LMFDB - Embedded newform 672.2.bo.a.125.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.8
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39544 - 0.229683i) q^{2} +(1.71200 + 0.262778i) q^{3} +(1.89449 + 0.641017i) q^{4} +(0.321849 + 0.777011i) q^{5} +(-2.32863 - 0.759907i) q^{6} +(0.967393 + 2.46255i) q^{7} +(-2.49641 - 1.32963i) q^{8} +(2.86190 + 0.899751i) q^{9} +O(q^{10})$	\(q+(-1.39544 - 0.229683i) q^{2} +(1.71200 + 0.262778i) q^{3} +(1.89449 + 0.641017i) q^{4} +(0.321849 + 0.777011i) q^{5} +(-2.32863 - 0.759907i) q^{6} +(0.967393 + 2.46255i) q^{7} +(-2.49641 - 1.32963i) q^{8} +(2.86190 + 0.899751i) q^{9} +(-0.270653 - 1.15819i) q^{10} +(-0.599335 - 1.44692i) q^{11} +(3.07493 + 1.59525i) q^{12} +(1.13642 + 0.470719i) q^{13} +(-0.784330 - 3.65853i) q^{14} +(0.346824 + 1.41482i) q^{15} +(3.17820 + 2.42880i) q^{16} +0.165815i q^{17} +(-3.78694 - 1.91288i) q^{18} +(1.27301 + 0.527297i) q^{19} +(0.111662 + 1.67835i) q^{20} +(1.00907 + 4.47010i) q^{21} +(0.504001 + 2.15675i) q^{22} +(-1.24300 + 1.24300i) q^{23} +(-3.92447 - 2.93233i) q^{24} +(3.03537 - 3.03537i) q^{25} +(-1.47768 - 0.917874i) q^{26} +(4.66313 + 2.29242i) q^{27} +(0.254181 + 5.28539i) q^{28} +(-2.41071 + 5.81996i) q^{29} +(-0.159011 - 2.05395i) q^{30} +2.57708i q^{31} +(-3.87712 - 4.11922i) q^{32} +(-0.645844 - 2.63463i) q^{33} +(0.0380849 - 0.231385i) q^{34} +(-1.60207 + 1.54424i) q^{35} +(4.84508 + 3.53909i) q^{36} +(0.423455 + 1.02231i) q^{37} +(-1.65529 - 1.02820i) q^{38} +(1.82185 + 1.10450i) q^{39} +(0.229671 - 2.36768i) q^{40} +(-1.44212 - 1.44212i) q^{41} +(-0.381394 - 6.46951i) q^{42} +(-5.03594 + 2.08595i) q^{43} +(-0.207933 - 3.12537i) q^{44} +(0.221980 + 2.51331i) q^{45} +(2.02003 - 1.44904i) q^{46} -12.1909i q^{47} +(4.80284 + 4.99327i) q^{48} +(-5.12830 + 4.76451i) q^{49} +(-4.93285 + 3.53850i) q^{50} +(-0.0435725 + 0.283876i) q^{51} +(1.85119 + 1.62023i) q^{52} +(2.78926 + 6.73386i) q^{53} +(-5.98058 - 4.26997i) q^{54} +(0.931380 - 0.931380i) q^{55} +(0.859271 - 7.43382i) q^{56} +(2.04083 + 1.23725i) q^{57} +(4.70074 - 7.56769i) q^{58} +(0.184087 + 0.444425i) q^{59} +(-0.249867 + 2.90268i) q^{60} +(4.35156 - 10.5056i) q^{61} +(0.591911 - 3.59615i) q^{62} +(0.552895 + 7.91797i) q^{63} +(4.46416 + 6.63862i) q^{64} +1.03451i q^{65} +(0.296105 + 3.82480i) q^{66} +(-5.54325 - 2.29609i) q^{67} +(-0.106290 + 0.314135i) q^{68} +(-2.45466 + 1.80139i) q^{69} +(2.59028 - 1.78692i) q^{70} +(9.01557 + 9.01557i) q^{71} +(-5.94814 - 6.05142i) q^{72} +(-1.36391 + 1.36391i) q^{73} +(-0.356098 - 1.52383i) q^{74} +(5.99419 - 4.39894i) q^{75} +(2.07370 + 1.81498i) q^{76} +(2.98333 - 2.87564i) q^{77} +(-2.28859 - 1.95970i) q^{78} +10.0284i q^{79} +(-0.864308 + 3.25120i) q^{80} +(7.38090 + 5.14999i) q^{81} +(1.68116 + 2.34362i) q^{82} +(0.535926 - 1.29384i) q^{83} +(-0.953724 + 9.11539i) q^{84} +(-0.128840 + 0.0533673i) q^{85} +(7.50644 - 1.75415i) q^{86} +(-5.65649 + 9.33030i) q^{87} +(-0.427686 + 4.40901i) q^{88} +(10.2497 - 10.2497i) q^{89} +(0.267505 - 3.55815i) q^{90} +(-0.0598082 + 3.25385i) q^{91} +(-3.15165 + 1.55807i) q^{92} +(-0.677198 + 4.41196i) q^{93} +(-2.80004 + 17.0116i) q^{94} +1.15885i q^{95} +(-5.55519 - 8.07093i) q^{96} -13.1901i q^{97} +(8.25055 - 5.47068i) q^{98} +(-0.413364 - 4.68020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.39544	−	0.229683i	−0.986723	−	0.162410i
$2$	−1.39544	−	0.229683i	−0.986723	−	0.162410i
$3$	1.71200	+	0.262778i	0.988424	+	0.151715i
$3$	1.71200	+	0.262778i	0.988424	+	0.151715i
$4$	1.89449	+	0.641017i	0.947246	+	0.320508i
$5$	0.321849	+	0.777011i	0.143935	+	0.347490i	0.979363	−	0.202110i	$-0.0647800\pi$
$5$	0.321849	+	0.777011i	0.143935	+	0.347490i	−0.835428	+	0.549600i	$0.814780\pi$
$6$	−2.32863	−	0.759907i	−0.950661	−	0.310231i
$7$	0.967393	+	2.46255i	0.365640	+	0.930756i
$7$	0.967393	+	2.46255i	0.365640	+	0.930756i
$8$	−2.49641	−	1.32963i	−0.882615	−	0.470096i
$9$	2.86190	+	0.899751i	0.953965	+	0.299917i
$10$	−0.270653	−	1.15819i	−0.0855881	−	0.366253i
$11$	−0.599335	−	1.44692i	−0.180706	−	0.436264i	0.807406	−	0.589996i	$-0.200871\pi$
$11$	−0.599335	−	1.44692i	−0.180706	−	0.436264i	−0.988113	+	0.153732i	$0.950871\pi$
$12$	3.07493	+	1.59525i	0.887655	+	0.460509i
$13$	1.13642	+	0.470719i	0.315185	+	0.130554i	0.534667	−	0.845063i	$-0.320437\pi$
$13$	1.13642	+	0.470719i	0.315185	+	0.130554i	−0.219483	+	0.975616i	$0.570437\pi$
$14$	−0.784330	−	3.65853i	−0.209621	−	0.977783i
$15$	0.346824	+	1.41482i	0.0895495	+	0.365305i
$16$	3.17820	+	2.42880i	0.794549	+	0.607200i
$17$			0.165815i			0.0402161i	0.999798	+	0.0201080i	$0.00640102\pi$
$17$			0.165815i			0.0402161i	−0.999798	+	0.0201080i	$0.993599\pi$
$18$	−3.78694	−	1.91288i	−0.892590	−	0.450869i
$19$	1.27301	+	0.527297i	0.292048	+	0.120970i	0.523897	−	0.851781i	$-0.324478\pi$
$19$	1.27301	+	0.527297i	0.292048	+	0.120970i	−0.231849	+	0.972752i	$0.574478\pi$
$20$	0.111662	+	1.67835i	0.0249684	+	0.375291i
$21$	1.00907	+	4.47010i	0.220198	+	0.975455i
$22$	0.504001	+	2.15675i	0.107453	+	0.459820i
$23$	−1.24300	+	1.24300i	−0.259184	+	0.259184i	−0.824722	−	0.565538i	$-0.808669\pi$
$23$	−1.24300	+	1.24300i	−0.259184	+	0.259184i	0.565538	+	0.824722i	$0.308669\pi$
$24$	−3.92447	−	2.93233i	−0.801078	−	0.598560i
$25$	3.03537	−	3.03537i	0.607075	−	0.607075i
$26$	−1.47768	−	0.917874i	−0.289797	−	0.180010i
$27$	4.66313	+	2.29242i	0.897421	+	0.441176i
$28$	0.254181	+	5.28539i	0.0480358	+	0.998846i
$29$	−2.41071	+	5.81996i	−0.447657	+	1.08074i	0.525540	+	0.850769i	$0.323863\pi$
$29$	−2.41071	+	5.81996i	−0.447657	+	1.08074i	−0.973197	+	0.229971i	$0.926137\pi$
$30$	−0.159011	−	2.05395i	−0.0290313	−	0.374998i
$31$			2.57708i			0.462857i	0.972852	+	0.231428i	$0.0743399\pi$
$31$			2.57708i			0.462857i	−0.972852	+	0.231428i	$0.925660\pi$
$32$	−3.87712	−	4.11922i	−0.685384	−	0.728182i
$33$	−0.645844	−	2.63463i	−0.112427	−	0.458630i
$34$	0.0380849	−	0.231385i	0.00653151	−	0.0396821i
$35$	−1.60207	+	1.54424i	−0.270800	+	0.261025i
$36$	4.84508	+	3.53909i	0.807514	+	0.589849i
$37$	0.423455	+	1.02231i	0.0696156	+	0.168067i	0.954858	−	0.297064i	$-0.0960074\pi$
$37$	0.423455	+	1.02231i	0.0696156	+	0.168067i	−0.885242	+	0.465131i	$0.846007\pi$
$38$	−1.65529	−	1.02820i	−0.268524	−	0.166796i
$39$	1.82185	+	1.10450i	0.291729	+	0.176861i
$40$	0.229671	−	2.36768i	0.0363142	−	0.374363i
$41$	−1.44212	−	1.44212i	−0.225221	−	0.225221i	0.585472	−	0.810693i	$-0.300909\pi$
$41$	−1.44212	−	1.44212i	−0.225221	−	0.225221i	−0.810693	+	0.585472i	$0.800909\pi$
$42$	−0.381394	−	6.46951i	−0.0588504	−	0.998267i
$43$	−5.03594	+	2.08595i	−0.767973	+	0.318105i	−0.732051	−	0.681250i	$-0.761437\pi$
$43$	−5.03594	+	2.08595i	−0.767973	+	0.318105i	−0.0359221	+	0.999355i	$0.511437\pi$
$44$	−0.207933	−	3.12537i	−0.0313471	−	0.471167i
$45$	0.221980	+	2.51331i	0.0330909	+	0.374662i
$46$	2.02003	−	1.44904i	0.297837	−	0.213649i
$47$		−	12.1909i		−	1.77822i	−0.457690	−	0.889112i	$-0.651323\pi$
$47$		−	12.1909i		−	1.77822i	0.457690	−	0.889112i	$-0.348677\pi$
$48$	4.80284	+	4.99327i	0.693230	+	0.720716i
$49$	−5.12830	+	4.76451i	−0.732615	+	0.680644i
$50$	−4.93285	+	3.53850i	−0.697610	+	0.500420i
$51$	−0.0435725	+	0.283876i	−0.00610137	+	0.0397505i
$52$	1.85119	+	1.62023i	0.256714	+	0.224686i
$53$	2.78926	+	6.73386i	0.383134	+	0.924967i	0.991356	+	0.131200i	$0.0418830\pi$
$53$	2.78926	+	6.73386i	0.383134	+	0.924967i	−0.608222	+	0.793767i	$0.708117\pi$
$54$	−5.98058	−	4.26997i	−0.813854	−	0.581069i
$55$	0.931380	−	0.931380i	0.125587	−	0.125587i
$56$	0.859271	−	7.43382i	0.114825	−	0.993386i
$57$	2.04083	+	1.23725i	0.270315	+	0.163878i
$58$	4.70074	−	7.56769i	0.617237	−	0.993687i
$59$	0.184087	+	0.444425i	0.0239661	+	0.0578592i	0.935410	−	0.353566i	$-0.115031\pi$
$59$	0.184087	+	0.444425i	0.0239661	+	0.0578592i	−0.911443	+	0.411425i	$0.865031\pi$
$60$	−0.249867	+	2.90268i	−0.0322577	+	0.374735i
$61$	4.35156	−	10.5056i	0.557161	−	1.34511i	−0.354844	−	0.934926i	$-0.615466\pi$
$61$	4.35156	−	10.5056i	0.557161	−	1.34511i	0.912005	−	0.410180i	$-0.134534\pi$
$62$	0.591911	−	3.59615i	0.0751728	−	0.456711i
$63$	0.552895	+	7.91797i	0.0696582	+	0.997571i
$64$	4.46416	+	6.63862i	0.558020	+	0.829827i
$65$			1.03451i			0.128315i
$66$	0.296105	+	3.82480i	0.0364480	+	0.470800i
$67$	−5.54325	−	2.29609i	−0.677216	−	0.280512i	0.0174468	−	0.999848i	$-0.494446\pi$
$67$	−5.54325	−	2.29609i	−0.677216	−	0.280512i	−0.694662	+	0.719336i	$0.744446\pi$
$68$	−0.106290	+	0.314135i	−0.0128896	+	0.0380945i
$69$	−2.45466	+	1.80139i	−0.295506	+	0.216862i
$70$	2.59028	−	1.78692i	0.309598	−	0.213578i
$71$	9.01557	+	9.01557i	1.06995	+	1.06995i	0.997362	+	0.0725895i	$0.0231263\pi$
$71$	9.01557	+	9.01557i	1.06995	+	1.06995i	0.0725895	+	0.997362i	$0.476874\pi$
$72$	−5.94814	−	6.05142i	−0.700995	−	0.713166i
$73$	−1.36391	+	1.36391i	−0.159633	+	0.159633i	−0.782404	−	0.622771i	$-0.786007\pi$
$73$	−1.36391	+	1.36391i	−0.159633	+	0.159633i	0.622771	+	0.782404i	$0.286007\pi$
$74$	−0.356098	−	1.52383i	−0.0413955	−	0.177142i
$75$	5.99419	−	4.39894i	0.692150	−	0.507945i
$76$	2.07370	+	1.81498i	0.237869	+	0.208192i
$77$	2.98333	−	2.87564i	0.339982	−	0.327709i
$78$	−2.28859	−	1.95970i	−0.259132	−	0.221893i
$79$			10.0284i			1.12828i	0.825679	+	0.564141i	$0.190792\pi$
