LMFDB - Embedded newform 930.2.z.c.469.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.4
Character	$\chi$	$=$	930.469
Dual form			930.2.z.c.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(2.12126 + 2.91966i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(2.12126 + 2.91966i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.25185 - 1.85280i) q^{10} +(3.84919 - 2.79660i) q^{11} +(0.951057 - 0.309017i) q^{12} +(1.38848 + 0.451145i) q^{13} +(-2.91966 - 2.12126i) q^{14} +(-0.0762803 + 2.23477i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.12831 - 5.68214i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.574481 + 1.76807i) q^{19} +(1.76313 + 1.37527i) q^{20} +(1.11521 + 3.43226i) q^{21} +(-2.79660 + 3.84919i) q^{22} +(0.863131 - 1.18800i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.23607 + 2.65626i) q^{25} -1.45994 q^{26} +(0.587785 + 0.809017i) q^{27} +(3.43226 + 1.11521i) q^{28} +(-0.853303 - 2.62620i) q^{29} +(-0.618034 - 2.14896i) q^{30} +(-5.26576 - 1.80882i) q^{31} +1.00000i q^{32} +(4.52499 - 1.47026i) q^{33} +(-2.17038 + 6.67975i) q^{34} +(-4.96322 + 6.36295i) q^{35} +1.00000 q^{36} +3.41709i q^{37} +(-1.09273 - 1.50401i) q^{38} +(1.18111 + 0.858129i) q^{39} +(-2.10182 - 0.763128i) q^{40} +(-0.0188545 - 0.0580282i) q^{41} +(-2.12126 - 2.91966i) q^{42} +(-10.0782 + 3.27461i) q^{43} +(1.47026 - 4.52499i) q^{44} +(-0.763128 + 2.10182i) q^{45} +(-0.453775 + 1.39658i) q^{46} +(3.59085 + 1.16674i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-1.86156 + 5.72929i) q^{49} +(3.20791 - 3.83527i) q^{50} +(5.68214 - 4.12831i) q^{51} +(1.38848 - 0.451145i) q^{52} +(-2.47015 + 3.39987i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(8.38871 + 6.54336i) q^{55} -3.60890 q^{56} +1.85906i q^{57} +(1.62308 + 2.23398i) q^{58} +(3.58839 - 11.0439i) q^{59} +(1.25185 + 1.85280i) q^{60} +1.14596 q^{61} +(5.56699 + 0.0930792i) q^{62} +3.60890i q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.111364 + 3.26261i) q^{65} +(-3.84919 + 2.79660i) q^{66} -7.32216i q^{67} -7.02351i q^{68} +(1.18800 - 0.863131i) q^{69} +(2.75405 - 7.58524i) q^{70} +(-0.562572 - 0.408732i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-0.0648550 - 0.0892652i) q^{73} +(-1.05594 - 3.24985i) q^{74} +(-4.84957 + 1.21724i) q^{75} +(1.50401 + 1.09273i) q^{76} +(16.3302 + 5.30601i) q^{77} +(-1.38848 - 0.451145i) q^{78} +(10.2182 + 7.42399i) q^{79} +(2.23477 + 0.0762803i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.0358634 + 0.0493617i) q^{82} +(-15.1636 + 4.92696i) q^{83} +(2.91966 + 2.12126i) q^{84} +(14.7621 + 5.35983i) q^{85} +(8.57303 - 6.22867i) q^{86} -2.76135i q^{87} +4.75786i q^{88} +(-11.1963 + 8.13458i) q^{89} +(0.0762803 - 2.23477i) q^{90} +(1.62814 + 5.01088i) q^{91} -1.46845i q^{92} +(-4.44908 - 3.34750i) q^{93} -3.77564 q^{94} +(-3.44446 + 2.32726i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-4.84881 - 6.67382i) q^{97} -6.02413i q^{98} +4.75786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	$ 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	0.618034	+	2.14896i	0.276393	+	0.961045i
$5$	0.618034	+	2.14896i	0.276393	+	0.961045i
$6$	−1.00000			−0.408248
$7$	2.12126	+	2.91966i	0.801759	+	1.10353i	0.992543	+	0.121895i	$0.0388972\pi$
$7$	2.12126	+	2.91966i	0.801759	+	1.10353i	−0.190784	+	0.981632i	$0.561103\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−1.25185	−	1.85280i	−0.395870	−	0.585907i
$11$	3.84919	−	2.79660i	1.16057	−	0.843206i	0.170723	−	0.985319i	$-0.445390\pi$
$11$	3.84919	−	2.79660i	1.16057	−	0.843206i	0.989850	+	0.142113i	$0.0453896\pi$
$12$	0.951057	−	0.309017i	0.274546	−	0.0892055i
$13$	1.38848	+	0.451145i	0.385095	+	0.125125i	0.495165	−	0.868799i	$-0.335107\pi$
$13$	1.38848	+	0.451145i	0.385095	+	0.125125i	−0.110070	+	0.993924i	$0.535107\pi$
$14$	−2.91966	−	2.12126i	−0.780312	−	0.566930i
$15$	−0.0762803	+	2.23477i	−0.0196955	+	0.577014i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	4.12831	−	5.68214i	1.00126	−	1.37812i	0.0767163	−	0.997053i	$-0.475556\pi$
$17$	4.12831	−	5.68214i	1.00126	−	1.37812i	0.924547	−	0.381068i	$-0.124444\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	0.574481	+	1.76807i	0.131795	+	0.405623i	0.995078	−	0.0990975i	$-0.0315956\pi$
$19$	0.574481	+	1.76807i	0.131795	+	0.405623i	−0.863283	+	0.504720i	$0.831596\pi$
$20$	1.76313	+	1.37527i	0.394247	+	0.307521i
$21$	1.11521	+	3.43226i	0.243359	+	0.748982i
$22$	−2.79660	+	3.84919i	−0.596237	+	0.820650i
$23$	0.863131	−	1.18800i	0.179975	−	0.247715i	−0.709492	−	0.704713i	$-0.751076\pi$
$23$	0.863131	−	1.18800i	0.179975	−	0.247715i	0.889467	+	0.456999i	$0.151076\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	−4.23607	+	2.65626i	−0.847214	+	0.531252i
$26$	−1.45994			−0.286317
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	3.43226	+	1.11521i	0.648637	+	0.210755i
$29$	−0.853303	−	2.62620i	−0.158454	−	0.487673i	0.840040	−	0.542524i	$-0.182531\pi$
$29$	−0.853303	−	2.62620i	−0.158454	−	0.487673i	−0.998495	+	0.0548517i	$0.982531\pi$
$30$	−0.618034	−	2.14896i	−0.112837	−	0.392345i
$31$	−5.26576	−	1.80882i	−0.945758	−	0.324873i
$31$	−5.26576	−	1.80882i	−0.945758	−	0.324873i
$32$			1.00000i			0.176777i
$33$	4.52499	−	1.47026i	0.787700	−	0.255939i
$34$	−2.17038	+	6.67975i	−0.372218	+	1.14557i
$35$	−4.96322	+	6.36295i	−0.838938	+	1.07553i
$36$	1.00000			0.166667
$37$			3.41709i			0.561766i	0.959742	+	0.280883i	$0.0906273\pi$
$37$			3.41709i			0.561766i	−0.959742	+	0.280883i	$0.909373\pi$
$38$	−1.09273	−	1.50401i	−0.177264	−	0.243983i
$39$	1.18111	+	0.858129i	0.189129	+	0.137411i
$40$	−2.10182	−	0.763128i	−0.332327	−	0.120661i
$41$	−0.0188545	−	0.0580282i	−0.00294458	−	0.00906248i	0.949573	−	0.313545i	$-0.101517\pi$
$41$	−0.0188545	−	0.0580282i	−0.00294458	−	0.00906248i	−0.952518	+	0.304482i	$0.901517\pi$
$42$	−2.12126	−	2.91966i	−0.327317	−	0.450513i
$43$	−10.0782	+	3.27461i	−1.53691	+	0.499373i	−0.950522	−	0.310657i	$-0.899451\pi$
$43$	−10.0782	+	3.27461i	−1.53691	+	0.499373i	−0.586389	+	0.810030i	$0.699451\pi$
$44$	1.47026	−	4.52499i	0.221650	−	0.682168i
$45$	−0.763128	+	2.10182i	−0.113760	+	0.313320i
$46$	−0.453775	+	1.39658i	−0.0669055	+	0.205914i
$47$	3.59085	+	1.16674i	0.523779	+	0.170186i	0.558960	−	0.829195i	$-0.311201\pi$
$47$	3.59085	+	1.16674i	0.523779	+	0.170186i	−0.0351807	+	0.999381i	$0.511201\pi$
$48$	0.587785	−	0.809017i	0.0848395	−	0.116772i
$49$	−1.86156	+	5.72929i	−0.265937	+	0.818470i
$50$	3.20791	−	3.83527i	0.453667	−	0.542389i
$51$	5.68214	−	4.12831i	0.795658	−	0.578080i
$52$	1.38848	−	0.451145i	0.192548	−	0.0625625i
$53$	−2.47015	+	3.39987i	−0.339302	+	0.467008i	−0.944237	−	0.329266i	$-0.893199\pi$
$53$	−2.47015	+	3.39987i	−0.339302	+	0.467008i	0.604936	+	0.796274i	$0.293199\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	8.38871	+	6.54336i	1.13113	+	0.882307i
$56$	−3.60890			−0.482259
$57$			1.85906i			0.246238i
$58$	1.62308	+	2.23398i	0.213121	+	0.293336i
$59$	3.58839	−	11.0439i	0.467168	−	1.43780i	−0.389066	−	0.921210i	$-0.627202\pi$
$59$	3.58839	−	11.0439i	0.467168	−	1.43780i	0.856235	−	0.516587i	$-0.172798\pi$
$60$	1.25185	+	1.85280i	0.161613	+	0.239196i
$61$	1.14596			0.146726			0.0733628	−	0.997305i	$-0.476627\pi$
$61$	1.14596			0.146726			0.0733628	+	0.997305i	$0.476627\pi$
$62$	5.56699	+	0.0930792i	0.707008	+	0.0118211i
$63$			3.60890i			0.454678i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−0.111364	+	3.26261i	−0.0138130	+	0.404678i
$66$	−3.84919	+	2.79660i	−0.473802	+	0.344237i
$67$		−	7.32216i		−	0.894544i	−0.894398	−	0.447272i	$-0.852396\pi$
$67$		−	7.32216i		−	0.894544i	0.894398	−	0.447272i	$-0.147604\pi$
$68$		−	7.02351i		−	0.851725i
$69$	1.18800	−	0.863131i	0.143018	−	0.103909i
$70$	2.75405	−	7.58524i	0.329172	−	0.906610i
$71$	−0.562572	−	0.408732i	−0.0667650	−	0.0485076i	0.553902	−	0.832582i	$-0.313138\pi$
$71$	−0.562572	−	0.408732i	−0.0667650	−	0.0485076i	−0.620667	+	0.784074i	$0.713138\pi$
$72$	−0.951057	+	0.309017i	−0.112083	+	0.0364180i
$73$	−0.0648550	−	0.0892652i	−0.00759070	−	0.0104477i	0.805205	−	0.592997i	$-0.202055\pi$
$73$	−0.0648550	−	0.0892652i	−0.00759070	−	0.0104477i	−0.812795	+	0.582549i	$0.802055\pi$
$74$	−1.05594	−	3.24985i	−0.122750	−	0.377787i
$75$	−4.84957	+	1.21724i	−0.559980	+	0.140555i
$76$	1.50401	+	1.09273i	0.172522	+	0.125344i
$77$	16.3302	+	5.30601i	1.86100	+	0.604676i
$78$	−1.38848	−	0.451145i	−0.157215	−	0.0510821i
$79$	10.2182	+	7.42399i	1.14964	+	0.835264i	0.988433	−	0.151656i	$-0.0484606\pi$
$79$	10.2182	+	7.42399i	1.14964	+	0.835264i	0.161209	+	0.986920i	$0.448461\pi$
$80$	2.23477	+	0.0762803i	0.249854	+	0.00852839i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	0.0358634	+	0.0493617i	0.00396045	+	0.00545109i
$83$	−15.1636	+	4.92696i	−1.66443	+	0.540805i	−0.981792	−	0.189957i	$-0.939165\pi$
$83$	−15.1636	+	4.92696i	−1.66443	+	0.540805i	−0.682633	+	0.730761i	$0.739165\pi$
$84$	2.91966	+	2.12126i	0.318561	+	0.231448i
$85$	14.7621	+	5.35983i	1.60118	+	0.581356i
