LMFDB - Embedded newform 784.2.x.m.765.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			765.1
Character	$\chi$	$=$	784.765
Dual form			784.2.x.m.165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40268 + 0.180222i) q^{2} +(-0.152579 + 0.569433i) q^{3} +(1.93504 - 0.505589i) q^{4} +(0.414228 + 1.54592i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(2.29710 + 1.32623i) q^{9} +O(q^{10})$	\(q+(-1.40268 + 0.180222i) q^{2} +(-0.152579 + 0.569433i) q^{3} +(1.93504 - 0.505589i) q^{4} +(0.414228 + 1.54592i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(2.29710 + 1.32623i) q^{9} +(-0.859639 - 2.09378i) q^{10} +(-5.26900 - 1.41182i) q^{11} +(-0.00734784 + 1.17902i) q^{12} +(-4.66311 - 4.66311i) q^{13} -0.943500 q^{15} +(3.48876 - 1.95667i) q^{16} +(-2.66615 - 4.61791i) q^{17} +(-3.46112 - 1.44630i) q^{18} +(-3.49592 + 0.936730i) q^{19} +(1.58315 + 2.78199i) q^{20} +(7.64518 + 1.03075i) q^{22} +(2.25586 + 1.30242i) q^{23} +(-0.202178 - 1.65511i) q^{24} +(2.11185 - 1.21928i) q^{25} +(7.38127 + 5.70048i) q^{26} +(-2.35625 + 2.35625i) q^{27} +(-1.22279 - 1.22279i) q^{29} +(1.32343 - 0.170039i) q^{30} +(-0.416854 - 0.722013i) q^{31} +(-4.54099 + 3.37334i) q^{32} +(1.60788 - 2.78493i) q^{33} +(4.57201 + 5.99696i) q^{34} +(5.11551 + 1.40492i) q^{36} +(-1.62137 - 6.05105i) q^{37} +(4.73485 - 1.94398i) q^{38} +(3.36683 - 1.94384i) q^{39} +(-2.72203 - 3.61693i) q^{40} +0.263382i q^{41} +(1.25233 - 1.25233i) q^{43} +(-10.9095 - 0.0679900i) q^{44} +(-1.09872 + 4.10050i) q^{45} +(-3.39898 - 1.42033i) q^{46} +(-5.37795 + 9.31488i) q^{47} +(0.581880 + 2.28516i) q^{48} +(-2.74251 + 2.09086i) q^{50} +(3.03639 - 0.813598i) q^{51} +(-11.3809 - 6.66570i) q^{52} +(-0.0650529 - 0.0174309i) q^{53} +(2.88043 - 3.72973i) q^{54} -8.73026i q^{55} -2.13362i q^{57} +(1.93556 + 1.49482i) q^{58} +(-4.92700 - 1.32019i) q^{59} +(-1.82571 + 0.477023i) q^{60} +(6.09793 - 1.63393i) q^{61} +(0.714837 + 0.937629i) q^{62} +(5.76162 - 5.55011i) q^{64} +(5.27720 - 9.14038i) q^{65} +(-1.75344 + 4.19615i) q^{66} +(3.48077 - 12.9904i) q^{67} +(-7.49387 - 7.58786i) q^{68} +(-1.08584 + 1.08584i) q^{69} +2.05301i q^{71} +(-7.42864 - 1.04874i) q^{72} +(4.74814 - 2.74134i) q^{73} +(3.36480 + 8.19549i) q^{74} +(0.372072 + 1.38859i) q^{75} +(-6.29115 + 3.58011i) q^{76} +(-4.37227 + 3.33337i) q^{78} +(-2.60788 + 4.51698i) q^{79} +(4.46999 + 4.58283i) q^{80} +(2.99648 + 5.19006i) q^{81} +(-0.0474672 - 0.369441i) q^{82} +(-5.84045 - 5.84045i) q^{83} +(6.03452 - 6.03452i) q^{85} +(-1.53093 + 1.98232i) q^{86} +(0.882871 - 0.509726i) q^{87} +(15.3149 - 1.87077i) q^{88} +(-5.47892 - 3.16326i) q^{89} +(0.802163 - 5.94971i) q^{90} +(5.02367 + 1.37970i) q^{92} +(0.474741 - 0.127207i) q^{93} +(5.86481 - 14.0351i) q^{94} +(-2.89622 - 5.01639i) q^{95} +(-1.22803 - 3.10049i) q^{96} -18.8089 q^{97} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	$ 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.40268	+	0.180222i	−0.991847	+	0.127436i
$2$	−1.40268	+	0.180222i	−0.991847	+	0.127436i
$3$	−0.152579	+	0.569433i	−0.0880916	+	0.328762i	−0.995882	−	0.0906624i	$-0.971102\pi$
$3$	−0.152579	+	0.569433i	−0.0880916	+	0.328762i	0.907790	+	0.419425i	$0.137768\pi$
$4$	1.93504	−	0.505589i	0.967520	−	0.252794i
$5$	0.414228	+	1.54592i	0.185248	+	0.691356i	0.994577	+	0.104000i	$0.0331643\pi$
$5$	0.414228	+	1.54592i	0.185248	+	0.691356i	−0.809329	+	0.587356i	$0.800169\pi$
$6$	0.111396	−	0.826233i	0.0454772	−	0.337308i
$7$		0			0
$7$		0			0
$8$	−2.62313	+	1.05792i	−0.927416	+	0.374030i
$9$	2.29710	+	1.32623i	0.765701	+	0.442078i
$10$	−0.859639	−	2.09378i	−0.271842	−	0.662112i
$11$	−5.26900	−	1.41182i	−1.58866	−	0.425681i	−0.647069	−	0.762431i	$-0.724006\pi$
$11$	−5.26900	−	1.41182i	−1.58866	−	0.425681i	−0.941594	+	0.336750i	$0.890672\pi$
$12$	−0.00734784	+	1.17902i	−0.00212114	+	0.340353i
$13$	−4.66311	−	4.66311i	−1.29332	−	1.29332i	−0.932724	−	0.360591i	$-0.882575\pi$
$13$	−4.66311	−	4.66311i	−1.29332	−	1.29332i	−0.360591	−	0.932724i	$-0.617425\pi$
$14$		0			0
$15$	−0.943500			−0.243611
$16$	3.48876	−	1.95667i	0.872190	−	0.489167i
$17$	−2.66615	−	4.61791i	−0.646637	−	1.12001i	−0.983921	−	0.178605i	$-0.942842\pi$
$17$	−2.66615	−	4.61791i	−0.646637	−	1.12001i	0.337284	−	0.941403i	$-0.390492\pi$
$18$	−3.46112	−	1.44630i	−0.815795	−	0.340895i
$19$	−3.49592	+	0.936730i	−0.802020	+	0.214901i	−0.636471	−	0.771301i	$-0.719606\pi$
$19$	−3.49592	+	0.936730i	−0.802020	+	0.214901i	−0.165549	+	0.986202i	$0.552940\pi$
$20$	1.58315	+	2.78199i	0.354002	+	0.622071i
$21$		0			0
$22$	7.64518	+	1.03075i	1.62996	+	0.219757i
$23$	2.25586	+	1.30242i	0.470379	+	0.271574i	0.716399	−	0.697691i	$-0.245789\pi$
$23$	2.25586	+	1.30242i	0.470379	+	0.271574i	−0.246019	+	0.969265i	$0.579123\pi$
$24$	−0.202178	−	1.65511i	−0.0412695	−	0.337849i
$25$	2.11185	−	1.21928i	0.422370	−	0.243855i
$26$	7.38127	+	5.70048i	1.44759	+	1.11796i
$27$	−2.35625	+	2.35625i	−0.453461	+	0.453461i
$28$		0			0
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	0.584399	−	0.811466i	$-0.301330\pi$
$29$	−1.22279	−	1.22279i	−0.227067	−	0.227067i	−0.811466	+	0.584399i	$0.801330\pi$
$30$	1.32343	−	0.170039i	0.241624	−	0.0310448i
$31$	−0.416854	−	0.722013i	−0.0748692	−	0.129677i	0.826160	−	0.563435i	$-0.190521\pi$
$31$	−0.416854	−	0.722013i	−0.0748692	−	0.129677i	−0.901029	+	0.433758i	$0.857187\pi$
$32$	−4.54099	+	3.37334i	−0.802741	+	0.596327i
$33$	1.60788	−	2.78493i	0.279896	−	0.484794i
$34$	4.57201	+	5.99696i	0.784094	+	1.02847i
$35$		0			0
$36$	5.11551	+	1.40492i	0.852586	+	0.234154i
$37$	−1.62137	−	6.05105i	−0.266552	−	0.994786i	−0.961294	−	0.275526i	$-0.911148\pi$
$37$	−1.62137	−	6.05105i	−0.266552	−	0.994786i	0.694741	−	0.719260i	$-0.255519\pi$
$38$	4.73485	−	1.94398i	0.768095	−	0.315355i
$39$	3.36683	−	1.94384i	0.539124	−	0.311263i
$40$	−2.72203	−	3.61693i	−0.430390	−	0.571886i
$41$			0.263382i			0.0411333i	0.999788	+	0.0205667i	$0.00654703\pi$
$41$			0.263382i			0.0411333i	−0.999788	+	0.0205667i	$0.993453\pi$
$42$		0			0
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	−0.605140	−	0.796119i	$-0.706883\pi$
$43$	1.25233	−	1.25233i	0.190979	−	0.190979i	0.796119	+	0.605140i	$0.206883\pi$
$44$	−10.9095	−	0.0679900i	−1.64467	−	0.0102499i
$45$	−1.09872	+	4.10050i	−0.163788	+	0.611266i
$46$	−3.39898	−	1.42033i	−0.501153	−	0.209416i
$47$	−5.37795	+	9.31488i	−0.784455	+	1.35872i	0.144870	+	0.989451i	$0.453724\pi$
$47$	−5.37795	+	9.31488i	−0.784455	+	1.35872i	−0.929324	+	0.369265i	$0.879610\pi$
$48$	0.581880	+	2.28516i	0.0839872	+	0.329835i
$49$		0			0
$50$	−2.74251	+	2.09086i	−0.387850	+	0.295692i
$51$	3.03639	−	0.813598i	0.425180	−	0.113927i
$52$	−11.3809	−	6.66570i	−1.57825	−	0.924366i
$53$	−0.0650529	−	0.0174309i	−0.00893571	−	0.00239432i	0.254348	−	0.967113i	$-0.418139\pi$
$53$	−0.0650529	−	0.0174309i	−0.00893571	−	0.00239432i	−0.263284	+	0.964718i	$0.584806\pi$
$54$	2.88043	−	3.72973i	0.391977	−	0.507551i
$55$		−	8.73026i		−	1.17719i
$56$		0			0
$57$		−	2.13362i		−	0.282605i
$58$	1.93556	+	1.49482i	0.254152	+	0.196279i
$59$	−4.92700	−	1.32019i	−0.641441	−	0.171874i	−0.0765850	−	0.997063i	$-0.524402\pi$
$59$	−4.92700	−	1.32019i	−0.641441	−	0.171874i	−0.564856	+	0.825189i	$0.691068\pi$
$60$	−1.82571	+	0.477023i	−0.235698	+	0.0615834i
$61$	6.09793	−	1.63393i	0.780760	−	0.209204i	0.153640	−	0.988127i	$-0.450900\pi$
$61$	6.09793	−	1.63393i	0.780760	−	0.209204i	0.627120	+	0.778923i	$0.284234\pi$
$62$	0.714837	+	0.937629i	0.0907844	+	0.119079i
$63$		0			0
$64$	5.76162	−	5.55011i	0.720203	−	0.693764i
$65$	5.27720	−	9.14038i	0.654557	−	1.13373i
$66$	−1.75344	+	4.19615i	−0.215834	+	0.516510i
$67$	3.48077	−	12.9904i	0.425244	−	1.58703i	−0.338146	−	0.941094i	$-0.609800\pi$
$67$	3.48077	−	12.9904i	0.425244	−	1.58703i	0.763390	−	0.645938i	$-0.223533\pi$
$68$	−7.49387	−	7.58786i	−0.908765	−	0.920163i
$69$	−1.08584	+	1.08584i	−0.130720	+	0.130720i
$70$		0			0
$71$			2.05301i			0.243647i	0.992552	+	0.121824i	$0.0388743\pi$
$71$			2.05301i			0.243647i	−0.992552	+	0.121824i	$0.961126\pi$
$72$	−7.42864	−	1.04874i	−0.875474	−	0.123595i
$73$	4.74814	−	2.74134i	0.555728	−	0.320850i	−0.195701	−	0.980664i	$-0.562698\pi$
$73$	4.74814	−	2.74134i	0.555728	−	0.320850i	0.751429	+	0.659814i	$0.229365\pi$
$74$	3.36480	+	8.19549i	0.391151	+	0.952707i
$75$	0.372072	+	1.38859i	0.0429632	+	0.160341i
$76$	−6.29115	+	3.58011i	−0.721645	+	0.410667i
$77$		0			0
$78$	−4.37227	+	3.33337i	−0.495062	+	0.377429i
$79$	−2.60788	+	4.51698i	−0.293409	+	0.508200i	−0.974614	−	0.223893i	$-0.928123\pi$
$79$	−2.60788	+	4.51698i	−0.293409	+	0.508200i	0.681204	+	0.732093i	$0.261457\pi$
$80$	4.46999	+	4.58283i	0.499760	+	0.512376i
$81$	2.99648	+	5.19006i	0.332943	+	0.576674i
$82$	−0.0474672	−	0.369441i	−0.00524187	−	0.0407980i
$83$	−5.84045	−	5.84045i	−0.641073	−	0.641073i	0.309746	−	0.950819i	$-0.399756\pi$