$79$			10.0284i			1.12828i	−0.825679	+	0.564141i	$0.809208\pi$
$80$	−0.864308	+	3.25120i	−0.0966326	+	0.363495i
$81$	7.38090	+	5.14999i	0.820099	+	0.572221i
$82$	1.68116	+	2.34362i	0.185653	+	0.258809i
$83$	0.535926	−	1.29384i	0.0588255	−	0.142017i	−0.891734	−	0.452560i	$-0.850511\pi$
$83$	0.535926	−	1.29384i	0.0588255	−	0.142017i	0.950559	+	0.310543i	$0.100511\pi$
$84$	−0.953724	+	9.11539i	−0.104060	+	0.994571i
$85$	−0.128840	+	0.0533673i	−0.0139747	+	0.00578850i
$86$	7.50644	−	1.75415i	0.809441	−	0.189155i
$87$	−5.65649	+	9.33030i	−0.606439	+	1.00031i
$88$	−0.427686	+	4.40901i	−0.0455915	+	0.470002i
$89$	10.2497	−	10.2497i	1.08647	−	1.08647i	0.0905795	−	0.995889i	$-0.471128\pi$
$89$	10.2497	−	10.2497i	1.08647	−	1.08647i	0.995889	−	0.0905795i	$-0.0288719\pi$
$90$	0.267505	−	3.55815i	0.0281975	−	0.375062i
$91$	−0.0598082	+	3.25385i	−0.00626960	+	0.341096i
$92$	−3.15165	+	1.55807i	−0.328582	+	0.162440i
$93$	−0.677198	+	4.41196i	−0.0702222	+	0.457499i
$94$	−2.80004	+	17.0116i	−0.288802	+	1.75461i
$95$			1.15885i			0.118896i
$96$	−5.55519	−	8.07093i	−0.566974	−	0.823735i
$97$		−	13.1901i		−	1.33925i	−0.742697	−	0.669627i	$-0.766454\pi$
$97$		−	13.1901i		−	1.33925i	0.742697	−	0.669627i	$-0.233546\pi$
$98$	8.25055	−	5.47068i	0.833432	−	0.552623i
$99$	−0.413364	−	4.68020i	−0.0415446	−	0.470377i
$100$	7.69622	−	3.80476i	0.769622	−	0.380476i
$101$	5.05862	+	12.2126i	0.503351	+	1.21520i	0.947648	+	0.319318i	$0.103454\pi$
$101$	5.05862	+	12.2126i	0.503351	+	1.21520i	−0.444296	+	0.895880i	$0.646546\pi$
$102$	0.126004	−	0.386123i	0.0124763	−	0.0382318i
$103$	0.491789	+	0.491789i	0.0484574	+	0.0484574i	0.730920	−	0.682463i	$-0.239091\pi$
$103$	0.491789	+	0.491789i	0.0484574	+	0.0484574i	−0.682463	+	0.730920i	$0.739091\pi$
$104$	−2.21108	−	2.68612i	−0.216814	−	0.263396i
$105$	−3.14855	+	2.22276i	−0.307267	+	0.216919i
$106$	−2.34558	−	10.0373i	−0.227823	−	0.974911i
$107$	−3.25308	−	7.85363i	−0.314487	−	0.759239i	−0.999528	−	0.0307338i	$-0.990216\pi$
$107$	−3.25308	−	7.85363i	−0.314487	−	0.759239i	0.685041	−	0.728505i	$-0.259784\pi$
$108$	7.36479	+	7.33211i	0.708677	+	0.705533i
$109$	3.97252	−	9.59052i	0.380499	−	0.918605i	−0.611371	−	0.791344i	$-0.709382\pi$
$109$	3.97252	−	9.59052i	0.380499	−	0.918605i	0.991869	−	0.127261i	$-0.0406185\pi$
$110$	−1.51361	+	1.08576i	−0.144317	+	0.103523i
$111$	0.456315	+	1.86147i	0.0433115	+	0.176683i
$112$	−2.90648	+	10.1761i	−0.274637	+	0.961548i
$113$	0.277797			0.0261330			0.0130665	−	0.999915i	$-0.495841\pi$
$113$	0.277797			0.0261330			0.0130665	+	0.999915i	$0.495841\pi$
$114$	−2.56367	−	2.19525i	−0.240110	−	0.205604i
$115$	−1.36589	−	0.565769i	−0.127370	−	0.0527582i
$116$	−8.29776	+	9.48056i	−0.770427	+	0.880248i
$117$	2.82877	+	2.36964i	0.261520	+	0.219073i
$118$	−0.154805	−	0.662449i	−0.0142509	−	0.0609834i
$119$	−0.408328	+	0.160408i	−0.0374313	+	0.0147046i
$120$	1.01537	−	3.99312i	0.0926903	−	0.364520i
$121$	6.04379	−	6.04379i	0.549435	−	0.549435i
$122$	−8.48530	+	13.6604i	−0.768223	+	1.23676i
$123$	−2.08995	−	2.84787i	−0.188445	−	0.256784i
$124$	−1.65195	+	4.88225i	−0.148349	+	0.438439i
$125$	7.22051	+	2.99083i	0.645822	+	0.267508i
$126$	1.04709	−	11.1760i	0.0932826	−	0.995640i
$127$	−10.2436			−0.908969			−0.454485	−	0.890755i	$-0.650177\pi$
$127$	−10.2436			−0.908969			−0.454485	+	0.890755i	$0.650177\pi$
$128$	−4.70468	−	10.2891i	−0.415839	−	0.909438i
$129$	−9.16967	+	2.24782i	−0.807345	+	0.197910i
$130$	0.237609	−	1.44359i	0.0208397	−	0.126611i
$131$	−8.30158	−	3.43863i	−0.725313	−	0.300434i	−0.0106884	−	0.999943i	$-0.503402\pi$
$131$	−8.30158	−	3.43863i	−0.725313	−	0.300434i	−0.714624	+	0.699509i	$0.753402\pi$
$132$	0.465295	−	5.40527i	0.0404987	−	0.470469i
$133$	−0.0669969	+	3.64495i	−0.00580937	+	0.316057i
$134$	7.20788	+	4.47724i	0.622666	+	0.386774i
$135$	−0.280411	+	4.36112i	−0.0241339	+	0.375345i
$136$	0.220473	−	0.413943i	0.0189054	−	0.0354953i
$137$	6.44132	−	6.44132i	0.550319	−	0.550319i	−0.376214	−	0.926533i	$-0.622774\pi$
$137$	6.44132	−	6.44132i	0.550319	−	0.550319i	0.926533	+	0.376214i	$0.122774\pi$
$138$	3.83907	−	1.94993i	0.326803	−	0.165989i
$139$	−2.60635	−	6.29230i	−0.221068	−	0.533706i	0.773967	−	0.633225i	$-0.218269\pi$
$139$	−2.60635	−	6.29230i	−0.221068	−	0.533706i	−0.995036	+	0.0995197i	$0.968269\pi$
$140$	−4.02500	+	1.89860i	−0.340175	+	0.160461i
$141$	3.20349	−	20.8708i	0.269783	−	1.75764i
$142$	−10.5099	−	14.6514i	−0.881975	−	1.22952i
$143$		−	1.92642i		−	0.161096i
$144$	6.91035	+	9.81056i	0.575862	+	0.817547i
$145$	−5.29806			−0.439980
$146$	2.21651	−	1.58998i	0.183440	−	0.131588i
$147$	−10.0317	+	6.80924i	−0.827398	+	0.561616i
$148$	0.146914	+	2.20820i	0.0120762	+	0.181513i
$149$	−3.40062	−	8.20983i	−0.278590	−	0.672575i	0.721207	−	0.692719i	$-0.243588\pi$
$149$	−3.40062	−	8.20983i	−0.278590	−	0.672575i	−0.999797	+	0.0201440i	$0.993588\pi$
$150$	−9.37488	+	4.76167i	−0.765456	+	0.388789i
$151$	−11.4450	−	11.4450i	−0.931379	−	0.931379i	0.0664134	−	0.997792i	$-0.478844\pi$
$151$	−11.4450	−	11.4450i	−0.931379	−	0.931379i	−0.997792	+	0.0664134i	$0.978844\pi$
$152$	−2.47684	−	3.00898i	−0.200899	−	0.244061i
$153$	−0.149192	+	0.474545i	−0.0120615	+	0.0383647i
$154$	−4.82353	+	3.32755i	−0.388691	+	0.268142i
$155$	−2.00242	+	0.829428i	−0.160838	+	0.0666213i
$156$	2.74348	+	3.26029i	0.219654	+	0.261032i
$157$	−1.88745	+	4.55670i	−0.150635	+	0.363664i	−0.981127	−	0.193367i	$-0.938059\pi$
$157$	−1.88745	+	4.55670i	−0.150635	+	0.363664i	0.830492	+	0.557030i	$0.188059\pi$
$158$	2.30335	−	13.9940i	0.183245	−	1.11330i
$159$	3.00570	+	12.2613i	0.238368	+	0.972387i
$160$	1.95283	−	4.33833i	0.154385	−	0.342975i
$161$	−4.26343	−	1.85849i	−0.336006	−	0.146469i
$162$	−9.11671	−	8.88175i	−0.716277	−	0.697816i
$163$	−17.6484	−	7.31021i	−1.38233	−	0.572580i	−0.437227	−	0.899351i	$-0.644039\pi$
$163$	−17.6484	−	7.31021i	−1.38233	−	0.572580i	−0.945104	+	0.326771i	$0.894039\pi$
$164$	−1.80766	−	3.65651i	−0.141155	−	0.285525i
$165$	1.83927	−	1.34978i	0.143187	−	0.105080i
$166$	−1.04502	+	1.68238i	−0.0811096	+	0.130578i
$167$	−13.2264	+	13.2264i	−1.02349	+	1.02349i	−0.0237746	+	0.999717i	$0.507568\pi$
$167$	−13.2264	+	13.2264i	−1.02349	+	1.02349i	−0.999717	+	0.0237746i	$0.992432\pi$
$168$	3.42451	−	12.5009i	0.264207	−	0.964466i
$169$	−8.12252	−	8.12252i	−0.624810	−	0.624810i
$170$	0.192046	−	0.0448784i	0.0147293	−	0.00344201i
$171$	3.16878	+	2.65446i	0.242323	+	0.202992i
$172$	−10.8777	+	0.723701i	−0.829415	+	0.0551817i
$173$	5.91916	−	14.2901i	0.450025	−	1.08646i	−0.522286	−	0.852770i	$-0.674921\pi$
$173$	5.91916	−	14.2901i	0.450025	−	1.08646i	0.972312	−	0.233687i	$-0.0750792\pi$
$174$	10.0363	−	11.7207i	0.760849	−	0.888540i
$175$	10.4112	+	4.53836i	0.787010	+	0.343068i
$176$	1.60949	−	6.05427i	0.121319	−	0.456358i
$177$	0.198372	+	0.809230i	0.0149105	+	0.0608254i
$178$	−16.6570	+	11.9487i	−1.24850	+	0.895590i
$179$	−13.8650	−	5.74307i	−1.03632	−	0.429257i	−0.201330	−	0.979524i	$-0.564526\pi$
$179$	−13.8650	−	5.74307i	−1.03632	−	0.429257i	−0.834989	+	0.550266i	$0.814526\pi$
$180$	−1.19053	+	4.90373i	−0.0887371	+	0.365503i
$181$	−4.66611	−	11.2650i	−0.346829	−	0.837320i	−0.996990	−	0.0775239i	$-0.975299\pi$
$181$	−4.66611	−	11.2650i	−0.346829	−	0.837320i	0.650161	−	0.759796i	$-0.274701\pi$
$182$	0.830812	−	4.52680i	0.0615839	−	0.335549i
$183$	10.2105	−	16.8421i	0.754784	−	1.24501i
$184$	4.75579	−	1.45032i	0.350601	−	0.106919i
$185$	−0.658059	+	0.658059i	−0.0483815	+	0.0483815i
$186$	1.95834	−	6.00107i	0.143592	−	0.440020i
$187$	0.239922	−	0.0993788i	0.0175448	−	0.00726730i
$188$	7.81456	−	23.0955i	0.569936	−	1.68441i
$189$	−1.13411	+	13.7009i	−0.0824943	+	0.996592i
$190$	0.266169	−	1.61710i	0.0193099	−	0.117317i
$191$			8.44039i			0.610725i	0.952236	+	0.305362i	$0.0987776\pi$
$191$			8.44039i			0.610725i	−0.952236	+	0.305362i	$0.901222\pi$
$192$	5.89817	+	12.5384i	0.425664	+	0.904882i
$193$	17.4061			1.25292			0.626460	−	0.779454i	$-0.284503\pi$
$193$	17.4061			1.25292			0.626460	+	0.779454i	$0.284503\pi$
$194$	−3.02955	+	18.4060i	−0.217509	+	1.32147i
$195$	−0.271845	+	1.77108i	−0.0194673	+	0.126829i
$196$	−12.7697	+	5.73899i	−0.912118	+	0.409928i
$197$	−12.5900	+	5.21494i	−0.896999	+	0.371549i	−0.783066	−	0.621939i	$-0.786345\pi$
$197$	−12.5900	+	5.21494i	−0.896999	+	0.371549i	−0.113933	+	0.993488i	$0.536345\pi$
$198$	−0.498138	+	6.62586i	−0.0354011	+	0.470880i
$199$	−11.6249	−	11.6249i	−0.824068	−	0.824068i	0.162620	−	0.986689i	$-0.448005\pi$
$199$	−11.6249	−	11.6249i	−0.824068	−	0.824068i	−0.986689	+	0.162620i	$0.948005\pi$
$200$	−11.6135	+	3.54162i	−0.821197	+	0.250430i
$201$	−8.88669	−	5.38755i	−0.626819	−	0.380008i
$202$	−4.25396	−	18.2038i	−0.299308	−	1.28081i
$203$	−16.6640	−	0.306298i	−1.16959	−	0.0214979i
$204$	−0.264517	+	0.509869i	−0.0185199	+	0.0356980i
$205$	0.656399	−	1.58469i	0.0458449	−	0.110679i
$206$	−0.573305	−	0.799216i	−0.0399440	−	0.0556840i
$207$	−4.67574	+	2.43895i	−0.324987	+	0.169519i
$208$	2.46847	+	4.25616i	0.171157	+	0.295112i
$209$		−	2.15797i		−	0.149270i
$210$	4.90413	−	2.37855i	0.338417	−	0.164136i
$211$	−4.97946	+	12.0215i	−0.342800	+	0.827592i	0.654630	+	0.755949i	$0.272824\pi$
$211$	−4.97946	+	12.0215i	−0.342800	+	0.827592i	−0.997430	+	0.0716433i	$0.977176\pi$