$86$	8.57303	−	6.22867i	0.924453	−	0.671655i
$87$		−	2.76135i		−	0.296048i
$88$			4.75786i			0.507189i
$89$	−11.1963	+	8.13458i	−1.18680	+	0.862264i	−0.992923	−	0.118761i	$-0.962108\pi$
$89$	−11.1963	+	8.13458i	−1.18680	+	0.862264i	−0.193882	+	0.981025i	$0.562108\pi$
$90$	0.0762803	−	2.23477i	0.00804065	−	0.235565i
$91$	1.62814	+	5.01088i	0.170675	+	0.525283i
$92$		−	1.46845i		−	0.153096i
$93$	−4.44908	−	3.34750i	−0.461348	−	0.347119i
$94$	−3.77564			−0.389428
$95$	−3.44446	+	2.32726i	−0.353395	+	0.238772i
$96$	−0.309017	+	0.951057i	−0.0315389	+	0.0970668i
$97$	−4.84881	−	6.67382i	−0.492322	−	0.677624i	0.488492	−	0.872569i	$-0.337547\pi$
$97$	−4.84881	−	6.67382i	−0.492322	−	0.677624i	−0.980814	+	0.194945i	$0.937547\pi$
$98$		−	6.02413i		−	0.608529i
$99$	4.75786			0.478183
$100$	−1.86574	+	4.63886i	−0.186574	+	0.463886i
$101$	−8.12334	−	5.90195i	−0.808302	−	0.587266i	0.105036	−	0.994468i	$-0.466504\pi$
$101$	−8.12334	−	5.90195i	−0.808302	−	0.587266i	−0.913338	+	0.407203i	$0.866504\pi$
$102$	−4.12831	+	5.68214i	−0.408764	+	0.562615i
$103$	−10.8951	+	3.54004i	−1.07353	+	0.348811i	−0.791861	−	0.610701i	$-0.790888\pi$
$103$	−10.8951	+	3.54004i	−1.07353	+	0.348811i	−0.281668	+	0.959512i	$0.590888\pi$
$104$	−1.18111	+	0.858129i	−0.115818	+	0.0841464i
$105$	−6.68657	+	4.51780i	−0.652542	+	0.440892i
$106$	1.29864	−	3.99679i	0.126135	−	0.388203i
$107$	4.32324	−	5.95042i	0.417943	−	0.575249i	−0.547190	−	0.837008i	$-0.684303\pi$
$107$	4.32324	−	5.95042i	0.417943	−	0.575249i	0.965133	+	0.261759i	$0.0843026\pi$
$108$	0.951057	+	0.309017i	0.0915155	+	0.0297352i
$109$	0.653799	−	2.01219i	0.0626225	−	0.192732i	−0.914850	−	0.403793i	$-0.867692\pi$
$109$	0.653799	−	2.01219i	0.0626225	−	0.192732i	0.977473	+	0.211060i	$0.0676917\pi$
$110$	−10.0001	−	3.63085i	−0.953477	−	0.346188i
$111$	−1.05594	+	3.24985i	−0.100225	+	0.308462i
$112$	3.43226	−	1.11521i	0.324319	−	0.105377i
$113$	10.6477	+	14.6553i	1.00165	+	1.37866i	0.924307	+	0.381651i	$0.124644\pi$
$113$	10.6477	+	14.6553i	1.00165	+	1.37866i	0.0773450	+	0.997004i	$0.475356\pi$
$114$	−0.574481	−	1.76807i	−0.0538050	−	0.165595i
$115$	3.08641	+	1.12061i	0.287809	+	0.104498i
$116$	−2.23398	−	1.62308i	−0.207420	−	0.150699i
$117$	0.858129	+	1.18111i	0.0793340	+	0.109194i
$118$			11.6123i			1.06900i
$119$	25.3471			2.32357
$120$	−1.76313	−	1.37527i	−0.160951	−	0.125545i
$121$	3.59610	−	11.0676i	0.326918	−	1.00615i
$122$	−1.08988	+	0.354122i	−0.0986727	+	0.0320607i
$123$		−	0.0610145i		−	0.00550149i
$124$	−5.32328	+	1.63177i	−0.478045	+	0.146537i
$125$	−8.32624	−	7.46149i	−0.744721	−	0.667376i
$126$	−1.11521	−	3.43226i	−0.0993508	−	0.305770i
$127$	9.13105	+	2.96686i	0.810250	+	0.263266i	0.684703	−	0.728822i	$-0.259932\pi$
$127$	9.13105	+	2.96686i	0.810250	+	0.263266i	0.125546	+	0.992088i	$0.459932\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−10.5968			−0.933000
$130$	−0.902290	−	3.13734i	−0.0791360	−	0.275163i
$131$	7.14509	−	5.19121i	0.624269	−	0.453558i	−0.230141	−	0.973157i	$-0.573919\pi$
$131$	7.14509	−	5.19121i	0.624269	−	0.453558i	0.854410	+	0.519599i	$0.173919\pi$
$132$	2.79660	−	3.84919i	0.243413	−	0.335029i
$133$	−3.94354	+	5.42782i	−0.341948	+	0.470651i
$134$	2.26267	+	6.96379i	0.195465	+	0.601580i
$135$	−1.37527	+	1.76313i	−0.118365	+	0.151746i
$136$	2.17038	+	6.67975i	0.186109	+	0.572784i
$137$	−19.5346	−	6.34719i	−1.66896	−	0.542277i	−0.686237	−	0.727378i	$-0.740739\pi$
$137$	−19.5346	−	6.34719i	−1.66896	−	0.542277i	−0.982719	+	0.185102i	$0.940739\pi$
$138$	−0.863131	+	1.18800i	−0.0734746	+	0.101129i
$139$	−6.76507	+	20.8207i	−0.573806	+	1.76599i	0.0664040	+	0.997793i	$0.478847\pi$
$139$	−6.76507	+	20.8207i	−0.573806	+	1.76599i	−0.640210	+	0.768200i	$0.721153\pi$
$140$	−0.275288	+	8.06504i	−0.0232660	+	0.681620i
$141$	3.05456	+	2.21927i	0.257240	+	0.186896i
$142$	0.661343	+	0.214883i	0.0554987	+	0.0180326i
$143$	6.60620	−	2.14648i	0.552438	−	0.179498i
$144$	0.809017	−	0.587785i	0.0674181	−	0.0489821i
$145$	5.11623	−	3.45680i	0.424880	−	0.287071i
$146$	0.0892652	+	0.0648550i	0.00738764	+	0.00536744i
$147$	−3.54090	+	4.87363i	−0.292048	+	0.401970i
$148$	2.00852	+	2.76448i	0.165099	+	0.227239i
$149$	−16.4769			−1.34984			−0.674919	−	0.737892i	$-0.735822\pi$
$149$	−16.4769			−1.34984			−0.674919	+	0.737892i	$0.735822\pi$
$150$	4.23607	−	2.65626i	0.345874	−	0.216883i
$151$	13.5149	−	9.81914i	1.09983	−	0.799070i	0.118794	−	0.992919i	$-0.462097\pi$
$151$	13.5149	−	9.81914i	1.09983	−	0.799070i	0.981031	+	0.193849i	$0.0620972\pi$
$152$	−1.76807	−	0.574481i	−0.143409	−	0.0465965i
$153$	6.67975	−	2.17038i	0.540026	−	0.175465i
$154$	−17.1706			−1.38365
$155$	0.632661	−	12.4338i	0.0508166	−	0.998708i
$156$	1.45994			0.116888
$157$	−3.03062	+	0.984708i	−0.241870	+	0.0785883i	−0.427443	−	0.904042i	$-0.640586\pi$
$157$	−3.03062	+	0.984708i	−0.241870	+	0.0785883i	0.185574	+	0.982630i	$0.440586\pi$
$158$	−12.0123	−	3.90302i	−0.955645	−	0.310508i
$159$	−3.39987	+	2.47015i	−0.269627	+	0.195896i
$160$	−2.14896	+	0.618034i	−0.169890	+	0.0488599i
$161$	5.29947			0.417657
$162$	−0.587785	−	0.809017i	−0.0461808	−	0.0635624i
$163$	−6.65695	+	9.16250i	−0.521412	+	0.717663i	−0.985791	−	0.167974i	$-0.946278\pi$
$163$	−6.65695	+	9.16250i	−0.521412	+	0.717663i	0.464379	+	0.885637i	$0.346278\pi$
$164$	−0.0493617	−	0.0358634i	−0.00385450	−	0.00280046i
$165$	5.95613	+	8.81536i	0.463684	+	0.686275i
$166$	12.8990	−	9.37164i	1.00115	−	0.727381i
$167$	−14.3567	+	4.66478i	−1.11095	+	0.360971i	−0.806309	−	0.591495i	$-0.798538\pi$
$167$	−14.3567	+	4.66478i	−1.11095	+	0.360971i	−0.304646	+	0.952466i	$0.598538\pi$
$168$	−3.43226	−	1.11521i	−0.264805	−	0.0860403i
$169$	−8.79287	−	6.38840i	−0.676375	−	0.491415i
$170$	−15.6959	−	0.535755i	−1.20382	−	0.0410905i
$171$	−0.574481	+	1.76807i	−0.0439316	+	0.135208i
$172$	−6.22867	+	8.57303i	−0.474932	+	0.653687i
$173$	7.17916	+	2.33265i	0.545821	+	0.177348i	0.568932	−	0.822385i	$-0.307357\pi$
$173$	7.17916	+	2.33265i	0.545821	+	0.177348i	−0.0231102	+	0.999733i	$0.507357\pi$
$174$	0.853303	+	2.62620i	0.0646888	+	0.199092i
$175$	−16.7412	−	6.73326i	−1.26551	−	0.508987i
$176$	−1.47026	−	4.52499i	−0.110825	−	0.341084i
$177$	6.82552	−	9.39452i	0.513038	−	0.706136i
$178$	8.13458	−	11.1963i	0.609713	−	0.839198i
$179$	18.7183	−	13.5997i	1.39907	−	1.01649i	0.404273	−	0.914638i	$-0.367525\pi$
$179$	18.7183	−	13.5997i	1.39907	−	1.01649i	0.994800	−	0.101848i	$-0.0324754\pi$
$180$	0.618034	+	2.14896i	0.0460655	+	0.160174i
$181$	21.9422			1.63095			0.815476	−	0.578791i	$-0.196475\pi$
$181$	21.9422			1.63095			0.815476	+	0.578791i	$0.196475\pi$
$182$	−3.09690	−	4.26251i	−0.229557	−	0.315958i
$183$	1.08988	+	0.354122i	0.0805659	+	0.0261775i
$184$	0.453775	+	1.39658i	0.0334527	+	0.102957i
$185$	−7.34320	+	2.11188i	−0.539882	+	0.155268i
$186$	5.26576	+	1.80882i	0.386104	+	0.132629i
$187$		−	33.4169i		−	2.44368i
$188$	3.59085	−	1.16674i	0.261889	−	0.0850931i
$189$	−1.11521	+	3.43226i	−0.0811196	+	0.249661i
$190$	2.55672	−	3.27776i	0.185484	−	0.237793i
$191$	−2.46610			−0.178441			−0.0892204	−	0.996012i	$-0.528438\pi$
$191$	−2.46610			−0.178441			−0.0892204	+	0.996012i	$0.528438\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−15.9972	−	22.0182i	−1.15150	−	1.58491i	−0.738622	−	0.674120i	$-0.764523\pi$
$193$	−15.9972	−	22.0182i	−1.15150	−	1.58491i	−0.412880	−	0.910785i	$-0.635477\pi$
$194$	6.67382	+	4.84881i	0.479152	+	0.348125i
$195$	−1.11412	+	3.06852i	−0.0797836	+	0.219741i
$196$	1.86156	+	5.72929i	0.132969	+	0.409235i
$197$	−0.902462	−	1.24213i	−0.0642978	−	0.0884983i	0.775657	−	0.631155i	$-0.217419\pi$
$197$	−0.902462	−	1.24213i	−0.0642978	−	0.0884983i	−0.839955	+	0.542656i	$0.817419\pi$
$198$	−4.52499	+	1.47026i	−0.321577	+	0.104487i
$199$	0.937390	−	2.88499i	0.0664498	−	0.204511i	−0.912318	−	0.409481i	$-0.865710\pi$
$199$	0.937390	−	2.88499i	0.0664498	−	0.204511i	0.978768	+	0.204970i	$0.0657097\pi$
$200$	0.340937	−	4.98836i	0.0241079	−	0.352731i
$201$	2.26267	−	6.96379i	0.159597	−	0.491188i
$202$	9.54955	+	3.10284i	0.671904	+	0.218315i
$203$	5.85753	−	8.06219i	0.411118	−	0.565855i
$204$	2.17038	−	6.67975i	0.151957	−	0.467676i
$205$	0.113048	−	0.0763810i	0.00789559	−	0.00533468i
$206$	9.26795	−	6.73356i	0.645729	−	0.469149i
$207$	1.39658	−	0.453775i	0.0970687	−	0.0315395i
$208$	0.858129	−	1.18111i	0.0595005	−	0.0818954i
$209$	7.15586	+	5.19904i	0.494981	+	0.359625i
$210$	4.96322	−	6.36295i	0.342495	−	0.439085i
$211$	14.2666			0.982157			0.491078	−	0.871115i	$-0.336603\pi$
$211$	14.2666			0.982157			0.491078	+	0.871115i	$0.336603\pi$
$212$			4.20247i			0.288627i
$213$	−0.408732	−	0.562572i	−0.0280059	−	0.0385468i
$214$	−2.27286	+	6.99514i	−0.155370	+	0.478178i
$215$	−13.2657	−	19.6338i	−0.904711	−	1.33902i
$216$	−1.00000			−0.0680414
$217$	−5.88889	−	19.2112i	−0.399764	−	1.30414i
$218$			2.11574i			0.143296i
$219$	−0.0340963	−	0.104938i	−0.00230401	−	0.00709102i
$220$	10.6327	+	0.362931i	0.716857	+	0.0244688i
$221$	8.29555	−	6.02707i	0.558019	−	0.405425i
$222$		−	3.41709i		−	0.229340i
