LMFDB - Embedded newform 930.2.z.c.349.7

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			349.7
Character	$\chi$	$=$	930.349
Dual form			930.2.z.c.469.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.618034 + 2.14896i) q^{5} -1.00000 q^{6} +(-2.12126 + 2.91966i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(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} +(-0.0762803 + 2.23477i) 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} +(-1.25185 - 1.85280i) 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} +(-0.763128 + 2.10182i) 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} +(-7.58524 - 2.75405i) q^{35} +1.00000 q^{36} +3.41709i q^{37} +(1.09273 - 1.50401i) q^{38} +(1.18111 - 0.858129i) q^{39} +(-1.37527 + 1.76313i) 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} +(1.76313 + 1.37527i) 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} +(-4.84957 + 1.21724i) 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} +(-3.63085 + 10.0001i) q^{55} -3.60890 q^{56} +1.85906i q^{57} +(-1.62308 + 2.23398i) q^{58} +(3.58839 + 11.0439i) q^{59} +(0.0762803 - 2.23477i) q^{60} +1.14596 q^{61} +(-5.56699 + 0.0930792i) q^{62} +3.60890i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-1.82762 - 2.70497i) q^{65} +(-3.84919 - 2.79660i) q^{66} -7.32216i q^{67} -7.02351i q^{68} +(1.18800 + 0.863131i) q^{69} +(-6.36295 - 4.96322i) 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} +(3.20791 - 3.83527i) 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} +(-1.85280 + 1.25185i) 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} +(9.65925 - 12.3833i) q^{85} +(8.57303 + 6.22867i) q^{86} -2.76135i q^{87} +4.75786i q^{88} +(-11.1963 - 8.13458i) q^{89} +(1.25185 + 1.85280i) q^{90} +(1.62814 - 5.01088i) q^{91} -1.46845i q^{92} +(4.44908 - 3.34750i) q^{93} -3.77564 q^{94} +(4.15456 + 0.141809i) 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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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	0.190784	+	0.981632i	$0.438897\pi$
$7$	−2.12126	+	2.91966i	−0.801759	+	1.10353i	−0.992543	+	0.121895i	$0.961103\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−0.0762803	+	2.23477i	−0.0241219	+	0.706695i
$11$	3.84919	+	2.79660i	1.16057	+	0.843206i	0.989850	−	0.142113i	$-0.0453896\pi$
$11$	3.84919	+	2.79660i	1.16057	+	0.843206i	0.170723	+	0.985319i	$0.445390\pi$
$12$	−0.951057	−	0.309017i	−0.274546	−	0.0892055i
$13$	−1.38848	+	0.451145i	−0.385095	+	0.125125i	−0.495165	−	0.868799i	$-0.664893\pi$
$13$	−1.38848	+	0.451145i	−0.385095	+	0.125125i	0.110070	+	0.993924i	$0.464893\pi$
$14$	−2.91966	+	2.12126i	−0.780312	+	0.566930i
$15$	−1.25185	−	1.85280i	−0.323226	−	0.478391i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.12831	−	5.68214i	−1.00126	−	1.37812i	−0.924547	−	0.381068i	$-0.875556\pi$
$17$	−4.12831	−	5.68214i	−1.00126	−	1.37812i	−0.0767163	−	0.997053i	$-0.524444\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	0.574481	−	1.76807i	0.131795	−	0.405623i	−0.863283	−	0.504720i	$-0.831596\pi$
