LMFDB - Embedded newform 504.2.cs.b.85.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.35
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.b.421.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38870 + 0.267418i) q^{2} +(1.16981 - 1.27732i) q^{3} +(1.85698 + 0.742726i) q^{4} +(0.563250 + 0.325193i) q^{5} +(1.96609 - 1.46099i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 + 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +O(q^{10})$	\(q+(1.38870 + 0.267418i) q^{2} +(1.16981 - 1.27732i) q^{3} +(1.85698 + 0.742726i) q^{4} +(0.563250 + 0.325193i) q^{5} +(1.96609 - 1.46099i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 + 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +(0.695224 + 0.602218i) q^{10} +(-2.20106 + 1.27078i) q^{11} +(3.12101 - 1.50310i) q^{12} +(-0.330225 - 0.190655i) q^{13} +(-0.462760 - 1.33636i) q^{14} +(1.07427 - 0.339038i) q^{15} +(2.89672 + 2.75845i) q^{16} +4.11399 q^{17} +(0.433805 - 4.22040i) q^{18} +0.275717i q^{19} +(0.804413 + 1.02222i) q^{20} +(-1.69110 - 0.374424i) q^{21} +(-3.39644 + 1.17613i) q^{22} +(-0.974828 + 1.68845i) q^{23} +(4.73610 - 1.25275i) q^{24} +(-2.28850 - 3.96380i) q^{25} +(-0.407598 - 0.353071i) q^{26} +(-4.12496 - 3.15985i) q^{27} +(-0.285268 - 1.97955i) q^{28} +(-7.40561 + 4.27563i) q^{29} +(1.58250 - 0.183543i) q^{30} +(-3.59920 + 6.23399i) q^{31} +(3.28501 + 4.60529i) q^{32} +(-0.951622 + 4.29802i) q^{33} +(5.71309 + 1.10015i) q^{34} -0.650385i q^{35} +(1.73104 - 5.74487i) q^{36} -2.84592i q^{37} +(-0.0737316 + 0.382888i) q^{38} +(-0.629828 + 0.198772i) q^{39} +(0.843730 + 1.63467i) q^{40} +(5.98003 - 10.3577i) q^{41} +(-2.24830 - 0.972192i) q^{42} +(-5.05692 + 2.91961i) q^{43} +(-5.03115 + 0.725027i) q^{44} +(0.823632 - 1.76880i) q^{45} +(-1.80526 + 2.08407i) q^{46} +(4.62536 + 8.01136i) q^{47} +(6.91203 - 0.473177i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.11805 - 6.11651i) q^{50} +(4.81258 - 5.25488i) q^{51} +(-0.471614 - 0.599309i) q^{52} +5.56863i q^{53} +(-4.88334 - 5.49118i) q^{54} -1.65299 q^{55} +(0.133215 - 2.82529i) q^{56} +(0.352179 + 0.322536i) q^{57} +(-11.4275 + 3.95718i) q^{58} +(-0.981080 - 0.566427i) q^{59} +(2.24671 + 0.168304i) q^{60} +(1.17619 - 0.679073i) q^{61} +(-6.66529 + 7.69466i) q^{62} +(-2.45652 + 1.72207i) q^{63} +(3.33036 + 7.27384i) q^{64} +(-0.123999 - 0.214773i) q^{65} +(-2.47089 + 5.71419i) q^{66} +(-8.47415 - 4.89255i) q^{67} +(7.63957 + 3.05556i) q^{68} +(1.01633 + 3.22033i) q^{69} +(0.173925 - 0.903190i) q^{70} +3.65788 q^{71} +(3.94017 - 7.51499i) q^{72} +4.35806 q^{73} +(0.761050 - 3.95213i) q^{74} +(-7.74015 - 1.71374i) q^{75} +(-0.204782 + 0.512000i) q^{76} +(2.20106 + 1.27078i) q^{77} +(-0.927797 + 0.107608i) q^{78} +(-7.28376 - 12.6158i) q^{79} +(0.734550 + 2.49569i) q^{80} +(-8.86156 + 1.57248i) q^{81} +(11.0743 - 12.7846i) q^{82} +(-4.69138 + 2.70857i) q^{83} +(-2.86223 - 1.95132i) q^{84} +(2.31720 + 1.33784i) q^{85} +(-7.80330 + 2.70216i) q^{86} +(-3.20180 + 14.4610i) q^{87} +(-7.18064 - 0.338573i) q^{88} +5.64356 q^{89} +(1.61679 - 2.23607i) q^{90} +0.381311i q^{91} +(-3.06429 + 2.41138i) q^{92} +(3.75243 + 11.8899i) q^{93} +(4.28086 + 12.3623i) q^{94} +(-0.0896612 + 0.155298i) q^{95} +(9.72527 + 1.19130i) q^{96} +(1.96718 + 3.40725i) q^{97} +(-0.925940 + 1.06894i) q^{98} +(4.37674 + 6.24339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	$ 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) $ 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.38870	+	0.267418i	0.981959	+	0.189093i
$2$	1.38870	+	0.267418i	0.981959	+	0.189093i
$3$	1.16981	−	1.27732i	0.675390	−	0.737461i
$3$	1.16981	−	1.27732i	0.675390	−	0.737461i
$4$	1.85698	+	0.742726i	0.928488	+	0.371363i
$5$	0.563250	+	0.325193i	0.251893	+	0.145431i	0.620631	−	0.784103i	$-0.286877\pi$
$5$	0.563250	+	0.325193i	0.251893	+	0.145431i	−0.368738	+	0.929534i	$0.620210\pi$
$6$	1.96609	−	1.46099i	0.802654	−	0.596445i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	2.38016	+	1.52801i	0.841515	+	0.540234i
$9$	−0.263093	−	2.98844i	−0.0876977	−	0.996147i
$10$	0.695224	+	0.602218i	0.219849	+	0.190438i
$11$	−2.20106	+	1.27078i	−0.663643	+	0.383155i	−0.793664	−	0.608357i	$-0.791829\pi$
$11$	−2.20106	+	1.27078i	−0.663643	+	0.383155i	0.130020	+	0.991511i	$0.458496\pi$
$12$	3.12101	−	1.50310i	0.900957	−	0.433909i
$13$	−0.330225	−	0.190655i	−0.0915878	−	0.0528783i	0.453507	−	0.891253i	$-0.350173\pi$
$13$	−0.330225	−	0.190655i	−0.0915878	−	0.0528783i	−0.545094	+	0.838375i	$0.683506\pi$
$14$	−0.462760	−	1.33636i	−0.123678	−	0.357157i
$15$	1.07427	−	0.339038i	0.277375	−	0.0875391i
$16$	2.89672	+	2.75845i	0.724179	+	0.689612i
$17$	4.11399			0.997788			0.498894	−	0.866663i	$-0.333740\pi$
$17$	4.11399			0.997788			0.498894	+	0.866663i	$0.333740\pi$
$18$	0.433805	−	4.22040i	0.102249	−	0.994759i
$19$			0.275717i			0.0632538i	0.999500	+	0.0316269i	$0.0100688\pi$
$19$			0.275717i			0.0632538i	−0.999500	+	0.0316269i	$0.989931\pi$
$20$	0.804413	+	1.02222i	0.179872	+	0.228574i
$21$	−1.69110	−	0.374424i	−0.369027	−	0.0817061i
$22$	−3.39644	+	1.17613i	−0.724123	+	0.250752i
$23$	−0.974828	+	1.68845i	−0.203266	+	0.352066i	−0.949579	−	0.313529i	$-0.898489\pi$
$23$	−0.974828	+	1.68845i	−0.203266	+	0.352066i	0.746313	+	0.665595i	$0.231822\pi$
$24$	4.73610	−	1.25275i	0.966752	−	0.255716i
$25$	−2.28850	−	3.96380i	−0.457700	−	0.792759i
$26$	−0.407598	−	0.353071i	−0.0799366	−	0.0692429i
$27$	−4.12496	−	3.15985i	−0.793850	−	0.608114i
$28$	−0.285268	−	1.97955i	−0.0539107	−	0.374100i
$29$	−7.40561	+	4.27563i	−1.37519	+	0.793965i	−0.991575	−	0.129530i	$-0.958653\pi$
$29$	−7.40561	+	4.27563i	−1.37519	+	0.793965i	−0.383611	+	0.923495i	$0.625320\pi$
$30$	1.58250	−	0.183543i	0.288924	−	0.0335101i
$31$	−3.59920	+	6.23399i	−0.646435	+	1.11966i	0.337533	+	0.941314i	$0.390408\pi$
$31$	−3.59920	+	6.23399i	−0.646435	+	1.11966i	−0.983968	+	0.178345i	$0.942926\pi$
$32$	3.28501	+	4.60529i	0.580714	+	0.814108i
$33$	−0.951622	+	4.29802i	−0.165656	+	0.748190i
$34$	5.71309	+	1.10015i	0.979787	+	0.188675i
$35$		−	0.650385i		−	0.109935i
$36$	1.73104	−	5.74487i	0.288506	−	0.957478i
$37$		−	2.84592i		−	0.467867i	−0.972253	−	0.233933i	$-0.924840\pi$
$37$		−	2.84592i		−	0.467867i	0.972253	−	0.233933i	$-0.0751598\pi$
$38$	−0.0737316	+	0.382888i	−0.0119608	+	0.0621127i
$39$	−0.629828	+	0.198772i	−0.100853	+	0.0318290i
$40$	0.843730	+	1.63467i	0.133405	+	0.258463i
$41$	5.98003	−	10.3577i	0.933924	−	1.61760i	0.157382	−	0.987538i	$-0.449694\pi$
$41$	5.98003	−	10.3577i	0.933924	−	1.61760i	0.776542	−	0.630066i	$-0.216972\pi$
$42$	−2.24830	−	0.972192i	−0.346920	−	0.150013i
$43$	−5.05692	+	2.91961i	−0.771173	+	0.445237i	−0.833293	−	0.552832i	$-0.813547\pi$
$43$	−5.05692	+	2.91961i	−0.771173	+	0.445237i	0.0621198	+	0.998069i	$0.480214\pi$
$44$	−5.03115	+	0.725027i	−0.758474	+	0.109302i
$45$	0.823632	−	1.76880i	0.122780	−	0.263677i
$46$	−1.80526	+	2.08407i	−0.266172	+	0.307279i
$47$	4.62536	+	8.01136i	0.674678	+	1.16858i	0.976563	+	0.215233i	$0.0690509\pi$
$47$	4.62536	+	8.01136i	0.674678	+	1.16858i	−0.301885	+	0.953344i	$0.597616\pi$
$48$	6.91203	−	0.473177i	0.997665	−	0.0682973i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−2.11805	−	6.11651i	−0.299537	−	0.865005i
$51$	4.81258	−	5.25488i	0.673896	−	0.735830i
$52$	−0.471614	−	0.599309i	−0.0654012	−	0.0831091i
$53$			5.56863i			0.764911i	0.923974	+	0.382455i	$0.124921\pi$
$53$			5.56863i			0.764911i	−0.923974	+	0.382455i	$0.875079\pi$
$54$	−4.88334	−	5.49118i	−0.664538	−	0.747254i
$55$	−1.65299			−0.222890
$56$	0.133215	−	2.82529i	0.0178016	−	0.377545i
$57$	0.352179	+	0.322536i	0.0466472	+	0.0427210i
$58$	−11.4275	+	3.95718i	−1.50051	+	0.519603i
$59$	−0.981080	−	0.566427i	−0.127726	−	0.0737425i	0.434776	−	0.900539i	$-0.356828\pi$
$59$	−0.981080	−	0.566427i	−0.127726	−	0.0737425i	−0.562502	+	0.826796i	$0.690161\pi$
$60$	2.24671	+	0.168304i	0.290049	+	0.0217280i
$61$	1.17619	−	0.679073i	0.150596	−	0.0869464i	−0.422809	−	0.906219i	$-0.638956\pi$
$61$	1.17619	−	0.679073i	0.150596	−	0.0869464i	0.573404	+	0.819273i	$0.305622\pi$
$62$	−6.66529	+	7.69466i	−0.846492	+	0.977223i
$63$	−2.45652	+	1.72207i	−0.309492	+	0.216960i
$64$	3.33036	+	7.27384i	0.416295	+	0.909229i
$65$	−0.123999	−	0.214773i	−0.0153802	−	0.0266393i
$66$	−2.47089	+	5.71419i	−0.304145	+	0.703368i
$67$	−8.47415	−	4.89255i	−1.03528	−	0.597720i	−0.116789	−	0.993157i	$-0.537260\pi$
$67$	−8.47415	−	4.89255i	−1.03528	−	0.597720i	−0.918493	+	0.395437i	$0.870593\pi$
$68$	7.63957	+	3.05556i	0.926434	+	0.370541i
$69$	1.01633	+	3.22033i	0.122352	+	0.387682i
$70$	0.173925	−	0.903190i	0.0207880	−	0.107952i
$71$	3.65788			0.434110			0.217055	−	0.976159i	$-0.430355\pi$
$71$	3.65788			0.434110			0.217055	+	0.976159i	$0.430355\pi$
$72$	3.94017	−	7.51499i	0.464353	−	0.885650i
$73$	4.35806			0.510073			0.255036	−	0.966931i	$-0.417913\pi$
$73$	4.35806			0.510073			0.255036	+	0.966931i	$0.417913\pi$
$74$	0.761050	−	3.95213i	0.0884702	−	0.459426i
$75$	−7.74015	−	1.71374i	−0.893755	−	0.197886i
$76$	−0.204782	+	0.512000i	−0.0234901	+	0.0587304i
$77$	2.20106	+	1.27078i	0.250834	+	0.144819i
$78$	−0.927797	+	0.107608i	−0.105052	+	0.0121842i
$79$	−7.28376	−	12.6158i	−0.819487	−	1.41939i	−0.906061	−	0.423147i	$-0.860925\pi$