$223$			9.75569i			0.653290i	0.945147	+	0.326645i	$0.105918\pi$
$223$			9.75569i			0.653290i	−0.945147	+	0.326645i	$0.894082\pi$
$224$	−2.91966	+	2.12126i	−0.195078	+	0.141732i
$225$	−4.98836	−	0.340937i	−0.332558	−	0.0227291i
$226$	−14.6553	−	10.6477i	−0.974856	−	0.708275i
$227$	4.35350	−	1.41454i	0.288952	−	0.0938861i	−0.160955	−	0.986962i	$-0.551457\pi$
$227$	4.35350	−	1.41454i	0.288952	−	0.0938861i	0.449906	+	0.893076i	$0.351457\pi$
$228$	1.09273	+	1.50401i	0.0723676	+	0.0996055i
$229$	−1.53614	−	4.72776i	−0.101511	−	0.312419i	0.887385	−	0.461030i	$-0.152520\pi$
$229$	−1.53614	−	4.72776i	−0.101511	−	0.312419i	−0.988896	+	0.148611i	$0.952520\pi$
$230$	−3.28164	−	0.112013i	−0.216385	−	0.00738595i
$231$	13.8913	+	10.0926i	0.913982	+	0.664047i
$232$	2.62620	+	0.853303i	0.172418	+	0.0560221i
$233$	−20.0005	−	6.49857i	−1.31028	−	0.425735i	−0.431133	−	0.902289i	$-0.641886\pi$
$233$	−20.0005	−	6.49857i	−1.31028	−	0.425735i	−0.879146	+	0.476553i	$0.841886\pi$
$234$	−1.18111	−	0.858129i	−0.0772117	−	0.0560976i
$235$	−0.288007	+	8.43768i	−0.0187875	+	0.550413i
$236$	−3.58839	−	11.0439i	−0.233584	−	0.718898i
$237$	7.42399	+	10.2182i	0.482240	+	0.663746i
$238$	−24.1065	+	7.83269i	−1.56259	+	0.507718i
$239$	−18.5584	−	13.4835i	−1.20044	−	0.872174i	−0.206116	−	0.978528i	$-0.566082\pi$
$239$	−18.5584	−	13.4835i	−1.20044	−	0.872174i	−0.994328	+	0.106354i	$0.966082\pi$
$240$	2.10182	+	0.763128i	0.135672	+	0.0492597i
$241$	−1.36289	+	0.990198i	−0.0877915	+	0.0637842i	−0.630815	−	0.775933i	$-0.717279\pi$
$241$	−1.36289	+	0.990198i	−0.0877915	+	0.0637842i	0.543024	+	0.839717i	$0.317279\pi$
$242$			11.6372i			0.748068i
$243$			1.00000i			0.0641500i
$244$	0.927103	−	0.673580i	0.0593517	−	0.0431215i
$245$	−13.4625	−	0.459523i	−0.860090	−	0.0293578i
$246$	0.0188545	+	0.0580282i	0.00120212	+	0.00369974i
$247$			2.71410i			0.172694i
$248$	4.55850	−	3.19689i	0.289465	−	0.203003i
$249$	−15.9440			−1.01041
$250$	10.2244	+	4.52335i	0.646651	+	0.286081i
$251$	2.78675	−	8.57672i	0.175898	−	0.541358i	−0.823775	−	0.566916i	$-0.808136\pi$
$251$	2.78675	−	8.57672i	0.175898	−	0.541358i	0.999673	+	0.0255582i	$0.00813633\pi$
$252$	2.12126	+	2.91966i	0.133627	+	0.183921i
$253$		−	6.98666i		−	0.439248i
$254$	−9.60095			−0.602417
$255$	12.3833	+	9.65925i	0.775475	+	0.604886i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	11.7459	−	16.1669i	0.732690	−	1.00846i	−0.266316	−	0.963886i	$-0.585807\pi$
$257$	11.7459	−	16.1669i	0.732690	−	1.00846i	0.999006	−	0.0445752i	$-0.0141934\pi$
$258$	10.0782	−	3.27461i	0.627441	−	0.203868i
$259$	−9.97674	+	7.24853i	−0.619924	+	0.450401i
$260$	1.82762	+	2.70497i	0.113344	+	0.167755i
$261$	0.853303	−	2.62620i	0.0528182	−	0.162558i
$262$	−5.19121	+	7.14509i	−0.320714	+	0.441425i
$263$	16.7182	+	5.43209i	1.03089	+	0.334957i	0.775142	−	0.631787i	$-0.217678\pi$
$263$	16.7182	+	5.43209i	1.03089	+	0.334957i	0.255749	+	0.966743i	$0.417678\pi$
$264$	−1.47026	+	4.52499i	−0.0904882	+	0.278494i
$265$	−8.83283	−	3.20702i	−0.542597	−	0.197006i
$266$	2.07324	−	6.38078i	0.127119	−	0.391231i
$267$	−13.1620	+	4.27660i	−0.805503	+	0.261724i
$268$	−4.30386	−	5.92375i	−0.262900	−	0.361851i
$269$	0.808606	+	2.48863i	0.0493016	+	0.151735i	0.972676	−	0.232165i	$-0.0745809\pi$
$269$	0.808606	+	2.48863i	0.0493016	+	0.151735i	−0.923375	+	0.383900i	$0.874581\pi$
$270$	0.763128	−	2.10182i	0.0464425	−	0.127913i
$271$	20.4486	+	14.8568i	1.24216	+	0.902485i	0.997741	−	0.0671835i	$-0.0214013\pi$
$271$	20.4486	+	14.8568i	1.24216	+	0.902485i	0.244424	+	0.969669i	$0.421401\pi$
$272$	−4.12831	−	5.68214i	−0.250316	−	0.344530i
$273$			5.26876i			0.318880i
$274$	20.5399			1.24086
$275$	−8.87692	+	22.0710i	−0.535299	+	1.33093i
$276$	0.453775	−	1.39658i	0.0273140	−	0.0840640i
$277$	−20.4670	+	6.65014i	−1.22975	+	0.399568i	−0.850622	−	0.525778i	$-0.823774\pi$
$277$	−20.4670	+	6.65014i	−1.22975	+	0.399568i	−0.379123	+	0.925346i	$0.623774\pi$
$278$		−	21.8922i		−	1.31301i
$279$	−3.19689	−	4.55850i	−0.191393	−	0.272910i
$280$	−2.23042	−	7.75538i	−0.133293	−	0.463473i
$281$	−2.57782	−	7.93372i	−0.153780	−	0.473286i	0.844255	−	0.535941i	$-0.180043\pi$
$281$	−2.57782	−	7.93372i	−0.153780	−	0.473286i	−0.998035	+	0.0626553i	$0.980043\pi$
$282$	−3.59085	−	1.16674i	−0.213832	−	0.0694782i
$283$	−14.8727	−	20.4706i	−0.884093	−	1.21685i	−0.975270	−	0.221015i	$-0.929063\pi$
$283$	−14.8727	−	20.4706i	−0.884093	−	1.21685i	0.0911772	−	0.995835i	$-0.470937\pi$
$284$	−0.695377			−0.0412630
$285$	−3.99504	+	1.14896i	−0.236646	+	0.0680586i
$286$	−5.61957	+	4.08285i	−0.332292	+	0.241424i
$287$	0.129427	−	0.178141i	0.00763985	−	0.0105154i
$288$	−0.587785	+	0.809017i	−0.0346356	+	0.0476718i
$289$	−9.99042	−	30.7473i	−0.587672	−	1.80867i
$290$	−3.79761	+	4.86861i	−0.223003	+	0.285895i
$291$	−2.54917	−	7.84555i	−0.149435	−	0.459914i
$292$	−0.104938	−	0.0340963i	−0.00614101	−	0.00199533i
$293$	−2.19404	+	3.01984i	−0.128177	+	0.176421i	−0.868282	−	0.496070i	$-0.834776\pi$
$293$	−2.19404	+	3.01984i	−0.128177	+	0.176421i	0.740105	+	0.672491i	$0.234776\pi$
$294$	1.86156	−	5.72929i	0.108568	−	0.334139i
$295$	25.9507	+	0.885787i	1.51091	+	0.0515725i
$296$	−2.76448	−	2.00852i	−0.160682	−	0.116743i
$297$	4.52499	+	1.47026i	0.262567	+	0.0853131i
$298$	15.6704	−	5.09164i	0.907764	−	0.294951i
$299$	1.73440	−	1.26012i	0.100303	−	0.0728744i
$300$	−3.20791	+	3.83527i	−0.185209	+	0.221430i
$301$	−30.9392	−	22.4786i	−1.78330	−	1.29565i
$302$	−9.81914	+	13.5149i	−0.565028	+	0.777694i
$303$	−5.90195	−	8.12334i	−0.339058	−	0.466673i
$304$	1.85906			0.106624
$305$	0.708244	+	2.46263i	0.0405539	+	0.141010i
$306$	−5.68214	+	4.12831i	−0.324826	+	0.236000i
$307$	11.5598	+	3.75601i	0.659752	+	0.214367i	0.619709	−	0.784831i	$-0.287250\pi$
$307$	11.5598	+	3.75601i	0.659752	+	0.214367i	0.0400430	+	0.999198i	$0.487250\pi$
$308$	16.3302	−	5.30601i	0.930501	−	0.302338i
$309$	−11.4558			−0.651699
$310$	3.24056	+	12.0208i	0.184052	+	0.682733i
$311$	8.23572			0.467005			0.233503	−	0.972356i	$-0.424981\pi$
$311$	8.23572			0.467005			0.233503	+	0.972356i	$0.424981\pi$
$312$	−1.38848	+	0.451145i	−0.0786073	+	0.0255410i
$313$	−18.0260	−	5.85702i	−1.01889	−	0.331058i	−0.248502	−	0.968631i	$-0.579938\pi$
$313$	−18.0260	−	5.85702i	−1.01889	−	0.331058i	−0.770390	+	0.637573i	$0.779938\pi$
$314$	2.57800	−	1.87303i	0.145485	−	0.105701i
$315$	−7.75538	+	2.23042i	−0.436966	+	0.125670i
$316$	12.6304			0.710518
$317$	1.10814	+	1.52522i	0.0622391	+	0.0856647i	0.839002	−	0.544129i	$-0.183140\pi$
$317$	1.10814	+	1.52522i	0.0622391	+	0.0856647i	−0.776763	+	0.629793i	$0.783140\pi$
$318$	2.47015	−	3.39987i	0.138519	−	0.190655i
$319$	−10.6289	−	7.72238i	−0.595107	−	0.432370i
$320$	1.85280	−	1.25185i	0.103575	−	0.0699806i
$321$	5.95042	−	4.32324i	0.332120	−	0.241300i
$322$	−5.04010	+	1.63763i	−0.280874	+	0.0912614i
$323$	12.4180	+	4.03487i	0.690959	+	0.224506i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−7.08006	+	1.77709i	−0.392731	+	0.0985752i
$326$	3.49976	−	10.7712i	0.193834	−	0.596560i
$327$	1.24360	−	1.71167i	0.0687712	−	0.0946554i
$328$	0.0580282	+	0.0188545i	0.00320407	+	0.00104107i
$329$	4.21063	+	12.9590i	0.232140	+	0.714453i
$330$	−8.38871	−	6.54336i	−0.461783	−	0.360200i
$331$	−0.622406	−	1.91557i	−0.0342105	−	0.105289i	0.932493	−	0.361188i	$-0.117629\pi$
$331$	−0.622406	−	1.91557i	−0.0342105	−	0.105289i	−0.966704	+	0.255899i	$0.917629\pi$
$332$	−9.37164	+	12.8990i	−0.514336	+	0.707922i
$333$	−2.00852	+	2.76448i	−0.110066	+	0.151493i
$334$	12.2125	−	8.87293i	0.668240	−	0.485505i
$335$	15.7350	−	4.52534i	0.859697	−	0.247246i
$336$	3.60890			0.196881
$337$	7.85244	+	10.8080i	0.427750	+	0.588747i	0.967435	−	0.253120i	$-0.0814567\pi$
$337$	7.85244	+	10.8080i	0.427750	+	0.588747i	−0.539685	+	0.841867i	$0.681457\pi$
$338$	10.3366	+	3.35858i	0.562239	+	0.182683i
$339$	5.59783	+	17.2283i	0.304032	+	0.935715i
$340$	15.0932	−	4.34077i	0.818546	−	0.235411i
$341$	−25.3274	+	7.76373i	−1.37156	+	0.420429i
$342$		−	1.85906i		−	0.100526i
$343$	3.34943	−	1.08830i	0.180852	−	0.0587624i
$344$	3.27461	−	10.0782i	0.176555	−	0.543380i
$345$	2.58906	+	2.01952i	0.139390	+	0.108727i
$346$	−7.54862			−0.405816
$347$			25.3627i			1.36154i	0.732496	+	0.680771i	$0.238355\pi$
$347$			25.3627i			1.36154i	−0.732496	+	0.680771i	$0.761645\pi$
$348$	−1.62308	−	2.23398i	−0.0870062	−	0.119754i
$349$	1.92426	+	1.39806i	0.103003	+	0.0748363i	0.638095	−	0.769958i	$-0.279723\pi$
$349$	1.92426	+	1.39806i	0.103003	+	0.0748363i	−0.535091	+	0.844794i	$0.679723\pi$
$350$	18.0025	+	1.23041i	0.962273	+	0.0657680i
$351$	0.451145	+	1.38848i	0.0240803	+	0.0741116i
$352$	2.79660	+	3.84919i	0.149059	+	0.205162i
$353$	22.6504	−	7.35956i	1.20556	−	0.391710i	0.363755	−	0.931495i	$-0.381494\pi$
$353$	22.6504	−	7.35956i	1.20556	−	0.391710i	0.841803	+	0.539785i	$0.181494\pi$
$354$	−3.58839	+	11.0439i	−0.190721	+	0.586978i
$355$	0.530662	−	1.46156i	0.0281646	−	0.0775713i
$356$	−4.27660	+	13.1620i	−0.226660	+	0.697586i
$357$	24.1065	+	7.83269i	1.27585	+	0.414550i
