LMFDB - Embedded newform 192.2.r.a.157.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [192,2,Mod(13,192)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(192, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.r (of order $16$, degree $8$, 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:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			157.12
Character	$\chi$	$=$	192.157
Dual form			192.2.r.a.181.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.914936 - 1.07837i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.325783 - 1.97329i) q^{4} +(-1.12099 + 1.67768i) q^{5} +(1.10774 - 0.879159i) q^{6} +(3.63169 - 1.50430i) q^{7} +(-2.42601 - 1.45412i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})$	\(q+(0.914936 - 1.07837i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.325783 - 1.97329i) q^{4} +(-1.12099 + 1.67768i) q^{5} +(1.10774 - 0.879159i) q^{6} +(3.63169 - 1.50430i) q^{7} +(-2.42601 - 1.45412i) q^{8} +(0.923880 + 0.382683i) q^{9} +(0.783533 + 2.74382i) q^{10} +(0.181766 + 0.913800i) q^{11} +(0.0654458 - 1.99893i) q^{12} +(-2.94399 - 4.40600i) q^{13} +(1.70057 - 5.29266i) q^{14} +(-1.42675 + 1.42675i) q^{15} +(-3.78773 + 1.28573i) q^{16} +(2.67163 + 2.67163i) q^{17} +(1.25797 - 0.646157i) q^{18} +(-6.32808 + 4.22829i) q^{19} +(3.67574 + 1.66547i) q^{20} +(3.85539 - 0.766884i) q^{21} +(1.15172 + 0.640057i) q^{22} +(-3.18943 + 7.69996i) q^{23} +(-2.09572 - 1.89947i) q^{24} +(0.355428 + 0.858079i) q^{25} +(-7.44489 - 0.856480i) q^{26} +(0.831470 + 0.555570i) q^{27} +(-4.15156 - 6.67630i) q^{28} +(0.769671 - 3.86940i) q^{29} +(0.233185 + 2.84395i) q^{30} -4.08619i q^{31} +(-2.07903 + 5.26095i) q^{32} +0.931702i q^{33} +(5.32538 - 0.436646i) q^{34} +(-1.54736 + 7.77911i) q^{35} +(0.454160 - 1.94775i) q^{36} +(2.30594 + 1.54078i) q^{37} +(-1.23011 + 10.6927i) q^{38} +(-2.02786 - 4.89568i) q^{39} +(5.15908 - 2.44002i) q^{40} +(0.846170 - 2.04283i) q^{41} +(2.70044 - 4.85920i) q^{42} +(3.25306 - 0.647073i) q^{43} +(1.74397 - 0.656378i) q^{44} +(-1.67768 + 1.12099i) q^{45} +(5.38532 + 10.4844i) q^{46} +(-1.41580 - 1.41580i) q^{47} +(-3.96578 + 0.522075i) q^{48} +(5.97654 - 5.97654i) q^{49} +(1.25052 + 0.401803i) q^{50} +(2.09908 + 3.14150i) q^{51} +(-7.73520 + 7.24475i) q^{52} +(-2.22367 - 11.1792i) q^{53} +(1.35985 - 0.388324i) q^{54} +(-1.73682 - 0.719415i) q^{55} +(-10.9980 - 1.63146i) q^{56} +(-7.03139 + 2.91250i) q^{57} +(-3.46846 - 4.37024i) q^{58} +(-4.86163 + 7.27594i) q^{59} +(3.28020 + 2.35057i) q^{60} +(-7.71722 - 1.53505i) q^{61} +(-4.40645 - 3.73861i) q^{62} +3.93092 q^{63} +(3.77109 + 7.05541i) q^{64} +10.6920 q^{65} +(1.00472 + 0.852448i) q^{66} +(10.8476 + 2.15772i) q^{67} +(4.40152 - 6.14226i) q^{68} +(-4.63033 + 6.92978i) q^{69} +(6.97306 + 8.78603i) q^{70} +(-8.29620 + 3.43640i) q^{71} +(-1.68488 - 2.27182i) q^{72} +(-1.40360 - 0.581389i) q^{73} +(3.77132 - 1.07695i) q^{74} +(0.181196 + 0.910932i) q^{75} +(10.4052 + 11.1096i) q^{76} +(2.03474 + 3.04521i) q^{77} +(-7.13474 - 2.29245i) q^{78} +(7.55405 - 7.55405i) q^{79} +(2.08896 - 7.79588i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-1.42875 - 2.78155i) q^{82} +(3.83208 - 2.56051i) q^{83} +(-2.76930 - 7.35795i) q^{84} +(-7.47700 + 1.48727i) q^{85} +(2.27855 - 4.10004i) q^{86} +(1.50976 - 3.64489i) q^{87} +(0.887804 - 2.48120i) q^{88} +(-2.90446 - 7.01198i) q^{89} +(-0.326123 + 2.83480i) q^{90} +(-17.3196 - 11.5726i) q^{91} +(16.2333 + 3.78514i) q^{92} +(0.797177 - 4.00768i) q^{93} +(-2.82214 + 0.231397i) q^{94} -15.3564i q^{95} +(-3.06545 + 4.75426i) q^{96} -5.94812i q^{97} +(-0.976796 - 11.9131i) q^{98} +(-0.181766 + 0.913800i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.914936	−	1.07837i	0.646958	−	0.762526i
$2$	0.914936	−	1.07837i	0.646958	−	0.762526i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$3$	0.980785	+	0.195090i	0.566257	+	0.112635i
$4$	−0.325783	−	1.97329i	−0.162892	−	0.986644i
$5$	−1.12099	+	1.67768i	−0.501322	+	0.750281i	−0.992693	−	0.120670i	$-0.961496\pi$
$5$	−1.12099	+	1.67768i	−0.501322	+	0.750281i	0.491371	+	0.870950i	$0.336496\pi$
$6$	1.10774	−	0.879159i	0.452231	−	0.358915i
$7$	3.63169	−	1.50430i	1.37265	−	0.568571i	0.430145	−	0.902760i	$-0.358462\pi$
$7$	3.63169	−	1.50430i	1.37265	−	0.568571i	0.942506	+	0.334189i	$0.108462\pi$
$8$	−2.42601	−	1.45412i	−0.857726	−	0.514108i
$9$	0.923880	+	0.382683i	0.307960	+	0.127561i
$10$	0.783533	+	2.74382i	0.247775	+	0.867671i
$11$	0.181766	+	0.913800i	0.0548045	+	0.275521i	0.998464	−	0.0553958i	$-0.0176420\pi$
$11$	0.181766	+	0.913800i	0.0548045	+	0.275521i	−0.943660	+	0.330917i	$0.892642\pi$
$12$	0.0654458	−	1.99893i	0.0188926	−	0.577041i
$13$	−2.94399	−	4.40600i	−0.816517	−	1.22200i	−0.972189	−	0.234196i	$-0.924754\pi$
$13$	−2.94399	−	4.40600i	−0.816517	−	1.22200i	0.155672	−	0.987809i	$-0.450246\pi$
$14$	1.70057	−	5.29266i	0.454497	−	1.41452i
$15$	−1.42675	+	1.42675i	−0.368385	+	0.368385i
$16$	−3.78773	+	1.28573i	−0.946933	+	0.321432i
$17$	2.67163	+	2.67163i	0.647965	+	0.647965i	0.952501	−	0.304536i	$-0.0985014\pi$
$17$	2.67163	+	2.67163i	0.647965	+	0.647965i	−0.304536	+	0.952501i	$0.598501\pi$
$18$	1.25797	−	0.646157i	0.296506	−	0.152301i
$19$	−6.32808	+	4.22829i	−1.45176	+	0.970036i	−0.454927	+	0.890529i	$0.650335\pi$
$19$	−6.32808	+	4.22829i	−1.45176	+	0.970036i	−0.996834	+	0.0795077i	$0.974665\pi$
$20$	3.67574	+	1.66547i	0.821921	+	0.372411i
$21$	3.85539	−	0.766884i	0.841314	−	0.167348i
$22$	1.15172	+	0.640057i	0.245548	+	0.136461i
$23$	−3.18943	+	7.69996i	−0.665041	+	1.60555i	0.124758	+	0.992187i	$0.460185\pi$
$23$	−3.18943	+	7.69996i	−0.665041	+	1.60555i	−0.789800	+	0.613365i	$0.789815\pi$
$24$	−2.09572	−	1.89947i	−0.427786	−	0.387727i
$25$	0.355428	+	0.858079i	0.0710856	+	0.171616i
$26$	−7.44489	−	0.856480i	−1.46006	−	0.167969i
$27$	0.831470	+	0.555570i	0.160016	+	0.106920i
$28$	−4.15156	−	6.67630i	−0.784570	−	1.26170i
$29$	0.769671	−	3.86940i	0.142924	−	0.718529i	−0.841154	−	0.540795i	$-0.818123\pi$
$29$	0.769671	−	3.86940i	0.142924	−	0.718529i	0.984079	−	0.177734i	$-0.0568766\pi$
$30$	0.233185	+	2.84395i	0.0425736	+	0.519232i
$31$		−	4.08619i		−	0.733902i	−0.930240	−	0.366951i	$-0.880402\pi$
$31$		−	4.08619i		−	0.733902i	0.930240	−	0.366951i	$-0.119598\pi$
$32$	−2.07903	+	5.26095i	−0.367525	+	0.930014i
$33$			0.931702i			0.162189i
$34$	5.32538	−	0.436646i	0.913296	−	0.0748842i
$35$	−1.54736	+	7.77911i	−0.261552	+	1.31491i
$36$	0.454160	−	1.94775i	0.0756933	−	0.324625i
$37$	2.30594	+	1.54078i	0.379094	+	0.253302i	0.730488	−	0.682925i	$-0.239292\pi$
$37$	2.30594	+	1.54078i	0.379094	+	0.253302i	−0.351395	+	0.936227i	$0.614292\pi$
$38$	−1.23011	+	10.6927i	−0.199551	+	1.73458i
$39$	−2.02786	−	4.89568i	−0.324717	−	0.783937i
$40$	5.15908	−	2.44002i	0.815721	−	0.385802i
$41$	0.846170	−	2.04283i	0.132149	−	0.319037i	−0.843929	−	0.536455i	$-0.819763\pi$
$41$	0.846170	−	2.04283i	0.132149	−	0.319037i	0.976079	+	0.217417i	$0.0697633\pi$
$42$	2.70044	−	4.85920i	0.416687	−	0.749791i
$43$	3.25306	−	0.647073i	0.496086	−	0.0986777i	0.0592949	−	0.998241i	$-0.481115\pi$
$43$	3.25306	−	0.647073i	0.496086	−	0.0986777i	0.436791	+	0.899563i	$0.356115\pi$
$44$	1.74397	−	0.656378i	0.262914	−	0.0989527i
$45$	−1.67768	+	1.12099i	−0.250094	+	0.167107i
$46$	5.38532	+	10.4844i	0.794022	+	1.54584i
$47$	−1.41580	−	1.41580i	−0.206516	−	0.206516i	0.596269	−	0.802785i	$-0.296649\pi$
$47$	−1.41580	−	1.41580i	−0.206516	−	0.206516i	−0.802785	+	0.596269i	$0.796649\pi$
$48$	−3.96578	+	0.522075i	−0.572412	+	0.0753550i
$49$	5.97654	−	5.97654i	0.853792	−	0.853792i
$50$	1.25052	+	0.401803i	0.176851	+	0.0568235i
$51$	2.09908	+	3.14150i	0.293931	+	0.439898i
$52$	−7.73520	+	7.24475i	−1.07268	+	1.00467i
$53$	−2.22367	−	11.1792i	−0.305445	−	1.53558i	−0.763002	−	0.646396i	$-0.776276\pi$
$53$	−2.22367	−	11.1792i	−0.305445	−	1.53558i	0.457557	−	0.889180i	$-0.348724\pi$
$54$	1.35985	−	0.388324i	0.185053	−	0.0528443i
$55$	−1.73682	−	0.719415i	−0.234193	−	0.0970058i
$56$	−10.9980	−	1.63146i	−1.46966	−	0.218013i
$57$	−7.03139	+	2.91250i	−0.931330	+	0.385770i
$58$	−3.46846	−	4.37024i	−0.455431	−	0.573841i
$59$	−4.86163	+	7.27594i	−0.632930	+	0.947246i	0.366926	+	0.930250i	$0.380410\pi$
$59$	−4.86163	+	7.27594i	−0.632930	+	0.947246i	−0.999856	+	0.0169960i	$0.994590\pi$
$60$	3.28020	+	2.35057i	0.423472	+	0.303458i
$61$	−7.71722	−	1.53505i	−0.988089	−	0.196543i	−0.325513	−	0.945538i	$-0.605537\pi$
$61$	−7.71722	−	1.53505i	−0.988089	−	0.196543i	−0.662576	+	0.748995i	$0.730537\pi$
$62$	−4.40645	−	3.73861i	−0.559619	−	0.474803i
$63$	3.93092			0.495249
$64$	3.77109	+	7.05541i	0.471387	+	0.881927i
$65$	10.6920			1.32618
$66$	1.00472	+	0.852448i	0.123673	+	0.104929i
$67$	10.8476	+	2.15772i	1.32524	+	0.263608i	0.806456	−	0.591295i	$-0.201383\pi$
$67$	10.8476	+	2.15772i	1.32524	+	0.263608i	0.518789	+	0.854902i	$0.326383\pi$
$68$	4.40152	−	6.14226i	0.533762	−	0.744859i
$69$	−4.63033	+	6.92978i	−0.557426	+	0.834247i
$70$	6.97306	+	8.78603i	0.833440	+	1.05013i
$71$	−8.29620	+	3.43640i	−0.984577	+	0.407825i	−0.816119	−	0.577884i	$-0.803879\pi$
$71$	−8.29620	+	3.43640i	−0.984577	+	0.407825i	−0.168458	+	0.985709i	$0.553879\pi$
$72$	−1.68488	−	2.27182i	−0.198565	−	0.267737i
$73$	−1.40360	−	0.581389i	−0.164279	−	0.0680464i	0.299029	−	0.954244i	$-0.403337\pi$
