LMFDB - Embedded newform 192.2.r.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("192.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	192.13
Dual form			192.2.r.a.133.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.968999 + 1.03007i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.122081 - 1.99627i) q^{4} +(2.48770 - 0.494834i) q^{5} +(0.233418 - 1.39482i) q^{6} +(-1.03562 - 2.50021i) q^{7} +(2.17459 + 1.80863i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})$	\(q+(-0.968999 + 1.03007i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.122081 - 1.99627i) q^{4} +(2.48770 - 0.494834i) q^{5} +(0.233418 - 1.39482i) q^{6} +(-1.03562 - 2.50021i) q^{7} +(2.17459 + 1.80863i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-1.90087 + 3.04199i) q^{10} +(2.08207 - 3.11604i) q^{11} +(1.21058 + 1.59201i) q^{12} +(1.29938 + 0.258462i) q^{13} +(3.57890 + 1.35594i) q^{14} +(-1.79353 + 1.79353i) q^{15} +(-3.97019 + 0.487414i) q^{16} +(5.07106 + 5.07106i) q^{17} +(0.580839 + 1.28943i) q^{18} +(-0.175108 + 0.880326i) q^{19} +(-1.29152 - 4.90571i) q^{20} +(2.25013 + 1.50349i) q^{21} +(1.19221 + 5.16411i) q^{22} +(1.40742 + 0.582973i) q^{23} +(-2.81293 - 0.295685i) q^{24} +(1.32439 - 0.548579i) q^{25} +(-1.52533 + 1.08800i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-4.86466 + 2.37260i) q^{28} +(-2.18042 - 3.26322i) q^{29} +(-0.109529 - 3.58539i) q^{30} -1.17860i q^{31} +(3.34504 - 4.56187i) q^{32} +3.74763i q^{33} +(-10.1374 + 0.309685i) q^{34} +(-3.81350 - 5.70730i) q^{35} +(-1.89103 - 0.651151i) q^{36} +(-1.91664 - 9.63560i) q^{37} +(-0.737116 - 1.03341i) q^{38} +(-1.22399 + 0.506991i) q^{39} +(6.30470 + 3.42327i) q^{40} +(-2.73651 - 1.13350i) q^{41} +(-3.72906 + 0.860906i) q^{42} +(-0.985566 - 0.658534i) q^{43} +(-6.47464 - 3.77597i) q^{44} +(0.494834 - 2.48770i) q^{45} +(-1.96429 + 0.884840i) q^{46} +(8.11274 + 8.11274i) q^{47} +(3.03030 - 2.61099i) q^{48} +(-0.228775 + 0.228775i) q^{49} +(-0.718255 + 1.89578i) q^{50} +(-7.03376 - 1.39910i) q^{51} +(0.357331 - 2.62546i) q^{52} +(-4.98567 + 7.46158i) q^{53} +(-1.19932 - 0.749424i) q^{54} +(3.63764 - 8.78205i) q^{55} +(2.26991 - 7.30998i) q^{56} +(-0.343486 - 0.829249i) q^{57} +(5.47416 + 0.916083i) q^{58} +(-13.5501 + 2.69529i) q^{59} +(3.79933 + 3.36142i) q^{60} +(11.2449 - 7.51358i) q^{61} +(1.21404 + 1.14206i) q^{62} -2.70620 q^{63} +(1.45770 + 7.86607i) q^{64} +3.36035 q^{65} +(-3.86031 - 3.63145i) q^{66} +(-10.1072 + 6.75338i) q^{67} +(9.50412 - 10.7423i) q^{68} +(-1.49411 + 0.297197i) q^{69} +(9.57418 + 1.60221i) q^{70} +(2.01550 + 4.86585i) q^{71} +(2.50314 - 1.31693i) q^{72} +(-5.31946 + 12.8423i) q^{73} +(11.7826 + 7.36262i) q^{74} +(-0.796413 + 1.19192i) q^{75} +(1.77875 + 0.242091i) q^{76} +(-9.94697 - 1.97858i) q^{77} +(0.663805 - 1.75206i) q^{78} +(-4.97742 + 4.97742i) q^{79} +(-9.63545 + 3.17713i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(3.81925 - 1.72043i) q^{82} +(1.10617 - 5.56107i) q^{83} +(2.72667 - 4.67541i) q^{84} +(15.1246 + 10.1059i) q^{85} +(1.63335 - 0.377081i) q^{86} +(3.62590 + 1.50190i) q^{87} +(10.1634 - 3.01041i) q^{88} +(-15.2973 + 6.33633i) q^{89} +(2.08301 + 2.92029i) q^{90} +(-0.699450 - 3.51637i) q^{91} +(0.991953 - 2.88077i) q^{92} +(0.654795 + 0.979969i) q^{93} +(-16.2179 + 0.495437i) q^{94} +2.27663i q^{95} +(-0.246861 + 5.65147i) q^{96} +1.54734i q^{97} +(-0.0139711 - 0.457337i) q^{98} +(-2.08207 - 3.11604i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) $ 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$133$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

Coefficient data

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

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

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

$2$	−0.968999	+	1.03007i	−0.685186	+	0.728368i
$2$	−0.968999	+	1.03007i	−0.685186	+	0.728368i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$4$	−0.122081	−	1.99627i	−0.0610406	−	0.998135i
$5$	2.48770	−	0.494834i	1.11253	−	0.221296i	0.395589	−	0.918428i	$-0.370540\pi$
$5$	2.48770	−	0.494834i	1.11253	−	0.221296i	0.716944	+	0.697131i	$0.245540\pi$
$6$	0.233418	−	1.39482i	0.0952926	−	0.569432i
$7$	−1.03562	−	2.50021i	−0.391427	−	0.944989i	−0.989629	−	0.143644i	$-0.954118\pi$
$7$	−1.03562	−	2.50021i	−0.391427	−	0.944989i	0.598202	−	0.801345i	$-0.295882\pi$
$8$	2.17459	+	1.80863i	0.768834	+	0.639448i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	−1.90087	+	3.04199i	−0.601106	+	0.961963i
$11$	2.08207	−	3.11604i	0.627768	−	0.939521i	−0.372168	−	0.928166i	$-0.621385\pi$
$11$	2.08207	−	3.11604i	0.627768	−	0.939521i	0.999936	−	0.0113556i	$-0.00361467\pi$
$12$	1.21058	+	1.59201i	0.349463	+	0.459575i
$13$	1.29938	+	0.258462i	0.360382	+	0.0716844i	0.371961	−	0.928249i	$-0.378686\pi$
$13$	1.29938	+	0.258462i	0.360382	+	0.0716844i	−0.0115786	+	0.999933i	$0.503686\pi$
$14$	3.57890	+	1.35594i	0.956500	+	0.362390i
$15$	−1.79353	+	1.79353i	−0.463088	+	0.463088i
$16$	−3.97019	+	0.487414i	−0.992548	+	0.121853i
$17$	5.07106	+	5.07106i	1.22991	+	1.22991i	0.963996	+	0.265916i	$0.0856743\pi$
$17$	5.07106	+	5.07106i	1.22991	+	1.22991i	0.265916	+	0.963996i	$0.414326\pi$
$18$	0.580839	+	1.28943i	0.136905	+	0.303921i
$19$	−0.175108	+	0.880326i	−0.0401725	+	0.201961i	−0.995659	−	0.0930733i	$-0.970331\pi$
$19$	−0.175108	+	0.880326i	−0.0401725	+	0.201961i	0.955487	+	0.295034i	$0.0953309\pi$
$20$	−1.29152	−	4.90571i	−0.288793	−	1.09695i
$21$	2.25013	+	1.50349i	0.491018	+	0.328088i
$22$	1.19221	+	5.16411i	0.254180	+	1.10099i
$23$	1.40742	+	0.582973i	0.293468	+	0.121558i	0.524560	−	0.851374i	$-0.324230\pi$
$23$	1.40742	+	0.582973i	0.293468	+	0.121558i	−0.231092	+	0.972932i	$0.574230\pi$
$24$	−2.81293	−	0.295685i	−0.574187	−	0.0603564i
$25$	1.32439	−	0.548579i	0.264877	−	0.109716i
$26$	−1.52533	+	1.08800i	−0.299141	+	0.213374i
$27$	0.195090	+	0.980785i	0.0375451	+	0.188752i
$28$	−4.86466	+	2.37260i	−0.919334	+	0.448380i
$29$	−2.18042	−	3.26322i	−0.404893	−	0.605965i	0.571855	−	0.820354i	$-0.306224\pi$
$29$	−2.18042	−	3.26322i	−0.404893	−	0.605965i	−0.976748	+	0.214389i	$0.931224\pi$
$30$	−0.109529	−	3.58539i	−0.0199972	−	0.654599i
$31$		−	1.17860i		−	0.211683i	−0.994383	−	0.105841i	$-0.966246\pi$
$31$		−	1.17860i		−	0.211683i	0.994383	−	0.105841i	$-0.0337536\pi$
$32$	3.34504	−	4.56187i	0.591326	−	0.806433i
$33$			3.74763i			0.652378i
$34$	−10.1374	+	0.309685i	−1.73855	+	0.0531105i
$35$	−3.81350	−	5.70730i	−0.644598	−	0.964710i
$36$	−1.89103	−	0.651151i	−0.315172	−	0.108525i
$37$	−1.91664	−	9.63560i	−0.315094	−	1.58408i	−0.736002	−	0.676980i	$-0.763288\pi$
$37$	−1.91664	−	9.63560i	−0.315094	−	1.58408i	0.420908	−	0.907103i	$-0.361712\pi$
$38$	−0.737116	−	1.03341i	−0.119576	−	0.167641i
$39$	−1.22399	+	0.506991i	−0.195994	+	0.0811836i
$40$	6.30470	+	3.42327i	0.996861	+	0.541267i
$41$	−2.73651	−	1.13350i	−0.427371	−	0.177023i	0.158621	−	0.987339i	$-0.449295\pi$
$41$	−2.73651	−	1.13350i	−0.427371	−	0.177023i	−0.585992	+	0.810317i	$0.699295\pi$
$42$	−3.72906	+	0.860906i	−0.575407	+	0.132841i
$43$	−0.985566	−	0.658534i	−0.150297	−	0.100426i	0.478148	−	0.878279i	$-0.341308\pi$
$43$	−0.985566	−	0.658534i	−0.150297	−	0.100426i	−0.628445	+	0.777854i	$0.716308\pi$
$44$	−6.47464	−	3.77597i	−0.976088	−	0.569248i
$45$	0.494834	−	2.48770i	0.0737655	−	0.370844i
$46$	−1.96429	+	0.884840i	−0.289619	+	0.130463i
$47$	8.11274	+	8.11274i	1.18336	+	1.18336i	0.978867	+	0.204498i	$0.0655562\pi$
$47$	8.11274	+	8.11274i	1.18336	+	1.18336i	0.204498	+	0.978867i	$0.434444\pi$
$48$	3.03030	−	2.61099i	0.437386	−	0.376864i
$49$	−0.228775	+	0.228775i	−0.0326822	+	0.0326822i
$50$	−0.718255	+	1.89578i	−0.101577	+	0.268104i
$51$	−7.03376	−	1.39910i	−0.984923	−	0.195913i
$52$	0.357331	−	2.62546i	0.0495528	−	0.364086i
$53$	−4.98567	+	7.46158i	−0.684835	+	1.02493i	0.312352	+	0.949966i	$0.398883\pi$
$53$	−4.98567	+	7.46158i	−0.684835	+	1.02493i	−0.997186	+	0.0749609i	$0.976117\pi$
$54$	−1.19932	−	0.749424i	−0.163207	−	0.101984i
$55$	3.63764	−	8.78205i	0.490500	−	1.18417i
$56$	2.26991	−	7.30998i	0.303329	−	0.976837i
$57$	−0.343486	−	0.829249i	−0.0454958	−	0.109837i
$58$	5.47416	+	0.916083i	0.718793	+	0.120288i
$59$	−13.5501	+	2.69529i	−1.76408	+	0.350897i	−0.967350	−	0.253443i	$-0.918437\pi$
$59$	−13.5501	+	2.69529i	−1.76408	+	0.350897i	−0.796727	+	0.604339i	$0.793437\pi$
$60$	3.79933	+	3.36142i	0.490491	+	0.433957i
$61$	11.2449	−	7.51358i	1.43976	−	0.962015i	0.441868	−	0.897080i	$-0.354316\pi$
$61$	11.2449	−	7.51358i	1.43976	−	0.962015i	0.997890	−	0.0649348i	$-0.0206839\pi$
$62$	1.21404	+	1.14206i	0.154183	+	0.145042i
$63$	−2.70620			−0.340950
$64$	1.45770	+	7.86607i	0.182212	+	0.983259i
$65$	3.36035			0.416800
$66$	−3.86031	−	3.63145i	−0.475172	−	0.447000i
$67$	−10.1072	+	6.75338i	−1.23479	+	0.825057i	−0.989520	−	0.144399i	$-0.953875\pi$
$67$	−10.1072	+	6.75338i	−1.23479	+	0.825057i	−0.245266	+	0.969456i	$0.578875\pi$
$68$	9.50412	−	10.7423i	1.15254	−	1.30269i
$69$	−1.49411	+	0.297197i	−0.179870	+	0.0357783i
$70$	9.57418	+	1.60221i	1.14433	+	0.191500i
$71$	2.01550	+	4.86585i	0.239196	+	0.577470i	0.997200	−	0.0747798i	$-0.0238254\pi$
$71$	2.01550	+	4.86585i	0.239196	+	0.577470i	−0.758004	+	0.652250i	$0.773825\pi$
$72$	2.50314	−	1.31693i	0.294998	−	0.155201i
$73$	−5.31946	+	12.8423i	−0.622595	+	1.50308i	0.226050	+	0.974116i	$0.427419\pi$