$358$	−13.5997	+	18.7183i	−0.718764	+	0.989294i
$359$	5.82073	−	17.9144i	0.307206	−	0.945484i	−0.671638	−	0.740879i	$-0.734409\pi$
$359$	5.82073	−	17.9144i	0.307206	−	0.945484i	0.978845	−	0.204605i	$-0.0655909\pi$
$360$	−1.25185	−	1.85280i	−0.0659783	−	0.0976512i
$361$	12.5753	−	9.13648i	0.661857	−	0.480867i
$362$	−20.8683	+	6.78051i	−1.09681	+	0.356376i
$363$	6.84018	−	9.41470i	0.359016	−	0.494144i
$364$	4.26251	+	3.09690i	0.223416	+	0.162322i
$365$	0.151745	−	0.194540i	0.00794269	−	0.0101827i
$366$	−1.14596			−0.0599004
$367$		−	3.48767i		−	0.182055i	−0.995848	−	0.0910274i	$-0.970985\pi$
$367$		−	3.48767i		−	0.182055i	0.995848	−	0.0910274i	$-0.0290151\pi$
$368$	−0.863131	−	1.18800i	−0.0449938	−	0.0619287i
$369$	0.0188545	−	0.0580282i	0.000981526	−	0.00302083i
$370$	6.33119	−	4.27769i	0.329143	−	0.222386i
$371$	−15.1663			−0.787395
$372$	−5.56699	−	0.0930792i	−0.288635	−	0.00482593i
$373$		−	0.0418393i		−	0.00216636i	−0.999999	−	0.00108318i	$-0.999655\pi$
$373$		−	0.0418393i		−	0.00216636i	0.999999	−	0.00108318i	$-0.000344786\pi$
$374$	10.3264	+	31.7813i	0.533964	+	1.64337i
$375$	−5.61300	−	9.66924i	−0.289854	−	0.499318i
$376$	−3.05456	+	2.21927i	−0.157527	+	0.114450i
$377$		−	4.03139i		−	0.207627i
$378$		−	3.60890i		−	0.185622i
$379$	2.05336	−	1.49185i	0.105474	−	0.0766314i	−0.533798	−	0.845612i	$-0.679236\pi$
$379$	2.05336	−	1.49185i	0.105474	−	0.0766314i	0.639272	+	0.768981i	$0.279236\pi$
$380$	−1.41870	+	3.90740i	−0.0727777	+	0.200445i
$381$	7.76733	+	5.64330i	0.397933	+	0.289115i
$382$	2.34540	−	0.762067i	0.120001	−	0.0389907i
$383$	14.3342	+	19.7293i	0.732444	+	1.00812i	0.999018	+	0.0443078i	$0.0141082\pi$
$383$	14.3342	+	19.7293i	0.732444	+	1.00812i	−0.266574	+	0.963814i	$0.585892\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	−1.30978	+	38.3723i	−0.0667525	+	1.95563i
$386$	22.0182	+	15.9972i	1.12070	+	0.814234i
$387$	−10.0782	−	3.27461i	−0.512304	−	0.166458i
$388$	−7.84555	−	2.54917i	−0.398297	−	0.129415i
$389$	−11.1760	−	8.11983i	−0.566645	−	0.411692i	0.267240	−	0.963630i	$-0.413888\pi$
$389$	−11.1760	−	8.11983i	−0.566645	−	0.411692i	−0.833885	+	0.551938i	$0.813888\pi$
$390$	0.111364	−	3.26261i	0.00563915	−	0.165209i
$391$	−3.18709	−	9.80886i	−0.161178	−	0.496055i
$392$	−3.54090	−	4.87363i	−0.178842	−	0.246155i
$393$	8.39956	−	2.72918i	0.423702	−	0.137669i
$394$	1.24213	+	0.902462i	0.0625778	+	0.0454654i
$395$	−9.63864	+	26.5469i	−0.484973	+	1.33572i
$396$	3.84919	−	2.79660i	0.193429	−	0.140534i
$397$		−	12.3636i		−	0.620512i	−0.950653	−	0.310256i	$-0.899585\pi$
$397$		−	12.3636i		−	0.620512i	0.950653	−	0.310256i	$-0.100415\pi$
$398$			3.03346i			0.152053i
$399$	−5.42782	+	3.94354i	−0.271731	+	0.197424i
$400$	1.21724	+	4.84957i	0.0608619	+	0.242479i
$401$	8.40258	+	25.8605i	0.419605	+	1.29141i	0.908067	+	0.418826i	$0.137558\pi$
$401$	8.40258	+	25.8605i	0.419605	+	1.29141i	−0.488462	+	0.872585i	$0.662442\pi$
$402$			7.32216i			0.365196i
$403$	−6.49536	−	4.88713i	−0.323557	−	0.243445i
$404$	−10.0410			−0.499558
$405$	−1.85280	+	1.25185i	−0.0920664	+	0.0622050i
$406$	−3.07948	+	9.47768i	−0.152832	+	0.470369i
$407$	9.55623	+	13.1530i	0.473685	+	0.651971i
$408$			7.02351i			0.347715i
$409$	−4.97280			−0.245889			−0.122945	−	0.992414i	$-0.539234\pi$
$409$	−4.97280			−0.245889			−0.122945	+	0.992414i	$0.539234\pi$
$410$	−0.0839117	+	0.107576i	−0.00414410	+	0.00531281i
$411$	−16.6171	−	12.0731i	−0.819664	−	0.595520i
$412$	−6.73356	+	9.26795i	−0.331739	+	0.456599i
$413$	39.8564	−	12.9501i	1.96120	−	0.637234i
$414$	−1.18800	+	0.863131i	−0.0583869	+	0.0424206i
$415$	−19.9595	−	29.5410i	−0.979773	−	1.45011i
$416$	−0.451145	+	1.38848i	−0.0221192	+	0.0680759i
$417$	−12.8679	+	17.7112i	−0.630145	+	0.867321i
$418$	−8.41222	−	2.73330i	−0.411455	−	0.133690i
$419$	−7.59511	+	23.3753i	−0.371045	+	1.14196i	0.575063	+	0.818109i	$0.304978\pi$
$419$	−7.59511	+	23.3753i	−0.371045	+	1.14196i	−0.946108	+	0.323851i	$0.895022\pi$
$420$	−2.75405	+	7.58524i	−0.134384	+	0.370122i
$421$	−9.02472	+	27.7752i	−0.439838	+	1.35368i	0.448209	+	0.893929i	$0.352062\pi$
$421$	−9.02472	+	27.7752i	−0.439838	+	1.35368i	−0.888047	+	0.459753i	$0.847938\pi$
$422$	−13.5684	+	4.40864i	−0.660499	+	0.214609i
$423$	2.21927	+	3.05456i	0.107904	+	0.148518i
$424$	−1.29864	−	3.99679i	−0.0630673	−	0.194101i
$425$	−2.39457	+	35.0358i	−0.116154	+	1.69949i
$426$	0.562572	+	0.408732i	0.0272567	+	0.0198032i
$427$	2.43088	+	3.34582i	0.117639	+	0.161916i
$428$		−	7.35513i		−	0.355524i
$429$	6.94617			0.335364
$430$	18.6836	+	14.5736i	0.901003	+	0.702800i
$431$	−6.37766	+	19.6284i	−0.307201	+	0.945468i	0.671645	+	0.740873i	$0.265588\pi$
$431$	−6.37766	+	19.6284i	−0.307201	+	0.945468i	−0.978847	+	0.204595i	$0.934412\pi$
$432$	0.951057	−	0.309017i	0.0457577	−	0.0148676i
$433$			21.7651i			1.04597i	0.852343	+	0.522983i	$0.175181\pi$
$433$			21.7651i			1.04597i	−0.852343	+	0.522983i	$0.824819\pi$
$434$	11.5372	+	16.4511i	0.553805	+	0.789680i
$435$	5.93403	−	1.70661i	0.284515	−	0.0818255i
$436$	−0.653799	−	2.01219i	−0.0313113	−	0.0963662i
$437$	2.59632	+	0.843594i	0.124199	+	0.0403546i
$438$	0.0648550	+	0.0892652i	0.00309889	+	0.00426526i
$439$	0.0890232			0.00424885			0.00212442	−	0.999998i	$-0.499324\pi$
$439$	0.0890232			0.00424885			0.00212442	+	0.999998i	$0.499324\pi$
$440$	−10.2245	+	2.94052i	−0.487432	+	0.140184i
$441$	−4.87363	+	3.54090i	−0.232077	+	0.168614i
$442$	−6.02707	+	8.29555i	−0.286679	+	0.394579i
$443$	1.39467	−	1.91960i	0.0662629	−	0.0912031i	−0.774599	−	0.632452i	$-0.782048\pi$
$443$	1.39467	−	1.91960i	0.0662629	−	0.0912031i	0.840862	+	0.541249i	$0.182048\pi$
$444$	1.05594	+	3.24985i	0.0501127	+	0.154231i
$445$	−24.4006	−	19.0330i	−1.15670	−	0.902249i
$446$	−3.01468	−	9.27822i	−0.142749	−	0.439336i
$447$	−15.6704	−	5.09164i	−0.741187	−	0.240826i
$448$	2.12126	−	2.91966i	0.100220	−	0.137941i
$449$	2.67592	−	8.23565i	0.126285	−	0.388664i	−0.867848	−	0.496829i	$-0.834497\pi$
$449$	2.67592	−	8.23565i	0.126285	−	0.388664i	0.994133	+	0.108165i	$0.0344975\pi$
$450$	4.84957	−	1.21724i	0.228611	−	0.0573812i
$451$	−0.234856	−	0.170633i	−0.0110589	−	0.00803479i
$452$	17.2283	+	5.59783i	0.810353	+	0.263300i
$453$	15.8877	−	5.16222i	0.746469	−	0.242542i
$454$	−3.70330	+	2.69061i	−0.173805	+	0.126277i
$455$	−9.76195	+	6.59570i	−0.457647	+	0.309211i
$456$	−1.50401	−	1.09273i	−0.0704317	−	0.0511716i
$457$	9.48548	−	13.0556i	0.443712	−	0.610717i	−0.527320	−	0.849667i	$-0.676803\pi$
$457$	9.48548	−	13.0556i	0.443712	−	0.610717i	0.971032	+	0.238950i	$0.0768031\pi$
$458$	2.92192	+	4.02167i	0.136532	+	0.187920i
$459$	7.02351			0.327829
$460$	3.15563	−	0.907550i	0.147132	−	0.0423147i
$461$	−12.0611	+	8.76292i	−0.561742	+	0.408130i	−0.832096	−	0.554631i	$-0.812859\pi$
$461$	−12.0611	+	8.76292i	−0.561742	+	0.408130i	0.270354	+	0.962761i	$0.412859\pi$
$462$	−16.3302	−	5.30601i	−0.759751	−	0.246858i
$463$	34.5736	−	11.2336i	1.60677	−	0.522072i	0.638002	−	0.770035i	$-0.279761\pi$
$463$	34.5736	−	11.2336i	1.60677	−	0.522072i	0.968769	+	0.247964i	$0.0797613\pi$
$464$	−2.76135			−0.128192
$465$	4.44396	−	11.6298i	0.206084	−	0.539317i
$466$	21.0298			0.974187
$467$	35.3724	−	11.4932i	1.63684	−	0.531841i	0.661009	−	0.750378i	$-0.270128\pi$
$467$	35.3724	−	11.4932i	1.63684	−	0.531841i	0.975829	+	0.218537i	$0.0701285\pi$
$468$	1.38848	+	0.451145i	0.0641826	+	0.0208542i
$469$	21.3782	−	15.5322i	0.987154	−	0.717209i
$470$	−2.33347	−	8.11371i	−0.107635	−	0.374257i
$471$	−3.18658			−0.146830
$472$	6.82552	+	9.39452i	0.314170	+	0.432418i
$473$	−29.6351	+	40.7892i	−1.36262	+	1.87549i
$474$	−10.2182	−	7.42399i	−0.469340	−	0.340995i
$475$	−7.12999	−	5.96369i	−0.327147	−	0.273633i
$476$	20.5062	−	14.8987i	0.939902	−	0.682879i
$477$	−3.99679	+	1.29864i	−0.183000	+	0.0594605i
$478$	21.8167	+	7.08868i	0.997874	+	0.324229i
$479$	19.9834	+	14.5188i	0.913066	+	0.663381i	0.941788	−	0.336206i	$-0.109144\pi$
$479$	19.9834	+	14.5188i	0.913066	+	0.663381i	−0.0287223	+	0.999587i	$0.509144\pi$
$480$	−2.23477	−	0.0762803i	−0.102003	−	0.00348170i
$481$	−1.54160	+	4.74457i	−0.0702910	+	0.216334i
$482$	0.990198	−	1.36289i	0.0451023	−	0.0620780i
$483$	5.04010	+	1.63763i	0.229332	+	0.0745146i
$484$	−3.59610	−	11.0676i	−0.163459	−	0.503075i
$485$	11.3450	−	14.5446i	0.515152	−	0.660434i
$486$	−0.309017	−	0.951057i	−0.0140173	−	0.0431408i
$487$	7.56882	−	10.4176i	0.342976	−	0.472066i	−0.602332	−	0.798246i	$-0.705762\pi$
$487$	7.56882	−	10.4176i	0.342976	−	0.472066i	0.945308	+	0.326180i	$0.105762\pi$
$488$	−0.673580	+	0.927103i	−0.0304915	+	0.0419680i
$489$	−9.16250	+	6.65695i	−0.414343	+	0.301038i
$490$	12.9456	−	3.72312i	0.584824	−	0.168193i
$491$	6.83606			0.308507			0.154253	−	0.988031i	$-0.450703\pi$
$491$	6.83606			0.308507			0.154253	+	0.988031i	$0.450703\pi$
$492$	−0.0358634	−	0.0493617i	−0.00161685	−	0.00222540i
$493$	−18.4451	−	5.99318i	−0.830727	−	0.269919i
$494$	−0.838705	−	2.58127i	−0.0377351	−	0.116137i
$495$	2.94052	+	10.2245i	0.132166	+	0.459555i
$496$	−3.34750	+	4.44908i	−0.150307	+	0.199769i
