LMFDB - Embedded newform 261.2.x.a.101.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(2,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([14, 3]))

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

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

chi := DirichletCharacter("261.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$261 = 3^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	261.x (of order $84$ , degree $24$ , 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			101.23
Character	$\chi$	$=$	261.101
Dual form			261.2.x.a.230.23

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.745238 - 1.70810i) q^{2} +(0.812584 - 1.52961i) q^{3} +(-1.00189 - 1.07979i) q^{4} +(1.35206 + 0.203790i) q^{5} +(-2.00716 - 2.52790i) q^{6} +(0.641683 + 0.595395i) q^{7} +(0.927004 - 0.324373i) q^{8} +(-1.67941 - 2.48587i) q^{9} +(1.35570 - 2.15759i) q^{10} +(-1.50068 + 1.29144i) q^{11} +(-2.46577 + 0.655091i) q^{12} +(-3.81944 + 5.60209i) q^{13} +(1.49520 - 0.652350i) q^{14} +(1.41038 - 1.90253i) q^{15} +(0.356931 - 4.76292i) q^{16} +(1.87992 + 1.87992i) q^{17} +(-5.49769 + 1.01605i) q^{18} +(-0.513681 - 0.322767i) q^{19} +(-1.13457 - 1.66411i) q^{20} +(1.43214 - 0.497716i) q^{21} +(1.08755 + 3.52576i) q^{22} +(-1.70995 - 0.671108i) q^{23} +(0.257105 - 1.68154i) q^{24} +(-2.99132 - 0.922701i) q^{25} +(6.72256 + 10.6989i) q^{26} +(-5.16708 + 0.548869i) q^{27} -1.28940i q^{28} +(2.83848 + 4.57636i) q^{29} +(-2.19865 - 3.82692i) q^{30} +(-5.24680 + 3.87232i) q^{31} +(-6.13295 - 3.24136i) q^{32} +(0.755973 + 3.34487i) q^{33} +(4.61208 - 1.81011i) q^{34} +(0.746259 + 0.935779i) q^{35} +(-1.00161 + 4.30399i) q^{36} +(-1.08510 - 3.10104i) q^{37} +(-0.934134 + 0.636882i) q^{38} +(5.46540 + 10.3944i) q^{39} +(1.31947 - 0.249657i) q^{40} +(9.96635 + 2.67047i) q^{41} +(0.217136 - 2.81717i) q^{42} +(6.90448 - 9.35524i) q^{43} +(2.89801 + 0.326527i) q^{44} +(-1.76407 - 3.70330i) q^{45} +(-2.42064 + 2.42064i) q^{46} +(-0.531191 - 0.617255i) q^{47} +(-6.99537 - 4.41623i) q^{48} +(-0.465849 - 6.21632i) q^{49} +(-3.80532 + 4.42186i) q^{50} +(4.40313 - 1.34795i) q^{51} +(9.87573 - 1.48853i) q^{52} +(-2.21260 - 1.76449i) q^{53} +(-2.91318 + 9.23495i) q^{54} +(-2.29220 + 1.44029i) q^{55} +(0.787972 + 0.343789i) q^{56} +(-0.911117 + 0.523456i) q^{57} +(9.93224 - 1.43794i) q^{58} +(7.63000 - 4.40518i) q^{59} +(-3.46738 + 0.383223i) q^{60} +(-5.21702 + 0.195207i) q^{61} +(2.70420 + 11.8479i) q^{62} +(0.402424 - 2.59506i) q^{63} +(-2.63860 + 2.10422i) q^{64} +(-6.30577 + 6.79601i) q^{65} +(6.27676 + 1.20144i) q^{66} +(3.56723 - 0.267327i) q^{67} +(0.146428 - 3.91338i) q^{68} +(-2.41601 + 2.07023i) q^{69} +(2.15455 - 0.577309i) q^{70} +(2.38011 - 1.14620i) q^{71} +(-2.36317 - 1.75966i) q^{72} +(-0.147552 + 1.30956i) q^{73} +(-6.10556 - 0.457548i) q^{74} +(-3.84208 + 3.82579i) q^{75} +(0.166135 + 0.878043i) q^{76} +(-1.73188 - 0.0648024i) q^{77} +(21.8278 - 1.58915i) q^{78} +(-0.830478 + 4.38918i) q^{79} +(1.45323 - 6.36702i) q^{80} +(-3.35913 + 8.34962i) q^{81} +(11.9888 - 15.0334i) q^{82} +(2.58232 - 8.37166i) q^{83} +(-1.97228 - 1.04775i) q^{84} +(2.15865 + 2.92487i) q^{85} +(-10.8342 - 18.7654i) q^{86} +(9.30654 - 0.623094i) q^{87} +(-0.972231 + 1.68395i) q^{88} +(-6.10911 + 0.688332i) q^{89} +(-7.64028 + 0.253381i) q^{90} +(-5.78633 + 1.32069i) q^{91} +(0.988541 + 2.51876i) q^{92} +(1.65967 + 11.1721i) q^{93} +(-1.45020 + 0.447327i) q^{94} +(-0.628751 - 0.541084i) q^{95} +(-9.94155 + 6.74714i) q^{96} +(5.89206 + 11.1483i) q^{97} +(-10.9653 - 3.83692i) q^{98} +(5.73063 + 1.56164i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100})$ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$ .

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{1}{6}\right)$

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

)

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

$2$	0.745238	−	1.70810i	0.526963	−	1.20781i	−0.425999	−	0.904723i	$-0.640077\pi$
$2$	0.745238	−	1.70810i	0.526963	−	1.20781i	0.952962	−	0.303089i	$-0.0980178\pi$
$3$	0.812584	−	1.52961i	0.469146	−	0.883121i
$3$	0.812584	−	1.52961i	0.469146	−	0.883121i
$4$	−1.00189	−	1.07979i	−0.500947	−	0.539893i
$5$	1.35206	+	0.203790i	0.604660	+	0.0911379i	0.444235	−	0.895910i	$-0.353475\pi$
$5$	1.35206	+	0.203790i	0.604660	+	0.0911379i	0.160425	+	0.987048i	$0.448714\pi$
$6$	−2.00716	−	2.52790i	−0.819422	−	1.03201i
$7$	0.641683	+	0.595395i	0.242533	+	0.225038i	0.792068	−	0.610433i	$-0.209004\pi$
$7$	0.641683	+	0.595395i	0.242533	+	0.225038i	−0.549535	+	0.835471i	$0.685195\pi$
$8$	0.927004	−	0.324373i	0.327745	−	0.114683i
$9$	−1.67941	−	2.48587i	−0.559805	−	0.828624i
$10$	1.35570	−	2.15759i	0.428711	−	0.682290i
$11$	−1.50068	+	1.29144i	−0.452473	+	0.389385i	−0.848791	−	0.528729i	$-0.822669\pi$
$11$	−1.50068	+	1.29144i	−0.452473	+	0.389385i	0.396318	+	0.918113i	$0.370288\pi$
$12$	−2.46577	+	0.655091i	−0.711807	+	0.189109i
$13$	−3.81944	+	5.60209i	−1.05932	+	1.55374i	−0.248338	+	0.968673i	$0.579884\pi$
$13$	−3.81944	+	5.60209i	−1.05932	+	1.55374i	−0.810985	+	0.585067i	$0.801068\pi$
$14$	1.49520	−	0.652350i	0.399610	−	0.174348i
$15$	1.41038	−	1.90253i	0.364159	−	0.491231i
$16$	0.356931	−	4.76292i	0.0892328	−	1.19073i
$17$	1.87992	+	1.87992i	0.455947	+	0.455947i	0.897322	−	0.441376i	$-0.145509\pi$
$17$	1.87992	+	1.87992i	0.455947	+	0.455947i	−0.441376	+	0.897322i	$0.645509\pi$
$18$	−5.49769	+	1.01605i	−1.29582	+	0.239485i
$19$	−0.513681	−	0.322767i	−0.117846	−	0.0740479i	0.471819	−	0.881695i	$-0.343598\pi$
$19$	−0.513681	−	0.322767i	−0.117846	−	0.0740479i	−0.589666	+	0.807648i	$0.700740\pi$
$20$	−1.13457	−	1.66411i	−0.253698	−	0.372107i
$21$	1.43214	−	0.497716i	0.312519	−	0.108611i
$22$	1.08755	+	3.52576i	0.231867	+	0.751694i
$23$	−1.70995	−	0.671108i	−0.356550	−	0.139936i	0.180303	−	0.983611i	$-0.442292\pi$
$23$	−1.70995	−	0.671108i	−0.356550	−	0.139936i	−0.536854	+	0.843675i	$0.680387\pi$
$24$	0.257105	−	1.68154i	0.0524813	−	0.343242i
$25$	−2.99132	−	0.922701i	−0.598265	−	0.184540i
$26$	6.72256	+	10.6989i	1.31840	+	2.09823i
$27$	−5.16708	+	0.548869i	−0.994406	+	0.105630i
$28$		−	1.28940i		−	0.243674i
$29$	2.83848	+	4.57636i	0.527092	+	0.849808i
$29$	2.83848	+	4.57636i	0.527092	+	0.849808i
$30$	−2.19865	−	3.82692i	−0.401416	−	0.698697i
$31$	−5.24680	+	3.87232i	−0.942354	+	0.695489i	−0.952525	−	0.304459i	$-0.901524\pi$
$31$	−5.24680	+	3.87232i	−0.942354	+	0.695489i	0.0101714	+	0.999948i	$0.496762\pi$
$32$	−6.13295	−	3.24136i	−1.08416	−	0.572996i
$33$	0.755973	+	3.34487i	0.131598	+	0.582267i
$34$	4.61208	−	1.81011i	0.790965	−	0.310431i
$35$	0.746259	+	0.935779i	0.126141	+	0.158176i
$36$	−1.00161	+	4.30399i	−0.166936	+	0.717331i
$37$	−1.08510	−	3.10104i	−0.178390	−	0.509808i	0.819617	−	0.572911i	$-0.194186\pi$
$37$	−1.08510	−	3.10104i	−0.178390	−	0.509808i	−0.998007	+	0.0631032i	$0.979900\pi$
$38$	−0.934134	+	0.636882i	−0.151537	+	0.103316i
$39$	5.46540	+	10.3944i	0.875164	+	1.66444i
$40$	1.31947	−	0.249657i	0.208627	−	0.0394743i
$41$	9.96635	+	2.67047i	1.55648	+	0.417058i	0.931548	−	0.363619i	$-0.118459\pi$
$41$	9.96635	+	2.67047i	1.55648	+	0.417058i	0.624934	+	0.780677i	$0.285126\pi$
$42$	0.217136	−	2.81717i	0.0335048	−	0.434698i
$43$	6.90448	−	9.35524i	1.05292	−	1.42666i	0.154255	−	0.988031i	$-0.450702\pi$
$43$	6.90448	−	9.35524i	1.05292	−	1.42666i	0.898668	−	0.438629i	$-0.144536\pi$
$44$	2.89801	+	0.326527i	0.436891	+	0.0492258i
$45$	−1.76407	−	3.70330i	−0.262973	−	0.552056i
$46$	−2.42064	+	2.42064i	−0.356905	+	0.356905i
$47$	−0.531191	−	0.617255i	−0.0774821	−	0.0900359i	0.717893	−	0.696154i	$-0.245107\pi$
$47$	−0.531191	−	0.617255i	−0.0774821	−	0.0900359i	−0.795375	+	0.606118i	$0.792726\pi$
$48$	−6.99537	−	4.41623i	−1.00969	−	0.637429i
$49$	−0.465849	−	6.21632i	−0.0665498	−	0.888045i
$50$	−3.80532	+	4.42186i	−0.538153	+	0.625346i
$51$	4.40313	−	1.34795i	0.616561	−	0.188751i
$52$	9.87573	−	1.48853i	1.36952	−	0.206422i
$53$	−2.21260	−	1.76449i	−0.303924	−	0.242371i	0.459637	−	0.888107i	$-0.347979\pi$
$53$	−2.21260	−	1.76449i	−0.303924	−	0.242371i	−0.763561	+	0.645735i	$0.776551\pi$
$54$	−2.91318	+	9.23495i	−0.396434	+	1.25672i
$55$	−2.29220	+	1.44029i	−0.309080	+	0.194208i
$56$	0.787972	+	0.343789i	0.105297	+	0.0459407i
$57$	−0.911117	+	0.523456i	−0.120680	+	0.0693335i
$58$	9.93224	−	1.43794i	1.30417	−	0.188811i
$59$	7.63000	−	4.40518i	0.993341	−	0.573506i	0.0870696	−	0.996202i	$-0.472250\pi$
$59$	7.63000	−	4.40518i	0.993341	−	0.573506i	0.906271	+	0.422697i	$0.138916\pi$
$60$	−3.46738	+	0.383223i	−0.447637	+	0.0494739i
$61$	−5.21702	+	0.195207i	−0.667971	+	0.0249937i	−0.369226	−	0.929340i	$-0.620377\pi$
$61$	−5.21702	+	0.195207i	−0.667971	+	0.0249937i	−0.298744	+	0.954333i	$0.596568\pi$
$62$	2.70420	+	11.8479i	0.343434	+	1.50468i
$63$	0.402424	−	2.59506i	0.0507007	−	0.326946i
$64$	−2.63860	+	2.10422i	−0.329825	+	0.263027i
$65$	−6.30577	+	6.79601i	−0.782135	+	0.842941i
$66$	6.27676	+	1.20144i	0.772616	+	0.147887i
$67$	3.56723	−	0.267327i	0.435807	−	0.0326592i	0.144979	−	0.989435i	$-0.453689\pi$
$67$	3.56723	−	0.267327i	0.435807	−	0.0326592i	0.290827	+	0.956776i	$0.406069\pi$