$212$	0.967705	+	14.5452i	0.0664622	+	0.998968i
$213$	13.0656	+	17.8038i	0.895239	+	1.21989i
$214$	2.73562	+	11.7064i	0.187003	+	0.800234i
$215$	−3.24162	−	3.24162i	−0.221077	−	0.221077i
$216$	−8.59304	−	11.9231i	−0.584682	−	0.811262i
$217$	−6.34618	+	2.49305i	−0.430807	+	0.169239i
$218$	−7.74619	+	12.4705i	−0.524638	+	0.844612i
$219$	−2.69342	+	1.97661i	−0.182004	+	0.133567i
$220$	2.36152	−	1.16746i	0.159214	−	0.0787102i
$221$	−0.0780522	+	0.188435i	−0.00525036	+	0.0126755i
$222$	−0.209211	−	2.70238i	−0.0140413	−	0.181372i
$223$		−	20.3447i		−	1.36238i	−0.732106	−	0.681191i	$-0.761462\pi$
$223$		−	20.3447i		−	1.36238i	0.732106	−	0.681191i	$-0.238538\pi$
$224$	6.39308	−	13.5325i	0.427156	−	0.904178i
$225$	11.4180	−	5.95584i	0.761200	−	0.397056i
$226$	−0.387649	−	0.0638053i	−0.0257860	−	0.00424427i
$227$	−16.0142	−	6.63330i	−1.06290	−	0.440267i	−0.218420	−	0.975855i	$-0.570090\pi$
$227$	−16.0142	−	6.63330i	−1.06290	−	0.440267i	−0.844480	+	0.535588i	$0.820090\pi$
$228$	3.07324	+	3.65217i	0.203530	+	0.241871i
$229$	2.06190	−	0.854066i	0.136254	−	0.0564383i	−0.313515	−	0.949583i	$-0.601506\pi$
$229$	2.06190	−	0.854066i	0.136254	−	0.0564383i	0.449769	+	0.893145i	$0.351506\pi$
$230$	1.77606	+	1.10322i	0.117110	+	0.0727439i
$231$	5.86311	−	4.13914i	0.385765	−	0.272335i
$232$	13.7565	−	11.3237i	0.903160	−	0.743436i
$233$	11.2099	−	11.2099i	0.734386	−	0.734386i	−0.237100	−	0.971485i	$-0.576197\pi$
$233$	11.2099	−	11.2099i	0.734386	−	0.734386i	0.971485	+	0.237100i	$0.0761968\pi$
$234$	−3.40311	−	3.95640i	−0.222468	−	0.258638i
$235$	9.47245	−	3.92362i	0.617915	−	0.255949i
$236$	0.0638671	+	0.959962i	0.00415739	+	0.0624882i
$237$	−2.63524	+	17.1686i	−0.171177	+	1.11522i
$238$	0.606639	−	0.130054i	0.0393226	−	0.00843013i
$239$	12.5593			0.812394			0.406197	−	0.913785i	$-0.366855\pi$
$239$	12.5593			0.812394			0.406197	+	0.913785i	$0.366855\pi$
$240$	−2.33404	+	5.33894i	−0.150662	+	0.344627i
$241$	21.5549			1.38847			0.694236	−	0.719747i	$-0.255742\pi$
$241$	21.5549			1.38847			0.694236	+	0.719747i	$0.255742\pi$
$242$	−9.82189	+	7.04557i	−0.631375	+	0.452907i
$243$	11.2828	+	10.7563i	0.723792	+	0.690018i
$244$	14.9783	−	17.1134i	0.958886	−	1.09557i
$245$	−5.35261	−	2.45130i	−0.341966	−	0.156608i
$246$	2.26229	+	4.45405i	0.144239	+	0.283980i
$247$	1.19846	+	1.19846i	0.0762560	+	0.0762560i
$248$	3.42656	−	6.43345i	0.217587	−	0.408524i
$249$	1.25750	−	2.07422i	0.0796907	−	0.131449i
$250$	−9.38882	−	5.83195i	−0.593801	−	0.368845i
$251$	7.78437	+	18.7931i	0.491345	+	1.18621i	0.954036	+	0.299692i	$0.0968839\pi$
$251$	7.78437	+	18.7931i	0.491345	+	1.18621i	−0.462691	+	0.886520i	$0.653116\pi$
$252$	−4.02810	+	15.3549i	−0.253746	+	0.967271i
$253$	2.54351	+	1.05356i	0.159909	+	0.0662365i
$254$	14.2942	+	2.35277i	0.896901	+	0.147626i
$255$	−0.234598	+	0.0575086i	−0.0146911	+	0.00360133i
$256$	4.20185	+	15.4384i	0.262615	+	0.964901i
$257$	−0.508541			−0.0317219			−0.0158610	−	0.999874i	$-0.505049\pi$
$257$	−0.508541			−0.0317219			−0.0158610	+	0.999874i	$0.505049\pi$
$258$	13.3120	−	1.03058i	0.828768	−	0.0641610i
$259$	−2.10785	+	2.03176i	−0.130975	+	0.126247i
$260$	−0.663136	+	1.95986i	−0.0411260	+	0.121546i
$261$	−12.1357	+	14.4871i	−0.751182	+	0.896728i
$262$	10.7945	+	6.70512i	0.666889	+	0.414244i
$263$	12.9789	+	12.9789i	0.800313	+	0.800313i	0.983144	−	0.182831i	$-0.0585261\pi$
$263$	12.9789	+	12.9789i	0.800313	+	0.800313i	−0.182831	+	0.983144i	$0.558526\pi$
$264$	−1.89079	+	7.43585i	−0.116370	+	0.457645i
$265$	−4.33457	+	4.33457i	−0.266270	+	0.266270i
$266$	0.930673	−	5.07091i	0.0570632	−	0.310918i
$267$	20.2409	−	14.8541i	1.23873	−	0.909059i
$268$	−9.02980	−	7.90323i	−0.551583	−	0.482767i
$269$	8.45970	−	20.4235i	0.515797	−	1.24524i	−0.424667	−	0.905350i	$-0.639609\pi$
$269$	8.45970	−	20.4235i	0.515797	−	1.24524i	0.940464	−	0.339894i	$-0.110391\pi$
$270$	1.39297	−	6.02126i	0.0847735	−	0.366442i
$271$	23.6001			1.43360			0.716801	−	0.697278i	$-0.245606\pi$
$271$	23.6001			1.43360			0.716801	+	0.697278i	$0.245606\pi$
$272$	−0.402732	+	0.526993i	−0.0244192	+	0.0319536i
$273$	−0.957430	+	5.55488i	−0.0579463	+	0.336196i
$274$	−10.4679	+	7.50899i	−0.632390	+	0.453635i
$275$	−6.21116	−	2.57275i	−0.374547	−	0.155142i
$276$	−5.80505	+	1.83924i	−0.349423	+	0.110709i
$277$	−20.6432	+	8.55070i	−1.24033	+	0.513762i	−0.903818	−	0.427917i	$-0.859248\pi$
$277$	−20.6432	+	8.55070i	−1.24033	+	0.513762i	−0.336513	+	0.941679i	$0.609248\pi$
$278$	2.19177	+	9.37914i	0.131454	+	0.562524i
$279$	−2.31873	+	7.37533i	−0.138819	+	0.441549i
$280$	6.05271	−	1.72490i	0.361719	−	0.103083i
$281$	−21.0524	−	21.0524i	−1.25588	−	1.25588i	−0.953042	−	0.302837i	$-0.902066\pi$
$281$	−21.0524	−	21.0524i	−1.25588	−	1.25588i	−0.302837	−	0.953042i	$-0.597934\pi$
$282$	−9.26395	+	28.3881i	−0.551660	+	1.69049i
$283$	−16.9455	+	7.01905i	−1.00730	+	0.417239i	−0.824471	−	0.565904i	$-0.808527\pi$
$283$	−16.9455	+	7.01905i	−1.00730	+	0.417239i	−0.182834	+	0.983144i	$0.558527\pi$
$284$	11.3008	+	22.8591i	0.670578	+	1.35644i
$285$	−0.304520	+	1.98396i	−0.0180382	+	0.117519i
$286$	−0.442467	+	2.68820i	−0.0261636	+	0.158957i
$287$	2.15620	−	4.94639i	0.127276	−	0.291976i
$288$	−7.38964	−	15.2772i	−0.435438	−	0.900219i
$289$	16.9725			0.998383
$290$	7.39311	+	1.21687i	0.434138	+	0.0714573i
$291$	3.46607	−	22.5815i	0.203185	−	1.32375i
$292$	−3.45820	+	1.70962i	−0.202376	+	0.100048i
$293$	9.03760	+	21.8187i	0.527982	+	1.27466i	0.932843	+	0.360283i	$0.117320\pi$
$293$	9.03760	+	21.8187i	0.527982	+	1.27466i	−0.404861	+	0.914378i	$0.632680\pi$
$294$	15.5625	−	7.19776i	0.907625	−	0.419782i
$295$	−0.286075	+	0.286075i	−0.0166559	+	0.0166559i
$296$	0.302178	−	3.11515i	0.0175637	−	0.181065i
$297$	0.522171	−	8.12112i	0.0302995	−	0.471235i
$298$	2.85970	+	12.2374i	0.165658	+	0.708892i
$299$	−1.99767	+	0.827464i	−0.115528	+	0.0478535i
$300$	14.1757	−	4.49137i	0.818437	−	0.259309i
$301$	−10.0085	−	10.3833i	−0.576880	−	0.598484i
$302$	13.3420	+	18.5995i	0.767748	+	1.07028i
$303$	5.45117	+	22.2373i	0.313161	+	1.27750i
$304$	2.76517	+	4.76774i	0.158593	+	0.273449i
$305$	9.56352			0.547605
$306$	0.317184	−	0.627931i	0.0181322	−	0.0358965i
$307$	−17.0929	−	7.08010i	−0.975542	−	0.404083i	−0.162769	−	0.986664i	$-0.552043\pi$
$307$	−17.0929	−	7.08010i	−0.975542	−	0.404083i	−0.812772	+	0.582582i	$0.802043\pi$
$308$	7.49522	−	3.53550i	0.427080	−	0.201454i
$309$	0.712712	+	0.971174i	0.0405448	+	0.0552482i
$310$	2.98475	−	0.697494i	0.169523	−	0.0396150i
$311$	0.0872943	+	0.0872943i	0.00495000	+	0.00495000i	0.709577	−	0.704627i	$-0.248886\pi$
$311$	0.0872943	+	0.0872943i	0.00495000	+	0.00495000i	−0.704627	+	0.709577i	$0.748886\pi$
$312$	−3.07952	−	5.17966i	−0.174343	−	0.293241i
$313$	4.13430	+	4.13430i	0.233684	+	0.233684i	0.814229	−	0.580544i	$-0.197160\pi$
$313$	4.13430	+	4.13430i	0.233684	+	0.233684i	−0.580544	+	0.814229i	$0.697160\pi$
$314$	3.68041	−	5.92507i	0.207697	−	0.334371i
$315$	−5.97441	+	2.97799i	−0.336620	+	0.167791i
$316$	−6.42836	+	18.9987i	−0.361624	+	1.06876i
$317$	−4.16797	+	10.0624i	−0.234097	+	0.565159i	−0.996652	−	0.0817641i	$-0.973945\pi$
$317$	−4.16797	+	10.0624i	−0.234097	+	0.565159i	0.762555	+	0.646923i	$0.223945\pi$
$318$	−1.37805	−	17.8003i	−0.0772771	−	0.998190i
$319$	9.86586			0.552382
$320$	−3.72150	+	5.60533i	−0.208038	+	0.313348i
$321$	−3.50552	−	14.3003i	−0.195659	−	0.798162i
$322$	5.52249	+	3.57264i	0.307756	+	0.199095i
$323$	−0.0874338	+	0.211084i	−0.00486495	+	0.0117450i
$324$	10.6818	+	14.4879i	0.593434	+	0.804883i
$325$	4.87825	−	2.02064i	0.270597	−	0.112085i
$326$	22.9482	+	14.2545i	1.27098	+	0.789483i
$327$	9.32114	−	15.3751i	0.515460	−	0.850244i
$328$	1.68264	+	5.51762i	0.0929083	+	0.304659i
$329$	30.0207	−	11.7934i	1.65509	−	0.650190i
$330$	−2.87661	+	1.46108i	−0.158352	+	0.0804299i
$331$	24.3963	−	10.1053i	1.34094	−	0.555437i	0.407187	−	0.913345i	$-0.366510\pi$
$331$	24.3963	−	10.1053i	1.34094	−	0.555437i	0.933757	+	0.357907i	$0.116510\pi$
$332$	1.84468	−	2.10763i	0.101240	−	0.115671i
$333$	0.292059	+	3.30675i	0.0160047	+	0.181209i
$334$	21.4945	−	15.4188i	1.17613	−	0.843678i
$335$		−	5.04616i		−	0.275701i
$336$	−7.64994	+	16.6577i	−0.417339	+	0.908751i
$337$			21.2947i			1.16000i	0.814617	+	0.579999i	$0.196947\pi$
$337$			21.2947i			1.16000i	−0.814617	+	0.579999i	$0.803053\pi$
$338$	9.46887	+	13.2001i	0.515039	+	0.717990i
$339$	0.475589	+	0.0729989i	0.0258305	+	0.00396475i
$340$	−0.278296	+	0.0185153i	−0.0150927	+	0.00100413i
$341$	3.72883	−	1.54453i	0.201928	−	0.0836411i
$342$	−3.81215	−	4.43195i	−0.206138	−	0.239652i
$343$	−16.6939	−	8.01955i	−0.901387	−	0.433015i
$344$	15.3453	+	1.48854i	0.827365	+	0.0802566i
$345$	−2.18973	−	1.32752i	−0.117891	−	0.0714714i
$346$	−11.5420	+	18.5814i	−0.620503	+	0.998944i
$347$	−20.2939	+	8.40601i	−1.08943	+	0.451258i	−0.853809	−	0.520586i	$-0.825714\pi$
$347$	−20.2939	+	8.40601i	−1.08943	+	0.451258i	−0.235625	+	0.971844i	$0.575714\pi$
$348$	−16.6970	+	14.0503i	−0.895056	+	0.753173i
$349$	4.99299	−	12.0541i	0.267269	−	0.645243i	−0.732084	−	0.681214i	$-0.761452\pi$
$349$	4.99299	−	12.0541i	0.267269	−	0.645243i	0.999353	+	0.0359707i	$0.0114523\pi$
$350$	−13.4857	−	8.72427i	−0.720843	−	0.466332i
