LMFDB - Embedded newform 504.2.cz.b.187.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (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:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.3
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40451 - 0.165416i) q^{2} +(0.410054 - 1.68281i) q^{3} +(1.94528 + 0.464656i) q^{4} +3.30804 q^{5} +(-0.854288 + 2.29569i) q^{6} +(-0.351034 - 2.62236i) q^{7} +(-2.65529 - 0.974392i) q^{8} +(-2.66371 - 1.38009i) q^{9} +O(q^{10})$	\(q+(-1.40451 - 0.165416i) q^{2} +(0.410054 - 1.68281i) q^{3} +(1.94528 + 0.464656i) q^{4} +3.30804 q^{5} +(-0.854288 + 2.29569i) q^{6} +(-0.351034 - 2.62236i) q^{7} +(-2.65529 - 0.974392i) q^{8} +(-2.66371 - 1.38009i) q^{9} +(-4.64616 - 0.547203i) q^{10} -2.13958 q^{11} +(1.57960 - 3.08300i) q^{12} +(-1.42190 - 2.46280i) q^{13} +(0.0592486 + 3.74119i) q^{14} +(1.35647 - 5.56680i) q^{15} +(3.56819 + 1.80777i) q^{16} +(3.14298 - 1.81460i) q^{17} +(3.51291 + 2.37896i) q^{18} +(-5.23140 - 3.02035i) q^{19} +(6.43504 + 1.53710i) q^{20} +(-4.55688 - 0.484586i) q^{21} +(3.00506 + 0.353922i) q^{22} +5.73325i q^{23} +(-2.72853 + 4.06880i) q^{24} +5.94311 q^{25} +(1.58968 + 3.69422i) q^{26} +(-3.41469 + 3.91661i) q^{27} +(0.535638 - 5.26432i) q^{28} +(7.57832 + 4.37535i) q^{29} +(-2.82601 + 7.59423i) q^{30} +(1.97299 - 3.41732i) q^{31} +(-4.71251 - 3.12926i) q^{32} +(-0.877345 + 3.60052i) q^{33} +(-4.71450 + 2.02872i) q^{34} +(-1.16123 - 8.67487i) q^{35} +(-4.54039 - 3.92236i) q^{36} +(3.38972 + 1.95705i) q^{37} +(6.84792 + 5.10746i) q^{38} +(-4.72748 + 1.38290i) q^{39} +(-8.78379 - 3.22332i) q^{40} +(-3.98965 + 2.30342i) q^{41} +(6.32001 + 1.43439i) q^{42} +(4.33651 - 7.51105i) q^{43} +(-4.16208 - 0.994170i) q^{44} +(-8.81166 - 4.56538i) q^{45} +(0.948372 - 8.05238i) q^{46} +(-1.65247 - 2.86216i) q^{47} +(4.50528 - 5.26331i) q^{48} +(-6.75355 + 1.84107i) q^{49} +(-8.34713 - 0.983086i) q^{50} +(-1.76484 - 6.03314i) q^{51} +(-1.62163 - 5.45151i) q^{52} +(5.94310 - 3.43125i) q^{53} +(5.44383 - 4.93606i) q^{54} -7.07782 q^{55} +(-1.62311 + 7.30517i) q^{56} +(-7.22784 + 7.56495i) q^{57} +(-9.92004 - 7.39878i) q^{58} +(-1.04047 - 0.600718i) q^{59} +(5.22536 - 10.1987i) q^{60} +(-2.98129 - 5.16375i) q^{61} +(-3.33636 + 4.47328i) q^{62} +(-2.68403 + 7.46967i) q^{63} +(6.10112 + 5.17458i) q^{64} +(-4.70369 - 8.14703i) q^{65} +(1.82782 - 4.91182i) q^{66} +(-0.545905 + 0.945534i) q^{67} +(6.95713 - 2.06950i) q^{68} +(9.64798 + 2.35094i) q^{69} +(0.195997 + 12.3760i) q^{70} +13.2647i q^{71} +(5.72818 + 6.26003i) q^{72} +(2.01411 - 1.16285i) q^{73} +(-4.43715 - 3.30941i) q^{74} +(2.43700 - 10.0011i) q^{75} +(-8.77309 - 8.30621i) q^{76} +(0.751066 + 5.61076i) q^{77} +(6.86853 - 1.16030i) q^{78} +(0.479167 - 0.276647i) q^{79} +(11.8037 + 5.98016i) q^{80} +(5.19072 + 7.35231i) q^{81} +(5.98450 - 2.57522i) q^{82} +(10.4733 + 6.04677i) q^{83} +(-8.63922 - 3.06003i) q^{84} +(10.3971 - 6.00277i) q^{85} +(-7.33310 + 9.83199i) q^{86} +(10.4704 - 10.9588i) q^{87} +(5.68121 + 2.08479i) q^{88} +(-10.3266 - 5.96208i) q^{89} +(11.6208 + 7.86970i) q^{90} +(-5.95921 + 4.59325i) q^{91} +(-2.66399 + 11.1527i) q^{92} +(-4.94167 - 4.72146i) q^{93} +(1.84745 + 4.29326i) q^{94} +(-17.3057 - 9.99143i) q^{95} +(-7.19833 + 6.64710i) q^{96} +(7.83942 + 4.52609i) q^{97} +(9.78995 - 1.46866i) q^{98} +(5.69923 + 2.95281i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.40451	−	0.165416i	−0.993136	−	0.116967i
$2$	−1.40451	−	0.165416i	−0.993136	−	0.116967i
$3$	0.410054	−	1.68281i	0.236745	−	0.971572i
$3$	0.410054	−	1.68281i	0.236745	−	0.971572i
$4$	1.94528	+	0.464656i	0.972638	+	0.232328i
$5$	3.30804			1.47940			0.739700	−	0.672937i	$-0.234968\pi$
$5$	3.30804			1.47940			0.739700	+	0.672937i	$0.234968\pi$
$6$	−0.854288	+	2.29569i	−0.348761	+	0.937212i
$7$	−0.351034	−	2.62236i	−0.132678	−	0.991159i
$7$	−0.351034	−	2.62236i	−0.132678	−	0.991159i
$8$	−2.65529	−	0.974392i	−0.938786	−	0.344500i
$9$	−2.66371	−	1.38009i	−0.887904	−	0.460029i
$10$	−4.64616	−	0.547203i	−1.46924	−	0.173041i
$11$	−2.13958			−0.645109			−0.322554	−	0.946551i	$-0.604541\pi$
$11$	−2.13958			−0.645109			−0.322554	+	0.946551i	$0.604541\pi$
$12$	1.57960	−	3.08300i	0.455990	−	0.889985i
$13$	−1.42190	−	2.46280i	−0.394363	−	0.683057i	0.598656	−	0.801006i	$-0.295701\pi$
$13$	−1.42190	−	2.46280i	−0.394363	−	0.683057i	−0.993020	+	0.117949i	$0.962368\pi$
$14$	0.0592486	+	3.74119i	0.0158349	+	0.999875i
$15$	1.35647	−	5.56680i	0.350240	−	1.43734i
$16$	3.56819	+	1.80777i	0.892047	+	0.451942i
$17$	3.14298	−	1.81460i	0.762286	−	0.440106i	−0.0678302	−	0.997697i	$-0.521608\pi$
$17$	3.14298	−	1.81460i	0.762286	−	0.440106i	0.830116	+	0.557591i	$0.188274\pi$
$18$	3.51291	+	2.37896i	0.828001	+	0.560727i
$19$	−5.23140	−	3.02035i	−1.20017	−	0.692916i	−0.239573	−	0.970878i	$-0.577008\pi$
$19$	−5.23140	−	3.02035i	−1.20017	−	0.692916i	−0.960592	+	0.277963i	$0.910341\pi$
$20$	6.43504	+	1.53710i	1.43892	+	0.343706i
$21$	−4.55688	−	0.484586i	−0.994393	−	0.105745i
$22$	3.00506	+	0.353922i	0.640680	+	0.0754563i
$23$			5.73325i			1.19547i	0.801696	+	0.597733i	$0.203932\pi$
$23$			5.73325i			1.19547i	−0.801696	+	0.597733i	$0.796068\pi$
$24$	−2.72853	+	4.06880i	−0.556959	+	0.830540i
$25$	5.94311			1.18862
$26$	1.58968	+	3.69422i	0.311761	+	0.724496i
$27$	−3.41469	+	3.91661i	−0.657158	+	0.753753i
$28$	0.535638	−	5.26432i	0.101226	−	0.994863i
$29$	7.57832	+	4.37535i	1.40726	+	0.812481i	0.995123	−	0.0986413i	$-0.0314497\pi$
$29$	7.57832	+	4.37535i	1.40726	+	0.812481i	0.412136	+	0.911123i	$0.364783\pi$
$30$	−2.82601	+	7.59423i	−0.515957	+	1.38651i
$31$	1.97299	−	3.41732i	0.354359	−	0.613769i	−0.632649	−	0.774439i	$-0.718032\pi$
$31$	1.97299	−	3.41732i	0.354359	−	0.613769i	0.987008	+	0.160670i	$0.0513656\pi$
$32$	−4.71251	−	3.12926i	−0.833062	−	0.553179i
$33$	−0.877345	+	3.60052i	−0.152726	+	0.626769i
$34$	−4.71450	+	2.02872i	−0.808531	+	0.347923i
$35$	−1.16123	−	8.67487i	−0.196284	−	1.46632i
$36$	−4.54039	−	3.92236i	−0.756731	−	0.653727i
$37$	3.38972	+	1.95705i	0.557266	+	0.321738i	0.752047	−	0.659109i	$-0.229066\pi$
$37$	3.38972	+	1.95705i	0.557266	+	0.321738i	−0.194782	+	0.980847i	$0.562400\pi$
$38$	6.84792	+	5.10746i	1.11088	+	0.828539i
$39$	−4.72748	+	1.38290i	−0.757003	+	0.221442i
$40$	−8.78379	−	3.22332i	−1.38884	−	0.509652i
$41$	−3.98965	+	2.30342i	−0.623078	+	0.359734i	−0.778066	−	0.628182i	$-0.783799\pi$
$41$	−3.98965	+	2.30342i	−0.623078	+	0.359734i	0.154988	+	0.987916i	$0.450466\pi$
$42$	6.32001	+	1.43439i	0.975199	+	0.221330i
$43$	4.33651	−	7.51105i	0.661311	−	1.14542i	−0.318960	−	0.947768i	$-0.603334\pi$
$43$	4.33651	−	7.51105i	0.661311	−	1.14542i	0.980271	−	0.197656i	$-0.0633330\pi$
$44$	−4.16208	−	0.994170i	−0.627457	−	0.149877i
$45$	−8.81166	−	4.56538i	−1.31356	−	0.680567i
$46$	0.948372	−	8.05238i	0.139830	−	1.18726i
$47$	−1.65247	−	2.86216i	−0.241037	−	0.417488i	0.719973	−	0.694002i	$-0.244154\pi$
$47$	−1.65247	−	2.86216i	−0.241037	−	0.417488i	−0.961010	+	0.276514i	$0.910821\pi$
$48$	4.50528	−	5.26331i	0.650281	−	0.759693i
$49$	−6.75355	+	1.84107i	−0.964793	+	0.263011i
$50$	−8.34713	−	0.983086i	−1.18046	−	0.139029i
$51$	−1.76484	−	6.03314i	−0.247127	−	0.844808i
$52$	−1.62163	−	5.45151i	−0.224879	−	0.755989i
$53$	5.94310	−	3.43125i	0.816347	−	0.471318i	−0.0328082	−	0.999462i	$-0.510445\pi$
$53$	5.94310	−	3.43125i	0.816347	−	0.471318i	0.849155	+	0.528144i	$0.177112\pi$
$54$	5.44383	−	4.93606i	0.740811	−	0.671713i
$55$	−7.07782			−0.954373
$56$	−1.62311	+	7.30517i	−0.216897	+	0.976194i
$57$	−7.22784	+	7.56495i	−0.957350	+	1.00200i
$58$	−9.92004	−	7.39878i	−1.30257	−	0.971507i
$59$	−1.04047	−	0.600718i	−0.135458	−	0.0782069i	0.430739	−	0.902476i	$-0.358253\pi$
$59$	−1.04047	−	0.600718i	−0.135458	−	0.0782069i	−0.566198	+	0.824269i	$0.691586\pi$
$60$	5.22536	−	10.1987i	0.674591	−	1.31664i
$61$	−2.98129	−	5.16375i	−0.381715	−	0.661150i	0.609592	−	0.792715i	$-0.291333\pi$
$61$	−2.98129	−	5.16375i	−0.381715	−	0.661150i	−0.991308	+	0.131565i	$0.958000\pi$
$62$	−3.33636	+	4.47328i	−0.423718	+	0.568107i
$63$	−2.68403	+	7.46967i	−0.338157	+	0.941090i
$64$	6.10112	+	5.17458i	0.762640	+	0.646823i
$65$	−4.70369	−	8.14703i	−0.583421	−	1.01051i
$66$	1.82782	−	4.91182i	0.224989	−	0.604603i
$67$	−0.545905	+	0.945534i	−0.0666929	+	0.115515i	−0.897444	−	0.441129i	$-0.854578\pi$
$67$	−0.545905	+	0.945534i	−0.0666929	+	0.115515i	0.830751	+	0.556644i	$0.187911\pi$
$68$	6.95713	−	2.06950i	0.843676	−	0.250963i
$69$	9.64798	+	2.35094i	1.16148	+	0.283020i
$70$	0.195997	+	12.3760i	0.0234261	+	1.47921i
$71$			13.2647i			1.57423i	0.616804	+	0.787117i	$0.288427\pi$
$71$			13.2647i			1.57423i	−0.616804	+	0.787117i	$0.711573\pi$
$72$	5.72818	+	6.26003i	0.675072	+	0.737752i
$73$	2.01411	−	1.16285i	0.235734	−	0.136101i	−0.377481	−	0.926018i	$-0.623210\pi$
$73$	2.01411	−	1.16285i	0.235734	−	0.136101i	0.613214	+	0.789917i	$0.289876\pi$
$74$	−4.43715	−	3.30941i	−0.515808	−	0.384711i
$75$	2.43700	−	10.0011i	0.281400	−	1.15483i
$76$	−8.77309	−	8.30621i	−1.00634	−	0.952788i