$83$	−5.84045	−	5.84045i	−0.641073	−	0.641073i	−0.950819	+	0.309746i	$0.899756\pi$
$84$		0			0
$85$	6.03452	−	6.03452i	0.654535	−	0.654535i
$86$	−1.53093	+	1.98232i	−0.165084	+	0.213760i
$87$	0.882871	−	0.509726i	0.0946537	−	0.0546483i
$88$	15.3149	−	1.87077i	1.63257	−	0.199425i
$89$	−5.47892	−	3.16326i	−0.580764	−	0.335304i	0.180673	−	0.983543i	$-0.442172\pi$
$89$	−5.47892	−	3.16326i	−0.580764	−	0.335304i	−0.761437	+	0.648239i	$0.775506\pi$
$90$	0.802163	−	5.94971i	0.0845554	−	0.627154i
$91$		0			0
$92$	5.02367	+	1.37970i	0.523754	+	0.143844i
$93$	0.474741	−	0.127207i	0.0492284	−	0.0131907i
$94$	5.86481	−	14.0351i	0.604909	−	1.44761i
$95$	−2.89622	−	5.01639i	−0.297146	−	0.514671i
$96$	−1.22803	−	3.10049i	−0.125335	−	0.316443i
$97$	−18.8089			−1.90976			−0.954878	−	0.296999i	$-0.904014\pi$
$97$	−18.8089			−1.90976			−0.954878	+	0.296999i	$0.904014\pi$
$98$		0			0
$99$	−10.2310	−	10.2310i	−1.02826	−	1.02826i
$100$	3.47006	−	3.42707i	0.347006	−	0.342707i
$101$	−3.94130	−	1.05607i	−0.392174	−	0.105083i	0.0573431	−	0.998355i	$-0.481737\pi$
$101$	−3.94130	−	1.05607i	−0.392174	−	0.105083i	−0.449517	+	0.893272i	$0.648404\pi$
$102$	−4.11246	+	1.68844i	−0.407195	+	0.167181i
$103$	−6.70338	−	3.87020i	−0.660504	−	0.381342i	0.131965	−	0.991254i	$-0.457871\pi$
$103$	−6.70338	−	3.87020i	−0.660504	−	0.381342i	−0.792469	+	0.609912i	$0.791205\pi$
$104$	17.1651	+	7.29876i	1.68318	+	0.715703i
$105$		0			0
$106$	0.0943901	+	0.0127260i	0.00916798	+	0.00123606i
$107$	−0.854476	−	3.18895i	−0.0826053	−	0.308287i	0.912245	−	0.409646i	$-0.134348\pi$
$107$	−0.854476	−	3.18895i	−0.0826053	−	0.308287i	−0.994850	+	0.101359i	$0.967681\pi$
$108$	−3.36815	+	5.75074i	−0.324100	+	0.553365i
$109$	−1.80387	+	6.73214i	−0.172779	+	0.644822i	0.824140	+	0.566387i	$0.191659\pi$
$109$	−1.80387	+	6.73214i	−0.172779	+	0.644822i	−0.996919	+	0.0784353i	$0.975008\pi$
$110$	1.57339	+	12.2458i	0.150016	+	1.16759i
$111$	3.69306			0.350529
$112$		0			0
$113$	5.24381			0.493296			0.246648	−	0.969105i	$-0.420671\pi$
$113$	5.24381			0.493296			0.246648	+	0.969105i	$0.420671\pi$
$114$	0.384525	+	2.99279i	0.0360141	+	0.280301i
$115$	−1.07900	+	4.02688i	−0.100617	+	0.375508i
$116$	−2.98438	−	1.74792i	−0.277093	−	0.162290i
$117$	−4.52728	−	16.8960i	−0.418547	−	1.56204i
$118$	7.14895	+	0.963849i	0.658114	+	0.0887295i
$119$		0			0
$120$	2.47492	−	0.998145i	0.225929	−	0.0911178i
$121$	16.2428	+	9.37781i	1.47662	+	0.852528i
$122$	−8.25899	+	3.39087i	−0.747734	+	0.306995i
$123$	−0.149978	−	0.0401866i	−0.0135231	−	0.00362350i
$124$	−1.17167	−	1.18637i	−0.105219	−	0.106539i
$125$	8.41814	+	8.41814i	0.752941	+	0.752941i
$126$		0			0
$127$	−17.6789			−1.56875			−0.784373	−	0.620290i	$-0.787015\pi$
$127$	−17.6789			−1.56875			−0.784373	+	0.620290i	$0.787015\pi$
$128$	−7.08148	+	8.82342i	−0.625920	+	0.779887i
$129$	0.522040	+	0.904200i	0.0459631	+	0.0796104i
$130$	−5.75495	+	13.7721i	−0.504742	+	1.20790i
$131$	−2.97672	+	0.797610i	−0.260077	+	0.0696875i	−0.386502	−	0.922289i	$-0.626317\pi$
$131$	−2.97672	+	0.797610i	−0.260077	+	0.0696875i	0.126424	+	0.991976i	$0.459650\pi$
$132$	1.70328	−	6.20188i	0.148252	−	0.539804i
$133$		0			0
$134$	−2.54126	+	18.8487i	−0.219531	+	1.62828i
$135$	−4.61860	−	2.66655i	−0.397506	−	0.229500i
$136$	11.8790	+	9.29281i	1.01862	+	0.796852i
$137$	7.40148	−	4.27325i	0.632351	−	0.365088i	−0.149311	−	0.988790i	$-0.547705\pi$
$137$	7.40148	−	4.27325i	0.632351	−	0.365088i	0.781662	+	0.623702i	$0.214372\pi$
$138$	1.32740	−	1.71878i	0.112996	−	0.146312i
$139$	5.72549	−	5.72549i	0.485629	−	0.485629i	−0.421295	−	0.906924i	$-0.638424\pi$
$139$	5.72549	−	5.72549i	0.485629	−	0.485629i	0.906924	+	0.421295i	$0.138424\pi$
$140$		0			0
$141$	−4.48364	−	4.48364i	−0.377591	−	0.377591i
$142$	−0.369997	−	2.87972i	−0.0310495	−	0.241661i
$143$	17.9865	+	31.1535i	1.50410	+	2.60518i
$144$	10.6090	+	0.132240i	0.884086	+	0.0110200i
$145$	1.38382	−	2.39685i	0.114920	−	0.199048i
$146$	−6.16609	+	4.70095i	−0.510309	+	0.389054i
$147$		0			0
$148$	−6.19676	−	10.8893i	−0.509371	−	0.895092i
$149$	0.144637	+	0.539794i	0.0118492	+	0.0442217i	0.971597	−	0.236640i	$-0.0760463\pi$
$149$	0.144637	+	0.539794i	0.0118492	+	0.0442217i	−0.959748	+	0.280862i	$0.909380\pi$
$150$	−0.772154	−	1.88070i	−0.0630461	−	0.153558i
$151$	−3.21780	+	1.85780i	−0.261861	+	0.151185i	−0.625183	−	0.780478i	$-0.714976\pi$
$151$	−3.21780	+	1.85780i	−0.261861	+	0.151185i	0.363322	+	0.931663i	$0.381642\pi$
$152$	8.17928	−	6.15556i	0.663427	−	0.499282i
$153$		−	14.1437i		−	1.14345i
$154$		0			0
$155$	0.943500	−	0.943500i	0.0757837	−	0.0757837i
$156$	5.53216	−	5.46363i	0.442927	−	0.437441i
$157$	−1.46242	+	5.45784i	−0.116714	+	0.435583i	−0.999409	−	0.0343627i	$-0.989060\pi$
$157$	−1.46242	+	5.45784i	−0.116714	+	0.435583i	0.882695	+	0.469946i	$0.155727\pi$
$158$	2.84397	−	6.80589i	0.226254	−	0.541448i
$159$	0.0198514	−	0.0343837i	0.00157432	−	0.00272681i
$160$	−7.09591	−	5.62267i	−0.560981	−	0.444511i
$161$		0			0
$162$	−5.13848	−	6.73998i	−0.403717	−	0.529543i
$163$	−4.60580	+	1.23412i	−0.360754	+	0.0966638i	−0.434643	−	0.900603i	$-0.643126\pi$
$163$	−4.60580	+	1.23412i	−0.360754	+	0.0966638i	0.0738892	+	0.997266i	$0.476459\pi$
$164$	0.133163	+	0.509654i	0.0103983	+	0.0397973i
$165$	4.97130	+	1.33206i	0.387015	+	0.103700i
$166$	9.24489	+	7.13973i	0.717542	+	0.554150i
$167$			12.4233i			0.961345i	0.876900	+	0.480673i	$0.159607\pi$
$167$			12.4233i			0.961345i	−0.876900	+	0.480673i	$0.840393\pi$
$168$		0			0
$169$			30.4893i			2.34533i
$170$	−7.37696	+	9.55207i	−0.565787	+	0.732610i
$171$	−9.27282	−	2.48464i	−0.709110	−	0.190005i
$172$	1.79015	−	3.05648i	0.136498	−	0.233054i
$173$	12.6481	−	3.38906i	0.961620	−	0.257665i	0.256334	−	0.966588i	$-0.417485\pi$
$173$	12.6481	−	3.38906i	0.961620	−	0.257665i	0.705286	+	0.708923i	$0.250819\pi$
$174$	−1.14652	+	0.874097i	−0.0869178	+	0.0662651i
$175$		0			0
$176$	−21.1448	+	5.38417i	−1.59385	+	0.405847i
$177$	1.50352	−	2.60417i	0.113011	−	0.195741i
$178$	8.25527	+	3.44962i	0.618759	+	0.258560i
$179$	−3.64387	+	13.5991i	−0.272355	+	1.01644i	0.685238	+	0.728319i	$0.259698\pi$
$179$	−3.64387	+	13.5991i	−0.272355	+	1.01644i	−0.957593	+	0.288124i	$0.906968\pi$
$180$	−0.0529119	+	8.49013i	−0.00394382	+	0.632817i
$181$	5.08125	−	5.08125i	0.377687	−	0.377687i	−0.492580	−	0.870267i	$-0.663946\pi$
$181$	5.08125	−	5.08125i	0.377687	−	0.377687i	0.870267	+	0.492580i	$0.163946\pi$
$182$		0			0
$183$			3.72167i			0.275114i
$184$	−7.29527	−	1.02991i	−0.537814	−	0.0759258i
$185$	8.68281	−	5.01302i	0.638373	−	0.368565i
$186$	−0.642986	+	0.263989i	−0.0471460	+	0.0193566i
$187$	7.52827	+	28.0959i	0.550522	+	2.05458i
$188$	−5.69705	+	20.7437i	−0.415500	+	1.51289i
$189$		0			0
$190$	4.96654	+	6.51445i	0.360311	+	0.472608i
$191$	−10.3964	+	18.0070i	−0.752254	+	1.30294i	0.194474	+	0.980908i	$0.437700\pi$
$191$	−10.3964	+	18.0070i	−0.752254	+	1.30294i	−0.946728	+	0.322035i	$0.895633\pi$
$192$	2.28131	+	4.12769i	0.164640	+	0.297890i
$193$	−6.67236	−	11.5569i	−0.480287	−	0.831882i	0.519457	−	0.854496i	$-0.326134\pi$
$193$	−6.67236	−	11.5569i	−0.480287	−	0.831882i	−0.999744	+	0.0226149i	$0.992801\pi$
$194$	26.3829	−	3.38978i	1.89418	−	0.243372i
$195$	4.39965	+	4.39965i	0.315065	+	0.315065i
$196$		0			0
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	−0.700145	−	0.714000i	$-0.746882\pi$
$197$	0.194462	−	0.194462i	0.0138549	−	0.0138549i	0.714000	+	0.700145i	$0.246882\pi$
$198$	16.1947	+	12.5070i	1.15091	+	0.888836i
$199$	12.4710	−	7.20013i	0.884045	−	0.510403i	0.0120548	−	0.999927i	$-0.496163\pi$
$199$	12.4710	−	7.20013i	0.884045	−	0.510403i	0.871990	+	0.489524i	$0.162829\pi$
$200$	−4.24976	+	5.43248i	−0.300503	+	0.384134i
$201$	6.86608	+	3.96413i	0.484296	+	0.279608i
$202$	5.71872	+	0.771019i	0.402367	+	0.0542487i
$203$		0			0
$204$	5.46419	−	3.10951i	0.382570	−	0.217709i
$205$	−0.407167	+	0.109100i	−0.0284378	+	0.00761987i
$206$	10.1002	+	4.22056i	0.703715	+	0.294061i
$207$	3.45463	+	5.98359i	0.240113	+	0.415888i
$208$	−25.3927	−	7.14432i	−1.76066	−	0.495369i
$209$	19.7425			1.36562
$210$		0			0
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	0.921081	−	0.389370i	$-0.127307\pi$
$211$	7.72356	+	7.72356i	0.531711	+	0.531711i	−0.389370	+	0.921081i	$0.627307\pi$
$212$	−0.134693		0.000839429i	−0.00925075		5.76522e-5i
$213$	−1.16905	−	0.313247i	−0.0801021	−	0.0214633i
$214$	1.77328	+	4.31909i	0.121219	+	0.295247i
$215$	2.45476	+	1.41725i	0.167413	+	0.0966559i
$216$	3.68804	−	8.67348i	0.250939	−	0.590156i
$217$		0			0
$218$	1.31698	−	9.76815i	0.0891971	−	0.661583i
$219$	0.836543	+	3.12202i	0.0565284	+	0.210967i
$220$	−4.41392	−	16.8934i	−0.297587	−	1.13895i
$221$	−9.10127	+	33.9664i	−0.612218	+	2.28483i
$222$	−5.18019	+	0.665570i	−0.347671	+	0.0446701i
$223$	7.06285			0.472963			0.236482	−	0.971636i	$-0.424006\pi$
