LMFDB - Embedded newform 945.2.u.a.584.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [945,2,Mod(89,945)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(945, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3, 5]))

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

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

chi := DirichletCharacter("945.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 945 = 3^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	945.u (of order $6$, degree $2$, not 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:	$7.54586299101$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			584.16
Character	$\chi$	$=$	945.584
Dual form			945.2.u.a.89.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.466107 + 0.807321i) q^{2} +(0.565488 + 0.979455i) q^{4} +(1.03266 + 1.98333i) q^{5} +(2.46700 + 0.955995i) q^{7} -2.91874 q^{8} +O(q^{10})$	\(q+(-0.466107 + 0.807321i) q^{2} +(0.565488 + 0.979455i) q^{4} +(1.03266 + 1.98333i) q^{5} +(2.46700 + 0.955995i) q^{7} -2.91874 q^{8} +(-2.08252 - 0.0907533i) q^{10} -1.22224i q^{11} +(-1.31924 + 2.28500i) q^{13} +(-1.92168 + 1.54606i) q^{14} +(0.229469 - 0.397451i) q^{16} +(6.76575 + 3.90621i) q^{17} +(2.02157 - 1.16715i) q^{19} +(-1.35862 + 2.13300i) q^{20} +(0.986737 + 0.569693i) q^{22} -6.98285 q^{23} +(-2.86721 + 4.09623i) q^{25} +(-1.22982 - 2.13011i) q^{26} +(0.458704 + 2.95692i) q^{28} +(5.69293 - 3.28681i) q^{29} +(-3.58046 + 2.06718i) q^{31} +(-2.70483 - 4.68490i) q^{32} +(-6.30712 + 3.64142i) q^{34} +(0.651524 + 5.88009i) q^{35} +(-0.395403 + 0.228286i) q^{37} +2.17607i q^{38} +(-3.01408 - 5.78883i) q^{40} +(2.67616 - 4.63525i) q^{41} +(6.97446 - 4.02671i) q^{43} +(1.19712 - 0.691160i) q^{44} +(3.25476 - 5.63740i) q^{46} +(-3.96077 - 2.28675i) q^{47} +(5.17215 + 4.71687i) q^{49} +(-1.97055 - 4.22404i) q^{50} -2.98407 q^{52} +(-1.18144 + 2.04632i) q^{53} +(2.42410 - 1.26216i) q^{55} +(-7.20052 - 2.79030i) q^{56} +6.12803i q^{58} +(-3.41014 - 5.90653i) q^{59} +(-0.253608 - 0.146420i) q^{61} -3.85410i q^{62} +5.96083 q^{64} +(-5.89424 - 0.256863i) q^{65} +(-12.7855 + 7.38170i) q^{67} +8.83566i q^{68} +(-5.05080 - 2.21476i) q^{70} +2.44979i q^{71} +(3.51808 - 6.09350i) q^{73} -0.425622i q^{74} +(2.28634 + 1.32002i) q^{76} +(1.16845 - 3.01525i) q^{77} +(-5.75444 + 9.96698i) q^{79} +(1.02524 + 0.0446786i) q^{80} +(2.49476 + 4.32105i) q^{82} +(-1.79536 + 1.03655i) q^{83} +(-0.760557 + 17.4525i) q^{85} +7.50751i q^{86} +3.56739i q^{88} +(0.840189 + 1.45525i) q^{89} +(-5.43902 + 4.37589i) q^{91} +(-3.94872 - 6.83939i) q^{92} +(3.69228 - 2.13174i) q^{94} +(4.40245 + 2.80416i) q^{95} +(-2.93872 - 5.09001i) q^{97} +(-6.21881 + 1.97701i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 38 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 38 * q^4 + 6 * q^5	$ 88 q - 38 q^{4} + 6 q^{5} - 6 q^{10} + 12 q^{14} - 26 q^{16} - 12 q^{19} - 6 q^{20} - 2 q^{25} - 12 q^{26} - 6 q^{29} - 6 q^{31} + 12 q^{34} + 6 q^{41} - 84 q^{44} - 18 q^{46} + 10 q^{49} - 30 q^{50} + 90 q^{56} + 6 q^{59} + 12 q^{61} - 8 q^{64} - 54 q^{65} - 30 q^{70} + 48 q^{76} + 8 q^{79} - 69 q^{80} - 7 q^{85} + 72 q^{89} + 20 q^{91} - 6 q^{94} + 93 q^{95}+O(q^{100}) $ 88 * q - 38 * q^4 + 6 * q^5 - 6 * q^10 + 12 * q^14 - 26 * q^16 - 12 * q^19 - 6 * q^20 - 2 * q^25 - 12 * q^26 - 6 * q^29 - 6 * q^31 + 12 * q^34 + 6 * q^41 - 84 * q^44 - 18 * q^46 + 10 * q^49 - 30 * q^50 + 90 * q^56 + 6 * q^59 + 12 * q^61 - 8 * q^64 - 54 * q^65 - 30 * q^70 + 48 * q^76 + 8 * q^79 - 69 * q^80 - 7 * q^85 + 72 * q^89 + 20 * q^91 - 6 * q^94 + 93 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/945\mathbb{Z}\right)^\times$.

$n$	$136$	$596$	$757$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.466107	+	0.807321i	−0.329587	+	0.570862i	−0.982430	−	0.186631i	$-0.940243\pi$
$2$	−0.466107	+	0.807321i	−0.329587	+	0.570862i	0.652843	+	0.757494i	$0.273576\pi$
$3$		0			0
$3$		0			0
$4$	0.565488	+	0.979455i	0.282744	+	0.489727i
$5$	1.03266	+	1.98333i	0.461821	+	0.886973i
$5$	1.03266	+	1.98333i	0.461821	+	0.886973i
$6$		0			0
$7$	2.46700	+	0.955995i	0.932437	+	0.361332i
$7$	2.46700	+	0.955995i	0.932437	+	0.361332i
$8$	−2.91874			−1.03193
$9$		0			0
$10$	−2.08252	−	0.0907533i	−0.658550	−	0.0286987i
$11$		−	1.22224i		−	0.368518i	−0.982878	−	0.184259i	$-0.941011\pi$
$11$		−	1.22224i		−	0.368518i	0.982878	−	0.184259i	$-0.0589885\pi$
$12$		0			0
$13$	−1.31924	+	2.28500i	−0.365892	+	0.633744i	−0.988919	−	0.148456i	$-0.952570\pi$
$13$	−1.31924	+	2.28500i	−0.365892	+	0.633744i	0.623026	+	0.782201i	$0.285903\pi$
$14$	−1.92168	+	1.54606i	−0.513590	+	0.413203i
$15$		0			0
$16$	0.229469	−	0.397451i	0.0573671	−	0.0993628i
$17$	6.76575	+	3.90621i	1.64093	+	0.947394i	0.980502	+	0.196509i	$0.0629604\pi$
$17$	6.76575	+	3.90621i	1.64093	+	0.947394i	0.660433	+	0.750885i	$0.270373\pi$
$18$		0			0
$19$	2.02157	−	1.16715i	0.463779	−	0.267763i	−0.249853	−	0.968284i	$-0.580382\pi$
$19$	2.02157	−	1.16715i	0.463779	−	0.267763i	0.713632	+	0.700521i	$0.247049\pi$
$20$	−1.35862	+	2.13300i	−0.303798	+	0.476953i
$21$		0			0
$22$	0.986737	+	0.569693i	0.210373	+	0.121459i
$23$	−6.98285			−1.45603			−0.728013	−	0.685564i	$-0.759556\pi$
$23$	−6.98285			−1.45603			−0.728013	+	0.685564i	$0.759556\pi$
$24$		0			0
$25$	−2.86721	+	4.09623i	−0.573442	+	0.819246i
$26$	−1.22982	−	2.13011i	−0.241187	−	0.417748i
$27$		0			0
$28$	0.458704	+	2.95692i	0.0866870	+	0.558805i
$29$	5.69293	−	3.28681i	1.05715	−	0.610346i	0.132508	−	0.991182i	$-0.457697\pi$
$29$	5.69293	−	3.28681i	1.05715	−	0.610346i	0.924643	+	0.380836i	$0.124364\pi$
$30$		0			0
$31$	−3.58046	+	2.06718i	−0.643069	+	0.371276i	−0.785796	−	0.618486i	$-0.787746\pi$
$31$	−3.58046	+	2.06718i	−0.643069	+	0.371276i	0.142727	+	0.989762i	$0.454413\pi$
$32$	−2.70483	−	4.68490i	−0.478150	−	0.828181i
$33$		0			0
$34$	−6.30712	+	3.64142i	−1.08166	+	0.624498i
$35$	0.651524	+	5.88009i	0.110128	+	0.993917i
$36$		0			0
$37$	−0.395403	+	0.228286i	−0.0650038	+	0.0375300i	−0.532150	−	0.846650i	$-0.678616\pi$
$37$	−0.395403	+	0.228286i	−0.0650038	+	0.0375300i	0.467146	+	0.884180i	$0.345282\pi$
$38$			2.17607i			0.353005i
$39$		0			0
$40$	−3.01408	−	5.78883i	−0.476568	−	0.915295i
$41$	2.67616	−	4.63525i	0.417947	−	0.723905i	−0.577786	−	0.816188i	$-0.696083\pi$
$41$	2.67616	−	4.63525i	0.417947	−	0.723905i	0.995733	+	0.0922834i	$0.0294166\pi$
$42$		0			0
$43$	6.97446	−	4.02671i	1.06360	−	0.614067i	0.137171	−	0.990547i	$-0.456199\pi$
$43$	6.97446	−	4.02671i	1.06360	−	0.614067i	0.926425	+	0.376480i	$0.122866\pi$
$44$	1.19712	−	0.691160i	0.180473	−	0.104196i
$45$		0			0
$46$	3.25476	−	5.63740i	0.479888	−	0.831190i
$47$	−3.96077	−	2.28675i	−0.577737	−	0.333557i	0.182496	−	0.983207i	$-0.441582\pi$
$47$	−3.96077	−	2.28675i	−0.577737	−	0.333557i	−0.760234	+	0.649650i	$0.774916\pi$
$48$		0			0
$49$	5.17215	+	4.71687i	0.738878	+	0.673839i
$50$	−1.97055	−	4.22404i	−0.278677	−	0.597370i
$51$		0			0
$52$	−2.98407			−0.413816
$53$	−1.18144	+	2.04632i	−0.162284	+	0.281084i	−0.935687	−	0.352830i	$-0.885219\pi$
$53$	−1.18144	+	2.04632i	−0.162284	+	0.281084i	0.773404	+	0.633914i	$0.218553\pi$
$54$		0			0
$55$	2.42410	−	1.26216i	0.326865	−	0.170189i
$56$	−7.20052	−	2.79030i	−0.962211	−	0.372870i
$57$		0			0
$58$			6.12803i			0.804649i
$59$	−3.41014	−	5.90653i	−0.443962	−	0.768965i	0.554017	−	0.832505i	$-0.313094\pi$
$59$	−3.41014	−	5.90653i	−0.443962	−	0.768965i	−0.997979	+	0.0635404i	$0.979761\pi$
$60$		0			0
$61$	−0.253608	−	0.146420i	−0.0324711	−	0.0187472i	0.483677	−	0.875247i	$-0.339301\pi$
