LMFDB - Embedded newform 504.2.cc.b.293.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.20
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995788 - 1.00419i) q^{2} +(0.539289 - 1.64595i) q^{3} +(-0.0168127 + 1.99993i) q^{4} +(0.194059 + 0.112040i) q^{5} +(-2.18988 + 1.09747i) q^{6} +(-0.784223 - 2.52685i) q^{7} +(2.02506 - 1.97462i) q^{8} +(-2.41834 - 1.77529i) q^{9} +O(q^{10})$	\(q+(-0.995788 - 1.00419i) q^{2} +(0.539289 - 1.64595i) q^{3} +(-0.0168127 + 1.99993i) q^{4} +(0.194059 + 0.112040i) q^{5} +(-2.18988 + 1.09747i) q^{6} +(-0.784223 - 2.52685i) q^{7} +(2.02506 - 1.97462i) q^{8} +(-2.41834 - 1.77529i) q^{9} +(-0.0807318 - 0.306441i) q^{10} +(1.00451 + 1.73985i) q^{11} +(3.28273 + 1.10621i) q^{12} +(1.86199 - 3.22507i) q^{13} +(-1.75653 + 3.30372i) q^{14} +(0.289067 - 0.258991i) q^{15} +(-3.99943 - 0.0672486i) q^{16} -4.50401 q^{17} +(0.625414 + 4.19629i) q^{18} +3.18997 q^{19} +(-0.227335 + 0.386221i) q^{20} +(-4.58201 - 0.0719078i) q^{21} +(0.746878 - 2.74125i) q^{22} +(-4.96153 - 2.86454i) q^{23} +(-2.15805 - 4.39805i) q^{24} +(-2.47489 - 4.28664i) q^{25} +(-5.09275 + 1.34168i) q^{26} +(-4.22623 + 3.02308i) q^{27} +(5.06672 - 1.52591i) q^{28} +(-3.01540 - 5.22282i) q^{29} +(-0.547927 - 0.0323795i) q^{30} +(9.21726 + 5.32159i) q^{31} +(3.91506 + 4.08318i) q^{32} +(3.40544 - 0.715087i) q^{33} +(4.48503 + 4.52290i) q^{34} +(0.130923 - 0.578224i) q^{35} +(3.59111 - 4.80665i) q^{36} -7.59321i q^{37} +(-3.17653 - 3.20335i) q^{38} +(-4.30417 - 4.80400i) q^{39} +(0.614219 - 0.156306i) q^{40} +(-5.47156 + 9.47702i) q^{41} +(4.49050 + 4.67284i) q^{42} +(-4.40539 + 2.54345i) q^{43} +(-3.49648 + 1.97969i) q^{44} +(-0.270397 - 0.615462i) q^{45} +(2.06408 + 7.83482i) q^{46} +(-3.71247 - 6.43019i) q^{47} +(-2.26754 + 6.54662i) q^{48} +(-5.76999 + 3.96324i) q^{49} +(-1.84015 + 6.75386i) q^{50} +(-2.42896 + 7.41339i) q^{51} +(6.41861 + 3.77808i) q^{52} +3.21900 q^{53} +(7.24418 + 1.23361i) q^{54} +0.450180i q^{55} +(-6.57768 - 3.56849i) q^{56} +(1.72031 - 5.25055i) q^{57} +(-2.24203 + 8.22886i) q^{58} +(8.74993 + 5.05177i) q^{59} +(0.513103 + 0.582468i) q^{60} +(0.189238 + 0.327769i) q^{61} +(-3.83453 - 14.5551i) q^{62} +(-2.58938 + 7.50301i) q^{63} +(0.201734 - 7.99746i) q^{64} +(0.722675 - 0.417236i) q^{65} +(-4.10918 - 2.70765i) q^{66} +(7.13938 + 4.12192i) q^{67} +(0.0757247 - 9.00769i) q^{68} +(-7.39060 + 6.62164i) q^{69} +(-0.711021 + 0.444316i) q^{70} +3.61002i q^{71} +(-8.40280 + 1.18023i) q^{72} -7.27725i q^{73} +(-7.62505 + 7.56122i) q^{74} +(-8.39030 + 1.76183i) q^{75} +(-0.0536322 + 6.37972i) q^{76} +(3.60860 - 3.90267i) q^{77} +(-0.538115 + 9.10599i) q^{78} +(-3.54286 - 6.13642i) q^{79} +(-0.768593 - 0.461148i) q^{80} +(2.69669 + 8.58649i) q^{81} +(14.9653 - 3.94259i) q^{82} +(8.02064 - 4.63072i) q^{83} +(0.220847 - 9.16249i) q^{84} +(-0.874044 - 0.504629i) q^{85} +(6.94095 + 1.89113i) q^{86} +(-10.2227 + 2.14660i) q^{87} +(5.46974 + 1.53979i) q^{88} -3.85271 q^{89} +(-0.348786 + 0.884400i) q^{90} +(-9.60950 - 2.17582i) q^{91} +(5.81230 - 9.87455i) q^{92} +(13.7299 - 12.3013i) q^{93} +(-2.76033 + 10.1312i) q^{94} +(0.619043 + 0.357405i) q^{95} +(8.83207 - 4.24200i) q^{96} +(15.5292 - 8.96577i) q^{97} +(9.72554 + 1.84765i) q^{98} +(0.659514 - 5.99084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.995788	−	1.00419i	−0.704128	−	0.710073i
$2$	−0.995788	−	1.00419i	−0.704128	−	0.710073i
$3$	0.539289	−	1.64595i	0.311358	−	0.950293i
$3$	0.539289	−	1.64595i	0.311358	−	0.950293i
$4$	−0.0168127	+	1.99993i	−0.00840637	+	0.999965i
$5$	0.194059	+	0.112040i	0.0867859	+	0.0501059i	0.542765	−	0.839885i	$-0.317377\pi$
$5$	0.194059	+	0.112040i	0.0867859	+	0.0501059i	−0.455979	+	0.889991i	$0.650711\pi$
$6$	−2.18988	+	1.09747i	−0.894013	+	0.448041i
$7$	−0.784223	−	2.52685i	−0.296409	−	0.955061i
$7$	−0.784223	−	2.52685i	−0.296409	−	0.955061i
$8$	2.02506	−	1.97462i	0.715967	−	0.698134i
$9$	−2.41834	−	1.77529i	−0.806112	−	0.591763i
$10$	−0.0807318	−	0.306441i	−0.0255296	−	0.0969053i
$11$	1.00451	+	1.73985i	0.302870	+	0.524586i	0.976785	−	0.214223i	$-0.0687219\pi$
$11$	1.00451	+	1.73985i	0.302870	+	0.524586i	−0.673915	+	0.738809i	$0.735389\pi$
$12$	3.28273	+	1.10621i	0.947642	+	0.319336i
$13$	1.86199	−	3.22507i	0.516424	−	0.894473i	−0.483394	−	0.875403i	$-0.660596\pi$
$13$	1.86199	−	3.22507i	0.516424	−	0.894473i	0.999818	−	0.0190702i	$-0.00607062\pi$
$14$	−1.75653	+	3.30372i	−0.469453	+	0.882957i
$15$	0.289067	−	0.258991i	0.0746368	−	0.0668711i
$16$	−3.99943	−	0.0672486i	−0.999859	−	0.0168122i
$17$	−4.50401			−1.09238			−0.546191	−	0.837661i	$-0.683923\pi$
$17$	−4.50401			−1.09238			−0.546191	+	0.837661i	$0.683923\pi$
$18$	0.625414	+	4.19629i	0.147411	+	0.989075i
$19$	3.18997			0.731829			0.365915	−	0.930648i	$-0.380756\pi$
$19$	3.18997			0.731829			0.365915	+	0.930648i	$0.380756\pi$
$20$	−0.227335	+	0.386221i	−0.0508337	+	0.0863617i
$21$	−4.58201	−	0.0719078i	−0.999877	−	0.0156916i
$22$	0.746878	−	2.74125i	0.159235	−	0.584436i
$23$	−4.96153	−	2.86454i	−1.03455	−	0.597298i	−0.116266	−	0.993218i	$-0.537092\pi$
$23$	−4.96153	−	2.86454i	−1.03455	−	0.597298i	−0.918285	+	0.395920i	$0.870426\pi$
$24$	−2.15805	−	4.39805i	−0.440510	−	0.897748i
$25$	−2.47489	−	4.28664i	−0.494979	−	0.857328i
$26$	−5.09275	+	1.34168i	−0.998770	+	0.263125i
$27$	−4.22623	+	3.02308i	−0.813338	+	0.581792i
$28$	5.06672	−	1.52591i	0.957519	−	0.288369i
$29$	−3.01540	−	5.22282i	−0.559945	−	0.969853i	−0.997500	−	0.0706616i	$-0.977489\pi$
$29$	−3.01540	−	5.22282i	−0.559945	−	0.969853i	0.437555	−	0.899191i	$-0.355844\pi$
$30$	−0.547927	−	0.0323795i	−0.100037	−	0.00591167i
$31$	9.21726	+	5.32159i	1.65547	+	0.955785i	0.974767	+	0.223225i	$0.0716584\pi$
$31$	9.21726	+	5.32159i	1.65547	+	0.955785i	0.680702	+	0.732561i	$0.261675\pi$
$32$	3.91506	+	4.08318i	0.692091	+	0.721810i
$33$	3.40544	−	0.715087i	0.592811	−	0.124481i
$34$	4.48503	+	4.52290i	0.769177	+	0.775670i
$35$	0.130923	−	0.578224i	0.0221301	−	0.0977377i
$36$	3.59111	−	4.80665i	0.598519	−	0.801109i
$37$		−	7.59321i		−	1.24832i	−0.781298	−	0.624158i	$-0.785442\pi$
$37$		−	7.59321i		−	1.24832i	0.781298	−	0.624158i	$-0.214558\pi$
$38$	−3.17653	−	3.20335i	−0.515302	−	0.519652i
$39$	−4.30417	−	4.80400i	−0.689218	−	0.769256i
$40$	0.614219	−	0.156306i	0.0971165	−	0.0247141i
$41$	−5.47156	+	9.47702i	−0.854514	+	1.48006i	0.0225804	+	0.999745i	$0.492812\pi$
$41$	−5.47156	+	9.47702i	−0.854514	+	1.48006i	−0.877095	+	0.480317i	$0.840522\pi$
$42$	4.49050	+	4.67284i	0.692900	+	0.721034i
$43$	−4.40539	+	2.54345i	−0.671815	+	0.387873i	−0.796764	−	0.604290i	$-0.793457\pi$
$43$	−4.40539	+	2.54345i	−0.671815	+	0.387873i	0.124949	+	0.992163i	$0.460123\pi$
$44$	−3.49648	+	1.97969i	−0.527113	+	0.298449i
$45$	−0.270397	−	0.615462i	−0.0403084	−	0.0917477i
$46$	2.06408	+	7.83482i	0.304332	+	1.15518i
$47$	−3.71247	−	6.43019i	−0.541520	−	0.937940i	−0.998817	−	0.0486261i	$-0.984516\pi$
$47$	−3.71247	−	6.43019i	−0.541520	−	0.937940i	0.457297	−	0.889314i	$-0.348818\pi$
$48$	−2.26754	+	6.54662i	−0.327291	+	0.944924i
$49$	−5.76999	+	3.96324i	−0.824284	+	0.566177i
$50$	−1.84015	+	6.75386i	−0.260237	+	0.955140i
$51$	−2.42896	+	7.41339i	−0.340122	+	1.03808i
$52$	6.41861	+	3.77808i	0.890100	+	0.523925i
$53$	3.21900			0.442163			0.221082	−	0.975255i	$-0.429041\pi$
$53$	3.21900			0.442163			0.221082	+	0.975255i	$0.429041\pi$
$54$	7.24418	+	1.23361i	0.985809	+	0.167873i
$55$			0.450180i			0.0607022i
$56$	−6.57768	−	3.56849i	−0.878980	−	0.476859i
$57$	1.72031	−	5.25055i	0.227861	−	0.695452i
$58$	−2.24203	+	8.22886i	−0.294393	+	1.08050i
$59$	8.74993	+	5.05177i	1.13914	+	0.657685i	0.946218	−	0.323529i	$-0.104869\pi$
$59$	8.74993	+	5.05177i	1.13914	+	0.657685i	0.192925	+	0.981214i	$0.438203\pi$
$60$	0.513103	+	0.582468i	0.0662413	+	0.0751963i
$61$	0.189238	+	0.327769i	0.0242294	+	0.0419666i	0.877886	−	0.478870i	$-0.158953\pi$
$61$	0.189238	+	0.327769i	0.0242294	+	0.0419666i	−0.853656	+	0.520836i	$0.825620\pi$
$62$	−3.83453	−	14.5551i	−0.486986	−	1.84850i
$63$	−2.58938	+	7.50301i	−0.326232	+	0.945290i
$64$	0.201734	−	7.99746i	0.0252167	−	0.999682i
$65$	0.722675	−	0.417236i	0.0896367	−	0.0517518i
$66$	−4.10918	−	2.70765i	−0.505806	−	0.333289i
$67$	7.13938	+	4.12192i	0.872214	+	0.503573i	0.868083	−	0.496419i	$-0.165352\pi$
$67$	7.13938	+	4.12192i	0.872214	+	0.503573i	0.00413042	+	0.999991i	$0.498685\pi$
$68$	0.0757247	−	9.00769i	0.00918297	−	1.09234i
$69$	−7.39060	+	6.62164i	−0.889724	+	0.797152i
$70$	−0.711021	+	0.444316i	−0.0849833	+	0.0531059i
$71$			3.61002i			0.428431i	0.976786	+	0.214215i	$0.0687194\pi$
$71$			3.61002i			0.428431i	−0.976786	+	0.214215i	$0.931281\pi$
$72$	−8.40280	+	1.18023i	−0.990280	+	0.139092i
$73$		−	7.27725i		−	0.851737i	−0.904785	−	0.425869i	$-0.859969\pi$
$73$		−	7.27725i		−	0.851737i	0.904785	−	0.425869i	$-0.140031\pi$
$74$	−7.62505	+	7.56122i	−0.886395	+	0.878974i
$75$	−8.39030	+	1.76183i	−0.968829	+	0.203438i
$76$	−0.0536322	+	6.37972i	−0.00615203	+	0.731804i
$77$	3.60860	−	3.90267i	0.411239	−	0.444751i
$78$	−0.538115	+	9.10599i	−0.0609296	+	1.03105i
$79$	−3.54286	−	6.13642i	−0.398603	−	0.690401i	0.594951	−	0.803762i	$-0.297172\pi$