$73$	−5.31946	+	12.8423i	−0.622595	+	1.50308i	−0.848645	+	0.528962i	$0.822581\pi$
$74$	11.7826	+	7.36262i	1.36969	+	0.855887i
$75$	−0.796413	+	1.19192i	−0.0919618	+	0.137631i
$76$	1.77875	+	0.242091i	0.204036	+	0.0277698i
$77$	−9.94697	−	1.97858i	−1.13356	−	0.225480i
$78$	0.663805	−	1.75206i	0.0751611	−	0.198382i
$79$	−4.97742	+	4.97742i	−0.560003	+	0.560003i	−0.929308	−	0.369305i	$-0.879596\pi$
$79$	−4.97742	+	4.97742i	−0.560003	+	0.560003i	0.369305	+	0.929308i	$0.379596\pi$
$80$	−9.63545	+	3.17713i	−1.07728	+	0.355213i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	3.81925	−	1.72043i	0.421766	−	0.189990i
$83$	1.10617	−	5.56107i	0.121417	−	0.610407i	−0.871381	−	0.490608i	$-0.836775\pi$
$83$	1.10617	−	5.56107i	0.121417	−	0.610407i	0.992798	−	0.119799i	$-0.0382251\pi$
$84$	2.72667	−	4.67541i	0.297504	−	0.510129i
$85$	15.1246	+	10.1059i	1.64049	+	1.09614i
$86$	1.63335	−	0.377081i	0.176128	−	0.0406617i
$87$	3.62590	+	1.50190i	0.388737	+	0.161020i
$88$	10.1634	−	3.01041i	1.08342	−	0.320911i
$89$	−15.2973	+	6.33633i	−1.62151	+	0.671650i	−0.994242	−	0.107157i	$-0.965825\pi$
$89$	−15.2973	+	6.33633i	−1.62151	+	0.671650i	−0.627264	+	0.778807i	$0.715825\pi$
$90$	2.08301	+	2.92029i	0.219568	+	0.307826i
$91$	−0.699450	−	3.51637i	−0.0733223	−	0.368616i
$92$	0.991953	−	2.88077i	0.103418	−	0.300341i
$93$	0.654795	+	0.979969i	0.0678990	+	0.101618i
$94$	−16.2179	+	0.495437i	−1.67275	+	0.0511005i
$95$			2.27663i			0.233578i
$96$	−0.246861	+	5.65147i	−0.0251952	+	0.576800i
$97$			1.54734i			0.157109i	0.996910	+	0.0785545i	$0.0250304\pi$
$97$			1.54734i			0.157109i	−0.996910	+	0.0785545i	$0.974970\pi$
$98$	−0.0139711	−	0.457337i	−0.00141129	−	0.0461981i
$99$	−2.08207	−	3.11604i	−0.209256	−	0.313174i
$100$	−1.25679	−	2.57686i	−0.125679	−	0.257686i
$101$	−0.535980	−	2.69455i	−0.0533320	−	0.268118i	0.944914	−	0.327318i	$-0.106145\pi$
$101$	−0.535980	−	2.69455i	−0.0533320	−	0.268118i	−0.998246	+	0.0592003i	$0.981145\pi$
$102$	8.25688	−	5.88952i	0.817553	−	0.583150i
$103$	9.87745	−	4.09137i	0.973254	−	0.403135i	0.161331	−	0.986900i	$-0.448421\pi$
$103$	9.87745	−	4.09137i	0.973254	−	0.403135i	0.811922	+	0.583765i	$0.198421\pi$
$104$	2.35815	+	2.91214i	0.231235	+	0.285559i
$105$	6.34161	+	2.62678i	0.618878	+	0.256348i
$106$	−2.85483	−	12.3658i	−0.277286	−	1.20108i
$107$	15.7205	+	10.5041i	1.51976	+	1.01547i	0.985408	+	0.170209i	$0.0544442\pi$
$107$	15.7205	+	10.5041i	1.51976	+	1.01547i	0.534352	+	0.845262i	$0.320556\pi$
$108$	1.93410	−	0.509188i	0.186108	−	0.0489967i
$109$	2.73773	−	13.7635i	0.262227	−	1.31830i	−0.595150	−	0.803614i	$-0.702908\pi$
$109$	2.73773	−	13.7635i	0.262227	−	1.31830i	0.857377	−	0.514689i	$-0.172092\pi$
$110$	5.52123	+	12.2568i	0.526429	+	1.16864i
$111$	6.94688	+	6.94688i	0.659369	+	0.659369i
$112$	5.33024	+	9.42152i	0.503661	+	0.890250i
$113$	3.28452	−	3.28452i	0.308981	−	0.308981i	−0.535533	−	0.844514i	$-0.679889\pi$
$113$	3.28452	−	3.28452i	0.308981	−	0.308981i	0.844514	+	0.535533i	$0.179889\pi$
$114$	1.18702	+	0.449727i	0.111175	+	0.0421208i
$115$	3.78972	+	0.753822i	0.353393	+	0.0702942i
$116$	−6.24809	+	4.75108i	−0.580120	+	0.441126i
$117$	0.736037	−	1.10156i	0.0680467	−	0.101839i
$118$	10.3537	−	16.5693i	0.953139	−	1.52533i
$119$	7.42700	−	17.9304i	0.680832	−	1.64367i
$120$	−7.14403	+	0.656358i	−0.652158	+	0.0599170i
$121$	−1.16516	−	2.81295i	−0.105924	−	0.255723i
$122$	−3.15677	+	18.8636i	−0.285800	+	1.70783i
$123$	2.90506	−	0.577853i	0.261941	−	0.0521032i
$124$	−2.35280	+	0.143885i	−0.211288	+	0.0129212i
$125$	−7.52163	+	5.02579i	−0.672755	+	0.449520i
$126$	2.62231	−	2.78757i	0.233614	−	0.248337i
$127$	−16.2160			−1.43894			−0.719469	−	0.694524i	$-0.755615\pi$
$127$	−16.2160			−1.43894			−0.719469	+	0.694524i	$0.755615\pi$
$128$	−9.51510	−	6.12069i	−0.841024	−	0.540998i
$129$	1.18533			0.104363
$130$	−3.25618	+	3.46139i	−0.285586	+	0.303584i
$131$	6.53370	−	4.36568i	0.570852	−	0.381431i	−0.236384	−	0.971660i	$-0.575962\pi$
$131$	6.53370	−	4.36568i	0.570852	−	0.381431i	0.807236	+	0.590229i	$0.200962\pi$
$132$	7.48128	−	0.457515i	0.651162	−	0.0398215i
$133$	2.38234	−	0.473877i	0.206575	−	0.0410903i
$134$	2.83738	−	16.9551i	0.245112	−	1.46470i
$135$	0.970652	+	2.34336i	0.0835404	+	0.201684i
$136$	1.85580	+	20.1992i	0.159133	+	1.73206i
$137$	−5.99553	+	14.4745i	−0.512232	+	1.23664i	0.430349	+	0.902662i	$0.358390\pi$
$137$	−5.99553	+	14.4745i	−0.512232	+	1.23664i	−0.942582	+	0.333976i	$0.891610\pi$
$138$	1.14166	−	1.82702i	0.0971845	−	0.155526i
$139$	−8.54998	+	12.7960i	−0.725200	+	1.08534i	0.267362	+	0.963596i	$0.413848\pi$
$139$	−8.54998	+	12.7960i	−0.725200	+	1.08534i	−0.992562	+	0.121742i	$0.961152\pi$
$140$	−10.9278	+	8.30952i	−0.923564	+	0.702283i
$141$	−11.2527	−	2.23830i	−0.947648	−	0.188499i
$142$	−6.96517	−	2.63890i	−0.584504	−	0.221452i
$143$	3.51077	−	3.51077i	0.293585	−	0.293585i
$144$	−1.06902	+	3.85450i	−0.0890846	+	0.321209i
$145$	−7.03897	−	7.03897i	−0.584555	−	0.584555i
$146$	−8.07390	−	17.9236i	−0.668201	−	1.48337i
$147$	0.0631190	−	0.317321i	0.00520597	−	0.0261722i
$148$	−19.0013	+	5.00246i	−1.56190	+	0.411200i
$149$	−5.14406	−	3.43715i	−0.421418	−	0.281582i	0.326726	−	0.945119i	$-0.394055\pi$
$149$	−5.14406	−	3.43715i	−0.421418	−	0.281582i	−0.748144	+	0.663537i	$0.769055\pi$
$150$	−0.456031	−	1.97532i	−0.0372348	−	0.161285i
$151$	7.20927	+	2.98618i	0.586682	+	0.243012i	0.656223	−	0.754567i	$-0.272153\pi$
$151$	7.20927	+	2.98618i	0.586682	+	0.243012i	−0.0695403	+	0.997579i	$0.522153\pi$
$152$	−1.97297	+	1.59764i	−0.160029	+	0.129586i
$153$	6.62566	−	2.74444i	0.535652	−	0.221875i
$154$	11.6767	−	8.32882i	0.940933	−	0.671156i
$155$	−0.583211	−	2.93200i	−0.0468446	−	0.235504i
$156$	1.16152	+	2.38151i	0.0929958	+	0.190674i
$157$	−2.35440	−	3.52361i	−0.187902	−	0.281215i	0.725544	−	0.688176i	$-0.241588\pi$
$157$	−2.35440	−	3.52361i	−0.187902	−	0.281215i	−0.913445	+	0.406961i	$0.866588\pi$
$158$	−0.303966	−	9.95020i	−0.0241823	−	0.791595i
$159$		−	8.97397i		−	0.711682i
$160$	6.06409	−	13.0038i	0.479408	−	1.02804i
$161$		−	4.12258i		−	0.324905i
$162$	1.41355	−	0.0431823i	0.111059	−	0.00339272i
$163$	0.421255	+	0.630453i	0.0329952	+	0.0493809i	0.847601	−	0.530635i	$-0.178046\pi$
$163$	0.421255	+	0.630453i	0.0329952	+	0.0493809i	−0.814605	+	0.580016i	$0.803046\pi$
$164$	−1.92869	+	5.60119i	−0.150606	+	0.437379i
$165$	1.85445	+	9.32297i	0.144369	+	0.725792i
$166$	4.65641	+	6.52810i	0.361407	+	0.506679i
$167$	−4.29271	+	1.77810i	−0.332180	+	0.137593i	−0.542538	−	0.840031i	$-0.682537\pi$
$167$	−4.29271	+	1.77810i	−0.332180	+	0.137593i	0.210359	+	0.977624i	$0.432537\pi$
$168$	2.17385	+	7.33912i	0.167716	+	0.566225i
$169$	−10.3889	−	4.30321i	−0.799143	−	0.331016i
$170$	−25.0655	+	5.78672i	−1.92244	+	0.443822i
$171$	0.746304	+	0.498664i	0.0570713	+	0.0381338i
$172$	−1.19429	+	2.04785i	−0.0910640	+	0.156147i
$173$	−0.507123	+	2.54948i	−0.0385558	+	0.193833i	−0.995263	−	0.0972189i	$-0.969005\pi$
$173$	−0.507123	+	2.54948i	−0.0385558	+	0.193833i	0.956707	+	0.291052i	$0.0940053\pi$
$174$	−5.06055	+	2.27959i	−0.383639	+	0.172815i
$175$	−2.74312	−	2.74312i	−0.207360	−	0.207360i
$176$	−6.74742	+	13.3861i	−0.508606	+	1.00902i
$177$	9.76910	−	9.76910i	0.734291	−	0.734291i
$178$	8.29618	−	21.8971i	0.621825	−	1.64126i
$179$	5.89092	+	1.17178i	0.440308	+	0.0875827i	0.410266	−	0.911966i	$-0.365436\pi$
$179$	5.89092	+	1.17178i	0.440308	+	0.0875827i	0.0300421	+	0.999549i	$0.490436\pi$
$180$	−5.02653	−	0.684122i	−0.374655	−	0.0509914i
$181$	−8.06106	+	12.0642i	−0.599174	+	0.896728i	−0.999810	−	0.0195100i	$-0.993789\pi$
$181$	−8.06106	+	12.0642i	−0.599174	+	0.896728i	0.400635	+	0.916238i	$0.368789\pi$
$182$	4.29987	+	2.68688i	0.318728	+	0.199165i
$183$	−5.17544	+	12.4946i	−0.382580	+	0.923629i
$184$	2.00618	+	3.81324i	0.147898	+	0.281116i
$185$	−9.53605	−	23.0221i	−0.701104	−	1.69262i
$186$	−1.64393	−	0.275106i	−0.120539	−	0.0201718i
$187$	26.3599	−	5.24331i	1.92763	−	0.383429i
$188$	15.2048	−	17.1856i	1.10893	−	1.25339i
$189$	2.25013	−	1.50349i	0.163673	−	0.109363i
$190$	−2.34509	−	2.20606i	−0.170131	−	0.160044i
$191$	6.10598			0.441814			0.220907	−	0.975295i	$-0.429098\pi$
$191$	6.10598			0.441814			0.220907	+	0.975295i	$0.429098\pi$
$192$	−5.58219	−	5.73055i	−0.402860	−	0.413567i
$193$	−4.93795			−0.355442			−0.177721	−	0.984081i	$-0.556872\pi$
$193$	−4.93795			−0.355442			−0.177721	+	0.984081i	$0.556872\pi$
$194$	−1.59387	−	1.49937i	−0.114433	−	0.107649i
$195$	−2.79403	+	1.86691i	−0.200085	+	0.133692i
$196$	0.484627	+	0.428768i	0.0346162	+	0.0306263i
$197$	2.32724	−	0.462917i	0.165809	−	0.0329814i	−0.111488	−	0.993766i	$-0.535562\pi$
$197$	2.32724	−	0.462917i	0.165809	−	0.0329814i	0.277297	+	0.960784i	$0.410562\pi$
$198$	5.22726	+	0.874764i	0.371485	+	0.0621668i
$199$	−0.328761	−	0.793700i	−0.0233053	−	0.0562639i	0.911798	−	0.410638i	$-0.134694\pi$
$199$	−0.328761	−	0.793700i	−0.0233053	−	0.0562639i	−0.935104	+	0.354374i	$0.884694\pi$
$200$	3.87218	+	1.20239i	0.273804	+	0.0850220i
$201$	4.65181	−	11.2305i	0.328114	−	0.792136i
$202$	3.29494	+	2.05892i	0.231831	+	0.144865i
$203$	−5.90065	+	8.83094i	−0.414144	+	0.619811i
$204$	−1.93430	+	14.2121i	−0.135428	+	0.995045i
$205$	−7.36850	−	1.46569i	−0.514638	−	0.102368i
$206$	−5.35685	+	14.1390i	−0.373229	+	0.985110i
$207$	1.07719	−	1.07719i	0.0748702	−	0.0748702i
$208$	−5.28475	−	0.392810i	−0.366431	−	0.0272364i
$209$	2.37854	+	2.37854i	0.164527	+	0.164527i