$223$	7.06285			0.472963			0.236482	+	0.971636i	$0.424006\pi$
$224$		0			0
$225$	6.46817			0.431212
$226$	−7.35540	+	0.945049i	−0.489274	+	0.0628637i
$227$	4.32747	−	16.1503i	0.287224	−	1.07193i	−0.659975	−	0.751288i	$-0.729433\pi$
$227$	4.32747	−	16.1503i	0.287224	−	1.07193i	0.947199	−	0.320647i	$-0.103900\pi$
$228$	−1.07873	−	4.12864i	−0.0714409	−	0.273426i
$229$	3.43264	+	12.8108i	0.226835	+	0.846561i	0.981661	+	0.190636i	$0.0610549\pi$
$229$	3.43264	+	12.8108i	0.226835	+	0.846561i	−0.754826	+	0.655926i	$0.772278\pi$
$230$	0.787761	−	5.84289i	0.0519434	−	0.385269i
$231$		0			0
$232$	4.50115	+	1.91393i	0.295515	+	0.125656i
$233$	−21.1644	−	12.2193i	−1.38653	−	0.800511i	−0.393604	−	0.919280i	$-0.628772\pi$
$233$	−21.1644	−	12.2193i	−1.38653	−	0.800511i	−0.992922	+	0.118769i	$0.962105\pi$
$234$	9.39537	+	22.8839i	0.614194	+	1.49596i
$235$	−16.6277	−	4.45539i	−1.08467	−	0.290638i
$236$	−10.2014	−	0.0635769i	−0.664056	−	0.00413851i
$237$	−2.17421	−	2.17421i	−0.141230	−	0.141230i
$238$		0			0
$239$	−6.27660			−0.406000			−0.203000	−	0.979179i	$-0.565069\pi$
$239$	−6.27660			−0.406000			−0.203000	+	0.979179i	$0.565069\pi$
$240$	−3.29165	+	1.84612i	−0.212475	+	0.119166i
$241$	−7.50621	−	13.0011i	−0.483517	−	0.837476i	0.516304	−	0.856406i	$-0.327308\pi$
$241$	−7.50621	−	13.0011i	−0.483517	−	0.837476i	−0.999821	+	0.0189293i	$0.993974\pi$
$242$	−24.4736	−	10.2268i	−1.57323	−	0.657402i
$243$	−13.0687	+	3.50175i	−0.838358	+	0.224637i
$244$	10.9736	−	6.24477i	0.702515	−	0.399781i
$245$		0			0
$246$	0.217615	+	0.0293396i	0.0138746	+	0.00187063i
$247$	20.6700	+	11.9338i	1.31520	+	0.759330i
$248$	1.85729	+	1.45294i	0.117938	+	0.0922615i
$249$	4.21688	−	2.43462i	0.267234	−	0.154288i
$250$	−13.3251	−	10.2909i	−0.842754	−	0.650851i
$251$	−11.7926	+	11.7926i	−0.744339	+	0.744339i	−0.973410	−	0.229071i	$-0.926431\pi$
$251$	−11.7926	+	11.7926i	−0.744339	+	0.744339i	0.229071	+	0.973410i	$0.426431\pi$
$252$		0			0
$253$	−10.0473	−	10.0473i	−0.631671	−	0.631671i
$254$	24.7979	−	3.18612i	1.55596	−	0.199915i
$255$	2.51551	+	4.35700i	0.157528	+	0.272846i
$256$	8.34290	−	13.6527i	0.521431	−	0.853293i
$257$	10.1988	−	17.6649i	0.636186	−	1.10191i	−0.350076	−	0.936721i	$-0.613844\pi$
$257$	10.1988	−	17.6649i	0.636186	−	1.10191i	0.986263	−	0.165186i	$-0.0528223\pi$
$258$	−0.895214	−	1.17422i	−0.0557336	−	0.0731039i
$259$		0			0
$260$	5.59033	−	20.3551i	0.346697	−	1.26237i
$261$	−1.18717	−	4.43058i	−0.0734841	−	0.274246i
$262$	4.03165	−	1.65526i	0.249076	−	0.102263i
$263$	20.2176	−	11.6726i	1.24667	−	0.719764i	0.276225	−	0.961093i	$-0.410917\pi$
$263$	20.2176	−	11.6726i	1.24667	−	0.719764i	0.970443	+	0.241329i	$0.0775832\pi$
$264$	−1.27145	+	9.00624i	−0.0782525	+	0.554296i
$265$		−	0.107787i		−	0.00662130i
$266$		0			0
$267$	2.63723	−	2.63723i	0.161396	−	0.161396i
$268$	0.167625	−	26.8968i	0.0102394	−	1.64298i
$269$	−8.07837	+	30.1489i	−0.492547	+	1.83821i	0.0508094	+	0.998708i	$0.483820\pi$
$269$	−8.07837	+	30.1489i	−0.492547	+	1.83821i	−0.543356	+	0.839502i	$0.682847\pi$
$270$	6.95900	+	2.90795i	0.423512	+	0.176972i
$271$	0.731959	−	1.26779i	0.0444633	−	0.0770127i	−0.842937	−	0.538012i	$-0.819176\pi$
$271$	0.731959	−	1.26779i	0.0444633	−	0.0770127i	0.887401	+	0.460999i	$0.152509\pi$
$272$	−18.3373	−	10.8940i	−1.11186	−	0.660546i
$273$		0			0
$274$	−9.61180	+	7.32792i	−0.580670	+	0.442696i
$275$	−12.8487	+	3.44281i	−0.774808	+	0.207609i
$276$	−1.55216	+	2.65013i	−0.0934288	+	0.159519i
$277$	1.90198	+	0.509633i	0.114279	+	0.0306209i	0.315505	−	0.948924i	$-0.397826\pi$
$277$	1.90198	+	0.509633i	0.114279	+	0.0306209i	−0.201226	+	0.979545i	$0.564493\pi$
$278$	−6.99918	+	9.06290i	−0.419783	+	0.543557i
$279$		−	2.21138i		−	0.132392i
$280$		0			0
$281$		−	5.66742i		−	0.338090i	−0.985608	−	0.169045i	$-0.945932\pi$
$281$		−	5.66742i		−	0.338090i	0.985608	−	0.169045i	$-0.0540683\pi$
$282$	7.09718	+	5.48108i	0.422631	+	0.326393i
$283$	−22.7600	−	6.09854i	−1.35294	−	0.362520i	−0.491724	−	0.870751i	$-0.663633\pi$
$283$	−22.7600	−	6.09854i	−1.35294	−	0.362520i	−0.861221	+	0.508231i	$0.830300\pi$
$284$	1.03798	+	3.97266i	0.0615927	+	0.235734i
$285$	3.29840	−	0.883805i	0.195381	−	0.0523521i
$286$	−30.8438	−	40.4569i	−1.82383	−	2.39226i
$287$		0			0
$288$	−14.9050	+	1.72649i	−0.878283	+	0.101734i
$289$	−5.71672	+	9.90165i	−0.336278	+	0.582450i
$290$	−1.50910	+	3.61142i	−0.0886173	+	0.212070i
$291$	2.86985	−	10.7104i	0.168234	−	0.627856i
$292$	7.80186	−	7.70521i	0.456569	−	0.450913i
$293$	−17.1121	+	17.1121i	−0.999698	+	0.999698i	−1.00000		0.000302098i	$-0.999904\pi$
$293$	−17.1121	+	17.1121i	−0.999698	+	0.999698i	0.000302098		1.00000i	$0.499904\pi$
$294$		0			0
$295$		−	8.16360i		−	0.475303i
$296$	10.6546	+	14.1574i	0.619285	+	0.822882i
$297$	15.7417	−	9.08849i	0.913427	−	0.527367i
$298$	−0.300163	−	0.731093i	−0.0173880	−	0.0423511i
$299$	−4.44599	−	16.5927i	−0.257118	−	0.959579i
$300$	1.42203	+	2.49887i	0.0821010	+	0.144272i
$301$		0			0
$302$	4.17874	−	3.18582i	0.240459	−	0.183323i
$303$	1.20272	−	2.08317i	0.0690944	−	0.119675i
$304$	−10.3636	+	10.1084i	−0.594391	+	0.579756i
$305$	5.05186	+	8.75008i	0.289269	+	0.501028i
$306$	2.54901	+	19.8392i	0.145717	+	1.13413i
$307$	9.59837	+	9.59837i	0.547808	+	0.547808i	0.925806	−	0.377998i	$-0.123388\pi$
$307$	9.59837	+	9.59837i	0.547808	+	0.547808i	−0.377998	+	0.925806i	$0.623388\pi$
$308$		0			0
$309$	3.22662	−	3.22662i	0.183556	−	0.183556i
$310$	−1.15339	+	1.49347i	−0.0655083	+	0.0848235i
$311$	16.6161	−	9.59331i	0.942213	−	0.543987i	0.0515594	−	0.998670i	$-0.483581\pi$
$311$	16.6161	−	9.59331i	0.942213	−	0.543987i	0.890653	+	0.454683i	$0.150248\pi$
$312$	−6.77520	+	8.66076i	−0.383570	+	0.490319i
$313$	−4.36445	−	2.51982i	−0.246693	−	0.142428i	0.371556	−	0.928411i	$-0.378824\pi$
$313$	−4.36445	−	2.51982i	−0.246693	−	0.142428i	−0.618249	+	0.785982i	$0.712158\pi$
$314$	1.06769	−	7.91918i	0.0602535	−	0.446905i
$315$		0			0
$316$	−2.76262	+	10.0591i	−0.155409	+	0.565866i
$317$	−7.54861	+	2.02264i	−0.423972	+	0.113603i	−0.464495	−	0.885576i	$-0.653764\pi$
$317$	−7.54861	+	2.02264i	−0.423972	+	0.113603i	0.0405232	+	0.999179i	$0.487098\pi$
$318$	−0.0216486	+	0.0518071i	−0.00121399	+	0.00290520i
$319$	4.71652	+	8.16926i	0.264075	+	0.457391i
$320$	10.9666	+	6.60799i	0.613054	+	0.369398i
$321$	1.94627			0.108630
$322$		0			0
$323$	13.6464	+	13.6464i	0.759306	+	0.759306i
$324$	8.42235	+	8.52799i	0.467909	+	0.473777i
$325$	−15.5334	−	4.16216i	−0.861638	−	0.230875i
$326$	6.23806	−	2.56115i	0.345494	−	0.141849i
$327$	−3.55827	−	2.05437i	−0.196773	−	0.113607i
$328$	−0.278636	−	0.690885i	−0.0153851	−	0.0381477i
$329$		0			0
$330$	−7.21323	−	0.972515i	−0.397075	−	0.0535352i
$331$	−5.39940	−	20.1508i	−0.296778	−	1.10759i	−0.939795	−	0.341739i	$-0.888984\pi$
$331$	−5.39940	−	20.1508i	−0.296778	−	1.10759i	0.643017	−	0.765852i	$-0.277682\pi$
$332$	−14.2544	−	8.34865i	−0.782311	−	0.458191i
$333$	4.30064	−	16.0502i	0.235673	−	0.879545i
$334$	−2.23895	−	17.4260i	−0.122510	−	0.953507i
$335$	21.5239			1.17598
$336$		0			0
$337$	16.7111			0.910311			0.455156	−	0.890412i	$-0.349584\pi$
$337$	16.7111			0.910311			0.455156	+	0.890412i	$0.349584\pi$
$338$	−5.49484	−	42.7668i	−0.298880	−	2.32621i
$339$	−0.800096	+	2.98600i	−0.0434552	+	0.162177i
$340$	8.62605	−	14.7280i	0.467813	−	0.798739i
$341$	1.17705	+	4.39281i	0.0637408	+	0.237884i
$342$	13.4546	+	1.81400i	0.727542	+	0.0980900i
$343$		0			0
$344$	−1.96017	+	4.60990i	−0.105685	+	0.248549i
$345$	−2.12840	−	1.22883i	−0.114589	−	0.0661582i
$346$	−17.1305	+	7.03325i	−0.920944	+	0.378110i
$347$	−7.62139	−	2.04215i	−0.409138	−	0.109628i	0.0483791	−	0.998829i	$-0.484594\pi$
$347$	−7.62139	−	2.04215i	−0.409138	−	0.109628i	−0.457517	+	0.889201i	$0.651261\pi$
$348$	1.45068	−	1.43271i	0.0777646	−	0.0768013i
$349$	17.9789	+	17.9789i	0.962388	+	0.962388i	0.999318	−	0.0369299i	$-0.0117578\pi$
$349$	17.9789	+	17.9789i	0.962388	+	0.962388i	−0.0369299	+	0.999318i	$0.511758\pi$
$350$		0			0
$351$	21.9750			1.17294
$352$	28.6890	−	11.3630i	1.52913	−	0.605652i
$353$	−12.5159	−	21.6782i	−0.666155	−	1.15381i	−0.978971	−	0.204000i	$-0.934606\pi$
$353$	−12.5159	−	21.6782i	−0.666155	−	1.15381i	0.312816	−	0.949814i	$-0.398728\pi$
$354$	−1.63963	+	3.92379i	−0.0871453	+	0.208547i
$355$	−3.17379	+	0.850413i	−0.168447	+	0.0451352i
$356$	−12.2012	−	3.35095i	−0.646664	−	0.177600i
$357$		0			0
$358$	2.66033	−	19.7319i	0.140603	−	1.04286i
$359$	−15.5806	−	8.99548i	−0.822314	−	0.474763i	0.0288999	−	0.999582i	$-0.490800\pi$
$359$	−15.5806	−	8.99548i	−0.822314	−	0.474763i	−0.851214	+	0.524819i	$0.824133\pi$
$360$	−1.45589	−	11.9185i	−0.0767321	−	0.628160i
$361$	−5.11046	+	2.95053i	−0.268972	+	0.155291i
$362$	−6.21164	+	8.04314i	−0.326476	+	0.422738i
$363$	−7.81836	+	7.81836i	−0.410357	+	0.410357i
$364$		0			0