$68$	0.146428	−	3.91338i	0.0177571	−	0.474567i
$69$	−2.41601	+	2.07023i	−0.290854	+	0.249227i
$70$	2.15455	−	0.577309i	0.257518	−	0.0690017i
$71$	2.38011	−	1.14620i	0.282467	−	0.136029i	−0.287286	−	0.957845i	$-0.592753\pi$
$71$	2.38011	−	1.14620i	0.282467	−	0.136029i	0.569753	+	0.821816i	$0.307039\pi$
$72$	−2.36317	−	1.75966i	−0.278503	−	0.207378i
$73$	−0.147552	+	1.30956i	−0.0172696	+	0.153272i	−0.999387	−	0.0349949i	$-0.988858\pi$
$73$	−0.147552	+	1.30956i	−0.0172696	+	0.153272i	0.982118	+	0.188267i	$0.0602871\pi$
$74$	−6.10556	−	0.457548i	−0.709757	−	0.0531889i
$75$	−3.84208	+	3.82579i	−0.443645	+	0.441764i
$76$	0.166135	+	0.878043i	0.0190570	+	0.100718i
$77$	−1.73188	−	0.0648024i	−0.197366	−	0.00738492i
$78$	21.8278	−	1.58915i	2.47151	−	0.179936i
$79$	−0.830478	+	4.38918i	−0.0934361	+	0.493822i	0.904319	+	0.426857i	$0.140379\pi$
$79$	−0.830478	+	4.38918i	−0.0934361	+	0.493822i	−0.997755	+	0.0669648i	$0.978668\pi$
$80$	1.45323	−	6.36702i	0.162476	−	0.711854i
$81$	−3.35913	+	8.34962i	−0.373237	+	0.927736i
$82$	11.9888	−	15.0334i	1.32394	−	1.66016i
$83$	2.58232	−	8.37166i	0.283446	−	0.918909i	−0.696144	−	0.717902i	$-0.745102\pi$
$83$	2.58232	−	8.37166i	0.283446	−	0.918909i	0.979590	−	0.201007i	$-0.0644214\pi$
$84$	−1.97228	−	1.04775i	−0.215194	−	0.114319i
$85$	2.15865	+	2.92487i	0.234139	+	0.317247i
$86$	−10.8342	−	18.7654i	−1.16829	−	2.02353i
$87$	9.30654	−	0.623094i	0.997766	−	0.0668027i
$88$	−0.972231	+	1.68395i	−0.103640	+	0.179510i
$89$	−6.10911	+	0.688332i	−0.647565	+	0.0729630i	−0.429637	−	0.903002i	$-0.641358\pi$
$89$	−6.10911	+	0.688332i	−0.647565	+	0.0729630i	−0.217928	+	0.975965i	$0.569930\pi$
$90$	−7.64028	+	0.253381i	−0.805356	+	0.0267087i
$91$	−5.78633	+	1.32069i	−0.606572	+	0.138446i
$92$	0.988541	+	2.51876i	0.103063	+	0.262599i
$93$	1.65967	+	11.1721i	0.172100	+	1.15850i
$94$	−1.45020	+	0.447327i	−0.149577	+	0.0461383i
$95$	−0.628751	−	0.541084i	−0.0645085	−	0.0555141i
$96$	−9.94155	+	6.74714i	−1.01465	+	0.688628i
$97$	5.89206	+	11.1483i	0.598248	+	1.13194i	0.978342	+	0.206993i	$0.0663678\pi$
$97$	5.89206	+	11.1483i	0.598248	+	1.13194i	−0.380094	+	0.924948i	$0.624108\pi$
$98$	−10.9653	−	3.83692i	−1.10766	−	0.387587i
$99$	5.73063	+	1.56164i	0.575950	+	0.156951i
$100$	2.00067	+	4.15444i	0.200067	+	0.415444i
$101$	0.217512	+	0.160531i	0.0216433	+	0.0159735i	0.604588	−	0.796538i	$-0.293338\pi$
$101$	0.217512	+	0.160531i	0.0216433	+	0.0159735i	−0.582945	+	0.812512i	$0.698100\pi$
$102$	0.978942	−	8.52554i	0.0969297	−	0.844155i
$103$	−7.16022	−	4.88176i	−0.705518	−	0.481014i	0.156639	−	0.987656i	$-0.449934\pi$
$103$	−7.16022	−	4.88176i	−0.705518	−	0.481014i	−0.862156	+	0.506642i	$0.830887\pi$
$104$	−1.72347	+	6.43209i	−0.169000	+	0.630718i
$105$	2.03777	−	0.381086i	0.198866	−	0.0371902i
$106$	−4.66285	+	2.46439i	−0.452896	+	0.239362i
$107$	−5.12213	+	10.6362i	−0.495175	+	1.02824i	0.492294	+	0.870429i	$0.336159\pi$
$107$	−5.12213	+	10.6362i	−0.495175	+	1.02824i	−0.987469	+	0.157813i	$0.949556\pi$
$108$	5.76953	+	5.02943i	0.555173	+	0.483957i
$109$	−16.8665	−	3.84967i	−1.61552	−	0.368732i	−0.683161	−	0.730268i	$-0.739395\pi$
$109$	−16.8665	−	3.84967i	−1.61552	−	0.368732i	−0.932358	+	0.361536i	$0.882252\pi$
$110$	0.751921	+	4.98867i	0.0716929	+	0.475651i
$111$	−5.62512	−	0.860074i	−0.533913	−	0.0816346i
$112$	3.06485	−	2.84377i	0.289601	−	0.268711i
$113$	−2.61645	+	4.95056i	−0.246135	+	0.465710i	−0.975968	−	0.217916i	$-0.930074\pi$
$113$	−2.61645	+	4.95056i	−0.246135	+	0.465710i	0.729833	+	0.683626i	$0.239598\pi$
$114$	0.215119	+	1.94638i	0.0201477	+	0.182295i
$115$	−2.17520	−	1.25585i	−0.202838	−	0.117109i
$116$	2.09762	−	7.64997i	0.194760	−	0.710282i
$117$	20.3405	+	0.0864121i	1.88048	+	0.00798880i
$118$	−1.83834	−	16.3157i	−0.169233	−	1.50199i
$119$	0.0870179	+	2.32560i	0.00797692	+	0.213188i
$120$	0.690302	−	2.22114i	0.0630157	−	0.202762i
$121$	−1.05524	+	7.00104i	−0.0959307	+	0.636458i
$122$	−3.55449	+	9.05668i	−0.321808	+	0.819954i
$123$	12.1833	−	13.0746i	1.09853	−	1.17890i
$124$	9.43801	+	1.78577i	0.847559	+	0.160367i
$125$	−10.0160	−	4.82347i	−0.895862	−	0.431424i
$126$	−4.13273	−	2.62132i	−0.368172	−	0.233526i
$127$	0.888177	−	2.53826i	0.0788130	−	0.225235i	−0.897734	−	0.440537i	$-0.854788\pi$
$127$	0.888177	−	2.53826i	0.0788130	−	0.225235i	0.976547	+	0.215303i	$0.0690738\pi$
$128$	−1.96293	−	7.32575i	−0.173500	−	0.647511i
$129$	−8.69940	−	18.1631i	−0.765939	−	1.59917i
$130$	6.90898	+	15.8356i	0.605958	+	1.38887i
$131$	−4.68162	−	10.7304i	−0.409035	−	0.937519i	−0.992141	−	0.125123i	$-0.960068\pi$
$131$	−4.68162	−	10.7304i	−0.409035	−	0.937519i	0.583106	−	0.812396i	$-0.301837\pi$
$132$	2.85433	−	4.16749i	0.248438	−	0.362734i
$133$	−0.137446	−	0.512957i	−0.0119181	−	0.0444790i
$134$	2.20181	−	6.29242i	0.190208	−	0.543583i
$135$	−7.09807	−	0.310897i	−0.610904	−	0.0267578i
$136$	2.35248	+	1.13290i	0.201724	+	0.0971451i
$137$	1.74425	+	0.330030i	0.149021	+	0.0281964i	0.259887	−	0.965639i	$-0.416315\pi$
$137$	1.74425	+	0.330030i	0.149021	+	0.0281964i	−0.110866	+	0.993835i	$0.535362\pi$
$138$	1.73567	+	5.66962i	0.147750	+	0.482630i
$139$	2.93973	−	7.49030i	0.249344	−	0.635319i	−0.750324	−	0.661070i	$-0.770102\pi$
$139$	2.93973	−	7.49030i	0.249344	−	0.635319i	0.999668	+	0.0257511i	$0.00819772\pi$
$140$	0.262768	−	1.74335i	0.0222079	−	0.147340i
$141$	−1.37580	+	0.310943i	−0.115863	+	0.0261862i
$142$	−0.184081	−	4.91967i	−0.0154477	−	0.412849i
$143$	−1.50301	−	13.3396i	−0.125688	−	1.11551i
$144$	−12.4394	+	7.11163i	−1.03662	+	0.592635i
$145$	2.90518	+	6.76597i	0.241262	+	0.561883i
$146$	2.12690	+	1.22797i	0.176024	+	0.101627i
$147$	−9.88708	−	4.33871i	−0.815473	−	0.357851i
$148$	−2.26130	+	4.27859i	−0.185878	+	0.351698i
$149$	−2.34204	+	2.17310i	−0.191867	+	0.178027i	−0.770257	−	0.637734i	$-0.779872\pi$
$149$	−2.34204	+	2.17310i	−0.191867	+	0.178027i	0.578389	+	0.815761i	$0.303681\pi$
$150$	3.67158	+	9.41379i	0.299784	+	0.768633i
$151$	2.24806	+	14.9149i	0.182945	+	1.21376i	0.872167	+	0.489208i	$0.162714\pi$
$151$	2.24806	+	14.9149i	0.182945	+	1.21376i	−0.689223	+	0.724550i	$0.742048\pi$
$152$	−0.580881	−	0.132582i	−0.0471157	−	0.0107538i
$153$	1.51607	−	7.83039i	0.122567	−	0.633050i
$154$	−1.40135	+	2.90994i	−0.112924	+	0.234490i
$155$	−7.88314	+	4.16636i	−0.633189	+	0.334650i
$156$	5.74799	−	16.3156i	0.460208	−	1.30629i
$157$	−5.30062	+	19.7822i	−0.423035	+	1.57879i	0.345141	+	0.938551i	$0.387831\pi$
$157$	−5.30062	+	19.7822i	−0.423035	+	1.57879i	−0.768176	+	0.640238i	$0.778836\pi$
$158$	6.87828	+	4.68953i	0.547206	+	0.373079i
$159$	−4.49691	+	1.95062i	−0.356628	+	0.154694i
$160$	−7.63156	−	5.63235i	−0.603328	−	0.445276i
$161$	−0.697674	−	1.44874i	−0.0549844	−	0.114176i
$162$	11.7587	+	11.9602i	0.923849	+	0.939683i
$163$	−12.5429	−	4.38895i	−0.982436	−	0.343769i	−0.209190	−	0.977875i	$-0.567083\pi$
$163$	−12.5429	−	4.38895i	−0.982436	−	0.343769i	−0.773246	+	0.634106i	$0.781368\pi$
$164$	−7.10169	−	13.4370i	−0.554548	−	1.04926i
$165$	0.340469	+	4.67653i	0.0265055	+	0.364067i
$166$	−12.3752	−	10.6497i	−0.960504	−	0.826581i
$167$	12.9271	−	3.98749i	1.00033	−	0.308561i	0.249012	−	0.968500i	$-0.419894\pi$
$167$	12.9271	−	3.98749i	1.00033	−	0.308561i	0.751319	+	0.659939i	$0.229418\pi$
$168$	1.16616	−	0.925933i	0.0899709	−	0.0714373i
$169$	−12.0459	−	30.6924i	−0.926605	−	2.36095i
$170$	6.60469	−	1.50748i	0.506557	−	0.115618i
$171$	0.0603252	+	1.81901i	0.00461318	+	0.139103i
$172$	−17.0192	+	1.91760i	−1.29770	+	0.146216i
$173$	5.47716	−	9.48672i	0.416421	−	0.721262i	−0.579156	−	0.815217i	$-0.696618\pi$
$173$	5.47716	−	9.48672i	0.416421	−	0.721262i	0.995576	+	0.0939550i	$0.0299510\pi$
$174$	5.87128	−	16.3609i	0.445101	−	1.24032i
$175$	−1.37011	−	2.37310i	−0.103571	−	0.179390i
$176$	5.61539	+	7.60859i	0.423276	+	0.573519i
$177$	−0.538197	−	15.2505i	−0.0404533	−	1.14630i
$178$	−3.37700	+	10.9480i	−0.253117	+	0.820585i
$179$	9.80697	−	12.2976i	0.733008	−	0.919162i	−0.265988	−	0.963976i	$-0.585698\pi$
$179$	9.80697	−	12.2976i	0.733008	−	0.919162i	0.998995	+	0.0448140i	$0.0142695\pi$
$180$	−2.23135	+	5.61514i	−0.166315	+	0.418528i
$181$	−5.74725	+	25.1803i	−0.427190	+	1.87164i	0.0597637	+	0.998213i	$0.480965\pi$
$181$	−5.74725	+	25.1803i	−0.427190	+	1.87164i	−0.486953	+	0.873428i	$0.661892\pi$
$182$	−2.05631	+	10.8679i	−0.152424	+	0.805581i
$183$	−3.94067	+	8.13862i	−0.291303	+	0.601624i
$184$	−1.80282	−	0.0674569i	−0.132906	−	0.00497299i
$185$	−0.835161	−	4.41393i	−0.0614022	−	0.324519i
$186$	20.3200	+	5.49103i	1.48994	+	0.402622i
$187$	−5.24896	−	0.393355i	−0.383842	−	0.0287650i
$188$	−0.134306	+	1.19200i	−0.00979525	+	0.0869352i
$189$	−3.64242	−	2.72425i	−0.264947	−	0.198160i
$190$	−1.39280	+	0.670736i	−0.101044	+	0.0486603i
$191$	22.7493	−	6.09567i	1.64608	−	0.441067i	0.687572	−	0.726117i	$-0.258677\pi$
$191$	22.7493	−	6.09567i	1.64608	−	0.441067i	0.958513	+	0.285050i	$0.0920100\pi$
$192$	1.07454	+	5.74589i	0.0775485	+	0.414674i
$193$	0.0439409	−	1.17434i	0.00316293	−	0.0845312i	−0.996825	−	0.0796233i	$-0.974628\pi$