$210$	−8.85078	+	3.98694i	−0.610762	+	0.275125i
$211$	1.46894	−	7.38488i	0.101126	−	0.508396i	−0.896708	−	0.442622i	$-0.854048\pi$
$211$	1.46894	−	7.38488i	0.101126	−	0.508396i	0.997835	−	0.0657740i	$-0.0209516\pi$
$212$	15.5040	+	9.04183i	1.06482	+	0.620995i
$213$	−4.37915	−	2.92605i	−0.300054	−	0.200490i
$214$	−26.0531	+	6.01473i	−1.78095	+	0.411158i
$215$	−2.77766	−	1.15054i	−0.189435	−	0.0784664i
$216$	−1.34964	+	2.48565i	−0.0918313	+	0.169127i
$217$	−2.94674	+	1.22058i	−0.200038	+	0.0828584i
$218$	11.5245	+	16.1569i	0.780536	+	1.09428i
$219$	−2.71183	−	13.6333i	−0.183249	−	0.921254i
$220$	−17.9754	−	6.18960i	−1.21190	−	0.417302i
$221$	5.27853	+	7.89988i	0.355073	+	0.531404i
$222$	−13.8873	+	0.424239i	−0.932054	+	0.0284731i
$223$			7.41178i			0.496330i	0.968718	+	0.248165i	$0.0798275\pi$
$223$			7.41178i			0.496330i	−0.968718	+	0.248165i	$0.920173\pi$
$224$	−14.8698	−	3.63893i	−0.993531	−	0.243137i
$225$		−	1.43350i		−	0.0955670i
$226$	0.200582	+	6.56597i	0.0133425	+	0.436762i
$227$	−10.7831	−	16.1380i	−0.715697	−	1.07112i	−0.993867	−	0.110584i	$-0.964728\pi$
$227$	−10.7831	−	16.1380i	−0.715697	−	1.07112i	0.278170	−	0.960532i	$-0.410272\pi$
$228$	−1.61347	+	0.786927i	−0.106855	+	0.0521155i
$229$	1.92839	+	9.69468i	0.127432	+	0.640642i	0.990719	+	0.135929i	$0.0434018\pi$
$229$	1.92839	+	9.69468i	0.127432	+	0.640642i	−0.863287	+	0.504713i	$0.831598\pi$
$230$	−4.44872	+	3.17321i	−0.293340	+	0.209236i
$231$	9.36984	−	3.88112i	0.616490	−	0.255359i
$232$	1.16046	−	11.0397i	0.0761878	−	0.724795i
$233$	16.9792	+	7.03302i	1.11235	+	0.460748i	0.861745	−	0.507342i	$-0.169372\pi$
$233$	16.9792	+	7.03302i	1.11235	+	0.460748i	0.250600	+	0.968091i	$0.419372\pi$
$234$	0.421460	+	1.82558i	0.0275517	+	0.119342i
$235$	24.1965	+	16.1676i	1.57841	+	1.05466i
$236$	7.03474	+	26.7207i	0.457923	+	1.73937i
$237$	1.37327	−	6.90388i	0.0892033	−	0.448455i
$238$	11.2727	+	25.0248i	0.730704	+	1.62212i
$239$	10.8731	+	10.8731i	0.703320	+	0.703320i	0.965122	−	0.261801i	$-0.0843165\pi$
$239$	10.8731	+	10.8731i	0.703320	+	0.703320i	−0.261801	+	0.965122i	$0.584317\pi$
$240$	6.24647	−	7.99485i	0.403208	−	0.516066i
$241$	12.1331	−	12.1331i	0.781559	−	0.781559i	−0.198535	−	0.980094i	$-0.563618\pi$
$241$	12.1331	−	12.1331i	0.781559	−	0.781559i	0.980094	+	0.198535i	$0.0636182\pi$
$242$	4.02658	+	1.52555i	0.258838	+	0.0980661i
$243$	0.980785	+	0.195090i	0.0629174	+	0.0125150i
$244$	−16.3719	−	21.5305i	−1.04810	−	1.37835i
$245$	−0.455918	+	0.682330i	−0.0291276	+	0.0435925i
$246$	−2.21977	+	3.55235i	−0.141528	+	0.226490i
$247$	−0.455061	+	1.09862i	−0.0289549	+	0.0699032i
$248$	2.13165	−	2.56297i	0.135360	−	0.162749i
$249$	2.16982	+	5.23842i	0.137507	+	0.331971i
$250$	2.11154	−	12.6178i	0.133546	−	0.798018i
$251$	18.0513	−	3.59062i	1.13939	−	0.226638i	0.410889	−	0.911686i	$-0.365219\pi$
$251$	18.0513	−	3.59062i	1.13939	−	0.226638i	0.728499	+	0.685047i	$0.240219\pi$
$252$	0.330376	+	5.40231i	0.0208118	+	0.340314i
$253$	4.74692	−	3.17179i	0.298436	−	0.199409i
$254$	15.7133	−	16.7036i	0.985941	−	1.04808i
$255$	−18.1902			−1.13911
$256$	15.5249	−	3.87025i	0.970303	−	0.241891i
$257$	2.13377			0.133101			0.0665504	−	0.997783i	$-0.478801\pi$
$257$	2.13377			0.133101			0.0665504	+	0.997783i	$0.478801\pi$
$258$	−1.14858	+	1.22097i	−0.0715077	+	0.0760144i
$259$	−22.1061	+	14.7708i	−1.37361	+	0.917814i
$260$	−0.410235	−	6.70817i	−0.0254417	−	0.416023i
$261$	−3.84923	+	0.765660i	−0.238262	+	0.0473932i
$262$	−1.83420	+	10.9605i	−0.113317	+	0.677142i
$263$	−3.24496	−	7.83402i	−0.200093	−	0.483066i	0.791702	−	0.610907i	$-0.209195\pi$
$263$	−3.24496	−	7.83402i	−0.200093	−	0.483066i	−0.991795	+	0.127841i	$0.959195\pi$
$264$	−6.77808	+	8.14956i	−0.417162	+	0.501571i
$265$	−8.71060	+	21.0292i	−0.535088	+	1.29182i
$266$	−1.82036	+	2.91316i	−0.111613	+	0.178617i
$267$	9.19893	−	13.7672i	0.562965	−	0.842537i
$268$	14.7155	+	19.3522i	0.898891	+	1.18212i
$269$	7.03261	+	1.39887i	0.428786	+	0.0852908i	0.404765	−	0.914421i	$-0.367353\pi$
$269$	7.03261	+	1.39887i	0.428786	+	0.0852908i	0.0240206	+	0.999711i	$0.492353\pi$
$270$	−3.35438	−	1.27088i	−0.204141	−	0.0773431i
$271$	21.1369	−	21.1369i	1.28398	−	1.28398i	0.345591	−	0.938385i	$-0.387678\pi$
$271$	21.1369	−	21.1369i	1.28398	−	1.28398i	0.938385	−	0.345591i	$-0.112322\pi$
$272$	−22.6048	−	17.6614i	−1.37062	−	1.07088i
$273$	2.53517	+	2.53517i	0.153435	+	0.153435i
$274$	−9.10004	−	20.2016i	−0.549754	−	1.22042i
$275$	1.04807	−	5.26902i	0.0632012	−	0.317734i
$276$	0.775689	+	2.94637i	0.0466910	+	0.177351i
$277$	1.73301	+	1.15796i	0.104127	+	0.0695752i	0.606543	−	0.795050i	$-0.292556\pi$
$277$	1.73301	+	1.15796i	0.104127	+	0.0695752i	−0.502417	+	0.864626i	$0.667556\pi$
$278$	−4.89578	−	21.2063i	−0.293629	−	1.27187i
$279$	−1.08888	−	0.451030i	−0.0651898	−	0.0270025i
$280$	2.02961	−	19.3083i	0.121293	−	1.15389i
$281$	−12.9674	+	5.37127i	−0.773570	+	0.320423i	−0.734318	−	0.678806i	$-0.762498\pi$
$281$	−12.9674	+	5.37127i	−0.773570	+	0.320423i	−0.0392525	+	0.999229i	$0.512498\pi$
$282$	13.2095	−	9.42213i	0.786612	−	0.561080i
$283$	1.25802	+	6.32449i	0.0747815	+	0.375952i	0.999994	−	0.00349759i	$-0.00111332\pi$
$283$	1.25802	+	6.32449i	0.0747815	+	0.375952i	−0.925212	+	0.379450i	$0.876113\pi$
$284$	9.46749	−	4.61751i	0.561792	−	0.273999i
$285$	−1.26483	−	1.89295i	−0.0749221	−	0.112129i
$286$	0.214399	+	7.01826i	0.0126777	+	0.414999i
$287$			8.01571i			0.473152i
$288$	−2.93453	−	4.83617i	−0.172919	−	0.284974i
$289$			34.4312i			2.02537i
$290$	14.0714	−	0.429863i	0.826299	−	0.0252424i
$291$	−0.859658	−	1.28657i	−0.0503940	−	0.0754200i
$292$	26.2861	+	9.05127i	1.53828	+	0.529686i
$293$	−4.14068	−	20.8166i	−0.241901	−	1.21612i	−0.890498	−	0.454987i	$-0.849644\pi$
$293$	−4.14068	−	20.8166i	−0.241901	−	1.21612i	0.648597	−	0.761132i	$-0.275356\pi$
$294$	0.265700	+	0.372500i	0.0154959	+	0.0217247i
$295$	−32.3749	+	13.4101i	−1.88494	+	0.780768i
$296$	13.2594	−	24.4200i	0.770684	−	1.41938i
$297$	3.46236	+	1.43416i	0.200906	+	0.0832181i
$298$	8.52509	−	1.96814i	0.493845	−	0.114011i
$299$	1.67809	+	1.12127i	0.0970467	+	0.0648445i
$300$	2.47661	+	1.44434i	0.142987	+	0.0833893i
$301$	−0.625800	+	3.14611i	−0.0360705	+	0.181339i
$302$	−10.0617	+	4.53244i	−0.578988	+	0.260813i
$303$	1.94266	+	1.94266i	0.111603	+	0.111603i
$304$	0.266128	−	3.58041i	0.0152635	−	0.205351i
$305$	24.2559	−	24.2559i	1.38889	−	1.38889i
$306$	−3.59330	+	9.48423i	−0.205415	+	0.542178i
$307$	12.4035	+	2.46722i	0.707907	+	0.140812i	0.535897	−	0.844284i	$-0.319974\pi$
$307$	12.4035	+	2.46722i	0.707907	+	0.140812i	0.172011	+	0.985095i	$0.444974\pi$
$308$	−2.73543	+	20.0984i	−0.155866	+	1.14521i
$309$	−5.93975	+	8.88947i	−0.337901	+	0.505704i
$310$	3.58529	+	2.24036i	0.203631	+	0.127244i
$311$	4.24466	−	10.2475i	0.240693	−	0.581083i	−0.756659	−	0.653809i	$-0.773170\pi$
$311$	4.24466	−	10.2475i	0.240693	−	0.581083i	0.997352	+	0.0727261i	$0.0231699\pi$
$312$	−3.57863	−	1.11124i	−0.202600	−	0.0629116i
$313$	−7.04950	−	17.0190i	−0.398461	−	0.961971i	−0.988031	−	0.154253i	$-0.950703\pi$
$313$	−7.04950	−	17.0190i	−0.398461	−	0.961971i	0.589570	−	0.807717i	$-0.299297\pi$
$314$	5.91097	+	0.989182i	0.333576	+	0.0558228i
$315$	−6.73222	+	1.33912i	−0.379318	+	0.0754510i
$316$	10.5439	+	9.32863i	0.593142	+	0.524776i
$317$	16.5011	−	11.0257i	0.926796	−	0.619265i	0.00211077	−	0.999998i	$-0.499328\pi$
$317$	16.5011	−	11.0257i	0.926796	−	0.619265i	0.924685	+	0.380732i	$0.124328\pi$
$318$	9.24380	+	8.69577i	0.518367	+	0.487635i
$319$	−14.7081			−0.823496
$320$	7.51871	+	18.8471i	0.420309	+	1.05359i
$321$	−18.9069			−1.05528
$322$	4.24654	+	3.99478i	0.236651	+	0.222620i
$323$	−5.35216	+	3.57620i	−0.297802	+	0.198985i
$324$	−1.32525	+	1.49790i	−0.0736251	+	0.0832167i
$325$	1.86266	−	0.370506i	0.103322	−	0.0205520i
$326$	−1.05761	−	0.176987i	−0.0585753	−	0.00980239i
$327$	5.37025	+	12.9649i	0.296975	+	0.716962i
$328$	−3.90070	−	7.41423i	−0.215380	−	0.409383i
$329$	11.8818	−	28.6852i	0.655066	−	1.58147i
$330$	−11.4003	−	7.12374i	−0.627564	−	0.392149i
$331$	−3.55473	+	5.32002i	−0.195385	+	0.292415i	−0.916207	−	0.400706i	$-0.868765\pi$
$331$	−3.55473	+	5.32002i	−0.195385	+	0.292415i	0.720821	+	0.693121i	$0.243765\pi$
$332$	−11.2364	−	1.52930i	−0.616680	−	0.0839315i
$333$	−9.63560	−	1.91664i	−0.528028	−	0.105031i
$334$	2.32807	−	6.14475i	0.127386	−	0.336226i
$335$	−21.8017	+	21.8017i	−1.19116	+	1.19116i
$336$	−9.66625	−	4.87239i	−0.527337	−	0.265810i
$337$	−5.12662	−	5.12662i	−0.279265	−	0.279265i	0.553551	−	0.832815i	$-0.313272\pi$
$337$	−5.12662	−	5.12662i	−0.279265	−	0.279265i	−0.832815	+	0.553551i	$0.813272\pi$
$338$	14.4994	−	6.53143i	0.788663	−	0.355263i
$339$	−0.906196	+	4.55576i	−0.0492178	+	0.247435i
$340$	18.3277	−	31.4265i	0.993961	−	1.70434i
$341$	−3.67256	−	2.45393i	−0.198880	−	0.132888i
$342$	−1.23683	+	0.285539i	−0.0668799	+	0.0154402i
$343$	−16.6925	−	6.91427i	−0.901312	−	0.373336i
$344$	−0.952157	−	3.21457i	−0.0513369	−	0.173318i
$345$	−3.56984	+	1.47867i	−0.192193	+	0.0796091i
$346$	−2.13473	−	2.99281i	−0.114764	−	0.160895i
$347$	−2.23237	−	11.2229i	−0.119840	−	0.602476i	−0.993298	−	0.115577i	$-0.963128\pi$
$347$	−2.23237	−	11.2229i	−0.119840	−	0.602476i	0.873459	−	0.486899i	$-0.161872\pi$
$348$	2.55554	−	7.42163i	0.136991	−	0.397841i
$349$	2.28795	+	3.42416i	0.122471	+	0.183291i	0.887639	−	0.460540i	$-0.152344\pi$
$349$	2.28795	+	3.42416i	0.122471	+	0.183291i	−0.765168	+	0.643831i	$0.777344\pi$