$73$	−1.40360	−	0.581389i	−0.164279	−	0.0680464i	−0.463307	+	0.886198i	$0.653337\pi$
$74$	3.77132	−	1.07695i	0.438407	−	0.125193i
$75$	0.181196	+	0.910932i	0.0209227	+	0.105185i
$76$	10.4052	+	11.1096i	1.19356	+	1.27436i
$77$	2.03474	+	3.04521i	0.231881	+	0.347034i
$78$	−7.13474	−	2.29245i	−0.807851	−	0.259569i
$79$	7.55405	−	7.55405i	0.849897	−	0.849897i	−0.140223	−	0.990120i	$-0.544782\pi$
$79$	7.55405	−	7.55405i	0.849897	−	0.849897i	0.990120	+	0.140223i	$0.0447818\pi$
$80$	2.08896	−	7.79588i	0.233553	−	0.871606i
$81$	0.707107	+	0.707107i	0.0785674	+	0.0785674i
$82$	−1.42875	−	2.78155i	−0.157779	−	0.307171i
$83$	3.83208	−	2.56051i	0.420625	−	0.281053i	−0.327192	−	0.944958i	$-0.606102\pi$
$83$	3.83208	−	2.56051i	0.420625	−	0.281053i	0.747817	+	0.663905i	$0.231102\pi$
$84$	−2.76930	−	7.35795i	−0.302156	−	0.802818i
$85$	−7.47700	+	1.48727i	−0.810994	+	0.161317i
$86$	2.27855	−	4.10004i	0.245703	−	0.442119i
$87$	1.50976	−	3.64489i	0.161864	−	0.390773i
$88$	0.887804	−	2.48120i	0.0946402	−	0.264497i
$89$	−2.90446	−	7.01198i	−0.307872	−	0.743268i	−0.999774	−	0.0212767i	$-0.993227\pi$
$89$	−2.90446	−	7.01198i	−0.307872	−	0.743268i	0.691902	−	0.721992i	$-0.256773\pi$
$90$	−0.326123	+	2.83480i	−0.0343764	+	0.298814i
$91$	−17.3196	−	11.5726i	−1.81559	−	1.21314i
$92$	16.2333	+	3.78514i	1.69244	+	0.394628i
$93$	0.797177	−	4.00768i	0.0826634	−	0.415577i
$94$	−2.82214	+	0.231397i	−0.291081	+	0.0238668i
$95$		−	15.3564i		−	1.57553i
$96$	−3.06545	+	4.75426i	−0.312866	+	0.485230i
$97$		−	5.94812i		−	0.603940i	−0.953317	−	0.301970i	$-0.902356\pi$
$97$		−	5.94812i		−	0.603940i	0.953317	−	0.301970i	$-0.0976442\pi$
$98$	−0.976796	−	11.9131i	−0.0986713	−	1.20341i
$99$	−0.181766	+	0.913800i	−0.0182682	+	0.0918403i
$100$	1.57744	−	0.980909i	0.157744	−	0.0980909i
$101$	2.66956	+	1.78374i	0.265631	+	0.177489i	0.681252	−	0.732049i	$-0.261436\pi$
$101$	2.66956	+	1.78374i	0.265631	+	0.177489i	−0.415621	+	0.909538i	$0.636436\pi$
$102$	5.30824	+	0.610674i	0.525594	+	0.0604658i
$103$	0.870540	+	2.10167i	0.0857769	+	0.207084i	0.960948	−	0.276731i	$-0.0892510\pi$
$103$	0.870540	+	2.10167i	0.0857769	+	0.207084i	−0.875171	+	0.483814i	$0.839251\pi$
$104$	0.735340	+	14.9699i	0.0721060	+	1.46792i
$105$	−3.03526	+	7.32777i	−0.296211	+	0.715117i
$106$	−14.0898	−	7.83027i	−1.36853	−	0.760543i
$107$	−5.54477	+	1.10292i	−0.536033	+	0.106624i	−0.455681	−	0.890143i	$-0.650604\pi$
$107$	−5.54477	+	1.10292i	−0.536033	+	0.106624i	−0.0803517	+	0.996767i	$0.525604\pi$
$108$	0.825421	−	1.82172i	0.0794262	−	0.175296i
$109$	9.70640	−	6.48561i	0.929705	−	0.621209i	0.00421890	−	0.999991i	$-0.498657\pi$
$109$	9.70640	−	6.48561i	0.929705	−	0.621209i	0.925486	+	0.378782i	$0.123657\pi$
$110$	−2.36488	+	1.21472i	−0.225482	+	0.115819i
$111$	1.96104	+	1.96104i	0.186134	+	0.186134i
$112$	−11.8218	+	10.3672i	−1.11705	+	0.979612i
$113$	8.10737	−	8.10737i	0.762677	−	0.762677i	−0.214129	−	0.976805i	$-0.568691\pi$
$113$	8.10737	−	8.10737i	0.762677	−	0.762677i	0.976805	+	0.214129i	$0.0686912\pi$
$114$	−3.29251	+	10.2472i	−0.308372	+	0.959740i
$115$	−9.34274	−	13.9824i	−0.871215	−	1.30387i
$116$	−7.88618	−	0.258197i	−0.732213	−	0.0239730i
$117$	−1.03379	−	5.19723i	−0.0955742	−	0.480484i
$118$	3.39811	+	11.8997i	0.312821	+	1.09545i
$119$	13.7215	+	5.68361i	1.25784	+	0.521016i
$120$	5.53597	−	1.38665i	0.505363	−	0.126584i
$121$	9.36068	−	3.87732i	0.850971	−	0.352484i
$122$	−8.71612	+	6.91758i	−0.789121	+	0.626288i
$123$	1.22845	−	1.83850i	0.110765	−	0.165772i
$124$	−8.06323	+	1.33121i	−0.724100	+	0.119547i
$125$	−11.7328	−	2.33380i	−1.04941	−	0.208741i
$126$	3.59654	−	4.23900i	0.320405	−	0.377640i
$127$	9.92782			0.880951			0.440476	−	0.897765i	$-0.354810\pi$
$127$	9.92782			0.880951			0.440476	+	0.897765i	$0.354810\pi$
$128$	11.0587	+	2.38860i	0.977459	+	0.211125i
$129$	3.31679			0.292027
$130$	9.78253	−	11.5300i	0.857985	−	1.01125i
$131$	1.26079	+	0.250788i	0.110156	+	0.0219114i	0.249861	−	0.968282i	$-0.419615\pi$
$131$	1.26079	+	0.250788i	0.110156	+	0.0219114i	−0.139704	+	0.990193i	$0.544615\pi$
$132$	1.83852	−	0.303533i	0.160022	−	0.0264192i
$133$	−16.6211	+	24.8752i	−1.44123	+	2.15695i
$134$	12.2517	−	9.72360i	1.05838	−	0.839991i
$135$	−1.86414	+	0.772151i	−0.160439	+	0.0664562i
$136$	−2.59655	−	10.3663i	−0.222652	−	0.888900i
$137$	−7.43980	−	3.08167i	−0.635625	−	0.263285i	0.0415158	−	0.999138i	$-0.486781\pi$
$137$	−7.43980	−	3.08167i	−0.635625	−	0.263285i	−0.677141	+	0.735853i	$0.736781\pi$
$138$	3.23644	+	11.3335i	0.275504	+	0.964775i
$139$	−0.726573	−	3.65273i	−0.0616271	−	0.309821i	0.937661	−	0.347552i	$-0.112987\pi$
$139$	−0.726573	−	3.65273i	−0.0616271	−	0.309821i	−0.999288	+	0.0377312i	$0.987987\pi$
$140$	15.8545	+	0.519084i	1.33995	+	0.0438706i
$141$	−1.11239	−	1.66481i	−0.0936802	−	0.140202i
$142$	−3.88477	+	12.0905i	−0.326002	+	1.01461i
$143$	3.49108	−	3.49108i	0.291939	−	0.291939i
$144$	−3.99143	−	0.261643i	−0.332619	−	0.0218036i
$145$	5.62881	+	5.62881i	0.467447	+	0.467447i
$146$	−1.91116	+	0.981669i	−0.158168	+	0.0812435i
$147$	7.02767	−	4.69574i	0.579632	−	0.387298i
$148$	2.28916	−	5.05224i	0.188168	−	0.415291i
$149$	12.5338	−	2.49312i	1.02680	−	0.204244i	0.347176	−	0.937800i	$-0.387141\pi$
$149$	12.5338	−	2.49312i	1.02680	−	0.204244i	0.679629	+	0.733556i	$0.262141\pi$
$150$	1.14811	+	0.638048i	0.0937426	+	0.0520964i
$151$	−2.30327	+	5.56058i	−0.187437	+	0.452514i	−0.989465	−	0.144773i	$-0.953755\pi$
$151$	−2.30327	+	5.56058i	−0.187437	+	0.452514i	0.802027	+	0.597287i	$0.203755\pi$
$152$	21.5004	−	1.05613i	1.74392	−	0.0856631i
$153$	1.44587	+	3.49065i	0.116892	+	0.282202i
$154$	5.14554	+	0.591957i	0.414639	+	0.0477012i
$155$	6.85532	+	4.58058i	0.550632	+	0.367921i
$156$	−8.99995	+	5.59648i	−0.720573	+	0.448077i
$157$	−2.62506	+	13.1971i	−0.209503	+	1.05324i	0.722661	+	0.691203i	$0.242919\pi$
$157$	−2.62506	+	13.1971i	−0.209503	+	1.05324i	−0.932163	+	0.362038i	$0.882081\pi$
$158$	−1.23462	−	15.0576i	−0.0982212	−	1.19792i
$159$		−	11.3982i		−	0.903934i
$160$	−6.49561	−	9.38542i	−0.513523	−	0.741983i
$161$			32.7617i			2.58199i
$162$	1.40948	−	0.115568i	0.110739	−	0.00907991i
$163$	−3.13385	+	15.7549i	−0.245462	+	1.23402i	0.639659	+	0.768659i	$0.279076\pi$
$163$	−3.13385	+	15.7549i	−0.245462	+	1.23402i	−0.885121	+	0.465361i	$0.845924\pi$
$164$	−4.30677	−	1.00421i	−0.336302	−	0.0784160i
$165$	−1.56310	−	1.04443i	−0.121687	−	0.0813086i
$166$	0.744915	−	6.47512i	0.0578166	−	0.502567i
$167$	−5.52601	−	13.3410i	−0.427616	−	1.03236i	−0.980041	−	0.198794i	$-0.936298\pi$
$167$	−5.52601	−	13.3410i	−0.427616	−	1.03236i	0.552426	−	0.833562i	$-0.313702\pi$
$168$	−10.4684	−	3.74571i	−0.807651	−	0.288988i
$169$	−5.77084	+	13.9320i	−0.443911	+	1.07170i
$170$	−5.23714	+	9.42376i	−0.401671	+	0.722769i
$171$	−7.46448	+	1.48478i	−0.570823	+	0.113544i
$172$	−2.33665	−	6.20841i	−0.178168	−	0.473387i
$173$	−0.203918	+	0.136254i	−0.0155036	+	0.0103592i	−0.563298	−	0.826254i	$-0.690468\pi$
$173$	−0.203918	+	0.136254i	−0.0155036	+	0.0103592i	0.547794	+	0.836613i	$0.315468\pi$
$174$	−2.54922	−	4.96293i	−0.193256	−	0.376239i
$175$	2.58161	+	2.58161i	0.195151	+	0.195151i
$176$	−1.86338	−	3.22753i	−0.140458	−	0.243284i
$177$	−6.18768	+	6.18768i	−0.465094	+	0.465094i
$178$	−10.2189	−	3.28342i	−0.765941	−	0.246103i
$179$	5.66279	+	8.47496i	0.423257	+	0.633448i	0.980411	−	0.196960i	$-0.0631070\pi$
$179$	5.66279	+	8.47496i	0.423257	+	0.633448i	−0.557155	+	0.830409i	$0.688107\pi$
$180$	2.75859	+	2.94534i	0.205613	+	0.219533i
$181$	3.65189	+	18.3593i	0.271443	+	1.36464i	0.840265	+	0.542176i	$0.182399\pi$
$181$	3.65189	+	18.3593i	0.271443	+	1.36464i	−0.568822	+	0.822461i	$0.692601\pi$
$182$	−28.3259	+	8.08885i	−2.09966	+	0.599585i
$183$	−7.26946	−	3.01111i	−0.537374	−	0.222588i
$184$	18.9342	−	14.0424i	1.39585	−	1.03522i
$185$	−5.16986	+	2.14143i	−0.380096	+	0.157441i
$186$	−3.59241	−	4.52642i	−0.263408	−	0.331894i
$187$	−1.95572	+	2.92694i	−0.143017	+	0.214039i
$188$	−2.33254	+	3.25504i	−0.170118	+	0.237398i
$189$	3.85539	+	0.766884i	0.280438	+	0.0557826i
$190$	−16.5599	−	14.0501i	−1.20138	−	1.01930i
$191$	4.23754			0.306618			0.153309	−	0.988178i	$-0.451007\pi$
$191$	4.23754			0.306618			0.153309	+	0.988178i	$0.451007\pi$
$192$	2.32219	+	7.65555i	0.167590	+	0.552492i
$193$	−23.8234			−1.71485			−0.857424	−	0.514611i	$-0.827936\pi$
$193$	−23.8234			−1.71485			−0.857424	+	0.514611i	$0.827936\pi$
$194$	−6.41430	−	5.44215i	−0.460520	−	0.390723i
$195$	10.4866	+	2.08591i	0.750961	+	0.149375i
$196$	−13.7405	−	9.84638i	−0.981464	−	0.703313i
$197$	8.52138	−	12.7531i	0.607123	−	0.908624i	−0.392816	−	0.919617i	$-0.628499\pi$
$197$	8.52138	−	12.7531i	0.607123	−	0.908624i	0.999940	+	0.0109929i	$0.00349923\pi$
$198$	0.819114	+	1.03208i	0.0582119	+	0.0733468i
$199$	−7.47005	+	3.09419i	−0.529538	+	0.219342i	−0.631401	−	0.775457i	$-0.717520\pi$
$199$	−7.47005	+	3.09419i	−0.529538	+	0.219342i	0.101863	+	0.994798i	$0.467520\pi$
$200$	0.385473	−	2.59854i	0.0272571	−	0.183745i
$201$	10.2182	+	4.23252i	0.720737	+	0.298539i
$202$	4.36602	−	1.24678i	0.307192	−	0.0877228i
$203$	−3.02551	−	15.2103i	−0.212349	−	1.06755i
$204$	5.51524	−	5.16555i	0.386144	−	0.361661i
$205$	2.47867	+	3.70960i	0.173118	+	0.259089i