$193$	0.0439409	−	1.17434i	0.00316293	−	0.0845312i	0.999988	−	0.00490786i	$-0.00156223\pi$
$194$	23.4335	−	1.75610i	1.68243	−	0.126080i
$195$	5.27127	+	15.1677i	0.377484	+	1.08618i
$196$	−6.24556	+	6.73111i	−0.446111	+	0.480793i
$197$	6.28633	−	5.01318i	0.447883	−	0.357175i	−0.373425	−	0.927661i	$-0.621817\pi$
$197$	6.28633	−	5.01318i	0.447883	−	0.357175i	0.821307	+	0.570486i	$0.193245\pi$
$198$	6.93813	−	8.62473i	0.493072	−	0.612933i
$199$	−4.15148	−	18.1888i	−0.294291	−	1.28937i	−0.878489	−	0.477762i	$-0.841448\pi$
$199$	−4.15148	−	18.1888i	−0.294291	−	1.28937i	0.584199	−	0.811611i	$-0.301409\pi$
$200$	−3.07227	+	0.114956i	−0.217242	+	0.00812863i
$201$	2.48977	−	5.67370i	0.175615	−	0.400192i
$202$	0.436303	−	0.251900i	0.0306982	−	0.0177236i
$203$	−0.903334	+	4.62658i	−0.0634016	+	0.324723i
$204$	−5.86696	−	3.40393i	−0.410770	−	0.238323i
$205$	12.9309	+	5.64169i	0.903133	+	0.394033i
$206$	−13.6746	+	8.59233i	−0.952756	+	0.598656i
$207$	1.20343	+	5.37780i	0.0836444	+	0.373783i
$208$	25.3190	+	20.1912i	1.75556	+	1.40001i
$209$	1.18771	−	0.179018i	0.0821555	−	0.0123829i
$210$	0.867693	−	3.76473i	0.0598765	−	0.259791i
$211$	−4.37845	+	5.08786i	−0.301425	+	0.350262i	−0.888175	−	0.459506i	$-0.848026\pi$
$211$	−4.37845	+	5.08786i	−0.301425	+	0.350262i	0.586749	+	0.809769i	$0.300407\pi$
$212$	0.311521	+	4.15696i	0.0213954	+	0.285502i
$213$	0.180799	−	4.57202i	0.0123881	−	0.313270i
$214$	14.3506	+	16.6757i	0.980984	+	1.13992i
$215$	11.2418	−	11.2418i	0.766683	−	0.766683i
$216$	−4.61187	+	2.18487i	−0.313798	+	0.148661i
$217$	−5.67234	−	0.639119i	−0.385064	−	0.0433863i
$218$	−19.1452	+	25.9408i	−1.29668	+	1.75694i
$219$	1.88322	+	1.28982i	0.127256	+	0.0871581i
$220$	3.85174	+	1.03207i	0.259684	+	0.0695822i
$221$	−17.7117	+	3.35123i	−1.19142	+	0.225428i
$222$	−5.66115	+	8.96733i	−0.379951	+	0.601848i
$223$	16.5743	−	11.3001i	1.10989	−	0.756713i	0.137604	−	0.990487i	$-0.456060\pi$
$223$	16.5743	−	11.3001i	1.10989	−	0.756713i	0.972291	+	0.233774i	$0.0751076\pi$
$224$	−2.00552	−	5.73145i	−0.133999	−	0.382948i
$225$	2.72996	+	8.98565i	0.181997	+	0.599044i
$226$	6.50620	+	8.15851i	0.432786	+	0.542696i
$227$	21.3724	−	8.38803i	1.41853	−	0.556733i	0.472653	−	0.881249i	$-0.343296\pi$
$227$	21.3724	−	8.38803i	1.41853	−	0.556733i	0.945880	+	0.324515i	$0.105201\pi$
$228$	1.47806	+	0.459363i	0.0978871	+	0.0304220i
$229$	9.12726	+	4.82390i	0.603146	+	0.318772i	0.740818	−	0.671706i	$-0.234438\pi$
$229$	9.12726	+	4.82390i	0.603146	+	0.318772i	−0.137672	+	0.990478i	$0.543962\pi$
$230$	−3.76616	+	2.77956i	−0.248334	+	0.183278i
$231$	−1.50642	+	2.59645i	−0.0991153	+	0.170834i
$232$	4.11573	+	3.32158i	0.270211	+	0.218072i
$233$		−	25.1236i		−	1.64590i	−0.568112	−	0.822952i	$-0.692326\pi$
$233$		−	25.1236i		−	1.64590i	0.568112	−	0.822952i	$-0.307674\pi$
$234$	15.3061	−	34.6793i	1.00059	−	2.26706i
$235$	−0.592412	−	0.942818i	−0.0386447	−	0.0615027i
$236$	−12.4011	−	3.82523i	−0.807243	−	0.249001i
$237$	6.03890	+	4.83689i	0.392269	+	0.314190i
$238$	4.03722	+	1.58449i	0.261694	+	0.102707i
$239$	6.41371	+	20.7927i	0.414868	+	1.34497i	0.886318	+	0.463077i	$0.153255\pi$
$239$	6.41371	+	20.7927i	0.414868	+	1.34497i	−0.471450	+	0.881893i	$0.656269\pi$
$240$	−8.55818	−	7.39661i	−0.552428	−	0.477449i
$241$	1.38758	+	2.03521i	0.0893819	+	0.131099i	0.868325	−	0.495995i	$-0.165197\pi$
$241$	1.38758	+	2.03521i	0.0893819	+	0.131099i	−0.778944	+	0.627094i	$0.784244\pi$
$242$	11.1721	+	7.01990i	0.718170	+	0.451256i
$243$	10.0421	+	11.9229i	0.644201	+	0.764857i
$244$	5.43768	+	5.43768i	0.348112	+	0.348112i
$245$	0.636970	−	8.49978i	0.0406945	−	0.543031i
$246$	−13.2534	−	30.5540i	−0.845006	−	1.94805i
$247$	3.77015	−	1.64490i	0.239889	−	0.104662i
$248$	−3.60773	+	5.29158i	−0.229091	+	0.336015i
$249$	−10.7070	−	10.7526i	−0.678531	−	0.681419i
$250$	−15.7033	+	13.5138i	−0.993166	+	0.854688i
$251$	−13.6166	+	21.6707i	−0.859471	+	1.36784i	0.0694595	+	0.997585i	$0.477873\pi$
$251$	−13.6166	+	21.6707i	−0.859471	+	1.36784i	−0.928930	+	0.370255i	$0.879270\pi$
$252$	−3.20529	+	2.16544i	−0.201914	+	0.136410i
$253$	3.43280	−	1.20119i	0.215818	−	0.0755180i
$254$	−3.67372	−	3.40871i	−0.230509	−	0.213881i
$255$	6.22800	−	0.925194i	0.390012	−	0.0579379i
$256$	−20.6504	−	3.11255i	−1.29065	−	0.194534i
$257$	8.79240	+	9.47595i	0.548455	+	0.591094i	0.945061	−	0.326895i	$-0.106002\pi$
$257$	8.79240	+	9.47595i	0.548455	+	0.591094i	−0.396606	+	0.917989i	$0.629812\pi$
$258$	−37.5075	+	1.32366i	−2.33512	+	0.0824073i
$259$	1.15005	−	2.63595i	0.0714608	−	0.163790i
$260$	13.6559			0.846906
$261$	6.60926	−	14.7417i	0.409103	−	0.912488i
$262$	−21.8176			−1.34789
$263$	0.431847	−	0.989803i	0.0266288	−	0.0610339i	−0.902740	−	0.430187i	$-0.858448\pi$
$263$	0.431847	−	0.989803i	0.0266288	−	0.0610339i	0.929368	+	0.369153i	$0.120352\pi$
$264$	1.78577	+	2.85549i	0.109907	+	0.175743i
$265$	−2.63199	−	2.83661i	−0.161682	−	0.174251i
$266$	−0.978614	−	0.147502i	−0.0600027	−	0.00904395i
$267$	−3.91129	+	9.90389i	−0.239367	+	0.606108i
$268$	−3.86264	−	3.58401i	−0.235948	−	0.218928i
$269$	−26.3887	+	9.23380i	−1.60895	+	0.562995i	−0.977226	−	0.212201i	$-0.931937\pi$
$269$	−26.3887	+	9.23380i	−1.60895	+	0.562995i	−0.631721	+	0.775196i	$0.717651\pi$
$270$	−5.82080	+	11.8925i	−0.354242	+	0.723757i
$271$	−2.86674	+	4.56239i	−0.174142	+	0.277146i	−0.922379	−	0.386286i	$-0.873758\pi$
$271$	−2.86674	+	4.56239i	−0.174142	+	0.277146i	0.748237	+	0.663432i	$0.230901\pi$
$272$	9.62488	−	8.28288i	0.583594	−	0.502223i
$273$	−2.68173	+	9.92400i	−0.162306	+	0.600628i
$274$	1.86361	−	2.73341i	0.112585	−	0.165131i
$275$	5.68065	−	2.47844i	0.342556	−	0.149456i
$276$	4.65600	+	0.534623i	0.280258	+	0.0321805i
$277$	−1.63171	+	21.7737i	−0.0980400	+	1.30825i	0.703664	+	0.710533i	$0.251546\pi$
$277$	−1.63171	+	21.7737i	−0.0980400	+	1.30825i	−0.801704	+	0.597721i	$0.796073\pi$
$278$	−10.6034	−	10.6034i	−0.635951	−	0.635951i
$279$	18.4377	+	6.53966i	1.10383	+	0.391519i
$280$	0.995326	+	0.625405i	0.0594821	+	0.0373751i
$281$	−8.53140	−	12.5133i	−0.508941	−	0.746479i	0.482661	−	0.875807i	$-0.339670\pi$
$281$	−8.53140	−	12.5133i	−0.508941	−	0.746479i	−0.991602	+	0.129328i	$0.958718\pi$
$282$	−0.494172	+	2.58173i	−0.0294275	+	0.153740i
$283$	3.84383	+	12.4614i	0.228492	+	0.740753i	0.995121	+	0.0986624i	$0.0314564\pi$
$283$	3.84383	+	12.4614i	0.228492	+	0.740753i	−0.766629	+	0.642090i	$0.778067\pi$
$284$	−3.62227	−	1.42163i	−0.214942	−	0.0843585i
$285$	−1.33856	+	0.522068i	−0.0792895	+	0.0309246i
$286$	−23.9055	−	7.37386i	−1.41356	−	0.436025i
$287$	4.80525	+	7.64751i	0.283645	+	0.451418i
$288$	2.24216	+	20.6893i	0.132120	+	1.21913i
$289$		−	9.93183i		−	0.584225i
$290$	13.7220	+	0.0799071i	0.805785	+	0.00469231i
$291$	21.8404	+	0.0463918i	1.28031	+	0.00271953i
$292$	1.56187	−	1.15271i	0.0914017	−	0.0674575i
$293$	−15.4113	−	8.14510i	−0.900337	−	0.475842i	−0.0480073	−	0.998847i	$-0.515287\pi$
$293$	−15.4113	−	8.14510i	−0.900337	−	0.475842i	−0.852330	+	0.523005i	$0.824811\pi$
$294$	−14.7792	+	13.6548i	−0.861941	+	0.796364i
$295$	11.2140	−	4.40115i	0.652902	−	0.256245i
$296$	−2.01179	−	2.52270i	−0.116933	−	0.146629i
$297$	7.04532	−	7.49667i	0.408811	−	0.435001i
$298$	1.96650	+	5.61992i	0.113916	+	0.325553i
$299$	10.2907	−	7.01607i	0.595125	−	0.405750i
$300$	7.98038	+	0.315581i	0.460748	+	0.0182201i
$301$	10.0005	−	1.89220i	0.576422	−	0.109065i
$302$	27.1515	+	7.27523i	1.56240	+	0.418643i
$303$	0.422298	−	0.202264i	0.0242604	−	0.0116198i
$304$	−1.72066	+	2.33141i	−0.0986867	+	0.133716i
$305$	−7.09351	−	0.799246i	−0.406173	−	0.0457647i
$306$	−12.2453	−	8.42512i	−0.700017	−	0.481632i
$307$	0.758844	−	0.758844i	0.0433095	−	0.0433095i	−0.685120	−	0.728430i	$-0.740250\pi$
$307$	0.758844	−	0.758844i	0.0433095	−	0.0433095i	0.728430	+	0.685120i	$0.240250\pi$
$308$	1.66519	+	1.93498i	0.0948830	+	0.110256i
$309$	−13.2855	+	6.98551i	−0.755784	+	0.397392i
$310$	1.24176	+	16.5702i	0.0705273	+	0.941122i
$311$	−3.99183	+	4.63859i	−0.226356	+	0.263030i	−0.859653	−	0.510879i	$-0.829320\pi$
$311$	−3.99183	+	4.63859i	−0.226356	+	0.263030i	0.633297	+	0.773909i	$0.281701\pi$
$312$	8.43812	+	7.86285i	0.477714	+	0.445146i
$313$	20.5336	−	3.09494i	1.16063	−	0.174936i	0.459636	−	0.888108i	$-0.347980\pi$
$313$	20.5336	−	3.09494i	1.16063	−	0.174936i	0.700990	+	0.713171i	$0.252742\pi$
$314$	29.8398	+	23.7964i	1.68396	+	1.34291i
$315$	1.07295	−	3.42667i	0.0604539	−	0.193071i
$316$	5.57142	−	3.50076i	0.313417	−	0.196933i
$317$	−9.19212	−	4.01048i	−0.516281	−	0.225251i	0.125564	−	0.992086i	$-0.459926\pi$
$317$	−9.19212	−	4.01048i	−0.516281	−	0.225251i	−0.641845	+	0.766834i	$0.721831\pi$
$318$	−0.0194036	+	9.13486i	−0.00108810	+	0.512257i
$319$	−10.1698	−	3.20193i	−0.569397	−	0.179274i
$320$	−3.99637	+	2.30731i	−0.223404	+	0.128982i
$321$	12.1071	+	16.4777i	0.675753	+	0.919695i
$322$	−2.99453	+	0.112047i	−0.166878	+	0.00624415i
$323$	−0.358902	−	1.57245i	−0.0199698	−	0.0874936i
$324$	12.3813	−	4.73830i	0.687850	−	0.263239i
$325$	16.5942	−	13.2335i	0.920483	−	0.734061i
$326$	−16.8442	+	18.1538i	−0.932916	+	1.00544i
$327$	−19.5940	+	22.6710i	−1.08355	+	1.25371i
$328$	10.1051	−	0.757271i	0.557959	−	0.0418133i