$350$	5.48368	−	0.167520i	0.293115	−	0.00895430i
$351$			1.32483i			0.0707143i
$352$	−7.25036	−	19.9214i	−0.386445	−	1.06182i
$353$			6.97075i			0.371015i	0.982643	+	0.185508i	$0.0593930\pi$
$353$			6.97075i			0.371015i	−0.982643	+	0.185508i	$0.940607\pi$
$354$	0.596590	+	19.5291i	0.0317084	+	1.03796i
$355$	7.42174	+	11.1074i	0.393905	+	0.589521i
$356$	14.5165	+	29.7639i	0.769375	+	1.57748i
$357$	3.78625	+	19.0348i	0.200390	+	1.00743i
$358$	−6.91531	+	4.93260i	−0.365485	+	0.260696i
$359$	−13.9273	+	5.76889i	−0.735057	+	0.304471i	−0.718628	−	0.695394i	$-0.755230\pi$
$359$	−13.9273	+	5.76889i	−0.735057	+	0.304471i	−0.0164287	+	0.999865i	$0.505230\pi$
$360$	5.57539	−	4.51476i	0.293849	−	0.237948i
$361$	16.8094	+	6.96268i	0.884705	+	0.366457i
$362$	−4.61582	−	19.9937i	−0.242602	−	1.05084i
$363$	2.53159	+	1.69155i	0.132874	+	0.0887836i
$364$	−6.93425	+	1.82558i	−0.363453	+	0.0956862i
$365$	−6.87839	+	34.5800i	−0.360032	+	1.81000i
$366$	−7.85531	−	17.4383i	−0.410604	−	0.911517i
$367$	−18.8325	−	18.8325i	−0.983048	−	0.983048i	0.0168106	−	0.999859i	$-0.494649\pi$
$367$	−18.8325	−	18.8325i	−0.983048	−	0.983048i	−0.999859	+	0.0168106i	$0.994649\pi$
$368$	−5.87189	−	1.62852i	−0.306093	−	0.0848924i
$369$	−2.09443	+	2.09443i	−0.109032	+	0.109032i
$370$	32.9547	+	12.4856i	1.71323	+	0.649094i
$371$	23.8188	+	4.73784i	1.23661	+	0.245977i
$372$	1.87635	−	1.42678i	0.0972840	−	0.0739752i
$373$	−12.9811	+	19.4277i	−0.672138	+	1.00593i	0.326026	+	0.945361i	$0.394290\pi$
$373$	−12.9811	+	19.4277i	−0.672138	+	1.00593i	−0.998164	+	0.0605650i	$0.980710\pi$
$374$	−20.1418	+	32.2333i	−1.04151	+	1.66674i
$375$	3.46183	−	8.35758i	0.178768	−	0.431584i
$376$	2.96893	+	32.3149i	0.153111	+	1.66651i
$377$	−1.98976	−	4.80371i	−0.102478	−	0.247403i
$378$	−0.631677	+	3.77466i	−0.0324900	+	0.194148i
$379$	−5.42693	+	1.07948i	−0.278763	+	0.0554493i	−0.332492	−	0.943106i	$-0.607889\pi$
$379$	−5.42693	+	1.07948i	−0.278763	+	0.0554493i	0.0537289	+	0.998556i	$0.482889\pi$
$380$	4.54478	−	0.277934i	0.233142	−	0.0142577i
$381$	13.4831	−	9.00914i	0.690761	−	0.461552i
$382$	−5.91669	+	6.28958i	−0.302724	+	0.321803i
$383$	−11.5193			−0.588611			−0.294306	−	0.955711i	$-0.595088\pi$
$383$	−11.5193			−0.588611			−0.294306	+	0.955711i	$0.595088\pi$
$384$	11.3120	−	0.197135i	0.577263	−	0.0100600i
$385$	−25.7241			−1.31102
$386$	4.78487	−	5.08643i	0.243544	−	0.258892i
$387$	−0.985566	+	0.658534i	−0.0500992	+	0.0334752i
$388$	3.08892	−	0.188901i	0.156816	−	0.00959002i
$389$	3.30427	−	0.657260i	0.167533	−	0.0333244i	−0.110611	−	0.993864i	$-0.535281\pi$
$389$	3.30427	−	0.657260i	0.167533	−	0.0333244i	0.278144	+	0.960539i	$0.410281\pi$
$390$	0.784367	−	4.68708i	0.0397180	−	0.237339i
$391$	4.18083	+	10.0934i	0.211434	+	0.510446i
$392$	−0.911264	+	0.0837224i	−0.0460258	+	0.00422862i
$393$	−3.00713	+	7.25986i	−0.151690	+	0.366211i
$394$	−1.77826	+	2.84578i	−0.0895873	+	0.143368i
$395$	−9.91932	+	14.8453i	−0.499095	+	0.746949i
$396$	−5.96628	+	4.53679i	−0.299817	+	0.227982i
$397$	14.8508	+	2.95400i	0.745339	+	0.148257i	0.553128	−	0.833097i	$-0.313434\pi$
$397$	14.8508	+	2.95400i	0.745339	+	0.148257i	0.192211	+	0.981354i	$0.438434\pi$
$398$	1.13613	+	0.430448i	0.0569493	+	0.0215764i
$399$	−1.71757	+	1.71757i	−0.0859861	+	0.0859861i
$400$	−4.99068	+	2.82349i	−0.249534	+	0.141174i
$401$	12.1595	+	12.1595i	0.607218	+	0.607218i	0.942218	−	0.335000i	$-0.108736\pi$
$401$	12.1595	+	12.1595i	0.607218	+	0.607218i	−0.335000	+	0.942218i	$0.608736\pi$
$402$	7.06055	+	15.6740i	0.352148	+	0.781748i
$403$	0.304623	−	1.53144i	0.0151743	−	0.0762866i
$404$	−5.31362	+	1.39891i	−0.264363	+	0.0695986i
$405$	−2.10897	−	1.40917i	−0.104796	−	0.0700221i
$406$	−3.37875	−	14.6352i	−0.167685	−	0.726335i
$407$	−34.0155	−	14.0897i	−1.68609	−	0.698399i
$408$	−12.7651	−	15.7640i	−0.631966	−	0.780432i
$409$	19.7638	−	8.18645i	0.977259	−	0.404794i	0.163850	−	0.986485i	$-0.447609\pi$
$409$	19.7638	−	8.18645i	0.977259	−	0.404794i	0.813410	+	0.581691i	$0.197609\pi$
$410$	8.64983	−	6.16981i	0.427184	−	0.304705i
$411$	−3.05649	−	15.3660i	−0.150766	−	0.757950i
$412$	−9.37334	−	19.2186i	−0.461791	−	0.946831i
$413$	20.7716	+	31.0868i	1.02210	+	1.52968i
$414$	0.0657832	+	2.15338i	0.00323307	+	0.105833i
$415$		−	14.3816i		−	0.705967i
$416$	5.52554	−	5.06302i	0.270912	−	0.248235i
$417$		−	15.3896i		−	0.753630i
$418$	−4.75487	+	0.145255i	−0.232568	+	0.00710467i
$419$	−4.48029	−	6.70523i	−0.218877	−	0.327572i	0.705740	−	0.708471i	$-0.250615\pi$
$419$	−4.48029	−	6.70523i	−0.218877	−	0.327572i	−0.924617	+	0.380899i	$0.875615\pi$
$420$	4.46958	−	12.9803i	0.218093	−	0.633371i
$421$	−3.19573	−	16.0660i	−0.155750	−	0.783010i	−0.977132	−	0.212632i	$-0.931797\pi$
$421$	−3.19573	−	16.0660i	−0.155750	−	0.783010i	0.821382	−	0.570379i	$-0.193203\pi$
$422$	6.18352	+	8.66905i	0.301009	+	0.422003i
$423$	10.5998	−	4.39058i	0.515380	−	0.213477i
$424$	−24.3371	+	7.20865i	−1.18191	+	0.350083i
$425$	9.49791	+	3.93416i	0.460716	+	0.190835i
$426$	7.25742	−	1.67548i	0.351623	−	0.0811772i
$427$	−30.4309	−	20.3333i	−1.47265	−	0.983996i
$428$	19.0499	−	32.6648i	0.920810	−	1.57891i
$429$	−0.968619	+	4.86958i	−0.0467654	+	0.235105i
$430$	3.87669	−	1.74630i	0.186950	−	0.0842141i
$431$	0.519240	+	0.519240i	0.0250109	+	0.0250109i	0.719502	−	0.694491i	$-0.244370\pi$
$431$	0.519240	+	0.519240i	0.0250109	+	0.0250109i	−0.694491	+	0.719502i	$0.744370\pi$
$432$	−1.25259	−	3.79882i	−0.0602655	−	0.182771i
$433$	−10.8591	+	10.8591i	−0.521857	+	0.521857i	−0.918132	−	0.396275i	$-0.870303\pi$
$433$	−10.8591	+	10.8591i	−0.521857	+	0.521857i	0.396275	+	0.918132i	$0.370303\pi$
$434$	1.59811	−	4.21808i	0.0767117	−	0.202475i
$435$	9.76333	+	1.94205i	0.468116	+	0.0931140i
$436$	−27.8099	−	3.78498i	−1.33185	−	0.181268i
$437$	−0.759657	+	1.13691i	−0.0363393	+	0.0543856i
$438$	16.6710	+	10.4173i	0.796572	+	0.497758i
$439$	15.8491	−	38.2632i	0.756438	−	1.82620i	0.237507	−	0.971386i	$-0.423670\pi$
$439$	15.8491	−	38.2632i	0.756438	−	1.82620i	0.518930	−	0.854816i	$-0.326330\pi$
$440$	23.7939	−	12.5182i	1.13433	−	0.596782i
$441$	0.123812	+	0.298909i	0.00589583	+	0.0142338i
$442$	−13.2523	−	2.21773i	−0.630348	−	0.105487i
$443$	−37.4120	+	7.44170i	−1.77750	+	0.353566i	−0.971259	−	0.238026i	$-0.923500\pi$
$443$	−37.4120	+	7.44170i	−1.77750	+	0.353566i	−0.806238	+	0.591592i	$0.798500\pi$
$444$	13.0198	−	14.7159i	0.617891	−	0.698388i
$445$	−34.9195	+	23.3325i	−1.65534	+	1.10607i
$446$	−7.63464	−	7.18201i	−0.361511	−	0.340078i
$447$	6.18671			0.292621
$448$	18.1572	−	11.7908i	0.857847	−	0.557063i
$449$	10.5229			0.496604			0.248302	−	0.968683i	$-0.420127\pi$
$449$	10.5229			0.496604			0.248302	+	0.968683i	$0.420127\pi$
$450$	1.47661	+	1.38907i	0.0696080	+	0.0654812i
$451$	−9.22963	+	6.16704i	−0.434606	+	0.290395i
$452$	−6.95776	−	6.15581i	−0.327266	−	0.289545i
$453$	−7.65332	+	1.52234i	−0.359584	+	0.0715258i
$454$	27.0720	+	4.53041i	1.27055	+	0.212623i
$455$	−3.48004	−	8.40157i	−0.163147	−	0.393872i
$456$	0.752864	−	2.42452i	0.0352561	−	0.113538i
$457$	16.1237	−	38.9260i	0.754234	−	1.82088i	0.220109	−	0.975475i	$-0.429359\pi$
$457$	16.1237	−	38.9260i	0.754234	−	1.82088i	0.534125	−	0.845406i	$-0.320641\pi$
$458$	−11.8548	−	7.40776i	−0.553938	−	0.346142i
$459$	−3.98430	+	5.96293i	−0.185971	+	0.278326i
$460$	1.04218	−	7.65733i	0.0485918	−	0.357025i
$461$	−27.2337	−	5.41713i	−1.26840	−	0.252301i	−0.485384	−	0.874301i	$-0.661320\pi$
$461$	−27.2337	−	5.41713i	−1.26840	−	0.252301i	−0.783017	+	0.622000i	$0.786320\pi$
$462$	−5.08156	+	13.4124i	−0.236415	+	0.624000i
$463$	−7.23627	+	7.23627i	−0.336298	+	0.336298i	−0.854972	−	0.518674i	$-0.826426\pi$
$463$	−7.23627	+	7.23627i	−0.336298	+	0.336298i	0.518674	+	0.854972i	$0.326426\pi$
$464$	10.2472	+	11.8929i	0.475715	+	0.552112i
$465$	2.11385	+	2.11385i	0.0980276	+	0.0980276i
$466$	−23.6973	+	10.6748i	−1.09776	+	0.494499i
$467$	−0.606832	+	3.05075i	−0.0280808	+	0.141172i	−0.992282	−	0.123998i	$-0.960428\pi$
$467$	−0.606832	+	3.05075i	−0.0280808	+	0.141172i	0.964202	+	0.265170i	$0.0854282\pi$
$468$	−2.28886	−	1.33485i	−0.105803	−	0.0617035i
$469$	27.3520	+	18.2760i	1.26300	+	0.843909i
$470$	−40.1001	+	9.25768i	−1.84968	+	0.427025i
$471$	3.91523	+	1.62174i	0.180404	+	0.0747259i
$472$	−34.3408	−	18.6461i	−1.58066	−	0.858255i
$473$	−4.10404	+	1.69995i	−0.188704	+	0.0781637i
$474$	5.78077	+	8.10441i	0.265520	+	0.372248i
$475$	0.251018	+	1.26195i	0.0115175	+	0.0579023i
$476$	−36.7006	−	12.6373i	−1.68217	−	0.579232i
$477$	4.98567	+	7.46158i	0.228278	+	0.341642i
$478$	−21.7360	+	0.664008i	−0.994181	+	0.0303710i
$479$			6.57738i			0.300528i	0.988646	+	0.150264i	$0.0480124\pi$
$479$			6.57738i			0.300528i	−0.988646	+	0.150264i	$0.951988\pi$
$480$	2.18242	+	14.1813i	0.0996134	+	0.647285i
$481$		−	13.0156i		−	0.593462i
$482$	0.740954	+	24.2548i	0.0337496	+	1.10478i
$483$	2.29038	+	3.42780i	0.104216	+	0.155970i
$484$	−5.47317	+	2.66939i	−0.248780	+	0.121336i
$485$	0.765678	+	3.84932i	0.0347677	+	0.174789i
$486$	−1.15134	+	0.821233i	−0.0522257	+	0.0372519i
$487$	−34.7725	+	14.4032i	−1.57569	+	0.652673i	−0.987724	−	0.156210i	$-0.950072\pi$
$487$	−34.7725	+	14.4032i	−1.57569	+	0.652673i	−0.587969	+	0.808883i	$0.700072\pi$
$488$	38.0423	+	3.99887i	1.72209	+	0.181020i
$489$	−0.700522	−	0.290166i	−0.0316787	−	0.0131217i
$490$	−0.261062	−	1.13080i	−0.0117936	−	0.0510845i
$491$	−13.6760	−	9.13801i	−0.617189	−	0.412393i	0.207294	−	0.978279i	$-0.433534\pi$