$351$	4.22017	+	4.80016i	0.225256	+	0.256214i
$352$	−3.63650	+	8.07868i	−0.193826	+	0.430595i
$353$	−4.43402			−0.235999			−0.118000	−	0.993014i	$-0.537648\pi$
$353$	−4.43402			−0.235999			−0.118000	+	0.993014i	$0.537648\pi$
$354$	−0.0909492	−	1.17479i	−0.00483390	−	0.0624395i
$355$	−4.10355	+	9.90685i	−0.217794	+	0.525801i
$356$	25.9883	−	12.8478i	1.37738	−	0.680930i
$357$	−0.741209	+	0.167320i	−0.0392290	+	0.00885550i
$358$	18.0287	+	11.1987i	0.952844	+	0.591867i
$359$	−1.91654	−	1.91654i	−0.101151	−	0.101151i	0.654720	−	0.755871i	$-0.272786\pi$
$359$	−1.91654	−	1.91654i	−0.101151	−	0.101151i	−0.755871	+	0.654720i	$0.772786\pi$
$360$	2.78762	−	6.56941i	0.146920	−	0.346238i
$361$	−12.0925	−	12.0925i	−0.636448	−	0.636448i
$362$	3.92389	+	16.7913i	0.206235	+	0.882532i
$363$	11.9351	−	8.75880i	0.626433	−	0.459718i
$364$	−2.19908	+	6.12605i	−0.115263	+	0.321092i
$365$	−1.49874	−	0.620800i	−0.0784478	−	0.0324941i
$366$	−18.1165	+	21.1569i	−0.946964	+	1.10589i
$367$	6.41751			0.334991			0.167496	−	0.985873i	$-0.446432\pi$
$367$	6.41751			0.334991			0.167496	+	0.985873i	$0.446432\pi$
$368$	−6.96952	+	0.931499i	−0.363311	+	0.0485578i
$369$	−2.82965	−	5.42475i	−0.147306	−	0.282401i
$370$	1.06943	−	0.767135i	0.0555968	−	0.0398815i
$371$	−13.8842	+	13.3830i	−0.720830	+	0.694809i
$372$	−4.11109	+	7.92432i	−0.213150	+	0.410857i
$373$	−30.3347	+	12.5651i	−1.57067	+	0.650594i	−0.986902	−	0.161324i	$-0.948424\pi$
$373$	−30.3347	+	12.5651i	−1.57067	+	0.650594i	−0.583772	+	0.811918i	$0.698424\pi$
$374$	−0.357621	+	0.0835710i	−0.0184922	+	0.00432135i
$375$	11.5756	+	7.01769i	0.597761	+	0.362392i
$376$	−16.2094	+	30.4335i	−0.835935	+	1.56949i
$377$	−5.47913	+	5.47913i	−0.282189	+	0.282189i
$378$	4.72944	−	18.8582i	0.243256	−	0.969962i
$379$	13.1729	+	31.8022i	0.676646	+	1.63357i	0.770084	+	0.637943i	$0.220214\pi$
$379$	13.1729	+	31.8022i	0.676646	+	1.63357i	−0.0934376	+	0.995625i	$0.529786\pi$
$380$	−0.742843	+	2.19543i	−0.0381071	+	0.112623i
$381$	−17.5370	−	2.69178i	−0.898447	−	0.137904i
$382$	1.93861	−	11.7780i	0.0991881	−	0.602617i
$383$	8.61741			0.440329			0.220164	−	0.975463i	$-0.429341\pi$
$383$	8.61741			0.440329			0.220164	+	0.975463i	$0.429341\pi$
$384$	−5.35066	−	18.8513i	−0.273050	−	0.962000i
$385$	3.19458	+	1.39256i	0.162811	+	0.0709714i
$386$	−24.2891	−	3.99789i	−1.23628	−	0.203487i
$387$	−16.2892	+	1.43869i	−0.828025	+	0.0731328i
$388$	8.45509	−	24.9886i	0.429242	−	1.26860i
$389$	−3.79626	+	1.57246i	−0.192478	+	0.0797270i	−0.476840	−	0.878990i	$-0.658218\pi$
$389$	−3.79626	+	1.57246i	−0.192478	+	0.0797270i	0.284363	+	0.958717i	$0.408218\pi$
$390$	0.786130	−	2.40899i	0.0398072	−	0.121984i
$391$	−0.206109	−	0.206109i	−0.0104234	−	0.0104234i
$392$	19.1374	−	5.07542i	0.966585	−	0.256348i
$393$	−13.3087	−	8.06841i	−0.671336	−	0.406997i
$394$	18.7663	−	4.38542i	0.945433	−	0.220934i
$395$	−7.79217	+	3.22762i	−0.392066	+	0.162399i
$396$	2.21697	−	9.13156i	0.111407	−	0.458878i
$397$	−35.0256	−	14.5081i	−1.75789	−	0.728140i	−0.996840	−	0.0794414i	$-0.974686\pi$
$397$	−35.0256	−	14.5081i	−1.75789	−	0.728140i	−0.761046	−	0.648698i	$-0.775314\pi$
$398$	13.5518	+	18.8919i	0.679290	+	0.946965i
$399$	−1.07251	+	6.22255i	−0.0536927	+	0.311517i
$400$	17.0193	−	2.27469i	0.850967	−	0.113735i
$401$	−1.11939			−0.0558999			−0.0279500	−	0.999609i	$-0.508898\pi$
$401$	−1.11939			−0.0558999			−0.0279500	+	0.999609i	$0.508898\pi$
$402$	11.1634	+	9.55911i	0.556779	+	0.476765i
$403$	−1.21308	+	2.92863i	−0.0604277	+	0.145885i
$404$	1.75504	+	26.3793i	0.0873164	+	1.31242i
$405$	−1.62607	+	7.39255i	−0.0808000	+	0.367339i
$406$	23.1833	+	4.25487i	1.15057	+	0.211166i
$407$	1.22541	−	1.22541i	0.0607416	−	0.0607416i
$408$	0.486225	−	0.650735i	0.0240717	−	0.0322162i
$409$	11.7970	+	11.7970i	0.583322	+	0.583322i	0.935815	−	0.352493i	$-0.114666\pi$
$409$	11.7970	+	11.7970i	0.583322	+	0.583322i	−0.352493	+	0.935815i	$0.614666\pi$
$410$	−1.27994	+	2.06057i	−0.0632117	+	0.101764i
$411$	12.7202	−	9.33491i	0.627440	−	0.460457i
$412$	0.616445	+	1.24693i	0.0303701	+	0.0614320i
$413$	−0.916334	+	0.883256i	−0.0450899	+	0.0434622i
$414$	7.08489	−	2.32947i	0.348204	−	0.114487i
$415$	1.17781			0.0578166
$416$	−2.46702	−	6.50617i	−0.120956	−	0.318991i
$417$	−2.80861	−	11.4573i	−0.137538	−	0.561067i
$418$	−0.495650	+	3.01132i	−0.0242430	+	0.147288i
$419$	−3.98473	−	1.65053i	−0.194667	−	0.0806337i	0.283220	−	0.959055i	$-0.408597\pi$
$419$	−3.98473	−	1.65053i	−0.194667	−	0.0806337i	−0.477887	+	0.878421i	$0.658597\pi$
$420$	−7.38972	+	2.19272i	−0.360581	+	0.106994i
$421$	−0.829840	−	2.00341i	−0.0404439	−	0.0976403i	0.902367	−	0.430969i	$-0.141828\pi$
$421$	−0.829840	−	2.00341i	−0.0404439	−	0.0976403i	−0.942811	+	0.333329i	$0.891828\pi$
$422$	9.70965	−	15.6315i	0.472658	−	0.760930i
$423$	10.9688	−	34.8890i	0.533320	−	1.69636i
$424$	1.99042	−	20.5192i	0.0966631	−	0.996500i
$425$	0.503311	+	0.503311i	0.0244142	+	0.0244142i
$426$	−14.1430	−	27.8450i	−0.685229	−	1.34909i
$427$	30.0803	+	0.552897i	1.45569	+	0.0267566i
$428$	−1.12862	−	16.9639i	−0.0545541	−	0.819981i
$429$	0.506221	−	3.29804i	0.0244406	−	0.159231i
$430$	3.77893	+	5.26802i	0.182236	+	0.254047i
$431$	−21.7012			−1.04531			−0.522654	−	0.852545i	$-0.675058\pi$
$431$	−21.7012			−1.04531			−0.522654	+	0.852545i	$0.675058\pi$
$432$	9.25252	+	18.6116i	0.445162	+	0.895450i
$433$	35.7603			1.71853			0.859264	−	0.511532i	$-0.170922\pi$
$433$	35.7603			1.71853			0.859264	+	0.511532i	$0.170922\pi$
$434$	9.42831	−	2.02128i	0.452573	−	0.0970245i
$435$	−9.07028	−	1.39221i	−0.434887	−	0.0667514i
$436$	13.6736	−	15.6227i	0.654846	−	0.748192i
$437$	−2.23779	+	0.926922i	−0.107048	+	0.0443407i
$438$	4.21249	−	2.13960i	0.201280	−	0.102234i
$439$	15.6600	−	15.6600i	0.747409	−	0.747409i	−0.226583	−	0.973992i	$-0.572755\pi$
$439$	15.6600	−	15.6600i	0.747409	−	0.747409i	0.973992	+	0.226583i	$0.0727553\pi$
$440$	−3.56350	+	1.08672i	−0.169883	+	0.0518072i
$441$	−18.9635	+	9.02132i	−0.903026	+	0.429587i
$442$	0.152197	−	0.245022i	0.00723929	−	0.0116545i
$443$	22.4961	−	9.31817i	1.06882	−	0.442720i	0.222246	−	0.974991i	$-0.428661\pi$
$443$	22.4961	−	9.31817i	1.06882	−	0.442720i	0.846574	+	0.532271i	$0.178661\pi$
$444$	−0.328750	+	3.81905i	−0.0156018	+	0.181244i
$445$	11.2630	+	4.66529i	0.533918	+	0.221156i
$446$	−4.67283	+	28.3898i	−0.221265	+	1.34429i
$447$	−3.66451	−	14.9488i	−0.173325	−	0.707056i
$448$	−12.0293	+	17.4154i	−0.568333	+	0.822799i
$449$		−	7.72616i		−	0.364620i	−0.983241	−	0.182310i	$-0.941643\pi$
$449$		−	7.72616i		−	0.364620i	0.983241	−	0.182310i	$-0.0583574\pi$
$450$	−17.3011	+	5.68848i	−0.815580	+	0.268158i
$451$	−1.22232	+	2.95095i	−0.0575570	+	0.138955i
$452$	0.526284	+	0.178073i	0.0247543	+	0.00837583i
$453$	−16.5863	−	22.6013i	−0.779294	−	1.06190i
$454$	20.8232	+	12.9345i	0.977283	+	0.607048i
$455$	−2.54753	+	1.00077i	−0.119430	+	0.0469170i
$456$	−3.44967	−	5.80224i	−0.161545	−	0.271715i
$457$	−5.84818	−	5.84818i	−0.273566	−	0.273566i	0.556968	−	0.830534i	$-0.311965\pi$
$457$	−5.84818	−	5.84818i	−0.273566	−	0.273566i	−0.830534	+	0.556968i	$0.811965\pi$
$458$	−3.07341	+	0.718213i	−0.143611	+	0.0335599i
$459$	−0.380117	+	0.773218i	−0.0177424	+	0.0360907i
$460$	−2.22499	−	1.94740i	−0.103741	−	0.0907980i
$461$	−10.7031	+	25.8395i	−0.498493	+	1.20347i	0.451803	+	0.892118i	$0.350781\pi$
$461$	−10.7031	+	25.8395i	−0.498493	+	1.20347i	−0.950295	+	0.311350i	$0.899219\pi$
$462$	−9.13230	+	4.42925i	−0.424873	+	0.206067i
$463$			13.8579i			0.644030i	0.946735	+	0.322015i	$0.104360\pi$
$463$			13.8579i			0.644030i	−0.946735	+	0.322015i	$0.895640\pi$
$464$	−21.7972	+	12.6418i	−1.01191	+	0.586883i
$465$	−3.64610	+	0.893792i	−0.169084	+	0.0414486i
$466$	−18.2175	+	13.0680i	−0.843907	+	0.605364i
$467$	6.39245	−	15.4327i	0.295807	−	0.714142i	−0.704184	−	0.710017i	$-0.748687\pi$
$467$	6.39245	−	15.4327i	0.295807	−	0.714142i	0.999991	−	0.00412456i	$-0.00131289\pi$
$468$	3.84011	+	6.30255i	0.177509	+	0.291335i
$469$	0.291734	−	15.8717i	0.0134710	−	0.732889i
$470$	−14.1194	+	3.29950i	−0.651280	+	0.152195i
$471$	−4.42871	+	7.30509i	−0.204064	+	0.336601i
$472$	0.131364	−	1.35424i	0.00604654	−	0.0623338i
$473$	6.03643	+	6.03643i	0.277555	+	0.277555i
$474$	7.62064	−	23.3524i	0.350028	−	1.07261i
$475$	5.46460	−	2.26351i	0.250733	−	0.103857i
$476$	−0.876398	+	0.0421471i	−0.0401696	+	0.00193181i
$477$	1.92376	+	21.7812i	0.0880830	+	0.997295i
$478$	−17.5257	−	2.88466i	−0.801608	−	0.131941i
$479$	7.64704			0.349402			0.174701	−	0.984622i	$-0.444104\pi$
$479$	7.64704			0.349402			0.174701	+	0.984622i	$0.444104\pi$
$480$	4.48327	−	6.91406i	0.204632	−	0.315582i
$481$			1.36110i			0.0620608i
$482$	−30.0785	−	4.95079i	−1.37004	−	0.225502i
$483$	−6.81063	−	4.30207i	−0.309895	−	0.195751i
$484$	15.3241	−	7.57574i	0.696549	−	0.344352i
$485$	10.2489	−	4.24522i	0.465377	−	0.192766i
$486$	−13.2739	−	17.6012i	−0.602116	−	0.798409i
$487$	15.7143	−	15.7143i	0.712082	−	0.712082i	−0.254888	−	0.966971i	$-0.582039\pi$
$487$	15.7143	−	15.7143i	0.712082	−	0.712082i	0.966971	+	0.254888i	$0.0820387\pi$
$488$	−24.8319	+	20.4404i	−1.12409	+	0.925292i
$489$	−28.2931	−	17.1527i	−1.27946	−	0.775672i
$490$	6.90621	+	4.65004i	0.311991	+	0.210067i