$329$	0.0266542	−	0.712350i	0.00146950	−	0.0392731i
$330$	8.24172	+	2.90357i	0.453692	+	0.159836i
$331$	−7.14355	+	1.91411i	−0.392645	+	0.105209i	−0.449739	−	0.893160i	$-0.648483\pi$
$331$	−7.14355	+	1.91411i	−0.392645	+	0.105209i	0.0570942	+	0.998369i	$0.481816\pi$
$332$	−11.6268	+	5.59917i	−0.638104	+	0.307295i
$333$	−5.88646	+	7.90536i	−0.322576	+	0.433211i
$334$	2.82274	−	25.0525i	0.154453	−	1.37081i
$335$	4.87759	+	0.365525i	0.266491	+	0.0199708i
$336$	−1.85941	−	6.99883i	−0.101439	−	0.381817i
$337$	−1.71118	−	9.04380i	−0.0932139	−	0.492647i	−0.997796	−	0.0663489i	$-0.978865\pi$
$337$	−1.71118	−	9.04380i	−0.0932139	−	0.492647i	0.904583	−	0.426298i	$-0.140183\pi$
$338$	−61.4028	−	2.29753i	−3.33987	−	0.124969i
$339$	5.44635	+	8.02489i	0.295805	+	0.435852i
$340$	0.995490	−	5.26129i	0.0539880	−	0.285334i
$341$	2.87292	−	12.5871i	0.155577	−	0.681628i
$342$	3.15201	+	1.25255i	0.170441	+	0.0677302i
$343$	7.22267	−	9.05695i	0.389988	−	0.489029i
$344$	3.36590	−	10.9120i	0.181477	−	0.588334i
$345$	−3.68849	+	2.30672i	−0.198582	+	0.124190i
$346$	−12.1225	−	16.4254i	−0.651711	−	0.883036i
$347$	−5.57920	−	9.66345i	−0.299507	−	0.518761i	0.676516	−	0.736428i	$-0.263489\pi$
$347$	−5.57920	−	9.66345i	−0.299507	−	0.518761i	−0.976023	+	0.217666i	$0.930155\pi$
$348$	−9.99698	−	9.42479i	−0.535894	−	0.505222i
$349$	−2.72924	+	4.72718i	−0.146093	+	0.253040i	−0.929780	−	0.368115i	$-0.880003\pi$
$349$	−2.72924	+	4.72718i	−0.146093	+	0.253040i	0.783687	+	0.621156i	$0.213336\pi$
$350$	−5.07456	+	0.571766i	−0.271247	+	0.0305622i
$351$	16.6606	−	31.0428i	0.889275	−	1.65694i
$352$	13.3896	−	3.05610i	0.713670	−	0.162891i
$353$	11.3756	+	28.9845i	0.605460	+	1.54269i	0.823840	+	0.566823i	$0.191828\pi$
$353$	11.3756	+	28.9845i	0.605460	+	1.54269i	−0.218380	+	0.975864i	$0.570077\pi$
$354$	−26.4505	−	10.4460i	−1.40583	−	0.555196i
$355$	3.45164	−	1.06469i	0.183194	−	0.0565078i
$356$	6.86394	+	5.90689i	0.363788	+	0.313065i
$357$	3.62797	+	1.75664i	0.192013	+	0.0929714i
$358$	−13.6970	−	25.9159i	−0.723907	−	1.36970i
$359$	−16.2729	−	5.69413i	−0.858850	−	0.300525i	−0.135307	−	0.990804i	$-0.543202\pi$
$359$	−16.2729	−	5.69413i	−0.858850	−	0.300525i	−0.723543	+	0.690279i	$0.757488\pi$
$360$	−2.83655	−	2.86076i	−0.149500	−	0.150775i
$361$	−8.08410	−	16.7868i	−0.425479	−	0.883516i
$362$	38.7276	+	28.5823i	2.03548	+	1.50225i
$363$	9.85140	+	7.30304i	0.517064	+	0.383310i
$364$	7.22335	+	4.92480i	0.378606	+	0.258129i
$365$	−0.466375	+	1.74053i	−0.0244112	+	0.0911037i
$366$	10.9649	+	12.7963i	0.573143	+	0.668873i
$367$	32.6599	−	17.2612i	1.70483	−	0.901029i	0.728413	−	0.685138i	$-0.240258\pi$
$367$	32.6599	−	17.2612i	1.70483	−	0.901029i	0.976418	−	0.215891i	$-0.0692655\pi$
$368$	−3.80677	+	7.90483i	−0.198441	+	0.412068i
$369$	−10.0992	−	29.2599i	−0.525742	−	1.52321i
$370$	−8.16185	−	1.86289i	−0.424314	−	0.0968469i
$371$	−0.369220	−	2.44961i	−0.0191689	−	0.127178i
$372$	10.4007	−	12.9854i	0.539252	−	0.673261i
$373$	8.75453	−	8.12302i	0.453293	−	0.420594i	−0.420200	−	0.907432i	$-0.638040\pi$
$373$	8.75453	−	8.12302i	0.453293	−	0.420594i	0.873493	+	0.486838i	$0.161850\pi$
$374$	−4.58362	+	8.67263i	−0.237013	+	0.448451i
$375$	−15.5169	+	11.4012i	−0.801289	+	0.588754i
$376$	−0.692637	−	0.399894i	−0.0357200	−	0.0206230i
$377$	−36.4786	−	1.57770i	−1.87874	−	0.0812557i
$378$	−7.36778	+	4.19142i	−0.378958	+	0.215583i
$379$	2.94657	+	26.1515i	0.151355	+	1.34331i	0.808030	+	0.589141i	$0.200534\pi$
$379$	2.94657	+	26.1515i	0.151355	+	1.34331i	−0.656675	+	0.754174i	$0.728038\pi$
$380$	0.0456875	+	1.22103i	0.00234372	+	0.0626373i
$381$	−3.16084	−	3.42112i	−0.161935	−	0.175269i
$382$	6.54164	−	43.4010i	0.334700	−	2.22059i
$383$	12.0080	−	30.5959i	0.613581	−	1.56338i	−0.198668	−	0.980067i	$-0.563661\pi$
$383$	12.0080	−	30.5959i	0.613581	−	1.56338i	0.812248	−	0.583312i	$-0.198243\pi$
$384$	−12.8006	−	2.95027i	−0.653227	−	0.150555i
$385$	−2.32840	−	0.440558i	−0.118666	−	0.0224529i
$386$	−1.97316	−	0.950222i	−0.100431	−	0.0483650i
$387$	−34.8514	−	1.45234i	−1.77160	−	0.0738264i
$388$	6.13457	−	17.5316i	0.311436	−	0.890032i
$389$	−0.932673	−	3.48078i	−0.0472884	−	0.176483i	0.938243	−	0.345978i	$-0.112453\pi$
$389$	−0.932673	−	3.48078i	−0.0472884	−	0.176483i	−0.985531	+	0.169495i	$0.945786\pi$
$390$	29.8364	+	2.29967i	1.51082	+	0.116448i
$391$	−1.95294	−	4.47620i	−0.0987646	−	0.226371i
$392$	−2.44825	−	5.61144i	−0.123655	−	0.283421i
$393$	−20.2175	−	1.55829i	−1.01984	−	0.0786052i
$394$	−3.87822	−	14.4737i	−0.195382	−	0.729176i
$395$	−2.01733	+	5.76520i	−0.101503	+	0.290079i
$396$	−4.05525	−	7.75245i	−0.203784	−	0.389575i
$397$	8.72050	+	4.19957i	0.437669	+	0.210770i	0.639725	−	0.768604i	$-0.279048\pi$
$397$	8.72050	+	4.19957i	0.437669	+	0.210770i	−0.202056	+	0.979374i	$0.564762\pi$
$398$	−34.1623	−	6.46385i	−1.71240	−	0.324004i
$399$	−0.896311	−	0.206581i	−0.0448717	−	0.0103420i
$400$	−5.46245	+	13.9181i	−0.273122	+	0.695904i
$401$	−5.06488	+	33.6033i	−0.252928	+	1.67807i	0.396804	+	0.917903i	$0.370119\pi$
$401$	−5.06488	+	33.6033i	−0.252928	+	1.67807i	−0.649732	+	0.760163i	$0.725119\pi$
$402$	−7.83580	−	8.48104i	−0.390814	−	0.422996i
$403$	−1.65322	−	44.1832i	−0.0823526	−	2.20092i
$404$	−0.0445849	−	0.395702i	−0.00221818	−	0.0196869i
$405$	−6.24333	+	10.6046i	−0.310233	+	0.526949i
$406$	7.22949	+	4.99090i	0.358794	+	0.247694i
$407$	5.63321	+	3.25234i	0.279228	+	0.161212i
$408$	3.64448	−	2.67781i	0.180429	−	0.132571i
$409$	12.4331	−	23.5246i	0.614777	−	1.16322i	−0.358488	−	0.933534i	$-0.616708\pi$
$409$	12.4331	−	23.5246i	0.614777	−	1.16322i	0.973266	−	0.229681i	$-0.0737684\pi$
$410$	19.2732	−	17.8829i	0.951835	−	0.883174i
$411$	1.92217	−	2.39984i	0.0948135	−	0.118376i
$412$	1.90254	+	12.6225i	0.0937313	+	0.621866i
$413$	7.51886	+	1.71613i	0.369979	+	0.0844452i
$414$	10.0827	+	1.95215i	0.495537	+	0.0959429i
$415$	5.19752	−	10.7928i	0.255136	−	0.529795i
$416$	41.5828	−	21.9772i	2.03877	−	1.07752i
$417$	−9.06847	−	10.5831i	−0.444085	−	0.518258i
$418$	0.579344	−	2.16214i	0.0283366	−	0.105754i
$419$	−17.9261	−	12.2218i	−0.875748	−	0.597075i	0.0398342	−	0.999206i	$-0.487317\pi$
$419$	−17.9261	−	12.2218i	−0.875748	−	0.597075i	−0.915582	+	0.402132i	$0.868269\pi$
$420$	−2.45313	−	1.81855i	−0.119700	−	0.0887362i
$421$	10.6818	+	7.88354i	0.520600	+	0.384220i	0.822186	−	0.569219i	$-0.192754\pi$
$421$	10.6818	+	7.88354i	0.520600	+	0.384220i	−0.301586	+	0.953439i	$0.597516\pi$
$422$	5.42760	+	11.2705i	0.264211	+	0.548640i
$423$	−0.642328	+	2.35710i	−0.0312310	+	0.114606i
$424$	−2.62344	−	0.917982i	−0.127406	−	0.0445812i
$425$	−3.88884	−	7.35804i	−0.188636	−	0.356917i
$426$	−7.67475	−	3.71607i	−0.371843	−	0.180044i
$427$	−3.46390	−	2.98092i	−0.167630	−	0.144257i
$428$	16.6167	−	5.12556i	0.803197	−	0.247753i
$429$	−21.6256	−	8.54050i	−1.04410	−	0.412339i
$430$	−10.8243	−	27.5799i	−0.521996	−	1.33002i
$431$	18.0179	−	4.11247i	0.867893	−	0.198091i	0.234684	−	0.972072i	$-0.424595\pi$
$431$	18.0179	−	4.11247i	0.867893	−	0.198091i	0.633209	+	0.773981i	$0.281737\pi$
$432$	0.769925	+	24.8063i	0.0370430	+	1.19349i
$433$	20.5135	−	2.31132i	0.985818	−	0.111075i	0.395690	−	0.918384i	$-0.370506\pi$
$433$	20.5135	−	2.31132i	0.985818	−	0.111075i	0.590129	+	0.807309i	$0.299077\pi$
$434$	−5.31893	+	9.21265i	−0.255317	+	0.442222i
$435$	12.7100	+	1.05412i	0.609398	+	0.0505413i
$436$	12.7416	+	22.0692i	0.610214	+	1.05692i
$437$	0.661759	+	0.896652i	0.0316562	+	0.0428927i
$438$	3.60660	−	2.25550i	0.172330	−	0.107772i
$439$	−3.69531	+	11.9799i	−0.176368	+	0.571770i	0.823622	+	0.567140i	$0.191950\pi$
$439$	−3.69531	+	11.9799i	−0.176368	+	0.571770i	−0.999989	+	0.00463024i	$0.998526\pi$
$440$	−1.65769	+	2.07868i	−0.0790273	+	0.0990971i
$441$	−14.6706	+	11.5978i	−0.698601	+	0.552277i
$442$	−7.47518	+	32.7509i	−0.355558	+	1.55780i
$443$	2.28030	−	12.0517i	0.108340	−	0.572592i	−0.885761	−	0.464141i	$-0.846363\pi$
$443$	2.28030	−	12.0517i	0.108340	−	0.572592i	0.994102	−	0.108451i	$-0.0345892\pi$
$444$	4.70708	+	6.93562i	0.223388	+	0.329150i
$445$	−8.40017	−	0.314312i	−0.398206	−	0.0148998i
$446$	−6.95004	−	36.7319i	−0.329094	−	1.73930i
$447$	1.42089	+	5.34823i	0.0672056	+	0.252963i
$448$	−2.94599	−	0.220771i	−0.139185	−	0.0104305i
$449$	−3.02417	+	26.8402i	−0.142719	+	1.26667i	0.694377	+	0.719612i	$0.255680\pi$
$449$	−3.02417	+	26.8402i	−0.142719	+	1.26667i	−0.837096	+	0.547056i	$0.815748\pi$
$450$	17.3829	+	2.03340i	0.819438	+	0.0958555i
$451$	−18.4051	+	8.86343i	−0.866662	+	0.417363i
$452$	7.96695	−	2.13474i	0.374734	−	0.100410i
$453$	24.6407	+	8.68095i	1.15772	+	0.407867i
$454$	1.59987	−	42.7573i	0.0750854	−	2.00670i
$455$	−8.09261	+	0.606457i	−0.379387	+	0.0284312i
$456$	−0.674814	+	0.780788i	−0.0316011	+	0.0365637i
$457$	−19.5098	+	21.0265i	−0.912628	+	0.983579i	−0.999921	−	0.0126034i	$-0.995988\pi$
$457$	−19.5098	+	21.0265i	−0.912628	+	0.983579i	0.0872923	+	0.996183i	$0.472179\pi$
$458$	15.0417	−	11.9954i	0.702853	−	0.560506i
$459$	−10.7455	−	8.68185i	−0.501557	−	0.405234i
$460$	0.823269	+	3.60698i	0.0383851	+	0.168176i
$461$	25.2871	−	0.946175i	1.17774	−	0.0440678i	0.558659	−	0.829398i	$-0.311316\pi$