$61$	−0.253608	−	0.146420i	−0.0324711	−	0.0187472i	−0.516148	+	0.856500i	$0.672634\pi$
$62$		−	3.85410i		−	0.489472i
$63$		0			0
$64$	5.96083			0.745104
$65$	−5.89424	−	0.256863i	−0.731091	−	0.0318600i
$66$		0			0
$67$	−12.7855	+	7.38170i	−1.56200	+	0.901819i	−0.564941	+	0.825132i	$0.691101\pi$
$67$	−12.7855	+	7.38170i	−1.56200	+	0.901819i	−0.997055	+	0.0766872i	$0.975566\pi$
$68$			8.83566i			1.07148i
$69$		0			0
$70$	−5.05080	−	2.21476i	−0.603687	−	0.264715i
$71$			2.44979i			0.290736i	0.989378	+	0.145368i	$0.0464366\pi$
$71$			2.44979i			0.290736i	−0.989378	+	0.145368i	$0.953563\pi$
$72$		0			0
$73$	3.51808	−	6.09350i	0.411761	−	0.713190i	−0.583322	−	0.812241i	$-0.698247\pi$
$73$	3.51808	−	6.09350i	0.411761	−	0.713190i	0.995082	+	0.0990508i	$0.0315806\pi$
$74$		−	0.425622i		−	0.0494776i
$75$		0			0
$76$	2.28634	+	1.32002i	0.262262	+	0.151417i
$77$	1.16845	−	3.01525i	0.133157	−	0.343620i
$78$		0			0
$79$	−5.75444	+	9.96698i	−0.647425	+	1.12137i	0.336311	+	0.941751i	$0.390821\pi$
$79$	−5.75444	+	9.96698i	−0.647425	+	1.12137i	−0.983736	+	0.179622i	$0.942513\pi$
$80$	1.02524	+	0.0446786i	0.114625	+	0.00499522i
$81$		0			0
$82$	2.49476	+	4.32105i	0.275500	+	0.477180i
$83$	−1.79536	+	1.03655i	−0.197066	+	0.113776i	−0.595286	−	0.803514i	$-0.702961\pi$
$83$	−1.79536	+	1.03655i	−0.197066	+	0.113776i	0.398220	+	0.917290i	$0.369628\pi$
$84$		0			0
$85$	−0.760557	+	17.4525i	−0.0824940	+	1.89299i
$86$			7.50751i			0.809555i
$87$		0			0
$88$			3.56739i			0.380285i
$89$	0.840189	+	1.45525i	0.0890599	+	0.154256i	0.907114	−	0.420885i	$-0.138280\pi$
$89$	0.840189	+	1.45525i	0.0890599	+	0.154256i	−0.818054	+	0.575141i	$0.804947\pi$
$90$		0			0
$91$	−5.43902	+	4.37589i	−0.570164	+	0.458718i
$92$	−3.94872	−	6.83939i	−0.411683	−	0.713056i
$93$		0			0
$94$	3.69228	−	2.13174i	0.380830	−	0.219872i
$95$	4.40245	+	2.80416i	0.451682	+	0.287701i
$96$		0			0
$97$	−2.93872	−	5.09001i	−0.298382	−	0.516812i	0.677384	−	0.735629i	$-0.263114\pi$
$97$	−2.93872	−	5.09001i	−0.298382	−	0.516812i	−0.975766	+	0.218817i	$0.929780\pi$
$98$	−6.21881	+	1.97701i	−0.628194	+	0.199709i
$99$		0			0
$100$	−5.63345	−	0.491930i	−0.563345	−	0.0491930i
$101$	−8.90434			−0.886015			−0.443008	−	0.896518i	$-0.646089\pi$
$101$	−8.90434			−0.886015			−0.443008	+	0.896518i	$0.646089\pi$
$102$		0			0
$103$	2.57886			0.254103			0.127051	−	0.991896i	$-0.459449\pi$
$103$	2.57886			0.254103			0.127051	+	0.991896i	$0.459449\pi$
$104$	3.85053	−	6.66932i	0.377576	−	0.653980i
$105$		0			0
$106$	−1.10136	−	1.90761i	−0.106973	−	0.185283i
$107$	3.63085	+	6.28881i	0.351007	+	0.607962i	0.986426	−	0.164205i	$-0.0525060\pi$
$107$	3.63085	+	6.28881i	0.351007	+	0.607962i	−0.635419	+	0.772167i	$0.719173\pi$
$108$		0			0
$109$	1.44439	−	2.50177i	0.138348	−	0.239626i	−0.788523	−	0.615005i	$-0.789154\pi$
$109$	1.44439	−	2.50177i	0.138348	−	0.239626i	0.926871	+	0.375379i	$0.122487\pi$
$110$	−0.110922	+	2.54533i	−0.0105760	+	0.242687i
$111$		0			0
$112$	0.946060	−	0.761140i	0.0893942	−	0.0719210i
$113$	0.369769	−	0.640458i	0.0347849	−	0.0602492i	−0.848109	−	0.529822i	$-0.822259\pi$
$113$	0.369769	−	0.640458i	0.0347849	−	0.0602492i	0.882894	+	0.469573i	$0.155592\pi$
$114$		0			0
$115$	−7.21094	−	13.8493i	−0.672424	−	1.29146i
$116$	6.43857	+	3.71731i	0.597806	+	0.345144i
$117$		0			0
$118$	6.35796			0.585297
$119$	12.9568	+	16.1046i	1.18774	+	1.47631i
$120$		0			0
$121$	9.50614			0.864195
$122$	0.236417	−	0.136495i	0.0214042	−	0.0123577i
$123$		0			0
$124$	−4.04941	−	2.33793i	−0.363648	−	0.209952i
$125$	−11.0850	−	1.45660i	−0.991477	−	0.130282i
$126$		0			0
$127$		−	20.9575i		−	1.85968i	−0.367964	−	0.929840i	$-0.619945\pi$
$127$		−	20.9575i		−	1.85968i	0.367964	−	0.929840i	$-0.380055\pi$
$128$	2.63127	−	4.55749i	0.232574	−	0.402829i
$129$		0			0
$130$	2.95472	−	4.63882i	0.259146	−	0.406852i
$131$	10.6395			0.929579			0.464789	−	0.885421i	$-0.346130\pi$
$131$	10.6395			0.929579			0.464789	+	0.885421i	$0.346130\pi$
$132$		0			0
$133$	6.10299	−	0.946752i	0.529196	−	0.0820938i
$134$		−	13.7627i		−	1.18891i
$135$		0			0
$136$	−19.7475	−	11.4012i	−1.69333	−	0.977645i
$137$	20.1675			1.72302			0.861512	−	0.507738i	$-0.169518\pi$
$137$	20.1675			1.72302			0.861512	+	0.507738i	$0.169518\pi$
$138$		0			0
$139$	2.84855	+	1.64461i	0.241610	+	0.139494i	0.615917	−	0.787811i	$-0.288786\pi$
$139$	2.84855	+	1.64461i	0.241610	+	0.139494i	−0.374306	+	0.927305i	$0.622119\pi$
$140$	−5.39086	+	3.96326i	−0.455611	+	0.334957i
$141$		0			0
$142$	−1.97776	−	1.14186i	−0.165970	−	0.0958230i
$143$	2.79281	+	1.61243i	0.233546	+	0.134838i
$144$		0			0
$145$	12.3977	+	7.89679i	1.02957	+	0.655793i
$146$	3.27961	+	5.68045i	0.271422	+	0.470117i
$147$		0			0
$148$	−0.447191	−	0.258186i	−0.0367589	−	0.0212228i
$149$			14.9815i			1.22733i	0.789565	+	0.613667i	$0.210306\pi$
$149$			14.9815i			1.22733i	−0.789565	+	0.613667i	$0.789694\pi$
$150$		0			0
$151$	−4.01090			−0.326403			−0.163201	−	0.986593i	$-0.552182\pi$
$151$	−4.01090			−0.326403			−0.163201	+	0.986593i	$0.552182\pi$
$152$	−5.90043	+	3.40661i	−0.478588	+	0.276313i
$153$		0			0
$154$	1.88965	+	2.34875i	0.152273	+	0.189267i
$155$	−7.79731	−	4.96653i	−0.626295	−	0.398921i
$156$		0			0
$157$	−8.82065	−	15.2778i	−0.703965	−	1.21930i	−0.967064	−	0.254534i	$-0.918078\pi$
$157$	−8.82065	−	15.2778i	−0.703965	−	1.21930i	0.263099	−	0.964769i	$-0.415255\pi$
$158$	−5.36437	−	9.29136i	−0.426766	−	0.739181i
$159$		0			0
$160$	6.49853	−	10.2025i	0.513754	−	0.806578i
$161$	−17.2267	−	6.67557i	−1.35765	−	0.526109i
$162$		0			0
$163$	−3.84106	+	2.21764i	−0.300855	+	0.173699i	−0.642827	−	0.766011i	$-0.722239\pi$
$163$	−3.84106	+	2.21764i	−0.300855	+	0.173699i	0.341972	+	0.939710i	$0.388905\pi$
$164$	6.05336			0.472688
$165$		0			0
$166$		−	1.93258i		−	0.149997i
$167$	−9.39299	−	5.42305i	−0.726852	−	0.419648i	0.0904177	−	0.995904i	$-0.471180\pi$
$167$	−9.39299	−	5.42305i	−0.726852	−	0.419648i	−0.817269	+	0.576256i	$0.804513\pi$
$168$		0			0
$169$	3.01919	+	5.22939i	0.232245	+	0.402261i
$170$	−13.7353	−	8.74876i	−1.05345	−	0.670999i
$171$		0			0
$172$	7.88795	+	4.55411i	0.601451	+	0.347248i
$173$	12.6196	+	7.28595i	0.959454	+	0.553941i	0.896005	−	0.444044i	$-0.146457\pi$
$173$	12.6196	+	7.28595i	0.959454	+	0.553941i	0.0634488	+	0.997985i	$0.479790\pi$
$174$		0			0
$175$	−10.9894	+	7.36435i	−0.830719	+	0.556693i
$176$	−0.485779	−	0.280465i	−0.0366170	−	0.0211408i
$177$		0			0
$178$	−1.56647			−0.117412
$179$	19.7353	+	11.3942i	1.47509	+	0.851643i	0.999606	−	0.0280824i	$-0.00894008\pi$
$179$	19.7353	+	11.3942i	1.47509	+	0.851643i	0.475483	+	0.879725i	$0.342273\pi$
$180$		0			0
$181$		−	15.1269i		−	1.12437i	−0.827010	−	0.562187i	$-0.809960\pi$
$181$		−	15.1269i		−	1.12437i	0.827010	−	0.562187i	$-0.190040\pi$
$182$	−0.997585	−	6.43067i	−0.0739459	−	0.476673i
$183$		0			0
$184$	20.3811			1.50252
$185$	−0.861085	−	0.548472i	−0.0633082	−	0.0403245i
$186$		0			0
$187$	4.77430	−	8.26934i	0.349132	−	0.604714i
$188$		−	5.17252i		−	0.377245i
$189$		0			0
$190$	−4.31587	+	2.24715i	−0.313106	+	0.163025i
$191$	4.29370	+	2.47897i	0.310682	+	0.179372i	0.647231	−	0.762294i	$-0.275927\pi$
$191$	4.29370	+	2.47897i	0.310682	+	0.179372i	−0.336550	+	0.941666i	$0.609260\pi$
$192$		0			0
$193$	20.9257	−	12.0815i	1.50627	−	0.869644i	0.506295	−	0.862360i	$-0.331015\pi$
$193$	20.9257	−	12.0815i	1.50627	−	0.869644i	0.999973	−	0.00728397i	$-0.00231858\pi$
$194$	5.47903			0.393371
$195$		0			0
$196$	−1.69518	+	7.73322i	−0.121084	+	0.552373i
$197$	3.15321			0.224657			0.112328	−	0.993671i	$-0.464169\pi$