$79$	−7.28376	−	12.6158i	−0.819487	−	1.41939i	0.0865743	−	0.996245i	$-0.472408\pi$
$80$	0.734550	+	2.49569i	0.0821252	+	0.279026i
$81$	−8.86156	+	1.57248i	−0.984618	+	0.174720i
$82$	11.0743	−	12.7846i	1.22295	−	1.41182i
$83$	−4.69138	+	2.70857i	−0.514946	+	0.297304i	−0.734864	−	0.678214i	$-0.762754\pi$
$83$	−4.69138	+	2.70857i	−0.514946	+	0.297304i	0.219919	+	0.975518i	$0.429421\pi$
$84$	−2.86223	−	1.95132i	−0.312295	−	0.212906i
$85$	2.31720	+	1.33784i	0.251336	+	0.145109i
$86$	−7.80330	+	2.70216i	−0.841452	+	0.291381i
$87$	−3.20180	+	14.4610i	−0.343269	+	1.55038i
$88$	−7.18064	−	0.338573i	−0.765459	−	0.0360920i
$89$	5.64356			0.598216			0.299108	−	0.954219i	$-0.403311\pi$
$89$	5.64356			0.598216			0.299108	+	0.954219i	$0.403311\pi$
$90$	1.61679	−	2.23607i	0.170424	−	0.235703i
$91$			0.381311i			0.0399722i
$92$	−3.06429	+	2.41138i	−0.319474	+	0.251404i
$93$	3.75243	+	11.8899i	0.389109	+	1.23293i
$94$	4.28086	+	12.3623i	0.441537	+	1.27507i
$95$	−0.0896612	+	0.155298i	−0.00919904	+	0.0159332i
$96$	9.72527	+	1.19130i	0.992581	+	0.121586i
$97$	1.96718	+	3.40725i	0.199736	+	0.345954i	0.948443	−	0.316948i	$-0.102658\pi$
$97$	1.96718	+	3.40725i	0.199736	+	0.345954i	−0.748706	+	0.662902i	$0.769325\pi$
$98$	−0.925940	+	1.06894i	−0.0935341	+	0.107979i
$99$	4.37674	+	6.24339i	0.439878	+	0.627485i
$100$	−1.30567	−	9.06040i	−0.130567	−	0.906040i
$101$	−3.76919	+	2.17615i	−0.375049	+	0.216535i	−0.675662	−	0.737212i	$-0.736142\pi$
$101$	−3.76919	+	2.17615i	−0.375049	+	0.216535i	0.300613	+	0.953746i	$0.402809\pi$
$102$	8.08847	−	6.01048i	0.800878	−	0.595126i
$103$	3.49728	−	6.05747i	0.344597	−	0.596860i	−0.640683	−	0.767805i	$-0.721349\pi$
$103$	3.49728	−	6.05747i	0.344597	−	0.596860i	0.985281	+	0.170945i	$0.0546822\pi$
$104$	−0.494665	−	0.958378i	−0.0485059	−	0.0939767i
$105$	−0.830750	−	0.760827i	−0.0810729	−	0.0742491i
$106$	−1.48915	+	7.73316i	−0.144639	+	0.751111i
$107$			7.87245i			0.761059i	0.924769	+	0.380529i	$0.124258\pi$
$107$			7.87245i			0.761059i	−0.924769	+	0.380529i	$0.875742\pi$
$108$	−5.31306	−	8.93149i	−0.511249	−	0.859433i
$109$			7.52943i			0.721188i	0.932723	+	0.360594i	$0.117426\pi$
$109$			7.52943i			0.721188i	−0.932723	+	0.360594i	$0.882574\pi$
$110$	−2.29551	−	0.442040i	−0.218869	−	0.0421468i
$111$	−3.63515	−	3.32919i	−0.345033	−	0.315992i
$112$	0.940527	−	3.88785i	0.0888715	−	0.367368i
$113$	6.82840	−	11.8271i	0.642362	−	1.11260i	−0.342542	−	0.939503i	$-0.611288\pi$
$113$	6.82840	−	11.8271i	0.642362	−	1.11260i	0.984904	−	0.173101i	$-0.0553788\pi$
$114$	0.402819	+	0.542085i	0.0377274	+	0.0507709i
$115$	−1.09814	+	0.634014i	−0.102402	+	0.0591221i
$116$	−16.9277	+	2.43940i	−1.57169	+	0.226493i
$117$	−0.482882	+	1.03702i	−0.0446425	+	0.0958723i
$118$	−1.21095	−	1.04896i	−0.111477	−	0.0965642i
$119$	−2.05699	−	3.56282i	−0.188564	−	0.326603i
$120$	3.07499	+	0.834533i	0.280707	+	0.0761821i
$121$	−2.27023	+	3.93216i	−0.206385	+	0.357469i
$122$	1.81497	−	0.628495i	0.164320	−	0.0569013i
$123$	−6.23463	−	19.7550i	−0.562157	−	1.78125i
$124$	−11.3138	+	8.90316i	−1.01601	+	0.799527i
$125$		−	6.22874i		−	0.557116i
$126$	−3.87188	+	1.73452i	−0.344934	+	0.154523i
$127$	−7.61942			−0.676114			−0.338057	−	0.941126i	$-0.609770\pi$
$127$	−7.61942			−0.676114			−0.338057	+	0.941126i	$0.609770\pi$
$128$	2.67972	+	10.9918i	0.236856	+	0.971545i
$129$	−2.18635	+	9.87470i	−0.192497	+	0.869419i
$130$	−0.114764	−	0.331415i	−0.0100655	−	0.0290670i
$131$	15.2196	+	8.78704i	1.32974	+	0.767727i	0.985260	−	0.171065i	$-0.0547208\pi$
$131$	15.2196	+	8.78704i	1.32974	+	0.767727i	0.344483	+	0.938792i	$0.388054\pi$
$132$	−4.95939	+	7.27453i	−0.431660	+	0.633167i
$133$	0.238778	−	0.137858i	0.0207047	−	0.0119538i
$134$	−10.4597	−	9.06042i	−0.903580	−	0.782701i
$135$	−1.29583	−	3.12120i	−0.111527	−	0.268630i
$136$	9.79196	+	6.28622i	0.839654	+	0.539039i
$137$	4.80166	+	8.31673i	0.410234	+	0.710546i	0.994915	−	0.100717i	$-0.0321137\pi$
$137$	4.80166	+	8.31673i	0.410234	+	0.710546i	−0.584681	+	0.811263i	$0.698780\pi$
$138$	0.550204	+	4.74386i	0.0468365	+	0.403824i
$139$	−13.0905	−	7.55779i	−1.11032	−	0.641043i	−0.171407	−	0.985200i	$-0.554831\pi$
$139$	−13.0905	−	7.55779i	−1.11032	−	0.641043i	−0.938912	+	0.344157i	$0.888165\pi$
$140$	0.483058	−	1.20775i	0.0408259	−	0.102074i
$141$	15.6439	+	3.46370i	1.31745	+	0.291696i
$142$	5.07969	+	0.978181i	0.426278	+	0.0820871i
$143$	0.969124			0.0810422
$144$	7.48135	−	9.38240i	0.623446	−	0.781866i
$145$	−5.56162			−0.461867
$146$	6.05204	+	1.16542i	0.500871	+	0.0964511i
$147$	0.521287	+	1.65174i	0.0429950	+	0.136234i
$148$	2.11374	−	5.28481i	0.173748	−	0.434409i
$149$	11.3580	+	6.55754i	0.930483	+	0.537215i	0.886964	−	0.461838i	$-0.152810\pi$
$149$	11.3580	+	6.55754i	0.930483	+	0.537215i	0.0435188	+	0.999053i	$0.486143\pi$
$150$	−10.2905	−	4.44972i	−0.840212	−	0.363318i
$151$	−8.95009	−	15.5020i	−0.728348	−	1.26154i	−0.957581	−	0.288164i	$-0.906955\pi$
$151$	−8.95009	−	15.5020i	−0.728348	−	1.26154i	0.229233	−	0.973372i	$-0.426378\pi$
$152$	−0.421299	+	0.656252i	−0.0341718	+	0.0532290i
$153$	−1.08236	−	12.2944i	−0.0875037	−	0.993944i
$154$	2.71678	+	2.35333i	0.218924	+	0.189637i
$155$	−4.05450	+	2.34087i	−0.325665	+	0.188023i
$156$	−1.31721	−	0.0986740i	−0.105461	−	0.00790024i
$157$	4.60492	+	2.65865i	0.367512	+	0.212183i	0.672371	−	0.740214i	$-0.265276\pi$
$157$	4.60492	+	2.65865i	0.367512	+	0.212183i	−0.304859	+	0.952398i	$0.598609\pi$
$158$	−6.74126	−	19.4674i	−0.536306	−	1.54874i
$159$	7.11293	+	6.51424i	0.564092	+	0.516613i
$160$	0.352678	+	3.66219i	0.0278817	+	0.289522i
$161$	1.94966			0.153654
$162$	−12.7266	−	0.186040i	−0.999893	−	0.0146167i
$163$		−	6.57875i		−	0.515288i	−0.966240	−	0.257644i	$-0.917054\pi$
$163$		−	6.57875i		−	0.515288i	0.966240	−	0.257644i	$-0.0829461\pi$
$164$	18.7977	−	14.7925i	1.46786	−	1.15510i
$165$	−1.93369	+	2.11140i	−0.150537	+	0.164372i
$166$	−7.23924	+	2.50683i	−0.561874	+	0.194568i
$167$	−2.30277	+	3.98852i	−0.178194	+	0.308641i	−0.941262	−	0.337677i	$-0.890359\pi$
$167$	−2.30277	+	3.98852i	−0.178194	+	0.308641i	0.763068	+	0.646318i	$0.223692\pi$
$168$	−3.45296	−	3.47521i	−0.266402	−	0.268118i
$169$	−6.42730	−	11.1324i	−0.494408	−	0.856339i
$170$	2.86014	+	2.47752i	0.219363	+	0.190017i
$171$	0.823964	−	0.0725392i	0.0630101	−	0.00554721i
$172$	−11.5591	+	1.66575i	−0.881369	+	0.127012i
$173$	10.1139	−	5.83924i	0.768943	−	0.443950i	−0.0635543	−	0.997978i	$-0.520244\pi$
$173$	10.1139	−	5.83924i	0.768943	−	0.443950i	0.832497	+	0.554029i	$0.186910\pi$
$174$	−8.31347	+	19.2258i	−0.630242	+	1.45750i
$175$	−2.28850	+	3.96380i	−0.172994	+	0.299635i
$176$	−9.88122	−	2.39041i	−0.744825	−	0.180184i
$177$	−1.87119	+	0.590542i	−0.140647	+	0.0443879i
$178$	7.83721	+	1.50919i	0.587424	+	0.113118i
$179$		−	21.7056i		−	1.62235i	−0.584803	−	0.811176i	$-0.698828\pi$
$179$		−	21.7056i		−	1.62235i	0.584803	−	0.811176i	$-0.301172\pi$
$180$	2.84320	−	2.67288i	0.211919	−	0.199225i
$181$		−	26.5849i		−	1.97604i	−0.154315	−	0.988022i	$-0.549317\pi$
$181$		−	26.5849i		−	1.97604i	0.154315	−	0.988022i	$-0.450683\pi$
$182$	−0.101969	+	0.529526i	−0.00755846	+	0.0392511i
$183$	0.508523	−	2.29676i	0.0375911	−	0.169781i
$184$	−4.90022	+	2.52924i	−0.361249	+	0.186458i
$185$	0.925473	−	1.60297i	0.0680421	−	0.117852i
$186$	2.03143	+	17.5150i	0.148952	+	1.28426i
$187$	−9.05511	+	5.22797i	−0.662175	+	0.382307i
$188$	2.63894	+	18.3123i	0.192464	+	1.33556i
$189$	−0.674030	+	5.15225i	−0.0490284	+	0.374771i
$190$	−0.166042	+	0.191685i	−0.0120459	+	0.0139063i
$191$	7.12851	+	12.3469i	0.515801	+	0.893394i	0.999832	+	0.0183428i	$0.00583902\pi$
$191$	7.12851	+	12.3469i	0.515801	+	0.893394i	−0.484031	+	0.875051i	$0.660828\pi$
$192$	13.1869	+	4.25506i	0.951683	+	0.307083i
$193$	5.40052	−	9.35398i	0.388738	−	0.673314i	−0.603542	−	0.797331i	$-0.706244\pi$
$193$	5.40052	−	9.35398i	0.388738	−	0.673314i	0.992280	+	0.124017i	$0.0395778\pi$
$194$	1.82066	+	5.25770i	0.130716	+	0.377481i
$195$	−0.419390	−	0.0928568i	−0.0300331	−	0.00664961i
$196$	−1.57171	+	1.23683i	−0.112265	+	0.0883447i
$197$		−	10.8319i		−	0.771740i	−0.922553	−	0.385870i	$-0.873901\pi$
$197$		−	10.8319i		−	0.771740i	0.922553	−	0.385870i	$-0.126099\pi$
$198$	4.40838	+	9.84062i	0.313290	+	0.699342i
$199$	−7.90135			−0.560112			−0.280056	−	0.959984i	$-0.590353\pi$
$199$	−7.90135			−0.560112			−0.280056	+	0.959984i	$0.590353\pi$
$200$	0.609723	−	12.9313i	0.0431139	−	0.914384i
$201$	−16.1625	+	5.10085i	−1.14001	+	0.359786i
$202$	−5.81622	+	2.01406i	−0.409228	+	0.141709i
$203$	7.40561	+	4.27563i	0.519772	+	0.300090i
$204$	12.8398	−	6.18375i	0.898964	−	0.432949i
$205$	6.73651	−	3.88933i	0.470498	−	0.271642i
$206$	6.47655	−	7.47677i	0.451242	−	0.520931i
$207$	5.30231	+	2.46900i	0.368536	+	0.171607i
$208$	−0.430655	−	1.46318i	−0.0298605	−	0.101453i
$209$	−0.350376	−	0.606869i	−0.0242360	−	0.0419780i
$210$	−0.950205	−	1.27872i	−0.0655703	−	0.0882399i
$211$	19.8758	+	11.4753i	1.36831	+	0.789994i	0.990712	−	0.135976i	$-0.0434170\pi$
$211$	19.8758	+	11.4753i	1.36831	+	0.789994i	0.377597	+	0.925970i	$0.376750\pi$
$212$	−4.13597	+	10.3408i	−0.284059	+	0.710210i
$213$	4.27902	−	4.67228i	0.293193	−	0.320139i
