LMFDB - Embedded newform 768.2.z.a.661.26

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, 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:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			661.26
Character	$\chi$	$=$	768.661
Dual form			768.2.z.a.445.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.400870 + 1.35621i) q^{2} +(-0.941544 - 0.336890i) q^{3} +(-1.67861 - 1.08733i) q^{4} +(-2.94925 - 2.18731i) q^{5} +(0.834330 - 1.14188i) q^{6} +(0.901442 + 0.0887843i) q^{7} +(2.14754 - 1.84067i) q^{8} +(0.773010 + 0.634393i) q^{9} +O(q^{10})$	\(q+(-0.400870 + 1.35621i) q^{2} +(-0.941544 - 0.336890i) q^{3} +(-1.67861 - 1.08733i) q^{4} +(-2.94925 - 2.18731i) q^{5} +(0.834330 - 1.14188i) q^{6} +(0.901442 + 0.0887843i) q^{7} +(2.14754 - 1.84067i) q^{8} +(0.773010 + 0.634393i) q^{9} +(4.14872 - 3.12298i) q^{10} +(-2.24299 - 2.47475i) q^{11} +(1.21417 + 1.58927i) q^{12} +(0.0701152 - 0.472678i) q^{13} +(-0.481771 + 1.18695i) q^{14} +(2.03997 + 3.05303i) q^{15} +(1.63544 + 3.65039i) q^{16} +(-0.569532 + 0.852364i) q^{17} +(-1.17025 + 0.794055i) q^{18} +(0.537204 - 0.896270i) q^{19} +(2.57231 + 6.87844i) q^{20} +(-0.818837 - 0.387281i) q^{21} +(4.25543 - 2.04990i) q^{22} +(-1.77130 + 0.946779i) q^{23} +(-2.64211 + 1.00958i) q^{24} +(2.46232 + 8.11719i) q^{25} +(0.612943 + 0.284573i) q^{26} +(-0.514103 - 0.857729i) q^{27} +(-1.41663 - 1.12920i) q^{28} +(3.87197 - 0.190218i) q^{29} +(-4.95830 + 1.54276i) q^{30} +(-3.63567 + 8.77728i) q^{31} +(-5.60629 + 0.754674i) q^{32} +(1.27815 + 3.08573i) q^{33} +(-0.927676 - 1.11409i) q^{34} +(-2.46438 - 2.23358i) q^{35} +(-0.607788 - 1.90541i) q^{36} +(-1.94043 - 0.486053i) q^{37} +(1.00018 + 1.08785i) q^{38} +(-0.225257 + 0.421426i) q^{39} +(-10.3598 + 0.731234i) q^{40} +(-0.613452 + 2.02228i) q^{41} +(0.853481 - 0.955265i) q^{42} +(2.34167 + 6.54452i) q^{43} +(1.07423 + 6.59300i) q^{44} +(-0.892185 - 3.56180i) q^{45} +(-0.573970 - 2.78179i) q^{46} +(-7.04312 + 1.40096i) q^{47} +(-0.310063 - 3.98796i) q^{48} +(-6.06078 - 1.20556i) q^{49} +(-11.9957 + 0.0854896i) q^{50} +(0.823392 - 0.610669i) q^{51} +(-0.631651 + 0.717203i) q^{52} +(-6.04786 - 0.297112i) q^{53} +(1.36935 - 0.353394i) q^{54} +(1.20207 + 12.2048i) q^{55} +(2.09931 - 1.46859i) q^{56} +(-0.807745 + 0.662899i) q^{57} +(-1.29418 + 5.32746i) q^{58} +(0.174788 + 1.17832i) q^{59} +(-0.104667 - 7.34294i) q^{60} +(3.14751 - 1.48866i) q^{61} +(-10.4464 - 8.44928i) q^{62} +(0.640500 + 0.640500i) q^{63} +(1.22390 - 7.90583i) q^{64} +(-1.24068 + 1.24068i) q^{65} +(-4.69726 + 0.496465i) q^{66} +(4.29727 + 9.08581i) q^{67} +(1.88282 - 0.811518i) q^{68} +(1.98672 - 0.294701i) q^{69} +(4.01710 - 2.44684i) q^{70} +(1.41071 + 1.71896i) q^{71} +(2.82778 - 0.0604664i) q^{72} +(13.1310 - 1.29329i) q^{73} +(1.43705 - 2.43679i) q^{74} +(0.416213 - 8.47222i) q^{75} +(-1.87629 + 0.920370i) q^{76} +(-1.80220 - 2.42999i) q^{77} +(-0.481243 - 0.474432i) q^{78} +(-1.69132 + 8.50282i) q^{79} +(3.16121 - 14.3431i) q^{80} +(0.195090 + 0.980785i) q^{81} +(-2.49672 - 1.64264i) q^{82} +(13.5674 - 3.39846i) q^{83} +(0.953404 + 1.54044i) q^{84} +(3.54408 - 1.26809i) q^{85} +(-9.81444 + 0.552290i) q^{86} +(-3.70971 - 1.12533i) q^{87} +(-9.37211 - 1.18605i) q^{88} +(-4.51607 - 2.41389i) q^{89} +(5.18820 + 0.217829i) q^{90} +(0.105171 - 0.419867i) q^{91} +(4.00277 + 0.336710i) q^{92} +(6.38012 - 7.03938i) q^{93} +(0.923373 - 10.1136i) q^{94} +(-3.54477 + 1.46829i) q^{95} +(5.53281 + 1.17814i) q^{96} +(5.33421 + 2.20950i) q^{97} +(4.06458 - 7.73641i) q^{98} +(-0.163884 - 3.33595i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{64}\right)$

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 $

$2$	−0.400870	+	1.35621i	−0.283458	+	0.958985i
$2$	−0.400870	+	1.35621i	−0.283458	+	0.958985i
$3$	−0.941544	−	0.336890i	−0.543601	−	0.194503i
$3$	−0.941544	−	0.336890i	−0.543601	−	0.194503i
$4$	−1.67861	−	1.08733i	−0.839304	−	0.543663i
$5$	−2.94925	−	2.18731i	−1.31895	−	0.978197i	−0.999532	−	0.0305815i	$-0.990264\pi$
$5$	−2.94925	−	2.18731i	−1.31895	−	0.978197i	−0.319414	−	0.947615i	$-0.603486\pi$
$6$	0.834330	−	1.14188i	0.340614	−	0.466171i
$7$	0.901442	+	0.0887843i	0.340713	+	0.0335573i	0.266927	−	0.963717i	$-0.413992\pi$
$7$	0.901442	+	0.0887843i	0.340713	+	0.0335573i	0.0737861	+	0.997274i	$0.476492\pi$
$8$	2.14754	−	1.84067i	0.759272	−	0.650774i
$9$	0.773010	+	0.634393i	0.257670	+	0.211464i
$10$	4.14872	−	3.12298i	1.31194	−	0.987572i
$11$	−2.24299	−	2.47475i	−0.676286	−	0.746166i	0.302027	−	0.953299i	$-0.402337\pi$
$11$	−2.24299	−	2.47475i	−0.676286	−	0.746166i	−0.978313	+	0.207133i	$0.933587\pi$
$12$	1.21417	+	1.58927i	0.350502	+	0.458783i
$13$	0.0701152	−	0.472678i	0.0194464	−	0.131097i	−0.977279	−	0.211957i	$-0.932016\pi$
$13$	0.0701152	−	0.472678i	0.0194464	−	0.131097i	0.996726	+	0.0808593i	$0.0257665\pi$
$14$	−0.481771	+	1.18695i	−0.128759	+	0.317227i
$15$	2.03997	+	3.05303i	0.526717	+	0.788288i
$16$	1.63544	+	3.65039i	0.408861	+	0.912597i
$17$	−0.569532	+	0.852364i	−0.138132	+	0.206729i	−0.894086	−	0.447896i	$-0.852173\pi$
$17$	−0.569532	+	0.852364i	−0.138132	+	0.206729i	0.755954	+	0.654625i	$0.227173\pi$
$18$	−1.17025	+	0.794055i	−0.275830	+	0.187161i
$19$	0.537204	−	0.896270i	0.123243	−	0.205618i	−0.789923	−	0.613206i	$-0.789880\pi$
$19$	0.537204	−	0.896270i	0.123243	−	0.205618i	0.913166	+	0.407587i	$0.133630\pi$
$20$	2.57231	+	6.87844i	0.575186	+	1.53807i
$21$	−0.818837	−	0.387281i	−0.178685	−	0.0845116i
$22$	4.25543	−	2.04990i	0.907260	−	0.437041i
$23$	−1.77130	+	0.946779i	−0.369341	+	0.197417i	−0.645617	−	0.763661i	$-0.723400\pi$
$23$	−1.77130	+	0.946779i	−0.369341	+	0.197417i	0.276276	+	0.961078i	$0.410900\pi$
$24$	−2.64211	+	1.00958i	−0.539318	+	0.206080i
$25$	2.46232	+	8.11719i	0.492464	+	1.62344i
$26$	0.612943	+	0.284573i	0.120208	+	0.0558094i
$27$	−0.514103	−	0.857729i	−0.0989391	−	0.165070i
$28$	−1.41663	−	1.12920i	−0.267718	−	0.213398i
$29$	3.87197	−	0.190218i	0.719007	−	0.0353226i	0.313725	−	0.949514i	$-0.398423\pi$
$29$	3.87197	−	0.190218i	0.719007	−	0.0353226i	0.405283	+	0.914191i	$0.367173\pi$
$30$	−4.95830	+	1.54276i	−0.905258	+	0.281668i
$31$	−3.63567	+	8.77728i	−0.652986	+	1.57645i	0.155438	+	0.987846i	$0.450321\pi$
$31$	−3.63567	+	8.77728i	−0.652986	+	1.57645i	−0.808424	+	0.588601i	$0.799679\pi$
$32$	−5.60629	+	0.754674i	−0.991061	+	0.133409i
$33$	1.27815	+	3.08573i	0.222497	+	0.537156i
$34$	−0.927676	−	1.11409i	−0.159095	−	0.191065i
$35$	−2.46438	−	2.23358i	−0.416556	−	0.377545i
$36$	−0.607788	−	1.90541i	−0.101298	−	0.317569i
$37$	−1.94043	−	0.486053i	−0.319005	−	0.0799065i	0.0801705	−	0.996781i	$-0.474454\pi$
$37$	−1.94043	−	0.486053i	−0.319005	−	0.0799065i	−0.399175	+	0.916875i	$0.630704\pi$
$38$	1.00018	+	1.08785i	0.162251	+	0.176472i
$39$	−0.225257	+	0.421426i	−0.0360700	+	0.0674822i
$40$	−10.3598	+	0.731234i	−1.63802	+	0.115618i
$41$	−0.613452	+	2.02228i	−0.0958051	+	0.315827i	−0.991724	−	0.128391i	$-0.959019\pi$
$41$	−0.613452	+	2.02228i	−0.0958051	+	0.315827i	0.895918	+	0.444219i	$0.146519\pi$
$42$	0.853481	−	0.955265i	0.131695	−	0.147401i
$43$	2.34167	+	6.54452i	0.357101	+	0.998030i	0.976980	+	0.213332i	$0.0684317\pi$
$43$	2.34167	+	6.54452i	0.357101	+	0.998030i	−0.619879	+	0.784697i	$0.712818\pi$
$44$	1.07423	+	6.59300i	0.161946	+	0.993931i
$45$	−0.892185	−	3.56180i	−0.132999	−	0.530962i
$46$	−0.573970	−	2.78179i	−0.0846273	−	0.410152i
$47$	−7.04312	+	1.40096i	−1.02734	+	0.204352i	−0.679866	−	0.733336i	$-0.737962\pi$
$47$	−7.04312	+	1.40096i	−1.02734	+	0.204352i	−0.347479	+	0.937688i	$0.612962\pi$
$48$	−0.310063	−	3.98796i	−0.0447538	−	0.575613i
$49$	−6.06078	−	1.20556i	−0.865826	−	0.172224i
$50$	−11.9957	+	0.0854896i	−1.69644	+	0.0120900i
$51$	0.823392	−	0.610669i	0.115298	−	0.0855108i
$52$	−0.631651	+	0.717203i	−0.0875942	+	0.0994581i
$53$	−6.04786	−	0.297112i	−0.830738	−	0.0408115i	−0.370745	−	0.928735i	$-0.620898\pi$
$53$	−6.04786	−	0.297112i	−0.830738	−	0.0408115i	−0.459992	+	0.887923i	$0.652148\pi$
$54$	1.36935	−	0.353394i	0.186345	−	0.0480908i
$55$	1.20207	+	12.2048i	0.162087	+	1.64569i
$56$	2.09931	−	1.46859i	0.280532	−	0.196248i
$57$	−0.807745	+	0.662899i	−0.106988	+	0.0878032i
$58$	−1.29418	+	5.32746i	−0.169934	+	0.699529i
$59$	0.174788	+	1.17832i	0.0227554	+	0.153405i	0.997576	−	0.0695863i	$-0.0221679\pi$
$59$	0.174788	+	1.17832i	0.0227554	+	0.153405i	−0.974820	+	0.222991i	$0.928418\pi$
$60$	−0.104667	−	7.34294i	−0.0135125	−	0.947970i
$61$	3.14751	−	1.48866i	0.402998	−	0.190604i	−0.215300	−	0.976548i	$-0.569073\pi$
$61$	3.14751	−	1.48866i	0.402998	−	0.190604i	0.618297	+	0.785944i	$0.287823\pi$
$62$	−10.4464	−	8.44928i	−1.32669	−	1.07306i
$63$	0.640500	+	0.640500i	0.0806954	+	0.0806954i
$64$	1.22390	−	7.90583i	0.152987	−	0.988228i
$65$	−1.24068	+	1.24068i	−0.153888	+	0.153888i
$66$	−4.69726	+	0.496465i	−0.578193	+	0.0611106i
$67$	4.29727	+	9.08581i	0.524995	+	1.11001i	0.976057	+	0.217516i	$0.0697954\pi$
$67$	4.29727	+	9.08581i	0.524995	+	1.11001i	−0.451062	+	0.892493i	$0.648955\pi$
$68$	1.88282	−	0.811518i	0.228325	−	0.0984110i
$69$	1.98672	−	0.294701i	0.239172	−	0.0354779i
$70$	4.01710	−	2.44684i	0.480136	−	0.292453i
$71$	1.41071	+	1.71896i	0.167421	+	0.204003i	0.849962	−	0.526845i	$-0.176625\pi$
$71$	1.41071	+	1.71896i	0.167421	+	0.204003i	−0.682541	+	0.730847i	$0.739125\pi$
$72$	2.82778	−	0.0604664i	0.333257	−	0.00712604i
$73$	13.1310	−	1.29329i	1.53687	−	0.151368i	0.706151	−	0.708061i	$-0.250430\pi$
