LMFDB - Embedded newform 630.2.bt.a.317.19

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			317.19
Character	$\chi$	$=$	630.317
Dual form			630.2.bt.a.473.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.32691 + 1.11325i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59332 - 1.56887i) q^{5} +(-0.993564 - 1.41874i) q^{6} +(-2.14973 + 1.54229i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.521364 + 2.95435i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.32691 + 1.11325i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59332 - 1.56887i) q^{5} +(-0.993564 - 1.41874i) q^{6} +(-2.14973 + 1.54229i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.521364 + 2.95435i) q^{9} +(1.13297 + 1.92779i) q^{10} -1.06334i q^{11} +(0.592512 + 1.62755i) q^{12} +(-5.82989 - 1.56211i) q^{13} +(2.47565 - 0.933346i) q^{14} +(-0.367651 - 3.85549i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.39089 + 0.372689i) q^{17} +(0.261043 - 2.98862i) q^{18} +(-1.99067 - 1.14931i) q^{19} +(-0.595421 - 2.15534i) q^{20} +(-4.56944 - 0.346706i) q^{21} +(-0.275212 + 1.02711i) q^{22} +(-6.29233 - 6.29233i) q^{23} +(-0.151081 - 1.72545i) q^{24} +(0.0773246 + 4.99940i) q^{25} +(5.22693 + 3.01777i) q^{26} +(-2.59712 + 4.50055i) q^{27} +(-2.63287 + 0.260796i) q^{28} +(1.36331 - 2.36131i) q^{29} +(-0.642752 + 3.81928i) q^{30} +(-3.84082 + 6.65250i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.18376 - 1.41095i) q^{33} +(-1.24704 - 0.719980i) q^{34} +(5.84485 + 0.915280i) q^{35} +(-1.02566 + 2.81922i) q^{36} +(-2.54274 + 0.681326i) q^{37} +(1.62537 + 1.62537i) q^{38} +(-5.99670 - 8.56288i) q^{39} +(0.0172908 + 2.23600i) q^{40} +(-0.580119 + 0.334932i) q^{41} +(4.32401 + 1.51755i) q^{42} +(-0.513911 - 1.91794i) q^{43} +(0.531669 - 0.920878i) q^{44} +(3.80428 - 5.52517i) q^{45} +(4.44935 + 7.70650i) q^{46} +(1.50997 + 0.404596i) q^{47} +(-0.300646 + 1.70576i) q^{48} +(2.24269 - 6.63101i) q^{49} +(1.21925 - 4.84906i) q^{50} +(1.43069 + 2.04293i) q^{51} +(-4.26777 - 4.26777i) q^{52} +(1.78346 - 6.65595i) q^{53} +(3.67345 - 3.67502i) q^{54} +(-1.66823 + 1.69424i) q^{55} +(2.61065 + 0.429526i) q^{56} +(-1.36196 - 3.74114i) q^{57} +(-1.92800 + 1.92800i) q^{58} +(-4.05084 + 7.01626i) q^{59} +(1.60935 - 3.52278i) q^{60} +(-0.761761 - 1.31941i) q^{61} +(5.43175 - 5.43175i) q^{62} +(-5.67725 - 5.54696i) q^{63} +1.00000i q^{64} +(6.83812 + 11.6353i) q^{65} +(-1.50860 + 1.05649i) q^{66} +(-14.2804 + 3.82641i) q^{67} +(1.01821 + 1.01821i) q^{68} +(-1.34442 - 15.3542i) q^{69} +(-5.40880 - 2.39685i) q^{70} +1.27742i q^{71} +(1.72038 - 2.45770i) q^{72} +(9.82391 + 2.63231i) q^{73} +2.63244 q^{74} +(-5.46297 + 6.71982i) q^{75} +(-1.14931 - 1.99067i) q^{76} +(1.63998 + 2.28589i) q^{77} +(3.57613 + 9.82317i) q^{78} +(12.5375 - 7.23854i) q^{79} +(0.562018 - 2.16429i) q^{80} +(-8.45636 + 3.08058i) q^{81} +(0.647038 - 0.173373i) q^{82} +(-9.19959 + 2.46502i) q^{83} +(-3.78390 - 2.58498i) q^{84} +(-1.63144 - 2.77594i) q^{85} +1.98560i q^{86} +(4.43770 - 1.61555i) q^{87} +(-0.751894 + 0.751894i) q^{88} +(-3.87841 + 6.71760i) q^{89} +(-5.10467 + 4.35228i) q^{90} +(14.9419 - 5.63325i) q^{91} +(-2.30315 - 8.59548i) q^{92} +(-12.5023 + 4.55147i) q^{93} +(-1.35380 - 0.781619i) q^{94} +(1.36865 + 4.95431i) q^{95} +(0.731885 - 1.56982i) q^{96} +(0.457480 - 0.122581i) q^{97} +(-3.88250 + 5.82462i) q^{98} +(3.14147 - 0.554386i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.32691	+	1.11325i	0.766090	+	0.642733i
$3$	1.32691	+	1.11325i	0.766090	+	0.642733i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−1.59332	−	1.56887i	−0.712553	−	0.701618i
$5$	−1.59332	−	1.56887i	−0.712553	−	0.701618i
$6$	−0.993564	−	1.41874i	−0.405621	−	0.579199i
$7$	−2.14973	+	1.54229i	−0.812522	+	0.582931i
$7$	−2.14973	+	1.54229i	−0.812522	+	0.582931i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.521364	+	2.95435i	0.173788	+	0.984783i
$10$	1.13297	+	1.92779i	0.358278	+	0.609620i
$11$		−	1.06334i		−	0.320608i	−0.987068	−	0.160304i	$-0.948752\pi$
$11$		−	1.06334i		−	0.320608i	0.987068	−	0.160304i	$-0.0512475\pi$
$12$	0.592512	+	1.62755i	0.171043	+	0.469834i
$13$	−5.82989	−	1.56211i	−1.61692	−	0.433252i	−0.666825	−	0.745214i	$-0.732347\pi$
$13$	−5.82989	−	1.56211i	−1.61692	−	0.433252i	−0.950095	+	0.311962i	$0.899014\pi$
$14$	2.47565	−	0.933346i	0.661647	−	0.249447i
$15$	−0.367651	−	3.85549i	−0.0949270	−	0.995484i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.39089	+	0.372689i	0.337342	+	0.0903904i	0.423513	−	0.905890i	$-0.360797\pi$
$17$	1.39089	+	0.372689i	0.337342	+	0.0903904i	−0.0861717	+	0.996280i	$0.527463\pi$
$18$	0.261043	−	2.98862i	0.0615285	−	0.704425i
$19$	−1.99067	−	1.14931i	−0.456691	−	0.263671i	0.253961	−	0.967214i	$-0.418267\pi$
$19$	−1.99067	−	1.14931i	−0.456691	−	0.263671i	−0.710652	+	0.703544i	$0.751600\pi$
$20$	−0.595421	−	2.15534i	−0.133140	−	0.481948i
$21$	−4.56944	−	0.346706i	−0.997134	−	0.0756575i
$22$	−0.275212	+	1.02711i	−0.0586754	+	0.218980i
$23$	−6.29233	−	6.29233i	−1.31204	−	1.31204i	−0.919909	−	0.392133i	$-0.871737\pi$
$23$	−6.29233	−	6.29233i	−1.31204	−	1.31204i	−0.392133	−	0.919909i	$-0.628263\pi$
$24$	−0.151081	−	1.72545i	−0.0308392	−	0.352206i
$25$	0.0773246	+	4.99940i	0.0154649	+	0.999880i
$26$	5.22693	+	3.01777i	1.02509	+	0.591834i
$27$	−2.59712	+	4.50055i	−0.499816	+	0.866132i
$28$	−2.63287	+	0.260796i	−0.497565	+	0.0492859i
$29$	1.36331	−	2.36131i	0.253159	−	0.438485i	−0.711235	−	0.702955i	$-0.751864\pi$
$29$	1.36331	−	2.36131i	0.253159	−	0.438485i	0.964394	+	0.264470i	$0.0851970\pi$
$30$	−0.642752	+	3.81928i	−0.117350	+	0.697301i
$31$	−3.84082	+	6.65250i	−0.689833	+	1.19482i	0.282059	+	0.959397i	$0.408983\pi$
$31$	−3.84082	+	6.65250i	−0.689833	+	1.19482i	−0.971892	+	0.235428i	$0.924351\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	1.18376	−	1.41095i	0.206066	−	0.245615i
$34$	−1.24704	−	0.719980i	−0.213866	−	0.123476i
$35$	5.84485	+	0.915280i	0.987960	+	0.154711i
$36$	−1.02566	+	2.81922i	−0.170943	+	0.469871i
$37$	−2.54274	+	0.681326i	−0.418025	+	0.112009i	−0.461699	−	0.887036i	$-0.652760\pi$
$37$	−2.54274	+	0.681326i	−0.418025	+	0.112009i	0.0436748	+	0.999046i	$0.486093\pi$
$38$	1.62537	+	1.62537i	0.263671	+	0.263671i
$39$	−5.99670	−	8.56288i	−0.960241	−	1.37116i
$40$	0.0172908	+	2.23600i	0.00273392	+	0.353543i
$41$	−0.580119	+	0.334932i	−0.0905993	+	0.0523075i	−0.544615	−	0.838686i	$-0.683324\pi$
$41$	−0.580119	+	0.334932i	−0.0905993	+	0.0523075i	0.454016	+	0.890994i	$0.349991\pi$
$42$	4.32401	+	1.51755i	0.667209	+	0.234163i
$43$	−0.513911	−	1.91794i	−0.0783707	−	0.292483i	0.915606	−	0.402077i	$-0.131712\pi$
$43$	−0.513911	−	1.91794i	−0.0783707	−	0.292483i	−0.993976	+	0.109594i	$0.965045\pi$
$44$	0.531669	−	0.920878i	0.0801521	−	0.138828i
$45$	3.80428	−	5.52517i	0.567108	−	0.823643i
$46$	4.44935	+	7.70650i	0.656021	+	1.13626i
$47$	1.50997	+	0.404596i	0.220252	+	0.0590164i	0.367257	−	0.930119i	$-0.380297\pi$
$47$	1.50997	+	0.404596i	0.220252	+	0.0590164i	−0.147005	+	0.989136i	$0.546963\pi$
$48$	−0.300646	+	1.70576i	−0.0433946	+	0.246205i
$49$	2.24269	−	6.63101i	0.320384	−	0.947288i
$50$	1.21925	−	4.84906i	0.172428	−	0.685761i
$51$	1.43069	+	2.04293i	0.200337	+	0.286068i
$52$	−4.26777	−	4.26777i	−0.591834	−	0.591834i
$53$	1.78346	−	6.65595i	0.244976	−	0.914264i	−0.728419	−	0.685132i	$-0.759744\pi$
$53$	1.78346	−	6.65595i	0.244976	−	0.914264i	0.973395	−	0.229132i	$-0.0735888\pi$
$54$	3.67345	−	3.67502i	0.499894	−	0.500106i
$55$	−1.66823	+	1.69424i	−0.224945	+	0.228451i
$56$	2.61065	+	0.429526i	0.348863	+	0.0573978i
$57$	−1.36196	−	3.74114i	−0.180396	−	0.495526i
$58$	−1.92800	+	1.92800i	−0.253159	+	0.253159i
$59$	−4.05084	+	7.01626i	−0.527375	+	0.913440i	0.472116	+	0.881536i	$0.343490\pi$
$59$	−4.05084	+	7.01626i	−0.527375	+	0.913440i	−0.999491	+	0.0319035i	$0.989843\pi$
$60$	1.60935	−	3.52278i	0.207766	−	0.454789i
$61$	−0.761761	−	1.31941i	−0.0975335	−	0.168933i	0.813130	−	0.582083i	$-0.197762\pi$
$61$	−0.761761	−	1.31941i	−0.0975335	−	0.168933i	−0.910663	+	0.413150i	$0.864429\pi$
$62$	5.43175	−	5.43175i	0.689833	−	0.689833i
$63$	−5.67725	−	5.54696i	−0.715267	−	0.698852i
$64$			1.00000i			0.125000i
$65$	6.83812	+	11.6353i	0.848164	+	1.44318i
$66$	−1.50860	+	1.05649i	−0.185696	+	0.130046i
$67$	−14.2804	+	3.82641i	−1.74462	+	0.467470i	−0.983465	−	0.181097i	$-0.942035\pi$
$67$	−14.2804	+	3.82641i	−1.74462	+	0.467470i	−0.761158	+	0.648567i	$0.775369\pi$
$68$	1.01821	+	1.01821i	0.123476	+	0.123476i
$69$	−1.34442	−	15.3542i	−0.161849	−	1.84843i
$70$	−5.40880	−	2.39685i	−0.646475	−	0.286479i
$71$			1.27742i			0.151602i	0.997123	+	0.0758011i	$0.0241514\pi$
$71$			1.27742i			0.151602i	−0.997123	+	0.0758011i	$0.975849\pi$
$72$	1.72038	−	2.45770i	0.202749	−	0.289643i
$73$	9.82391	+	2.63231i	1.14980	+	0.308089i	0.782886	−	0.622165i	$-0.213747\pi$
$73$	9.82391	+	2.63231i	1.14980	+	0.308089i	0.366916	+	0.930254i	$0.380414\pi$
$74$	2.63244			0.306015
$75$	−5.46297	+	6.71982i	−0.630809	+	0.775938i
$76$	−1.14931	−	1.99067i	−0.131835	−	0.228345i
$77$	1.63998	+	2.28589i	0.186893	+	0.260501i
$78$	3.57613	+	9.82317i	0.404917	+	1.11225i
$79$	12.5375	−	7.23854i	1.41058	−	0.814399i	0.415138	−	0.909758i	$-0.363733\pi$