$214$	−2.10523	+	10.9325i	−0.143911	+	0.747328i
$215$	−3.79775			−0.259004
$216$	−4.98980	−	13.8240i	−0.339513	−	0.940601i
$217$	7.19840			0.488659
$218$	−2.01350	+	10.4561i	−0.136372	+	0.708178i
$219$	5.09810	−	5.56664i	0.344498	−	0.376159i
$220$	−3.06957	−	1.22772i	−0.206950	−	0.0827730i
$221$	−1.35854	−	0.784353i	−0.0913852	−	0.0527613i
$222$	−4.15785	−	5.59534i	−0.279057	−	0.375535i
$223$	−6.27529	−	10.8691i	−0.420225	−	0.727850i	0.575737	−	0.817635i	$-0.304715\pi$
$223$	−6.27529	−	10.8691i	−0.420225	−	0.727850i	−0.995961	+	0.0897849i	$0.971382\pi$
$224$	2.34579	−	5.14755i	0.156735	−	0.343935i
$225$	−11.2435	+	7.88189i	−0.749566	+	0.525460i
$226$	12.6454	−	14.5983i	0.841159	−	0.971065i
$227$	16.1277	−	9.31131i	1.07043	−	0.618013i	0.142131	−	0.989848i	$-0.454605\pi$
$227$	16.1277	−	9.31131i	1.07043	−	0.618013i	0.928299	+	0.371835i	$0.121271\pi$
$228$	0.414431	+	0.860514i	0.0274464	+	0.0569889i
$229$	25.5878	+	14.7731i	1.69089	+	0.976234i	0.953802	+	0.300435i	$0.0971318\pi$
$229$	25.5878	+	14.7731i	1.69089	+	0.976234i	0.737085	+	0.675800i	$0.236202\pi$
$230$	−1.69454	+	0.586792i	−0.111735	+	0.0386919i
$231$	4.19801	−	1.32488i	0.276209	−	0.0871709i
$232$	−24.1598	−	1.13915i	−1.58617	−	0.0747891i
$233$	23.2846			1.52543			0.762714	−	0.646736i	$-0.223866\pi$
$233$	23.2846			1.52543			0.762714	+	0.646736i	$0.223866\pi$
$234$	−0.947895	+	1.31097i	−0.0619659	+	0.0857011i
$235$			6.01654i			0.392475i
$236$	−1.40114	−	1.78051i	−0.0912066	−	0.115902i
$237$	−24.6351	−	5.45443i	−1.60022	−	0.354303i
$238$	−1.90379	−	5.49776i	−0.123404	−	0.356367i
$239$	0.280507	−	0.485852i	0.0181445	−	0.0314272i	−0.856811	−	0.515631i	$-0.827557\pi$
$239$	0.280507	−	0.485852i	0.0181445	−	0.0314272i	0.874955	+	0.484204i	$0.160891\pi$
$240$	4.04708	+	1.98122i	0.261238	+	0.127887i
$241$	12.0450	+	20.8626i	0.775890	+	1.34388i	0.934293	+	0.356506i	$0.116032\pi$
$241$	12.0450	+	20.8626i	0.775890	+	1.34388i	−0.158404	+	0.987374i	$0.550635\pi$
$242$	−4.20420	+	4.85349i	−0.270256	+	0.311994i
$243$	−8.35778	+	13.1586i	−0.536152	+	0.844121i
$244$	2.68852	−	0.387436i	0.172115	−	0.0248031i
$245$	−0.563250	+	0.325193i	−0.0359847	+	0.0207758i
$246$	−3.37520	−	29.1010i	−0.215195	−	1.85541i
$247$	0.0525669	−	0.0910485i	0.00334475	−	0.00579328i
$248$	−18.0923	+	9.33831i	−1.14886	+	0.592983i
$249$	−2.02831	+	9.16090i	−0.128539	+	0.580549i
$250$	1.66568	−	8.64985i	0.105347	−	0.547065i
$251$			2.14312i			0.135272i	0.997710	+	0.0676362i	$0.0215457\pi$
$251$			2.14312i			0.135272i	−0.997710	+	0.0676362i	$0.978454\pi$
$252$	−5.84072	+	1.37331i	−0.367931	+	0.0865107i
$253$		−	4.95517i		−	0.311529i
$254$	−10.5811	−	2.03757i	−0.663916	−	0.127848i
$255$	4.41953	−	1.39480i	0.276762	−	0.0873455i
$256$	0.781936	+	15.9809i	0.0488710	+	0.998805i
$257$	−5.28744	+	9.15811i	−0.329821	+	0.571267i	−0.982476	−	0.186388i	$-0.940322\pi$
$257$	−5.28744	+	9.15811i	−0.329821	+	0.571267i	0.652655	+	0.757655i	$0.273655\pi$
$258$	−5.67685	+	13.1283i	−0.353425	+	0.817334i
$259$	−2.46464	+	1.42296i	−0.153145	+	0.0884185i
$260$	−0.0707462	−	0.490926i	−0.00438749	−	0.0304460i
$261$	14.7258	+	21.0063i	0.911506	+	1.30026i
$262$	18.7857	+	16.2726i	1.16058	+	1.00532i
$263$	5.47502	+	9.48302i	0.337604	+	0.584748i	0.983982	−	0.178270i	$-0.0570501\pi$
$263$	5.47502	+	9.48302i	0.337604	+	0.584748i	−0.646377	+	0.763018i	$0.723717\pi$
$264$	−8.83245	+	8.77591i	−0.543600	+	0.540120i
$265$	−1.81088	+	3.13654i	−0.111241	+	0.192676i
$266$	0.368457	−	0.127591i	0.0225915	−	0.00782309i
$267$	6.60188	−	7.20863i	0.404029	−	0.441161i
$268$	−12.1025	−	15.3793i	−0.739275	−	0.939441i
$269$		−	18.7007i		−	1.14020i	−0.821575	−	0.570100i	$-0.806904\pi$
$269$		−	18.7007i		−	1.14020i	0.821575	−	0.570100i	$-0.193096\pi$
$270$	−0.964852	−	4.68093i	−0.0587190	−	0.284872i
$271$	25.0803			1.52352			0.761759	−	0.647861i	$-0.224336\pi$
$271$	25.0803			1.52352			0.761759	+	0.647861i	$0.224336\pi$
$272$	11.9170	+	11.3482i	0.722577	+	0.688086i
$273$	0.487056	+	0.446061i	0.0294779	+	0.0269968i
$274$	4.44403	+	12.8335i	0.268474	+	0.775299i
$275$	10.0742	+	5.81636i	0.607499	+	0.350740i
$276$	−0.504524	+	6.73493i	−0.0303688	+	0.405395i
$277$	0.187030	−	0.107982i	0.0112375	−	0.00648800i	−0.494371	−	0.869251i	$-0.664601\pi$
$277$	0.187030	−	0.107982i	0.0112375	−	0.00648800i	0.505608	+	0.862763i	$0.331268\pi$
$278$	−16.1577	−	13.9961i	−0.969072	−	0.839432i
$279$	19.5769	+	9.11587i	1.17204	+	0.545753i
$280$	0.993796	−	1.54802i	0.0593907	−	0.0925121i
$281$	−6.20406	−	10.7457i	−0.370103	−	0.641038i	0.619478	−	0.785014i	$-0.287344\pi$
$281$	−6.20406	−	10.7457i	−0.370103	−	0.641038i	−0.989581	+	0.143977i	$0.954011\pi$
$282$	20.7984	+	8.99348i	1.23853	+	0.535554i
$283$	4.76875	+	2.75324i	0.283473	+	0.163663i	0.634995	−	0.772517i	$-0.281002\pi$
$283$	4.76875	+	2.75324i	0.283473	+	0.163663i	−0.351522	+	0.936180i	$0.614336\pi$
$284$	6.79259	+	2.71680i	0.403066	+	0.161212i
$285$	0.0934784	+	0.296195i	0.00553718	+	0.0175451i
$286$	1.34582	+	0.259161i	0.0795801	+	0.0153245i
$287$	−11.9601			−0.705980
$288$	12.8984	−	11.0287i	0.760044	−	0.649872i
$289$	−0.0751273			−0.00441925
$290$	−7.72342	−	1.48727i	−0.453535	−	0.0873357i
$291$	6.65337	+	1.47312i	0.390027	+	0.0863557i
$292$	8.09282	+	3.23685i	0.473596	+	0.189422i
$293$	−26.0114	−	15.0177i	−1.51960	−	0.877344i	−0.999733	−	0.0230994i	$-0.992647\pi$
$293$	−26.0114	−	15.0177i	−1.51960	−	0.877344i	−0.519871	−	0.854245i	$-0.674020\pi$
$294$	0.282206	+	2.43318i	0.0164586	+	0.141906i
$295$	−0.368396	−	0.638080i	−0.0214488	−	0.0371505i
$296$	4.34860	−	6.77376i	0.252757	−	0.393717i
$297$	13.0948	+	1.71309i	0.759835	+	0.0994034i
$298$	14.0192	+	12.1438i	0.812113	+	0.703471i
$299$	0.643824	−	0.371712i	0.0372333	−	0.0214967i
$300$	−13.1004	−	8.93118i	−0.756353	−	0.515642i
$301$	5.05692	+	2.91961i	0.291476	+	0.168284i
$302$	−8.28348	−	23.9210i	−0.476661	−	1.37650i
$303$	−1.62960	+	7.36014i	−0.0936183	+	0.422829i
$304$	−0.760551	+	0.798674i	−0.0436206	+	0.0458071i
$305$	0.883318			0.0505787
$306$	1.78467	−	17.3627i	0.102023	−	0.992558i
$307$		−	5.85643i		−	0.334244i	−0.985936	−	0.167122i	$-0.946553\pi$
$307$		−	5.85643i		−	0.334244i	0.985936	−	0.167122i	$-0.0534474\pi$
$308$	3.14347	+	3.99459i	0.179116	+	0.227613i
$309$	−3.64617	−	11.5532i	−0.207424	−	0.657240i
$310$	−6.25647	+	2.16652i	−0.355344	+	0.123050i
$311$	−4.70853	+	8.15541i	−0.266996	+	0.462451i	−0.968085	−	0.250623i	$-0.919364\pi$
$311$	−4.70853	+	8.15541i	−0.266996	+	0.462451i	0.701089	+	0.713074i	$0.252698\pi$
$312$	−1.80282	−	0.489273i	−0.102065	−	0.0276996i
$313$	1.37620	+	2.38365i	0.0777875	+	0.134732i	0.902295	−	0.431119i	$-0.141881\pi$
$313$	1.37620	+	2.38365i	0.0777875	+	0.134732i	−0.824508	+	0.565851i	$0.808548\pi$
$314$	5.68388	+	4.92350i	0.320760	+	0.277849i
$315$	−1.94364	+	0.171112i	−0.109512	+	0.00964107i
$316$	−4.15565	−	28.8371i	−0.233774	−	1.62222i
$317$	−25.3262	+	14.6221i	−1.42246	+	0.821257i	−0.996509	−	0.0834890i	$-0.973394\pi$
$317$	−25.3262	+	14.6221i	−1.42246	+	0.821257i	−0.425951	+	0.904746i	$0.640060\pi$
$318$	8.13570	+	10.9484i	0.456227	+	0.613958i
$319$	10.8668	−	18.8218i	0.608422	−	1.05382i
$320$	−0.489571	+	5.18000i	−0.0273678	+	0.289571i
$321$	10.0556	+	9.20926i	0.561251	+	0.514011i
$322$	2.70749	+	0.521372i	0.150882	+	0.0290549i
$323$			1.13430i			0.0631139i
$324$	−17.6236	−	3.66166i	−0.979090	−	0.203426i
$325$			1.74526i			0.0968095i
$326$	1.75927	−	9.13591i	0.0974372	−	0.505991i
$327$	9.61749	+	8.80799i	0.531848	+	0.487083i
$328$	30.0602	−	15.5155i	1.65980	−	0.856701i
$329$	4.62536	−	8.01136i	0.255004	−	0.441681i
$330$	−3.24994	+	2.41500i	−0.178903	+	0.132942i
$331$	18.5309	−	10.6988i	1.01855	−	0.588059i	0.104865	−	0.994486i	$-0.466559\pi$
$331$	18.5309	−	10.6988i	1.01855	−	0.588059i	0.913683	+	0.406427i	$0.133225\pi$
$332$	−10.7235	+	1.54534i	−0.588529	+	0.0848115i
$333$	−8.50487	+	0.748742i	−0.466064	+	0.0410308i
$334$	−4.26446	+	4.92306i	−0.233341	+	0.269378i
$335$	−3.18204	−	5.51146i	−0.173854	−	0.301123i
$336$	−3.86580	−	5.74940i	−0.210896	−	0.313656i
$337$	−5.78431	+	10.0187i	−0.315091	+	0.545754i	−0.979457	−	0.201654i	$-0.935369\pi$
$337$	−5.78431	+	10.0187i	−0.315091	+	0.545754i	0.664366	+	0.747408i	$0.268702\pi$
$338$	−5.94859	−	17.1784i	−0.323561	−	0.934379i
$339$	−7.11912	−	22.5576i	−0.386657	−	1.22516i
$340$	3.30934	+	4.20538i	0.179474	+	0.228069i
$341$		−	18.2952i		−	0.990739i
$342$	1.16364	+	0.119607i	0.0629223	+	0.00646762i
$343$	1.00000			0.0539949
$344$	−16.4975	−	0.777871i	−0.889486	−	0.0419400i
$345$	−0.474780	+	2.14436i	−0.0255613	+	0.115448i
$346$	15.6066	−	5.40433i	0.839019	−	0.290539i
$347$	4.96639	+	2.86735i	0.266610	+	0.153927i	0.627346	−	0.778741i	$-0.284141\pi$
$347$	4.96639	+	2.86735i	0.266610	+	0.153927i	−0.360736	+	0.932668i	$0.617475\pi$
$348$	−16.6862	+	24.4757i	−0.894476	+	1.31203i
$349$	1.81499	−	1.04789i	0.0971543	−	0.0560920i	−0.450636	−	0.892708i	$-0.648803\pi$
$349$	1.81499	−	1.04789i	0.0971543	−	0.0560920i	0.547790	+	0.836616i	$0.315469\pi$
$350$	−4.23803	+	4.89254i	−0.226532	+	0.261517i
$351$	0.759722	+	1.82991i	0.0405510	+	0.0976732i
$352$	−13.0828	−	5.96197i	−0.697316	−	0.317774i
$353$	−13.4873	−	23.3606i	−0.717855	−	1.24336i	−0.961848	−	0.273585i	$-0.911791\pi$