$73$	13.1310	−	1.29329i	1.53687	−	0.151368i	0.830718	+	0.556693i	$0.187930\pi$
$74$	1.43705	−	2.43679i	0.167054	−	0.283271i
$75$	0.416213	−	8.47222i	0.0480602	−	0.978288i
$76$	−1.87629	+	0.920370i	−0.215225	+	0.105574i
$77$	−1.80220	−	2.42999i	−0.205380	−	0.276923i
$78$	−0.481243	−	0.474432i	−0.0544901	−	0.0537189i
$79$	−1.69132	+	8.50282i	−0.190288	+	0.956642i	0.761097	+	0.648638i	$0.224661\pi$
$79$	−1.69132	+	8.50282i	−0.190288	+	0.956642i	−0.951385	+	0.308004i	$0.900339\pi$
$80$	3.16121	−	14.3431i	0.353434	−	1.60361i
$81$	0.195090	+	0.980785i	0.0216767	+	0.108976i
$82$	−2.49672	−	1.64264i	−0.275717	−	0.181399i
$83$	13.5674	−	3.39846i	1.48922	−	0.373030i	0.588880	−	0.808221i	$-0.299569\pi$
$83$	13.5674	−	3.39846i	1.48922	−	0.373030i	0.900338	+	0.435191i	$0.143319\pi$
$84$	0.953404	+	1.54044i	0.104025	+	0.168075i
$85$	3.54408	−	1.26809i	0.384410	−	0.137544i
$86$	−9.81444	+	0.552290i	−1.05832	+	0.0595550i
$87$	−3.70971	−	1.12533i	−0.397723	−	0.120648i
$88$	−9.37211	−	1.18605i	−0.999070	−	0.126434i
$89$	−4.51607	−	2.41389i	−0.478703	−	0.255872i	0.214353	−	0.976756i	$-0.431236\pi$
$89$	−4.51607	−	2.41389i	−0.478703	−	0.255872i	−0.693055	+	0.720884i	$0.743736\pi$
$90$	5.18820	+	0.217829i	0.546884	+	0.0229612i
$91$	0.105171	−	0.419867i	0.0110249	−	0.0440140i
$92$	4.00277	+	0.336710i	0.417318	+	0.0351044i
$93$	6.38012	−	7.03938i	0.661588	−	0.729950i
$94$	0.923373	−	10.1136i	0.0952387	−	1.04313i
$95$	−3.54477	+	1.46829i	−0.363686	+	0.150644i
$96$	5.53281	+	1.17814i	0.564690	+	0.120244i
$97$	5.33421	+	2.20950i	0.541607	+	0.224341i	0.636678	−	0.771129i	$-0.280308\pi$
$97$	5.33421	+	2.20950i	0.541607	+	0.224341i	−0.0950713	+	0.995470i	$0.530308\pi$
$98$	4.06458	−	7.73641i	0.410585	−	0.781496i
$99$	−0.163884	−	3.33595i	−0.0164710	−	0.335275i
$100$	4.69276	−	16.3029i	0.469276	−	1.63029i
$101$	−9.25836	+	5.54925i	−0.921241	+	0.552171i	−0.894301	−	0.447466i	$-0.852326\pi$
$101$	−9.25836	+	5.54925i	−0.921241	+	0.552171i	−0.0269403	+	0.999637i	$0.508576\pi$
$102$	0.498122	+	1.36149i	0.0493215	+	0.134808i
$103$	4.93039	−	1.49562i	0.485805	−	0.147367i	−0.0378746	−	0.999282i	$-0.512059\pi$
$103$	4.93039	−	1.49562i	0.485805	−	0.147367i	0.523680	+	0.851915i	$0.324559\pi$
$104$	−0.719467	−	1.14416i	−0.0705495	−	0.112194i
$105$	1.56785	+	2.93324i	0.153007	+	0.286255i
$106$	2.82735	−	8.08306i	0.274617	−	0.785096i
$107$	−3.11699	+	6.59032i	−0.301331	+	0.637111i	−0.996667	−	0.0815738i	$-0.974005\pi$
$107$	−3.11699	+	6.59032i	−0.301331	+	0.637111i	0.695336	+	0.718684i	$0.255255\pi$
$108$	−0.0696544	+	1.99879i	−0.00670249	+	0.192333i
$109$	−14.8118	−	8.87784i	−1.41871	−	0.850343i	−0.420338	−	0.907367i	$-0.638089\pi$
$109$	−14.8118	−	8.87784i	−1.41871	−	0.850343i	−0.998373	+	0.0570247i	$0.981839\pi$
$110$	−17.0341	−	3.26227i	−1.62414	−	0.311046i
$111$	1.66325	+	1.11135i	0.157869	+	0.105485i
$112$	1.15016	+	3.43581i	0.108680	+	0.324654i
$113$	14.0825	−	9.40966i	1.32477	−	0.885186i	0.326575	−	0.945171i	$-0.394105\pi$
$113$	14.0825	−	9.40966i	1.32477	−	0.885186i	0.998199	+	0.0599851i	$0.0191053\pi$
$114$	−0.575230	−	1.36121i	−0.0538752	−	0.127489i
$115$	7.29491	+	1.08210i	0.680254	+	0.100906i
$116$	−6.70635	−	3.89080i	−0.622669	−	0.361251i
$117$	0.354063	−	0.320904i	0.0327332	−	0.0296676i
$118$	−1.66812	−	0.235305i	−0.153563	−	0.0216616i
$119$	−0.589076	+	0.717791i	−0.0540005	+	0.0657998i
$120$	10.0005	+	2.80161i	0.912919	+	0.255751i
$121$	−0.0152306	+	0.154639i	−0.00138460	+	0.0140581i
$122$	0.757196	+	4.86545i	0.0685533	+	0.440497i
$123$	1.25888	−	1.69740i	0.113509	−	0.153049i
$124$	15.6466	−	10.7804i	1.40511	−	0.968113i
$125$	4.30780	−	12.0395i	0.385301	−	1.07684i
$126$	−1.12541	+	0.611895i	−0.100259	+	0.0545119i
$127$			10.9018i			0.967374i	0.875241	+	0.483687i	$0.160703\pi$
$127$			10.9018i			0.967374i	−0.875241	+	0.483687i	$0.839297\pi$
$128$	10.2313	+	4.82906i	0.904330	+	0.426833i
$129$		−	6.95084i		−	0.611987i
$130$	−1.18527	−	2.17998i	−0.103955	−	0.191197i
$131$	−6.38032	+	17.8318i	−0.557451	+	1.55797i	0.250128	+	0.968213i	$0.419527\pi$
$131$	−6.38032	+	17.8318i	−0.557451	+	1.55797i	−0.807579	+	0.589759i	$0.799223\pi$
$132$	1.20968	−	6.56949i	0.105289	−	0.571801i
$133$	0.563833	−	0.760240i	0.0488905	−	0.0659212i
$134$	−14.0449	+	2.18577i	−1.21330	+	0.188822i
$135$	−0.359904	+	3.65416i	−0.0309756	+	0.314500i
$136$	0.345824	+	2.87881i	0.0296541	+	0.246856i
$137$	−5.06040	+	6.16612i	−0.432339	+	0.526807i	−0.942918	−	0.333024i	$-0.891931\pi$
$137$	−5.06040	+	6.16612i	−0.432339	+	0.526807i	0.510579	+	0.859831i	$0.329431\pi$
$138$	−0.396737	+	2.81254i	−0.0337725	+	0.239419i
$139$	−2.70514	+	2.45179i	−0.229447	+	0.207958i	−0.778184	−	0.628037i	$-0.783859\pi$
$139$	−2.70514	+	2.45179i	−0.229447	+	0.207958i	0.548737	+	0.835995i	$0.315109\pi$
$140$	1.70809	+	6.42890i	0.144360	+	0.543341i
$141$	7.10338	+	1.05369i	0.598213	+	0.0887364i
$142$	−2.89678	+	1.22414i	−0.243092	+	0.102728i
$143$	−1.32703	+	0.886692i	−0.110972	+	0.0741489i
$144$	−1.05157	+	3.85930i	−0.0876305	+	0.321608i
$145$	−11.8355	−	7.90822i	−0.982884	−	0.656742i
$146$	−3.50985	+	18.3268i	−0.290477	+	1.51674i
$147$	5.30035	+	3.17691i	0.437166	+	0.262027i
$148$	2.72872	+	2.92577i	0.224300	+	0.240497i
$149$	−5.43335	+	11.4879i	−0.445118	+	0.941122i	0.549302	+	0.835624i	$0.314894\pi$
$149$	−5.43335	+	11.4879i	−0.445118	+	0.941122i	−0.994419	+	0.105498i	$0.966356\pi$
$150$	11.3233	+	3.96073i	0.924540	+	0.323392i
$151$	6.82975	+	12.7776i	0.555797	+	1.03982i	0.990273	+	0.139139i	$0.0444336\pi$
$151$	6.82975	+	12.7776i	0.555797	+	1.03982i	−0.434476	+	0.900683i	$0.643066\pi$
$152$	−0.496065	−	2.91359i	−0.0402362	−	0.236324i
$153$	−0.980988	+	0.297579i	−0.0793082	+	0.0240579i
$154$	4.01802	−	1.47005i	0.323781	−	0.118460i
$155$	29.9212	−	17.9341i	2.40333	−	1.44050i
$156$	0.836345	−	0.462481i	0.0669612	−	0.0370281i
$157$	−0.994756	−	20.2487i	−0.0793901	−	1.61602i	−0.626815	−	0.779168i	$-0.715642\pi$
$157$	−0.994756	−	20.2487i	−0.0793901	−	1.61602i	0.547425	−	0.836855i	$-0.315608\pi$
$158$	−10.8536	−	5.70230i	−0.863466	−	0.453651i
$159$	5.59423	+	2.31721i	0.443652	+	0.183767i
$160$	18.1851	+	10.0370i	1.43766	+	0.793494i
$161$	−1.68078	+	0.696202i	−0.132464	+	0.0548684i
$162$	−1.40836	−	0.128584i	−0.110651	−	0.0101025i
$163$	−14.9882	+	16.5369i	−1.17397	+	1.29527i	−0.227015	+	0.973891i	$0.572897\pi$
$163$	−14.9882	+	16.5369i	−1.17397	+	1.29527i	−0.946950	+	0.321380i	$0.895853\pi$
$164$	3.22862	−	2.72759i	0.252113	−	0.212989i
$165$	2.97987	−	11.8963i	0.231983	−	0.926126i
$166$	−0.829742	+	19.7626i	−0.0644004	+	1.53388i
$167$	−15.6214	−	8.34979i	−1.20882	−	0.646127i	−0.261123	−	0.965305i	$-0.584093\pi$
$167$	−15.6214	−	8.34979i	−1.20882	−	0.646127i	−0.947694	+	0.319179i	$0.896593\pi$
$168$	−2.47134	+	0.675502i	−0.190668	+	0.0521161i
$169$	12.2217	+	3.70742i	0.940132	+	0.285186i
$170$	0.299084	+	5.31486i	0.0229387	+	0.407631i
$171$	0.983852	−	0.352028i	0.0752370	−	0.0269202i
$172$	3.18529	−	13.5318i	0.242876	−	1.03179i
$173$	−6.13759	+	1.53739i	−0.466632	+	0.116885i	−0.469163	−	0.883112i	$-0.655444\pi$
$173$	−6.13759	+	1.53739i	−0.466632	+	0.116885i	0.00253093	+	0.999997i	$0.499194\pi$
$174$	3.01329	−	4.58004i	0.228437	−	0.347212i
$175$	1.49896	+	7.53579i	0.113311	+	0.569652i
$176$	5.36553	−	12.2351i	0.404442	−	0.922254i
$177$	0.232395	−	1.16833i	0.0174679	−	0.0878169i
$178$	5.08410	−	5.15708i	0.381069	−	0.386540i
$179$	5.83565	+	7.86846i	0.436177	+	0.588116i	0.965532	−	0.260284i	$-0.0838162\pi$
$179$	5.83565	+	7.86846i	0.436177	+	0.588116i	−0.529355	+	0.848400i	$0.677566\pi$
$180$	−2.37521	+	6.94896i	−0.177038	+	0.517945i
$181$	0.103413	−	2.10502i	0.00768663	−	0.156465i	−0.991884	−	0.127149i	$-0.959417\pi$
$181$	0.103413	−	2.10502i	0.00768663	−	0.156465i	0.999570	−	0.0293156i	$-0.00933277\pi$
$182$	0.527267	+	0.310946i	0.0390836	+	0.0230488i
$183$	−3.46504	+	0.341276i	−0.256143	+	0.0252279i
$184$	−2.06124	+	5.29362i	−0.151957	+	0.390251i
$185$	4.65967	+	5.67782i	0.342586	+	0.417442i
$186$	6.98927	+	11.4747i	0.512478	+	0.841362i
$187$	3.38684	−	0.502391i	0.247670	−	0.0367384i
$188$	13.3459	+	5.30650i	0.973353	+	0.387017i
$189$	−0.387281	−	0.818837i	−0.0281705	−	0.0595616i
$190$	−0.570321	−	5.39605i	−0.0413754	−	0.391471i
$191$	1.06139	−	1.06139i	0.0767996	−	0.0767996i	−0.667664	−	0.744463i	$-0.732706\pi$
$191$	1.06139	−	1.06139i	0.0767996	−	0.0767996i	0.744463	+	0.667664i	$0.232706\pi$
$192$	−3.81574	+	7.03137i	−0.275378	+	0.507445i
$193$	−18.4702	−	18.4702i	−1.32952	−	1.32952i	−0.905790	−	0.423726i	$-0.860722\pi$
$193$	−18.4702	−	18.4702i	−1.32952	−	1.32952i	−0.423726	−	0.905790i	$-0.639278\pi$
$194$	−5.13487	+	6.34858i	−0.368662	+	0.455802i
$195$	1.58613	−	0.750184i	0.113585	−	0.0537218i
$196$	8.86283	+	8.61372i	0.633059	+	0.615265i
$197$	1.14812	+	7.74003i	0.0818005	+	0.551454i	0.990871	+	0.134812i	$0.0430431\pi$
$197$	1.14812	+	7.74003i	0.0818005	+	0.551454i	−0.909071	+	0.416642i	$0.863207\pi$
$198$	4.58994	+	1.11502i	0.326193	+	0.0792408i
$199$	7.52423	−	6.17498i	0.533379	−	0.437733i	−0.328754	−	0.944416i	$-0.606629\pi$
$199$	7.52423	−	6.17498i	0.533379	−	0.437733i	0.862132	+	0.506683i	$0.169129\pi$
$200$	20.2290	+	12.8997i	1.43040	+	0.912147i
$201$	−0.985150	−	10.0024i	−0.0694872	−	0.705515i
$202$	−3.81454	−	14.7808i	−0.268390	−	1.03997i
$203$	3.50725	+	0.172300i	0.246160	+	0.0120931i
$204$	−2.04615	+	0.129778i	−0.143259	+	0.00908626i
$205$	6.23259	−	4.62240i	0.435303	−	0.322843i