$497$		−	2.50954i		−	0.112568i
$498$	15.1636	−	4.92696i	0.679499	−	0.220783i
$499$	−5.28459	+	16.2643i	−0.236571	+	0.728091i	0.760338	+	0.649527i	$0.225033\pi$
$499$	−5.28459	+	16.2643i	−0.236571	+	0.728091i	−0.996909	+	0.0785631i	$0.974967\pi$
$500$	−11.1218	−	1.14243i	−0.497383	−	0.0510910i
$501$	−15.0955			−0.674419
$502$			9.01810i			0.402498i
$503$	−16.6478	−	22.9137i	−0.742289	−	1.02167i	−0.998484	−	0.0550480i	$-0.982469\pi$
$503$	−16.6478	−	22.9137i	−0.742289	−	1.02167i	0.256195	−	0.966625i	$-0.417531\pi$
$504$	−2.91966	−	2.12126i	−0.130052	−	0.0944883i
$505$	7.66256	−	21.1043i	0.340980	−	0.939131i
$506$	2.15900	+	6.64471i	0.0959791	+	0.295393i
$507$	−6.38840	−	8.79287i	−0.283719	−	0.390505i
$508$	9.13105	−	2.96686i	0.405125	−	0.131633i
$509$	−6.05326	+	18.6300i	−0.268306	+	0.825761i	0.722607	+	0.691259i	$0.242944\pi$
$509$	−6.05326	+	18.6300i	−0.268306	+	0.825761i	−0.990913	+	0.134502i	$0.957056\pi$
$510$	−14.7621	−	5.35983i	−0.653678	−	0.237337i
$511$	0.123050	−	0.378709i	0.00544341	−	0.0167531i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−1.09273	+	1.50401i	−0.0482451	+	0.0664036i
$514$	−6.17519	+	19.0053i	−0.272376	+	0.838287i
$515$	−14.3410	−	21.2253i	−0.631939	−	0.935301i
$516$	−8.57303	+	6.22867i	−0.377406	+	0.274202i
$517$	17.0847	−	5.55117i	0.751386	−	0.244140i
$518$	7.24853	−	9.97674i	0.318482	−	0.438353i
$519$	6.10696	+	4.43697i	0.268066	+	0.194761i
$520$	−2.57405	−	2.00781i	−0.112880	−	0.0880484i
$521$	−7.05812			−0.309222			−0.154611	−	0.987975i	$-0.549412\pi$
$521$	−7.05812			−0.309222			−0.154611	+	0.987975i	$0.549412\pi$
$522$			2.76135i			0.120861i
$523$	8.17216	+	11.2480i	0.357343	+	0.491841i	0.949406	−	0.314051i	$-0.101686\pi$
$523$	8.17216	+	11.2480i	0.357343	+	0.491841i	−0.592063	+	0.805892i	$0.701686\pi$
$524$	2.72918	−	8.39956i	0.119225	−	0.366936i
$525$	−13.8411	−	11.5770i	−0.604075	−	0.505262i
$526$	−17.5786			−0.766463
$527$	−32.0166	+	22.4534i	−1.39467	+	0.978085i
$528$		−	4.75786i		−	0.207059i
$529$	6.44105	+	19.8235i	0.280046	+	0.861891i
$530$	9.39155	+	0.320566i	0.407943	+	0.0139245i
$531$	9.39452	−	6.82552i	0.407688	−	0.296202i
$532$			6.70915i			0.290878i
$533$		−	0.0890772i		−	0.00385836i
$534$	11.1963	−	8.13458i	0.484511	−	0.352018i
$535$	15.4591	+	5.61290i	0.668357	+	0.242667i
$536$	5.92375	+	4.30386i	0.255867	+	0.185898i
$537$	22.0047	−	7.14976i	0.949573	−	0.308535i
$538$	−1.53806	−	2.11696i	−0.0663105	−	0.0912685i
$539$	8.85704	+	27.2592i	0.381500	+	1.17414i
$540$	−0.0762803	+	2.23477i	−0.00328258	+	0.0961690i
$541$	−9.90951	−	7.19968i	−0.426043	−	0.309538i	0.354022	−	0.935237i	$-0.384814\pi$
$541$	−9.90951	−	7.19968i	−0.426043	−	0.309538i	−0.780065	+	0.625699i	$0.784814\pi$
$542$	−24.0388	−	7.81067i	−1.03255	−	0.335497i
$543$	20.8683	+	6.78051i	0.895544	+	0.290980i
$544$	5.68214	+	4.12831i	0.243620	+	0.177000i
$545$	4.72818	+	0.161389i	0.202533	+	0.00691314i
$546$	−1.62814	−	5.01088i	−0.0696778	−	0.214446i
$547$	7.19840	+	9.90775i	0.307782	+	0.423625i	0.934688	−	0.355470i	$-0.115679\pi$
$547$	7.19840	+	9.90775i	0.307782	+	0.423625i	−0.626906	+	0.779095i	$0.715679\pi$
$548$	−19.5346	+	6.34719i	−0.834478	+	0.271138i
$549$	0.927103	+	0.673580i	0.0395678	+	0.0287477i
$550$	1.62213	−	23.7339i	0.0691679	−	1.01202i
$551$	4.15309	−	3.01740i	0.176928	−	0.128546i
$552$			1.46845i			0.0625012i
$553$			45.5820i			1.93834i
$554$	17.4103	−	12.6493i	0.739693	−	0.537418i
$555$	−7.63640	−	0.260657i	−0.324147	−	0.0110643i
$556$	6.76507	+	20.8207i	0.286903	+	0.882996i
$557$		−	40.0470i		−	1.69685i	−0.529318	−	0.848423i	$-0.677552\pi$
$557$		−	40.0470i		−	1.69685i	0.529318	−	0.848423i	$-0.322448\pi$
$558$	4.44908	+	3.34750i	0.188344	+	0.141711i
$559$	−15.4707			−0.654341
$560$	4.51780	+	6.68657i	0.190912	+	0.282559i
$561$	10.3264	−	31.7813i	0.435980	−	1.34181i
$562$	4.90331	+	6.74882i	0.206834	+	0.284682i
$563$		−	13.9292i		−	0.587044i	−0.955952	−	0.293522i	$-0.905173\pi$
$563$		−	13.9292i		−	0.587044i	0.955952	−	0.293522i	$-0.0948275\pi$
$564$	3.77564			0.158983
$565$	−24.9130	+	31.9390i	−1.04810	+	1.34368i
$566$	20.4706	+	14.8727i	0.860443	+	0.625148i
$567$	−2.12126	+	2.91966i	−0.0890844	+	0.122614i
$568$	0.661343	−	0.214883i	0.0277493	−	0.00901631i
$569$	−0.397530	+	0.288822i	−0.0166653	+	0.0121081i	−0.596087	−	0.802920i	$-0.703279\pi$
$569$	−0.397530	+	0.288822i	−0.0166653	+	0.0121081i	0.579421	+	0.815028i	$0.303279\pi$
$570$	3.44446	−	2.32726i	0.144273	−	0.0974783i
$571$	2.21668	−	6.82223i	0.0927651	−	0.285502i	−0.893900	−	0.448267i	$-0.852041\pi$
$571$	2.21668	−	6.82223i	0.0927651	−	0.285502i	0.986665	+	0.162765i	$0.0520414\pi$
$572$	4.08285	−	5.61957i	0.170713	−	0.234966i
$573$	−2.34540	−	0.762067i	−0.0979805	−	0.0318358i
$574$	−0.0680440	+	0.209418i	−0.00284010	+	0.00874093i
$575$	−0.500648	+	7.32514i	−0.0208785	+	0.305480i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	16.1432	−	5.24526i	0.672052	−	0.218363i	0.0469398	−	0.998898i	$-0.485053\pi$
$577$	16.1432	−	5.24526i	0.672052	−	0.218363i	0.625112	+	0.780535i	$0.285053\pi$
$578$	19.0029	+	26.1553i	0.790417	+	1.08792i
$579$	−8.41021	−	25.8840i	−0.349516	−	1.07570i
$580$	2.10726	−	5.80385i	0.0874992	−	0.240992i
$581$	−46.5510	−	33.8213i	−1.93126	−	1.40314i
$582$	4.84881	+	6.67382i	0.200990	+	0.276639i
$583$			19.9948i			0.828099i
$584$	0.110338			0.00456581
$585$	−2.00781	+	2.57405i	−0.0830128	+	0.106424i
$586$	1.15348	−	3.55004i	0.0476497	−	0.146651i
$587$	−5.44686	+	1.76979i	−0.224816	+	0.0730471i	−0.419259	−	0.907867i	$-0.637710\pi$
$587$	−5.44686	+	1.76979i	−0.224816	+	0.0730471i	0.194443	+	0.980914i	$0.437710\pi$
$588$			6.02413i			0.248431i
$589$	0.173040	−	10.3494i	0.00712998	−	0.426438i
$590$	−24.9543	+	7.17678i	−1.02735	+	0.295463i
$591$	−0.474453	−	1.46021i	−0.0195164	−	0.0600652i
$592$	3.24985	+	1.05594i	0.133568	+	0.0433988i
$593$	7.35011	+	10.1166i	0.301833	+	0.415437i	0.932813	−	0.360362i	$-0.117347\pi$
$593$	7.35011	+	10.1166i	0.301833	+	0.415437i	−0.630980	+	0.775799i	$0.717347\pi$
$594$	−4.75786			−0.195217
$595$	15.6654	+	54.4700i	0.642218	+	2.23305i
$596$	−13.3301	+	9.68487i	−0.546021	+	0.396708i
$597$	1.78302	−	2.45412i	0.0729742	−	0.100440i
$598$	−1.26012	+	1.73440i	−0.0515300	+	0.0709249i
$599$	4.34762	+	13.3806i	0.177639	+	0.546717i	0.999744	−	0.0226190i	$-0.00720047\pi$
$599$	4.34762	+	13.3806i	0.177639	+	0.546717i	−0.822105	+	0.569336i	$0.807200\pi$
$600$	1.86574	−	4.63886i	0.0761685	−	0.189381i
$601$	4.53166	+	13.9470i	0.184850	+	0.568910i	0.999946	−	0.0104163i	$-0.00331567\pi$
$601$	4.53166	+	13.9470i	0.184850	+	0.568910i	−0.815096	+	0.579326i	$0.803316\pi$
$602$	36.3712	+	11.8177i	1.48238	+	0.481654i
$603$	4.30386	−	5.92375i	0.175267	−	0.241234i
$604$	5.16222	−	15.8877i	0.210048	−	0.646461i
$605$	26.0064	+	0.887689i	1.05731	+	0.0360897i
$606$	8.12334	+	5.90195i	0.329988	+	0.239750i
$607$	41.1077	+	13.3567i	1.66851	+	0.542132i	0.982629	−	0.185582i	$-0.0594170\pi$
$607$	41.1077	+	13.3567i	1.66851	+	0.542132i	0.685881	+	0.727714i	$0.259417\pi$
$608$	−1.76807	+	0.574481i	−0.0717047	+	0.0232983i
$609$	8.06219	−	5.85753i	0.326697	−	0.237359i
$610$	−1.43457	−	2.12324i	−0.0580842	−	0.0859675i
$611$	4.45946	+	3.23998i	0.180410	+	0.131076i
$612$	4.12831	−	5.68214i	0.166877	−	0.229687i
$613$	−19.7779	−	27.2220i	−0.798823	−	1.09949i	−0.992953	−	0.118509i	$-0.962188\pi$
$613$	−19.7779	−	27.2220i	−0.798823	−	1.09949i	0.194130	−	0.980976i	$-0.437812\pi$
$614$	−12.1547			−0.490523
$615$	0.131118	−	0.0377090i	0.00528718	−	0.00152057i
$616$	−13.8913	+	10.0926i	−0.559697	+	0.406644i
$617$	−35.6727	−	11.5908i	−1.43613	−	0.466626i	−0.515440	−	0.856926i	$-0.672372\pi$
$617$	−35.6727	−	11.5908i	−1.43613	−	0.466626i	−0.920688	+	0.390299i	$0.872372\pi$
$618$	10.8951	−	3.54004i	0.438266	−	0.142401i
$619$	3.81405			0.153300			0.0766498	−	0.997058i	$-0.475578\pi$
$619$	3.81405			0.153300			0.0766498	+	0.997058i	$0.475578\pi$
$620$	−6.79658	−	10.4310i	−0.272957	−	0.418920i
$621$	1.46845			0.0589267
$622$	−7.83264	+	2.54498i	−0.314060	+	0.102044i
$623$	−47.5004	−	15.4338i	−1.90306	−	0.618343i
$624$	1.18111	−	0.858129i	0.0472823	−	0.0343526i
$625$	10.8885	−	22.5042i	0.435542	−	0.900169i
$626$	18.9537			0.757542
$627$	5.19904	+	7.15586i	0.207630	+	0.285778i
$628$	−1.87303	+	2.57800i	−0.0747419	+	0.102873i
$629$	19.4164	+	14.1068i	0.774182	+	0.562476i
$630$	6.68657	−	4.51780i	0.266399	−	0.179993i
$631$	35.6539	−	25.9041i	1.41936	−	1.03122i	0.427481	−	0.904024i	$-0.359401\pi$
$631$	35.6539	−	25.9041i	1.41936	−	1.03122i	0.991877	−	0.127200i	$-0.0405990\pi$
$632$	−12.0123	+	3.90302i	−0.477822	+	0.155254i
$633$	13.5684	+	4.40864i	0.539295	+	0.175228i
$634$	−1.52522	−	1.10814i	−0.0605741	−	0.0440097i
$635$	−0.732363	+	21.4559i	−0.0290629	+	0.851451i
$636$	−1.29864	+	3.99679i	−0.0514943	+	0.158483i
$637$	−5.16948	+	7.11518i	−0.204822	+	0.281914i
$638$	12.4951	+	4.05990i	0.494685	+	0.160733i
$639$	−0.214883	−	0.661343i	−0.00850066	−	0.0261623i
$640$	−1.37527	+	1.76313i	−0.0543625	+	0.0696937i