$206$	3.06288	+	0.984126i	0.213401	+	0.0685673i
$207$	−5.89329	+	5.89329i	−0.409612	+	0.409612i
$208$	16.8160	+	12.9036i	1.16598	+	0.894701i
$209$	−5.01404	−	5.01404i	−0.346829	−	0.346829i
$210$	5.12501	+	9.97759i	0.353659	+	0.688519i
$211$	17.5561	−	11.7306i	1.20861	−	0.807568i	0.222708	−	0.974885i	$-0.428510\pi$
$211$	17.5561	−	11.7306i	1.20861	−	0.807568i	0.985903	+	0.167317i	$0.0535104\pi$
$212$	−21.3353	+	8.02993i	−1.46531	+	0.551498i
$213$	−8.80719	+	1.75186i	−0.603459	+	0.120035i
$214$	−3.88375	+	6.98844i	−0.265487	+	0.477720i
$215$	−2.56106	+	6.18294i	−0.174663	+	0.421673i
$216$	−1.20929	−	2.55687i	−0.0822820	−	0.173973i
$217$	−6.14685	−	14.8398i	−0.417275	−	1.00739i
$218$	1.88682	−	16.4011i	0.127792	−	1.11082i
$219$	−1.26320	−	0.844046i	−0.0853594	−	0.0570353i
$220$	−0.853785	+	3.66162i	−0.0575622	+	0.246866i
$221$	3.90593	−	19.6364i	0.262741	−	1.32089i
$222$	3.90896	−	0.320509i	0.262352	−	0.0215111i
$223$			17.0292i			1.14036i	0.821520	+	0.570180i	$0.193127\pi$
$223$			17.0292i			1.14036i	−0.821520	+	0.570180i	$0.806873\pi$
$224$	0.363618	+	22.2336i	0.0242952	+	1.48555i
$225$			0.928778i			0.0619185i
$226$	−1.32505	−	16.1605i	−0.0881413	−	1.07498i
$227$	−2.87749	+	14.4661i	−0.190986	+	0.960149i	0.759766	+	0.650196i	$0.225313\pi$
$227$	−2.87749	+	14.4661i	−0.190986	+	0.960149i	−0.950752	+	0.309953i	$0.899687\pi$
$228$	8.03790	+	12.9261i	0.532323	+	0.856053i
$229$	2.00107	+	1.33707i	0.132234	+	0.0883560i	0.619928	−	0.784659i	$-0.287162\pi$
$229$	2.00107	+	1.33707i	0.132234	+	0.0883560i	−0.487694	+	0.873015i	$0.662162\pi$
$230$	−23.6263	−	2.71803i	−1.55787	−	0.179222i
$231$	1.40156	+	3.38366i	0.0922157	+	0.222628i
$232$	−7.49378	+	8.26802i	−0.491991	+	0.542822i
$233$	−8.74599	+	21.1147i	−0.572969	+	1.38327i	0.326047	+	0.945354i	$0.394283\pi$
$233$	−8.74599	+	21.1147i	−0.572969	+	1.38327i	−0.899016	+	0.437916i	$0.855717\pi$
$234$	−6.55042	−	3.64032i	−0.428214	−	0.237975i
$235$	3.96237	−	0.788164i	0.258476	−	0.0514141i
$236$	15.9414	+	7.22301i	1.03769	+	0.470178i
$237$	8.88263	−	5.93518i	0.576989	−	0.385531i
$238$	18.6833	−	9.59672i	1.21106	−	0.622063i
$239$	−5.69317	−	5.69317i	−0.368260	−	0.368260i	0.498582	−	0.866842i	$-0.333854\pi$
$239$	−5.69317	−	5.69317i	−0.368260	−	0.368260i	−0.866842	+	0.498582i	$0.833854\pi$
$240$	3.56973	−	7.23855i	0.230425	−	0.467246i
$241$	17.2207	−	17.2207i	1.10928	−	1.10928i	0.116036	−	0.993245i	$-0.462981\pi$
$241$	17.2207	−	17.2207i	1.10928	−	1.10928i	0.993245	−	0.116036i	$-0.0370189\pi$
$242$	4.38322	−	13.6418i	0.281764	−	0.876930i
$243$	0.555570	+	0.831470i	0.0356398	+	0.0533388i
$244$	−0.514954	+	15.7284i	−0.0329666	+	1.00691i
$245$	3.32708	+	16.7264i	0.212559	+	1.06861i
$246$	−0.858642	−	3.00684i	−0.0547450	−	0.191709i
$247$	37.2597	+	15.4335i	2.37078	+	0.982008i
$248$	−5.94180	+	9.91316i	−0.377305	+	0.629486i
$249$	4.25797	−	1.76371i	0.269838	−	0.111771i
$250$	−13.2515	+	10.5171i	−0.838096	+	0.665158i
$251$	4.95027	−	7.40860i	0.312458	−	0.467627i	−0.641689	−	0.766965i	$-0.721766\pi$
$251$	4.95027	−	7.40860i	0.312458	−	0.467627i	0.954147	+	0.299338i	$0.0967659\pi$
$252$	−1.28063	−	7.75683i	−0.0806719	−	0.488634i
$253$	−7.61595	−	1.51491i	−0.478811	−	0.0952414i
$254$	9.08332	−	10.7059i	0.569938	−	0.671748i
$255$	−7.62348			−0.477401
$256$	12.6938	−	9.73999i	0.793363	−	0.608749i
$257$	−9.02201			−0.562777			−0.281389	−	0.959594i	$-0.590795\pi$
$257$	−9.02201			−0.562777			−0.281389	+	0.959594i	$0.590795\pi$
$258$	3.03465	−	3.57674i	0.188929	−	0.222678i
$259$	10.6922	+	2.12682i	0.664384	+	0.132154i
$260$	−3.48329	−	21.0985i	−0.216024	−	1.30847i
$261$	2.19184	−	3.28032i	0.135671	−	0.203046i
$262$	1.42399	−	1.13015i	0.0879743	−	0.0698211i
$263$	−28.2079	+	11.6841i	−1.73937	+	0.720471i	−0.740547	+	0.672005i	$0.765434\pi$
$263$	−28.2079	+	11.6841i	−1.73937	+	0.720471i	−0.998825	+	0.0484669i	$0.984566\pi$
$264$	1.35480	−	2.26032i	0.0833824	−	0.139113i
$265$	21.2478	+	8.80111i	1.30524	+	0.540648i
$266$	11.6175	+	40.6829i	0.712317	+	2.49443i
$267$	−1.48068	−	7.44388i	−0.0906161	−	0.455558i
$268$	0.723838	−	22.1084i	0.0442154	−	1.35048i
$269$	1.35668	+	2.03042i	0.0827184	+	0.123797i	0.870522	−	0.492130i	$-0.163782\pi$
$269$	1.35668	+	2.03042i	0.0827184	+	0.123797i	−0.787803	+	0.615927i	$0.788782\pi$
$270$	−0.872898	+	2.71671i	−0.0531229	+	0.165333i
$271$	−9.97526	+	9.97526i	−0.605954	+	0.605954i	−0.941886	−	0.335932i	$-0.890949\pi$
$271$	−9.97526	+	9.97526i	−0.605954	+	0.605954i	0.335932	+	0.941886i	$0.390949\pi$
$272$	−13.5544	−	6.68441i	−0.821856	−	0.405302i
$273$	−14.7291	−	14.7291i	−0.891447	−	0.891447i
$274$	−10.1301	+	5.20337i	−0.611984	+	0.314347i
$275$	−0.719508	+	0.480760i	−0.0433879	+	0.0289909i
$276$	15.1829	+	6.87937i	0.913905	+	0.414089i
$277$	2.76307	−	0.549608i	0.166017	−	0.0330228i	−0.111382	−	0.993778i	$-0.535528\pi$
$277$	2.76307	−	0.549608i	0.166017	−	0.0330228i	0.277399	+	0.960755i	$0.410528\pi$
$278$	−4.60378	−	2.55850i	−0.276116	−	0.153448i
$279$	1.56372	−	3.77515i	0.0936174	−	0.226012i
$280$	15.0657	−	16.6222i	0.900345	−	0.993367i
$281$	−10.0149	−	24.1782i	−0.597441	−	1.44235i	−0.876181	−	0.481983i	$-0.839917\pi$
$281$	−10.0149	−	24.1782i	−0.597441	−	1.44235i	0.278740	−	0.960367i	$-0.410083\pi$
$282$	−2.81305	−	0.323621i	−0.167515	−	0.0192714i
$283$	−23.2829	−	15.5572i	−1.38403	−	0.924777i	−0.999999	−	0.00145540i	$-0.999537\pi$
$283$	−23.2829	−	15.5572i	−1.38403	−	0.924777i	−0.384028	−	0.923322i	$-0.625463\pi$
$284$	9.48376	+	15.2513i	0.562758	+	0.904996i
$285$	2.99588	−	15.0613i	0.177460	−	0.892154i
$286$	−0.570577	−	6.95881i	−0.0337389	−	0.411483i
$287$		−	8.69184i		−	0.513063i
$288$	−3.93406	+	4.06487i	−0.231816	+	0.239525i
$289$		−	2.72482i		−	0.160283i
$290$	11.2200	−	0.919964i	0.658859	−	0.0540221i
$291$	1.16042	−	5.83383i	0.0680250	−	0.341985i
$292$	−0.689979	+	2.95911i	−0.0403780	+	0.173169i
$293$	22.4850	+	15.0240i	1.31359	+	0.877710i	0.997475	−	0.0710121i	$-0.0226229\pi$
$293$	22.4850	+	15.0240i	1.31359	+	0.877710i	0.316111	+	0.948722i	$0.397623\pi$
$294$	1.36610	−	11.8748i	0.0796728	−	0.692550i
$295$	−6.75685	−	16.3125i	−0.393399	−	0.949750i
$296$	−3.35377	−	7.09105i	−0.194934	−	0.412159i
$297$	−0.356547	+	0.860781i	−0.0206890	+	0.0499476i
$298$	8.77907	−	15.7971i	0.508558	−	0.915103i
$299$	43.3157	−	8.61602i	2.50501	−	0.498277i
$300$	1.73850	−	0.654317i	0.100372	−	0.0377770i
$301$	10.8407	−	7.24353i	0.624848	−	0.417510i
$302$	3.88905	+	7.57137i	0.223790	+	0.435683i
$303$	2.27028	+	2.27028i	0.130424	+	0.130424i
$304$	18.5326	−	24.1518i	1.06292	−	1.38520i
$305$	11.2262	−	11.2262i	0.642813	−	0.642813i
$306$	5.08711	+	1.63453i	0.290811	+	0.0934397i
$307$	−0.868349	−	1.29958i	−0.0495593	−	0.0741707i	0.805863	−	0.592103i	$-0.201702\pi$
$307$	−0.868349	−	1.29958i	−0.0495593	−	0.0741707i	−0.855422	+	0.517932i	$0.826702\pi$
$308$	5.34619	−	5.00722i	0.304628	−	0.285313i
$309$	0.443798	+	2.23112i	0.0252468	+	0.126924i
$310$	11.2118	−	3.20166i	0.636785	−	0.181842i
$311$	−12.8769	−	5.33380i	−0.730184	−	0.302452i	−0.0135565	−	0.999908i	$-0.504315\pi$
$311$	−12.8769	−	5.33380i	−0.730184	−	0.302452i	−0.716628	+	0.697456i	$0.754315\pi$
$312$	−2.19928	+	14.8257i	−0.124510	+	0.839342i
$313$	−26.3763	+	10.9254i	−1.49087	+	0.617541i	−0.971507	−	0.237010i	$-0.923832\pi$
$313$	−26.3763	+	10.9254i	−1.49087	+	0.617541i	−0.519368	+	0.854551i	$0.673832\pi$
$314$	11.8296	+	14.9053i	0.667584	+	0.841154i
$315$	−4.40651	+	6.59482i	−0.248279	+	0.371576i
$316$	−17.3673	−	12.4453i	−0.976987	−	0.700105i
$317$	−12.4568	−	2.47781i	−0.699644	−	0.139168i	−0.167563	−	0.985861i	$-0.553590\pi$
$317$	−12.4568	−	2.47781i	−0.699644	−	0.139168i	−0.532081	+	0.846694i	$0.678590\pi$
$318$	−12.2915	−	10.4286i	−0.689273	−	0.584807i
$319$	3.67575			0.205803
$320$	−16.0641	−	1.58236i	−0.898009	−	0.0884565i
$321$	−5.65340			−0.315542
$322$	35.3294	+	29.9749i	1.96883	+	1.67044i
$323$	−28.2027	−	5.60986i	−1.56924	−	0.312141i
$324$	1.16496	−	1.62569i	0.0647201	−	0.0903161i
$325$	2.73432	−	4.09219i	0.151673	−	0.226994i
$326$	14.1224	+	17.7942i	0.782169	+	0.985530i
$327$	10.7852	−	4.46737i	0.596422	−	0.247046i
$328$	−5.02334	+	3.72552i	−0.277367	+	0.205707i
$329$	−7.27156	−	3.01198i	−0.400894	−	0.166056i
$330$	−2.55642	+	0.730019i	−0.140726	+	0.0401862i
$331$	1.80743	+	9.08654i	0.0993451	+	0.499442i	0.998134	+	0.0610600i	$0.0194481\pi$
$331$	1.80743	+	9.08654i	0.0993451	+	0.499442i	−0.898789	+	0.438381i	$0.855552\pi$
$332$	−6.30105	−	6.72762i	−0.345815	−	0.369226i
$333$	1.54078	+	2.30594i	0.0844341	+	0.126365i
$334$	−19.4425	−	6.24703i	−1.06385	−	0.341822i
$335$	−15.7800	+	15.7800i	−0.862154	+	0.862154i
$336$	−13.6172	+	7.86173i	−0.742877	+	0.428893i
$337$	14.9074	+	14.9074i	0.812059	+	0.812059i	0.984942	−	0.172883i	$-0.0553084\pi$
$337$	14.9074	+	14.9074i	0.812059	+	0.812059i	−0.172883	+	0.984942i	$0.555308\pi$
$338$	9.74401	+	18.9701i	0.530004	+	1.03184i
$339$	9.53325	−	6.36992i	0.517775	−	0.345966i
$340$	5.37069	+	14.2697i	0.291266	+	0.773885i
$341$	3.73396	−	0.742731i	0.202205	−	0.0402212i
$342$	−5.22838	+	9.40798i	−0.282718	+	0.508726i
$343$	2.18440	−	5.27360i	0.117946	−	0.284748i
$344$	−8.83288	−	3.16051i	−0.476237	−	0.170403i
$345$	−6.43539	−	15.5364i	−0.346470	−	0.836452i
$346$	−0.0396395	+	0.344564i	−0.00213103	+	0.0185239i
