LMFDB - Embedded newform 442.2.m.b.373.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [442,2,Mod(237,442)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(442, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("442.237");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 442 = 2 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	442.m (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52938776934$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.6
Character	$\chi$	$=$	442.373
Dual form			442.2.m.b.237.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.340479 - 0.196576i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.77611i q^{5} +(-0.340479 + 0.196576i) q^{6} +(-2.18274 + 1.26021i) q^{7} -1.00000 q^{8} +(-1.42272 - 2.46422i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.340479 - 0.196576i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.77611i q^{5} +(-0.340479 + 0.196576i) q^{6} +(-2.18274 + 1.26021i) q^{7} -1.00000 q^{8} +(-1.42272 - 2.46422i) q^{9} +(-1.53816 - 0.888055i) q^{10} +(-2.98453 - 1.72312i) q^{11} +0.393151i q^{12} +(2.99263 + 2.01101i) q^{13} +2.52041i q^{14} +(-0.349140 + 0.604728i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.52068 + 3.26285i) q^{17} -2.84543 q^{18} +(-3.66553 - 6.34888i) q^{19} +(-1.53816 + 0.888055i) q^{20} +0.990903 q^{21} +(-2.98453 + 1.72312i) q^{22} +(-0.147983 - 0.0854382i) q^{23} +(0.340479 + 0.196576i) q^{24} +1.84543 q^{25} +(3.23790 - 1.58619i) q^{26} +2.29814i q^{27} +(2.18274 + 1.26021i) q^{28} +(-3.57292 - 2.06282i) q^{29} +(0.349140 + 0.604728i) q^{30} -9.12805i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.677447 + 1.17337i) q^{33} +(1.56537 + 3.81440i) q^{34} +(2.23827 + 3.87679i) q^{35} +(-1.42272 + 2.46422i) q^{36} +(9.10280 + 5.25550i) q^{37} -7.33106 q^{38} +(-0.623613 - 1.27298i) q^{39} +1.77611i q^{40} +(-0.111611 - 0.0644385i) q^{41} +(0.495452 - 0.858147i) q^{42} +(-2.65978 - 4.60687i) q^{43} +3.44624i q^{44} +(-4.37672 + 2.52690i) q^{45} +(-0.147983 + 0.0854382i) q^{46} -2.05317 q^{47} +(0.340479 - 0.196576i) q^{48} +(-0.323759 + 0.560767i) q^{49} +(0.922716 - 1.59819i) q^{50} +(1.49963 - 0.615426i) q^{51} +(0.245269 - 3.59720i) q^{52} -4.26638 q^{53} +(1.99025 + 1.14907i) q^{54} +(-3.06045 + 5.30086i) q^{55} +(2.18274 - 1.26021i) q^{56} +2.88221i q^{57} +(-3.57292 + 2.06282i) q^{58} +(0.0723702 + 0.125349i) q^{59} +0.698280 q^{60} +(13.4493 - 7.76493i) q^{61} +(-7.90512 - 4.56403i) q^{62} +(6.21084 + 3.58583i) q^{63} +1.00000 q^{64} +(3.57177 - 5.31524i) q^{65} +1.35489 q^{66} +(4.08704 - 7.07896i) q^{67} +(4.08605 + 0.551551i) q^{68} +(0.0335901 + 0.0581798i) q^{69} +4.47653 q^{70} +(4.14584 - 2.39360i) q^{71} +(1.42272 + 2.46422i) q^{72} -9.40225i q^{73} +(9.10280 - 5.25550i) q^{74} +(-0.628331 - 0.362767i) q^{75} +(-3.66553 + 6.34888i) q^{76} +8.68595 q^{77} +(-1.41424 - 0.0964278i) q^{78} +2.76824i q^{79} +(1.53816 + 0.888055i) q^{80} +(-3.81639 + 6.61018i) q^{81} +(-0.111611 + 0.0644385i) q^{82} +6.67445 q^{83} +(-0.495452 - 0.858147i) q^{84} +(5.79517 + 4.47701i) q^{85} -5.31955 q^{86} +(0.811001 + 1.40470i) q^{87} +(2.98453 + 1.72312i) q^{88} +(-7.64870 + 13.2479i) q^{89} +5.05380i q^{90} +(-9.06643 - 0.618179i) q^{91} +0.170876i q^{92} +(-1.79435 + 3.10791i) q^{93} +(-1.02659 + 1.77810i) q^{94} +(-11.2763 + 6.51039i) q^{95} -0.393151i q^{96} +(5.50775 - 3.17990i) q^{97} +(0.323759 + 0.560767i) q^{98} +9.80605i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9} + 12 q^{13} - 12 q^{16} + 5 q^{17} + 24 q^{18} + 8 q^{19} - 4 q^{21} - 48 q^{25} - 6 q^{26} + 12 q^{32} - 6 q^{33} + 10 q^{34} - 10 q^{35} + 12 q^{36} + 16 q^{38} - 2 q^{42} - 4 q^{43} + 12 q^{47} + 20 q^{49} - 24 q^{50} + 16 q^{51} - 18 q^{52} - 44 q^{53} - 12 q^{55} + 14 q^{59} + 24 q^{64} - 12 q^{66} + 6 q^{67} + 5 q^{68} + 10 q^{69} - 20 q^{70} - 12 q^{72} + 8 q^{76} - 28 q^{77} - 4 q^{81} - 4 q^{83} + 2 q^{84} + 13 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 6 q^{94} - 20 q^{98}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9 + 12 * q^13 - 12 * q^16 + 5 * q^17 + 24 * q^18 + 8 * q^19 - 4 * q^21 - 48 * q^25 - 6 * q^26 + 12 * q^32 - 6 * q^33 + 10 * q^34 - 10 * q^35 + 12 * q^36 + 16 * q^38 - 2 * q^42 - 4 * q^43 + 12 * q^47 + 20 * q^49 - 24 * q^50 + 16 * q^51 - 18 * q^52 - 44 * q^53 - 12 * q^55 + 14 * q^59 + 24 * q^64 - 12 * q^66 + 6 * q^67 + 5 * q^68 + 10 * q^69 - 20 * q^70 - 12 * q^72 + 8 * q^76 - 28 * q^77 - 4 * q^81 - 4 * q^83 + 2 * q^84 + 13 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 6 * q^94 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/442\mathbb{Z}\right)^\times$.

$n$	$105$	$171$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.340479	−	0.196576i	−0.196576	−	0.113493i	0.398482	−	0.917176i	$-0.369537\pi$
$3$	−0.340479	−	0.196576i	−0.196576	−	0.113493i	−0.595057	+	0.803683i	$0.702871\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		−	1.77611i		−	0.794301i	−0.917754	−	0.397150i	$-0.869999\pi$
$5$		−	1.77611i		−	0.794301i	0.917754	−	0.397150i	$-0.130001\pi$
$6$	−0.340479	+	0.196576i	−0.139000	+	0.0802516i
$7$	−2.18274	+	1.26021i	−0.824999	+	0.476313i	−0.852137	−	0.523318i	$-0.824694\pi$
$7$	−2.18274	+	1.26021i	−0.824999	+	0.476313i	0.0271384	+	0.999632i	$0.491361\pi$
$8$	−1.00000			−0.353553
$9$	−1.42272	−	2.46422i	−0.474239	−	0.821406i
$10$	−1.53816	−	0.888055i	−0.486408	−	0.280828i
$11$	−2.98453	−	1.72312i	−0.899871	−	0.519541i	−0.0227125	−	0.999742i	$-0.507230\pi$
$11$	−2.98453	−	1.72312i	−0.899871	−	0.519541i	−0.877158	+	0.480201i	$0.840564\pi$
$12$			0.393151i			0.113493i
$13$	2.99263	+	2.01101i	0.830007	+	0.557753i
$13$	2.99263	+	2.01101i	0.830007	+	0.557753i
$14$			2.52041i			0.673609i
$15$	−0.349140	+	0.604728i	−0.0901475	+	0.156140i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.52068	+	3.26285i	−0.611355	+	0.791356i
$17$	−2.52068	+	3.26285i	−0.611355	+	0.791356i
$18$	−2.84543			−0.670675
$19$	−3.66553	−	6.34888i	−0.840930	−	1.45653i	−0.889109	−	0.457695i	$-0.848675\pi$
$19$	−3.66553	−	6.34888i	−0.840930	−	1.45653i	0.0481788	−	0.998839i	$-0.484658\pi$
$20$	−1.53816	+	0.888055i	−0.343942	+	0.198575i
$21$	0.990903			0.216233
$22$	−2.98453	+	1.72312i	−0.636305	+	0.367371i
$23$	−0.147983	−	0.0854382i	−0.0308567	−	0.0178151i	0.484492	−	0.874796i	$-0.339004\pi$
$23$	−0.147983	−	0.0854382i	−0.0308567	−	0.0178151i	−0.515349	+	0.856980i	$0.672338\pi$
$24$	0.340479	+	0.196576i	0.0695000	+	0.0401258i
$25$	1.84543			0.369086
$26$	3.23790	−	1.58619i	0.635005	−	0.311078i
$27$			2.29814i			0.442277i
$28$	2.18274	+	1.26021i	0.412499	+	0.238157i
$29$	−3.57292	−	2.06282i	−0.663474	−	0.383057i	0.130126	−	0.991498i	$-0.458462\pi$
$29$	−3.57292	−	2.06282i	−0.663474	−	0.383057i	−0.793599	+	0.608441i	$0.791795\pi$
$30$	0.349140	+	0.604728i	0.0637439	+	0.110408i
$31$		−	9.12805i		−	1.63945i	−0.572760	−	0.819723i	$-0.694127\pi$
$31$		−	9.12805i		−	1.63945i	0.572760	−	0.819723i	$-0.305873\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.677447	+	1.17337i	0.117928	+	0.204258i
$34$	1.56537	+	3.81440i	0.268458	+	0.654164i
$35$	2.23827	+	3.87679i	0.378336	+	0.655297i
$36$	−1.42272	+	2.46422i	−0.237119	+	0.410703i
$37$	9.10280	+	5.25550i	1.49649	+	0.864000i	0.999992	−	0.00403741i	$-0.00128515\pi$
$37$	9.10280	+	5.25550i	1.49649	+	0.864000i	0.496499	+	0.868037i	$0.334618\pi$
$38$	−7.33106			−1.18926
$39$	−0.623613	−	1.27298i	−0.0998579	−	0.203841i
$40$			1.77611i			0.280828i
$41$	−0.111611	−	0.0644385i	−0.0174307	−	0.0100636i	0.491259	−	0.871013i	$-0.336537\pi$
$41$	−0.111611	−	0.0644385i	−0.0174307	−	0.0100636i	−0.508690	+	0.860950i	$0.669870\pi$
$42$	0.495452	−	0.858147i	0.0764499	−	0.132415i
$43$	−2.65978	−	4.60687i	−0.405612	−	0.702541i	0.588780	−	0.808293i	$-0.299608\pi$
$43$	−2.65978	−	4.60687i	−0.405612	−	0.702541i	−0.994392	+	0.105752i	$0.966275\pi$
$44$			3.44624i			0.519541i
$45$	−4.37672	+	2.52690i	−0.652443	+	0.376688i
$46$	−0.147983	+	0.0854382i	−0.0218190	+	0.0125972i
$47$	−2.05317			−0.299486			−0.149743	−	0.988725i	$-0.547845\pi$
$47$	−2.05317			−0.299486			−0.149743	+	0.988725i	$0.547845\pi$
$48$	0.340479	−	0.196576i	0.0491439	−	0.0283732i
$49$	−0.323759	+	0.560767i	−0.0462513	+	0.0801095i
$50$	0.922716	−	1.59819i	0.130492	−	0.226018i
$51$	1.49963	−	0.615426i	0.209991	−	0.0861769i
$52$	0.245269	−	3.59720i	0.0340127	−	0.498842i
$53$	−4.26638			−0.586032			−0.293016	−	0.956108i	$-0.594659\pi$
$53$	−4.26638			−0.586032			−0.293016	+	0.956108i	$0.594659\pi$
$54$	1.99025	+	1.14907i	0.270838	+	0.156369i
$55$	−3.06045	+	5.30086i	−0.412671	+	0.714768i
$56$	2.18274	−	1.26021i	0.291681	−	0.168402i
$57$			2.88221i			0.381759i
$58$	−3.57292	+	2.06282i	−0.469147	+	0.270862i
$59$	0.0723702	+	0.125349i	0.00942180	+	0.0163190i	0.870698	−	0.491818i	$-0.163668\pi$
$59$	0.0723702	+	0.125349i	0.00942180	+	0.0163190i	−0.861276	+	0.508137i	$0.830334\pi$
$60$	0.698280			0.0901475