$641$	6.84597	+	21.0697i	0.270400	+	0.832204i	0.990400	+	0.138231i	$0.0441415\pi$
$641$	6.84597	+	21.0697i	0.270400	+	0.832204i	−0.720001	+	0.693974i	$0.755858\pi$
$642$	−4.32324	+	5.95042i	−0.170625	+	0.234845i
$643$	1.46975	−	2.02294i	0.0579614	−	0.0797770i	−0.779052	−	0.626959i	$-0.784299\pi$
$643$	1.46975	−	2.02294i	0.0579614	−	0.0797770i	0.837014	+	0.547182i	$0.184299\pi$
$644$	4.28736	−	3.11495i	0.168946	−	0.122746i
$645$	−6.54921	−	22.7722i	−0.257875	−	0.896655i
$646$	−13.0571			−0.513725
$647$	22.1839	+	30.5335i	0.872138	+	1.20040i	0.978537	+	0.206072i	$0.0660681\pi$
$647$	22.1839	+	30.5335i	0.872138	+	1.20040i	−0.106398	+	0.994324i	$0.533932\pi$
$648$	−0.951057	−	0.309017i	−0.0373610	−	0.0121393i
$649$	−17.0730	−	52.5454i	−0.670175	−	2.06259i
$650$	6.18439	−	3.87797i	0.242572	−	0.152107i
$651$	0.335913	−	20.0907i	0.0131655	−	0.787416i
$652$			11.3255i			0.443540i
$653$	−2.92742	+	0.951175i	−0.114559	+	0.0372224i	−0.365735	−	0.930719i	$-0.619182\pi$
$653$	−2.92742	+	0.951175i	−0.114559	+	0.0372224i	0.251177	+	0.967941i	$0.419182\pi$
$654$	−0.653799	+	2.01219i	−0.0255655	+	0.0786827i
$655$	15.5716	+	12.1462i	0.608433	+	0.474590i
$656$	−0.0610145			−0.00238221
$657$		−	0.110338i		−	0.00430469i
$658$	−8.00910	−	11.0236i	−0.312227	−	0.429744i
$659$	−17.0461	−	12.3847i	−0.664023	−	0.482441i	0.203996	−	0.978972i	$-0.434607\pi$
$659$	−17.0461	−	12.3847i	−0.664023	−	0.482441i	−0.868019	+	0.496531i	$0.834607\pi$
$660$	10.0001	+	3.63085i	0.389255	+	0.141331i
$661$	−7.18228	−	22.1048i	−0.279358	−	0.859777i	−0.988033	−	0.154241i	$-0.950707\pi$
$661$	−7.18228	−	22.1048i	−0.279358	−	0.859777i	0.708675	−	0.705535i	$-0.249293\pi$
$662$	1.18389	+	1.62948i	0.0460130	+	0.0633315i
$663$	9.75201	−	3.16862i	0.378737	−	0.123059i
$664$	4.92696	−	15.1636i	0.191203	−	0.588463i
$665$	−14.1014	−	5.11994i	−0.546829	−	0.198543i
$666$	1.05594	−	3.24985i	0.0409168	−	0.125929i
$667$	−3.85643	−	1.25303i	−0.149322	−	0.0485175i
$668$	−8.87293	+	12.2125i	−0.343304	+	0.472517i
$669$	−3.01468	+	9.27822i	−0.116554	+	0.358717i
$670$	−13.5665	+	9.16625i	−0.524120	+	0.354123i
$671$	4.41103	−	3.20480i	0.170286	−	0.123720i
$672$	−3.43226	+	1.11521i	−0.132402	+	0.0430202i
$673$	−29.0407	+	39.9710i	−1.11944	+	1.54077i	−0.312705	+	0.949850i	$0.601235\pi$
$673$	−29.0407	+	39.9710i	−1.11944	+	1.54077i	−0.806730	+	0.590920i	$0.798765\pi$
$674$	−10.8080	−	7.85244i	−0.416307	−	0.302465i
$675$	−4.63886	−	1.86574i	−0.178550	−	0.0718123i
$676$	−10.8686			−0.418023
$677$		−	28.0295i		−	1.07726i	−0.842542	−	0.538630i	$-0.818942\pi$
$677$		−	28.0295i		−	1.07726i	0.842542	−	0.538630i	$-0.181058\pi$
$678$	−10.6477	−	14.6553i	−0.408923	−	0.562834i
$679$	9.19970	−	28.3138i	0.353052	−	1.08658i
$680$	−13.0132	+	8.79238i	−0.499032	+	0.337173i
$681$	4.57754			0.175412
$682$	21.6887	−	15.2103i	0.830503	−	0.582434i
$683$		−	19.9503i		−	0.763377i	−0.924291	−	0.381688i	$-0.875343\pi$
$683$		−	19.9503i		−	0.763377i	0.924291	−	0.381688i	$-0.124657\pi$
$684$	0.574481	+	1.76807i	0.0219658	+	0.0676038i
$685$	1.56679	−	45.9019i	0.0598640	−	1.75382i
$686$	−2.84919	+	2.07006i	−0.108783	+	0.0790353i
$687$		−	4.97106i		−	0.189658i
$688$			10.5968i			0.404001i
$689$	−4.96359	+	3.60626i	−0.189098	+	0.137388i
$690$	−3.08641	−	1.12061i	−0.117497	−	0.0426610i
$691$	15.6437	+	11.3658i	0.595116	+	0.432377i	0.844142	−	0.536120i	$-0.180110\pi$
$691$	15.6437	+	11.3658i	0.595116	+	0.432377i	−0.249026	+	0.968497i	$0.580110\pi$
$692$	7.17916	−	2.33265i	0.272911	−	0.0886741i
$693$	10.0926	+	13.8913i	0.383388	+	0.527688i
$694$	−7.83752	−	24.1214i	−0.297508	−	0.915636i
$695$	−48.9240	−	1.66995i	−1.85579	−	0.0633446i
$696$	2.23398	+	1.62308i	0.0846787	+	0.0615227i
$697$	−0.407562	−	0.132425i	−0.0154375	−	0.00501595i
$698$	−2.26211	−	0.735003i	−0.0856219	−	0.0278203i
$699$	−17.0135	−	12.3610i	−0.643508	−	0.467536i
$700$	−17.5016	+	4.39289i	−0.661498	+	0.166036i
$701$	−6.09569	−	18.7606i	−0.230231	−	0.708578i	−0.997718	−	0.0675138i	$-0.978493\pi$
$701$	−6.09569	−	18.7606i	−0.230231	−	0.708578i	0.767487	−	0.641064i	$-0.221507\pi$
$702$	−0.858129	−	1.18111i	−0.0323880	−	0.0445782i
$703$	−6.04165	+	1.96305i	−0.227865	+	0.0740379i
$704$	−3.84919	−	2.79660i	−0.145072	−	0.105401i
$705$	−2.88130	+	7.93571i	−0.108516	+	0.298876i
$706$	−19.2676	+	13.9987i	−0.725145	+	0.526848i
$707$		−	36.2369i		−	1.36283i
$708$		−	11.6123i		−	0.436416i
$709$	−33.7050	+	24.4881i	−1.26582	+	0.919669i	−0.999028	−	0.0440857i	$-0.985963\pi$
$709$	−33.7050	+	24.4881i	−1.26582	+	0.919669i	−0.266789	+	0.963755i	$0.585963\pi$
$710$	−0.0530436	+	1.55401i	−0.00199069	+	0.0583208i
$711$	3.90302	+	12.0123i	0.146375	+	0.450495i
$712$		−	13.8394i		−	0.518653i
$713$	−6.69391	+	4.69446i	−0.250689	+	0.175809i
$714$	−25.3471			−0.948592
$715$	8.69556	+	12.8699i	0.325196	+	0.481305i
$716$	7.14976	−	22.0047i	0.267199	−	0.822354i
$717$	−13.4835	−	18.5584i	−0.503550	−	0.693077i
$718$			18.8363i			0.702964i
$719$	44.5420			1.66114			0.830568	−	0.556917i	$-0.188016\pi$
$719$	44.5420			1.66114			0.830568	+	0.556917i	$0.188016\pi$
$720$	1.76313	+	1.37527i	0.0657079	+	0.0512535i
$721$	−33.4471	−	24.3007i	−1.24563	−	0.905006i
$722$	−9.13648	+	12.5753i	−0.340024	+	0.468004i
$723$	−1.60217	+	0.520578i	−0.0595855	+	0.0193605i
$724$	17.7516	−	12.8973i	0.659734	−	0.479325i
$725$	10.5905	+	8.85816i	0.393322	+	0.328984i
$726$	−3.59610	+	11.0676i	−0.133464	+	0.410759i
$727$	4.36308	−	6.00526i	0.161818	−	0.222723i	−0.720407	−	0.693551i	$-0.756045\pi$
$727$	4.36308	−	6.00526i	0.161818	−	0.222723i	0.882225	+	0.470829i	$0.156045\pi$
$728$	−5.01088	−	1.62814i	−0.185716	−	0.0603427i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	−0.0842019	+	0.231910i	−0.00311645	+	0.00858338i
$731$	−22.9992	+	70.7843i	−0.850657	+	2.61805i
$732$	1.08988	−	0.354122i	0.0402830	−	0.0130887i
$733$	23.3386	+	32.1229i	0.862032	+	1.18649i	0.981081	+	0.193597i	$0.0620155\pi$
$733$	23.3386	+	32.1229i	0.862032	+	1.18649i	−0.119049	+	0.992888i	$0.537985\pi$
$734$	1.07775	+	3.31697i	0.0397804	+	0.122432i
$735$	−12.6616	−	4.59718i	−0.467031	−	0.169570i
$736$	1.18800	+	0.863131i	0.0437902	+	0.0318154i
$737$	−20.4771	−	28.1844i	−0.754285	−	1.03818i
$738$			0.0610145i			0.00224597i
$739$	−33.5282			−1.23335			−0.616677	−	0.787216i	$-0.711522\pi$
$739$	−33.5282			−1.23335			−0.616677	+	0.787216i	$0.711522\pi$
$740$	−4.69944	+	6.02477i	−0.172755	+	0.221475i
$741$	−0.838705	+	2.58127i	−0.0308106	+	0.0948252i
$742$	14.4240	−	4.68664i	0.529522	−	0.172052i
$743$		−	39.1380i		−	1.43583i	−0.696128	−	0.717917i	$-0.745096\pi$
$743$		−	39.1380i		−	1.43583i	0.696128	−	0.717917i	$-0.254904\pi$
$744$	5.32328	−	1.63177i	0.195161	−	0.0598236i
$745$	−10.1833	−	35.4082i	−0.373086	−	1.29726i
$746$	0.0129291	+	0.0397915i	0.000473366	+	0.00145687i
$747$	−15.1636	−	4.92696i	−0.554809	−	0.180268i
$748$	−19.6419	−	27.0348i	−0.718180	−	0.988490i
$749$	26.5439			0.969893
$750$	8.32624	+	7.46149i	0.304031	+	0.272455i
$751$	1.37401	−	0.998277i	0.0501383	−	0.0364276i	−0.562434	−	0.826842i	$-0.690135\pi$
$751$	1.37401	−	0.998277i	0.0501383	−	0.0364276i	0.612572	+	0.790415i	$0.290135\pi$
$752$	2.21927	−	3.05456i	0.0809283	−	0.111388i
$753$	5.30071	−	7.29580i	0.193168	−	0.265874i
$754$	1.24577	+	3.83408i	0.0453682	+	0.139629i
$755$	29.4536	+	22.9744i	1.07193	+	0.836124i
$756$	1.11521	+	3.43226i	0.0405598	+	0.124830i
$757$	−8.10615	−	2.63385i	−0.294623	−	0.0957288i	0.157976	−	0.987443i	$-0.449503\pi$
$757$	−8.10615	−	2.63385i	−0.294623	−	0.0957288i	−0.452599	+	0.891714i	$0.649503\pi$
$758$	−1.49185	+	2.05336i	−0.0541866	+	0.0745814i
$759$	2.15900	−	6.64471i	0.0783666	−	0.241188i
$760$	0.141809	−	4.15456i	0.00514397	−	0.150702i
$761$	−4.88155	−	3.54666i	−0.176956	−	0.128566i	0.495781	−	0.868447i	$-0.334882\pi$
$761$	−4.88155	−	3.54666i	−0.176956	−	0.128566i	−0.672738	+	0.739881i	$0.734882\pi$
$762$	−9.13105	−	2.96686i	−0.330783	−	0.107478i
$763$	7.26177	−	2.35949i	0.262894	−	0.0854193i
$764$	−1.99512	+	1.44954i	−0.0721808	+	0.0524424i
$765$	8.79238	+	13.0132i	0.317889	+	0.470492i
$766$	−19.7293	−	14.3342i	−0.712850	−	0.517916i
$767$	9.96482	−	13.7154i	0.359809	−	0.495234i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	2.33805			0.0843122			0.0421561	−	0.999111i	$-0.486577\pi$
$769$	2.33805			0.0843122			0.0421561	+	0.999111i	$0.486577\pi$
$770$	−10.6120	−	36.8990i	−0.382431	−	1.32975i
$771$	16.1669	−	11.7459i	0.582235	−	0.423019i
$772$	−25.8840	−	8.41021i	−0.931584	−	0.302690i
$773$	40.2459	−	13.0767i	1.44754	−	0.470336i	0.523304	−	0.852146i	$-0.324699\pi$
$773$	40.2459	−	13.0767i	1.44754	−	0.470336i	0.924241	+	0.381810i	$0.124699\pi$
$774$	10.5968			0.380896
$775$	27.1108	−	6.32495i	0.973848	−	0.227199i
$776$	8.24929			0.296132
$777$	−11.7284	+	3.81078i	−0.420753	+	0.136711i
$778$	13.1382	+	4.26885i	0.471026	+	0.153046i
$779$	0.0917663	−	0.0666722i	0.00328787	−	0.00238878i
$780$	0.902290	+	3.13734i	0.0323072	+	0.112335i
$781$	−3.30851			−0.118388
$782$	6.06221	+	8.34392i	0.216784	+	0.298378i
$783$	1.62308	−	2.23398i	0.0580041	−	0.0798358i