$197$	3.15321			0.224657			0.112328	+	0.993671i	$0.464169\pi$
$198$		0			0
$199$	13.1981	+	7.61991i	0.935587	+	0.540161i	0.888574	−	0.458733i	$-0.151697\pi$
$199$	13.1981	+	7.61991i	0.935587	+	0.540161i	0.0470127	+	0.998894i	$0.485030\pi$
$200$	8.36864	−	11.9558i	0.591752	−	0.845405i
$201$		0			0
$202$	4.15038	−	7.18866i	0.292019	−	0.505792i
$203$	17.1866	−	2.66615i	1.20626	−	0.187127i
$204$		0			0
$205$	11.9568	+	0.521062i	0.835101	+	0.0363926i
$206$	−1.20203	+	2.08197i	−0.0837491	+	0.145058i
$207$		0			0
$208$	0.605450	+	1.04867i	0.0419804	+	0.0727122i
$209$	−1.42653	−	2.47083i	−0.0986755	−	0.170911i
$210$		0			0
$211$	6.36733	−	11.0285i	0.438345	−	0.759235i	−0.559217	−	0.829021i	$-0.688898\pi$
$211$	6.36733	−	11.0285i	0.438345	−	0.759235i	0.997562	+	0.0697858i	$0.0222316\pi$
$212$	−2.67237			−0.183539
$213$		0			0
$214$	−6.76945			−0.462750
$215$	15.1886	+	9.67443i	1.03585	+	0.659791i
$216$		0			0
$217$	−10.8092	+	1.67682i	−0.733775	+	0.113830i
$218$	1.34649	+	2.33218i	0.0911955	+	0.157955i
$219$		0			0
$220$	2.60703	+	1.66056i	0.175766	+	0.111955i
$221$	−17.8513	+	10.3065i	−1.20081	+	0.693289i
$222$		0			0
$223$	−10.5055	−	18.1961i	−0.703501	−	1.21850i	−0.967230	−	0.253902i	$-0.918286\pi$
$223$	−10.5055	−	18.1961i	−0.703501	−	1.21850i	0.263729	−	0.964597i	$-0.415048\pi$
$224$	−2.19406	−	14.1434i	−0.146597	−	0.944998i
$225$		0			0
$226$	0.344704	+	0.597044i	0.0229293	+	0.0397148i
$227$		−	11.0151i		−	0.731100i	−0.930792	−	0.365550i	$-0.880881\pi$
$227$		−	11.0151i		−	0.731100i	0.930792	−	0.365550i	$-0.119119\pi$
$228$		0			0
$229$		−	7.09863i		−	0.469091i	−0.972105	−	0.234545i	$-0.924640\pi$
$229$		−	7.09863i		−	0.469091i	0.972105	−	0.234545i	$-0.0753601\pi$
$230$	14.5419	+	0.633717i	0.958865	+	0.0417860i
$231$		0			0
$232$	−16.6162	+	9.59336i	−1.09091	+	0.629835i
$233$	−7.15918	−	12.4001i	−0.469013	−	0.812355i	0.530359	−	0.847773i	$-0.322057\pi$
$233$	−7.15918	−	12.4001i	−0.469013	−	0.812355i	−0.999373	+	0.0354182i	$0.988724\pi$
$234$		0			0
$235$	0.445241	−	10.2170i	0.0290443	−	0.666481i
$236$	3.85679	−	6.68015i	0.251055	−	0.434841i
$237$		0			0
$238$	−19.0408	+	2.95379i	−1.23423	+	0.191466i
$239$	5.40175	+	3.11870i	0.349410	+	0.201732i	0.664425	−	0.747355i	$-0.268676\pi$
$239$	5.40175	+	3.11870i	0.349410	+	0.201732i	−0.315015	+	0.949087i	$0.602010\pi$
$240$		0			0
$241$			19.0013i			1.22398i	0.790865	+	0.611991i	$0.209631\pi$
$241$			19.0013i			1.22398i	−0.790865	+	0.611991i	$0.790369\pi$
$242$	−4.43088	+	7.67451i	−0.284828	+	0.493336i
$243$		0			0
$244$		−	0.331196i		−	0.0212027i
$245$	−4.01403	+	15.1290i	−0.256447	+	0.966558i
$246$		0			0
$247$			6.15903i			0.391890i
$248$	10.4504	−	6.03355i	0.663602	−	0.383131i
$249$		0			0
$250$	6.34276	−	8.27026i	0.401151	−	0.523057i
$251$	12.5655			0.793127			0.396564	−	0.918007i	$-0.370203\pi$
$251$	12.5655			0.793127			0.396564	+	0.918007i	$0.370203\pi$
$252$		0			0
$253$			8.53469i			0.536571i
$254$	16.9195	+	9.76845i	1.06162	+	0.612927i
$255$		0			0
$256$	8.41374	+	14.5730i	0.525858	+	0.910814i
$257$			11.3181i			0.706002i	0.935623	+	0.353001i	$0.114839\pi$
$257$			11.3181i			0.706002i	−0.935623	+	0.353001i	$0.885161\pi$
$258$		0			0
$259$	−1.19370	+	0.185177i	−0.0741727	+	0.0115064i
$260$	−3.08154	−	5.91840i	−0.191109	−	0.367044i
$261$		0			0
$262$	−4.95915	+	8.58950i	−0.306377	+	0.530661i
$263$	−11.8680			−0.731811			−0.365905	−	0.930652i	$-0.619241\pi$
$263$	−11.8680			−0.731811			−0.365905	+	0.930652i	$0.619241\pi$
$264$		0			0
$265$	−5.27857	−	0.230033i	−0.324260	−	0.0141308i
$266$	−2.08031	+	5.36836i	−0.127552	+	0.329155i
$267$		0			0
$268$	−14.4601	−	8.34854i	−0.883291	−	0.509968i
$269$	11.6488	−	20.1764i	0.710243	−	1.23018i	−0.254523	−	0.967067i	$-0.581918\pi$
$269$	11.6488	−	20.1764i	0.710243	−	1.23018i	0.964766	−	0.263110i	$-0.0847482\pi$
$270$		0			0
$271$	11.9390	−	6.89299i	0.725243	−	0.418719i	−0.0914362	−	0.995811i	$-0.529146\pi$
$271$	11.9390	−	6.89299i	0.725243	−	0.418719i	0.816679	+	0.577092i	$0.195812\pi$
$272$	3.10505	−	1.79270i	0.188271	−	0.108699i
$273$		0			0
$274$	−9.40020	+	16.2816i	−0.567887	+	0.983609i
$275$	5.00656	+	3.50441i	0.301907	+	0.211324i
$276$		0			0
$277$			1.12137i			0.0673764i	0.999432	+	0.0336882i	$0.0107253\pi$
$277$			1.12137i			0.0673764i	−0.999432	+	0.0336882i	$0.989275\pi$
$278$	−2.65545	+	1.53313i	−0.159264	+	0.0919508i
$279$		0			0
$280$	−1.90163	−	17.1625i	−0.113644	−	1.02565i
$281$	−7.62415	+	4.40180i	−0.454818	+	0.262590i	−0.709863	−	0.704340i	$-0.751243\pi$
$281$	−7.62415	+	4.40180i	−0.454818	+	0.262590i	0.255045	+	0.966929i	$0.417910\pi$
$282$		0			0
$283$	−5.81878	−	10.0784i	−0.345890	−	0.599100i	0.639625	−	0.768687i	$-0.279090\pi$
$283$	−5.81878	−	10.0784i	−0.345890	−	0.599100i	−0.985515	+	0.169588i	$0.945756\pi$
$284$	−2.39946	+	1.38533i	−0.142381	+	0.0822040i
$285$		0			0
$286$	−2.60349	+	1.50313i	−0.153948	+	0.0888818i
$287$	11.0334	−	8.87675i	0.651279	−	0.523978i
$288$		0			0
$289$	22.0169	+	38.1344i	1.29511	+	2.24320i
$290$	−12.1539	+	6.32819i	−0.713702	+	0.371604i
$291$		0			0
$292$	7.95775			0.465692
$293$	16.4546	+	9.50008i	0.961289	+	0.555000i	0.896569	−	0.442903i	$-0.146051\pi$
$293$	16.4546	+	9.50008i	0.961289	+	0.555000i	0.0647194	+	0.997904i	$0.479385\pi$
$294$		0			0
$295$	8.19308	−	12.8629i	0.477020	−	0.748907i
$296$	1.15408	−	0.666307i	0.0670794	−	0.0387283i
$297$		0			0
$298$	−12.0949	−	6.98300i	−0.700639	−	0.404514i
$299$	9.21209	−	15.9558i	0.532749	−	0.922748i
$300$		0			0
$301$	21.0555	−	3.26632i	1.21362	−	0.188268i
$302$	1.86951	−	3.23809i	0.107578	−	0.186331i
$303$		0			0
$304$		−	1.07130i		−	0.0614432i
$305$	0.0285088	−	0.654191i	0.00163241	−	0.0374589i
$306$		0			0
$307$	12.8703			0.734544			0.367272	−	0.930114i	$-0.380292\pi$
$307$	12.8703			0.734544			0.367272	+	0.930114i	$0.380292\pi$
$308$	3.61405	−	0.560645i	0.205930	−	0.0319457i
$309$		0			0
$310$	7.64396	−	3.97999i	0.434148	−	0.226048i
$311$	−14.4633	−	25.0512i	−0.820141	−	1.42053i	−0.905577	−	0.424182i	$-0.860562\pi$
$311$	−14.4633	−	25.0512i	−0.820141	−	1.42053i	0.0854366	−	0.996344i	$-0.472771\pi$
$312$		0			0
$313$	−16.0805	+	27.8523i	−0.908925	+	1.57430i	−0.0933639	+	0.995632i	$0.529762\pi$
$313$	−16.0805	+	27.8523i	−0.908925	+	1.57430i	−0.815561	+	0.578672i	$0.803571\pi$
$314$	16.4455			0.928071
$315$		0			0
$316$	−13.0163			−0.732223
$317$	−0.880096	+	1.52437i	−0.0494311	+	0.0856172i	−0.889682	−	0.456580i	$-0.849074\pi$
$317$	−0.880096	+	1.52437i	−0.0494311	+	0.0856172i	0.840251	+	0.542197i	$0.182407\pi$
$318$		0			0
$319$	−4.01726	−	6.95810i	−0.224923	−	0.389579i
$320$	6.15554	+	11.8223i	0.344105	+	0.660887i
$321$		0			0
$322$	13.4188	−	10.7959i	0.747801	−	0.601633i
$323$	18.2365			1.01471
$324$		0			0
$325$	−5.57733	−	11.9555i	−0.309375	−	0.663172i
$326$		−	4.13463i		−	0.228996i
$327$		0			0
$328$	−7.81103	+	13.5291i	−0.431292	+	0.747019i
$329$	−7.58508	−	9.42788i	−0.418179	−	0.519776i
$330$		0			0
$331$	1.85966	−	3.22103i	0.102216	−	0.177044i	−0.810381	−	0.585903i	$-0.800740\pi$
$331$	1.85966	−	3.22103i	0.102216	−	0.177044i	0.912597	+	0.408859i	$0.134073\pi$
$332$	−2.03051	−	1.17232i	−0.111439	−	0.0643392i
$333$		0			0
$334$	8.75628	−	5.05544i	0.479122	−	0.276621i
$335$	−27.8435	−	17.7350i	−1.52125	−	0.968969i
$336$		0			0
$337$	23.7054	+	13.6863i	1.29132	+	0.745542i	0.978887	−	0.204400i	$-0.0655243\pi$
$337$	23.7054	+	13.6863i	1.29132	+	0.745542i	0.312428	+	0.949941i	$0.398858\pi$
$338$	−5.62906			−0.306181
$339$		0			0
$340$	−17.5240	+	9.12427i	−0.950375	+	0.494833i
$341$	2.52658	+	4.37616i	0.136822	+	0.236982i