$61$	13.4493	−	7.76493i	1.72200	−	0.994197i	0.807213	−	0.590260i	$-0.200975\pi$
$61$	13.4493	−	7.76493i	1.72200	−	0.994197i	0.914787	−	0.403938i	$-0.132359\pi$
$62$	−7.90512	−	4.56403i	−1.00395	−	0.579632i
$63$	6.21084	+	3.58583i	0.782493	+	0.451772i
$64$	1.00000			0.125000
$65$	3.57177	−	5.31524i	0.443024	−	0.659275i
$66$	1.35489			0.166776
$67$	4.08704	−	7.07896i	0.499311	−	0.864833i	−0.500688	−	0.865628i	$-0.666920\pi$
$67$	4.08704	−	7.07896i	0.499311	−	0.864833i	1.00000		0.000794879i	$0.000253018\pi$
$68$	4.08605	+	0.551551i	0.495506	+	0.0668854i
$69$	0.0335901	+	0.0581798i	0.00404378	+	0.00700403i
$70$	4.47653			0.535048
$71$	4.14584	−	2.39360i	0.492021	−	0.284068i	−0.233392	−	0.972383i	$-0.574982\pi$
$71$	4.14584	−	2.39360i	0.492021	−	0.284068i	0.725412	+	0.688315i	$0.241649\pi$
$72$	1.42272	+	2.46422i	0.167669	+	0.290411i
$73$		−	9.40225i		−	1.10045i	−0.835016	−	0.550225i	$-0.814542\pi$
$73$		−	9.40225i		−	1.10045i	0.835016	−	0.550225i	$-0.185458\pi$
$74$	9.10280	−	5.25550i	1.05818	−	0.610940i
$75$	−0.628331	−	0.362767i	−0.0725534	−	0.0418887i
$76$	−3.66553	+	6.34888i	−0.420465	+	0.728267i
$77$	8.68595			0.989856
$78$	−1.41424	−	0.0964278i	−0.160131	−	0.0109183i
$79$			2.76824i			0.311452i	0.987800	+	0.155726i	$0.0497716\pi$
$79$			2.76824i			0.311452i	−0.987800	+	0.155726i	$0.950228\pi$
$80$	1.53816	+	0.888055i	0.171971	+	0.0992876i
$81$	−3.81639	+	6.61018i	−0.424043	+	0.734465i
$82$	−0.111611	+	0.0644385i	−0.0123253	+	0.00711604i
$83$	6.67445			0.732616			0.366308	−	0.930494i	$-0.380622\pi$
$83$	6.67445			0.732616			0.366308	+	0.930494i	$0.380622\pi$
$84$	−0.495452	−	0.858147i	−0.0540582	−	0.0936316i
$85$	5.79517	+	4.47701i	0.628575	+	0.485600i
$86$	−5.31955			−0.573622
$87$	0.811001	+	1.40470i	0.0869485	+	0.150599i
$88$	2.98453	+	1.72312i	0.318152	+	0.183685i
$89$	−7.64870	+	13.2479i	−0.810761	+	1.40428i	0.101572	+	0.994828i	$0.467613\pi$
$89$	−7.64870	+	13.2479i	−0.810761	+	1.40428i	−0.912332	+	0.409450i	$0.865721\pi$
$90$			5.05380i			0.532717i
$91$	−9.06643	−	0.618179i	−0.950420	−	0.0648028i
$92$			0.170876i			0.0178151i
$93$	−1.79435	+	3.10791i	−0.186066	+	0.322275i
$94$	−1.02659	+	1.77810i	−0.105884	+	0.183397i
$95$	−11.2763	+	6.51039i	−1.15693	+	0.667952i
$96$		−	0.393151i		−	0.0401258i
$97$	5.50775	−	3.17990i	0.559228	−	0.322870i	−0.193608	−	0.981079i	$-0.562019\pi$
$97$	5.50775	−	3.17990i	0.559228	−	0.322870i	0.752835	+	0.658209i	$0.228686\pi$
$98$	0.323759	+	0.560767i	0.0327046	+	0.0566460i
$99$			9.80605i			0.985545i
$100$	−0.922716	−	1.59819i	−0.0922716	−	0.159819i
$101$	8.47701	−	14.6826i	0.843494	−	1.46097i	−0.0434292	−	0.999057i	$-0.513828\pi$
$101$	8.47701	−	14.6826i	0.843494	−	1.46097i	0.886923	−	0.461917i	$-0.152838\pi$
$102$	0.216843	−	1.60643i	0.0214706	−	0.159061i
$103$	7.33106			0.722351			0.361175	−	0.932498i	$-0.382376\pi$
$103$	7.33106			0.722351			0.361175	+	0.932498i	$0.382376\pi$
$104$	−2.99263	−	2.01101i	−0.293452	−	0.197196i
$105$		−	1.75995i		−	0.171754i
$106$	−2.13319	+	3.69479i	−0.207194	+	0.358870i
$107$	3.24534	+	1.87370i	0.313739	+	0.181137i	0.648599	−	0.761131i	$-0.275355\pi$
$107$	3.24534	+	1.87370i	0.313739	+	0.181137i	−0.334859	+	0.942268i	$0.608689\pi$
$108$	1.99025	−	1.14907i	0.191512	−	0.110569i
$109$		−	5.85268i		−	0.560585i	−0.959915	−	0.280293i	$-0.909568\pi$
$109$		−	5.85268i		−	0.560585i	0.959915	−	0.280293i	$-0.0904315\pi$
$110$	3.06045	+	5.30086i	0.291803	+	0.505417i
$111$	−2.06621	−	3.57878i	−0.196116	−	0.339682i
$112$		−	2.52041i		−	0.238157i
$113$	9.22173	−	5.32417i	0.867507	−	0.500856i	0.000988279	−	1.00000i	$-0.499685\pi$
$113$	9.22173	−	5.32417i	0.867507	−	0.500856i	0.866519	+	0.499144i	$0.166352\pi$
$114$	2.49607	+	1.44111i	0.233778	+	0.134972i
$115$	−0.151748	+	0.262835i	−0.0141505	+	0.0245095i
$116$			4.12565i			0.383057i
$117$	0.697896	−	10.2356i	0.0645205	−	0.946280i
$118$	0.144740			0.0133244
$119$	1.39014	−	10.2985i	0.127434	−	0.944065i
$120$	0.349140	−	0.604728i	0.0318720	−	0.0552039i
$121$	0.438294	+	0.759147i	0.0398449	+	0.0690134i
$122$		−	15.5299i		−	1.40601i
$123$	0.0253341	+	0.0438799i	0.00228430	+	0.00395652i
$124$	−7.90512	+	4.56403i	−0.709901	+	0.409862i
$125$		−	12.1582i		−	1.08747i
$126$	6.21084	−	3.58583i	0.553306	−	0.319451i
$127$	−10.3400	+	17.9094i	−0.917525	+	1.58920i	−0.114362	+	0.993439i	$0.536482\pi$
$127$	−10.3400	+	17.9094i	−0.917525	+	1.58920i	−0.803163	+	0.595760i	$0.796851\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$			2.09139i			0.184136i
$130$	−2.81725	−	5.75087i	−0.247089	−	0.504385i
$131$			16.6476i			1.45451i	0.686368	+	0.727255i	$0.259204\pi$
$131$			16.6476i			1.45451i	−0.686368	+	0.727255i	$0.740796\pi$
$132$	0.677447	−	1.17337i	0.0589642	−	0.102129i
$133$	16.0018	+	9.23865i	1.38753	+	0.801093i
$134$	−4.08704	−	7.07896i	−0.353067	−	0.611529i
$135$	4.08175			0.351301
$136$	2.52068	−	3.26285i	0.216147	−	0.279787i
$137$	−6.44230	−	11.1584i	−0.550403	−	0.953326i	−0.998245	−	0.0592132i	$-0.981141\pi$
$137$	−6.44230	−	11.1584i	−0.550403	−	0.953326i	0.447843	−	0.894112i	$-0.352193\pi$
$138$	0.0671803			0.00571876
$139$	−6.77086	+	3.90916i	−0.574297	+	0.331570i	−0.758864	−	0.651250i	$-0.774245\pi$
$139$	−6.77086	+	3.90916i	−0.574297	+	0.331570i	0.184567	+	0.982820i	$0.440912\pi$
$140$	2.23827	−	3.87679i	0.189168	−	0.327649i
$141$	0.699062	+	0.403604i	0.0588717	+	0.0339896i
$142$		−	4.78720i		−	0.401733i
$143$	−5.46640	−	11.1586i	−0.457123	−	0.933128i
$144$	2.84543			0.237119
$145$	−3.66380	+	6.34589i	−0.304262	+	0.526998i
$146$	−8.14259	−	4.70112i	−0.673885	−	0.389068i
$147$	0.220466	−	0.127286i	0.0181837	−	0.0104984i
$148$		−	10.5110i		−	0.864000i
$149$	2.66432	+	4.61475i	0.218270	+	0.378055i	0.954279	−	0.298917i	$-0.0966253\pi$
$149$	2.66432	+	4.61475i	0.218270	+	0.378055i	−0.736009	+	0.676972i	$0.763292\pi$
$150$	−0.628331	+	0.362767i	−0.0513030	+	0.0296198i
$151$	4.68595			0.381338			0.190669	−	0.981654i	$-0.438934\pi$
$151$	4.68595			0.381338			0.190669	+	0.981654i	$0.438934\pi$
$152$	3.66553	+	6.34888i	0.297314	+	0.514963i
$153$	11.6266	+	1.56940i	0.939953	+	0.126879i
$154$	4.34298	−	7.52226i	0.349967	−	0.606161i
$155$	−16.2124			−1.30221
$156$	−0.790630	+	1.17656i	−0.0633011	+	0.0941999i
$157$	−19.4414			−1.55159			−0.775797	−	0.630983i	$-0.782652\pi$
$157$	−19.4414			−1.55159			−0.775797	+	0.630983i	$0.782652\pi$
$158$	2.39737	+	1.38412i	0.190724	+	0.110115i
$159$	1.45261	+	0.838666i	0.115200	+	0.0665105i
$160$	1.53816	−	0.888055i	0.121602	−	0.0702069i
$161$	0.430679			0.0339423
$162$	3.81639	+	6.61018i	0.299844	+	0.519345i
$163$	5.58408	−	3.22397i	0.437379	−	0.252521i	−0.265106	−	0.964219i	$-0.585407\pi$
$163$	5.58408	−	3.22397i	0.437379	−	0.252521i	0.702485	+	0.711699i	$0.252074\pi$
$164$			0.128877i			0.0100636i
$165$	2.08404	−	1.20322i	0.162242	−	0.0936706i
$166$	3.33722	−	5.78024i	0.259019	−	0.448634i
$167$	−19.3237	−	11.1566i	−1.49531	−	0.863320i	−0.495329	−	0.868705i	$-0.664953\pi$
$167$	−19.3237	−	11.1566i	−1.49531	−	0.863320i	−0.999986	+	0.00538475i	$0.998286\pi$
$168$	−0.990903			−0.0764499
$169$	4.91169	+	12.0364i	0.377822	+	0.925878i
$170$	6.77479	−	2.78026i	0.519603	−	0.213237i
$171$	−10.4300	+	18.0653i	−0.797603	+	1.38149i
$172$	−2.65978	+	4.60687i	−0.202806	+	0.351270i
$173$	−19.1708	+	11.0683i	−1.45753	+	0.841506i	−0.998889	−	0.0471148i	$-0.984997\pi$
$173$	−19.1708	+	11.0683i	−1.45753	+	0.841506i	−0.458642	+	0.888621i	$0.651664\pi$
$174$	1.62200			0.122964
$175$	−4.02810	+	2.32563i	−0.304496	+	0.175801i
$176$	2.98453	−	1.72312i	0.224968	−	0.129885i
$177$		−	0.0569049i		−	0.00427723i
$178$	7.64870	+	13.2479i	0.573294	+	0.992975i
$179$	4.71131	−	8.16023i	0.352140	−	0.609925i	−0.634484	−	0.772936i	$-0.718787\pi$
$179$	4.71131	−	8.16023i	0.352140	−	0.609925i	0.986624	+	0.163011i	$0.0521207\pi$
$180$	4.37672	+	2.52690i	0.326221	+	0.188344i
$181$			15.0540i			1.11895i	0.828847	+	0.559476i	$0.188998\pi$
$181$			15.0540i			1.11895i	−0.828847	+	0.559476i	$0.811002\pi$
$182$	−5.06857	+	7.54267i	−0.375708	+	0.559100i
$183$	−6.10558			−0.451338
$184$	0.147983	+	0.0854382i	0.0109095	+	0.00629859i
$185$	9.33436	−	16.1676i	0.686275	−	1.18866i
$186$	1.79435	+	3.10791i	0.131568	+	0.227883i
$187$	13.1453	−	5.39463i	0.961282	−	0.394495i
$188$	1.02659	+	1.77810i	0.0748716	+	0.129681i
$189$	−2.89613	−	5.01624i	−0.210662	−	0.364878i
$190$			13.0208i			0.944626i
$191$	−8.29594	−	14.3690i	−0.600273	−	1.03970i	−0.992779	−	0.119954i	$-0.961725\pi$
$191$	−8.29594	−	14.3690i	−0.600273	−	1.03970i	0.392506	−	0.919749i	$-0.371608\pi$
$192$	−0.340479	−	0.196576i	−0.0245719	−	0.0141866i
$193$	7.46974	+	4.31266i	0.537684	+	0.310432i	0.744140	−	0.668024i	$-0.232860\pi$
$193$	7.46974	+	4.31266i	0.537684	+	0.310432i	−0.206456	+	0.978456i	$0.566193\pi$
$194$		−	6.35981i		−	0.456608i
$195$	−2.26096	+	1.10760i	−0.161911	+	0.0793172i
$196$	0.647518			0.0462513
$197$	0.873453	+	0.504289i	0.0622310	+	0.0359291i	0.530793	−	0.847502i	$-0.321894\pi$