$353$	−13.4873	−	23.3606i	−0.717855	−	1.24336i	0.243993	−	0.969777i	$-0.421543\pi$
$354$	−2.75644	+	0.319698i	−0.146503	+	0.0169918i
$355$	2.06030	+	1.18952i	0.109349	+	0.0631329i
$356$	10.4799	+	4.19162i	0.555436	+	0.222155i
$357$	−6.95714	−	1.54038i	−0.368211	−	0.0815254i
$358$	5.80445	−	30.1425i	0.306775	−	1.59308i
$359$	0.0285211			0.00150528			0.000752642	−	1.00000i	$-0.499760\pi$
$359$	0.0285211			0.00150528			0.000752642		1.00000i	$0.499760\pi$
$360$	4.66312	−	2.95151i	0.245768	−	0.155558i
$361$	18.9240			0.995999
$362$	7.10928	−	36.9185i	0.373656	−	1.94039i
$363$	2.36689	+	7.49969i	0.124229	+	0.393632i
$364$	−0.283209	+	0.708084i	−0.0148442	+	0.0371137i
$365$	2.45468	+	1.41721i	0.128484	+	0.0741802i
$366$	1.32038	−	3.05352i	0.0690173	−	0.159610i
$367$	−2.07713	−	3.59770i	−0.108425	−	0.187798i	0.806707	−	0.590951i	$-0.201248\pi$
$367$	−2.07713	−	3.59770i	−0.108425	−	0.187798i	−0.915133	+	0.403153i	$0.867914\pi$
$368$	−7.48130	+	2.20195i	−0.389990	+	0.114785i
$369$	−32.5267	−	15.1459i	−1.69327	−	0.788466i
$370$	1.71387	−	1.97855i	0.0890997	−	0.102860i
$371$	4.82258	−	2.78432i	0.250376	−	0.144555i
$372$	−1.86277	+	24.8663i	−0.0965802	+	1.28926i
$373$	7.80969	+	4.50893i	0.404370	+	0.233463i	0.688368	−	0.725362i	$-0.258327\pi$
$373$	7.80969	+	4.50893i	0.404370	+	0.233463i	−0.283998	+	0.958825i	$0.591661\pi$
$374$	−13.9729	+	4.83859i	−0.722521	+	0.250197i
$375$	−7.95610	−	7.28644i	−0.410851	−	0.376270i
$376$	−1.23233	+	26.1360i	−0.0635527	+	1.34786i
$377$	3.26069			0.167934
$378$	−2.31383	+	6.97468i	−0.119010	+	0.358739i
$379$			29.5716i			1.51899i	0.650513	+	0.759495i	$0.274554\pi$
$379$			29.5716i			1.51899i	−0.650513	+	0.759495i	$0.725446\pi$
$380$	−0.281842	+	0.221790i	−0.0144582	+	0.0113776i
$381$	−8.91326	+	9.73243i	−0.456640	+	0.498608i
$382$	6.59758	+	19.0525i	0.337561	+	0.974811i
$383$	0.000970819	−	0.00168151i	4.96065e−5	−	8.59210e-5i	−0.866001	−	0.500043i	$-0.833318\pi$
$383$	0.000970819	−	0.00168151i	4.96065e−5	−	8.59210e-5i	0.866050	+	0.499957i	$0.166651\pi$
$384$	17.1748	+	9.43541i	0.876447	+	0.481499i
$385$	0.826497	+	1.43154i	0.0421222	+	0.0729578i
$386$	10.0011	−	11.5457i	0.509044	−	0.587659i
$387$	10.0555	+	14.3442i	0.511152	+	0.729156i
$388$	1.12235	+	7.78825i	0.0569785	+	0.395388i
$389$	−26.4825	+	15.2897i	−1.34272	+	0.775219i	−0.987206	−	0.159453i	$-0.949027\pi$
$389$	−26.4825	+	15.2897i	−1.34272	+	0.775219i	−0.355513	+	0.934671i	$0.615694\pi$
$390$	−0.557575	−	0.241103i	−0.0282339	−	0.0122087i
$391$	−4.01043	+	6.94626i	−0.202816	+	0.351288i
$392$	−2.51338	+	1.29728i	−0.126945	+	0.0655224i
$393$	29.0279	−	9.16114i	1.46426	−	0.462118i
$394$	2.89664	−	15.0422i	0.145931	−	0.757818i
$395$		−	9.47450i		−	0.476714i
$396$	3.49036	+	14.8445i	0.175397	+	0.745966i
$397$		−	30.5066i		−	1.53108i	−0.643386	−	0.765542i	$-0.722471\pi$
$397$		−	30.5066i		−	1.53108i	0.643386	−	0.765542i	$-0.277529\pi$
$398$	−10.9726	−	2.11296i	−0.550007	−	0.105913i
$399$	0.103235	−	0.466264i	0.00516822	−	0.0233424i
$400$	4.30479	−	17.7947i	0.215240	−	0.889735i
$401$	−12.2503	+	21.2182i	−0.611753	+	1.05959i	0.379192	+	0.925318i	$0.376202\pi$
$401$	−12.2503	+	21.2182i	−0.611753	+	1.05959i	−0.990945	+	0.134269i	$0.957131\pi$
$402$	−23.8089	+	2.76141i	−1.18748	+	0.137727i
$403$	2.37709	−	1.37241i	0.118411	−	0.0683647i
$404$	−8.61558	+	1.24157i	−0.428641	+	0.0617705i
$405$	−5.50264	−	1.99602i	−0.273428	−	0.0991829i
$406$	9.14079	+	7.91796i	0.453650	+	0.392962i
$407$	3.61654	+	6.26403i	0.179265	+	0.310497i
$408$	19.4842	−	5.15379i	0.964613	−	0.255151i
$409$	7.03943	−	12.1926i	0.348077	−	0.602887i	−0.637831	−	0.770177i	$-0.720168\pi$
$409$	7.03943	−	12.1926i	0.348077	−	0.602887i	0.985908	+	0.167289i	$0.0535014\pi$
$410$	10.3951	−	3.59964i	0.513376	−	0.177774i
$411$	16.2402	+	3.59572i	0.801068	+	0.177364i
$412$	10.9934	−	8.65105i	0.541606	−	0.426207i
$413$			1.13285i			0.0557441i
$414$	6.70306	+	4.84662i	0.329438	+	0.238199i
$415$	−3.52323			−0.172948
$416$	−0.206770	−	2.14708i	−0.0101377	−	0.105269i
$417$	−24.9671	+	7.87956i	−1.22264	+	0.385863i
$418$	−0.324279	−	0.936455i	−0.0158610	−	0.0458035i
$419$	10.3174	+	5.95675i	0.504038	+	0.291006i	0.730379	−	0.683042i	$-0.239343\pi$
$419$	10.3174	+	5.95675i	0.504038	+	0.291006i	−0.226342	+	0.974048i	$0.572677\pi$
$420$	−0.977598	−	2.02986i	−0.0477019	−	0.0990469i
$421$	−3.18434	+	1.83848i	−0.155195	+	0.0896021i	−0.575587	−	0.817741i	$-0.695226\pi$
$421$	−3.18434	+	1.83848i	−0.155195	+	0.0896021i	0.420391	+	0.907343i	$0.361893\pi$
$422$	24.5329	+	21.2509i	1.19424	+	1.03448i
$423$	22.7246	−	15.9304i	1.10491	−	0.774560i
$424$	−8.50894	+	13.2543i	−0.413230	+	0.643684i
$425$	−9.41485	−	16.3070i	−0.456687	−	0.791006i
$426$	7.19172	−	5.34411i	0.348440	−	0.258923i
$427$	−1.17619	−	0.679073i	−0.0569198	−	0.0328626i
$428$	−5.84707	+	14.6189i	−0.282629	+	0.706634i
$429$	1.13369	−	1.23788i	0.0547351	−	0.0597655i
$430$	−5.27393	−	1.01559i	−0.254332	−	0.0489759i
$431$	12.3366			0.594235			0.297118	−	0.954841i	$-0.403975\pi$
$431$	12.3366			0.594235			0.297118	+	0.954841i	$0.403975\pi$
$432$	−3.23257	−	20.5317i	−0.155527	−	0.987832i
$433$	−27.7226			−1.33226			−0.666131	−	0.745835i	$-0.732051\pi$
$433$	−27.7226			−1.33226			−0.666131	+	0.745835i	$0.732051\pi$
$434$	9.99641	+	1.92498i	0.479843	+	0.0924019i
$435$	−6.50603	+	7.10396i	−0.311940	+	0.340609i
$436$	−5.59230	+	13.9820i	−0.267823	+	0.669615i
$437$	−0.465535	−	0.268777i	−0.0222695	−	0.0128573i
$438$	8.56836	−	6.36708i	0.409412	−	0.304231i
$439$	−10.8249	−	18.7493i	−0.516644	−	0.894853i	−0.999813	−	0.0193264i	$-0.993848\pi$
$439$	−10.8249	−	18.7493i	−0.516644	−	0.894853i	0.483169	−	0.875527i	$-0.339486\pi$
$440$	−3.93440	−	2.52579i	−0.187565	−	0.120413i
$441$	2.71961	+	1.26638i	0.129505	+	0.0603036i
$442$	−1.67685	−	1.45253i	−0.0797598	−	0.0690897i
$443$	−19.7049	+	11.3766i	−0.936206	+	0.540519i	−0.888769	−	0.458356i	$-0.848439\pi$
$443$	−19.7049	+	11.3766i	−0.936206	+	0.540519i	−0.0474369	+	0.998874i	$0.515105\pi$
$444$	−4.27772	−	8.88214i	−0.203012	−	0.421528i
$445$	3.17874	+	1.83524i	0.150687	+	0.0869989i
$446$	−5.80790	−	16.7721i	−0.275012	−	0.794181i
$447$	21.6628	−	6.83672i	1.02461	−	0.323366i
$448$	4.63415	−	6.52110i	0.218943	−	0.308093i
$449$	−35.3042			−1.66611			−0.833055	−	0.553191i	$-0.813410\pi$
$449$	−35.3042			−1.66611			−0.833055	+	0.553191i	$0.813410\pi$
$450$	−17.7216	+	7.93888i	−0.835404	+	0.374242i
$451$			30.3972i			1.43135i
$452$	21.4645	−	16.8911i	1.00961	−	0.794490i
$453$	−30.2709	−	6.70226i	−1.42225	−	0.314900i
$454$	24.8865	−	8.61779i	1.16798	−	0.404453i
$455$	−0.123999	+	0.214773i	−0.00581318	+	0.0100687i
$456$	0.345404	+	1.30582i	0.0161750	+	0.0611507i
$457$	7.67088	+	13.2864i	0.358829	+	0.621509i	0.987765	−	0.155947i	$-0.0498429\pi$
$457$	7.67088	+	13.2864i	0.358829	+	0.621509i	−0.628937	+	0.777456i	$0.716510\pi$
$458$	31.5832	+	27.3580i	1.47578	+	1.27836i
$459$	−16.9700	−	12.9996i	−0.792094	−	0.606769i
$460$	−2.51013	+	0.361728i	−0.117035	+	0.0168657i
$461$	2.84349	−	1.64169i	0.132435	−	0.0764612i	−0.432319	−	0.901721i	$-0.642305\pi$
$461$	2.84349	−	1.64169i	0.132435	−	0.0764612i	0.564754	+	0.825260i	$0.308971\pi$
$462$	6.18407	−	0.717243i	0.287709	−	0.0333692i
$463$	−17.6350	+	30.5448i	−0.819569	+	1.41954i	0.0864309	+	0.996258i	$0.472454\pi$
$463$	−17.6350	+	30.5448i	−0.819569	+	1.41954i	−0.906000	+	0.423278i	$0.860880\pi$
$464$	−33.2460	−	8.04269i	−1.54341	−	0.373373i
$465$	−1.75295	+	7.91726i	−0.0812913	+	0.367154i
$466$	32.3354	+	6.22673i	1.49791	+	0.288447i
$467$			30.4858i			1.41071i	0.708852	+	0.705357i	$0.249213\pi$
$467$			30.4858i			1.41071i	−0.708852	+	0.705357i	$0.750787\pi$
$468$	−1.66692	+	1.56707i	−0.0770534	+	0.0724377i
$469$			9.78510i			0.451834i
$470$	−1.60893	+	8.35516i	−0.0742143	+	0.385395i
$471$	8.78282	−	2.77184i	0.404691	−	0.127720i
$472$	−1.46963	−	2.84729i	−0.0676450	−	0.131057i
$473$	7.42038	−	12.8525i	0.341189	−	0.590957i
$474$	−32.7521	−	14.1624i	−1.50435	−	0.650502i
$475$	1.09289	−	0.630978i	0.0501451	−	0.0289513i
$476$	−1.17359	−	8.14384i	−0.0537914	−	0.373272i
$477$	16.6415	−	1.46507i	0.761964	−	0.0670809i
$478$	0.519465	−	0.599690i	0.0237598	−	0.0274292i
$479$	−20.7437	−	35.9292i	−0.947806	−	1.64165i	−0.750034	−	0.661399i	$-0.769963\pi$
$479$	−20.7437	−	35.9292i	−0.947806	−	1.64165i	−0.197771	−	0.980248i	$-0.563370\pi$
$480$	5.09036	+	3.83358i	0.232342	+	0.174978i
$481$	−0.542590	+	0.939794i	−0.0247400	+	0.0428509i
$482$	11.1479	+	32.1930i	0.507774	+	1.46635i
$483$	2.28072	−	2.49033i	0.103777	−	0.113314i
$484$	−7.13629	+	5.61577i	−0.324377	+	0.255262i
$485$			2.55885i			0.116191i
$486$	−15.1253	+	16.0383i	−0.686097	+	0.727510i
$487$	24.4657			1.10865			0.554324	−	0.832301i	$-0.312977\pi$
$487$	24.4657			1.10865			0.554324	+	0.832301i	$0.312977\pi$
$488$	3.83715	+	0.180925i	0.173700	+	0.00819009i
$489$	−8.40317	−	7.69588i	−0.380005	−	0.348020i
$490$	−0.869148	+	0.300972i	−0.0392641	+	0.0135965i
$491$	−9.36735	−	5.40824i	−0.422743	−	0.244070i	0.273507	−	0.961870i	$-0.411816\pi$
$491$	−9.36735	−	5.40824i	−0.422743	−	0.244070i	−0.696250	+	0.717799i	$0.745149\pi$
$492$	3.09498	−	41.3151i	0.139532	−	1.86263i
$493$	−30.4666	+	17.5899i	−1.37214	+	0.792208i
$494$	0.0973476	−	0.112382i	0.00437988	−	0.00505630i