$79$	12.5375	−	7.23854i	1.41058	−	0.814399i	0.995443	+	0.0953589i	$0.0303999\pi$
$80$	0.562018	−	2.16429i	0.0628355	−	0.241975i
$81$	−8.45636	+	3.08058i	−0.939596	+	0.342287i
$82$	0.647038	−	0.173373i	0.0714534	−	0.0191459i
$83$	−9.19959	+	2.46502i	−1.00979	+	0.270571i	−0.725540	−	0.688180i	$-0.758410\pi$
$83$	−9.19959	+	2.46502i	−1.00979	+	0.270571i	−0.284246	+	0.958751i	$0.591743\pi$
$84$	−3.78390	−	2.58498i	−0.412857	−	0.282044i
$85$	−1.63144	−	2.77594i	−0.176954	−	0.301093i
$86$			1.98560i			0.214113i
$87$	4.43770	−	1.61555i	0.475772	−	0.173205i
$88$	−0.751894	+	0.751894i	−0.0801521	+	0.0801521i
$89$	−3.87841	+	6.71760i	−0.411111	+	0.712064i	−0.995011	−	0.0997606i	$-0.968192\pi$
$89$	−3.87841	+	6.71760i	−0.411111	+	0.712064i	0.583901	+	0.811825i	$0.301526\pi$
$90$	−5.10467	+	4.35228i	−0.538079	+	0.458771i
$91$	14.9419	−	5.63325i	1.56634	−	0.590525i
$92$	−2.30315	−	8.59548i	−0.240120	−	0.896141i
$93$	−12.5023	+	4.55147i	−1.29643	+	0.471965i
$94$	−1.35380	−	0.781619i	−0.139634	−	0.0806179i
$95$	1.36865	+	4.95431i	0.140421	+	0.508302i
$96$	0.731885	−	1.56982i	0.0746977	−	0.160219i
$97$	0.457480	−	0.122581i	0.0464501	−	0.0124463i	−0.235519	−	0.971870i	$-0.575679\pi$
$97$	0.457480	−	0.122581i	0.0464501	−	0.0124463i	0.281969	+	0.959423i	$0.409012\pi$
$98$	−3.88250	+	5.82462i	−0.392192	+	0.588375i
$99$	3.14147	−	0.554386i	0.315730	−	0.0557179i
$100$	−2.43274	+	4.36827i	−0.243274	+	0.436827i
$101$		−	5.99193i		−	0.596219i	−0.954532	−	0.298110i	$-0.903644\pi$
$101$		−	5.99193i		−	0.596219i	0.954532	−	0.298110i	$-0.0963561\pi$
$102$	−0.853193	−	2.34361i	−0.0844787	−	0.232052i
$103$	−12.7641	+	12.7641i	−1.25768	+	1.25768i	−0.305487	+	0.952196i	$0.598819\pi$
$103$	−12.7641	+	12.7641i	−1.25768	+	1.25768i	−0.952196	+	0.305487i	$0.901181\pi$
$104$	3.01777	+	5.22693i	0.295917	+	0.512543i
$105$	6.73664	+	7.72125i	0.657429	+	0.753517i
$106$	−3.44537	+	5.96756i	−0.334644	+	0.579620i
$107$	0.638382	+	2.38247i	0.0617147	+	0.230323i	0.989894	−	0.141812i	$-0.0452928\pi$
$107$	0.638382	+	2.38247i	0.0617147	+	0.230323i	−0.928179	+	0.372134i	$0.878626\pi$
$108$	−4.49945	+	2.59903i	−0.432959	+	0.250092i
$109$	−14.2932	+	8.25216i	−1.36904	+	0.790413i	−0.990805	−	0.135298i	$-0.956801\pi$
$109$	−14.2932	+	8.25216i	−1.36904	+	0.790413i	−0.378231	+	0.925711i	$0.623468\pi$
$110$	2.04989	−	1.20474i	0.195449	−	0.114867i
$111$	−4.13247	−	1.92665i	−0.392237	−	0.182869i
$112$	−2.41053	−	1.09058i	−0.227773	−	0.103050i
$113$	1.97602	−	7.37460i	0.185888	−	0.693744i	−0.808550	−	0.588427i	$-0.799747\pi$
$113$	1.97602	−	7.37460i	0.185888	−	0.693744i	0.994439	−	0.105317i	$-0.0335859\pi$
$114$	0.347278	+	3.96616i	0.0325256	+	0.371465i
$115$	0.153866	+	19.8975i	0.0143481	+	1.85545i
$116$	2.36131	−	1.36331i	0.219242	−	0.126580i
$117$	1.57554	−	18.0380i	0.145659	−	1.66761i
$118$	5.72876	−	5.72876i	0.527375	−	0.527375i
$119$	−3.56484	+	1.34398i	−0.326789	+	0.123203i
$120$	−2.46628	+	2.98621i	−0.225139	+	0.272603i
$121$	9.86931			0.897210
$122$	0.394317	+	1.47161i	0.0356998	+	0.133233i
$123$	−1.14262	−	0.201392i	−0.103027	−	0.0181589i
$124$	−6.65250	+	3.84082i	−0.597412	+	0.344916i
$125$	7.72018	−	8.08695i	0.690514	−	0.723319i
$126$	4.04815	+	6.82734i	0.360638	+	0.608227i
$127$	11.9378	+	11.9378i	1.05931	+	1.05931i	0.998126	+	0.0611858i	$0.0194882\pi$
$127$	11.9378	+	11.9378i	1.05931	+	1.05931i	0.0611858	+	0.998126i	$0.480512\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	1.45323	−	3.11704i	0.127950	−	0.274440i
$130$	−3.59369	−	13.0086i	−0.315188	−	1.14093i
$131$		−	5.91576i		−	0.516862i	−0.966030	−	0.258431i	$-0.916794\pi$
$131$		−	5.91576i		−	0.516862i	0.966030	−	0.258431i	$-0.0832055\pi$
$132$	1.73064	−	0.630040i	0.150633	−	0.0548380i
$133$	6.05198	−	0.599474i	0.524773	−	0.0519810i
$134$	14.7841			1.27715
$135$	11.1988	−	3.09628i	0.963839	−	0.266486i
$136$	−0.719980	−	1.24704i	−0.0617378	−	0.106933i
$137$	3.00033	−	3.00033i	0.256336	−	0.256336i	−0.567226	−	0.823562i	$-0.691984\pi$
$137$	3.00033	−	3.00033i	0.256336	−	0.256336i	0.823562	+	0.567226i	$0.191984\pi$
$138$	−2.67536	+	15.1790i	−0.227742	+	1.29212i
$139$	16.5661	−	9.56443i	1.40512	−	0.811244i	0.410205	−	0.911993i	$-0.365457\pi$
$139$	16.5661	−	9.56443i	1.40512	−	0.811244i	0.994912	+	0.100749i	$0.0321239\pi$
$140$	4.60415	+	3.71508i	0.389122	+	0.313982i
$141$	1.55318	+	2.21783i	0.130801	+	0.186775i
$142$	0.330621	−	1.23390i	0.0277451	−	0.103546i
$143$	−1.66106	+	6.19914i	−0.138904	+	0.518398i
$144$	−2.29786	+	1.92869i	−0.191488	+	0.160724i
$145$	−5.87676	+	1.62348i	−0.488038	+	0.134823i
$146$	−8.80788	−	5.08523i	−0.728945	−	0.420857i
$147$	10.3578	−	6.30208i	0.854296	−	0.519786i
$148$	−2.54274	−	0.681326i	−0.209012	−	0.0560047i
$149$	15.7856			1.29320			0.646602	−	0.762828i	$-0.276189\pi$
$149$	15.7856			1.29320			0.646602	+	0.762828i	$0.276189\pi$
$150$	7.01604	−	5.07693i	0.572857	−	0.414530i
$151$	18.3040			1.48956			0.744780	−	0.667311i	$-0.232555\pi$
$151$	18.3040			1.48956			0.744780	+	0.667311i	$0.232555\pi$
$152$	0.594929	+	2.22030i	0.0482551	+	0.180090i
$153$	−0.375892	+	4.30350i	−0.0303891	+	0.347917i
$154$	−0.992462	−	2.63246i	−0.0799749	−	0.212129i
$155$	16.5565	−	4.57382i	1.32985	−	0.367378i
$156$	−0.911853	−	10.4140i	−0.0730067	−	0.833789i
$157$	−1.83476	+	0.491622i	−0.146430	+	0.0392357i	−0.331289	−	0.943529i	$-0.607484\pi$
$157$	−1.83476	+	0.491622i	−0.146430	+	0.0392357i	0.184860	+	0.982765i	$0.440817\pi$
$158$	−13.9838	+	3.74694i	−1.11249	+	0.298091i
$159$	9.77619	−	6.84639i	0.775302	−	0.542954i
$160$	−1.10303	+	1.94508i	−0.0872019	+	0.153772i
$161$	23.2314	+	3.82222i	1.83089	+	0.301233i
$162$	8.96553	−	0.786946i	0.704399	−	0.0618283i
$163$	−1.82884	−	6.82534i	−0.143246	−	0.534602i	−0.999827	−	0.0185894i	$-0.994082\pi$
$163$	−1.82884	−	6.82534i	−0.143246	−	0.534602i	0.856581	−	0.516013i	$-0.172584\pi$
$164$	−0.669863			−0.0523075
$165$	−4.09969	+	0.390937i	−0.319161	+	0.0304344i
$166$	9.52412			0.739215
$167$	−2.66520	−	0.714139i	−0.206240	−	0.0552617i	0.154220	−	0.988037i	$-0.450713\pi$
$167$	−2.66520	−	0.714139i	−0.206240	−	0.0552617i	−0.360460	+	0.932775i	$0.617380\pi$
$168$	2.98592	+	3.47624i	0.230369	+	0.268198i
$169$	20.2891	+	11.7139i	1.56070	+	0.901069i
$170$	0.857383	+	3.10360i	0.0657583	+	0.238035i
$171$	2.35761	−	6.48034i	0.180291	−	0.495564i
$172$	0.513911	−	1.91794i	0.0391853	−	0.146242i
$173$	−2.94795	+	11.0019i	−0.224129	+	0.836460i	0.758623	+	0.651530i	$0.225873\pi$
$173$	−2.94795	+	11.0019i	−0.224129	+	0.836460i	−0.982752	+	0.184930i	$0.940794\pi$
$174$	−4.70463	+	0.411938i	−0.356657	+	0.0312289i
$175$	−7.87675	−	10.6281i	−0.595426	−	0.803410i
$176$	0.920878	−	0.531669i	0.0694138	−	0.0400761i
$177$	−13.1859	+	4.80034i	−0.991115	+	0.360816i
$178$	5.48490	−	5.48490i	0.411111	−	0.411111i
$179$	−8.36582	−	14.4900i	−0.625291	−	1.08304i	−0.988485	−	0.151322i	$-0.951647\pi$
$179$	−8.36582	−	14.4900i	−0.625291	−	1.08304i	0.363194	−	0.931714i	$-0.381686\pi$
$180$	6.05718	−	2.88280i	0.451476	−	0.214871i
$181$	−16.8133			−1.24972			−0.624860	−	0.780737i	$-0.714844\pi$
$181$	−16.8133			−1.24972			−0.624860	+	0.780737i	$0.714844\pi$
$182$	−15.8908	+	1.57405i	−1.17790	+	0.116676i
$183$	0.458042	−	2.59876i	0.0338594	−	0.192106i
$184$			8.89870i			0.656021i
$185$	5.12031	+	2.90365i	0.376453	+	0.213481i
$186$	13.2543	−	1.16055i	0.971852	−	0.0850955i
$187$	0.396295	−	1.47899i	0.0289799	−	0.108155i
$188$	1.10538	+	1.10538i	0.0806179	+	0.0806179i
$189$	−1.35805	−	13.6805i	−0.0987835	−	0.995109i
$190$	−0.0397452	−	5.13973i	−0.00288342	−	0.372875i
$191$	−19.7116	+	11.3805i	−1.42628	+	0.823462i	−0.996825	−	0.0796268i	$-0.974627\pi$
$191$	−19.7116	+	11.3805i	−1.42628	+	0.823462i	−0.429454	+	0.903089i	$0.641294\pi$
$192$	−1.11325	+	1.32691i	−0.0803417	+	0.0957613i
$193$	0.398743	+	1.48813i	0.0287022	+	0.107118i	0.978791	−	0.204862i	$-0.0656745\pi$
$193$	0.398743	+	1.48813i	0.0287022	+	0.107118i	−0.950089	+	0.311980i	$0.899008\pi$
$194$	−0.473618			−0.0340038
$195$	−3.87936	+	23.0514i	−0.277807	+	1.65075i
$196$	5.25773	−	4.62128i	0.375552	−	0.330092i
$197$	−3.78826	+	3.78826i	−0.269902	+	0.269902i	−0.829061	−	0.559158i	$-0.811124\pi$
$197$	−3.78826	+	3.78826i	−0.269902	+	0.269902i	0.559158	+	0.829061i	$0.311124\pi$
$198$	−3.17791	−	0.277577i	−0.225845	−	0.0197266i
$199$	17.7428	−	10.2438i	1.25776	−	0.726165i	0.285118	−	0.958493i	$-0.407967\pi$
$199$	17.7428	−	10.2438i	1.25776	−	0.726165i	0.972638	+	0.232327i	$0.0746340\pi$
$200$	3.48043	−	3.58979i	0.246104	−	0.253836i
$201$	−23.2084	−	10.8203i	−1.63700	−	0.763203i
$202$	−1.55083	+	5.78776i	−0.109116	+	0.407225i
$203$	0.711090	+	7.17880i	0.0499087	+	0.503853i
$204$	0.217550	+	2.48458i	0.0152315	+	0.173955i
$205$	1.44978	+	0.376475i	0.101257	+	0.0262942i
$206$	15.6328	−	9.02558i	1.08919	−	0.628842i
$207$	15.3091	−	21.8703i	1.06406	−	1.52009i
$208$	−1.56211	−	5.82989i	−0.108313	−	0.404230i
$209$	−1.22211	+	2.11675i	−0.0845350	+	0.146419i
$210$	−4.50869	−	9.20173i	−0.311129	−	0.634979i
$211$	9.45709	+	16.3802i	0.651053	+	1.12766i	0.982868	+	0.184312i	$0.0590058\pi$
$211$	9.45709	+	16.3802i	0.651053	+	1.12766i	−0.331815	+	0.943345i	$0.607661\pi$
$212$	4.87249	−	4.87249i	0.334644	−	0.334644i
$213$	−1.42209	+	1.69502i	−0.0974398	+	0.116141i