$365$	6.20470	+	6.20470i	0.324769	+	0.324769i
$366$	−0.670726	−	5.22032i	−0.0350594	−	0.272870i
$367$	5.15387	+	8.92677i	0.269030	+	0.465974i	0.968612	−	0.248579i	$-0.0799636\pi$
$367$	5.15387	+	8.92677i	0.269030	+	0.465974i	−0.699582	+	0.714553i	$0.746630\pi$
$368$	10.4186	+	0.129866i	0.543105	+	0.00676971i
$369$	−0.349306	+	0.605015i	−0.0181841	+	0.0314958i
$370$	−11.2758	+	8.59651i	−0.586199	+	0.446911i
$371$		0			0
$372$	0.854329	−	0.486174i	0.0442949	−	0.0252069i
$373$	5.87673	+	21.9323i	0.304286	+	1.13561i	0.933558	+	0.358425i	$0.116686\pi$
$373$	5.87673	+	21.9323i	0.304286	+	1.13561i	−0.629273	+	0.777184i	$0.716647\pi$
$374$	−15.6233	−	38.0529i	−0.807861	−	1.96767i
$375$	−6.07800	+	3.50914i	−0.313867	+	0.181211i
$376$	4.25269	−	30.1236i	0.219316	−	1.55350i
$377$			11.4040i			0.587338i
$378$		0			0
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	−0.173622	−	0.984812i	$-0.555547\pi$
$379$	15.7922	−	15.7922i	0.811190	−	0.811190i	0.984812	+	0.173622i	$0.0555471\pi$
$380$	−8.14053	−	8.24263i	−0.417600	−	0.422838i
$381$	2.69743	−	10.0669i	0.138193	−	0.515745i
$382$	11.3375	−	27.1318i	0.580079	−	1.38818i
$383$	9.18163	−	15.9031i	0.469160	−	0.812608i	−0.530219	−	0.847861i	$-0.677890\pi$
$383$	9.18163	−	15.9031i	0.469160	−	0.812608i	0.999378	+	0.0352526i	$0.0112236\pi$
$384$	−3.94386	−	5.37870i	−0.201259	−	0.274481i
$385$		0			0
$386$	11.4420	+	15.0081i	0.582383	+	0.763893i
$387$	4.53762	−	1.21585i	0.230660	−	0.0618052i
$388$	−36.3960	+	9.50957i	−1.84773	+	0.482775i
$389$	−19.0634	−	5.10801i	−0.966551	−	0.258987i	−0.259180	−	0.965829i	$-0.583452\pi$
$389$	−19.0634	−	5.10801i	−0.966551	−	0.258987i	−0.707371	+	0.706842i	$0.750119\pi$
$390$	−6.96423	−	5.37840i	−0.352647	−	0.272346i
$391$		−	13.8898i		−	0.702438i
$392$		0			0
$393$		−	1.81674i		−	0.0916426i
$394$	−0.237723	+	0.307815i	−0.0119763	+	0.0155075i
$395$	−8.06314	−	2.16051i	−0.405701	−	0.108707i
$396$	−24.9701	−	14.6248i	−1.25480	−	0.734922i
$397$	−1.54108	+	0.412931i	−0.0773446	+	0.0207244i	−0.297284	−	0.954789i	$-0.596081\pi$
$397$	−1.54108	+	0.412931i	−0.0773446	+	0.0207244i	0.219939	+	0.975514i	$0.429414\pi$
$398$	−16.1952	+	12.3470i	−0.811793	+	0.618901i
$399$		0			0
$400$	4.98201	−	8.38595i	0.249101	−	0.419297i
$401$	7.17349	−	12.4248i	0.358227	−	0.620467i	−0.629438	−	0.777051i	$-0.716715\pi$
$401$	7.17349	−	12.4248i	0.358227	−	0.620467i	0.987665	+	0.156584i	$0.0500481\pi$
$402$	−10.3454	−	4.32300i	−0.515980	−	0.215612i
$403$	−1.42299	+	5.31066i	−0.0708841	+	0.264543i
$404$	−8.16050	−	0.0508576i	−0.406000	−	0.00253026i
$405$	−6.78219	+	6.78219i	−0.337010	+	0.337010i
$406$		0			0
$407$			34.1721i			1.69385i
$408$	−7.10413	+	5.34642i	−0.351707	+	0.264687i
$409$	33.9931	−	19.6259i	1.68085	−	0.970438i	0.719749	−	0.694234i	$-0.244257\pi$
$409$	33.9931	−	19.6259i	1.68085	−	0.970438i	0.961099	−	0.276204i	$-0.0890765\pi$
$410$	0.551464	−	0.226413i	0.0272349	−	0.0111817i
$411$	1.30402	+	4.86666i	0.0643224	+	0.240055i
$412$	−14.9280	−	4.09984i	−0.735451	−	0.201984i
$413$		0			0
$414$	−5.92412	−	7.77048i	−0.291155	−	0.381898i
$415$	6.60959	−	11.4481i	0.324452	−	0.561967i
$416$	36.9054	+	5.44490i	1.80944	+	0.266958i
$417$	2.38669	+	4.13387i	0.116877	+	0.202437i
$418$	−27.6925	+	3.55804i	−1.35448	+	0.174029i
$419$	4.41473	+	4.41473i	0.215673	+	0.215673i	0.806672	−	0.590999i	$-0.201266\pi$
$419$	4.41473	+	4.41473i	0.215673	+	0.215673i	−0.590999	+	0.806672i	$0.701266\pi$
$420$		0			0
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	−0.867178	−	0.497998i	$-0.834069\pi$
$421$	−7.57494	+	7.57494i	−0.369180	+	0.369180i	0.497998	+	0.867178i	$0.334069\pi$
$422$	−12.2257	−	9.44175i	−0.595136	−	0.459617i
$423$	−24.7074	+	14.2648i	−1.20132	+	0.693580i
$424$	0.189083	−	0.0230972i	0.00918267	−	0.00112170i
$425$	−11.2610	−	6.50155i	−0.546239	−	0.315371i
$426$	1.69626	+	0.228697i	0.0821842	+	0.0110804i
$427$		0			0
$428$	−3.26574	−	5.73873i	−0.157856	−	0.277392i
$429$	−20.4842	+	5.48872i	−0.988985	+	0.264998i
$430$	−3.69867	−	1.54556i	−0.178365	−	0.0745334i
$431$	9.26979	+	16.0558i	0.446510	+	0.773378i	0.998156	−	0.0607001i	$-0.0193333\pi$
$431$	9.26979	+	16.0558i	0.446510	+	0.773378i	−0.551646	+	0.834078i	$0.686000\pi$
$432$	−3.61000	+	12.8308i	−0.173686	+	0.617323i
$433$	−7.21190			−0.346582			−0.173291	−	0.984871i	$-0.555440\pi$
$433$	−7.21190			−0.346582			−0.173291	+	0.984871i	$0.555440\pi$
$434$		0			0
$435$	1.15370	+	1.15370i	0.0553159	+	0.0553159i
$436$	−0.0868700	+	13.9390i	−0.00416032	+	0.667556i
$437$	−9.10633	−	2.44003i	−0.435615	−	0.116723i
$438$	−1.73606	−	4.22844i	−0.0829523	−	0.202043i
$439$	13.1302	+	7.58073i	0.626671	+	0.361809i	0.779462	−	0.626450i	$-0.215493\pi$
$439$	13.1302	+	7.58073i	0.626671	+	0.361809i	−0.152791	+	0.988259i	$0.548826\pi$
$440$	9.23590	+	22.9006i	0.440304	+	1.09174i
$441$		0			0
$442$	6.64471	−	49.2843i	0.316056	−	2.34422i
$443$	−0.775043	−	2.89250i	−0.0368234	−	0.137427i	0.945067	−	0.326877i	$-0.105996\pi$
$443$	−0.775043	−	2.89250i	−0.0368234	−	0.137427i	−0.981890	+	0.189450i	$0.939330\pi$
$444$	7.14621	−	1.86717i	0.339144	−	0.0886118i
$445$	2.62062	−	9.78027i	0.124229	−	0.463629i
$446$	−9.90694	+	1.27288i	−0.469107	+	0.0602726i
$447$	−0.329445			−0.0155822
$448$		0			0
$449$	4.29509			0.202698			0.101349	−	0.994851i	$-0.467684\pi$
$449$	4.29509			0.202698			0.101349	+	0.994851i	$0.467684\pi$
$450$	−9.07280	+	1.16571i	−0.427696	+	0.0549520i
$451$	0.371849	−	1.38776i	0.0175097	−	0.0653470i
$452$	10.1470	−	2.65121i	0.477274	−	0.124702i
$453$	−0.566922	−	2.11578i	−0.0266363	−	0.0994082i
$454$	−3.15942	+	23.4337i	−0.148279	+	1.09980i
$455$		0			0
$456$	2.25719	+	5.59676i	0.105703	+	0.262093i
$457$	24.0610	+	13.8916i	1.12553	+	0.649823i	0.942806	−	0.333342i	$-0.108176\pi$
$457$	24.0610	+	13.8916i	1.12553	+	0.649823i	0.182721	+	0.983165i	$0.441510\pi$
$458$	−7.12370	−	17.3508i	−0.332868	−	0.810752i
$459$	17.1631	+	4.59884i	0.801104	+	0.214655i
$460$	−0.0519619	+	8.33769i	−0.00242274	+	0.388747i
$461$	6.50912	+	6.50912i	0.303160	+	0.303160i	0.842249	−	0.539089i	$-0.181231\pi$
$461$	6.50912	+	6.50912i	0.303160	+	0.303160i	−0.539089	+	0.842249i	$0.681231\pi$
$462$		0			0
$463$	−39.1018			−1.81722			−0.908608	−	0.417650i	$-0.862854\pi$
$463$	−39.1018			−1.81722			−0.908608	+	0.417650i	$0.862854\pi$
$464$	−6.65863	−	1.87343i	−0.309119	−	0.0869718i
$465$	0.393302	+	0.681219i	0.0182389	+	0.0315908i
$466$	31.8891	+	13.3255i	1.47724	+	0.617291i
$467$	22.4873	−	6.02544i	1.04059	−	0.278824i	0.302230	−	0.953235i	$-0.402269\pi$
$467$	22.4873	−	6.02544i	1.04059	−	0.278824i	0.738356	+	0.674411i	$0.235602\pi$
$468$	−17.3029	−	30.4055i	−0.799827	−	1.40550i
$469$		0			0
$470$	24.1264	+	3.25282i	1.11287	+	0.150041i
$471$	−2.88474	−	1.66551i	−0.132922	−	0.0767424i
$472$	14.3208	−	1.74934i	0.659169	−	0.0805200i
$473$	−8.36662	+	4.83047i	−0.384698	+	0.222105i
$474$	3.44157	+	2.65789i	0.158077	+	0.122081i
$475$	−6.24073	+	6.24073i	−0.286344	+	0.286344i
$476$		0			0
$477$	−0.126316	−	0.126316i	−0.00578361	−	0.00578361i
$478$	8.80408	−	1.13118i	0.402689	−	0.0517390i
$479$	−18.6282	−	32.2650i	−0.851145	−	1.47423i	−0.880175	−	0.474649i	$-0.842575\pi$
$479$	−18.6282	−	32.2650i	−0.851145	−	1.47423i	0.0290300	−	0.999579i	$-0.490758\pi$
$480$	4.28442	−	3.18274i	0.195556	−	0.145272i
$481$	−20.6561	+	35.7774i	−0.941836	+	1.63131i
$482$	12.8719	+	16.8837i	0.586300	+	0.769031i
$483$		0			0
$484$	36.1719	+	9.93424i	1.64418	+	0.451556i
$485$	−7.79117	−	29.0770i	−0.353779	−	1.32032i
$486$	17.7002	−	7.26711i	0.802895	−	0.329643i
$487$	−33.2743	+	19.2110i	−1.50780	+	0.870531i	−0.507846	+	0.861448i	$0.669558\pi$
$487$	−33.2743	+	19.2110i	−1.50780	+	0.870531i	−0.999959	+	0.00908353i	$0.997109\pi$
$488$	−14.2671	+	10.7371i	−0.645841	+	0.486047i
$489$		−	2.81100i		−	0.127118i
$490$		0			0
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	−0.458773	−	0.888554i	$-0.651711\pi$
$491$	9.52330	−	9.52330i	0.429781	−	0.429781i	0.888554	+	0.458773i	$0.151711\pi$
$492$	−0.310532	−	0.00193529i	−0.0139999	−	8.72495e-5i
$493$	−2.38659	+	8.90689i	−0.107487	+	0.401146i
$494$	−31.1442	−	13.0142i	−1.40124	−	0.585535i
$495$	11.5784	−	20.0543i	0.520409	−	0.901374i
$496$	−2.86704	−	1.70328i	−0.128734	−	0.0764797i
$497$		0			0
$498$	−5.47618	+	4.17497i	−0.245393	+	0.187085i
$499$	−13.3623	+	3.58042i	−0.598180	+	0.160282i	−0.545189	−	0.838313i	$-0.683542\pi$
$499$	−13.3623	+	3.58042i	−0.598180	+	0.160282i	−0.0529909	+	0.998595i	$0.516875\pi$
$500$	20.5456	+	12.0333i	0.918825	+	0.538147i
$501$	−7.07425	−	1.89554i	−0.316054	−	0.0846865i
$502$	14.4159	−	18.6665i	0.643415	−	0.833126i
$503$			11.0554i			0.492938i	0.969151	+	0.246469i	$0.0792703\pi$
$503$			11.0554i			0.492938i	−0.969151	+	0.246469i	$0.920730\pi$
$504$		0			0
$505$		−	6.53038i		−	0.290598i
$506$	15.9040	+	12.2825i	0.707018	+	0.546023i