$79$	−3.54286	−	6.13642i	−0.398603	−	0.690401i	−0.993554	+	0.113361i	$0.963838\pi$
$80$	−0.768593	−	0.461148i	−0.0859313	−	0.0515579i
$81$	2.69669	+	8.58649i	0.299633	+	0.954055i
$82$	14.9653	−	3.94259i	1.65264	−	0.435387i
$83$	8.02064	−	4.63072i	0.880380	−	0.508287i	0.00959607	−	0.999954i	$-0.496945\pi$
$83$	8.02064	−	4.63072i	0.880380	−	0.508287i	0.870784	+	0.491667i	$0.163612\pi$
$84$	0.220847	−	9.16249i	0.0240964	−	0.999710i
$85$	−0.874044	−	0.504629i	−0.0948034	−	0.0547347i
$86$	6.94095	+	1.89113i	0.748462	+	0.203925i
$87$	−10.2227	+	2.14660i	−1.09599	+	0.230140i
$88$	5.46974	+	1.53979i	0.583076	+	0.164142i
$89$	−3.85271			−0.408387			−0.204193	−	0.978931i	$-0.565457\pi$
$89$	−3.85271			−0.408387			−0.204193	+	0.978931i	$0.565457\pi$
$90$	−0.348786	+	0.884400i	−0.0367653	+	0.0932240i
$91$	−9.60950	−	2.17582i	−1.00735	−	0.228087i
$92$	5.81230	−	9.87455i	0.605974	−	1.02949i
$93$	13.7299	−	12.3013i	1.42372	−	1.27559i
$94$	−2.76033	+	10.1312i	−0.284706	+	1.04495i
$95$	0.619043	+	0.357405i	0.0635125	+	0.0366690i
$96$	8.83207	−	4.24200i	0.901419	−	0.432947i
$97$	15.5292	−	8.96577i	1.57675	−	0.910336i	0.581439	−	0.813590i	$-0.302490\pi$
$97$	15.5292	−	8.96577i	1.57675	−	0.910336i	0.995309	−	0.0967455i	$-0.0308433\pi$
$98$	9.72554	+	1.84765i	0.982428	+	0.186641i
$99$	0.659514	−	5.99084i	0.0662837	−	0.602102i
$100$	8.61459	−	4.87754i	0.861459	−	0.487754i
$101$	12.8320	−	7.40857i	1.27683	−	0.737180i	0.300569	−	0.953760i	$-0.402823\pi$
$101$	12.8320	−	7.40857i	1.27683	−	0.737180i	0.976265	+	0.216580i	$0.0694901\pi$
$102$	9.86321	−	4.94302i	0.976604	−	0.489432i
$103$	1.35694	+	0.783432i	0.133704	+	0.0771939i	0.565360	−	0.824844i	$-0.308737\pi$
$103$	1.35694	+	0.783432i	0.133704	+	0.0771939i	−0.431656	+	0.902038i	$0.642071\pi$
$104$	−2.59764	−	10.2077i	−0.254720	−	1.00095i
$105$	−0.881125	−	0.527324i	−0.0859890	−	0.0514615i
$106$	−3.20544	−	3.23250i	−0.311340	−	0.313968i
$107$	−3.88615			−0.375688			−0.187844	−	0.982199i	$-0.560150\pi$
$107$	−3.88615			−0.375688			−0.187844	+	0.982199i	$0.560150\pi$
$108$	−5.97489	−	8.50298i	−0.574934	−	0.818200i
$109$		−	0.989706i		−	0.0947966i	−0.998876	−	0.0473983i	$-0.984907\pi$
$109$		−	0.989706i		−	0.0947966i	0.998876	−	0.0473983i	$-0.0150930\pi$
$110$	0.452068	−	0.448284i	0.0431030	−	0.0427422i
$111$	−12.4981	−	4.09493i	−1.18626	−	0.388673i
$112$	2.96652	+	10.1587i	0.280310	+	0.959910i
$113$	2.54716	+	1.47060i	0.239617	+	0.138343i	0.615000	−	0.788527i	$-0.289156\pi$
$113$	2.54716	+	1.47060i	0.239617	+	0.138343i	−0.375384	+	0.926869i	$0.622489\pi$
$114$	−6.98564	+	3.50090i	−0.654265	+	0.327890i
$115$	−0.641887	−	1.11178i	−0.0598563	−	0.103674i
$116$	10.4960	−	5.94277i	0.974526	−	0.551772i
$117$	−10.2284	+	4.49372i	−0.945612	+	0.415445i
$118$	−3.64011	−	13.8171i	−0.335099	−	1.27197i
$119$	3.53215	+	11.3810i	0.323791	+	1.04329i
$120$	0.0739690	−	1.09527i	0.00675241	−	0.0999840i
$121$	3.48194	−	6.03089i	0.316540	−	0.548263i
$122$	0.140703	−	0.516420i	0.0127387	−	0.0467545i
$123$	12.6480	+	14.1168i	1.14043	+	1.27287i
$124$	−10.7978	+	18.3444i	−0.969668	+	1.64738i
$125$		−	2.22955i		−	0.199417i
$126$	10.1130	−	4.87116i	0.900933	−	0.433957i
$127$	6.11690			0.542787			0.271394	−	0.962468i	$-0.412515\pi$
$127$	6.11690			0.542787			0.271394	+	0.962468i	$0.412515\pi$
$128$	−8.23188	+	7.76119i	−0.727603	+	0.685999i
$129$	1.81063	+	8.62272i	0.159417	+	0.759188i
$130$	−1.13862	−	0.310227i	−0.0998633	−	0.0272087i
$131$	3.42788	+	1.97909i	0.299496	+	0.172914i	0.642216	−	0.766523i	$-0.278015\pi$
$131$	3.42788	+	1.97909i	0.299496	+	0.172914i	−0.342721	+	0.939437i	$0.611348\pi$
$132$	1.37287	+	6.82266i	0.119493	+	0.593837i
$133$	−2.50165	−	8.06059i	−0.216920	−	0.698942i
$134$	−2.97010	−	11.2739i	−0.256577	−	0.973915i
$135$	−1.15884	+	0.113149i	−0.0997375	+	0.00973832i
$136$	−9.12088	+	8.89371i	−0.782109	+	0.762629i
$137$	4.66326	−	2.69233i	0.398409	−	0.230022i	−0.287388	−	0.957814i	$-0.592787\pi$
$137$	4.66326	−	2.69233i	0.398409	−	0.230022i	0.685797	+	0.727793i	$0.259454\pi$
$138$	14.0089	+	0.827851i	1.19252	+	0.0704714i
$139$	7.83653	−	13.5733i	0.664686	−	1.15127i	−0.314684	−	0.949196i	$-0.601899\pi$
$139$	7.83653	−	13.5733i	0.664686	−	1.15127i	0.979370	−	0.202074i	$-0.0647681\pi$
$140$	1.15421	+	0.271559i	0.0975482	+	0.0229509i
$141$	−12.5859	+	2.64283i	−1.05992	+	0.222567i
$142$	3.62516	−	3.59481i	0.304217	−	0.301670i
$143$	7.48154			0.625638
$144$	9.55259	+	7.26278i	0.796049	+	0.605232i
$145$		−	1.35138i		−	0.112226i
$146$	−7.30777	+	7.24659i	−0.604795	+	0.599732i
$147$	3.41162	+	11.6345i	0.281386	+	0.959595i
$148$	15.1859	+	0.127663i	1.24827	+	0.0104938i
$149$	6.11071	−	10.5841i	0.500609	−	0.867080i	−0.499391	−	0.866377i	$-0.666443\pi$
$149$	6.11071	−	10.5841i	0.500609	−	0.867080i	1.00000		0.000703058i	$-0.000223790\pi$
$150$	10.1242	+	6.67109i	0.826636	+	0.544692i
$151$	4.94695	+	8.56836i	0.402577	+	0.697283i	0.994036	−	0.109051i	$-0.0347813\pi$
$151$	4.94695	+	8.56836i	0.402577	+	0.697283i	−0.591459	+	0.806335i	$0.701448\pi$
$152$	6.45988	−	6.29899i	0.523966	−	0.510915i
$153$	10.8922	+	7.99591i	0.880582	+	0.646431i
$154$	−7.51245	+	0.262497i	−0.605370	+	0.0211526i
$155$	1.19246	+	2.06541i	0.0957809	+	0.165897i
$156$	9.68003	−	8.52726i	0.775023	−	0.682727i
$157$	−3.25505	+	5.63792i	−0.259781	+	0.449955i	−0.966183	−	0.257856i	$-0.916984\pi$
$157$	−3.25505	+	5.63792i	−0.259781	+	0.449955i	0.706402	+	0.707811i	$0.250317\pi$
$158$	−2.63422	+	9.66829i	−0.209567	+	0.769168i
$159$	1.73597	−	5.29832i	0.137671	−	0.420184i
$160$	0.302274	+	1.23102i	0.0238968	+	0.0973208i
$161$	−3.34733	+	14.7835i	−0.263807	+	1.16510i
$162$	5.93717	−	11.2583i	0.466468	−	0.884538i
$163$			12.3947i			0.970829i	0.874284	+	0.485414i	$0.161331\pi$
$163$			12.3947i			0.970829i	−0.874284	+	0.485414i	$0.838669\pi$
$164$	−18.8614	−	11.1021i	−1.47283	−	0.866926i
$165$	0.740976	+	0.242777i	0.0576849	+	0.0189002i
$166$	−12.6370	−	3.44307i	−0.980821	−	0.267234i
$167$	3.46690	−	6.00485i	0.268277	−	0.464669i	−0.700140	−	0.714005i	$-0.746879\pi$
$167$	3.46690	−	6.00485i	0.268277	−	0.464669i	0.968417	+	0.249336i	$0.0802125\pi$
$168$	−9.42084	+	8.90212i	−0.726833	+	0.686814i
$169$	−0.434048	−	0.751793i	−0.0333883	−	0.0578302i
$170$	0.363616	+	1.38021i	0.0278881	+	0.105858i
$171$	−7.71442	−	5.66312i	−0.589936	−	0.433070i
$172$	−5.01266	−	8.85323i	−0.382211	−	0.675052i
$173$	−10.4873	+	6.05484i	−0.797334	+	0.460341i	−0.842538	−	0.538637i	$-0.818939\pi$
$173$	−10.4873	+	6.05484i	−0.797334	+	0.460341i	0.0452043	+	0.998978i	$0.485606\pi$
$174$	12.3352	+	8.12801i	0.935132	+	0.616183i
$175$	−8.89085	+	9.61538i	−0.672085	+	0.726855i
$176$	−3.90045	−	7.02599i	−0.294008	−	0.529604i
$177$	13.0337	−	11.6776i	0.979675	−	0.877744i
$178$	3.83649	+	3.86887i	0.287557	+	0.289984i
$179$	9.28719			0.694157			0.347079	−	0.937836i	$-0.387174\pi$
$179$	9.28719			0.694157			0.347079	+	0.937836i	$0.387174\pi$
$180$	1.23543	−	0.530427i	0.0920833	−	0.0395357i
$181$	6.13624			0.456103			0.228052	−	0.973649i	$-0.426765\pi$
$181$	6.13624			0.456103			0.228052	+	0.973649i	$0.426765\pi$
$182$	7.38408	+	11.8165i	0.547345	+	0.875894i
$183$	0.641547	−	0.134714i	0.0474245	−	0.00995838i
$184$	−15.7038	+	3.99628i	−1.15770	+	0.294610i
$185$	0.850744	−	1.47353i	0.0625479	−	0.108336i
$186$	−26.0249	−	1.53794i	−1.90824	−	0.112767i
$187$	−4.52430	−	7.83632i	−0.330849	−	0.573048i
$188$	12.9223	−	7.31658i	0.942459	−	0.533616i
$189$	10.9532	+	8.30829i	0.796727	+	0.604340i
$190$	−0.257532	−	0.977539i	−0.0186833	−	0.0709182i
$191$	18.7449	−	10.8224i	1.35634	−	0.783081i	0.367208	−	0.930139i	$-0.380314\pi$
$191$	18.7449	−	10.8224i	1.35634	−	0.783081i	0.989128	+	0.147058i	$0.0469805\pi$
$192$	−13.0547	−	4.64498i	−0.942139	−	0.335223i
$193$	−2.30173	+	3.98672i	−0.165682	+	0.286970i	−0.936897	−	0.349605i	$-0.886316\pi$
$193$	−2.30173	+	3.98672i	−0.165682	+	0.286970i	0.771215	+	0.636575i	$0.219649\pi$
$194$	−24.4671	−	6.66630i	−1.75664	−	0.478612i
$195$	−0.297022	−	1.41450i	−0.0212702	−	0.101294i
$196$	−7.82918	−	11.6062i	−0.559227	−	0.829014i
$197$	−12.6570			−0.901777			−0.450889	−	0.892580i	$-0.648893\pi$
$197$	−12.6570			−0.901777			−0.450889	+	0.892580i	$0.648893\pi$
$198$	−6.67271	+	5.30333i	−0.474209	+	0.376891i
$199$			15.4636i			1.09619i	0.836417	+	0.548094i	$0.184646\pi$
$199$			15.4636i			1.09619i	−0.836417	+	0.548094i	$0.815354\pi$
$200$	−13.4763	−	3.79373i	−0.952919	−	0.268257i
$201$	10.6347	−	9.52819i	0.750113	−	0.672066i
$202$	−20.2176	−	5.50848i	−1.42251	−	0.387575i
$203$	−10.8326	+	11.7153i	−0.760297	+	0.822254i
$204$	−14.7854	−	4.98239i	−1.03519	−	0.348837i
$205$	−2.12361	+	1.22607i	−0.148320	+	0.0856324i
$206$	−0.564511	−	2.14277i	−0.0393313	−	0.149294i
$207$	6.91326	+	15.7356i	0.480505	+	1.09370i
$208$	−7.66381	+	12.7732i	−0.531389	+	0.885665i
$209$	3.20434	+	5.55009i	0.221649	+	0.383908i
$210$	0.347878	+	1.40992i	0.0240059	+	0.0972940i
$211$	−11.4454	−	6.60799i	−0.787932	−	0.454913i	0.0513022	−	0.998683i	$-0.483663\pi$
$211$	−11.4454	−	6.60799i	−0.787932	−	0.454913i	−0.839234	+	0.543771i	$0.816996\pi$