$491$	2.59925	+	6.27514i	0.117302	+	0.283193i	0.971616	−	0.236566i	$-0.0760218\pi$
$491$	2.59925	+	6.27514i	0.117302	+	0.283193i	−0.854313	+	0.519759i	$0.826022\pi$
$492$	−2.13387	−	6.73496i	−0.0962023	−	0.303635i
$493$	−0.965037	−	0.399731i	−0.0434631	−	0.0180030i
$494$	−1.39711	−	1.94764i	−0.0628588	−	0.0876284i
$495$	3.50352	−	1.82750i	0.157472	−	0.0821401i
$496$	−6.25921	+	8.19045i	−0.281047	+	0.367762i
$497$	−13.4797	+	30.9229i	−0.604647	+	1.38708i
$498$	−2.23117	+	2.60563i	−0.0999813	+	0.116761i
$499$	7.36689	−	17.7852i	0.329787	−	0.796177i	−0.668820	−	0.743424i	$-0.733200\pi$
$499$	7.36689	−	17.7852i	0.329787	−	0.796177i	0.998608	−	0.0527529i	$-0.0167996\pi$
$500$	11.7620	+	10.2946i	0.526013	+	0.460387i
$501$	−26.1193	+	19.1681i	−1.16692	+	0.856366i
$502$	−6.54613	−	28.0126i	−0.292168	−	1.25026i
$503$	−15.3002	−	15.3002i	−0.682200	−	0.682200i	0.278295	−	0.960496i	$-0.410231\pi$
$503$	−15.3002	−	15.3002i	−0.682200	−	0.682200i	−0.960496	+	0.278295i	$0.910231\pi$
$504$	9.14773	−	20.5017i	0.407472	−	0.913218i
$505$	−7.86121	+	7.86121i	−0.349819	+	0.349819i
$506$	−3.30732	−	2.05437i	−0.147028	−	0.0913280i
$507$	−11.7714	−	16.0402i	−0.522784	−	0.712370i
$508$	−19.4063	−	6.56629i	−0.861017	−	0.291332i
$509$	17.2973	+	7.16476i	0.766688	+	0.317572i	0.731530	−	0.681809i	$-0.238807\pi$
$509$	17.2973	+	7.16476i	0.766688	+	0.317572i	0.0351578	+	0.999382i	$0.488807\pi$
$510$	0.340576	−	0.0263665i	0.0150810	−	0.00116753i
$511$	−4.67812	−	2.03926i	−0.206948	−	0.0902114i
$512$	−2.31747	−	22.5084i	−0.102419	−	0.994741i
$513$	4.72742	+	5.37713i	0.208721	+	0.237406i
$514$	0.709637	+	0.116803i	0.0313007	+	0.00515197i
$515$	−0.223844	+	0.540407i	−0.00986374	+	0.0238132i
$516$	−18.8128	−	1.61943i	−0.828186	−	0.0712915i
$517$	−17.6393	+	7.30643i	−0.775774	+	0.321336i
$518$	3.40803	−	2.35105i	0.149740	−	0.103299i
$519$	13.8887	−	22.9093i	0.609648	−	1.00561i
$520$	1.37551	−	2.58256i	0.0603202	−	0.113253i
$521$	19.2217	+	19.2217i	0.842118	+	0.842118i	0.989134	−	0.147016i	$-0.0469669\pi$
$521$	19.2217	+	19.2217i	0.842118	+	0.842118i	−0.147016	+	0.989134i	$0.546967\pi$
$522$	20.2621	−	17.4285i	0.886846	−	0.762823i
$523$	0.00283245	+	0.00683815i	0.000123855	+	0.000299011i	0.923941	−	0.382534i	$-0.124948\pi$
$523$	0.00283245	+	0.00683815i	0.000123855	+	0.000299011i	−0.923818	+	0.382833i	$0.874948\pi$
$524$	−13.5231	−	11.8359i	−0.590758	−	0.517054i
$525$	16.6313	+	10.5055i	0.725851	+	0.458498i
$526$	−15.1302	−	21.0923i	−0.659709	−	0.919667i
$527$	−0.427318			−0.0186143
$528$	4.34637	−	9.94198i	0.189151	−	0.432669i
$529$			19.9099i			0.865647i
$530$	7.04419	−	5.05304i	0.305980	−	0.219490i
$531$	0.126965	+	1.43753i	0.00550983	+	0.0623835i
$532$	−2.46340	+	6.86238i	−0.106802	+	0.297522i
$533$	−0.960014	−	2.31768i	−0.0415828	−	0.100390i
$534$	−31.6567	+	16.0790i	−1.36992	+	0.695807i
$535$	5.05536	−	5.05536i	0.218562	−	0.218562i
$536$	10.7853	+	13.1025i	0.465853	+	0.565940i
$537$	−22.2277	−	13.4756i	−0.959198	−	0.581513i
$538$	−16.4959	+	26.5567i	−0.711190	+	1.14494i
$539$	9.96745	+	4.56472i	0.429328	+	0.196617i
$540$	−3.32679	+	8.08235i	−0.143162	+	0.347809i
$541$	−17.9108	−	7.41888i	−0.770043	−	0.318962i	−0.0371533	−	0.999310i	$-0.511829\pi$
$541$	−17.9108	−	7.41888i	−0.770043	−	0.318962i	−0.732890	+	0.680347i	$0.761829\pi$
$542$	−32.9324	−	5.42054i	−1.41457	−	0.232832i
$543$	−5.02820	−	20.5118i	−0.215781	−	0.880247i
$544$	0.683028	−	0.642884i	0.0292846	−	0.0275634i
$545$	8.73049			0.373973
$546$	2.61189	−	7.53158i	0.111779	−	0.322322i
$547$	5.04265	+	2.08874i	0.215608	+	0.0893079i	0.487873	−	0.872914i	$-0.337773\pi$
$547$	5.04265	+	2.08874i	0.215608	+	0.0893079i	−0.272265	+	0.962222i	$0.587773\pi$
$548$	16.3320	−	8.07403i	0.697669	−	0.344905i
$549$	21.9062	−	26.1506i	0.934932	−	1.11608i
$550$	8.07637	+	5.01671i	0.344378	+	0.213913i
$551$	−6.13770	+	6.13770i	−0.261475	+	0.261475i
$552$	8.52303	−	1.23323i	0.362764	−	0.0524896i
$553$	−24.6954	+	9.70139i	−1.05016	+	0.412545i
$554$	30.7703	−	7.19057i	1.30730	−	0.305498i
$555$	−1.29952	+	0.953675i	−0.0551616	+	0.0404812i
$556$	−0.904249	−	13.5914i	−0.0383487	−	0.576405i
$557$	−22.6781	−	9.39358i	−0.960902	−	0.398019i	−0.153584	−	0.988136i	$-0.549082\pi$
$557$	−22.6781	−	9.39358i	−0.960902	−	0.398019i	−0.807318	+	0.590117i	$0.799082\pi$
$558$	4.92963	−	9.75923i	0.208688	−	0.413141i
$559$	−6.70481			−0.283583
$560$	−8.84236	+	1.01678i	−0.373658	+	0.0429670i
$561$	0.436861	−	0.107091i	0.0184443	−	0.00452137i
$562$	24.5419	+	34.2126i	1.03524	+	1.44317i
$563$	3.60981	−	8.71484i	0.152135	−	0.367287i	−0.829376	−	0.558691i	$-0.811304\pi$
$563$	3.60981	−	8.71484i	0.152135	−	0.367287i	0.981511	+	0.191404i	$0.0613040\pi$
$564$	19.4475	−	37.4861i	0.818889	−	1.57845i
$565$	0.0894086	+	0.215851i	0.00376145	+	0.00908094i
$566$	25.2585	−	5.90256i	1.06170	−	0.248103i
$567$	−5.54188	+	23.1579i	−0.232737	+	0.972540i
$568$	−10.5192	−	34.4940i	−0.441376	−	1.44734i
$569$	20.5804	+	20.5804i	0.862776	+	0.862776i	0.991660	−	0.128884i	$-0.0411394\pi$
$569$	20.5804	+	20.5804i	0.862776	+	0.862776i	−0.128884	+	0.991660i	$0.541139\pi$
$570$	0.880620	−	2.69854i	0.0368851	−	0.113029i
$571$	1.34168	+	3.23910i	0.0561474	+	0.135552i	0.949464	−	0.313876i	$-0.101628\pi$
$571$	1.34168	+	3.23910i	0.0561474	+	0.135552i	−0.893316	+	0.449428i	$0.851628\pi$
$572$	1.23487	−	3.64959i	0.0516325	−	0.152597i
$573$	−2.21794	+	14.4500i	−0.0926560	+	0.603655i
$574$	−4.14494	+	6.40714i	−0.173006	+	0.267429i
$575$			7.54597i			0.314689i
$576$	6.80286	+	23.0157i	0.283452	+	0.958986i
$577$			42.4713i			1.76810i	0.467389	+	0.884052i	$0.345195\pi$
$577$			42.4713i			1.76810i	−0.467389	+	0.884052i	$0.654805\pi$
$578$	−23.6841	−	3.89830i	−0.985127	−	0.162148i
$579$	29.7993	+	4.57394i	1.23842	+	0.190086i
$580$	−10.0371	−	3.39614i	−0.416769	−	0.141017i
$581$	3.70459	+	0.0680932i	0.153692	+	0.00282498i
$582$	−10.0233	+	30.7150i	−0.415478	+	1.27318i
$583$	8.07168	−	8.07168i	0.334295	−	0.334295i
$584$	5.21837	−	1.59138i	0.215938	−	0.0658519i
$585$	−0.930799	+	2.96065i	−0.0384838	+	0.122408i
$586$	−7.60002	−	32.5224i	−0.313954	−	1.34349i
$587$	10.2412	−	4.24204i	0.422699	−	0.175088i	−0.161186	−	0.986924i	$-0.551532\pi$
$587$	10.2412	−	4.24204i	0.422699	−	0.175088i	0.583885	+	0.811836i	$0.301532\pi$
$588$	−23.3697	+	6.46957i	−0.963752	+	0.266801i
$589$	−1.35889	+	3.28064i	−0.0559919	+	0.135176i
$590$	0.464906	−	0.333493i	0.0191399	−	0.0137297i
$591$	−22.9244	+	5.61962i	−0.942985	+	0.231160i
$592$	−1.13717	+	4.27759i	−0.0467373	+	0.175808i
$593$		−	43.7639i		−	1.79717i	−0.438803	−	0.898583i	$-0.644597\pi$
$593$		−	43.7639i		−	1.79717i	0.438803	−	0.898583i	$-0.355403\pi$
$594$	−2.59394	+	11.2126i	−0.106431	+	0.460058i
$595$	−0.256059	−	0.265648i	−0.0104974	−	0.0108905i
$596$	−1.17981	−	17.7333i	−0.0483270	−	0.726384i
$597$	−16.8471	−	22.9566i	−0.689506	−	0.939553i
$598$	2.97768	−	0.695842i	0.121767	−	0.0284551i
$599$	−6.42233	+	6.42233i	−0.262409	+	0.262409i	−0.826032	−	0.563623i	$-0.809407\pi$
$599$	−6.42233	+	6.42233i	−0.262409	+	0.262409i	0.563623	+	0.826032i	$0.309407\pi$
$600$	−20.8129	+	3.01150i	−0.849685	+	0.122944i
$601$	23.6557	+	23.6557i	0.964938	+	0.964938i	0.999406	−	0.0344681i	$-0.0109737\pi$
$601$	23.6557	+	23.6557i	0.964938	+	0.964938i	−0.0344681	+	0.999406i	$0.510974\pi$
$602$	11.5814	+	16.7880i	0.472021	+	0.684230i
$603$	−13.7983	−	11.5587i	−0.561910	−	0.470707i
$604$	−14.3460	−	29.0188i	−0.583730	−	1.18076i
$605$	6.64128	+	2.75091i	0.270006	+	0.111840i
$606$	−2.49924	−	32.2827i	−0.101525	−	1.31140i
$607$			12.7373i			0.516989i	0.966013	+	0.258495i	$0.0832264\pi$
$607$			12.7373i			0.516989i	−0.966013	+	0.258495i	$0.916774\pi$
$608$	−2.76355	−	7.28819i	−0.112077	−	0.295575i
$609$	−28.4484	−	4.90332i	−1.15279	−	0.198693i
$610$	−13.3453	−	2.19658i	−0.540335	−	0.0889369i
$611$	5.73848	−	13.8539i	0.232154	−	0.560469i
$612$	−0.586835	+	0.803387i	−0.0237214	+	0.0324750i
$613$	4.02386	+	9.71446i	0.162522	+	0.392363i	0.984071	−	0.177774i	$-0.0568897\pi$
$613$	4.02386	+	9.71446i	0.162522	+	0.392363i	−0.821549	+	0.570138i	$0.806890\pi$
$614$	22.2259	+	13.8058i	0.896962	+	0.557156i
$615$	1.54018	−	2.54050i	0.0621059	−	0.102443i
$616$	−11.2712	+	3.21205i	−0.454128	+	0.129417i
$617$	1.88885	−	1.88885i	0.0760424	−	0.0760424i	−0.668063	−	0.744105i	$-0.732876\pi$
$617$	1.88885	−	1.88885i	0.0760424	−	0.0760424i	0.744105	+	0.668063i	$0.232876\pi$
$618$	−0.771482	−	1.51891i	−0.0310336	−	0.0610995i
$619$	−18.0088	−	43.4771i	−0.723835	−	1.74749i	−0.662120	−	0.749398i	$-0.730343\pi$
$619$	−18.0088	−	43.4771i	−0.723835	−	1.74749i	−0.0617149	−	0.998094i	$-0.519657\pi$
$620$	−4.32524	+	0.287762i	−0.173706	+	0.0115568i
$621$	−8.64578	+	2.94681i	−0.346943	+	0.118251i
$622$	−0.101764	−	0.141864i	−0.00408035	−	0.00568822i
$623$	35.1560	+	15.3249i	1.40849	+	0.613981i
$624$	3.10759	+	7.93521i	0.124403	+	0.317663i
$625$		−	14.8903i		−	0.595613i
$626$	−4.81958	−	6.71873i	−0.192629	−	0.268535i
$627$	0.567067	−	3.69445i	0.0226465	−	0.147542i
$628$	−6.49667	+	7.42274i	−0.259245	+	0.296199i
$629$	−0.169515	+	0.0702153i	−0.00675899	+	0.00279967i
$630$	9.02090	−	2.78338i	0.359401	−	0.110893i
$631$	−22.2010	−	22.2010i	−0.883809	−	0.883809i	0.110110	−	0.993919i	$-0.464880\pi$