$784$	4.87363	+	3.54090i	0.174058	+	0.126461i
$785$	−3.98913	−	5.90410i	−0.142378	−	0.210726i
$786$	−7.14509	+	5.19121i	−0.254857	+	0.185164i
$787$	−22.0525	+	7.16529i	−0.786087	+	0.255415i	−0.674437	−	0.738332i	$-0.735614\pi$
$787$	−22.0525	+	7.16529i	−0.786087	+	0.255415i	−0.111650	+	0.993748i	$0.535614\pi$
$788$	−1.46021	−	0.474453i	−0.0520180	−	0.0169017i
$789$	14.2214	+	10.3324i	0.506295	+	0.367845i
$790$	0.963454	−	28.2261i	0.0342781	−	1.00424i
$791$	−20.2020	+	62.1753i	−0.718300	+	2.21070i
$792$	−2.79660	+	3.84919i	−0.0993728	+	0.136775i
$793$	1.59115	+	0.516995i	0.0565033	+	0.0183590i
$794$	3.82057	+	11.7585i	0.135587	+	0.417293i
$795$	−7.40950	−	5.77956i	−0.262788	−	0.204980i
$796$	−0.937390	−	2.88499i	−0.0332249	−	0.102256i
$797$	−22.1383	+	30.4707i	−0.784178	+	1.07933i	0.210631	+	0.977566i	$0.432448\pi$
$797$	−22.1383	+	30.4707i	−0.784178	+	1.07933i	−0.994809	+	0.101763i	$0.967552\pi$
$798$	3.94354	−	5.42782i	0.139600	−	0.192143i
$799$	21.4537	−	15.5870i	0.758978	−	0.551430i
$800$	−2.65626	−	4.23607i	−0.0939130	−	0.149768i
$801$	−13.8394			−0.488991
$802$	−15.9827	−	21.9982i	−0.564367	−	0.776785i
$803$	−0.499278	−	0.162225i	−0.0176191	−	0.00572481i
$804$	−2.26267	−	6.96379i	−0.0797983	−	0.245594i
$805$	3.27525	+	11.3884i	0.115438	+	0.401387i
$806$	7.68766	+	2.64076i	0.270786	+	0.0930167i
$807$			2.61670i			0.0921123i
$808$	9.54955	−	3.10284i	0.335952	−	0.109157i
$809$	−3.01539	+	9.28042i	−0.106015	+	0.326282i	−0.989967	−	0.141296i	$-0.954873\pi$
$809$	−3.01539	+	9.28042i	−0.106015	+	0.326282i	0.883952	+	0.467578i	$0.154873\pi$
$810$	1.37527	−	1.76313i	0.0483222	−	0.0619500i
$811$	−35.9698			−1.26307			−0.631535	−	0.775347i	$-0.717575\pi$
$811$	−35.9698			−1.26307			−0.631535	+	0.775347i	$0.717575\pi$
$812$		−	9.96542i		−	0.349718i
$813$	14.8568	+	20.4486i	0.521050	+	0.717164i
$814$	−13.1530	−	9.55623i	−0.461013	−	0.334946i
$815$	−23.8041	−	8.64278i	−0.833821	−	0.302744i
$816$	−2.17038	−	6.67975i	−0.0759786	−	0.233838i
$817$	−11.5795	−	15.9378i	−0.405114	−	0.557592i
$818$	4.72941	−	1.53668i	0.165360	−	0.0537287i
$819$	−1.62814	+	5.01088i	−0.0568916	+	0.175094i
$820$	0.0465618	−	0.128241i	0.00162601	−	0.00447838i
$821$	−2.49192	+	7.66935i	−0.0869688	+	0.267662i	−0.985078	−	0.172111i	$-0.944941\pi$
$821$	−2.49192	+	7.66935i	−0.0869688	+	0.267662i	0.898109	+	0.439773i	$0.144941\pi$
$822$	19.5346	+	6.34719i	0.681348	+	0.221384i
$823$	8.23342	−	11.3323i	0.286999	−	0.395020i	−0.641037	−	0.767510i	$-0.721496\pi$
$823$	8.23342	−	11.3323i	0.286999	−	0.395020i	0.928036	+	0.372489i	$0.121496\pi$
$824$	3.54004	−	10.8951i	0.123323	−	0.379550i
$825$	−15.2628	+	18.2477i	−0.531382	+	0.635303i
$826$	−33.9039	+	24.6326i	−1.17967	+	0.857078i
$827$	−33.7356	+	10.9614i	−1.17310	+	0.381164i	−0.829800	−	0.558061i	$-0.811545\pi$
$827$	−33.7356	+	10.9614i	−1.17310	+	0.381164i	−0.343302	+	0.939225i	$0.611545\pi$
$828$	0.863131	−	1.18800i	0.0299959	−	0.0412858i
$829$	26.0371	+	18.9170i	0.904304	+	0.657015i	0.939568	−	0.342363i	$-0.111227\pi$
$829$	26.0371	+	18.9170i	0.904304	+	0.657015i	−0.0352637	+	0.999378i	$0.511227\pi$
$830$	28.1113	+	21.9274i	0.975757	+	0.761110i
$831$	−21.5203			−0.746531
$832$		−	1.45994i		−	0.0506142i
$833$	24.8695	+	34.2300i	0.861678	+	1.18600i
$834$	6.76507	−	20.8207i	0.234255	−	0.720964i
$835$	−18.8974	−	27.9690i	−0.653970	−	0.967907i
$836$	8.84513			0.305915
$837$	−1.63177	−	5.32328i	−0.0564022	−	0.184000i
$838$		−	24.5783i		−	0.849043i
$839$	1.01478	+	3.12316i	0.0350340	+	0.107823i	0.967044	−	0.254608i	$-0.0819466\pi$
$839$	1.01478	+	3.12316i	0.0350340	+	0.107823i	−0.932010	+	0.362432i	$0.881947\pi$
$840$	0.275288	−	8.06504i	0.00949832	−	0.278270i
$841$	17.2927	−	12.5639i	0.596300	−	0.433237i
$842$		−	29.2046i		−	1.00646i
$843$		−	8.34201i		−	0.287314i
$844$	11.5420	−	8.38573i	0.397291	−	0.288649i
$845$	8.29412	−	22.8438i	0.285326	−	0.785850i
$846$	−3.05456	−	2.21927i	−0.105018	−	0.0762999i
$847$	39.9420	−	12.9779i	1.37242	−	0.445927i
$848$	2.47015	+	3.39987i	0.0848254	+	0.116752i
$849$	−7.81907	−	24.0646i	−0.268350	−	0.825895i
$850$	−8.54928	−	34.0610i	−0.293238	−	1.16828i
$851$	4.05950	+	2.94940i	0.139158	+	0.101104i
$852$	−0.661343	−	0.214883i	−0.0226572	−	0.00736178i
$853$	−52.6602	−	17.1103i	−1.80305	−	0.585847i	−0.803100	−	0.595844i	$-0.796818\pi$
$853$	−52.6602	−	17.1103i	−1.80305	−	0.585847i	−0.999950	+	0.00999739i	$0.996818\pi$
$854$	−3.34582	−	2.43088i	−0.114492	−	0.0831830i
$855$	−4.15456	−	0.141809i	−0.142083	−	0.00484978i
$856$	2.27286	+	6.99514i	0.0776848	+	0.239089i
$857$	21.2293	+	29.2196i	0.725179	+	0.998123i	0.999336	+	0.0364380i	$0.0116012\pi$
$857$	21.2293	+	29.2196i	0.725179	+	0.998123i	−0.274157	+	0.961685i	$0.588399\pi$
$858$	−6.60620	+	2.14648i	−0.225532	+	0.0732797i
$859$	18.2241	+	13.2406i	0.621797	+	0.451762i	0.853549	−	0.521013i	$-0.174446\pi$
$859$	18.2241	+	13.2406i	0.621797	+	0.451762i	−0.231752	+	0.972775i	$0.574446\pi$
$860$	−22.2726	−	8.08675i	−0.759490	−	0.275756i
$861$	0.178141	−	0.129427i	0.00607104	−	0.00441087i
$862$		−	20.6385i		−	0.702952i
$863$		−	43.6032i		−	1.48427i	−0.670251	−	0.742134i	$-0.733814\pi$
$863$		−	43.6032i		−	1.48427i	0.670251	−	0.742134i	$-0.266186\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	−0.575810	+	16.8694i	−0.0195781	+	0.573577i
$866$	−6.72580	−	20.6999i	−0.228552	−	0.703410i
$867$		−	32.3297i		−	1.09797i
$868$	−16.0563	−	12.0808i	−0.544985	−	0.410048i
$869$	60.0939			2.03854
$870$	−5.11623	+	3.45680i	−0.173456	+	0.117196i
$871$	3.30336	−	10.1667i	0.111930	−	0.344485i
$872$	1.24360	+	1.71167i	0.0421136	+	0.0579644i
$873$		−	8.24929i		−	0.279196i
$874$	−2.72993			−0.0923412
$875$	4.12291	−	40.1375i	0.139380	−	1.35689i
$876$	−0.0892652	−	0.0648550i	−0.00301599	−	0.00219125i
$877$	−19.9736	+	27.4913i	−0.674461	+	0.928316i	−0.999851	−	0.0172637i	$-0.994505\pi$
$877$	−19.9736	+	27.4913i	−0.674461	+	0.928316i	0.325390	+	0.945580i	$0.394505\pi$
$878$	−0.0846661	+	0.0275097i	−0.00285734	+	0.000928407i
$879$	−3.01984	+	2.19404i	−0.101857	+	0.0740033i
$880$	8.81536	−	5.95613i	0.297166	−	0.200781i
$881$	6.74982	−	20.7738i	0.227407	−	0.699888i	−0.770631	−	0.637282i	$-0.780059\pi$
$881$	6.74982	−	20.7738i	0.227407	−	0.699888i	0.998038	−	0.0626061i	$-0.0199412\pi$
$882$	3.54090	−	4.87363i	0.119228	−	0.164104i
$883$	2.27348	+	0.738699i	0.0765087	+	0.0248592i	0.347021	−	0.937857i	$-0.387193\pi$
$883$	2.27348	+	0.738699i	0.0765087	+	0.0248592i	−0.270513	+	0.962716i	$0.587193\pi$
$884$	3.16862	−	9.75201i	0.106572	−	0.327996i
$885$	24.4069	+	8.86164i	0.820428	+	0.297881i
$886$	−0.733223	+	2.25663i	−0.0246331	+	0.0758129i
$887$	−18.2323	+	5.92403i	−0.612180	+	0.198909i	−0.598665	−	0.800999i	$-0.704302\pi$
$887$	−18.2323	+	5.92403i	−0.612180	+	0.198909i	−0.0135148	+	0.999909i	$0.504302\pi$
$888$	−2.00852	−	2.76448i	−0.0674014	−	0.0927700i
$889$	10.7071	+	32.9530i	0.359104	+	1.10521i
$890$	29.0879	+	10.5612i	0.975027	+	0.354013i
$891$	3.84919	+	2.79660i	0.128953	+	0.0936896i
$892$	5.73425	+	7.89252i	0.191997	+	0.264261i
$893$			7.01914i			0.234886i
$894$	16.4769			0.551069
$895$	40.7937	+	31.8199i	1.36358	+	1.06362i
$896$	−1.11521	+	3.43226i	−0.0372566	+	0.114664i
$897$	2.03891	−	0.662482i	0.0680772	−	0.0221196i
$898$			8.65947i			0.288970i
$899$	−0.257024	+	15.3724i	−0.00857223	+	0.512698i
$900$	−4.23607	+	2.65626i	−0.141202	+	0.0885421i
$901$	9.12098	+	28.0715i	0.303864	+	0.935197i
$902$	0.276090	+	0.0897071i	0.00919279	+	0.00298692i
$903$	−22.4786	−	30.9392i	−0.748042	−	1.02959i
$904$	−18.1150			−0.602494
$905$	13.5610	+	47.1529i	0.450784	+	1.56742i
$906$	−13.5149	+	9.81914i	−0.449002	+	0.326219i
$907$	11.4403	−	15.7463i	0.379870	−	0.522846i	−0.575680	−	0.817675i	$-0.695263\pi$
$907$	11.4403	−	15.7463i	0.379870	−	0.522846i	0.955550	+	0.294829i	$0.0952627\pi$
$908$	2.69061	−	3.70330i	0.0892910	−	0.122898i
$909$	−3.10284	−	9.54955i	−0.102915	−	0.316739i
$910$	7.24599	−	9.28949i	0.240202	−	0.307944i
$911$	10.2766	+	31.6282i	0.340480	+	1.04789i	0.963959	+	0.266049i	$0.0857184\pi$
$911$	10.2766	+	31.6282i	0.340480	+	1.04789i	−0.623480	+	0.781840i	$0.714282\pi$
$912$	1.76807	+	0.574481i	0.0585466	+	0.0190230i
$913$	−44.5890	+	61.3714i	−1.47568	+	2.03110i
$914$	−4.98681	+	15.3478i	−0.164949	+	0.507661i
$915$	−0.0874143	+	2.56096i	−0.00288983	+	0.0846627i
$916$	−4.02167	−	2.92192i	−0.132880	−	0.0965428i
$917$	30.3131	+	9.84933i	1.00103	+	0.325254i
$918$	−6.67975	+	2.17038i	−0.220465	+	0.0716333i
$919$	30.2965	−	22.0117i	0.999391	−	0.726100i	0.0374334	−	0.999299i	$-0.488082\pi$
$919$	30.2965	−	22.0117i	0.999391	−	0.726100i	0.961958	+	0.273199i	$0.0880818\pi$
$920$	−2.72074	+	1.83828i	−0.0897001	+	0.0606062i
$921$	9.83335	+	7.14435i	0.324020	+	0.235414i
$922$	8.76292	−	12.0611i	0.288591	−	0.397212i
$923$	−0.596723	−	0.821319i	−0.0196414	−	0.0270340i
$924$	17.1706			0.564872
$925$	−9.07669	−	14.4750i	−0.298440	−	0.475936i
$926$	−29.4101	+	21.3677i	−0.966474	+	0.702185i
$927$	−10.8951	−	3.54004i	−0.357843	−	0.116270i
$928$	2.62620	−	0.853303i	0.0862092	−	0.0280111i