$342$		0			0
$343$	8.25036	+	16.5811i	0.445478	+	0.895293i
$344$	−20.3566	+	11.7529i	−1.09756	+	0.633675i
$345$		0			0
$346$	−11.7642	+	6.79207i	−0.632448	+	0.365144i
$347$	3.61918	+	6.26861i	0.194288	+	0.336516i	0.946667	−	0.322214i	$-0.104427\pi$
$347$	3.61918	+	6.26861i	0.194288	+	0.336516i	−0.752379	+	0.658730i	$0.771094\pi$
$348$		0			0
$349$	23.6947	−	13.6801i	1.26835	−	0.732281i	0.293672	−	0.955906i	$-0.405123\pi$
$349$	23.6947	−	13.6801i	1.26835	−	0.732281i	0.974675	+	0.223625i	$0.0717893\pi$
$350$	−0.823172	−	12.3045i	−0.0440004	−	0.657705i
$351$		0			0
$352$	−5.72605	+	3.30594i	−0.305199	+	0.176207i
$353$		−	11.6326i		−	0.619139i	−0.950877	−	0.309569i	$-0.899815\pi$
$353$		−	11.6326i		−	0.619139i	0.950877	−	0.309569i	$-0.100185\pi$
$354$		0			0
$355$	−4.85874	+	2.52981i	−0.257875	+	0.134268i
$356$	−0.950235	+	1.64586i	−0.0503624	+	0.0872302i
$357$		0			0
$358$	−18.3976	+	10.6218i	−0.972341	+	0.561381i
$359$	−18.0869	+	10.4425i	−0.954588	+	0.551131i	−0.894503	−	0.447062i	$-0.852470\pi$
$359$	−18.0869	+	10.4425i	−0.954588	+	0.551131i	−0.0600846	+	0.998193i	$0.519137\pi$
$360$		0			0
$361$	−6.77551	+	11.7355i	−0.356606	+	0.617660i
$362$	12.2123	+	7.05075i	0.641862	+	0.370579i
$363$		0			0
$364$	−7.36169	−	2.85276i	−0.385857	−	0.149525i
$365$	15.7184	+	0.684988i	0.822740	+	0.0358539i
$366$		0			0
$367$	21.8050			1.13821			0.569105	−	0.822265i	$-0.307290\pi$
$367$	21.8050			1.13821			0.569105	+	0.822265i	$0.307290\pi$
$368$	−1.60235	+	2.77534i	−0.0835280	+	0.144675i
$369$		0			0
$370$	0.844151	−	0.439525i	0.0438853	−	0.0228498i
$371$	−4.87089	+	3.91881i	−0.252884	+	0.203455i
$372$		0			0
$373$		−	3.08620i		−	0.159797i	−0.996803	−	0.0798987i	$-0.974540\pi$
$373$		−	3.08620i		−	0.159797i	0.996803	−	0.0798987i	$-0.0254597\pi$
$374$	4.45067	+	7.70879i	0.230139	+	0.398612i
$375$		0			0
$376$	11.5604	+	6.67443i	0.596185	+	0.344207i
$377$			17.3444i			0.893284i
$378$		0			0
$379$	10.7760			0.553524			0.276762	−	0.960939i	$-0.410739\pi$
$379$	10.7760			0.553524			0.276762	+	0.960939i	$0.410739\pi$
$380$	−0.257015	+	5.89772i	−0.0131846	+	0.302547i
$381$		0			0
$382$	−4.00265	+	2.31093i	−0.204793	+	0.118238i
$383$		−	13.0249i		−	0.665541i	−0.943008	−	0.332770i	$-0.892017\pi$
$383$		−	13.0249i		−	0.665541i	0.943008	−	0.332770i	$-0.107983\pi$
$384$		0			0
$385$	7.18686	−	0.796316i	0.366276	−	0.0405840i
$386$			22.5251i			1.14650i
$387$		0			0
$388$	3.32362	−	5.75669i	0.168731	−	0.292251i
$389$		−	7.97528i		−	0.404363i	−0.979348	−	0.202181i	$-0.935197\pi$
$389$		−	7.97528i		−	0.404363i	0.979348	−	0.202181i	$-0.0648030\pi$
$390$		0			0
$391$	−47.2442	−	27.2765i	−2.38924	−	1.37943i
$392$	−15.0962	−	13.7673i	−0.762471	−	0.695355i
$393$		0			0
$394$	−1.46973	+	2.54565i	−0.0740440	+	0.128248i
$395$	−25.7102	−	1.12042i	−1.29362	−	0.0563743i
$396$		0			0
$397$	7.08543	+	12.2723i	0.355607	+	0.615930i	0.987222	−	0.159353i	$-0.0509407\pi$
$397$	7.08543	+	12.2723i	0.355607	+	0.615930i	−0.631614	+	0.775283i	$0.717607\pi$
$398$	−12.3034	+	7.10339i	−0.616715	+	0.356061i
$399$		0			0
$400$	0.970118	+	2.07953i	0.0485059	+	0.103977i
$401$			9.28015i			0.463429i	0.972784	+	0.231714i	$0.0744335\pi$
$401$			9.28015i			0.463429i	−0.972784	+	0.231714i	$0.925567\pi$
$402$		0			0
$403$		−	10.9084i		−	0.543388i
$404$	−5.03530	−	8.72140i	−0.250516	−	0.433906i
$405$		0			0
$406$	−5.85836	+	15.1178i	−0.290746	+	0.750285i
$407$	0.279019	+	0.483275i	0.0138305	+	0.0239551i
$408$		0			0
$409$	−19.5041	+	11.2607i	−0.964417	+	0.556806i	−0.897530	−	0.440954i	$-0.854640\pi$
$409$	−19.5041	+	11.2607i	−0.964417	+	0.556806i	−0.0668871	+	0.997761i	$0.521307\pi$
$410$	−5.99382	+	9.41012i	−0.296014	+	0.464733i
$411$		0			0
$412$	1.45832	+	2.52588i	0.0718461	+	0.124441i
$413$	−2.76618	−	17.8315i	−0.136115	−	0.877429i
$414$		0			0
$415$	−3.90983	−	2.49039i	−0.191926	−	0.122248i
$416$	14.2733			0.699806
$417$		0			0
$418$	2.65967			0.130089
$419$	−3.40062	+	5.89004i	−0.166131	+	0.287747i	−0.937056	−	0.349178i	$-0.886461\pi$
$419$	−3.40062	+	5.89004i	−0.166131	+	0.287747i	0.770925	+	0.636926i	$0.219794\pi$
$420$		0			0
$421$	−16.6544	−	28.8462i	−0.811685	−	1.40588i	−0.911684	−	0.410893i	$-0.865217\pi$
$421$	−16.6544	−	28.8462i	−0.811685	−	1.40588i	0.0999985	−	0.994988i	$-0.468116\pi$
$422$	5.93571	+	10.2810i	0.288946	+	0.500469i
$423$		0			0
$424$	3.44833	−	5.97268i	0.167466	−	0.290059i
$425$	−35.3995	+	16.5142i	−1.71713	+	0.801054i
$426$		0			0
$427$	−0.485672	−	0.603666i	−0.0235033	−	0.0292135i
$428$	−4.10640	+	7.11250i	−0.198490	+	0.343796i
$429$		0			0
$430$	−14.8899	+	7.75273i	−0.718053	+	0.373870i
$431$	−23.9228	−	13.8118i	−1.15232	−	0.665292i	−0.202868	−	0.979206i	$-0.565026\pi$
$431$	−23.9228	−	13.8118i	−1.15232	−	0.665292i	−0.949451	+	0.313914i	$0.898360\pi$
$432$		0			0
$433$	−6.73121			−0.323481			−0.161741	−	0.986833i	$-0.551711\pi$
$433$	−6.73121			−0.323481			−0.161741	+	0.986833i	$0.551711\pi$
$434$	3.68450	−	9.50806i	0.176862	−	0.456401i
$435$		0			0
$436$	3.26715			0.156468
$437$	−14.1163	+	8.15005i	−0.675274	+	0.389870i
$438$		0			0
$439$	−14.7061	−	8.49057i	−0.701884	−	0.405233i	0.106165	−	0.994349i	$-0.466143\pi$
$439$	−14.7061	−	8.49057i	−0.701884	−	0.405233i	−0.808049	+	0.589116i	$0.799476\pi$
$440$	−7.07532	+	3.68392i	−0.337302	+	0.175624i
$441$		0			0
$442$		−	19.2157i		−	0.913997i
$443$	−11.9714	+	20.7352i	−0.568781	+	0.985157i	0.427906	+	0.903823i	$0.359251\pi$
$443$	−11.9714	+	20.7352i	−0.568781	+	0.985157i	−0.996687	+	0.0813338i	$0.974082\pi$
$444$		0			0
$445$	−2.01861	+	3.16916i	−0.0956914	+	0.150233i
$446$	19.5868			0.927460
$447$		0			0
$448$	14.7053	+	5.69852i	0.694762	+	0.269230i
$449$			0.967708i			0.0456690i	0.999739	+	0.0228345i	$0.00726907\pi$
$449$			0.967708i			0.0456690i	−0.999739	+	0.0228345i	$0.992731\pi$
$450$		0			0
$451$	−5.66537	−	3.27090i	−0.266772	−	0.154021i
$452$	0.836400			0.0393409
$453$		0			0
$454$	8.89274	+	5.13423i	0.417357	+	0.240961i
$455$	−14.2955	−	6.26855i	−0.670184	−	0.293874i
$456$		0			0
$457$	16.9046	+	9.75990i	0.790766	+	0.456549i	0.840232	−	0.542227i	$-0.182419\pi$
$457$	16.9046	+	9.75990i	0.790766	+	0.456549i	−0.0494662	+	0.998776i	$0.515752\pi$
$458$	5.73087	+	3.30872i	0.267786	+	0.154606i
$459$		0			0
$460$	9.48707	−	14.8944i	0.442337	−	0.694456i
$461$	−1.38530	−	2.39941i	−0.0645199	−	0.111752i	0.831961	−	0.554834i	$-0.187218\pi$
$461$	−1.38530	−	2.39941i	−0.0645199	−	0.111752i	−0.896481	+	0.443082i	$0.853885\pi$
$462$		0			0
$463$	−17.0428	−	9.83967i	−0.792046	−	0.457288i	0.0486362	−	0.998817i	$-0.484513\pi$
$463$	−17.0428	−	9.83967i	−0.792046	−	0.457288i	−0.840682	+	0.541528i	$0.817846\pi$
$464$		−	3.01688i		−	0.140055i
$465$		0			0
$466$	13.3478			0.618323
$467$	−13.4844	+	7.78521i	−0.623983	+	0.360257i	−0.778418	−	0.627746i	$-0.783978\pi$
$467$	−13.4844	+	7.78521i	−0.623983	+	0.360257i	0.154435	+	0.988003i	$0.450644\pi$
$468$		0			0
$469$	−38.5986	+	5.98778i	−1.78232	+	0.276490i
$470$	8.04083	+	5.12165i	0.370896	+	0.236244i
$471$		0			0
$472$	9.95331	+	17.2396i	0.458138	+	0.793518i
$473$	−4.92158	−	8.52444i	−0.226295	−	0.391954i
$474$		0			0
$475$	−1.01533	+	11.6273i	−0.0465865	+	0.533496i
$476$	−8.44685	+	21.7975i	−0.387161	+	0.999089i
$477$		0			0
$478$	−5.03559	+	2.90730i	−0.230322	+	0.132977i
$479$	−9.34514			−0.426990			−0.213495	−	0.976944i	$-0.568485\pi$
$479$	−9.34514			−0.426990			−0.213495	+	0.976944i	$0.568485\pi$
$480$		0			0
$481$		−	1.20466i		−	0.0549277i
$482$	−15.3402	−	8.85664i	−0.698725	−	0.403409i
$483$		0			0
$484$	5.37561	+	9.31083i	0.244346	+	0.423220i