$495$	0.434891	+	4.93988i	0.0195469	+	0.222031i
$496$	−27.6220	+	8.12992i	−1.24026	+	0.365044i
$497$	−1.82894	−	3.16781i	−0.0820391	−	0.142096i
$498$	−5.26650	+	12.1793i	−0.235997	+	0.545769i
$499$	−23.9022	−	13.8000i	−1.07001	−	0.617771i	−0.141826	−	0.989892i	$-0.545297\pi$
$499$	−23.9022	−	13.8000i	−1.07001	−	0.617771i	−0.928184	+	0.372121i	$0.878631\pi$
$500$	4.62625	−	11.5666i	0.206892	−	0.517275i
$501$	2.40081	+	7.60718i	0.107260	+	0.339864i
$502$	−0.573108	+	2.97615i	−0.0255791	+	0.132832i
$503$	−24.9186			−1.11106			−0.555532	−	0.831495i	$-0.687485\pi$
$503$	−24.9186			−1.11106			−0.555532	+	0.831495i	$0.687485\pi$
$504$	−8.47826	+	0.345210i	−0.377652	+	0.0153769i
$505$	−2.83067			−0.125963
$506$	1.32510	−	6.88124i	0.0589078	−	0.305909i
$507$	−21.7384	−	4.81308i	−0.965435	−	0.213756i
$508$	−14.1491	−	5.65914i	−0.627763	−	0.251084i
$509$	−7.06763	−	4.08050i	−0.313267	−	0.180865i	0.335120	−	0.942175i	$-0.391223\pi$
$509$	−7.06763	−	4.08050i	−0.313267	−	0.180865i	−0.648388	+	0.761310i	$0.724556\pi$
$510$	6.51040	−	0.755091i	0.288285	−	0.0334360i
$511$	−2.17903	−	3.77419i	−0.0963947	−	0.166961i
$512$	−3.18770	+	22.4018i	−0.140878	+	0.990027i
$513$	0.871225	−	1.13732i	0.0384655	−	0.0502140i
$514$	−9.79170	+	11.3039i	−0.431893	+	0.498594i
$515$	3.93969	−	2.27458i	0.173603	−	0.100230i
$516$	−11.3942	+	16.7132i	−0.501601	+	0.735758i
$517$	−20.3614	−	11.7556i	−0.895492	−	0.517012i
$518$	−3.80317	+	1.31698i	−0.167102	+	0.0578647i
$519$	4.37271	−	19.7494i	0.191941	−	0.866905i
$520$	0.0330371	−	0.700668i	0.00144877	−	0.0307263i
$521$	−6.49477			−0.284541			−0.142270	−	0.989828i	$-0.545440\pi$
$521$	−6.49477			−0.284541			−0.142270	+	0.989828i	$0.545440\pi$
$522$	14.8323	+	33.1094i	0.649192	+	1.44916i
$523$			32.9112i			1.43911i	0.694437	+	0.719553i	$0.255653\pi$
$523$			32.9112i			1.43911i	−0.694437	+	0.719553i	$0.744347\pi$
$524$	21.7361	+	27.6213i	0.949545	+	1.20664i
$525$	2.38593	+	7.56003i	0.104131	+	0.329947i
$526$	5.06724	+	14.6332i	0.220942	+	0.638037i
$527$	−14.8070	+	25.6466i	−0.645005	+	1.11718i
$528$	−14.6125	+	9.82516i	−0.635925	+	0.427585i
$529$	9.59942	+	16.6267i	0.417366	+	0.722899i
$530$	−3.35353	+	3.87145i	−0.145668	+	0.168165i
$531$	−1.43462	+	3.08092i	−0.0622571	+	0.133701i
$532$	0.545796	−	0.0786533i	0.0236632	−	0.00341005i
$533$	−3.94951	+	2.28025i	−0.171072	+	0.0987685i
$534$	11.0958	−	8.24516i	0.480160	−	0.356803i
$535$	−2.56006	+	4.43416i	−0.110681	+	0.191705i
$536$	−12.6940	−	24.5937i	−0.548297	−	1.06228i
$537$	−27.7250	−	25.3914i	−1.19642	−	1.09572i
$538$	5.00089	−	25.9696i	0.215604	−	1.11963i
$539$		−	2.54156i		−	0.109473i
$540$	−0.0881260	−	6.75843i	−0.00379234	−	0.290837i
$541$		−	13.1641i		−	0.565967i	−0.959125	−	0.282984i	$-0.908676\pi$
$541$		−	13.1641i		−	0.565967i	0.959125	−	0.282984i	$-0.0913242\pi$
$542$	34.8290	+	6.70691i	1.49603	+	0.288086i
$543$	−33.9575	−	31.0993i	−1.45726	−	1.33460i
$544$	13.5145	+	18.9461i	0.579429	+	0.812307i
$545$	−2.44852	+	4.24095i	−0.104883	+	0.181662i
$546$	0.557090	+	0.749692i	0.0238412	+	0.0320838i
$547$	−10.4271	+	6.02009i	−0.445830	+	0.257400i	−0.706068	−	0.708144i	$-0.749533\pi$
$547$	−10.4271	+	6.02009i	−0.445830	+	0.257400i	0.260237	+	0.965545i	$0.416199\pi$
$548$	2.73953	+	19.0103i	0.117027	+	0.812079i
$549$	−2.33882	−	3.33631i	−0.0998183	−	0.142390i
$550$	12.4347	+	10.7712i	0.530217	+	0.459286i
$551$	−1.17886	−	2.04185i	−0.0502213	−	0.0869858i
$552$	−2.50167	+	9.21788i	−0.106478	+	0.392339i
$553$	−7.28376	+	12.6158i	−0.309737	+	0.536480i
$554$	0.288605	−	0.0999393i	0.0122616	−	0.00424601i
$555$	−0.964874	−	3.05729i	−0.0409566	−	0.129775i
$556$	−18.6953	−	23.7573i	−0.792858	−	1.00753i
$557$		−	28.4395i		−	1.20502i	−0.798111	−	0.602510i	$-0.794167\pi$
$557$		−	28.4395i		−	1.20502i	0.798111	−	0.602510i	$-0.205833\pi$
$558$	24.7486	+	17.8944i	1.04769	+	0.757531i
$559$	2.22656			0.0941734
$560$	1.79405	−	1.88398i	0.0758126	−	0.0796128i
$561$	−3.91496	+	17.6820i	−0.165290	+	0.746535i
$562$	−5.74198	−	16.5817i	−0.242211	−	0.699457i
$563$	14.8259	+	8.55971i	0.624835	+	0.360749i	0.778749	−	0.627335i	$-0.215855\pi$
$563$	14.8259	+	8.55971i	0.624835	+	0.360749i	−0.153914	+	0.988084i	$0.549188\pi$
$564$	26.4777	+	18.0511i	1.11491	+	0.760088i
$565$	7.69220	−	4.44109i	0.323613	−	0.186838i
$566$	5.88610	+	5.09867i	0.247411	+	0.214313i
$567$	5.79259	+	6.88810i	0.243266	+	0.289273i
$568$	8.70635	+	5.58928i	0.365310	+	0.234521i
$569$	4.24083	+	7.34533i	0.177785	+	0.307932i	0.941122	−	0.338068i	$-0.109774\pi$
$569$	4.24083	+	7.34533i	0.177785	+	0.307932i	−0.763337	+	0.646001i	$0.776440\pi$
$570$	0.0506058	+	0.436323i	0.00211964	+	0.0182756i
$571$	2.82466	+	1.63082i	0.118208	+	0.0682476i	0.557938	−	0.829882i	$-0.311593\pi$
$571$	2.82466	+	1.63082i	0.118208	+	0.0682476i	−0.439730	+	0.898130i	$0.644926\pi$
$572$	1.79964	+	0.719793i	0.0752467	+	0.0300961i
$573$	24.1100	+	5.33818i	1.00721	+	0.223006i
$574$	−16.6089	−	3.19833i	−0.693244	−	0.133496i
$575$	8.92357			0.372139
$576$	20.8612	−	11.8663i	0.869218	−	0.494429i
$577$	−13.7437			−0.572157			−0.286078	−	0.958206i	$-0.592352\pi$
$577$	−13.7437			−0.572157			−0.286078	+	0.958206i	$0.592352\pi$
$578$	−0.104329	−	0.0200904i	−0.00433952	−	0.000835649i
$579$	−5.63044	−	17.8406i	−0.233993	−	0.741428i
$580$	−10.3278	−	4.13076i	−0.428838	−	0.171520i
$581$	4.69138	+	2.70857i	0.194631	+	0.112370i
$582$	8.84559	+	3.82495i	0.366662	+	0.158549i
$583$	−7.07651	−	12.2569i	−0.293079	−	0.507628i
$584$	10.3729	+	6.65917i	0.429234	+	0.275559i
$585$	−0.609214	+	0.427070i	−0.0251879	+	0.0176572i
$586$	−32.1061	−	27.8110i	−1.32629	−	1.14886i
$587$	−22.3911	+	12.9275i	−0.924179	+	0.533575i	−0.884966	−	0.465656i	$-0.845818\pi$
$587$	−22.3911	+	12.9275i	−0.924179	+	0.533575i	−0.0392129	+	0.999231i	$0.512485\pi$
$588$	−0.258776	+	3.45442i	−0.0106717	+	0.142458i
$589$	−1.71882	−	0.992360i	−0.0708227	−	0.0408895i
$590$	−0.340957	−	0.984618i	−0.0140370	−	0.0405361i
$591$	−13.8358	−	12.6712i	−0.569129	−	0.521225i
$592$	7.85033	−	8.24383i	0.322646	−	0.338819i
$593$	−15.3377			−0.629842			−0.314921	−	0.949118i	$-0.601978\pi$
$593$	−15.3377			−0.629842			−0.314921	+	0.949118i	$0.601978\pi$
$594$	17.7266	+	5.88073i	0.727330	+	0.241289i
$595$		−	2.67568i		−	0.109692i
$596$	16.2211	+	20.6131i	0.664441	+	0.844344i
$597$	−9.24307	+	10.0926i	−0.378294	+	0.413061i
$598$	0.993481	−	0.344027i	0.0406265	−	0.0140683i
$599$	−9.73061	+	16.8539i	−0.397582	+	0.688632i	−0.993427	−	0.114467i	$-0.963484\pi$
$599$	−9.73061	+	16.8539i	−0.397582	+	0.688632i	0.595845	+	0.803099i	$0.296817\pi$
$600$	−15.8042	−	15.9060i	−0.645204	−	0.649360i
$601$	18.9584	+	32.8369i	0.773328	+	1.33944i	0.935729	+	0.352719i	$0.114743\pi$
$601$	18.9584	+	32.8369i	0.773328	+	1.33944i	−0.162401	+	0.986725i	$0.551924\pi$
$602$	6.24179	+	5.40678i	0.254396	+	0.220364i
$603$	−12.3916	+	26.6117i	−0.504625	+	1.08371i
$604$	−5.10635	−	35.4343i	−0.207775	−	1.44180i
$605$	−2.55742	+	1.47653i	−0.103974	+	0.0600294i
$606$	−4.23126	+	9.78525i	−0.171883	+	0.397498i
$607$	9.93800	−	17.2131i	0.403371	−	0.698659i	−0.590759	−	0.806848i	$-0.701172\pi$
$607$	9.93800	−	17.2131i	0.403371	−	0.698659i	0.994130	+	0.108189i	$0.0345051\pi$
$608$	−1.26976	+	0.905734i	−0.0514954	+	0.0367324i
$609$	14.1245	−	4.45766i	0.572353	−	0.180634i
$610$	1.22666	+	0.236215i	0.0496662	+	0.00956406i
$611$		−	3.52740i		−	0.142703i
$612$	7.12145	−	23.6343i	0.287868	−	0.955360i
$613$			14.8585i			0.600129i	0.953919	+	0.300065i	$0.0970083\pi$
$613$			14.8585i			0.600129i	−0.953919	+	0.300065i	$0.902992\pi$
$614$	1.56611	−	8.13283i	0.0632032	−	0.328214i
$615$	2.91252	−	13.1544i	0.117444	−	0.530439i
$616$	3.29711	+	6.38790i	0.132844	+	0.257376i
$617$	−17.3444	+	30.0414i	−0.698259	+	1.20942i	0.270811	+	0.962633i	$0.412708\pi$
$617$	−17.3444	+	30.0414i	−0.698259	+	1.20942i	−0.969070	+	0.246787i	$0.920625\pi$
$618$	−1.97390	−	17.0190i	−0.0794021	−	0.684605i
$619$	23.7452	−	13.7093i	0.954400	−	0.551023i	0.0599547	−	0.998201i	$-0.480904\pi$
$619$	23.7452	−	13.7093i	0.954400	−	0.551023i	0.894445	+	0.447178i	$0.147571\pi$
$620$	−9.26773	+	1.33555i	−0.372201	+	0.0536370i
$621$	9.35639	−	3.88449i	0.375459	−	0.155879i
$622$	−8.71963	+	10.0663i	−0.349625	+	0.403621i
$623$	−2.82178	−	4.88746i	−0.113052	−	0.195812i
$624$	−2.37273	−	1.16156i	−0.0949854	−	0.0464996i
$625$	−9.41696	+	16.3106i	−0.376678	+	0.652426i
$626$	1.27370	+	3.67820i	0.0509073	+	0.147010i
$627$	−1.18504	−	0.262378i	−0.0473259	−	0.0104784i
$628$	6.57657	+	8.35724i	0.262434	+	0.333490i
$629$		−	11.7081i		−	0.466832i
$630$	−2.74489	−	0.282140i	−0.109359	−	0.0112407i
$631$	3.12371			0.124353			0.0621765	−	0.998065i	$-0.480196\pi$
$631$	3.12371			0.124353			0.0621765	+	0.998065i	$0.480196\pi$
$632$	1.94061	−	41.1574i	0.0771932	−	1.63715i
$633$	37.9086	−	11.9639i	1.50673	−	0.475521i
$634$	−39.0807	+	13.5330i	−1.55209	+	0.537464i
$635$	−4.29164	−	2.47778i	−0.170308	−	0.0983277i
$636$	8.37024	+	17.3797i	0.331902	+	0.689151i
$637$	0.330225	−	0.190655i	0.0130840	−	0.00755404i
$638$	20.1240	−	23.2319i	0.796716	−	0.919759i
$639$	−0.962362	−	10.9314i	−0.0380705	−	0.432438i
$640$	−2.06509	+	7.06255i	−0.0816299	+	0.279172i
$641$	21.4463	+	37.1460i	0.847077	+	1.46718i	0.883805	+	0.467855i	$0.154973\pi$
