0.652527 + 2.56402i) q^{28} +(1.59174 - 2.75698i) q^{29} +(2.38041 - 3.05510i) q^{30} +(-3.12555 + 5.41362i) q^{31} +(0.965926 - 0.258819i) q^{32} +(0.703009 + 2.32083i) q^{33} +(2.32511 + 1.34240i) q^{34} +(0.464351 + 5.89783i) q^{35} +(-2.99373 + 0.193831i) q^{36} +(1.56810 + 5.85224i) q^{37} +(0.690166 - 0.690166i) q^{38} +(-0.186522 - 5.76773i) q^{39} +(2.22678 - 0.203572i) q^{40} +(-1.30462 + 0.753225i) q^{41} +(3.17581 - 3.30367i) q^{42} +(-3.55140 + 0.951596i) q^{43} +(-0.700028 + 1.21248i) q^{44} +(-6.67057 - 0.709589i) q^{45} +(0.444560 + 0.770000i) q^{46} +(-1.62966 + 6.08198i) q^{47} +(-1.26369 - 1.18452i) q^{48} +(-0.176325 + 6.99778i) q^{49} +(4.98422 + 0.396914i) q^{50} +(-0.150305 - 4.64779i) q^{51} +(2.35590 - 2.35590i) q^{52} +(-0.151267 - 0.0405318i) q^{53} +(3.02161 + 4.22728i) q^{54} +(-2.00296 + 2.40603i) q^{55} +(2.64554 + 0.0333249i) q^{56} +(-1.64624 - 0.384539i) q^{57} +(-2.25107 - 2.25107i) q^{58} +(6.30314 - 10.9174i) q^{59} +(-2.33490 - 3.09002i) q^{60} +(0.788770 + 1.36619i) q^{61} +(4.42020 + 4.42020i) q^{62} +(-7.76331 - 1.65258i) q^{63} -1.00000i q^{64} +(6.08597 - 4.29691i) q^{65} +(2.42370 - 0.0783800i) q^{66} +(-1.40294 - 5.23584i) q^{67} +(1.89845 - 1.89845i) q^{68} +(0.726491 - 1.35787i) q^{69} +(5.81705 + 1.07794i) q^{70} -4.15268i q^{71} +(-0.587608 + 2.94189i) q^{72} +(-2.49135 + 9.29786i) q^{73} +6.05868 q^{74} +(-3.97191 - 7.69571i) q^{75} +(-0.488021 - 0.845277i) q^{76} +(-2.65205 + 2.58607i) q^{77} +(-5.61948 - 1.31263i) q^{78} +(-3.35565 + 1.93738i) q^{79} +(0.379698 - 2.20359i) q^{80} +(3.45736 - 8.30943i) q^{81} +(0.389898 + 1.45512i) q^{82} +(-4.20762 - 15.7031i) q^{83} +(-2.36914 - 3.92265i) q^{84} +(4.90424 - 3.46257i) q^{85} +3.67669i q^{86} +(-1.25422 + 5.36943i) q^{87} +(0.989989 + 0.989989i) q^{88} +(-6.92869 + 12.0008i) q^{89} +(-2.41188 + 6.25962i) q^{90} +(7.68889 - 4.31098i) q^{91} +(0.858823 - 0.230121i) q^{92} +(2.46280 - 10.5434i) q^{93} +(5.45296 + 3.14827i) q^{94} +(-0.754451 - 2.04795i) q^{95} +(-1.47122 + 0.914056i) q^{96} +(3.30188 + 12.3228i) q^{97} +(6.71370 + 1.98147i) q^{98} +(-2.33071 - 3.49417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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