$491$	−13.6760	−	9.13801i	−0.617189	−	0.412393i	−0.824483	+	0.565886i	$0.808534\pi$
$492$	−1.50820	−	5.72874i	−0.0679950	−	0.258272i
$493$	5.49097	−	27.6050i	0.247301	−	1.24327i
$494$	−0.690694	−	1.53330i	−0.0310758	−	0.0689865i
$495$	−6.72149	−	6.72149i	−0.302108	−	0.302108i
$496$	0.574466	+	4.67927i	0.0257943	+	0.210105i
$497$	10.0783	−	10.0783i	0.452075	−	0.452075i
$498$	−7.49848	−	2.84095i	−0.336015	−	0.127306i
$499$	9.11046	+	1.81218i	0.407840	+	0.0811244i	0.394747	−	0.918790i	$-0.370832\pi$
$499$	9.11046	+	1.81218i	0.407840	+	0.0811244i	0.0130930	+	0.999914i	$0.495832\pi$
$500$	10.9511	+	14.4016i	0.489748	+	0.644061i
$501$	2.58140	−	3.86333i	0.115328	−	0.172601i
$502$	−13.7931	+	22.0734i	−0.615616	+	0.985183i
$503$	−9.68194	+	23.3743i	−0.431696	+	1.04221i	0.547044	+	0.837104i	$0.315753\pi$
$503$	−9.68194	+	23.3743i	−0.431696	+	1.04221i	−0.978740	+	0.205103i	$0.934247\pi$
$504$	−5.88489	−	4.89453i	−0.262134	−	0.218020i
$505$	−2.66671	−	6.43801i	−0.118667	−	0.286488i
$506$	−1.33260	+	7.96311i	−0.0592413	+	0.354004i
$507$	11.0288	−	2.19376i	0.489804	−	0.0974281i
$508$	1.97967	+	32.3716i	0.0878336	+	1.43626i
$509$	13.6661	−	9.13142i	0.605741	−	0.404743i	−0.214531	−	0.976717i	$-0.568822\pi$
$509$	13.6661	−	9.13142i	0.605741	−	0.404743i	0.820272	+	0.571974i	$0.193822\pi$
$510$	17.6263	−	18.7371i	0.780505	−	0.829695i
$511$	37.6173			1.66409
$512$	−11.0569	+	19.7419i	−0.488653	+	0.872478i
$513$	−0.897572			−0.0396288
$514$	−2.06762	+	2.19793i	−0.0911988	+	0.0969464i
$515$	22.5476	−	15.0658i	0.993564	−	0.663878i
$516$	−0.144707	−	2.36624i	−0.00637035	−	0.104168i
$517$	42.1709	−	8.38832i	1.85467	−	0.368918i
$518$	6.20583	−	37.0837i	0.272669	−	1.62936i
$519$	−0.994757	−	2.40156i	−0.0436650	−	0.105417i
$520$	7.30739	+	6.07764i	0.320450	+	0.266522i
$521$	−1.43079	+	3.45423i	−0.0626840	+	0.151333i	−0.952118	−	0.305732i	$-0.901099\pi$
$521$	−1.43079	+	3.45423i	−0.0626840	+	0.151333i	0.889434	+	0.457064i	$0.151099\pi$
$522$	2.94122	−	4.70690i	0.128734	−	0.206015i
$523$	13.5669	−	20.3043i	0.593240	−	0.887846i	−0.406427	−	0.913683i	$-0.633225\pi$
$523$	13.5669	−	20.3043i	0.593240	−	0.887846i	0.999666	+	0.0258378i	$0.00822533\pi$
$524$	−9.51272	−	12.5101i	−0.415565	−	0.546505i
$525$	3.80482	+	0.756825i	0.166056	+	0.0330305i
$526$	11.2139	+	4.24863i	0.488951	+	0.185249i
$527$	5.97674	−	5.97674i	0.260351	−	0.260351i
$528$	−1.82665	−	14.8788i	−0.0794946	−	0.647517i
$529$	−14.6225	−	14.6225i	−0.635760	−	0.635760i
$530$	−13.2210	−	29.3498i	−0.574283	−	1.27488i
$531$	−2.69529	+	13.5501i	−0.116966	+	0.588026i
$532$	−1.23683	−	4.69794i	−0.0536232	−	0.203682i
$533$	−3.26279	−	2.18012i	−0.141327	−	0.0944316i
$534$	5.26737	+	22.8159i	0.227941	+	0.987340i
$535$	44.3057	+	18.3520i	1.91550	+	0.793427i
$536$	−34.1933	−	3.59428i	−1.47693	−	0.155249i
$537$	−5.54913	+	2.29852i	−0.239462	+	0.0991886i
$538$	−8.25553	+	5.88856i	−0.355921	+	0.253874i
$539$	0.236546	+	1.18920i	0.0101888	+	0.0512224i
$540$	4.55948	−	2.22376i	0.196209	−	0.0956956i
$541$	−0.214975	−	0.321732i	−0.00924248	−	0.0138324i	0.826820	−	0.562467i	$-0.190148\pi$
$541$	−0.214975	−	0.321732i	−0.00924248	−	0.0138324i	−0.836062	+	0.548635i	$0.815148\pi$
$542$	1.29081	+	42.2541i	0.0554451	+	1.81497i
$543$		−	14.5095i		−	0.622664i
$544$	40.0964	−	6.17061i	1.71912	−	0.264563i
$545$		−	35.5941i		−	1.52468i
$546$	−5.06797	+	0.154820i	−0.216889	+	0.00662569i
$547$	23.5964	+	35.3145i	1.00891	+	1.50994i	0.852827	+	0.522194i	$0.174886\pi$
$547$	23.5964	+	35.3145i	1.00891	+	1.50994i	0.156082	+	0.987744i	$0.450114\pi$
$548$	29.6269	+	10.2016i	1.26560	+	0.435792i
$549$	−2.63842	−	13.2642i	−0.112605	−	0.566103i
$550$	4.41187	+	6.18526i	0.188123	+	0.263740i
$551$	3.25451	−	1.34806i	0.138647	−	0.0574293i
$552$	−3.78660	−	2.05602i	−0.161169	−	0.0875099i
$553$	17.5993	+	7.28986i	0.748398	+	0.309996i
$554$	−2.87207	+	0.663057i	−0.122022	+	0.0281706i
$555$	20.7193	+	13.8442i	0.879485	+	0.587653i
$556$	26.5880	+	15.5059i	1.12758	+	0.657598i
$557$	−5.66591	+	28.4845i	−0.240073	+	1.20693i	0.653121	+	0.757254i	$0.273459\pi$
$557$	−5.66591	+	28.4845i	−0.240073	+	1.20693i	−0.893194	+	0.449672i	$0.851541\pi$
$558$	1.51972	−	0.684576i	0.0643348	−	0.0289804i
$559$	−1.11041	−	1.11041i	−0.0469655	−	0.0469655i
$560$	17.9221	+	20.8003i	0.757348	+	0.878974i
$561$	−19.0044	+	19.0044i	−0.802368	+	0.802368i
$562$	7.03262	−	18.5621i	0.296653	−	0.782993i
$563$	−7.88970	−	1.56936i	−0.332511	−	0.0661406i	0.0260114	−	0.999662i	$-0.491719\pi$
$563$	−7.88970	−	1.56936i	−0.332511	−	0.0661406i	−0.358523	+	0.933521i	$0.616719\pi$
$564$	−3.09451	+	22.7367i	−0.130302	+	0.957387i
$565$	6.54560	−	9.79618i	0.275375	−	0.412128i
$566$	−7.73368	−	4.83258i	−0.325071	−	0.203129i
$567$	−1.03562	+	2.50021i	−0.0434919	+	0.104999i
$568$	−4.41764	+	14.2265i	−0.185360	+	0.596932i
$569$	13.3546	+	32.2408i	0.559854	+	1.35161i	0.909882	+	0.414867i	$0.136172\pi$
$569$	13.3546	+	32.2408i	0.559854	+	1.35161i	−0.350028	+	0.936739i	$0.613828\pi$
$570$	3.17549	+	0.531408i	0.133007	+	0.0222582i
$571$	36.8376	−	7.32745i	1.54160	−	0.306644i	0.650168	−	0.759791i	$-0.274699\pi$
$571$	36.8376	−	7.32745i	1.54160	−	0.306644i	0.891436	+	0.453146i	$0.149699\pi$
$572$	−7.43704	−	6.57985i	−0.310958	−	0.275117i
$573$	−5.07694	+	3.39230i	−0.212092	+	0.141716i
$574$	−8.25672	−	7.76721i	−0.344629	−	0.324197i
$575$	2.18378			0.0910698
$576$	7.82514	+	1.66348i	0.326048	+	0.0693117i
$577$	8.63210			0.359359			0.179679	−	0.983725i	$-0.442494\pi$
$577$	8.63210			0.359359			0.179679	+	0.983725i	$0.442494\pi$
$578$	−35.4665	−	33.3638i	−1.47521	−	1.38775i
$579$	4.10576	−	2.74338i	0.170629	−	0.114011i
$580$	−13.1924	+	14.9110i	−0.547783	+	0.619146i
$581$	−15.0494	+	2.99351i	−0.624354	+	0.124192i
$582$	2.15826	+	0.361178i	0.0894628	+	0.0149713i
$583$	12.8701	+	31.0711i	0.533024	+	1.28683i
$584$	−34.7946	+	18.3058i	−1.43981	+	0.757500i
$585$	1.28595	−	3.10456i	0.0531675	−	0.128358i
$586$	25.4548	+	15.9061i	1.05153	+	0.657075i
$587$	−12.1112	+	18.1258i	−0.499885	+	0.748130i	−0.992517	−	0.122107i	$-0.961035\pi$
$587$	−12.1112	+	18.1258i	−0.499885	+	0.748130i	0.492632	+	0.870238i	$0.336035\pi$
$588$	−0.641163	−	0.0872637i	−0.0264411	−	0.00359870i
$589$	1.03755	+	0.206382i	0.0427515	+	0.00850381i
$590$	17.5579	−	46.3428i	0.722848	−	1.90790i
$591$	−1.67785	+	1.67785i	−0.0690174	+	0.0690174i
$592$	12.3060	+	37.3210i	0.505772	+	1.53388i
$593$	22.6004	+	22.6004i	0.928088	+	0.928088i	0.997582	−	0.0694947i	$-0.0221387\pi$
$593$	22.6004	+	22.6004i	0.928088	+	0.928088i	−0.0694947	+	0.997582i	$0.522139\pi$
$594$	−4.83230	+	2.17677i	−0.198272	+	0.0893139i
$595$	9.60359	−	48.2805i	0.393709	−	1.97931i
$596$	−6.23349	+	10.6885i	−0.255334	+	0.437820i
$597$	0.714311	+	0.477287i	0.0292348	+	0.0195341i
$598$	−2.78105	+	0.642045i	−0.113726	+	0.0262552i
$599$	13.6094	+	5.63718i	0.556063	+	0.230329i	0.642975	−	0.765887i	$-0.277700\pi$
$599$	13.6094	+	5.63718i	0.556063	+	0.230329i	−0.0869118	+	0.996216i	$0.527700\pi$
$600$	−3.88761	+	1.15151i	−0.158711	+	0.0470103i
$601$	17.3171	−	7.17298i	0.706379	−	0.292592i	−0.000426008	−	1.00000i	$-0.500136\pi$
$601$	17.3171	−	7.17298i	0.706379	−	0.292592i	0.706805	+	0.707408i	$0.250136\pi$
$602$	−2.63431	−	3.69319i	−0.107366	−	0.150523i
$603$	2.37147	+	11.9222i	0.0965739	+	0.485510i
$604$	5.08110	−	14.7562i	0.206747	−	0.600422i
$605$	−4.29052	−	6.42122i	−0.174434	−	0.261060i
$606$	−3.88352	+	0.118637i	−0.157757	+	0.00481928i
$607$		−	26.9686i		−	1.09462i	−0.836929	−	0.547312i	$-0.815651\pi$
$607$		−	26.9686i		−	1.09462i	0.836929	−	0.547312i	$-0.184349\pi$
$608$	3.43019	+	3.74355i	0.139113	+	0.151821i
$609$		−	10.6209i		−	0.430380i
$610$	1.48128	+	48.4891i	0.0599754	+	1.96327i
$611$	8.44466	+	12.6383i	0.341635	+	0.511292i
$612$	−6.28751	−	12.8916i	−0.254157	−	0.521110i
$613$	−7.50424	−	37.7264i	−0.303093	−	1.52375i	−0.769190	−	0.639020i	$-0.779340\pi$
$613$	−7.50424	−	37.7264i	−0.303093	−	1.52375i	0.466097	−	0.884734i	$-0.345660\pi$
$614$	−14.5604	+	10.3858i	−0.587611	+	0.419135i
$615$	6.94097	−	2.87505i	0.279887	−	0.115933i
$616$	−18.0521	−	22.2930i	−0.727339	−	0.898211i
$617$	−38.5138	−	15.9529i	−1.55051	−	0.642241i	−0.567099	−	0.823650i	$-0.691934\pi$
$617$	−38.5138	−	15.9529i	−1.55051	−	0.642241i	−0.983408	+	0.181409i	$0.941934\pi$
$618$	−3.40114	−	14.7322i	−0.136814	−	0.592618i
$619$	−13.1146	−	8.76287i	−0.527119	−	0.352209i	0.263361	−	0.964697i	$-0.415169\pi$
$619$	−13.1146	−	8.76287i	−0.527119	−	0.352209i	−0.790480	+	0.612488i	$0.790169\pi$
$620$	−5.78186	+	1.52219i	−0.232205	+	0.0611326i
$621$	−0.297197	+	1.49411i	−0.0119261	+	0.0599566i
$622$	6.44257	+	14.3021i	0.258323	+	0.573463i
$623$	31.6843	+	31.6843i	1.26940	+	1.26940i
$624$	4.61234	−	2.60944i	0.184641	−	0.104461i
$625$	−21.2928	+	21.2928i	−0.851713	+	0.851713i
$626$	24.3617	+	9.22993i	0.973689	+	0.368902i
$627$	−3.29913	−	0.656238i	−0.131755	−	0.0262076i
$628$	−6.74666	+	5.13019i	−0.269221	+	0.204717i
$629$	39.1433	−	58.5821i	1.56075	−	2.33582i
$630$	5.14413	−	8.23225i	0.204947	−	0.327981i
$631$	4.55227	−	10.9901i	0.181223	−	0.437511i	−0.806996	−	0.590557i	$-0.798908\pi$
$631$	4.55227	−	10.9901i	0.181223	−	0.437511i	0.988219	+	0.153046i	$0.0489082\pi$
$632$	−19.8262	+	1.82153i	−0.788643	+	0.0724566i
$633$	2.88144	+	6.95640i	0.114527	+	0.276492i
$634$	−4.63236	+	27.6812i	−0.183974	+	1.09936i
$635$	−40.3406	+	8.02424i	−1.60087	+	0.318432i