$206$	0.0519264	+	7.28618i	0.00361789	+	0.507652i
$207$	−1.96986	−	0.391830i	−0.136915	−	0.0272341i
$208$	1.84013	−	0.517091i	0.127590	−	0.0358538i
$209$	−3.42299	+	0.680874i	−0.236773	+	0.0470971i
$210$	−4.60660	+	0.950486i	−0.317885	+	0.0655898i
$211$	−3.64343	−	14.5454i	−0.250824	−	1.00135i	−0.956247	−	0.292560i	$-0.905493\pi$
$211$	−3.64343	−	14.5454i	−0.250824	−	1.00135i	0.705423	−	0.708787i	$-0.250757\pi$
$212$	9.82892	+	7.07473i	0.675053	+	0.485895i
$213$	−0.749148	−	2.09373i	−0.0513308	−	0.143460i
$214$	−7.68835	−	6.86915i	−0.525565	−	0.469566i
$215$	7.40876	−	24.4234i	0.505273	−	1.66566i
$216$	−2.68285	−	0.895719i	−0.182545	−	0.0609459i
$217$	−4.05663	+	7.58942i	−0.275382	+	0.515203i
$218$	17.9778	−	16.5290i	1.21761	−	1.11949i
$219$	−12.7991	−	3.20601i	−0.864885	−	0.216642i
$220$	11.2528	−	21.7941i	0.758663	−	1.46936i
$221$	0.362961	+	0.328969i	0.0244154	+	0.0221288i
$222$	−2.17397	+	1.81021i	−0.145908	+	0.121494i
$223$	−8.95574	−	21.6211i	−0.599721	−	1.44785i	−0.873867	−	0.486166i	$-0.838395\pi$
$223$	−8.95574	−	21.6211i	−0.599721	−	1.44785i	0.274146	−	0.961688i	$-0.411605\pi$
$224$	−5.12075	+	0.182544i	−0.342144	+	0.0121968i
$225$	−3.24609	+	7.83675i	−0.216406	+	0.522450i
$226$	7.11620	+	22.8709i	0.473362	+	1.52135i
$227$	−16.4863	+	0.809919i	−1.09423	+	0.0537562i	−0.588168	−	0.808739i	$-0.700151\pi$
$227$	−16.4863	+	0.809919i	−1.09423	+	0.0537562i	−0.506065	+	0.862495i	$0.668901\pi$
$228$	2.07667	−	0.234465i	0.137531	−	0.0155278i
$229$	−9.15833	−	15.2797i	−0.605199	−	1.00971i	−0.996010	−	0.0892431i	$-0.971555\pi$
$229$	−9.15833	−	15.2797i	−0.605199	−	1.00971i	0.390810	−	0.920471i	$-0.372195\pi$
$230$	−4.39186	+	9.45964i	−0.289591	+	0.623750i
$231$	0.878214	+	2.89508i	0.0577823	+	0.190483i
$232$	7.96511	−	7.53551i	0.522935	−	0.494730i
$233$	3.46699	−	1.85315i	0.227130	−	0.121404i	−0.353907	−	0.935281i	$-0.615147\pi$
$233$	3.46699	−	1.85315i	0.227130	−	0.121404i	0.581037	+	0.813877i	$0.302647\pi$
$234$	0.293280	+	0.608825i	0.0191723	+	0.0398001i
$235$	23.8363	+	11.2737i	1.55491	+	0.735417i
$236$	0.987823	−	2.16799i	0.0643018	−	0.141124i
$237$	4.45696	−	7.43599i	0.289511	−	0.483020i
$238$	−0.737333	−	1.08665i	−0.0477942	−	0.0704372i
$239$	−4.59452	+	6.87619i	−0.297195	+	0.444783i	−0.949774	−	0.312937i	$-0.898687\pi$
$239$	−4.59452	+	6.87619i	−0.297195	+	0.444783i	0.652579	+	0.757721i	$0.273687\pi$
$240$	−7.80848	+	12.4397i	−0.504035	+	0.802981i
$241$	3.75588	+	5.62108i	0.241938	+	0.362085i	0.932489	−	0.361198i	$-0.117632\pi$
$241$	3.75588	+	5.62108i	0.241938	+	0.362085i	−0.690552	+	0.723283i	$0.742632\pi$
$242$	−0.203617	−	0.0826459i	−0.0130890	−	0.00531268i
$243$	0.146730	−	0.989177i	0.00941276	−	0.0634557i
$244$	−6.90210	−	0.923494i	−0.441862	−	0.0591206i
$245$	15.2378	+	16.8124i	0.973509	+	1.07410i
$246$	1.79738	+	2.38774i	0.114597	+	0.152237i
$247$	−0.385981	−	0.316766i	−0.0245594	−	0.0201554i
$248$	8.34829	+	25.5417i	0.530117	+	1.62190i
$249$	−13.9192	−	1.37092i	−0.882095	−	0.0868788i
$250$	14.6012	+	10.6685i	0.923461	+	0.674738i
$251$	−8.00627	−	5.93785i	−0.505351	−	0.374794i	0.312780	−	0.949826i	$-0.398740\pi$
$251$	−8.00627	−	5.93785i	−0.505351	−	0.374794i	−0.818131	+	0.575032i	$0.804990\pi$
$252$	−0.378715	−	1.77158i	−0.0238568	−	0.111599i
$253$	6.31604	+	2.25992i	0.397086	+	0.142080i
$254$	−14.7851	−	4.37018i	−0.927697	−	0.274210i
$255$	−3.76412			−0.235718
$256$	−10.6507	+	11.9400i	−0.665666	+	0.746250i
$257$	10.2292			0.638078			0.319039	−	0.947742i	$-0.396640\pi$
$257$	10.2292			0.638078			0.319039	+	0.947742i	$0.396640\pi$
$258$	9.42679	+	2.78638i	0.586886	+	0.173472i
$259$	−1.70603	−	0.610428i	−0.106008	−	0.0379301i
$260$	3.43165	−	0.733592i	0.212822	−	0.0454954i
$261$	3.11375	+	2.30931i	0.192736	+	0.142943i
$262$	−21.6260	−	15.8013i	−1.33606	−	0.976206i
$263$	−0.335964	−	0.0330896i	−0.0207164	−	0.00204039i	0.0876536	−	0.996151i	$-0.472063\pi$
$263$	−0.335964	−	0.0330896i	−0.0207164	−	0.00204039i	−0.108370	+	0.994111i	$0.534563\pi$
$264$	8.42468	+	4.27409i	0.518503	+	0.263052i
$265$	17.1868	+	14.1048i	1.05578	+	0.866453i
$266$	0.805021	+	1.06943i	0.0493590	+	0.0655711i
$267$	3.43887	+	3.79420i	0.210455	+	0.232201i
$268$	2.66582	−	19.9240i	0.162841	−	1.21705i
$269$	2.40540	−	16.2159i	0.146660	−	0.988699i	−0.783460	−	0.621442i	$-0.786547\pi$
$269$	2.40540	−	16.2159i	0.146660	−	0.988699i	0.930120	−	0.367257i	$-0.119703\pi$
$270$	−4.81153	−	1.95295i	−0.292821	−	0.118853i
$271$	−8.22007	−	12.3022i	−0.499334	−	0.747306i	0.493115	−	0.869964i	$-0.335858\pi$
$271$	−8.22007	−	12.3022i	−0.499334	−	0.747306i	−0.992449	+	0.122658i	$0.960858\pi$
$272$	−4.04290	−	0.685017i	−0.245137	−	0.0415353i
$273$	−0.240472	+	0.359892i	−0.0145540	+	0.0217816i
$274$	−6.33398	−	9.33477i	−0.382650	−	0.563934i
$275$	14.5651	−	24.3004i	0.878307	−	1.46537i
$276$	−3.65535	−	1.66552i	−0.220026	−	0.100253i
$277$	16.8706	+	7.97921i	1.01366	+	0.479425i	0.860865	−	0.508834i	$-0.169923\pi$
$277$	16.8706	+	7.97921i	1.01366	+	0.479425i	0.152793	+	0.988258i	$0.451173\pi$
$278$	−2.24074	−	4.65158i	−0.134390	−	0.278983i
$279$	−8.37866	+	4.47849i	−0.501617	+	0.268120i
$280$	−9.40365	−	0.260620i	−0.561976	−	0.0155750i
$281$	7.76847	+	25.6092i	0.463428	+	1.52772i	0.808130	+	0.589005i	$0.200480\pi$
$281$	7.76847	+	25.6092i	0.463428	+	1.52772i	−0.344702	+	0.938712i	$0.612020\pi$
$282$	−4.27655	+	9.21128i	−0.254665	+	0.548524i
$283$	−10.9441	−	18.2591i	−0.650557	−	1.08539i	−0.989493	−	0.144580i	$-0.953817\pi$
$283$	−10.9441	−	18.2591i	−0.650557	−	1.08539i	0.338936	−	0.940809i	$-0.389933\pi$
$284$	−0.498964	−	4.41936i	−0.0296080	−	0.262241i
$285$	3.83221	−	0.188265i	0.227001	−	0.0111518i
$286$	−0.670575	−	2.15518i	−0.0396519	−	0.127438i
$287$	−0.732538	+	1.76850i	−0.0432403	+	0.104391i
$288$	−4.81248	−	2.97322i	−0.283578	−	0.175199i
$289$	6.10346	+	14.7351i	0.359027	+	0.866768i
$290$	15.4697	−	12.8812i	0.908412	−	0.756412i
$291$	−4.27804	−	3.87739i	−0.250783	−	0.227296i
$292$	−23.4480	−	12.1068i	−1.37219	−	0.708495i
$293$	−11.9907	−	3.00350i	−0.700502	−	0.175467i	−0.123663	−	0.992324i	$-0.539464\pi$
$293$	−11.9907	−	3.00350i	−0.700502	−	0.175467i	−0.576839	+	0.816858i	$0.695714\pi$
$294$	−6.43330	+	5.91486i	−0.375198	+	0.344962i
$295$	2.06187	−	3.85749i	0.120047	−	0.224592i
$296$	−5.06182	+	2.52787i	−0.294212	+	0.146929i
$297$	−0.969542	+	3.19615i	−0.0562585	+	0.185459i
$298$	−13.4019	−	11.9739i	−0.776350	−	0.693629i
$299$	0.323327	+	0.903637i	0.0186985	+	0.0522587i
$300$	−9.91072	+	13.7690i	−0.572196	+	0.794952i
$301$	1.52983	+	6.10741i	0.0881777	+	0.352025i
$302$	−20.0669	+	4.14043i	−1.15472	+	0.238255i
$303$	10.5866	−	2.10581i	0.608186	−	0.120976i
$304$	4.15030	+	0.495202i	0.238036	+	0.0284018i
$305$	−12.5390	−	2.49416i	−0.717980	−	0.142815i
$306$	−0.0103317	−	1.44972i	−0.000590623	−	0.0828747i
$307$	−21.2615	+	15.7686i	−1.21346	+	0.899963i	−0.997081	−	0.0763468i	$-0.975674\pi$
$307$	−21.2615	+	15.7686i	−1.21346	+	0.899963i	−0.216378	+	0.976310i	$0.569424\pi$
$308$	0.382999	+	6.03858i	0.0218234	+	0.344080i
$309$	−5.14603	−	0.252808i	−0.292748	−	0.0143818i
$310$	12.3279	+	47.7686i	0.700175	+	2.71308i
$311$	0.326766	+	3.31771i	0.0185292	+	0.188130i	0.999994	−	0.00351328i	$-0.00111831\pi$
$311$	0.326766	+	3.31771i	0.0185292	+	0.188130i	−0.981465	+	0.191643i	$0.938618\pi$
$312$	0.291955	+	1.31965i	0.0165287	+	0.0747107i
$313$	12.9987	−	10.6677i	0.734728	−	0.602976i	−0.190811	−	0.981627i	$-0.561112\pi$
$313$	12.9987	−	10.6677i	0.734728	−	0.602976i	0.925540	+	0.378651i	$0.123612\pi$
$314$	27.8603	+	6.76800i	1.57225	+	0.381940i
$315$	−0.488021	−	3.28997i	−0.0274969	−	0.185369i
$316$	12.0844	−	12.4339i	0.679800	−	0.699460i
$317$	12.7149	−	6.01369i	0.714139	−	0.337762i	−0.0357187	−	0.999362i	$-0.511372\pi$
$317$	12.7149	−	6.01369i	0.714139	−	0.337762i	0.749857	+	0.661599i	$0.230122\pi$
$318$	−5.38518	+	6.65805i	−0.301986	+	0.373365i
$319$	−9.15552	−	9.15552i	−0.512611	−	0.512611i
$320$	−20.9021	+	20.6392i	−1.16846	+	1.15377i
$321$	5.15500	−	5.15500i	0.287724	−	0.287724i
$322$	−0.270422	−	2.55858i	−0.0150700	−	0.142584i
$323$	0.457994	+	0.968347i	0.0254835	+	0.0538803i
$324$	0.738954	−	1.85848i	0.0410530	−	0.103249i
$325$	4.00946	−	0.594747i	0.222405	−	0.0329906i
$326$	−16.4192	−	26.9563i	−0.909376	−	1.49297i
$327$	10.9551	+	13.3488i	0.605818	+	0.738191i
$328$	2.40493	+	5.47210i	0.132790	+	0.302146i
$329$	−6.47335	+	0.637569i	−0.356887	+	0.0351503i
$330$	14.9393	+	8.81020i	0.822384	+	0.484985i
$331$	−1.52691	+	31.0810i	−0.0839266	+	1.70837i	0.475689	+	0.879613i	$0.342199\pi$
$331$	−1.52691	+	31.0810i	−0.0839266	+	1.70837i	−0.559616	+	0.828752i	$0.689051\pi$
$332$	−26.4696	−	9.04753i	−1.45271	−	0.496548i
$333$	−1.19162	−	1.60672i	−0.0653006	−	0.0880477i
$334$	17.5862	−	17.8387i	0.962274	−	0.976088i
$335$	7.19980	−	36.1958i	0.393367	−	1.97759i
$336$	0.0745644	−	3.62245i	0.00406782	−	0.197621i
$337$	−3.13578	−	15.7647i	−0.170817	−	0.858755i	−0.967210	−	0.253976i	$-0.918261\pi$
$337$	−3.13578	−	15.7647i	−0.170817	−	0.858755i	0.796393	−	0.604779i	$-0.206739\pi$
$338$	−9.92735	+	15.0890i	−0.539977	+	0.820734i
$339$	−16.4294	+	4.11534i	−0.892320	+	0.223515i
$340$	−7.32795	−	1.72494i	−0.397414	−	0.0935482i
$341$	29.8764	−	10.6899i	1.61790	−	0.578892i
$342$	0.0830270	+	1.47543i	0.00448959	+	0.0797819i
$343$	−11.4240	−	3.46543i	−0.616838	−	0.187116i
$344$	17.0751	+	9.74442i	0.920628	+	0.525384i
$345$	−6.50393	−	3.47642i	−0.350160	−	0.187164i