$212$	−0.0541202	+	6.43776i	−0.00371699	+	0.442148i
$213$	5.94193	+	1.94684i	0.407134	+	0.133395i
$214$	3.86978	+	3.90245i	0.264533	+	0.266766i
$215$	−1.13987			−0.0777388
$216$	−2.58893	+	14.4671i	−0.176154	+	0.984363i
$217$	6.21849	−	27.4640i	0.422139	−	1.86438i
$218$	−0.993857	+	0.985537i	−0.0673125	+	0.0667490i
$219$	−11.9780	−	3.92454i	−0.809400	−	0.265196i
$220$	−0.900328	−	0.00756876i	−0.0607001	−	0.000510286i
$221$	−8.38643	+	14.5257i	−0.564133	+	0.977106i
$222$	8.33333	+	16.6282i	0.559296	+	1.11601i
$223$	−8.18863	+	4.72770i	−0.548351	+	0.316591i	−0.748457	−	0.663184i	$-0.769205\pi$
$223$	−8.18863	+	4.72770i	−0.548351	+	0.316591i	0.200106	+	0.979774i	$0.435871\pi$
$224$	7.24731	−	13.0949i	0.484231	−	0.874940i
$225$	−1.62491	+	14.7602i	−0.108327	+	0.984013i
$226$	−1.05966	−	4.02225i	−0.0704875	−	0.267556i
$227$	8.98099	−	5.18517i	0.596089	−	0.344152i	−0.171412	−	0.985199i	$-0.554833\pi$
$227$	8.98099	−	5.18517i	0.596089	−	0.344152i	0.767501	+	0.641047i	$0.221500\pi$
$228$	10.4718	+	3.52878i	0.693512	+	0.233699i
$229$	12.7073	−	22.0098i	0.839725	−	1.45445i	−0.0503992	−	0.998729i	$-0.516049\pi$
$229$	12.7073	−	22.0098i	0.839725	−	1.45445i	0.890124	−	0.455718i	$-0.150617\pi$
$230$	−0.477261	+	1.75168i	−0.0314697	+	0.115502i
$231$	−4.47755	−	8.04427i	−0.294601	−	0.529274i
$232$	−16.4195	−	4.62225i	−1.07799	−	0.303466i
$233$		−	2.64486i		−	0.173270i	−0.996240	−	0.0866352i	$-0.972389\pi$
$233$		−	2.64486i		−	0.173270i	0.996240	−	0.0866352i	$-0.0276115\pi$
$234$	14.6978	+	5.79647i	0.960828	+	0.378927i
$235$		−	1.66378i		−	0.108533i
$236$	−10.2503	+	17.4143i	−0.667237	+	1.13357i
$237$	−12.0109	+	2.52209i	−0.780191	+	0.163827i
$238$	7.91143	−	14.8800i	0.512822	−	0.964526i
$239$	−5.97586	−	3.45017i	−0.386547	−	0.223173i	0.294116	−	0.955770i	$-0.404975\pi$
$239$	−5.97586	−	3.45017i	−0.386547	−	0.223173i	−0.680663	+	0.732597i	$0.738308\pi$
$240$	−1.17352	+	1.01638i	−0.0757505	+	0.0656069i
$241$	0.525473	−	0.303382i	0.0338487	−	0.0195426i	−0.482980	−	0.875631i	$-0.660446\pi$
$241$	0.525473	−	0.303382i	0.0338487	−	0.0195426i	0.516829	+	0.856089i	$0.327112\pi$
$242$	−9.52346	+	2.50895i	−0.612191	+	0.161281i
$243$	15.5873	+	0.191961i	0.999924	+	0.0123143i
$244$	−0.658697	+	0.372951i	−0.0421688	+	0.0238758i
$245$	−1.56376	+	0.122632i	−0.0999050	+	0.00783469i
$246$	1.58128	−	26.7584i	0.100819	−	1.70605i
$247$	5.93971	−	10.2879i	0.377935	−	0.654602i
$248$	29.1736	−	7.42407i	1.85253	−	0.471429i
$249$	−3.29651	−	15.6989i	−0.208908	−	0.994878i
$250$	−2.23890	+	2.22016i	−0.141601	+	0.140415i
$251$			25.2201i			1.59188i	0.605377	+	0.795939i	$0.293022\pi$
$251$			25.2201i			1.59188i	−0.605377	+	0.795939i	$0.706978\pi$
$252$	−14.9619	−	5.30473i	−0.942514	−	0.334167i
$253$		−	11.5098i		−	0.723615i
$254$	−6.09114	−	6.14256i	−0.382192	−	0.385418i
$255$	−1.30196	+	1.16650i	−0.0815318	+	0.0730488i
$256$	15.9910	+	0.537913i	0.999435	+	0.0336196i
$257$	−10.6733	+	18.4867i	−0.665782	+	1.15317i	0.313290	+	0.949657i	$0.398569\pi$
$257$	−10.6733	+	18.4867i	−0.665782	+	1.15317i	−0.979073	+	0.203511i	$0.934765\pi$
$258$	6.85589	−	10.4046i	0.426829	−	0.647764i
$259$	−19.1869	+	5.95477i	−1.19222	+	0.370011i
$260$	0.822293	+	1.45231i	0.0509964	+	0.0900686i
$261$	−1.97978	+	17.9837i	−0.122545	+	1.11316i
$262$	−1.42606	−	5.41302i	−0.0881020	−	0.334417i
$263$	−8.89018	+	5.13274i	−0.548192	+	0.316499i	−0.748392	−	0.663256i	$-0.769174\pi$
$263$	−8.89018	+	5.13274i	−0.548192	+	0.316499i	0.200201	+	0.979755i	$0.435841\pi$
$264$	5.48420	−	8.17255i	0.337529	−	0.502986i
$265$	0.624676	+	0.360657i	0.0383735	+	0.0221550i
$266$	−5.60329	+	10.5388i	−0.343560	+	0.646174i
$267$	−2.07772	+	6.34139i	−0.127155	+	0.388087i
$268$	−8.36358	+	14.2089i	−0.510887	+	0.867950i
$269$		−	1.37215i		−	0.0836615i	−0.999125	−	0.0418308i	$-0.986681\pi$
$269$		−	1.37215i		−	0.0836615i	0.999125	−	0.0418308i	$-0.0133190\pi$
$270$	1.26759	+	1.05103i	0.0771429	+	0.0639638i
$271$			15.8831i			0.964828i	0.875943	+	0.482414i	$0.160240\pi$
$271$			15.8831i			0.964828i	−0.875943	+	0.482414i	$0.839760\pi$
$272$	18.0135	+	0.302888i	1.09223	+	0.0183653i
$273$	−8.76359	+	14.6434i	−0.530396	+	0.886260i
$274$	−7.34724	−	2.00182i	−0.443863	−	0.120935i
$275$	4.97209	−	8.61191i	0.299828	−	0.519318i
$276$	−13.1186	−	14.8920i	−0.789645	−	0.896394i
$277$	−21.9652	+	12.6816i	−1.31976	+	0.761963i	−0.983690	−	0.179874i	$-0.942431\pi$
$277$	−21.9652	+	12.6816i	−1.31976	+	0.761963i	−0.336070	+	0.941837i	$0.609098\pi$
$278$	−21.4337	+	5.64670i	−1.28551	+	0.338667i
$279$	−12.8431	−	29.2327i	−0.768894	−	1.75012i
$280$	−0.876646	−	1.42946i	−0.0523896	−	0.0854267i
$281$	9.19271	−	5.30741i	0.548391	−	0.316614i	−0.200082	−	0.979779i	$-0.564121\pi$
$281$	9.19271	−	5.30741i	0.548391	−	0.316614i	0.748473	+	0.663165i	$0.230787\pi$
$282$	15.1868	+	10.0070i	0.904361	+	0.595908i
$283$	−10.4056	+	18.0230i	−0.618546	+	1.07135i	0.371205	+	0.928551i	$0.378945\pi$
$283$	−10.4056	+	18.0230i	−0.618546	+	1.07135i	−0.989751	+	0.142803i	$0.954389\pi$
$284$	−7.21978	−	0.0606944i	−0.428415	−	0.00360155i
$285$	0.922115	−	0.826173i	0.0546214	−	0.0489383i
$286$	−7.45002	−	7.51292i	−0.440529	−	0.444248i
$287$	28.2380	+	6.39374i	1.66684	+	0.377410i
$288$	−2.21911	−	16.8248i	−0.130762	−	0.991414i
$289$	3.28606			0.193298
$290$	−1.35705	+	1.34569i	−0.0796887	+	0.0790216i
$291$	−6.38255	−	30.3954i	−0.374152	−	1.78181i
$292$	14.5540	+	0.122351i	0.851707	+	0.00716002i
$293$	14.5206	+	8.38348i	0.848303	+	0.489768i	0.860078	−	0.510162i	$-0.170415\pi$
$293$	14.5206	+	8.38348i	0.848303	+	0.489768i	−0.0117746	+	0.999931i	$0.503748\pi$
$294$	8.28602	−	15.0114i	0.483250	−	0.875482i
$295$	1.13200	+	1.96069i	0.0659077	+	0.114156i
$296$	−14.9937	−	15.3767i	−0.871492	−	0.893752i
$297$	−9.50499	−	4.31632i	−0.551535	−	0.250459i
$298$	−16.7134	+	4.40314i	−0.968182	+	0.255067i
$299$	−18.4767	+	10.6675i	−1.06853	+	0.616919i
$300$	−3.38246	−	16.8096i	−0.195287	−	0.970505i
$301$	9.88174	+	9.13714i	0.569574	+	0.526656i
$302$	3.67819	−	13.5000i	0.211656	−	0.776836i
$303$	−5.27401	−	25.1163i	−0.302984	−	1.44289i
$304$	−12.7581	−	0.214521i	−0.731726	−	0.0123036i
$305$			0.0848089i			0.00485614i
$306$	−2.81687	−	18.9001i	−0.161029	−	1.08045i
$307$	−0.789650			−0.0450677			−0.0225339	−	0.999746i	$-0.507173\pi$
$307$	−0.789650			−0.0450677			−0.0225339	+	0.999746i	$0.507173\pi$
$308$	7.74440	+	7.28257i	0.441278	+	0.414963i
$309$	2.02128	−	1.81097i	0.114987	−	0.103023i
$310$	0.886629	−	3.25417i	0.0503572	−	0.184825i
$311$	13.1909	−	22.8473i	0.747986	−	1.29555i	−0.200800	−	0.979632i	$-0.564354\pi$
$311$	13.1909	−	22.8473i	0.747986	−	1.29555i	0.948786	−	0.315918i	$-0.102313\pi$
$312$	−18.2023	−	1.22929i	−1.03050	−	0.0695948i
$313$	−22.9717	+	13.2627i	−1.29844	+	0.749653i	−0.980134	−	0.198337i	$-0.936446\pi$
$313$	−22.9717	+	13.2627i	−1.29844	+	0.749653i	−0.318302	+	0.947989i	$0.603113\pi$
$314$	8.90291	−	2.34546i	0.502420	−	0.132362i
$315$	−1.34313	+	1.16591i	−0.0756769	+	0.0656917i
$316$	12.3320	−	6.98230i	0.693727	−	0.392785i
$317$	14.4111	+	24.9608i	0.809409	+	1.40194i	0.913274	+	0.407346i	$0.133546\pi$
$317$	14.4111	+	24.9608i	0.809409	+	1.40194i	−0.103864	+	0.994591i	$0.533121\pi$
$318$	−7.04920	+	3.53276i	−0.395300	+	0.198107i
$319$	6.05796	−	10.4927i	0.339181	−	0.587479i
$320$	0.935185	−	1.52938i	0.0522784	−	0.0854948i
$321$	−2.09576	+	6.39643i	−0.116974	+	0.357014i
$322$	18.1787	−	11.3599i	1.01306	−	0.633061i
$323$	−14.3676			−0.799437
$324$	−17.2177	+	5.24883i	−0.956540	+	0.291602i
$325$	−18.4330			−1.02248
$326$	12.4467	−	12.3425i	0.689359	−	0.683588i
$327$	−1.62901	−	0.533737i	−0.0900845	−	0.0295157i
$328$	7.63330	+	29.9958i	0.421479	+	1.65624i
$329$	−13.3368	+	14.4236i	−0.735279	+	0.795198i
$330$	−0.494060	−	0.985838i	−0.0271971	−	0.0542686i
$331$	12.7196	−	7.34367i	0.699133	−	0.403645i	−0.107891	−	0.994163i	$-0.534410\pi$
$331$	12.7196	−	7.34367i	0.699133	−	0.403645i	0.807024	+	0.590518i	$0.201077\pi$
$332$	9.12626	+	16.1186i	0.500869	+	0.884621i
$333$	−13.4801	+	18.3629i	−0.738707	+	1.00628i
$334$	−9.48233	+	2.49811i	−0.518850	+	0.136691i
$335$	0.923641	+	1.59979i	0.0504639	+	0.0874061i
$336$	18.3206	+	0.595725i	0.999472	+	0.0324994i
$337$	−8.28231	+	14.3454i	−0.451166	+	0.781442i	−0.998459	−	0.0554988i	$-0.982325\pi$
$337$	−8.28231	+	14.3454i	−0.451166	+	0.781442i	0.547293	+	0.836941i	$0.315658\pi$
$338$	−0.322727	+	1.18450i	−0.0175540	+	0.0644280i
$339$	3.79420	−	3.39943i	0.206073	−	0.184632i
$340$	1.02392	−	1.73954i	0.0555298	−	0.0943399i
$341$			21.3823i			1.15791i
$342$	1.99505	+	13.3860i	0.107880	+	0.723834i
$343$	14.5395	+	11.4719i	0.785058	+	0.619422i
$344$	−3.89882	+	13.8496i	−0.210210	+	0.746721i
$345$	−2.17610	+	0.456947i	−0.117158	+	0.0246012i
$346$	16.5233	+	4.50194i	0.888301	+	0.242026i
$347$	14.1179	−	24.4529i	0.757888	−	1.31270i	−0.186038	−	0.982543i	$-0.559565\pi$
$347$	14.1179	−	24.4529i	0.757888	−	1.31270i	0.943926	−	0.330158i	$-0.107102\pi$
$348$	−4.12117	−	20.4808i	−0.220918	−	1.09788i
$349$	−0.485151	−	0.840306i	−0.0259695	−	0.0449806i	0.852749	−	0.522322i	$-0.174934\pi$
$349$	−0.485151	−	0.840306i	−0.0259695	−	0.0449806i	−0.878718	+	0.477341i	$0.841601\pi$