$19$	0.574481	−	1.76807i	0.131795	−	0.405623i	0.995078	+	0.0990975i	$0.0315956\pi$
$20$	−0.763128	+	2.10182i	−0.170641	+	0.469981i
$21$	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	$-0.248924\pi$
$23$	−0.863131	−	1.18800i	−0.179975	−	0.247715i	−0.889467	+	0.456999i	$0.848924\pi$
$24$	−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	−0.998495	−	0.0548517i	$-0.982531\pi$
$29$	−0.853303	+	2.62620i	−0.158454	+	0.487673i	0.840040	+	0.542524i	$0.182531\pi$
$30$	−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
$35$	−7.58524	−	2.75405i	−1.28214	−	0.465519i
$36$	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
$40$	−1.37527	+	1.76313i	−0.217450	+	0.278775i
$41$	−0.0188545	+	0.0580282i	−0.00294458	+	0.00906248i	−0.952518	−	0.304482i	$-0.901517\pi$
$41$	−0.0188545	+	0.0580282i	−0.00294458	+	0.00906248i	0.949573	+	0.313545i	$0.101517\pi$
$42$	2.12126	−	2.91966i	0.327317	−	0.450513i
$43$	10.0782	+	3.27461i	1.53691	+	0.499373i	0.950522	−	0.310657i	$-0.100549\pi$
$43$	10.0782	+	3.27461i	1.53691	+	0.499373i	0.586389	+	0.810030i	$0.300549\pi$
$44$	1.47026	+	4.52499i	0.221650	+	0.682168i
$45$	1.76313	+	1.37527i	0.262832	+	0.205014i
$46$	−0.453775	−	1.39658i	−0.0669055	−	0.205914i
$47$	−3.59085	+	1.16674i	−0.523779	+	0.170186i	−0.558960	−	0.829195i	$-0.688799\pi$
$47$	−3.59085	+	1.16674i	−0.523779	+	0.170186i	0.0351807	+	0.999381i	$0.488799\pi$
$48$	−0.587785	−	0.809017i	−0.0848395	−	0.116772i
$49$	−1.86156	−	5.72929i	−0.265937	−	0.818470i
$50$	−4.84957	+	1.21724i	−0.685833	+	0.172143i
$51$	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	$-0.106801\pi$
$53$	2.47015	+	3.39987i	0.339302	+	0.467008i	−0.604936	+	0.796274i	$0.706801\pi$
$54$	−0.809017	+	0.587785i	−0.110093	+	0.0799874i
$55$	−3.63085	+	10.0001i	−0.489584	+	1.34842i
$56$	−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	0.856235	+	0.516587i	$0.172798\pi$
$59$	3.58839	+	11.0439i	0.467168	+	1.43780i	−0.389066	+	0.921210i	$0.627202\pi$
$60$	0.0762803	−	2.23477i	0.00984774	−	0.288507i
$61$	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
$65$	−1.82762	−	2.70497i	−0.226689	−	0.335510i
$66$	−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
$70$	−6.36295	−	4.96322i	−0.760517	−	0.593219i
$71$	−0.562572	+	0.408732i	−0.0667650	+	0.0485076i	−0.620667	−	0.784074i	$-0.713138\pi$
$71$	−0.562572	+	0.408732i	−0.0667650	+	0.0485076i	0.553902	+	0.832582i	$0.313138\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	0.0648550	−	0.0892652i	0.00759070	−	0.0104477i	−0.805205	−	0.592997i	$-0.797945\pi$
$73$	0.0648550	−	0.0892652i	0.00759070	−	0.0104477i	0.812795	+	0.582549i	$0.197945\pi$
$74$	−1.05594	+	3.24985i	−0.122750	+	0.377787i
$75$	3.20791	−	3.83527i	0.370418	−	0.442859i
$76$	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	0.161209	−	0.986920i	$-0.448461\pi$
$79$	10.2182	−	7.42399i	1.14964	−	0.835264i	0.988433	+	0.151656i	$0.0484606\pi$