$197$	0.873453	+	0.504289i	0.0622310	+	0.0359291i	−0.468562	+	0.883431i	$0.655228\pi$
$198$	8.49229	+	4.90302i	0.603521	+	0.348443i
$199$	−14.4836	+	8.36211i	−1.02671	+	0.592774i	−0.916042	−	0.401083i	$-0.868634\pi$
$199$	−14.4836	+	8.36211i	−1.02671	+	0.592774i	−0.110673	+	0.993857i	$0.535301\pi$
$200$	−1.84543			−0.130492
$201$	−2.78310	+	1.60682i	−0.196305	+	0.113337i
$202$	−8.47701	−	14.6826i	−0.596440	−	1.03306i
$203$	10.3983			0.729820
$204$	−1.28279	−	0.991009i	−0.0898134	−	0.0693845i
$205$	−0.114450	+	0.198233i	−0.00799352	+	0.0138452i
$206$	3.66553	−	6.34888i	0.255390	−	0.442348i
$207$			0.486217i			0.0337944i
$208$	−3.23790	+	1.58619i	−0.224508	+	0.109983i
$209$			25.2646i			1.74759i
$210$	−1.52416	−	0.879977i	−0.105177	−	0.0607242i
$211$	19.2628	+	11.1214i	1.32610	+	0.765627i	0.984695	−	0.174288i	$-0.0557623\pi$
$211$	19.2628	+	11.1214i	1.32610	+	0.765627i	0.341410	+	0.939915i	$0.389096\pi$
$212$	2.13319	+	3.69479i	0.146508	+	0.253759i
$213$	−1.88209			−0.128959
$214$	3.24534	−	1.87370i	0.221847	−	0.128084i
$215$	−8.18230	+	4.72406i	−0.558029	+	0.322178i
$216$		−	2.29814i		−	0.156369i
$217$	11.5032	+	19.9242i	0.780890	+	1.35254i
$218$	−5.06857	−	2.92634i	−0.343287	−	0.198197i
$219$	−1.84825	+	3.20127i	−0.124893	+	0.216322i
$220$	6.12091			0.412671
$221$	−14.1051	+	4.69538i	−0.948811	+	0.315846i
$222$	−4.13242			−0.277350
$223$	4.50037	−	7.79486i	0.301367	−	0.521983i	−0.675079	−	0.737745i	$-0.735890\pi$
$223$	4.50037	−	7.79486i	0.301367	−	0.521983i	0.976446	+	0.215763i	$0.0692238\pi$
$224$	−2.18274	−	1.26021i	−0.145841	−	0.0842011i
$225$	−2.62553	−	4.54754i	−0.175035	−	0.303170i
$226$		−	10.6483i		−	0.708317i
$227$	−23.6011	+	13.6261i	−1.56646	+	0.904397i	−0.569884	+	0.821725i	$0.693012\pi$
$227$	−23.6011	+	13.6261i	−1.56646	+	0.904397i	−0.996577	+	0.0826718i	$0.973655\pi$
$228$	2.49607	−	1.44111i	0.165306	−	0.0954397i
$229$	−18.9943			−1.25518			−0.627588	−	0.778545i	$-0.715958\pi$
$229$	−18.9943			−1.25518			−0.627588	+	0.778545i	$0.715958\pi$
$230$	0.151748	+	0.262835i	0.0100059	+	0.0173308i
$231$	−2.95738	−	1.70745i	−0.194582	−	0.112342i
$232$	3.57292	+	2.06282i	0.234573	+	0.135431i
$233$		−	17.4119i		−	1.14069i	−0.821404	−	0.570347i	$-0.806809\pi$
$233$		−	17.4119i		−	1.14069i	0.821404	−	0.570347i	$-0.193191\pi$
$234$	−8.51533	−	5.72219i	−0.556665	−	0.374071i
$235$			3.64666i			0.237882i
$236$	0.0723702	−	0.125349i	0.00471090	−	0.00815952i
$237$	0.544169	−	0.942528i	0.0353476	−	0.0612238i
$238$	−8.22372	−	6.35316i	−0.533065	−	0.411814i
$239$	−10.8422			−0.701324			−0.350662	−	0.936502i	$-0.614043\pi$
$239$	−10.8422			−0.701324			−0.350662	+	0.936502i	$0.614043\pi$
$240$	−0.349140	−	0.604728i	−0.0225369	−	0.0390350i
$241$	3.13875	−	1.81216i	0.202185	−	0.116731i	−0.395489	−	0.918471i	$-0.629425\pi$
$241$	3.13875	−	1.81216i	0.202185	−	0.116731i	0.597674	+	0.801739i	$0.296092\pi$
$242$	0.876587			0.0563492
$243$	8.56954	−	4.94763i	0.549736	−	0.317390i
$244$	−13.4493	−	7.76493i	−0.861000	−	0.497099i
$245$	0.995984	+	0.575031i	0.0636311	+	0.0367374i
$246$	0.0506681			0.00323048
$247$	1.79808	−	26.3713i	0.114409	−	1.67796i
$248$			9.12805i			0.579632i
$249$	−2.27251	−	1.31203i	−0.144014	−	0.0831467i
$250$	−10.5293	−	6.07912i	−0.665934	−	0.384477i
$251$	−0.151225	−	0.261930i	−0.00954527	−	0.0165329i	0.861213	−	0.508244i	$-0.169705\pi$
$251$	−0.151225	−	0.261930i	−0.00954527	−	0.0165329i	−0.870759	+	0.491711i	$0.836372\pi$
$252$		−	7.17166i		−	0.451772i
$253$	0.294441	+	0.509986i	0.0185113	+	0.0320626i
$254$	10.3400	+	17.9094i	0.648788	+	1.12373i
$255$	−1.09306	−	2.66352i	−0.0684503	−	0.166796i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.14104	−	3.70838i	0.133554	−	0.231323i	−0.791490	−	0.611182i	$-0.790694\pi$
$257$	2.14104	−	3.70838i	0.133554	−	0.231323i	0.925044	+	0.379859i	$0.124028\pi$
$258$	1.81120	+	1.04569i	0.112760	+	0.0651021i
$259$	−26.4921			−1.64614
$260$	−6.38902	−	0.435625i	−0.396230	−	0.0270163i
$261$			11.7392i			0.726641i
$262$	14.4173	+	8.32381i	0.890701	+	0.514247i
$263$	−3.03662	+	5.25958i	−0.187246	+	0.324320i	−0.944331	−	0.328997i	$-0.893289\pi$
$263$	−3.03662	+	5.25958i	−0.187246	+	0.324320i	0.757085	+	0.653316i	$0.226623\pi$
$264$	−0.677447	−	1.17337i	−0.0416940	−	0.0722161i
$265$			7.57756i			0.465486i
$266$	16.0018	−	9.23865i	0.981134	−	0.566458i
$267$	5.20844	−	3.00710i	0.318751	−	0.184031i
$268$	−8.17408			−0.499311
$269$	1.82831	−	1.05557i	0.111474	−	0.0643595i	−0.443226	−	0.896410i	$-0.646166\pi$
$269$	1.82831	−	1.05557i	0.111474	−	0.0643595i	0.554700	+	0.832050i	$0.312833\pi$
$270$	2.04087	−	3.53490i	0.124204	−	0.215127i
$271$	6.75132	−	11.6936i	0.410113	−	0.710337i	−0.584788	−	0.811186i	$-0.698822\pi$
$271$	6.75132	−	11.6936i	0.410113	−	0.710337i	0.994902	+	0.100849i	$0.0321558\pi$
$272$	−1.56537	−	3.81440i	−0.0949143	−	0.231282i
$273$	2.96541	+	1.99272i	0.179475	+	0.120605i
$274$	−12.8846			−0.778387
$275$	−5.50775	−	3.17990i	−0.332130	−	0.191755i
$276$	0.0335901	−	0.0581798i	0.00202189	−	0.00350201i
$277$	−5.42837	+	3.13407i	−0.326159	+	0.188308i	−0.654135	−	0.756378i	$-0.726967\pi$
$277$	−5.42837	+	3.13407i	−0.326159	+	0.188308i	0.327975	+	0.944686i	$0.393634\pi$
$278$			7.81831i			0.468911i
$279$	−22.4935	+	12.9866i	−1.34665	+	0.777489i
$280$	−2.23827	−	3.87679i	−0.133762	−	0.231683i
$281$	9.45270			0.563901			0.281950	−	0.959429i	$-0.409019\pi$
$281$	9.45270			0.563901			0.281950	+	0.959429i	$0.409019\pi$
$282$	0.699062	−	0.403604i	0.0416286	−	0.0240343i
$283$	18.7041	+	10.7988i	1.11184	+	0.641923i	0.939306	−	0.343081i	$-0.111470\pi$
$283$	18.7041	+	10.7988i	1.11184	+	0.641923i	0.172536	+	0.985003i	$0.444804\pi$
$284$	−4.14584	−	2.39360i	−0.246010	−	0.142034i
$285$	5.11913			0.303231
$286$	−12.3968	−	0.845256i	−0.733039	−	0.0499811i
$287$	0.324823			0.0191737
$288$	1.42272	−	2.46422i	0.0838343	−	0.145205i
$289$	−4.29233	−	16.4492i	−0.252490	−	0.967599i
$290$	3.66380	+	6.34589i	0.215146	+	0.372644i
$291$	−2.50037			−0.146574
$292$	−8.14259	+	4.70112i	−0.476509	+	0.275112i
$293$	14.6759	+	25.4195i	0.857377	+	1.48502i	0.874422	+	0.485166i	$0.161241\pi$
$293$	14.6759	+	25.4195i	0.857377	+	1.48502i	−0.0170454	+	0.999855i	$0.505426\pi$
$294$		−	0.254572i		−	0.0148470i
$295$	0.222633	−	0.128537i	0.0129622	−	0.00748374i
$296$	−9.10280	−	5.25550i	−0.529090	−	0.305470i
$297$	3.95997	−	6.85887i	0.229781	−	0.397992i
$298$	5.32865			0.308680
$299$	−0.271043	−	0.553281i	−0.0156748	−	0.0319971i
$300$			0.725534i			0.0418887i
$301$	11.6112	+	6.70373i	0.669259	+	0.386397i
$302$	2.34298	−	4.05816i	0.134823	−	0.233521i
$303$	−5.77248	+	3.33275i	−0.331621	+	0.191461i
$304$	7.33106			0.420465
$305$	−13.7914	−	23.8874i	−0.789691	−	1.36779i
$306$	7.17243	−	9.28421i	0.410020	−	0.530743i
$307$	10.0439			0.573236			0.286618	−	0.958045i	$-0.407469\pi$
$307$	10.0439			0.573236			0.286618	+	0.958045i	$0.407469\pi$
$308$	−4.34298	−	7.52226i	−0.247464	−	0.428620i
$309$	−2.49607	−	1.44111i	−0.141997	−	0.0819817i
$310$	−8.10621	+	14.0404i	−0.460402	+	0.797439i
$311$		−	21.5147i		−	1.21999i	−0.792407	−	0.609993i	$-0.791172\pi$
$311$		−	21.5147i		−	1.21999i	0.792407	−	0.609993i	$-0.208828\pi$
$312$	0.623613	+	1.27298i	0.0353051	+	0.0720685i
$313$			4.68654i			0.264899i	0.991190	+	0.132449i	$0.0422842\pi$
$313$			4.68654i			0.264899i	−0.991190	+	0.132449i	$0.957716\pi$
$314$	−9.72071	+	16.8368i	−0.548571	+	0.950153i
$315$	6.36883	−	11.0311i	0.358843	−	0.621535i
$316$	2.39737	−	1.38412i	0.134863	−	0.0778629i
$317$		−	30.9882i		−	1.74047i	−0.492638	−	0.870234i	$-0.663967\pi$
$317$		−	30.9882i		−	1.74047i	0.492638	−	0.870234i	$-0.336033\pi$
$318$	1.45261	−	0.838666i	0.0814584	−	0.0470300i
$319$	7.10899	+	12.3131i	0.398027	+	0.689403i
$320$		−	1.77611i		−	0.0992876i
$321$	−0.736648	−	1.27591i	−0.0411157	−	0.0712144i
$322$	0.215340	−	0.372979i	0.0120004	−	0.0207853i
$323$	29.9551	+	4.04345i	1.66674	+	0.224984i
$324$	7.63278			0.424043
$325$	5.52270	+	3.71118i	0.306344	+	0.205859i
$326$		−	6.44794i		−	0.357118i
$327$	−1.15049	+	1.99272i	−0.0636225	+	0.110197i
$328$	0.111611	+	0.0644385i	0.00616267	+	0.00355802i
$329$	4.48155	−	2.58742i	0.247076	−	0.142649i
$330$		−	2.40644i		−	0.132470i
$331$	5.93213	+	10.2748i	0.326059	+	0.564751i	0.981726	−	0.190299i	$-0.0609457\pi$
$331$	5.93213	+	10.2748i	0.326059	+	0.564751i	−0.655667	+	0.755050i	$0.727612\pi$
$332$	−3.33722	−	5.78024i	−0.183154	−	0.317232i
$333$		−	29.9084i		−	1.63897i
$334$	−19.3237	+	11.1566i	−1.05735	+	0.610460i
$335$	−12.5730	−	7.25903i	−0.686937	−	0.396603i
$336$	−0.495452	+	0.858147i	−0.0270291	+	0.0468158i
$337$			3.61745i			0.197055i	0.995134	+	0.0985275i	$0.0314133\pi$
$337$			3.61745i			0.197055i	−0.995134	+	0.0985275i	$0.968587\pi$
$338$	12.8797	+	1.76456i	0.700563	+	0.0959796i
$339$	−4.18641			−0.227374
$340$	0.979615	−	7.25727i	0.0531271	−	0.393581i
$341$	−15.7287	+	27.2430i	−0.851759	+	1.47529i