$350$	18.5091	−	0.646737i	0.989354	−	0.0345696i
$351$	1.88042	+	19.2588i	0.100370	+	1.02796i
$352$	−3.17143	+	10.9132i	−0.169038	+	0.581676i
$353$	−7.34447	−	12.7210i	−0.390907	−	0.677070i	0.601663	−	0.798750i	$-0.294505\pi$
$353$	−7.34447	−	12.7210i	−0.390907	−	0.677070i	−0.992569	+	0.121680i	$0.961172\pi$
$354$	−24.7054	−	1.45996i	−1.31308	−	0.0775960i
$355$	−0.404467	+	0.700558i	−0.0214669	+	0.0371817i
$356$	0.0647747	−	7.70516i	0.00343305	−	0.408372i
$357$	20.6374	+	0.323873i	1.09225	+	0.0171412i
$358$	−9.24807	−	9.32614i	−0.488776	−	0.492902i
$359$			0.545972i			0.0288153i	0.999896	+	0.0144076i	$0.00458625\pi$
$359$			0.545972i			0.0288153i	−0.999896	+	0.0144076i	$0.995414\pi$
$360$	−1.76287	−	0.712416i	−0.0929116	−	0.0375476i
$361$	−8.82409			−0.464426
$362$	−6.11040	−	6.16198i	−0.321155	−	0.323866i
$363$	−8.04881	−	8.98350i	−0.422453	−	0.471512i
$364$	4.51304	−	19.1817i	0.236548	−	1.00540i
$365$	0.815344	−	1.41222i	0.0426770	−	0.0739188i
$366$	−0.774125	−	0.510091i	−0.0404641	−	0.0266629i
$367$	5.91301	−	3.41388i	0.308657	−	0.178203i	−0.337669	−	0.941265i	$-0.609638\pi$
$367$	5.91301	−	3.41388i	0.308657	−	0.178203i	0.646325	+	0.763062i	$0.276305\pi$
$368$	19.6507	+	11.7902i	1.02436	+	0.614607i
$369$	30.0565	−	13.2050i	1.56468	−	0.687426i
$370$	−2.32687	+	0.613013i	−0.120968	+	0.0318690i
$371$	−2.52441	−	8.13394i	−0.131061	−	0.422293i
$372$	24.3709	+	27.6656i	1.26357	+	1.43439i
$373$	28.5225	+	16.4675i	1.47684	+	0.852653i	0.999658	−	0.0261520i	$-0.00832538\pi$
$373$	28.5225	+	16.4675i	1.47684	+	0.852653i	0.477181	+	0.878805i	$0.341659\pi$
$374$	−3.36394	+	12.3466i	−0.173945	+	0.638427i
$375$	−3.66974	−	1.20237i	−0.189505	−	0.0620902i
$376$	−20.2152	−	5.69079i	−1.04252	−	0.293480i
$377$	−22.4586			−1.15668
$378$	−2.56391	−	19.2724i	−0.131873	−	0.991267i
$379$			1.43271i			0.0735933i	0.999323	+	0.0367967i	$0.0117154\pi$
$379$			1.43271i			0.0735933i	−0.999323	+	0.0367967i	$0.988285\pi$
$380$	−0.725192	+	1.23203i	−0.0372016	+	0.0632020i
$381$	3.29878	−	10.0681i	0.169001	−	0.515807i
$382$	−29.5338	−	8.04675i	−1.51108	−	0.411707i
$383$	0.0237067	−	0.0410612i	0.00121136	−	0.00209813i	−0.865419	−	0.501049i	$-0.832948\pi$
$383$	0.0237067	−	0.0410612i	0.00121136	−	0.00209813i	0.866630	+	0.498951i	$0.166281\pi$
$384$	8.33521	+	17.7348i	0.425354	+	0.905027i
$385$	1.13754	−	0.353042i	0.0579744	−	0.0179927i
$386$	6.29547	−	1.65854i	0.320431	−	0.0844173i
$387$	15.1691	+	1.66992i	0.771087	+	0.0848867i
$388$	17.6698	+	31.2080i	0.897049	+	1.58434i
$389$	−5.35013	−	9.26669i	−0.271262	−	0.469840i	0.697923	−	0.716173i	$-0.254108\pi$
$389$	−5.35013	−	9.26669i	−0.271262	−	0.469840i	−0.969185	+	0.246333i	$0.920774\pi$
$390$	−1.12466	+	1.70681i	−0.0569495	+	0.0864277i
$391$	22.3468	+	12.9019i	1.13012	+	0.652478i
$392$	−3.85868	+	19.4193i	−0.194893	+	0.980825i
$393$	5.10611	−	4.57484i	0.257569	−	0.230770i
$394$	12.6037	+	12.7101i	0.634967	+	0.640327i
$395$		−	1.58777i		−	0.0798894i
$396$	11.9702	+	1.41970i	0.601524	+	0.0713429i
$397$	10.0443			0.504108			0.252054	−	0.967713i	$-0.418894\pi$
$397$	10.0443			0.504108			0.252054	+	0.967713i	$0.418894\pi$
$398$	15.5285	−	15.3985i	0.778373	−	0.771857i
$399$	−14.6165	−	0.229384i	−0.731739	−	0.0114836i
$400$	9.60991	+	17.3106i	0.480495	+	0.865529i
$401$	−9.24865	−	5.33971i	−0.461855	−	0.266652i	0.250969	−	0.967995i	$-0.419251\pi$
$401$	−9.24865	−	5.33971i	−0.461855	−	0.266652i	−0.712824	+	0.701343i	$0.752584\pi$
$402$	−20.1580	−	1.19123i	−1.00539	−	0.0594133i
$403$	34.3250	−	19.8175i	1.70985	−	0.987182i
$404$	14.6009	+	25.7877i	0.726421	+	1.28299i
$405$	−0.438714	+	1.96843i	−0.0217999	+	0.0978119i
$406$	22.5514	−	0.787981i	1.11921	−	0.0391068i
$407$	13.2111	−	7.62742i	0.654849	−	0.378077i
$408$	9.71986	+	19.8088i	0.481205	+	0.980683i
$409$	−5.10080	−	2.94495i	−0.252218	−	0.145618i	0.368561	−	0.929603i	$-0.379850\pi$
$409$	−5.10080	−	2.94495i	−0.252218	−	0.145618i	−0.620780	+	0.783985i	$0.713184\pi$
$410$	3.34588	+	0.911617i	0.165241	+	0.0450215i
$411$	−1.91662	−	9.12746i	−0.0945398	−	0.450224i
$412$	−1.58962	+	2.70062i	−0.0783151	+	0.133050i
$413$	5.90320	−	26.0715i	0.290477	−	1.28289i
$414$	8.91744	−	22.6116i	0.438268	−	1.11130i
$415$	2.07531			0.101873
$416$	20.4583	−	5.02348i	1.00305	−	0.246297i
$417$	−18.1148	−	20.2185i	−0.887088	−	0.990104i
$418$	2.38252	−	8.74449i	0.116533	−	0.427707i
$419$	14.3453	+	8.28228i	0.700815	+	0.404616i	0.807651	−	0.589661i	$-0.200739\pi$
$419$	14.3453	+	8.28228i	0.700815	+	0.404616i	−0.106836	+	0.994277i	$0.534072\pi$
$420$	1.06942	−	1.75332i	0.0521826	−	0.0855534i
$421$	−31.0738	+	17.9404i	−1.51444	+	0.874364i	−0.514586	+	0.857439i	$0.672054\pi$
$421$	−31.0738	+	17.9404i	−1.51444	+	0.874364i	−0.999857	+	0.0169248i	$0.994612\pi$
$422$	4.76146	+	18.0735i	0.231784	+	0.879806i
$423$	−2.43745	+	22.1411i	−0.118513	+	1.07654i
$424$	6.51866	−	6.35630i	0.316574	−	0.308689i
$425$	11.1469	+	19.3071i	0.540706	+	0.936530i
$426$	−3.96189	−	7.90550i	−0.191954	−	0.383023i
$427$	0.679821	−	0.735220i	0.0328988	−	0.0355798i
$428$	0.0653369	−	7.77203i	0.00315818	−	0.375675i
$429$	4.03471	−	12.3143i	0.194798	−	0.594539i
$430$	1.13507	+	1.14466i	0.0547381	+	0.0552002i
$431$		−	7.54421i		−	0.363392i	−0.983355	−	0.181696i	$-0.941841\pi$
$431$		−	7.54421i		−	0.363392i	0.983355	−	0.181696i	$-0.0581586\pi$
$432$	17.1058	−	11.8064i	0.823004	−	0.568035i
$433$			1.43470i			0.0689471i	0.999406	+	0.0344736i	$0.0109755\pi$
$433$			1.43470i			0.0689471i	−0.999406	+	0.0344736i	$0.989025\pi$
$434$	−33.7715	+	21.1037i	−1.62108	+	1.01301i
$435$	−2.22431	−	0.728785i	−0.106648	−	0.0349426i
$436$	1.97934	+	0.0166397i	0.0947933	+	0.000796896i
$437$	−15.8271	−	9.13780i	−0.757115	−	0.437120i
$438$	7.98657	+	15.9363i	0.381613	+	0.761464i
$439$	1.32217	−	0.763355i	0.0631037	−	0.0364329i	−0.468116	−	0.883667i	$-0.655067\pi$
$439$	1.32217	−	0.763355i	0.0631037	−	0.0364329i	0.531220	+	0.847234i	$0.321734\pi$
$440$	0.888935	+	0.911641i	0.0423783	+	0.0434608i
$441$	20.9897	+	0.658965i	0.999508	+	0.0313793i
$442$	22.9378	−	6.04294i	1.09104	−	0.287433i
$443$	7.02505	+	12.1677i	0.333770	+	0.578107i	0.983248	−	0.182274i	$-0.0583458\pi$
$443$	7.02505	+	12.1677i	0.333770	+	0.578107i	−0.649478	+	0.760381i	$0.725012\pi$
$444$	8.39970	−	24.9264i	0.398632	−	1.18296i
$445$	−0.747655	−	0.431659i	−0.0354422	−	0.0204626i
$446$	12.9017	+	3.51518i	0.610912	+	0.166449i
$447$	−14.1254	−	15.7658i	−0.668111	−	0.745697i
$448$	−20.3666	+	5.76204i	−0.962232	+	0.272231i
$449$			33.6622i			1.58862i	0.607516	+	0.794308i	$0.292166\pi$
$449$			33.6622i			1.58862i	−0.607516	+	0.794308i	$0.707834\pi$
$450$	16.4402	−	13.0663i	0.774997	−	0.615951i
$451$	−21.9849			−1.03523
$452$	−2.98393	+	5.06941i	−0.140352	+	0.238445i
$453$	16.7710	−	3.52163i	0.787969	−	0.165461i
$454$	−14.1501	−	3.85532i	−0.664096	−	0.180939i
$455$	−1.62103	−	1.49889i	−0.0759952	−	0.0702689i
$456$	−6.88411	−	14.0296i	−0.322378	−	0.656998i
$457$	−14.9039	−	25.8143i	−0.697175	−	1.20754i	−0.969442	−	0.245321i	$-0.921107\pi$
$457$	−14.9039	−	25.8143i	−0.697175	−	1.20754i	0.272267	−	0.962222i	$-0.412227\pi$
$458$	−34.7559	+	9.15642i	−1.62404	+	0.427851i
$459$	19.0350	−	13.6160i	0.888475	−	0.635539i
$460$	2.23428	−	1.26504i	0.104174	−	0.0589827i
$461$	−5.83258	+	3.36744i	−0.271650	+	0.156837i	−0.629637	−	0.776889i	$-0.716797\pi$
$461$	−5.83258	+	3.36744i	−0.271650	+	0.156837i	0.357987	+	0.933727i	$0.383463\pi$
$462$	−3.61932	+	12.5067i	−0.168386	+	0.581865i
$463$	−4.34234	+	7.52115i	−0.201805	+	0.349537i	−0.949110	−	0.314944i	$-0.898014\pi$
$463$	−4.34234	+	7.52115i	−0.201805	+	0.349537i	0.747305	+	0.664481i	$0.231348\pi$
$464$	11.7087	+	21.0911i	0.543560	+	0.979130i
$465$	4.04265	−	0.848890i	0.187473	−	0.0393663i
$466$	−2.65595	+	2.63372i	−0.123035	+	0.122005i
$467$		−	11.8122i		−	0.546602i	−0.961929	−	0.273301i	$-0.911884\pi$
$467$		−	11.8122i		−	0.546602i	0.961929	−	0.273301i	$-0.0881156\pi$
$468$	−8.81516	−	20.5315i	−0.407481	−	0.949071i
$469$	4.81663	−	21.2727i	0.222411	−	0.982281i
$470$	−1.67076	+	1.65678i	−0.0770666	+	0.0764214i
$471$	7.52434	+	8.39813i	0.346703	+	0.386966i
$472$	27.6945	−	7.04766i	1.27474	−	0.324395i
$473$	−8.85047	−	5.10982i	−0.406945	−	0.234950i
$474$	14.4930	+	9.54980i	0.665684	+	0.438637i
$475$	−7.89484	−	13.6743i	−0.362240	−	0.627418i
$476$	−22.8205	+	6.87270i	−1.04598	+	0.315009i
$477$	−7.78461	−	5.71465i	−0.356433	−	0.261656i
$478$	2.48606	+	9.43656i	0.113710	+	0.431618i
$479$	−10.7923	−	18.6929i	−0.493115	−	0.854100i	0.506854	−	0.862032i	$-0.330808\pi$
$479$	−10.7923	−	18.6929i	−0.493115	−	0.854100i	−0.999969	+	0.00793209i	$0.997475\pi$
$480$	2.18922	+	0.166347i	0.0999237	+	0.00759268i
$481$	−24.4886	−	14.1385i	−1.11658	−	0.644660i
$482$	−0.827915	−	0.225573i	−0.0377105	−	0.0102746i
$483$	22.5278	+	13.4821i	1.02505	+	0.613458i
$484$	12.0028	+	7.06502i	0.545583	+	0.321137i
$485$	4.01810			0.182453
$486$	−15.3289	−	15.8438i	−0.695331	−	0.718690i
$487$	−11.3462			−0.514146			−0.257073	−	0.966392i	$-0.582758\pi$
$487$	−11.3462			−0.514146			−0.257073	+	0.966392i	$0.582758\pi$