$641$	21.4463	+	37.1460i	0.847077	+	1.46718i	−0.0367285	+	0.999325i	$0.511694\pi$
$642$	11.5015	+	15.4780i	0.453930	+	0.610866i
$643$	−35.2154	−	20.3316i	−1.38876	−	0.801801i	−0.395585	−	0.918429i	$-0.629458\pi$
$643$	−35.2154	−	20.3316i	−1.38876	−	0.801801i	−0.993176	+	0.116628i	$0.962791\pi$
$644$	3.62046	+	1.44806i	0.142666	+	0.0570615i
$645$	−4.44264	+	4.85094i	−0.174929	+	0.191006i
$646$	−0.303331	+	1.57520i	−0.0119344	+	0.0619753i
$647$	12.0632			0.474254			0.237127	−	0.971479i	$-0.423794\pi$
$647$	12.0632			0.474254			0.237127	+	0.971479i	$0.423794\pi$
$648$	−23.4947	−	9.79782i	−0.922961	−	0.384895i
$649$	2.87922			0.113019
$650$	−0.466713	+	2.42364i	−0.0183060	+	0.0950630i
$651$	8.42075	−	9.19466i	0.330035	−	0.360367i
$652$	4.88621	−	12.2166i	0.191359	−	0.478438i
$653$	−14.9305	−	8.62010i	−0.584274	−	0.337331i	0.178556	−	0.983930i	$-0.442857\pi$
$653$	−14.9305	−	8.62010i	−0.584274	−	0.337331i	−0.762830	+	0.646599i	$0.776191\pi$
$654$	11.0004	+	14.8035i	0.430149	+	0.578864i
$655$	5.71496	+	9.89861i	0.223302	+	0.386771i
$656$	45.8937	−	13.5078i	1.79185	−	0.527390i
$657$	−1.14658	−	13.0238i	−0.0447322	−	0.508108i
$658$	8.56562	−	9.88847i	0.333923	−	0.385493i
$659$	22.6656	−	13.0860i	0.882926	−	0.509757i	0.0113038	−	0.999936i	$-0.496402\pi$
$659$	22.6656	−	13.0860i	0.882926	−	0.509757i	0.871622	+	0.490179i	$0.163068\pi$
$660$	−5.15900	+	2.48462i	−0.200814	+	0.0967138i
$661$	−4.47602	−	2.58423i	−0.174097	−	0.100515i	0.410419	−	0.911897i	$-0.365382\pi$
$661$	−4.47602	−	2.58423i	−0.174097	−	0.100515i	−0.584516	+	0.811382i	$0.698716\pi$
$662$	28.5949	−	9.90195i	1.11137	−	0.384850i
$663$	−2.59110	+	0.817746i	−0.100630	+	0.0317586i
$664$	−15.3050	−	0.721642i	−0.593948	−	0.0280051i
$665$	0.179322			0.00695382
$666$	−12.0109	−	1.23457i	−0.465415	−	0.0478388i
$667$		−	16.6720i		−	0.645543i
$668$	−7.23857	+	5.69625i	−0.280069	+	0.220395i
$669$	−21.2242	−	4.69924i	−0.820577	−	0.181683i
$670$	−2.94504	−	8.50470i	−0.113777	−	0.328565i
$671$	−1.72591	+	2.98936i	−0.0666278	+	0.115403i
$672$	−3.83094	−	9.01798i	−0.147782	−	0.347876i
$673$	8.77902	+	15.2057i	0.338406	+	0.586137i	0.984133	−	0.177432i	$-0.0567789\pi$
$673$	8.77902	+	15.2057i	0.338406	+	0.586137i	−0.645727	+	0.763568i	$0.723446\pi$
$674$	−10.7119	+	12.3662i	−0.412605	+	0.476327i
$675$	−3.08503	+	23.5818i	−0.118743	+	0.907666i
$676$	−3.66701	−	25.4463i	−0.141039	−	0.978705i
$677$	32.4915	−	18.7590i	1.24875	−	0.720967i	0.277891	−	0.960613i	$-0.410365\pi$
$677$	32.4915	−	18.7590i	1.24875	−	0.720967i	0.970860	+	0.239645i	$0.0770312\pi$
$678$	−3.85403	−	33.2295i	−0.148013	−	1.27617i
$679$	1.96718	−	3.40725i	0.0754933	−	0.130758i
$680$	3.47109	+	6.72499i	0.133110	+	0.257892i
$681$	6.97276	−	31.4926i	0.267197	−	1.20680i
$682$	4.89245	−	25.4065i	0.187342	−	0.972865i
$683$		−	22.0581i		−	0.844031i	−0.906589	−	0.422015i	$-0.861323\pi$
$683$		−	22.0581i		−	0.844031i	0.906589	−	0.422015i	$-0.138677\pi$
$684$	1.58396	+	0.477276i	0.0605641	+	0.0182491i
$685$			6.24587i			0.238642i
$686$	1.38870	+	0.267418i	0.0530208	+	0.0102101i
$687$	48.8028	−	15.4021i	1.86194	−	0.587625i
$688$	−22.7021	−	5.49195i	−0.865508	−	0.209379i
$689$	1.06169	−	1.83890i	0.0404471	−	0.0700565i
$690$	−1.23277	+	2.85090i	−0.0469306	+	0.108532i
$691$	−17.9747	+	10.3777i	−0.683791	+	0.394787i	−0.801282	−	0.598287i	$-0.795848\pi$
$691$	−17.9747	+	10.3777i	−0.683791	+	0.394787i	0.117491	+	0.993074i	$0.462515\pi$
$692$	23.1182	−	3.33150i	0.878821	−	0.126645i
$693$	3.21857	−	6.91206i	0.122263	−	0.262567i
$694$	6.13005	+	5.30998i	0.232693	+	0.201564i
$695$	−4.91548	−	8.51385i	−0.186455	−	0.322949i
$696$	−29.7174	+	29.5272i	−1.12643	+	1.11922i
$697$	24.6018	−	42.6115i	0.931858	−	1.61403i
$698$	2.80070	−	0.969838i	0.106008	−	0.0367089i
$699$	27.2386	−	29.7419i	1.03026	−	1.12494i
$700$	−7.19370	+	5.66095i	−0.271896	+	0.213964i
$701$			39.1099i			1.47716i	0.674165	+	0.738580i	$0.264503\pi$
$701$			39.1099i			1.47716i	−0.674165	+	0.738580i	$0.735497\pi$
$702$	0.565677	+	2.74436i	0.0213501	+	0.103579i
$703$	0.784669			0.0295944
$704$	−16.5738	−	11.7780i	−0.624647	−	0.443899i
$705$	7.68504	+	7.03820i	0.289435	+	0.265074i
$706$	−12.4827	−	36.0477i	−0.469794	−	1.35667i
$707$	3.76919	+	2.17615i	0.141755	+	0.0818424i
$708$	−3.91336	−	0.293155i	−0.147073	−	0.0110175i
$709$	−25.9908	+	15.0058i	−0.976105	+	0.563554i	−0.901092	−	0.433628i	$-0.857233\pi$
$709$	−25.9908	+	15.0058i	−0.976105	+	0.563554i	−0.0750129	+	0.997183i	$0.523900\pi$
$710$	2.54304	+	2.20284i	0.0954387	+	0.0826711i
$711$	−35.7854	+	25.0862i	−1.34206	+	0.940807i
$712$	13.4326	+	8.62342i	0.503408	+	0.323176i
$713$	−7.01720	−	12.1541i	−0.262796	−	0.455176i
$714$	−9.24946	−	3.99958i	−0.346152	−	0.149681i
$715$	0.545859	+	0.315152i	0.0204140	+	0.0117860i
$716$	16.1213	−	40.3067i	0.602481	−	1.50633i
$717$	−0.292449	−	0.926651i	−0.0109217	−	0.0346064i
$718$	0.0396072	+	0.00762704i	0.00147813	+	0.000284639i
$719$	29.5953			1.10372			0.551860	−	0.833937i	$-0.313918\pi$
$719$	29.5953			1.10372			0.551860	+	0.833937i	$0.313918\pi$
$720$	7.26496	−	2.85176i	0.270749	−	0.106279i
$721$	−6.99456			−0.260491
$722$	26.2797	+	5.06061i	0.978030	+	0.188336i
$723$	40.7387	+	9.01992i	1.51509	+	0.335454i
$724$	19.7453	−	49.3676i	0.733829	−	1.83473i
$725$	33.8955	+	19.5696i	1.25885	+	0.726795i
$726$	1.28135	+	11.0478i	0.0475552	+	0.410021i
$727$	24.1526	+	41.8335i	0.895770	+	1.55152i	0.832849	+	0.553500i	$0.186708\pi$
$727$	24.1526	+	41.8335i	0.895770	+	1.55152i	0.0629205	+	0.998019i	$0.479959\pi$
$728$	−0.582647	+	0.907582i	−0.0215943	+	0.0336372i
$729$	7.03067	+	26.0686i	0.260395	+	0.965502i
$730$	3.02983	+	2.62451i	0.112139	+	0.0971373i
$731$	−20.8041	+	12.0112i	−0.769467	+	0.444252i
$732$	2.65017	−	3.88733i	0.0979533	−	0.143680i
$733$	−15.2976	−	8.83209i	−0.565031	−	0.326221i	0.190131	−	0.981759i	$-0.439109\pi$
$733$	−15.2976	−	8.83209i	−0.565031	−	0.326221i	−0.755162	+	0.655538i	$0.772442\pi$
$734$	−1.92243	−	5.55159i	−0.0709580	−	0.204913i
$735$	−0.243520	+	1.09986i	−0.00898238	+	0.0405691i
$736$	−10.9781	+	1.05722i	−0.404659	+	0.0389697i
$737$	24.8694			0.916077
$738$	−41.1196	−	29.7314i	−1.51363	−	1.09443i
$739$		−	7.14501i		−	0.262833i	−0.991327	−	0.131417i	$-0.958047\pi$
$739$		−	7.14501i		−	0.262833i	0.991327	−	0.131417i	$-0.0419526\pi$
$740$	2.90915	−	2.28930i	0.106942	−	0.0841562i
$741$	−0.0548049	−	0.173654i	−0.00201331	−	0.00637934i
$742$	7.44169	−	2.57694i	0.273193	−	0.0946024i
$743$	17.1692	−	29.7380i	0.629878	−	1.09098i	−0.357697	−	0.933838i	$-0.616438\pi$
$743$	17.1692	−	29.7380i	0.629878	−	1.09098i	0.987576	−	0.157144i	$-0.0502286\pi$
$744$	−9.23652	+	34.0337i	−0.338627	+	1.24774i
$745$	4.26493	+	7.38707i	0.156255	+	0.270641i
$746$	9.63955	+	8.34999i	0.352929	+	0.305715i
$747$	9.32867	+	13.3073i	0.341318	+	0.486889i
$748$	−20.6981	+	2.98275i	−0.756796	+	0.109060i
$749$	6.81774	−	3.93623i	0.249115	−	0.143827i
$750$	−9.10011	−	12.2463i	−0.332289	−	0.447171i
$751$	−12.5390	+	21.7181i	−0.457553	+	0.792505i	−0.998831	−	0.0483387i	$-0.984607\pi$
$751$	−12.5390	+	21.7181i	−0.457553	+	0.792505i	0.541278	+	0.840844i	$0.317941\pi$
$752$	−8.70056	+	35.9655i	−0.317277	+	1.31153i
$753$	2.73745	+	2.50704i	0.0997582	+	0.0913616i
$754$	4.52811	+	0.871965i	0.164904	+	0.0317551i
$755$		−	11.6420i		−	0.423696i
$756$	−5.07837	+	9.06698i	−0.184698	+	0.329763i
$757$		−	51.0824i		−	1.85662i	−0.371808	−	0.928310i	$-0.621262\pi$
$757$		−	51.0824i		−	1.85662i	0.371808	−	0.928310i	$-0.378738\pi$
$758$	−7.90797	+	41.0661i	−0.287230	+	1.49159i
$759$	−6.32934	−	5.79660i	−0.229740	−	0.210403i
$760$	−0.450705	+	0.232631i	−0.0163488	+	0.00843840i
$761$	9.50244	−	16.4587i	0.344463	−	0.596628i	−0.640793	−	0.767714i	$-0.721394\pi$
$761$	9.50244	−	16.4587i	0.344463	−	0.596628i	0.985256	+	0.171086i	$0.0547276\pi$
$762$	−14.9805	+	11.1319i	−0.542685	+	0.403265i
$763$	6.52068	−	3.76471i	0.236064	−	0.136292i
$764$	4.06708	+	28.2225i	0.147142	+	1.02105i
$765$	3.38841	−	7.27680i	0.122508	−	0.263093i
$766$	0.00179784	−	0.00207550i	6.49586e−5	−	7.49907e-5i
$767$	0.215985	+	0.374096i	0.00779875	+	0.0135078i
$768$	21.3274	+	17.6958i	0.769587	+	0.638542i
$769$	−16.2156	+	28.0862i	−0.584749	+	1.01282i	0.410158	+	0.912015i	$0.365474\pi$
$769$	−16.2156	+	28.0862i	−0.584749	+	1.01282i	−0.994907	+	0.100800i	$0.967860\pi$
$770$	0.764939	+	2.20899i	0.0275665	+	0.0796066i
$771$	5.51254	+	17.4670i	0.198529	+	0.629058i
$772$	16.9761	−	13.3590i	0.610982	−	0.480801i
$773$			32.3434i			1.16331i	0.813436	+	0.581655i	$0.197595\pi$
$773$			32.3434i			1.16331i	−0.813436	+	0.581655i	$0.802405\pi$
$774$	10.1282	+	22.6088i	0.364052	+	0.812656i
$775$	32.9471			1.18349
$776$	−0.524113	+	11.1157i	−0.0188146	+	0.399030i
$777$	−1.06558	+	4.81273i	−0.0382276	+	0.172656i
$778$	−40.8650	+	14.1509i	−1.46508	+	0.507335i
$779$	2.85580	+	1.64880i	0.102320	+	0.0590742i
$780$	−0.709830	−	0.483925i	−0.0254160	−	0.0173273i
$781$	−8.05119	+	4.64836i	−0.288094	+	0.166331i
$782$	−7.42683	+	8.57382i	−0.265583	+	0.306599i
$783$	44.0582	+	5.76380i	1.57451	+	0.205982i
$784$	−3.83724	+	1.12941i	−0.137044	+	0.0403360i
$785$	1.72915	+	2.99497i	0.0617159	+	0.106895i
$786$	42.7609	−	4.95951i	1.52523	−	0.176900i