$214$		−	2.46652i		−	0.168608i
$215$	−2.19017	+	3.86215i	−0.149368	+	0.263396i
$216$	5.01881	−	1.34593i	0.341487	−	0.0915790i
$217$	−2.00335	−	20.2248i	−0.135996	−	1.37295i
$218$	15.9419	−	4.27163i	1.07972	−	0.289311i
$219$	10.1050	+	14.4293i	0.682833	+	0.975040i
$220$	−2.29185	+	0.633134i	−0.154517	+	0.0426859i
$221$	−7.52658	−	4.34547i	−0.506292	−	0.292308i
$222$	3.49301	+	2.93056i	0.234435	+	0.196686i
$223$	1.91332	+	7.14063i	0.128126	+	0.478172i	0.999932	−	0.0116795i	$-0.00371778\pi$
$223$	1.91332	+	7.14063i	0.128126	+	0.478172i	−0.871806	+	0.489851i	$0.837051\pi$
$224$	2.04613	+	1.67731i	0.136713	+	0.112070i
$225$	−14.7297	+	2.83495i	−0.981978	+	0.188997i
$226$	−3.81738	+	6.61189i	−0.253928	+	0.439816i
$227$	−16.9754	+	16.9754i	−1.12670	+	1.12670i	−0.135989	+	0.990710i	$0.543421\pi$
$227$	−16.9754	+	16.9754i	−1.12670	+	1.12670i	−0.990710	+	0.135989i	$0.956579\pi$
$228$	0.691074	−	3.92090i	0.0457675	−	0.259668i
$229$		−	3.50598i		−	0.231682i	−0.993268	−	0.115841i	$-0.963044\pi$
$229$		−	3.50598i		−	0.231682i	0.993268	−	0.115841i	$-0.0369563\pi$
$230$	5.00123	−	19.2593i	0.329771	−	1.26992i
$231$	−0.368666	+	4.85886i	−0.0242564	+	0.319690i
$232$	−2.63370	+	0.705699i	−0.172911	+	0.0463314i
$233$	12.2425	−	3.28038i	0.802035	−	0.214905i	0.165558	−	0.986200i	$-0.447058\pi$
$233$	12.2425	−	3.28038i	0.802035	−	0.214905i	0.636477	+	0.771295i	$0.280391\pi$
$234$	−6.19042	+	17.0155i	−0.404680	+	1.11234i
$235$	−1.77111	−	3.01359i	−0.115534	−	0.196585i
$236$	−7.01626	+	4.05084i	−0.456720	+	0.263687i
$237$	24.6944	+	4.35248i	1.60407	+	0.282724i
$238$	3.79122	−	0.375536i	0.245748	−	0.0243424i
$239$	2.02058	+	3.49975i	0.130700	+	0.226380i	0.923947	−	0.382521i	$-0.124944\pi$
$239$	2.02058	+	3.49975i	0.130700	+	0.226380i	−0.793246	+	0.608901i	$0.791611\pi$
$240$	3.15513	−	2.24614i	0.203663	−	0.144988i
$241$	−15.8387			−1.02026			−0.510130	−	0.860097i	$-0.670403\pi$
$241$	−15.8387			−1.02026			−0.510130	+	0.860097i	$0.670403\pi$
$242$	−9.53302	−	2.55437i	−0.612806	−	0.164201i
$243$	−14.6502	−	5.32637i	−0.939814	−	0.341687i
$244$		−	1.52352i		−	0.0975335i
$245$	−13.9765	+	7.04684i	−0.892925	+	0.450206i
$246$	1.05157	+	0.490263i	0.0670454	+	0.0312580i
$247$	9.81002	+	9.81002i	0.624197	+	0.624197i
$248$	7.41990	−	1.98816i	0.471164	−	0.126248i
$249$	−14.9512	−	6.97056i	−0.947493	−	0.441741i
$250$	−9.55018	+	5.81326i	−0.604007	+	0.367663i
$251$			10.5488i			0.665836i	0.942956	+	0.332918i	$0.108033\pi$
$251$			10.5488i			0.665836i	−0.942956	+	0.332918i	$0.891967\pi$
$252$	−2.14316	−	7.64244i	−0.135007	−	0.481428i
$253$	−6.69087	+	6.69087i	−0.420652	+	0.420652i
$254$	−8.44133	−	14.6208i	−0.529656	−	0.917391i
$255$	0.925537	−	5.49961i	0.0579594	−	0.344399i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.10242	+	3.10242i	−0.193524	+	0.193524i	−0.797217	−	0.603693i	$-0.793695\pi$
$257$	−3.10242	+	3.10242i	−0.193524	+	0.193524i	0.603693	+	0.797217i	$0.293695\pi$
$258$	−2.21046	+	2.63471i	−0.137617	+	0.164030i
$259$	4.41541	−	5.38632i	0.274361	−	0.334689i
$260$	0.104360	+	13.4955i	0.00647210	+	0.836954i
$261$	7.68692	+	2.79658i	0.475809	+	0.173104i
$262$	−1.53111	+	5.71419i	−0.0945924	+	0.353024i
$263$	−1.98839	−	1.98839i	−0.122609	−	0.122609i	0.643140	−	0.765749i	$-0.277631\pi$
$263$	−1.98839	−	1.98839i	−0.122609	−	0.122609i	−0.765749	+	0.643140i	$0.777631\pi$
$264$	−1.83474	+	0.160650i	−0.112920	+	0.00988731i
$265$	−13.2839	+	7.80704i	−0.816023	+	0.479582i
$266$	−6.00092	−	0.987320i	−0.367940	−	0.0605365i
$267$	−12.6246	+	4.59601i	−0.772615	+	0.281271i
$268$	−14.2804	−	3.82641i	−0.872312	−	0.233735i
$269$	−0.818317	−	1.41737i	−0.0498936	−	0.0864183i	0.840000	−	0.542586i	$-0.182555\pi$
$269$	−0.818317	−	1.41737i	−0.0498936	−	0.0864183i	−0.889894	+	0.456168i	$0.849222\pi$
$270$	−11.6186	+	0.0923184i	−0.707084	+	0.00561832i
$271$	−1.81683	+	3.14683i	−0.110364	+	0.191157i	−0.915917	−	0.401367i	$-0.868535\pi$
$271$	−1.81683	+	3.14683i	−0.110364	+	0.191157i	0.805553	+	0.592524i	$0.201868\pi$
$272$	0.372689	+	1.39089i	0.0225976	+	0.0843354i
$273$	26.0977	+	9.15925i	1.57951	+	0.554343i
$274$	−3.67464	+	2.12156i	−0.221993	+	0.128168i
$275$	5.31605	−	0.0822222i	0.320570	−	0.00495818i
$276$	6.51282	−	13.9694i	0.392026	−	0.840858i
$277$	−0.813249	−	0.813249i	−0.0488634	−	0.0488634i	0.682253	−	0.731116i	$-0.261000\pi$
$277$	−0.813249	−	0.813249i	−0.0488634	−	0.0488634i	−0.731116	+	0.682253i	$0.761000\pi$
$278$	−18.4771	+	4.95091i	−1.10818	+	0.296936i
$279$	−21.6563	−	7.87876i	−1.29653	−	0.471689i
$280$	−3.48573	−	4.78013i	−0.208312	−	0.285668i
$281$	−22.3933	−	12.9288i	−1.33587	−	0.771268i	−0.349682	−	0.936868i	$-0.613710\pi$
$281$	−22.3933	−	12.9288i	−1.33587	−	0.771268i	−0.986193	+	0.165601i	$0.947044\pi$
$282$	−0.926237	−	2.54425i	−0.0551566	−	0.151508i
$283$	1.92196	+	7.17287i	0.114249	+	0.426383i	0.999230	−	0.0392449i	$-0.0124952\pi$
$283$	1.92196	+	7.17287i	0.114249	+	0.426383i	−0.884981	+	0.465628i	$0.845829\pi$
$284$	−0.638711	+	1.10628i	−0.0379005	+	0.0656457i
$285$	−3.69930	+	8.09756i	−0.219128	+	0.479658i
$286$	3.20891	−	5.55800i	0.189747	−	0.328651i
$287$	0.730537	−	1.61472i	0.0431223	−	0.0953141i
$288$	2.71874	−	1.26824i	0.160203	−	0.0747318i
$289$	−12.9267	−	7.46326i	−0.760397	−	0.439015i
$290$	6.09670	−	0.0471453i	0.358011	−	0.00276847i
$291$	0.743497	+	0.346634i	0.0435846	+	0.0203200i
$292$	7.19160	+	7.19160i	0.420857	+	0.420857i
$293$	6.83404	−	25.5050i	0.399249	−	1.49002i	−0.415172	−	0.909743i	$-0.636278\pi$
$293$	6.83404	−	25.5050i	0.399249	−	1.49002i	0.814421	−	0.580275i	$-0.197055\pi$
$294$	−11.6360	+	3.40654i	−0.678623	+	0.198674i
$295$	17.4619	−	4.82392i	1.01667	−	0.280859i
$296$	2.27976	+	1.31622i	0.132509	+	0.0765038i
$297$	4.78561	+	2.76162i	0.277689	+	0.160245i
$298$	−15.2477	−	4.08561i	−0.883275	−	0.236673i
$299$	26.8542	+	46.5129i	1.55302	+	2.68991i
$300$	−8.09098	+	3.08805i	−0.467133	+	0.178289i
$301$	4.06279	+	3.33046i	0.234175	+	0.191965i
$302$	−17.6803	−	4.73743i	−1.01739	−	0.272608i
$303$	6.67050	−	7.95073i	0.383210	−	0.456758i
$304$		−	2.29863i		−	0.131835i
$305$	−0.856247	+	3.29734i	−0.0490286	+	0.188805i
$306$	1.47691	−	4.05957i	0.0844293	−	0.232070i
$307$	4.70855	+	4.70855i	0.268731	+	0.268731i	0.828589	−	0.559858i	$-0.189144\pi$
$307$	4.70855	+	4.70855i	0.268731	+	0.268731i	−0.559858	+	0.828589i	$0.689144\pi$
$308$	0.277315	+	2.79963i	0.0158015	+	0.159524i
$309$	−31.1463	+	2.72718i	−1.77185	+	0.155144i
$310$	−17.1762	+	0.132822i	−0.975541	+	0.00754378i
$311$	−25.2288	−	14.5659i	−1.43060	−	0.825955i	−0.433431	−	0.901187i	$-0.642697\pi$
$311$	−25.2288	−	14.5659i	−1.43060	−	0.825955i	−0.997166	+	0.0752317i	$0.976030\pi$
$312$	−1.81456	+	10.2952i	−0.102730	+	0.582850i
$313$	−9.71191	−	2.60230i	−0.548950	−	0.147091i	−0.0263249	−	0.999653i	$-0.508380\pi$
$313$	−9.71191	−	2.60230i	−0.548950	−	0.147091i	−0.522625	+	0.852563i	$0.675047\pi$
$314$	1.89948			0.107194
$315$	0.343234	+	17.7449i	0.0193391	+	0.999813i
$316$	14.4771			0.814399
$317$	−18.7875	−	5.03409i	−1.05521	−	0.282743i	−0.310807	−	0.950473i	$-0.600599\pi$
$317$	−18.7875	−	5.03409i	−1.05521	−	0.282743i	−0.744403	+	0.667730i	$0.767266\pi$
$318$	−11.2150	+	4.08285i	−0.628909	+	0.228955i
$319$	−2.51087	−	1.44965i	−0.140582	−	0.0811651i
$320$	1.56887	−	1.59332i	0.0877022	−	0.0890692i
$321$	−1.80521	+	3.87200i	−0.100757	+	0.216114i
$322$	−21.4506	−	9.70471i	−1.19539	−	0.540823i
$323$	−2.34048	−	2.34048i	−0.130228	−	0.130228i
$324$	−8.86371	−	1.56032i	−0.492428	−	0.0866844i
$325$	7.35884	−	29.2667i	0.408195	−	1.62343i
$326$			7.06611i			0.391356i
$327$	−28.1524	−	4.96196i	−1.55683	−	0.274397i
$328$	0.647038	+	0.173373i	0.0357267	+	0.00957294i
$329$	−3.87004	+	1.45904i	−0.213362	+	0.0804396i
$330$	4.06118	+	0.683463i	0.223561	+	0.0376234i
$331$	9.44913	+	16.3664i	0.519371	+	0.899577i	0.999747	+	0.0225142i	$0.00716708\pi$
$331$	9.44913	+	16.3664i	0.519371	+	0.899577i	−0.480375	+	0.877063i	$0.659500\pi$
$332$	−9.19959	−	2.46502i	−0.504893	−	0.135286i
$333$	−3.33857	−	7.15694i	−0.182953	−	0.392198i
$334$	2.38955	+	1.37961i	0.130751	+	0.0754889i
$335$	28.7563	+	16.3073i	1.57112	+	0.890961i
$336$	−1.98446	−	4.13061i	−0.108261	−	0.225343i
$337$	6.36015	−	23.7364i	0.346459	−	1.29300i	−0.544439	−	0.838801i	$-0.683257\pi$
$337$	6.36015	−	23.7364i	0.346459	−	1.29300i	0.890898	−	0.454203i	$-0.150076\pi$
$338$	−16.5659	−	16.5659i	−0.901069	−	0.901069i
$339$	10.8317	−	7.58562i	0.588300	−	0.411994i
$340$	−0.0248981	−	3.21975i	−0.00135029	−	0.174616i
$341$	7.07386	+	4.08410i	0.383071	+	0.221166i
$342$	−3.95451	+	5.64934i	−0.213836	+	0.305481i
$343$	5.40577	+	17.7138i	0.291884	+	0.956454i
$344$	−0.992800	+	1.71958i	−0.0535282	+	0.0927135i
$345$	−21.9467	+	26.5734i	−1.18157	+	1.43066i
$346$	5.69501	−	9.86405i	0.306166	−	0.530294i
$347$	−6.86482	−	25.6199i	−0.368523	−	1.37535i	−0.862582	−	0.505918i	$-0.831154\pi$
$347$	−6.86482	−	25.6199i	−0.368523	−	1.37535i	0.494059	−	0.869429i	$-0.335513\pi$
$348$	4.65094	+	0.819746i	0.249316	+	0.0439430i
$349$	−16.8403	−	9.72273i	−0.901439	−	0.520446i	−0.0237719	−	0.999717i	$-0.507568\pi$
$349$	−16.8403	−	9.72273i	−0.901439	−	0.520446i	−0.877667	+	0.479272i	$0.840901\pi$
$350$	4.85760	+	12.3046i	0.259650	+	0.657710i