$461$	25.2871	−	0.946175i	1.17774	−	0.0440678i	0.619077	+	0.785330i	$0.287507\pi$
$462$	3.31236	+	4.50810i	0.154105	+	0.209736i
$463$	−21.0334	+	12.1436i	−0.977504	+	0.564362i	−0.901516	−	0.432747i	$-0.857544\pi$
$463$	−21.0334	+	12.1436i	−0.977504	+	0.564362i	−0.0759880	+	0.997109i	$0.524211\pi$
$464$	22.8099	−	11.8860i	1.05892	−	0.551794i
$465$	−0.0328043	+	15.4437i	−0.00152126	+	0.716182i
$466$	−42.9138	−	18.7231i	−1.98794	−	0.867330i
$467$	−0.0640516	+	0.0402463i	−0.00296395	+	0.00186238i	−0.533513	−	0.845792i	$-0.679129\pi$
$467$	−0.0640516	+	0.0402463i	−0.00296395	+	0.00186238i	0.530549	+	0.847654i	$0.321986\pi$
$468$	−20.2857	−	22.0500i	−0.937709	−	1.01926i
$469$	2.44820	+	1.95237i	0.113047	+	0.0901521i
$470$	−2.05192	+	0.309277i	−0.0946480	+	0.0142659i
$471$	25.9518	+	24.1825i	1.19580	+	1.11427i
$472$	5.64412	−	6.55858i	0.259792	−	0.301883i
$473$	1.72031	+	22.9560i	0.0791001	+	1.05552i
$474$	12.7623	−	6.71044i	0.586193	−	0.308221i
$475$	1.23877	+	1.43948i	0.0568386	+	0.0660477i
$476$	2.42397	−	2.42397i	0.111102	−	0.111102i
$477$	−0.670425	+	8.46355i	−0.0306966	+	0.387520i
$478$	40.2959	+	4.54025i	1.84309	+	0.207666i
$479$	−4.92324	+	6.67075i	−0.224948	+	0.304794i	−0.902508	−	0.430674i	$-0.858276\pi$
$479$	−4.92324	+	6.67075i	−0.224948	+	0.304794i	0.677559	+	0.735468i	$0.263038\pi$
$480$	−14.8166	+	7.09656i	−0.676282	+	0.323912i
$481$	21.5168	+	5.76541i	0.981081	+	0.262880i
$482$	4.51042	−	0.853418i	0.205444	−	0.0388721i
$483$	−2.78292	−	0.110050i	−0.126627	−	0.00500743i
$484$	8.61686	−	5.87487i	0.391675	−	0.267040i
$485$	5.69451	+	16.2740i	0.258574	+	0.738963i
$486$	27.8494	−	8.26752i	1.26327	−	0.375022i
$487$	−10.0298	−	12.5770i	−0.454495	−	0.569919i	0.500804	−	0.865561i	$-0.333038\pi$
$487$	−10.0298	−	12.5770i	−0.454495	−	0.569919i	−0.955299	+	0.295642i	$0.904466\pi$
$488$	−4.77288	+	1.87322i	−0.216058	+	0.0847965i
$489$	−16.9055	+	15.6194i	−0.764495	+	0.706332i
$490$	−14.0438	−	7.42237i	−0.634435	−	0.335309i
$491$	−26.1044	+	19.2659i	−1.17807	+	0.869457i	−0.993553	−	0.113371i	$-0.963835\pi$
$491$	−26.1044	+	19.2659i	−1.17807	+	0.869457i	−0.184520	+	0.982829i	$0.559073\pi$
$492$	−26.3242	−	0.0559159i	−1.18678	−	0.00252088i
$493$	−3.26706	+	13.9393i	−0.147141	+	0.627793i
$494$		−	7.66564i		−	0.344894i
$495$	7.42992	+	3.27928i	0.333950	+	0.147393i
$496$	16.5708	+	26.3722i	0.744050	+	1.18415i
$497$	2.20972	+	0.681607i	0.0991193	+	0.0305743i
$498$	−26.3459	+	10.2755i	−1.18059	+	0.460455i
$499$	15.4765	+	6.07409i	0.692824	+	0.271913i	0.685514	−	0.728060i	$-0.259578\pi$
$499$	15.4765	+	6.07409i	0.692824	+	0.271913i	0.00731065	+	0.999973i	$0.497673\pi$
$500$	4.82670	+	15.6478i	0.215857	+	0.699790i
$501$	4.40507	−	23.0136i	0.196804	−	1.02817i
$502$	26.8681	+	39.4083i	1.19918	+	1.75888i
$503$	18.6961	+	11.7475i	0.833619	+	0.523797i	0.879915	−	0.475130i	$-0.157599\pi$
$503$	18.6961	+	11.7475i	0.833619	+	0.523797i	−0.0462967	+	0.998928i	$0.514742\pi$
$504$	−0.468717	−	2.53616i	−0.0208783	−	0.112970i
$505$	0.261375	+	0.261375i	0.0116311	+	0.0116311i
$506$	0.506498	−	6.75875i	0.0225166	−	0.300463i
$507$	−56.7356	−	6.51464i	−2.51972	−	0.289326i
$508$	−3.63064	+	1.58403i	−0.161084	+	0.0702800i
$509$	−2.45815	+	3.60545i	−0.108956	+	0.159809i	−0.876844	−	0.480775i	$-0.840355\pi$
$509$	−2.45815	+	3.60545i	−0.108956	+	0.159809i	0.767888	+	0.640584i	$0.221308\pi$
$510$	3.06101	−	11.3276i	0.135544	−	0.501593i
$511$	−0.874385	+	0.752470i	−0.0386805	+	0.0332873i
$512$	−12.6360	+	20.1100i	−0.558437	+	0.888747i
$513$	2.83139	+	1.38582i	0.125009	+	0.0611855i
$514$	22.7383	−	7.95649i	1.00295	−	0.350946i
$515$	−8.68620	−	8.05962i	−0.382760	−	0.355149i
$516$	−10.8963	+	27.5910i	−0.479685	+	1.21462i
$517$	1.59430	+	0.240302i	0.0701172	+	0.0105685i
$518$	−3.64541	−	3.92882i	−0.160170	−	0.172622i
$519$	−10.0603	−	16.0867i	−0.441600	−	0.706127i
$520$	−3.64104	+	8.34535i	−0.159670	+	0.365968i
$521$	37.6657			1.65017			0.825083	−	0.565012i	$-0.191128\pi$
$521$	37.6657			1.65017			0.825083	+	0.565012i	$0.191128\pi$
$522$	−20.2549	−	22.2754i	−0.886532	−	0.974967i
$523$	−18.0455			−0.789076			−0.394538	−	0.918880i	$-0.629095\pi$
$523$	−18.0455			−0.789076			−0.394538	+	0.918880i	$0.629095\pi$
$524$	−6.89603	+	15.8059i	−0.301254	+	0.690482i
$525$	−4.74325	+	0.167391i	−0.207012	+	0.00730555i
$526$	−1.36886	−	1.47528i	−0.0596850	−	0.0643252i
$527$	−17.1432	−	2.58392i	−0.746769	−	0.112557i
$528$	16.2012	−	2.40675i	0.705065	−	0.104740i
$529$	−14.3866	−	13.3488i	−0.625506	−	0.580385i
$530$	−6.80667	+	2.38176i	−0.295663	+	0.103457i
$531$	−23.7646	−	11.5691i	−1.03130	−	0.502055i
$532$	−0.416177	+	0.662341i	−0.0180435	+	0.0287161i
$533$	−53.0261	+	45.6327i	−2.29682	+	1.97657i
$534$	14.0020	+	14.0616i	0.605927	+	0.608507i
$535$	−9.09300	+	13.3370i	−0.393125	+	0.576608i
$536$	3.22012	−	1.40493i	0.139088	−	0.0606835i
$537$	−10.8415	−	24.9936i	−0.467844	−	1.07856i
$538$	−3.89357	+	51.9560i	−0.167864	+	2.23998i
$539$	8.72711	+	8.72711i	0.375903	+	0.375903i
$540$	6.77581	+	7.97587i	0.291584	+	0.343227i
$541$	−0.155229	−	0.0975368i	−0.00667381	−	0.00419343i	0.528691	−	0.848814i	$-0.322683\pi$
$541$	−0.155229	−	0.0975368i	−0.00667381	−	0.00419343i	−0.535365	+	0.844621i	$0.679826\pi$
$542$	5.65664	+	8.29676i	0.242973	+	0.356377i
$543$	33.8460	+	29.2522i	1.45247	+	1.25533i
$544$	−5.43595	−	17.6229i	−0.233064	−	0.755576i
$545$	−22.0200	−	8.64223i	−0.943235	−	0.370192i
$546$	14.9527	+	11.9764i	0.639916	+	0.512543i
$547$	−39.8633	−	12.2962i	−1.70443	−	0.525747i	−0.718881	−	0.695133i	$-0.755345\pi$
$547$	−39.8633	−	12.2962i	−1.70443	−	0.525747i	−0.985550	+	0.169386i	$0.945821\pi$
$548$	−1.39119	−	2.21407i	−0.0594288	−	0.0945804i
$549$	9.24680	+	12.6410i	0.394644	+	0.539505i
$550$		−	11.5502i		−	0.492501i
$551$	0.0190244	−	3.26695i	0.000810465	−	0.139177i
$552$	−1.56813	+	2.70280i	−0.0667440	+	0.115039i
$553$	−3.14620	+	2.32200i	−0.133790	+	0.0987415i
$554$	35.9757	+	19.0137i	1.52846	+	0.807815i
$555$	−7.43023	−	2.30922i	−0.315396	−	0.0980209i
$556$	−11.0332	+	4.33022i	−0.467912	+	0.183642i
$557$	−11.9270	−	14.9559i	−0.505361	−	0.633703i	0.462068	−	0.886845i	$-0.347108\pi$
$557$	−11.9270	−	14.9559i	−0.505361	−	0.633703i	−0.967429	+	0.253141i	$0.918536\pi$
$558$	24.9109	−	26.6198i	1.05456	−	1.12691i
$559$	26.0376	+	74.4113i	1.10127	+	3.14726i
$560$	4.72340	−	3.22036i	0.199600	−	0.136085i
$561$	−4.86690	+	7.70923i	−0.205481	+	0.325484i
$562$	−27.7319	+	5.24716i	−1.16980	+	0.221338i
$563$	11.5889	+	3.10524i	0.488414	+	0.130870i	0.494618	−	0.869111i	$-0.335308\pi$
$563$	11.5889	+	3.10524i	0.488414	+	0.130870i	−0.00620361	+	0.999981i	$0.501975\pi$
$564$	1.71415	+	1.17403i	0.0721789	+	0.0494357i
$565$	−4.54648	+	6.16026i	−0.191272	+	0.259164i
$566$	24.1499	+	2.72104i	1.01510	+	0.114374i
$567$	−7.12682	+	3.35780i	−0.299298	+	0.141014i
$568$	1.83457	−	1.83457i	0.0769770	−	0.0769770i
$569$	−14.3748	−	16.7038i	−0.602624	−	0.700262i	0.370945	−	0.928655i	$-0.379034\pi$
$569$	−14.3748	−	16.7038i	−0.602624	−	0.700262i	−0.973569	+	0.228393i	$0.926653\pi$
$570$	−0.105800	+	2.67547i	−0.00443149	+	0.112063i
$571$	0.176989	+	2.36175i	0.00740674	+	0.0988361i	0.999682	−	0.0252202i	$-0.00802870\pi$
$571$	0.176989	+	2.36175i	0.00740674	+	0.0988361i	−0.992275	+	0.124056i	$0.960410\pi$
$572$	−12.8980	+	14.9878i	−0.539293	+	0.626669i
$573$	9.16175	−	39.7509i	0.382738	−	1.66062i
$574$	16.6438	−	2.50865i	0.694698	−	0.104709i
$575$	4.49580	+	3.58528i	0.187488	+	0.149516i
$576$	9.66212	+	3.02538i	0.402589	+	0.126058i
$577$	14.8629	−	9.33897i	0.618750	−	0.388787i	−0.185872	−	0.982574i	$-0.559511\pi$
$577$	14.8629	−	9.33897i	0.618750	−	0.388787i	0.804622	+	0.593787i	$0.202368\pi$
$578$	−16.9646	−	7.40158i	−0.705634	−	0.307865i
$579$	−1.76058	−	1.02147i	−0.0731674	−	0.0424507i
$580$	4.39511	−	9.91576i	0.182497	−	0.411729i
$581$	6.64147	−	3.83446i	0.275535	−	0.159080i
$582$	16.3555	−	37.2711i	0.677959	−	1.54494i
$583$	5.59915	−	0.209505i	0.231893	−	0.00867683i
$584$	0.288004	+	1.26183i	0.0119177	+	0.0522148i
$585$	27.4840	+	4.26204i	1.13632	+	0.176214i
$586$	−25.3978	+	20.2540i	−1.04917	+	0.836687i
$587$	−16.8728	+	18.1846i	−0.696415	+	0.750557i	−0.977915	−	0.209004i	$-0.932978\pi$
$587$	−16.8728	+	18.1846i	−0.696415	+	0.750557i	0.281500	+	0.959561i	$0.409168\pi$
$588$	5.22093	+	15.0229i	0.215308	+	0.619532i
$589$	3.94504	−	0.295640i	0.162553	−	0.0121816i
$590$	0.839440	−	22.4345i	0.0345592	−	0.923614i
$591$	−2.56004	−	13.6893i	−0.105306	−	0.563101i
$592$	−15.1573	+	4.06139i	−0.622961	+	0.166922i
$593$	26.1866	−	12.6108i	1.07536	−	0.517864i	0.189527	−	0.981876i	$-0.439305\pi$
$593$	26.1866	−	12.6108i	1.07536	−	0.517864i	0.885829	+	0.464011i	$0.153590\pi$
$594$	−7.55465	−	17.6210i	−0.309971	−	0.722997i
$595$	−0.356282	+	3.16209i	−0.0146061	+	0.129633i
$596$	4.69295	+	0.351688i	0.192231	+	0.0144057i
$597$	−31.1953	−	8.42980i	−1.27674	−	0.345009i
$598$	−4.31516	−	22.8062i	−0.176460	−	0.932614i
$599$	45.1406	+	1.68904i	1.84440	+	0.0690124i	0.936600	−	0.350400i	$-0.113954\pi$
$599$	45.1406	+	1.68904i	1.84440	+	0.0690124i	0.907796	+	0.419413i	$0.137764\pi$