$347$	5.22340	+	3.49017i	0.280407	+	0.187362i	0.687818	−	0.725883i	$-0.258569\pi$
$347$	5.22340	+	3.49017i	0.280407	+	0.187362i	−0.407412	+	0.913245i	$0.633569\pi$
$348$	−7.68428	−	1.79175i	−0.411920	−	0.0960480i
$349$	−1.25156	+	6.29200i	−0.0669943	+	0.336803i	−0.999717	−	0.0237915i	$-0.992426\pi$
$349$	−1.25156	+	6.29200i	−0.0669943	+	0.336803i	0.932723	+	0.360595i	$0.117426\pi$
$350$	5.14595	−	0.421934i	0.275063	−	0.0225533i
$351$		−	5.29905i		−	0.282842i
$352$	−5.18536	−	0.943559i	−0.276380	−	0.0502918i
$353$		−	24.7949i		−	1.31970i	−0.751398	−	0.659849i	$-0.770620\pi$
$353$		−	24.7949i		−	1.31970i	0.751398	−	0.659849i	$-0.229380\pi$
$354$	1.01130	+	12.3340i	0.0537502	+	0.655543i
$355$	3.53478	−	17.7705i	0.187606	−	0.943161i
$356$	−12.8904	+	8.01572i	−0.683191	+	0.424832i
$357$	12.3490	+	8.25132i	0.653577	+	0.436706i
$358$	14.3203	+	1.64744i	0.756850	+	0.0870701i
$359$	10.4442	+	25.2146i	0.551226	+	1.33078i	0.916559	+	0.399900i	$0.130955\pi$
$359$	10.4442	+	25.2146i	0.551226	+	1.33078i	−0.365333	+	0.930877i	$0.619045\pi$
$360$	5.70012	−	0.279996i	0.300423	−	0.0147571i
$361$	14.8952	−	35.9602i	0.783958	−	1.89264i
$362$	23.1395	+	12.8595i	1.21618	+	0.675879i
$363$	9.93725	−	1.97664i	0.521570	−	0.103747i
$364$	−17.1936	+	37.9468i	−0.901191	+	1.98895i
$365$	2.54880	−	1.70305i	0.133410	−	0.0891419i
$366$	−9.89820	+	5.08423i	−0.517387	+	0.265757i
$367$	15.2385	+	15.2385i	0.795441	+	0.795441i	0.982373	−	0.186932i	$-0.0598544\pi$
$367$	15.2385	+	15.2385i	0.795441	+	0.795441i	−0.186932	+	0.982373i	$0.559854\pi$
$368$	2.18063	−	33.2661i	0.113673	−	1.73412i
$369$	1.56352	−	1.56352i	0.0813935	−	0.0813935i
$370$	−2.42083	+	7.53432i	−0.125853	+	0.391690i
$371$	−24.8925	−	37.2542i	−1.29235	−	1.93414i
$372$	−8.16801	−	0.267424i	−0.423492	−	0.0138653i
$373$	−3.96187	−	19.9177i	−0.205138	−	1.03130i	−0.936863	−	0.349698i	$-0.886284\pi$
$373$	−3.96187	−	19.9177i	−0.205138	−	1.03130i	0.731724	−	0.681601i	$-0.238716\pi$
$374$	1.36698	+	4.78697i	0.0706849	+	0.247528i
$375$	−11.0521	−	4.57791i	−0.570726	−	0.236402i
$376$	1.37602	+	5.49351i	0.0709627	+	0.283306i
$377$	−19.3145	+	8.00031i	−0.994746	+	0.412037i
$378$	4.35442	−	3.45590i	0.223967	−	0.177752i
$379$	−5.93359	+	8.88025i	−0.304788	+	0.456148i	−0.951971	−	0.306187i	$-0.900947\pi$
$379$	−5.93359	+	8.88025i	−0.304788	+	0.456148i	0.647183	+	0.762334i	$0.275947\pi$
$380$	−30.3025	+	5.00285i	−1.55449	+	0.256641i
$381$	9.73706	+	1.93682i	0.498845	+	0.0992263i
$382$	3.87708	−	4.56966i	0.198369	−	0.233804i
$383$	5.97541			0.305329			0.152664	−	0.988278i	$-0.451215\pi$
$383$	5.97541			0.305329			0.152664	+	0.988278i	$0.451215\pi$
$384$	10.3802	+	4.50015i	0.529713	+	0.229647i
$385$	−7.38981			−0.376620
$386$	−21.7969	+	25.6906i	−1.10943	+	1.30762i
$387$	3.25306	+	0.647073i	0.165362	+	0.0328926i
$388$	−11.7373	+	1.93780i	−0.595874	+	0.0983768i
$389$	−7.25359	+	10.8558i	−0.367772	+	0.550409i	−0.968490	−	0.249051i	$-0.919881\pi$
$389$	−7.25359	+	10.8558i	−0.367772	+	0.550409i	0.600719	+	0.799461i	$0.294881\pi$
$390$	11.8440	−	9.40000i	0.599742	−	0.475987i
$391$	−29.0924	+	12.0505i	−1.47126	+	0.609418i
$392$	−23.1898	+	5.80859i	−1.17126	+	0.293378i
$393$	1.18764	+	0.491937i	0.0599086	+	0.0248150i
$394$	−5.95615	−	20.8576i	−0.300066	−	1.05079i
$395$	4.20526	+	21.1413i	0.211590	+	1.06373i
$396$	1.86241	+	0.0609760i	0.0935895	+	0.00306416i
$397$	2.28774	+	3.42384i	0.114818	+	0.171838i	0.884428	−	0.466677i	$-0.154549\pi$
$397$	2.28774	+	3.42384i	0.114818	+	0.171838i	−0.769609	+	0.638515i	$0.779549\pi$
$398$	−3.49792	+	10.8865i	−0.175335	+	0.545691i
$399$	−21.1546	+	21.1546i	−1.05905	+	1.05905i
$400$	−2.44952	−	2.79319i	−0.122476	−	0.139659i
$401$	10.5794	+	10.5794i	0.528311	+	0.528311i	0.920069	−	0.391757i	$-0.128133\pi$
$401$	10.5794	+	10.5794i	0.528311	+	0.528311i	−0.391757	+	0.920069i	$0.628133\pi$
$402$	13.9133	−	7.14657i	0.693930	−	0.356439i
$403$	−18.0038	+	12.0297i	−0.896831	+	0.599244i
$404$	2.65014	−	5.84893i	0.131849	−	0.290995i
$405$	−1.97896	+	0.393639i	−0.0983352	+	0.0195601i
$406$	−19.1705	−	10.6538i	−0.951417	−	0.528739i
$407$	−0.988822	+	2.38723i	−0.0490141	+	0.118330i
$408$	−0.524301	−	10.6736i	−0.0259568	−	0.528424i
$409$	5.04673	+	12.1839i	0.249545	+	0.602454i	0.998166	−	0.0605444i	$-0.0192837\pi$
$409$	5.04673	+	12.1839i	0.249545	+	0.602454i	−0.748621	+	0.662998i	$0.769284\pi$
$410$	6.26816	+	0.721106i	0.309562	+	0.0356129i
$411$	−6.69565	−	4.47389i	−0.330272	−	0.220681i
$412$	3.86359	−	2.40252i	0.190346	−	0.118363i
$413$	−6.71077	+	33.7373i	−0.330215	+	1.66010i
$414$	0.963190	+	11.7472i	0.0473382	+	0.577342i
$415$			9.29930i			0.456484i
$416$	29.3004	−	6.32799i	1.43657	−	0.310255i
$417$		−	3.72429i		−	0.182379i
$418$	−9.99454	+	0.819487i	−0.488849	+	0.0400824i
$419$	1.47369	−	7.40872i	0.0719942	−	0.361940i	−0.927948	−	0.372710i	$-0.878429\pi$
$419$	1.47369	−	7.40872i	0.0719942	−	0.361940i	0.999942	+	0.0107708i	$0.00342852\pi$
$420$	15.4486	+	3.60218i	0.753816	+	0.175768i
$421$	−27.1237	−	18.1235i	−1.32193	−	0.883284i	−0.323902	−	0.946091i	$-0.604995\pi$
$421$	−27.1237	−	18.1235i	−1.32193	−	0.883284i	−0.998026	+	0.0628072i	$0.979995\pi$
$422$	3.41272	−	29.6648i	0.166128	−	1.44406i
$423$	−0.766228	−	1.84984i	−0.0372553	−	0.0899422i
$424$	−10.8611	+	30.3543i	−0.527463	+	1.47413i
$425$	−1.34290	+	3.24204i	−0.0651400	+	0.157262i
$426$	−6.16886	+	11.1003i	−0.298882	+	0.537811i
$427$	−30.3358	+	6.03416i	−1.46805	+	0.292013i
$428$	3.98278	+	10.5821i	0.192515	+	0.511506i
$429$	4.10508	−	2.74293i	0.198195	−	0.132430i
$430$	4.32432	+	8.41878i	0.208537	+	0.405990i
$431$	11.7782	+	11.7782i	0.567338	+	0.567338i	0.931382	−	0.364044i	$-0.118604\pi$
$431$	11.7782	+	11.7782i	0.567338	+	0.567338i	−0.364044	+	0.931382i	$0.618604\pi$
$432$	−3.86370	−	1.03531i	−0.185892	−	0.0498112i
$433$	1.08234	−	1.08234i	0.0520140	−	0.0520140i	−0.680621	−	0.732635i	$-0.738290\pi$
$433$	1.08234	−	1.08234i	0.0520140	−	0.0520140i	0.732635	+	0.680621i	$0.238290\pi$
$434$	−21.6268	−	6.94887i	−1.03812	−	0.333556i
$435$	4.42253	+	6.61878i	0.212044	+	0.317346i
$436$	−15.9602	−	17.0406i	−0.764353	−	0.816098i
$437$	−12.3747	−	62.2118i	−0.591962	−	2.97599i
$438$	−2.06595	+	0.589959i	−0.0987148	+	0.0281893i
$439$	1.05221	+	0.435839i	0.0502192	+	0.0208015i	0.407652	−	0.913138i	$-0.366348\pi$
$439$	1.05221	+	0.435839i	0.0502192	+	0.0208015i	−0.357432	+	0.933939i	$0.616348\pi$
$440$	3.16744	+	4.27085i	0.151002	+	0.203605i
$441$	7.80873	−	3.23448i	0.371844	−	0.154023i
$442$	−17.6018	−	22.1782i	−0.837231	−	1.05491i
$443$	0.905372	−	1.35499i	0.0430155	−	0.0643773i	−0.809339	−	0.587342i	$-0.800174\pi$
$443$	0.905372	−	1.35499i	0.0430155	−	0.0643773i	0.852354	+	0.522965i	$0.175174\pi$
$444$	3.23082	−	4.50857i	0.153328	−	0.213967i
$445$	15.0197	+	2.98761i	0.712003	+	0.141626i
$446$	18.3639	+	15.5806i	0.869555	+	0.737765i
$447$	12.7793			0.604440
$448$	24.3089	+	19.9503i	1.14849	+	0.942561i
$449$	−10.4707			−0.494142			−0.247071	−	0.968997i	$-0.579468\pi$
$449$	−10.4707			−0.494142			−0.247071	+	0.968997i	$0.579468\pi$
$450$	1.00157	+	0.849772i	0.0472145	+	0.0400587i
$451$	2.02055	+	0.401912i	0.0951438	+	0.0189253i
$452$	−18.6394	−	13.3569i	−0.876724	−	0.628257i
$453$	−3.34383	+	5.00439i	−0.157107	+	0.235127i
$454$	12.9672	+	16.3386i	0.608579	+	0.766807i
$455$	38.8302	−	16.0840i	1.82039	−	0.754029i
$456$	21.2934	+	3.15870i	0.997153	+	0.147919i
$457$	−7.42503	−	3.07555i	−0.347328	−	0.143868i	0.202198	−	0.979345i	$-0.435192\pi$
$457$	−7.42503	−	3.07555i	−0.347328	−	0.143868i	−0.549526	+	0.835477i	$0.685192\pi$
$458$	3.27271	−	0.934565i	0.152924	−	0.0436694i
$459$	0.737100	+	3.70565i	0.0344049	+	0.172965i
$460$	−24.5476	+	22.9912i	−1.14454	+	1.07197i
$461$	12.5156	+	18.7310i	0.582912	+	0.872389i	0.999323	−	0.0367872i	$-0.0117124\pi$
$461$	12.5156	+	18.7310i	0.582912	+	0.872389i	−0.416411	+	0.909176i	$0.636712\pi$
$462$	4.93118	+	1.58443i	0.229419	+	0.0737142i
$463$	−9.68667	+	9.68667i	−0.450178	+	0.450178i	−0.895413	−	0.445236i	$-0.853120\pi$
$463$	−9.68667	+	9.68667i	−0.450178	+	0.450178i	0.445236	+	0.895413i	$0.353120\pi$
$464$	2.05969	+	15.6458i	0.0956187	+	0.726339i
$465$	5.82997	+	5.82997i	0.270358	+	0.270358i
$466$	14.7675	+	28.7501i	0.684092	+	1.33182i
$467$	9.03088	−	6.03424i	0.417899	−	0.279231i	−0.328792	−	0.944402i	$-0.606641\pi$
$467$	9.03088	−	6.03424i	0.417899	−	0.279231i	0.746691	+	0.665171i	$0.231641\pi$
$468$	−9.91884	+	3.73314i	−0.458499	+	0.172565i
$469$	42.6410	−	8.48182i	1.96898	−	0.391654i
$470$	2.77538	−	4.99403i	0.128019	−	0.230358i
$471$	−5.14924	+	12.4314i	−0.237265	+	0.572807i
$472$	22.3744	−	10.5822i	1.02987	−	0.487083i
$473$	1.18259	+	2.85503i	0.0543756	+	0.131274i
$474$	1.72669	−	15.0091i	0.0793094	−	0.689391i
$475$	−5.87738	−	3.92714i	−0.269673	−	0.180190i
$476$	6.74518	−	28.9280i	0.309165	−	1.32591i
$477$	2.22367	−	11.1792i	0.101815	−	0.511859i
$478$	−11.3483	+	0.930482i	−0.519057	+	0.0425593i
$479$		−	35.0050i		−	1.59942i	−0.600387	−	0.799710i	$-0.704987\pi$
$479$		−	35.0050i		−	1.59942i	0.600387	−	0.799710i	$-0.295013\pi$
$480$	−4.53980	−	10.4723i	−0.207212	−	0.477994i
$481$		−	14.6960i		−	0.670080i
$482$	−2.81452	−	34.3262i	−0.128198	−	1.56351i
$483$	−6.39150	+	32.1322i	−0.290823	+	1.46207i
$484$	−10.7006	−	17.2082i	−0.486392	−	0.782189i