$485$	7.06047	−	11.0847i	0.320599	−	0.503332i
$486$		0			0
$487$	−7.99734	−	4.61727i	−0.362394	−	0.209228i	0.307736	−	0.951472i	$-0.400429\pi$
$487$	−7.99734	−	4.61727i	−0.362394	−	0.209228i	−0.670130	+	0.742243i	$0.733762\pi$
$488$	0.740215	+	0.427363i	0.0335080	+	0.0193458i
$489$		0			0
$490$	−10.3430	−	10.2924i	−0.467250	−	0.464961i
$491$	−2.31216	−	1.33493i	−0.104347	−	0.0602445i	0.446919	−	0.894575i	$-0.352521\pi$
$491$	−2.31216	−	1.33493i	−0.104347	−	0.0602445i	−0.551265	+	0.834330i	$0.685855\pi$
$492$		0			0
$493$	51.3559			2.31295
$494$	−4.97232	−	2.87077i	−0.223715	−	0.129162i
$495$		0			0
$496$			1.89741i			0.0851962i
$497$	−2.34198	+	6.04362i	−0.105052	+	0.271093i
$498$		0			0
$499$	−11.8540			−0.530660			−0.265330	−	0.964158i	$-0.585481\pi$
$499$	−11.8540			−0.530660			−0.265330	+	0.964158i	$0.585481\pi$
$500$	−4.84180	−	11.6810i	−0.216532	−	0.522390i
$501$		0			0
$502$	−5.85687	+	10.1444i	−0.261405	+	0.452766i
$503$			7.62907i			0.340164i	0.985430	+	0.170082i	$0.0544032\pi$
$503$			7.62907i			0.340164i	−0.985430	+	0.170082i	$0.945597\pi$
$504$		0			0
$505$	−9.19519	−	17.6603i	−0.409181	−	0.785871i
$506$	−6.89024	−	3.97808i	−0.306308	−	0.176847i
$507$		0			0
$508$	20.5270	−	11.8512i	0.910736	−	0.525814i
$509$	5.09548			0.225853			0.112927	−	0.993603i	$-0.463977\pi$
$509$	5.09548			0.225853			0.112927	+	0.993603i	$0.463977\pi$
$510$		0			0
$511$	14.5045	−	11.6694i	0.641640	−	0.516223i
$512$	−5.16173			−0.228118
$513$		0			0
$514$	−9.13732	−	5.27543i	−0.403030	−	0.232689i
$515$	2.66310	+	5.11474i	0.117350	+	0.225382i
$516$		0			0
$517$	−2.79495	+	4.84099i	−0.122922	+	0.212906i
$518$	0.406893	−	1.05001i	0.0178779	−	0.0461348i
$519$		0			0
$520$	17.2038	+	0.749717i	0.754435	+	0.0328773i
$521$	−2.29742	+	3.97925i	−0.100652	+	0.174334i	−0.911953	−	0.410294i	$-0.865426\pi$
$521$	−2.29742	+	3.97925i	−0.100652	+	0.174334i	0.811302	+	0.584628i	$0.198759\pi$
$522$		0			0
$523$	−9.14719	−	15.8434i	−0.399979	−	0.692784i	0.593744	−	0.804654i	$-0.297649\pi$
$523$	−9.14719	−	15.8434i	−0.399979	−	0.692784i	−0.993723	+	0.111870i	$0.964316\pi$
$524$	6.01652	+	10.4209i	0.262833	+	0.455240i
$525$		0			0
$526$	5.53175	−	9.58127i	0.241196	−	0.417763i
$527$	−32.2993			−1.40698
$528$		0			0
$529$	25.7602			1.12001
$530$	2.64609	−	4.15428i	0.114939	−	0.180450i
$531$		0			0
$532$	4.37847	+	5.44222i	0.189831	+	0.235950i
$533$	7.06103	+	12.2301i	0.305847	+	0.529743i
$534$		0			0
$535$	−8.72335	+	13.6954i	−0.377143	+	0.592104i
$536$	37.3175	−	21.5453i	1.61187	−	0.930614i
$537$		0			0
$538$	10.8592	+	18.8087i	0.468174	+	0.810902i
$539$	5.76513	−	6.32158i	0.248322	−	0.272290i
$540$		0			0
$541$	−4.72439	−	8.18288i	−0.203117	−	0.351809i	0.746414	−	0.665482i	$-0.231774\pi$
$541$	−4.72439	−	8.18288i	−0.203117	−	0.351809i	−0.949531	+	0.313672i	$0.898441\pi$
$542$			12.8515i			0.552019i
$543$		0			0
$544$		−	42.2624i		−	1.81199i
$545$	6.45340	+	0.281231i	0.276433	+	0.0120466i
$546$		0			0
$547$	−25.4387	+	14.6870i	−1.08768	+	0.627972i	−0.932958	−	0.359986i	$-0.882781\pi$
$547$	−25.4387	+	14.6870i	−1.08768	+	0.627972i	−0.154722	+	0.987958i	$0.549448\pi$
$548$	11.4045	+	19.7531i	0.487175	+	0.843812i
$549$		0			0
$550$	−5.16277	+	2.40847i	−0.220141	+	0.102698i
$551$	7.67242	−	13.2890i	0.326856	−	0.566131i
$552$		0			0
$553$	−23.7246	+	19.0873i	−1.00887	+	0.811674i
$554$	−0.905303	−	0.522677i	−0.0384627	−	0.0222064i
$555$		0			0
$556$			3.72003i			0.157764i
$557$	−15.8036	+	27.3726i	−0.669620	+	1.15982i	0.308391	+	0.951260i	$0.400210\pi$
$557$	−15.8036	+	27.3726i	−0.669620	+	1.15982i	−0.978011	+	0.208556i	$0.933124\pi$
$558$		0			0
$559$			21.2488i			0.898730i
$560$	2.48656	+	1.09035i	0.105076	+	0.0460756i
$561$		0			0
$562$		−	8.20684i		−	0.346185i
$563$	28.4061	−	16.4003i	1.19717	−	0.691189i	0.237250	−	0.971449i	$-0.423754\pi$
$563$	28.4061	−	16.4003i	1.19717	−	0.691189i	0.959924	+	0.280260i	$0.0904208\pi$
$564$		0			0
$565$	1.65209	+	0.0719957i	0.0695039	+	0.00302888i
$566$	10.8487			0.456005
$567$		0			0
$568$		−	7.15029i		−	0.300020i
$569$	−11.4939	−	6.63602i	−0.481850	−	0.278197i	0.239337	−	0.970937i	$-0.423070\pi$
$569$	−11.4939	−	6.63602i	−0.481850	−	0.278197i	−0.721187	+	0.692740i	$0.756403\pi$
$570$		0			0
$571$	−3.07377	−	5.32392i	−0.128633	−	0.222799i	0.794514	−	0.607246i	$-0.207726\pi$
$571$	−3.07377	−	5.32392i	−0.128633	−	0.222799i	−0.923147	+	0.384446i	$0.874392\pi$
$572$			3.64724i			0.152499i
$573$		0			0
$574$	2.02366	+	13.0450i	0.0844659	+	0.544487i
$575$	20.0213	−	28.6034i	0.834946	−	1.19284i
$576$		0			0
$577$	−12.0072	+	20.7971i	−0.499866	+	0.865793i	−1.00000		0.000155138i	$-0.999951\pi$
$577$	−12.0072	+	20.7971i	−0.499866	+	0.865793i	0.500134	+	0.865948i	$0.333284\pi$
$578$	−41.0489			−1.70741
$579$		0			0
$580$	−0.723778	+	16.6086i	−0.0300533	+	0.689633i
$581$	−5.42009	+	0.840814i	−0.224863	+	0.0348829i
$582$		0			0
$583$	2.50109	+	1.44400i	0.103584	+	0.0598045i
$584$	−10.2684	+	17.7853i	−0.424908	+	0.735963i
$585$		0			0
$586$	−15.3392	+	8.85610i	−0.633657	+	0.365842i
$587$	36.2012	−	20.9007i	1.49418	−	0.862666i	0.494204	−	0.869346i	$-0.335460\pi$
$587$	36.2012	−	20.9007i	1.49418	−	0.862666i	0.999978	+	0.00668002i	$0.00212633\pi$
$588$		0			0
$589$	−4.82542	+	8.35787i	−0.198828	+	0.344380i
$590$	6.56563	+	12.6099i	0.270303	+	0.519143i
$591$		0			0
$592$			0.209538i			0.00861194i
$593$	−5.44034	+	3.14098i	−0.223408	+	0.128985i	−0.607527	−	0.794299i	$-0.707838\pi$
$593$	−5.44034	+	3.14098i	−0.223408	+	0.128985i	0.384119	+	0.923283i	$0.374505\pi$
$594$		0			0
$595$	−18.5608	+	42.3282i	−0.760919	+	1.73529i
$596$	−14.6737	+	8.47188i	−0.601060	+	0.347022i
$597$		0			0
$598$	8.58764	+	14.8742i	0.351175	+	0.608252i
$599$	−1.04632	+	0.604096i	−0.0427517	+	0.0246827i	−0.521223	−	0.853420i	$-0.674524\pi$
$599$	−1.04632	+	0.604096i	−0.0427517	+	0.0246827i	0.478472	+	0.878103i	$0.341191\pi$
$600$		0			0
$601$	−5.25953	+	3.03659i	−0.214541	+	0.123865i	−0.603420	−	0.797424i	$-0.706196\pi$
$601$	−5.25953	+	3.03659i	−0.214541	+	0.123865i	0.388879	+	0.921289i	$0.372862\pi$
$602$	−7.17714	+	18.5210i	−0.292518	+	0.754859i
$603$		0			0
$604$	−2.26812	−	3.92850i	−0.0922885	−	0.159848i
$605$	9.81665	+	18.8538i	0.399104	+	0.766517i
$606$		0			0
$607$	−13.8765			−0.563230			−0.281615	−	0.959527i	$-0.590870\pi$
$607$	−13.8765			−0.563230			−0.281615	+	0.959527i	$0.590870\pi$
$608$	−10.9360	−	6.31389i	−0.443512	−	0.256062i
$609$		0			0
$610$	0.514854	+	0.327939i	0.0208458	+	0.0132779i
$611$	10.4504	−	6.03356i	0.422779	−	0.244092i
$612$		0			0
$613$	−5.50993	−	3.18116i	−0.222544	−	0.128486i	0.384584	−	0.923090i	$-0.374345\pi$
$613$	−5.50993	−	3.18116i	−0.222544	−	0.128486i	−0.607128	+	0.794604i	$0.707678\pi$
$614$	−5.99892	+	10.3904i	−0.242097	+	0.419324i
$615$		0			0
$616$	−3.41041	+	8.80074i	−0.137409	+	0.354592i
$617$	−16.6269	+	28.7986i	−0.669374	+	1.15939i	0.308706	+	0.951158i	$0.400104\pi$
$617$	−16.6269	+	28.7986i	−0.669374	+	1.15939i	−0.978080	+	0.208232i	$0.933229\pi$
$618$		0			0
$619$			2.35605i			0.0946976i	0.998878	+	0.0473488i	$0.0150772\pi$
$619$			2.35605i			0.0946976i	−0.998878	+	0.0473488i	$0.984923\pi$
$620$	0.455206	−	10.4456i	0.0182815	−	0.419506i
$621$		0			0
$622$	26.9659			1.08123
$623$	0.681532	+	4.39332i	0.0273050	+	0.176014i
$624$		0			0
$625$	−8.55822	−	23.4895i	−0.342329	−	0.939580i
$626$	−14.9905	−	25.9643i	−0.599140	−	1.03774i
$627$		0			0
$628$	9.97595	−	17.2789i	0.398084	−	0.689501i
$629$	−3.56693			−0.142223
$630$		0			0
$631$	31.0399			1.23568			0.617839	−	0.786304i	$-0.288008\pi$