$507$	−17.3616	−	4.65203i	−0.771056	−	0.206604i
$508$	−34.2093	+	8.93823i	−1.51779	+	0.396570i
$509$	−0.236650	+	0.0634101i	−0.0104893	+	0.00281060i	−0.264060	−	0.964506i	$-0.585062\pi$
$509$	−0.236650	+	0.0634101i	−0.0104893	+	0.00281060i	0.253571	+	0.967317i	$0.418395\pi$
$510$	−4.31369	−	5.65814i	−0.191014	−	0.250546i
$511$		0			0
$512$	−9.24192	+	20.6540i	−0.408439	+	0.912786i
$513$	6.03011	−	10.4445i	0.266236	−	0.461134i
$514$	−11.1221	+	26.6163i	−0.490576	+	1.17400i
$515$	3.20629	−	11.9660i	0.141286	−	0.527286i
$516$	1.46732	+	1.48573i	0.0645953	+	0.0654054i
$517$	41.4874	−	41.4874i	1.82461	−	1.82461i
$518$		0			0
$519$			7.71937i			0.338843i
$520$	−4.17302	+	29.5593i	−0.182999	+	1.29626i
$521$	−25.9687	+	14.9930i	−1.13771	+	0.656857i	−0.945862	−	0.324568i	$-0.894781\pi$
$521$	−25.9687	+	14.9930i	−1.13771	+	0.656857i	−0.191847	+	0.981425i	$0.561448\pi$
$522$	2.46371	+	6.00075i	0.107834	+	0.262646i
$523$	−0.545124	−	2.03443i	−0.0238366	−	0.0889594i	0.952983	−	0.303024i	$-0.0979963\pi$
$523$	−0.545124	−	2.03443i	−0.0238366	−	0.0889594i	−0.976819	+	0.214065i	$0.931330\pi$
$524$	−5.35681	+	3.04840i	−0.234013	+	0.133170i
$525$		0			0
$526$	−26.2552	+	20.0166i	−1.14478	+	0.872766i
$527$	−2.22279	+	3.84999i	−0.0968263	+	0.167708i
$528$	0.160323	−	12.8620i	0.00697716	−	0.559748i
$529$	−8.10740	−	14.0424i	−0.352495	−	0.610540i
$530$	0.0194256	+	0.151191i	0.000843793	+	0.00656731i
$531$	−9.56695	−	9.56695i	−0.415170	−	0.415170i
$532$		0			0
$533$	1.22818	−	1.22818i	0.0531983	−	0.0531983i
$534$	−3.22391	+	4.17449i	−0.139512	+	0.180648i
$535$	4.57591	−	2.64190i	0.197834	−	0.114219i
$536$	4.61227	+	37.7579i	0.199220	+	1.63089i
$537$	−7.18780	−	4.14988i	−0.310176	−	0.179080i
$538$	5.89790	−	43.7452i	0.254277	−	1.88599i
$539$		0			0
$540$	−10.2854	−	2.82477i	−0.442611	−	0.121559i
$541$	−16.5066	+	4.42294i	−0.709676	+	0.190157i	−0.595561	−	0.803310i	$-0.703070\pi$
$541$	−16.5066	+	4.42294i	−0.709676	+	0.190157i	−0.114115	+	0.993467i	$0.536403\pi$
$542$	−0.798223	+	1.91022i	−0.0342866	+	0.0820511i
$543$	2.11814	+	3.66873i	0.0908982	+	0.157440i
$544$	27.6847	+	11.9761i	1.18697	+	0.513469i
$545$	−11.1545			−0.477808
$546$		0			0
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	0.918918	−	0.394449i	$-0.129065\pi$
$547$	12.2663	+	12.2663i	0.524468	+	0.524468i	−0.394449	+	0.918918i	$0.629065\pi$
$548$	12.1617	−	12.0110i	0.519520	−	0.513085i
$549$	16.1745	+	4.33395i	0.690312	+	0.184969i
$550$	17.4022	−	7.14479i	0.742033	−	0.304655i
$551$	5.42021	+	3.12936i	0.230909	+	0.133315i
$552$	1.69957	−	3.99703i	0.0723385	−	0.170125i
$553$		0			0
$554$	−2.75972	−	0.372076i	−0.117249	−	0.0158080i
$555$	1.52977	+	5.70916i	0.0649349	+	0.242340i
$556$	8.18430	−	13.9738i	0.347092	−	0.592620i
$557$	−0.851813	+	3.17901i	−0.0360925	+	0.134699i	−0.981621	−	0.190840i	$-0.938879\pi$
$557$	−0.851813	+	3.17901i	−0.0360925	+	0.134699i	0.945529	+	0.325539i	$0.105546\pi$
$558$	0.398540	+	3.10187i	0.0168715	+	0.131313i
$559$	−11.6795			−0.493992
$560$		0			0
$561$	−17.1474			−0.723964
$562$	1.02139	+	7.94959i	0.0430849	+	0.335333i
$563$	4.41321	−	16.4703i	0.185994	−	0.694141i	−0.808421	−	0.588605i	$-0.799677\pi$
$563$	4.41321	−	16.4703i	0.185994	−	0.694141i	0.994415	−	0.105536i	$-0.0336558\pi$
$564$	−10.9429	−	6.40915i	−0.460779	−	0.269874i
$565$	2.17213	+	8.10650i	0.0913822	+	0.341043i
$566$	33.0242	+	4.45245i	1.38811	+	0.187151i
$567$		0			0
$568$	−2.17191	−	5.38531i	−0.0911315	−	0.225963i
$569$	6.92621	+	3.99885i	0.290362	+	0.167641i	0.638105	−	0.769949i	$-0.279719\pi$
$569$	6.92621	+	3.99885i	0.290362	+	0.167641i	−0.347743	+	0.937590i	$0.613052\pi$
$570$	−4.46733	+	1.83414i	−0.187116	+	0.0768238i
$571$	−30.1231	−	8.07146i	−1.26061	−	0.337780i	−0.434185	−	0.900824i	$-0.642964\pi$
$571$	−30.1231	−	8.07146i	−1.26061	−	0.337780i	−0.826427	+	0.563044i	$0.809630\pi$
$572$	50.5553	+	51.1894i	2.11382	+	2.14034i
$573$	−8.66753	−	8.66753i	−0.362091	−	0.362091i
$574$		0			0
$575$	6.35204			0.264899
$576$	20.5958	−	5.10792i	0.858157	−	0.212830i
$577$	21.7100	+	37.6028i	0.903798	+	1.56542i	0.822523	+	0.568732i	$0.192566\pi$
$577$	21.7100	+	37.6028i	0.903798	+	1.56542i	0.0812747	+	0.996692i	$0.474101\pi$
$578$	6.23425	−	14.9192i	0.259311	−	0.620555i
$579$	7.59893	−	2.03613i	0.315801	−	0.0846185i
$580$	1.46593	−	5.33765i	0.0608695	−	0.221634i
$581$		0			0
$582$	−2.09524	+	15.5405i	−0.0868503	+	0.644176i
$583$	0.318155	+	0.183687i	0.0131766	+	0.00760752i
$584$	−9.55488	+	12.2140i	−0.395384	+	0.505420i
$585$	24.2446	−	13.9976i	1.00239	−	0.578730i
$586$	20.9188	−	27.0868i	0.864149	−	1.11894i
$587$	18.2274	−	18.2274i	0.752326	−	0.752326i	−0.222587	−	0.974913i	$-0.571450\pi$
$587$	18.2274	−	18.2274i	0.752326	−	0.752326i	0.974913	+	0.222587i	$0.0714502\pi$
$588$		0			0
$589$	2.13362	+	2.13362i	0.0879143	+	0.0879143i
$590$	1.47126	+	11.4509i	0.0605708	+	0.471428i
$591$	0.0810624	+	0.140404i	0.00333446	+	0.00577546i
$592$	−17.4965	−	17.9382i	−0.719101	−	0.737254i
$593$	−19.8757	+	34.4257i	−0.816197	+	1.41370i	0.0922677	+	0.995734i	$0.470588\pi$
$593$	−19.8757	+	34.4257i	−0.816197	+	1.41370i	−0.908465	+	0.417961i	$0.862745\pi$
$594$	−20.4427	+	15.5853i	−0.838774	+	0.639471i
$595$		0			0
$596$	0.552793	+	0.971396i	0.0226433	+	0.0397899i
$597$	2.19718	+	8.19998i	0.0899246	+	0.335603i
$598$	9.22669	+	22.4730i	0.377307	+	0.918989i
$599$	32.5016	−	18.7648i	1.32798	−	0.766708i	0.342991	−	0.939339i	$-0.388560\pi$
$599$	32.5016	−	18.7648i	1.32798	−	0.766708i	0.984987	+	0.172631i	$0.0552267\pi$
$600$	−2.44501	−	3.24884i	−0.0998171	−	0.132633i
$601$		−	3.99899i		−	0.163122i	−0.996668	−	0.0815611i	$-0.974009\pi$
$601$		−	3.99899i		−	0.163122i	0.996668	−	0.0815611i	$-0.0259906\pi$
$602$		0			0
$603$	25.2240	−	25.2240i	1.02720	−	1.02720i
$604$	−5.28729	+	5.22179i	−0.215137	+	0.212472i
$605$	−7.76910	+	28.9947i	−0.315859	+	1.17880i
$606$	−1.31160	+	3.13879i	−0.0532802	+	0.127504i
$607$	−12.1836	+	21.1026i	−0.494517	+	0.856529i	−0.999980	−	0.00631933i	$-0.997988\pi$
$607$	−12.1836	+	21.1026i	−0.494517	+	0.856529i	0.505463	+	0.862848i	$0.331322\pi$
$608$	12.7151	−	16.0466i	0.515663	−	0.650776i
$609$		0			0
$610$	−8.66311	−	11.3631i	−0.350759	−	0.460080i
$611$	68.5144	−	18.3584i	2.77179	−	0.742700i
$612$	−7.15092	−	27.3687i	−0.289059	−	1.10631i
$613$	22.8354	+	6.11872i	0.922312	+	0.247133i	0.688573	−	0.725167i	$-0.258237\pi$
$613$	22.8354	+	6.11872i	0.922312	+	0.247133i	0.233739	+	0.972299i	$0.424904\pi$
$614$	−15.1933	−	11.7336i	−0.613152	−	0.473531i
$615$		−	0.248501i		−	0.0100205i
$616$		0			0
$617$			2.64202i			0.106364i	0.998585	+	0.0531819i	$0.0169363\pi$
$617$			2.64202i			0.106364i	−0.998585	+	0.0531819i	$0.983064\pi$
$618$	−3.94441	+	5.10743i	−0.158668	+	0.205451i
$619$	36.8516	+	9.87436i	1.48119	+	0.396884i	0.906752	−	0.421664i	$-0.138554\pi$
$619$	36.8516	+	9.87436i	1.48119	+	0.396884i	0.574439	+	0.818548i	$0.305220\pi$
$620$	1.34869	−	2.30273i	0.0541646	−	0.0924800i
$621$	−8.38421	+	2.24654i	−0.336447	+	0.0901507i
$622$	−21.5782	+	16.4510i	−0.865207	+	0.659623i
$623$		0			0
$624$	7.94260	−	13.3693i	0.317959	−	0.535202i
$625$	−3.43035	+	5.94155i	−0.137214	+	0.237662i
$626$	6.57606	+	2.74793i	0.262832	+	0.109830i
$627$	−3.01230	+	11.2421i	−0.120300	+	0.448964i
$628$	−0.0704267	+	11.3005i	−0.00281033	+	0.450940i
$629$	−23.6204	+	23.6204i	−0.941805	+	0.941805i
$630$		0			0
$631$		−	18.9710i		−	0.755223i	−0.925964	−	0.377611i	$-0.876746\pi$
$631$		−	18.9710i		−	0.755223i	0.925964	−	0.377611i	$-0.123254\pi$
$632$	2.06222	−	14.6075i	0.0820305	−	0.581057i
$633$	−5.57650	+	3.21960i	−0.221646	+	0.127967i
$634$	10.2238	−	4.19755i	0.406038	−	0.166706i
$635$	−7.32308	−	27.3301i	−0.290607	−	1.08456i
$636$	0.0210293	−	0.0765705i	0.000833867	−	0.00303622i
$637$		0			0
$638$	−8.08807	−	10.6089i	−0.320210	−	0.420009i
$639$	−2.72277	+	4.71597i	−0.107711	+	0.186561i
$640$	−16.5736	−	7.29248i	−0.655130	−	0.288261i
$641$	−15.6881	−	27.1726i	−0.619643	−	1.07325i	−0.989551	−	0.144184i	$-0.953944\pi$
$641$	−15.6881	−	27.1726i	−0.619643	−	1.07325i	0.369908	−	0.929068i	$-0.379389\pi$
$642$	−2.73000	+	0.350760i	−0.107744	+	0.0138434i
$643$	−13.5690	−	13.5690i	−0.535110	−	0.535110i	0.386978	−	0.922089i	$-0.373519\pi$
$643$	−13.5690	−	13.5690i	−0.535110	−	0.535110i	−0.922089	+	0.386978i	$0.873519\pi$
$644$		0			0
$645$	−1.18158	+	1.18158i	−0.0465245	+	0.0465245i
$646$	−21.6009	−	16.6822i	−0.849878	−	0.656352i
$647$	34.3455	−	19.8294i	1.35026	−	0.779573i	0.361974	−	0.932188i	$-0.382103\pi$
$647$	34.3455	−	19.8294i	1.35026	−	0.779573i	0.988286	+	0.152615i	$0.0487695\pi$
$648$	−13.3508	−	10.4442i	−0.524470	−	0.410286i
$649$	24.0965	+	13.9121i	0.945871	+	0.546099i
$650$	22.5386	+	3.03874i	0.884035	+	0.119189i
$651$		0			0
$652$	−8.28845	+	4.71671i	−0.324601	+	0.184721i
$653$	−4.05251	+	1.08587i	−0.158587	+	0.0424933i	−0.337239	−	0.941419i	$-0.609493\pi$