$485$	9.97903	+	6.66777i	0.453124	+	0.302768i
$486$	1.40495	+	0.161629i	0.0637297	+	0.00733163i
$487$	−8.65463	−	20.8941i	−0.392179	−	0.946803i	−0.989465	−	0.144775i	$-0.953754\pi$
$487$	−8.65463	−	20.8941i	−0.392179	−	0.946803i	0.597286	−	0.802028i	$-0.296246\pi$
$488$	16.4899	+	14.9458i	0.746465	+	0.676564i
$489$	−6.14726	+	14.8408i	−0.277989	+	0.671124i
$490$	21.0813	+	11.7157i	0.952358	+	0.529262i
$491$	38.9578	−	7.74919i	1.75814	−	0.349716i	0.792555	−	0.609800i	$-0.208750\pi$
$491$	38.9578	−	7.74919i	1.75814	−	0.349716i	0.965586	+	0.260084i	$0.0837504\pi$
$492$	−4.02810	−	1.82513i	−0.181601	−	0.0822831i
$493$	12.3939	−	8.28131i	0.558191	−	0.372971i
$494$	50.7333	−	26.0593i	2.28260	−	1.17246i
$495$	−1.32930	−	1.32930i	−0.0597478	−	0.0597478i
$496$	5.25374	+	15.4774i	0.235900	+	0.694956i
$497$	−24.9599	+	24.9599i	−1.11960	+	1.11960i
$498$	1.99383	−	6.20537i	0.0893458	−	0.278069i
$499$	8.21585	+	12.2959i	0.367792	+	0.550439i	0.968495	−	0.249033i	$-0.0801127\pi$
$499$	8.21585	+	12.2959i	0.367792	+	0.550439i	−0.600703	+	0.799472i	$0.705113\pi$
$500$	−0.782905	+	23.9125i	−0.0350126	+	1.06940i
$501$	−2.81714	−	14.1627i	−0.125860	−	0.632743i
$502$	−3.46007	−	12.1166i	−0.154430	−	0.540792i
$503$	2.51569	+	1.04203i	0.112169	+	0.0464620i	0.438062	−	0.898945i	$-0.355665\pi$
$503$	2.51569	+	1.04203i	0.112169	+	0.0464620i	−0.325893	+	0.945407i	$0.605665\pi$
$504$	−9.53646	−	5.71601i	−0.424788	−	0.254611i
$505$	−5.98510	+	2.47911i	−0.266333	+	0.110319i
$506$	−8.60175	+	6.82680i	−0.382394	+	0.303488i
$507$	−8.37797	+	12.5385i	−0.372079	+	0.556855i
$508$	−3.23432	−	19.5904i	−0.143500	−	0.869185i
$509$	−11.1316	−	2.21422i	−0.493401	−	0.0981436i	−0.0578827	−	0.998323i	$-0.518435\pi$
$509$	−11.1316	−	2.21422i	−0.493401	−	0.0981436i	−0.435518	+	0.900180i	$0.643435\pi$
$510$	−6.97500	+	8.22097i	−0.308858	+	0.364031i
$511$	−5.97201			−0.264186
$512$	1.11066	−	22.6001i	0.0490848	−	0.998795i
$513$	−7.61072			−0.336022
$514$	−8.25456	+	9.72910i	−0.364093	+	0.429132i
$515$	−4.50179	−	0.895462i	−0.198373	−	0.0394588i
$516$	−1.08055	−	6.54498i	−0.0475688	−	0.288127i
$517$	1.03642	−	1.55111i	0.0455816	−	0.0682176i
$518$	12.0762	−	9.58434i	0.530599	−	0.421112i
$519$	−0.226582	+	0.0938532i	−0.00994584	+	0.00411970i
$520$	−25.9390	−	15.5475i	−1.13750	−	0.681801i
$521$	18.4035	+	7.62298i	0.806272	+	0.333969i	0.747465	−	0.664301i	$-0.231271\pi$
$521$	18.4035	+	7.62298i	0.806272	+	0.333969i	0.0588062	+	0.998269i	$0.481271\pi$
$522$	−1.53202	−	5.36490i	−0.0670546	−	0.234815i
$523$	4.22835	+	21.2573i	0.184893	+	0.929518i	0.956124	+	0.292963i	$0.0946413\pi$
$523$	4.22835	+	21.2573i	0.184893	+	0.929518i	−0.771231	+	0.636555i	$0.780359\pi$
$524$	0.0841302	−	2.56961i	0.00367524	−	0.112254i
$525$	2.02836	+	3.03565i	0.0885248	+	0.132487i
$526$	−13.2086	+	41.1088i	−0.575922	+	1.79243i
$527$	10.9168	−	10.9168i	0.475543	−	0.475543i
$528$	−1.19792	−	3.52904i	−0.0521326	−	0.153582i
$529$	−32.8534	−	32.8534i	−1.42841	−	1.42841i
$530$	28.9312	−	14.8606i	1.25669	−	0.645503i
$531$	−7.27594	+	4.86163i	−0.315749	+	0.210977i
$532$	54.5007	+	24.6942i	2.36291	+	1.07063i
$533$	−11.4918	+	2.28587i	−0.497767	+	0.0990120i
$534$	−9.38202	−	5.21395i	−0.406000	−	0.225630i
$535$	4.36528	−	10.5387i	0.188727	−	0.455628i
$536$	−23.1789	−	21.0083i	−1.00117	−	0.907422i
$537$	3.90060	+	9.41687i	0.168323	+	0.406368i
$538$	3.43083	+	0.394692i	0.147914	+	0.0170164i
$539$	6.54770	+	4.37503i	0.282029	+	0.188446i
$540$	2.13098	+	3.42692i	0.0917028	+	0.147471i
$541$	−0.981180	+	4.93272i	−0.0421842	+	0.212074i	−0.996128	−	0.0879096i	$-0.971981\pi$
$541$	−0.981180	+	4.93272i	−0.0421842	+	0.212074i	0.953944	+	0.299984i	$0.0969813\pi$
$542$	1.63034	+	19.8838i	0.0700291	+	0.854082i
$543$			18.7190i			0.803309i
$544$	−19.6097	+	8.50090i	−0.840759	+	0.364473i
$545$			23.5545i			1.00896i
$546$	−29.3597	+	2.40730i	−1.25648	+	0.103023i
$547$	5.70608	−	28.6864i	0.243974	−	1.22654i	−0.643414	−	0.765519i	$-0.722482\pi$
$547$	5.70608	−	28.6864i	0.243974	−	1.22654i	0.887388	−	0.461023i	$-0.152518\pi$
$548$	−3.65725	+	15.6848i	−0.156230	+	0.670023i
$549$	−6.54234	−	4.37145i	−0.279220	−	0.186569i
$550$	−0.139865	+	1.21576i	−0.00596385	+	0.0518403i
$551$	11.4904	+	27.7402i	0.489507	+	1.18177i
$552$	21.3100	−	10.0787i	0.907012	−	0.428978i
$553$	16.0705	−	38.7975i	0.683386	−	1.64984i
$554$	1.93535	−	3.48248i	0.0822250	−	0.147956i
$555$	−5.48830	+	1.09169i	−0.232965	+	0.0463397i
$556$	−6.97118	+	2.62374i	−0.295644	+	0.111271i
$557$	−34.5957	+	23.1161i	−1.46587	+	0.979462i	−0.470596	+	0.882349i	$0.655961\pi$
$557$	−34.5957	+	23.1161i	−1.46587	+	0.979462i	−0.995273	+	0.0971133i	$0.969039\pi$
$558$	−2.64032	−	5.14030i	−0.111774	−	0.217606i
$559$	−12.4280	−	12.4280i	−0.525648	−	0.525648i
$560$	−4.14084	−	31.4547i	−0.174983	−	1.32920i
$561$	−2.48916	+	2.48916i	−0.105092	+	0.105092i
$562$	−35.2362	−	11.3216i	−1.48635	−	0.477575i
$563$	2.43472	+	3.64381i	0.102611	+	0.153568i	0.879222	−	0.476412i	$-0.158063\pi$
$563$	2.43472	+	3.64381i	0.102611	+	0.153568i	−0.776611	+	0.629980i	$0.783063\pi$
$564$	−2.92275	+	2.73743i	−0.123070	+	0.115267i
$565$	4.51329	+	22.6898i	0.189875	+	0.954568i
$566$	−38.0788	+	10.8739i	−1.60057	+	0.457065i
$567$	3.63169	+	1.50430i	0.152517	+	0.0631745i
$568$	25.1236	+	3.72688i	1.05416	+	0.156377i
$569$	41.8738	−	17.3447i	1.75544	−	0.727127i	0.758269	−	0.651941i	$-0.226045\pi$
$569$	41.8738	−	17.3447i	1.75544	−	0.727127i	0.997170	−	0.0751853i	$-0.0239548\pi$
$570$	−13.5007	−	17.0108i	−0.565481	−	0.712504i
$571$	2.82473	−	4.22751i	0.118211	−	0.176916i	−0.767645	−	0.640875i	$-0.778572\pi$
$571$	2.82473	−	4.22751i	0.118211	−	0.176916i	0.885857	+	0.463959i	$0.153572\pi$
$572$	−8.02625	−	5.75158i	−0.335594	−	0.240485i
$573$	4.15612	+	0.826704i	0.173624	+	0.0345360i
$574$	−9.37306	−	7.95248i	−0.391224	−	0.331930i
$575$	−7.74078			−0.322813
$576$	0.784046	+	7.96149i	0.0326686	+	0.331729i
$577$	−9.85867			−0.410422			−0.205211	−	0.978718i	$-0.565788\pi$
$577$	−9.85867			−0.410422			−0.205211	+	0.978718i	$0.565788\pi$
$578$	−2.93837	−	2.49304i	−0.122220	−	0.103697i
$579$	−23.3657	−	4.64772i	−0.971044	−	0.193153i
$580$	9.27349	−	12.9410i	0.385061	−	0.537347i
$581$	10.0652	−	15.0636i	0.417573	−	0.624942i
$582$	−5.22934	−	6.58895i	−0.216763	−	0.273121i
$583$	9.81133	−	4.06399i	0.406344	−	0.168313i
$584$	2.55974	+	3.45145i	0.105923	+	0.142822i
$585$	9.87816	+	4.09167i	0.408411	+	0.169170i
$586$	36.7738	−	10.5012i	1.51911	−	0.433802i
$587$	−7.72386	−	38.8305i	−0.318798	−	1.60271i	−0.724884	−	0.688871i	$-0.758107\pi$
$587$	−7.72386	−	38.8305i	−0.318798	−	1.60271i	0.406086	−	0.913835i	$-0.366893\pi$
$588$	−11.5555	−	12.3378i	−0.476543	−	0.508803i
$589$	17.2776	+	25.8578i	0.711911	+	1.06545i
$590$	−23.7731	−	7.63847i	−0.978722	−	0.314471i
$591$	10.8457	−	10.8457i	0.446131	−	0.446131i
$592$	−10.7153	−	2.87124i	−0.440396	−	0.118007i
$593$	27.2869	+	27.2869i	1.12054	+	1.12054i	0.991661	+	0.128877i	$0.0411371\pi$
$593$	27.2869	+	27.2869i	1.12054	+	1.12054i	0.128877	+	0.991661i	$0.458863\pi$
$594$	0.602026	+	1.17205i	0.0247014	+	0.0480898i
$595$	−24.9169	+	16.6489i	−1.02149	+	0.682539i
$596$	−9.00293	−	23.9205i	−0.368774	−	0.979821i
$597$	−7.93016	+	1.57741i	−0.324560	+	0.0645590i
$598$	30.3398	−	54.5936i	1.24069	−	2.23250i
$599$	−7.78170	+	18.7867i	−0.317952	+	0.767604i	0.681411	+	0.731901i	$0.261367\pi$
$599$	−7.78170	+	18.7867i	−0.317952	+	0.767604i	−0.999362	+	0.0357022i	$0.988633\pi$
$600$	0.885017	−	2.47341i	0.0361307	−	0.100977i
$601$	15.4558	+	37.3137i	0.630456	+	1.52206i	0.839050	+	0.544054i	$0.183111\pi$
$601$	15.4558	+	37.3137i	0.630456	+	1.52206i	−0.208594	+	0.978002i	$0.566889\pi$
$602$	2.10732	−	18.3177i	0.0858879	−	0.746575i
$603$	9.19615	+	6.14467i	0.374496	+	0.250230i
$604$	11.7230	+	2.73347i	0.477002	+	0.111223i
$605$	−3.98832	+	20.0507i	−0.162148	+	0.815175i
$606$	4.52536	−	0.371050i	0.183830	−	0.0150729i
$607$			20.2438i			0.821669i	0.911710	+	0.410835i	$0.134763\pi$
$607$			20.2438i			0.821669i	−0.911710	+	0.410835i	$0.865237\pi$
$608$	−9.08853	−	42.0825i	−0.368588	−	1.70667i
$609$		−	15.5083i		−	0.628426i
$610$	−1.83480	−	22.3774i	−0.0742888	−	0.906034i
$611$	−2.06991	+	10.4062i	−0.0837397	+	0.420988i
$612$	6.41701	−	3.99032i	0.259392	−	0.161299i
$613$	−5.54943	−	3.70801i	−0.224139	−	0.149765i	0.438431	−	0.898765i	$-0.355534\pi$
$613$	−5.54943	−	3.70801i	−0.224139	−	0.149765i	−0.662570	+	0.749000i	$0.730534\pi$
$614$	−2.19591	−	0.252624i	−0.0886199	−	0.0101951i
$615$	1.70734	+	4.12188i	0.0688466	+	0.166210i
$616$	−0.508231	−	10.3465i	−0.0204772	−	0.416872i
$617$	6.15245	−	14.8533i	0.247688	−	0.597973i	−0.750319	−	0.661076i	$-0.770100\pi$
$617$	6.15245	−	14.8533i	0.247688	−	0.597973i	0.998007	+	0.0631038i	$0.0200999\pi$
$618$	2.81203	+	1.56275i	0.113116	+	0.0628632i
$619$	46.9305	−	9.33507i	1.88630	−	0.375208i	0.889624	−	0.456695i	$-0.150967\pi$
$619$	46.9305	−	9.33507i	1.88630	−	0.375208i	0.996674	+	0.0814867i	$0.0259668\pi$
$620$	6.80545	−	15.0198i	0.273313	−	0.603209i
$621$	−6.92978	+	4.63033i	−0.278082	+	0.185809i
$622$	−17.5334	+	9.00607i	−0.703026	+	0.361111i
$623$	−21.0962	−	21.0962i	−0.845201	−	0.845201i
$624$	13.9755	+	15.9363i	0.559468	+	0.637961i
$625$	13.7840	−	13.7840i	0.551359	−	0.551359i
$626$	−12.3509	+	38.4395i	−0.493642	+	1.53635i