$631$	31.0399			1.23568			0.617839	+	0.786304i	$0.288008\pi$
$632$	16.7957	−	29.0910i	0.668098	−	1.15718i
$633$		0			0
$634$	−0.820438	−	1.42104i	−0.0325838	−	0.0564367i
$635$	41.5657	−	21.6421i	1.64949	−	0.858840i
$636$		0			0
$637$	−17.6014	+	5.59564i	−0.697392	+	0.221707i
$638$	7.48989			0.296528
$639$		0			0
$640$	11.7562	+	0.512321i	0.464706	+	0.0202513i
$641$		−	10.0094i		−	0.395349i	−0.980268	−	0.197675i	$-0.936661\pi$
$641$		−	10.0094i		−	0.395349i	0.980268	−	0.197675i	$-0.0633390\pi$
$642$		0			0
$643$	3.49908	−	6.06058i	0.137990	−	0.239006i	−0.788746	−	0.614720i	$-0.789269\pi$
$643$	3.49908	−	6.06058i	0.137990	−	0.239006i	0.926736	+	0.375714i	$0.122602\pi$
$644$	−3.20306	−	20.6477i	−0.126218	−	0.813634i
$645$		0			0
$646$	−8.50018	+	14.7227i	−0.334435	+	0.579259i
$647$	5.28314	+	3.05022i	0.207702	+	0.119917i	0.600243	−	0.799818i	$-0.295071\pi$
$647$	5.28314	+	3.05022i	0.207702	+	0.119917i	−0.392541	+	0.919734i	$0.628404\pi$
$648$		0			0
$649$	−7.21917	+	4.16799i	−0.283377	+	0.163608i
$650$	12.2516	+	1.06984i	0.480546	+	0.0419627i
$651$		0			0
$652$	−4.34416	−	2.50810i	−0.170130	−	0.0982248i
$653$	0.967764			0.0378715			0.0189358	−	0.999821i	$-0.493972\pi$
$653$	0.967764			0.0378715			0.0189358	+	0.999821i	$0.493972\pi$
$654$		0			0
$655$	10.9870	+	21.1017i	0.429299	+	0.824511i
$656$	−1.22819	−	2.12729i	−0.0479528	−	0.0830567i
$657$		0			0
$658$	11.1468	−	1.72919i	0.434547	−	0.0674109i
$659$	6.50034	−	3.75297i	0.253217	−	0.146195i	−0.368019	−	0.929818i	$-0.619964\pi$
$659$	6.50034	−	3.75297i	0.253217	−	0.146195i	0.621237	+	0.783623i	$0.286631\pi$
$660$		0			0
$661$	15.3382	−	8.85552i	0.596587	−	0.344440i	−0.171111	−	0.985252i	$-0.554736\pi$
$661$	15.3382	−	8.85552i	0.596587	−	0.344440i	0.767698	+	0.640812i	$0.221402\pi$
$662$	1.73360	+	3.00269i	0.0673784	+	0.116703i
$663$		0			0
$664$	5.24019	−	3.02543i	0.203359	−	0.117409i
$665$	8.18006	+	11.1266i	0.317209	+	0.431470i
$666$		0			0
$667$	−39.7529	+	22.9513i	−1.53924	+	0.888679i
$668$		−	12.2667i		−	0.474612i
$669$		0			0
$670$	27.2959	−	14.2122i	1.05453	−	0.549065i
$671$	−0.178960	+	0.309968i	−0.00690868	+	0.0119662i
$672$		0			0
$673$	−42.8848	+	24.7595i	−1.65309	+	0.954410i	−0.677295	+	0.735712i	$0.736848\pi$
$673$	−42.8848	+	24.7595i	−1.65309	+	0.954410i	−0.975792	+	0.218699i	$0.929819\pi$
$674$	−22.0985	+	12.7586i	−0.851203	+	0.491442i
$675$		0			0
$676$	−3.41463	+	5.91432i	−0.131332	+	0.227474i
$677$	−16.0817	−	9.28479i	−0.618071	−	0.356844i	0.158046	−	0.987432i	$-0.449480\pi$
$677$	−16.0817	−	9.28479i	−0.618071	−	0.356844i	−0.776118	+	0.630588i	$0.782814\pi$
$678$		0			0
$679$	−2.38379	−	15.3664i	−0.0914813	−	0.589710i
$680$	2.21987	−	50.9394i	0.0851281	−	1.95344i
$681$		0			0
$682$	−4.71062			−0.180379
$683$	11.3039	−	19.5790i	0.432532	−	0.749168i	−0.564558	−	0.825393i	$-0.690953\pi$
$683$	11.3039	−	19.5790i	0.432532	−	0.749168i	0.997091	+	0.0762251i	$0.0242867\pi$
$684$		0			0
$685$	20.8262	+	39.9988i	0.795729	+	1.52827i
$686$	−17.2318	−	1.06786i	−0.657913	−	0.0407710i
$687$		0			0
$688$		−	3.69601i		−	0.140909i
$689$	−3.11723	−	5.39920i	−0.118757	−	0.205693i
$690$		0			0
$691$	30.7721	+	17.7663i	1.17063	+	0.675861i	0.953828	−	0.300355i	$-0.0971051\pi$
$691$	30.7721	+	17.7663i	1.17063	+	0.675861i	0.216799	+	0.976216i	$0.430438\pi$
$692$			16.4805i			0.626494i
$693$		0			0
$694$	−6.74770			−0.256139
$695$	−0.320213	+	7.34794i	−0.0121464	+	0.278723i
$696$		0			0
$697$	36.2125	−	20.9073i	1.37165	−	0.791920i
$698$			25.5056i			0.965402i
$699$		0			0
$700$	−13.4274	−	6.59914i	−0.507509	−	0.249424i
$701$		−	40.9221i		−	1.54561i	−0.634645	−	0.772804i	$-0.718854\pi$
$701$		−	40.9221i		−	1.54561i	0.634645	−	0.772804i	$-0.281146\pi$
$702$		0			0
$703$	−0.532888	+	0.922990i	−0.0200983	+	0.0348112i
$704$		−	7.28554i		−	0.274584i
$705$		0			0
$706$	9.39121	+	5.42202i	0.353443	+	0.204060i
$707$	−21.9670	−	8.51251i	−0.826153	−	0.320146i
$708$		0			0
$709$	−1.56103	+	2.70378i	−0.0586257	+	0.101543i	−0.893849	−	0.448369i	$-0.852005\pi$
$709$	−1.56103	+	2.70378i	−0.0586257	+	0.101543i	0.835223	+	0.549911i	$0.185339\pi$
$710$	0.222326	−	5.10172i	0.00834375	−	0.191464i
$711$		0			0
$712$	−2.45230	−	4.24750i	−0.0919036	−	0.159182i
$713$	25.0018	−	14.4348i	0.936324	−	0.540587i
$714$		0			0
$715$	−0.313947	+	7.20416i	−0.0117410	+	0.269420i
$716$			25.7732i			0.963188i
$717$		0			0
$718$		−	19.4692i		−	0.726584i
$719$	6.26983	+	10.8597i	0.233825	+	0.404997i	0.958931	−	0.283641i	$-0.0915424\pi$
$719$	6.26983	+	10.8597i	0.233825	+	0.404997i	−0.725105	+	0.688638i	$0.758209\pi$
$720$		0			0
$721$	6.36204	+	2.46538i	0.236935	+	0.0918155i
$722$	−6.31623	−	10.9400i	−0.235066	−	0.407146i
$723$		0			0
$724$	14.8161	−	8.55409i	0.550636	−	0.317910i
$725$	−2.85927	+	32.7435i	−0.106191	+	1.21606i
$726$		0			0
$727$	−10.2656	−	17.7805i	−0.380730	−	0.659444i	0.610437	−	0.792065i	$-0.290994\pi$
$727$	−10.2656	−	17.7805i	−0.380730	−	0.659444i	−0.991167	+	0.132621i	$0.957661\pi$
$728$	15.8751	−	12.7721i	0.588370	−	0.473365i
$729$		0			0
$730$	−7.87948	+	12.3705i	−0.291633	+	0.457854i
$731$	62.9166			2.32705
$732$		0			0
$733$	47.2325			1.74457			0.872286	−	0.488996i	$-0.162637\pi$
$733$	47.2325			1.74457			0.872286	+	0.488996i	$0.162637\pi$
$734$	−10.1634	+	17.6036i	−0.375140	+	0.649761i
$735$		0			0
$736$	18.8874	+	32.7139i	0.696199	+	1.20585i
$737$	9.02218	+	15.6269i	0.332336	+	0.575623i
$738$		0			0
$739$	5.92336	−	10.2596i	0.217894	−	0.377404i	−0.736270	−	0.676688i	$-0.763414\pi$
$739$	5.92336	−	10.2596i	0.217894	−	0.377404i	0.954164	+	0.299284i	$0.0967478\pi$
$740$	0.0502701	−	1.15355i	0.00184796	−	0.0424053i
$741$		0			0
$742$	−0.893384	−	5.75896i	−0.0327971	−	0.211418i
$743$	−21.9727	+	38.0579i	−0.806101	+	1.39621i	0.109444	+	0.993993i	$0.465093\pi$
$743$	−21.9727	+	38.0579i	−0.806101	+	1.39621i	−0.915545	+	0.402215i	$0.868240\pi$
$744$		0			0
$745$	−29.7133	+	15.4709i	−1.08861	+	0.566810i
$746$	2.49155	+	1.43850i	0.0912223	+	0.0526672i
$747$		0			0
$748$	10.7993			0.394860
$749$	2.94521	+	18.9855i	0.107616	+	0.693717i
$750$		0			0
$751$	11.9637			0.436562			0.218281	−	0.975886i	$-0.429955\pi$
$751$	11.9637			0.436562			0.218281	+	0.975886i	$0.429955\pi$
$752$	−1.81774	+	1.04947i	−0.0662863	+	0.0382704i
$753$		0			0
$754$	−14.0025	−	8.08436i	−0.509942	−	0.294415i
$755$	−4.14192	−	7.95495i	−0.150740	−	0.289510i
$756$		0			0
$757$		−	12.5653i		−	0.456693i	−0.973580	−	0.228346i	$-0.926668\pi$
$757$		−	12.5653i		−	0.456693i	0.973580	−	0.228346i	$-0.0733318\pi$
$758$	−5.02275	+	8.69965i	−0.182434	+	0.315986i
$759$		0			0
$760$	−12.8496	−	8.18462i	−0.466104	−	0.296887i
$761$	−43.6251			−1.58141			−0.790705	−	0.612197i	$-0.790286\pi$
$761$	−43.6251			−1.58141			−0.790705	+	0.612197i	$0.790286\pi$
$762$		0			0
$763$	5.95499	−	4.79101i	0.215585	−	0.173446i
$764$			5.60732i			0.202866i
$765$		0			0
$766$	10.5153	+	6.07099i	0.379932	+	0.219354i
$767$	17.9952			0.649770
$768$		0			0
$769$	−36.5174	−	21.0833i	−1.31685	−	0.760284i	−0.333630	−	0.942704i	$-0.608274\pi$
$769$	−36.5174	−	21.0833i	−1.31685	−	0.760284i	−0.983221	+	0.182420i	$0.941607\pi$
$770$	−2.70696	+	6.17327i	−0.0975522	+	0.222469i
$771$		0			0
$772$	23.6665	+	13.6639i	0.851777	+	0.491774i
$773$	−44.6003	−	25.7500i	−1.60416	−	0.926163i	−0.990643	−	0.136482i	$-0.956420\pi$
$773$	−44.6003	−	25.7500i	−1.60416	−	0.926163i	−0.613518	−	0.789681i	$-0.710246\pi$
$774$		0			0
$775$	1.79828	−	20.5934i	0.0645961	−	0.739737i
$776$	8.57736	+	14.8564i	0.307909	+	0.533314i
$777$		0			0
$778$	6.43861	+	3.71733i	0.230835	+	0.133273i
$779$		−	12.4940i		−	0.447642i