$351$	22.1713	−	22.1807i	1.18342	−	1.18392i
$352$	−1.02711	+	0.275212i	−0.0547449	+	0.0146689i
$353$	1.80455	+	1.80455i	0.0960464	+	0.0960464i	0.753497	−	0.657451i	$-0.228365\pi$
$353$	1.80455	+	1.80455i	0.0960464	+	0.0960464i	−0.657451	+	0.753497i	$0.728365\pi$
$354$	13.9790	−	1.22401i	0.742978	−	0.0650552i
$355$	2.00410	−	2.03534i	0.106367	−	0.108025i
$356$	−6.71760	+	3.87841i	−0.356032	+	0.205555i
$357$	−6.22640	−	2.18521i	−0.329536	−	0.115654i
$358$	4.33047	+	16.1615i	0.228872	+	0.854163i
$359$	−8.37289	+	14.5023i	−0.441904	+	0.765400i	−0.997831	−	0.0658311i	$-0.979030\pi$
$359$	−8.37289	+	14.5023i	−0.441904	+	0.765400i	0.555927	+	0.831231i	$0.312363\pi$
$360$	−6.59691	+	1.21685i	−0.347688	+	0.0641338i
$361$	−6.85816	−	11.8787i	−0.360956	−	0.625193i
$362$	16.2404	+	4.35160i	0.853575	+	0.228715i
$363$	13.0957	+	10.9870i	0.687344	+	0.576667i
$364$	15.7567	+	2.59242i	0.825876	+	0.135880i
$365$	−11.5229	−	19.6065i	−0.603135	−	1.02625i
$366$	−1.11504	+	2.39166i	−0.0582842	+	0.125014i
$367$	−4.78601	−	4.78601i	−0.249828	−	0.249828i	0.571072	−	0.820900i	$-0.306528\pi$
$367$	−4.78601	−	4.78601i	−0.249828	−	0.249828i	−0.820900	+	0.571072i	$0.806528\pi$
$368$	2.30315	−	8.59548i	0.120060	−	0.448070i
$369$	−1.29196	−	1.53925i	−0.0672566	−	0.0801302i
$370$	−4.19432	−	4.12995i	−0.218052	−	0.214706i
$371$	6.43145	+	17.0591i	0.333904	+	0.885664i
$372$	−13.1030	−	2.30946i	−0.679361	−	0.119740i
$373$	10.4639	−	10.4639i	0.541799	−	0.541799i	−0.382257	−	0.924056i	$-0.624853\pi$
$373$	10.4639	−	10.4639i	0.541799	−	0.541799i	0.924056	+	0.382257i	$0.124853\pi$
$374$	−0.765582	+	1.32603i	−0.0395873	+	0.0685672i
$375$	19.2467	−	2.13616i	0.993897	−	0.110311i
$376$	−0.781619	−	1.35380i	−0.0403089	−	0.0698171i
$377$	−11.6366	+	11.6366i	−0.599313	+	0.599313i
$378$	−2.22900	+	13.5658i	−0.114647	+	0.697751i
$379$		−	18.3985i		−	0.945067i	−0.881313	−	0.472534i	$-0.843340\pi$
$379$		−	18.3985i		−	0.945067i	0.881313	−	0.472534i	$-0.156660\pi$
$380$	−1.29187	+	4.97489i	−0.0662715	+	0.255206i
$381$	2.55064	+	29.1302i	0.130673	+	1.49238i
$382$	21.9854	−	5.89097i	1.12487	−	0.301408i
$383$	11.7457	+	11.7457i	0.600175	+	0.600175i	0.940359	−	0.340184i	$-0.110489\pi$
$383$	11.7457	+	11.7457i	0.600175	+	0.600175i	−0.340184	+	0.940359i	$0.610489\pi$
$384$	1.41874	−	0.993564i	0.0723999	−	0.0507026i
$385$	0.973252	−	6.21505i	0.0496015	−	0.316748i
$386$		−	1.54063i		−	0.0784158i
$387$	5.39834	−	2.51822i	0.274413	−	0.128008i
$388$	0.457480	+	0.122581i	0.0232250	+	0.00622313i
$389$	−20.4092			−1.03479			−0.517393	−	0.855748i	$-0.673098\pi$
$389$	−20.4092			−1.03479			−0.517393	+	0.855748i	$0.673098\pi$
$390$	9.71331	−	21.2619i	0.491853	−	1.07664i
$391$	−6.40688	−	11.0970i	−0.324010	−	0.561202i
$392$	−6.27465	+	3.10302i	−0.316918	+	0.156726i
$393$	6.58570	−	7.84966i	0.332205	−	0.395963i
$394$	4.63965	−	2.67870i	0.233742	−	0.134951i
$395$	−31.3326	−	8.13638i	−1.57651	−	0.409386i
$396$	2.99779	+	1.09062i	0.150644	+	0.0548059i
$397$	0.737528	−	0.197620i	0.0370154	−	0.00991826i	−0.240264	−	0.970708i	$-0.577234\pi$
$397$	0.737528	−	0.197620i	0.0370154	−	0.00991826i	0.277279	+	0.960789i	$0.410567\pi$
$398$	−19.7895	+	5.30259i	−0.991960	+	0.265795i
$399$	8.69777	+	5.94190i	0.435433	+	0.297467i
$400$	−4.29095	+	2.56667i	−0.214547	+	0.128333i
$401$		−	24.8806i		−	1.24248i	−0.783622	−	0.621238i	$-0.786630\pi$
$401$		−	24.8806i		−	1.24248i	0.783622	−	0.621238i	$-0.213370\pi$
$402$	19.6171	+	16.4584i	0.978414	+	0.820869i
$403$	32.7835	−	32.7835i	1.63306	−	1.63306i
$404$	2.99597	−	5.18916i	0.149055	−	0.258171i
$405$	18.3067	+	8.35854i	0.909667	+	0.415339i
$406$	1.17115	−	7.11823i	0.0581232	−	0.353272i
$407$	0.724480	+	2.70380i	0.0359112	+	0.134022i
$408$	0.432919	−	2.45622i	0.0214327	−	0.121601i
$409$	−13.8679	−	8.00665i	−0.685725	−	0.395903i	0.116284	−	0.993216i	$-0.462902\pi$
$409$	−13.8679	−	8.00665i	−0.685725	−	0.395903i	−0.802009	+	0.597313i	$0.796235\pi$
$410$	−1.30294	−	0.738877i	−0.0643475	−	0.0364905i
$411$	7.32127	−	0.641052i	0.361132	−	0.0316207i
$412$	−17.4361	+	4.67198i	−0.859014	+	0.230172i
$413$	−2.11289	−	21.3307i	−0.103969	−	1.04961i
$414$	−20.4480	+	17.1628i	−1.00496	+	0.843507i
$415$	18.5252	+	10.5054i	0.909365	+	0.515687i
$416$			6.03554i			0.295917i
$417$	32.6292	+	5.75102i	1.59786	+	0.281629i
$418$	1.72832	−	1.72832i	0.0845350	−	0.0845350i
$419$	8.38194	+	14.5179i	0.409485	+	0.709248i	0.994832	−	0.101534i	$-0.0323752\pi$
$419$	8.38194	+	14.5179i	0.409485	+	0.709248i	−0.585347	+	0.810783i	$0.699042\pi$
$420$	1.97347	+	10.0551i	0.0962957	+	0.490640i
$421$	5.23727	−	9.07122i	0.255249	−	0.442104i	−0.709714	−	0.704490i	$-0.751176\pi$
$421$	5.23727	−	9.07122i	0.255249	−	0.442104i	0.964963	+	0.262386i	$0.0845092\pi$
$422$	−4.89535	−	18.2697i	−0.238302	−	0.889355i
$423$	−0.408073	+	4.67193i	−0.0198412	+	0.227157i
$424$	−5.96756	+	3.44537i	−0.289810	+	0.167322i
$425$	−1.75567	+	6.98246i	−0.0851626	+	0.338699i
$426$	1.81233	−	1.26920i	0.0878079	−	0.0614930i
$427$	3.67249	+	1.66152i	0.177724	+	0.0804065i
$428$	−0.638382	+	2.38247i	−0.0308574	+	0.115161i
$429$	−9.10524	+	6.37652i	−0.439605	+	0.307861i
$430$	3.11514	−	3.16369i	0.150225	−	0.152567i
$431$	−9.93195	+	5.73421i	−0.478405	+	0.276207i	−0.719752	−	0.694232i	$-0.755744\pi$
$431$	−9.93195	+	5.73421i	−0.478405	+	0.276207i	0.241346	+	0.970439i	$0.422411\pi$
$432$	−5.19615	+	0.00110582i	−0.250000	+	5.32036e-5i
$433$	−16.8219	+	16.8219i	−0.808411	+	0.808411i	−0.984393	−	0.175983i	$-0.943690\pi$
$433$	−16.8219	+	16.8219i	−0.808411	+	0.808411i	0.175983	+	0.984393i	$0.443690\pi$
$434$	−3.29947	+	20.0541i	−0.158380	+	0.962629i
$435$	−9.60525	−	4.38808i	−0.460537	−	0.210392i
$436$	−16.5043			−0.790413
$437$	5.29409	+	19.7578i	0.253251	+	0.945144i
$438$	−6.02612	−	16.5530i	−0.287939	−	0.790932i
$439$	−31.3041	+	18.0734i	−1.49406	+	0.862597i	−0.999977	−	0.00681713i	$-0.997830\pi$
$439$	−31.3041	+	18.0734i	−1.49406	+	0.862597i	−0.494085	+	0.869414i	$0.664497\pi$
$440$	2.37763	−	0.0183860i	0.113349	−	0.000876518i
$441$	20.7596	+	3.16851i	0.988552	+	0.150881i
$442$	6.14542	+	6.14542i	0.292308	+	0.292308i
$443$	10.3471	−	38.6158i	0.491604	−	1.83469i	−0.0566727	−	0.998393i	$-0.518049\pi$
$443$	10.3471	−	38.6158i	0.491604	−	1.83469i	0.548276	−	0.836297i	$-0.315284\pi$
$444$	−2.61550	−	3.73476i	−0.124126	−	0.177244i
$445$	16.7185	−	4.61857i	0.792535	−	0.218941i
$446$		−	7.39252i		−	0.350046i
$447$	20.9460	+	17.5732i	0.990711	+	0.831185i
$448$	−1.54229	−	2.14973i	−0.0728663	−	0.101565i
$449$	20.4371			0.964488			0.482244	−	0.876037i	$-0.339822\pi$
$449$	20.4371			0.964488			0.482244	+	0.876037i	$0.339822\pi$
$450$	14.9615	+	1.07397i	0.705292	+	0.0506272i
$451$	0.356146	+	0.616862i	0.0167702	+	0.0290469i
$452$	5.39858	−	5.39858i	0.253928	−	0.253928i
$453$	24.2877	+	20.3769i	1.14114	+	0.957389i
$454$	20.7906	−	12.0034i	0.975750	−	0.563350i
$455$	−32.6450	−	14.4663i	−1.53042	−	0.678191i
$456$	−1.68233	+	3.60844i	−0.0787824	+	0.168981i
$457$	4.53995	−	16.9433i	0.212370	−	0.792575i	−0.774706	−	0.632322i	$-0.782102\pi$
$457$	4.53995	−	16.9433i	0.212370	−	0.792575i	0.987076	−	0.160254i	$-0.0512313\pi$
$458$	−0.907415	+	3.38652i	−0.0424007	+	0.158242i
$459$	−5.28963	+	5.29188i	−0.246899	+	0.247004i
$460$	−9.81550	+	17.3087i	−0.457650	+	0.807021i
$461$	−28.3736	−	16.3815i	−1.32149	−	0.762964i	−0.337525	−	0.941316i	$-0.609590\pi$
$461$	−28.3736	−	16.3815i	−1.32149	−	0.762964i	−0.983967	+	0.178353i	$0.942923\pi$
$462$	1.61367	−	4.59788i	0.0750747	−	0.213913i
$463$	−25.2416	−	6.76347i	−1.17308	−	0.314325i	−0.380900	−	0.924616i	$-0.624386\pi$
$463$	−25.2416	−	6.76347i	−1.17308	−	0.314325i	−0.792178	+	0.610291i	$0.791053\pi$
$464$	2.72661			0.126580
$465$	27.0608	+	12.3625i	1.25491	+	0.573296i
$466$	−12.6744			−0.587131
$467$	3.16265	+	11.8032i	0.146350	+	0.546185i	0.999692	+	0.0248332i	$0.00790547\pi$
$467$	3.16265	+	11.8032i	0.146350	+	0.546185i	−0.853342	+	0.521352i	$0.825428\pi$
$468$	10.3834	−	14.8336i	0.479974	−	0.685681i
$469$	24.7975	−	30.2502i	1.14504	−	1.39682i
$470$	0.930785	+	3.36930i	0.0429339	+	0.155414i
$471$	−2.98185	−	1.39020i	−0.137396	−	0.0640571i
$472$	7.82563	−	2.09687i	0.360204	−	0.0965163i
$473$	−2.03942	+	0.546461i	−0.0937727	+	0.0251263i
$474$	−22.7265	−	10.5956i	−1.04386	−	0.486670i
$475$	5.59195	−	10.0410i	0.256576	−	0.460714i
$476$	−3.75924	−	0.618500i	−0.172304	−	0.0283489i
$477$	20.5938	+	1.79878i	0.942926	+	0.0823605i
$478$	−1.04593	−	3.90346i	−0.0478397	−	0.178540i
$479$	−24.9089			−1.13812			−0.569059	−	0.822296i	$-0.692693\pi$
$479$	−24.9089			−1.13812			−0.569059	+	0.822296i	$0.692693\pi$
$480$	−3.62897	+	1.35300i	−0.165639	+	0.0617557i
$481$	15.8882			0.724441
$482$	15.2990	+	4.09935i	0.696850	+	0.186720i
$483$	26.5708	+	30.9340i	1.20902	+	1.40755i
$484$	8.54707	+	4.93466i	0.388503	+	0.224303i
$485$	−0.921225	−	0.522413i	−0.0418307	−	0.0237216i
$486$	12.7725	+	8.93664i	0.579372	+	0.405374i
$487$	−3.69711	+	13.7978i	−0.167532	+	0.625238i	0.830172	+	0.557508i	$0.188242\pi$
$487$	−3.69711	+	13.7978i	−0.167532	+	0.625238i	−0.997704	+	0.0677299i	$0.978424\pi$
$488$	−0.394317	+	1.47161i	−0.0178499	+	0.0666166i
$489$	5.17158	−	11.0925i	0.233867	−	0.501622i
$490$	15.3241	−	3.18935i	0.692272	−	0.144080i