$627$	−3.93951	−	5.89589i	−0.157329	−	0.235459i
$628$	26.8968	+	0.880614i	1.07330	+	0.0351403i
$629$	2.04422	+	10.2770i	0.0815084	+	0.409770i
$630$	3.08000	+	10.7857i	0.122710	+	0.429713i
$631$	19.7077	+	8.16320i	0.784552	+	0.324972i	0.738751	−	0.673979i	$-0.235416\pi$
$631$	19.7077	+	8.16320i	0.784552	+	0.324972i	0.0458010	+	0.998951i	$0.485416\pi$
$632$	−29.3107	+	7.34177i	−1.16592	+	0.292040i
$633$	19.5073	−	8.08018i	0.775345	−	0.321158i
$634$	−14.0692	+	11.1661i	−0.558759	+	0.443461i
$635$	−11.1290	+	16.6557i	−0.441640	+	0.660961i
$636$	−22.4919	+	3.71334i	−0.891861	+	0.147243i
$637$	−43.9275	−	8.73773i	−1.74047	−	0.346202i
$638$	3.36308	−	3.96384i	0.133146	−	0.156930i
$639$	−8.97974			−0.355233
$640$	−16.4040	+	15.8753i	−0.648424	+	0.627527i
$641$	16.3818			0.647041			0.323521	−	0.946221i	$-0.395133\pi$
$641$	16.3818			0.647041			0.323521	+	0.946221i	$0.395133\pi$
$642$	−5.17250	+	6.09648i	−0.204142	+	0.240609i
$643$	7.26507	+	1.44511i	0.286506	+	0.0569896i	0.336251	−	0.941772i	$-0.390841\pi$
$643$	7.26507	+	1.44511i	0.286506	+	0.0569896i	−0.0497450	+	0.998762i	$0.515841\pi$
$644$	64.6483	−	10.6732i	2.54750	−	0.420584i
$645$	−3.71808	+	5.56450i	−0.146399	+	0.219102i
$646$	−31.8532	+	25.2804i	−1.25325	+	0.994644i
$647$	24.2188	−	10.0318i	0.952139	−	0.394389i	0.148105	−	0.988972i	$-0.452683\pi$
$647$	24.2188	−	10.0318i	0.952139	−	0.394389i	0.804034	+	0.594583i	$0.202683\pi$
$648$	−0.687236	−	2.74367i	−0.0269972	−	0.107781i
$649$	−7.53243	−	3.12003i	−0.295674	−	0.122472i
$650$	−1.91119	−	6.69272i	−0.0749632	−	0.262510i
$651$	−3.13363	−	15.7538i	−0.122817	−	0.617442i
$652$	32.1099	+	1.05129i	1.25752	+	0.0411718i
$653$	6.35562	+	9.51185i	0.248715	+	0.372228i	0.934730	−	0.355360i	$-0.115642\pi$
$653$	6.35562	+	9.51185i	0.248715	+	0.372228i	−0.686015	+	0.727587i	$0.740642\pi$
$654$	5.05025	−	15.7178i	0.197481	−	0.614615i
$655$	−1.83408	+	1.83408i	−0.0716633	+	0.0716633i
$656$	−0.578531	+	8.82565i	−0.0225878	+	0.344584i
$657$	−1.07427	−	1.07427i	−0.0419111	−	0.0419111i
$658$	−9.90105	+	5.08570i	−0.385983	+	0.198261i
$659$	−8.68363	+	5.80221i	−0.338266	+	0.226022i	−0.713088	−	0.701075i	$-0.752704\pi$
$659$	−8.68363	+	5.80221i	−0.338266	+	0.226022i	0.374822	+	0.927097i	$0.377704\pi$
$660$	−1.55173	+	3.42470i	−0.0604009	+	0.133306i
$661$	−16.9443	+	3.37042i	−0.659055	+	0.131094i	−0.513277	−	0.858223i	$-0.671569\pi$
$661$	−16.9443	+	3.37042i	−0.659055	+	0.131094i	−0.145778	+	0.989317i	$0.546569\pi$
$662$	11.4524	+	6.36452i	0.445109	+	0.247364i
$663$	7.66176	−	18.4971i	0.297558	−	0.718369i
$664$	−13.0200	+	0.639555i	−0.505272	+	0.0248195i
$665$	−23.1005	−	55.7696i	−0.895800	−	2.16265i
$666$	3.89638	+	0.448250i	0.150982	+	0.0173693i
$667$	27.3394	+	18.2676i	1.05858	+	0.707324i
$668$	−24.5253	+	15.2507i	−0.948913	+	0.590067i
$669$	−3.32224	+	16.7020i	−0.128445	+	0.645737i
$670$	2.57906	+	31.4544i	0.0996377	+	1.21519i
$671$		−	7.33102i		−	0.283011i
$672$	−3.98094	+	21.8774i	−0.153568	+	0.843938i
$673$			42.9813i			1.65681i	0.560131	+	0.828404i	$0.310751\pi$
$673$			42.9813i			1.65681i	−0.560131	+	0.828404i	$0.689249\pi$
$674$	29.7151	−	2.43644i	1.14458	−	0.0938483i
$675$	−0.181196	+	0.910932i	−0.00697422	+	0.0350618i
$676$	29.3720	+	6.84870i	1.12969	+	0.263412i
$677$	−29.8747	−	19.9616i	−1.14818	−	0.767188i	−0.172201	−	0.985062i	$-0.555088\pi$
$677$	−29.8747	−	19.9616i	−1.14818	−	0.767188i	−0.975977	+	0.217874i	$0.930088\pi$
$678$	1.85316	−	16.1085i	0.0711703	−	0.618643i
$679$	−8.94773	−	21.6017i	−0.343382	−	0.828999i
$680$	20.3020	+	7.26429i	0.778545	+	0.278573i
$681$	−5.64439	+	13.6268i	−0.216294	+	0.522179i
$682$	2.61539	−	4.70616i	0.100149	−	0.180208i
$683$	−33.7453	+	6.71236i	−1.29123	+	0.256841i	−0.792476	−	0.609903i	$-0.791208\pi$
$683$	−33.7453	+	6.71236i	−1.29123	+	0.256841i	−0.498753	+	0.866744i	$0.666208\pi$
$684$	5.36170	+	14.2459i	0.205010	+	0.544704i
$685$	13.5100	−	9.02708i	0.516190	−	0.344907i
$686$	−3.68834	−	7.18061i	−0.140821	−	0.274157i
$687$	1.70177	+	1.70177i	0.0649264	+	0.0649264i
$688$	−11.4897	+	6.63349i	−0.438042	+	0.252899i
$689$	−42.7089	+	42.7089i	−1.62708	+	1.62708i
$690$	−22.6420	−	7.27506i	−0.861968	−	0.276957i
$691$	−4.48755	−	6.71610i	−0.170715	−	0.255492i	0.736240	−	0.676720i	$-0.236599\pi$
$691$	−4.48755	−	6.71610i	−0.170715	−	0.255492i	−0.906955	+	0.421228i	$0.861599\pi$
$692$	0.335301	+	0.358000i	0.0127462	+	0.0136091i
$693$	0.714507	+	3.59207i	0.0271419	+	0.136452i
$694$	8.54278	−	2.43950i	0.324280	−	0.0926023i
$695$	6.94259	+	2.87571i	0.263347	+	0.109082i
$696$	−8.96280	+	6.64719i	−0.339734	+	0.251961i
$697$	7.71834	−	3.19704i	0.292353	−	0.121097i
$698$	5.64004	+	7.10643i	0.213479	+	0.268982i
$699$	−12.6972	+	19.0027i	−0.480253	+	0.718749i
$700$	4.25321	−	5.93531i	0.160756	−	0.224333i
$701$	26.2397	+	5.21940i	0.991059	+	0.197134i	0.663889	−	0.747831i	$-0.268905\pi$
$701$	26.2397	+	5.21940i	0.991059	+	0.197134i	0.327171	+	0.944965i	$0.393905\pi$
$702$	−5.71436	−	4.84829i	−0.215675	−	0.182987i
$703$	−21.1070			−0.796066
$704$	−5.76178	+	4.72846i	−0.217155	+	0.178211i
$705$	4.03999			0.152155
$706$	−26.7382	−	22.6857i	−1.00630	−	0.853789i
$707$	12.3783	+	2.46220i	0.465534	+	0.0926005i
$708$	14.2259	+	10.1942i	0.534642	+	0.383122i
$709$	11.5780	−	17.3277i	0.434821	−	0.650756i	−0.547750	−	0.836642i	$-0.684516\pi$
$709$	11.5780	−	17.3277i	0.434821	−	0.650756i	0.982571	+	0.185886i	$0.0595155\pi$
$710$	−15.9292	−	20.0707i	−0.597811	−	0.753240i
$711$	9.86985	−	4.08822i	0.370148	−	0.153320i
$712$	−3.14998	+	21.2346i	−0.118050	+	0.795800i
$713$	31.4635	+	13.0326i	1.17832	+	0.488075i
$714$	20.1965	−	5.76739i	0.755837	−	0.215839i
$715$	1.94345	+	9.77038i	0.0726809	+	0.365392i
$716$	14.8787	−	13.9353i	0.556043	−	0.520787i
$717$	−4.47309	−	6.69446i	−0.167051	−	0.250009i
$718$	36.7466	+	11.8070i	1.37137	+	0.440632i
$719$	−19.1699	+	19.1699i	−0.714917	+	0.714917i	−0.967560	−	0.252643i	$-0.918700\pi$
$719$	−19.1699	+	19.1699i	−0.714917	+	0.714917i	0.252643	+	0.967560i	$0.418700\pi$
$720$	4.91331	−	6.40304i	0.183108	−	0.238627i
$721$	6.32307	+	6.32307i	0.235483	+	0.235483i
$722$	−25.1504	−	48.9639i	−0.936002	−	1.82225i
$723$	20.2494	−	13.5302i	0.753082	−	0.503193i
$724$	35.0385	−	13.1874i	1.30219	−	0.490106i
$725$	3.59381	−	0.714853i	0.133471	−	0.0265490i
$726$	6.96039	−	12.5246i	0.258324	−	0.464831i
$727$	12.2581	−	29.5937i	0.454628	−	1.09757i	−0.515915	−	0.856640i	$-0.672548\pi$
$727$	12.2581	−	29.5937i	0.454628	−	1.09757i	0.970543	−	0.240929i	$-0.0774520\pi$
$728$	25.1897	+	53.2600i	0.933594	+	1.97395i
$729$	0.382683	+	0.923880i	0.0141735	+	0.0342178i
$730$	0.495460	−	4.30675i	0.0183378	−	0.159400i
$731$	10.4197	+	6.96221i	0.385386	+	0.257507i
$732$	−3.57352	+	15.3257i	−0.132081	+	0.566455i
$733$	3.25188	−	16.3483i	0.120111	−	0.603839i	−0.873103	−	0.487536i	$-0.837896\pi$
$733$	3.25188	−	16.3483i	0.120111	−	0.603839i	0.993214	−	0.116303i	$-0.0371042\pi$
$734$	30.3750	−	2.49055i	1.12116	−	0.0919278i
$735$			17.0540i			0.629048i
$736$	−33.8782	−	32.7879i	−1.24877	−	1.20858i
$737$			10.3047i			0.379580i
$738$	−0.255539	−	3.11658i	−0.00940651	−	0.114723i
$739$	5.42650	−	27.2809i	0.199617	−	1.00354i	−0.742905	−	0.669397i	$-0.766552\pi$
$739$	5.42650	−	27.2809i	0.199617	−	1.00354i	0.942522	−	0.334145i	$-0.108448\pi$
$740$	5.90991	+	9.50398i	0.217252	+	0.349373i
$741$	33.5328	+	22.4059i	1.23186	+	0.823102i
$742$	−62.9490	−	7.24182i	−2.31093	−	0.265856i
$743$	−8.07244	−	19.4886i	−0.296149	−	0.714967i	−0.999989	−	0.00460903i	$-0.998533\pi$
$743$	−8.07244	−	19.4886i	−0.296149	−	0.714967i	0.703840	−	0.710358i	$-0.251467\pi$
$744$	−7.76159	+	8.56350i	−0.284554	+	0.313953i
$745$	−9.86755	+	23.8224i	−0.361519	+	0.872784i
$746$	−25.1036	−	13.9510i	−0.919107	−	0.510783i
$747$	4.52024	−	0.899132i	0.165387	−	0.0328975i
$748$	6.41284	+	2.90565i	0.234477	+	0.106241i
$749$	−18.4778	+	12.3465i	−0.675163	+	0.451130i
$750$	−15.0486	+	7.72976i	−0.549498	+	0.282251i
$751$	−24.6642	−	24.6642i	−0.900011	−	0.900011i	0.0954259	−	0.995437i	$-0.469579\pi$
$751$	−24.6642	−	24.6642i	−0.900011	−	0.900011i	−0.995437	+	0.0954259i	$0.969579\pi$
$752$	7.18303	+	3.54234i	0.261938	+	0.129176i
$753$	6.30050	−	6.30050i	0.229603	−	0.229603i
$754$	−9.04417	+	28.1480i	−0.329369	+	1.02509i
$755$	−6.74693	−	10.0975i	−0.245546	−	0.367486i
$756$	0.257262	−	7.85762i	0.00935653	−	0.285779i
$757$	−0.337628	−	1.69737i	−0.0122713	−	0.0616920i	0.974164	−	0.225840i	$-0.0725126\pi$
$757$	−0.337628	−	1.69737i	−0.0122713	−	0.0616920i	−0.986436	+	0.164148i	$0.947513\pi$
$758$	4.14737	+	14.5235i	0.150639	+	0.527517i
$759$	−7.17407	−	2.97160i	−0.260402	−	0.107862i
$760$	−22.3299	+	37.2547i	−0.809991	+	1.35137i
$761$	−32.4673	+	13.4484i	−1.17694	+	0.487503i	−0.883480	−	0.468469i	$-0.844806\pi$
$761$	−32.4673	+	13.4484i	−1.17694	+	0.487503i	−0.293457	+	0.955972i	$0.594806\pi$
$762$	10.9974	−	8.72813i	0.398394	−	0.316187i
$763$	25.4944	−	38.1551i	0.922959	−	1.38131i
$764$	−1.38052	−	8.36189i	−0.0499455	−	0.302523i
$765$	−7.47700	−	1.48727i	−0.270331	−	0.0537723i
$766$	5.46712	−	6.44373i	0.197535	−	0.232821i
$767$	46.3704			1.67434
$768$	14.3501	−	7.07640i	0.517814	−	0.255348i
$769$	−36.9462			−1.33231			−0.666157	−	0.745812i	$-0.732062\pi$
$769$	−36.9462			−1.33231			−0.666157	+	0.745812i	$0.732062\pi$