$346$	0.375356	−	8.94015i	0.0201793	−	0.480625i
$347$	5.97004	−	23.8337i	0.320488	−	1.27946i	−0.568937	−	0.822381i	$-0.692645\pi$
$347$	5.97004	−	23.8337i	0.320488	−	1.27946i	0.889425	−	0.457080i	$-0.151105\pi$
$348$	5.00355	+	5.92266i	0.268219	+	0.317488i
$349$	−23.9548	+	26.4301i	−1.28227	+	1.41477i	−0.420645	+	0.907225i	$0.638196\pi$
$349$	−23.9548	+	26.4301i	−1.28227	+	1.41477i	−0.861626	+	0.507543i	$0.830554\pi$
$350$	−10.8210	−	0.987963i	−0.578406	−	0.0528089i
$351$	−0.441476	+	0.182865i	−0.0235642	+	0.00976063i
$352$	14.4425	+	12.1815i	0.769785	+	0.649274i
$353$	0.830347	+	0.343941i	0.0441949	+	0.0183061i	0.404671	−	0.914462i	$-0.367386\pi$
$353$	0.830347	+	0.343941i	0.0441949	+	0.0183061i	−0.360476	+	0.932768i	$0.617386\pi$
$354$	1.49134	+	0.783524i	0.0792637	+	0.0416438i
$355$	−0.400645	−	8.15531i	−0.0212640	−	0.432839i
$356$	4.95602	+	8.96242i	0.262669	+	0.475007i
$357$	0.796458	−	0.477378i	0.0421530	−	0.0252655i
$358$	−13.0106	+	4.76013i	−0.687632	+	0.251581i
$359$	−8.87348	+	2.69174i	−0.468325	+	0.142065i	−0.515622	−	0.856816i	$-0.672439\pi$
$359$	−8.87348	+	2.69174i	−0.468325	+	0.142065i	0.0472975	+	0.998881i	$0.484939\pi$
$360$	−8.47210	−	6.00692i	−0.446519	−	0.316592i
$361$	8.44183	+	15.7935i	0.444307	+	0.831239i
$362$	2.81339	+	0.984089i	0.147869	+	0.0517226i
$363$	0.0664366	−	0.140468i	0.00348702	−	0.00737268i
$364$	−0.633073	+	0.590436i	−0.0331820	+	0.0309472i
$365$	−41.5555	−	24.9074i	−2.17512	−	1.30371i
$366$	0.926186	−	4.83612i	0.0484125	−	0.252788i
$367$	−24.0498	−	16.0695i	−1.25539	−	0.838823i	−0.263342	−	0.964703i	$-0.584825\pi$
$367$	−24.0498	−	16.0695i	−1.25539	−	0.838823i	−0.992046	+	0.125880i	$0.959825\pi$
$368$	−6.35297	−	4.91752i	−0.331171	−	0.256344i
$369$	−1.75713	+	1.17407i	−0.0914723	+	0.0611198i
$370$	−9.56824	+	4.04342i	−0.497429	+	0.210207i
$371$	−5.42542	−	0.804785i	−0.281674	−	0.0417823i
$372$	−18.3638	+	4.87908i	−0.952120	+	0.252968i
$373$	−19.0088	+	17.2286i	−0.984237	+	0.892061i	−0.994163	−	0.107890i	$-0.965591\pi$
$373$	−19.0088	+	17.2286i	−0.984237	+	0.892061i	0.00992552	+	0.999951i	$0.496841\pi$
$374$	−0.676336	+	4.79466i	−0.0349725	+	0.247926i
$375$	−8.11196	+	9.88445i	−0.418900	+	0.510431i
$376$	−12.5467	+	15.9727i	−0.647047	+	0.823728i
$377$	0.181572	−	1.84353i	0.00935144	−	0.0949468i
$378$	1.26576	−	0.196987i	0.0651038	−	0.0101319i
$379$	4.31926	−	5.82385i	0.221865	−	0.299151i	−0.678225	−	0.734855i	$-0.737250\pi$
$379$	4.31926	−	5.82385i	0.221865	−	0.299151i	0.900090	+	0.435704i	$0.143500\pi$
$380$	7.54680	+	1.38964i	0.387142	+	0.0712869i
$381$	3.67269	−	10.2645i	0.188158	−	0.525865i
$382$	1.01399	+	1.86495i	0.0518802	+	0.0954191i
$383$			21.3526i			1.09106i	0.838090	+	0.545532i	$0.183672\pi$
$383$			21.3526i			1.09106i	−0.838090	+	0.545532i	$0.816328\pi$
$384$	−8.00639	−	7.99361i	−0.408574	−	0.407922i
$385$			11.1086i			0.566148i
$386$	32.4537	−	17.6453i	1.65185	−	0.898125i
$387$	−2.34167	+	6.54452i	−0.119034	+	0.332677i
$388$	−6.55159	−	9.50891i	−0.332607	−	0.482742i
$389$	−19.3071	+	26.0325i	−0.978906	+	1.31990i	−0.0316250	+	0.999500i	$0.510068\pi$
$389$	−19.3071	+	26.0325i	−0.978906	+	1.31990i	−0.947281	+	0.320403i	$0.896182\pi$
$390$	0.381575	+	2.45185i	0.0193218	+	0.124154i
$391$	0.201810	−	2.04901i	0.0102060	−	0.103623i
$392$	−15.2348	+	8.56687i	−0.769476	+	0.432692i
$393$	12.0147	−	14.6400i	0.606062	−	0.738488i
$394$	−10.9573	−	1.54565i	−0.552023	−	0.0778685i
$395$	23.5865	−	21.3775i	1.18676	−	1.07562i
$396$	−3.35216	+	5.77794i	−0.168453	+	0.290352i
$397$	−32.0635	−	4.75618i	−1.60922	−	0.238706i	−0.719261	−	0.694740i	$-0.755519\pi$
$397$	−32.0635	−	4.75618i	−1.60922	−	0.238706i	−0.889962	+	0.456034i	$0.849269\pi$
$398$	5.35833	+	12.6798i	0.268589	+	0.635581i
$399$	−0.786990	+	0.525850i	−0.0393988	+	0.0263254i
$400$	−25.6039	+	22.2636i	−1.28019	+	1.11318i
$401$	−20.2403	−	13.5242i	−1.01075	−	0.675364i	−0.0642092	−	0.997936i	$-0.520453\pi$
$401$	−20.2403	−	13.5242i	−1.01075	−	0.675364i	−0.946545	+	0.322572i	$0.895453\pi$
$402$	13.9603	+	2.67359i	0.696275	+	0.133346i
$403$	3.89391	+	2.33392i	0.193970	+	0.116261i
$404$	21.5750	+	0.751852i	1.07340	+	0.0374060i
$405$	1.56992	−	3.31931i	0.0780097	−	0.164938i
$406$	−1.63962	+	4.68749i	−0.0813731	+	0.232636i
$407$	3.14950	+	5.89230i	0.156115	+	0.292070i
$408$	0.644233	−	2.82703i	0.0318943	−	0.139959i
$409$	−9.58094	+	2.90635i	−0.473747	+	0.143710i	−0.518124	−	0.855305i	$-0.673370\pi$
$409$	−9.58094	+	2.90635i	−0.473747	+	0.143710i	0.0443775	+	0.999015i	$0.485870\pi$
$410$	3.77049	+	10.3057i	0.186211	+	0.508961i
$411$	6.84189	−	4.10087i	0.337486	−	0.202281i
$412$	−9.90240	−	2.85039i	−0.487856	−	0.140428i
$413$	0.0529445	+	1.07771i	0.00260523	+	0.0530306i
$414$	1.32106	−	2.51447i	0.0649266	−	0.123580i
$415$	−47.4473	−	19.6533i	−2.32909	−	0.964742i
$416$	−0.0363681	+	2.70288i	−0.00178309	+	0.132520i
$417$	3.37299	−	1.39714i	0.165176	−	0.0684181i
$418$	0.448763	−	4.91523i	0.0219497	−	0.240412i
$419$	−0.725366	+	0.800318i	−0.0354364	+	0.0390981i	−0.758411	−	0.651776i	$-0.774024\pi$
$419$	−0.725366	+	0.800318i	−0.0354364	+	0.0390981i	0.722975	+	0.690874i	$0.242774\pi$
$420$	0.557586	−	6.62853i	0.0272074	−	0.323439i
$421$	7.57281	−	30.2323i	0.369076	−	1.47343i	−0.446500	−	0.894784i	$-0.647330\pi$
$421$	7.57281	−	30.2323i	0.369076	−	1.47343i	0.815576	−	0.578650i	$-0.196420\pi$
$422$	21.1872	+	0.889552i	1.03137	+	0.0433027i
$423$	−6.33317	−	3.38515i	−0.307929	−	0.164592i
$424$	−13.5349	+	10.4940i	−0.657315	+	0.509635i
$425$	−8.32117	−	2.52420i	−0.403636	−	0.122442i
$426$	3.13985	−	0.176689i	0.152126	−	0.00856063i
$427$	2.96947	−	1.06249i	0.143703	−	0.0514177i
$428$	12.3980	−	7.67338i	0.599282	−	0.370907i
$429$	1.54817	−	0.387797i	0.0747465	−	0.0187230i
$430$	30.1533	+	19.8384i	1.45412	+	0.956694i
$431$	4.15017	+	20.8643i	0.199907	+	1.00500i	0.942233	+	0.334959i	$0.108723\pi$
$431$	4.15017	+	20.8643i	0.199907	+	1.00500i	−0.742326	+	0.670039i	$0.766277\pi$
$432$	2.29026	−	3.27944i	0.110190	−	0.157782i
$433$	−2.61502	+	13.1466i	−0.125670	+	0.631785i	0.865686	+	0.500587i	$0.166882\pi$
$433$	−2.61502	+	13.1466i	−0.125670	+	0.631785i	−0.991356	+	0.131198i	$0.958118\pi$
$434$	−8.66666	−	8.54401i	−0.416013	−	0.410125i
$435$	8.47944	+	11.4332i	0.406558	+	0.548180i
$436$	15.2100	+	31.0076i	0.728429	+	1.48500i
$437$	−0.102978	+	2.09617i	−0.00492613	+	0.100274i
$438$	9.47881	−	16.0731i	0.452915	−	0.768002i
$439$	−14.3527	+	1.41362i	−0.685018	+	0.0674684i	−0.434538	−	0.900653i	$-0.643088\pi$
$439$	−14.3527	+	1.41362i	−0.685018	+	0.0674684i	−0.250480	+	0.968122i	$0.580588\pi$
$440$	25.0464	+	23.9977i	1.19404	+	1.14405i
$441$	−3.92025	−	4.77683i	−0.186678	−	0.227468i
$442$	−0.591650	+	0.360378i	−0.0281419	+	0.0171414i
$443$	22.5976	−	3.35204i	1.07364	−	0.159260i	0.413579	−	0.910468i	$-0.364279\pi$
$443$	22.5976	−	3.35204i	1.07364	−	0.159260i	0.660065	+	0.751208i	$0.270529\pi$
$444$	−1.58355	−	3.67402i	−0.0751519	−	0.174361i
$445$	8.03910	+	16.9972i	0.381090	+	0.805747i
$446$	32.9128	−	3.47863i	1.55847	−	0.164718i
$447$	8.98588	−	8.98588i	0.425018	−	0.425018i
$448$	1.80518	−	7.01798i	0.0852869	−	0.331568i
$449$	4.10886	+	4.10886i	0.193909	+	0.193909i	0.797383	−	0.603474i	$-0.206217\pi$
$449$	4.10886	+	4.10886i	0.193909	+	0.193909i	−0.603474	+	0.797383i	$0.706217\pi$
$450$	−9.32701	−	7.54389i	−0.439680	−	0.355622i
$451$	6.38061	−	3.01780i	0.300451	−	0.142103i
$452$	−33.8704	+	0.482793i	−1.59313	+	0.0227087i
$453$	−2.12588	−	14.3315i	−0.0998825	−	0.673353i
$454$	5.51043	−	22.6835i	0.258617	−	1.06459i
$455$	−1.22856	+	1.00825i	−0.0575956	+	0.0472675i
$456$	−0.514492	+	2.91040i	−0.0240933	+	0.136292i
$457$	−3.10887	−	31.5649i	−0.145427	−	1.47654i	−0.740057	−	0.672544i	$-0.765202\pi$
$457$	−3.10887	−	31.5649i	−0.145427	−	1.47654i	0.594631	−	0.803999i	$-0.297298\pi$
$458$	24.3938	−	6.29542i	1.13985	−	0.294166i
$459$	1.02390	+	0.0503007i	0.0477913	+	0.00234784i
$460$	−11.0687	−	9.74836i	−0.516080	−	0.454520i
$461$	−3.96452	+	2.94029i	−0.184646	+	0.136943i	−0.684074	−	0.729412i	$-0.739794\pi$
$461$	−3.96452	+	2.94029i	−0.184646	+	0.136943i	0.499428	+	0.866355i	$0.333544\pi$
$462$	−4.27839	+	0.0304908i	−0.199049	+	0.00141856i
$463$	−1.74504	−	0.347110i	−0.0810988	−	0.0161315i	0.154374	−	0.988012i	$-0.450664\pi$
$463$	−1.74504	−	0.347110i	−0.0810988	−	0.0161315i	−0.235473	+	0.971881i	$0.575664\pi$
$464$	7.02676	+	13.8231i	0.326209	+	0.641722i
$465$	−34.2139	+	6.80557i	−1.58663	+	0.315601i
$466$	1.12344	+	5.44484i	0.0520425	+	0.252227i
$467$	−8.33913	−	33.2917i	−0.385889	−	1.54055i	−0.782549	−	0.622589i	$-0.786081\pi$
$467$	−8.33913	−	33.2917i	−0.385889	−	1.54055i	0.396660	−	0.917965i	$-0.370169\pi$
$468$	−0.943261	+	0.153690i	−0.0436023	+	0.00710432i
$469$	3.06706	+	8.57186i	0.141624	+	0.395812i
$470$	−24.8448	+	27.8077i	−1.14600	+	1.28267i
$471$	−5.88498	+	19.4002i	−0.271166	+	0.893913i
$472$	2.54427	+	2.20878i	0.117109	+	0.101667i
$473$	10.9437	−	20.4743i	0.503194	−	0.941410i
$474$	8.29810	+	9.02544i	0.381144	+	0.414552i
$475$	8.59796	+	2.15368i	0.394501	+	0.0988175i
$476$	1.76930	−	0.564372i	0.0810958	−	0.0258679i
$477$	−4.48657	−	4.06639i	−0.205426	−	0.186187i
$478$	−7.48374	−	8.98758i	−0.342298	−	0.411083i
$479$	−7.76359	−	18.7430i	−0.354727	−	0.856388i	−0.996023	−	0.0890939i	$-0.971603\pi$
$479$	−7.76359	−	18.7430i	−0.354727	−	0.856388i	0.641296	−	0.767294i	$-0.278397\pi$
$480$	−13.7407	−	15.5766i	−0.627173	−	0.710973i
$481$	−0.365800	+	0.883119i	−0.0166790	+	0.0402668i