$491$	−17.5334	+	10.1229i	−0.791271	+	0.456841i	−0.840410	−	0.541951i	$-0.817686\pi$
$491$	−17.5334	+	10.1229i	−0.791271	+	0.456841i	0.0491386	+	0.998792i	$0.484352\pi$
$492$	−0.888846	−	0.745723i	−0.0400723	−	0.0336198i
$493$	2.77625	−	2.77625i	0.125036	−	0.125036i
$494$	−6.93673	−	12.0148i	−0.312098	−	0.540570i
$495$	−5.87512	−	4.04523i	−0.264067	−	0.181820i
$496$	−7.68165			−0.344916
$497$	−1.97016	−	2.74612i	−0.0883736	−	0.123180i
$498$	12.6376	+	10.6027i	0.566305	+	0.475118i
$499$		−	21.5210i		−	0.963411i	−0.876333	−	0.481706i	$-0.840017\pi$
$499$		−	21.5210i		−	0.963411i	0.876333	−	0.481706i	$-0.159983\pi$
$500$	10.7294	−	3.14341i	0.479831	−	0.140578i
$501$	−2.74146	−	3.91462i	−0.122479	−	0.174892i
$502$	2.73024	−	10.1894i	0.121856	−	0.454774i
$503$	17.0865	+	17.0865i	0.761849	+	0.761849i	0.976657	−	0.214807i	$-0.0689123\pi$
$503$	17.0865	+	17.0865i	0.761849	+	0.761849i	−0.214807	+	0.976657i	$0.568912\pi$
$504$	0.0921296	+	7.93672i	0.00410378	+	0.353530i
$505$	−9.40053	+	9.54705i	−0.418318	+	0.424838i
$506$	8.19461	−	4.73116i	0.364295	−	0.210326i
$507$	13.8812	+	38.1300i	0.616488	+	1.69341i
$508$	4.36955	+	16.3074i	0.193868	+	0.723524i
$509$	6.96145			0.308561			0.154281	−	0.988027i	$-0.450694\pi$
$509$	6.96145			0.308561			0.154281	+	0.988027i	$0.450694\pi$
$510$	−2.31740	+	5.07266i	−0.102616	+	0.224621i
$511$	−25.1786	+	9.49256i	−1.11383	+	0.419926i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	10.3426	−	5.97421i	0.456635	−	0.263768i
$514$	3.79967	−	2.19374i	0.167596	−	0.0967618i
$515$	40.3624	−	0.312119i	1.77858	−	0.0137536i
$516$	2.81705	−	1.97282i	0.124014	−	0.0868486i
$517$	0.430222	−	1.60561i	0.0189212	−	0.0706147i
$518$	−5.65904	+	4.05999i	−0.248644	+	0.178386i
$519$	−16.1595	+	11.3167i	−0.709324	+	0.496749i
$520$	3.39208	−	13.0626i	0.148753	−	0.572835i
$521$	−32.7545	+	18.9108i	−1.43500	+	0.828498i	−0.997496	−	0.0707184i	$-0.977471\pi$
$521$	−32.7545	+	18.9108i	−1.43500	+	0.828498i	−0.437504	+	0.899216i	$0.644137\pi$
$522$	−6.70119	−	4.69081i	−0.293303	−	0.205311i
$523$	−5.96516	−	22.2623i	−0.260838	−	0.973461i	−0.964749	−	0.263173i	$-0.915231\pi$
$523$	−5.96516	−	22.2623i	−0.260838	−	0.973461i	0.703911	−	0.710289i	$-0.251436\pi$
$524$	2.95788	−	5.12320i	0.129216	−	0.223808i
$525$	1.37999	−	22.8713i	0.0602279	−	0.998185i
$526$	1.40600	+	2.43527i	0.0613046	+	0.106183i
$527$	−7.82150	+	7.82150i	−0.340710	+	0.340710i
$528$	1.81380	+	0.319689i	0.0789354	+	0.0139127i
$529$			56.1868i			2.44291i
$530$	14.8519	−	4.10289i	0.645124	−	0.178218i
$531$	−22.8405	−	8.30958i	−0.991191	−	0.360605i
$532$	5.54090	+	2.50683i	0.240229	+	0.108685i
$533$	3.90523	−	1.04640i	0.169154	−	0.0453247i
$534$	13.3840	−	1.17190i	0.579182	−	0.0507133i
$535$	2.72064	−	4.79758i	0.117623	−	0.207417i
$536$	12.8034	+	7.39206i	0.553023	+	0.319288i
$537$	5.03031	−	28.5401i	0.217074	−	1.23160i
$538$	0.423592	+	1.58087i	0.0182623	+	0.0681560i
$539$	−7.05101	−	2.38473i	−0.303709	−	0.102718i
$540$	11.2466	+	2.91794i	0.483976	+	0.125568i
$541$	6.86834	−	11.8963i	0.295293	−	0.511462i	−0.679760	−	0.733435i	$-0.737916\pi$
$541$	6.86834	−	11.8963i	0.295293	−	0.511462i	0.975053	+	0.221972i	$0.0712494\pi$
$542$	2.56938	−	2.56938i	0.110364	−	0.110364i
$543$	−22.3096	−	18.7173i	−0.957399	−	0.803237i
$544$		−	1.43996i		−	0.0617378i
$545$	35.7201	+	9.27572i	1.53008	+	0.397328i
$546$	−22.8379	−	15.6017i	−0.977371	−	0.667693i
$547$	−1.20895	+	0.323937i	−0.0516910	+	0.0138506i	−0.284572	−	0.958655i	$-0.591851\pi$
$547$	−1.20895	+	0.323937i	−0.0516910	+	0.0138506i	0.232881	+	0.972505i	$0.425185\pi$
$548$	4.09853	−	1.09820i	0.175081	−	0.0469127i
$549$	3.50084	−	2.93840i	0.149412	−	0.125408i
$550$	−5.15620	−	1.29648i	−0.219861	−	0.0552819i
$551$	−5.42778	+	3.13373i	−0.231231	+	0.133501i
$552$	−9.90645	+	11.8077i	−0.421646	+	0.502571i
$553$	−15.7884	+	34.8974i	−0.671390	+	1.48399i
$554$	0.575054	+	0.996022i	0.0244317	+	0.0423169i
$555$	3.56169	+	9.55305i	0.151185	+	0.405504i
$556$	19.1289			0.811244
$557$	12.9010	+	3.45682i	0.546634	+	0.146470i	0.521558	−	0.853216i	$-0.325351\pi$
$557$	12.9010	+	3.45682i	0.546634	+	0.146470i	0.0250751	+	0.999686i	$0.492017\pi$
$558$	18.8792	+	13.2154i	0.799220	+	0.559451i
$559$			11.9842i			0.506877i
$560$	2.12977	+	5.51943i	0.0899991	+	0.233238i
$561$	2.17233	−	1.52131i	0.0917158	−	0.0642298i
$562$	18.2841	+	18.2841i	0.771268	+	0.771268i
$563$	1.54576	−	0.414186i	0.0651462	−	0.0174559i	−0.226099	−	0.974104i	$-0.572597\pi$
$563$	1.54576	−	0.414186i	0.0651462	−	0.0174559i	0.291245	+	0.956649i	$0.405931\pi$
$564$	0.236175	+	2.69729i	0.00994476	+	0.113576i
$565$	−14.7182	+	8.64998i	−0.619199	+	0.363907i
$566$		−	7.42590i		−	0.312134i
$567$	13.4278	−	19.6646i	0.563913	−	0.825835i
$568$	0.903274	−	0.903274i	0.0379005	−	0.0379005i
$569$	−7.16263	−	12.4060i	−0.300273	−	0.520088i	0.675925	−	0.736971i	$-0.263745\pi$
$569$	−7.16263	−	12.4060i	−0.300273	−	0.520088i	−0.976198	+	0.216882i	$0.930411\pi$
$570$	5.66905	−	6.86419i	0.237450	−	0.287509i
$571$	−21.1964	+	36.7133i	−0.887044	+	1.53640i	−0.0436902	+	0.999045i	$0.513911\pi$
$571$	−21.1964	+	36.7133i	−0.887044	+	1.53640i	−0.843353	+	0.537359i	$0.819422\pi$
$572$	−4.53809	+	4.53809i	−0.189747	+	0.189747i
$573$	−38.8247	−	6.84300i	−1.62192	−	0.285870i
$574$	−1.12357	+	1.37063i	−0.0468967	+	0.0572088i
$575$	30.9713	−	31.9444i	1.29159	−	1.33218i
$576$	−2.95435	+	0.521364i	−0.123098	+	0.0217235i
$577$	1.00681	−	3.75747i	0.0419141	−	0.156425i	−0.941797	−	0.336182i	$-0.890864\pi$
$577$	1.00681	−	3.75747i	0.0419141	−	0.156425i	0.983711	+	0.179756i	$0.0575310\pi$
$578$	10.5546	+	10.5546i	0.439015	+	0.439015i
$579$	−1.12756	+	2.41851i	−0.0468598	+	0.100510i
$580$	−5.90117	−	1.53240i	−0.245033	−	0.0636296i
$581$	15.9749	−	19.4876i	0.662749	−	0.808481i
$582$	−0.628447	−	0.527254i	−0.0260500	−	0.0218554i
$583$	−7.07752	−	1.89642i	−0.293121	−	0.0785415i
$584$	−5.08523	−	8.80788i	−0.210428	−	0.364473i
$585$	−30.8094	+	26.2684i	−1.27381	+	1.08606i
$586$	−13.2024	+	22.8672i	−0.545384	+	0.944633i
$587$	−9.57665	−	35.7406i	−0.395271	−	1.47517i	−0.821318	−	0.570470i	$-0.806761\pi$
$587$	−9.57665	−	35.7406i	−0.395271	−	1.47517i	0.426048	−	0.904701i	$-0.359906\pi$
$588$	12.1211	−	0.278862i	0.499868	−	0.0115001i
$589$	15.2916	−	8.82863i	0.630081	−	0.363777i
$590$	−18.1154	+	0.140085i	−0.745798	+	0.00576720i
$591$	−9.24393	+	0.809400i	−0.380245	+	0.0332943i
$592$	−1.86142	−	1.86142i	−0.0765038	−	0.0765038i
$593$	23.4283	−	6.27760i	0.962086	−	0.257790i	0.256603	−	0.966517i	$-0.417397\pi$
$593$	23.4283	−	6.27760i	0.962086	−	0.257790i	0.705483	+	0.708727i	$0.250730\pi$
$594$	−3.90779	−	3.90612i	−0.160338	−	0.160270i
$595$	7.78845	+	3.45137i	0.319296	+	0.141492i
$596$	13.6707	+	7.89278i	0.559974	+	0.323301i
$597$	34.9470	+	6.15954i	1.43028	+	0.252093i
$598$	−13.9008	−	51.8784i	−0.568445	−	2.12147i
$599$	21.9480	−	38.0150i	0.896770	−	1.55325i	0.0651718	−	0.997874i	$-0.479240\pi$
$599$	21.9480	−	38.0150i	0.896770	−	1.55325i	0.831598	−	0.555377i	$-0.187426\pi$
$600$	8.61453	−	0.888732i	0.351687	−	0.0362823i
$601$	8.92883	−	15.4652i	0.364215	−	0.630838i	−0.624435	−	0.781077i	$-0.714671\pi$
$601$	8.92883	−	15.4652i	0.364215	−	0.630838i	0.988650	+	0.150238i	$0.0480041\pi$
$602$	−3.06237	−	4.26850i	−0.124813	−	0.173971i
$603$	−18.7498	−	40.1942i	−0.763551	−	1.63683i
$604$	15.8517	+	9.15200i	0.644998	+	0.372390i
$605$	−15.7250	−	15.4836i	−0.639310	−	0.629499i
$606$	−8.50101	+	5.95337i	−0.345330	+	0.241839i
$607$	9.62529	+	9.62529i	0.390679	+	0.390679i	0.874929	−	0.484251i	$-0.160908\pi$
$607$	9.62529	+	9.62529i	0.390679	+	0.390679i	−0.484251	+	0.874929i	$0.660908\pi$
$608$	−0.594929	+	2.22030i	−0.0241275	+	0.0900452i
$609$	−7.04823	+	10.3172i	−0.285608	+	0.418075i
$610$	1.68049	−	2.96337i	0.0680409	−	0.119983i
$611$	−8.17094	−	4.71750i	−0.330561	−	0.190849i
$612$	−2.47728	+	3.53899i	−0.100138	+	0.143055i
$613$	−19.1774	−	5.13857i	−0.774568	−	0.207545i	−0.150180	−	0.988659i	$-0.547985\pi$
$613$	−19.1774	−	5.13857i	−0.774568	−	0.207545i	−0.624389	+	0.781114i	$0.714652\pi$
$614$	−3.32945	−	5.76677i	−0.134366	−	0.232728i
$615$	1.50461	+	2.11351i	0.0606716	+	0.0852248i
$616$	0.456731	−	2.77601i	0.0184022	−	0.111848i
$617$	−25.5343	−	6.84189i	−1.02797	−	0.275444i	−0.294851	−	0.955543i	$-0.595270\pi$
$617$	−25.5343	−	6.84189i	−1.02797	−	0.275444i	−0.733120	+	0.680099i	$0.761937\pi$
$618$	30.7909	+	5.42702i	1.23859	+	0.218307i
$619$		−	5.21889i		−	0.209765i	−0.994485	−	0.104883i	$-0.966553\pi$
$619$		−	5.21889i		−	0.209765i	0.994485	−	0.104883i	$-0.0334467\pi$
$620$	16.6253	+	4.31723i	0.667688	+	0.173384i
$621$	44.6609	−	11.9770i	1.79218	−	0.480622i
$622$	20.5993	+	20.5993i	0.825955	+	0.825955i
$623$	−2.02295	−	20.4227i	−0.0810478	−	0.818217i
$624$	4.41732	−	9.47474i	0.176834	−	0.379293i
$625$	−24.9880	+	0.773153i	−0.999522	+	0.0309261i
$626$	8.70746	+	5.02726i	0.348020	+	0.200930i
$627$	−3.97810	+	1.44823i	−0.158870	+	0.0578366i
$628$	−1.83476	−	0.491622i	−0.0732148	−	0.0196178i
$629$	−3.79061			−0.151142
$630$	4.26118	−	17.2291i	0.169770	−	0.686424i
$631$	−0.742517			−0.0295591			−0.0147796	−	0.999891i	$-0.504705\pi$
$631$	−0.742517			−0.0295591			−0.0147796	+	0.999891i	$0.504705\pi$