$631$	−22.2010	−	22.2010i	−0.883809	−	0.883809i	−0.993919	+	0.110110i	$0.964880\pi$
$632$	13.3341	−	25.0350i	0.530400	−	0.995839i
$633$	−11.6838	+	19.2723i	−0.464390	+	0.766005i
$634$	8.12730	−	13.0841i	0.322776	−	0.519636i
$635$	−3.29687	−	7.95936i	−0.130832	−	0.315858i
$636$	−2.16544	+	25.1557i	−0.0858654	+	0.997488i
$637$	−8.07062	+	3.00047i	−0.319770	+	0.118883i
$638$	−13.7672	−	2.26602i	−0.545048	−	0.0897126i
$639$	17.6899	+	33.9134i	0.699800	+	1.34159i
$640$	6.48057	−	6.96713i	0.256167	−	0.275400i
$641$			12.5846i			0.497062i	0.968624	+	0.248531i	$0.0799477\pi$
$641$			12.5846i			0.497062i	−0.968624	+	0.248531i	$0.920052\pi$
$642$	1.60720	+	20.7603i	0.0634312	+	0.819342i
$643$	−18.8376	+	45.4779i	−0.742882	+	1.79347i	−0.149145	+	0.988815i	$0.547652\pi$
$643$	−18.8376	+	45.4779i	−0.742882	+	1.79347i	−0.593737	+	0.804659i	$0.702348\pi$
$644$	−6.88572	−	6.25382i	−0.271335	−	0.246435i
$645$	−4.69783	−	6.40148i	−0.184977	−	0.252058i
$646$	0.170491	−	0.274472i	0.00670787	−	0.0107990i
$647$	23.9078	−	23.9078i	0.939913	−	0.939913i	−0.0583813	−	0.998294i	$-0.518594\pi$
$647$	23.9078	−	23.9078i	0.939913	−	0.939913i	0.998294	+	0.0583813i	$0.0185939\pi$
$648$	−11.5782	−	22.6704i	−0.454834	−	0.890576i
$649$	0.532719	−	0.532719i	0.0209111	−	0.0209111i
$650$	−7.27140	+	1.69922i	−0.285208	+	0.0666490i
$651$	−11.5198	+	2.60046i	−0.451496	+	0.101920i
$652$	−28.7488	−	25.1621i	−1.12589	−	0.985423i
$653$	9.21532	+	3.81711i	0.360623	+	0.149375i	0.555636	−	0.831426i	$-0.312475\pi$
$653$	9.21532	+	3.81711i	0.360623	+	0.149375i	−0.195013	+	0.980801i	$0.562475\pi$
$654$	−16.5385	+	19.3141i	−0.646705	+	0.755240i
$655$		−	7.55714i		−	0.295282i
$656$	−1.08072	−	8.08596i	−0.0421949	−	0.315704i
$657$	−5.13054	+	2.67618i	−0.200161	+	0.104408i
$658$	−44.6007	+	9.56168i	−1.73872	+	0.372753i
$659$	30.3877	+	12.5870i	1.18374	+	0.490320i	0.885711	−	0.464238i	$-0.153672\pi$
$659$	30.3877	+	12.5870i	1.18374	+	0.490320i	0.298026	+	0.954558i	$0.403672\pi$
$660$	4.34971	−	1.37814i	0.169312	−	0.0536440i
$661$	15.2627	+	36.8475i	0.593652	+	1.43320i	0.879952	+	0.475063i	$0.157575\pi$
$661$	15.2627	+	36.8475i	0.593652	+	1.43320i	−0.286300	+	0.958140i	$0.592425\pi$
$662$	−36.3646	+	8.49788i	−1.41335	+	0.330280i
$663$	−0.183142	+	0.302090i	−0.00711264	+	0.0117322i
$664$	−3.05822	+	2.51737i	−0.118682	+	0.0976931i
$665$	−2.85373	+	1.12106i	−0.110663	+	0.0434730i
$666$	0.351956	−	4.68145i	0.0136380	−	0.181402i
$667$	−4.23772	−	10.2308i	−0.164085	−	0.396136i
$668$	−33.5357	+	16.5790i	−1.29754	+	0.641461i
$669$	5.34613	−	34.8301i	0.206693	−	1.34661i
$670$	−1.15902	+	7.04160i	−0.0447767	+	0.272041i
$671$	−17.8089			−0.687503
$672$	14.5010	−	21.4877i	0.559388	−	0.828906i
$673$	−20.4498			−0.788280			−0.394140	−	0.919050i	$-0.628958\pi$
$673$	−20.4498			−0.788280			−0.394140	+	0.919050i	$0.628958\pi$
$674$	4.89104	−	29.7154i	0.188396	−	1.14460i
$675$	21.1127	−	7.19601i	0.812628	−	0.276975i
$676$	−10.1814	−	20.5947i	−0.391591	−	0.792105i
$677$	4.72921	+	11.4173i	0.181758	+	0.438803i	0.988329	−	0.152334i	$-0.0486790\pi$
$677$	4.72921	+	11.4173i	0.181758	+	0.438803i	−0.806571	+	0.591138i	$0.798679\pi$
$678$	−0.646888	−	0.211100i	−0.0248436	−	0.00810725i
$679$	32.4813	−	12.7600i	1.24652	−	0.489685i
$680$	0.392597	+	0.0380830i	0.0150554	+	0.00146042i
$681$	−25.6732	−	15.5644i	−0.983800	−	0.596428i
$682$	−5.55811	+	1.29885i	−0.212831	+	0.0497355i
$683$	17.1700	+	41.4519i	0.656990	+	1.58611i	0.802429	+	0.596747i	$0.203540\pi$
$683$	17.1700	+	41.4519i	0.656990	+	1.58611i	−0.145439	+	0.989367i	$0.546460\pi$
$684$	4.30167	+	7.06010i	0.164479	+	0.269949i
$685$	7.07810	+	2.93185i	0.270440	+	0.112020i
$686$	21.4534	+	15.0251i	0.819093	+	0.573661i
$687$	3.75440	−	0.920342i	0.143239	−	0.0351132i
$688$	−21.0716	−	5.60172i	−0.803346	−	0.213564i
$689$			8.96541i			0.341555i
$690$	2.75072	+	2.35542i	0.104718	+	0.0896692i
$691$	36.7355	+	15.2163i	1.39748	+	0.578856i	0.949097	−	0.314984i	$-0.101999\pi$
$691$	36.7355	+	15.2163i	1.39748	+	0.578856i	0.448386	+	0.893840i	$0.351999\pi$
$692$	20.3740	−	23.2782i	0.774503	−	0.884905i
$693$	11.1253	−	5.54552i	0.422616	−	0.210657i
$694$	30.2496	−	7.06890i	1.14826	−	0.268332i
$695$	4.05033	−	4.05033i	0.153638	−	0.153638i
$696$	26.5268	−	15.7712i	1.00550	−	0.597807i
$697$	0.239125	−	0.239125i	0.00905752	−	0.00905752i
$698$	−9.73604	+	15.6740i	−0.368514	+	0.593269i
$699$	22.1371	−	16.2457i	0.837302	−	0.614468i
$700$	16.8147	+	15.2716i	0.635535	+	0.577213i
$701$	5.34836	−	12.9121i	0.202005	−	0.487683i	−0.790118	−	0.612955i	$-0.789981\pi$
$701$	5.34836	−	12.9121i	0.202005	−	0.487683i	0.992122	+	0.125273i	$0.0399806\pi$
$702$	−4.78647	−	7.66763i	−0.180654	−	0.289396i
$703$			1.52470i			0.0575051i
$704$	6.93004	−	10.4381i	0.261186	−	0.393399i
$705$	17.2479	−	4.22809i	0.649593	−	0.159239i
$706$	6.18740	+	1.01842i	0.232866	+	0.0383288i
$707$	−25.1804	+	24.2715i	−0.947007	+	0.912822i
$708$	−0.142916	+	1.66024i	−0.00537111	+	0.0623956i
$709$	0.680550	+	1.64299i	0.0255586	+	0.0617039i	0.936144	−	0.351618i	$-0.114368\pi$
$709$	0.680550	+	1.64299i	0.0255586	+	0.0617039i	−0.910585	+	0.413322i	$0.864368\pi$
$710$	8.00168	−	12.8819i	0.300298	−	0.483448i
$711$	−9.02305	+	28.7002i	−0.338391	+	1.07634i
$712$	−39.2159	+	11.9592i	−1.46968	+	0.448190i
$713$	−3.20332	−	3.20332i	−0.119965	−	0.119965i
$714$	1.07274	−	0.0632409i	0.0401464	−	0.00236673i
$715$	1.49685	−	0.620017i	0.0559791	−	0.0231873i
$716$	−22.5857	−	19.7679i	−0.844068	−	0.738761i
$717$	21.5016	+	3.30031i	0.802990	+	0.123252i
$718$	2.23421	+	3.11460i	0.0833800	+	0.116236i
$719$			23.0656i			0.860201i	0.902781	+	0.430100i	$0.141522\pi$
$719$			23.0656i			0.860201i	−0.902781	+	0.430100i	$0.858478\pi$
$720$	−5.39883	+	8.52693i	−0.201203	+	0.317780i
$721$	−0.735301	+	1.68681i	−0.0273841	+	0.0628200i
$722$	14.0969	+	19.6518i	0.524633	+	0.731364i
$723$	36.9020	+	5.66414i	1.37240	+	0.210652i
$724$	−1.61886	−	24.3325i	−0.0601645	−	0.904310i
$725$	10.3484	+	24.9832i	0.384329	+	0.927851i
$726$	−18.6665	+	9.48106i	−0.692779	+	0.351875i
$727$	−9.52897	+	9.52897i	−0.353410	+	0.353410i	−0.861377	−	0.507967i	$-0.830397\pi$
$727$	−9.52897	+	9.52897i	−0.353410	+	0.353410i	0.507967	+	0.861377i	$0.330397\pi$
$728$	4.47572	−	8.04343i	0.165881	−	0.298109i
$729$	16.4896	+	21.3797i	0.610728	+	0.791841i
$730$	1.94881	+	1.21052i	0.0721289	+	0.0448035i
$731$	−0.345883	−	0.835034i	−0.0127929	−	0.0308849i
$732$	30.1398	−	25.3621i	1.11400	−	0.937411i
$733$	−3.17917	+	7.67520i	−0.117425	+	0.283490i	−0.971654	−	0.236408i	$-0.924030\pi$
$733$	−3.17917	+	7.67520i	−0.117425	+	0.283490i	0.854229	+	0.519898i	$0.174030\pi$
$734$	−8.95523	−	1.47399i	−0.330543	−	0.0544061i
$735$	−8.51953	−	5.60317i	−0.314248	−	0.206676i
$736$	9.93948	+	0.300932i	0.366374	+	0.0110925i
$737$			9.39678i			0.346135i
$738$	2.70262	+	8.21982i	0.0994850	+	0.302576i
$739$	22.1450	+	9.17275i	0.814616	+	0.337425i	0.750794	−	0.660536i	$-0.229671\pi$
$739$	22.1450	+	9.17275i	0.814616	+	0.337425i	0.0638218	+	0.997961i	$0.479671\pi$
$740$	−1.66851	+	0.824860i	−0.0613358	+	0.0303225i
$741$	1.73683	+	2.36669i	0.0638041	+	0.0869425i
$742$	22.4483	−	15.4861i	0.824104	−	0.568514i
$743$	19.1540	+	19.1540i	0.702690	+	0.702690i	0.964987	−	0.262297i	$-0.0844800\pi$
$743$	19.1540	+	19.1540i	0.702690	+	0.702690i	−0.262297	+	0.964987i	$0.584480\pi$
$744$	7.55685	−	10.1136i	0.277047	−	0.370784i
$745$	5.28464	−	5.28464i	0.193614	−	0.193614i
$746$	45.2162	−	10.5664i	1.65548	−	0.386863i
$747$	2.69790	−	3.22063i	0.0987109	−	0.117837i
$748$	0.518233	−	0.0344785i	0.0189485	−	0.00126066i
$749$	16.1929	−	15.6084i	0.591677	−	0.570319i
$750$	−14.5412	−	12.4515i	−0.530968	−	0.454663i
$751$			29.3567i			1.07124i	0.844459	+	0.535620i	$0.179922\pi$
$751$			29.3567i			1.07124i	−0.844459	+	0.535620i	$0.820078\pi$
$752$	29.6092	−	38.7450i	1.07974	−	1.41289i
$753$	8.38843	+	34.2194i	0.305691	+	1.24702i
$754$	8.90424	−	6.38732i	0.324273	−	0.232612i
$755$	5.20932	−	12.5764i	0.189587	−	0.457703i
$756$	−10.9310	+	25.2292i	−0.397558	+	0.917577i
$757$	−25.7976	+	10.6857i	−0.937631	+	0.388379i	−0.798568	−	0.601904i	$-0.794409\pi$
$757$	−25.7976	+	10.6857i	−0.937631	+	0.388379i	−0.139063	+	0.990284i	$0.544409\pi$
$758$	−11.0775	−	47.4035i	−0.402354	−	1.72177i
$759$	4.07764	+	2.47207i	0.148009	+	0.0897303i
$760$	1.54085	−	2.89297i	0.0558923	−	0.104939i
$761$	13.7440	−	13.7440i	0.498219	−	0.498219i	−0.412664	−	0.910883i	$-0.635402\pi$
$761$	13.7440	−	13.7440i	0.498219	−	0.498219i	0.910883	+	0.412664i	$0.135402\pi$
$762$	23.8535	+	7.78416i	0.864122	+	0.281990i
$763$	27.4601	+	0.504738i	0.994123	+	0.0182727i
$764$	−5.41043	+	15.9902i	−0.195742	+	0.578507i
$765$	−0.416744	+	0.0368077i	−0.0150674	+	0.00133078i
$766$	−12.0251	−	1.97927i	−0.434483	−	0.0715140i
$767$			0.591704i			0.0213652i
$768$	3.13670	+	27.5347i	0.113186	+	0.993574i
$769$			17.4378i			0.628822i	0.949287	+	0.314411i	$0.101807\pi$
$769$			17.4378i			0.628822i	−0.949287	+	0.314411i	$0.898193\pi$
$770$	−4.13799	−	2.67697i	−0.149123	−	0.0964713i
$771$	−0.870623	−	0.133633i	−0.0313547	−	0.00481268i
$772$	32.9757	+	11.1576i	1.18682	+	0.401571i
$773$	−17.4037	−	42.0162i	−0.625967	−	1.51122i	−0.844593	−	0.535409i	$-0.820157\pi$
$773$	−17.4037	−	42.0162i	−0.625967	−	1.51122i	0.218626	−	0.975809i	$-0.429843\pi$