$482$	−9.12897	+	2.84044i	−0.415813	+	0.129379i
$483$	1.81707	−	0.0892671i	0.0826797	−	0.00406179i
$484$	0.193709	−	0.243017i	0.00880496	−	0.0110462i
$485$	−10.8991	−	18.1840i	−0.494901	−	0.825692i
$486$	1.28271	+	0.595528i	0.0581849	+	0.0270137i
$487$	7.04114	+	23.2115i	0.319064	+	1.05181i	0.959005	+	0.283390i	$0.0914590\pi$
$487$	7.04114	+	23.2115i	0.319064	+	1.05181i	−0.639940	+	0.768424i	$0.721041\pi$
$488$	4.01929	−	8.99049i	0.181945	−	0.406980i
$489$	19.6832	−	10.5209i	0.890103	−	0.475770i
$490$	−28.9095	+	13.9261i	−1.30600	+	0.629118i
$491$	21.2723	+	10.0610i	0.960004	+	0.454048i	0.842305	−	0.539001i	$-0.181198\pi$
$491$	21.2723	+	10.0610i	0.960004	+	0.454048i	0.117699	+	0.993049i	$0.462448\pi$
$492$	−3.95879	+	1.48046i	−0.178476	+	0.0667441i
$493$	−2.04308	+	3.40867i	−0.0920155	+	0.153519i
$494$	0.584330	−	0.396489i	0.0262902	−	0.0178389i
$495$	−6.81342	+	10.1970i	−0.306241	+	0.458322i
$496$	−37.9864	+	1.08315i	−1.70564	+	0.0486347i
$497$	1.11906	+	1.67479i	0.0501967	+	0.0751246i
$498$	7.43906	−	18.3278i	0.333352	−	0.821290i
$499$	0.123442	−	0.832179i	0.00552603	−	0.0372535i	−0.986238	−	0.165331i	$-0.947131\pi$
$499$	0.123442	−	0.832179i	0.00552603	−	0.0372535i	0.991764	+	0.128078i	$0.0408807\pi$
$500$	−20.3219	+	15.5256i	−0.908825	+	0.694325i
$501$	11.8952	+	13.1244i	0.531440	+	0.586354i
$502$	11.2624	−	8.47787i	0.502667	−	0.378386i
$503$	9.95035	+	8.16604i	0.443664	+	0.364106i	0.829542	−	0.558444i	$-0.188601\pi$
$503$	9.95035	+	8.16604i	0.443664	+	0.364106i	−0.385878	+	0.922550i	$0.626101\pi$
$504$	2.55445	+	0.196555i	0.113784	+	0.00875528i
$505$	39.4432	+	3.88481i	1.75520	+	0.172872i
$506$	−5.59683	+	7.65994i	−0.248809	+	0.340526i
$507$	−10.2583	−	7.60807i	−0.455587	−	0.337886i
$508$	11.8538	−	18.2998i	0.525926	−	0.811920i
$509$	9.55034	+	3.41717i	0.423311	+	0.151463i	0.539923	−	0.841714i	$-0.318453\pi$
$509$	9.55034	+	3.41717i	0.423311	+	0.151463i	−0.116612	+	0.993178i	$0.537203\pi$
$510$	1.50892	−	5.10493i	0.0668161	−	0.226050i
$511$	11.9517			0.528711
$512$	−11.9236	−	19.2309i	−0.526954	−	0.849894i
$513$	−1.04493			−0.0461350
$514$	−4.10056	+	13.8729i	−0.180868	+	0.611907i
$515$	−17.8123	−	6.37336i	−0.784905	−	0.280844i
$516$	−7.55783	+	11.6677i	−0.332715	+	0.513643i
$517$	19.2647	+	14.2876i	0.847259	+	0.628370i
$518$	1.51176	−	2.06903i	0.0664231	−	0.0909081i
$519$	6.29674	+	0.620175i	0.276396	+	0.0272226i
$520$	−0.380739	+	4.94810i	−0.0166965	+	0.216989i
$521$	−1.92440	−	1.57932i	−0.0843095	−	0.0691910i	0.591295	−	0.806456i	$-0.298617\pi$
$521$	−1.92440	−	1.57932i	−0.0843095	−	0.0691910i	−0.675604	+	0.737265i	$0.736117\pi$
$522$	−4.38012	+	3.29716i	−0.191713	+	0.144313i
$523$	16.5835	+	18.2971i	0.725145	+	0.800074i	0.986254	−	0.165235i	$-0.0528382\pi$
$523$	16.5835	+	18.2971i	0.725145	+	0.800074i	−0.261109	+	0.965309i	$0.584088\pi$
$524$	30.0990	−	22.9951i	1.31488	−	1.00455i
$525$	1.12739	−	7.60026i	0.0492034	−	0.331703i
$526$	0.179554	−	0.442373i	0.00782894	−	0.0192884i
$527$	−5.41081	−	8.09786i	−0.235699	−	0.352748i
$528$	−9.17376	+	9.71228i	−0.399237	+	0.422673i
$529$	−10.5370	+	15.7697i	−0.458131	+	0.685641i
$530$	−26.0188	+	17.6547i	−1.13018	+	0.766871i
$531$	−0.612408	+	1.02174i	−0.0265762	+	0.0443398i
$532$	−1.77308	+	0.663075i	−0.0768729	+	0.0287479i
$533$	0.912875	+	0.431758i	0.0395410	+	0.0187015i
$534$	−6.52427	+	3.14284i	−0.282333	+	0.136004i
$535$	23.6079	−	12.6187i	1.02066	−	0.545553i
$536$	25.9525	+	11.6023i	1.12098	+	0.501145i
$537$	−2.84371	−	9.37447i	−0.122715	−	0.404538i
$538$	21.0279	+	9.76267i	0.906576	+	0.420899i
$539$	10.6108	+	17.7030i	0.457038	+	0.762522i
$540$	4.57740	−	5.74257i	0.196980	−	0.247121i
$541$	−16.4988	+	0.810535i	−0.709340	+	0.0348476i	−0.400540	−	0.916279i	$-0.631177\pi$
$541$	−16.4988	+	0.810535i	−0.709340	+	0.0348476i	−0.308800	+	0.951127i	$0.599927\pi$
$542$	19.9795	−	6.21655i	0.858195	−	0.267024i
$543$	−0.806528	+	1.94713i	−0.0346114	+	0.0835594i
$544$	2.54970	−	5.20841i	0.109318	−	0.223309i
$545$	24.2650	+	58.5810i	1.03940	+	2.50933i
$546$	−0.391691	−	0.470400i	−0.0167628	−	0.0201313i
$547$	−0.302804	−	0.274445i	−0.0129469	−	0.0117344i	0.665060	−	0.746790i	$-0.268406\pi$
$547$	−0.302804	−	0.274445i	−0.0129469	−	0.0117344i	−0.678007	+	0.735056i	$0.737156\pi$
$548$	15.1990	−	4.84818i	0.649269	−	0.207104i
$549$	3.37746	+	0.846009i	0.144146	+	0.0361068i
$550$	27.1177	+	29.4946i	1.15630	+	1.25765i
$551$	1.90955	−	3.57252i	0.0813496	−	0.152194i
$552$	3.72411	−	4.28976i	0.158509	−	0.182584i
$553$	−2.27954	+	7.51464i	−0.0969359	+	0.319555i
$554$	−17.5844	+	19.6815i	−0.747090	+	0.836186i
$555$	−2.47448	−	6.91572i	−0.105036	−	0.293556i
$556$	7.20676	−	1.17423i	0.305635	−	0.0497985i
$557$	−7.36479	−	29.4019i	−0.312056	−	1.24580i	−0.899639	−	0.436634i	$-0.856170\pi$
$557$	−7.36479	−	29.4019i	−0.312056	−	1.24580i	0.587583	−	0.809164i	$-0.300080\pi$
$558$	−2.71501	−	13.1585i	−0.114936	−	0.557044i
$559$	3.25764	−	0.647984i	0.137783	−	0.0274068i
$560$	4.12309	−	12.6488i	0.174232	−	0.534511i
$561$	−3.35811	−	0.667970i	−0.141780	−	0.0282017i
$562$	−37.8456	+	0.269714i	−1.59642	+	0.0113772i
$563$	−20.4089	+	15.1363i	−0.860132	+	0.637918i	−0.933179	−	0.359411i	$-0.882978\pi$
$563$	−20.4089	+	15.1363i	−0.860132	+	0.637918i	0.0730471	+	0.997328i	$0.476728\pi$
$564$	−10.7781	−	9.49242i	−0.453839	−	0.399703i
$565$	−62.1149	−	3.05151i	−2.61319	−	0.128378i
$566$	29.1503	−	7.52293i	1.22528	−	0.316213i
$567$	0.0887843	+	0.901442i	0.00372859	+	0.0378570i
$568$	6.19360	+	1.09489i	0.259878	+	0.0459405i
$569$	−26.2075	+	21.5079i	−1.09867	+	0.901659i	−0.995664	−	0.0930210i	$-0.970348\pi$
$569$	−26.2075	+	21.5079i	−1.09867	+	0.901659i	−0.103011	+	0.994680i	$0.532848\pi$
$570$	−1.28089	+	5.27275i	−0.0536507	+	0.220851i
$571$	3.81770	+	25.7368i	0.159766	+	1.07705i	0.909617	+	0.415447i	$0.136375\pi$
$571$	3.81770	+	25.7368i	0.159766	+	1.07705i	−0.749852	+	0.661606i	$0.769875\pi$
$572$	3.19168	−	0.0454946i	0.133451	−	0.00190223i
$573$	−1.35692	+	0.641775i	−0.0566861	+	0.0268105i
$574$	−2.10481	−	1.70241i	−0.0878530	−	0.0710574i
$575$	−12.0467	−	12.0467i	−0.502381	−	0.502381i
$576$	5.96149	−	5.33485i	0.248395	−	0.222286i
$577$	8.32172	−	8.32172i	0.346438	−	0.346438i	−0.512343	−	0.858781i	$-0.671222\pi$
$577$	8.32172	−	8.32172i	0.346438	−	0.346438i	0.858781	+	0.512343i	$0.171222\pi$
$578$	−22.4305	+	2.37073i	−0.932986	+	0.0986095i
$579$	11.1681	+	23.6130i	0.464131	+	0.981322i
$580$	11.2683	+	26.1438i	0.467892	+	1.08556i
$581$	12.5320	−	1.85894i	0.519914	−	0.0771219i
$582$	6.97348	−	4.24758i	0.289060	−	0.176068i
$583$	12.8300	+	15.6334i	0.531364	+	0.647469i
$584$	25.8189	−	26.9472i	1.06839	−	1.11508i
$585$	−1.74614	+	0.171980i	−0.0721941	+	0.00711050i
$586$	8.88007	−	15.0578i	0.366832	−	0.622033i
$587$	1.38810	−	28.2553i	0.0572929	−	1.16622i	−0.782263	−	0.622949i	$-0.785934\pi$
$587$	1.38810	−	28.2553i	0.0572929	−	1.16622i	0.839555	−	0.543274i	$-0.182816\pi$
$588$	−5.44287	−	11.0960i	−0.224460	−	0.457591i
$589$	5.91372	+	7.97373i	0.243671	+	0.328552i
$590$	4.40502	+	4.34268i	0.181352	+	0.178785i
$591$	1.52653	−	7.67437i	0.0627929	−	0.315681i
$592$	−1.39918	−	7.87823i	−0.0575061	−	0.323793i
$593$	3.51983	+	17.6954i	0.144542	+	0.726662i	0.983276	+	0.182121i	$0.0582962\pi$
$593$	3.51983	+	17.6954i	0.144542	+	0.726662i	−0.838734	+	0.544541i	$0.816704\pi$
$594$	−3.94599	−	2.59614i	−0.161906	−	0.106521i
$595$	3.30737	−	0.828453i	0.135589	−	0.0339633i
$596$	21.6115	−	13.3758i	0.885242	−	0.547893i
$597$	−9.16468	+	3.27918i	−0.375085	+	0.134208i
$598$	−1.35513	+	0.0762577i	−0.0554155	+	0.00311841i
$599$	27.1262	+	8.22865i	1.10835	+	0.336213i	0.790828	−	0.612039i	$-0.209650\pi$
$599$	27.1262	+	8.22865i	1.10835	+	0.336213i	0.317519	+	0.948252i	$0.397150\pi$
$600$	−14.7007	−	18.9606i	−0.600153	−	0.774062i
$601$	40.7581	+	21.7856i	1.66256	+	0.888655i	0.988720	+	0.149773i	$0.0478543\pi$
$601$	40.7581	+	21.7856i	1.66256	+	0.888655i	0.673835	+	0.738882i	$0.264646\pi$
$602$	−8.89618	−	0.373510i	−0.362581	−	0.0152231i
$603$	−2.44214	+	9.74959i	−0.0994518	+	0.397034i
$604$	2.42891	−	28.8747i	0.0988311	−	1.17489i
$605$	0.383163	−	0.422755i	0.0155778	−	0.0171874i
$606$	−1.38794	+	15.2019i	−0.0563811	+	0.617533i
$607$	−4.93864	+	2.04565i	−0.200453	+	0.0830304i	−0.480652	−	0.876912i	$-0.659600\pi$
$607$	−4.93864	+	2.04565i	−0.200453	+	0.0830304i	0.280198	+	0.959942i	$0.409600\pi$
$608$	−2.33533	+	5.43016i	−0.0947100	+	0.220222i
$609$	−3.24418	−	1.34378i	−0.131461	−	0.0544529i
$610$	8.40910	−	16.0057i	0.340475	−	0.648050i
$611$	0.168375	+	3.42736i	0.00681173	+	0.138656i
$612$	1.97026	+	0.567135i	0.0796430	+	0.0229251i
$613$	14.6861	−	8.80248i	0.593164	−	0.355529i	−0.185809	−	0.982586i	$-0.559491\pi$
$613$	14.6861	−	8.80248i	0.593164	−	0.355529i	0.778974	+	0.627057i	$0.215741\pi$
$614$	−12.8625	−	35.1562i	−0.519086	−	1.41879i
$615$	−7.42550	+	2.25250i	−0.299425	+	0.0908295i
$616$	−8.34311	−	1.90126i	−0.336153	−	0.0766038i
$617$	−6.29093	−	11.7695i	−0.253263	−	0.473822i	0.722873	−	0.690981i	$-0.242821\pi$
$617$	−6.29093	−	11.7695i	−0.253263	−	0.473822i	−0.976136	+	0.217159i	$0.930321\pi$
$618$	2.40575	−	6.87776i	0.0967735	−	0.276664i
$619$	6.65135	−	14.0631i	0.267340	−	0.565244i	−0.725004	−	0.688745i	$-0.758162\pi$
$619$	6.65135	−	14.0631i	0.267340	−	0.565244i	0.992344	+	0.123501i	$0.0394122\pi$
$620$	−69.7261	−	2.42984i	−2.80027	−	0.0975846i
$621$	1.72271	+	1.03255i	0.0691299	+	0.0414349i