$929$	−35.7204			−1.17195			−0.585975	−	0.810329i	$-0.699288\pi$
$929$	−35.7204			−1.17195			−0.585975	+	0.810329i	$0.699288\pi$
$930$	−0.632661	+	12.4338i	−0.0207458	+	0.407721i
$931$	−11.1992			−0.367039
$932$	−20.0005	+	6.49857i	−0.655139	+	0.212868i
$933$	7.83264	+	2.54498i	0.256429	+	0.0833189i
$934$	−30.0895	+	21.8613i	−0.984559	+	0.715324i
$935$	71.8115	−	20.6528i	2.34849	−	0.675417i
$936$	−1.45994			−0.0477195
$937$	−12.5618	−	17.2899i	−0.410377	−	0.564836i	0.552933	−	0.833226i	$-0.313509\pi$
$937$	−12.5618	−	17.2899i	−0.410377	−	0.564836i	−0.963310	+	0.268390i	$0.913509\pi$
$938$	−15.5322	+	21.3782i	−0.507144	+	0.698023i
$939$	−15.3339	−	11.1407i	−0.500402	−	0.363563i
$940$	4.72654	+	6.99551i	0.154163	+	0.228168i
$941$	29.9894	−	21.7886i	0.977628	−	0.710288i	0.0204506	−	0.999791i	$-0.493490\pi$
$941$	29.9894	−	21.7886i	0.977628	−	0.710288i	0.957177	+	0.289503i	$0.0934899\pi$
$942$	3.03062	−	0.984708i	0.0987429	−	0.0320835i
$943$	−0.0852113	−	0.0276868i	−0.00277486	−	0.000901607i
$944$	−9.39452	−	6.82552i	−0.305766	−	0.222152i
$945$	−8.06504	−	0.275288i	−0.262356	−	0.00895511i
$946$	15.5801	−	47.9506i	0.506553	−	1.55901i
$947$	2.50403	−	3.44650i	0.0813700	−	0.111996i	−0.766392	−	0.642374i	$-0.777950\pi$
$947$	2.50403	−	3.44650i	0.0813700	−	0.111996i	0.847762	+	0.530377i	$0.177950\pi$
$948$	12.0123	+	3.90302i	0.390140	+	0.126764i
$949$	−0.0497784	−	0.153202i	−0.00161587	−	0.00497315i
$950$	8.62391	+	3.46852i	0.279797	+	0.112534i
$951$	0.582581	+	1.79300i	0.0188915	+	0.0581420i
$952$	−14.8987	+	20.5062i	−0.482868	+	0.664611i
$953$	7.38490	−	10.1644i	0.239220	−	0.329258i	−0.672479	−	0.740116i	$-0.734771\pi$
$953$	7.38490	−	10.1644i	0.239220	−	0.329258i	0.911700	+	0.410857i	$0.134771\pi$
$954$	3.39987	−	2.47015i	0.110075	−	0.0799741i
$955$	−1.52413	−	5.29955i	−0.0493198	−	0.171490i
$956$	−22.9395			−0.741915
$957$	−7.72238	−	10.6289i	−0.249629	−	0.343585i
$958$	−23.4919	−	7.63299i	−0.758990	−	0.246611i
$959$	−22.9063	−	70.4985i	−0.739684	−	2.27651i
$960$	2.14896	−	0.618034i	0.0693574	−	0.0199470i
$961$	24.4564	+	19.0496i	0.788915	+	0.614502i
$962$		−	4.98873i		−	0.160843i
$963$	6.99514	−	2.27286i	0.225415	−	0.0732419i
$964$	−0.520578	+	1.60217i	−0.0167667	+	0.0516025i
$965$	37.4295	−	47.9853i	1.20490	−	1.54470i
$966$	−5.29947			−0.170508
$967$			19.6233i			0.631043i	0.948918	+	0.315521i	$0.102179\pi$
$967$			19.6233i			0.631043i	−0.948918	+	0.315521i	$0.897821\pi$
$968$	6.84018	+	9.41470i	0.219852	+	0.302600i
$969$	10.5634	+	7.67478i	0.339346	+	0.246549i
$970$	−6.29527	+	17.3385i	−0.202129	+	0.556706i
$971$	0.725131	+	2.23172i	0.0232706	+	0.0716194i	0.962017	−	0.272988i	$-0.0880120\pi$
$971$	0.725131	+	2.23172i	0.0232706	+	0.0716194i	−0.938747	+	0.344608i	$0.888012\pi$
$972$	0.587785	+	0.809017i	0.0188532	+	0.0259492i
$973$	−75.1399	+	24.4144i	−2.40888	+	0.782691i
$974$	−3.97916	+	12.2466i	−0.127501	+	0.392407i
$975$	−7.28269	−	0.497746i	−0.233233	−	0.0159406i
$976$	0.354122	−	1.08988i	0.0113352	−	0.0348861i
$977$	19.6638	+	6.38915i	0.629100	+	0.204407i	0.606176	−	0.795330i	$-0.292703\pi$
$977$	19.6638	+	6.38915i	0.629100	+	0.204407i	0.0229237	+	0.999737i	$0.492703\pi$
$978$	6.65695	−	9.16250i	0.212866	−	0.292985i
$979$	−20.3475	+	62.6231i	−0.650308	+	2.00144i
$980$	−11.1615	+	7.54132i	−0.356542	+	0.240899i
$981$	1.71167	−	1.24360i	0.0546493	−	0.0397051i
$982$	−6.50148	+	2.11246i	−0.207470	+	0.0674113i
$983$	20.5920	−	28.3425i	0.656784	−	0.903985i	−0.342586	−	0.939486i	$-0.611303\pi$
$983$	20.5920	−	28.3425i	0.656784	−	0.903985i	0.999370	+	0.0355014i	$0.0113028\pi$
$984$	0.0493617	+	0.0358634i	0.00157359	+	0.00114328i
$985$	2.11154	−	2.70704i	0.0672794	−	0.0862534i
$986$	19.3943			0.617642
$987$			13.6259i			0.433717i
$988$	1.59531	+	2.19576i	0.0507536	+	0.0698563i
$989$	−4.80858	+	14.7993i	−0.152904	+	0.470590i
$990$	−5.95613	−	8.81536i	−0.189298	−	0.280171i
$991$	31.5904			1.00350			0.501752	−	0.865012i	$-0.332689\pi$
$991$	31.5904			1.00350			0.501752	+	0.865012i	$0.332689\pi$
$992$	1.80882	−	5.26576i	0.0574300	−	0.167188i
$993$		−	2.01415i		−	0.0639170i
$994$	0.775492	+	2.38672i	0.0245971	+	0.0757021i
$995$	6.77907	+	0.231393i	0.214911	+	0.00733565i
$996$	−12.8990	+	9.37164i	−0.408719	+	0.296952i
$997$		−	15.3213i		−	0.485231i	−0.970122	−	0.242616i	$-0.921995\pi$
$997$		−	15.3213i		−	0.485231i	0.970122	−	0.242616i	$-0.0780054\pi$
$998$		−	17.1013i		−	0.541332i
$999$	−2.76448	+	2.00852i	−0.0874644	+	0.0635466i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.c.469.4	yes	32
5.4	even	2	inner	930.2.z.c.469.5	yes	32
31.8	even	5	inner	930.2.z.c.349.7	yes	32
155.39	even	10	inner	930.2.z.c.349.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.c.349.2	✓	32	155.39	even	10	inner
930.2.z.c.349.7	yes	32	31.8	even	5	inner
930.2.z.c.469.4	yes	32	1.1	even	1	trivial
930.2.z.c.469.5	yes	32	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(2.12126 + 2.91966i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.809017 - 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(2.12126 + 2.91966i) q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.25185 - 1.85280i) q^{10} +(3.84919 - 2.79660i) q^{11} +(0.951057 - 0.309017i) q^{12} +(1.38848 + 0.451145i) q^{13} +(-2.91966 - 2.12126i) q^{14} +(-0.0762803 + 2.23477i) q^{15} +(0.309017 - 0.951057i) q^{16} +(4.12831 - 5.68214i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(0.574481 + 1.76807i) q^{19} +(1.76313 + 1.37527i) q^{20} +(1.11521 + 3.43226i) q^{21} +(-2.79660 + 3.84919i) q^{22} +(0.863131 - 1.18800i) q^{23} +(-0.809017 + 0.587785i) q^{24} +(-4.23607 + 2.65626i) q^{25} -1.45994 q^{26} +(0.587785 + 0.809017i) q^{27} +(3.43226 + 1.11521i) q^{28} +(-0.853303 - 2.62620i) q^{29} +(-0.618034 - 2.14896i) q^{30} +(-5.26576 - 1.80882i) q^{31} +1.00000i q^{32} +(4.52499 - 1.47026i) q^{33} +(-2.17038 + 6.67975i) q^{34} +(-4.96322 + 6.36295i) q^{35} +1.00000 q^{36} +3.41709i q^{37} +(-1.09273 - 1.50401i) q^{38} +(1.18111 + 0.858129i) q^{39} +(-2.10182 - 0.763128i) q^{40} +(-0.0188545 - 0.0580282i) q^{41} +(-2.12126 - 2.91966i) q^{42} +(-10.0782 + 3.27461i) q^{43} +(1.47026 - 4.52499i) q^{44} +(-0.763128 + 2.10182i) q^{45} +(-0.453775 + 1.39658i) q^{46} +(3.59085 + 1.16674i) q^{47} +(0.587785 - 0.809017i) q^{48} +(-1.86156 + 5.72929i) q^{49} +(3.20791 - 3.83527i) q^{50} +(5.68214 - 4.12831i) q^{51} +(1.38848 - 0.451145i) q^{52} +(-2.47015 + 3.39987i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(8.38871 + 6.54336i) q^{55} -3.60890 q^{56} +1.85906i q^{57} +(1.62308 + 2.23398i) q^{58} +(3.58839 - 11.0439i) q^{59} +(1.25185 + 1.85280i) q^{60} +1.14596 q^{61} +(5.56699 + 0.0930792i) q^{62} +3.60890i q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.111364 + 3.26261i) q^{65} +(-3.84919 + 2.79660i) q^{66} -7.32216i q^{67} -7.02351i q^{68} +(1.18800 - 0.863131i) q^{69} +(2.75405 - 7.58524i) q^{70} +(-0.562572 - 0.408732i) q^{71} +(-0.951057 + 0.309017i) q^{72} +(-0.0648550 - 0.0892652i) q^{73} +(-1.05594 - 3.24985i) q^{74} +(-4.84957 + 1.21724i) q^{75} +(1.50401 + 1.09273i) q^{76} +(16.3302 + 5.30601i) q^{77} +(-1.38848 - 0.451145i) q^{78} +(10.2182 + 7.42399i) q^{79} +(2.23477 + 0.0762803i) q^{80} +(0.309017 + 0.951057i) q^{81} +(0.0358634 + 0.0493617i) q^{82} +(-15.1636 + 4.92696i) q^{83} +(2.91966 + 2.12126i) q^{84} +(14.7621 + 5.35983i) q^{85} +(8.57303 - 6.22867i) q^{86} -2.76135i q^{87} +4.75786i q^{88} +(-11.1963 + 8.13458i) q^{89} +(0.0762803 - 2.23477i) q^{90} +(1.62814 + 5.01088i) q^{91} -1.46845i q^{92} +(-4.44908 - 3.34750i) q^{93} -3.77564 q^{94} +(-3.44446 + 2.32726i) q^{95} +(-0.309017 + 0.951057i) q^{96} +(-4.84881 - 6.67382i) q^{97} -6.02413i q^{98} +4.75786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9	\( 32 q + 8 q^{4} - 16 q^{5} - 32 q^{6} + 8 q^{9} - 4 q^{11} - 4 q^{14} - 8 q^{16} - 16 q^{19} + 16 q^{20} - 4 q^{21} - 8 q^{24} - 64 q^{25} - 16 q^{26} + 4 q^{29} + 16 q^{30} - 24 q^{31} - 12 q^{34} + 32 q^{36} + 4 q^{39} - 48 q^{41} + 4 q^{44} + 16 q^{45} + 8 q^{46} - 28 q^{49} + 8 q^{51} - 8 q^{54} - 8 q^{55} - 16 q^{56} - 8 q^{59} + 32 q^{61} + 8 q^{64} - 8 q^{65} + 4 q^{66} - 12 q^{69} - 8 q^{70} + 32 q^{71} + 4 q^{74} - 24 q^{76} + 64 q^{79} + 24 q^{80} - 8 q^{81} + 4 q^{84} + 28 q^{85} + 84 q^{86} - 128 q^{89} - 28 q^{91} + 40 q^{94} + 8 q^{95} + 8 q^{96} - 16 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^5 - 32 * q^6 + 8 * q^9 - 4 * q^11 - 4 * q^14 - 8 * q^16 - 16 * q^19 + 16 * q^20 - 4 * q^21 - 8 * q^24 - 64 * q^25 - 16 * q^26 + 4 * q^29 + 16 * q^30 - 24 * q^31 - 12 * q^34 + 32 * q^36 + 4 * q^39 - 48 * q^41 + 4 * q^44 + 16 * q^45 + 8 * q^46 - 28 * q^49 + 8 * q^51 - 8 * q^54 - 8 * q^55 - 16 * q^56 - 8 * q^59 + 32 * q^61 + 8 * q^64 - 8 * q^65 + 4 * q^66 - 12 * q^69 - 8 * q^70 + 32 * q^71 + 4 * q^74 - 24 * q^76 + 64 * q^79 + 24 * q^80 - 8 * q^81 + 4 * q^84 + 28 * q^85 + 84 * q^86 - 128 * q^89 - 28 * q^91 + 40 * q^94 + 8 * q^95 + 8 * q^96 - 16 * q^99

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