$770$	−6.76121	+	7.96899i	−0.243657	+	0.287182i
$771$	−8.84865	−	1.76011i	−0.318676	−	0.0633887i
$772$	7.76128	+	47.0105i	0.279335	+	1.69194i
$773$	−18.1200	+	27.1184i	−0.651729	+	0.975382i	0.347559	+	0.937658i	$0.387011\pi$
$773$	−18.1200	+	27.1184i	−0.651729	+	0.975382i	−0.999288	+	0.0377238i	$0.987989\pi$
$774$	3.67413	−	2.91598i	0.132064	−	0.104813i
$775$	3.50628	−	1.45235i	0.125949	−	0.0521698i
$776$	−8.64925	+	14.4302i	−0.310490	+	0.518015i
$777$	10.0719	+	4.17191i	0.361326	+	0.149666i
$778$	5.07001	+	17.7544i	0.181769	+	0.636527i
$779$	3.28306	+	16.5051i	0.117628	+	0.591356i
$780$	0.699749	−	21.3726i	0.0250550	−	0.765263i
$781$	−4.64815	−	6.95644i	−0.166324	−	0.248921i
$782$	−13.6228	+	42.3979i	−0.487149	+	1.51614i
$783$	2.78968	−	2.78968i	0.0996950	−	0.0996950i
$784$	−14.9533	+	30.3217i	−0.534047	+	1.08292i
$785$	−19.1978	−	19.1978i	−0.685198	−	0.685198i
$786$	1.61711	−	0.830632i	0.0576804	−	0.0296276i
$787$	−12.9448	+	8.64946i	−0.461433	+	0.308320i	−0.764470	−	0.644659i	$-0.776999\pi$
$787$	−12.9448	+	8.64946i	−0.461433	+	0.308320i	0.303037	+	0.952979i	$0.401999\pi$
$788$	−27.9418	−	12.6604i	−0.995384	−	0.451007i
$789$	−29.9453	+	5.95649i	−1.06608	+	0.212057i
$790$	26.6458	+	14.8081i	0.948014	+	0.526848i
$791$	17.2476	−	41.6393i	0.613253	−	1.48052i
$792$	1.76974	−	1.95258i	0.0628849	−	0.0693820i
$793$	15.9560	+	38.5213i	0.566615	+	1.36793i
$794$	5.78532	+	0.665558i	0.205313	+	0.0236198i
$795$	19.1225	+	12.7772i	0.678204	+	0.453162i
$796$	8.53935	+	13.7325i	0.302669	+	0.486736i
$797$	0.996002	−	5.00724i	0.0352802	−	0.177366i	−0.959128	−	0.282974i	$-0.908679\pi$
$797$	0.996002	−	5.00724i	0.0352802	−	0.177366i	0.994408	+	0.105608i	$0.0336790\pi$
$798$	3.45747	+	42.1677i	0.122393	+	1.49272i
$799$		−	7.56500i		−	0.267631i
$800$	−5.25326	+	0.0859138i	−0.185731	+	0.00303751i
$801$		−	7.58971i		−	0.268169i
$802$	21.0881	−	1.72908i	0.744646	−	0.0610561i
$803$	0.276147	−	1.38828i	0.00974501	−	0.0489915i
$804$	5.02306	−	21.5424i	0.177150	−	0.759741i
$805$	−54.9637	−	36.7255i	−1.93721	−	1.29441i
$806$	−3.49974	+	30.4212i	−0.123273	+	1.07154i
$807$	0.934499	+	2.25608i	0.0328959	+	0.0794178i
$808$	−3.88262	−	8.20924i	−0.136590	−	0.288800i
$809$	−2.11979	+	5.11762i	−0.0745277	+	0.179926i	−0.956753	−	0.290902i	$-0.906045\pi$
$809$	−2.11979	+	5.11762i	−0.0745277	+	0.179926i	0.882225	+	0.470828i	$0.156045\pi$
$810$	−1.38613	+	2.49421i	−0.0487036	+	0.0876377i
$811$	−1.25611	+	0.249856i	−0.0441081	+	0.00877364i	−0.217095	−	0.976150i	$-0.569658\pi$
$811$	−1.25611	+	0.249856i	−0.0441081	+	0.00877364i	0.172987	+	0.984924i	$0.444658\pi$
$812$	−29.0286	+	10.9255i	−1.01870	+	0.383408i
$813$	−11.7297	+	7.83751i	−0.411377	+	0.274874i
$814$	1.66962	+	3.25048i	0.0585200	+	0.113929i
$815$	−22.9187	−	22.9187i	−0.802806	−	0.802806i
$816$	−11.9899	−	9.20031i	−0.419730	−	0.322075i
$817$	−17.8496	+	17.8496i	−0.624478	+	0.624478i
$818$	17.7562	+	5.70521i	0.620832	+	0.199478i
$819$	−11.5726	−	17.3196i	−0.404379	−	0.605196i
$820$	6.51259	−	6.09966i	0.227429	−	0.213009i
$821$	0.145926	+	0.733621i	0.00509286	+	0.0256036i	0.983248	−	0.182272i	$-0.0583451\pi$
$821$	0.145926	+	0.733621i	0.00509286	+	0.0256036i	−0.978155	+	0.207875i	$0.933345\pi$
$822$	−10.9506	+	3.12709i	−0.381947	+	0.109070i
$823$	−10.3861	−	4.30205i	−0.362035	−	0.149960i	0.194248	−	0.980952i	$-0.437773\pi$
$823$	−10.3861	−	4.30205i	−0.362035	−	0.149960i	−0.556284	+	0.830992i	$0.687773\pi$
$824$	0.944129	−	6.36455i	0.0328903	−	0.221720i
$825$	−0.799474	+	0.331153i	−0.0278341	+	0.0115293i
$826$	30.2415	+	38.1042i	1.05224	+	1.32581i
$827$	−0.420781	+	0.629743i	−0.0146320	+	0.0218983i	−0.838714	−	0.544573i	$-0.816692\pi$
$827$	−0.420781	+	0.629743i	−0.0146320	+	0.0218983i	0.824082	+	0.566471i	$0.191692\pi$
$828$	13.5491	+	9.70923i	0.470864	+	0.337419i
$829$	−30.4343	−	6.05377i	−1.05703	−	0.210256i	−0.364172	−	0.931332i	$-0.618648\pi$
$829$	−30.4343	−	6.05377i	−1.05703	−	0.210256i	−0.692856	+	0.721076i	$0.743648\pi$
$830$	10.0281	+	8.50826i	0.348081	+	0.295326i
$831$	2.81720			0.0977275
$832$	19.9841	−	37.3865i	0.692823	−	1.29614i
$833$	31.9342			1.10645
$834$	−4.01618	−	3.40749i	−0.139069	−	0.117992i
$835$	28.5765	+	5.68421i	0.988930	+	0.196710i
$836$	−8.26066	+	11.5276i	−0.285701	+	0.398692i
$837$	2.27017	−	3.39754i	0.0784684	−	0.117436i
$838$	−6.64104	−	8.36769i	−0.229411	−	0.289057i
$839$	5.83833	−	2.41832i	0.201562	−	0.0834895i	−0.279619	−	0.960111i	$-0.590208\pi$
$839$	5.83833	−	2.41832i	0.201562	−	0.0834895i	0.481181	+	0.876622i	$0.340208\pi$
$840$	18.0190	−	13.3636i	0.621715	−	0.461090i
$841$	12.4127	+	5.14150i	0.428023	+	0.177293i
$842$	−44.3603	+	12.6677i	−1.52876	+	0.436557i
$843$	−5.10557	−	25.6674i	−0.175845	−	0.884033i
$844$	−28.8673	−	30.8216i	−0.993655	−	1.06092i
$845$	−16.9044	−	25.2993i	−0.581531	−	0.870322i
$846$	−2.69587	−	0.866203i	−0.0926858	−	0.0297807i
$847$	28.1625	−	28.1625i	0.967675	−	0.967675i
$848$	22.7960	+	39.4846i	0.782819	+	1.35591i
$849$	−19.8005	−	19.8005i	−0.679552	−	0.679552i
$850$	2.26747	+	4.41440i	0.0777735	+	0.151413i
$851$	−19.2185	+	12.8414i	−0.658803	+	0.440198i
$852$	6.32616	+	16.8084i	0.216731	+	0.575846i
$853$	−5.95691	+	1.18490i	−0.203961	+	0.0405703i	−0.296013	−	0.955184i	$-0.595657\pi$
$853$	−5.95691	+	1.18490i	−0.203961	+	0.0405703i	0.0920526	+	0.995754i	$0.470657\pi$
$854$	−21.2482	+	38.2342i	−0.727098	+	1.30835i
$855$	5.87662	−	14.1874i	0.200976	−	0.485200i
$856$	15.0555	+	5.38703i	0.514585	+	0.184125i
$857$	16.2301	+	39.1829i	0.554410	+	1.33846i	0.914137	+	0.405406i	$0.132870\pi$
$857$	16.2301	+	39.1829i	0.554410	+	1.33846i	−0.359727	+	0.933058i	$0.617130\pi$
$858$	0.797984	−	6.93642i	0.0272427	−	0.236805i
$859$	0.688418	+	0.459986i	0.0234885	+	0.0156945i	0.567259	−	0.823539i	$-0.308004\pi$
$859$	0.688418	+	0.459986i	0.0234885	+	0.0156945i	−0.543771	+	0.839234i	$0.683004\pi$
$860$	13.0351	+	3.03941i	0.444493	+	0.103643i
$861$	1.69569	−	8.52483i	0.0577891	−	0.290525i
$862$	23.4777	−	1.92502i	0.799654	−	0.0655663i
$863$			11.1655i			0.380077i	0.981777	+	0.190039i	$0.0608613\pi$
$863$			11.1655i			0.380077i	−0.981777	+	0.190039i	$0.939139\pi$
$864$	−4.65148	+	3.21927i	−0.158247	+	0.109522i
$865$		−	0.494848i		−	0.0168253i
$866$	−0.176896	−	2.15744i	−0.00601117	−	0.0733128i
$867$	0.531586	−	2.67246i	0.0180536	−	0.0907616i
$868$	−27.2807	+	16.9641i	−0.925966	+	0.575798i
$869$	8.27596	+	5.52982i	0.280743	+	0.187586i
$870$	11.1839	+	1.28662i	0.379168	+	0.0436205i
$871$	−22.4284	−	54.1468i	−0.759956	−	1.83470i
$872$	−32.9787	+	1.61995i	−1.11680	+	0.0548585i
$873$	2.27625	−	5.49534i	0.0770392	−	0.185989i
$874$	−78.4097	−	43.5753i	−2.65225	−	1.47396i
$875$	−46.1206	+	9.17397i	−1.55916	+	0.310137i
$876$	−1.25401	+	2.76764i	−0.0423692	+	0.0935099i
$877$	21.6503	−	14.4663i	0.731078	−	0.488491i	−0.133462	−	0.991054i	$-0.542610\pi$
$877$	21.6503	−	14.4663i	0.731078	−	0.488491i	0.864541	+	0.502563i	$0.167610\pi$
$878$	1.43270	−	0.735911i	0.0483514	−	0.0248358i
$879$	19.1219	+	19.1219i	0.644966	+	0.644966i
$880$	7.50358	+	0.491868i	0.252946	+	0.0165809i
$881$	23.6671	−	23.6671i	0.797365	−	0.797365i	−0.185314	−	0.982679i	$-0.559330\pi$
$881$	23.6671	−	23.6671i	0.797365	−	0.797365i	0.982679	+	0.185314i	$0.0593303\pi$
$882$	3.65651	−	11.3801i	0.123121	−	0.383187i
$883$	4.39972	+	6.58465i	0.148062	+	0.221591i	0.898086	−	0.439820i	$-0.144958\pi$
$883$	4.39972	+	6.58465i	0.148062	+	0.221591i	−0.750023	+	0.661411i	$0.769958\pi$
$884$	−40.0208	−	1.31030i	−1.34605	−	0.0440701i
$885$	−3.44461	−	17.3172i	−0.115789	−	0.582113i
$886$	−0.632824	−	2.21606i	−0.0212601	−	0.0744498i
$887$	−31.0612	−	12.8660i	−1.04293	−	0.431997i	−0.205569	−	0.978643i	$-0.565904\pi$
$887$	−31.0612	−	12.8660i	−1.04293	−	0.431997i	−0.837364	+	0.546646i	$0.815904\pi$
$888$	−1.90593	−	7.60909i	−0.0639588	−	0.255344i
$889$	36.0548	−	14.9344i	1.20924	−	0.500883i
$890$	16.9638	−	13.4634i	0.568629	−	0.451294i
$891$	−0.517626	+	0.774682i	−0.0173411	+	0.0259528i
$892$	33.6035	−	5.54784i	1.12513	−	0.185755i
$893$	14.9458	+	2.97290i	0.500141	+	0.0994842i
$894$	11.6922	−	13.7809i	0.391047	−	0.460901i
$895$	−20.5662			−0.687452
$896$	43.7549	−	7.96088i	1.46175	−	0.265954i
$897$	44.1643			1.47460
$898$	−9.58001	+	11.2913i	−0.319689	+	0.376796i
$899$	−15.8111	−	3.14502i	−0.527330	−	0.104892i
$900$	1.83275	−	0.302580i	0.0610915	−	0.0100860i
$901$	23.9257	−	35.8074i	0.797081	−	1.19292i
$902$	2.28208	−	1.81118i	0.0759850	−	0.0603058i
$903$	12.0456	−	4.98943i	0.400851	−	0.166038i
$904$	−31.4576	+	7.87954i	−1.04627	+	0.262069i
$905$	−34.8947	−	14.4539i	−1.15994	−	0.480463i
$906$	2.33722	+	8.18460i	0.0776490	+	0.271915i
$907$	7.37557	+	37.0795i	0.244902	+	1.23120i	0.885978	+	0.463727i	$0.153488\pi$
$907$	7.37557	+	37.0795i	0.244902	+	1.23120i	−0.641077	+	0.767477i	$0.721512\pi$
$908$	29.4832	+	0.965294i	0.978435	+	0.0320344i
$909$	1.78374	+	2.66956i	0.0591630	+	0.0885438i
$910$	18.1826	−	56.5893i	0.602747	−	1.87592i
$911$	21.8792	−	21.8792i	0.724889	−	0.724889i	−0.244708	−	0.969597i	$-0.578692\pi$
$911$	21.8792	−	21.8792i	0.724889	−	0.724889i	0.969597	+	0.244708i	$0.0786921\pi$
$912$	22.8883	−	20.0722i	0.757908	−	0.664657i
$913$	3.03634	+	3.03634i	0.100488	+	0.100488i
$914$	−10.1100	+	5.19303i	−0.334410	+	0.171770i