$780$		0			0
$781$	2.99422			0.107142
$782$	44.0417	−	25.4275i	1.57493	−	0.909286i
$783$		0			0
$784$	3.06157	−	0.973302i	0.109342	−	0.0347608i
$785$	21.1922	−	33.2711i	0.756382	−	1.18750i
$786$		0			0
$787$	−20.3087	−	35.1756i	−0.723925	−	1.25388i	−0.959415	−	0.281998i	$-0.909003\pi$
$787$	−20.3087	−	35.1756i	−0.723925	−	1.25388i	0.235490	−	0.971877i	$-0.424331\pi$
$788$	1.78310	+	3.08842i	0.0635204	+	0.110020i
$789$		0			0
$790$	12.8883	−	20.2342i	0.458544	−	0.719900i
$791$	1.52449	−	1.22651i	0.0542047	−	0.0436097i
$792$		0			0
$793$	0.669141	−	0.386329i	0.0237619	−	0.0137189i
$794$	−13.2103			−0.468815
$795$		0			0
$796$			17.2359i			0.610910i
$797$	5.22831	+	3.01857i	0.185196	+	0.106923i	0.589732	−	0.807599i	$-0.299233\pi$
$797$	5.22831	+	3.01857i	0.185196	+	0.106923i	−0.404536	+	0.914522i	$0.632567\pi$
$798$		0			0
$799$	−17.8650	−	30.9431i	−0.632019	−	1.09469i
$800$	26.9457	+	2.35299i	0.952675	+	0.0831906i
$801$		0			0
$802$	−7.49206	−	4.32555i	−0.264554	−	0.152740i
$803$	−7.44769	−	4.29993i	−0.262823	−	0.151741i
$804$		0			0
$805$	−4.54950	−	41.0598i	−0.160349	−	1.44717i
$806$	8.80662	+	5.08450i	0.310200	+	0.179094i
$807$		0			0
$808$	25.9895			0.914306
$809$	27.0425	+	15.6130i	0.950763	+	0.548923i	0.893318	−	0.449426i	$-0.148371\pi$
$809$	27.0425	+	15.6130i	0.950763	+	0.548923i	0.0574449	+	0.998349i	$0.481705\pi$
$810$		0			0
$811$			29.4580i			1.03441i	0.855862	+	0.517205i	$0.173028\pi$
$811$			29.4580i			1.03441i	−0.855862	+	0.517205i	$0.826972\pi$
$812$	12.3302	+	15.3258i	0.432705	+	0.537831i
$813$		0			0
$814$	−0.520211			−0.0182334
$815$	−8.36484	−	5.32803i	−0.293008	−	0.186633i
$816$		0			0
$817$	9.39956	−	16.2805i	0.328849	−	0.569583i
$818$		−	20.9948i		−	0.734065i
$819$		0			0
$820$	6.25109	+	12.0058i	0.218297	+	0.419261i
$821$	1.73638	+	1.00250i	0.0606001	+	0.0349875i	0.529994	−	0.848001i	$-0.322194\pi$
$821$	1.73638	+	1.00250i	0.0606001	+	0.0349875i	−0.469394	+	0.882989i	$0.655528\pi$
$822$		0			0
$823$	−10.7145	+	6.18599i	−0.373482	+	0.215630i	−0.674979	−	0.737837i	$-0.735847\pi$
$823$	−10.7145	+	6.18599i	−0.373482	+	0.215630i	0.301496	+	0.953467i	$0.402514\pi$
$824$	−7.52703			−0.262217
$825$		0			0
$826$	15.6851	+	6.07817i	0.545753	+	0.211487i
$827$	−1.40242			−0.0487669			−0.0243834	−	0.999703i	$-0.507762\pi$
$827$	−1.40242			−0.0487669			−0.0243834	+	0.999703i	$0.507762\pi$
$828$		0			0
$829$	−21.8022	−	12.5875i	−0.757221	−	0.437181i	0.0710764	−	0.997471i	$-0.477357\pi$
$829$	−21.8022	−	12.5875i	−0.757221	−	0.437181i	−0.828297	+	0.560289i	$0.810690\pi$
$830$	3.83294	−	1.99570i	0.133043	−	0.0692718i
$831$		0			0
$832$	−7.86379	+	13.6205i	−0.272628	+	0.472205i
$833$	16.5684	+	52.1166i	0.574060	+	1.80573i
$834$		0			0
$835$	1.05589	−	24.2296i	0.0365407	−	0.838500i
$836$	1.61338	−	2.79445i	0.0557998	−	0.0966482i
$837$		0			0
$838$	−3.17010	−	5.49078i	−0.109509	−	0.189676i
$839$	−17.9747	−	31.1331i	−0.620555	−	1.07483i	−0.989383	−	0.145335i	$-0.953574\pi$
$839$	−17.9747	−	31.1331i	−0.620555	−	1.07483i	0.368828	−	0.929498i	$-0.379759\pi$
$840$		0			0
$841$	7.10629	−	12.3084i	0.245044	−	0.424429i
$842$	31.0509			1.07009
$843$		0			0
$844$	14.4026			0.495758
$845$	−7.25381	+	11.3883i	−0.249539	+	0.391768i
$846$		0			0
$847$	23.4516	+	9.08782i	0.805807	+	0.312261i
$848$	0.542209	+	0.939133i	0.0186195	+	0.0322500i
$849$		0			0
$850$	3.16775	−	36.2762i	0.108653	−	1.24426i
$851$	2.76104	−	1.59409i	0.0946472	−	0.0546446i
$852$		0			0
$853$	−13.1411	−	22.7610i	−0.449942	−	0.779323i	0.548440	−	0.836190i	$-0.315222\pi$
$853$	−13.1411	−	22.7610i	−0.449942	−	0.779323i	−0.998382	+	0.0568674i	$0.981889\pi$
$854$	0.713728	−	0.110720i	0.0244233	−	0.00378876i
$855$		0			0
$856$	−10.5975	−	18.3554i	−0.362215	−	0.627375i
$857$		−	10.7581i		−	0.367490i	−0.982974	−	0.183745i	$-0.941178\pi$
$857$		−	10.7581i		−	0.367490i	0.982974	−	0.183745i	$-0.0588221\pi$
$858$		0			0
$859$			53.5068i			1.82563i	0.408374	+	0.912814i	$0.366096\pi$
$859$			53.5068i			1.82563i	−0.408374	+	0.912814i	$0.633904\pi$
$860$	−0.886708	+	20.3473i	−0.0302365	+	0.693837i
$861$		0			0
$862$	22.3011	−	12.8756i	0.759580	−	0.438544i
$863$	−11.7535	−	20.3577i	−0.400094	−	0.692983i	0.593643	−	0.804728i	$-0.297689\pi$
$863$	−11.7535	−	20.3577i	−0.400094	−	0.692983i	−0.993737	+	0.111746i	$0.964356\pi$
$864$		0			0
$865$	−1.41861	+	32.5529i	−0.0482342	+	1.10683i
$866$	3.13747	−	5.43425i	0.106615	−	0.184663i
$867$		0			0
$868$	−7.75484	−	9.63888i	−0.263216	−	0.327165i
$869$	12.1820	+	7.03328i	0.413246	+	0.238588i
$870$		0			0
$871$		−	38.9531i		−	1.31987i
$872$	−4.21581	+	7.30200i	−0.142765	+	0.247277i
$873$		0			0
$874$		−	15.1952i		−	0.513985i
$875$	−25.9543	−	14.1907i	−0.877415	−	0.479732i
$876$		0			0
$877$			3.65277i			0.123345i	0.998096	+	0.0616727i	$0.0196435\pi$
$877$			3.65277i			0.123345i	−0.998096	+	0.0616727i	$0.980357\pi$
$878$	13.7092	−	7.91503i	0.462664	−	0.267119i
$879$		0			0
$880$	0.0546078	−	1.25309i	0.00184083	−	0.0422416i
$881$	19.1800			0.646192			0.323096	−	0.946366i	$-0.395276\pi$
$881$	19.1800			0.646192			0.323096	+	0.946366i	$0.395276\pi$
$882$		0			0
$883$		−	2.92260i		−	0.0983533i	−0.998790	−	0.0491767i	$-0.984340\pi$
$883$		−	2.92260i		−	0.0983533i	0.998790	−	0.0491767i	$-0.0156597\pi$
$884$	−20.1895	−	11.6564i	−0.679045	−	0.392047i
$885$		0			0
$886$	−11.1600	−	19.3296i	−0.374926	−	0.649391i
$887$		−	52.1516i		−	1.75108i	−0.483146	−	0.875540i	$-0.660506\pi$
$887$		−	52.1516i		−	1.75108i	0.483146	−	0.875540i	$-0.339494\pi$
$888$		0			0
$889$	20.0353	−	51.7022i	0.671962	−	1.73404i
$890$	−1.61764	−	3.10684i	−0.0542234	−	0.104141i
$891$		0			0
$892$	11.8815	−	20.5793i	0.397822	−	0.689047i
$893$	−10.6759			−0.357256
$894$		0			0
$895$	−2.21851	+	50.9081i	−0.0741565	+	1.70167i
$896$	10.8483	−	8.72784i	0.362415	−	0.291577i
$897$		0			0
$898$	−0.781251	−	0.451056i	−0.0260707	−	0.0150519i
$899$	−13.5889	+	23.5366i	−0.453214	+	0.784989i
$900$		0			0
$901$	−15.9867	+	9.22993i	−0.532594	+	0.307494i
$902$	5.28134	−	3.04918i	0.175849	−	0.101527i
$903$		0			0
$904$	−1.07926	+	1.86933i	−0.0358956	+	0.0621730i
$905$	30.0017	−	15.6210i	0.997289	−	0.519260i
$906$		0			0
$907$			41.1035i			1.36482i	0.730969	+	0.682410i	$0.239068\pi$
$907$			41.1035i			1.36482i	−0.730969	+	0.682410i	$0.760932\pi$
$908$	10.7888	−	6.22893i	0.358040	−	0.206714i
$909$		0			0
$910$	11.7240	−	8.61926i	0.388646	−	0.285726i
$911$	−30.4358	+	17.5721i	−1.00838	+	0.582190i	−0.910718	−	0.413029i	$-0.864471\pi$
$911$	−30.4358	+	17.5721i	−1.00838	+	0.582190i	−0.0976655	+	0.995219i	$0.531138\pi$
$912$		0			0
$913$	1.26691	+	2.19435i	0.0419286	+	0.0726225i
$914$	−15.7587	+	9.09832i	−0.521253	+	0.300946i
$915$		0			0
$916$	6.95279	−	4.01419i	0.229727	−	0.132633i
$917$	26.2476	+	10.1713i	0.866774	+	0.335887i
$918$		0			0
$919$	−21.9116	−	37.9519i	−0.722795	−	1.25192i	−0.959875	−	0.280428i	$-0.909524\pi$
$919$	−21.9116	−	37.9519i	−0.722795	−	1.25192i	0.237080	−	0.971490i	$-0.423810\pi$
$920$	21.0469	+	40.4226i	0.693895	+	1.33269i
$921$		0			0
$922$	2.58279			0.0850598
$923$	−5.59776	−	3.23187i	−0.184252	−	0.106378i
$924$		0			0
$925$	0.198591	−	2.27420i	0.00652962	−	0.0747754i
$926$	15.8875	−	9.17268i	0.522097	−	0.301433i
$927$		0			0
$928$	−30.7968	−	17.7805i	−1.01095	−	0.583674i
$929$	9.47376	−	16.4090i	0.310824	−	0.538363i	−0.667717	−	0.744415i	$-0.732728\pi$
$929$	9.47376	−	16.4090i	0.310824	−	0.538363i	0.978541	+	0.206052i	$0.0660617\pi$
$930$		0			0
$931$	15.9611	+	3.49879i	0.523105	+	0.114668i
$932$	8.09686	−	14.0242i	0.265222	−	0.459377i
$933$		0			0