$77$	0.751066	+	5.61076i	0.0855919	+	0.639405i
$78$	6.86853	−	1.16030i	0.777708	−	0.131378i
$79$	0.479167	−	0.276647i	0.0539105	−	0.0311252i	−0.472802	−	0.881168i	$-0.656758\pi$
$79$	0.479167	−	0.276647i	0.0539105	−	0.0311252i	0.526713	+	0.850043i	$0.323424\pi$
$80$	11.8037	+	5.98016i	1.31969	+	0.668602i
$81$	5.19072	+	7.35231i	0.576746	+	0.816923i
$82$	5.98450	−	2.57522i	0.660878	−	0.284385i
$83$	10.4733	+	6.04677i	1.14960	+	0.663719i	0.948789	−	0.315912i	$-0.102310\pi$
$83$	10.4733	+	6.04677i	1.14960	+	0.663719i	0.200806	+	0.979631i	$0.435644\pi$
$84$	−8.63922	−	3.06003i	−0.942617	−	0.333877i
$85$	10.3971	−	6.00277i	1.12772	−	0.651092i
$86$	−7.33310	+	9.83199i	−0.790749	+	1.06021i
$87$	10.4704	−	10.9588i	1.12255	−	1.17490i
$88$	5.68121	+	2.08479i	0.605619	+	0.222240i
$89$	−10.3266	−	5.96208i	−1.09462	−	0.631979i	−0.159818	−	0.987147i	$-0.551091\pi$
$89$	−10.3266	−	5.96208i	−1.09462	−	0.631979i	−0.934803	+	0.355167i	$0.884424\pi$
$90$	11.6208	+	7.86970i	1.22494	+	0.829539i
$91$	−5.95921	+	4.59325i	−0.624695	+	0.481504i
$92$	−2.66399	+	11.1527i	−0.277740	+	1.16275i
$93$	−4.94167	−	4.72146i	−0.512428	−	0.489592i
$94$	1.84745	+	4.29326i	0.190550	+	0.442816i
$95$	−17.3057	−	9.99143i	−1.77552	−	1.02510i
$96$	−7.19833	+	6.64710i	−0.734677	+	0.678417i
$97$	7.83942	+	4.52609i	0.795973	+	0.459555i	0.842061	−	0.539382i	$-0.181342\pi$
$97$	7.83942	+	4.52609i	0.795973	+	0.459555i	−0.0460882	+	0.998937i	$0.514676\pi$
$98$	9.78995	−	1.46866i	0.988934	−	0.148357i
$99$	5.69923	+	2.95281i	0.572794	+	0.296769i
$100$	11.5610	+	2.76150i	1.15610	+	0.276150i
$101$	5.20996			0.518410			0.259205	−	0.965822i	$-0.416539\pi$
$101$	5.20996			0.518410			0.259205	+	0.965822i	$0.416539\pi$
$102$	1.48075	+	8.76551i	0.146616	+	0.867915i
$103$	12.1069			1.19293			0.596465	−	0.802639i	$-0.296572\pi$
$103$	12.1069			1.19293			0.596465	+	0.802639i	$0.296572\pi$
$104$	1.37582	+	7.92493i	0.134910	+	0.777103i
$105$	−15.0743	−	1.60303i	−1.47110	−	0.156439i
$106$	−8.91470	+	3.83612i	−0.865872	+	0.372597i
$107$	8.37423	−	14.5046i	0.809567	−	1.40221i	−0.103597	−	0.994619i	$-0.533035\pi$
$107$	8.37423	−	14.5046i	0.809567	−	1.40221i	0.913164	−	0.407592i	$-0.133632\pi$
$108$	−8.46240	+	6.03223i	−0.814294	+	0.580452i
$109$	−3.01855	+	1.74276i	−0.289125	+	0.166926i	−0.637547	−	0.770411i	$-0.720051\pi$
$109$	−3.01855	+	1.74276i	−0.289125	+	0.166926i	0.348422	+	0.937338i	$0.386718\pi$
$110$	9.94084	+	1.17079i	0.947822	+	0.111630i
$111$	4.68332	−	4.90176i	0.444521	−	0.465254i
$112$	3.48806	−	9.99167i	0.329591	−	0.944124i
$113$	7.42220	+	12.8556i	0.698222	+	1.20936i	0.969082	+	0.246737i	$0.0793584\pi$
$113$	7.42220	+	12.8556i	0.698222	+	1.20936i	−0.270861	+	0.962619i	$0.587308\pi$
$114$	11.4029	−	9.42942i	1.06798	−	0.883146i
$115$			18.9658i			1.76857i
$116$	12.7089	+	12.0326i	1.17999	+	1.11720i
$117$	0.388646	+	8.52253i	0.0359304	+	0.787908i
$118$	1.36198	+	1.01582i	0.125381	+	0.0935141i
$119$	−5.86184	−	7.60505i	−0.537354	−	0.697154i
$120$	−9.02608	+	13.4597i	−0.823964	+	1.22870i
$121$	−6.42218			−0.583835
$122$	3.33307	+	7.74567i	0.301762	+	0.701260i
$123$	2.24026	+	7.65835i	0.201997	+	0.690530i
$124$	5.42589	−	5.73086i	0.487259	−	0.514647i
$125$	3.11983			0.279046
$126$	5.00535	−	10.0472i	0.445912	−	0.895077i
$127$			15.3766i			1.36446i	0.731139	+	0.682228i	$0.238989\pi$
$127$			15.3766i			1.36446i	−0.731139	+	0.682228i	$0.761011\pi$
$128$	−7.71310	−	8.27696i	−0.681748	−	0.731587i
$129$	−10.8615	−	10.3775i	−0.956300	−	0.913685i
$130$	5.25871	+	12.2206i	0.461219	+	1.07182i
$131$		−	15.5136i		−	1.35543i	−0.735325	−	0.677715i	$-0.762970\pi$
$131$		−	15.5136i		−	1.35543i	0.735325	−	0.677715i	$-0.237030\pi$
$132$	−3.37968	+	6.59633i	−0.294163	+	0.574137i
$133$	−6.08405	+	14.7789i	−0.527554	+	1.28149i
$134$	0.923133	−	1.23771i	0.0797465	−	0.106922i
$135$	−11.2959	+	12.9563i	−0.972199	+	1.11510i
$136$	−10.1137	+	1.75580i	−0.867240	+	0.150558i
$137$	−6.06106			−0.517832			−0.258916	−	0.965900i	$-0.583365\pi$
$137$	−6.06106			−0.517832			−0.258916	+	0.965900i	$0.583365\pi$
$138$	−13.1618	−	4.89784i	−1.12040	−	0.416932i
$139$	14.3119	−	8.26300i	1.21392	−	0.700859i	0.250312	−	0.968165i	$-0.419467\pi$
$139$	14.3119	−	8.26300i	1.21392	−	0.700859i	0.963612	+	0.267306i	$0.0861336\pi$
$140$	1.77191	−	17.4146i	0.149754	−	1.47180i
$141$	−5.49407	+	1.60715i	−0.462684	+	0.135347i
$142$	2.19420	−	18.6304i	0.184133	−	1.56343i
$143$	3.04227	+	5.26936i	0.254407	+	0.440646i
$144$	−7.00975	−	9.73978i	−0.584146	−	0.811649i
$145$	25.0694	+	14.4738i	2.08190	+	1.20198i
$146$	−3.02118	+	1.30006i	−0.250035	+	0.107594i
$147$	0.328862	+	12.1199i	0.0271241	+	0.999632i
$148$	5.68457	+	5.38206i	0.467269	+	0.442402i
$149$			8.30689i			0.680527i	0.940330	+	0.340264i	$0.110516\pi$
$149$			8.30689i			0.680527i	−0.940330	+	0.340264i	$0.889484\pi$
$150$	−5.07712	+	13.6435i	−0.414545	+	1.11399i
$151$			10.8056i			0.879344i	0.898158	+	0.439672i	$0.144905\pi$
$151$			10.8056i			0.879344i	−0.898158	+	0.439672i	$0.855095\pi$
$152$	10.9479	+	13.1173i	0.887990	+	1.06396i
$153$	−10.8763	+	0.495984i	−0.879298	+	0.0400979i
$154$	−0.126767	−	8.00458i	−0.0102152	−	0.645028i
$155$	6.52672	−	11.3046i	0.524239	−	0.908009i
$156$	−9.83882	+	0.493479i	−0.787736	+	0.0395099i
$157$	−2.21033	+	3.82841i	−0.176404	+	0.305540i	−0.940646	−	0.339389i	$-0.889780\pi$
$157$	−2.21033	+	3.82841i	−0.176404	+	0.305540i	0.764242	+	0.644929i	$0.223113\pi$
$158$	−0.718755	+	0.309291i	−0.0571811	+	0.0246059i
$159$	−3.33715	−	11.4081i	−0.264654	−	0.904722i
$160$	−15.5892	−	10.3517i	−1.23243	−	0.818373i
$161$	15.0346	−	2.01256i	1.18490	−	0.158612i
$162$	−6.07420	−	11.1850i	−0.477234	−	0.878776i
$163$	−3.54000	+	6.13146i	−0.277274	+	0.480253i	−0.970706	−	0.240269i	$-0.922764\pi$
$163$	−3.54000	+	6.13146i	−0.277274	+	0.480253i	0.693432	+	0.720522i	$0.256098\pi$
$164$	−8.83126	+	2.62698i	−0.689605	+	0.205133i
$165$	−2.90229	+	11.9106i	−0.225943	+	0.927242i
$166$	−13.7096	−	10.2252i	−1.06407	−	0.793628i
$167$	−3.23753	−	5.60756i	−0.250527	−	0.433926i	0.713144	−	0.701018i	$-0.247271\pi$
$167$	−3.23753	−	5.60756i	−0.250527	−	0.433926i	−0.963671	+	0.267092i	$0.913937\pi$
$168$	11.6277	+	5.72690i	0.897094	+	0.441840i
$169$	2.45642	−	4.25464i	0.188955	−	0.327280i
$170$	−15.5958	+	6.71108i	−1.19614	+	0.514716i
$171$	9.76659	+	15.2651i	0.746870	+	1.16735i
$172$	11.9258	−	12.5961i	0.909330	−	0.960442i
$173$	2.69667	+	4.67077i	0.205024	+	0.355112i	0.950140	−	0.311822i	$-0.100939\pi$
$173$	2.69667	+	4.67077i	0.205024	+	0.355112i	−0.745116	+	0.666935i	$0.767606\pi$
$174$	−16.5185	+	13.6597i	−1.25226	+	1.03554i
$175$	−2.08623	−	15.5850i	−0.157704	−	1.17811i
$176$	−7.63444	−	3.86787i	−0.575467	−	0.291551i
$177$	−1.43755	+	1.50460i	−0.108053	+	0.113092i
$178$	13.5176	+	10.0820i	1.01319	+	0.755676i
$179$	−8.16391	−	14.1403i	−0.610200	−	1.05690i	−0.991206	−	0.132324i	$-0.957756\pi$
$179$	−8.16391	−	14.1403i	−0.610200	−	1.05690i	0.381007	−	0.924572i	$-0.375577\pi$
$180$	−15.0198	−	12.9753i	−1.11951	−	0.967122i
$181$	18.8205			1.39892			0.699458	−	0.714674i	$-0.253425\pi$
$181$	18.8205			1.39892			0.699458	+	0.714674i	$0.253425\pi$
$182$	9.12955	−	5.46550i	0.676727	−	0.405130i
$183$	−9.91210	+	2.89953i	−0.732724	+	0.214340i
$184$	5.58643	−	15.2234i	0.411837	−	1.12229i
$185$	11.2133	+	6.47400i	0.824418	+	0.475978i
$186$	6.15960	+	7.44875i	0.451644	+	0.546169i
$187$	−6.72468	+	3.88249i	−0.491757	+	0.283916i
$188$	−1.88458	−	6.33551i	−0.137447	−	0.462064i
$189$	11.4694	+	7.57969i	0.834280	+	0.551342i
$190$	22.6532	+	16.8957i	1.64343	+	1.22574i
$191$	1.04968	−	0.606035i	0.0759525	−	0.0438512i	−0.461543	−	0.887118i	$-0.652704\pi$
$191$	1.04968	−	0.606035i	0.0759525	−	0.0438512i	0.537495	+	0.843267i	$0.319371\pi$
$192$	11.2096	−	8.14518i	0.808986	−	0.587828i
$193$	6.04512	−	10.4704i	0.435137	−	0.753679i	−0.562170	−	0.827022i	$-0.690033\pi$
$193$	6.04512	−	10.4704i	0.435137	−	0.753679i	0.997307	+	0.0733424i	$0.0233666\pi$
$194$	−10.2618	−	7.65369i	−0.736756	−	0.549503i
$195$	−15.6387	+	4.57470i	−1.11991	+	0.327601i
$196$	−13.9930	+	0.443320i	−0.999499	+	0.0316657i
$197$		−	14.8067i		−	1.05493i	−0.849575	−	0.527467i	$-0.823142\pi$
$197$		−	14.8067i		−	1.05493i	0.849575	−	0.527467i	$-0.176858\pi$
$198$	−7.51616	−	5.08999i	−0.534150	−	0.361730i
$199$	−0.696824	−	1.20693i	−0.0493966	−	0.0855573i	0.840270	−	0.542168i	$-0.182396\pi$
$199$	−0.696824	−	1.20693i	−0.0493966	−	0.0855573i	−0.889666	+	0.456611i	$0.849063\pi$
$200$	−15.7807	−	5.79092i	−1.11586	−	0.409480i
$201$	1.36731	+	1.30637i	0.0964423	+	0.0921446i
$202$	−7.31742	−	0.861811i	−0.514852	−	0.0606368i
$203$	8.81349	−	21.4090i	0.618585	−	1.50262i
$204$	−0.629770	−	12.5562i	−0.0440927	−	0.879107i
$205$	−13.1979	+	7.61981i	−0.921781	+	0.532190i
$206$	−17.0042	−	2.00268i	−1.18474	−	0.139533i
$207$	7.91239	−	15.2717i	0.549949	−	1.06146i
$208$	−0.621434	−	11.3582i	−0.0430887	−	0.787549i
$209$	11.1930	+	6.46229i	0.774237	+	0.447006i
$210$	20.9068	+	4.74500i	1.44271	+	0.327436i
$211$	11.5259	+	19.9635i	0.793476	+	1.37434i	0.923802	+	0.382870i	$0.125064\pi$