$342$	10.4300	+	18.0653i	0.563991	+	0.976861i
$343$		−	19.2749i		−	1.04075i
$344$	2.65978	+	4.60687i	0.143406	+	0.248386i
$345$	0.103334	−	0.0596598i	0.00556330	−	0.00321197i
$346$			22.1366i			1.19007i
$347$	−1.59558	+	0.921207i	−0.0856551	+	0.0494530i	−0.542216	−	0.840239i	$-0.682414\pi$
$347$	−1.59558	+	0.921207i	−0.0856551	+	0.0494530i	0.456561	+	0.889692i	$0.349081\pi$
$348$	0.811001	−	1.40470i	0.0434742	−	0.0752996i
$349$	11.3613	−	19.6783i	0.608155	−	1.05335i	−0.383390	−	0.923587i	$-0.625243\pi$
$349$	11.3613	−	19.6783i	0.608155	−	1.05335i	0.991544	−	0.129768i	$-0.0414233\pi$
$350$			4.65125i			0.248620i
$351$	−4.62158	+	6.87748i	−0.246682	+	0.367093i
$352$		−	3.44624i		−	0.183685i
$353$	−10.1891	+	17.6481i	−0.542312	+	0.939312i	0.456459	+	0.889745i	$0.349118\pi$
$353$	−10.1891	+	17.6481i	−0.542312	+	0.939312i	−0.998771	+	0.0495673i	$0.984216\pi$
$354$	−0.0492811	−	0.0284524i	−0.00261926	−	0.00151223i
$355$	−4.25130	−	7.36347i	−0.225636	−	0.390812i
$356$	15.2974			0.810761
$357$	−2.49775	+	3.23317i	−0.132195	+	0.171117i
$358$	−4.71131	−	8.16023i	−0.249001	−	0.431282i
$359$	23.3694			1.23339			0.616695	−	0.787202i	$-0.288471\pi$
$359$	23.3694			1.23339			0.616695	+	0.787202i	$0.288471\pi$
$360$	4.37672	−	2.52690i	0.230673	−	0.133179i
$361$	−17.3722	+	30.0896i	−0.914328	+	1.58366i
$362$	13.0371	+	7.52698i	0.685215	+	0.395609i
$363$		−	0.344631i		−	0.0180885i
$364$	3.99786	+	8.16085i	0.209545	+	0.427745i
$365$	−16.6994			−0.874088
$366$	−3.05279	+	5.28759i	−0.159572	+	0.276387i
$367$	−10.6618	−	6.15561i	−0.556543	−	0.321320i	0.195214	−	0.980761i	$-0.437460\pi$
$367$	−10.6618	−	6.15561i	−0.556543	−	0.321320i	−0.751757	+	0.659440i	$0.770793\pi$
$368$	0.147983	−	0.0854382i	0.00771416	−	0.00445377i
$369$			0.366711i			0.0190902i
$370$	−9.33436	−	16.1676i	−0.485270	−	0.840512i
$371$	9.31240	−	5.37652i	0.483476	−	0.279135i
$372$	3.58870			0.186066
$373$	5.95835	+	10.3202i	0.308512	+	0.534358i	0.978037	−	0.208431i	$-0.0668357\pi$
$373$	5.95835	+	10.3202i	0.308512	+	0.534358i	−0.669525	+	0.742789i	$0.733502\pi$
$374$	1.90078	−	14.0815i	0.0982869	−	0.728138i
$375$	−2.39001	+	4.13962i	−0.123420	+	0.213769i
$376$	2.05317			0.105884
$377$	−6.54406	−	13.3584i	−0.337036	−	0.687994i
$378$	−5.79226			−0.297922
$379$	8.80729	+	5.08489i	0.452400	+	0.261193i	0.708843	−	0.705366i	$-0.249217\pi$
$379$	8.80729	+	5.08489i	0.452400	+	0.261193i	−0.256443	+	0.966559i	$0.582551\pi$
$380$	11.2763	+	6.51039i	0.578463	+	0.333976i
$381$	7.04109	−	4.06517i	0.360726	−	0.208265i
$382$	−16.5919			−0.848915
$383$	−3.37109	−	5.83890i	−0.172255	−	0.298354i	0.766953	−	0.641703i	$-0.221772\pi$
$383$	−3.37109	−	5.83890i	−0.172255	−	0.298354i	−0.939208	+	0.343349i	$0.888439\pi$
$384$	−0.340479	+	0.196576i	−0.0173750	+	0.0100315i
$385$		−	15.4272i		−	0.786244i
$386$	7.46974	−	4.31266i	0.380200	−	0.219509i
$387$	−7.56821	+	13.1085i	−0.384714	+	0.666344i
$388$	−5.50775	−	3.17990i	−0.279614	−	0.161435i
$389$	11.0873			0.562146			0.281073	−	0.959686i	$-0.409310\pi$
$389$	11.0873			0.562146			0.281073	+	0.959686i	$0.409310\pi$
$390$	−0.171266	+	2.51185i	−0.00867241	+	0.127193i
$391$	0.651791	−	0.267484i	0.0329625	−	0.0135273i
$392$	0.323759	−	0.560767i	0.0163523	−	0.0283230i
$393$	3.27252	−	5.66816i	0.165077	−	0.285921i
$394$	0.873453	−	0.504289i	0.0440039	−	0.0254057i
$395$	4.91671			0.247386
$396$	8.49229	−	4.90302i	0.426754	−	0.246386i
$397$	20.6149	−	11.9020i	1.03463	−	0.597345i	0.116324	−	0.993211i	$-0.462889\pi$
$397$	20.6149	−	11.9020i	1.03463	−	0.597345i	0.918308	+	0.395866i	$0.129555\pi$
$398$			16.7242i			0.838309i
$399$	−3.63219	−	6.29113i	−0.181837	−	0.314950i
$400$	−0.922716	+	1.59819i	−0.0461358	+	0.0799096i
$401$	−13.2096	−	7.62655i	−0.659654	−	0.380852i	0.132491	−	0.991184i	$-0.457702\pi$
$401$	−13.2096	−	7.62655i	−0.659654	−	0.380852i	−0.792145	+	0.610333i	$0.791036\pi$
$402$			3.21365i			0.160282i
$403$	18.3566	−	27.3169i	0.914407	−	1.36075i
$404$	−16.9540			−0.843494
$405$	11.7404	+	6.77833i	0.583386	+	0.336818i
$406$	5.19917	−	9.00522i	0.258030	−	0.446922i
$407$	−18.1117	−	31.3705i	−0.897766	−	1.55498i
$408$	−1.49963	+	0.615426i	−0.0742430	+	0.0304681i
$409$	8.32494	+	14.4192i	0.411642	+	0.712985i	0.995069	−	0.0991806i	$-0.0316221\pi$
$409$	8.32494	+	14.4192i	0.411642	+	0.712985i	−0.583428	+	0.812165i	$0.698289\pi$
$410$	0.114450	+	0.198233i	0.00565227	+	0.00979003i
$411$			5.06560i			0.249867i
$412$	−3.66553	−	6.34888i	−0.180588	−	0.312787i
$413$	−0.315931	−	0.182403i	−0.0155459	−	0.00897546i
$414$	0.421077	+	0.243109i	0.0206948	+	0.0119481i
$415$		−	11.8546i		−	0.581917i
$416$	−0.245269	+	3.59720i	−0.0120253	+	0.176367i
$417$	3.07378			0.150524
$418$	21.8798	+	12.6323i	1.07018	+	0.617866i
$419$	32.9339	+	19.0144i	1.60892	+	0.928913i	0.989611	+	0.143769i	$0.0459224\pi$
$419$	32.9339	+	19.0144i	1.60892	+	0.928913i	0.619314	+	0.785144i	$0.287411\pi$
$420$	−1.52416	+	0.879977i	−0.0743716	+	0.0429385i
$421$	21.1387			1.03024			0.515120	−	0.857118i	$-0.327748\pi$
$421$	21.1387			1.03024			0.515120	+	0.857118i	$0.327748\pi$
$422$	19.2628	−	11.1214i	0.937698	−	0.541380i
$423$	2.92108	+	5.05947i	0.142028	+	0.246000i
$424$	4.26638			0.207194
$425$	−4.65175	+	6.02136i	−0.225643	+	0.292079i
$426$	−0.941047	+	1.62994i	−0.0455939	+	0.0789709i
$427$	−19.5708	+	33.8977i	−0.947099	+	1.64042i
$428$		−	3.74740i		−	0.181137i
$429$	−0.332314	+	4.87382i	−0.0160442	+	0.235310i
$430$			9.44811i			0.455628i
$431$	5.78500	+	3.33997i	0.278654	+	0.160881i	0.632814	−	0.774304i	$-0.281900\pi$
$431$	5.78500	+	3.33997i	0.278654	+	0.160881i	−0.354160	+	0.935185i	$0.615233\pi$
$432$	−1.99025	−	1.14907i	−0.0957558	−	0.0552846i
$433$	−12.1772	−	21.0915i	−0.585199	−	1.01359i	−0.994851	−	0.101352i	$-0.967683\pi$
$433$	−12.1772	−	21.0915i	−0.585199	−	1.01359i	0.409652	−	0.912242i	$-0.365650\pi$
$434$	23.0065			1.10435
$435$	2.49489	−	1.44043i	0.119621	−	0.0690632i
$436$	−5.06857	+	2.92634i	−0.242741	+	0.140146i
$437$			1.25271i			0.0599250i
$438$	1.84825	+	3.20127i	0.0883129	+	0.152962i
$439$	3.95737	+	2.28479i	0.188875	+	0.109047i	0.591456	−	0.806337i	$-0.298553\pi$
$439$	3.95737	+	2.28479i	0.188875	+	0.109047i	−0.402581	+	0.915384i	$0.631887\pi$
$440$	3.06045	−	5.30086i	0.145901	−	0.252709i
$441$	1.84247			0.0877366
$442$	−2.98622	+	14.5631i	−0.142040	+	0.692694i
$443$	19.8946			0.945223			0.472612	−	0.881271i	$-0.343311\pi$
$443$	19.8946			0.945223			0.472612	+	0.881271i	$0.343311\pi$
$444$	−2.06621	+	3.57878i	−0.0980579	+	0.169841i
$445$	23.5298	+	13.5849i	1.11542	+	0.643988i
$446$	−4.50037	−	7.79486i	−0.213098	−	0.369097i
$447$		−	2.09496i		−	0.0990884i
$448$	−2.18274	+	1.26021i	−0.103125	+	0.0595392i
$449$	12.9261	−	7.46288i	0.610020	−	0.352195i	−0.162953	−	0.986634i	$-0.552102\pi$
$449$	12.9261	−	7.46288i	0.610020	−	0.352195i	0.772973	+	0.634439i	$0.218769\pi$
$450$	−5.25105			−0.247537
$451$	0.222071	+	0.384638i	0.0104569	+	0.0181119i
$452$	−9.22173	−	5.32417i	−0.433754	−	0.250428i
$453$	−1.59547	−	0.921144i	−0.0749617	−	0.0432791i
$454$			27.2522i			1.27901i
$455$	−1.09795	+	16.1030i	−0.0514729	+	0.754919i
$456$		−	2.88221i		−	0.134972i
$457$	14.1941	−	24.5850i	0.663974	−	1.15004i	−0.315589	−	0.948896i	$-0.602202\pi$
$457$	14.1941	−	24.5850i	0.663974	−	1.15004i	0.979562	−	0.201140i	$-0.0644647\pi$
$458$	−9.49713	+	16.4495i	−0.443772	+	0.768635i
$459$	−7.49847	−	5.79287i	−0.349999	−	0.270388i
$460$	0.303495			0.0141505
$461$	−3.97305	−	6.88152i	−0.185043	−	0.320504i	0.758548	−	0.651617i	$-0.225909\pi$
$461$	−3.97305	−	6.88152i	−0.185043	−	0.320504i	−0.943591	+	0.331113i	$0.892576\pi$
$462$	−2.95738	+	1.70745i	−0.137590	+	0.0794376i
$463$	11.2493			0.522800			0.261400	−	0.965231i	$-0.415816\pi$
$463$	11.2493			0.522800			0.261400	+	0.965231i	$0.415816\pi$
$464$	3.57292	−	2.06282i	0.165868	−	0.0957642i
$465$	5.51999	+	3.18697i	0.255983	+	0.147792i
$466$	−15.0792	−	8.70597i	−0.698530	−	0.403296i
$467$	−5.12618			−0.237211			−0.118606	−	0.992941i	$-0.537842\pi$
$467$	−5.12618			−0.237211			−0.118606	+	0.992941i	$0.537842\pi$
$468$	−9.21323	+	4.51340i	−0.425882	+	0.208632i
$469$			20.6021i			0.951315i
$470$	3.15810	+	1.82333i	0.145672	+	0.0841040i
$471$	6.61939	+	3.82171i	0.305005	+	0.176095i
$472$	−0.0723702	−	0.125349i	−0.00333111	−	0.00576965i
$473$			18.3325i			0.842928i
$474$	−0.544169	−	0.942528i	−0.0249945	−	0.0432918i
$475$	−6.76449	−	11.7164i	−0.310376	−	0.537587i
$476$	−9.61386	+	3.94537i	−0.440650	+	0.180836i
$477$	6.06984	+	10.5133i	0.277919	+	0.481370i
$478$	−5.42110	+	9.38962i	−0.247955	+	0.429471i
$479$	−10.7251	−	6.19216i	−0.490044	−	0.282927i	0.234549	−	0.972104i	$-0.424639\pi$
$479$	−10.7251	−	6.19216i	−0.490044	−	0.282927i	−0.724593	+	0.689177i	$0.757972\pi$
$480$	−0.698280			−0.0318720
$481$	16.6725	+	34.0336i	0.760199	+	1.55180i
$482$		−	3.62432i		−	0.165083i
$483$	−0.146637	−	0.0846610i	−0.00667222	−	0.00385221i
$484$	0.438294	−	0.759147i	0.0199224	−	0.0345067i