$774$	23.0610	+	1.73374i	0.828909	+	0.0623181i
$775$	7.82239	+	7.82239i	0.280989	+	0.280989i
$776$	−17.5380	+	32.9280i	−0.629578	+	1.18205i
$777$	−4.14253	+	2.92448i	−0.148613	+	0.104915i
$778$	5.65861	−	1.32234i	0.202871	−	0.0474080i
$779$	−1.07541	−	2.59626i	−0.0385304	−	0.0930206i
$780$	−1.65030	+	3.18103i	−0.0590902	+	0.113899i
$781$	7.64149	−	18.4482i	0.273434	−	0.660128i
$782$	0.240272	+	0.334952i	0.00859212	+	0.0119778i
$783$	−24.5832	+	21.6129i	−0.878533	+	0.772383i
$784$	−27.8708	+	2.68690i	−0.995385	+	0.0959607i
$785$	−4.14807			−0.148051
$786$	16.7183	+	14.3157i	0.596323	+	0.510626i
$787$	−35.0364	−	14.5126i	−1.24891	−	0.517317i	−0.342425	−	0.939545i	$-0.611248\pi$
$787$	−35.0364	−	14.5126i	−1.24891	−	0.517317i	−0.906490	+	0.422228i	$0.861248\pi$
$788$	−27.1945	+	1.80927i	−0.968763	+	0.0644526i
$789$	18.8093	+	25.6305i	0.669630	+	0.912469i
$790$	11.6148	−	2.71421i	0.413236	−	0.0965674i
$791$	0.268739	+	0.684089i	0.00955526	+	0.0243234i
$792$	−5.19101	+	12.2333i	−0.184454	+	0.434692i
$793$	9.89037	−	9.89037i	0.351217	−	0.351217i
$794$	45.5438	+	28.2899i	1.61629	+	1.00397i
$795$	−8.55981	+	6.28176i	−0.303585	+	0.222791i
$796$	−14.5715	−	29.4751i	−0.516474	−	1.04472i
$797$	12.2065	+	5.05611i	0.432377	+	0.179097i	0.588247	−	0.808681i	$-0.299818\pi$
$797$	12.2065	+	5.05611i	0.432377	+	0.179097i	−0.155870	+	0.987778i	$0.549818\pi$
$798$	2.92584	−	8.43685i	0.103573	−	0.298661i
$799$	2.02143			0.0715131
$800$	−24.2719	−	0.734865i	−0.858140	−	0.0259814i
$801$	38.5558	−	20.1114i	1.36230	−	0.710603i
$802$	1.56205	+	0.257106i	0.0551577	+	0.00907873i
$803$	2.79091	+	1.15603i	0.0984890	+	0.0407955i
$804$	−13.3822	−	15.9032i	−0.471955	−	0.560862i
$805$	0.0718850	−	3.91089i	0.00253361	−	0.137841i
$806$	2.36543	−	3.80809i	0.0833187	−	0.134134i
$807$	19.8499	−	32.7421i	0.698748	−	1.15258i
$808$	3.60983	−	37.2138i	0.126994	−	1.30918i
$809$	−38.8991	+	38.8991i	−1.36762	+	1.36762i	−0.503796	+	0.863823i	$0.668064\pi$
$809$	−38.8991	+	38.8991i	−1.36762	+	1.36762i	−0.863823	+	0.503796i	$0.831936\pi$
$810$	3.96702	−	9.94237i	0.139387	−	0.349339i
$811$	3.15699	+	7.62165i	0.110857	+	0.267632i	0.969566	−	0.244832i	$-0.0787327\pi$
$811$	3.15699	+	7.62165i	0.110857	+	0.267632i	−0.858709	+	0.512464i	$0.828733\pi$
$812$	−31.3735	−	11.2622i	−1.10100	−	0.395226i
$813$	40.4033	+	6.20157i	1.41701	+	0.217499i
$814$	−1.99145	+	1.42853i	−0.0698002	+	0.0500700i
$815$		−	16.0658i		−	0.562760i
$816$	−0.827959	+	0.796383i	−0.0289844	+	0.0278790i
$817$	−7.51071			−0.262766
$818$	−13.7523	−	19.1715i	−0.480840	−	0.670315i
$819$	−3.09882	+	9.25836i	−0.108281	+	0.323513i
$820$	2.25935	−	2.58141i	0.0789001	−	0.0901469i
$821$	−4.37037	−	10.5510i	−0.152527	−	0.368233i	0.829084	−	0.559124i	$-0.188862\pi$
$821$	−4.37037	−	10.5510i	−0.152527	−	0.368233i	−0.981611	+	0.190891i	$0.938862\pi$
$822$	−19.8943	+	10.1047i	−0.693893	+	0.352441i
$823$	6.73214	+	6.73214i	0.234668	+	0.234668i	0.814638	−	0.579970i	$-0.196936\pi$
$823$	6.73214	+	6.73214i	0.234668	+	0.234668i	−0.579970	+	0.814638i	$0.696936\pi$
$824$	−0.573810	−	1.88161i	−0.0199896	−	0.0655488i
$825$	−9.95745	−	6.03670i	−0.346674	−	0.210171i
$826$	1.48156	−	1.02206i	0.0515499	−	0.0355621i
$827$	−28.5233	+	11.8147i	−0.991851	+	0.410838i	−0.818803	−	0.574075i	$-0.805362\pi$
$827$	−28.5233	+	11.8147i	−0.991851	+	0.410838i	−0.173048	+	0.984913i	$0.555362\pi$
$828$	−10.4216	+	1.62335i	−0.362174	+	0.0564152i
$829$	17.2497	−	41.6444i	0.599106	−	1.44637i	−0.275389	−	0.961333i	$-0.588807\pi$
$829$	17.2497	−	41.6444i	0.599106	−	1.44637i	0.874494	−	0.485036i	$-0.161193\pi$
$830$	−1.64357	−	0.270524i	−0.0570490	−	0.00939003i
$831$	−37.5882	+	9.21424i	−1.30392	+	0.319638i
$832$	1.94822	+	9.64559i	0.0675423	+	0.334401i
$833$	−0.790027	−	0.850350i	−0.0273728	−	0.0294629i
$834$	1.28769	+	16.6331i	0.0445889	+	0.575955i
$835$	−14.5340	−	6.02018i	−0.502970	−	0.208337i
$836$	1.38330	−	4.08826i	0.0478423	−	0.141396i
$837$	−5.90774	+	12.0173i	−0.204201	+	0.415377i
$838$	5.18135	+	3.21844i	0.178987	+	0.111179i
$839$	−35.8955	+	35.8955i	−1.23925	+	1.23925i	−0.278940	+	0.960308i	$0.589983\pi$
$839$	−35.8955	+	35.8955i	−1.23925	+	1.23925i	−0.960308	+	0.278940i	$0.910017\pi$
$840$	10.8155	−	1.36251i	0.373171	−	0.0470112i
$841$	−7.55434	−	7.55434i	−0.260495	−	0.260495i
$842$	0.697840	+	2.98623i	0.0240492	+	0.102912i
$843$	−30.5096	−	41.5738i	−1.05081	−	1.43188i
$844$	−17.1395	+	19.5827i	−0.589966	+	0.674063i
$845$	3.69707	−	8.92551i	0.127183	−	0.307047i
$846$	−23.3196	+	46.1661i	−0.801746	+	1.58722i
$847$	20.7299	+	9.03642i	0.712286	+	0.310495i
$848$	−7.49041	+	28.1761i	−0.257222	+	0.967570i
$849$	−30.8551	+	7.56373i	−1.05895	+	0.259586i
$850$	−0.586737	−	0.817941i	−0.0201249	−	0.0280551i
$851$	−1.79709	−	0.744381i	−0.0616036	−	0.0255170i
$852$	13.3401	+	42.1043i	0.457025	+	1.44247i
$853$	0.723413	+	1.74647i	0.0247692	+	0.0597981i	0.935780	−	0.352584i	$-0.114697\pi$
$853$	0.723413	+	1.74647i	0.0247692	+	0.0597981i	−0.911011	+	0.412382i	$0.864697\pi$
$854$	−41.8481	−	7.68046i	−1.43201	−	0.262820i
$855$	−1.04268	+	3.31651i	−0.0356588	+	0.113422i
$856$	−2.32140	+	23.9313i	−0.0793438	+	0.817955i
$857$	−4.56010	+	4.56010i	−0.155770	+	0.155770i	−0.780689	−	0.624919i	$-0.785132\pi$
$857$	−4.56010	+	4.56010i	−0.155770	+	0.155770i	0.624919	+	0.780689i	$0.285132\pi$
$858$	−1.46390	+	4.48594i	−0.0499768	+	0.153147i
$859$	−30.7556	+	12.7394i	−1.04937	+	0.434663i	−0.839666	−	0.543102i	$-0.817250\pi$
$859$	−30.7556	+	12.7394i	−1.04937	+	0.434663i	−0.209702	+	0.977765i	$0.567250\pi$
$860$	−4.06329	−	8.21915i	−0.138557	−	0.280271i
$861$	4.99121	−	7.90162i	0.170100	−	0.269287i
$862$	30.2826	+	4.98439i	1.03143	+	0.169769i
$863$		−	31.8382i		−	1.08378i	−0.840448	−	0.541892i	$-0.817708\pi$
$863$		−	31.8382i		−	1.08378i	0.840448	−	0.541892i	$-0.182292\pi$
$864$	−8.63655	−	28.0964i	−0.293822	−	0.955860i
$865$	13.0087			0.442308
$866$	−49.9012	−	8.21353i	−1.69571	−	0.279107i
$867$	29.0569	+	4.45999i	0.986826	+	0.151469i
$868$	−13.6209	+	0.655045i	−0.462322	+	0.0222337i
$869$	14.5103	−	6.01036i	0.492228	−	0.203888i
$870$	12.3372	+	4.02603i	0.418272	+	0.136495i
$871$	−5.21862	−	5.21862i	−0.176826	−	0.176826i
$872$	−22.6689	+	18.6599i	−0.767666	+	0.631904i
$873$	11.8678	−	37.7488i	0.401665	−	1.27760i
$874$	3.33559	−	0.779480i	0.112828	−	0.0263663i
$875$	−0.380007	+	20.6742i	−0.0128466	+	0.698914i
$876$	−6.36969	+	2.01814i	−0.215212	+	0.0681866i
$877$	−5.50635	+	13.2935i	−0.185936	+	0.448889i	−0.989170	−	0.146774i	$-0.953111\pi$
$877$	−5.50635	+	13.2935i	−0.185936	+	0.448889i	0.803234	+	0.595664i	$0.203111\pi$
$878$	−25.4493	+	18.2557i	−0.858873	+	0.616099i
$879$	9.73891	+	39.7285i	0.328485	+	1.34001i
$880$	5.22225	−	0.697970i	0.176042	−	0.0235286i
$881$		−	40.9679i		−	1.38024i	−0.723693	−	0.690122i	$-0.757557\pi$
$881$		−	40.9679i		−	1.38024i	0.723693	−	0.690122i	$-0.242443\pi$
$882$	28.5345	−	8.23309i	0.960806	−	0.277222i
$883$	−8.85150	+	21.3694i	−0.297877	+	0.719138i	0.702099	+	0.712080i	$0.252247\pi$
$883$	−8.85150	+	21.3694i	−0.297877	+	0.719138i	−0.999975	+	0.00705786i	$0.997753\pi$
$884$	−0.268659	+	0.306955i	−0.00903598	+	0.0103240i
$885$	−0.564935	+	0.414587i	−0.0189901	+	0.0139362i
$886$	−33.5321	+	7.83596i	−1.12653	+	0.263254i
$887$	−18.5518	−	18.5518i	−0.622908	−	0.622908i	0.323366	−	0.946274i	$-0.395186\pi$
$887$	−18.5518	−	18.5518i	−0.622908	−	0.622908i	−0.946274	+	0.323366i	$0.895186\pi$
$888$	1.33592	−	5.25374i	0.0448306	−	0.176304i
$889$	−9.90955	−	25.2253i	−0.332355	−	0.846029i
$890$	−14.6453	−	9.09704i	−0.490911	−	0.304934i
$891$	3.02801	−	13.7662i	0.101442	−	0.461184i
$892$	13.0413	−	38.5429i	0.436655	−	1.29051i
$893$	6.42822	−	15.5191i	0.215112	−	0.519327i
$894$	1.68010	+	21.7019i	0.0561909	+	0.725819i
$895$		−	12.6217i		−	0.421896i
$896$	20.7862	−	21.5391i	0.694418	−	0.719572i
$897$	−3.63746	+	0.891675i	−0.121451	+	0.0297721i
$898$	−1.77457	+	10.7814i	−0.0592181	+	0.359779i
$899$	−14.9985	−	6.21258i	−0.500228	−	0.207201i
$900$	25.4491	−	3.96416i	0.848304	−	0.132139i
$901$	−1.11658	+	0.462501i	−0.0371985	+	0.0154081i
$902$	2.38346	−	3.83712i	0.0793605	−	0.127762i
$903$	−14.4061	−	20.4062i	−0.479403	−	0.679077i
$904$	−0.693497	−	0.369368i	−0.0230654	−	0.0122850i
$905$	7.25124	−	7.25124i	0.241039	−	0.241039i
$906$	17.9540	+	35.3483i	0.596483	+	1.17437i
$907$	−10.6666	+	4.41826i	−0.354180	+	0.146706i	−0.552677	−	0.833395i	$-0.686394\pi$
$907$	−10.6666	+	4.41826i	−0.354180	+	0.146706i	0.198498	+	0.980101i	$0.436394\pi$
$908$	−26.0867	−	22.8321i	−0.865717	−	0.757709i
$909$	3.48895	+	39.5026i	0.115721	+	1.31022i
$910$	3.78477	−	0.811395i	0.125464	−	0.0268975i
$911$	−53.2305			−1.76361			−0.881803	−	0.471619i	$-0.843670\pi$
$911$	−53.2305			−1.76361			−0.881803	+	0.471619i	$0.843670\pi$
$912$	3.48112	+	8.88900i	0.115271	+	0.294344i
$913$	−2.19329			−0.0725871
$914$	6.81754	+	9.50399i	0.225504	+	0.314364i
$915$	16.3728	+	2.51308i	0.541267	+	0.0830798i
$916$	4.45372	−	0.296310i	0.147155	−	0.00979035i
$917$	0.436902	−	23.7696i	0.0144278	−	0.784940i
$918$	0.708025	−	0.991671i	0.0233683	−	0.0327300i
$919$	14.6794	+	14.6794i	0.484229	+	0.484229i	0.906479	−	0.422250i	$-0.138760\pi$