$600$	−2.32064	+	4.79279i	−0.0947397	+	0.195665i
$601$	−5.08154	+	26.8566i	−0.207280	+	1.09550i	0.712083	+	0.702095i	$0.247752\pi$
$601$	−5.08154	+	26.8566i	−0.207280	+	1.09550i	−0.919364	+	0.393408i	$0.871296\pi$
$602$	4.22070	−	18.4921i	0.172023	−	0.753682i
$603$	−6.65540	−	8.41873i	−0.271029	−	0.342837i
$604$	13.8526	−	17.3706i	0.563653	−	0.706799i
$605$	−2.85349	+	9.25079i	−0.116011	+	0.376098i
$606$	−0.0307755	−	0.872063i	−0.00125017	−	0.0354251i
$607$	−2.64813	−	3.58808i	−0.107484	−	0.145636i	0.747554	−	0.664201i	$-0.231228\pi$
$607$	−2.64813	−	3.58808i	−0.107484	−	0.145636i	−0.855038	+	0.518565i	$0.826466\pi$
$608$	2.10417	+	3.64454i	0.0853355	+	0.147806i
$609$	6.34284	+	5.14124i	0.257025	+	0.208333i
$610$	−6.65155	+	11.5208i	−0.269313	+	0.466464i
$611$	5.48677	−	0.618210i	0.221971	−	0.0250101i
$612$	−9.97409	+	6.20819i	−0.403179	+	0.250951i
$613$	8.92879	−	2.03794i	0.360630	−	0.0823115i	−0.0383668	−	0.999264i	$-0.512216\pi$
$613$	8.92879	−	2.03794i	0.360630	−	0.0823115i	0.398997	+	0.916952i	$0.369358\pi$
$614$	−0.730665	−	1.86170i	−0.0294872	−	0.0751323i
$615$	19.1370	−	15.1949i	0.771679	−	0.612717i
$616$	−1.62648	+	0.501703i	−0.0655328	+	0.0202142i
$617$	12.0861	+	10.4009i	0.486566	+	0.418724i	0.861059	−	0.508506i	$-0.169802\pi$
$617$	12.0861	+	10.4009i	0.486566	+	0.418724i	−0.374492	+	0.927230i	$0.622183\pi$
$618$	2.03114	+	27.8988i	0.0817046	+	1.12226i
$619$	−12.1815	−	23.0486i	−0.489618	−	0.926402i	−0.997873	−	0.0651949i	$-0.979233\pi$
$619$	−12.1815	−	23.0486i	−0.489618	−	0.926402i	0.508255	−	0.861207i	$-0.330291\pi$
$620$	12.3969	+	4.33785i	0.497869	+	0.174212i
$621$	9.20383	+	2.52913i	0.369337	+	0.101490i
$622$	4.94833	+	10.2753i	0.198410	+	0.412002i
$623$	−4.32994	−	3.19564i	−0.173475	−	0.128031i
$624$	51.4586	−	22.3211i	2.05999	−	0.893561i
$625$	0.372965	+	0.254283i	0.0149186	+	0.0101713i
$626$	10.0159	−	37.3799i	0.400317	−	1.49400i
$627$	0.691284	−	1.96220i	0.0276072	−	0.0783626i
$628$	26.6711	−	14.0961i	1.06429	−	0.562496i
$629$	3.78980	−	7.86960i	0.151109	−	0.313781i
$630$	−5.05350	−	4.38639i	−0.201336	−	0.174758i
$631$	−14.7631	−	3.36959i	−0.587711	−	0.134141i	−0.0816830	−	0.996658i	$-0.526030\pi$
$631$	−14.7631	−	3.36959i	−0.587711	−	0.134141i	−0.506028	+	0.862517i	$0.668887\pi$
$632$	0.653875	+	4.33817i	0.0260097	+	0.172563i
$633$	4.22457	+	10.8316i	0.167912	+	0.430519i
$634$	−13.7006	+	12.7123i	−0.544122	+	0.504872i
$635$	1.71814	−	3.25089i	0.0681825	−	0.129007i
$636$	6.61167	+	2.90138i	0.262170	+	0.115047i
$637$	36.6037	+	21.1331i	1.45029	+	0.837325i
$638$	−13.0481	+	14.9848i	−0.516580	+	0.593255i
$639$	−6.84650	−	3.99170i	−0.270843	−	0.157909i
$640$	−1.16108	−	10.3049i	−0.0458958	−	0.407337i
$641$	−0.883080	−	23.6008i	−0.0348795	−	0.932176i	−0.901388	−	0.433013i	$-0.857451\pi$
$641$	−0.883080	−	23.6008i	−0.0348795	−	0.932176i	0.866508	−	0.499163i	$-0.166359\pi$
$642$	37.1683	−	8.40040i	1.46692	−	0.331537i
$643$	−5.72269	+	37.9676i	−0.225681	+	1.49730i	0.533157	+	0.846016i	$0.321006\pi$
$643$	−5.72269	+	37.9676i	−0.225681	+	1.49730i	−0.758838	+	0.651280i	$0.774233\pi$
$644$	−0.865327	+	2.20482i	−0.0340987	+	0.0868820i
$645$	−8.06066	−	26.3304i	−0.317388	−	1.03676i
$646$	−2.95338	−	0.558810i	−0.116199	−	0.0219861i
$647$	40.4946	+	19.5011i	1.59201	+	0.766669i	0.999250	−	0.0387137i	$-0.0123260\pi$
$647$	40.4946	+	19.5011i	1.59201	+	0.766669i	0.592755	+	0.805383i	$0.298040\pi$
$648$	−0.405539	+	8.82975i	−0.0159311	+	0.346865i
$649$	−5.76117	+	16.4645i	−0.226146	+	0.646288i
$650$	−10.2375	−	38.2068i	−0.401547	−	1.49859i
$651$	−5.58686	+	8.15713i	−0.218966	+	0.319703i
$652$	7.82754	+	17.9409i	0.306550	+	0.702620i
$653$	6.94122	+	15.9094i	0.271631	+	0.622585i	0.997896	−	0.0648298i	$-0.0206504\pi$
$653$	6.94122	+	15.9094i	0.271631	+	0.622585i	−0.726265	+	0.687414i	$0.758746\pi$
$654$	24.1223	+	50.3638i	0.943256	+	1.96938i
$655$	−4.14309	−	15.4622i	−0.161884	−	0.604159i
$656$	16.2765	−	46.5157i	0.635492	−	1.81613i
$657$	3.50320	−	1.83250i	0.136673	−	0.0714925i
$658$	−1.19690	−	0.576399i	−0.0466602	−	0.0224704i
$659$	−5.12045	−	0.968842i	−0.199464	−	0.0377407i	0.0852192	−	0.996362i	$-0.472841\pi$
$659$	−5.12045	−	0.968842i	−0.199464	−	0.0377407i	−0.284684	+	0.958622i	$0.591889\pi$
$660$	4.70853	−	5.05302i	0.183279	−	0.196688i
$661$	0.431643	−	1.09981i	0.0167890	−	0.0427776i	−0.922233	−	0.386633i	$-0.873638\pi$
$661$	0.431643	−	1.09981i	0.0167890	−	0.0427776i	0.939022	+	0.343856i	$0.111733\pi$
$662$	−2.05415	+	13.6284i	−0.0798368	+	0.529683i
$663$	−9.26616	+	29.8151i	−0.359868	+	1.15792i
$664$	−0.321722	−	8.59820i	−0.0124852	−	0.333675i
$665$	−0.0813002	−	0.721560i	−0.00315269	−	0.0279809i
$666$	9.11636	+	15.9461i	0.353252	+	0.617897i
$667$	−1.78244	−	9.73028i	−0.0690165	−	0.376758i
$668$	−17.2572	−	9.96347i	−0.667703	−	0.385498i
$669$	−3.81683	−	34.5345i	−0.147567	−	1.33518i
$670$	4.25932	−	8.05903i	0.164552	−	0.311348i
$671$	7.57700	−	7.03042i	0.292507	−	0.271407i
$672$	−10.3965	−	1.58962i	−0.401055	−	0.0613208i
$673$	−1.68779	−	11.1978i	−0.0650596	−	0.431642i	−0.997521	−	0.0703721i	$-0.977581\pi$
$673$	−1.68779	−	11.1978i	−0.0650596	−	0.431642i	0.932461	−	0.361270i	$-0.117657\pi$
$674$	−16.7230	−	3.81691i	−0.644146	−	0.147022i
$675$	15.9629	+	3.12583i	0.614411	+	0.120313i
$676$	−21.0725	+	43.7575i	−0.810480	+	1.68298i
$677$	−34.0609	+	18.0017i	−1.30907	+	0.691862i	−0.968654	−	0.248413i	$-0.920091\pi$
$677$	−34.0609	+	18.0017i	−1.30907	+	0.691862i	−0.340414	+	0.940276i	$0.610567\pi$
$678$	17.7662	−	3.32247i	0.682306	−	0.127599i
$679$	−2.85682	+	10.6618i	−0.109635	+	0.409162i
$680$	2.94983	+	2.01116i	0.113121	+	0.0771244i
$681$	4.53642	−	39.5074i	0.173836	−	1.51393i
$682$	−19.3590	−	14.2876i	−0.741295	−	0.547101i
$683$	−15.0454	−	31.2422i	−0.575698	−	1.19545i	−0.961993	−	0.273074i	$-0.911960\pi$
$683$	−15.0454	−	31.2422i	−0.575698	−	1.19545i	0.386295	−	0.922375i	$-0.373755\pi$
$684$	1.90370	−	1.88759i	0.0727896	−	0.0721738i
$685$	2.29108	+	0.801682i	0.0875375	+	0.0306307i
$686$	−10.0876	−	19.0867i	−0.385146	−	0.728732i
$687$	14.7953	−	10.0413i	0.564478	−	0.383101i
$688$	−42.0938	−	36.2246i	−1.60481	−	1.38105i
$689$	18.3357	−	5.65582i	0.698536	−	0.215470i
$690$	1.19131	+	8.01939i	0.0453525	+	0.305293i
$691$	−6.04815	−	15.4104i	−0.230082	−	0.586241i	0.768478	−	0.639876i	$-0.221014\pi$
$691$	−6.04815	−	15.4104i	−0.230082	−	0.586241i	−0.998561	+	0.0536355i	$0.982919\pi$
$692$	−15.7312	+	3.59053i	−0.598009	+	0.136492i
$693$	2.74746	+	4.41407i	0.104367	+	0.167677i
$694$	−20.6640	+	2.32827i	−0.784395	+	0.0883801i
$695$	5.50114	−	9.52826i	0.208670	−	0.361428i
$696$	8.42509	−	3.59640i	0.319352	−	0.136321i
$697$	13.7156	+	23.7562i	0.519516	+	0.899829i
$698$	6.04058	+	8.18470i	0.228639	+	0.309795i
$699$	−38.4293	−	20.4150i	−1.45353	−	0.772168i
$700$	−1.18973	+	3.85702i	−0.0449677	+	0.145782i
$701$	−12.9825	+	16.2795i	−0.490342	+	0.614870i	−0.964020	−	0.265828i	$-0.914355\pi$
$701$	−12.9825	+	16.2795i	−0.490342	+	0.614870i	0.473678	+	0.880698i	$0.342926\pi$
$702$	−40.6083	−	51.5923i	−1.53266	−	1.94723i
$703$	−0.443518	+	1.94318i	−0.0167276	+	0.0732884i
$704$	1.24223	−	6.56537i	0.0468185	−	0.247442i
$705$	−1.92353	+	0.140040i	−0.0724443	+	0.00527423i
$706$	57.9860	+	2.16968i	2.18233	+	0.0816571i
$707$	0.0439944	+	0.232516i	0.00165458	+	0.00874467i
$708$	−15.9280	+	15.8605i	−0.598613	+	0.596075i
$709$	22.3001	+	1.67116i	0.837498	+	0.0627618i	0.486571	−	0.873641i	$-0.338247\pi$
$709$	22.3001	+	1.67116i	0.837498	+	0.0627618i	0.350927	+	0.936403i	$0.385866\pi$
$710$	0.753692	−	6.68920i	0.0282856	−	0.251041i
$711$	12.3057	−	5.30679i	0.461499	−	0.199020i
$712$	−5.43990	+	2.61972i	−0.203869	+	0.0981780i
$713$	11.5705	−	3.10032i	0.433320	−	0.116108i
$714$	5.70423	−	4.88784i	0.213476	−	0.182923i
$715$	0.686317	−	18.3422i	0.0256668	−	0.685960i
$716$	−23.1043	+	1.73143i	−0.863447	+	0.0647064i
$717$	37.0164	+	7.08536i	1.38240	+	0.264608i
$718$	−21.8533	+	23.5523i	−0.815560	+	0.878964i
$719$	−32.3845	+	25.8258i	−1.20774	+	0.963138i	−0.999887	−	0.0150224i	$-0.995218\pi$
$719$	−32.3845	+	25.8258i	−1.20774	+	0.963138i	−0.207850	+	0.978161i	$0.566647\pi$
$720$	−18.2682	+	7.08031i	−0.680814	+	0.263868i
$721$	−1.68802	−	7.39570i	−0.0628651	−	0.275430i
$722$	−34.6982	+	1.29832i	−1.29133	+	0.0483183i
$723$	4.24060	−	0.468681i	0.157709	−	0.0174304i
$724$	32.9475	−	19.0222i	1.22448	−	0.706956i
$725$	−4.26820	−	16.3084i	−0.158517	−	0.605680i
$726$	19.8160	−	11.3847i	0.735440	−	0.422526i
$727$	−4.78198	−	2.08636i	−0.177354	−	0.0773787i	0.309339	−	0.950952i	$-0.399892\pi$
$727$	−4.78198	−	2.08636i	−0.177354	−	0.0773787i	−0.486693	+	0.873573i	$0.661797\pi$
$728$	−4.93555	+	3.10121i	−0.182924	+	0.114939i
$729$	26.3975	−	5.67211i	0.977685	−	0.210078i
$730$	2.62545	+	2.09373i	0.0971723	+	0.0774924i
$731$	30.5669	−	4.60722i	1.13056	−	0.170404i
$732$	12.7361	−	3.89896i	0.470740	−	0.144110i
$733$	28.7208	−	33.3742i	1.06083	−	1.23270i	0.0892416	−	0.996010i	$-0.471556\pi$
$733$	28.7208	−	33.3742i	1.06083	−	1.23270i	0.971585	−	0.236692i	$-0.0760634\pi$
$734$	−5.14462	−	68.6502i	−0.189891	−	2.53392i