$485$	−5.64786	−	9.78238i	−0.256456	−	0.444195i
$486$		−	9.89525i		−	0.448858i
$487$	14.3966	−	8.31186i	0.652370	−	0.376646i	−0.136993	−	0.990572i	$-0.543744\pi$
$487$	14.3966	−	8.31186i	0.652370	−	0.376646i	0.789364	+	0.613926i	$0.210411\pi$
$488$	−13.4493	+	7.76493i	−0.608819	+	0.351502i
$489$	−2.53501			−0.114637
$490$	0.995984	−	0.575031i	0.0449940	−	0.0259773i
$491$	−1.09580	+	1.89797i	−0.0494526	+	0.0856544i	−0.889692	−	0.456561i	$-0.849081\pi$
$491$	−1.09580	+	1.89797i	−0.0494526	+	0.0856544i	0.840240	+	0.542215i	$0.182414\pi$
$492$	0.0253341	−	0.0438799i	0.00114215	−	0.00197826i
$493$	15.7369	−	6.45815i	0.708752	−	0.290861i
$494$	−21.9392	−	14.7428i	−0.987090	−	0.663311i
$495$	17.4166			0.782819
$496$	7.90512	+	4.56403i	0.354951	+	0.204931i
$497$	−6.03286	+	10.4492i	−0.270611	+	0.468712i
$498$	−2.27251	+	1.31203i	−0.101834	+	0.0587936i
$499$		−	18.3644i		−	0.822104i	−0.911612	−	0.411052i	$-0.865162\pi$
$499$		−	18.3644i		−	0.822104i	0.911612	−	0.411052i	$-0.134838\pi$
$500$	−10.5293	+	6.07912i	−0.470887	+	0.271867i
$501$	4.38621	+	7.59715i	0.195962	+	0.339415i
$502$	−0.302451			−0.0134990
$503$	12.0338	−	6.94775i	0.536563	−	0.309785i	−0.207122	−	0.978315i	$-0.566410\pi$
$503$	12.0338	−	6.94775i	0.536563	−	0.309785i	0.743685	+	0.668530i	$0.233076\pi$
$504$	−6.21084	−	3.58583i	−0.276653	−	0.159726i
$505$	−26.0779	−	15.0561i	−1.16045	−	0.669988i
$506$	0.588882			0.0261790
$507$	0.693740	−	5.06366i	0.0308101	−	0.224885i
$508$	20.6800			0.917525
$509$	8.54701	−	14.8039i	0.378840	−	0.656169i	−0.612054	−	0.790816i	$-0.709657\pi$
$509$	8.54701	−	14.8039i	0.378840	−	0.656169i	0.990894	+	0.134646i	$0.0429899\pi$
$510$	−2.85321	−	0.385137i	−0.126342	−	0.0170541i
$511$	11.8488	+	20.5227i	0.524159	+	0.907870i
$512$	−1.00000			−0.0441942
$513$	14.5906	−	8.42390i	0.644191	−	0.371924i
$514$	−2.14104	−	3.70838i	−0.0944371	−	0.163570i
$515$		−	13.0208i		−	0.573764i
$516$	1.81120	−	1.04569i	0.0797334	−	0.0460341i
$517$	6.12777	+	3.53787i	0.269499	+	0.155595i
$518$	−13.2460	+	22.9428i	−0.581998	+	1.00805i
$519$	8.70302			0.382020
$520$	−3.57177	+	5.31524i	−0.156633	+	0.233089i
$521$		−	18.7005i		−	0.819284i	−0.912246	−	0.409642i	$-0.865654\pi$
$521$		−	18.7005i		−	0.819284i	0.912246	−	0.409642i	$-0.134346\pi$
$522$	10.1665	+	5.86962i	0.444975	+	0.256906i
$523$	−21.6437	+	37.4880i	−0.946414	+	1.63924i	−0.193518	+	0.981097i	$0.561990\pi$
$523$	−21.6437	+	37.4880i	−0.946414	+	1.63924i	−0.752896	+	0.658140i	$0.771343\pi$
$524$	14.4173	−	8.32381i	0.629821	−	0.363627i
$525$	1.82864			0.0798086
$526$	3.03662	+	5.25958i	0.132403	+	0.229329i
$527$	29.7834	+	23.0089i	1.29739	+	1.00228i
$528$	−1.35489			−0.0589642
$529$	−11.4854	−	19.8933i	−0.499365	−	0.864926i
$530$	6.56236	+	3.78878i	0.285051	+	0.164574i
$531$	0.205925	−	0.356672i	0.00893636	−	0.0154782i
$532$		−	18.4773i		−	0.801093i
$533$	−0.204423	−	0.417291i	−0.00885456	−	0.0180749i
$534$		−	6.01419i		−	0.260259i
$535$	3.32790	−	5.76409i	0.143878	−	0.249203i
$536$	−4.08704	+	7.07896i	−0.176533	+	0.305765i
$537$	−3.20821	+	1.85226i	−0.138444	+	0.0799308i
$538$		−	2.11115i		−	0.0910181i
$539$	1.93254	−	1.11575i	0.0832403	−	0.0480588i
$540$	−2.04087	−	3.53490i	−0.0878252	−	0.152118i
$541$		−	26.0933i		−	1.12184i	−0.827871	−	0.560919i	$-0.810448\pi$
$541$		−	26.0933i		−	1.12184i	0.827871	−	0.560919i	$-0.189552\pi$
$542$	−6.75132	−	11.6936i	−0.289994	−	0.502284i
$543$	2.95924	−	5.12555i	0.126993	−	0.219959i
$544$	−4.08605	−	0.551551i	−0.175188	−	0.0236476i
$545$	−10.3950			−0.445273
$546$	3.20845	−	1.57176i	0.137309	−	0.0672652i
$547$		−	7.11102i		−	0.304045i	−0.988377	−	0.152023i	$-0.951421\pi$
$547$		−	7.11102i		−	0.304045i	0.988377	−	0.152023i	$-0.0485787\pi$
$548$	−6.44230	+	11.1584i	−0.275201	+	0.476663i
$549$	−38.2689	−	22.0946i	−1.63328	−	0.942974i
$550$	−5.50775	+	3.17990i	−0.234851	+	0.135592i
$551$			30.2454i			1.28850i
$552$	−0.0335901	−	0.0581798i	−0.00142969	−	0.00247630i
$553$	−3.48856	−	6.04236i	−0.148349	−	0.256947i
$554$			6.26815i			0.266308i
$555$	−6.35630	+	3.66981i	−0.269810	+	0.155775i
$556$	6.77086	+	3.90916i	0.287148	+	0.165785i
$557$	−1.75872	+	3.04618i	−0.0745191	+	0.129071i	−0.900877	−	0.434074i	$-0.857076\pi$
$557$	−1.75872	+	3.04618i	−0.0745191	+	0.129071i	0.826358	+	0.563145i	$0.190409\pi$
$558$			25.9732i			1.09954i
$559$	1.30472	−	19.1355i	0.0551838	−	0.809345i
$560$	−4.47653			−0.189168
$561$	−5.53616	−	0.747293i	−0.233737	−	0.0315507i
$562$	4.72635	−	8.18628i	0.199369	−	0.345317i
$563$	13.5862	+	23.5319i	0.572588	+	0.991752i	0.996299	+	0.0859542i	$0.0273939\pi$
$563$	13.5862	+	23.5319i	0.572588	+	0.991752i	−0.423711	+	0.905797i	$0.639273\pi$
$564$		−	0.807208i		−	0.0339896i
$565$	−9.45631	−	16.3788i	−0.397830	−	0.689062i
$566$	18.7041	−	10.7988i	0.786191	−	0.453908i
$567$		−	19.2378i		−	0.807910i
$568$	−4.14584	+	2.39360i	−0.173956	+	0.100433i
$569$	5.32688	−	9.22642i	0.223314	−	0.386792i	−0.732498	−	0.680769i	$-0.761646\pi$
$569$	5.32688	−	9.22642i	0.223314	−	0.386792i	0.955812	+	0.293977i	$0.0949790\pi$
$570$	2.55957	−	4.43330i	0.107208	−	0.185690i
$571$			33.9714i			1.42166i	0.703364	+	0.710830i	$0.251681\pi$
$571$			33.9714i			1.42166i	−0.703364	+	0.710830i	$0.748319\pi$
$572$	−6.93042	+	10.3133i	−0.289776	+	0.431222i
$573$			6.52312i			0.272507i
$574$	0.162412	−	0.281305i	0.00677893	−	0.0117414i
$575$	−0.273093	−	0.157670i	−0.0113888	−	0.00657531i
$576$	−1.42272	−	2.46422i	−0.0592798	−	0.102676i
$577$	−12.3286			−0.513244			−0.256622	−	0.966512i	$-0.582610\pi$
$577$	−12.3286			−0.513244			−0.256622	+	0.966512i	$0.582610\pi$
$578$	−16.3916	−	4.50733i	−0.681800	−	0.187480i
$579$	−1.69553	−	2.93674i	−0.0704637	−	0.122047i
$580$	7.32760			0.304262
$581$	−14.5686	+	8.41118i	−0.604407	+	0.348955i
$582$	−1.25018	+	2.16538i	−0.0518217	+	0.0897579i
$583$	12.7331	+	7.35149i	0.527353	+	0.304467i
$584$			9.40225i			0.389068i
$585$	−18.1795	−	1.23954i	−0.751631	−	0.0512487i
$586$	29.3519			1.21251
$587$	0.412347	−	0.714205i	0.0170194	−	0.0294784i	−0.857390	−	0.514667i	$-0.827916\pi$
$587$	0.412347	−	0.714205i	0.0170194	−	0.0294784i	0.874410	+	0.485188i	$0.161249\pi$
$588$	−0.220466	−	0.127286i	−0.00909187	−	0.00524919i
$589$	−57.9529	+	33.4591i	−2.38791	+	1.37866i
$590$		−	0.257075i		−	0.0105836i
$591$	−0.198262	−	0.343399i	−0.00815539	−	0.0141256i
$592$	−9.10280	+	5.25550i	−0.374123	+	0.216000i
$593$	−1.91348			−0.0785774			−0.0392887	−	0.999228i	$-0.512509\pi$
$593$	−1.91348			−0.0785774			−0.0392887	+	0.999228i	$0.512509\pi$
$594$	−3.95997	−	6.85887i	−0.162480	−	0.281423i
$595$	−18.2913	−	2.46904i	−0.749871	−	0.101221i
$596$	2.66432	−	4.61475i	0.109135	−	0.189027i
$597$	6.57514			0.269103
$598$	−0.614677	−	0.0419107i	−0.0251360	−	0.00171386i
$599$	31.1134			1.27126			0.635629	−	0.771995i	$-0.280741\pi$
$599$	31.1134			1.27126			0.635629	+	0.771995i	$0.280741\pi$
$600$	0.628331	+	0.362767i	0.0256515	+	0.0148099i
$601$	7.83325	+	4.52253i	0.319525	+	0.184478i	0.651181	−	0.758923i	$-0.274274\pi$
$601$	7.83325	+	4.52253i	0.319525	+	0.184478i	−0.331656	+	0.943400i	$0.607607\pi$
$602$	11.6112	−	6.70373i	0.473238	−	0.273224i
$603$	−23.2588			−0.947171
$604$	−2.34298	−	4.05816i	−0.0953344	−	0.165124i
$605$	1.34833	−	0.778458i	0.0548174	−	0.0316488i
$606$			6.66549i			0.270767i
$607$	−24.7375	+	14.2822i	−1.00407	+	0.579698i	−0.909449	−	0.415816i	$-0.863496\pi$
$607$	−24.7375	+	14.2822i	−1.00407	+	0.579698i	−0.0946173	+	0.995514i	$0.530163\pi$
$608$	3.66553	−	6.34888i	0.148657	−	0.257481i
$609$	−3.54041	−	2.04406i	−0.143465	−	0.0828294i
$610$	−27.5827			−1.11679
$611$	−6.14439	−	4.12895i	−0.248576	−	0.167039i
$612$	−4.45415	−	10.8536i	−0.180048	−	0.438731i
$613$	−5.28651	+	9.15650i	−0.213520	+	0.369828i	−0.952814	−	0.303556i	$-0.901826\pi$
$613$	−5.28651	+	9.15650i	−0.213520	+	0.369828i	0.739294	+	0.673383i	$0.235160\pi$
$614$	5.02195	−	8.69827i	0.202669	−	0.351034i
$615$	0.0779355	−	0.0449961i	0.00314266	−	0.00181442i
$616$	−8.68595			−0.349967
$617$	18.0174	−	10.4024i	0.725355	−	0.418784i	−0.0913657	−	0.995817i	$-0.529123\pi$
$617$	18.0174	−	10.4024i	0.725355	−	0.418784i	0.816720	+	0.577034i	$0.195790\pi$
$618$	−2.49607	+	1.44111i	−0.100407	+	0.0579698i
$619$		−	14.0519i		−	0.564794i	−0.959298	−	0.282397i	$-0.908871\pi$
$619$		−	14.0519i		−	0.564794i	0.959298	−	0.282397i	$-0.0911295\pi$
$620$	8.10621	+	14.0404i	0.325553	+	0.563875i
$621$	0.196349	−	0.340086i	0.00787921	−	0.0136472i
$622$	−18.6323	−	10.7573i	−0.747086	−	0.431330i
$623$		−	38.5558i		−	1.54470i
$624$	1.41424	+	0.0964278i	0.0566150	+	0.00386020i
$625$	−12.3672			−0.494689
$626$	4.05866	+	2.34327i	0.162217	+	0.0936559i
$627$	4.96641	−	8.60207i	0.198339	−	0.343533i
$628$	9.72071	+	16.8368i	0.387899	+	0.671860i
$629$	−40.0932	+	16.4536i	−1.59862	+	0.656048i
$630$	−6.36883	−	11.0311i	−0.253740	−	0.439491i
$631$	−13.2440	−	22.9393i	−0.527236	−	0.913200i	−0.999496	−	0.0317405i	$-0.989895\pi$