$211$	11.5259	+	19.9635i	0.793476	+	1.37434i	−0.130326	+	0.991471i	$0.541602\pi$
$212$	13.1553	−	3.91323i	0.903510	−	0.268761i
$213$	22.3220	+	5.43925i	1.52948	+	0.372692i
$214$	−14.1609	+	18.9866i	−0.968023	+	1.29789i
$215$	14.3453	−	24.8468i	0.978343	−	1.69454i
$216$	12.8833	−	7.07249i	0.876599	−	0.481222i
$217$	−9.65403	−	3.97430i	−0.655358	−	0.269793i
$218$	4.52786	−	1.94840i	0.306665	−	0.131962i
$219$	−1.13096	−	3.86620i	−0.0764231	−	0.261254i
$220$	−13.7683	−	3.28875i	−0.928259	−	0.221728i
$221$	−8.93800	−	5.16036i	−0.601235	−	0.347123i
$222$	−7.38858	+	6.10985i	−0.495889	+	0.410066i
$223$	−6.88017	+	11.9168i	−0.460730	+	0.798008i	−0.998998	−	0.0447658i	$-0.985746\pi$
$223$	−6.88017	+	11.9168i	−0.460730	+	0.798008i	0.538267	+	0.842774i	$0.319079\pi$
$224$	−6.55179	+	13.4564i	−0.437760	+	0.899092i
$225$	−15.8307	−	8.20201i	−1.05538	−	0.546801i
$226$	−8.29800	−	19.2836i	−0.551975	−	1.28272i
$227$			15.7500i			1.04536i	0.852528	+	0.522681i	$0.175068\pi$
$227$			15.7500i			1.04536i	−0.852528	+	0.522681i	$0.824932\pi$
$228$	−17.5752	+	11.3575i	−1.16395	+	0.752166i
$229$	−6.24137			−0.412441			−0.206221	−	0.978506i	$-0.566116\pi$
$229$	−6.24137			−0.412441			−0.206221	+	0.978506i	$0.566116\pi$
$230$	3.13725	−	26.6376i	0.206864	−	1.75643i
$231$	9.74983	+	1.03681i	0.641492	+	0.0682172i
$232$	−15.8593	−	19.0021i	−1.04122	−	1.24755i
$233$	−9.55163	+	16.5439i	−0.625748	+	1.08383i	0.362648	+	0.931926i	$0.381873\pi$
$233$	−9.55163	+	16.5439i	−0.625748	+	1.08383i	−0.988396	+	0.151901i	$0.951460\pi$
$234$	0.863907	−	12.0342i	0.0564754	−	0.786702i
$235$	−5.46642	−	9.46812i	−0.356590	−	0.617632i
$236$	−1.74488	−	1.65202i	−0.113582	−	0.107538i
$237$	−0.269061	−	0.919788i	−0.0174774	−	0.0597467i
$238$	6.97499	+	11.6510i	0.452121	+	0.755221i
$239$	12.6835	−	7.32284i	0.820430	−	0.473675i	−0.0301350	−	0.999546i	$-0.509594\pi$
$239$	12.6835	−	7.32284i	0.820430	−	0.473675i	0.850565	+	0.525871i	$0.176260\pi$
$240$	14.9036	−	17.4112i	0.962026	−	1.12389i
$241$			26.1516i			1.68457i	0.539031	+	0.842286i	$0.318791\pi$
$241$			26.1516i			1.68457i	−0.539031	+	0.842286i	$0.681209\pi$
$242$	9.02000	+	1.06233i	0.579827	+	0.0682893i
$243$	14.5010	−	5.72015i	0.930241	−	0.366948i
$244$	−3.40006	−	11.4302i	−0.217667	−	0.731742i
$245$	−22.3410	+	6.09034i	−1.42731	+	0.389098i
$246$	−1.87964	−	11.1268i	−0.119841	−	0.709417i
$247$			17.1785i			1.09304i
$248$	−8.56867	+	7.15151i	−0.544111	+	0.454121i
$249$	14.4702	−	15.1451i	0.917011	−	0.959782i
$250$	−4.38183	−	0.516071i	−0.277131	−	0.0326392i
$251$			15.8604i			1.00110i	0.865707	+	0.500551i	$0.166869\pi$
$251$			15.8604i			1.00110i	−0.865707	+	0.500551i	$0.833131\pi$
$252$	−8.69201	+	13.2834i	−0.547545	+	0.836776i
$253$		−	12.2668i		−	0.771205i
$254$	2.54354	−	21.5966i	0.159596	−	1.35509i
$255$	−5.83816	−	19.9578i	−0.365600	−	1.24981i
$256$	9.46396	+	12.9009i	0.591497	+	0.806307i
$257$			19.7262i			1.23049i	0.788336	+	0.615245i	$0.210943\pi$
$257$			19.7262i			1.23049i	−0.788336	+	0.615245i	$0.789057\pi$
$258$	13.5384	+	16.3719i	0.842865	+	1.01927i
$259$	3.94219	−	9.57605i	0.244956	−	0.595027i
$260$	−5.36440	−	18.0338i	−0.332686	−	1.11841i
$261$	−14.1481	−	22.1134i	−0.875745	−	1.36879i
$262$	−2.56620	+	21.7890i	−0.158540	+	1.34613i
$263$			21.9428i			1.35305i	0.736419	+	0.676526i	$0.236515\pi$
$263$			21.9428i			1.35305i	−0.736419	+	0.676526i	$0.763485\pi$
$264$	5.83792	−	8.70553i	0.359299	−	0.535789i
$265$	19.6600	−	11.3507i	1.20770	−	0.697268i
$266$	10.9897	−	19.7506i	0.673824	−	1.21099i
$267$	−14.2675	+	14.9330i	−0.873159	+	0.913885i
$268$	−1.50128	+	1.58567i	−0.0917054	+	0.0968600i
$269$	−10.8060	−	18.7166i	−0.658856	−	1.14117i	−0.980912	−	0.194452i	$-0.937707\pi$
$269$	−10.8060	−	18.7166i	−0.658856	−	1.14117i	0.322056	−	0.946721i	$-0.395626\pi$
$270$	18.0084	−	16.3287i	1.09596	−	0.993732i
$271$	1.17755	−	2.03957i	0.0715309	−	0.123895i	−0.828042	−	0.560667i	$-0.810545\pi$
$271$	1.17755	−	2.03957i	0.0715309	−	0.123895i	0.899572	+	0.436772i	$0.143878\pi$
$272$	14.4951	−	0.793065i	0.878897	−	0.0480866i
$273$	5.28598	+	11.9117i	0.319922	+	0.720930i
$274$	8.51280	+	1.00260i	0.514277	+	0.0605691i
$275$	−12.7158			−0.766790
$276$	17.6756	+	9.05622i	1.06395	+	0.545120i
$277$		−	27.6102i		−	1.65893i	−0.558556	−	0.829467i	$-0.688644\pi$
$277$		−	27.6102i		−	1.65893i	0.558556	−	0.829467i	$-0.311356\pi$
$278$	−21.4680	+	9.23801i	−1.28757	+	0.554059i
$279$	−9.97168	+	6.37985i	−0.596989	+	0.381952i
$280$	−5.36931	+	24.1658i	−0.320878	+	1.44418i
$281$	−8.25805	+	14.3034i	−0.492634	+	0.853267i	−0.999964	−	0.00848473i	$-0.997299\pi$
$281$	−8.25805	+	14.3034i	−0.492634	+	0.853267i	0.507330	+	0.861752i	$0.330633\pi$
$282$	7.98231	−	1.34845i	0.475339	−	0.0802988i
$283$	−22.3051	−	12.8778i	−1.32590	−	0.765508i	−0.341236	−	0.939978i	$-0.610845\pi$
$283$	−22.3051	−	12.8778i	−1.32590	−	0.765508i	−0.984663	+	0.174470i	$0.944179\pi$
$284$	−6.16353	+	25.8035i	−0.365738	+	1.53116i
$285$	−23.9099	+	25.0251i	−1.41630	+	1.48236i
$286$	−3.40125	−	7.90409i	−0.201120	−	0.467379i
$287$	7.44091	+	9.65371i	0.439223	+	0.569840i
$288$	8.23412	+	14.8391i	0.485200	+	0.874403i
$289$	−1.91443	+	3.31590i	−0.112614	+	0.195053i
$290$	−32.8159	−	24.4754i	−1.92701	−	1.43725i
$291$	10.8311	−	11.3363i	0.634933	−	0.664547i
$292$	4.45832	−	1.32619i	0.260904	−	0.0776094i
$293$	9.26491	+	16.0473i	0.541262	+	0.937493i	0.998832	+	0.0483191i	$0.0153864\pi$
$293$	9.26491	+	16.0473i	0.541262	+	0.937493i	−0.457570	+	0.889173i	$0.651280\pi$
$294$	1.54294	−	17.0769i	0.0899859	−	0.995943i
$295$	−3.44193	−	1.98720i	−0.200397	−	0.115699i
$296$	−7.09374	−	8.49945i	−0.412315	−	0.494021i
$297$	7.30602	−	8.37992i	0.423938	−	0.486252i
$298$	1.37409	−	11.6671i	0.0795991	−	0.675856i
$299$	14.1198	−	8.15209i	0.816571	−	0.471448i
$300$	9.38771	−	18.3226i	0.542000	−	1.05786i
$301$	−21.2189	−	8.73525i	−1.22304	−	0.503492i
$302$	1.78741	−	15.1765i	0.102854	−	0.873308i
$303$	2.13636	−	8.76738i	0.122731	−	0.503673i
$304$	−13.2065	−	20.2343i	−0.757447	−	1.16052i
$305$	−9.86222	−	17.0819i	−0.564709	−	0.978104i
$306$	15.3579	+	1.10250i	0.877952	+	0.0630260i
$307$		−	0.148447i		−	0.00847233i	−0.999991	−	0.00423616i	$-0.998652\pi$
$307$		−	0.148447i		−	0.00847233i	0.999991	−	0.00423616i	$-0.00134842\pi$
$308$	−1.14604	+	11.2635i	−0.0653018	+	0.641795i
$309$	4.96449	−	20.3737i	0.282420	−	1.15902i
$310$	−11.0368	+	14.7978i	−0.626848	+	0.840457i
$311$	−2.24744	+	3.89268i	−0.127441	+	0.220734i	−0.922684	−	0.385556i	$-0.874010\pi$
$311$	−2.24744	+	3.89268i	−0.127441	+	0.220734i	0.795244	+	0.606290i	$0.207343\pi$
$312$	13.9003	+	0.934406i	0.786951	+	0.0529003i
$313$	20.4782	−	11.8231i	1.15749	−	0.668280i	0.206792	−	0.978385i	$-0.433698\pi$
$313$	20.4782	−	11.8231i	1.15749	−	0.668280i	0.950702	+	0.310105i	$0.100364\pi$
$314$	3.73771	−	5.01140i	0.210931	−	0.282810i
$315$	−8.87889	+	24.7099i	−0.500269	+	1.39225i
$316$	1.06066	−	0.315507i	0.0596666	−	0.0177487i
$317$	24.4544	−	14.1187i	1.37350	−	0.792988i	0.382129	−	0.924109i	$-0.375191\pi$
$317$	24.4544	−	14.1187i	1.37350	−	0.792988i	0.991366	+	0.131121i	$0.0418577\pi$
$318$	2.79997	+	16.5748i	0.157014	+	0.929467i
$319$	−16.2144	−	9.36141i	−0.907835	−	0.524139i
$320$	20.1827	+	17.1177i	1.12825	+	0.956909i
$321$	−20.9746	−	20.0399i	−1.17069	−	1.11852i
$322$	−21.4492	+	0.339687i	−1.19532	+	0.0189300i
$323$	−21.9229			−1.21982
$324$	6.68108	+	16.7142i	0.371171	+	0.928565i
$325$	−8.45049	−	14.6367i	−0.468749	−	0.811896i
$326$	5.98620	−	8.02610i	0.331545	−	0.444525i
$327$	1.69497	+	5.79428i	0.0937321	+	0.320424i
$328$	12.8381	−	2.22878i	0.708865	−	0.123064i
$329$	−6.92553	+	5.33808i	−0.381817	+	0.294298i
$330$	6.04649	−	16.2485i	0.332849	−	0.894449i
$331$	7.04653	+	12.2050i	0.387312	+	0.670845i	0.992087	−	0.125552i	$-0.0400701\pi$
$331$	7.04653	+	12.2050i	0.387312	+	0.670845i	−0.604775	+	0.796397i	$0.706737\pi$
$332$	17.5638	+	16.6291i	0.963939	+	0.912641i
$333$	−6.32832	−	9.89113i	−0.346790	−	0.542031i
$334$	3.61955	+	8.41139i	0.198053	+	0.460251i
$335$	−1.80587	+	3.12786i	−0.0986653	+	0.170893i
$336$	−15.3838	−	9.96687i	−0.839255	−	0.543738i
$337$	−12.9013	−	22.3456i	−0.702777	−	1.21724i	−0.967488	−	0.252917i	$-0.918610\pi$
$337$	−12.9013	−	22.3456i	−0.702777	−	1.21724i	0.264711	−	0.964328i	$-0.414723\pi$
$338$	−4.15384	+	5.56934i	−0.225939	+	0.302932i
$339$	24.6771	−	7.21866i	1.34028	−	0.392064i
$340$	23.0145	−	6.84597i	1.24813	−	0.371275i
$341$	−4.22138	+	7.31164i	−0.228600	+	0.395947i
$342$	−11.1921	−	23.0555i	−0.605201	−	1.24670i
$343$	7.19869	+	17.0640i	0.388693	+	0.921368i
$344$	−18.8334	+	15.7186i	−1.01543	+	0.847488i
$345$	31.9159	+	7.77700i	1.71829	+	0.418700i
$346$	−3.01487	−	7.00620i	−0.162080	−	0.376656i
$347$	−11.9807	+	20.7512i	−0.643157	+	1.11398i	0.341567	+	0.939857i	$0.389042\pi$
$347$	−11.9807	+	20.7512i	−0.643157	+	1.11398i	−0.984724	+	0.174123i	$0.944291\pi$
$348$	25.4599	−	16.4527i	1.36479	−	0.881955i
$349$	4.07603	−	7.05989i	0.218185	−	0.377907i	−0.736068	−	0.676907i	$-0.763320\pi$