$735$	−12.4838	−	7.88110i	−0.460470	−	0.290699i
$736$	8.31176	+	9.65844i	0.306376	+	0.356015i
$737$	−5.00805	+	5.00805i	−0.184474	+	0.184474i
$738$	−57.5053	−	4.55517i	−2.11680	−	0.167678i
$739$	−33.0017	−	3.71839i	−1.21399	−	0.136783i	−0.518344	−	0.855172i	$-0.673451\pi$
$739$	−33.0017	−	3.71839i	−1.21399	−	0.136783i	−0.695642	+	0.718389i	$0.744880\pi$
$740$	−3.92935	+	5.32408i	−0.144446	+	0.195717i
$741$	0.547507	−	7.10347i	0.0201132	−	0.260953i
$742$	−4.45935	−	1.19488i	−0.163708	−	0.0438654i
$743$	18.3312	−	3.46845i	0.672506	−	0.127245i	0.161566	−	0.986862i	$-0.448345\pi$
$743$	18.3312	−	3.46845i	0.672506	−	0.127245i	0.510939	+	0.859617i	$0.329298\pi$
$744$	5.16246	+	9.81828i	0.189265	+	0.359956i
$745$	−3.60944	+	2.46087i	−0.132240	+	0.0901594i
$746$	−7.35075	−	21.0072i	−0.269130	−	0.769130i
$747$	−25.1477	+	7.64018i	−0.920105	+	0.279540i
$748$	4.83417	+	6.06185i	0.176755	+	0.221643i
$749$	−9.61953	+	3.77539i	−0.351490	+	0.137950i
$750$	7.91058	+	35.0011i	0.288854	+	1.27806i
$751$	21.2915	+	11.2529i	0.776938	+	0.410624i	0.808215	−	0.588887i	$-0.200434\pi$
$751$	21.2915	+	11.2529i	0.776938	+	0.410624i	−0.0312774	+	0.999511i	$0.509958\pi$
$752$	−3.12953	+	2.30970i	−0.114122	+	0.0842261i
$753$	22.0830	+	38.4373i	0.804751	+	1.40073i
$754$	−29.8801	+	61.1334i	−1.08817	+	2.22635i
$755$			20.6240i			0.750584i
$756$	0.707713	+	6.66245i	0.0257393	+	0.242311i
$757$	−3.40759	−	5.42314i	−0.123851	−	0.197108i	0.779044	−	0.626970i	$-0.215705\pi$
$757$	−3.40759	−	5.42314i	−0.123851	−	0.197108i	−0.902895	+	0.429862i	$0.858562\pi$
$758$	46.8655	+	14.4561i	1.70223	+	0.525068i
$759$	0.952087	−	6.22691i	0.0345586	−	0.226022i
$760$	−0.758368	−	0.297638i	−0.0275089	−	0.0107964i
$761$	−7.82491	−	25.3677i	−0.283653	−	0.919579i	−0.979509	−	0.201399i	$-0.935451\pi$
$761$	−7.82491	−	25.3677i	−0.283653	−	0.919579i	0.695857	−	0.718181i	$-0.255025\pi$
$762$	−8.19920	+	2.84949i	−0.297026	+	0.103226i
$763$	−8.53088	−	12.5125i	−0.308839	−	0.452983i
$764$	−29.3744	−	18.4572i	−1.06273	−	0.667757i
$765$	3.64558	−	10.2782i	0.131806	−	0.371609i
$766$	−43.3122	−	43.3122i	−1.56493	−	1.56493i
$767$	−4.46410	+	59.5693i	−0.161189	+	2.15092i
$768$	−21.5412	+	29.0579i	−0.777300	+	1.04854i
$769$	−34.0307	+	14.8474i	−1.22718	+	0.535412i	−0.910653	−	0.413172i	$-0.864421\pi$
$769$	−34.0307	+	14.8474i	−1.22718	+	0.535412i	−0.316524	+	0.948584i	$0.602516\pi$
$770$	−2.48773	+	3.64884i	−0.0896517	+	0.131495i
$771$	21.6391	−	5.74894i	0.779312	−	0.207043i
$772$	−1.31206	+	1.12912i	−0.0472222	+	0.0406380i
$773$	0.573614	−	0.912901i	0.0206315	−	0.0328348i	−0.836249	−	0.548349i	$-0.815256\pi$
$773$	0.573614	−	0.912901i	0.0206315	−	0.0328348i	0.856881	+	0.515515i	$0.172399\pi$
$774$	−28.4533	+	58.4475i	−1.02273	+	2.10085i
$775$	19.2679	−	6.74213i	0.692123	−	0.242184i
$776$	9.07818	+	8.42332i	0.325888	+	0.302380i
$777$	−3.09746	−	3.90106i	−0.111121	−	0.139950i
$778$	−6.64061	−	1.00091i	−0.238077	−	0.0358844i
$779$	−4.25758	−	4.58858i	−0.152544	−	0.164403i
$780$	11.0966	−	20.8883i	0.397322	−	0.747920i
$781$	−2.09154	+	4.79386i	−0.0748412	+	0.171538i
$782$	−9.10122			−0.325459
$783$	−17.1785	−	22.0885i	−0.613909	−	0.789377i
$784$	−29.7741			−1.06336
$785$	−11.1982	+	25.6665i	−0.399680	+	0.916076i
$786$	−17.7286	+	33.3724i	−0.632358	+	1.19035i
$787$	−7.67269	−	8.26919i	−0.273502	−	0.294765i	0.581332	−	0.813666i	$-0.302532\pi$
$787$	−7.67269	−	8.26919i	−0.273502	−	0.294765i	−0.854834	+	0.518901i	$0.826341\pi$
$788$	−11.7114	−	1.76521i	−0.417201	−	0.0628830i
$789$	−1.16310	−	1.46485i	−0.0414075	−	0.0521502i
$790$	8.34417	+	7.74226i	0.296872	+	0.275457i
$791$	−4.62647	+	1.61887i	−0.164498	+	0.0575604i
$792$	5.81888	−	0.411213i	0.206765	−	0.0146118i
$793$	18.8325	−	29.9718i	0.668763	−	1.06433i
$794$	13.6722	−	11.7658i	0.485207	−	0.417554i
$795$	−6.47761	+	1.72093i	−0.229737	+	0.0610351i
$796$	−15.4807	+	22.7060i	−0.548698	+	0.804793i
$797$	29.5312	−	12.8843i	1.04605	−	0.456386i	0.194631	−	0.980876i	$-0.437649\pi$
$797$	29.5312	−	12.8843i	1.04605	−	0.456386i	0.851416	+	0.524491i	$0.175744\pi$
$798$	−1.02083	+	1.37704i	−0.0361369	+	0.0487467i
$799$	0.161793	−	2.15898i	0.00572383	−	0.0763793i
$800$	15.3548	+	15.3548i	0.542875	+	0.542875i
$801$	11.9708	+	14.0305i	0.422969	+	0.495743i
$802$	53.6233	+	33.6938i	1.89350	+	1.18977i
$803$	−1.46979	−	2.15579i	−0.0518678	−	0.0760761i
$804$	−8.62086	+	2.99603i	−0.304034	+	0.105662i
$805$	−0.648060	−	2.10096i	−0.0228411	−	0.0740491i
$806$	−76.7015	−	30.1031i	−2.70170	−	1.06034i
$807$	−7.31891	+	47.8677i	−0.257638	+	1.68502i
$808$	0.253707	+	0.0782582i	0.00892538	+	0.00275312i
$809$	28.3087	+	45.0530i	0.995280	+	1.58398i	0.797131	+	0.603807i	$0.206350\pi$
$809$	28.3087	+	45.0530i	0.995280	+	1.58398i	0.198149	+	0.980172i	$0.436507\pi$
$810$	13.4611	+	18.5672i	0.472974	+	0.652386i
$811$		−	16.1915i		−	0.568559i	−0.958741	−	0.284279i	$-0.908246\pi$
$811$		−	16.1915i		−	0.568559i	0.958741	−	0.284279i	$-0.0917544\pi$
$812$	5.90076	−	3.65994i	0.207076	−	0.128439i
$813$	4.64922	+	8.09233i	0.163055	+	0.283810i
$814$	9.75341	−	7.19835i	0.341857	−	0.252302i
$815$	−16.0643	−	8.49026i	−0.562710	−	0.297401i
$816$	−4.84855	−	21.4529i	−0.169733	−	0.751000i
$817$	−6.56626	+	2.57707i	−0.229724	+	0.0901602i
$818$	−30.9168	−	38.7684i	−1.08098	−	1.35551i
$819$	13.0007	+	12.1661i	0.454282	+	0.425117i
$820$	−6.86357	−	19.6150i	−0.239686	−	0.684984i
$821$	9.09088	−	6.19806i	0.317274	−	0.216314i	−0.394203	−	0.919024i	$-0.628979\pi$
$821$	9.09088	−	6.19806i	0.317274	−	0.216314i	0.711476	+	0.702710i	$0.248027\pi$
$822$	−2.66671	−	5.07172i	−0.0930123	−	0.176896i
$823$	−6.71314	+	1.27019i	−0.234005	+	0.0442762i	−0.301591	−	0.953437i	$-0.597518\pi$
$823$	−6.71314	+	1.27019i	−0.234005	+	0.0442762i	0.0675862	+	0.997713i	$0.478470\pi$
$824$	−8.22107	−	2.20283i	−0.286394	−	0.0767391i
$825$	0.824954	−	10.7031i	0.0287212	−	0.372635i
$826$	8.53467	−	11.5641i	0.296959	−	0.402365i
$827$	−12.0306	−	1.35552i	−0.418344	−	0.0471360i	−0.0997161	−	0.995016i	$-0.531793\pi$
$827$	−12.0306	−	1.35552i	−0.418344	−	0.0471360i	−0.318628	+	0.947880i	$0.603222\pi$
$828$	4.60115	−	6.68743i	0.159901	−	0.232404i
$829$	16.9213	−	16.9213i	0.587700	−	0.587700i	−0.349308	−	0.937008i	$-0.613583\pi$
$829$	16.9213	−	16.9213i	0.587700	−	0.587700i	0.937008	+	0.349308i	$0.113583\pi$
$830$	−14.5618	−	16.9211i	−0.505446	−	0.587339i
$831$	31.9793	+	20.1888i	1.10935	+	0.700343i
$832$	−1.71002	−	22.8186i	−0.0592843	−	0.791094i
$833$	10.8104	−	12.5619i	0.374558	−	0.435244i
$834$	−24.8353	+	7.60293i	−0.859975	+	0.263268i
$835$	18.2909	−	2.75691i	0.632982	−	0.0954066i
$836$	−1.38326	−	1.10311i	−0.0478410	−	0.0381519i
$837$	24.9853	−	22.8884i	0.863617	−	0.791139i
$838$	−34.2353	+	21.5115i	−1.18264	+	0.743102i
$839$	−36.4249	−	15.8920i	−1.25753	−	0.548654i	−0.337803	−	0.941217i	$-0.609684\pi$
$839$	−36.4249	−	15.8920i	−1.25753	−	0.548654i	−0.919725	+	0.392563i	$0.871588\pi$
$840$	1.76541	−	1.01427i	0.0609125	−	0.0349955i
$841$	−12.8861	+	25.9798i	−0.444347	+	0.895855i
$842$	21.4264	−	12.3705i	0.738402	−	0.426317i
$843$	−26.0729	+	2.88164i	−0.897999	+	0.0992489i
$844$	9.88054	−	0.369704i	0.340102	−	0.0127257i
$845$	−10.0319	−	43.9528i	−0.345109	−	1.51202i
$846$	3.54748	+	2.85376i	0.121965	+	0.0981144i
$847$	−4.84551	+	3.86417i	−0.166494	+	0.132774i
$848$	−9.19386	+	9.90863i	−0.315719	+	0.340264i
$849$	22.1845	+	4.24636i	0.761370	+	0.145735i
$850$	−15.4664	+	1.15905i	−0.530493	+	0.0397550i
$851$	−0.225659	+	6.03086i	−0.00773548	+	0.206735i
$852$	−5.11794	+	4.38546i	−0.175338	+	0.150243i
$853$	6.19296	−	1.65940i	0.212043	−	0.0568167i	−0.151234	−	0.988498i	$-0.548325\pi$
$853$	6.19296	−	1.65940i	0.212043	−	0.0568167i	0.363277	+	0.931681i	$0.381658\pi$
$854$	−7.67315	+	3.69520i	−0.262570	+	0.126447i
$855$	−0.289133	+	2.47170i	−0.00988813	+	0.0845304i
$856$	−1.29814	+	11.5213i	−0.0443695	+	0.393790i
$857$	−11.1081	−	0.832434i	−0.379444	−	0.0284354i	−0.116357	−	0.993207i	$-0.537122\pi$
$857$	−11.1081	−	0.832434i	−0.379444	−	0.0284354i	−0.263087	+	0.964772i	$0.584741\pi$
$858$	−30.7043	+	30.5742i	−1.04823	+	1.04378i
$859$	6.58433	+	34.7990i	0.224654	+	1.18733i	0.895271	+	0.445523i	$0.146982\pi$
$859$	6.58433	+	34.7990i	0.224654	+	1.18733i	−0.670616	+	0.741804i	$0.733970\pi$
$860$	−23.4018	−	0.875633i	−0.797994	−	0.0298588i
$861$	15.6024	−	1.13591i	0.531727	−	0.0387118i
$862$	6.40311	−	33.8413i	0.218091	−	1.15264i
$863$	0.622299	−	2.72647i	0.0211833	−	0.0928101i	−0.963231	−	0.268674i	$-0.913415\pi$
$863$	0.622299	−	2.72647i	0.0211833	−	0.0928101i	0.984415	+	0.175864i	$0.0562718\pi$
$864$	33.4685	+	13.3822i	1.13862	+	0.455271i
$865$	9.33876	−	11.7104i	0.317527	−	0.398167i
$866$	11.3395	−	36.7618i	0.385332	−	1.24922i
$867$	−15.1918	−	8.07045i	−0.515942	−	0.274087i
$868$	4.99297	+	6.76524i	0.169473	+	0.229627i
$869$	−4.42209	−	7.65929i	−0.150009	−	0.259824i
$870$	11.2725	−	20.9244i	0.382174	−	0.709405i
$871$	−12.1272	+	21.0050i	−0.410916	+	0.711727i
$872$	−16.8841	+	1.90238i	−0.571766	+	0.0644226i
$873$	17.8181	−	33.3696i	0.603052	−	1.12939i
$874$	2.02474	−	0.462135i	0.0684880	−	0.0156319i