$632$	−13.9838	−	3.74694i	−0.556245	−	0.149045i
$633$	−5.68648	+	32.2630i	−0.226017	+	1.28234i
$634$	16.8444	+	9.72512i	0.668977	+	0.386234i
$635$	−0.291915	−	37.7496i	−0.0115843	−	1.49805i
$636$	11.8896	−	1.04106i	0.471454	−	0.0412806i
$637$	−23.4330	+	35.1547i	−0.928450	+	1.39288i
$638$	2.05012	+	2.05012i	0.0811651	+	0.0811651i
$639$	−3.77395	+	0.666002i	−0.149295	+	0.0263466i
$640$	−1.92779	+	1.13297i	−0.0762025	+	0.0447848i
$641$			39.1499i			1.54633i	0.634207	+	0.773163i	$0.281327\pi$
$641$			39.1499i			1.54633i	−0.634207	+	0.773163i	$0.718673\pi$
$642$	2.74584	−	3.27284i	0.108370	−	0.129169i
$643$	17.0799	+	4.57654i	0.673564	+	0.180481i	0.579360	−	0.815072i	$-0.303303\pi$
$643$	17.0799	+	4.57654i	0.673564	+	0.180481i	0.0942044	+	0.995553i	$0.469969\pi$
$644$	18.2079	+	14.9258i	0.717491	+	0.588161i
$645$	−7.20567	+	2.68651i	−0.283723	+	0.105781i
$646$	1.65497	+	2.86648i	0.0651138	+	0.112780i
$647$	−0.715746	−	0.191784i	−0.0281389	−	0.00753979i	0.244722	−	0.969593i	$-0.421303\pi$
$647$	−0.715746	−	0.191784i	−0.0281389	−	0.00753979i	−0.272861	+	0.962053i	$0.587970\pi$
$648$	8.15785	+	3.80125i	0.320471	+	0.149327i
$649$	7.46066	+	4.30741i	0.292857	+	0.169081i
$650$	−14.6829	+	26.3649i	−0.575910	+	1.03412i
$651$	19.8569	−	29.0666i	0.778253	−	1.13921i
$652$	1.82884	−	6.82534i	0.0716231	−	0.267301i
$653$	25.8329	+	25.8329i	1.01092	+	1.01092i	0.999940	+	0.0109787i	$0.00349469\pi$
$653$	25.8329	+	25.8329i	1.01092	+	1.01092i	0.0109787	+	0.999940i	$0.496505\pi$
$654$	25.9089	+	12.0793i	1.01312	+	0.472336i
$655$	−9.28103	+	9.42569i	−0.362640	+	0.368292i
$656$	−0.580119	−	0.334932i	−0.0226498	−	0.0130769i
$657$	−2.65493	+	30.3957i	−0.103579	+	1.18585i
$658$	4.11580	−	0.407687i	0.160450	−	0.0158933i
$659$	−14.1819	+	24.5638i	−0.552449	+	0.956870i	0.445648	+	0.895208i	$0.352973\pi$
$659$	−14.1819	+	24.5638i	−0.552449	+	0.956870i	−0.998097	+	0.0616618i	$0.980360\pi$
$660$	−3.74591	−	1.71129i	−0.145809	−	0.0666117i
$661$	−13.3960	+	23.2025i	−0.521044	+	0.902474i	0.478657	+	0.878002i	$0.341124\pi$
$661$	−13.3960	+	23.2025i	−0.521044	+	0.902474i	−0.999701	+	0.0244719i	$0.992210\pi$
$662$	−4.89123	−	18.2543i	−0.190103	−	0.709474i
$663$	−5.14949	−	14.1450i	−0.199989	−	0.549345i
$664$	8.24813	+	4.76206i	0.320089	+	0.184804i
$665$	−10.5832	−	8.53959i	−0.410400	−	0.331151i
$666$	1.37246	+	7.77716i	0.0531818	+	0.301359i
$667$	−23.4365	+	6.27980i	−0.907466	+	0.243155i
$668$	−1.95106	−	1.95106i	−0.0754889	−	0.0754889i
$669$	−5.41047	+	11.6049i	−0.209181	+	0.448673i
$670$	−23.5558	−	23.1943i	−0.910040	−	0.896073i
$671$	−1.40298	+	0.810010i	−0.0541614	+	0.0312701i
$672$	0.847766	+	4.50348i	0.0327033	+	0.173725i
$673$	3.59852	+	13.4299i	0.138713	+	0.517683i	0.999955	+	0.00948855i	$0.00302035\pi$
$673$	3.59852	+	13.4299i	0.138713	+	0.517683i	−0.861242	+	0.508195i	$0.830313\pi$
$674$	−12.2869	+	21.2815i	−0.473272	+	0.819732i
$675$	−22.7009	−	12.6360i	−0.873758	−	0.486361i
$676$	11.7139	+	20.2891i	0.450534	+	0.780349i
$677$	25.0351	+	6.70813i	0.962176	+	0.257814i	0.705521	−	0.708689i	$-0.250713\pi$
$677$	25.0351	+	6.70813i	0.962176	+	0.257814i	0.256655	+	0.966503i	$0.417380\pi$
$678$	−12.4260	+	4.52368i	−0.477216	+	0.173731i
$679$	−0.794403	+	0.969084i	−0.0304864	+	0.0371900i
$680$	−0.809284	+	3.11649i	−0.0310346	+	0.119512i
$681$	−41.4227	+	3.62697i	−1.58732	+	0.138986i
$682$	−5.77578	−	5.77578i	−0.221166	−	0.221166i
$683$	−9.01354	+	33.6390i	−0.344894	+	1.28716i	0.547843	+	0.836581i	$0.315449\pi$
$683$	−9.01354	+	33.6390i	−0.344894	+	1.28716i	−0.892737	+	0.450579i	$0.851218\pi$
$684$	5.28192	−	4.43334i	0.201959	−	0.169513i
$685$	−9.48760	+	0.0733669i	−0.362503	+	0.00280320i
$686$	−0.636914	−	18.5093i	−0.0243175	−	0.706689i
$687$	3.90303	−	4.65211i	0.148910	−	0.177489i
$688$	1.40403	−	1.40403i	0.0535282	−	0.0535282i
$689$	−20.7947	+	36.0175i	−0.792214	+	1.37216i
$690$	28.0765	−	19.9877i	1.06886	−	0.760920i
$691$	−0.205609	−	0.356125i	−0.00782173	−	0.0135476i	0.862088	−	0.506759i	$-0.169156\pi$
$691$	−0.205609	−	0.356125i	−0.00782173	−	0.0135476i	−0.869910	+	0.493211i	$0.835823\pi$
$692$	−8.05396	+	8.05396i	−0.306166	+	0.306166i
$693$	−5.89830	+	6.03684i	−0.224058	+	0.229321i
$694$			26.5236i			1.00682i
$695$	−41.4003	−	10.7508i	−1.57040	−	0.407800i
$696$	−4.28030	−	1.99556i	−0.162244	−	0.0756417i
$697$	−0.931709	+	0.249651i	−0.0352910	+	0.00945620i
$698$	13.7500	+	13.7500i	0.520446	+	0.520446i
$699$	19.8966	+	9.27621i	0.752558	+	0.350858i
$700$	−1.50741	−	13.1426i	−0.0569748	−	0.496743i
$701$		−	3.08417i		−	0.116488i	−0.998302	−	0.0582438i	$-0.981450\pi$
$701$		−	3.08417i		−	0.116488i	0.998302	−	0.0582438i	$-0.0185501\pi$
$702$	−27.1566	+	15.6866i	−1.02496	+	0.592052i
$703$	5.84482	+	1.56612i	0.220442	+	0.0590672i
$704$	1.06334			0.0400761
$705$	1.00477	−	5.97044i	0.0378420	−	0.224860i
$706$	−1.27601	−	2.21011i	−0.0480232	−	0.0831786i
$707$	9.24129	+	12.8810i	0.347555	+	0.484441i
$708$	−13.8195	−	2.43574i	−0.519369	−	0.0915408i
$709$	20.0690	−	11.5868i	0.753708	−	0.435153i	−0.0733244	−	0.997308i	$-0.523361\pi$
$709$	20.0690	−	11.5868i	0.753708	−	0.435153i	0.827032	+	0.562155i	$0.190028\pi$
$710$	−2.46260	+	1.44729i	−0.0924198	+	0.0543157i
$711$	27.9218	+	33.2663i	1.04715	+	1.24758i
$712$	7.49251	−	2.00761i	0.280794	−	0.0752385i
$713$	66.0275	−	17.6920i	2.47275	−	0.662571i
$714$	5.44866	+	3.72226i	0.203911	+	0.139302i
$715$	12.3722	−	7.27123i	0.462694	−	0.271929i
$716$		−	16.7316i		−	0.625291i
$717$	−1.21496	+	6.89324i	−0.0453735	+	0.257433i
$718$	11.8410	−	11.8410i	0.441904	−	0.441904i
$719$	−7.72927	+	13.3875i	−0.288253	+	0.499269i	−0.973393	−	0.229143i	$-0.926408\pi$
$719$	−7.72927	+	13.3875i	−0.288253	+	0.499269i	0.685140	+	0.728412i	$0.259741\pi$
$720$	6.68707	+	0.532017i	0.249213	+	0.0198271i
$721$	7.75344	−	47.1253i	0.288753	−	1.75504i
$722$	3.55004	+	13.2489i	0.132119	+	0.493075i
$723$	−21.0165	−	17.6324i	−0.781611	−	0.655755i
$724$	−14.5607	−	8.40664i	−0.541145	−	0.312430i
$725$	11.9106	+	6.63312i	0.442348	+	0.246348i
$726$	−9.80579	−	14.0020i	−0.363927	−	0.519663i
$727$	−30.9185	+	8.28458i	−1.14670	+	0.307258i	−0.781643	−	0.623726i	$-0.785618\pi$
$727$	−30.9185	+	8.28458i	−1.14670	+	0.307258i	−0.365060	+	0.930984i	$0.618952\pi$
$728$	−14.5488	−	6.58222i	−0.539216	−	0.243953i
$729$	−13.5100	−	23.3769i	−0.500369	−	0.865813i
$730$	6.05571	+	21.9208i	0.224132	+	0.811324i
$731$		−	2.85918i		−	0.105751i
$732$	1.69606	−	2.02157i	0.0626880	−	0.0747195i
$733$	24.3933	−	24.3933i	0.900988	−	0.900988i	−0.0945338	−	0.995522i	$-0.530136\pi$
$733$	24.3933	−	24.3933i	0.900988	−	0.900988i	0.995522	+	0.0945338i	$0.0301361\pi$
$734$	3.38422	+	5.86164i	0.124914	+	0.216357i
$735$	−26.3904	−	6.20877i	−0.973423	−	0.229014i
$736$	−4.44935	+	7.70650i	−0.164005	+	0.284065i
$737$	4.06877	+	15.1848i	0.149875	+	0.559341i
$738$	0.849548	+	1.82119i	0.0312723	+	0.0670388i
$739$	12.8962	−	7.44565i	0.474396	−	0.273893i	−0.243682	−	0.969855i	$-0.578355\pi$
$739$	12.8962	−	7.44565i	0.474396	−	0.273893i	0.718078	+	0.695962i	$0.245022\pi$
$740$	2.98249	+	5.07479i	0.109639	+	0.186553i
$741$	2.09601	+	23.9380i	0.0769989	+	0.879383i
$742$	−1.79708	−	18.1424i	−0.0659729	−	0.666028i
$743$	−5.54455	+	20.6925i	−0.203410	+	0.759135i	0.786519	+	0.617566i	$0.211881\pi$
$743$	−5.54455	+	20.6925i	−0.203410	+	0.759135i	−0.989928	+	0.141569i	$0.954785\pi$
$744$	12.0588	+	5.62208i	0.442098	+	0.206116i
$745$	−25.1514	−	24.7654i	−0.921477	−	0.907335i
$746$	−12.8156	+	7.39908i	−0.469212	+	0.270900i
$747$	−12.0789	−	25.8936i	−0.441943	−	0.947399i
$748$	1.08270	−	1.08270i	0.0395873	−	0.0395873i
$749$	−5.04682	−	4.13711i	−0.184407	−	0.151167i
$750$	−19.1438	−	2.91805i	−0.699033	−	0.106552i
$751$	−10.0182			−0.365568			−0.182784	−	0.983153i	$-0.558511\pi$
$751$	−10.0182			−0.365568			−0.182784	+	0.983153i	$0.558511\pi$
$752$	0.404596	+	1.50997i	0.0147541	+	0.0550630i
$753$	−11.7434	+	13.9973i	−0.427955	+	0.510090i
$754$	14.2518	−	8.22829i	0.519020	−	0.299657i
$755$	−29.1641	−	28.7165i	−1.06139	−	1.04510i
$756$	5.66414	−	12.5267i	0.206003	−	0.455591i
$757$	32.2032	+	32.2032i	1.17044	+	1.17044i	0.982104	+	0.188340i	$0.0603107\pi$
$757$	32.2032	+	32.2032i	1.17044	+	1.17044i	0.188340	+	0.982104i	$0.439689\pi$
$758$	−4.76188	+	17.7716i	−0.172959	+	0.645493i
$759$	−16.3268	+	1.42957i	−0.592624	+	0.0518902i
$760$	2.53545	−	4.47101i	0.0919703	−	0.162181i
$761$			11.8367i			0.429079i	0.976715	+	0.214539i	$0.0688250\pi$
$761$			11.8367i			0.429079i	−0.976715	+	0.214539i	$0.931175\pi$
$762$	5.07571	−	28.7977i	0.183874	−	1.04323i
$763$	17.9992	−	39.7841i	0.651616	−	1.44028i
$764$	−22.7609			−0.823462
$765$	7.35052	−	6.26711i	0.265759	−	0.226588i
$766$	−8.30544	−	14.3854i	−0.300088	−	0.519767i
$767$	34.5762	−	34.5762i	1.24847	−	1.24847i
$768$	−1.62755	+	0.592512i	−0.0587293	+	0.0213804i
$769$	−1.77019	+	1.02202i	−0.0638346	+	0.0368549i	−0.531578	−	0.847010i	$-0.678401\pi$
$769$	−1.77019	+	1.02202i	−0.0638346	+	0.0368549i	0.467743	+	0.883865i	$0.345067\pi$
$770$	−2.54866	+	5.75138i	−0.0918474	+	0.207265i
$771$	−7.57038	+	0.662864i	−0.272641	+	0.0238725i
$772$	−0.398743	+	1.48813i	−0.0143511	+	0.0535590i
$773$	10.2247	−	38.1591i	0.367757	−	1.37249i	−0.495887	−	0.868387i	$-0.665157\pi$