$653$	−4.05251	+	1.08587i	−0.158587	+	0.0424933i	0.178652	+	0.983912i	$0.442826\pi$
$654$	5.36137	+	2.24035i	0.209646	+	0.0876046i
$655$	−2.46608	−	4.27138i	−0.0963577	−	0.166896i
$656$	0.515351	+	0.918876i	0.0201211	+	0.0358761i
$657$	14.5426			0.567362
$658$		0			0
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	0.216391	−	0.976307i	$-0.430571\pi$
$659$	−19.5078	−	19.5078i	−0.759915	−	0.759915i	−0.976307	+	0.216391i	$0.930571\pi$
$660$	10.2931	+	0.0641486i	0.400660	+	0.00249698i
$661$	16.3569	+	4.38283i	0.636212	+	0.170472i	0.562487	−	0.826806i	$-0.309845\pi$
$661$	16.3569	+	4.38283i	0.636212	+	0.170472i	0.0737248	+	0.997279i	$0.476511\pi$
$662$	11.2053	+	27.2922i	0.435505	+	1.06074i
$663$	−17.9529	−	10.3651i	−0.697234	−	0.402548i
$664$	21.4990	+	9.14155i	0.834323	+	0.354761i
$665$		0			0
$666$	−3.13983	+	23.2884i	−0.121666	+	0.902407i
$667$	−1.16586	−	4.35104i	−0.0451422	−	0.168473i
$668$	6.28109	+	24.0396i	0.243023	+	0.930121i
$669$	−1.07764	+	4.02182i	−0.0416641	+	0.155493i
$670$	−30.1913	+	3.87909i	−1.16639	+	0.149862i
$671$	−34.4368			−1.32942
$672$		0			0
$673$	−30.9400			−1.19265			−0.596324	−	0.802744i	$-0.703373\pi$
$673$	−30.9400			−1.19265			−0.596324	+	0.802744i	$0.703373\pi$
$674$	−23.4404	+	3.01171i	−0.902890	+	0.116007i
$675$	−2.10313	+	7.84897i	−0.0809493	+	0.302107i
$676$	15.4150	+	58.9979i	0.592886	+	2.26915i
$677$	0.00451508	+	0.0168505i	0.000173529	+	0.000647617i	0.966013	−	0.258495i	$-0.0832266\pi$
$677$	0.00451508	+	0.0168505i	0.000173529	+	0.000647617i	−0.965839	+	0.259143i	$0.916560\pi$
$678$	0.584138	−	4.33260i	0.0224337	−	0.166393i
$679$		0			0
$680$	−9.44530	+	22.2133i	−0.362211	+	0.851843i
$681$	8.53625	+	4.92841i	0.327110	+	0.188857i
$682$	−2.44271	−	5.94959i	−0.0935361	−	0.227822i
$683$	19.3087	+	5.17376i	0.738829	+	0.197969i	0.608557	−	0.793510i	$-0.291749\pi$
$683$	19.3087	+	5.17376i	0.738829	+	0.197969i	0.130271	+	0.991478i	$0.458415\pi$
$684$	−19.1995	−	0.119654i	−0.734110	−	0.00457510i
$685$	9.67199	+	9.67199i	0.369548	+	0.369548i
$686$		0			0
$687$	−7.81864			−0.298300
$688$	1.91869	−	6.81949i	0.0731493	−	0.259991i
$689$	0.222067	+	0.384631i	0.00846008	+	0.0146533i
$690$	3.20694	+	1.34008i	0.122086	+	0.0510160i
$691$	43.0783	−	11.5428i	1.63878	−	0.439109i	0.682337	−	0.731038i	$-0.260964\pi$
$691$	43.0783	−	11.5428i	1.63878	−	0.439109i	0.956440	+	0.291929i	$0.0942972\pi$
$692$	22.7612	−	12.9527i	0.865250	−	0.492388i
$693$		0			0
$694$	11.0584	+	1.49094i	0.419773	+	0.0565954i
$695$	11.2228	+	6.47948i	0.425705	+	0.245781i
$696$	−1.77664	+	2.27108i	−0.0673433	+	0.0860851i
$697$	1.21627	−	0.702215i	0.0460696	−	0.0265983i
$698$	−28.4589	−	21.9785i	−1.07718	−	0.831898i
$699$	10.1873	−	10.1873i	0.385319	−	0.385319i
$700$		0			0
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	0.312816	−	0.949814i	$-0.398728\pi$
$701$	−16.8654	−	16.8654i	−0.636998	−	0.636998i	−0.949814	+	0.312816i	$0.898728\pi$
$702$	−30.8239	+	3.96037i	−1.16337	+	0.149475i
$703$	11.3364	+	19.6352i	0.427560	+	0.740556i
$704$	−38.1938	+	21.1091i	−1.43948	+	0.795580i
$705$	5.07410	−	8.78859i	0.191102	−	0.330998i
$706$	21.4627	+	28.1520i	0.807761	+	1.05951i
$707$		0			0
$708$	1.59273	−	5.79933i	0.0598583	−	0.217952i
$709$	7.91870	+	29.5530i	0.297393	+	1.10989i	0.939298	+	0.343102i	$0.111478\pi$
$709$	7.91870	+	29.5530i	0.297393	+	1.10989i	−0.641905	+	0.766784i	$0.721856\pi$
$710$	4.29855	−	1.76485i	0.161322	−	0.0662335i
$711$	−11.9811	+	6.91731i	−0.449328	+	0.259419i
$712$	17.7184	+	2.50139i	0.664024	+	0.0937434i
$713$		−	2.17168i		−	0.0813300i
$714$		0			0
$715$	−40.7102	+	40.7102i	−1.52248	+	1.52248i
$716$	−0.175480	+	28.1571i	−0.00655798	+	1.05228i
$717$	0.957679	−	3.57411i	0.0357652	−	0.133477i
$718$	23.4759	+	9.80983i	0.876111	+	0.366100i
$719$	20.1849	−	34.9613i	0.752769	−	1.30383i	−0.193706	−	0.981060i	$-0.562051\pi$
$719$	20.1849	−	34.9613i	0.752769	−	1.30383i	0.946476	−	0.322775i	$-0.104616\pi$
$720$	4.19012	+	16.4555i	0.156157	+	0.613260i
$721$		0			0
$722$	6.63661	−	5.05967i	0.246989	−	0.188302i
$723$	8.54857	−	2.29058i	0.317925	−	0.0851876i
$724$	7.26341	−	12.4015i	0.269942	−	0.460897i
$725$	−4.07327	−	1.09143i	−0.151277	−	0.0405347i
$726$	9.55764	−	12.3757i	0.354717	−	0.459306i
$727$			3.43634i			0.127447i	0.997968	+	0.0637234i	$0.0202976\pi$
$727$			3.43634i			0.127447i	−0.997968	+	0.0637234i	$0.979702\pi$
$728$		0			0
$729$			10.0029i			0.370476i
$730$	−9.82146	−	7.58501i	−0.363508	−	0.280734i
$731$	−9.12207	−	2.44425i	−0.337392	−	0.0904039i
$732$	1.88163	+	7.20157i	0.0695471	+	0.266178i
$733$	−37.3462	+	10.0069i	−1.37941	+	0.369613i	−0.870908	−	0.491446i	$-0.836469\pi$
$733$	−37.3462	+	10.0069i	−1.37941	+	0.369613i	−0.508506	+	0.861059i	$0.669802\pi$
$734$	−8.83805	−	11.5926i	−0.326218	−	0.427890i
$735$		0			0
$736$	−14.6373	+	1.69549i	−0.539540	+	0.0624967i
$737$	−36.6804	+	63.5323i	−1.35114	+	2.34024i
$738$	0.380928	−	0.911597i	0.0140222	−	0.0335563i
$739$	−10.3802	+	38.7393i	−0.381841	+	1.42505i	0.461247	+	0.887272i	$0.347402\pi$
$739$	−10.3802	+	38.7393i	−0.381841	+	1.42505i	−0.843087	+	0.537777i	$0.819264\pi$
$740$	14.2671	−	14.0903i	0.524467	−	0.517971i
$741$	−9.94932	+	9.94932i	−0.365497	+	0.365497i
$742$		0			0
$743$		−	34.1733i		−	1.25370i	−0.779141	−	0.626848i	$-0.784344\pi$
$743$		−	34.1733i		−	1.25370i	0.779141	−	0.626848i	$-0.215656\pi$
$744$	−1.11073	+	0.835916i	−0.0407215	+	0.0306462i
$745$	−0.774565	+	0.447195i	−0.0283779	+	0.0163840i
$746$	−12.1959	−	29.7049i	−0.446523	−	1.08757i
$747$	−5.67032	−	21.1619i	−0.207466	−	0.774274i
$748$	28.7725	+	50.5605i	1.05203	+	1.84867i
$749$		0			0
$750$	7.89309	−	6.01760i	0.288215	−	0.219732i
$751$	−4.27895	+	7.41136i	−0.156141	+	0.270445i	−0.933474	−	0.358645i	$-0.883239\pi$
$751$	−4.27895	+	7.41136i	−0.156141	+	0.270445i	0.777333	+	0.629090i	$0.216572\pi$
$752$	−0.536240	+	43.0203i	−0.0195547	+	1.56879i
$753$	−4.91577	−	8.51437i	−0.179141	−	0.310281i
$754$	−2.05526	−	15.9962i	−0.0748481	−	0.582549i
$755$	−4.20490	−	4.20490i	−0.153032	−	0.153032i
$756$		0			0
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	−0.996306	−	0.0858779i	$-0.972631\pi$
$757$	−25.0492	+	25.0492i	−0.910428	+	0.910428i	0.0858779	+	0.996306i	$0.472631\pi$
$758$	−19.3053	+	24.9975i	−0.701202	+	0.907952i
$759$	7.25431	−	4.18827i	0.263315	−	0.152025i
$760$	12.9041	+	10.0947i	0.468080	+	0.366173i
$761$	24.6145	+	14.2112i	0.892274	+	0.515155i	0.874686	−	0.484691i	$-0.161068\pi$
$761$	24.6145	+	14.2112i	0.892274	+	0.515155i	0.0175884	+	0.999845i	$0.494401\pi$
$762$	−1.96935	+	14.6069i	−0.0713421	+	0.529151i
$763$		0			0
$764$	−11.0132	+	40.1006i	−0.398445	+	1.45079i
$765$	21.8651	−	5.85873i	0.790533	−	0.211823i
$766$	−10.0128	+	23.9617i	−0.361779	+	0.865771i
$767$	16.8190	+	29.1314i	0.607299	+	1.05187i
$768$	6.50135	+	6.83384i	0.234597	+	0.246595i
$769$	12.0189			0.433413			0.216707	−	0.976237i	$-0.430469\pi$
$769$	12.0189			0.433413			0.216707	+	0.976237i	$0.430469\pi$
$770$		0			0
$771$	8.50286	+	8.50286i	0.306223	+	0.306223i
$772$	−18.7543	−	18.9895i	−0.674982	−	0.683448i
$773$	6.92456	+	1.85543i	0.249059	+	0.0667352i	0.381189	−	0.924497i	$-0.375515\pi$
$773$	6.92456	+	1.85543i	0.249059	+	0.0667352i	−0.132130	+	0.991232i	$0.542182\pi$
$774$	−6.14572	+	2.52323i	−0.220903	+	0.0906958i
$775$	−1.76066	−	1.01652i	−0.0632449	−	0.0365145i
$776$	49.3382	−	19.8983i	1.77114	−	0.714306i
$777$		0			0
$778$	27.6604	+	3.72929i	0.991675	+	0.133701i
$779$	−0.246718	−	0.920763i	−0.00883957	−	0.0329897i
$780$	10.7379	+	6.28908i	0.384479	+	0.225185i
$781$	2.89849	−	10.8173i	0.103716	−	0.387074i
$782$	2.50325	+	19.4830i	0.0895160	+	0.696711i
$783$	5.76241			0.205932
$784$		0			0
$785$	−9.04315			−0.322764
$786$	0.327417	+	2.54831i	0.0116786	+	0.0908954i
$787$	−6.20908	+	23.1726i	−0.221330	+	0.826014i	0.762512	+	0.646974i	$0.223966\pi$
$787$	−6.20908	+	23.1726i	−0.221330	+	0.826014i	−0.983842	+	0.179040i	$0.942701\pi$
$788$	0.277974	−	0.474610i	0.00990243	−	0.0169073i
$789$	3.56200	+	13.2936i	0.126810	+	0.473263i
$790$	11.6994	+	1.57736i	0.416246	+	0.0561199i
$791$		0			0
$792$	37.6609	+	16.0137i	1.33822	+	0.569023i
$793$	−36.0546	−	20.8161i	−1.28033	−	0.739202i
$794$	2.08723	−	0.856948i	0.0740730	−	0.0304120i
$795$	0.0613774	+	0.0164460i	0.00217683	+	0.000583281i
$796$	20.4916	−	20.2377i	0.726304	−	0.717307i
$797$	−35.5609	−	35.5609i	−1.25963	−	1.25963i	−0.951268	−	0.308366i	$-0.900218\pi$
$797$	−35.5609	−	35.5609i	−1.25963	−	1.25963i	−0.308366	−	0.951268i	$-0.599782\pi$
$798$		0			0
$799$	57.3537			2.02903
$800$	−5.47685	+	12.6607i	−0.193636	+	0.447623i
$801$	−8.39042	−	14.5326i	−0.296461	−	0.513486i
$802$	−7.82290	+	18.7209i	−0.276236	+	0.661059i
$803$	−28.8883	+	7.74059i	−1.01944	+	0.273159i
$804$	15.2904	+	4.19934i	0.539249	+	0.148099i
$805$		0			0