$349$	4.07603	−	7.05989i	0.218185	−	0.377907i	0.954253	+	0.299000i	$0.0966531\pi$
$350$	0.352121	+	22.2343i	0.0188216	+	1.18847i
$351$	14.5012	+	2.84068i	0.774015	+	0.151624i
$352$	10.0828	+	6.69530i	0.537416	+	0.356861i
$353$			5.79374i			0.308369i	0.988042	+	0.154185i	$0.0492751\pi$
$353$			5.79374i			0.308369i	−0.988042	+	0.154185i	$0.950725\pi$
$354$	2.26793	−	1.87542i	0.120539	−	0.0996775i
$355$			43.8802i			2.32892i
$356$	−17.3178	−	16.3962i	−0.917843	−	0.868998i
$357$	−15.2015	+	6.74589i	−0.804551	+	0.357030i
$358$	9.12723	+	21.2106i	0.482389	+	1.12102i
$359$	−22.8845	−	13.2124i	−1.20780	−	0.697322i	−0.245520	−	0.969392i	$-0.578959\pi$
$359$	−22.8845	−	13.2124i	−1.20780	−	0.697322i	−0.962278	+	0.272069i	$0.912292\pi$
$360$	18.9490	+	20.7084i	0.998701	+	1.09143i
$361$	8.74502	+	15.1468i	0.460264	+	0.797201i
$362$	−26.4335	−	3.11321i	−1.38931	−	0.163627i
$363$	−2.63344	+	10.8073i	−0.138220	+	0.567238i
$364$	−13.7266	+	6.16616i	−0.719469	+	0.323194i
$365$	6.66275	−	3.84674i	0.348744	−	0.201348i
$366$	14.4012	−	2.43279i	0.752765	−	0.127164i
$367$	−13.3379			−0.696232			−0.348116	−	0.937451i	$-0.613178\pi$
$367$	−13.3379			−0.696232			−0.348116	+	0.937451i	$0.613178\pi$
$368$	−10.3644	+	20.4573i	−0.540281	+	1.06641i
$369$	13.8062	−	0.629593i	0.718722	−	0.0327753i
$370$	−14.6782	−	10.9476i	−0.763086	−	0.569141i
$371$	−11.0842	−	14.3805i	−0.575463	−	0.746596i
$372$	−7.41906	−	11.4807i	−0.384660	−	0.595247i
$373$			23.4954i			1.21655i	0.793727	+	0.608274i	$0.208138\pi$
$373$			23.4954i			1.21655i	−0.793727	+	0.608274i	$0.791862\pi$
$374$	10.0871	−	4.34062i	0.521590	−	0.224448i
$375$	1.27930	−	5.25009i	0.0660628	−	0.271114i
$376$	1.59892	+	9.21000i	0.0824578	+	0.474970i
$377$		−	24.8852i		−	1.28165i
$378$	−14.8551	−	12.5430i	−0.764064	−	0.645140i
$379$	7.39951			0.380087			0.190044	−	0.981776i	$-0.439137\pi$
$379$	7.39951			0.380087			0.190044	+	0.981776i	$0.439137\pi$
$380$	−29.0217	−	27.4772i	−1.48878	−	1.40955i
$381$	25.8760	+	6.30525i	1.32567	+	0.323028i
$382$	−1.57454	+	0.677546i	−0.0805602	+	0.0346663i
$383$	11.6517			0.595375			0.297688	−	0.954663i	$-0.403785\pi$
$383$	11.6517			0.595375			0.297688	+	0.954663i	$0.403785\pi$
$384$	−17.0914	+	9.58570i	−0.872189	+	0.489168i
$385$	2.48455	+	18.5606i	0.126625	+	0.945936i
$386$	−10.2224	+	13.7058i	−0.520306	+	0.697609i
$387$	−21.9171	+	14.0225i	−1.11411	+	0.712804i
$388$	13.1468	+	12.4471i	0.667425	+	0.631907i
$389$			19.5978i			0.993646i	0.867852	+	0.496823i	$0.165500\pi$
$389$			19.5978i			0.993646i	−0.867852	+	0.496823i	$0.834500\pi$
$390$	22.7213	−	3.83831i	1.15054	−	0.194360i
$391$	10.4036	+	18.0195i	0.526131	+	0.911286i
$392$	19.7266	+	1.69202i	0.996342	+	0.0854598i
$393$	−26.1065	−	6.36142i	−1.31690	−	0.320891i
$394$	−2.44927	+	20.7961i	−0.123392	+	1.04769i
$395$	1.58510	−	0.915159i	0.0797552	−	0.0460467i
$396$	9.71453	+	8.39221i	0.488174	+	0.421725i
$397$	9.64936	−	16.7132i	0.484288	−	0.838811i	−0.515550	−	0.856860i	$-0.672412\pi$
$397$	9.64936	−	16.7132i	0.484288	−	0.838811i	0.999837	+	0.0180492i	$0.00574554\pi$
$398$	0.779047	+	1.81041i	0.0390501	+	0.0907478i
$399$	22.3752	+	16.2984i	1.12016	+	0.815942i
$400$	21.2061	+	10.7438i	1.06031	+	0.537188i
$401$	−10.1551			−0.507123			−0.253561	−	0.967319i	$-0.581602\pi$
$401$	−10.1551			−0.507123			−0.253561	+	0.967319i	$0.581602\pi$
$402$	−1.70429	−	2.06099i	−0.0850025	−	0.102793i
$403$	−11.2216			−0.558985
$404$	10.1348	+	2.42084i	0.504225	+	0.120441i
$405$	17.1711	+	24.3217i	0.853238	+	1.20856i
$406$	−15.9200	+	28.6112i	−0.790096	+	1.41995i
$407$	−7.25258	−	4.18728i	−0.359497	−	0.207556i
$408$	−1.19247	+	17.7394i	−0.0590363	+	0.878230i
$409$	−7.11274	−	4.10654i	−0.351702	−	0.203055i	0.313732	−	0.949511i	$-0.398421\pi$
$409$	−7.11274	−	4.10654i	−0.351702	−	0.203055i	−0.665435	+	0.746456i	$0.731754\pi$
$410$	19.7970	−	8.51892i	0.977702	−	0.420720i
$411$	−2.48536	+	10.1996i	−0.122594	+	0.503111i
$412$	23.5513	+	5.62555i	1.16029	+	0.277151i
$413$	−1.21006	+	2.93937i	−0.0595431	+	0.144637i
$414$	−13.6392	+	20.1404i	−0.670329	+	0.989846i
$415$	34.6461	+	20.0029i	1.70071	+	0.981905i
$416$	−1.00602	+	16.0554i	−0.0493241	+	0.787183i
$417$	−8.03641	−	27.4726i	−0.393545	−	1.34534i
$418$	−14.6517	−	10.9278i	−0.716637	−	0.534498i
$419$	−16.1868	+	9.34543i	−0.790775	+	0.456554i	−0.840235	−	0.542222i	$-0.817583\pi$
$419$	−16.1868	+	9.34543i	−0.790775	+	0.456554i	0.0494605	+	0.998776i	$0.484250\pi$
$420$	−28.5789	−	10.1227i	−1.39451	−	0.493938i
$421$	−12.0139	−	6.93621i	−0.585520	−	0.338050i	0.177804	−	0.984066i	$-0.443101\pi$
$421$	−12.0139	−	6.93621i	−0.585520	−	0.338050i	−0.763324	+	0.646016i	$0.776434\pi$
$422$	−12.8859	−	29.9454i	−0.627277	−	1.45772i
$423$	0.451668	+	9.90451i	0.0219608	+	0.481574i
$424$	−19.1240	+	3.32005i	−0.928744	+	0.161236i
$425$	18.6791	−	10.7844i	0.906069	−	0.523119i
$426$	−30.4517	−	11.3319i	−1.47539	−	0.549032i
$427$	−12.4947	+	9.63067i	−0.604659	+	0.466061i
$428$	23.0298	−	24.3243i	1.11319	−	1.17576i
$429$	10.1148	−	2.95884i	0.488349	−	0.142854i
$430$	−24.2582	+	32.5246i	−1.16983	+	1.56847i
$431$	−7.80108	+	4.50395i	−0.375765	+	0.216948i	−0.675974	−	0.736926i	$-0.736277\pi$
$431$	−7.80108	+	4.50395i	−0.375765	+	0.216948i	0.300209	+	0.953873i	$0.402943\pi$
$432$	−19.2646	+	7.80225i	−0.926869	+	0.375386i
$433$		−	23.8787i		−	1.14754i	−0.819017	−	0.573769i	$-0.805481\pi$
$433$		−	23.8787i		−	1.14754i	0.819017	−	0.573769i	$-0.194519\pi$
$434$	12.9017	+	7.17886i	0.619303	+	0.344596i
$435$	34.6365	−	36.2520i	1.66069	−	1.73815i
$436$	−6.68170	+	1.98756i	−0.319995	+	0.0951870i
$437$	17.3164	−	29.9929i	0.828356	−	1.43476i
$438$	0.948907	+	5.61718i	0.0453405	+	0.268399i
$439$	15.4521	+	26.7638i	0.737488	+	1.27737i	0.953623	+	0.301004i	$0.0973217\pi$
$439$	15.4521	+	26.7638i	0.737488	+	1.27737i	−0.216135	+	0.976364i	$0.569345\pi$
$440$	18.7937	+	6.89657i	0.895953	+	0.328781i
$441$	20.5304	+	4.41640i	0.977636	+	0.210305i
$442$	11.6999	+	8.72624i	0.556506	+	0.415065i
$443$	−0.934840	−	1.61919i	−0.0444156	−	0.0769301i	0.842963	−	0.537972i	$-0.180809\pi$
$443$	−0.934840	−	1.61919i	−0.0444156	−	0.0769301i	−0.887379	+	0.461042i	$0.847476\pi$
$444$	11.3880	−	7.35913i	0.540449	−	0.349249i
$445$	−34.1609	−	19.7228i	−1.61938	−	0.934950i
$446$	11.6345	−	15.5991i	0.550908	−	0.738641i
$447$	13.9789	+	3.40627i	0.661181	+	0.161111i
$448$	11.4279	−	17.8158i	0.539919	−	0.841717i
$449$	−4.99072			−0.235527			−0.117763	−	0.993042i	$-0.537572\pi$
$449$	−4.99072			−0.235527			−0.117763	+	0.993042i	$0.537572\pi$
$450$	20.8776	+	14.1384i	0.984180	+	0.666492i
$451$	8.53618	−	4.92836i	0.401953	−	0.232068i
$452$	8.46478	+	28.4565i	0.398150	+	1.33848i
$453$	18.1837	+	4.43086i	0.854346	+	0.208180i
$454$	2.60530	−	22.1209i	0.122273	−	1.03819i
$455$	−19.7133	+	15.1946i	−0.924173	+	0.712336i
$456$	26.5632	−	13.0444i	1.24394	−	0.610860i
$457$	−18.9143	−	32.7605i	−0.884774	−	1.53247i	−0.845973	−	0.533226i	$-0.820980\pi$
$457$	−18.9143	−	32.7605i	−0.884774	−	1.53247i	−0.0388009	−	0.999247i	$-0.512354\pi$
$458$	8.76604	+	1.03242i	0.409610	+	0.0482419i
$459$	−3.62523	+	18.5062i	−0.169211	+	0.863794i
$460$	−8.81257	+	36.8937i	−0.410888	+	1.72018i
$461$	1.61662	−	2.80006i	0.0752933	−	0.130412i	−0.825920	−	0.563787i	$-0.809344\pi$
$461$	1.61662	−	2.80006i	0.0752933	−	0.130412i	0.901214	+	0.433375i	$0.142677\pi$
$462$	−13.5222	−	3.06899i	−0.629109	−	0.142782i
$463$	−13.4958	+	7.79182i	−0.627204	+	0.362117i	−0.779669	−	0.626192i	$-0.784612\pi$
$463$	−13.4958	+	7.79182i	−0.627204	+	0.362117i	0.152464	+	0.988309i	$0.451279\pi$
$464$	19.1313	+	29.3119i	0.888147	+	1.36077i
$465$	−16.3472	−	15.6188i	−0.758085	−	0.724302i
$466$	16.1520	−	21.6560i	0.748225	−	1.00320i
$467$	−17.5836	−	10.1519i	−0.813673	−	0.469774i	0.0345569	−	0.999403i	$-0.488998\pi$
$467$	−17.5836	−	10.1519i	−0.813673	−	0.469774i	−0.848230	+	0.529628i	$0.822331\pi$
$468$	−3.20402	+	16.7592i	−0.148106	+	0.774696i
$469$	2.67116	+	1.09964i	0.123343	+	0.0507768i
$470$	6.11144	+	14.2023i	0.281900	+	0.655102i
$471$	5.53614	+	5.28943i	0.255092	+	0.243724i
$472$	2.17743	+	2.60891i	0.100224	+	0.120085i
$473$	−9.27832	+	16.0705i	−0.426618	+	0.738923i
$474$	0.225750	+	1.33636i	0.0103690	+	0.0613808i
$475$	−31.0908	−	17.9503i	−1.42654	−	0.823614i
$476$	−7.86915	−	17.5177i	−0.360682	−	0.802920i
$477$	−20.5661	+	0.937861i	−0.941658	+	0.0429417i
$478$	−19.0254	+	8.18691i	−0.870202	+	0.374461i
$479$	3.61217			0.165044			0.0825221	−	0.996589i	$-0.473702\pi$
$479$	3.61217			0.165044			0.0825221	+	0.996589i	$0.473702\pi$
$480$	−23.8123	+	21.9889i	−1.08688	+	1.00365i
$481$		−	11.1309i		−	0.507526i
$482$	4.32589	−	36.7301i	0.197039	−	1.67301i
$483$	2.77825	−	26.1257i	0.126415	−	1.18876i
$484$	−12.4929	−	2.98411i	−0.567860	−	0.135641i
$485$	25.9331	+	14.9725i	1.17756	+	0.679865i
$486$	−21.3130	+	5.63529i	−0.966777	+	0.255622i
$487$	2.43745	−	1.40726i	0.110451	−	0.0637691i	−0.443757	−	0.896147i	$-0.646355\pi$
$487$	2.43745	−	1.40726i	0.110451	−	0.0637691i	0.554208	+	0.832378i	$0.313021\pi$
$488$	2.88468	+	16.6162i	0.130583	+	0.752179i