$631$	−13.2440	−	22.9393i	−0.527236	−	0.913200i	0.472260	−	0.881459i	$-0.343438\pi$
$632$		−	2.76824i		−	0.110115i
$633$	−4.37238	−	7.57319i	−0.173787	−	0.301007i
$634$	−26.8365	−	15.4941i	−1.06582	−	0.615349i
$635$	31.8090	+	18.3649i	1.26230	+	0.728790i
$636$		−	1.67733i		−	0.0665105i
$637$	−2.09660	+	1.02709i	−0.0830702	+	0.0406946i
$638$	14.2180			0.562895
$639$	−11.7967	−	6.81083i	−0.466670	−	0.269432i
$640$	−1.53816	−	0.888055i	−0.0608010	−	0.0351035i
$641$	−2.63903	+	1.52364i	−0.104235	+	0.0601803i	−0.551211	−	0.834366i	$-0.685834\pi$
$641$	−2.63903	+	1.52364i	−0.104235	+	0.0601803i	0.446976	+	0.894546i	$0.352501\pi$
$642$	−1.47330			−0.0581463
$643$	−38.1047	+	21.9997i	−1.50270	+	0.867585i	−0.502706	+	0.864457i	$0.667662\pi$
$643$	−38.1047	+	21.9997i	−1.50270	+	0.867585i	−0.999995	+	0.00312755i	$0.999004\pi$
$644$	−0.215340	−	0.372979i	−0.00848557	−	0.0146974i
$645$	3.71454			0.146260
$646$	18.4793	−	23.9201i	0.727057	−	0.941125i
$647$	18.5812	−	32.1837i	0.730504	−	1.26527i	−0.226164	−	0.974089i	$-0.572619\pi$
$647$	18.5812	−	32.1837i	0.730504	−	1.26527i	0.956668	−	0.291181i	$-0.0940482\pi$
$648$	3.81639	−	6.61018i	0.149922	−	0.259672i
$649$		−	0.498811i		−	0.0195800i
$650$	5.97533	−	2.92721i	0.234372	−	0.114815i
$651$		−	9.04502i		−	0.354502i
$652$	−5.58408	−	3.22397i	−0.218689	−	0.126260i
$653$	−13.7835	−	7.95790i	−0.539390	−	0.311417i	0.205442	−	0.978669i	$-0.434137\pi$
$653$	−13.7835	−	7.95790i	−0.539390	−	0.311417i	−0.744832	+	0.667252i	$0.767470\pi$
$654$	1.15049	+	1.99272i	0.0449879	+	0.0779213i
$655$	29.5680			1.15532
$656$	0.111611	−	0.0644385i	0.00435767	−	0.00251590i
$657$	−23.1692	+	13.3767i	−0.903916	+	0.521876i
$658$		−	5.17485i		−	0.201737i
$659$	6.69127	+	11.5896i	0.260655	+	0.451468i	0.966416	−	0.256982i	$-0.0827282\pi$
$659$	6.69127	+	11.5896i	0.260655	+	0.451468i	−0.705761	+	0.708450i	$0.749395\pi$
$660$	−2.08404	−	1.20322i	−0.0811211	−	0.0468353i
$661$	6.72296	−	11.6445i	0.261493	−	0.452919i	−0.705146	−	0.709062i	$-0.749118\pi$
$661$	6.72296	−	11.6445i	0.261493	−	0.452919i	0.966639	+	0.256143i	$0.0824518\pi$
$662$	11.8643			0.461118
$663$	5.72548	+	1.17404i	0.222359	+	0.0455958i
$664$	−6.67445			−0.259019
$665$	16.4089	−	28.4210i	0.636308	−	1.10212i
$666$	−25.9014	−	14.9542i	−1.00366	−	0.579463i
$667$	0.352488	+	0.610527i	0.0136484	+	0.0236397i
$668$			22.3131i			0.863320i
$669$	−3.06456	+	1.76932i	−0.118483	+	0.0684060i
$670$	−12.5730	+	7.25903i	−0.485738	+	0.280441i
$671$	−53.5197			−2.06610
$672$	0.495452	+	0.858147i	0.0191125	+	0.0331038i
$673$	−2.84795	−	1.64427i	−0.109781	−	0.0633818i	0.444104	−	0.895975i	$-0.353522\pi$
$673$	−2.84795	−	1.64427i	−0.109781	−	0.0633818i	−0.553885	+	0.832593i	$0.686855\pi$
$674$	3.13280	+	1.80873i	0.120671	+	0.0696695i
$675$			4.24106i			0.163238i
$676$	7.96800	−	10.2719i	0.306462	−	0.395071i
$677$			27.6386i			1.06224i	0.847298	+	0.531118i	$0.178228\pi$
$677$			27.6386i			1.06224i	−0.847298	+	0.531118i	$0.821772\pi$
$678$	−2.09320	+	3.62553i	−0.0803890	+	0.139238i
$679$	−8.01467	+	13.8818i	−0.307575	+	0.532735i
$680$	−5.79517	−	4.47701i	−0.222235	−	0.171685i
$681$	10.7142			0.410571
$682$	15.7287	+	27.2430i	0.602284	+	1.04319i
$683$	39.7272	−	22.9365i	1.52012	−	0.877642i	0.520401	−	0.853922i	$-0.325782\pi$
$683$	39.7272	−	22.9365i	1.52012	−	0.877642i	0.999719	−	0.0237196i	$-0.00755088\pi$
$684$	20.8600			0.797603
$685$	−19.8185	+	11.4422i	−0.757227	+	0.437185i
$686$	−16.6926	−	9.63745i	−0.637325	−	0.367960i
$687$	6.46715	+	3.73381i	0.246737	+	0.142454i
$688$	5.31955			0.202806
$689$	−12.7677	−	8.57972i	−0.486411	−	0.326861i
$690$		−	0.119320i		−	0.00454242i
$691$	−21.3175	−	12.3077i	−0.810956	−	0.468205i	0.0363320	−	0.999340i	$-0.488433\pi$
$691$	−21.3175	−	12.3077i	−0.810956	−	0.468205i	−0.847288	+	0.531134i	$0.821766\pi$
$692$	19.1708	+	11.0683i	0.728766	+	0.420753i
$693$	−12.3576	−	21.4041i	−0.469428	−	0.813074i
$694$			1.84241i			0.0699371i
$695$	6.94309	+	12.0258i	0.263367	+	0.456164i
$696$	−0.811001	−	1.40470i	−0.0307409	−	0.0532449i
$697$	0.491588	−	0.201740i	0.0186202	−	0.00764144i
$698$	−11.3613	−	19.6783i	−0.430030	−	0.744834i
$699$	−3.42276	+	5.92840i	−0.129461	+	0.224233i
$700$	4.02810	+	2.32563i	0.152248	+	0.0879004i
$701$	15.7971			0.596649			0.298325	−	0.954464i	$-0.403572\pi$
$701$	15.7971			0.596649			0.298325	+	0.954464i	$0.403572\pi$
$702$	3.64529	+	7.44114i	0.137582	+	0.280848i
$703$		−	77.0568i		−	2.90625i
$704$	−2.98453	−	1.72312i	−0.112484	−	0.0649426i
$705$	0.716845	−	1.24161i	0.0269979	−	0.0467618i
$706$	10.1891	+	17.6481i	0.383472	+	0.664194i
$707$			42.7311i			1.60707i
$708$	−0.0492811	+	0.0284524i	−0.00185210	+	0.00106931i
$709$	−22.6841	+	13.0967i	−0.851921	+	0.491857i	−0.861298	−	0.508099i	$-0.830348\pi$
$709$	−22.6841	+	13.0967i	−0.851921	+	0.491857i	0.00937777	+	0.999956i	$0.497015\pi$
$710$	−8.50260			−0.319097
$711$	6.82155	−	3.93842i	0.255828	−	0.147702i
$712$	7.64870	−	13.2479i	0.286647	−	0.496487i
$713$	−0.779884	+	1.35080i	−0.0292069	+	0.0505878i
$714$	1.55113	+	3.77970i	0.0580495	+	0.141452i
$715$	−19.8189	+	9.70892i	−0.741184	+	0.363093i
$716$	−9.42263			−0.352140
$717$	3.69154	+	2.13131i	0.137863	+	0.0795953i
$718$	11.6847	−	20.2385i	0.436069	−	0.755294i
$719$	−43.0030	+	24.8278i	−1.60374	+	0.925921i	−0.613012	+	0.790074i	$0.710042\pi$
$719$	−43.0030	+	24.8278i	−1.60374	+	0.925921i	−0.990730	+	0.135847i	$0.956624\pi$
$720$		−	5.05380i		−	0.188344i
$721$	−16.0018	+	9.23865i	−0.595939	+	0.344065i
$722$	17.3722	+	30.0896i	0.646527	+	1.11982i
$723$	−1.42490			−0.0529928
$724$	13.0371	−	7.52698i	0.484520	−	0.279738i
$725$	−6.59357	−	3.80680i	−0.244879	−	0.141381i
$726$	−0.298459	−	0.172316i	−0.0110769	−	0.00639523i
$727$	−16.3105			−0.604922			−0.302461	−	0.953162i	$-0.597808\pi$
$727$	−16.3105			−0.604922			−0.302461	+	0.953162i	$0.597808\pi$
$728$	9.06643	+	0.618179i	0.336024	+	0.0229112i
$729$	19.0080			0.704000
$730$	−8.34971	+	14.4621i	−0.309037	+	0.535267i
$731$	21.7359	+	2.93400i	0.803933	+	0.108518i
$732$	3.05279	+	5.28759i	0.112834	+	0.195435i
$733$	−19.8609			−0.733577			−0.366789	−	0.930304i	$-0.619543\pi$
$733$	−19.8609			−0.733577			−0.366789	+	0.930304i	$0.619543\pi$
$734$	−10.6618	+	6.15561i	−0.393535	+	0.227208i
$735$	−0.226074	−	0.391572i	−0.00833888	−	0.0144434i
$736$		−	0.170876i		−	0.00629859i
$737$	−24.3958	+	14.0849i	−0.898632	+	0.518825i
$738$	0.317581	+	0.183355i	0.0116903	+	0.00674940i
$739$	16.3121	−	28.2534i	0.600052	−	1.03932i	−0.392761	−	0.919641i	$-0.628480\pi$
$739$	16.3121	−	28.2534i	0.600052	−	1.03932i	0.992813	−	0.119679i	$-0.0381866\pi$
$740$	−18.6687			−0.686275
$741$	−5.79616	+	8.62541i	−0.212927	+	0.316862i
$742$		−	10.7530i		−	0.394756i
$743$	20.1057	+	11.6080i	0.737606	+	0.425857i	0.821198	−	0.570643i	$-0.193306\pi$
$743$	20.1057	+	11.6080i	0.737606	+	0.425857i	−0.0835924	+	0.996500i	$0.526639\pi$
$744$	1.79435	−	3.10791i	0.0657841	−	0.113941i
$745$	8.19630	−	4.73213i	0.300289	−	0.173372i
$746$	11.9167			0.436302
$747$	−9.49584	−	16.4473i	−0.347435	−	0.601775i
$748$	−11.2446	−	8.68688i	−0.411142	−	0.317624i
$749$	−9.44500			−0.345113
$750$	2.39001	+	4.13962i	0.0872710	+	0.151158i
$751$	23.4295	+	13.5270i	0.854955	+	0.493608i	0.862319	−	0.506365i	$-0.169011\pi$
$751$	23.4295	+	13.5270i	0.854955	+	0.493608i	−0.00736484	+	0.999973i	$0.502344\pi$
$752$	1.02659	−	1.77810i	0.0374358	−	0.0648407i
$753$			0.118909i			0.00433328i
$754$	−14.8408	−	1.01189i	−0.540469	−	0.0368510i
$755$		−	8.32277i		−	0.302897i
$756$	−2.89613	+	5.01624i	−0.105331	+	0.182439i
$757$	11.2802	−	19.5378i	0.409985	−	0.710115i	−0.584902	−	0.811104i	$-0.698867\pi$
$757$	11.2802	−	19.5378i	0.409985	−	0.710115i	0.994888	+	0.100988i	$0.0322005\pi$
$758$	8.80729	−	5.08489i	0.319895	−	0.184692i
$759$		−	0.231519i		−	0.00840362i
$760$	11.2763	−	6.51039i	0.409035	−	0.236157i
$761$	−14.4527	−	25.0328i	−0.523910	−	0.907438i	−0.999613	−	0.0278323i	$-0.991140\pi$
$761$	−14.4527	−	25.0328i	−0.523910	−	0.907438i	0.475703	−	0.879606i	$-0.342194\pi$
$762$		−	8.13035i		−	0.294531i
$763$	7.37559	+	12.7749i	0.267014	+	0.462482i
$764$	−8.29594	+	14.3690i	−0.300137	+	0.519852i
$765$	2.78743	−	20.6501i	0.100780	−	0.746605i
$766$	−6.74218			−0.243605
$767$	−0.0355003	+	0.520660i	−0.00128184	+	0.0188000i
$768$			0.393151i			0.0141866i
$769$	−14.9590	+	25.9097i	−0.539435	+	0.934329i	0.459499	+	0.888178i	$0.348029\pi$
$769$	−14.9590	+	25.9097i	−0.539435	+	0.934329i	−0.998934	+	0.0461509i	$0.985304\pi$
$770$	−13.3604	−	7.71361i	−0.481474	−	0.277979i
$771$	−1.45796	+	0.841751i	−0.0525070	+	0.0303149i
$772$		−	8.62532i		−	0.310432i
$773$	7.06086	+	12.2298i	0.253962	+	0.439874i	0.964613	−	0.263670i	$-0.0849330\pi$
$773$	7.06086	+	12.2298i	0.253962	+	0.439874i	−0.710651	+	0.703544i	$0.751600\pi$
$774$	7.56821	+	13.1085i	0.272034	+	0.471176i
$775$		−	16.8452i		−	0.605097i
$776$	−5.50775	+	3.17990i	−0.197717	+	0.114152i
$777$	9.02000	+	5.20770i	0.323591	+	0.186825i