$488$	1.03044	+	0.290079i	0.0466457	+	0.0131313i
$489$	20.4011	+	6.68433i	0.922571	+	0.302276i
$490$	1.68032	+	1.44820i	0.0759092	+	0.0654232i
$491$	15.8498	−	27.4527i	0.715293	−	1.23892i	−0.247553	−	0.968874i	$-0.579626\pi$
$491$	15.8498	−	27.4527i	0.715293	−	1.23892i	0.962846	−	0.270050i	$-0.0870403\pi$
$492$	−28.4452	+	25.0578i	−1.28241	+	1.12969i
$493$	13.5814	+	23.5236i	0.611674	+	1.05945i
$494$	−16.2457	+	4.27992i	−0.730929	+	0.192563i
$495$	0.799200	−	1.08869i	0.0359214	−	0.0489328i
$496$	−36.5060	−	21.9032i	−1.63917	−	0.983482i
$497$	9.12200	−	2.83106i	0.409177	−	0.126990i
$498$	−12.4821	+	18.9431i	−0.559337	+	0.848862i
$499$	−32.0295	−	18.4922i	−1.43384	−	0.827826i	−0.436426	−	0.899740i	$-0.643756\pi$
$499$	−32.0295	−	18.4922i	−1.43384	−	0.827826i	−0.997411	+	0.0719145i	$0.977089\pi$
$500$	4.45895	+	0.0374849i	0.199410	+	0.00167638i
$501$	−8.01405	−	8.94471i	−0.358041	−	0.399620i
$502$	25.3259	−	25.1139i	1.13035	−	1.12089i
$503$	12.0741			0.538359			0.269180	−	0.963090i	$-0.413247\pi$
$503$	12.0741			0.538359			0.269180	+	0.963090i	$0.413247\pi$
$504$	9.57194	+	20.3071i	0.426368	+	0.904550i
$505$	3.32023			0.147748
$506$	−11.5581	+	11.4613i	−0.513819	+	0.509518i
$507$	−1.47149	+	0.308990i	−0.0653514	+	0.0137227i
$508$	−0.102842	+	12.2334i	−0.00456287	+	0.542768i
$509$	−21.0323	−	12.1430i	−0.932239	−	0.538229i	−0.0447202	−	0.999000i	$-0.514240\pi$
$509$	−21.0323	−	12.1430i	−0.932239	−	0.538229i	−0.887519	+	0.460771i	$0.847573\pi$
$510$	2.46786	+	0.145838i	0.109279	+	0.00645780i
$511$	−18.3885	+	5.70699i	−0.813461	+	0.252462i
$512$	−15.3834	−	16.5937i	−0.679858	−	0.733344i
$513$	−13.4815	+	9.64353i	−0.595225	+	0.425772i
$514$	29.1926	−	7.69077i	1.28763	−	0.339225i
$515$	0.175552	+	0.304065i	0.00773573	+	0.0133987i
$516$	−17.2753	+	3.47616i	−0.760502	+	0.153030i
$517$	7.45840	−	12.9183i	0.328020	−	0.568148i
$518$	25.0859	+	13.3377i	1.10221	+	0.586026i
$519$	4.31032	+	20.5269i	0.189202	+	0.901031i
$520$	0.639575	−	2.27194i	0.0280472	−	0.0996311i
$521$	9.35023			0.409641			0.204820	−	0.978800i	$-0.434339\pi$
$521$	9.35023			0.409641			0.204820	+	0.978800i	$0.434339\pi$
$522$	20.0306	−	15.9199i	0.876715	−	0.696795i
$523$	25.5387			1.11673			0.558366	−	0.829595i	$-0.311429\pi$
$523$	25.5387			1.11673			0.558366	+	0.829595i	$0.311429\pi$
$524$	−4.01567	+	6.82225i	−0.175425	+	0.298032i
$525$	11.0317	+	19.8194i	0.481465	+	0.864990i
$526$	14.0070	+	3.81634i	0.610734	+	0.166400i
$527$	−41.5146	−	23.9685i	−1.80840	−	1.04408i
$528$	−13.6679	+	2.63093i	−0.594820	+	0.114497i
$529$	4.91120	+	8.50644i	0.213530	+	0.369845i
$530$	−0.259875	−	0.986434i	−0.0112883	−	0.0428479i
$531$	−12.1919	−	27.7505i	−0.529083	−	1.20427i
$532$	16.1627	−	4.86760i	0.700741	−	0.211037i
$533$	20.3760	+	35.2923i	0.882584	+	1.52868i
$534$	8.43697	−	4.22824i	0.365103	−	0.182974i
$535$	−0.754144	−	0.435405i	−0.0326045	−	0.0188242i
$536$	22.5969	−	5.75044i	0.976037	−	0.248381i
$537$	5.00848	−	15.2863i	0.216132	−	0.659652i
$538$	−1.37791	+	1.36637i	−0.0594058	+	0.0589085i
$539$	−12.6914	−	6.05785i	−0.546659	−	0.260930i
$540$	−0.206807	−	2.31951i	−0.00889954	−	0.0998158i
$541$		−	10.6421i		−	0.457539i	−0.973481	−	0.228769i	$-0.926530\pi$
$541$		−	10.6421i		−	0.457539i	0.973481	−	0.228769i	$-0.0734701\pi$
$542$	15.9497	−	15.8162i	0.685098	−	0.679363i
$543$	3.30921	−	10.1000i	0.142012	−	0.433432i
$544$	−17.6334	−	18.3906i	−0.756028	−	0.788492i
$545$	0.110887	−	0.192062i	0.00474987	−	0.00822701i
$546$	23.4315	−	5.78139i	1.00278	−	0.247421i
$547$	37.2026	−	21.4789i	1.59067	−	0.918372i	0.597474	−	0.801888i	$-0.296171\pi$
$547$	37.2026	−	21.4789i	1.59067	−	0.918372i	0.993193	−	0.116484i	$-0.0371623\pi$
$548$	5.30607	+	9.37145i	0.226664	+	0.400329i
$549$	0.124245	−	1.12861i	0.00530266	−	0.0481678i
$550$	−13.5992	+	3.58269i	−0.579871	+	0.152767i
$551$	−9.61902	−	16.6606i	−0.409784	−	0.709767i
$552$	−1.89117	+	28.0029i	−0.0804936	+	1.19188i
$553$	−12.7274	+	13.7646i	−0.541226	+	0.585331i
$554$	34.6074	+	9.42912i	1.47033	+	0.400605i
$555$	−1.96657	−	2.19494i	−0.0834763	−	0.0931702i
$556$	27.0138	+	15.9007i	1.14564	+	0.674341i
$557$	−29.7345			−1.25989			−0.629946	−	0.776639i	$-0.716923\pi$
$557$	−29.7345			−1.25989			−0.629946	+	0.776639i	$0.716923\pi$
$558$	−16.5663	+	42.0065i	−0.701309	+	1.77828i
$559$			18.9436i			0.801228i
$560$	−0.562504	+	2.30376i	−0.0237701	+	0.0973518i
$561$	−15.3381	+	3.22076i	−0.647576	+	0.135980i
$562$	−14.4837	−	3.94621i	−0.610956	−	0.166461i
$563$	−34.0287	−	19.6465i	−1.43414	−	0.828001i	−0.436706	−	0.899604i	$-0.643855\pi$
$563$	−34.0287	−	19.6465i	−1.43414	−	0.828001i	−0.997433	+	0.0716032i	$0.977188\pi$
$564$	−5.07388	−	25.2154i	−0.213649	−	1.06176i
$565$	0.329533	+	0.570768i	0.0138636	+	0.0240124i
$566$	28.4603	−	7.49784i	1.19628	−	0.315158i
$567$	19.5820	−	13.5479i	0.822367	−	0.568957i
$568$	7.12843	+	7.31051i	0.299102	+	0.306742i
$569$	31.1053	−	17.9587i	1.30400	−	0.752867i	0.322916	−	0.946428i	$-0.395337\pi$
$569$	31.1053	−	17.9587i	1.30400	−	0.752867i	0.981088	+	0.193561i	$0.0620037\pi$
$570$	−1.74787	−	0.103290i	−0.0732102	−	0.00432633i
$571$	−18.9149	−	10.9205i	−0.791565	−	0.457010i	0.0489482	−	0.998801i	$-0.484413\pi$
$571$	−18.9149	−	10.9205i	−0.791565	−	0.457010i	−0.840513	+	0.541791i	$0.817746\pi$
$572$	−0.125785	+	14.9625i	−0.00525934	+	0.625615i
$573$	−7.70424	−	36.6897i	−0.321849	−	1.53273i
$574$	−21.6985	−	34.7232i	−0.905677	−	1.44932i
$575$			28.3577i			1.18260i
$576$	−14.6857	+	18.9824i	−0.611903	+	0.790933i
$577$		−	9.91668i		−	0.412837i	−0.978464	−	0.206418i	$-0.933819\pi$
$577$		−	9.91668i		−	0.412837i	0.978464	−	0.206418i	$-0.0661808\pi$
$578$	−3.27222	−	3.29985i	−0.136106	−	0.137255i
$579$	5.32066	+	5.93854i	0.221119	+	0.246797i
$580$	2.70267	+	0.0227204i	0.112222	+	0.000943415i
$581$	−17.9911	−	16.6355i	−0.746398	−	0.690156i
$582$	−24.1673	+	36.6767i	−1.00177	+	1.52030i
$583$	3.23350	+	5.60059i	0.133918	+	0.231953i
$584$	−14.3698	−	14.7369i	−0.594627	−	0.609816i
$585$	−2.48838	−	0.273939i	−0.102882	−	0.0113260i
$586$	−6.04081	−	22.9297i	−0.249544	−	0.947217i
$587$	−20.2319	+	11.6809i	−0.835061	+	0.482123i	−0.855582	−	0.517667i	$-0.826801\pi$
$587$	−20.2319	+	11.6809i	−0.835061	+	0.482123i	0.0205215	+	0.999789i	$0.493467\pi$
$588$	−23.3255	+	6.62739i	−0.961926	+	0.273309i
$589$	29.4028	+	16.9757i	1.21152	+	0.699472i
$590$	0.841675	−	3.08918i	0.0346512	−	0.127179i
$591$	−6.82580	+	20.8329i	−0.280776	+	0.856952i
$592$	−0.510633	+	30.3685i	−0.0209869	+	1.24814i
$593$	26.4683			1.08692			0.543462	−	0.839434i	$-0.317113\pi$
$593$	26.4683			1.08692			0.543462	+	0.839434i	$0.317113\pi$
$594$	5.13052	+	13.8430i	0.210508	+	0.567985i
$595$	−0.589680	+	2.60432i	−0.0241745	+	0.106767i
$596$	21.0646	+	12.3989i	0.862841	+	0.507880i
$597$	25.4525	+	8.33936i	1.04170	+	0.341307i
$598$	29.1111	+	7.93160i	1.19044	+	0.324347i
$599$	9.86453	+	5.69529i	0.403054	+	0.232703i	0.687801	−	0.725899i	$-0.258576\pi$
$599$	9.86453	+	5.69529i	0.403054	+	0.232703i	−0.284747	+	0.958603i	$0.591910\pi$
$600$	−13.5119	+	20.1355i	−0.551622	+	0.822028i
$601$	17.1393	−	9.89538i	0.699127	−	0.403641i	−0.107895	−	0.994162i	$-0.534411\pi$
$601$	17.1393	−	9.89538i	0.699127	−	0.403641i	0.807022	+	0.590521i	$0.201078\pi$
$602$	−0.664653	−	19.0218i	−0.0270892	−	0.775272i
$603$	−9.94780	−	22.6426i	−0.405106	−	0.922080i
$604$	−17.2193	+	9.74949i	−0.700643	+	0.396701i
$605$	1.35140	−	0.780233i	0.0549424	−	0.0317210i
$606$	−19.9698	+	30.3066i	−0.811219	+	1.23112i
$607$	0.432069	+	0.249455i	0.0175371	+	0.0101251i	0.508743	−	0.860918i	$-0.330110\pi$
$607$	0.432069	+	0.249455i	0.0175371	+	0.0101251i	−0.491206	+	0.871044i	$0.663444\pi$
$608$	12.4889	+	13.0252i	0.506493	+	0.528242i
$609$	13.4410	+	24.1478i	0.544657	+	0.978520i
$610$	0.0851646	−	0.0844517i	0.00344821	−	0.00341935i
$611$	−27.6504			−1.11862
$612$	−16.1744	+	21.6492i	−0.653811	+	0.875117i
$613$			9.98361i			0.403234i	0.979464	+	0.201617i	$0.0646197\pi$
$613$			9.98361i			0.403234i	−0.979464	+	0.201617i	$0.935380\pi$
$614$	0.786324	+	0.792962i	0.0317335	+	0.0320013i
$615$	0.872814	+	4.15658i	0.0351952	+	0.167609i
$616$	−0.398670	−	15.0288i	−0.0160629	−	0.605527i
$617$	−36.2651	−	20.9377i	−1.45998	−	0.842919i	−0.460969	−	0.887416i	$-0.652498\pi$
$617$	−36.2651	−	20.9377i	−1.45998	−	0.842919i	−0.999010	+	0.0444967i	$0.985832\pi$
$618$	−3.83133	−	0.226412i	−0.154119	−	0.00910761i
$619$	12.8209	+	22.2065i	0.515317	+	0.892555i	0.999842	+	0.0177777i	$0.00565912\pi$
$619$	12.8209	+	22.2065i	0.515317	+	0.892555i	−0.484525	+	0.874777i	$0.661008\pi$
$620$	−4.15072	+	2.35012i	−0.166697	+	0.0943830i
$621$	29.6283	−	2.89289i	1.18894	−	0.116088i
$622$	−36.0784	+	9.50484i	−1.44661	+	0.381109i
$623$	3.02139	+	9.73525i	0.121049	+	0.390034i
$624$	16.8912	+	19.5027i	0.676188	+	0.780735i
$625$	−12.1247	+	21.0005i	−0.484987	+	0.840022i
$626$	36.1933	+	9.86119i	1.44657	+	0.394132i
$627$	10.8633	−	2.28111i	0.433837	−	0.0910986i
$628$	−11.2207	−	6.60466i	−0.447755	−	0.263555i
$629$			34.1998i			1.36364i
$630$	2.50828	+	0.187764i	0.0999322	+	0.00748068i
$631$	−17.5094			−0.697039			−0.348519	−	0.937302i	$-0.613315\pi$