$636$	−17.9145	+	1.09555i	−0.710355	+	0.0434415i
$637$	−0.356395	+	0.238135i	−0.0141209	+	0.00943527i
$638$	14.2521	−	15.1504i	0.564248	−	0.599808i
$639$	5.26676			0.208350
$640$	−26.6994	−	10.5180i	−1.05539	−	0.415762i
$641$	−32.2949			−1.27557			−0.637786	−	0.770214i	$-0.720149\pi$
$641$	−32.2949			−1.27557			−0.637786	+	0.770214i	$0.720149\pi$
$642$	18.3208	−	19.4754i	0.723063	−	0.768633i
$643$	14.5990	−	9.75476i	0.575730	−	0.384690i	−0.233347	−	0.972394i	$-0.574968\pi$
$643$	14.5990	−	9.75476i	0.575730	−	0.384690i	0.809077	+	0.587703i	$0.199968\pi$
$644$	−8.22979	+	0.503290i	−0.324299	+	0.0198324i
$645$	2.94875	−	0.586542i	0.116107	−	0.0230951i
$646$	1.50251	−	8.97843i	0.0591155	−	0.353252i
$647$	5.68203	+	13.7176i	0.223384	+	0.539296i	0.995345	−	0.0963732i	$-0.0307242\pi$
$647$	5.68203	+	13.7176i	0.223384	+	0.539296i	−0.771962	+	0.635669i	$0.780724\pi$
$648$	−0.258772	−	2.81656i	−0.0101655	−	0.110645i
$649$	−19.8137	+	47.8345i	−0.777756	+	1.87767i
$650$	−1.42327	+	2.27769i	−0.0558253	+	0.0893383i
$651$	1.77201	−	2.65200i	0.0694504	−	0.103940i
$652$	1.20713	−	0.917905i	0.0472747	−	0.0359480i
$653$	−3.38802	−	0.673919i	−0.132584	−	0.0263725i	0.128352	−	0.991729i	$-0.459031\pi$
$653$	−3.38802	−	0.673919i	−0.132584	−	0.0263725i	−0.260936	+	0.965356i	$0.584031\pi$
$654$	−18.5585	−	7.03128i	−0.725695	−	0.274945i
$655$	14.0936	−	14.0936i	0.550682	−	0.550682i
$656$	11.4169	+	3.16640i	0.445757	+	0.123627i
$657$	9.82907	+	9.82907i	0.383469	+	0.383469i
$658$	18.0343	+	40.0350i	0.703050	+	1.56073i
$659$	−1.47310	+	7.40579i	−0.0573840	+	0.288489i	−0.998812	−	0.0487246i	$-0.984484\pi$
$659$	−1.47310	+	7.40579i	−0.0573840	+	0.288489i	0.941428	+	0.337213i	$0.109484\pi$
$660$	18.3848	−	4.84015i	0.715626	−	0.188403i
$661$	−31.2110	−	20.8545i	−1.21397	−	0.811146i	−0.227287	−	0.973828i	$-0.572986\pi$
$661$	−31.2110	−	20.8545i	−1.21397	−	0.811146i	−0.986679	+	0.162682i	$0.947986\pi$
$662$	−2.03546	−	8.81671i	−0.0791104	−	0.342671i
$663$	−8.77788	−	3.63592i	−0.340905	−	0.141207i
$664$	12.4634	−	10.0924i	0.483674	−	0.391662i
$665$	5.69205	−	2.35773i	0.220728	−	0.0914287i
$666$	11.3112	−	8.06811i	0.438299	−	0.312633i
$667$	−1.16639	−	5.86385i	−0.0451629	−	0.227049i
$668$	4.07362	+	8.35233i	0.157613	+	0.323161i
$669$	−4.11777	−	6.16267i	−0.159202	−	0.238263i
$670$	−1.33141	−	43.5832i	−0.0514369	−	1.68376i
$671$		−	50.6832i		−	1.95660i
$672$	14.3855	−	5.23556i	0.554932	−	0.201966i
$673$			24.5793i			0.947463i	0.880669	+	0.473732i	$0.157093\pi$
$673$			24.5793i			0.947463i	−0.880669	+	0.473732i	$0.842907\pi$
$674$	10.2485	−	0.313078i	0.394756	−	0.0120593i
$675$	0.796413	+	1.19192i	0.0306539	+	0.0458769i
$676$	−7.32208	+	21.2643i	−0.281618	+	0.817858i
$677$	−4.42266	−	22.2342i	−0.169976	−	0.854529i	−0.967816	−	0.251659i	$-0.919024\pi$
$677$	−4.42266	−	22.2342i	−0.169976	−	0.854529i	0.797839	−	0.602870i	$-0.205976\pi$
$678$	−3.81464	−	5.34797i	−0.146500	−	0.205387i
$679$	3.86868	−	1.60246i	0.148466	−	0.0614967i
$680$	14.6119	+	49.3311i	0.560341	+	1.89176i
$681$	17.9316	+	7.42750i	0.687139	+	0.284622i
$682$	6.08642	−	1.40514i	0.233061	−	0.0538054i
$683$	−11.1901	−	7.47696i	−0.428176	−	0.286098i	0.322750	−	0.946484i	$-0.395393\pi$
$683$	−11.1901	−	7.47696i	−0.428176	−	0.286098i	−0.750926	+	0.660386i	$0.770393\pi$
$684$	0.904359	−	1.55070i	0.0345790	−	0.0592926i
$685$	−7.75260	+	38.9749i	−0.296211	+	1.48916i
$686$	23.2972	−	10.4945i	0.889492	−	0.400683i
$687$	−6.98947	−	6.98947i	−0.266665	−	0.266665i
$688$	4.23387	+	2.13413i	0.161415	+	0.0813629i
$689$	−8.40679	+	8.40679i	−0.320273	+	0.320273i
$690$	1.93603	−	5.11001i	0.0737035	−	0.194535i
$691$	−27.1853	−	5.40748i	−1.03418	−	0.205710i	−0.351314	−	0.936258i	$-0.614265\pi$
$691$	−27.1853	−	5.40748i	−1.03418	−	0.205710i	−0.682862	+	0.730547i	$0.739265\pi$
$692$	5.15136	+	0.701111i	0.195825	+	0.0266522i
$693$	−5.63451	+	8.43264i	−0.214037	+	0.320329i
$694$	13.7235	+	8.57547i	0.520937	+	0.325520i
$695$	−14.9379	+	36.0633i	−0.566627	+	1.36796i
$696$	5.16847	+	9.82393i	0.195910	+	0.372375i
$697$	−8.12895	−	19.6250i	−0.307906	−	0.743351i
$698$	−5.74415	−	0.961264i	−0.217419	−	0.0363844i
$699$	−18.0250	+	3.58540i	−0.681769	+	0.135612i
$700$	−5.14112	+	5.81089i	−0.194316	+	0.219631i
$701$	3.96263	−	2.64775i	0.149667	−	0.100004i	−0.478482	−	0.878097i	$-0.658813\pi$
$701$	3.96263	−	2.64775i	0.149667	−	0.100004i	0.628149	+	0.778093i	$0.283813\pi$
$702$	−1.36467	−	1.28376i	−0.0515060	−	0.0484524i
$703$	8.81809			0.332580
$704$	27.5460	+	11.8355i	1.03818	+	0.446067i
$705$	−29.1009			−1.09600
$706$	−7.18035	−	6.75465i	−0.270236	−	0.254215i
$707$	−6.18186	+	4.13059i	−0.232493	+	0.155347i
$708$	−20.6944	−	18.3092i	−0.777743	−	0.688100i
$709$	−27.5292	+	5.47589i	−1.03388	+	0.205651i	−0.682732	−	0.730669i	$-0.739208\pi$
$709$	−27.5292	+	5.47589i	−1.03388	+	0.205651i	−0.351147	+	0.936320i	$0.614208\pi$
$710$	−18.6331	−	3.11818i	−0.699287	−	0.117023i
$711$	2.69376	+	6.50331i	0.101024	+	0.243893i
$712$	−44.7254	−	13.8882i	−1.67615	−	0.520482i
$713$	0.687092	−	1.65879i	0.0257318	−	0.0621220i
$714$	−23.2760	−	14.5446i	−0.871082	−	0.544318i
$715$	6.99649	−	10.4710i	0.261654	−	0.391593i
$716$	1.62001	−	11.9029i	0.0605427	−	0.444833i
$717$	−15.0814	−	2.99987i	−0.563225	−	0.112032i
$718$	7.55323	−	19.9362i	0.281884	−	0.744011i
$719$	27.9001	−	27.9001i	1.04050	−	1.04050i	0.0413544	−	0.999145i	$-0.486833\pi$
$719$	27.9001	−	27.9001i	1.04050	−	1.04050i	0.999145	−	0.0413544i	$-0.0131673\pi$
$720$	−0.752047	+	10.1178i	−0.0280271	+	0.377069i
$721$	−20.4586	−	20.4586i	−0.761916	−	0.761916i
$722$	−23.4603	+	10.5680i	−0.873103	+	0.393300i
$723$	−3.34750	+	16.8290i	−0.124495	+	0.625879i
$724$	25.0676	+	14.6193i	0.931629	+	0.543320i
$725$	−4.67784	−	3.12564i	−0.173731	−	0.116083i
$726$	−4.19553	+	0.968596i	−0.155711	+	0.0359480i
$727$	39.8931	+	16.5243i	1.47955	+	0.612851i	0.969015	−	0.247004i	$-0.0794460\pi$
$727$	39.8931	+	16.5243i	1.47955	+	0.612851i	0.510539	+	0.859855i	$0.329446\pi$
$728$	4.83881	−	8.91173i	0.179338	−	0.330291i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	−28.9546	−	40.5932i	−1.07166	−	1.50242i
$731$	−1.65840	−	8.33733i	−0.0613381	−	0.308367i
$732$	25.5745	+	8.80623i	0.945260	+	0.325487i
$733$	−19.1036	−	28.5906i	−0.705608	−	1.05602i	−0.995104	−	0.0988380i	$-0.968487\pi$
$733$	−19.1036	−	28.5906i	−0.705608	−	1.05602i	0.289495	−	0.957179i	$-0.406513\pi$
$734$	37.6474	−	1.15008i	1.38959	−	0.0424503i
$735$		−	0.820631i		−	0.0302694i
$736$	7.36734	−	4.47041i	0.271564	−	0.164781i
$737$			45.5553i			1.67805i
$738$	−0.127905	−	4.18691i	−0.00470825	−	0.154122i
$739$	−14.1205	−	21.1327i	−0.519429	−	0.777381i	0.475310	−	0.879818i	$-0.342336\pi$
$739$	−14.1205	−	21.1327i	−0.519429	−	0.777381i	−0.994739	+	0.102438i	$0.967336\pi$
$740$	−44.7941	+	21.8471i	−1.64666	+	0.803115i
$741$	−0.231988	−	1.16628i	−0.00852230	−	0.0428445i
$742$	−27.9607	+	19.9440i	−1.02647	+	0.732166i
$743$	−5.41396	+	2.24254i	−0.198619	+	0.0822707i	−0.479776	−	0.877391i	$-0.659282\pi$
$743$	−5.41396	+	2.24254i	−0.198619	+	0.0822707i	0.281157	+	0.959662i	$0.409282\pi$
$744$	−0.348494	+	3.31532i	−0.0127764	+	0.121545i
$745$	−14.4977	−	6.00514i	−0.531154	−	0.220011i
$746$	−7.43309	−	32.1968i	−0.272145	−	1.17881i
$747$	−4.71445	−	3.15009i	−0.172493	−	0.115256i
$748$	−13.6851	−	51.9814i	−0.500377	−	1.90063i
$749$	9.98198	−	50.1828i	0.364734	−	1.83364i
$750$	5.25438	+	11.6644i	0.191863	+	0.425924i
$751$	1.91432	+	1.91432i	0.0698544	+	0.0698544i	0.741171	−	0.671316i	$-0.234271\pi$
$751$	1.91432	+	1.91432i	0.0698544	+	0.0698544i	−0.671316	+	0.741171i	$0.734271\pi$
$752$	−36.1634	−	28.2549i	−1.31874	−	1.03035i
$753$	−13.0143	+	13.0143i	−0.474266	+	0.474266i
$754$	6.87622	+	2.60520i	0.250417	+	0.0948757i
$755$	19.4122	+	3.86132i	0.706481	+	0.140528i
$756$	−3.27606	−	4.30831i	−0.119149	−	0.156692i
$757$	−17.6288	+	26.3834i	−0.640731	+	0.958922i	0.358942	+	0.933360i	$0.383137\pi$
$757$	−17.6288	+	26.3834i	−0.640731	+	0.958922i	−0.999673	+	0.0255619i	$0.991863\pi$
$758$	4.14675	−	6.63613i	0.150617	−	0.241035i
$759$	−2.18477	+	5.27450i	−0.0793020	+	0.191452i
$760$	−4.11759	+	4.95075i	−0.149361	+	0.179583i
$761$	9.24353	+	22.3158i	0.335078	+	0.808949i	0.998173	+	0.0604142i	$0.0192422\pi$
$761$	9.24353	+	22.3158i	0.335078	+	0.808949i	−0.663096	+	0.748534i	$0.730758\pi$
$762$	−3.78511	+	22.6184i	−0.137120	+	0.819378i
$763$	−37.2468	+	7.40885i	−1.34842	+	0.268218i
$764$	−0.745426	−	12.1892i	−0.0269685	−	0.440990i
$765$	15.1246	−	10.1059i	0.546831	−	0.365381i
$766$	11.1622	−	11.8657i	0.403308	−	0.428726i
$767$	−18.3033			−0.660896
$768$	−10.7582	+	11.8431i	−0.388205	+	0.427353i
$769$	33.8955			1.22230			0.611151	−	0.791514i	$-0.290707\pi$
$769$	33.8955			1.22230			0.611151	+	0.791514i	$0.290707\pi$
$770$	24.9267	−	26.4976i	0.898295	−	0.954908i
$771$	−1.77416	+	1.18546i	−0.0638950	+	0.0426932i
$772$	0.602831	+	9.85749i	0.0216964	+	0.354779i
$773$	21.7263	−	4.32163i	0.781440	−	0.155438i	0.211779	−	0.977318i	$-0.432074\pi$
$773$	21.7263	−	4.32163i	0.781440	−	0.155438i	0.569661	+	0.821880i	$0.307074\pi$
$774$	0.276678	−	1.65332i	0.00994497	−	0.0594274i
$775$	−0.646554	−	1.56092i	−0.0232249	−	0.0560699i
$776$	−2.79858	+	3.36484i	−0.100463	+	0.120791i
$777$	10.1743	−	24.5630i	0.365001	−	0.881191i
$778$	−2.52481	+	4.04051i	−0.0905189	+	0.144859i
$779$	1.47703	−	2.21053i	0.0529201	−	0.0792006i
$780$	4.06796	+	5.34972i	0.145656	+	0.191551i