$622$	−4.63050	−	0.886806i	−0.185666	−	0.0355577i
$623$	−3.85666	−	2.57694i	−0.154514	−	0.103243i
$624$	−1.90676	−	0.133057i	−0.0763316	−	0.00532653i
$625$	−3.77449	+	2.52203i	−0.150980	+	0.100881i
$626$	9.25690	+	21.9053i	0.369980	+	0.875511i
$627$	3.45227	+	0.512096i	0.137871	+	0.0204512i
$628$	−20.3472	+	35.0713i	−0.811940	+	1.39950i
$629$	1.51943	−	1.37713i	0.0605837	−	0.0549098i
$630$	4.65752	+	0.656991i	0.185560	+	0.0261751i
$631$	−19.4943	+	23.7539i	−0.776055	+	0.945626i	−0.999577	−	0.0290726i	$-0.990745\pi$
$631$	−19.4943	+	23.7539i	−0.776055	+	0.945626i	0.223522	+	0.974699i	$0.428245\pi$
$632$	12.0187	+	21.3733i	0.478077	+	0.850186i
$633$	−1.46975	+	14.9226i	−0.0584171	+	0.593119i
$634$	3.05881	+	19.6547i	0.121481	+	0.780590i
$635$	23.8456	−	32.1520i	0.946282	−	1.27591i
$636$	−6.87096	−	9.97244i	−0.272451	−	0.395433i
$637$	−0.994796	+	2.78027i	−0.0394153	+	0.110158i
$638$	16.0870	−	8.74663i	0.636889	−	0.346282i
$639$			2.22372i			0.0879690i
$640$	−19.6121	−	36.6213i	−0.775236	−	1.44758i
$641$			2.46684i			0.0974345i	0.998813	+	0.0487172i	$0.0155133\pi$
$641$			2.46684i			0.0974345i	−0.998813	+	0.0487172i	$0.984487\pi$
$642$	4.92477	+	9.05774i	0.194365	+	0.357480i
$643$	11.2911	−	31.5565i	0.445277	−	1.24447i	−0.483995	−	0.875071i	$-0.660815\pi$
$643$	11.2911	−	31.5565i	0.445277	−	1.24447i	0.929272	−	0.369396i	$-0.120435\pi$
$644$	3.57837	+	0.658907i	0.141008	+	0.0259646i
$645$	−15.2037	+	20.4998i	−0.598644	+	0.807178i
$646$	−1.49688	+	0.232955i	−0.0588939	+	0.00916549i
$647$	−3.44728	+	35.0008i	−0.135527	+	1.37603i	0.651285	+	0.758833i	$0.274230\pi$
$647$	−3.44728	+	35.0008i	−0.135527	+	1.37603i	−0.786812	+	0.617193i	$0.788270\pi$
$648$	2.22426	+	1.74718i	0.0873773	+	0.0686359i
$649$	2.52401	−	3.07552i	0.0990762	−	0.120725i
$650$	−0.800669	+	5.67608i	−0.0314048	+	0.222634i
$651$	6.37629	−	5.77914i	0.249907	−	0.226502i
$652$	43.1403	−	11.4619i	1.68950	−	0.448884i
$653$	24.4944	+	3.63340i	0.958539	+	0.142186i	0.607627	−	0.794223i	$-0.292122\pi$
$653$	24.4944	+	3.63340i	0.958539	+	0.142186i	0.350912	+	0.936408i	$0.385872\pi$
$654$	−22.4953	+	9.50626i	−0.879638	+	0.371724i
$655$	57.8209	−	38.6347i	2.25925	−	1.50958i
$656$	−8.38537	+	1.06799i	−0.327394	+	0.0416979i
$657$	10.9709	+	7.33050i	0.428014	+	0.285990i
$658$	1.73029	−	9.03480i	0.0674538	−	0.352213i
$659$	0.142150	+	0.0852014i	0.00553737	+	0.00331897i	0.516869	−	0.856065i	$-0.327098\pi$
$659$	0.142150	+	0.0852014i	0.00553737	+	0.00331897i	−0.511331	+	0.859384i	$0.670848\pi$
$660$	−17.9372	+	16.7291i	−0.698205	+	0.651181i
$661$	−13.5378	+	28.6232i	−0.526558	+	1.11331i	0.448993	+	0.893535i	$0.351783\pi$
$661$	−13.5378	+	28.6232i	−0.526558	+	1.11331i	−0.975550	+	0.219777i	$0.929467\pi$
$662$	−41.5402	−	14.5302i	−1.61451	−	0.564734i
$663$	−0.230918	−	0.432016i	−0.00896810	−	0.0167781i
$664$	22.8812	−	32.2714i	0.887963	−	1.25237i
$665$	−3.32577	+	1.00886i	−0.128968	+	0.0391220i
$666$	2.65673	−	0.972007i	0.102946	−	0.0376645i
$667$	−6.67832	+	4.00283i	−0.258586	+	0.154990i
$668$	17.1432	+	31.0015i	0.663290	+	1.19949i
$669$	1.14831	+	23.3743i	0.0443960	+	0.903702i
$670$	46.2030	+	24.2742i	1.78498	+	0.937796i
$671$	−10.7439	−	4.45027i	−0.414764	−	0.171801i
$672$	4.88291	+	1.55325i	0.188362	+	0.0599181i
$673$	26.0341	−	10.7837i	1.00354	−	0.415681i	0.180448	−	0.983585i	$-0.442245\pi$
$673$	26.0341	−	10.7837i	1.00354	−	0.415681i	0.823095	+	0.567904i	$0.192245\pi$
$674$	22.6372	+	2.06679i	0.871953	+	0.0796098i
$675$	5.69646	−	6.28507i	0.219257	−	0.241912i
$676$	−16.4843	−	19.5123i	−0.634011	−	0.750473i
$677$	−5.99474	+	23.9324i	−0.230397	+	0.919795i	0.738883	+	0.673834i	$0.235354\pi$
$677$	−5.99474	+	23.9324i	−0.230397	+	0.919795i	−0.969280	+	0.245961i	$0.920896\pi$
$678$	1.00477	−	23.9314i	0.0385879	−	0.919078i
$679$	4.61231	+	2.46533i	0.177004	+	0.0946108i
$680$	5.27694	−	9.24676i	0.202361	−	0.354597i
$681$	15.7954	+	4.79149i	0.605282	+	0.183610i
$682$	2.52126	+	44.8039i	0.0965440	+	1.71563i
$683$	−19.9160	+	7.12606i	−0.762065	+	0.272671i	−0.689103	−	0.724664i	$-0.741995\pi$
$683$	−19.9160	+	7.12606i	−0.762065	+	0.272671i	−0.0729620	+	0.997335i	$0.523245\pi$
$684$	−2.03427	−	0.478852i	−0.0777822	−	0.0183093i
$685$	28.4116	−	7.11675i	1.08555	−	0.271917i
$686$	9.27939	−	14.1042i	0.354289	−	0.538499i
$687$	3.47538	+	17.4719i	0.132594	+	0.666595i
$688$	−20.0604	+	19.2512i	−0.764794	+	0.733944i
$689$	−0.564485	+	2.83786i	−0.0215052	+	0.108114i
$690$	7.32199	−	7.42710i	0.278743	−	0.282745i
$691$	17.9091	+	24.1476i	0.681294	+	0.918618i	0.999568	−	0.0293804i	$-0.00935343\pi$
$691$	17.9091	+	24.1476i	0.681294	+	0.918618i	−0.318275	+	0.947999i	$0.603103\pi$
$692$	11.9742	+	4.09289i	0.455192	+	0.155589i
$693$	0.148447	−	3.02171i	0.00563904	−	0.114785i
$694$	29.9303	+	17.6508i	1.13614	+	0.670017i
$695$	13.3410	−	1.31397i	0.506052	−	0.0498417i
$696$	−10.0381	+	4.41165i	−0.380495	+	0.167223i
$697$	−1.37434	−	1.67464i	−0.0520568	−	0.0634314i
$698$	−26.2419	−	43.0827i	−0.993272	−	1.63071i
$699$	−3.88864	+	0.576825i	−0.147082	+	0.0218175i
$700$	5.67769	−	14.2795i	0.214597	−	0.539714i
$701$	18.9029	+	39.9669i	0.713953	+	1.50953i	0.854499	+	0.519453i	$0.173864\pi$
$701$	18.9029	+	39.9669i	0.713953	+	1.50953i	−0.140546	+	0.990074i	$0.544886\pi$
$702$	−0.0710293	−	0.672039i	−0.00268083	−	0.0253645i
$703$	−1.47804	+	1.47804i	−0.0557454	+	0.0557454i
$704$	−22.3101	+	14.7038i	−0.840845	+	0.554171i
$705$	−18.6449	−	18.6449i	−0.702208	−	0.702208i
$706$	−0.799317	+	0.988249i	−0.0300827	+	0.0371932i
$707$	−8.83856	+	4.18033i	−0.332408	+	0.157217i
$708$	−1.66045	+	1.70847i	−0.0624037	+	0.0642084i
$709$	−5.73165	−	38.6396i	−0.215257	−	1.45114i	−0.779950	−	0.625842i	$-0.784756\pi$
$709$	−5.73165	−	38.6396i	−0.215257	−	1.45114i	0.564694	−	0.825301i	$-0.308994\pi$
$710$	11.2209	+	2.72586i	0.421114	+	0.102300i
$711$	−6.70154	+	5.49981i	−0.251327	+	0.206259i
$712$	−14.1416	+	3.12864i	−0.529980	+	0.117251i
$713$	−1.87029	−	18.9894i	−0.0700429	−	0.711157i
$714$	0.328149	+	1.27153i	0.0122807	+	0.0475858i
$715$	5.85322	+	0.287550i	0.218898	+	0.0107538i
$716$	−1.24018	−	19.5533i	−0.0463475	−	0.730741i
$717$	6.64246	−	4.92638i	0.248067	−	0.183979i
$718$	−0.0934548	−	13.1133i	−0.00348770	−	0.489385i
$719$	−17.7178	−	3.52428i	−0.660761	−	0.131434i	−0.146692	−	0.989182i	$-0.546863\pi$
$719$	−17.7178	−	3.52428i	−0.660761	−	0.131434i	−0.514069	+	0.857749i	$0.671863\pi$
$720$	11.5428	−	9.08195i	0.430176	−	0.338464i
$721$	4.57724	−	0.910470i	0.170465	−	0.0339077i
$722$	−24.8034	+	5.11773i	−0.923088	+	0.190462i
$723$	−1.64265	−	6.55781i	−0.0610906	−	0.243888i
$724$	−2.46243	+	3.42106i	−0.0915157	+	0.127143i
$725$	11.0781	+	30.9611i	0.411429	+	1.14987i
$726$	0.163872	+	0.146411i	0.00608186	+	0.00543384i
$727$	6.67797	−	22.0143i	0.247672	−	0.816466i	−0.741658	−	0.670778i	$-0.765960\pi$
$727$	6.67797	−	22.0143i	0.247672	−	0.816466i	0.989331	−	0.145688i	$-0.0465396\pi$
$728$	−0.546975	−	1.09527i	−0.0202722	−	0.0405933i
$729$	−0.471397	+	0.881921i	−0.0174591	+	0.0326638i
$730$	50.4380	−	46.3733i	1.86679	−	1.71635i
$731$	−6.91197	−	1.73136i	−0.255648	−	0.0640366i
$732$	6.18752	+	3.19476i	0.228697	+	0.118082i
$733$	−34.4162	−	31.1930i	−1.27119	−	1.15214i	−0.980754	−	0.195246i	$-0.937449\pi$
$733$	−34.4162	−	31.1930i	−1.27119	−	1.15214i	−0.290437	−	0.956894i	$-0.593801\pi$
$734$	31.4345	−	26.1747i	1.16027	−	0.966127i
$735$	−8.68318	−	20.9630i	−0.320284	−	0.773233i
$736$	9.21590	−	6.64467i	0.339703	−	0.244926i
$737$	12.8464	−	31.0140i	0.473204	−	1.14242i
$738$	−0.887911	−	2.85368i	−0.0326845	−	0.105045i
$739$	−18.0879	+	0.888600i	−0.665373	+	0.0326877i	−0.378952	−	0.925416i	$-0.623716\pi$
$739$	−18.0879	+	0.888600i	−0.665373	+	0.0326877i	−0.286421	+	0.958104i	$0.592466\pi$
$740$	−1.64811	−	14.5974i	−0.0605856	−	0.536612i
$741$	0.256703	+	0.428283i	0.00943021	+	0.0157334i
$742$	3.26634	−	7.03539i	0.119911	−	0.258277i
$743$	10.4489	+	34.4455i	0.383334	+	1.26368i	0.910354	+	0.413831i	$0.135809\pi$
$743$	10.4489	+	34.4455i	0.383334	+	1.26368i	−0.527020	+	0.849853i	$0.676691\pi$
$744$	0.744447	−	26.8611i	0.0272928	−	0.984774i
$745$	41.1519	−	21.9961i	1.50769	−	0.805876i
$746$	−15.7455	−	32.6863i	−0.576483	−	1.19673i
$747$	12.6437	+	5.98003i	0.462610	+	0.218798i
$748$	−6.23144	−	2.83929i	−0.227844	−	0.103815i
$749$	−3.39490	+	5.66405i	−0.124047	+	0.206960i
$750$	−10.1535	−	14.9639i	−0.370755	−	0.546404i
$751$	3.60701	−	5.39827i	0.131622	−	0.196986i	−0.759805	−	0.650151i	$-0.774705\pi$
$751$	3.60701	−	5.39827i	0.131622	−	0.196986i	0.891426	+	0.453166i	$0.149705\pi$
$752$	−16.6327	−	23.4189i	−0.606532	−	0.854000i
$753$	5.53785	+	8.28798i	0.201810	+	0.302031i
$754$	2.42743	+	0.985266i	0.0884018	+	0.0358813i
$755$	7.80589	−	52.6230i	0.284085	−	1.91515i
$756$	−0.240250	+	1.79561i	−0.00873782	+	0.0653056i
$757$	−15.2194	−	16.7920i	−0.553157	−	0.610315i	0.398616	−	0.917118i	$-0.369491\pi$
$757$	−15.2194	−	16.7920i	−0.553157	−	0.610315i	−0.951773	+	0.306803i	$0.900741\pi$
$758$	6.16690	+	8.19242i	0.223992	+	0.297562i
$759$	−5.18549	−	4.25562i	−0.188221	−	0.154469i
$760$	−4.90992	+	9.67797i	−0.178102	+	0.351057i
$761$	−3.12136	−	0.307428i	−0.113149	−	0.0111442i	0.0412840	−	0.999147i	$-0.486855\pi$
$761$	−3.12136	−	0.307428i	−0.113149	−	0.0111442i	−0.154433	+	0.988003i	$0.549355\pi$
$762$	12.4485	+	9.09565i	0.450962	+	0.329501i
$763$	−12.5637	−	9.31791i	−0.454838	−	0.337331i
$764$	−2.93574	+	0.627580i	−0.106211	+	0.0227051i
$765$	3.54408	+	1.26809i	0.128137	+	0.0458480i