$806$	1.03890	−	7.70563i	0.0365938	−	0.271419i
$807$	−15.9352	−	9.20019i	−0.560945	−	0.323862i
$808$	11.4558	−	1.39936i	0.403012	−	0.0492295i
$809$	10.2729	−	5.93106i	0.361176	−	0.208525i	−0.308421	−	0.951250i	$-0.599800\pi$
$809$	10.2729	−	5.93106i	0.361176	−	0.208525i	0.669596	+	0.742725i	$0.266467\pi$
$810$	8.29096	−	10.7356i	0.291315	−	0.377209i
$811$	−20.4859	+	20.4859i	−0.719357	+	0.719357i	−0.968473	−	0.249117i	$-0.919860\pi$
$811$	−20.4859	+	20.4859i	−0.719357	+	0.719357i	0.249117	+	0.968473i	$0.419860\pi$
$812$		0			0
$813$	0.610240	+	0.610240i	0.0214020	+	0.0214020i
$814$	−6.15856	−	47.9326i	−0.215857	−	1.68004i
$815$	−3.81570	−	6.60898i	−0.133658	−	0.231503i
$816$	9.00129	−	8.77966i	0.315108	−	0.307350i
$817$	−3.20496	+	5.55116i	−0.112127	+	0.194210i
$818$	−44.1445	+	33.6552i	−1.54347	+	1.17673i
$819$		0			0
$820$	−0.732724	+	0.416972i	−0.0255878	+	0.0145613i
$821$	−10.6406	−	39.7113i	−0.371360	−	1.38594i	−0.858591	−	0.512662i	$-0.828659\pi$
$821$	−10.6406	−	39.7113i	−0.371360	−	1.38594i	0.487230	−	0.873274i	$-0.338007\pi$
$822$	−2.70620	−	6.59137i	−0.0943897	−	0.229900i
$823$	44.4787	−	25.6798i	1.55043	−	0.895140i	0.552322	−	0.833631i	$-0.313742\pi$
$823$	44.4787	−	25.6798i	1.55043	−	0.895140i	0.998107	−	0.0615092i	$-0.0195913\pi$
$824$	21.6782	+	3.06041i	0.755195	+	0.106614i
$825$		−	7.84180i		−	0.273016i
$826$		0			0
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	−0.990122	−	0.140210i	$-0.955222\pi$
$827$	−24.4414	+	24.4414i	−0.849912	+	0.849912i	0.140210	+	0.990122i	$0.455222\pi$
$828$	9.71008	+	9.83187i	0.337449	+	0.341681i
$829$	4.16759	−	15.5537i	0.144746	−	0.540201i	−0.855020	−	0.518595i	$-0.826455\pi$
$829$	4.16759	−	15.5537i	0.144746	−	0.540201i	0.999767	−	0.0216062i	$-0.00687801\pi$
$830$	−7.20795	+	17.2493i	−0.250192	+	0.598732i
$831$	−0.580404	+	1.00529i	−0.0201340	+	0.0348731i
$832$	−52.7479	−	0.986303i	−1.82870	−	0.0341939i
$833$		0			0
$834$	−4.09279	−	5.36838i	−0.141722	−	0.185892i
$835$	−19.2054	+	5.14608i	−0.664632	+	0.178087i
$836$	38.2026	−	9.98160i	1.32126	−	0.345221i
$837$	2.68346	+	0.719031i	0.0927539	+	0.0248533i
$838$	−6.98809	−	5.39683i	−0.241400	−	0.186430i
$839$		−	35.2906i		−	1.21837i	−0.793029	−	0.609184i	$-0.791497\pi$
$839$		−	35.2906i		−	1.21837i	0.793029	−	0.609184i	$-0.208503\pi$
$840$		0			0
$841$		−	26.0096i		−	0.896881i
$842$	9.26007	−	11.9904i	0.319123	−	0.413217i
$843$	3.22722	+	0.864730i	0.111151	+	0.0297829i
$844$	18.8503	+	11.0404i	0.648855	+	0.380028i
$845$	−47.1339	+	12.6295i	−1.62146	+	0.434468i
$846$	32.0858	−	24.4619i	1.10313	−	0.841016i
$847$		0			0
$848$	−0.261061	+	0.0664749i	−0.00896486	+	0.00228276i
$849$	6.94542	−	12.0298i	0.238366	−	0.412862i
$850$	16.9673	+	7.09013i	0.581975	+	0.243189i
$851$	4.22342	−	15.7620i	0.144777	−	0.540315i
$852$	−2.42054	−	0.0150852i	−0.0829262	−	0.000516810i
$853$	6.93449	−	6.93449i	0.237432	−	0.237432i	−0.578354	−	0.815786i	$-0.696305\pi$
$853$	6.93449	−	6.93449i	0.237432	−	0.237432i	0.815786	+	0.578354i	$0.196305\pi$
$854$		0			0
$855$		−	15.3642i		−	0.525445i
$856$	5.61505	+	7.46106i	0.191918	+	0.255014i
$857$	−25.2698	+	14.5895i	−0.863200	+	0.498369i	−0.865083	−	0.501630i	$-0.832734\pi$
$857$	−25.2698	+	14.5895i	−0.863200	+	0.498369i	0.00188263	+	0.999998i	$0.499401\pi$
$858$	27.7436	−	11.3906i	0.947151	−	0.388870i
$859$	0.595210	+	2.22135i	0.0203083	+	0.0757916i	0.975336	−	0.220724i	$-0.0708420\pi$
$859$	0.595210	+	2.22135i	0.0203083	+	0.0757916i	−0.955028	+	0.296516i	$0.904175\pi$
$860$	5.46660	+	1.50135i	0.186409	+	0.0511955i
$861$		0			0
$862$	−15.8962	−	20.8505i	−0.541426	−	0.710171i
$863$	16.8529	−	29.1902i	0.573681	−	0.993645i	−0.422503	−	0.906362i	$-0.638848\pi$
$863$	16.8529	−	29.1902i	0.573681	−	0.993645i	0.996184	−	0.0872830i	$-0.0278184\pi$
$864$	2.75129	−	18.6482i	0.0936007	−	0.634423i
$865$	10.4784	+	18.1491i	0.356277	+	0.617090i
$866$	10.1160	−	1.29974i	0.343756	−	0.0441671i
$867$	−4.76608	−	4.76608i	−0.161864	−	0.161864i
$868$		0			0
$869$	20.1181	−	20.1181i	0.682460	−	0.682460i
$870$	−1.82620	−	1.41036i	−0.0619141	−	0.0478156i
$871$	−76.8070	+	44.3445i	−2.60251	+	1.50256i
$872$	−2.39026	−	19.5676i	−0.0809443	−	0.662643i
$873$	−43.2060	−	24.9450i	−1.46230	−	0.844260i
$874$	13.2130	+	1.78143i	0.446938	+	0.0602579i
$875$		0			0
$876$	3.19720	+	5.61829i	0.108024	+	0.189824i
$877$	34.6760	−	9.29142i	1.17093	−	0.313749i	0.379605	−	0.925149i	$-0.376060\pi$
$877$	34.6760	−	9.29142i	1.17093	−	0.313749i	0.791322	+	0.611400i	$0.209393\pi$
$878$	−19.7837	−	8.26701i	−0.667669	−	0.278998i
$879$	−7.13324	−	12.3551i	−0.240598	−	0.416728i
$880$	−17.0822	−	30.4578i	−0.575842	−	1.02673i
$881$	−13.0482			−0.439606			−0.219803	−	0.975544i	$-0.570541\pi$
$881$	−13.0482			−0.439606			−0.219803	+	0.975544i	$0.570541\pi$
$882$		0			0
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	0.168325	−	0.985732i	$-0.446164\pi$
$883$	−24.2895	−	24.2895i	−0.817407	−	0.817407i	−0.985732	+	0.168325i	$0.946164\pi$
$884$	−0.438295	+	70.3278i	−0.0147415	+	2.36538i
$885$	4.64863	+	1.24560i	0.156262	+	0.0418702i
$886$	1.60843	+	3.91758i	0.0540363	+	0.131614i
$887$	−17.1896	−	9.92445i	−0.577172	−	0.333230i	0.182837	−	0.983143i	$-0.441472\pi$
$887$	−17.1896	−	9.92445i	−0.577172	−	0.333230i	−0.760009	+	0.649913i	$0.774805\pi$
$888$	−9.68736	+	3.90695i	−0.325087	+	0.131109i
$889$		0			0
$890$	−1.91327	+	14.1909i	−0.0641331	+	0.475680i
$891$	−8.46102	−	31.5770i	−0.283455	−	1.05787i
$892$	13.6669	−	3.57089i	0.457601	−	0.119562i
$893$	10.0754	−	37.6018i	0.337160	−	1.25830i
$894$	0.462108	−	0.0593733i	0.0154552	−	0.00198574i
$895$	−22.5325			−0.753178
$896$		0			0
$897$	10.1268			0.338124
$898$	−6.02466	+	0.774070i	−0.201045	+	0.0258311i
$899$	−0.373145	+	1.39260i	−0.0124451	+	0.0464457i
$900$	12.5162	−	3.27023i	0.417206	−	0.109008i
$901$	0.0929467	+	0.346882i	0.00309650	+	0.0115563i
$902$	−0.271481	+	2.01360i	−0.00903935	+	0.0670456i
$903$		0			0
$904$	−13.7552	+	5.54751i	−0.457491	+	0.184508i
$905$	9.96000	+	5.75041i	0.331082	+	0.191150i
$906$	1.17652	+	2.86560i	0.0390874	+	0.0952032i
$907$	54.1242	+	14.5025i	1.79716	+	0.481549i	0.993530	−	0.113573i	$-0.0362296\pi$
$907$	54.1242	+	14.5025i	1.79716	+	0.481549i	0.803635	+	0.595122i	$0.202896\pi$
$908$	0.208400	−	33.4394i	0.00691600	−	1.10973i
$909$	−7.65297	−	7.65297i	−0.253833	−	0.253833i
$910$		0			0
$911$	11.6260			0.385188			0.192594	−	0.981279i	$-0.438310\pi$
$911$	11.6260			0.385188			0.192594	+	0.981279i	$0.438310\pi$
$912$	−4.17479	−	7.44369i	−0.138241	−	0.246485i
$913$	22.5277	+	39.0191i	0.745557	+	1.29134i
$914$	−36.2536	−	15.1492i	−1.19916	−	0.501092i
$915$	−5.75339	+	1.54162i	−0.190201	+	0.0509643i
$916$	13.1193	+	23.0539i	0.433474	+	0.761722i
$917$		0			0
$918$	−24.9032	−	3.35754i	−0.821928	−	0.110815i
$919$	36.4646	+	21.0528i	1.20285	+	0.694468i	0.961189	−	0.275891i	$-0.0889729\pi$
$919$	36.4646	+	21.0528i	1.20285	+	0.694468i	0.241666	+	0.970360i	$0.422306\pi$
$920$	−1.42975	−	11.7045i	−0.0471374	−	0.385886i
$921$	−6.93014	+	4.00112i	−0.228356	+	0.131841i
$922$	−10.3033	−	7.95715i	−0.339322	−	0.262055i
$923$	9.57342	−	9.57342i	0.315113	−	0.315113i
$924$		0			0
$925$	−10.8020	−	10.8020i	−0.355167	−	0.355167i
$926$	54.8475	−	7.04701i	1.80240	−	0.231579i
$927$	−10.2656	−	17.7805i	−0.337165	−	0.583988i
$928$	9.67757	+	1.42780i	0.317682	+	0.0468697i
$929$	15.1619	−	26.2612i	0.497447	−	0.861603i	−0.502549	−	0.864549i	$-0.667604\pi$
$929$	15.1619	−	26.2612i	0.497447	−	0.861603i	0.999996	+	0.00294569i	$0.000937644\pi$
$930$	−0.674449	−	0.884653i	−0.0221160	−	0.0290089i
$931$		0			0
$932$	−47.1319	−	12.9443i	−1.54386	−	0.424005i
$933$	2.92748	+	10.9255i	0.0958414	+	0.357685i
$934$	−30.4566	+	12.5045i	−0.996570	+	0.409159i
$935$	−40.3156	+	23.2762i	−1.31846	+	0.761213i
$936$	29.7502	+	39.5310i	0.972417	+	1.29211i
$937$		−	17.7772i		−	0.580757i	−0.956912	−	0.290378i	$-0.906219\pi$
$937$		−	17.7772i		−	0.580757i	0.956912	−	0.290378i	$-0.0937812\pi$
$938$		0			0
$939$	2.10079	−	2.10079i	0.0685567	−	0.0685567i
$940$	−34.4280	−	0.214561i	−1.12292	−	0.00699820i
$941$	7.74494	−	28.9045i	0.252478	−	0.942260i	−0.716998	−	0.697075i	$-0.754484\pi$
$941$	7.74494	−	28.9045i	0.252478	−	0.942260i	0.969476	−	0.245186i	$-0.0788489\pi$
$942$	4.34654	+	1.81628i	0.141618	+	0.0591777i
$943$	−0.343034	+	0.594153i	−0.0111707	+	0.0193483i
$944$	−19.7723	+	5.03470i	−0.643533	+	0.163865i
$945$		0			0
$946$	10.8652	−	8.28347i	0.353257	−	0.269319i
$947$	−16.1871	+	4.33732i	−0.526010	+	0.140944i	−0.512045	−	0.858959i	$-0.671112\pi$
$947$	−16.1871	+	4.33732i	−0.526010	+	0.140944i	−0.0139648	+	0.999902i	$0.504445\pi$
$948$	−5.30644	−	3.10793i	−0.172345	−	0.100941i
$949$	−34.9243	−	9.35794i	−1.13369	−	0.303772i
$950$	7.62904	−	9.87848i	0.247519	−	0.320500i
$951$		−	4.60704i		−	0.149394i
$952$		0			0
$953$		−	14.1855i		−	0.459513i	−0.973248	−	0.229757i	$-0.926207\pi$