$934$		−	14.5150i		−	0.474944i
$935$	21.3311	+	0.929580i	0.697601	+	0.0304005i
$936$		0			0
$937$	−7.93569			−0.259248			−0.129624	−	0.991563i	$-0.541377\pi$
$937$	−7.93569			−0.259248			−0.129624	+	0.991563i	$0.541377\pi$
$938$	13.1570	−	33.9524i	0.429592	−	1.10859i
$939$		0			0
$940$	10.2588	−	5.34148i	0.334606	−	0.174220i
$941$	16.5698	+	28.6997i	0.540160	+	0.935585i	0.998894	+	0.0470111i	$0.0149696\pi$
$941$	16.5698	+	28.6997i	0.540160	+	0.935585i	−0.458734	+	0.888573i	$0.651697\pi$
$942$		0			0
$943$	−18.6873	+	32.3673i	−0.608541	+	1.05402i
$944$	−3.13008			−0.101875
$945$		0			0
$946$	9.17594			0.298336
$947$	25.7456	−	44.5926i	0.836619	−	1.44907i	−0.0560868	−	0.998426i	$-0.517862\pi$
$947$	25.7456	−	44.5926i	0.836619	−	1.44907i	0.892706	−	0.450640i	$-0.148804\pi$
$948$		0			0
$949$	9.28242	+	16.0776i	0.301320	+	0.521902i
$950$	−8.91369	−	6.23925i	−0.289198	−	0.202428i
$951$		0			0
$952$	−37.8174	−	47.0052i	−1.22567	−	1.52345i
$953$	−44.9621			−1.45647			−0.728233	−	0.685329i	$-0.759658\pi$
$953$	−44.9621			−1.45647			−0.728233	+	0.685329i	$0.759658\pi$
$954$		0			0
$955$	−0.482668	+	11.0758i	−0.0156188	+	0.358404i
$956$			7.05436i			0.228154i
$957$		0			0
$958$	4.35583	−	7.54453i	0.140731	−	0.243753i
$959$	49.7531	+	19.2800i	1.60661	+	0.622584i
$960$		0			0
$961$	−6.95356	+	12.0439i	−0.224308	+	0.388513i
$962$	0.972546	+	0.561500i	0.0313562	+	0.0181035i
$963$		0			0
$964$	−18.6109	+	10.7450i	−0.599417	+	0.346074i
$965$	45.5709	+	29.0266i	1.46698	+	0.934399i
$966$		0			0
$967$	22.8364	+	13.1846i	0.734368	+	0.423987i	0.820018	−	0.572338i	$-0.193963\pi$
$967$	22.8364	+	13.1846i	0.734368	+	0.423987i	−0.0856501	+	0.996325i	$0.527297\pi$
$968$	−27.7460			−0.891789
$969$		0			0
$970$	5.65800	+	10.8667i	0.181667	+	0.348910i
$971$	−10.4676	−	18.1304i	−0.335920	−	0.581831i	0.647741	−	0.761861i	$-0.275714\pi$
$971$	−10.4676	−	18.1304i	−0.335920	−	0.581831i	−0.983661	+	0.180030i	$0.942381\pi$
$972$		0			0
$973$	5.45511	+	6.78044i	0.174883	+	0.217371i
$974$	7.45523	−	4.30428i	0.238881	−	0.137918i
$975$		0			0
$976$	−0.116390	+	0.0671978i	−0.00372555	+	0.00215095i
$977$	−15.7894	−	27.3480i	−0.505147	−	0.874940i	−0.999982	−	0.00595340i	$-0.998105\pi$
$977$	−15.7894	−	27.3480i	−0.505147	−	0.874940i	0.494835	−	0.868987i	$-0.335228\pi$
$978$		0			0
$979$	1.77866	−	1.02691i	0.0568462	−	0.0328202i
$980$	−17.0881	+	4.62373i	−0.545859	+	0.147700i
$981$		0			0
$982$	2.15543	−	1.24444i	0.0687826	−	0.0397117i
$983$		−	27.2799i		−	0.870092i	−0.900408	−	0.435046i	$-0.856732\pi$
$983$		−	27.2799i		−	0.870092i	0.900408	−	0.435046i	$-0.143268\pi$
$984$		0			0
$985$	3.25620	+	6.25385i	0.103751	+	0.199264i
$986$	−23.9373	+	41.4607i	−0.762320	+	1.32038i
$987$		0			0
$988$	−6.03249	+	3.48286i	−0.191919	+	0.110805i
$989$	−48.7016	+	28.1179i	−1.54862	+	0.894097i
$990$		0			0
$991$	6.26637	−	10.8537i	0.199058	−	0.344778i	−0.749165	−	0.662383i	$-0.769545\pi$
$991$	6.26637	−	10.8537i	0.199058	−	0.344778i	0.948223	+	0.317605i	$0.102878\pi$
$992$	19.3690	+	11.1827i	0.614967	+	0.355051i
$993$		0			0
$994$	−3.78752	−	4.70770i	−0.120133	−	0.149319i
$995$	−1.48363	+	34.0450i	−0.0470344	+	1.07930i
$996$		0			0
$997$	−41.6673			−1.31962			−0.659808	−	0.751434i	$-0.729362\pi$
$997$	−41.6673			−1.31962			−0.659808	+	0.751434i	$0.729362\pi$
$998$	5.52525	−	9.57002i	0.174899	−	0.302934i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	945.2.u.a.584.16		88
3.2	odd	2		315.2.u.a.59.29	yes	88
5.4	even	2	inner	945.2.u.a.584.29		88
7.5	odd	6		945.2.bq.a.719.29		88
9.2	odd	6		945.2.bq.a.899.16		88
9.7	even	3		315.2.bq.a.164.29	yes	88
15.14	odd	2		315.2.u.a.59.16	✓	88
21.5	even	6		315.2.bq.a.194.16	yes	88
35.19	odd	6		945.2.bq.a.719.16		88
45.29	odd	6		945.2.bq.a.899.29		88
45.34	even	6		315.2.bq.a.164.16	yes	88
63.47	even	6	inner	945.2.u.a.89.29		88
63.61	odd	6		315.2.u.a.299.16	yes	88
105.89	even	6		315.2.bq.a.194.29	yes	88
315.124	odd	6		315.2.u.a.299.29	yes	88
315.299	even	6	inner	945.2.u.a.89.16		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.u.a.59.16	✓	88	15.14	odd	2
315.2.u.a.59.29	yes	88	3.2	odd	2
315.2.u.a.299.16	yes	88	63.61	odd	6
315.2.u.a.299.29	yes	88	315.124	odd	6
315.2.bq.a.164.16	yes	88	45.34	even	6
315.2.bq.a.164.29	yes	88	9.7	even	3
315.2.bq.a.194.16	yes	88	21.5	even	6
315.2.bq.a.194.29	yes	88	105.89	even	6
945.2.u.a.89.16		88	315.299	even	6	inner
945.2.u.a.89.29		88	63.47	even	6	inner
945.2.u.a.584.16		88	1.1	even	1	trivial
945.2.u.a.584.29		88	5.4	even	2	inner
945.2.bq.a.719.16		88	35.19	odd	6
945.2.bq.a.719.29		88	7.5	odd	6
945.2.bq.a.899.16		88	9.2	odd	6
945.2.bq.a.899.29		88	45.29	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.466107 + 0.807321i) q^{2} +(0.565488 + 0.979455i) q^{4} +(1.03266 + 1.98333i) q^{5} +(2.46700 + 0.955995i) q^{7} -2.91874 q^{8} +O(q^{10})\)	\(q+(-0.466107 + 0.807321i) q^{2} +(0.565488 + 0.979455i) q^{4} +(1.03266 + 1.98333i) q^{5} +(2.46700 + 0.955995i) q^{7} -2.91874 q^{8} +(-2.08252 - 0.0907533i) q^{10} -1.22224i q^{11} +(-1.31924 + 2.28500i) q^{13} +(-1.92168 + 1.54606i) q^{14} +(0.229469 - 0.397451i) q^{16} +(6.76575 + 3.90621i) q^{17} +(2.02157 - 1.16715i) q^{19} +(-1.35862 + 2.13300i) q^{20} +(0.986737 + 0.569693i) q^{22} -6.98285 q^{23} +(-2.86721 + 4.09623i) q^{25} +(-1.22982 - 2.13011i) q^{26} +(0.458704 + 2.95692i) q^{28} +(5.69293 - 3.28681i) q^{29} +(-3.58046 + 2.06718i) q^{31} +(-2.70483 - 4.68490i) q^{32} +(-6.30712 + 3.64142i) q^{34} +(0.651524 + 5.88009i) q^{35} +(-0.395403 + 0.228286i) q^{37} +2.17607i q^{38} +(-3.01408 - 5.78883i) q^{40} +(2.67616 - 4.63525i) q^{41} +(6.97446 - 4.02671i) q^{43} +(1.19712 - 0.691160i) q^{44} +(3.25476 - 5.63740i) q^{46} +(-3.96077 - 2.28675i) q^{47} +(5.17215 + 4.71687i) q^{49} +(-1.97055 - 4.22404i) q^{50} -2.98407 q^{52} +(-1.18144 + 2.04632i) q^{53} +(2.42410 - 1.26216i) q^{55} +(-7.20052 - 2.79030i) q^{56} +6.12803i q^{58} +(-3.41014 - 5.90653i) q^{59} +(-0.253608 - 0.146420i) q^{61} -3.85410i q^{62} +5.96083 q^{64} +(-5.89424 - 0.256863i) q^{65} +(-12.7855 + 7.38170i) q^{67} +8.83566i q^{68} +(-5.05080 - 2.21476i) q^{70} +2.44979i q^{71} +(3.51808 - 6.09350i) q^{73} -0.425622i q^{74} +(2.28634 + 1.32002i) q^{76} +(1.16845 - 3.01525i) q^{77} +(-5.75444 + 9.96698i) q^{79} +(1.02524 + 0.0446786i) q^{80} +(2.49476 + 4.32105i) q^{82} +(-1.79536 + 1.03655i) q^{83} +(-0.760557 + 17.4525i) q^{85} +7.50751i q^{86} +3.56739i q^{88} +(0.840189 + 1.45525i) q^{89} +(-5.43902 + 4.37589i) q^{91} +(-3.94872 - 6.83939i) q^{92} +(3.69228 - 2.13174i) q^{94} +(4.40245 + 2.80416i) q^{95} +(-2.93872 - 5.09001i) q^{97} +(-6.21881 + 1.97701i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 38 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 38 * q^4 + 6 * q^5	\( 88 q - 38 q^{4} + 6 q^{5} - 6 q^{10} + 12 q^{14} - 26 q^{16} - 12 q^{19} - 6 q^{20} - 2 q^{25} - 12 q^{26} - 6 q^{29} - 6 q^{31} + 12 q^{34} + 6 q^{41} - 84 q^{44} - 18 q^{46} + 10 q^{49} - 30 q^{50} + 90 q^{56} + 6 q^{59} + 12 q^{61} - 8 q^{64} - 54 q^{65} - 30 q^{70} + 48 q^{76} + 8 q^{79} - 69 q^{80} - 7 q^{85} + 72 q^{89} + 20 q^{91} - 6 q^{94} + 93 q^{95}+O(q^{100}) \) 88 * q - 38 * q^4 + 6 * q^5 - 6 * q^10 + 12 * q^14 - 26 * q^16 - 12 * q^19 - 6 * q^20 - 2 * q^25 - 12 * q^26 - 6 * q^29 - 6 * q^31 + 12 * q^34 + 6 * q^41 - 84 * q^44 - 18 * q^46 + 10 * q^49 - 30 * q^50 + 90 * q^56 + 6 * q^59 + 12 * q^61 - 8 * q^64 - 54 * q^65 - 30 * q^70 + 48 * q^76 + 8 * q^79 - 69 * q^80 - 7 * q^85 + 72 * q^89 + 20 * q^91 - 6 * q^94 + 93 * q^95

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