$766$	−28.9585	−	8.55959i	−1.04631	−	0.309271i
$767$	0.569223			0.0205535
$768$	14.0505	−	7.65394i	0.507005	−	0.276188i
$769$	21.0702			0.759811			0.379905	−	0.925025i	$-0.375957\pi$
$769$	21.0702			0.759811			0.379905	+	0.925025i	$0.375957\pi$
$770$	−15.0656	−	4.45311i	−0.542928	−	0.160479i
$771$	−9.63121	−	3.44610i	−0.346860	−	0.124108i
$772$	10.9211	+	51.0874i	0.393059	+	1.83868i
$773$	24.0012	+	17.8005i	0.863264	+	0.640240i	0.934007	−	0.357254i	$-0.116287\pi$
$773$	24.0012	+	17.8005i	0.863264	+	0.640240i	−0.0707429	+	0.997495i	$0.522537\pi$
$774$	−7.93703	−	5.79929i	−0.285291	−	0.208451i
$775$	−80.1990	−	7.89891i	−2.88083	−	0.283737i
$776$	15.5224	−	5.07350i	0.557222	−	0.182128i
$777$	1.40066	+	1.14949i	0.0502483	+	0.0412377i
$778$	−27.5660	−	36.6201i	−0.988288	−	1.31289i
$779$	1.48296	+	1.63619i	0.0531326	+	0.0586228i
$780$	−3.47819	−	0.465378i	−0.124539	−	0.0166632i
$781$	1.08979	−	7.34676i	0.0389957	−	0.262888i
$782$	2.69799	+	1.09508i	0.0964799	+	0.0391601i
$783$	−2.15375	−	3.22331i	−0.0769686	−	0.115192i
$784$	−5.51129	−	24.0958i	−0.196832	−	0.860565i
$785$	−41.3565	+	61.8944i	−1.47608	+	2.20911i
$786$	15.0385	+	22.1632i	0.536406	+	0.790534i
$787$	18.3083	−	30.5456i	0.652621	−	1.08883i	−0.336494	−	0.941686i	$-0.609241\pi$
$787$	18.3083	−	30.5456i	0.652621	−	1.08883i	0.989115	−	0.147146i	$-0.0470088\pi$
$788$	6.48869	−	14.2409i	0.231150	−	0.507309i
$789$	0.305178	+	0.144338i	0.0108646	+	0.00513858i
$790$	19.5373	+	40.5578i	0.695106	+	1.44298i
$791$	13.5300	−	7.23195i	0.481072	−	0.257139i
$792$	−6.49231	−	6.86243i	−0.230694	−	0.243846i
$793$	−0.482970	−	1.59214i	−0.0171508	−	0.0565385i
$794$	19.3037	−	41.5783i	0.685062	−	1.47556i
$795$	−11.4303	−	19.0704i	−0.405393	−	0.676357i
$796$	−19.3444	+	2.18407i	−0.685646	+	0.0774122i
$797$	52.6424	−	2.58616i	1.86469	−	0.0916063i	0.914746	−	0.404029i	$-0.132391\pi$
$797$	52.6424	−	2.58616i	1.86469	−	0.0916063i	0.949943	+	0.312423i	$0.101141\pi$
$798$	−0.397682	−	1.27812i	−0.0140778	−	0.0452450i
$799$	2.81715	−	6.80120i	0.0996636	−	0.240609i
$800$	−19.9303	−	43.6490i	−0.704643	−	1.54323i
$801$	−1.95961	−	4.73093i	−0.0692396	−	0.167159i
$802$	26.4553	−	22.0287i	0.934170	−	0.777861i
$803$	−32.6533	−	29.5952i	−1.15231	−	1.04439i
$804$	−9.22219	+	17.8613i	−0.325242	+	0.629919i
$805$	6.47986	+	1.62312i	0.228385	+	0.0572075i
$806$	−4.72624	+	4.34536i	−0.166475	+	0.153059i
$807$	−7.72775	+	14.4576i	−0.272030	+	0.508932i
$808$	−9.66843	+	28.9588i	−0.340134	+	1.01877i
$809$	−16.2582	+	53.5961i	−0.571608	+	1.88434i	−0.118321	+	0.992975i	$0.537751\pi$
$809$	−16.2582	+	53.5961i	−0.571608	+	1.88434i	−0.453287	+	0.891365i	$0.649749\pi$
$810$	3.87234	+	3.45974i	0.136060	+	0.121563i
$811$	5.49055	+	15.3450i	0.192799	+	0.538837i	0.998574	−	0.0533845i	$-0.0170009\pi$
$811$	5.49055	+	15.3450i	0.192799	+	0.538837i	−0.805775	+	0.592222i	$0.798251\pi$
$812$	−5.69994	−	4.10274i	−0.200029	−	0.143978i
$813$	3.59507	+	14.3523i	0.126085	+	0.503358i
$814$	−9.25372	+	1.90934i	−0.324343	+	0.0669222i
$815$	80.3754	−	15.9877i	2.81543	−	0.560023i
$816$	3.57579	+	2.00698i	0.125178	+	0.0702585i
$817$	7.12361	+	1.41697i	0.249224	+	0.0495736i
$818$	−0.100906	−	14.1588i	−0.00352808	−	0.495052i
$819$	0.347659	−	0.257841i	0.0121482	−	0.00900971i
$820$	−15.4881	+	0.982340i	−0.540869	+	0.0343048i
$821$	−20.0805	−	0.986493i	−0.700815	−	0.0344288i	−0.304459	−	0.952526i	$-0.598476\pi$
$821$	−20.0805	−	0.986493i	−0.700815	−	0.0344288i	−0.396356	+	0.918097i	$0.629726\pi$
$822$	2.81893	+	10.9230i	0.0983216	+	0.380982i
$823$	0.488947	+	4.96436i	0.0170436	+	0.173047i	0.999938	−	0.0111226i	$-0.00354050\pi$
$823$	0.488947	+	4.96436i	0.0170436	+	0.173047i	−0.982895	+	0.184169i	$0.941041\pi$
$824$	7.83529	−	12.2871i	0.272955	−	0.428041i
$825$	−21.9002	+	17.9730i	−0.762467	+	0.625741i
$826$	−1.48282	−	0.360217i	−0.0515940	−	0.0125336i
$827$	2.11930	+	14.2872i	0.0736954	+	0.496814i	0.994326	+	0.106379i	$0.0339255\pi$
$827$	2.11930	+	14.2872i	0.0736954	+	0.496814i	−0.920630	+	0.390435i	$0.872324\pi$
$828$	2.88058	+	2.79961i	0.100107	+	0.0972932i
$829$	−40.8658	+	19.3281i	−1.41933	+	0.671293i	−0.974513	−	0.224329i	$-0.927981\pi$
$829$	−40.8658	+	19.3281i	−1.41933	+	0.671293i	−0.444816	+	0.895622i	$0.646731\pi$
$830$	45.6741	−	56.4700i	1.58537	−	1.96010i
$831$	−13.1963	−	13.1963i	−0.457776	−	0.457776i
$832$	−3.65110	−	1.13283i	−0.126579	−	0.0392737i
$833$	4.47939	−	4.47939i	0.155202	−	0.155202i
$834$	0.542682	+	5.13455i	0.0187915	+	0.177795i
$835$	27.8077	+	58.7945i	0.962326	+	2.03467i
$836$	6.48618	+	2.57898i	0.224329	+	0.0891960i
$837$	9.39763	−	1.39401i	0.324830	−	0.0481839i
$838$	−0.794622	−	1.30457i	−0.0274497	−	0.0450657i
$839$	29.0306	+	35.3739i	1.00225	+	1.22124i	0.975135	+	0.221610i	$0.0711311\pi$
$839$	29.0306	+	35.3739i	1.00225	+	1.22124i	0.0271120	+	0.999632i	$0.491369\pi$
$840$	8.76615	+	3.41338i	0.302461	+	0.117773i
$841$	−13.9044	+	1.36946i	−0.479461	+	0.0472228i
$842$	37.9657	+	22.3895i	1.30838	+	0.771595i
$843$	1.31313	−	26.7293i	0.0452265	−	0.920606i
$844$	−9.69971	+	28.3776i	−0.333878	+	0.976798i
$845$	−27.9356	−	37.6668i	−0.961015	−	1.29578i
$846$	7.12975	−	7.23210i	0.245126	−	0.248645i
$847$	−0.0274590	+	0.138046i	−0.000943503	+	0.00474331i
$848$	−8.80636	−	22.5629i	−0.302412	−	0.774815i
$849$	4.15302	+	20.8787i	0.142531	+	0.716554i
$850$	6.75905	−	10.2734i	0.231833	−	0.352374i
$851$	3.89727	−	0.976214i	0.133597	−	0.0334642i
$852$	−1.01904	+	4.32912i	−0.0349118	+	0.148313i
$853$	−26.1349	+	9.35123i	−0.894843	+	0.320180i	−0.743844	−	0.668354i	$-0.766999\pi$
$853$	−26.1349	+	9.35123i	−0.894843	+	0.320180i	−0.151000	+	0.988534i	$0.548249\pi$
$854$	0.250593	+	4.45314i	0.00857511	+	0.152383i
$855$	−3.67162	−	1.11377i	−0.125567	−	0.0380903i
$856$	5.43671	+	19.8904i	0.185823	+	0.679838i
$857$	−9.60623	−	5.13464i	−0.328142	−	0.175396i	0.299096	−	0.954223i	$-0.403315\pi$
$857$	−9.60623	−	5.13464i	−0.328142	−	0.175396i	−0.627239	+	0.778827i	$0.715815\pi$
$858$	−0.0946815	+	2.25510i	−0.00323237	+	0.0769880i
$859$	7.48105	−	29.8660i	0.255250	−	1.01901i	−0.697822	−	0.716271i	$-0.745847\pi$
$859$	7.48105	−	29.8660i	0.255250	−	1.01901i	0.953072	−	0.302744i	$-0.0979026\pi$
$860$	−38.9926	+	32.9416i	−1.32964	+	1.12330i
$861$	1.28551	−	1.41834i	0.0438100	−	0.0483369i
$862$	−29.9600	−	2.73537i	−1.02044	−	0.0931671i
$863$	3.40067	−	1.40860i	0.115760	−	0.0479494i	−0.324052	−	0.946039i	$-0.605045\pi$
$863$	3.40067	−	1.40860i	0.115760	−	0.0479494i	0.439812	+	0.898090i	$0.355045\pi$
$864$	3.52951	+	4.42069i	0.120076	+	0.150395i
$865$	21.4640	+	8.89070i	0.729799	+	0.302293i
$866$	−16.7812	−	8.81658i	−0.570250	−	0.299600i
$867$	−0.782586	−	15.9299i	−0.0265780	−	0.541008i
$868$	15.0617	−	8.32877i	0.511226	−	0.282697i
$869$	24.8360	−	14.8861i	0.842503	−	0.504977i
$870$	−18.9050	+	6.91667i	−0.640938	+	0.234497i
$871$	4.59597	−	1.39417i	0.155728	−	0.0472397i
$872$	−48.1501	+	8.19799i	−1.63057	+	0.277619i
$873$	2.72171	+	5.09196i	0.0921158	+	0.172337i
$874$	−2.80157	−	0.979953i	−0.0947645	−	0.0331474i
$875$	4.95215	−	10.4704i	0.167413	−	0.353965i
$876$	17.9987	+	19.2985i	0.608120	+	0.652035i
$877$	17.1304	+	10.2676i	0.578453	+	0.346712i	0.773220	−	0.634138i	$-0.218645\pi$
$877$	17.1304	+	10.2676i	0.578453	+	0.346712i	−0.194766	+	0.980850i	$0.562395\pi$
$878$	3.83641	−	20.0320i	0.129472	−	0.676046i
$879$	10.2779	+	6.86746i	0.346664	+	0.231634i
$880$	−42.5863	+	24.3482i	−1.43558	+	0.820779i
$881$	11.4403	−	7.64418i	0.385434	−	0.257539i	−0.347724	−	0.937597i	$-0.613045\pi$
$881$	11.4403	−	7.64418i	0.385434	−	0.257539i	0.733158	+	0.680058i	$0.238045\pi$
$882$	8.04989	−	3.40179i	0.271054	−	0.114544i
$883$	−21.2793	−	3.15648i	−0.716105	−	0.106224i	−0.221272	−	0.975212i	$-0.571021\pi$
$883$	−21.2793	−	3.15648i	−0.716105	−	0.106224i	−0.494833	+	0.868988i	$0.664771\pi$
$884$	−0.251573	−	0.946866i	−0.00846130	−	0.0318466i
$885$	−3.24089	+	2.93737i	−0.108941	+	0.0987388i
$886$	−4.51263	+	31.9908i	−0.151605	+	1.07475i
$887$	32.4463	−	39.5359i	1.08944	−	1.32749i	0.148499	−	0.988913i	$-0.452556\pi$
$887$	32.4463	−	39.5359i	1.08944	−	1.32749i	0.940940	−	0.338573i	$-0.109944\pi$
$888$	5.61754	−	0.674820i	0.188512	−	0.0226455i
$889$	−0.967904	+	9.82729i	−0.0324625	+	0.329597i
$890$	−26.2745	+	4.08902i	−0.880722	+	0.137064i
$891$	1.98962	−	2.68269i	0.0666547	−	0.0898734i
$892$	−8.47599	+	46.0311i	−0.283797	+	1.54124i
$893$	−2.52795	+	7.06514i	−0.0845946	+	0.236426i
$894$	8.58457	+	15.7889i	0.287111	+	0.528060i
$895$		−	35.9705i		−	1.20236i
$896$	8.79421	+	5.26150i	0.293794	+	0.175774i
$897$		−	0.959740i		−	0.0320448i
$898$	−7.21959	+	3.92536i	−0.240921	+	0.130991i
$899$	−12.4076	+	34.6770i	−0.413817	+	1.15654i
$900$	13.9700	−	9.62527i	0.465667	−	0.320842i
$901$	3.69770	−	4.98577i	0.123188	−	0.166100i
$902$	1.53498	+	9.86318i	0.0511092	+	0.328408i
$903$	0.617125	−	6.26578i	0.0205366	−	0.208512i
$904$	12.9229	−	46.1289i	0.429808	−	1.53423i
$905$	−4.90933	+	5.98204i	−0.163192	+	0.198850i
$906$	20.2887	+	2.86193i	0.674048	+	0.0950813i
$907$	−38.4767	+	34.8733i	−1.27760	+	1.15795i	−0.298533	+	0.954399i	$0.596497\pi$
$907$	−38.4767	+	34.8733i	−1.27760	+	1.15795i	−0.979065	+	0.203548i	$0.934753\pi$
$908$	28.5546	+	16.5664i	0.947619	+	0.549776i
$909$	−10.6772	−	1.58381i	−0.354141	−	0.0525318i
$910$	−0.874907	−	2.07036i	−0.0290029	−	0.0686317i
$911$	−21.6056	+	14.4364i	−0.715825	+	0.478299i	−0.859376	−	0.511344i	$-0.829148\pi$