$631$	−17.5094			−0.697039			−0.348519	+	0.937302i	$0.613315\pi$
$632$	−19.2916	−	5.43080i	−0.767379	−	0.216026i
$633$	−17.0488	+	15.2749i	−0.677629	+	0.607125i
$634$	10.7151	−	39.3272i	0.425550	−	1.56188i
$635$	1.18704	+	0.685339i	0.0471063	+	0.0271968i
$636$	10.5671	+	3.56089i	0.419012	+	0.141199i
$637$	2.03802	+	25.9881i	0.0807495	+	1.02969i
$638$	−16.5692	+	4.36513i	−0.655979	+	0.172817i
$639$	6.40883	−	8.73024i	0.253529	−	0.345363i
$640$	−2.46704	+	0.583829i	−0.0975183	+	0.0230779i
$641$	−23.7236	+	13.6968i	−0.937025	+	0.540991i	−0.889026	−	0.457856i	$-0.848618\pi$
$641$	−23.7236	+	13.6968i	−0.937025	+	0.540991i	−0.0479982	+	0.998847i	$0.515284\pi$
$642$	8.51019	−	4.26494i	0.335870	−	0.168324i
$643$	−16.7696	+	29.0458i	−0.661329	+	1.14546i	0.318937	+	0.947776i	$0.396674\pi$
$643$	−16.7696	+	29.0458i	−0.661329	+	1.14546i	−0.980267	+	0.197680i	$0.936659\pi$
$644$	−29.5097	−	6.94298i	−1.16284	−	0.273592i
$645$	−0.614722	+	1.87618i	−0.0242046	+	0.0738746i
$646$	14.3071	+	14.4279i	0.562906	+	0.567658i
$647$	2.78223			0.109381			0.0546904	−	0.998503i	$-0.482583\pi$
$647$	2.78223			0.109381			0.0546904	+	0.998503i	$0.482583\pi$
$648$	22.4160	+	12.0632i	0.880585	+	0.473888i
$649$			20.2981i			0.796771i
$650$	18.3553	+	18.5103i	0.719955	+	0.726033i
$651$	−41.8509	−	25.0464i	−1.64027	−	0.981645i
$652$	−24.7885	−	0.208389i	−0.970794	−	0.00816115i
$653$	14.3839	−	24.9137i	0.562886	−	0.974948i	−0.434357	−	0.900741i	$-0.643024\pi$
$653$	14.3839	−	24.9137i	0.562886	−	0.974948i	0.997243	−	0.0742068i	$-0.0236425\pi$
$654$	1.08617	+	2.16733i	0.0424728	+	0.0847494i
$655$	0.443475	+	0.768122i	0.0173280	+	0.0300130i
$656$	22.5205	−	37.5348i	0.879277	−	1.46549i
$657$	−12.9192	+	17.5988i	−0.504027	+	0.686595i
$658$	27.7647	−	0.970141i	1.08238	−	0.0378200i
$659$	7.04796	+	12.2074i	0.274549	+	0.475533i	0.970021	−	0.243020i	$-0.0781380\pi$
$659$	7.04796	+	12.2074i	0.274549	+	0.475533i	−0.695472	+	0.718553i	$0.744805\pi$
$660$	−0.497994	+	1.47782i	−0.0193844	+	0.0575240i
$661$	−18.6479	+	32.2991i	−0.725319	+	1.25629i	0.233523	+	0.972351i	$0.424975\pi$
$661$	−18.6479	+	32.2991i	−0.725319	+	1.25629i	−0.958842	+	0.283939i	$0.908359\pi$
$662$	−20.0405	−	5.46022i	−0.778896	−	0.212218i
$663$	19.3860	+	21.6373i	0.752889	+	0.840321i
$664$	7.09836	−	25.2152i	0.275470	−	0.978540i
$665$	0.417642	−	1.84452i	0.0161955	−	0.0715273i
$666$	31.8633	−	4.74889i	1.23468	−	0.184016i
$667$			34.5509i			1.33782i
$668$	11.9510	+	7.03451i	0.462397	+	0.272173i
$669$	3.36556	+	16.0277i	0.130120	+	0.619667i
$670$	0.686753	−	2.52057i	0.0265316	−	0.0973781i
$671$	−0.380181	+	0.658492i	−0.0146767	+	0.0254208i
$672$	−17.6452	−	18.9907i	−0.680679	−	0.732581i
$673$	−5.31532	−	9.20641i	−0.204891	−	0.354881i	0.745207	−	0.666833i	$-0.232351\pi$
$673$	−5.31532	−	9.20641i	−0.204891	−	0.354881i	−0.950098	+	0.311952i	$0.899017\pi$
$674$	22.6530	−	5.96791i	0.872560	−	0.229875i
$675$	23.4183	+	10.6345i	0.901372	+	0.409323i
$676$	1.51083	−	0.855426i	0.0581089	−	0.0329010i
$677$	10.6587	−	6.15378i	0.409646	−	0.236509i	−0.280992	−	0.959710i	$-0.590663\pi$
$677$	10.6587	−	6.15378i	0.409646	−	0.236509i	0.690638	+	0.723201i	$0.257330\pi$
$678$	−7.19191	−	0.425003i	−0.276203	−	0.0163222i
$679$	−34.8335	−	32.2088i	−1.33679	−	1.23606i
$680$	−2.76644	+	0.704002i	−0.106088	+	0.0269972i
$681$	−3.69122	−	17.5786i	−0.141448	−	0.673614i
$682$	21.4719	−	21.2922i	0.822203	−	0.815320i
$683$	30.6662			1.17341			0.586706	−	0.809800i	$-0.300425\pi$
$683$	30.6662			1.17341			0.586706	+	0.809800i	$0.300425\pi$
$684$	11.4555	−	15.3331i	0.438014	−	0.586275i
$685$	1.20660			0.0461017
$686$	−2.95826	−	26.0240i	−0.112947	−	0.993601i
$687$	−29.3742	−	32.7853i	−1.12069	−	1.25084i
$688$	17.7901	−	9.87611i	0.678241	−	0.376523i
$689$	5.99375	−	10.3815i	0.228344	−	0.395503i
$690$	2.62580	+	1.73021i	0.0999626	+	0.0658680i
$691$	10.8266	+	18.7523i	0.411864	+	0.713369i	0.995094	−	0.0989380i	$-0.0315446\pi$
$691$	10.8266	+	18.7523i	0.411864	+	0.713369i	−0.583230	+	0.812307i	$0.698211\pi$
$692$	−11.9329	−	21.0756i	−0.453622	−	0.801175i
$693$	−15.6552	+	3.03166i	−0.594692	+	0.115163i
$694$	−38.6139	+	10.1728i	−1.46576	+	0.386154i
$695$	3.04150	−	1.75601i	0.115371	−	0.0666094i
$696$	−16.4628	+	24.5329i	−0.624022	+	0.929919i
$697$	24.6439	−	42.6846i	0.933456	−	1.61679i
$698$	−0.360723	+	1.32395i	−0.0136536	+	0.0501124i
$699$	−4.35332	−	1.42634i	−0.164658	−	0.0539492i
$700$	−19.0806	−	17.9427i	−0.721179	−	0.678172i
$701$	−21.5501			−0.813936			−0.406968	−	0.913442i	$-0.633414\pi$
$701$	−21.5501			−0.813936			−0.406968	+	0.913442i	$0.633414\pi$
$702$	17.4671	−	21.0660i	0.659254	−	0.795086i
$703$		−	24.2221i		−	0.913554i
$704$	14.1171	−	7.68250i	0.532057	−	0.289545i
$705$	−2.73851	−	0.897260i	−0.103138	−	0.0337928i
$706$	−5.46082	+	20.0427i	−0.205521	+	0.754316i
$707$	−28.7835	−	26.6147i	−1.08252	−	1.00095i
$708$	23.1353	+	26.2629i	0.869477	+	0.987019i
$709$	31.7385	−	18.3242i	1.19197	−	0.688182i	0.233213	−	0.972426i	$-0.425076\pi$
$709$	31.7385	−	18.3242i	1.19197	−	0.688182i	0.958752	+	0.284244i	$0.0917426\pi$
$710$	1.10626	−	0.291443i	0.0415172	−	0.0109377i
$711$	−2.32609	+	21.1295i	−0.0872351	+	0.792419i
$712$	−7.80198	+	7.60766i	−0.292391	+	0.285109i
$713$	−30.4878	−	52.8065i	−1.14178	−	1.97762i
$714$	−20.2252	−	21.0465i	−0.756911	−	0.787644i
$715$	1.45186	+	0.838233i	0.0542965	+	0.0313481i
$716$	−0.156143	+	18.5737i	−0.00583534	+	0.694133i
$717$	−8.90154	+	7.97537i	−0.332434	+	0.297846i
$718$	0.548262	−	0.543672i	0.0204609	−	0.0202897i
$719$	−31.3857			−1.17049			−0.585244	−	0.810857i	$-0.699001\pi$
$719$	−31.3857			−1.17049			−0.585244	+	0.810857i	$0.699001\pi$
$720$	1.04004	+	2.47968i	0.0387602	+	0.0924124i
$721$	0.915472	−	4.04319i	0.0340940	−	0.150576i
$722$	8.78692	+	8.86110i	0.327015	+	0.329776i
$723$	−0.215972	−	1.02852i	−0.00803207	−	0.0382509i
$724$	−0.103167	+	12.2720i	−0.00383417	+	0.456087i
$725$	−14.9256	+	25.8518i	−0.554322	+	0.960113i
$726$	−1.00628	+	17.0282i	−0.0373465	+	0.631977i
$727$	−33.8765	+	19.5586i	−1.25641	+	0.725389i	−0.972375	−	0.233425i	$-0.925007\pi$
$727$	−33.8765	+	19.5586i	−1.25641	+	0.725389i	−0.284035	+	0.958814i	$0.591673\pi$
$728$	−23.7562	+	14.5690i	−0.880464	+	0.539962i
$729$	8.72200	−	25.5524i	0.323037	−	0.946386i
$730$	−2.23005	+	0.587505i	−0.0825378	+	0.0217445i
$731$	19.8419	−	11.4557i	0.733879	−	0.423705i
$732$	0.258633	+	1.28531i	0.00955936	+	0.0475066i
$733$	−8.55944	+	14.8254i	−0.316150	+	0.547588i	−0.979681	−	0.200560i	$-0.935724\pi$
$733$	−8.55944	+	14.8254i	−0.316150	+	0.547588i	0.663531	+	0.748149i	$0.269057\pi$
$734$	−9.31630	−	2.53831i	−0.343871	−	0.0936909i
$735$	−0.641471	+	2.64001i	−0.0236610	+	0.0973784i
$736$	−7.72826	−	31.4737i	−0.284867	−	1.16013i
$737$			16.5620i			0.610068i
$738$	−43.1903	−	17.0332i	−1.58986	−	0.627001i
$739$			6.88141i			0.253137i	0.991958	+	0.126568i	$0.0403963\pi$
$739$			6.88141i			0.253137i	−0.991958	+	0.126568i	$0.959604\pi$
$740$	2.93266	+	1.72620i	0.107807	+	0.0634564i
$741$	−13.7302	−	15.3246i	−0.504390	−	0.562964i
$742$	−5.65427	+	10.6347i	−0.207575	+	0.390411i
$743$	−0.551758	−	0.318558i	−0.0202420	−	0.0116868i	0.489845	−	0.871810i	$-0.337053\pi$
$743$	−0.551758	−	0.318558i	−0.0202420	−	0.0116868i	−0.510087	+	0.860123i	$0.670387\pi$
$744$	3.51331	−	52.0222i	0.128804	−	1.90723i
$745$	2.37168	−	1.36929i	0.0868916	−	0.0501669i
$746$	−11.8658	−	45.0402i	−0.434438	−	1.64904i
$747$	−27.6175	−	3.04033i	−1.01047	−	0.111240i
$748$	15.7481	−	8.91653i	0.575809	−	0.326021i
$749$	3.04761	+	9.81974i	0.111357	+	0.358805i
$750$	2.44687	+	4.88244i	0.0893470	+	0.178282i
$751$	12.9137	−	22.3673i	0.471229	−	0.816193i	−0.528229	−	0.849102i	$-0.677144\pi$
$751$	12.9137	−	22.3673i	0.471229	−	0.816193i	0.999458	+	0.0329091i	$0.0104772\pi$
$752$	14.4154	+	25.9668i	0.525675	+	0.946912i
$753$	41.5111	+	13.6009i	1.51275	+	0.495645i
$754$	22.3640	+	22.5528i	0.814449	+	0.821325i
$755$			2.21703i			0.0806859i
$756$	−16.8002	+	21.7659i	−0.611016	+	0.791618i
$757$		−	25.3146i		−	0.920076i	−0.887899	−	0.460038i	$-0.847836\pi$
$757$		−	25.3146i		−	0.920076i	0.887899	−	0.460038i	$-0.152164\pi$
$758$	1.43872	−	1.42667i	0.0522566	−	0.0518192i
$759$	−18.9446	−	6.20710i	−0.687645	−	0.225303i
$760$	1.95934	−	0.498611i	0.0710727	−	0.0180865i
$761$	17.2664	−	29.9062i	0.625905	−	1.08410i	−0.362460	−	0.931999i	$-0.618063\pi$
$761$	17.2664	−	29.9062i	0.625905	−	1.08410i	0.988365	−	0.152100i	$-0.0486035\pi$
$762$	−13.3953	+	6.71313i	−0.485259	+	0.243191i
$763$	−2.50084	+	0.776150i	−0.0905366	+	0.0280985i
$764$	21.3289	+	37.6705i	0.771651	+	1.36287i
$765$	1.21787	+	2.77204i	0.0440321	+	0.100223i
$766$	−0.0648403	+	0.0170821i	−0.00234277	+	0.000617202i
$767$	32.5846	−	18.8127i	1.17656	−	0.679289i
$768$	9.50912	−	26.0303i	0.343131	−	0.939288i
$769$	23.0382	+	13.3011i	0.830780	+	0.479651i	0.854120	−	0.520077i	$-0.174097\pi$
$769$	23.0382	+	13.3011i	0.830780	+	0.479651i	−0.0233399	+	0.999728i	$0.507430\pi$
$770$	−1.48727	−	0.790756i	−0.0535975	−	0.0284969i
$771$	24.6723	+	27.5374i	0.888551	+	0.991737i
$772$	−7.93445	−	4.67033i	−0.285567	−	0.168089i