$787$	−46.1972	−	26.6720i	−1.64675	−	0.950753i	−0.978351	−	0.206951i	$-0.933646\pi$
$787$	−46.1972	−	26.6720i	−1.64675	−	0.950753i	−0.668401	−	0.743801i	$-0.733021\pi$
$788$	8.04513	−	20.1146i	0.286596	−	0.716552i
$789$	18.5176	+	4.09996i	0.659243	+	0.145963i
$790$	2.53365	−	13.1572i	0.0901432	−	0.468114i
$791$	−13.6568			−0.485580
$792$	0.877371	+	21.5480i	0.0311760	+	0.765675i
$793$	−0.517875			−0.0183903
$794$	8.15801	−	42.3646i	0.289517	−	1.50346i
$795$	1.88798	+	5.98222i	0.0669596	+	0.212167i
$796$	−14.6726	−	5.86854i	−0.520057	−	0.208005i
$797$	17.2656	+	9.96829i	0.611578	+	0.353095i	0.773583	−	0.633695i	$-0.218463\pi$
$797$	17.2656	+	9.96829i	0.611578	+	0.353095i	−0.162005	+	0.986790i	$0.551796\pi$
$798$	0.268050	−	0.619894i	0.00948886	−	0.0219440i
$799$	19.0287	+	32.9586i	0.673186	+	1.16599i
$800$	10.7367	−	23.5603i	0.379599	−	0.832983i
$801$	−1.48478	−	16.8654i	−0.0524622	−	0.595911i
$802$	−22.6862	+	26.1898i	−0.801076	+	0.924793i
$803$	−9.59235	+	5.53814i	−0.338507	+	0.195437i
$804$	−33.8019	−	2.53215i	−1.19210	−	0.0893020i
$805$	1.09814	+	0.634014i	0.0387045	+	0.0223460i
$806$	3.66807	−	1.27019i	0.129202	−	0.0447407i
$807$	−23.8868	−	21.8762i	−0.840854	−	0.770080i
$808$	−12.2965	−	0.579789i	−0.432589	−	0.0203969i
$809$	18.4879			0.649999			0.325000	−	0.945714i	$-0.394636\pi$
$809$	18.4879			0.649999			0.325000	+	0.945714i	$0.394636\pi$
$810$	−7.10774	−	4.24337i	−0.249741	−	0.149097i
$811$			9.08842i			0.319138i	0.987187	+	0.159569i	$0.0510104\pi$
$811$			9.08842i			0.319138i	−0.987187	+	0.159569i	$0.948990\pi$
$812$	10.5764	+	13.4401i	0.371159	+	0.471654i
$813$	29.3391	−	32.0355i	1.02897	−	1.12354i
$814$	3.34718	+	9.66599i	0.117319	+	0.338793i
$815$	2.13936	−	3.70548i	0.0749386	−	0.129797i
$816$	28.4360	−	1.94664i	0.995458	−	0.0681462i
$817$	−0.804987	−	1.39428i	−0.0281629	−	0.0487796i
$818$	13.0362	−	15.0495i	0.455799	−	0.526192i
$819$	1.13952	−	0.100320i	0.0398182	−	0.00350547i
$820$	15.3982	−	2.21900i	0.537730	−	0.0774910i
$821$	−20.5085	+	11.8406i	−0.715753	+	0.413240i	−0.813188	−	0.582002i	$-0.802270\pi$
$821$	−20.5085	+	11.8406i	−0.715753	+	0.413240i	0.0974345	+	0.995242i	$0.468936\pi$
$822$	21.5911	+	9.33628i	0.753077	+	0.325640i
$823$	−1.67747	+	2.90546i	−0.0584729	+	0.101278i	−0.893780	−	0.448506i	$-0.851956\pi$
$823$	−1.67747	+	2.90546i	−0.0584729	+	0.101278i	0.835307	+	0.549783i	$0.185290\pi$
$824$	17.5800	−	9.07388i	0.612428	−	0.316104i
$825$	19.2143	−	6.06399i	0.668955	−	0.211121i
$826$	−0.302945	+	1.57319i	−0.0105408	+	0.0547384i
$827$		−	0.683428i		−	0.0237651i	−0.999929	−	0.0118826i	$-0.996218\pi$
$827$		−	0.683428i		−	0.0237651i	0.999929	−	0.0118826i	$-0.00378243\pi$
$828$	8.01247	+	8.52303i	0.278453	+	0.296196i
$829$		−	0.172036i		−	0.00597507i	−0.999996	−	0.00298754i	$-0.999049\pi$
$829$		−	0.172036i		−	0.00597507i	0.999996	−	0.00298754i	$-0.000950964\pi$
$830$	−4.89271	−	0.942173i	−0.169828	−	0.0327033i
$831$	0.0808621	−	0.365215i	0.00280507	−	0.0126692i
$832$	0.287028	−	3.03695i	0.00995089	−	0.105287i
$833$	−2.05699	+	3.56282i	−0.0712706	+	0.123444i
$834$	−36.7789	+	4.26570i	−1.27355	+	0.147709i
$835$	−2.59408	+	1.49769i	−0.0897717	+	0.0518297i
$836$	−0.199902	−	1.38717i	−0.00691376	−	0.0479764i
$837$	34.5451	−	14.3421i	1.19405	−	0.495735i
$838$	12.7348	+	11.0312i	0.439917	+	0.381066i
$839$	−1.65731	−	2.87054i	−0.0572165	−	0.0991020i	0.835998	−	0.548732i	$-0.184889\pi$
$839$	−1.65731	−	2.87054i	−0.0572165	−	0.0991020i	−0.893215	+	0.449630i	$0.851556\pi$
$840$	−0.814770	−	3.08029i	−0.0281122	−	0.106280i
$841$	22.0620	−	38.2125i	0.760759	−	1.31767i
$842$	−4.91374	+	1.70155i	−0.169339	+	0.0586393i
$843$	−20.9833	−	4.64590i	−0.722704	−	0.160013i
$844$	28.3859	+	36.0717i	0.977084	+	1.24164i
$845$		−	8.36045i		−	0.287608i
$846$	35.8177	−	16.0455i	1.23144	−	0.551657i
$847$	4.54047			0.156012
$848$	−15.3608	+	16.1308i	−0.527492	+	0.553932i
$849$	9.09530	−	2.87046i	0.312150	−	0.0985139i
$850$	−8.71363	−	25.1632i	−0.298875	−	0.863092i
$851$	4.80520	+	2.77428i	0.164720	+	0.0951012i
$852$	11.4163	−	5.49817i	0.391114	−	0.188364i
$853$	31.9005	−	18.4178i	1.09225	−	0.630612i	0.158077	−	0.987427i	$-0.449470\pi$
$853$	31.9005	−	18.4178i	1.09225	−	0.630612i	0.934175	+	0.356814i	$0.116137\pi$
$854$	−1.45178	−	1.25756i	−0.0496788	−	0.0430329i
$855$	0.487687	+	0.227089i	0.0166786	+	0.00776629i
$856$	−12.0292	+	18.7377i	−0.411149	+	0.640442i
$857$	−18.4566	−	31.9677i	−0.630465	−	1.09200i	−0.987457	−	0.157890i	$-0.949531\pi$
$857$	−18.4566	−	31.9677i	−0.630465	−	1.09200i	0.356992	−	0.934108i	$-0.383802\pi$
$858$	1.90539	−	1.41588i	0.0650488	−	0.0483373i
$859$	12.9520	+	7.47782i	0.441915	+	0.255140i	0.704410	−	0.709794i	$-0.251212\pi$
$859$	12.9520	+	7.47782i	0.441915	+	0.255140i	−0.262495	+	0.964933i	$0.584545\pi$
$860$	−7.05233	−	2.82069i	−0.240482	−	0.0961846i
$861$	−13.9910	+	15.2768i	−0.476812	+	0.520633i
$862$	17.1319	+	3.29904i	0.583515	+	0.112366i
$863$	−39.2886			−1.33740			−0.668699	−	0.743533i	$-0.733149\pi$
$863$	−39.2886			−1.33740			−0.668699	+	0.743533i	$0.733149\pi$
$864$	1.00147	−	29.3768i	0.0340706	−	0.999419i
$865$	7.59552			0.258255
$866$	−38.4983	−	7.41351i	−1.30823	−	0.251921i
$867$	−0.0878846	+	0.0959616i	−0.00298472	+	0.00325903i
$868$	13.3672	+	5.34643i	0.453714	+	0.181470i
$869$	32.0639	+	18.5121i	1.08769	+	0.627980i
$870$	−10.9346	+	8.12545i	−0.370719	+	0.275478i
$871$	1.86558	+	3.23128i	0.0632128	+	0.109488i
$872$	−11.5051	+	17.9213i	−0.389610	+	0.606891i
$873$	9.66481	−	6.77521i	0.327104	−	0.229306i
$874$	−0.574612	−	0.497742i	−0.0194366	−	0.0168364i
$875$	−5.39425	+	3.11437i	−0.182359	+	0.105285i
$876$	13.6015	−	6.55063i	0.459554	−	0.221325i
$877$	33.2002	+	19.1681i	1.12109	+	0.647262i	0.941679	−	0.336512i	$-0.109247\pi$
$877$	33.2002	+	19.1681i	1.12109	+	0.647262i	0.179412	+	0.983774i	$0.442581\pi$
$878$	−10.0186	−	28.9319i	−0.338113	−	0.976403i
$879$	−49.6108	+	15.6571i	−1.67333	+	0.528100i
$880$	−4.78826	−	4.55970i	−0.161412	−	0.153707i
$881$	−16.0465			−0.540619			−0.270310	−	0.962773i	$-0.587126\pi$
$881$	−16.0465			−0.540619			−0.270310	+	0.962773i	$0.587126\pi$
$882$	3.43808	+	2.48589i	0.115766	+	0.0837042i
$883$		−	33.7695i		−	1.13643i	−0.822879	−	0.568216i	$-0.807634\pi$
$883$		−	33.7695i		−	1.13643i	0.822879	−	0.568216i	$-0.192366\pi$
$884$	−1.94021	−	2.46555i	−0.0652565	−	0.0829253i
$885$	−1.24599	−	0.275873i	−0.0418834	−	0.00927336i
$886$	−30.4064	+	10.5293i	−1.02152	+	0.353737i
$887$	−14.3815	+	24.9094i	−0.482882	+	0.836376i	−0.999807	−	0.0196546i	$-0.993743\pi$
$887$	−14.3815	+	24.9094i	−0.482882	+	0.836376i	0.516925	+	0.856031i	$0.327077\pi$
$888$	−3.56523	−	13.4786i	−0.119641	−	0.452311i
$889$	3.80971	+	6.59861i	0.127774	+	0.221310i
$890$	3.92353	+	3.39865i	0.131517	+	0.113923i
$891$	17.5065	−	14.7222i	0.586491	−	0.493213i
$892$	−3.58028	−	24.8445i	−0.119877	−	0.831856i
$893$	−2.20887	+	1.27529i	−0.0739169	+	0.0426760i
$894$	31.9113	−	3.70115i	1.06727	−	0.123785i
$895$	7.05850	−	12.2257i	0.235940	−	0.408659i
$896$	8.17929	−	7.81659i	0.273251	−	0.261134i
$897$	0.278356	−	1.25720i	0.00929404	−	0.0419767i
$898$	−49.0270	−	9.44097i	−1.63605	−	0.315049i
$899$		−	61.5554i		−	2.05299i
$900$	−26.7330	+	6.28566i	−0.891099	+	0.209522i
$901$			22.9093i			0.763219i
$902$	−8.12875	+	42.2126i	−0.270658	+	1.40553i
$903$	9.64491	−	3.04391i	0.320963	−	0.101295i
$904$	34.3247	−	17.7167i	1.14162	−	0.589247i
$905$	8.64523	−	14.9740i	0.287377	−	0.497752i
$906$	−40.2449	−	17.4024i	−1.33705	−	0.578156i
$907$	40.0377	−	23.1157i	1.32943	−	0.767546i	0.344217	−	0.938890i	$-0.388144\pi$
$907$	40.0377	−	23.1157i	1.32943	−	0.767546i	0.985211	+	0.171344i	$0.0548110\pi$
$908$	36.8644	−	5.31244i	1.22339	−	0.176300i
$909$	7.49493	+	10.6915i	0.248591	+	0.354614i
$910$	−0.229632	+	0.265096i	−0.00761223	+	0.00878785i
$911$	17.4088	+	30.1529i	0.576778	+	0.999009i	0.995846	+	0.0910543i	$0.0290237\pi$
$911$	17.4088	+	30.1529i	0.576778	+	0.999009i	−0.419068	+	0.907955i	$0.637643\pi$
$912$	0.130463	+	1.90576i	0.00432006	+	0.0631061i
$913$	6.88399	−	11.9234i	0.227827	−	0.394608i
$914$	7.09954	+	20.5021i	0.234832	+	0.678149i
$915$	1.03331	−	1.12828i	0.0341603	−	0.0372998i
$916$	36.5435	+	46.4380i	1.20743	+	1.53435i
$917$		−	17.5741i		−	0.580347i
$918$	−20.0900	−	22.5906i	−0.663068	−	0.745601i
$919$	25.8037			0.851185			0.425593	−	0.904915i	$-0.360066\pi$
$919$	25.8037			0.851185			0.425593	+	0.904915i	$0.360066\pi$
$920$	−3.58254	−	0.168920i	−0.118113	−	0.00556912i
$921$	−7.48054	−	6.85091i	−0.246492	−	0.225745i
$922$	4.38777	−	1.51942i	0.144504	−	0.0500393i
$923$	−1.20792	−	0.697393i	−0.0397592	−	0.0229550i
$924$	8.77962	+	0.657695i	0.288828	+	0.0216366i
$925$	−11.2807	+	6.51289i	−0.370906	+	0.214143i
$926$	−32.6580	+	37.7016i	−1.07321	+	1.23895i
$927$	−19.0225	−	8.85774i	−0.624781	−	0.290926i
$928$	−44.0180	−	20.0595i	−1.44496	−	0.658484i
$929$	15.8483	+	27.4501i	0.519966	+	0.900607i	0.999731	+	0.0232100i	$0.00738863\pi$
$929$	15.8483	+	27.4501i	0.519966	+	0.900607i	−0.479765	+	0.877397i	$0.659278\pi$
$930$	−4.55154	+	10.5259i	−0.149251	+	0.345159i
$931$	−0.238778	−	0.137858i	−0.00782563	−	0.00451813i
$932$	43.2390	+	17.2941i	1.41634	+	0.566487i
$933$	4.90899	+	15.5546i	0.160713	+	0.509234i