$911$	−21.6056	+	14.4364i	−0.715825	+	0.478299i	0.143551	+	0.989643i	$0.454148\pi$
$912$	−3.74086	−	1.86445i	−0.123872	−	0.0617381i
$913$	−38.8419	−	25.9533i	−1.28548	−	0.858929i
$914$	44.0548	+	8.43712i	1.45720	+	0.279075i
$915$	10.9657	+	6.57262i	0.362516	+	0.217284i
$916$	−1.24084	+	35.6068i	−0.0409984	+	1.17648i
$917$	−7.33467	+	15.5079i	−0.242212	+	0.512115i
$918$	−0.478667	+	1.36845i	−0.0157984	+	0.0451656i
$919$	−8.93355	−	16.7135i	−0.294691	−	0.551327i	0.690387	−	0.723441i	$-0.257440\pi$
$919$	−8.93355	−	16.7135i	−0.294691	−	0.551327i	−0.985077	+	0.172113i	$0.944940\pi$
$920$	17.6579	−	11.1036i	0.582164	−	0.366076i
$921$	25.3310	−	7.68406i	0.834683	−	0.253198i
$922$	−2.39839	−	6.55540i	−0.0789869	−	0.215890i
$923$	0.911426	−	0.546288i	0.0300000	−	0.0179813i
$924$	1.67372	−	5.81461i	0.0550615	−	0.191287i
$925$	−0.832585	−	16.9477i	−0.0273752	−	0.557235i
$926$	1.17029	−	2.22749i	0.0384580	−	0.0731999i
$927$	4.76005	+	1.97168i	0.156341	+	0.0647584i
$928$	−21.5638	+	3.98849i	−0.707868	+	0.130929i
$929$	−31.1310	+	12.8949i	−1.02137	+	0.423067i	−0.829592	−	0.558370i	$-0.811427\pi$
$929$	−31.1310	+	12.8949i	−1.02137	+	0.423067i	−0.191782	+	0.981437i	$0.561427\pi$
$930$	4.48554	−	49.1294i	0.147087	−	1.61102i
$931$	−4.33639	+	4.78446i	−0.142119	+	0.156804i
$932$	−7.83470	−	0.659048i	−0.256634	−	0.0215878i
$933$	0.810038	−	3.23385i	0.0265195	−	0.105872i
$934$	48.4934	+	2.03602i	1.58675	+	0.0666205i
$935$	−11.0875	−	5.92641i	−0.362601	−	0.193814i
$936$	0.169689	−	1.34087i	0.00554646	−	0.0438277i
$937$	−40.3754	−	12.2478i	−1.31901	−	0.400117i	−0.449166	−	0.893448i	$-0.648279\pi$
$937$	−40.3754	−	12.2478i	−1.31901	−	0.400117i	−0.869841	+	0.493332i	$0.835779\pi$
$938$	−12.8547	+	0.723378i	−0.419722	+	0.0236191i
$939$	−15.8327	+	5.66502i	−0.516680	+	0.184871i
$940$	−27.7536	−	44.8420i	−0.905221	−	1.46258i
$941$	36.2863	−	9.08923i	1.18290	−	0.296301i	0.398859	−	0.917012i	$-0.369406\pi$
$941$	36.2863	−	9.08923i	1.18290	−	0.296301i	0.784039	+	0.620712i	$0.213156\pi$
$942$	−23.9516	−	15.7582i	−0.780385	−	0.513430i
$943$	−0.828045	−	4.16286i	−0.0269649	−	0.135561i
$944$	−4.01548	+	2.56513i	−0.130693	+	0.0834877i
$945$	−0.648864	+	3.26206i	−0.0211076	+	0.106115i
$946$	23.3804	+	23.0495i	0.760163	+	0.749405i
$947$	3.23900	+	4.36729i	0.105254	+	0.141918i	0.852694	−	0.522411i	$-0.174967\pi$
$947$	3.23900	+	4.36729i	0.105254	+	0.141918i	−0.747440	+	0.664329i	$0.768717\pi$
$948$	−15.5668	+	7.63594i	−0.505587	+	0.248004i
$949$	0.309372	−	6.29742i	0.0100427	−	0.204423i
$950$	−6.36750	+	10.7973i	−0.206589	+	0.350310i
$951$	−13.9976	+	1.37864i	−0.453902	+	0.0447055i
$952$	0.0561471	+	2.62578i	0.00181974	+	0.0851021i
$953$	23.3014	+	28.3928i	0.754806	+	0.919734i	0.998746	−	0.0500566i	$-0.0159402\pi$
$953$	23.3014	+	28.3928i	0.754806	+	0.919734i	−0.243941	+	0.969790i	$0.578440\pi$
$954$	7.31341	−	4.45464i	0.236780	−	0.144224i
$955$	−5.45191	+	0.808714i	−0.176420	+	0.0261694i
$956$	15.1891	−	6.54667i	0.491249	−	0.211734i
$957$	5.53592	+	11.7047i	0.178951	+	0.378360i
$958$	28.5316	−	3.01557i	0.921813	−	0.0974285i
$959$	−5.10911	+	5.10911i	−0.164982	+	0.164982i
$960$	26.6334	−	12.3910i	0.859589	−	0.399919i
$961$	−41.9023	−	41.9023i	−1.35169	−	1.35169i
$962$	−1.05106	−	0.850117i	−0.0338874	−	0.0274089i
$963$	−6.59032	+	3.11699i	−0.212370	+	0.100444i
$964$	−0.192708	−	13.5194i	−0.00620670	−	0.435432i
$965$	14.0732	+	94.8736i	0.453031	+	3.05409i
$966$	−0.607345	+	2.50012i	−0.0195410	+	0.0804399i
$967$	13.1066	−	10.7563i	0.421480	−	0.345900i	−0.399623	−	0.916679i	$-0.630859\pi$
$967$	13.1066	−	10.7563i	0.421480	−	0.345900i	0.821103	+	0.570780i	$0.193359\pi$
$968$	0.251930	+	0.360128i	0.00809735	+	0.0115750i
$969$	−0.104995	−	1.06604i	−0.00337294	−	0.0342460i
$970$	29.0304	−	7.49200i	0.932109	−	0.240554i
$971$	−38.4748	−	1.89015i	−1.23472	−	0.0606577i	−0.578786	−	0.815479i	$-0.696473\pi$
$971$	−38.4748	−	1.89015i	−1.23472	−	0.0606577i	−0.655930	+	0.754822i	$0.727723\pi$
$972$	−1.32186	+	1.50089i	−0.0423987	+	0.0481412i
$973$	−2.65620	+	1.96997i	−0.0851540	+	0.0631545i
$974$	−34.3023	+	0.244462i	−1.09911	+	0.00783306i
$975$	−3.97545	−	0.790766i	−0.127316	−	0.0253248i
$976$	10.5818	+	9.05502i	0.338714	+	0.289844i
$977$	−9.47306	+	1.88431i	−0.303070	+	0.0602844i	−0.344283	−	0.938866i	$-0.611878\pi$
$977$	−9.47306	+	1.88431i	−0.303070	+	0.0602844i	0.0412126	+	0.999150i	$0.486878\pi$
$978$	6.37812	+	30.9120i	0.203950	+	0.988456i
$979$	4.15570	+	16.5905i	0.132817	+	0.530234i
$980$	−7.29781	−	44.7898i	−0.233120	−	1.43076i
$981$	−5.81762	−	16.2592i	−0.185742	−	0.519115i
$982$	−22.1723	+	24.8165i	−0.707546	+	0.791926i
$983$	7.58772	−	25.0134i	0.242011	−	0.797802i	−0.748830	−	0.662763i	$-0.769384\pi$
$983$	7.58772	−	25.0134i	0.242011	−	0.797802i	0.990840	−	0.135040i	$-0.0431162\pi$
$984$	−0.420851	−	5.96242i	−0.0134162	−	0.190075i
$985$	13.5438	−	25.3386i	0.431540	−	0.807355i
$986$	−3.80386	−	4.13727i	−0.121139	−	0.131757i
$987$	6.30973	+	1.58051i	0.200841	+	0.0503081i
$988$	0.303482	+	0.951414i	0.00965505	+	0.0302685i
$989$	−10.3440	−	9.37526i	−0.328920	−	0.298116i
$990$	−11.0980	−	13.3281i	−0.352717	−	0.423595i
$991$	−19.4639	−	46.9899i	−0.618290	−	1.49268i	−0.853688	−	0.520784i	$-0.825640\pi$
$991$	−19.4639	−	46.9899i	−0.618290	−	1.49268i	0.235399	−	0.971899i	$-0.424360\pi$
$992$	13.7586	−	51.9517i	0.436837	−	1.64947i
$993$	11.9085	−	28.7497i	0.377906	−	0.912345i
$994$	−2.71996	+	0.846306i	−0.0862720	+	0.0268432i
$995$	−35.6975	+	1.75370i	−1.13169	+	0.0555962i
$996$	21.8743	+	17.4360i	0.693113	+	0.552480i
$997$	16.0568	+	26.7892i	0.508524	+	0.848421i	0.999744	−	0.0226141i	$-0.00719892\pi$
$997$	16.0568	+	26.7892i	0.508524	+	0.848421i	−0.491220	+	0.871035i	$0.663449\pi$
$998$	1.07913	+	0.501009i	0.0341591	+	0.0158592i
$999$	0.580679	+	1.91424i	0.0183719	+	0.0605640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.661.26	yes	2048
256.189	even	64	inner	768.2.z.a.445.26	✓	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.445.26	✓	2048	256.189	even	64	inner
768.2.z.a.661.26	yes	2048	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.400870 + 1.35621i) q^{2} +(-0.941544 - 0.336890i) q^{3} +(-1.67861 - 1.08733i) q^{4} +(-2.94925 - 2.18731i) q^{5} +(0.834330 - 1.14188i) q^{6} +(0.901442 + 0.0887843i) q^{7} +(2.14754 - 1.84067i) q^{8} +(0.773010 + 0.634393i) q^{9} +O(q^{10})\)	\(q+(-0.400870 + 1.35621i) q^{2} +(-0.941544 - 0.336890i) q^{3} +(-1.67861 - 1.08733i) q^{4} +(-2.94925 - 2.18731i) q^{5} +(0.834330 - 1.14188i) q^{6} +(0.901442 + 0.0887843i) q^{7} +(2.14754 - 1.84067i) q^{8} +(0.773010 + 0.634393i) q^{9} +(4.14872 - 3.12298i) q^{10} +(-2.24299 - 2.47475i) q^{11} +(1.21417 + 1.58927i) q^{12} +(0.0701152 - 0.472678i) q^{13} +(-0.481771 + 1.18695i) q^{14} +(2.03997 + 3.05303i) q^{15} +(1.63544 + 3.65039i) q^{16} +(-0.569532 + 0.852364i) q^{17} +(-1.17025 + 0.794055i) q^{18} +(0.537204 - 0.896270i) q^{19} +(2.57231 + 6.87844i) q^{20} +(-0.818837 - 0.387281i) q^{21} +(4.25543 - 2.04990i) q^{22} +(-1.77130 + 0.946779i) q^{23} +(-2.64211 + 1.00958i) q^{24} +(2.46232 + 8.11719i) q^{25} +(0.612943 + 0.284573i) q^{26} +(-0.514103 - 0.857729i) q^{27} +(-1.41663 - 1.12920i) q^{28} +(3.87197 - 0.190218i) q^{29} +(-4.95830 + 1.54276i) q^{30} +(-3.63567 + 8.77728i) q^{31} +(-5.60629 + 0.754674i) q^{32} +(1.27815 + 3.08573i) q^{33} +(-0.927676 - 1.11409i) q^{34} +(-2.46438 - 2.23358i) q^{35} +(-0.607788 - 1.90541i) q^{36} +(-1.94043 - 0.486053i) q^{37} +(1.00018 + 1.08785i) q^{38} +(-0.225257 + 0.421426i) q^{39} +(-10.3598 + 0.731234i) q^{40} +(-0.613452 + 2.02228i) q^{41} +(0.853481 - 0.955265i) q^{42} +(2.34167 + 6.54452i) q^{43} +(1.07423 + 6.59300i) q^{44} +(-0.892185 - 3.56180i) q^{45} +(-0.573970 - 2.78179i) q^{46} +(-7.04312 + 1.40096i) q^{47} +(-0.310063 - 3.98796i) q^{48} +(-6.06078 - 1.20556i) q^{49} +(-11.9957 + 0.0854896i) q^{50} +(0.823392 - 0.610669i) q^{51} +(-0.631651 + 0.717203i) q^{52} +(-6.04786 - 0.297112i) q^{53} +(1.36935 - 0.353394i) q^{54} +(1.20207 + 12.2048i) q^{55} +(2.09931 - 1.46859i) q^{56} +(-0.807745 + 0.662899i) q^{57} +(-1.29418 + 5.32746i) q^{58} +(0.174788 + 1.17832i) q^{59} +(-0.104667 - 7.34294i) q^{60} +(3.14751 - 1.48866i) q^{61} +(-10.4464 - 8.44928i) q^{62} +(0.640500 + 0.640500i) q^{63} +(1.22390 - 7.90583i) q^{64} +(-1.24068 + 1.24068i) q^{65} +(-4.69726 + 0.496465i) q^{66} +(4.29727 + 9.08581i) q^{67} +(1.88282 - 0.811518i) q^{68} +(1.98672 - 0.294701i) q^{69} +(4.01710 - 2.44684i) q^{70} +(1.41071 + 1.71896i) q^{71} +(2.82778 - 0.0604664i) q^{72} +(13.1310 - 1.29329i) q^{73} +(1.43705 - 2.43679i) q^{74} +(0.416213 - 8.47222i) q^{75} +(-1.87629 + 0.920370i) q^{76} +(-1.80220 - 2.42999i) q^{77} +(-0.481243 - 0.474432i) q^{78} +(-1.69132 + 8.50282i) q^{79} +(3.16121 - 14.3431i) q^{80} +(0.195090 + 0.980785i) q^{81} +(-2.49672 - 1.64264i) q^{82} +(13.5674 - 3.39846i) q^{83} +(0.953404 + 1.54044i) q^{84} +(3.54408 - 1.26809i) q^{85} +(-9.81444 + 0.552290i) q^{86} +(-3.70971 - 1.12533i) q^{87} +(-9.37211 - 1.18605i) q^{88} +(-4.51607 - 2.41389i) q^{89} +(5.18820 + 0.217829i) q^{90} +(0.105171 - 0.419867i) q^{91} +(4.00277 + 0.336710i) q^{92} +(6.38012 - 7.03938i) q^{93} +(0.923373 - 10.1136i) q^{94} +(-3.54477 + 1.46829i) q^{95} +(5.53281 + 1.17814i) q^{96} +(5.33421 + 2.20950i) q^{97} +(4.06458 - 7.73641i) q^{98} +(-0.163884 - 3.33595i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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