$875$	−3.55525	−	9.05864i	−0.120189	−	0.306238i
$876$	−0.494051	−	3.32573i	−0.0166924	−	0.112366i
$877$	41.5666	−	12.8216i	1.40360	−	0.432955i	0.501757	−	0.865009i	$-0.332687\pi$
$877$	41.5666	−	12.8216i	1.40360	−	0.432955i	0.901848	+	0.432054i	$0.142211\pi$
$878$	17.7090	+	15.2399i	0.597651	+	0.514321i
$879$	−24.9818	+	16.9547i	−0.842615	+	0.571867i
$880$	6.04180	+	11.4316i	0.203669	+	0.385361i
$881$	44.0727	+	15.4217i	1.48485	+	0.519571i	0.946375	−	0.323071i	$-0.104715\pi$
$881$	44.0727	+	15.4217i	1.48485	+	0.519571i	0.538474	+	0.842642i	$0.319001\pi$
$882$	8.87717	+	33.7021i	0.298910	+	1.13481i
$883$	−22.5759	−	46.8793i	−0.759739	−	1.57761i	−0.815218	−	0.579154i	$-0.803383\pi$
$883$	−22.5759	−	46.8793i	−0.759739	−	1.57761i	0.0554797	−	0.998460i	$-0.482331\pi$
$884$	21.3639	+	15.7672i	0.718544	+	0.530310i
$885$	2.38023	−	20.7293i	0.0800106	−	0.696807i
$886$	−18.8861	−	12.8764i	−0.634492	−	0.432590i
$887$	0.690794	−	2.57808i	0.0231946	−	0.0865634i	−0.953358	−	0.301841i	$-0.902399\pi$
$887$	0.690794	−	2.57808i	0.0231946	−	0.0865634i	0.976553	+	0.215277i	$0.0690656\pi$
$888$	−5.49349	+	1.02734i	−0.184350	+	0.0344754i
$889$	2.08120	−	1.09994i	0.0698011	−	0.0368910i
$890$	−6.79701	+	14.1141i	−0.227836	+	0.473107i
$891$	−5.74207	−	16.8683i	−0.192367	−	0.565109i
$892$	−28.8074	−	6.57509i	−0.964542	−	0.220150i
$893$	0.0736330	+	0.488523i	0.00246403	+	0.0163478i
$894$	10.1942	+	1.55869i	0.340946	+	0.0521303i
$895$	15.7658	−	14.6285i	0.526991	−	0.488976i
$896$	3.10214	−	5.86953i	0.103635	−	0.196087i
$897$	−2.36981	−	21.4419i	−0.0791255	−	0.715923i
$898$	43.5921	+	25.1679i	1.45469	+	0.839865i
$899$	−32.6141	−	13.0197i	−1.08774	−	0.434233i
$900$	6.96745	−	11.9504i	0.232248	−	0.398348i
$901$	−0.842410	−	7.47660i	−0.0280647	−	0.249082i
$902$	1.42348	+	38.0432i	0.0473966	+	1.26670i
$903$	5.23194	−	16.8345i	0.174108	−	0.560217i
$904$	−0.819631	+	5.43790i	−0.0272605	+	0.180862i
$905$	−12.9021	+	32.8741i	−0.428882	+	1.09277i
$906$	33.1912	−	35.6195i	1.10270	−	1.18338i
$907$	21.8036	+	4.12546i	0.723975	+	0.136984i	0.534823	−	0.844964i	$-0.320378\pi$
$907$	21.8036	+	4.12546i	0.723975	+	0.136984i	0.189152	+	0.981948i	$0.439426\pi$
$908$	−30.4701	−	14.6736i	−1.01119	−	0.486962i
$909$	0.0337673	−	0.810307i	0.00111999	−	0.0268762i
$910$	−4.99503	+	14.2750i	−0.165584	+	0.473211i
$911$	−1.40020	−	5.22562i	−0.0463907	−	0.173133i	0.938844	−	0.344344i	$-0.111899\pi$
$911$	−1.40020	−	5.22562i	−0.0463907	−	0.173133i	−0.985234	+	0.171211i	$0.945232\pi$
$912$	2.16797	+	4.52641i	0.0717887	+	0.149884i
$913$	6.93629	+	15.8981i	0.229558	+	0.526152i
$914$	21.3761	+	48.9945i	0.707058	+	1.62059i
$915$	−6.98661	+	10.2008i	−0.230970	+	0.337230i
$916$	−3.93578	−	14.6885i	−0.130042	−	0.485322i
$917$	3.38470	−	9.67292i	0.111773	−	0.319428i
$918$	−22.8375	+	11.8844i	−0.753749	+	0.392244i
$919$	−37.7965	−	18.2018i	−1.24679	−	0.600423i	−0.310141	−	0.950690i	$-0.600376\pi$
$919$	−37.7965	−	18.2018i	−1.24679	−	0.600423i	−0.936650	+	0.350268i	$0.886091\pi$
$920$	−2.42378	−	0.458604i	−0.0799097	−	0.0151197i
$921$	−0.544111	−	1.77736i	−0.0179291	−	0.0585660i
$922$	17.2287	−	43.8981i	0.567398	−	1.44571i
$923$	−2.66957	+	17.7114i	−0.0878699	+	0.582979i
$924$	4.31288	−	0.974753i	0.141883	−	0.0320670i
$925$	0.384555	+	10.2774i	0.0126441	+	0.337920i
$926$	5.06770	+	44.9771i	0.166535	+	1.47804i
$927$	−0.110446	+	25.9979i	−0.00362753	+	0.853883i
$928$	−2.57464	−	37.2671i	−0.0845167	−	1.22335i
$929$	−7.03524	−	4.06180i	−0.230819	−	0.133263i	0.380131	−	0.924933i	$-0.375879\pi$
$929$	−7.03524	−	4.06180i	−0.230819	−	0.133263i	−0.610950	+	0.791669i	$0.709212\pi$
$930$	26.3549	+	11.5652i	0.864212	+	0.379239i
$931$	−1.76713	+	3.34356i	−0.0579152	+	0.109581i
$932$	−27.1281	+	25.1712i	−0.888611	+	0.824510i
$933$	3.85153	+	9.87518i	0.126094	+	0.323299i
$934$	0.0210111	+	0.139400i	0.000687506	+	0.00456130i
$935$	−7.01676	−	1.60153i	−0.229473	−	0.0523756i
$936$	18.8838	−	6.51781i	0.617235	−	0.213041i
$937$	4.50495	−	9.35463i	0.147170	−	0.305602i	−0.814332	−	0.580400i	$-0.802896\pi$
$937$	4.50495	−	9.35463i	0.147170	−	0.305602i	0.961502	+	0.274797i	$0.0886107\pi$
$938$	5.15934	−	2.72679i	0.168458	−	0.0890329i
$939$	11.9512	−	33.9232i	0.390012	−	1.10704i
$940$	−0.424507	+	1.58428i	−0.0138459	+	0.0516735i
$941$	25.2209	+	17.1953i	0.822177	+	0.560551i	0.899735	−	0.436437i	$-0.143760\pi$
$941$	25.2209	+	17.1953i	0.822177	+	0.560551i	−0.0775578	+	0.996988i	$0.524712\pi$
$942$	60.6466	−	26.3066i	1.97597	−	0.857117i
$943$	−15.2498	−	11.2549i	−0.496603	−	0.366509i
$944$	−18.2581	−	37.9134i	−0.594251	−	1.23398i
$945$	−4.36960	−	4.42565i	−0.142143	−	0.143966i
$946$	40.4933	+	14.1692i	1.31655	+	0.460681i
$947$	−1.46864	−	2.77881i	−0.0477245	−	0.0902992i	0.859100	−	0.511809i	$-0.171024\pi$
$947$	−1.46864	−	2.77881i	−0.0477245	−	0.0902992i	−0.906824	+	0.421509i	$0.861500\pi$
$948$	−0.827545	−	11.3668i	−0.0268774	−	0.369175i
$949$	−6.77270	−	5.82838i	−0.219851	−	0.189197i
$950$	3.38195	−	1.04319i	0.109725	−	0.0338457i
$951$	−13.6038	+	10.8015i	−0.441135	+	0.350263i
$952$	0.835028	+	2.12762i	0.0270634	+	0.0689564i
$953$	32.8184	−	7.49058i	1.06309	−	0.242644i	0.345007	−	0.938600i	$-0.387877\pi$
$953$	32.8184	−	7.49058i	1.06309	−	0.242644i	0.718084	+	0.695956i	$0.245019\pi$
$954$	13.9570	+	7.45252i	0.451875	+	0.241284i
$955$	32.0007	−	3.60562i	1.03552	−	0.116675i
$956$	16.0258	−	27.7575i	0.518312	−	0.897743i
$957$	−13.1615	+	12.9539i	−0.425451	+	0.418741i
$958$	7.72535	+	13.3807i	0.249595	+	0.432311i
$959$	0.922757	+	1.25029i	0.0297974	+	0.0403740i
$960$	0.281892	+	7.98777i	0.00909802	+	0.257804i
$961$	3.39670	−	11.0118i	0.109571	−	0.355220i
$962$	25.8831	−	32.4563i	0.834503	−	1.04643i
$963$	35.0425	−	5.12965i	1.12923	−	0.165301i
$964$	0.807377	−	3.53735i	0.0260039	−	0.113930i
$965$	0.298731	−	1.57883i	0.00961649	−	0.0508244i
$966$	−2.26191	+	4.67150i	−0.0727759	+	0.150303i
$967$	−15.9220	−	0.595759i	−0.512016	−	0.0191583i	−0.219865	−	0.975530i	$-0.570562\pi$
$967$	−15.9220	−	0.595759i	−0.512016	−	0.0191583i	−0.292152	+	0.956372i	$0.594371\pi$
$968$	1.29274	+	6.83229i	0.0415502	+	0.219598i
$969$	−2.69688	−	0.728769i	−0.0866362	−	0.0234114i
$970$	32.0414	+	2.40117i	1.02879	+	0.0770969i
$971$	0.665508	−	5.90655i	0.0213572	−	0.189550i	−0.978504	−	0.206229i	$-0.933881\pi$
$971$	0.665508	−	5.90655i	0.0213572	−	0.189550i	0.999861	+	0.0166790i	$0.00530933\pi$
$972$	2.81309	−	22.7888i	0.0902299	−	0.730952i
$973$	6.34606	−	3.05610i	0.203445	−	0.0979741i
$974$	−28.9575	+	7.75913i	−0.927857	+	0.248619i
$975$	−6.75783	−	36.1360i	−0.216424	−	1.15728i
$976$	−0.932362	+	24.9179i	−0.0298442	+	0.797602i
$977$	−7.81428	+	0.585599i	−0.250001	+	0.0187350i	−0.199141	−	0.979971i	$-0.563815\pi$
$977$	−7.81428	+	0.585599i	−0.250001	+	0.0187350i	−0.0508598	+	0.998706i	$0.516196\pi$
$978$	14.0808	+	40.5166i	0.450256	+	1.29558i
$979$	8.27891	−	8.92254i	0.264595	−	0.285166i
$980$	−9.81611	+	7.82809i	−0.313564	+	0.250059i
$981$	18.7561	+	48.3932i	0.598835	+	1.54508i
$982$	13.4542	+	58.9466i	0.429340	+	1.88106i
$983$	4.85770	−	0.181762i	0.154937	−	0.00579732i	0.0401896	−	0.999192i	$-0.487204\pi$
$983$	4.85770	−	0.181762i	0.154937	−	0.00579732i	0.114747	+	0.993395i	$0.463394\pi$
$984$	7.05289	−	16.0722i	0.224838	−	0.512362i
$985$	9.52115	−	5.49704i	0.303369	−	0.175150i
$986$	21.3750	+	15.9686i	0.680718	+	0.508542i
$987$	−1.06796	−	0.619615i	−0.0339935	−	0.0197226i
$988$	−5.55342	−	2.42293i	−0.176678	−	0.0770838i
$989$	−18.0847	+	11.3634i	−0.575060	+	0.361334i
$990$	11.1384	−	10.2472i	0.354002	−	0.325678i
$991$	−15.2873	−	12.1912i	−0.485618	−	0.387267i	0.349851	−	0.936805i	$-0.386232\pi$
$991$	−15.2873	−	12.1912i	−0.485618	−	0.387267i	−0.835469	+	0.549538i	$0.814804\pi$
$992$	44.7299	−	6.74195i	1.42018	−	0.214057i
$993$	−2.87689	+	12.4822i	−0.0912955	+	0.396111i
$994$	2.81102	−	3.26647i	0.0891602	−	0.103606i
$995$	−1.90635	−	25.4385i	−0.0604353	−	0.806453i
$996$	−0.883201	+	22.3343i	−0.0279853	+	0.707689i
$997$	18.7819	+	21.8249i	0.594828	+	0.691202i	0.972011	−	0.234936i	$-0.0754882\pi$
$997$	18.7819	+	21.8249i	0.594828	+	0.691202i	−0.377183	+	0.926139i	$0.623107\pi$
$998$	21.9089	−	21.9089i	0.693513	−	0.693513i
$999$	7.30887	+	15.4278i	0.231243	+	0.488113i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.101.23	yes	672
3.2	odd	2		783.2.be.a.710.6		672
9.4	even	3		783.2.be.a.449.23		672
9.5	odd	6	inner	261.2.x.a.14.6	✓	672
29.27	odd	28	inner	261.2.x.a.56.6	yes	672
87.56	even	28		783.2.be.a.143.23		672
261.85	odd	84		783.2.be.a.665.6		672
261.230	even	84	inner	261.2.x.a.230.23	yes	672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.6	✓	672	9.5	odd	6	inner
261.2.x.a.56.6	yes	672	29.27	odd	28	inner
261.2.x.a.101.23	yes	672	1.1	even	1	trivial
261.2.x.a.230.23	yes	672	261.230	even	84	inner
783.2.be.a.143.23		672	87.56	even	28
783.2.be.a.449.23		672	9.4	even	3
783.2.be.a.665.6		672	261.85	odd	84
783.2.be.a.710.6		672	3.2	odd	2

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	261.2.x.a.101.23

Level	$261$
Weight	$2$
Character	261.101
Analytic conductor	$2.084$
Analytic rank	$0$
Dimension	$672$
Inner twists	$4$