$953$		−	14.1855i		−	0.459513i	0.973248	−	0.229757i	$-0.0737930\pi$
$954$	0.199946	+	0.154416i	0.00647349	+	0.00499941i
$955$	−32.1438	−	8.61292i	−1.04015	−	0.278707i
$956$	−12.1455	+	3.17338i	−0.392813	+	0.102634i
$957$	−5.37149	+	1.43929i	−0.173636	+	0.0465255i
$958$	31.9444	+	41.9004i	1.03208	+	1.35374i
$959$		0			0
$960$	−5.43609	+	5.23653i	−0.175449	+	0.169008i
$961$	15.1525	−	26.2448i	0.488789	−	0.846608i
$962$	22.5261	−	53.9070i	0.726269	−	1.73803i
$963$	2.26647	−	8.45857i	0.0730359	−	0.272574i
$964$	−21.0980	−	21.3627i	−0.679522	−	0.688045i
$965$	15.1021	−	15.1021i	0.486154	−	0.486154i
$966$		0			0
$967$			8.54873i			0.274909i	0.990508	+	0.137454i	$0.0438920\pi$
$967$			8.54873i			0.274909i	−0.990508	+	0.137454i	$0.956108\pi$
$968$	−52.5280	−	7.41563i	−1.68832	−	0.238347i
$969$	−9.85287	+	5.68855i	−0.316520	+	0.182743i
$970$	16.1689	+	39.3817i	0.519151	+	1.26447i
$971$	9.33690	+	34.8458i	0.299635	+	1.11825i	0.937466	+	0.348077i	$0.113165\pi$
$971$	9.33690	+	34.8458i	0.299635	+	1.11825i	−0.637831	+	0.770177i	$0.720168\pi$
$972$	−23.5180	+	13.3834i	−0.754341	+	0.429273i
$973$		0			0
$974$	43.2111	−	32.9437i	1.38457	−	1.05558i
$975$	4.74015	−	8.21018i	0.151806	−	0.262936i
$976$	18.0771	−	17.6320i	0.578635	−	0.564387i
$977$	−6.61877	−	11.4640i	−0.211753	−	0.366767i	0.740510	−	0.672045i	$-0.234584\pi$
$977$	−6.61877	−	11.4640i	−0.211753	−	0.366767i	−0.952263	+	0.305278i	$0.901251\pi$
$978$	0.506603	+	3.94294i	0.0161994	+	0.126081i
$979$	24.4025	+	24.4025i	0.779906	+	0.779906i
$980$		0			0
$981$	−13.0721	+	13.0721i	−0.417359	+	0.417359i
$982$	−11.6419	+	15.0745i	−0.371507	+	0.481046i
$983$	17.2541	−	9.96166i	0.550320	−	0.317727i	−0.198931	−	0.980014i	$-0.563747\pi$
$983$	17.2541	−	9.96166i	0.550320	−	0.317727i	0.749251	+	0.662286i	$0.230414\pi$
$984$	0.435927	−	0.0532501i	0.0138968	−	0.00169755i
$985$	0.381174	+	0.220071i	0.0121452	+	0.00701205i
$986$	1.74242	−	12.9237i	0.0554899	−	0.411573i
$987$		0			0
$988$	46.0308	+	12.6419i	1.46444	+	0.402193i
$989$	4.45615	−	1.19402i	0.141697	−	0.0379677i
$990$	−12.6265	+	30.2165i	−0.401298	+	0.960344i
$991$	−27.1797	−	47.0767i	−0.863392	−	1.49544i	−0.868635	−	0.495453i	$-0.835002\pi$
$991$	−27.1797	−	47.0767i	−0.863392	−	1.49544i	0.00524220	−	0.999986i	$-0.498331\pi$
$992$	4.32852	+	1.87246i	0.137431	+	0.0594507i
$993$	12.2984			0.390278
$994$		0			0
$995$	16.2966	+	16.2966i	0.516638	+	0.516638i
$996$	6.92892	−	6.84309i	0.219551	−	0.216832i
$997$	19.6751	+	5.27193i	0.623117	+	0.166964i	0.556544	−	0.830818i	$-0.312127\pi$
$997$	19.6751	+	5.27193i	0.623117	+	0.166964i	0.0665726	+	0.997782i	$0.478794\pi$
$998$	18.0978	−	7.43039i	0.572877	−	0.235205i
$999$	18.0782	+	10.4374i	0.571968	+	0.330226i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.m.765.1		24
7.2	even	3		784.2.m.h.589.5		12
7.3	odd	6		784.2.x.l.557.4		24
7.4	even	3	inner	784.2.x.m.557.4		24
7.5	odd	6		112.2.m.d.29.5	✓	12
7.6	odd	2		784.2.x.l.765.1		24
16.5	even	4	inner	784.2.x.m.373.4		24
28.19	even	6		448.2.m.d.337.4		12
56.5	odd	6		896.2.m.g.673.4		12
56.19	even	6		896.2.m.h.673.3		12
112.5	odd	12		112.2.m.d.85.5	yes	12
112.19	even	12		896.2.m.h.225.3		12
112.37	even	12		784.2.m.h.197.5		12
112.53	even	12	inner	784.2.x.m.165.1		24
112.61	odd	12		896.2.m.g.225.4		12
112.69	odd	4		784.2.x.l.373.4		24
112.75	even	12		448.2.m.d.113.4		12
112.101	odd	12		784.2.x.l.165.1		24
224.5	odd	24		7168.2.a.bj.1.6		12
224.75	even	24		7168.2.a.bi.1.6		12
224.117	odd	24		7168.2.a.bj.1.7		12
224.187	even	24		7168.2.a.bi.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.d.29.5	✓	12	7.5	odd	6
112.2.m.d.85.5	yes	12	112.5	odd	12
448.2.m.d.113.4		12	112.75	even	12
448.2.m.d.337.4		12	28.19	even	6
784.2.m.h.197.5		12	112.37	even	12
784.2.m.h.589.5		12	7.2	even	3
784.2.x.l.165.1		24	112.101	odd	12
784.2.x.l.373.4		24	112.69	odd	4
784.2.x.l.557.4		24	7.3	odd	6
784.2.x.l.765.1		24	7.6	odd	2
784.2.x.m.165.1		24	112.53	even	12	inner
784.2.x.m.373.4		24	16.5	even	4	inner
784.2.x.m.557.4		24	7.4	even	3	inner
784.2.x.m.765.1		24	1.1	even	1	trivial
896.2.m.g.225.4		12	112.61	odd	12
896.2.m.g.673.4		12	56.5	odd	6
896.2.m.h.225.3		12	112.19	even	12
896.2.m.h.673.3		12	56.19	even	6
7168.2.a.bi.1.6		12	224.75	even	24
7168.2.a.bi.1.7		12	224.187	even	24
7168.2.a.bj.1.6		12	224.5	odd	24
7168.2.a.bj.1.7		12	224.117	odd	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40268 + 0.180222i) q^{2} +(-0.152579 + 0.569433i) q^{3} +(1.93504 - 0.505589i) q^{4} +(0.414228 + 1.54592i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(2.29710 + 1.32623i) q^{9} +O(q^{10})\)	\(q+(-1.40268 + 0.180222i) q^{2} +(-0.152579 + 0.569433i) q^{3} +(1.93504 - 0.505589i) q^{4} +(0.414228 + 1.54592i) q^{5} +(0.111396 - 0.826233i) q^{6} +(-2.62313 + 1.05792i) q^{8} +(2.29710 + 1.32623i) q^{9} +(-0.859639 - 2.09378i) q^{10} +(-5.26900 - 1.41182i) q^{11} +(-0.00734784 + 1.17902i) q^{12} +(-4.66311 - 4.66311i) q^{13} -0.943500 q^{15} +(3.48876 - 1.95667i) q^{16} +(-2.66615 - 4.61791i) q^{17} +(-3.46112 - 1.44630i) q^{18} +(-3.49592 + 0.936730i) q^{19} +(1.58315 + 2.78199i) q^{20} +(7.64518 + 1.03075i) q^{22} +(2.25586 + 1.30242i) q^{23} +(-0.202178 - 1.65511i) q^{24} +(2.11185 - 1.21928i) q^{25} +(7.38127 + 5.70048i) q^{26} +(-2.35625 + 2.35625i) q^{27} +(-1.22279 - 1.22279i) q^{29} +(1.32343 - 0.170039i) q^{30} +(-0.416854 - 0.722013i) q^{31} +(-4.54099 + 3.37334i) q^{32} +(1.60788 - 2.78493i) q^{33} +(4.57201 + 5.99696i) q^{34} +(5.11551 + 1.40492i) q^{36} +(-1.62137 - 6.05105i) q^{37} +(4.73485 - 1.94398i) q^{38} +(3.36683 - 1.94384i) q^{39} +(-2.72203 - 3.61693i) q^{40} +0.263382i q^{41} +(1.25233 - 1.25233i) q^{43} +(-10.9095 - 0.0679900i) q^{44} +(-1.09872 + 4.10050i) q^{45} +(-3.39898 - 1.42033i) q^{46} +(-5.37795 + 9.31488i) q^{47} +(0.581880 + 2.28516i) q^{48} +(-2.74251 + 2.09086i) q^{50} +(3.03639 - 0.813598i) q^{51} +(-11.3809 - 6.66570i) q^{52} +(-0.0650529 - 0.0174309i) q^{53} +(2.88043 - 3.72973i) q^{54} -8.73026i q^{55} -2.13362i q^{57} +(1.93556 + 1.49482i) q^{58} +(-4.92700 - 1.32019i) q^{59} +(-1.82571 + 0.477023i) q^{60} +(6.09793 - 1.63393i) q^{61} +(0.714837 + 0.937629i) q^{62} +(5.76162 - 5.55011i) q^{64} +(5.27720 - 9.14038i) q^{65} +(-1.75344 + 4.19615i) q^{66} +(3.48077 - 12.9904i) q^{67} +(-7.49387 - 7.58786i) q^{68} +(-1.08584 + 1.08584i) q^{69} +2.05301i q^{71} +(-7.42864 - 1.04874i) q^{72} +(4.74814 - 2.74134i) q^{73} +(3.36480 + 8.19549i) q^{74} +(0.372072 + 1.38859i) q^{75} +(-6.29115 + 3.58011i) q^{76} +(-4.37227 + 3.33337i) q^{78} +(-2.60788 + 4.51698i) q^{79} +(4.46999 + 4.58283i) q^{80} +(2.99648 + 5.19006i) q^{81} +(-0.0474672 - 0.369441i) q^{82} +(-5.84045 - 5.84045i) q^{83} +(6.03452 - 6.03452i) q^{85} +(-1.53093 + 1.98232i) q^{86} +(0.882871 - 0.509726i) q^{87} +(15.3149 - 1.87077i) q^{88} +(-5.47892 - 3.16326i) q^{89} +(0.802163 - 5.94971i) q^{90} +(5.02367 + 1.37970i) q^{92} +(0.474741 - 0.127207i) q^{93} +(5.86481 - 14.0351i) q^{94} +(-2.89622 - 5.01639i) q^{95} +(-1.22803 - 3.10049i) q^{96} -18.8089 q^{97} +(-10.2310 - 10.2310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8	\( 24 q - 2 q^{2} + 4 q^{3} + 6 q^{4} + 4 q^{5} - 8 q^{6} - 8 q^{8} - 4 q^{10} + 8 q^{12} - 48 q^{15} - 10 q^{16} - 8 q^{17} + 40 q^{20} + 28 q^{22} - 8 q^{24} - 20 q^{26} - 8 q^{27} - 8 q^{29} + 28 q^{30} - 8 q^{31} - 12 q^{32} - 16 q^{34} - 32 q^{36} + 20 q^{37} + 16 q^{38} - 8 q^{40} + 32 q^{43} - 14 q^{44} + 40 q^{45} + 28 q^{46} + 16 q^{47} - 32 q^{48} + 88 q^{50} + 16 q^{51} - 16 q^{52} - 4 q^{53} + 64 q^{54} - 14 q^{58} - 16 q^{59} - 60 q^{60} - 20 q^{61} - 16 q^{62} - 36 q^{64} - 32 q^{65} + 12 q^{66} - 24 q^{67} - 28 q^{68} + 8 q^{69} - 6 q^{72} + 38 q^{74} - 40 q^{75} - 96 q^{76} - 152 q^{78} - 24 q^{79} + 24 q^{80} + 44 q^{81} - 16 q^{82} + 40 q^{83} - 16 q^{85} - 38 q^{86} + 14 q^{88} + 80 q^{90} + 64 q^{92} + 48 q^{93} - 24 q^{94} - 16 q^{96} - 96 q^{97} + 64 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 + 4 * q^3 + 6 * q^4 + 4 * q^5 - 8 * q^6 - 8 * q^8 - 4 * q^10 + 8 * q^12 - 48 * q^15 - 10 * q^16 - 8 * q^17 + 40 * q^20 + 28 * q^22 - 8 * q^24 - 20 * q^26 - 8 * q^27 - 8 * q^29 + 28 * q^30 - 8 * q^31 - 12 * q^32 - 16 * q^34 - 32 * q^36 + 20 * q^37 + 16 * q^38 - 8 * q^40 + 32 * q^43 - 14 * q^44 + 40 * q^45 + 28 * q^46 + 16 * q^47 - 32 * q^48 + 88 * q^50 + 16 * q^51 - 16 * q^52 - 4 * q^53 + 64 * q^54 - 14 * q^58 - 16 * q^59 - 60 * q^60 - 20 * q^61 - 16 * q^62 - 36 * q^64 - 32 * q^65 + 12 * q^66 - 24 * q^67 - 28 * q^68 + 8 * q^69 - 6 * q^72 + 38 * q^74 - 40 * q^75 - 96 * q^76 - 152 * q^78 - 24 * q^79 + 24 * q^80 + 44 * q^81 - 16 * q^82 + 40 * q^83 - 16 * q^85 - 38 * q^86 + 14 * q^88 + 80 * q^90 + 64 * q^92 + 48 * q^93 - 24 * q^94 - 16 * q^96 - 96 * q^97 + 64 * q^99

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