$781$	19.3586	+	3.85066i	0.692705	+	0.137788i
$782$	−14.4481	−	5.47397i	−0.516664	−	0.195749i
$783$	2.77514	−	2.77514i	0.0991755	−	0.0991755i
$784$	0.796774	−	1.01979i	0.0284562	−	0.0364211i
$785$	−7.60065	−	7.60065i	−0.271279	−	0.271279i
$786$	−4.56424	−	10.1323i	−0.162801	−	0.361409i
$787$	1.48421	−	7.46162i	0.0529063	−	0.265978i	−0.945274	−	0.326278i	$-0.894206\pi$
$787$	1.48421	−	7.46162i	0.0529063	−	0.265978i	0.998180	+	0.0602996i	$0.0192056\pi$
$788$	−1.20822	−	4.58929i	−0.0430410	−	0.163487i
$789$	7.05043	+	4.71095i	0.251002	+	0.167714i
$790$	−5.67987	−	24.6027i	−0.202081	−	0.875324i
$791$	−11.6135	−	4.81046i	−0.412928	−	0.171040i
$792$	1.10812	−	10.5418i	0.0393752	−	0.374587i
$793$	16.5533	−	6.85659i	0.587824	−	0.243485i
$794$	−17.4332	+	12.4349i	−0.618681	+	0.441297i
$795$	−4.44063	−	22.3245i	−0.157493	−	0.791770i
$796$	−1.54430	+	0.753192i	−0.0547364	+	0.0266962i
$797$	23.0282	+	34.4641i	0.815700	+	1.22078i	0.972443	+	0.233142i	$0.0749006\pi$
$797$	23.0282	+	34.4641i	0.815700	+	1.22078i	−0.156743	+	0.987639i	$0.550099\pi$
$798$	−0.104890	−	3.43354i	−0.00371308	−	0.121546i
$799$			82.2804i			2.91087i
$800$	1.92758	−	7.87670i	0.0681503	−	0.278483i
$801$			16.5576i			0.585035i
$802$	−24.3077	+	0.742571i	−0.858336	+	0.0262211i
$803$	28.9416	+	43.3142i	1.02133	+	1.52853i
$804$	−22.9869	−	7.91525i	−0.810687	−	0.279149i
$805$	−2.03999	−	10.2557i	−0.0719004	−	0.361468i
$806$	1.28231	+	1.79775i	0.0451675	+	0.0633230i
$807$	−6.62457	+	2.74399i	−0.233196	+	0.0965930i
$808$	3.70792	−	6.82894i	0.130444	−	0.240241i
$809$	−17.2252	−	7.13493i	−0.605607	−	0.250851i	0.0587418	−	0.998273i	$-0.481291\pi$
$809$	−17.2252	−	7.13493i	−0.605607	−	0.250851i	−0.664349	+	0.747422i	$0.731291\pi$
$810$	3.49513	−	0.806899i	0.122806	−	0.0283516i
$811$	−14.3574	−	9.59329i	−0.504156	−	0.336866i	0.277345	−	0.960770i	$-0.410545\pi$
$811$	−14.3574	−	9.59329i	−0.504156	−	0.336866i	−0.781501	+	0.623904i	$0.785545\pi$
$812$	18.3493	+	10.7012i	0.643934	+	0.375538i
$813$	−5.83166	+	29.3178i	−0.204525	+	1.02822i
$814$	47.4743	−	21.3854i	1.66397	−	0.749558i
$815$	1.35993	+	1.35993i	0.0476361	+	0.0476361i
$816$	28.6073	+	2.12635i	1.00146	+	0.0744371i
$817$	0.752305	−	0.752305i	0.0263198	−	0.0263198i
$818$	−10.7185	+	28.2908i	−0.374765	+	0.989164i
$819$	−3.51637	−	0.699450i	−0.122872	−	0.0244408i
$820$	−2.02635	+	14.8885i	−0.0707632	+	0.519927i
$821$	4.13472	−	6.18805i	0.144303	−	0.215965i	−0.752277	−	0.658847i	$-0.771044\pi$
$821$	4.13472	−	6.18805i	0.144303	−	0.215965i	0.896579	+	0.442883i	$0.146044\pi$
$822$	18.7898	+	11.7413i	0.655369	+	0.409524i
$823$	−7.08641	+	17.1081i	−0.247017	+	0.596351i	−0.997948	−	0.0640294i	$-0.979605\pi$
$823$	−7.08641	+	17.1081i	−0.247017	+	0.596351i	0.750931	+	0.660380i	$0.229605\pi$
$824$	28.8792	+	8.96761i	1.00605	+	0.312402i
$825$	2.05587	+	4.96331i	0.0715762	+	0.172800i
$826$	−52.1492	−	8.72700i	−1.81450	−	0.303651i
$827$	10.1125	−	2.01151i	0.351647	−	0.0699469i	−0.0161064	−	0.999870i	$-0.505127\pi$
$827$	10.1125	−	2.01151i	0.351647	−	0.0699469i	0.367753	+	0.929923i	$0.380127\pi$
$828$	−2.28188	−	2.01887i	−0.0793007	−	0.0701605i
$829$	−1.71564	+	1.14635i	−0.0595865	+	0.0398144i	−0.585007	−	0.811028i	$-0.698908\pi$
$829$	−1.71564	+	1.14635i	−0.0595865	+	0.0398144i	0.525420	+	0.850843i	$0.323908\pi$
$830$	14.8141	+	13.9358i	0.514204	+	0.483719i
$831$	−2.08428			−0.0723027
$832$	−0.138986	+	10.5977i	−0.00481847	+	0.367411i
$833$	−2.32027			−0.0803925
$834$	15.8523	+	14.9125i	0.548920	+	0.516377i
$835$	−9.79910	+	6.54755i	−0.339112	+	0.226587i
$836$	4.45784	−	5.03859i	0.154178	−	0.174263i
$837$	1.15595	−	0.229933i	0.0399556	−	0.00794766i
$838$	11.2483	+	1.88236i	0.388564	+	0.0650250i
$839$	−17.0423	−	41.1438i	−0.588366	−	1.42044i	−0.885064	−	0.465470i	$-0.845885\pi$
$839$	−17.0423	−	41.1438i	−0.588366	−	1.42044i	0.296697	−	0.954972i	$-0.404115\pi$
$840$	9.03953	+	17.1818i	0.311893	+	0.592829i
$841$	5.20341	−	12.5622i	0.179428	−	0.433178i
$842$	19.6458	+	12.2761i	0.677038	+	0.423064i
$843$	7.79788	−	11.6703i	0.268573	−	0.401948i
$844$	−14.9215	−	2.03085i	−0.513621	−	0.0699049i
$845$	−27.9737	−	5.56432i	−0.962325	−	0.191418i
$846$	−5.74860	+	15.1730i	−0.197641	+	0.521658i
$847$	−5.82630	+	5.82630i	−0.200194	+	0.200194i
$848$	16.1572	−	32.0540i	0.554840	−	1.10074i
$849$	−4.55971	−	4.55971i	−0.156489	−	0.156489i
$850$	−13.2559	+	5.97129i	−0.454674	+	0.204814i
$851$	2.91978	−	14.6787i	0.100089	−	0.503180i
$852$	−5.30658	+	9.09918i	−0.181800	+	0.311733i
$853$	−22.1903	−	14.8271i	−0.759780	−	0.507669i	0.114303	−	0.993446i	$-0.463537\pi$
$853$	−22.1903	−	14.8271i	−0.759780	−	0.507669i	−0.874083	+	0.485777i	$0.838537\pi$
$854$	50.4322	−	11.6430i	1.72575	−	0.398414i
$855$	2.10334	+	0.871230i	0.0719326	+	0.0297954i
$856$	15.1876	+	51.2748i	0.519102	+	1.75254i
$857$	15.7925	−	6.54148i	0.539462	−	0.223453i	−0.0962795	−	0.995354i	$-0.530694\pi$
$857$	15.7925	−	6.54148i	0.539462	−	0.223453i	0.635742	+	0.771902i	$0.280694\pi$
$858$	−4.07741	−	5.71636i	−0.139200	−	0.195153i
$859$	0.265931	+	1.33692i	0.00907344	+	0.0456153i	0.985057	−	0.172230i	$-0.0550972\pi$
$859$	0.265931	+	1.33692i	0.00907344	+	0.0456153i	−0.975983	+	0.217845i	$0.930097\pi$
$860$	−1.95770	+	5.68542i	−0.0667569	+	0.193871i
$861$	−4.45329	−	6.66482i	−0.151768	−	0.227136i
$862$	−1.03800	+	0.0317095i	−0.0353543	+	0.00108003i
$863$			7.84585i			0.267076i	0.991044	+	0.133538i	$0.0426338\pi$
$863$			7.84585i			0.267076i	−0.991044	+	0.133538i	$0.957366\pi$
$864$	5.12680	+	2.39079i	0.174417	+	0.0813364i
$865$			6.59327i			0.224178i
$866$	−0.663157	−	21.7082i	−0.0225350	−	0.737673i
$867$	−19.1290	−	28.6285i	−0.649654	−	0.972276i
$868$	2.79635	+	5.73348i	0.0949143	+	0.194607i
$869$	5.14649	+	25.8732i	0.174583	+	0.877687i
$870$	−11.4611	+	8.17505i	−0.388568	+	0.277160i
$871$	−14.8785	+	6.16287i	−0.504138	+	0.208821i
$872$	30.8465	−	24.9784i	1.04460	−	0.845876i
$873$	1.42956	+	0.592143i	0.0483832	+	0.0200410i
$874$	−0.434985	−	1.88416i	−0.0147136	−	0.0637327i
$875$	20.3551	+	13.6008i	0.688126	+	0.459791i
$876$	−26.8847	+	7.07793i	−0.908351	+	0.239141i
$877$	0.971364	−	4.88338i	0.0328006	−	0.164900i	−0.960913	−	0.276850i	$-0.910710\pi$
$877$	0.971364	−	4.88338i	0.0328006	−	0.164900i	0.993714	+	0.111950i	$0.0357096\pi$
$878$	24.0559	+	53.4027i	0.811847	+	1.80225i
$879$	15.0079	+	15.0079i	0.506205	+	0.506205i
$880$	−10.1616	+	36.6394i	−0.342549	+	1.23512i
$881$	−28.4922	+	28.4922i	−0.959927	+	0.959927i	−0.999227	−	0.0393004i	$-0.987487\pi$
$881$	−28.4922	+	28.4922i	−0.959927	+	0.959927i	0.0393004	+	0.999227i	$0.487487\pi$
$882$	−0.427871	−	0.162108i	−0.0144072	−	0.00545845i
$883$	−7.03340	−	1.39903i	−0.236693	−	0.0470811i	0.0753184	−	0.997160i	$-0.476003\pi$
$883$	−7.03340	−	1.39903i	−0.236693	−	0.0470811i	−0.312011	+	0.950078i	$0.601003\pi$
$884$	15.1259	−	11.5018i	0.508739	−	0.386848i
$885$	19.4685	−	29.1367i	0.654426	−	0.979418i
$886$	28.5867	−	45.7479i	0.960389	−	1.53693i
$887$	−4.83693	+	11.6774i	−0.162408	+	0.392088i	−0.984044	−	0.177925i	$-0.943062\pi$
$887$	−4.83693	+	11.6774i	−0.162408	+	0.392088i	0.821636	+	0.570013i	$0.193062\pi$
$888$	2.54227	+	27.6710i	0.0853131	+	0.928578i
$889$	16.7936	+	40.5434i	0.563240	+	1.35978i
$890$	9.80295	−	58.5787i	0.328596	−	1.96356i
$891$	−3.67562	+	0.731126i	−0.123138	+	0.0244936i
$892$	14.7959	−	0.904839i	0.495404	−	0.0302962i
$893$	−8.56246	+	5.72125i	−0.286532	+	0.191454i
$894$	−5.99491	+	6.37273i	−0.200500	+	0.213136i
$895$	15.2347			0.509239
$896$	−5.44897	+	30.1284i	−0.182037	+	1.00652i
$897$	−2.01823			−0.0673866
$898$	−10.1966	+	10.8393i	−0.340266	+	0.361711i
$899$	−3.84603	+	2.56984i	−0.128272	+	0.0857088i
$900$	−2.86166	+	0.175004i	−0.0953888	+	0.00583346i
$901$	−63.1207	+	12.5555i	−2.10286	+	0.418284i
$902$	2.59103	−	15.4830i	0.0862719	−	0.515528i
$903$	−1.22755	−	2.96357i	−0.0408503	−	0.0986215i
$904$	13.0830	−	1.20200i	0.435133	−	0.0399778i
$905$	−14.0837	+	34.0011i	−0.468158	+	1.13023i
$906$	5.84795	−	9.35859i	0.194285	−	0.310918i
$907$	4.02145	−	6.01853i	0.133530	−	0.199842i	−0.758679	−	0.651465i	$-0.774155\pi$
$907$	4.02145	−	6.01853i	0.133530	−	0.199842i	0.892209	+	0.451623i	$0.149155\pi$
$908$	−30.8994	+	23.4960i	−1.02543	+	0.779744i
$909$	−2.69455	−	0.535980i	−0.0893727	−	0.0177773i
$910$	12.0263	+	4.55643i	0.398670	+	0.151044i
$911$	9.27344	−	9.27344i	0.307243	−	0.307243i	−0.536596	−	0.843839i	$-0.680290\pi$
$911$	9.27344	−	9.27344i	0.307243	−	0.307243i	0.843839	+	0.536596i	$0.180290\pi$
$912$	1.76789	+	3.12486i	0.0585408	+	0.103474i
$913$	−15.0254	−	15.0254i	−0.497268	−	0.497268i
$914$	24.4726	+	54.3277i	0.809482	+	1.79700i
$915$	−6.69218	+	33.6438i	−0.221237	+	1.11223i
$916$	19.1178	−	5.03313i	0.631669	−	0.166299i
$917$	−17.6815	−	11.8144i	−0.583895	−	0.390146i
$918$	−2.28144	−	9.88218i	−0.0752987	−	0.326161i
$919$	−3.67392	−	1.52179i	−0.121191	−	0.0501991i	0.321264	−	0.946990i	$-0.395892\pi$
$919$	−3.67392	−	1.52179i	−0.121191	−	0.0501991i	−0.442455	+	0.896791i	$0.645892\pi$
$920$	6.87770	+	8.49346i	0.226751	+	0.280021i
$921$	−11.6839	+	4.83962i	−0.384997	+	0.159471i
$922$	31.9695	−	22.8034i	1.05286	−	0.750990i
$923$	1.36126	+	6.84349i	0.0448063	+	0.225256i
$924$	−8.89164	−	18.2309i	−0.292513	−	0.599754i
$925$	−7.82426	−	11.7098i	−0.257260	−	0.385017i
$926$	−0.441912	−	14.4658i	−0.0145221	−	0.475376i
$927$		−	10.6913i		−	0.351147i
$928$	−22.1800	−	0.968843i	−0.728094	−	0.0318038i