$919$	14.6794	+	14.6794i	0.484229	+	0.484229i	−0.422250	+	0.906479i	$0.638760\pi$
$920$	2.65756	+	3.22852i	0.0876170	+	0.106441i
$921$	−27.4025	−	16.6128i	−0.902944	−	0.547409i
$922$	20.8704	−	33.5992i	0.687330	−	1.10653i
$923$	6.00163	+	14.4892i	0.197546	+	0.476919i
$924$	13.7609	−	4.08321i	0.452700	−	0.134328i
$925$	4.38844	+	1.81775i	0.144291	+	0.0597673i
$926$	3.18292	−	19.3378i	0.104597	−	0.635480i
$927$	0.964961	+	1.84994i	0.0316935	+	0.0607599i
$928$	33.3203	−	12.6344i	1.09379	−	0.414746i
$929$	2.05983			0.0675808			0.0337904	−	0.999429i	$-0.489242\pi$
$929$	2.05983			0.0675808			0.0337904	+	0.999429i	$0.489242\pi$
$930$	5.29319	−	0.409784i	0.173570	−	0.0134373i
$931$	−9.04068	+	3.36112i	−0.296296	+	0.110156i
$932$	28.4228	−	14.0513i	0.931021	−	0.460267i
$933$	0.126509	+	0.172387i	0.00414172	+	0.00564369i
$934$	−12.4649	+	20.0672i	−0.407864	+	0.656618i
$935$	0.154437	+	0.154437i	0.00505063	+	0.00505063i
$936$	−3.91104	−	9.67682i	−0.127836	−	0.316297i
$937$	−30.7612	+	30.7612i	−1.00493	+	1.00493i	−0.00493835	+	0.999988i	$0.501572\pi$
$937$	−30.7612	+	30.7612i	−1.00493	+	1.00493i	−0.999988	+	0.00493835i	$0.998428\pi$
$938$	−4.05257	+	22.0810i	−0.132321	+	0.720971i
$939$	5.99152	+	8.16432i	0.195526	+	0.266433i
$940$	20.4606	−	1.36126i	0.667351	−	0.0443994i
$941$	1.12969	−	2.72731i	0.0368268	−	0.0889078i	−0.904396	−	0.426694i	$-0.859678\pi$
$941$	1.12969	−	2.72731i	0.0368268	−	0.0889078i	0.941223	+	0.337786i	$0.109678\pi$
$942$	7.85784	−	9.17660i	0.256022	−	0.298990i
$943$	3.58512			0.116748
$944$	−0.494356	+	1.85958i	−0.0160899	+	0.0605242i
$945$	−11.0107	+	3.52839i	−0.358179	+	0.114778i
$946$	−7.03699	−	9.80993i	−0.228792	−	0.318948i
$947$	−11.4757	−	4.75338i	−0.372909	−	0.154464i	0.188354	−	0.982101i	$-0.439685\pi$
$947$	−11.4757	−	4.75338i	−0.372909	−	0.154464i	−0.561264	+	0.827637i	$0.689685\pi$
$948$	−15.9978	+	30.8365i	−0.519584	+	1.00152i
$949$	−2.19198	+	0.907948i	−0.0711547	+	0.0294733i
$950$	−8.14540	+	1.90346i	−0.264272	+	0.0617565i
$951$	−9.77974	+	16.1315i	−0.317130	+	0.523101i
$952$	1.23264	+	0.142480i	0.0399501	+	0.00461781i
$953$	−6.95641	−	6.95641i	−0.225340	−	0.225340i	0.585403	−	0.810743i	$-0.300936\pi$
$953$	−6.95641	−	6.95641i	−0.225340	−	0.225340i	−0.810743	+	0.585403i	$0.800936\pi$
$954$	2.31829	−	30.8362i	0.0750575	−	0.998359i
$955$	−6.55827	+	2.71653i	−0.212221	+	0.0879047i
$956$	23.7935	+	8.05073i	0.769537	+	0.260379i
$957$	16.8904	+	2.59253i	0.545988	+	0.0838045i
$958$	−10.6710	−	1.75640i	−0.344763	−	0.0567466i
$959$	22.0933	+	9.63078i	0.713431	+	0.310994i
$960$	−7.84416	+	8.61841i	−0.253169	+	0.278158i
$961$	24.3587			0.785764
$962$	0.312621	−	1.89933i	0.0100793	−	0.0612368i
$963$	−2.24366	−	25.4032i	−0.0723010	−	0.818607i
$964$	40.8355	+	13.8170i	1.31522	+	0.445017i
$965$	5.60213	+	13.5247i	0.180339	+	0.435377i
$966$	8.51570	+	7.56755i	0.273988	+	0.243482i
$967$	−0.135613	+	0.135613i	−0.00436103	+	0.00436103i	−0.709284	−	0.704923i	$-0.750982\pi$
$967$	−0.135613	+	0.135613i	−0.00436103	+	0.00436103i	0.704923	+	0.709284i	$0.250982\pi$
$968$	−23.1238	+	7.05179i	−0.743228	+	0.226653i
$969$	−0.205155	+	0.338400i	−0.00659053	+	0.0108710i
$970$	−15.2767	+	3.56995i	−0.490506	+	0.114624i
$971$	28.4585	−	11.7879i	0.913277	−	0.378292i	0.123967	−	0.992286i	$-0.460438\pi$
$971$	28.4585	−	11.7879i	0.913277	−	0.378292i	0.789310	+	0.613995i	$0.210438\pi$
$972$	14.4802	+	27.6102i	0.464452	+	0.885598i
$973$	12.9737	−	12.5054i	0.415919	−	0.400905i
$974$	−25.5376	+	18.3190i	−0.818278	+	0.586979i
$975$	8.88255	−	2.17744i	0.284469	−	0.0697339i
$976$	39.3462	−	22.8198i	1.25944	−	0.730443i
$977$	−7.14929			−0.228726			−0.114363	−	0.993439i	$-0.536483\pi$
$977$	−7.14929			−0.228726			−0.114363	+	0.993439i	$0.536483\pi$
$978$	35.5416	+	30.4340i	1.13650	+	0.973171i
$979$	−20.9736	−	8.68754i	−0.670319	−	0.277655i
$980$	−8.56915	−	8.07508i	−0.273731	−	0.257949i
$981$	19.9980	−	23.8728i	0.638488	−	0.762199i
$982$	−2.18580	−	9.35357i	−0.0697515	−	0.298484i
$983$	5.87649	+	5.87649i	0.187431	+	0.187431i	0.794584	−	0.607154i	$-0.207689\pi$
$983$	5.87649	+	5.87649i	0.187431	+	0.187431i	−0.607154	+	0.794584i	$0.707689\pi$
$984$	1.43078	+	9.88833i	0.0456115	+	0.315228i
$985$	−8.10413	−	8.10413i	−0.258219	−	0.258219i
$986$	1.25484	+	0.779453i	0.0399622	+	0.0248228i
$987$	54.4944	−	12.3015i	1.73458	−	0.391561i
$988$	1.50224	+	3.03870i	0.0477925	+	0.0966739i
$989$	3.66684	−	8.85254i	0.116599	−	0.281494i
$990$	−5.30869	+	1.74547i	−0.168721	+	0.0554745i
$991$	23.6616			0.751636			0.375818	−	0.926694i	$-0.377362\pi$
$991$	23.6616			0.751636			0.375818	+	0.926694i	$0.377362\pi$
$992$	10.6155	−	9.99163i	0.337044	−	0.317235i
$993$	44.4220	−	10.8895i	1.40969	−	0.345567i
$994$	25.9125	−	40.0549i	0.821896	−	1.27046i
$995$	5.29123	−	12.7741i	0.167743	−	0.404968i
$996$	3.71193	−	3.12352i	0.117617	−	0.0989727i
$997$	38.1577	−	15.8054i	1.20847	−	0.500563i	0.314741	−	0.949178i	$-0.398082\pi$
$997$	38.1577	−	15.8054i	1.20847	−	0.500563i	0.893725	+	0.448614i	$0.148082\pi$
$998$	−14.3650	+	23.1262i	−0.454716	+	0.732046i
$999$	−0.368936	+	5.73791i	−0.0116726	+	0.181540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.8	yes	496
3.2	odd	2	inner	672.2.bo.a.125.117	yes	496
7.6	odd	2	inner	672.2.bo.a.125.7	✓	496
21.20	even	2	inner	672.2.bo.a.125.118	yes	496
32.21	even	8	inner	672.2.bo.a.629.118	yes	496
96.53	odd	8	inner	672.2.bo.a.629.7	yes	496
224.181	odd	8	inner	672.2.bo.a.629.117	yes	496
672.629	even	8	inner	672.2.bo.a.629.8	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.7	✓	496	7.6	odd	2	inner
672.2.bo.a.125.8	yes	496	1.1	even	1	trivial
672.2.bo.a.125.117	yes	496	3.2	odd	2	inner
672.2.bo.a.125.118	yes	496	21.20	even	2	inner
672.2.bo.a.629.7	yes	496	96.53	odd	8	inner
672.2.bo.a.629.8	yes	496	672.629	even	8	inner
672.2.bo.a.629.117	yes	496	224.181	odd	8	inner
672.2.bo.a.629.118	yes	496	32.21	even	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39544 - 0.229683i) q^{2} +(1.71200 + 0.262778i) q^{3} +(1.89449 + 0.641017i) q^{4} +(0.321849 + 0.777011i) q^{5} +(-2.32863 - 0.759907i) q^{6} +(0.967393 + 2.46255i) q^{7} +(-2.49641 - 1.32963i) q^{8} +(2.86190 + 0.899751i) q^{9} +O(q^{10})\)	\(q+(-1.39544 - 0.229683i) q^{2} +(1.71200 + 0.262778i) q^{3} +(1.89449 + 0.641017i) q^{4} +(0.321849 + 0.777011i) q^{5} +(-2.32863 - 0.759907i) q^{6} +(0.967393 + 2.46255i) q^{7} +(-2.49641 - 1.32963i) q^{8} +(2.86190 + 0.899751i) q^{9} +(-0.270653 - 1.15819i) q^{10} +(-0.599335 - 1.44692i) q^{11} +(3.07493 + 1.59525i) q^{12} +(1.13642 + 0.470719i) q^{13} +(-0.784330 - 3.65853i) q^{14} +(0.346824 + 1.41482i) q^{15} +(3.17820 + 2.42880i) q^{16} +0.165815i q^{17} +(-3.78694 - 1.91288i) q^{18} +(1.27301 + 0.527297i) q^{19} +(0.111662 + 1.67835i) q^{20} +(1.00907 + 4.47010i) q^{21} +(0.504001 + 2.15675i) q^{22} +(-1.24300 + 1.24300i) q^{23} +(-3.92447 - 2.93233i) q^{24} +(3.03537 - 3.03537i) q^{25} +(-1.47768 - 0.917874i) q^{26} +(4.66313 + 2.29242i) q^{27} +(0.254181 + 5.28539i) q^{28} +(-2.41071 + 5.81996i) q^{29} +(-0.159011 - 2.05395i) q^{30} +2.57708i q^{31} +(-3.87712 - 4.11922i) q^{32} +(-0.645844 - 2.63463i) q^{33} +(0.0380849 - 0.231385i) q^{34} +(-1.60207 + 1.54424i) q^{35} +(4.84508 + 3.53909i) q^{36} +(0.423455 + 1.02231i) q^{37} +(-1.65529 - 1.02820i) q^{38} +(1.82185 + 1.10450i) q^{39} +(0.229671 - 2.36768i) q^{40} +(-1.44212 - 1.44212i) q^{41} +(-0.381394 - 6.46951i) q^{42} +(-5.03594 + 2.08595i) q^{43} +(-0.207933 - 3.12537i) q^{44} +(0.221980 + 2.51331i) q^{45} +(2.02003 - 1.44904i) q^{46} -12.1909i q^{47} +(4.80284 + 4.99327i) q^{48} +(-5.12830 + 4.76451i) q^{49} +(-4.93285 + 3.53850i) q^{50} +(-0.0435725 + 0.283876i) q^{51} +(1.85119 + 1.62023i) q^{52} +(2.78926 + 6.73386i) q^{53} +(-5.98058 - 4.26997i) q^{54} +(0.931380 - 0.931380i) q^{55} +(0.859271 - 7.43382i) q^{56} +(2.04083 + 1.23725i) q^{57} +(4.70074 - 7.56769i) q^{58} +(0.184087 + 0.444425i) q^{59} +(-0.249867 + 2.90268i) q^{60} +(4.35156 - 10.5056i) q^{61} +(0.591911 - 3.59615i) q^{62} +(0.552895 + 7.91797i) q^{63} +(4.46416 + 6.63862i) q^{64} +1.03451i q^{65} +(0.296105 + 3.82480i) q^{66} +(-5.54325 - 2.29609i) q^{67} +(-0.106290 + 0.314135i) q^{68} +(-2.45466 + 1.80139i) q^{69} +(2.59028 - 1.78692i) q^{70} +(9.01557 + 9.01557i) q^{71} +(-5.94814 - 6.05142i) q^{72} +(-1.36391 + 1.36391i) q^{73} +(-0.356098 - 1.52383i) q^{74} +(5.99419 - 4.39894i) q^{75} +(2.07370 + 1.81498i) q^{76} +(2.98333 - 2.87564i) q^{77} +(-2.28859 - 1.95970i) q^{78} +10.0284i q^{79} +(-0.864308 + 3.25120i) q^{80} +(7.38090 + 5.14999i) q^{81} +(1.68116 + 2.34362i) q^{82} +(0.535926 - 1.29384i) q^{83} +(-0.953724 + 9.11539i) q^{84} +(-0.128840 + 0.0533673i) q^{85} +(7.50644 - 1.75415i) q^{86} +(-5.65649 + 9.33030i) q^{87} +(-0.427686 + 4.40901i) q^{88} +(10.2497 - 10.2497i) q^{89} +(0.267505 - 3.55815i) q^{90} +(-0.0598082 + 3.25385i) q^{91} +(-3.15165 + 1.55807i) q^{92} +(-0.677198 + 4.41196i) q^{93} +(-2.80004 + 17.0116i) q^{94} +1.15885i q^{95} +(-5.55519 - 8.07093i) q^{96} -13.1901i q^{97} +(8.25055 - 5.47068i) q^{98} +(-0.413364 - 4.68020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

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Modular forms

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