$489$	8.86651	+	8.47139i	0.400957	+	0.383089i
$490$	32.3855	−	4.85836i	1.46303	−	0.219479i
$491$	11.8286	+	20.4878i	0.533819	+	0.924602i	0.999219	+	0.0395019i	$0.0125771\pi$
$491$	11.8286	+	20.4878i	0.533819	+	0.924602i	−0.465400	+	0.885100i	$0.654090\pi$
$492$	0.799418	+	15.9385i	0.0360406	+	0.718565i
$493$	31.7581			1.43031
$494$	2.84160	−	24.1273i	0.127850	−	1.08554i
$495$	18.8533	+	9.76801i	0.847391	+	0.439039i
$496$	13.2177	−	8.62694i	0.593493	−	0.387361i
$497$	34.7849	−	4.65637i	1.56032	−	0.208867i
$498$	−22.8287	+	18.8778i	−1.02298	+	0.845934i
$499$	18.5619			0.830943			0.415472	−	0.909606i	$-0.363617\pi$
$499$	18.5619			0.830943			0.415472	+	0.909606i	$0.363617\pi$
$500$	6.06893	+	1.44965i	0.271411	+	0.0648303i
$501$	−10.7640	+	3.14875i	−0.480901	+	0.140676i
$502$	2.62357	−	22.2761i	0.117096	−	0.994230i
$503$	−3.52330			−0.157096			−0.0785482	−	0.996910i	$-0.525028\pi$
$503$	−3.52330			−0.157096			−0.0785482	+	0.996910i	$0.525028\pi$
$504$	14.4053	−	17.2188i	0.641662	−	0.766988i
$505$	17.2347			0.766936
$506$	−2.02912	+	17.2287i	−0.0902054	+	0.765911i
$507$	−6.15249	−	5.87832i	−0.273242	−	0.261065i
$508$	−7.14485	+	29.9118i	−0.317001	+	1.32712i
$509$	−39.0796			−1.73217			−0.866086	−	0.499896i	$-0.833372\pi$
$509$	−39.0796			−1.73217			−0.866086	+	0.499896i	$0.833372\pi$
$510$	4.89839	+	28.9966i	0.216904	+	1.28399i
$511$	−3.75643	−	4.87353i	−0.166175	−	0.215592i
$512$	−11.1582	−	19.6849i	−0.493126	−	0.869958i
$513$	29.6932	−	10.1758i	1.31099	−	0.449273i
$514$	3.26304	−	27.7056i	0.143926	−	1.22204i
$515$	40.0501			1.76482
$516$	−16.3066	−	25.2339i	−0.717859	−	1.11086i
$517$	3.53559	+	6.12382i	0.155495	+	0.269325i
$518$	−7.12087	+	12.7975i	−0.312873	+	0.562291i
$519$	8.96581	−	2.62272i	0.393555	−	0.115125i
$520$	4.55126	+	26.2159i	0.199586	+	1.14965i
$521$	11.7479	−	6.78263i	0.514683	−	0.297152i	−0.220074	−	0.975483i	$-0.570630\pi$
$521$	11.7479	−	6.78263i	0.514683	−	0.297152i	0.734757	+	0.678331i	$0.237296\pi$
$522$	16.2132	+	33.3987i	0.709631	+	1.46182i
$523$	−31.1006	−	17.9559i	−1.35993	−	0.785157i	−0.370318	−	0.928905i	$-0.620751\pi$
$523$	−31.1006	−	17.9559i	−1.35993	−	0.785157i	−0.989614	+	0.143748i	$0.954085\pi$
$524$	7.20849	−	30.1782i	0.314904	−	1.31834i
$525$	−27.0820	−	2.87994i	−1.18196	−	0.125691i
$526$	3.62970	−	30.8188i	0.158262	−	1.34376i
$527$		−	14.3208i		−	0.623823i
$528$	−9.63943	+	11.2613i	−0.419502	+	0.490085i
$529$	−9.87014			−0.429137
$530$	−29.4901	+	12.6900i	−1.28097	+	0.551220i
$531$	1.94248	+	3.03609i	0.0842964	+	0.131755i
$532$	−18.7022	+	25.9220i	−0.810844	+	1.12386i
$533$	11.3457	+	6.55046i	0.491438	+	0.283732i
$534$	22.5090	−	18.6134i	0.974060	−	0.805481i
$535$	27.7023	−	47.9817i	1.19767	−	2.07443i
$536$	2.37086	−	1.97874i	0.102405	−	0.0854686i
$537$	−27.1431	+	7.94004i	−1.17131	+	0.342638i
$538$	12.0811	+	28.0751i	0.520854	+	1.21040i
$539$	14.4498	−	3.93913i	0.622396	−	0.169670i
$540$	−27.9939	+	19.9549i	−1.20467	+	0.858720i
$541$	−5.71435	−	3.29918i	−0.245679	−	0.141843i	0.372105	−	0.928191i	$-0.378636\pi$
$541$	−5.71435	−	3.29918i	−0.245679	−	0.141843i	−0.617784	+	0.786348i	$0.711969\pi$
$542$	−1.99125	+	2.66981i	−0.0855315	+	0.114678i
$543$	7.71742	−	31.6713i	0.331186	−	1.35915i
$544$	−20.4897	−	1.28387i	−0.878489	−	0.0550453i
$545$	−9.98548	+	5.76512i	−0.427731	+	0.246951i
$546$	−5.45380	−	17.6045i	−0.233401	−	0.753401i
$547$	6.60040	−	11.4322i	0.282213	−	0.488807i	−0.689717	−	0.724079i	$-0.742265\pi$
$547$	6.60040	−	11.4322i	0.282213	−	0.488807i	0.971929	+	0.235273i	$0.0755983\pi$
$548$	−11.7904	−	2.81631i	−0.503662	−	0.120307i
$549$	0.814874	+	17.8692i	0.0347780	+	0.762638i
$550$	17.8594	+	2.10339i	0.761527	+	0.0896890i
$551$	−26.4301	−	45.7783i	−1.12596	−	1.95022i
$552$	−23.3274	−	15.6433i	−0.992882	−	0.665825i
$553$	−0.893673	−	1.15944i	−0.0380028	−	0.0493042i
$554$	−4.56717	+	38.7786i	−0.194040	+	1.64755i
$555$	15.4926	−	16.2152i	0.657624	−	0.688296i
$556$	31.6801	−	9.42369i	1.34354	−	0.399653i
$557$	−25.8467	+	14.9226i	−1.09516	+	0.632291i	−0.934946	−	0.354791i	$-0.884552\pi$
$557$	−25.8467	+	14.9226i	−1.09516	+	0.632291i	−0.160215	+	0.987082i	$0.551219\pi$
$558$	15.0606	−	7.31107i	0.637567	−	0.309502i
$559$	−24.6643			−1.04319
$560$	11.5386	−	33.0528i	0.487596	−	1.39674i
$561$	3.77603	+	12.9084i	0.159424	+	0.544993i
$562$	13.9645	−	18.7231i	0.589056	−	0.789788i
$563$	−12.4482	−	7.18695i	−0.524628	−	0.302894i	0.214198	−	0.976790i	$-0.431286\pi$
$563$	−12.4482	−	7.18695i	−0.524628	−	0.302894i	−0.738826	+	0.673896i	$0.764619\pi$
$564$	−11.4343	+	0.573500i	−0.481469	+	0.0241487i
$565$	24.5529	+	42.5269i	1.03295	+	1.78912i
$566$	29.1974	+	21.7766i	1.22726	+	0.915339i
$567$	17.4583	−	16.1928i	0.733179	−	0.680035i
$568$	12.9250	−	35.2217i	0.542323	−	1.47787i
$569$	−6.79129	−	11.7629i	−0.284706	−	0.493125i	0.687832	−	0.725870i	$-0.258563\pi$
$569$	−6.79129	−	11.7629i	−0.284706	−	0.493125i	−0.972538	+	0.232745i	$0.925229\pi$
$570$	37.7212	−	31.1929i	1.57997	−	1.30653i
$571$	3.72225	−	6.44713i	0.155771	−	0.269804i	−0.777568	−	0.628798i	$-0.783547\pi$
$571$	3.72225	−	6.44713i	0.155771	−	0.269804i	0.933340	+	0.358995i	$0.116880\pi$
$572$	3.46961	+	11.6640i	0.145072	+	0.487695i
$573$	−0.589416	−	2.01493i	−0.0246232	−	0.0841748i
$574$	−8.85392	−	14.7895i	−0.369555	−	0.617303i
$575$			34.0733i			1.42096i
$576$	−9.11025	−	22.2037i	−0.379594	−	0.925153i
$577$	26.5754	−	15.3433i	1.10635	−	0.638751i	0.168468	−	0.985707i	$-0.446118\pi$
$577$	26.5754	−	15.3433i	1.10635	−	0.638751i	0.937881	+	0.346956i	$0.112785\pi$
$578$	3.23734	−	4.34052i	0.134655	−	0.180542i
$579$	−15.1410	−	14.4662i	−0.629237	−	0.601197i
$580$	42.0415	+	39.8042i	1.74568	+	1.65278i
$581$	12.1803	−	29.5874i	0.505325	−	1.22749i
$582$	−17.0876	+	14.1303i	−0.708305	+	0.585720i
$583$	−12.7157	+	7.34144i	−0.526632	+	0.304051i
$584$	−6.48112	+	1.12516i	−0.268190	+	0.0465596i
$585$	1.28566	+	28.1928i	0.0531553	+	1.16563i
$586$	−10.3581	−	24.0711i	−0.427891	−	0.994367i
$587$	13.3239	+	7.69254i	0.549935	+	0.317505i	0.749096	−	0.662462i	$-0.230488\pi$
$587$	13.3239	+	7.69254i	0.549935	+	0.317505i	−0.199161	+	0.979967i	$0.563822\pi$
$588$	−4.99185	+	23.7293i	−0.205861	+	0.978581i
$589$	−20.6430	+	11.9182i	−0.850580	+	0.491082i
$590$	4.50549	+	3.36038i	0.185488	+	0.138345i
$591$	−24.9169	−	6.07155i	−1.02494	−	0.249750i
$592$	8.55725	+	13.1110i	0.351701	+	0.538857i
$593$	4.16061	+	2.40213i	0.170856	+	0.0986436i	0.582989	−	0.812480i	$-0.301883\pi$
$593$	4.16061	+	2.40213i	0.170856	+	0.0986436i	−0.412134	+	0.911123i	$0.635216\pi$
$594$	−11.6475	+	10.5611i	−0.477904	+	0.433328i
$595$	−19.3912	−	25.1578i	−0.794961	−	1.03137i
$596$	−3.85985	+	16.1592i	−0.158105	+	0.661906i
$597$	−2.31678	+	0.677715i	−0.0948195	+	0.0277370i
$598$	−21.1799	+	9.11401i	−0.866110	+	0.372700i
$599$	−8.69398	−	5.01947i	−0.355227	−	0.205090i	0.311758	−	0.950161i	$-0.399082\pi$
$599$	−8.69398	−	5.01947i	−0.355227	−	0.205090i	−0.666985	+	0.745071i	$0.732415\pi$
$600$	−16.2159	+	24.1813i	−0.662013	+	0.987198i
$601$	−32.0527	−	18.5057i	−1.30746	−	0.754862i	−0.325787	−	0.945443i	$-0.605629\pi$
$601$	−32.0527	−	18.5057i	−1.30746	−	0.754862i	−0.981671	+	0.190581i	$0.938963\pi$
$602$	28.3572	+	15.7787i	1.15575	+	0.643091i
$603$	2.75905	−	1.76523i	0.112357	−	0.0718859i
$604$	−5.02087	+	21.0198i	−0.204296	+	0.855283i
$605$	−21.2448			−0.863725
$606$	−4.45080	+	11.9604i	−0.180802	+	0.485860i
$607$	28.9929			1.17679			0.588394	−	0.808575i	$-0.299761\pi$
$607$	28.9929			1.17679			0.588394	+	0.808575i	$0.299761\pi$
$608$	15.2016	+	30.6038i	0.616505	+	1.24115i
$609$	−32.4133	−	23.6103i	−1.31345	−	0.956737i
$610$	11.0259	+	25.6229i	0.446427	+	1.03744i
$611$	−4.69927	+	8.13938i	−0.190112	+	0.329284i
$612$	−21.3879	−	4.08892i	−0.864554	−	0.165285i
$613$	−18.5664	+	10.7193i	−0.749888	+	0.432948i	−0.825653	−	0.564178i	$-0.809193\pi$
$613$	−18.5664	+	10.7193i	−0.749888	+	0.432948i	0.0757655	+	0.997126i	$0.475860\pi$
$614$	−0.0245556	+	0.208495i	−0.000990981	+	0.00841417i
$615$	7.41085	+	25.3341i	0.298834	+	1.02157i
$616$	3.47278	−	15.6300i	0.139922	−	0.629751i
$617$	−14.3986	−	24.9391i	−0.579667	−	1.00401i	−0.995517	−	0.0945794i	$-0.969849\pi$
$617$	−14.3986	−	24.9391i	−0.579667	−	1.00401i	0.415851	−	0.909433i	$-0.363484\pi$
$618$	−10.3428	+	27.7937i	−0.416048	+	1.11803i
$619$		−	38.8755i		−	1.56254i	−0.624194	−	0.781270i	$-0.714572\pi$
$619$		−	38.8755i		−	1.56254i	0.624194	−	0.781270i	$-0.285428\pi$
$620$	17.9490	−	18.9579i	0.720850	−	0.761368i
$621$	−22.4549	−	19.5773i	−0.901085	−	0.785610i
$622$	3.80046	−	5.09553i	0.152384	−	0.204312i
$623$	−12.0097	+	29.1730i	−0.481160	+	1.16879i
$624$	−19.3685	−	3.61171i	−0.775361	−	0.144584i
$625$	−19.3950			−0.775800
$626$	−30.7174	+	13.2182i	−1.22772	+	0.528304i
$627$	15.4646	−	16.1858i	0.617595	−	0.646400i
$628$	−6.07860	+	6.42026i	−0.242562	+	0.256196i
$629$	14.2051			0.566394
$630$	16.5579	−	33.2366i	0.659681	−	1.32418i
$631$		−	0.692263i		−	0.0275585i	−0.999905	−	0.0137793i	$-0.995614\pi$