$778$	5.54363	−	9.60184i	0.198749	−	0.344243i
$779$			0.944805i			0.0338511i
$780$	2.08969	+	1.40425i	0.0748231	+	0.0502801i
$781$	−16.4979			−0.590340
$782$	0.0942470	−	0.698209i	0.00337027	−	0.0249679i
$783$	4.74065	−	8.21105i	0.169417	−	0.293439i
$784$	−0.323759	−	0.560767i	−0.0115628	−	0.0200274i
$785$			34.5301i			1.23243i
$786$	−3.27252	−	5.66816i	−0.116727	−	0.202177i
$787$	−9.66904	+	5.58242i	−0.344664	+	0.198992i	−0.662333	−	0.749210i	$-0.730433\pi$
$787$	−9.66904	+	5.58242i	−0.344664	+	0.198992i	0.317669	+	0.948202i	$0.397100\pi$
$788$		−	1.00858i		−	0.0359291i
$789$	2.06781	−	1.19385i	0.0736160	−	0.0425022i
$790$	2.45835	−	4.25799i	0.0874643	−	0.151493i
$791$	−13.4191	+	23.2426i	−0.477128	+	0.826411i
$792$		−	9.80605i		−	0.348443i
$793$	55.8640	+	3.80899i	1.98379	+	0.135261i
$794$		−	23.8040i		−	0.844774i
$795$	1.48956	−	2.58000i	0.0528293	−	0.0915031i
$796$	14.4836	+	8.36211i	0.513357	+	0.296387i
$797$	20.5264	+	35.5528i	0.727083	+	1.25934i	0.958111	+	0.286397i	$0.0924576\pi$
$797$	20.5264	+	35.5528i	0.727083	+	1.25934i	−0.231028	+	0.972947i	$0.574209\pi$
$798$	−7.26437			−0.257156
$799$	5.17540	−	6.69919i	0.183092	−	0.237000i
$800$	0.922716	+	1.59819i	0.0326229	+	0.0565046i
$801$	43.5277			1.53798
$802$	−13.2096	+	7.62655i	−0.466446	+	0.269303i
$803$	−16.2012	+	28.0613i	−0.571728	+	0.990263i
$804$	2.78310	+	1.60682i	0.0981524	+	0.0566683i
$805$		−	0.764934i		−	0.0269604i
$806$	−14.4788	−	29.5557i	−0.509995	−	1.04106i
$807$	−0.830001			−0.0292174
$808$	−8.47701	+	14.6826i	−0.298220	+	0.516532i
$809$	−0.691853	−	0.399441i	−0.0243242	−	0.0140436i	0.487789	−	0.872962i	$-0.337804\pi$
$809$	−0.691853	−	0.399441i	−0.0243242	−	0.0140436i	−0.512113	+	0.858918i	$0.671137\pi$
$810$	11.7404	−	6.77833i	0.412516	−	0.238166i
$811$			9.15833i			0.321592i	0.986988	+	0.160796i	$0.0514062\pi$
$811$			9.15833i			0.321592i	−0.986988	+	0.160796i	$0.948594\pi$
$812$	−5.19917	−	9.00522i	−0.182455	−	0.316021i
$813$	−4.59736	+	2.65429i	−0.161237	+	0.0930900i
$814$	−36.2235			−1.26963
$815$	−5.72612	−	9.91793i	−0.200577	−	0.347410i
$816$	−0.216843	+	1.60643i	−0.00759102	+	0.0562365i
$817$	−19.4990	+	33.7732i	−0.682183	+	1.18158i
$818$	16.6499			0.582149
$819$	11.3756	+	23.2211i	0.397497	+	0.811412i
$820$	0.228900			0.00799352
$821$	−16.8274	−	9.71531i	−0.587281	−	0.339067i	0.176741	−	0.984257i	$-0.443445\pi$
$821$	−16.8274	−	9.71531i	−0.587281	−	0.339067i	−0.764021	+	0.645191i	$0.776778\pi$
$822$	4.38693	+	2.53280i	0.153012	+	0.0883415i
$823$	22.4487	−	12.9608i	0.782514	−	0.451784i	−0.0548067	−	0.998497i	$-0.517454\pi$
$823$	22.4487	−	12.9608i	0.782514	−	0.451784i	0.837320	+	0.546713i	$0.184121\pi$
$824$	−7.33106			−0.255390
$825$	1.25018	+	2.16538i	0.0435258	+	0.0753889i
$826$	−0.315931	+	0.182403i	−0.0109926	+	0.00634661i
$827$			48.0859i			1.67211i	0.548645	+	0.836055i	$0.315144\pi$
$827$			48.0859i			1.67211i	−0.548645	+	0.836055i	$0.684856\pi$
$828$	0.421077	−	0.243109i	0.0146334	−	0.00844861i
$829$	9.78082	−	16.9409i	0.339702	−	0.588381i	−0.644675	−	0.764457i	$-0.723007\pi$
$829$	9.78082	−	16.9409i	0.339702	−	0.588381i	0.984377	+	0.176076i	$0.0563405\pi$
$830$	−10.2663	−	5.92728i	−0.356350	−	0.205739i
$831$	2.46433			0.0854866
$832$	2.99263	+	2.01101i	0.103751	+	0.0697192i
$833$	−1.01360	−	2.46989i	−0.0351193	−	0.0855766i
$834$	1.53689	−	2.66197i	0.0532181	−	0.0921765i
$835$	−19.8153	+	34.3211i	−0.685736	+	1.18773i
$836$	21.8798	−	12.6323i	0.756729	−	0.436897i
$837$	20.9775			0.725089
$838$	32.9339	−	19.0144i	1.13768	−	0.656841i
$839$	−26.1400	+	15.0920i	−0.902454	+	0.521032i	−0.877996	−	0.478669i	$-0.841119\pi$
$839$	−26.1400	+	15.0920i	−0.902454	+	0.521032i	−0.0244584	+	0.999701i	$0.507786\pi$
$840$			1.75995i			0.0607242i
$841$	−5.98952	−	10.3742i	−0.206535	−	0.357729i
$842$	10.5694	−	18.3067i	0.364245	−	0.630890i
$843$	−3.21844	−	1.85817i	−0.110849	−	0.0639988i
$844$		−	22.2427i		−	0.765627i
$845$	21.3780	−	8.72370i	0.735426	−	0.300104i
$846$	5.84217			0.200858
$847$	−1.91336	−	1.10468i	−0.0657440	−	0.0379573i
$848$	2.13319	−	3.69479i	0.0732540	−	0.126880i
$849$	−4.24556	−	7.35353i	−0.145707	−	0.252373i
$850$	2.88878	+	7.03921i	0.0990843	+	0.241443i
$851$	−0.898042	−	1.55545i	−0.0307845	−	0.0533203i
$852$	0.941047	+	1.62994i	0.0322397	+	0.0558409i
$853$			6.34844i			0.217367i	0.994076	+	0.108683i	$0.0346634\pi$
$853$			6.34844i			0.217367i	−0.994076	+	0.108683i	$0.965337\pi$
$854$	19.5708	+	33.8977i	0.669700	+	1.15995i
$855$	32.0860	+	18.5249i	1.09732	+	0.633537i
$856$	−3.24534	−	1.87370i	−0.110924	−	0.0640418i
$857$			27.9099i			0.953383i	0.879071	+	0.476692i	$0.158164\pi$
$857$			27.9099i			0.953383i	−0.879071	+	0.476692i	$0.841836\pi$
$858$	4.05470	+	2.72470i	0.138425	+	0.0930199i
$859$	−5.57228			−0.190124			−0.0950618	−	0.995471i	$-0.530305\pi$
$859$	−5.57228			−0.190124			−0.0950618	+	0.995471i	$0.530305\pi$
$860$	8.18230	+	4.72406i	0.279014	+	0.161089i
$861$	−0.110595	−	0.0638523i	−0.00376908	−	0.00217608i
$862$	5.78500	−	3.33997i	0.197038	−	0.113760i
$863$	−16.9075			−0.575537			−0.287769	−	0.957700i	$-0.592913\pi$
$863$	−16.9075			−0.575537			−0.287769	+	0.957700i	$0.592913\pi$
$864$	−1.99025	+	1.14907i	−0.0677096	+	0.0390921i
$865$	19.6585	+	34.0495i	0.668409	+	1.15772i
$866$	−24.3544			−0.827596
$867$	−1.77206	+	6.44437i	−0.0601823	+	0.218862i
$868$	11.5032	−	19.9242i	0.390445	−	0.676271i
$869$	4.77002	−	8.26192i	0.161812	−	0.280266i
$870$		−	2.88086i		−	0.0976702i
$871$	26.4669	−	12.9656i	0.896795	−	0.439324i
$872$			5.85268i			0.198197i
$873$	−15.6719	−	9.04820i	−0.530415	−	0.306235i
$874$	1.08487	+	0.626353i	0.0366964	+	0.0211867i
$875$	15.3219	+	26.5383i	0.517975	+	0.897158i
$876$	3.69650			0.124893
$877$	25.8995	−	14.9531i	0.874564	−	0.504930i	0.00570167	−	0.999984i	$-0.498185\pi$
$877$	25.8995	−	14.9531i	0.874564	−	0.504930i	0.868862	+	0.495054i	$0.164852\pi$
$878$	3.95737	−	2.28479i	0.133555	−	0.0771079i
$879$		−	11.5397i		−	0.389225i
$880$	−3.06045	−	5.30086i	−0.103168	−	0.178692i
$881$	−13.7255	−	7.92441i	−0.462423	−	0.266980i	0.250640	−	0.968080i	$-0.419359\pi$
$881$	−13.7255	−	7.92441i	−0.462423	−	0.266980i	−0.713063	+	0.701100i	$0.752692\pi$
$882$	0.921234	−	1.59562i	0.0310196	−	0.0537275i
$883$	45.1238			1.51854			0.759269	−	0.650777i	$-0.225557\pi$
$883$	45.1238			1.51854			0.759269	+	0.650777i	$0.225557\pi$
$884$	11.1189	+	9.86767i	0.373968	+	0.331886i
$885$	−0.101069			−0.00339741
$886$	9.94732	−	17.2293i	0.334187	−	0.578829i
$887$	10.9013	+	6.29384i	0.366028	+	0.211327i	0.671722	−	0.740803i	$-0.265555\pi$
$887$	10.9013	+	6.29384i	0.366028	+	0.211327i	−0.305694	+	0.952130i	$0.598888\pi$
$888$	2.06621	+	3.57878i	0.0693374	+	0.120096i
$889$		−	52.1220i		−	1.74812i
$890$	23.5298	−	13.5849i	0.788721	−	0.455368i
$891$	22.7803	−	13.1522i	0.763168	−	0.440616i
$892$	−9.00073			−0.301367
$893$	7.52597	+	13.0354i	0.251847	+	0.436212i
$894$	−1.81429	−	1.04748i	−0.0606790	−	0.0350330i
$895$	−14.4935	−	8.36781i	−0.484463	−	0.279705i
$896$			2.52041i			0.0842011i
$897$	−0.0164772	+	0.241661i	−0.000550159	+	0.00806882i
$898$		−	14.9258i		−	0.498079i
$899$	−18.8296	+	32.6137i	−0.628001	+	1.08773i
$900$	−2.62553	+	4.54754i	−0.0875175	+	0.151585i
$901$	10.7542	−	13.9205i	0.358274	−	0.463760i
$902$	0.444141			0.0147883
$903$	−2.63558	−	4.56496i	−0.0877066	−	0.151912i
$904$	−9.22173	+	5.32417i	−0.306710	+	0.177079i
$905$	26.7375			0.888784
$906$	−1.59547	+	0.921144i	−0.0530059	+	0.0306030i
$907$	20.3979	+	11.7767i	0.677300	+	0.391039i	0.798837	−	0.601548i	$-0.205449\pi$
$907$	20.3979	+	11.7767i	0.677300	+	0.391039i	−0.121537	+	0.992587i	$0.538782\pi$
$908$	23.6011	+	13.6261i	0.783231	+	0.452198i
$909$	−48.2415			−1.60007
$910$	13.3966	+	9.00234i	0.444093	+	0.298425i
$911$			10.4307i			0.345585i	0.984958	+	0.172793i	$0.0552790\pi$
$911$			10.4307i			0.345585i	−0.984958	+	0.172793i	$0.944721\pi$
$912$	−2.49607	−	1.44111i	−0.0826532	−	0.0477198i
$913$	−19.9201	−	11.5009i	−0.659259	−	0.380624i
$914$	−14.1941	−	24.5850i	−0.469500	−	0.813199i
$915$			10.8442i			0.358498i
$916$	9.49713	+	16.4495i	0.313794	+	0.543507i
$917$	−20.9794	−	36.3375i	−0.692802	−	1.19997i
$918$	−8.76601	+	3.59743i	−0.289322	+	0.118733i
$919$	−14.0455	−	24.3276i	−0.463319	−	0.802493i	0.535804	−	0.844342i	$-0.320008\pi$
$919$	−14.0455	−	24.3276i	−0.463319	−	0.802493i	−0.999124	+	0.0418492i	$0.986675\pi$
$920$	0.151748	−	0.262835i	0.00500297	−	0.00866540i
$921$	−3.41974	−	1.97439i	−0.112684	−	0.0650582i
$922$	−7.94610			−0.261691
$923$	17.2205	+	1.17415i	0.566820	+	0.0386477i
$924$			3.41489i			0.112342i
$925$	16.7986	+	9.69868i	0.552335	+	0.318891i
$926$	5.62466	−	9.74219i	0.184838	−	0.320148i
$927$	−10.4300	−	18.0653i	−0.342567	−	0.593343i
$928$		−	4.12565i		−	0.135431i
$929$	−11.9787	+	6.91589i	−0.393008	+	0.226903i	−0.683462	−	0.729986i	$-0.739527\pi$
$929$	−11.9787	+	6.91589i	−0.393008	+	0.226903i	0.290455	+	0.956889i	$0.406193\pi$