$773$		−	50.4085i		−	1.81307i	−0.422132	−	0.906534i	$-0.638718\pi$
$773$		−	50.4085i		−	1.81307i	0.422132	−	0.906534i	$-0.361282\pi$
$774$	−13.4283	−	16.8956i	−0.482669	−	0.607299i
$775$		−	52.6815i		−	1.89237i
$776$	13.7435	−	48.8204i	0.493362	−	1.75255i
$777$	−0.546011	+	34.7922i	−0.0195880	+	1.24816i
$778$	−3.97797	+	14.6002i	−0.142617	+	0.523444i
$779$	−17.4541	+	30.2314i	−0.625359	+	1.08315i
$780$	2.83389	−	0.570242i	0.101470	−	0.0204179i
$781$	−6.28091	+	3.62629i	−0.224749	+	0.129759i
$782$	−9.29661	−	35.2881i	−0.332446	−	1.26190i
$783$	28.5327	+	12.9570i	1.01968	+	0.463047i
$784$	23.3432	−	15.4627i	0.833686	−	0.552239i
$785$	−1.26335	+	0.729393i	−0.0450908	+	0.0260332i
$786$	−9.67864	−	0.571956i	−0.345226	−	0.0204010i
$787$	−25.1352	+	43.5355i	−0.895973	+	1.55187i	−0.0633782	+	0.997990i	$0.520187\pi$
$787$	−25.1352	+	43.5355i	−0.895973	+	1.55187i	−0.832595	+	0.553882i	$0.813146\pi$
$788$	0.212800	−	25.3132i	0.00758068	−	0.901745i
$789$	3.65390	+	17.4009i	0.130082	+	0.619487i
$790$	−1.59443	+	1.58108i	−0.0567273	+	0.0562524i
$791$	1.71846	−	7.58958i	0.0611013	−	0.269854i
$792$	−10.4941	−	13.4341i	−0.372891	−	0.477360i
$793$	1.40944			0.0500506
$794$	−10.0020	−	10.0864i	−0.354957	−	0.357953i
$795$	0.930506	−	0.833690i	0.0330016	−	0.0295680i
$796$	−30.9262	−	0.259986i	−1.09615	−	0.00921497i
$797$	0.211749	+	0.122253i	0.00750053	+	0.00433043i	0.503746	−	0.863852i	$-0.331955\pi$
$797$	0.211749	+	0.122253i	0.00750053	+	0.00433043i	−0.496245	+	0.868182i	$0.665288\pi$
$798$	14.3246	+	14.9062i	0.507084	+	0.527674i
$799$	16.7210	+	28.9616i	0.591547	+	1.02459i
$800$	7.81376	−	26.8879i	0.276258	−	0.950630i
$801$	9.31716	+	6.83968i	0.329206	+	0.241668i
$802$	3.84759	+	14.6047i	0.135863	+	0.515708i
$803$	12.6614	−	7.31003i	0.446809	−	0.257966i
$804$	18.8769	+	21.4288i	0.665737	+	0.755736i
$805$	−2.30593	+	2.49384i	−0.0812733	+	0.0878963i
$806$	−54.0811	−	14.7349i	−1.90492	−	0.519014i
$807$	−2.25850	−	0.739986i	−0.0795029	−	0.0260487i
$808$	11.3565	−	40.3412i	0.399520	−	1.41920i
$809$		−	35.7733i		−	1.25772i	−0.777518	−	0.628861i	$-0.783522\pi$
$809$		−	35.7733i		−	1.25772i	0.777518	−	0.628861i	$-0.216478\pi$
$810$	2.41355	−	1.51958i	0.0848034	−	0.0533926i
$811$	54.5728			1.91631			0.958156	−	0.286248i	$-0.0924082\pi$
$811$	54.5728			1.91631			0.958156	+	0.286248i	$0.0924082\pi$
$812$	−23.2477	−	21.8613i	−0.815834	−	0.767182i
$813$	26.1428	+	8.56556i	0.916869	+	0.300407i
$814$	−20.8148	−	5.67120i	−0.729560	−	0.198775i
$815$	−1.38871	+	2.40531i	−0.0486442	+	0.0842543i
$816$	10.2130	−	29.4860i	0.357527	−	1.03222i
$817$	−14.0531	+	8.11354i	−0.491654	+	0.283857i
$818$	2.12201	+	8.05474i	0.0741945	+	0.281627i
$819$	19.3763	+	22.3215i	0.677063	+	0.779976i
$820$	−2.41635	−	4.26769i	−0.0843825	−	0.149034i
$821$	−18.6433	−	32.2911i	−0.650654	−	1.12697i	−0.982964	−	0.183796i	$-0.941161\pi$
$821$	−18.6433	−	32.2911i	−0.650654	−	1.12697i	0.332310	−	0.943170i	$-0.392172\pi$
$822$	−7.25720	+	11.0137i	−0.253124	+	0.384146i
$823$	−6.44747	+	11.1673i	−0.224745	+	0.389269i	−0.956243	−	0.292574i	$-0.905488\pi$
$823$	−6.44747	+	11.1673i	−0.224745	+	0.389269i	0.731498	+	0.681843i	$0.238821\pi$
$824$	4.29488	−	1.09296i	0.149619	−	0.0380749i
$825$	−11.4934	−	12.8281i	−0.400150	−	0.446619i
$826$	−32.0592	+	20.0337i	−1.11548	+	0.697063i
$827$	−0.191099			−0.00664518			−0.00332259	−	0.999994i	$-0.501058\pi$
$827$	−0.191099			−0.00664518			−0.00332259	+	0.999994i	$0.501058\pi$
$828$	−31.5863	+	13.5615i	−1.09770	+	0.471294i
$829$	4.56157			0.158430			0.0792149	−	0.996858i	$-0.474759\pi$
$829$	4.56157			0.158430			0.0792149	+	0.996858i	$0.474759\pi$
$830$	−2.06656	−	2.08401i	−0.0717315	−	0.0723371i
$831$	9.02777	+	42.9927i	0.313170	+	1.49140i
$832$	−25.4167	−	15.5418i	−0.881166	−	0.538816i
$833$	25.9881	−	17.8504i	0.900433	−	0.618481i
$834$	−2.26475	+	38.3242i	−0.0784220	+	1.32706i
$835$	1.34557	−	0.776864i	0.0465653	−	0.0268845i
$836$	−11.1537	+	6.31515i	−0.385757	+	0.218414i
$837$	−55.0418	+	5.37426i	−1.90252	+	0.185761i
$838$	−5.96788	−	22.6529i	−0.206157	−	0.782531i
$839$	2.15948	+	3.74033i	0.0745535	+	0.129130i	0.900892	−	0.434043i	$-0.142914\pi$
$839$	2.15948	+	3.74033i	0.0745535	+	0.129130i	−0.826339	+	0.563174i	$0.809580\pi$
$840$	−2.82560	+	0.672027i	−0.0974923	+	0.0231871i
$841$	−3.68522	+	6.38299i	−0.127077	+	0.220103i
$842$	48.9586	+	13.3392i	1.68722	+	0.459700i
$843$	−3.77824	−	17.9930i	−0.130129	−	0.619712i
$844$	13.4079	−	22.7788i	0.461520	−	0.784080i
$845$		−	0.194523i		−	0.00669180i
$846$	24.6611	−	19.6002i	0.847867	−	0.673867i
$847$	−17.9698	−	4.06878i	−0.617450	−	0.139805i
$848$	−12.8742	−	0.216473i	−0.442101	−	0.00743371i
$849$	24.0534	+	26.8467i	0.825510	+	0.921375i
$850$	8.28806	−	30.4194i	0.284278	−	1.04338i
$851$	−21.7511	+	37.6739i	−0.745616	+	1.29145i
$852$	−3.99345	+	11.8507i	−0.136813	+	0.405999i
$853$	24.7758	+	42.9129i	0.848307	+	1.46931i	0.882718	+	0.469903i	$0.155711\pi$
$853$	24.7758	+	42.9129i	0.848307	+	1.46931i	−0.0344110	+	0.999408i	$0.510956\pi$
$854$	−1.41526	+	0.0494514i	−0.0484293	+	0.00169219i
$855$	−0.862557	−	1.96331i	−0.0294988	−	0.0671436i
$856$	−7.86969	+	7.67368i	−0.268980	+	0.262281i
$857$	3.31377	+	5.73962i	0.113196	+	0.196062i	0.917057	−	0.398756i	$-0.130558\pi$
$857$	3.31377	+	5.73962i	0.113196	+	0.196062i	−0.803861	+	0.594817i	$0.797224\pi$
$858$	−16.3836	+	8.21077i	−0.559328	+	0.280311i
$859$	17.2058	−	29.8012i	0.587053	−	1.01681i	−0.407563	−	0.913177i	$-0.633621\pi$
$859$	17.2058	−	29.8012i	0.587053	−	1.01681i	0.994616	−	0.103628i	$-0.0330453\pi$
$860$	0.0191644	−	2.27967i	0.000653502	−	0.0777361i
$861$	25.7522	−	43.0304i	0.877634	−	1.46647i
$862$	−7.57585	+	7.51243i	−0.258034	+	0.255874i
$863$			38.3595i			1.30577i	0.757457	+	0.652886i	$0.226442\pi$
$863$			38.3595i			1.30577i	−0.757457	+	0.652886i	$0.773558\pi$
$864$	−28.8897	−	5.42090i	−0.982847	−	0.184423i
$865$	−2.71354			−0.0922631
$866$	1.44071	−	1.42865i	0.0489575	−	0.0485476i
$867$	1.77214	−	5.40871i	0.0601849	−	0.183689i
$868$	54.8215	+	12.8983i	1.86076	+	0.437796i
$869$	7.11765	−	12.3281i	0.241450	−	0.418203i
$870$	1.48310	+	2.95936i	0.0502819	+	0.100332i
$871$	26.5870	−	15.3500i	0.900865	−	0.520115i
$872$	−1.95430	−	2.00421i	−0.0661808	−	0.0678712i
$873$	−53.4716	−	5.88653i	−1.80974	−	0.199229i
$874$	6.58434	+	24.9928i	0.222719	+	0.845395i
$875$	−5.63375	+	1.74847i	−0.190456	+	0.0591089i
$876$	8.05018	−	23.8892i	0.271990	−	0.807142i
$877$	−4.67213	−	2.69746i	−0.157767	−	0.0910866i	0.419038	−	0.907969i	$-0.362367\pi$
$877$	−4.67213	−	2.69746i	−0.157767	−	0.0910866i	−0.576805	+	0.816882i	$0.695701\pi$
$878$	−2.08316	−	0.567576i	−0.0703031	−	0.0191547i
$879$	21.6296	−	19.3792i	0.729550	−	0.653643i
$880$	0.0302740	−	1.80047i	0.00102054	−	0.0606937i
$881$	−45.7067			−1.53990			−0.769949	−	0.638106i	$-0.779718\pi$
$881$	−45.7067			−1.53990			−0.769949	+	0.638106i	$0.779718\pi$
$882$	−20.2395	−	21.7339i	−0.681500	−	0.731818i
$883$			57.2657i			1.92714i	0.267449	+	0.963572i	$0.413819\pi$
$883$			57.2657i			1.92714i	−0.267449	+	0.963572i	$0.586181\pi$
$884$	−28.9094	−	17.0165i	−0.972329	−	0.572327i
$885$	3.83768	−	0.805850i	0.129002	−	0.0270883i
$886$	5.22332	−	19.1710i	0.175481	−	0.644062i
$887$	−17.4323	+	30.1937i	−0.585320	+	1.01380i	0.409515	+	0.912303i	$0.365698\pi$
$887$	−17.4323	+	30.1937i	−0.585320	+	1.01380i	−0.994835	+	0.101501i	$0.967635\pi$
$888$	−33.3953	+	16.3865i	−1.12067	+	0.549895i
$889$	−4.79702	−	15.4565i	−0.160887	−	0.518395i
$890$	0.311036	+	1.18063i	0.0104260	+	0.0395749i
$891$	−12.2304	+	13.3170i	−0.409734	+	0.446137i
$892$	−9.31740	−	16.4562i	−0.311970	−	0.550993i
$893$	−11.8427	−	20.5121i	−0.396300	−	0.686412i
$894$	−1.76599	+	29.8841i	−0.0590636	+	0.999474i
$895$	1.80226	+	1.04054i	0.0602431	+	0.0347814i
$896$	26.0670	+	14.7143i	0.870838	+	0.491569i
$897$	7.59399	+	36.1647i	0.253556	+	1.20750i
$898$	33.8034	−	33.5204i	1.12803	−	1.11859i
$899$		−	64.1868i		−	2.14075i
$900$	−29.4920	−	3.49786i	−0.983067	−	0.116595i
$901$	−14.4984			−0.483011
$902$	21.8923	+	22.0771i	0.728932	+	0.735086i
$903$	20.3684	−	11.3373i	0.677819	−	0.377283i
$904$	8.06203	−	2.05162i	0.268139	−	0.0682358i
$905$	1.19079	+	0.687505i	0.0395833	+	0.0228535i
$906$	−20.2367	−	13.3345i	−0.672320	−	0.443010i
$907$	22.2277	−	12.8332i	0.738058	−	0.426118i	−0.0833048	−	0.996524i	$-0.526548\pi$
$907$	22.2277	−	12.8332i	0.738058	−	0.426118i	0.821363	+	0.570406i	$0.193214\pi$
$908$	10.2190	+	18.0485i	0.339129	+	0.598961i
$909$	−44.1845	−	4.86414i	−1.46551	−	0.161333i
$910$	0.109032	+	3.12041i	0.00361437	+	0.103440i
$911$	−26.8104	+	15.4790i	−0.888269	+	0.512842i	−0.873376	−	0.487047i	$-0.838074\pi$
$911$	−26.8104	+	15.4790i	−0.888269	+	0.512842i	−0.0148929	+	0.999889i	$0.504741\pi$
$912$	−7.23338	+	20.8835i	−0.239521	+	0.691523i
$913$	16.1136	+	9.30317i	0.533281	+	0.307890i
$914$	−11.0815	+	40.6720i	−0.366542	+	1.34531i
$915$	0.139592	+	0.0457365i	0.00461476	+	0.00151200i
$916$	43.8043	+	25.7838i	1.44734	+	0.851922i
$917$	2.31265	−	10.2138i	0.0763703	−	0.337290i
$918$	−32.6278	−	5.55618i	−1.07688	−	0.183381i
$919$	−35.2687			−1.16341			−0.581703	−	0.813401i	$-0.697613\pi$