$631$		−	0.692263i		−	0.0275585i	0.999905	−	0.0137793i	$-0.00438622\pi$
$632$	−1.54189	+	0.267682i	−0.0613331	+	0.0106478i
$633$	38.3210	−	11.2098i	1.52312	−	0.445551i
$634$	−36.6818	+	15.7847i	−1.45682	+	0.626891i
$635$			50.8665i			2.01858i
$636$	−1.19084	−	23.7425i	−0.0472198	−	0.941453i
$637$	14.1370	+	14.0148i	0.560130	+	0.555287i
$638$	21.2248	+	15.8303i	0.840296	+	0.626727i
$639$	18.3065	−	35.3334i	0.724193	−	1.39777i
$640$	−25.5152	−	27.3805i	−1.00858	−	1.08231i
$641$	−15.8086			−0.624403			−0.312202	−	0.950016i	$-0.601066\pi$
$641$	−15.8086			−0.624403			−0.312202	+	0.950016i	$0.601066\pi$
$642$	26.1440	+	31.6157i	1.03182	+	1.24777i
$643$	−15.3003	+	8.83365i	−0.603386	+	0.348365i	−0.770373	−	0.637594i	$-0.779930\pi$
$643$	−15.3003	+	8.83365i	−0.603386	+	0.348365i	0.166986	+	0.985959i	$0.446596\pi$
$644$	30.1817	+	3.07094i	1.18932	+	0.121012i
$645$	−35.9302	−	34.3290i	−1.41475	−	1.35170i
$646$	30.7909	+	3.62641i	1.21145	+	0.142679i
$647$	5.77505	+	10.0027i	0.227041	+	0.393246i	0.956930	−	0.290320i	$-0.0937617\pi$
$647$	5.77505	+	10.0027i	0.227041	+	0.393246i	−0.729889	+	0.683566i	$0.760428\pi$
$648$	−6.61882	−	24.5803i	−0.260012	−	0.965605i
$649$	2.22618	+	1.28529i	0.0873853	+	0.0504519i
$650$	9.44762	+	21.9551i	0.370566	+	0.861152i
$651$	−10.6467	+	14.6162i	−0.417276	+	0.572856i
$652$	−9.73530	+	10.2825i	−0.381264	+	0.402694i
$653$		−	19.8616i		−	0.777244i	−0.921397	−	0.388622i	$-0.872951\pi$
$653$		−	19.8616i		−	0.777244i	0.921397	−	0.388622i	$-0.127049\pi$
$654$	−1.42213	−	8.41848i	−0.0556097	−	0.329189i
$655$		−	51.3196i		−	2.00522i
$656$	−18.3999	+	1.00670i	−0.718394	+	0.0393051i
$657$	−6.96984	+	0.317840i	−0.271919	+	0.0124001i
$658$	10.6100	−	6.35177i	0.413619	−	0.247618i
$659$	−7.60340	+	13.1695i	−0.296186	+	0.513010i	−0.975260	−	0.221060i	$-0.929048\pi$
$659$	−7.60340	+	13.1695i	−0.296186	+	0.513010i	0.679074	+	0.734070i	$0.262382\pi$
$660$	−11.1801	+	21.8209i	−0.435185	+	0.849378i
$661$	−17.4961	+	30.3042i	−0.680520	+	1.17870i	0.294302	+	0.955713i	$0.404913\pi$
$661$	−17.4961	+	30.3042i	−0.680520	+	1.17870i	−0.974822	+	0.222983i	$0.928420\pi$
$662$	−7.87800	−	18.3075i	−0.306187	−	0.711543i
$663$	−12.3490	+	12.9249i	−0.479594	+	0.501963i
$664$	−21.9177	−	26.2610i	−0.850573	−	1.01913i
$665$	−20.1263	+	48.8890i	−0.780463	+	1.89583i
$666$	7.25201	+	14.9390i	0.281010	+	0.578873i
$667$	−25.0849	+	43.4484i	−0.971293	+	1.68233i
$668$	−3.69229	−	12.4126i	−0.142859	−	0.480257i
$669$	17.2325	+	16.4646i	0.666247	+	0.636557i
$670$	3.05376	−	4.09438i	0.117977	−	0.158180i
$671$	6.37872	+	11.0483i	0.246248	+	0.426513i
$672$	19.9580	+	16.5433i	0.769895	+	0.638170i
$673$	2.41265	−	4.17882i	0.0930007	−	0.161082i	−0.815772	−	0.578374i	$-0.803687\pi$
$673$	2.41265	−	4.17882i	0.0930007	−	0.161082i	0.908772	+	0.417292i	$0.137021\pi$
$674$	14.4236	+	33.5187i	0.555575	+	1.29109i
$675$	−20.2939	+	23.2769i	−0.781112	+	0.895927i
$676$	6.75535	−	7.13506i	0.259821	−	0.274425i
$677$	−3.41939	−	5.92256i	−0.131418	−	0.227623i	0.792805	−	0.609475i	$-0.208620\pi$
$677$	−3.41939	−	5.92256i	−0.131418	−	0.227623i	−0.924223	+	0.381852i	$0.875286\pi$
$678$	−35.8532	+	6.05667i	−1.37694	+	0.232605i
$679$	9.11714	−	22.1466i	0.349884	−	0.849909i
$680$	−33.4564	+	5.80824i	−1.28299	+	0.222736i
$681$	26.5042	+	6.45834i	1.01564	+	0.247484i
$682$	7.13841	−	9.57096i	0.273344	−	0.366491i
$683$	6.43661	+	11.1485i	0.246290	+	0.426587i	0.962494	−	0.271305i	$-0.0874551\pi$
$683$	6.43661	+	11.1485i	0.246290	+	0.426587i	−0.716204	+	0.697891i	$0.754122\pi$
$684$	11.9057	+	34.2330i	0.455225	+	1.30893i
$685$	−20.0502			−0.766080
$686$	−7.28795	−	25.1572i	−0.278255	−	0.960507i
$687$	−2.55930	+	10.5030i	−0.0976433	+	0.400716i
$688$	29.0517	−	18.9615i	1.10759	−	0.722899i
$689$	−16.9009	−	9.75776i	−0.643874	−	0.371741i
$690$	−43.5396	−	16.2022i	−1.65752	−	0.616809i
$691$	−12.9457	+	7.47421i	−0.492478	+	0.284332i	−0.725602	−	0.688115i	$-0.758439\pi$
$691$	−12.9457	+	7.47421i	−0.492478	+	0.284332i	0.233124	+	0.972447i	$0.425105\pi$
$692$	3.07547	+	10.3390i	0.116912	+	0.393028i
$693$	5.74272	−	15.9820i	0.218148	−	0.607105i
$694$	20.2595	−	27.1633i	0.769041	−	1.03111i
$695$	47.3444	−	27.3343i	1.79588	−	1.03685i
$696$	−38.4801	+	18.8964i	−1.45858	+	0.716266i
$697$	−8.35960	+	14.4792i	−0.316642	+	0.548440i
$698$	−6.89263	+	9.24142i	−0.260890	+	0.349793i
$699$	23.9236	+	22.8575i	0.904874	+	0.864550i
$700$	3.18335	−	31.2864i	0.120319	−	1.18252i
$701$			5.72767i			0.216331i	0.994133	+	0.108165i	$0.0344976\pi$
$701$			5.72767i			0.216331i	−0.994133	+	0.108165i	$0.965502\pi$
$702$	−19.8971	−	6.38848i	−0.750967	−	0.241118i
$703$	−11.8220	−	20.4763i	−0.445874	−	0.772276i
$704$	−13.0539	−	11.0715i	−0.491986	−	0.417271i
$705$	−18.1746	+	5.31652i	−0.684495	+	0.200232i
$706$	0.958377	−	8.13734i	0.0360690	−	0.306253i
$707$	−1.82887	−	13.6624i	−0.0687818	−	0.513827i
$708$	−3.49554	+	2.25889i	−0.131371	+	0.0848942i
$709$	10.3680	−	5.98599i	0.389380	−	0.224809i	−0.292511	−	0.956262i	$-0.594491\pi$
$709$	10.3680	−	5.98599i	0.389380	−	0.224809i	0.681891	+	0.731453i	$0.261158\pi$
$710$	7.25849	−	61.6300i	0.272406	−	2.31293i
$711$	−1.65816	+	0.0756158i	−0.0621859	+	0.00283581i
$712$	21.6108	+	25.8932i	0.809898	+	0.970390i
$713$	19.5923	+	11.3116i	0.733739	+	0.423624i
$714$	22.4665	−	6.96006i	0.840789	−	0.260474i
$715$	10.0639	+	17.4312i	0.376370	+	0.651891i
$716$	−9.31068	−	31.3002i	−0.347956	−	1.16974i
$717$	−7.12203	−	24.3468i	−0.265977	−	0.909246i
$718$	29.9559	+	22.3423i	1.11794	+	0.833808i
$719$	8.55690	−	14.8210i	0.319119	−	0.552730i	−0.661186	−	0.750222i	$-0.729946\pi$
$719$	8.55690	−	14.8210i	0.319119	−	0.552730i	0.980304	+	0.197492i	$0.0632798\pi$
$720$	−23.1885	−	32.2196i	−0.864185	−	1.20075i
$721$	−4.24994	−	31.7487i	−0.158276	−	1.18238i
$722$	−9.77691	−	22.7204i	−0.363859	−	0.845565i
$723$	44.0082	+	10.7236i	1.63668	+	0.398814i
$724$	36.6110	+	8.74505i	1.36064	+	0.325007i
$725$	45.0388	+	26.0031i	1.67270	+	0.965733i
$726$	5.48639	−	14.7433i	0.203619	−	0.547177i
$727$	4.46644	−	7.73610i	0.165651	−	0.286916i	−0.771235	−	0.636550i	$-0.780361\pi$
$727$	4.46644	−	7.73610i	0.165651	−	0.286916i	0.936886	+	0.349634i	$0.113694\pi$
$728$	20.2991	−	6.38981i	0.752333	−	0.236822i
$729$	−3.67974	−	26.7481i	−0.136287	−	0.990669i
$730$	−9.99419	+	4.30065i	−0.369902	+	0.159174i
$731$		−	31.4762i		−	1.16419i
$732$	−20.6291	+	1.03468i	−0.762472	+	0.0382428i
$733$	28.0771			1.03705			0.518527	−	0.855062i	$-0.326481\pi$
$733$	28.0771			1.03705			0.518527	+	0.855062i	$0.326481\pi$
$734$	18.7331	+	2.20630i	0.691453	+	0.0814360i
$735$	1.08789	+	40.0931i	0.0401273	+	1.47885i
$736$	17.9408	−	27.0180i	0.661307	−	0.995897i
$737$	1.16801	−	2.02305i	0.0430241	−	0.0745200i
$738$	−19.4950	−	1.39950i	−0.717622	−	0.0515163i
$739$	−2.63763	−	4.56851i	−0.0970269	−	0.168055i	0.813426	−	0.581669i	$-0.197600\pi$
$739$	−2.63763	−	4.56851i	−0.0970269	−	0.168055i	−0.910453	+	0.413613i	$0.864267\pi$
$740$	18.8048	+	17.8040i	0.691277	+	0.654490i
$741$	28.9082	+	7.04412i	1.06197	+	0.258772i
$742$	13.1891	+	22.0309i	0.484186	+	0.808781i
$743$	2.86769	−	1.65566i	0.105205	−	0.0607403i	−0.446474	−	0.894797i	$-0.647321\pi$
$743$	2.86769	−	1.65566i	0.105205	−	0.0607403i	0.551679	+	0.834056i	$0.313987\pi$
$744$	8.52102	+	17.3520i	0.312396	+	0.636154i
$745$			27.4795i			1.00677i
$746$	3.88652	−	32.9995i	0.142296	−	1.20820i
$747$	−19.5528	−	30.5609i	−0.715400	−	1.11817i
$748$	−14.8854	+	4.42786i	−0.544263	+	0.161899i
$749$	−40.9759	−	16.8686i	−1.49723	−	0.616367i
$750$	−2.66524	+	7.16217i	−0.0973206	+	0.261526i
$751$			10.5872i			0.386331i	0.981166	+	0.193166i	$0.0618754\pi$
$751$			10.5872i			0.386331i	−0.981166	+	0.193166i	$0.938125\pi$
$752$	−0.722204	−	13.2000i	−0.0263361	−	0.481354i
$753$	26.6901	+	6.50363i	0.972642	+	0.237006i
$754$	−4.11641	+	34.9514i	−0.149911	+	1.27285i
$755$			35.7452i			1.30090i
$756$	18.7893	+	20.0739i	0.683360	+	0.730082i
$757$		−	32.1399i		−	1.16814i	−0.811702	−	0.584072i	$-0.801459\pi$
$757$		−	32.1399i		−	1.16814i	0.811702	−	0.584072i	$-0.198541\pi$
$758$	−10.3927	−	1.22400i	−0.377478	−	0.0444576i
$759$	−20.6427	−	5.03004i	−0.749281	−	0.182579i
$760$	36.2160	+	43.3926i	1.31369	+	1.57402i
$761$			0.442762i			0.0160501i	0.999968	+	0.00802505i	$0.00255448\pi$
$761$			0.442762i			0.0160501i	−0.999968	+	0.00802505i	$0.997446\pi$
$762$	−35.3000	−	13.1361i	−1.27878	−	0.475870i
$763$	5.62976	+	7.30396i	0.203811	+	0.264421i
$764$	2.32352	−	0.691164i	0.0840621	−	0.0250054i
$765$	−35.9792	+	1.64073i	−1.30083	+	0.0593209i
$766$	−16.3649	−	1.92738i	−0.591289	−	0.0696392i
$767$			3.41664i			0.123368i
$768$	25.5905	−	10.6360i	0.923419	−	0.383793i
$769$	−10.1525	+	5.86155i	−0.366109	+	0.211373i	−0.671757	−	0.740771i	$-0.734460\pi$
$769$	−10.1525	+	5.86155i	−0.366109	+	0.211373i	0.305648	+	0.952144i	$0.401127\pi$
$770$	−0.419351	−	26.4795i	−0.0151124	−	0.954253i
$771$	33.1956	+	8.08883i	1.19551	+	0.291312i
$772$	16.6246	−	17.5590i	0.598331	−	0.631962i
$773$	8.75856	+	15.1703i	0.315023	+	0.545636i	0.979442	−	0.201724i	$-0.0646543\pi$