$934$	−8.15244	+	42.3356i	−0.266756	+	1.38526i
$935$	−6.80039			−0.222397
$936$	−2.73391	+	1.73042i	−0.0893607	+	0.0565606i
$937$	−30.3580			−0.991751			−0.495876	−	0.868394i	$-0.665153\pi$
$937$	−30.3580			−0.991751			−0.495876	+	0.868394i	$0.665153\pi$
$938$	−2.61671	+	13.5886i	−0.0854386	+	0.443683i
$939$	4.65458	+	1.03057i	0.151896	+	0.0336313i
$940$	−4.46864	+	11.1726i	−0.145751	+	0.364409i
$941$	30.5115	+	17.6158i	0.994646	+	0.574259i	0.906660	−	0.421862i	$-0.138623\pi$
$941$	30.5115	+	17.6158i	0.994646	+	0.574259i	0.0879864	+	0.996122i	$0.471957\pi$
$942$	12.9379	−	1.50057i	0.421541	−	0.0488913i
$943$	11.6590	+	20.1940i	0.379669	+	0.657606i
$944$	−1.27945	−	4.34704i	−0.0416426	−	0.141484i
$945$	−2.05512	+	2.68282i	−0.0668531	+	0.0872721i
$946$	13.7417	−	15.8639i	0.446780	−	0.515779i
$947$	6.48495	−	3.74408i	0.210732	−	0.121666i	−0.390919	−	0.920425i	$-0.627843\pi$
$947$	6.48495	−	3.74408i	0.210732	−	0.121666i	0.601652	+	0.798759i	$0.294510\pi$
$948$	−41.6956	−	28.4258i	−1.35421	−	0.923229i
$949$	−1.43914	−	0.830888i	−0.0467165	−	0.0269718i
$950$	1.68643	−	0.583982i	0.0547149	−	0.0189469i
$951$	−10.9497	+	49.4547i	−0.355069	+	1.60368i
$952$	0.548043	−	11.6232i	0.0177622	−	0.376710i
$953$	−25.2439			−0.817729			−0.408864	−	0.912595i	$-0.634075\pi$
$953$	−25.2439			−0.817729			−0.408864	+	0.912595i	$0.634075\pi$
$954$	23.5019	+	2.41570i	0.760902	+	0.0782111i
$955$			9.27256i			0.300053i
$956$	0.881749	−	0.693876i	0.0285178	−	0.0224416i
$957$	−11.3294	−	35.8983i	−0.366228	−	1.16043i
$958$	−19.1987	−	55.4421i	−0.620283	−	1.79125i
$959$	4.80166	−	8.31673i	0.155054	−	0.268561i
$960$	6.04381	+	6.68495i	0.195063	+	0.215756i
$961$	−10.4085	−	18.0280i	−0.335757	−	0.581548i
$962$	−1.00481	+	1.15999i	−0.0323964	+	0.0373997i
$963$	23.5264	−	2.07119i	0.758126	−	0.0667431i
$964$	6.87214	+	47.6876i	0.221337	+	1.53591i
$965$	6.08369	−	3.51242i	0.195841	−	0.113069i
$966$	3.83320	−	2.84842i	0.123331	−	0.0916464i
$967$	−25.9085	+	44.8748i	−0.833160	+	1.44308i	0.0623602	+	0.998054i	$0.480137\pi$
$967$	−25.9085	+	44.8748i	−0.833160	+	1.44308i	−0.895520	+	0.445021i	$0.853196\pi$
$968$	−11.4119	+	5.89024i	−0.366793	+	0.189320i
$969$	1.44886	+	1.32691i	0.0465440	+	0.0426265i
$970$	−0.684280	+	3.55347i	−0.0219709	+	0.114095i
$971$			56.9089i			1.82629i	0.407633	+	0.913146i	$0.366354\pi$
$971$			56.9089i			1.82629i	−0.407633	+	0.913146i	$0.633646\pi$
$972$	−25.2934	+	18.2276i	−0.811286	+	0.584649i
$973$			15.1156i			0.484583i
$974$	33.9755	+	6.54256i	1.08865	+	0.209637i
$975$	2.22925	+	2.04162i	0.0713932	+	0.0653841i
$976$	5.28027	+	1.27737i	0.169017	+	0.0408877i
$977$	−9.84868	+	17.0584i	−0.315087	+	0.545747i	−0.979456	−	0.201658i	$-0.935367\pi$
$977$	−9.84868	+	17.0584i	−0.315087	+	0.545747i	0.664369	+	0.747405i	$0.268700\pi$
$978$	−9.61147	−	12.9344i	−0.307341	−	0.413598i
$979$	−12.4218	+	7.17172i	−0.397002	+	0.229209i
$980$	−1.28747	+	0.185534i	−0.0411268	+	0.00592668i
$981$	22.5013	−	1.98094i	0.718410	−	0.0632466i
$982$	−11.5622	−	10.0154i	−0.368964	−	0.319605i
$983$	−18.9416	−	32.8078i	−0.604143	−	1.04641i	−0.992186	−	0.124766i	$-0.960182\pi$
$983$	−18.9416	−	32.8078i	−0.604143	−	1.04641i	0.388043	−	0.921641i	$-0.373151\pi$
$984$	15.3464	−	56.5466i	0.489225	−	1.80264i
$985$	3.52245	−	6.10107i	0.112235	−	0.194396i
$986$	−47.0128	+	16.2798i	−1.49719	+	0.518453i
$987$	−4.82228	−	15.2798i	−0.153495	−	0.486362i
$988$	0.165240	−	0.130032i	0.00525697	−	0.00413687i
$989$		−	11.3845i		−	0.362005i
$990$	−0.717076	+	6.97630i	−0.0227902	+	0.221722i
$991$	−50.1684			−1.59365			−0.796825	−	0.604210i	$-0.793489\pi$
$991$	−50.1684			−1.59365			−0.796825	+	0.604210i	$0.793489\pi$
$992$	−40.5328	+	3.90340i	−1.28692	+	0.123933i
$993$	8.01179	−	36.1854i	0.254246	−	1.14831i
$994$	−1.69272	−	4.88823i	−0.0536897	−	0.155045i
$995$	−4.45044	−	2.56946i	−0.141088	−	0.0814574i
$996$	−10.5706	+	15.5051i	−0.334941	+	0.491298i
$997$	−17.5464	+	10.1304i	−0.555699	+	0.320833i	−0.751417	−	0.659827i	$-0.770630\pi$
$997$	−17.5464	+	10.1304i	−0.555699	+	0.320833i	0.195718	+	0.980660i	$0.437296\pi$
$998$	−29.5027	−	25.5559i	−0.933891	−	0.808957i
$999$	−8.99269	+	11.7393i	−0.284516	+	0.371416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.b.85.35	yes	72
8.5	even	2	inner	504.2.cs.b.85.15	✓	72
9.7	even	3	inner	504.2.cs.b.421.15	yes	72
72.61	even	6	inner	504.2.cs.b.421.35	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.b.85.15	✓	72	8.5	even	2	inner
504.2.cs.b.85.35	yes	72	1.1	even	1	trivial
504.2.cs.b.421.15	yes	72	9.7	even	3	inner
504.2.cs.b.421.35	yes	72	72.61	even	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38870 + 0.267418i) q^{2} +(1.16981 - 1.27732i) q^{3} +(1.85698 + 0.742726i) q^{4} +(0.563250 + 0.325193i) q^{5} +(1.96609 - 1.46099i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 + 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +O(q^{10})\)	\(q+(1.38870 + 0.267418i) q^{2} +(1.16981 - 1.27732i) q^{3} +(1.85698 + 0.742726i) q^{4} +(0.563250 + 0.325193i) q^{5} +(1.96609 - 1.46099i) q^{6} +(-0.500000 - 0.866025i) q^{7} +(2.38016 + 1.52801i) q^{8} +(-0.263093 - 2.98844i) q^{9} +(0.695224 + 0.602218i) q^{10} +(-2.20106 + 1.27078i) q^{11} +(3.12101 - 1.50310i) q^{12} +(-0.330225 - 0.190655i) q^{13} +(-0.462760 - 1.33636i) q^{14} +(1.07427 - 0.339038i) q^{15} +(2.89672 + 2.75845i) q^{16} +4.11399 q^{17} +(0.433805 - 4.22040i) q^{18} +0.275717i q^{19} +(0.804413 + 1.02222i) q^{20} +(-1.69110 - 0.374424i) q^{21} +(-3.39644 + 1.17613i) q^{22} +(-0.974828 + 1.68845i) q^{23} +(4.73610 - 1.25275i) q^{24} +(-2.28850 - 3.96380i) q^{25} +(-0.407598 - 0.353071i) q^{26} +(-4.12496 - 3.15985i) q^{27} +(-0.285268 - 1.97955i) q^{28} +(-7.40561 + 4.27563i) q^{29} +(1.58250 - 0.183543i) q^{30} +(-3.59920 + 6.23399i) q^{31} +(3.28501 + 4.60529i) q^{32} +(-0.951622 + 4.29802i) q^{33} +(5.71309 + 1.10015i) q^{34} -0.650385i q^{35} +(1.73104 - 5.74487i) q^{36} -2.84592i q^{37} +(-0.0737316 + 0.382888i) q^{38} +(-0.629828 + 0.198772i) q^{39} +(0.843730 + 1.63467i) q^{40} +(5.98003 - 10.3577i) q^{41} +(-2.24830 - 0.972192i) q^{42} +(-5.05692 + 2.91961i) q^{43} +(-5.03115 + 0.725027i) q^{44} +(0.823632 - 1.76880i) q^{45} +(-1.80526 + 2.08407i) q^{46} +(4.62536 + 8.01136i) q^{47} +(6.91203 - 0.473177i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-2.11805 - 6.11651i) q^{50} +(4.81258 - 5.25488i) q^{51} +(-0.471614 - 0.599309i) q^{52} +5.56863i q^{53} +(-4.88334 - 5.49118i) q^{54} -1.65299 q^{55} +(0.133215 - 2.82529i) q^{56} +(0.352179 + 0.322536i) q^{57} +(-11.4275 + 3.95718i) q^{58} +(-0.981080 - 0.566427i) q^{59} +(2.24671 + 0.168304i) q^{60} +(1.17619 - 0.679073i) q^{61} +(-6.66529 + 7.69466i) q^{62} +(-2.45652 + 1.72207i) q^{63} +(3.33036 + 7.27384i) q^{64} +(-0.123999 - 0.214773i) q^{65} +(-2.47089 + 5.71419i) q^{66} +(-8.47415 - 4.89255i) q^{67} +(7.63957 + 3.05556i) q^{68} +(1.01633 + 3.22033i) q^{69} +(0.173925 - 0.903190i) q^{70} +3.65788 q^{71} +(3.94017 - 7.51499i) q^{72} +4.35806 q^{73} +(0.761050 - 3.95213i) q^{74} +(-7.74015 - 1.71374i) q^{75} +(-0.204782 + 0.512000i) q^{76} +(2.20106 + 1.27078i) q^{77} +(-0.927797 + 0.107608i) q^{78} +(-7.28376 - 12.6158i) q^{79} +(0.734550 + 2.49569i) q^{80} +(-8.86156 + 1.57248i) q^{81} +(11.0743 - 12.7846i) q^{82} +(-4.69138 + 2.70857i) q^{83} +(-2.86223 - 1.95132i) q^{84} +(2.31720 + 1.33784i) q^{85} +(-7.80330 + 2.70216i) q^{86} +(-3.20180 + 14.4610i) q^{87} +(-7.18064 - 0.338573i) q^{88} +5.64356 q^{89} +(1.61679 - 2.23607i) q^{90} +0.381311i q^{91} +(-3.06429 + 2.41138i) q^{92} +(3.75243 + 11.8899i) q^{93} +(4.28086 + 12.3623i) q^{94} +(-0.0896612 + 0.155298i) q^{95} +(9.72527 + 1.19130i) q^{96} +(1.96718 + 3.40725i) q^{97} +(-0.925940 + 1.06894i) q^{98} +(4.37674 + 6.24339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8	\( 72 q + 2 q^{6} - 36 q^{7} + 6 q^{8} - 8 q^{12} - 40 q^{17} - 21 q^{18} + 12 q^{20} + 12 q^{22} + 12 q^{23} - 12 q^{24} + 36 q^{25} - 14 q^{26} - 60 q^{30} - 15 q^{32} + 8 q^{33} + 6 q^{34} + 18 q^{36} - 3 q^{38} - 20 q^{39} + 21 q^{40} - 32 q^{41} - 13 q^{42} - 64 q^{44} + 12 q^{46} + 29 q^{48} - 36 q^{49} + 5 q^{50} - 9 q^{52} + 30 q^{54} - 3 q^{56} + 4 q^{57} + 9 q^{58} + 34 q^{60} - 12 q^{62} - 54 q^{64} + 40 q^{65} + 120 q^{66} + 55 q^{68} - 56 q^{71} + 15 q^{72} - 22 q^{74} + 12 q^{76} + 62 q^{78} + 94 q^{80} - 4 q^{81} + 12 q^{82} + 4 q^{84} - 3 q^{86} - 28 q^{87} - 12 q^{88} + 88 q^{89} - 83 q^{90} + 55 q^{92} - 18 q^{94} - 40 q^{95} - 83 q^{96}+O(q^{100}) \) 72 * q + 2 * q^6 - 36 * q^7 + 6 * q^8 - 8 * q^12 - 40 * q^17 - 21 * q^18 + 12 * q^20 + 12 * q^22 + 12 * q^23 - 12 * q^24 + 36 * q^25 - 14 * q^26 - 60 * q^30 - 15 * q^32 + 8 * q^33 + 6 * q^34 + 18 * q^36 - 3 * q^38 - 20 * q^39 + 21 * q^40 - 32 * q^41 - 13 * q^42 - 64 * q^44 + 12 * q^46 + 29 * q^48 - 36 * q^49 + 5 * q^50 - 9 * q^52 + 30 * q^54 - 3 * q^56 + 4 * q^57 + 9 * q^58 + 34 * q^60 - 12 * q^62 - 54 * q^64 + 40 * q^65 + 120 * q^66 + 55 * q^68 - 56 * q^71 + 15 * q^72 - 22 * q^74 + 12 * q^76 + 62 * q^78 + 94 * q^80 - 4 * q^81 + 12 * q^82 + 4 * q^84 - 3 * q^86 - 28 * q^87 - 12 * q^88 + 88 * q^89 - 83 * q^90 + 55 * q^92 - 18 * q^94 - 40 * q^95 - 83 * q^96

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