$915$	13.2007	−	8.82040i	0.436400	−	0.291593i
$916$	1.98651	−	4.38427i	0.0656361	−	0.144860i
$917$	4.95608	−	0.985825i	0.163664	−	0.0325548i
$918$	4.67048	+	2.59557i	0.154149	+	0.0856664i
$919$	−6.75257	+	16.3021i	−0.222747	+	0.537758i	−0.995261	−	0.0972391i	$-0.968999\pi$
$919$	−6.75257	+	16.3021i	−0.222747	+	0.537758i	0.772514	+	0.634997i	$0.218999\pi$
$920$	2.33359	+	47.5069i	0.0769363	+	1.56626i
$921$	−0.598129	−	1.44401i	−0.0197090	−	0.0475818i
$922$	31.6500	+	3.64111i	1.04234	+	0.119913i
$923$	39.5647	+	26.4363i	1.30229	+	0.870161i
$924$	6.22033	−	3.86801i	0.204634	−	0.127248i
$925$	−0.502515	+	2.52631i	−0.0165226	+	0.0830646i
$926$	1.58317	+	19.3085i	0.0520263	+	0.634518i
$927$			2.27483i			0.0747153i
$928$	18.7565	+	12.0938i	0.615713	+	0.396999i
$929$		−	22.3493i		−	0.733257i	−0.930367	−	0.366628i	$-0.880512\pi$
$929$		−	22.3493i		−	0.733257i	0.930367	−	0.366628i	$-0.119488\pi$
$930$	11.6209	−	0.952840i	0.381066	−	0.0312449i
$931$	−12.5495	+	63.0906i	−0.411293	+	2.06771i
$932$	44.5147	+	10.3795i	1.45813	+	0.339993i
$933$	−11.5889	−	7.74348i	−0.379405	−	0.253510i
$934$	1.75551	−	15.2596i	0.0574419	−	0.499310i
$935$	−2.71813	−	6.56214i	−0.0888923	−	0.214605i
$936$	−5.04938	+	14.1118i	−0.165044	+	0.461259i
$937$	−9.10596	+	21.9837i	−0.297479	+	0.718177i	0.702500	+	0.711683i	$0.252067\pi$
$937$	−9.10596	+	21.9837i	−0.297479	+	0.718177i	−0.999979	+	0.00649348i	$0.997933\pi$
$938$	29.8672	−	53.7433i	0.975199	−	1.75478i
$939$	−28.0009	+	5.56972i	−0.913775	+	0.181761i
$940$	−2.84615	−	7.56212i	−0.0928311	−	0.246649i
$941$	−7.02478	+	4.69380i	−0.229001	+	0.153014i	−0.664778	−	0.747041i	$-0.731474\pi$
$941$	−7.02478	+	4.69380i	−0.229001	+	0.153014i	0.435777	+	0.900055i	$0.356474\pi$
$942$	8.69445	+	16.9267i	0.283280	+	0.551503i
$943$	13.0309	+	13.0309i	0.424346	+	0.424346i
$944$	9.05964	−	33.8100i	0.294866	−	1.10042i
$945$	−5.60843	+	5.60843i	−0.182442	+	0.182442i
$946$	4.16078	+	1.33689i	0.135279	+	0.0434661i
$947$	−4.93617	−	7.38750i	−0.160404	−	0.240062i	0.742558	−	0.669782i	$-0.233612\pi$
$947$	−4.93617	−	7.38750i	−0.160404	−	0.240062i	−0.902962	+	0.429720i	$0.858612\pi$
$948$	−14.6056	−	15.5944i	−0.474369	−	0.506482i
$949$	1.57058	+	7.89585i	0.0509833	+	0.256310i
$950$	−9.61236	+	2.74494i	−0.311866	+	0.0890575i
$951$	−11.7341	−	4.86040i	−0.380503	−	0.157609i
$952$	−25.0238	−	33.7411i	−0.811026	−	1.09356i
$953$	39.3619	−	16.3042i	1.27506	−	0.528146i	0.360559	−	0.932737i	$-0.382586\pi$
$953$	39.3619	−	16.3042i	1.27506	−	0.528146i	0.914498	+	0.404591i	$0.132586\pi$
$954$	−10.0208	−	12.6262i	−0.324435	−	0.408787i
$955$	−4.75024	+	7.10924i	−0.153714	+	0.230050i
$956$	−9.37952	+	13.0890i	−0.303355	+	0.423328i
$957$	3.60513	+	0.717104i	0.116537	+	0.0231807i
$958$	−37.7485	−	32.0273i	−1.21960	−	1.03476i
$959$	−31.6548			−1.02219
$960$	−15.4467	−	4.68590i	−0.498540	−	0.151237i
$961$	14.3030			0.461388
$962$	−15.8478	−	13.4459i	−0.510953	−	0.433513i
$963$	−5.54477	−	1.10292i	−0.178678	−	0.0355412i
$964$	−39.5916	−	28.3711i	−1.27516	−	0.913773i
$965$	26.7058	−	39.9681i	0.859690	−	1.28662i
$966$	28.8028	+	36.2914i	0.926714	+	1.16766i
$967$	−30.8265	+	12.7688i	−0.991315	+	0.410616i	−0.818605	−	0.574357i	$-0.805252\pi$
$967$	−30.8265	+	12.7688i	−0.991315	+	0.410616i	−0.172710	+	0.984973i	$0.555252\pi$
$968$	−28.3472	−	4.20508i	−0.911114	−	0.135156i
$969$	−26.5664	−	11.0041i	−0.853434	−	0.353504i
$970$	16.3205	−	4.66054i	0.524021	−	0.149641i
$971$	6.84256	+	34.3999i	0.219588	+	1.10394i	0.920514	+	0.390710i	$0.127771\pi$
$971$	6.84256	+	34.3999i	0.219588	+	1.10394i	−0.700926	+	0.713234i	$0.747229\pi$
$972$	1.45973	−	1.36718i	0.0468210	−	0.0438523i
$973$	−8.13348	−	12.1726i	−0.260747	−	0.390236i
$974$	−30.4501	−	9.78385i	−0.975685	−	0.313495i
$975$	3.48013	−	3.48013i	0.111453	−	0.111453i
$976$	31.2044	−	4.10790i	0.998829	−	0.131491i
$977$	−17.0295	−	17.0295i	−0.544823	−	0.544823i	0.380116	−	0.924939i	$-0.375884\pi$
$977$	−17.0295	−	17.0295i	−0.544823	−	0.544823i	−0.924939	+	0.380116i	$0.875884\pi$
$978$	10.3796	+	20.2074i	0.331903	+	0.646163i
$979$	5.87961	−	3.92863i	0.187913	−	0.125560i
$980$	31.9220	−	12.0145i	1.01971	−	0.383788i
$981$	11.4495	−	2.27744i	0.365554	−	0.0727132i
$982$	27.2874	−	49.1011i	0.870775	−	1.56688i
$983$	−0.273304	+	0.659814i	−0.00871704	+	0.0210448i	−0.928178	−	0.372136i	$-0.878625\pi$
$983$	−0.273304	+	0.659814i	−0.00871704	+	0.0210448i	0.919461	+	0.393181i	$0.128625\pi$
$984$	−5.65363	+	2.67393i	−0.180231	+	0.0852417i
$985$	11.8433	+	28.5923i	0.377359	+	0.911026i
$986$	2.40923	−	20.9421i	0.0767256	−	0.666932i
$987$	−6.54423	−	4.37271i	−0.208305	−	0.139185i
$988$	18.3161	−	78.5521i	0.582712	−	2.49907i
$989$	−5.39295	+	27.1122i	−0.171486	+	0.862117i
$990$	−2.64972	+	0.217259i	−0.0842136	+	0.00690496i
$991$			19.8284i			0.629869i	0.949113	+	0.314935i	$0.101983\pi$
$991$			19.8284i			0.629869i	−0.949113	+	0.314935i	$0.898017\pi$
$992$	21.4973	+	8.49533i	0.682539	+	0.269727i
$993$			9.26456i			0.294002i
$994$	4.07940	+	49.7528i	0.129391	+	1.57806i
$995$	3.18278	−	16.0009i	0.100901	−	0.507263i
$996$	−4.86749	−	7.82762i	−0.154232	−	0.248028i
$997$	22.4752	+	15.0175i	0.711797	+	0.475608i	0.858002	−	0.513647i	$-0.171706\pi$
$997$	22.4752	+	15.0175i	0.711797	+	0.475608i	−0.146205	+	0.989254i	$0.546706\pi$
$998$	20.7765	+	2.39019i	0.657670	+	0.0756601i
$999$	1.06131	+	2.56222i	0.0335782	+	0.0810651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.157.12	✓	128
3.2	odd	2		576.2.bd.b.541.5		128
4.3	odd	2		768.2.r.a.721.3		128
64.11	odd	16		768.2.r.a.49.3		128
64.53	even	16	inner	192.2.r.a.181.12	yes	128
192.53	odd	16		576.2.bd.b.181.5		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.157.12	✓	128	1.1	even	1	trivial
192.2.r.a.181.12	yes	128	64.53	even	16	inner
576.2.bd.b.181.5		128	192.53	odd	16
576.2.bd.b.541.5		128	3.2	odd	2
768.2.r.a.49.3		128	64.11	odd	16
768.2.r.a.721.3		128	4.3	odd	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.r (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.914936 - 1.07837i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.325783 - 1.97329i) q^{4} +(-1.12099 + 1.67768i) q^{5} +(1.10774 - 0.879159i) q^{6} +(3.63169 - 1.50430i) q^{7} +(-2.42601 - 1.45412i) q^{8} +(0.923880 + 0.382683i) q^{9} +O(q^{10})\)	\(q+(0.914936 - 1.07837i) q^{2} +(0.980785 + 0.195090i) q^{3} +(-0.325783 - 1.97329i) q^{4} +(-1.12099 + 1.67768i) q^{5} +(1.10774 - 0.879159i) q^{6} +(3.63169 - 1.50430i) q^{7} +(-2.42601 - 1.45412i) q^{8} +(0.923880 + 0.382683i) q^{9} +(0.783533 + 2.74382i) q^{10} +(0.181766 + 0.913800i) q^{11} +(0.0654458 - 1.99893i) q^{12} +(-2.94399 - 4.40600i) q^{13} +(1.70057 - 5.29266i) q^{14} +(-1.42675 + 1.42675i) q^{15} +(-3.78773 + 1.28573i) q^{16} +(2.67163 + 2.67163i) q^{17} +(1.25797 - 0.646157i) q^{18} +(-6.32808 + 4.22829i) q^{19} +(3.67574 + 1.66547i) q^{20} +(3.85539 - 0.766884i) q^{21} +(1.15172 + 0.640057i) q^{22} +(-3.18943 + 7.69996i) q^{23} +(-2.09572 - 1.89947i) q^{24} +(0.355428 + 0.858079i) q^{25} +(-7.44489 - 0.856480i) q^{26} +(0.831470 + 0.555570i) q^{27} +(-4.15156 - 6.67630i) q^{28} +(0.769671 - 3.86940i) q^{29} +(0.233185 + 2.84395i) q^{30} -4.08619i q^{31} +(-2.07903 + 5.26095i) q^{32} +0.931702i q^{33} +(5.32538 - 0.436646i) q^{34} +(-1.54736 + 7.77911i) q^{35} +(0.454160 - 1.94775i) q^{36} +(2.30594 + 1.54078i) q^{37} +(-1.23011 + 10.6927i) q^{38} +(-2.02786 - 4.89568i) q^{39} +(5.15908 - 2.44002i) q^{40} +(0.846170 - 2.04283i) q^{41} +(2.70044 - 4.85920i) q^{42} +(3.25306 - 0.647073i) q^{43} +(1.74397 - 0.656378i) q^{44} +(-1.67768 + 1.12099i) q^{45} +(5.38532 + 10.4844i) q^{46} +(-1.41580 - 1.41580i) q^{47} +(-3.96578 + 0.522075i) q^{48} +(5.97654 - 5.97654i) q^{49} +(1.25052 + 0.401803i) q^{50} +(2.09908 + 3.14150i) q^{51} +(-7.73520 + 7.24475i) q^{52} +(-2.22367 - 11.1792i) q^{53} +(1.35985 - 0.388324i) q^{54} +(-1.73682 - 0.719415i) q^{55} +(-10.9980 - 1.63146i) q^{56} +(-7.03139 + 2.91250i) q^{57} +(-3.46846 - 4.37024i) q^{58} +(-4.86163 + 7.27594i) q^{59} +(3.28020 + 2.35057i) q^{60} +(-7.71722 - 1.53505i) q^{61} +(-4.40645 - 3.73861i) q^{62} +3.93092 q^{63} +(3.77109 + 7.05541i) q^{64} +10.6920 q^{65} +(1.00472 + 0.852448i) q^{66} +(10.8476 + 2.15772i) q^{67} +(4.40152 - 6.14226i) q^{68} +(-4.63033 + 6.92978i) q^{69} +(6.97306 + 8.78603i) q^{70} +(-8.29620 + 3.43640i) q^{71} +(-1.68488 - 2.27182i) q^{72} +(-1.40360 - 0.581389i) q^{73} +(3.77132 - 1.07695i) q^{74} +(0.181196 + 0.910932i) q^{75} +(10.4052 + 11.1096i) q^{76} +(2.03474 + 3.04521i) q^{77} +(-7.13474 - 2.29245i) q^{78} +(7.55405 - 7.55405i) q^{79} +(2.08896 - 7.79588i) q^{80} +(0.707107 + 0.707107i) q^{81} +(-1.42875 - 2.78155i) q^{82} +(3.83208 - 2.56051i) q^{83} +(-2.76930 - 7.35795i) q^{84} +(-7.47700 + 1.48727i) q^{85} +(2.27855 - 4.10004i) q^{86} +(1.50976 - 3.64489i) q^{87} +(0.887804 - 2.48120i) q^{88} +(-2.90446 - 7.01198i) q^{89} +(-0.326123 + 2.83480i) q^{90} +(-17.3196 - 11.5726i) q^{91} +(16.2333 + 3.78514i) q^{92} +(0.797177 - 4.00768i) q^{93} +(-2.82214 + 0.231397i) q^{94} -15.3564i q^{95} +(-3.06545 + 4.75426i) q^{96} -5.94812i q^{97} +(-0.976796 - 11.9131i) q^{98} +(-0.181766 + 0.913800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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