$773$	10.2247	−	38.1591i	0.367757	−	1.37249i	0.863644	−	0.504102i	$-0.168176\pi$
$774$	−5.86615	+	1.03522i	−0.210855	+	0.0372102i
$775$	−33.5555	−	18.6874i	−1.20535	−	0.671272i
$776$	−0.410165	−	0.236809i	−0.0147241	−	0.00850095i
$777$	11.8551	−	2.23170i	0.425301	−	0.0800616i
$778$	19.7138	+	5.28229i	0.706772	+	0.189379i
$779$	1.53977			0.0551678
$780$	−14.8853	+	18.0234i	−0.532980	+	0.645342i
$781$	1.35833			0.0486049
$782$	3.31645	+	12.3772i	0.118596	+	0.442606i
$783$	7.08655	+	12.2682i	0.253253	+	0.438431i
$784$	6.86397	−	1.37328i	0.245142	−	0.0490459i
$785$	3.69464	+	2.09518i	0.131867	+	0.0747801i
$786$	−8.39294	+	5.87769i	−0.299366	+	0.209650i
$787$	−9.54651	+	2.55798i	−0.340296	+	0.0911821i	−0.424920	−	0.905231i	$-0.639698\pi$
$787$	−9.54651	+	2.55798i	−0.340296	+	0.0911821i	0.0846239	+	0.996413i	$0.473031\pi$
$788$	−5.17486	+	1.38660i	−0.184347	+	0.0493956i
$789$	−0.424839	−	4.85197i	−0.0151247	−	0.172735i
$790$	28.1591	+	15.9686i	1.00185	+	0.568137i
$791$	7.12586	+	18.9010i	0.253367	+	0.672042i
$792$	−2.61337	−	1.82935i	−0.0928619	−	0.0650030i
$793$	2.37992	+	8.88197i	0.0845133	+	0.315408i
$794$	−0.763545			−0.0270972
$795$	−26.3176	−	4.42904i	−0.933391	−	0.157082i
$796$	20.4876			0.726165
$797$	−33.4328	−	8.95828i	−1.18425	−	0.317319i	−0.387638	−	0.921812i	$-0.626709\pi$
$797$	−33.4328	−	8.95828i	−1.18425	−	0.317319i	−0.796610	+	0.604493i	$0.793376\pi$
$798$	−6.86353	−	7.99058i	−0.242966	−	0.282864i
$799$	1.94942	+	1.12550i	0.0689657	+	0.0398173i
$800$	4.80904	−	1.36863i	0.170025	−	0.0483884i
$801$	−21.8682	−	7.95586i	−0.772675	−	0.281107i
$802$	−6.43956	+	24.0328i	−0.227389	+	0.848627i
$803$	2.79904	−	10.4461i	0.0987758	−	0.368636i
$804$	−14.6890	−	20.9748i	−0.518040	−	0.739726i
$805$	−31.0185	−	42.5370i	−1.09326	−	1.49923i
$806$	−40.1515	+	23.1815i	−1.41428	+	0.816532i
$807$	0.492048	−	2.79170i	0.0173209	−	0.0982725i
$808$	−4.23694	+	4.23694i	−0.149055	+	0.149055i
$809$	24.2689	+	42.0350i	0.853249	+	1.47787i	0.878260	+	0.478183i	$0.158705\pi$
$809$	24.2689	+	42.0350i	0.853249	+	1.47787i	−0.0250112	+	0.999687i	$0.507962\pi$
$810$	−15.5196	−	12.8119i	−0.545301	−	0.450163i
$811$	−23.1667			−0.813491			−0.406746	−	0.913541i	$-0.633336\pi$
$811$	−23.1667			−0.813491			−0.406746	+	0.913541i	$0.633336\pi$
$812$	−2.97358	+	6.57257i	−0.104352	+	0.230652i
$813$	−5.91396	+	2.15298i	−0.207412	+	0.0755083i
$814$		−	2.79918i		−	0.0981111i
$815$	−7.79411	+	13.7441i	−0.273016	+	0.481437i
$816$	−1.05389	+	2.26048i	−0.0368934	+	0.0791327i
$817$	−1.18129	+	4.40863i	−0.0413281	+	0.154239i
$818$	11.3231	+	11.3231i	0.395903	+	0.395903i
$819$	24.4328	+	41.2067i	0.853750	+	1.43988i
$820$	1.06731	+	1.05092i	0.0372719	+	0.0366999i
$821$	−4.38438	+	2.53133i	−0.153016	+	0.0883439i	−0.574553	−	0.818467i	$-0.694824\pi$
$821$	−4.38438	+	2.53133i	−0.153016	+	0.0883439i	0.421537	+	0.906811i	$0.361491\pi$
$822$	−7.23772	−	1.27568i	−0.252445	−	0.0444943i
$823$	7.25837	+	27.0886i	0.253011	+	0.944249i	0.969186	+	0.246329i	$0.0792244\pi$
$823$	7.25837	+	27.0886i	0.253011	+	0.944249i	−0.716175	+	0.697920i	$0.754109\pi$
$824$	18.0512			0.628842
$825$	7.14544	+	5.80898i	0.248772	+	0.202243i
$826$	−3.47988	+	21.1507i	−0.121081	+	0.735926i
$827$	30.1951	−	30.1951i	1.04999	−	1.04999i	0.0513028	−	0.998683i	$-0.483663\pi$
$827$	30.1951	−	30.1951i	1.04999	−	1.04999i	0.998683	−	0.0513028i	$-0.0163374\pi$
$828$	24.1933	−	11.2857i	0.840774	−	0.392205i
$829$	−17.9310	+	10.3525i	−0.622770	+	0.359556i	−0.777947	−	0.628330i	$-0.783739\pi$
$829$	−17.9310	+	10.3525i	−0.622770	+	0.359556i	0.155177	+	0.987887i	$0.450405\pi$
$830$	−15.1749	−	14.9421i	−0.526730	−	0.518646i
$831$	−0.173759	−	1.98445i	−0.00602763	−	0.0688399i
$832$	1.56211	−	5.82989i	0.0541565	−	0.202115i
$833$	5.59065	−	8.38722i	0.193704	−	0.290600i
$834$	−30.0289	−	14.0001i	−1.03982	−	0.484785i
$835$	3.12613	+	5.31919i	0.108184	+	0.184078i
$836$	−2.11675	+	1.22211i	−0.0732095	+	0.0422675i
$837$	−19.9649	−	34.5632i	−0.690087	−	1.19468i
$838$	−4.33881	−	16.1927i	−0.149882	−	0.559366i
$839$	26.0191	−	45.0663i	0.898278	−	1.55586i	0.0685836	−	0.997645i	$-0.478152\pi$
$839$	26.0191	−	45.0663i	0.898278	−	1.55586i	0.829694	−	0.558218i	$-0.188515\pi$
$840$	0.696226	−	10.2233i	0.0240221	−	0.352736i
$841$	10.7828	+	18.6764i	0.371821	+	0.644012i
$842$	−7.40662	+	7.40662i	−0.255249	+	0.255249i
$843$	−15.3209	−	42.0846i	−0.527681	−	1.44947i
$844$			18.9142i			0.651053i
$845$	−13.9494	−	50.4948i	−0.479874	−	1.73707i
$846$	1.60335	−	4.40712i	0.0551244	−	0.151520i
$847$	−21.2164	+	15.2213i	−0.729003	+	0.523011i
$848$	6.65595	−	1.78346i	0.228566	−	0.0612441i
$849$	−5.43491	+	11.6574i	−0.186525	+	0.400079i
$850$	3.50304	−	6.29014i	0.120153	−	0.215750i
$851$	20.2869	+	11.7127i	0.695427	+	0.401505i
$852$	−2.07907	+	0.756888i	−0.0712279	+	0.0259306i
$853$	−3.02845	−	11.3023i	−0.103692	−	0.386984i	0.894501	−	0.447065i	$-0.147531\pi$
$853$	−3.02845	−	11.3023i	−0.103692	−	0.386984i	−0.998194	+	0.0600809i	$0.980864\pi$
$854$	−3.11732	−	2.55541i	−0.106673	−	0.0874445i
$855$	−13.9232	+	6.62647i	−0.476164	+	0.226621i
$856$	1.23326	−	2.13607i	0.0421520	−	0.0730093i
$857$	40.4401	−	40.4401i	1.38141	−	1.38141i	0.539285	−	0.842124i	$-0.318695\pi$
$857$	40.4401	−	40.4401i	1.38141	−	1.38141i	0.842124	−	0.539285i	$-0.181305\pi$
$858$	10.4454	−	3.80264i	0.356598	−	0.129820i
$859$		−	9.94900i		−	0.339455i	−0.985491	−	0.169728i	$-0.945711\pi$
$859$		−	9.94900i		−	0.339455i	0.985491	−	0.169728i	$-0.0542888\pi$
$860$	−3.82782	+	2.24963i	−0.130527	+	0.0767119i
$861$	2.76694	−	1.32932i	0.0942971	−	0.0453031i
$862$	11.0776	−	2.96825i	0.377306	−	0.101099i
$863$	20.0072	−	5.36091i	0.681053	−	0.182488i	0.0983245	−	0.995154i	$-0.468652\pi$
$863$	20.0072	−	5.36091i	0.681053	−	0.182488i	0.582729	+	0.812667i	$0.301985\pi$
$864$	5.01938	+	1.34380i	0.170763	+	0.0457168i
$865$	21.9575	−	12.9046i	0.746579	−	0.438770i
$866$	20.6026	−	11.8949i	0.700104	−	0.404205i
$867$	−8.84414	−	24.2937i	−0.300363	−	0.825057i
$868$	8.37743	−	18.5168i	0.284348	−	0.628502i
$869$	−7.69702	−	13.3316i	−0.261103	−	0.452244i
$870$	8.14224	+	6.72458i	0.276048	+	0.227985i
$871$	89.2302			3.02345
$872$	15.9419	+	4.27163i	0.539862	+	0.144656i
$873$	0.600662	+	1.28765i	0.0203293	+	0.0435802i
$874$		−	20.4548i		−	0.691894i
$875$	−4.12390	+	29.2915i	−0.139413	+	0.990234i
$876$	1.53656	+	17.5486i	0.0519155	+	0.592913i
$877$	28.7133	+	28.7133i	0.969579	+	0.969579i	0.999551	−	0.0299722i	$-0.00954187\pi$
$877$	28.7133	+	28.7133i	0.969579	+	0.969579i	−0.0299722	+	0.999551i	$0.509542\pi$
$878$	34.9151	−	9.35548i	1.17833	−	0.315732i
$879$	37.4615	−	26.2348i	1.26354	−	0.884877i
$880$	−2.30137	−	0.597615i	−0.0775791	−	0.0201456i
$881$		−	42.0460i		−	1.41657i	−0.705928	−	0.708284i	$-0.749470\pi$
$881$		−	42.0460i		−	1.41657i	0.705928	−	0.708284i	$-0.250530\pi$
$882$	−19.2322	−	8.43352i	−0.647580	−	0.283971i
$883$	−13.3727	+	13.3727i	−0.450026	+	0.450026i	−0.895363	−	0.445337i	$-0.853084\pi$
$883$	−13.3727	+	13.3727i	−0.450026	+	0.450026i	0.445337	+	0.895363i	$0.353084\pi$
$884$	−4.34547	−	7.52658i	−0.146154	−	0.253146i
$885$	28.5405	+	13.0385i	0.959377	+	0.438283i
$886$	−19.9890	+	34.6219i	−0.671543	+	1.16315i
$887$	−18.7066	+	18.7066i	−0.628106	+	0.628106i	−0.947591	−	0.319486i	$-0.896490\pi$
$887$	−18.7066	+	18.7066i	−0.628106	+	0.628106i	0.319486	+	0.947591i	$0.396490\pi$
$888$	1.55975	+	4.28444i	0.0523419	+	0.143776i
$889$	−44.0748	−	7.25154i	−1.47822	−	0.243209i
$890$	−17.3443	+	0.134122i	−0.581381	+	0.00449577i
$891$	3.27570	+	8.99197i	0.109740	+	0.301242i
$892$	−1.91332	+	7.14063i	−0.0640629	+	0.239086i
$893$	−2.54085	−	2.54085i	−0.0850263	−	0.0850263i
$894$	−15.6840	−	22.3957i	−0.524551	−	0.749023i
$895$	−9.40348	+	36.2121i	−0.314324	+	1.21044i
$896$	0.933346	+	2.47565i	0.0311809	+	0.0827058i
$897$	−16.1473	+	91.6137i	−0.539141	+	3.05889i
$898$	−19.7407	−	5.28952i	−0.658757	−	0.176513i
$899$	10.4724	+	18.1388i	0.349275	+	0.604962i
$900$	−14.1737	−	4.90969i	−0.472458	−	0.163656i
$901$	4.96120	−	8.59304i	0.165281	−	0.286276i
$902$	−0.184354	−	0.688020i	−0.00613833	−	0.0229086i
$903$	1.68332	+	8.94210i	0.0560175	+	0.297574i
$904$	−6.61189	+	3.81738i	−0.219908	+	0.126964i
$905$	26.7889	+	26.3778i	0.890493	+	0.876826i
$906$	−18.1862	−	25.9687i	−0.604196	−	0.862751i
$907$	4.38403	+	4.38403i	0.145569	+	0.145569i	0.776135	−	0.630566i	$-0.217177\pi$
$907$	4.38403	+	4.38403i	0.145569	+	0.145569i	−0.630566	+	0.776135i	$0.717177\pi$
$908$	−23.1889	+	6.21344i	−0.769550	+	0.206200i
$909$	17.7023	−	3.12398i	0.587147	−	0.103616i
$910$	27.7885	+	22.4225i	0.921181	+	0.743300i
$911$	2.61631	+	1.51052i	0.0866821	+	0.0500459i	0.542714	−	0.839917i	$-0.317397\pi$
$911$	2.61631	+	1.51052i	0.0866821	+	0.0500459i	−0.456032	+	0.889963i	$0.650730\pi$
$912$	2.55894	−	3.05006i	0.0847349	−	0.100998i
$913$	2.62115	+	9.78228i	0.0867475	+	0.323746i
$914$	−8.77051	+	15.1910i	−0.290103	+	0.502473i
$915$	−4.80691	+	3.42205i	−0.158912	+	0.113129i
$916$	1.75299	−	3.03627i	0.0579205	−	0.100321i
$917$	9.12381	+	12.7173i	0.301295	+	0.419962i
$918$	6.47902	−	3.74251i	0.213840	−	0.123521i
$919$	−20.6682	−	11.9328i	−0.681781	−	0.393627i	0.118745	−	0.992925i	$-0.462113\pi$