$919$	−35.2687			−1.16341			−0.581703	+	0.813401i	$0.697613\pi$
$920$	−3.49521	−	0.983939i	−0.115234	−	0.0324395i
$921$	−0.425849	+	1.29973i	−0.0140322	+	0.0428275i
$922$	9.18958	+	2.50379i	0.302643	+	0.0824578i
$923$	11.6426	+	6.72184i	0.383220	+	0.221252i
$924$	16.1632	−	8.81953i	0.531732	−	0.290141i
$925$	−32.5494	+	18.7924i	−1.07022	+	0.617890i
$926$	11.8767	−	3.12892i	0.390294	−	0.102823i
$927$	−1.89073	−	4.30357i	−0.0620997	−	0.141348i
$928$	9.52023	−	32.7600i	0.312517	−	1.07540i
$929$	16.7827	+	29.0685i	0.550622	+	0.953705i	0.998230	+	0.0594752i	$0.0189427\pi$
$929$	16.7827	+	29.0685i	0.550622	+	0.953705i	−0.447608	+	0.894230i	$0.647724\pi$
$930$	−4.87807	−	3.21429i	−0.159958	−	0.105401i
$931$	−18.4061	+	12.6426i	−0.603235	+	0.414345i
$932$	5.28953	+	0.0444673i	0.173264	+	0.00145658i
$933$	−30.4919	−	34.0329i	−0.998260	−	1.11419i
$934$	−11.8617	+	11.7624i	−0.388127	+	0.384878i
$935$		−	2.02761i		−	0.0663100i
$936$	−11.8396	+	29.2972i	−0.386991	+	0.957609i
$937$		−	1.39520i		−	0.0455793i	−0.999740	−	0.0227896i	$-0.992745\pi$
$937$		−	1.39520i		−	0.0455793i	0.999740	−	0.0227896i	$-0.00725479\pi$
$938$	−26.1582	+	16.3462i	−0.854097	+	0.533724i
$939$	9.44145	+	44.9628i	0.308110	+	1.46730i
$940$	3.32745	+	0.0279728i	0.108530	+	0.000912372i
$941$	28.2201	+	16.2929i	0.919950	+	0.531133i	0.883619	−	0.468206i	$-0.155100\pi$
$941$	28.2201	+	16.2929i	0.919950	+	0.531133i	0.0363309	+	0.999340i	$0.488433\pi$
$942$	0.940708	−	15.9187i	0.0306499	−	0.518658i
$943$	54.2947	−	31.3470i	1.76808	−	1.02080i
$944$	−34.6550	−	20.7927i	−1.12793	−	0.676743i
$945$	1.19470	+	2.83950i	0.0388637	+	0.0923689i
$946$	3.68194	+	13.9759i	0.119710	+	0.454396i
$947$	8.73287	+	15.1258i	0.283780	+	0.491521i	0.972313	−	0.233684i	$-0.0750781\pi$
$947$	8.73287	+	15.1258i	0.283780	+	0.491521i	−0.688533	+	0.725205i	$0.741745\pi$
$948$	−4.84207	−	24.0633i	−0.157263	−	0.781541i
$949$	−23.4696	−	13.5502i	−0.761856	−	0.439858i
$950$	−5.87003	+	21.5446i	−0.190449	+	0.699000i
$951$	48.8561	−	10.2590i	1.58427	−	0.332670i
$952$	29.6259	+	16.0725i	0.960181	+	0.520912i
$953$			1.02607i			0.0332376i	0.999862	+	0.0166188i	$0.00529016\pi$
$953$			1.02607i			0.0332376i	−0.999862	+	0.0166188i	$0.994710\pi$
$954$	2.01320	+	13.5078i	0.0651799	+	0.437333i
$955$	4.85017			0.156948
$956$	7.00056	−	11.8933i	0.226414	−	0.384657i
$957$	−14.0035	−	15.6297i	−0.452670	−	0.505237i
$958$	−8.02441	+	29.4518i	−0.259257	+	0.951543i
$959$	−10.4602	−	9.67199i	−0.337777	−	0.312325i
$960$	−2.01295	−	2.36405i	−0.0649678	−	0.0762993i
$961$	41.1386	+	71.2541i	1.32705	+	2.29852i
$962$	10.1877	+	38.6703i	0.328463	+	1.24678i
$963$	9.39802	+	6.89904i	0.302847	+	0.222319i
$964$	0.597908	+	1.05601i	0.0192573	+	0.0340118i
$965$	−0.893344	+	0.515773i	−0.0287578	+	0.0166033i
$966$	−8.89424	−	36.0477i	−0.286167	−	1.15981i
$967$	3.58747	−	6.21368i	0.115365	−	0.199819i	−0.802560	−	0.596571i	$-0.796529\pi$
$967$	3.58747	−	6.21368i	0.115365	−	0.199819i	0.917926	+	0.396752i	$0.129863\pi$
$968$	−4.85760	−	19.0884i	−0.156129	−	0.613525i
$969$	−7.74831	+	23.6485i	−0.248911	+	0.759699i
$970$	−4.00118	−	4.03496i	−0.128470	−	0.129555i
$971$			35.0730i			1.12555i	0.826611	+	0.562773i	$0.190266\pi$
$971$			35.0730i			1.12555i	−0.826611	+	0.562773i	$0.809734\pi$
$972$	−0.645974	+	31.1702i	−0.0207196	+	0.999785i
$973$	−40.4433	−	9.15731i	−1.29655	−	0.293570i
$974$	11.2984	+	11.3938i	0.362025	+	0.365081i
$975$	−9.94068	+	30.3398i	−0.318357	+	0.971652i
$976$	−0.734802	−	1.32362i	−0.0235204	−	0.0423680i
$977$	42.9788	+	24.8138i	1.37501	+	0.793865i	0.991554	−	0.129693i	$-0.0413991\pi$
$977$	42.9788	+	24.8138i	1.37501	+	0.793865i	0.383460	+	0.923557i	$0.374732\pi$
$978$	−13.6028	−	27.1429i	−0.434971	−	0.867933i
$979$	−3.87007	−	6.70316i	−0.123688	−	0.214234i
$980$	−0.218965	−	3.12947i	−0.00699457	−	0.0999674i
$981$	−1.75701	+	2.39344i	−0.0560972	+	0.0764167i
$982$	−43.3510	+	11.4208i	−1.38338	+	0.364452i
$983$	−4.59185	−	7.95331i	−0.146457	−	0.253671i	0.783458	−	0.621444i	$-0.213454\pi$
$983$	−4.59185	−	7.95331i	−0.146457	−	0.253671i	−0.929916	+	0.367773i	$0.880120\pi$
$984$	53.4883	+	3.61233i	1.70514	+	0.115157i
$985$	−2.45622	−	1.41810i	−0.0782616	−	0.0451843i
$986$	10.0981	−	37.0628i	0.321590	−	1.18032i
$987$	16.5482	+	29.7302i	0.526736	+	0.946322i
$988$	20.4752	+	12.0520i	0.651402	+	0.383424i
$989$	29.1433			0.926703
$990$	−1.88909	+	0.281549i	−0.0600391	+	0.00894820i
$991$	14.9822			0.475926			0.237963	−	0.971274i	$-0.423520\pi$
$991$	14.9822			0.475926			0.237963	+	0.971274i	$0.423520\pi$
$992$	14.3571	+	58.4700i	0.455839	+	1.85642i
$993$	−5.22781	−	24.8963i	−0.165899	−	0.790059i
$994$	−11.9265	−	6.34112i	−0.378286	−	0.201128i
$995$	−1.73255	+	3.00086i	−0.0549255	+	0.0951337i
$996$	31.4521	−	6.32885i	0.996599	−	0.200537i
$997$	−10.4010	−	18.0151i	−0.329404	−	0.570545i	0.652990	−	0.757367i	$-0.273515\pi$
$997$	−10.4010	−	18.0151i	−0.329404	−	0.570545i	−0.982394	+	0.186822i	$0.940181\pi$
$998$	13.3248	+	50.5782i	0.421788	+	1.60102i
$999$	22.9549	+	32.0906i	0.726259	+	1.01530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.20	yes	168
7.6	odd	2	inner	504.2.cc.b.293.19	✓	168
8.5	even	2	inner	504.2.cc.b.293.51	yes	168
9.2	odd	6	inner	504.2.cc.b.461.52	yes	168
56.13	odd	2	inner	504.2.cc.b.293.52	yes	168
63.20	even	6	inner	504.2.cc.b.461.51	yes	168
72.29	odd	6	inner	504.2.cc.b.461.19	yes	168
504.461	even	6	inner	504.2.cc.b.461.20	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.19	✓	168	7.6	odd	2	inner
504.2.cc.b.293.20	yes	168	1.1	even	1	trivial
504.2.cc.b.293.51	yes	168	8.5	even	2	inner
504.2.cc.b.293.52	yes	168	56.13	odd	2	inner
504.2.cc.b.461.19	yes	168	72.29	odd	6	inner
504.2.cc.b.461.20	yes	168	504.461	even	6	inner
504.2.cc.b.461.51	yes	168	63.20	even	6	inner
504.2.cc.b.461.52	yes	168	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995788 - 1.00419i) q^{2} +(0.539289 - 1.64595i) q^{3} +(-0.0168127 + 1.99993i) q^{4} +(0.194059 + 0.112040i) q^{5} +(-2.18988 + 1.09747i) q^{6} +(-0.784223 - 2.52685i) q^{7} +(2.02506 - 1.97462i) q^{8} +(-2.41834 - 1.77529i) q^{9} +O(q^{10})\)	\(q+(-0.995788 - 1.00419i) q^{2} +(0.539289 - 1.64595i) q^{3} +(-0.0168127 + 1.99993i) q^{4} +(0.194059 + 0.112040i) q^{5} +(-2.18988 + 1.09747i) q^{6} +(-0.784223 - 2.52685i) q^{7} +(2.02506 - 1.97462i) q^{8} +(-2.41834 - 1.77529i) q^{9} +(-0.0807318 - 0.306441i) q^{10} +(1.00451 + 1.73985i) q^{11} +(3.28273 + 1.10621i) q^{12} +(1.86199 - 3.22507i) q^{13} +(-1.75653 + 3.30372i) q^{14} +(0.289067 - 0.258991i) q^{15} +(-3.99943 - 0.0672486i) q^{16} -4.50401 q^{17} +(0.625414 + 4.19629i) q^{18} +3.18997 q^{19} +(-0.227335 + 0.386221i) q^{20} +(-4.58201 - 0.0719078i) q^{21} +(0.746878 - 2.74125i) q^{22} +(-4.96153 - 2.86454i) q^{23} +(-2.15805 - 4.39805i) q^{24} +(-2.47489 - 4.28664i) q^{25} +(-5.09275 + 1.34168i) q^{26} +(-4.22623 + 3.02308i) q^{27} +(5.06672 - 1.52591i) q^{28} +(-3.01540 - 5.22282i) q^{29} +(-0.547927 - 0.0323795i) q^{30} +(9.21726 + 5.32159i) q^{31} +(3.91506 + 4.08318i) q^{32} +(3.40544 - 0.715087i) q^{33} +(4.48503 + 4.52290i) q^{34} +(0.130923 - 0.578224i) q^{35} +(3.59111 - 4.80665i) q^{36} -7.59321i q^{37} +(-3.17653 - 3.20335i) q^{38} +(-4.30417 - 4.80400i) q^{39} +(0.614219 - 0.156306i) q^{40} +(-5.47156 + 9.47702i) q^{41} +(4.49050 + 4.67284i) q^{42} +(-4.40539 + 2.54345i) q^{43} +(-3.49648 + 1.97969i) q^{44} +(-0.270397 - 0.615462i) q^{45} +(2.06408 + 7.83482i) q^{46} +(-3.71247 - 6.43019i) q^{47} +(-2.26754 + 6.54662i) q^{48} +(-5.76999 + 3.96324i) q^{49} +(-1.84015 + 6.75386i) q^{50} +(-2.42896 + 7.41339i) q^{51} +(6.41861 + 3.77808i) q^{52} +3.21900 q^{53} +(7.24418 + 1.23361i) q^{54} +0.450180i q^{55} +(-6.57768 - 3.56849i) q^{56} +(1.72031 - 5.25055i) q^{57} +(-2.24203 + 8.22886i) q^{58} +(8.74993 + 5.05177i) q^{59} +(0.513103 + 0.582468i) q^{60} +(0.189238 + 0.327769i) q^{61} +(-3.83453 - 14.5551i) q^{62} +(-2.58938 + 7.50301i) q^{63} +(0.201734 - 7.99746i) q^{64} +(0.722675 - 0.417236i) q^{65} +(-4.10918 - 2.70765i) q^{66} +(7.13938 + 4.12192i) q^{67} +(0.0757247 - 9.00769i) q^{68} +(-7.39060 + 6.62164i) q^{69} +(-0.711021 + 0.444316i) q^{70} +3.61002i q^{71} +(-8.40280 + 1.18023i) q^{72} -7.27725i q^{73} +(-7.62505 + 7.56122i) q^{74} +(-8.39030 + 1.76183i) q^{75} +(-0.0536322 + 6.37972i) q^{76} +(3.60860 - 3.90267i) q^{77} +(-0.538115 + 9.10599i) q^{78} +(-3.54286 - 6.13642i) q^{79} +(-0.768593 - 0.461148i) q^{80} +(2.69669 + 8.58649i) q^{81} +(14.9653 - 3.94259i) q^{82} +(8.02064 - 4.63072i) q^{83} +(0.220847 - 9.16249i) q^{84} +(-0.874044 - 0.504629i) q^{85} +(6.94095 + 1.89113i) q^{86} +(-10.2227 + 2.14660i) q^{87} +(5.46974 + 1.53979i) q^{88} -3.85271 q^{89} +(-0.348786 + 0.884400i) q^{90} +(-9.60950 - 2.17582i) q^{91} +(5.81230 - 9.87455i) q^{92} +(13.7299 - 12.3013i) q^{93} +(-2.76033 + 10.1312i) q^{94} +(0.619043 + 0.357405i) q^{95} +(8.83207 - 4.24200i) q^{96} +(15.5292 - 8.96577i) q^{97} +(9.72554 + 1.84765i) q^{98} +(0.659514 - 5.99084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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