$930$	5.51999	−	3.18697i	0.181008	−	0.104505i
$931$	4.74699			0.155576
$932$	−15.0792	+	8.70597i	−0.493935	+	0.285174i
$933$	−4.22926	+	7.32530i	−0.138460	+	0.239820i
$934$	−2.56309	+	4.43940i	−0.0838668	+	0.145262i
$935$	−9.58147	−	23.3476i	−0.313347	−	0.763547i
$936$	−0.697896	+	10.2356i	−0.0228115	+	0.334561i
$937$	10.9776			0.358623			0.179312	−	0.983792i	$-0.442613\pi$
$937$	10.9776			0.358623			0.179312	+	0.983792i	$0.442613\pi$
$938$	17.8419	+	10.3010i	0.582559	+	0.336341i
$939$	0.921259	−	1.59567i	0.0300641	−	0.0520726i
$940$	3.15810	−	1.82333i	0.103006	−	0.0594705i
$941$			31.4554i			1.02542i	0.858563	+	0.512708i	$0.171358\pi$
$941$			31.4554i			1.02542i	−0.858563	+	0.512708i	$0.828642\pi$
$942$	6.61939	−	3.82171i	0.215671	−	0.124518i
$943$	0.0110110	+	0.0190716i	0.000358568	+	0.000621058i
$944$	−0.144740			−0.00471090
$945$	−8.90940	+	5.14384i	−0.289823	+	0.167329i
$946$	15.8764	+	9.16623i	0.516186	+	0.298020i
$947$	35.7581	+	20.6449i	1.16198	+	0.670870i	0.951778	−	0.306788i	$-0.0992541\pi$
$947$	35.7581	+	20.6449i	1.16198	+	0.670870i	0.210203	+	0.977658i	$0.432587\pi$
$948$	−1.08834			−0.0353476
$949$	18.9080	−	28.1375i	0.613780	−	0.913381i
$950$	−13.5290			−0.438938
$951$	−6.09152	+	10.5508i	−0.197531	+	0.342134i
$952$	−1.39014	+	10.2985i	−0.0450546	+	0.333777i
$953$	16.7428	+	28.9994i	0.542353	+	0.939383i	0.998768	+	0.0496161i	$0.0157998\pi$
$953$	16.7428	+	28.9994i	0.542353	+	0.939383i	−0.456415	+	0.889767i	$0.650867\pi$
$954$	12.1397			0.393037
$955$	−25.5209	+	14.7345i	−0.825837	+	0.476797i
$956$	5.42110	+	9.38962i	0.175331	+	0.303682i
$957$		−	5.58982i		−	0.180693i
$958$	−10.7251	+	6.19216i	−0.346513	+	0.200060i
$959$	28.1238	+	16.2373i	0.908163	+	0.524328i
$960$	−0.349140	+	0.604728i	−0.0112684	+	0.0195175i
$961$	−52.3213			−1.68778
$962$	37.8102	+	2.57802i	1.21905	+	0.0831188i
$963$		−	10.6630i		−	0.343610i
$964$	−3.13875	−	1.81216i	−0.101092	−	0.0583657i
$965$	7.65976	−	13.2671i	0.246576	−	0.427083i
$966$	−0.146637	+	0.0846610i	−0.00471797	+	0.00272392i
$967$	−13.0454			−0.419513			−0.209756	−	0.977754i	$-0.567267\pi$
$967$	−13.0454			−0.419513			−0.209756	+	0.977754i	$0.567267\pi$
$968$	−0.438294	−	0.759147i	−0.0140873	−	0.0243999i
$969$	−9.40422	−	7.26515i	−0.302107	−	0.233390i
$970$	−11.2957			−0.362684
$971$	−17.1693	−	29.7381i	−0.550989	−	0.954341i	−0.998204	−	0.0599145i	$-0.980917\pi$
$971$	−17.1693	−	29.7381i	−0.550989	−	0.954341i	0.447214	−	0.894427i	$-0.352416\pi$
$972$	−8.56954	−	4.94763i	−0.274868	−	0.158695i
$973$	9.85269	−	17.0654i	0.315863	−	0.547090i
$974$		−	16.6237i		−	0.532658i
$975$	−1.15083	−	2.34921i	−0.0368562	−	0.0752348i
$976$			15.5299i			0.497099i
$977$	−5.41366	+	9.37674i	−0.173198	+	0.299988i	−0.939536	−	0.342449i	$-0.888744\pi$
$977$	−5.41366	+	9.37674i	−0.173198	+	0.299988i	0.766338	+	0.642438i	$0.222077\pi$
$978$	−1.26751	+	2.19539i	−0.0405304	+	0.0702007i
$979$	45.6556	−	26.3593i	1.45916	−	0.842446i
$980$		−	1.15006i		−	0.0367374i
$981$	−14.4223	+	8.32671i	−0.460468	+	0.265851i
$982$	1.09580	+	1.89797i	0.0349682	+	0.0605668i
$983$			0.651250i			0.0207717i	0.999946	+	0.0103858i	$0.00330597\pi$
$983$			0.651250i			0.0207717i	−0.999946	+	0.0103858i	$0.996694\pi$
$984$	−0.0253341	−	0.0438799i	−0.000807620	−	0.00139884i
$985$	0.895672	−	1.55135i	0.0285385	−	0.0494301i
$986$	2.27550	−	16.8576i	0.0724668	−	0.536855i
$987$	−2.03450			−0.0647588
$988$	−23.7372	+	11.6285i	−0.755182	+	0.369951i
$989$			0.908986i			0.0289041i
$990$	8.70831	−	15.0832i	0.276768	−	0.479377i
$991$	−15.6791	−	9.05231i	−0.498062	−	0.287556i	0.229851	−	0.973226i	$-0.426176\pi$
$991$	−15.6791	−	9.05231i	−0.498062	−	0.287556i	−0.727913	+	0.685670i	$0.759509\pi$
$992$	7.90512	−	4.56403i	0.250988	−	0.144908i
$993$		−	4.66445i		−	0.148022i
$994$	6.03286	+	10.4492i	0.191351	+	0.331429i
$995$	14.8520	+	25.7245i	0.470841	+	0.815520i
$996$			2.62407i			0.0831467i
$997$	20.9161	−	12.0759i	0.662420	−	0.382448i	−0.130779	−	0.991412i	$-0.541748\pi$
$997$	20.9161	−	12.0759i	0.662420	−	0.382448i	0.793198	+	0.608963i	$0.208414\pi$
$998$	−15.9040	−	9.18220i	−0.503434	−	0.290658i
$999$	−12.0779	+	20.9195i	−0.382127	+	0.661864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	442.2.m.b.373.6	yes	24
13.3	even	3	inner	442.2.m.b.237.7	yes	24
17.16	even	2	inner	442.2.m.b.373.7	yes	24
221.16	even	6	inner	442.2.m.b.237.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
442.2.m.b.237.6	✓	24	221.16	even	6	inner
442.2.m.b.237.7	yes	24	13.3	even	3	inner
442.2.m.b.373.6	yes	24	1.1	even	1	trivial
442.2.m.b.373.7	yes	24	17.16	even	2	inner

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:	\( N \)	\(=\)	\( 442 = 2 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	442.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.340479 - 0.196576i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.77611i q^{5} +(-0.340479 + 0.196576i) q^{6} +(-2.18274 + 1.26021i) q^{7} -1.00000 q^{8} +(-1.42272 - 2.46422i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.340479 - 0.196576i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.77611i q^{5} +(-0.340479 + 0.196576i) q^{6} +(-2.18274 + 1.26021i) q^{7} -1.00000 q^{8} +(-1.42272 - 2.46422i) q^{9} +(-1.53816 - 0.888055i) q^{10} +(-2.98453 - 1.72312i) q^{11} +0.393151i q^{12} +(2.99263 + 2.01101i) q^{13} +2.52041i q^{14} +(-0.349140 + 0.604728i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.52068 + 3.26285i) q^{17} -2.84543 q^{18} +(-3.66553 - 6.34888i) q^{19} +(-1.53816 + 0.888055i) q^{20} +0.990903 q^{21} +(-2.98453 + 1.72312i) q^{22} +(-0.147983 - 0.0854382i) q^{23} +(0.340479 + 0.196576i) q^{24} +1.84543 q^{25} +(3.23790 - 1.58619i) q^{26} +2.29814i q^{27} +(2.18274 + 1.26021i) q^{28} +(-3.57292 - 2.06282i) q^{29} +(0.349140 + 0.604728i) q^{30} -9.12805i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.677447 + 1.17337i) q^{33} +(1.56537 + 3.81440i) q^{34} +(2.23827 + 3.87679i) q^{35} +(-1.42272 + 2.46422i) q^{36} +(9.10280 + 5.25550i) q^{37} -7.33106 q^{38} +(-0.623613 - 1.27298i) q^{39} +1.77611i q^{40} +(-0.111611 - 0.0644385i) q^{41} +(0.495452 - 0.858147i) q^{42} +(-2.65978 - 4.60687i) q^{43} +3.44624i q^{44} +(-4.37672 + 2.52690i) q^{45} +(-0.147983 + 0.0854382i) q^{46} -2.05317 q^{47} +(0.340479 - 0.196576i) q^{48} +(-0.323759 + 0.560767i) q^{49} +(0.922716 - 1.59819i) q^{50} +(1.49963 - 0.615426i) q^{51} +(0.245269 - 3.59720i) q^{52} -4.26638 q^{53} +(1.99025 + 1.14907i) q^{54} +(-3.06045 + 5.30086i) q^{55} +(2.18274 - 1.26021i) q^{56} +2.88221i q^{57} +(-3.57292 + 2.06282i) q^{58} +(0.0723702 + 0.125349i) q^{59} +0.698280 q^{60} +(13.4493 - 7.76493i) q^{61} +(-7.90512 - 4.56403i) q^{62} +(6.21084 + 3.58583i) q^{63} +1.00000 q^{64} +(3.57177 - 5.31524i) q^{65} +1.35489 q^{66} +(4.08704 - 7.07896i) q^{67} +(4.08605 + 0.551551i) q^{68} +(0.0335901 + 0.0581798i) q^{69} +4.47653 q^{70} +(4.14584 - 2.39360i) q^{71} +(1.42272 + 2.46422i) q^{72} -9.40225i q^{73} +(9.10280 - 5.25550i) q^{74} +(-0.628331 - 0.362767i) q^{75} +(-3.66553 + 6.34888i) q^{76} +8.68595 q^{77} +(-1.41424 - 0.0964278i) q^{78} +2.76824i q^{79} +(1.53816 + 0.888055i) q^{80} +(-3.81639 + 6.61018i) q^{81} +(-0.111611 + 0.0644385i) q^{82} +6.67445 q^{83} +(-0.495452 - 0.858147i) q^{84} +(5.79517 + 4.47701i) q^{85} -5.31955 q^{86} +(0.811001 + 1.40470i) q^{87} +(2.98453 + 1.72312i) q^{88} +(-7.64870 + 13.2479i) q^{89} +5.05380i q^{90} +(-9.06643 - 0.618179i) q^{91} +0.170876i q^{92} +(-1.79435 + 3.10791i) q^{93} +(-1.02659 + 1.77810i) q^{94} +(-11.2763 + 6.51039i) q^{95} -0.393151i q^{96} +(5.50775 - 3.17990i) q^{97} +(0.323759 + 0.560767i) q^{98} +9.80605i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 24 q^{8} + 12 q^{9} + 12 q^{13} - 12 q^{16} + 5 q^{17} + 24 q^{18} + 8 q^{19} - 4 q^{21} - 48 q^{25} - 6 q^{26} + 12 q^{32} - 6 q^{33} + 10 q^{34} - 10 q^{35} + 12 q^{36} + 16 q^{38} - 2 q^{42} - 4 q^{43} + 12 q^{47} + 20 q^{49} - 24 q^{50} + 16 q^{51} - 18 q^{52} - 44 q^{53} - 12 q^{55} + 14 q^{59} + 24 q^{64} - 12 q^{66} + 6 q^{67} + 5 q^{68} + 10 q^{69} - 20 q^{70} - 12 q^{72} + 8 q^{76} - 28 q^{77} - 4 q^{81} - 4 q^{83} + 2 q^{84} + 13 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{89} + 6 q^{94} - 20 q^{98}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 24 * q^8 + 12 * q^9 + 12 * q^13 - 12 * q^16 + 5 * q^17 + 24 * q^18 + 8 * q^19 - 4 * q^21 - 48 * q^25 - 6 * q^26 + 12 * q^32 - 6 * q^33 + 10 * q^34 - 10 * q^35 + 12 * q^36 + 16 * q^38 - 2 * q^42 - 4 * q^43 + 12 * q^47 + 20 * q^49 - 24 * q^50 + 16 * q^51 - 18 * q^52 - 44 * q^53 - 12 * q^55 + 14 * q^59 + 24 * q^64 - 12 * q^66 + 6 * q^67 + 5 * q^68 + 10 * q^69 - 20 * q^70 - 12 * q^72 + 8 * q^76 - 28 * q^77 - 4 * q^81 - 4 * q^83 + 2 * q^84 + 13 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^89 + 6 * q^94 - 20 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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