$919$	−20.6682	−	11.9328i	−0.681781	−	0.393627i	−0.800526	+	0.599298i	$0.795446\pi$
$920$	13.9609	−	14.1785i	0.460276	−	0.467450i
$921$	1.00603	+	11.4896i	0.0331498	+	0.378595i
$922$	23.1670	+	23.1670i	0.762964	+	0.762964i
$923$	1.99548	−	7.44723i	0.0656820	−	0.245129i
$924$	−2.74870	+	4.02356i	−0.0904257	+	0.132366i
$925$	−3.60284	−	12.6595i	−0.118461	−	0.416242i
$926$	22.6310	+	13.0660i	0.743702	+	0.429376i
$927$	−44.3643	−	31.0549i	−1.45712	−	1.01998i
$928$	−2.63370	−	0.705699i	−0.0864555	−	0.0231657i
$929$	18.3298	+	31.7481i	0.601380	+	1.04162i	0.992612	+	0.121329i	$0.0387156\pi$
$929$	18.3298	+	31.7481i	0.601380	+	1.04162i	−0.391232	+	0.920292i	$0.627951\pi$
$930$	−22.9391	−	18.9451i	−0.752201	−	0.621234i
$931$	−12.0856	+	10.6226i	−0.396088	+	0.348142i
$932$	12.2425	+	3.28038i	0.401018	+	0.107452i
$933$	−17.2609	−	47.4135i	−0.565097	−	1.55225i
$934$		−	12.2195i		−	0.399835i
$935$	−2.95176	+	1.73477i	−0.0965329	+	0.0567331i
$936$	−13.8688	+	11.6407i	−0.453317	+	0.380488i
$937$	21.8202	+	21.8202i	0.712836	+	0.712836i	0.967128	−	0.254292i	$-0.0818424\pi$
$937$	21.8202	+	21.8202i	0.712836	+	0.712836i	−0.254292	+	0.967128i	$0.581842\pi$
$938$	−31.7819	+	22.8014i	−1.03771	+	0.744491i
$939$	−9.98980	−	14.2648i	−0.326005	−	0.465513i
$940$	−0.0270297	−	3.49540i	−0.000881611	−	0.114007i
$941$	39.5710	+	22.8463i	1.28998	+	0.744768i	0.978650	−	0.205535i	$-0.0658933\pi$
$941$	39.5710	+	22.8463i	1.28998	+	0.744768i	0.311327	+	0.950303i	$0.399227\pi$
$942$	2.52043	+	2.11459i	0.0821202	+	0.0688971i
$943$	5.75780	+	1.54280i	0.187500	+	0.0502404i
$944$	−8.10168			−0.263687
$945$	−19.2990	+	23.9280i	−0.627798	+	0.778377i
$946$	2.11136			0.0686464
$947$	32.1900	+	8.62529i	1.04604	+	0.280284i	0.740612	−	0.671932i	$-0.234536\pi$
$947$	32.1900	+	8.62529i	1.04604	+	0.280284i	0.305423	+	0.952217i	$0.401202\pi$
$948$	19.2097	+	16.1166i	0.623903	+	0.523442i
$949$	−53.1604	−	30.6921i	−1.72566	−	0.996309i
$950$	−8.00022	+	8.25158i	−0.259561	+	0.267717i
$951$	−19.3251	−	27.5949i	−0.626658	−	0.894825i
$952$	3.47106	+	1.57039i	0.112498	+	0.0508965i
$953$	−38.0214	−	38.0214i	−1.23164	−	1.23164i	−0.963336	−	0.268300i	$-0.913538\pi$
$953$	−38.0214	−	38.0214i	−1.23164	−	1.23164i	−0.268300	−	0.963336i	$-0.586462\pi$
$954$	−19.4265	−	7.06756i	−0.628957	−	0.228821i
$955$	49.2612	+	12.7921i	1.59406	+	0.413941i
$956$			4.04116i			0.130700i
$957$	−1.71787	−	4.71878i	−0.0555310	−	0.152536i
$958$	24.0602	+	6.44691i	0.777350	+	0.208290i
$959$	−1.82253	+	11.0773i	−0.0588524	+	0.357704i
$960$	3.85549	−	0.367651i	0.124436	−	0.0118659i
$961$	−14.0039	−	24.2554i	−0.451738	−	0.782433i
$962$	−15.3468	−	4.11218i	−0.494802	−	0.132582i
$963$	−6.70583	+	3.12814i	−0.216092	+	0.100803i
$964$	−13.7167	−	7.91935i	−0.441785	−	0.255065i
$965$	1.69935	−	2.99664i	0.0547040	−	0.0964652i
$966$	−17.6591	−	36.7570i	−0.568174	−	1.18264i
$967$	−5.54768	+	20.7042i	−0.178401	+	0.665803i	0.817546	+	0.575864i	$0.195334\pi$
$967$	−5.54768	+	20.7042i	−0.178401	+	0.665803i	−0.995947	+	0.0899397i	$0.971333\pi$
$968$	−6.97866	−	6.97866i	−0.224303	−	0.224303i
$969$	−0.500066	−	5.71112i	−0.0160644	−	0.183468i
$970$	0.754624	+	0.743043i	0.0242295	+	0.0238577i
$971$	8.79284	+	5.07655i	0.282176	+	0.162914i	0.634408	−	0.772998i	$-0.281244\pi$
$971$	8.79284	+	5.07655i	0.282176	+	0.162914i	−0.352232	+	0.935913i	$0.614577\pi$
$972$	−10.0243	−	11.9379i	−0.321530	−	0.382908i
$973$	−20.8615	+	46.1106i	−0.668789	+	1.47824i
$974$	7.14226	−	12.3708i	0.228853	−	0.396385i
$975$	42.3456	−	30.6420i	1.35614	−	0.981331i
$976$	0.761761	−	1.31941i	0.0243834	−	0.0422333i
$977$	13.0476	+	48.6943i	0.417430	+	1.55787i	0.779919	+	0.625881i	$0.215260\pi$
$977$	13.0476	+	48.6943i	0.417430	+	1.55787i	−0.362489	+	0.931988i	$0.618073\pi$
$978$	−7.86633	+	9.37607i	−0.251537	+	0.299814i
$979$	7.14308	+	4.12406i	0.228294	+	0.131806i
$980$	−15.6274	−	0.885495i	−0.499199	−	0.0282861i
$981$	−31.8317	−	37.9246i	−1.01631	−	1.21084i
$982$	19.5560	−	5.24001i	0.624056	−	0.167215i
$983$	−11.9386	−	11.9386i	−0.380782	−	0.380782i	0.490602	−	0.871384i	$-0.336777\pi$
$983$	−11.9386	−	11.9386i	−0.380782	−	0.380782i	−0.871384	+	0.490602i	$0.836777\pi$
$984$	0.665552	+	0.950363i	0.0212170	+	0.0302965i
$985$	11.9792	−	0.0926340i	0.381688	−	0.00295156i
$986$	−3.40020	+	1.96310i	−0.108284	+	0.0625180i
$987$	−6.75945	−	2.37229i	−0.215156	−	0.0755110i
$988$	3.59072	+	13.4007i	0.114236	+	0.426334i
$989$	−8.83463	+	15.3020i	−0.280925	+	0.486576i
$990$	4.62795	+	5.42799i	0.147086	+	0.172513i
$991$	−14.6352	−	25.3489i	−0.464902	−	0.805234i	0.534295	−	0.845298i	$-0.320577\pi$
$991$	−14.6352	−	25.3489i	−0.464902	−	0.805234i	−0.999197	+	0.0400639i	$0.987244\pi$
$992$	7.41990	+	1.98816i	0.235582	+	0.0631241i
$993$	−5.68169	+	32.2359i	−0.180303	+	1.02297i
$994$	1.19228	+	3.16246i	0.0378167	+	0.100307i
$995$	−44.3411	−	11.5144i	−1.40571	−	0.365032i
$996$	−9.46282	−	13.5123i	−0.299841	−	0.428153i
$997$	−33.2465	−	33.2465i	−1.05293	−	1.05293i	−0.998519	−	0.0544076i	$-0.982673\pi$
$997$	−33.2465	−	33.2465i	−1.05293	−	1.05293i	−0.0544076	−	0.998519i	$-0.517327\pi$
$998$	−5.57004	+	20.7877i	−0.176316	+	0.658022i
$999$	3.53746	−	13.2132i	0.111920	−	0.418049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.317.19	✓	192
5.3	odd	4	inner	630.2.bt.a.443.7	yes	192
7.4	even	3		630.2.cd.a.137.38	yes	192
9.5	odd	6		630.2.cd.a.527.23	yes	192
35.18	odd	12		630.2.cd.a.263.23	yes	192
45.23	even	12		630.2.cd.a.23.38	yes	192
63.32	odd	6	inner	630.2.bt.a.347.7	yes	192
315.158	even	12	inner	630.2.bt.a.473.19	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.19	✓	192	1.1	even	1	trivial
630.2.bt.a.347.7	yes	192	63.32	odd	6	inner
630.2.bt.a.443.7	yes	192	5.3	odd	4	inner
630.2.bt.a.473.19	yes	192	315.158	even	12	inner
630.2.cd.a.23.38	yes	192	45.23	even	12
630.2.cd.a.137.38	yes	192	7.4	even	3
630.2.cd.a.263.23	yes	192	35.18	odd	12
630.2.cd.a.527.23	yes	192	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.32691 + 1.11325i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59332 - 1.56887i) q^{5} +(-0.993564 - 1.41874i) q^{6} +(-2.14973 + 1.54229i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.521364 + 2.95435i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.32691 + 1.11325i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.59332 - 1.56887i) q^{5} +(-0.993564 - 1.41874i) q^{6} +(-2.14973 + 1.54229i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.521364 + 2.95435i) q^{9} +(1.13297 + 1.92779i) q^{10} -1.06334i q^{11} +(0.592512 + 1.62755i) q^{12} +(-5.82989 - 1.56211i) q^{13} +(2.47565 - 0.933346i) q^{14} +(-0.367651 - 3.85549i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.39089 + 0.372689i) q^{17} +(0.261043 - 2.98862i) q^{18} +(-1.99067 - 1.14931i) q^{19} +(-0.595421 - 2.15534i) q^{20} +(-4.56944 - 0.346706i) q^{21} +(-0.275212 + 1.02711i) q^{22} +(-6.29233 - 6.29233i) q^{23} +(-0.151081 - 1.72545i) q^{24} +(0.0773246 + 4.99940i) q^{25} +(5.22693 + 3.01777i) q^{26} +(-2.59712 + 4.50055i) q^{27} +(-2.63287 + 0.260796i) q^{28} +(1.36331 - 2.36131i) q^{29} +(-0.642752 + 3.81928i) q^{30} +(-3.84082 + 6.65250i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(1.18376 - 1.41095i) q^{33} +(-1.24704 - 0.719980i) q^{34} +(5.84485 + 0.915280i) q^{35} +(-1.02566 + 2.81922i) q^{36} +(-2.54274 + 0.681326i) q^{37} +(1.62537 + 1.62537i) q^{38} +(-5.99670 - 8.56288i) q^{39} +(0.0172908 + 2.23600i) q^{40} +(-0.580119 + 0.334932i) q^{41} +(4.32401 + 1.51755i) q^{42} +(-0.513911 - 1.91794i) q^{43} +(0.531669 - 0.920878i) q^{44} +(3.80428 - 5.52517i) q^{45} +(4.44935 + 7.70650i) q^{46} +(1.50997 + 0.404596i) q^{47} +(-0.300646 + 1.70576i) q^{48} +(2.24269 - 6.63101i) q^{49} +(1.21925 - 4.84906i) q^{50} +(1.43069 + 2.04293i) q^{51} +(-4.26777 - 4.26777i) q^{52} +(1.78346 - 6.65595i) q^{53} +(3.67345 - 3.67502i) q^{54} +(-1.66823 + 1.69424i) q^{55} +(2.61065 + 0.429526i) q^{56} +(-1.36196 - 3.74114i) q^{57} +(-1.92800 + 1.92800i) q^{58} +(-4.05084 + 7.01626i) q^{59} +(1.60935 - 3.52278i) q^{60} +(-0.761761 - 1.31941i) q^{61} +(5.43175 - 5.43175i) q^{62} +(-5.67725 - 5.54696i) q^{63} +1.00000i q^{64} +(6.83812 + 11.6353i) q^{65} +(-1.50860 + 1.05649i) q^{66} +(-14.2804 + 3.82641i) q^{67} +(1.01821 + 1.01821i) q^{68} +(-1.34442 - 15.3542i) q^{69} +(-5.40880 - 2.39685i) q^{70} +1.27742i q^{71} +(1.72038 - 2.45770i) q^{72} +(9.82391 + 2.63231i) q^{73} +2.63244 q^{74} +(-5.46297 + 6.71982i) q^{75} +(-1.14931 - 1.99067i) q^{76} +(1.63998 + 2.28589i) q^{77} +(3.57613 + 9.82317i) q^{78} +(12.5375 - 7.23854i) q^{79} +(0.562018 - 2.16429i) q^{80} +(-8.45636 + 3.08058i) q^{81} +(0.647038 - 0.173373i) q^{82} +(-9.19959 + 2.46502i) q^{83} +(-3.78390 - 2.58498i) q^{84} +(-1.63144 - 2.77594i) q^{85} +1.98560i q^{86} +(4.43770 - 1.61555i) q^{87} +(-0.751894 + 0.751894i) q^{88} +(-3.87841 + 6.71760i) q^{89} +(-5.10467 + 4.35228i) q^{90} +(14.9419 - 5.63325i) q^{91} +(-2.30315 - 8.59548i) q^{92} +(-12.5023 + 4.55147i) q^{93} +(-1.35380 - 0.781619i) q^{94} +(1.36865 + 4.95431i) q^{95} +(0.731885 - 1.56982i) q^{96} +(0.457480 - 0.122581i) q^{97} +(-3.88250 + 5.82462i) q^{98} +(3.14147 - 0.554386i) 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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