$773$	8.75856	+	15.1703i	0.315023	+	0.545636i	−0.664419	+	0.747360i	$0.731321\pi$
$774$	33.1023	−	16.0693i	1.18984	−	0.577598i
$775$	11.7257	−	20.3095i	0.421199	−	0.729539i
$776$	−16.4057	−	19.6568i	−0.588932	−	0.705636i
$777$	−14.4982	−	10.5607i	−0.520119	−	0.378862i
$778$	3.24178	−	27.5252i	0.116224	−	0.986825i
$779$	27.8286			0.997062
$780$	−32.5472	+	1.63245i	−1.16538	+	0.0584510i
$781$		−	28.3810i		−	1.01555i
$782$	−11.6312	−	27.0294i	−0.415929	−	0.966570i
$783$	−43.0142	+	14.7409i	−1.53720	+	0.526797i
$784$	−27.4262	−	5.63954i	−0.979507	−	0.201412i
$785$	−7.31186	+	12.6645i	−0.260972	+	0.452016i
$786$	35.6144	+	13.2531i	1.27032	+	0.472722i
$787$	−30.1428	−	17.4029i	−1.07447	−	0.620348i	−0.145073	−	0.989421i	$-0.546342\pi$
$787$	−30.1428	−	17.4029i	−1.07447	−	0.620348i	−0.929400	+	0.369073i	$0.879675\pi$
$788$	6.88003	−	28.8031i	0.245091	−	1.02607i
$789$	36.9256	+	8.99774i	1.31459	+	0.320328i
$790$	−2.37767	+	1.02315i	−0.0845936	+	0.0364019i
$791$	31.1066	−	23.9764i	1.10603	−	0.852504i
$792$	−12.2559	−	13.3939i	−0.435495	−	0.475930i
$793$	−8.47817	+	14.6846i	−0.301069	+	0.521466i
$794$	−16.3172	+	21.8776i	−0.579076	+	0.776407i
$795$	−11.0394	−	37.7384i	−0.391528	−	1.33844i
$796$	−0.794705	−	2.67160i	−0.0281676	−	0.0946925i
$797$	4.18351	+	7.24606i	0.148188	+	0.256668i	0.930558	−	0.366145i	$-0.119323\pi$
$797$	4.18351	+	7.24606i	0.148188	+	0.256668i	−0.782370	+	0.622814i	$0.785989\pi$
$798$	−28.7302	−	26.5925i	−1.01704	−	0.941364i
$799$	−10.3874	−	5.99714i	−0.367478	−	0.212164i
$800$	−28.0070	−	18.5975i	−0.990195	−	0.657521i
$801$	19.2790	+	30.1329i	0.681189	+	1.06469i
$802$	14.2629	+	1.67982i	0.503642	+	0.0593165i
$803$	−4.30936	+	2.48801i	−0.152074	+	0.0877999i
$804$	2.05277	+	3.17658i	0.0723957	+	0.112030i
$805$	49.7352	−	6.65764i	1.75293	−	0.234651i
$806$	15.7607	+	1.85623i	0.555149	+	0.0653828i
$807$	−35.9276	+	10.5097i	−1.26471	+	0.369959i
$808$	−13.8339	−	5.07654i	−0.486677	−	0.178592i
$809$	5.39028	+	9.33623i	0.189512	+	0.328245i	0.945088	−	0.326817i	$-0.105976\pi$
$809$	5.39028	+	9.33623i	0.189512	+	0.328245i	−0.755576	+	0.655061i	$0.772643\pi$
$810$	−20.0937	−	37.0004i	−0.706020	−	1.30006i
$811$		−	6.01258i		−	0.211130i	−0.994412	−	0.105565i	$-0.966335\pi$
$811$		−	6.01258i		−	0.211130i	0.994412	−	0.105565i	$-0.0336651\pi$
$812$	27.0925	−	37.5511i	0.950759	−	1.31779i
$813$	−2.94936	−	2.81792i	−0.103438	−	0.0988289i
$814$	9.49365	+	7.08075i	0.332752	+	0.248180i
$815$	−11.7105	+	20.2831i	−0.410199	+	0.710486i
$816$	4.60921	−	24.7178i	0.161355	−	0.865296i
$817$	−45.3720	+	26.1955i	−1.58737	+	0.916466i
$818$	9.31060	+	6.94423i	0.325537	+	0.242799i
$819$	22.2127	−	4.01087i	0.776175	−	0.140151i
$820$	−29.2141	+	8.69014i	−1.02020	+	0.303473i
$821$	−13.6618	+	7.88765i	−0.476801	+	0.275281i	−0.719082	−	0.694925i	$-0.755438\pi$
$821$	−13.6618	+	7.88765i	−0.476801	+	0.275281i	0.242282	+	0.970206i	$0.422104\pi$
$822$	5.17789	−	13.9143i	0.180600	−	0.485318i
$823$	47.6996	+	27.5394i	1.66271	+	0.959963i	0.971416	+	0.237385i	$0.0762904\pi$
$823$	47.6996	+	27.5394i	1.66271	+	0.959963i	0.691290	+	0.722578i	$0.257043\pi$
$824$	−32.1474	−	11.7969i	−1.11991	−	0.410964i
$825$	−5.21415	+	21.3983i	−0.181534	+	0.744992i
$826$	2.18575	−	3.92820i	0.0760521	−	0.136680i
$827$	−40.7048			−1.41545			−0.707723	−	0.706490i	$-0.750277\pi$
$827$	−40.7048			−1.41545			−0.707723	+	0.706490i	$0.750277\pi$
$828$	22.4879	−	26.0312i	0.781507	−	0.904645i
$829$	24.7044	+	42.7892i	0.858018	+	1.48613i	0.873817	+	0.486255i	$0.161637\pi$
$829$	24.7044	+	42.7892i	0.858018	+	1.48613i	−0.0157991	+	0.999875i	$0.505029\pi$
$830$	−45.3518	−	33.8253i	−1.57419	−	1.17409i
$831$	−46.4627	−	11.3217i	−1.61177	−	0.392744i
$832$	4.06879	−	22.3836i	0.141060	−	0.776010i
$833$	−17.8855	+	18.0415i	−0.619695	+	0.625100i
$834$	6.74278	+	39.9148i	0.233483	+	1.38214i
$835$	−10.7099	−	18.5500i	−0.370630	−	0.641950i
$836$	18.7707	+	17.7718i	0.649200	+	0.614652i
$837$	6.64716	+	19.3965i	0.229760	+	0.670442i
$838$	24.2803	−	10.4482i	0.838748	−	0.360926i
$839$	−16.7320	+	28.9806i	−0.577651	+	1.00052i	0.418097	+	0.908403i	$0.362697\pi$
$839$	−16.7320	+	28.9806i	−0.577651	+	1.00052i	−0.995748	+	0.0921191i	$0.970636\pi$
$840$	38.4647	+	18.9448i	1.32716	+	0.653658i
$841$	23.7873	+	41.2008i	0.820251	+	1.42072i
$842$	15.7262	+	11.7292i	0.541960	+	0.404216i
$843$	20.6836	+	19.7619i	0.712382	+	0.680636i
$844$	13.1449	+	44.1900i	0.452467	+	1.52108i
$845$	8.12592	−	14.0745i	0.279540	−	0.484178i
$846$	1.00399	−	13.9857i	0.0345181	−	0.480837i
$847$	2.25440	+	16.8413i	0.0774622	+	0.578673i
$848$	27.4090	−	1.49961i	0.941229	−	0.0514969i
$849$	−30.8173	+	32.2546i	−1.05765	+	1.10698i
$850$	−28.0188	+	12.0569i	−0.961037	+	0.413548i
$851$	−11.2203	+	19.4341i	−0.384626	+	0.666192i
$852$	40.8951	+	20.9529i	1.40104	+	0.717835i
$853$	17.0303	−	29.4973i	0.583105	−	1.00997i	−0.412003	−	0.911182i	$-0.635171\pi$
$853$	17.0303	−	29.4973i	0.583105	−	1.00997i	0.995109	−	0.0987857i	$-0.0314958\pi$
$854$	19.1419	−	11.4595i	0.655023	−	0.392136i
$855$	32.3082	+	50.4976i	1.10492	+	1.72698i
$856$	−36.3692	+	30.3541i	−1.24307	+	1.03748i
$857$		−	0.0416236i		−	0.00142183i	−1.00000		0.000710917i	$-0.999774\pi$
$857$		−	0.0416236i		−	0.00142183i	1.00000		0.000710917i	$-0.000226292\pi$
$858$	−14.6958	+	2.48255i	−0.501706	+	0.0847529i
$859$		−	4.16170i		−	0.141995i	−0.997476	−	0.0709977i	$-0.977382\pi$
$859$		−	4.16170i		−	0.141995i	0.997476	−	0.0709977i	$-0.0226183\pi$
$860$	39.4508	−	41.6683i	1.34526	−	1.42088i
$861$	19.2966	−	8.56310i	0.657625	−	0.291830i
$862$	11.7017	−	5.03541i	0.398561	−	0.171507i
$863$	−11.9396	−	6.89334i	−0.406429	−	0.234652i	0.282825	−	0.959172i	$-0.408728\pi$
$863$	−11.9396	−	6.89334i	−0.406429	−	0.234652i	−0.689254	+	0.724519i	$0.742062\pi$
$864$	28.3479	−	7.77164i	0.964414	−	0.264397i
$865$	8.92069	+	15.4511i	0.303312	+	0.525353i
$866$	−3.94992	+	33.5378i	−0.134224	+	1.13966i
$867$	4.79501	+	4.58133i	0.162847	+	0.155590i
$868$	−16.9331	−	12.2169i	−0.574746	−	0.414669i
$869$	−1.02522	+	0.591910i	−0.0347781	+	0.0200792i
$870$	−54.6438	+	45.1867i	−1.85260	+	1.53197i
$871$	3.10488			0.105205
$872$	9.71326	−	1.68628i	0.328933	−	0.0571048i
$873$	−14.6356	−	22.8753i	−0.495338	−	0.774211i
$874$	−29.2823	+	39.2608i	−0.990489	+	1.32802i
$875$	−1.09517	−	8.18133i	−0.0370234	−	0.276579i
$876$	−0.403574	−	8.04633i	−0.0136355	−	0.271860i
$877$		−	13.7303i		−	0.463639i	−0.972759	−	0.231820i	$-0.925532\pi$
$877$		−	13.7303i		−	0.463639i	0.972759	−	0.231820i	$-0.0744679\pi$
$878$	−17.2754	−	40.1460i	−0.583017	−	1.35486i
$879$	30.8037	−	9.01084i	1.03898	−	0.303928i
$880$	−25.2550	−	12.7950i	−0.851346	−	0.431321i
$881$		−	29.3023i		−	0.987219i	−0.869684	−	0.493610i	$-0.835677\pi$
$881$		−	29.3023i		−	0.987219i	0.869684	−	0.493610i	$-0.164323\pi$
$882$	−28.1045	−	9.59891i	−0.946327	−	0.323212i
$883$	16.0752			0.540972			0.270486	−	0.962724i	$-0.412816\pi$
$883$	16.0752			0.540972			0.270486	+	0.962724i	$0.412816\pi$
$884$	−14.9891	−	14.1914i	−0.504137	−	0.477309i
$885$	−4.75546	+	4.97726i	−0.159853	+	0.167309i
$886$	1.04515	+	2.42880i	0.0351125	+	0.0815972i
$887$	−33.3467			−1.11967			−0.559837	−	0.828603i	$-0.689136\pi$
$887$	−33.3467			−1.11967			−0.559837	+	0.828603i	$0.689136\pi$
$888$	−17.2118	+	8.45219i	−0.577590	+	0.283637i
$889$	40.3231	−	5.39772i	1.35239	−	0.181034i
$890$	44.7167	+	33.3515i	1.49891	+	1.11795i
$891$	−11.1060	−	15.7309i	−0.372064	−	0.527004i
$892$	−18.9210	+	19.9846i	−0.633523	+	0.669132i
$893$			19.9641i			0.668073i
$894$	−19.0700	−	7.09647i	−0.637798	−	0.237342i
$895$	−27.0065	−	46.7767i	−0.902729	−	1.56357i
$896$	−18.9976	+	23.1320i	−0.634666	+	0.772787i
$897$	−7.92854	−	27.1038i	−0.264726	−	0.904970i
$898$	7.00949	+	0.825545i	0.233910	+	0.0275488i
$899$	29.9039	−	17.2650i	0.997351	−	0.575821i
$900$	−26.9840	−	23.3110i	−0.899467	−	0.777033i
$901$	12.4527	−	21.5687i	0.414860	−	0.718558i
$902$	−12.8043	+	5.50990i	−0.426338	+	0.183460i
$903$	−23.4007	+	32.1256i	−0.778727	+	1.06907i
$904$	−7.18167	−	41.3675i	−0.238859	−	1.37586i
$905$	62.2589			2.06955
$906$	−24.8062	−	9.23106i	−0.824131	−	0.306681i
$907$	52.9652			1.75868			0.879341	−	0.476193i	$-0.157984\pi$
$907$	52.9652			1.75868			0.879341	+	0.476193i	$0.157984\pi$
$908$	−7.31832	+	30.6380i	−0.242867	+	1.01676i
$909$	−13.8778	−	7.19020i	−0.460298	−	0.238484i
$910$	30.2009	−	18.0801i	1.00115	−	0.599349i
$911$	25.4390	+	14.6872i	0.842833	+	0.486610i	0.858226	−	0.513272i	$-0.171567\pi$
$911$	25.4390	+	14.6872i	0.842833	+	0.486610i	−0.0153935	+	0.999882i	$0.504900\pi$
$912$	−39.4660	+	13.9269i	−1.30685	+	0.461167i
$913$	−22.4085	−	12.9376i	−0.741614	−	0.428171i
$914$	21.1461	+	49.1411i	0.699452	+	1.62544i
$915$	−32.7896	+	9.59177i	−1.08399	+	0.317094i
$916$	−12.1412	−	2.90009i	−0.401156	−	0.0958216i
$917$	−40.6823	+	5.44580i	−1.34345	+	0.179836i
$918$	8.15287	−	25.3924i	0.269085	−	0.838073i
$919$	−32.8150	−	18.9457i	−1.08247	−	0.624962i	−0.150906	−	0.988548i	$-0.548219\pi$
$919$	−32.8150	−	18.9457i	−1.08247	−	0.624962i	−0.931561	+	0.363586i	$0.881552\pi$