$929$		−	5.60648i		−	0.183943i	−0.995762	−	0.0919714i	$-0.970683\pi$
$929$		−	5.60648i		−	0.183943i	0.995762	−	0.0919714i	$-0.0293168\pi$
$930$	−4.22574	+	0.129091i	−0.138567	+	0.00423306i
$931$	−0.161337	−	0.241457i	−0.00528759	−	0.00791344i
$932$	11.9670	−	34.7537i	0.391991	−	1.13840i
$933$	2.16391	+	10.8787i	0.0708432	+	0.356153i
$934$	−2.55446	−	3.58125i	−0.0835846	−	0.117182i
$935$	62.9809	−	26.0876i	2.05970	−	0.853154i
$936$	3.59289	−	1.06422i	0.117437	−	0.0347850i
$937$	27.9259	+	11.5673i	0.912301	+	0.377887i	0.788937	−	0.614474i	$-0.210632\pi$
$937$	27.9259	+	11.5673i	0.912301	+	0.377887i	0.123364	+	0.992362i	$0.460632\pi$
$938$	−45.3296	+	10.4650i	−1.48007	+	0.341694i
$939$	15.3167	+	10.2343i	0.499841	+	0.333983i
$940$	29.3210	−	50.2766i	0.956344	−	1.63984i
$941$	−0.259617	+	1.30518i	−0.00846326	+	0.0425477i	−0.984786	−	0.173771i	$-0.944405\pi$
$941$	−0.259617	+	1.30518i	−0.00846326	+	0.0425477i	0.976323	+	0.216318i	$0.0694049\pi$
$942$	−5.46436	+	2.46149i	−0.178038	+	0.0801996i
$943$	−3.19062	−	3.19062i	−0.103901	−	0.103901i
$944$	52.4829	−	17.3053i	1.70817	−	0.563241i
$945$	4.85366	−	4.85366i	0.157890	−	0.157890i
$946$	2.22575	−	5.87469i	0.0723653	−	0.191003i
$947$	−15.3658	−	3.05644i	−0.499320	−	0.0993209i	−0.0609961	−	0.998138i	$-0.519428\pi$
$947$	−15.3658	−	3.05644i	−0.499320	−	0.0993209i	−0.438324	+	0.898817i	$0.644428\pi$
$948$	−13.9497	−	1.89858i	−0.453064	−	0.0616630i
$949$	−10.2312	+	15.3121i	−0.332119	+	0.497052i
$950$	−1.54313	−	0.964264i	−0.0500658	−	0.0312849i
$951$	−7.59464	+	18.3351i	−0.246273	+	0.594556i
$952$	48.5802	−	25.5585i	1.57449	−	0.828356i
$953$	−12.6010	−	30.4215i	−0.408186	−	0.985449i	−0.985615	−	0.169007i	$-0.945944\pi$
$953$	−12.6010	−	30.4215i	−0.408186	−	0.985449i	0.577429	−	0.816441i	$-0.304056\pi$
$954$	−12.5171	−	2.09469i	−0.405254	−	0.0678180i
$955$	15.1898	−	3.02145i	0.491532	−	0.0977718i
$956$	20.3782	−	23.0330i	0.659078	−	0.744940i
$957$	12.2293	−	8.17139i	0.395318	−	0.264143i
$958$	−6.77515	−	6.37348i	−0.218895	−	0.205918i
$959$	42.3983			1.36911
$960$	−16.7225	−	11.4936i	−0.539715	−	0.370955i
$961$	29.6109			0.955190
$962$	13.4070	+	12.6122i	0.432259	+	0.406632i
$963$	15.7205	−	10.5041i	0.506587	−	0.338490i
$964$	−25.7021	−	22.7397i	−0.827809	−	0.732395i
$965$	−12.2841	+	2.44347i	−0.395440	+	0.0786580i
$966$	−5.75025	−	0.962286i	−0.185011	−	0.0309610i
$967$	−7.13152	−	17.2170i	−0.229334	−	0.553662i	0.766763	−	0.641931i	$-0.221866\pi$
$967$	−7.13152	−	17.2170i	−0.229334	−	0.553662i	−0.996097	+	0.0882693i	$0.971866\pi$
$968$	2.55384	−	8.22437i	0.0820837	−	0.264341i
$969$	2.46333	−	5.94700i	0.0791336	−	0.191045i
$970$	−4.70701	−	2.94129i	−0.151133	−	0.0944392i
$971$	6.24720	−	9.34959i	0.200482	−	0.300043i	−0.717583	−	0.696474i	$-0.754751\pi$
$971$	6.24720	−	9.34959i	0.200482	−	0.300043i	0.918065	+	0.396431i	$0.129751\pi$
$972$	0.269718	−	1.98173i	0.00865120	−	0.0635640i
$973$	40.8470	+	8.12498i	1.30950	+	0.260475i
$974$	18.8582	−	49.7748i	0.604256	−	1.59489i
$975$	−1.34290	+	1.34290i	−0.0430073	+	0.0430073i
$976$	−40.9820	+	35.3113i	−1.31180	+	1.13029i
$977$	−28.5667	−	28.5667i	−0.913930	−	0.913930i	0.0826487	−	0.996579i	$-0.473662\pi$
$977$	−28.5667	−	28.5667i	−0.913930	−	0.913930i	−0.996579	+	0.0826487i	$0.973662\pi$
$978$	0.977695	−	0.440415i	0.0312632	−	0.0140829i
$979$	−12.1057	+	60.8595i	−0.386900	+	1.94508i
$980$	1.41777	+	0.826837i	0.0452891	+	0.0264123i
$981$	−11.6681	−	7.79639i	−0.372534	−	0.248920i
$982$	22.6648	−	5.23249i	0.723263	−	0.166975i
$983$	−36.9098	−	15.2885i	−1.17724	−	0.487629i	−0.293661	−	0.955910i	$-0.594874\pi$
$983$	−36.9098	−	15.2885i	−1.17724	−	0.487629i	−0.883580	+	0.468281i	$0.844874\pi$
$984$	7.36244	+	3.99759i	0.234706	+	0.127439i
$985$	5.56040	−	2.30319i	0.177169	−	0.0733859i
$986$	23.1143	+	32.4053i	0.736109	+	1.03199i
$987$	6.05730	+	30.4521i	0.192806	+	0.969301i
$988$	2.24869	+	0.774305i	0.0715403	+	0.0246339i
$989$	−1.00320	−	1.50139i	−0.0318999	−	0.0477416i
$990$	13.4367	−	0.410475i	0.427047	−	0.0130457i
$991$			9.07366i			0.288234i	0.989561	+	0.144117i	$0.0460342\pi$
$991$			9.07366i			0.288234i	−0.989561	+	0.144117i	$0.953966\pi$
$992$	−5.37662	−	3.94247i	−0.170708	−	0.125173i
$993$		−	6.39834i		−	0.203045i
$994$	0.615474	+	20.1473i	0.0195217	+	0.639032i
$995$	−1.21061	−	1.81180i	−0.0383789	−	0.0574380i
$996$	10.1924	−	4.97106i	0.322959	−	0.157514i
$997$	0.235475	+	1.18381i	0.00745756	+	0.0374917i	0.984335	−	0.176309i	$-0.0564157\pi$
$997$	0.235475	+	1.18381i	0.00745756	+	0.0374917i	−0.976877	+	0.213801i	$0.931416\pi$
$998$	−10.6947	+	7.62839i	−0.338535	+	0.241472i
$999$	9.07654	−	3.75963i	0.287169	−	0.118949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.r.a.13.5	✓	128
3.2	odd	2		576.2.bd.b.397.12		128
4.3	odd	2		768.2.r.a.145.15		128
64.5	even	16	inner	192.2.r.a.133.5	yes	128
64.59	odd	16		768.2.r.a.625.15		128
192.5	odd	16		576.2.bd.b.325.12		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.r.a.13.5	✓	128	1.1	even	1	trivial
192.2.r.a.133.5	yes	128	64.5	even	16	inner
576.2.bd.b.325.12		128	192.5	odd	16
576.2.bd.b.397.12		128	3.2	odd	2
768.2.r.a.145.15		128	4.3	odd	2
768.2.r.a.625.15		128	64.59	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.968999 + 1.03007i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.122081 - 1.99627i) q^{4} +(2.48770 - 0.494834i) q^{5} +(0.233418 - 1.39482i) q^{6} +(-1.03562 - 2.50021i) q^{7} +(2.17459 + 1.80863i) q^{8} +(0.382683 - 0.923880i) q^{9} +O(q^{10})\)	\(q+(-0.968999 + 1.03007i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.122081 - 1.99627i) q^{4} +(2.48770 - 0.494834i) q^{5} +(0.233418 - 1.39482i) q^{6} +(-1.03562 - 2.50021i) q^{7} +(2.17459 + 1.80863i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-1.90087 + 3.04199i) q^{10} +(2.08207 - 3.11604i) q^{11} +(1.21058 + 1.59201i) q^{12} +(1.29938 + 0.258462i) q^{13} +(3.57890 + 1.35594i) q^{14} +(-1.79353 + 1.79353i) q^{15} +(-3.97019 + 0.487414i) q^{16} +(5.07106 + 5.07106i) q^{17} +(0.580839 + 1.28943i) q^{18} +(-0.175108 + 0.880326i) q^{19} +(-1.29152 - 4.90571i) q^{20} +(2.25013 + 1.50349i) q^{21} +(1.19221 + 5.16411i) q^{22} +(1.40742 + 0.582973i) q^{23} +(-2.81293 - 0.295685i) q^{24} +(1.32439 - 0.548579i) q^{25} +(-1.52533 + 1.08800i) q^{26} +(0.195090 + 0.980785i) q^{27} +(-4.86466 + 2.37260i) q^{28} +(-2.18042 - 3.26322i) q^{29} +(-0.109529 - 3.58539i) q^{30} -1.17860i q^{31} +(3.34504 - 4.56187i) q^{32} +3.74763i q^{33} +(-10.1374 + 0.309685i) q^{34} +(-3.81350 - 5.70730i) q^{35} +(-1.89103 - 0.651151i) q^{36} +(-1.91664 - 9.63560i) q^{37} +(-0.737116 - 1.03341i) q^{38} +(-1.22399 + 0.506991i) q^{39} +(6.30470 + 3.42327i) q^{40} +(-2.73651 - 1.13350i) q^{41} +(-3.72906 + 0.860906i) q^{42} +(-0.985566 - 0.658534i) q^{43} +(-6.47464 - 3.77597i) q^{44} +(0.494834 - 2.48770i) q^{45} +(-1.96429 + 0.884840i) q^{46} +(8.11274 + 8.11274i) q^{47} +(3.03030 - 2.61099i) q^{48} +(-0.228775 + 0.228775i) q^{49} +(-0.718255 + 1.89578i) q^{50} +(-7.03376 - 1.39910i) q^{51} +(0.357331 - 2.62546i) q^{52} +(-4.98567 + 7.46158i) q^{53} +(-1.19932 - 0.749424i) q^{54} +(3.63764 - 8.78205i) q^{55} +(2.26991 - 7.30998i) q^{56} +(-0.343486 - 0.829249i) q^{57} +(5.47416 + 0.916083i) q^{58} +(-13.5501 + 2.69529i) q^{59} +(3.79933 + 3.36142i) q^{60} +(11.2449 - 7.51358i) q^{61} +(1.21404 + 1.14206i) q^{62} -2.70620 q^{63} +(1.45770 + 7.86607i) q^{64} +3.36035 q^{65} +(-3.86031 - 3.63145i) q^{66} +(-10.1072 + 6.75338i) q^{67} +(9.50412 - 10.7423i) q^{68} +(-1.49411 + 0.297197i) q^{69} +(9.57418 + 1.60221i) q^{70} +(2.01550 + 4.86585i) q^{71} +(2.50314 - 1.31693i) q^{72} +(-5.31946 + 12.8423i) q^{73} +(11.7826 + 7.36262i) q^{74} +(-0.796413 + 1.19192i) q^{75} +(1.77875 + 0.242091i) q^{76} +(-9.94697 - 1.97858i) q^{77} +(0.663805 - 1.75206i) q^{78} +(-4.97742 + 4.97742i) q^{79} +(-9.63545 + 3.17713i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(3.81925 - 1.72043i) q^{82} +(1.10617 - 5.56107i) q^{83} +(2.72667 - 4.67541i) q^{84} +(15.1246 + 10.1059i) q^{85} +(1.63335 - 0.377081i) q^{86} +(3.62590 + 1.50190i) q^{87} +(10.1634 - 3.01041i) q^{88} +(-15.2973 + 6.33633i) q^{89} +(2.08301 + 2.92029i) q^{90} +(-0.699450 - 3.51637i) q^{91} +(0.991953 - 2.88077i) q^{92} +(0.654795 + 0.979969i) q^{93} +(-16.2179 + 0.495437i) q^{94} +2.27663i q^{95} +(-0.246861 + 5.65147i) q^{96} +1.54734i q^{97} +(-0.0139711 - 0.457337i) q^{98} +(-2.08207 - 3.11604i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{22} - 80 q^{26} - 80 q^{28} - 80 q^{32} - 80 q^{34} - 80 q^{38} - 80 q^{40} - 16 q^{44} + 48 q^{50} - 32 q^{51} + 48 q^{52} + 16 q^{54} - 64 q^{55} + 112 q^{56} - 128 q^{59} + 96 q^{60} + 96 q^{62} - 32 q^{63} + 96 q^{64} + 96 q^{66} - 32 q^{67} + 96 q^{68} + 96 q^{70} - 128 q^{71} + 112 q^{74} - 64 q^{75} + 16 q^{76} + 48 q^{78} - 32 q^{79} + 48 q^{80} - 80 q^{82} - 80 q^{88} - 96 q^{94}+O(q^{100}) \) 128 * q - 16 * q^22 - 80 * q^26 - 80 * q^28 - 80 * q^32 - 80 * q^34 - 80 * q^38 - 80 * q^40 - 16 * q^44 + 48 * q^50 - 32 * q^51 + 48 * q^52 + 16 * q^54 - 64 * q^55 + 112 * q^56 - 128 * q^59 + 96 * q^60 + 96 * q^62 - 32 * q^63 + 96 * q^64 + 96 * q^66 - 32 * q^67 + 96 * q^68 + 96 * q^70 - 128 * q^71 + 112 * q^74 - 64 * q^75 + 16 * q^76 + 48 * q^78 - 32 * q^79 + 48 * q^80 - 80 * q^82 - 80 * q^88 - 96 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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