$920$	18.4801	−	50.3597i	0.609271	−	1.66031i
$921$	−0.249809	−	0.0608714i	−0.00823148	−	0.00200578i
$922$	−2.73372	+	3.66529i	−0.0900304	+	0.120710i
$923$	32.6683	−	18.8611i	1.07529	−	0.620820i
$924$	18.4843	+	6.54720i	0.608090	+	0.215387i
$925$	20.1454	+	11.6310i	0.662378	+	0.382424i
$926$	20.2439	−	8.71123i	0.665255	−	0.286269i
$927$	−32.2493	−	16.7086i	−1.05921	−	0.548782i
$928$	−22.0213	−	44.3334i	−0.722886	−	1.45531i
$929$	−9.77652	+	5.64447i	−0.320757	+	0.185189i	−0.651730	−	0.758451i	$-0.725956\pi$
$929$	−9.77652	+	5.64447i	−0.320757	+	0.185189i	0.330973	+	0.943640i	$0.392623\pi$
$930$	20.3762	+	24.6407i	0.668162	+	0.808001i
$931$	40.8912	+	10.7667i	1.34016	+	0.352864i
$932$	−26.2678	+	27.7442i	−0.860429	+	0.908792i
$933$	5.62908	+	5.37823i	0.184288	+	0.176075i
$934$	23.0170	+	17.1670i	0.753140	+	0.561722i
$935$	−22.2455	+	12.8434i	−0.727505	+	0.420025i
$936$	7.27231	−	23.0085i	0.237703	−	0.752055i
$937$			19.4082i			0.634039i	0.948419	+	0.317019i	$0.102682\pi$
$937$			19.4082i			0.634039i	−0.948419	+	0.317019i	$0.897318\pi$
$938$	−3.56977	−	1.98631i	−0.116557	−	0.0648553i
$939$	−11.4989	−	39.3090i	−0.375251	−	1.28280i
$940$	−6.23427	−	20.9581i	−0.203340	−	0.683578i
$941$	−5.56193	+	9.63355i	−0.181314	+	0.314045i	−0.942328	−	0.334690i	$-0.891368\pi$
$941$	−5.56193	+	9.63355i	−0.181314	+	0.314045i	0.761014	+	0.648735i	$0.224702\pi$
$942$	−6.90058	−	8.34480i	−0.224833	−	0.271888i
$943$	−13.2061	−	22.8736i	−0.430050	−	0.744868i
$944$	−2.62665	−	4.02441i	−0.0854902	−	0.130983i
$945$	37.9414	+	25.0739i	1.23423	+	0.815654i
$946$	15.6898	−	21.0364i	0.510119	−	0.683951i
$947$	4.07936	+	7.06565i	0.132561	+	0.229603i	0.924663	−	0.380786i	$-0.124347\pi$
$947$	4.07936	+	7.06565i	0.132561	+	0.229603i	−0.792102	+	0.610389i	$0.791013\pi$
$948$	−0.0960123	−	1.91426i	−0.00311833	−	0.0621723i
$949$	−5.72772	−	3.30690i	−0.185930	−	0.107346i
$950$	40.6979	+	30.3542i	1.32041	+	0.984819i
$951$	−13.7316	−	46.9416i	−0.445277	−	1.52218i
$952$	8.15457	+	25.9053i	0.264291	+	0.839597i
$953$	30.7401			0.995768			0.497884	−	0.867244i	$-0.334110\pi$
$953$	30.7401			0.995768			0.497884	+	0.867244i	$0.334110\pi$
$954$	29.0404	+	2.08474i	0.940217	+	0.0674958i
$955$	3.47239	−	2.00479i	0.112364	−	0.0648734i
$956$	28.0756	−	8.35146i	0.908029	−	0.270106i
$957$	−22.4023	+	23.4472i	−0.724163	+	0.757940i
$958$	−5.07332	−	0.597511i	−0.163911	−	0.0193047i
$959$	2.12764	+	15.8943i	0.0687050	+	0.513254i
$960$	37.0819	−	26.9446i	1.19681	−	0.869632i
$961$	7.71462	+	13.3621i	0.248859	+	0.431036i
$962$	−1.84123	+	15.6334i	−0.0593637	+	0.504042i
$963$	−42.3241	+	27.0789i	−1.36388	+	0.872604i
$964$	−12.1515	+	50.8720i	−0.391373	+	1.63848i
$965$	19.9975	−	34.6366i	0.643741	−	1.11499i
$966$	−8.22369	+	36.2342i	−0.264593	+	1.16582i
$967$	−13.5848	+	7.84318i	−0.436857	+	0.252220i	−0.702264	−	0.711917i	$-0.747827\pi$
$967$	−13.5848	+	7.84318i	−0.436857	+	0.252220i	0.265406	+	0.964137i	$0.414494\pi$
$968$	17.0528	+	6.25772i	0.548096	+	0.201131i
$969$	−8.98959	+	36.8922i	−0.288787	+	1.18515i
$970$	−33.9465	−	25.3187i	−1.08996	−	0.812934i
$971$	9.81489	+	5.66663i	0.314975	+	0.181851i	0.649151	−	0.760660i	$-0.275125\pi$
$971$	9.81489	+	5.66663i	0.314975	+	0.181851i	−0.334176	+	0.942511i	$0.608458\pi$
$972$	30.8664	−	4.38928i	0.990040	−	0.140786i
$973$	−26.6926	−	34.6305i	−0.855724	−	1.11020i
$974$	−3.65619	+	1.57331i	−0.117152	+	0.0504122i
$975$	−28.0959	+	8.21875i	−0.899790	+	0.263211i
$976$	−1.30296	−	23.8147i	−0.0417067	−	0.762290i
$977$	18.5566	−	32.1411i	0.593680	−	1.02828i	−0.400052	−	0.916492i	$-0.631008\pi$
$977$	18.5566	−	32.1411i	0.593680	−	1.02828i	0.993732	−	0.111791i	$-0.0356587\pi$
$978$	−11.0518	−	13.3648i	−0.353396	−	0.427358i
$979$	22.0947	+	12.7564i	0.706149	+	0.407695i
$980$	−46.2893	+	1.46652i	−1.47866	+	0.0468463i
$981$	10.4457	−	0.476348i	0.333506	−	0.0152086i
$982$	−13.2244	−	30.7319i	−0.422007	−	0.980695i
$983$	43.1048			1.37483			0.687415	−	0.726265i	$-0.258745\pi$
$983$	43.1048			1.37483			0.687415	+	0.726265i	$0.258745\pi$
$984$	1.51370	−	22.5180i	0.0482551	−	0.717848i
$985$		−	48.9812i		−	1.56067i
$986$	−44.6044	−	5.25329i	−1.42049	−	0.167299i
$987$	6.14314	+	13.8433i	0.195538	+	0.440636i
$988$	−7.98209	+	33.4169i	−0.253944	+	1.06313i
$989$	43.0627	+	24.8623i	1.36932	+	0.790574i
$990$	−24.8637	−	16.8379i	−0.790222	−	0.535143i
$991$	−34.3130	+	19.8106i	−1.08999	+	0.629304i	−0.933573	−	0.358387i	$-0.883327\pi$
$991$	−34.3130	+	19.8106i	−1.08999	+	0.629304i	−0.156414	+	0.987692i	$0.549993\pi$
$992$	−19.9914	+	9.93016i	−0.634728	+	0.315283i
$993$	23.4281	−	6.85330i	0.743468	−	0.217483i
$994$	−49.6258	+	0.785916i	−1.57404	+	0.0249278i
$995$	−2.30512	−	3.99258i	−0.0730772	−	0.126573i
$996$	35.1858	−	22.7377i	1.11490	−	0.720473i
$997$	−27.9430			−0.884965			−0.442482	−	0.896777i	$-0.645902\pi$
$997$	−27.9430			−0.884965			−0.442482	+	0.896777i	$0.645902\pi$
$998$	−26.0703	−	3.07043i	−0.825239	−	0.0971928i
$999$	−19.2399	+	6.59347i	−0.608722	+	0.208608i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.3	yes	180
7.3	odd	6		504.2.bf.b.115.65	✓	180
8.3	odd	2	inner	504.2.cz.b.187.56	yes	180
9.4	even	3		504.2.bf.b.355.65	yes	180
56.3	even	6		504.2.bf.b.115.66	yes	180
63.31	odd	6	inner	504.2.cz.b.283.56	yes	180
72.67	odd	6		504.2.bf.b.355.66	yes	180
504.283	even	6	inner	504.2.cz.b.283.3	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.65	✓	180	7.3	odd	6
504.2.bf.b.115.66	yes	180	56.3	even	6
504.2.bf.b.355.65	yes	180	9.4	even	3
504.2.bf.b.355.66	yes	180	72.67	odd	6
504.2.cz.b.187.3	yes	180	1.1	even	1	trivial
504.2.cz.b.187.56	yes	180	8.3	odd	2	inner
504.2.cz.b.283.3	yes	180	504.283	even	6	inner
504.2.cz.b.283.56	yes	180	63.31	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.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40451 - 0.165416i) q^{2} +(0.410054 - 1.68281i) q^{3} +(1.94528 + 0.464656i) q^{4} +3.30804 q^{5} +(-0.854288 + 2.29569i) q^{6} +(-0.351034 - 2.62236i) q^{7} +(-2.65529 - 0.974392i) q^{8} +(-2.66371 - 1.38009i) q^{9} +O(q^{10})\)	\(q+(-1.40451 - 0.165416i) q^{2} +(0.410054 - 1.68281i) q^{3} +(1.94528 + 0.464656i) q^{4} +3.30804 q^{5} +(-0.854288 + 2.29569i) q^{6} +(-0.351034 - 2.62236i) q^{7} +(-2.65529 - 0.974392i) q^{8} +(-2.66371 - 1.38009i) q^{9} +(-4.64616 - 0.547203i) q^{10} -2.13958 q^{11} +(1.57960 - 3.08300i) q^{12} +(-1.42190 - 2.46280i) q^{13} +(0.0592486 + 3.74119i) q^{14} +(1.35647 - 5.56680i) q^{15} +(3.56819 + 1.80777i) q^{16} +(3.14298 - 1.81460i) q^{17} +(3.51291 + 2.37896i) q^{18} +(-5.23140 - 3.02035i) q^{19} +(6.43504 + 1.53710i) q^{20} +(-4.55688 - 0.484586i) q^{21} +(3.00506 + 0.353922i) q^{22} +5.73325i q^{23} +(-2.72853 + 4.06880i) q^{24} +5.94311 q^{25} +(1.58968 + 3.69422i) q^{26} +(-3.41469 + 3.91661i) q^{27} +(0.535638 - 5.26432i) q^{28} +(7.57832 + 4.37535i) q^{29} +(-2.82601 + 7.59423i) q^{30} +(1.97299 - 3.41732i) q^{31} +(-4.71251 - 3.12926i) q^{32} +(-0.877345 + 3.60052i) q^{33} +(-4.71450 + 2.02872i) q^{34} +(-1.16123 - 8.67487i) q^{35} +(-4.54039 - 3.92236i) q^{36} +(3.38972 + 1.95705i) q^{37} +(6.84792 + 5.10746i) q^{38} +(-4.72748 + 1.38290i) q^{39} +(-8.78379 - 3.22332i) q^{40} +(-3.98965 + 2.30342i) q^{41} +(6.32001 + 1.43439i) q^{42} +(4.33651 - 7.51105i) q^{43} +(-4.16208 - 0.994170i) q^{44} +(-8.81166 - 4.56538i) q^{45} +(0.948372 - 8.05238i) q^{46} +(-1.65247 - 2.86216i) q^{47} +(4.50528 - 5.26331i) q^{48} +(-6.75355 + 1.84107i) q^{49} +(-8.34713 - 0.983086i) q^{50} +(-1.76484 - 6.03314i) q^{51} +(-1.62163 - 5.45151i) q^{52} +(5.94310 - 3.43125i) q^{53} +(5.44383 - 4.93606i) q^{54} -7.07782 q^{55} +(-1.62311 + 7.30517i) q^{56} +(-7.22784 + 7.56495i) q^{57} +(-9.92004 - 7.39878i) q^{58} +(-1.04047 - 0.600718i) q^{59} +(5.22536 - 10.1987i) q^{60} +(-2.98129 - 5.16375i) q^{61} +(-3.33636 + 4.47328i) q^{62} +(-2.68403 + 7.46967i) q^{63} +(6.10112 + 5.17458i) q^{64} +(-4.70369 - 8.14703i) q^{65} +(1.82782 - 4.91182i) q^{66} +(-0.545905 + 0.945534i) q^{67} +(6.95713 - 2.06950i) q^{68} +(9.64798 + 2.35094i) q^{69} +(0.195997 + 12.3760i) q^{70} +13.2647i q^{71} +(5.72818 + 6.26003i) q^{72} +(2.01411 - 1.16285i) q^{73} +(-4.43715 - 3.30941i) q^{74} +(2.43700 - 10.0011i) q^{75} +(-8.77309 - 8.30621i) q^{76} +(0.751066 + 5.61076i) q^{77} +(6.86853 - 1.16030i) q^{78} +(0.479167 - 0.276647i) q^{79} +(11.8037 + 5.98016i) q^{80} +(5.19072 + 7.35231i) q^{81} +(5.98450 - 2.57522i) q^{82} +(10.4733 + 6.04677i) q^{83} +(-8.63922 - 3.06003i) q^{84} +(10.3971 - 6.00277i) q^{85} +(-7.33310 + 9.83199i) q^{86} +(10.4704 - 10.9588i) q^{87} +(5.68121 + 2.08479i) q^{88} +(-10.3266 - 5.96208i) q^{89} +(11.6208 + 7.86970i) q^{90} +(-5.95921 + 4.59325i) q^{91} +(-2.66399 + 11.1527i) q^{92} +(-4.94167 - 4.72146i) q^{93} +(1.84745 + 4.29326i) q^{94} +(-17.3057 - 9.99143i) q^{95} +(-7.19833 + 6.64710i) q^{96} +(7.83942 + 4.52609i) q^{97} +(9.78995 - 1.46866i) q^{98} +(5.69923 + 2.95281i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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