$80$	−1.85280	+	1.25185i	−0.207149	+	0.139961i
$81$	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	$-0.0608347\pi$
$83$	15.1636	+	4.92696i	1.66443	+	0.540805i	0.682633	+	0.730761i	$0.260835\pi$
$84$	2.91966	−	2.12126i	0.318561	−	0.231448i
$85$	9.65925	−	12.3833i	1.04769	−	1.34316i
$86$	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	−0.193882	−	0.981025i	$-0.562108\pi$
$89$	−11.1963	−	8.13458i	−1.18680	−	0.862264i	−0.992923	+	0.118761i	$0.962108\pi$
$90$	1.25185	+	1.85280i	0.131957	+	0.195302i
$91$	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
$95$	4.15456	+	0.141809i	0.426249	+	0.0145493i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	4.84881	−	6.67382i	0.492322	−	0.677624i	−0.488492	−	0.872569i	$-0.662453\pi$
$97$	4.84881	−	6.67382i	0.492322	−	0.677624i	0.980814	+	0.194945i	$0.0624528\pi$
$98$		−	6.02413i		−	0.608529i
$99$	4.75786			0.478183
$100$	−4.98836	−	0.340937i	−0.498836	−	0.0340937i
$101$	−8.12334	+	5.90195i	−0.808302	+	0.587266i	−0.913338	−	0.407203i	$-0.866504\pi$
$101$	−8.12334	+	5.90195i	−0.808302	+	0.587266i	0.105036	+	0.994468i	$0.466504\pi$
$102$	4.12831	+	5.68214i	0.408764	+	0.562615i
$103$	10.8951	+	3.54004i	1.07353	+	0.348811i	0.791861	−	0.610701i	$-0.209112\pi$
$103$	10.8951	+	3.54004i	1.07353	+	0.348811i	0.281668	+	0.959512i	$0.409112\pi$
$104$	−1.18111	−	0.858129i	−0.115818	−	0.0841464i
$105$	8.06504	+	0.275288i	0.787067	+	0.0268653i
$106$	1.29864	+	3.99679i	0.126135	+	0.388203i
$107$	−4.32324	−	5.95042i	−0.417943	−	0.575249i	0.547190	−	0.837008i	$-0.315697\pi$
$107$	−4.32324	−	5.95042i	−0.417943	−	0.575249i	−0.965133	+	0.261759i	$0.915697\pi$
$108$	−0.951057	+	0.309017i	−0.0915155	+	0.0297352i
$109$	0.653799	+	2.01219i	0.0626225	+	0.192732i	0.977473	−	0.211060i	$-0.0676917\pi$
$109$	0.653799	+	2.01219i	0.0626225	+	0.192732i	−0.914850	+	0.403793i	$0.867692\pi$
$110$	−6.54336	+	8.38871i	−0.623885	+	0.799832i
$111$	−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	−0.0773450	+	0.997004i	$0.524644\pi$
$113$	−10.6477	+	14.6553i	−1.00165	+	1.37866i	−0.924307	+	0.381651i	$0.875356\pi$
$114$	−0.574481	+	1.76807i	−0.0538050	+	0.165595i
$115$	2.01952	−	2.58906i	0.188321	−	0.241431i
$116$	−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
$120$	0.763128	−	2.10182i	0.0696637	−	0.191869i
$121$	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	$-0.740068\pi$
$127$	−9.13105	+	2.96686i	−0.810250	+	0.263266i	−0.125546	+	0.992088i	$0.540068\pi$
$128$	−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	0.854410	−	0.519599i	$-0.173919\pi$
$131$	7.14509	+	5.19121i	0.624269	+	0.453558i	−0.230141	+	0.973157i	$0.573919\pi$
$132$	−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
$135$	−2.10182	−	0.763128i	−0.180896	−	0.0656796i
$136$	2.17038	−	6.67975i	0.186109	−	0.572784i
$137$	19.5346	−	6.34719i	1.66896	−	0.542277i	0.686237	−	0.727378i	$-0.259261\pi$
$137$	19.5346	−	6.34719i	1.66896	−	0.542277i	0.982719	+	0.185102i	$0.0592614\pi$
$138$	0.863131	+	1.18800i	0.0734746	+	0.101129i
$139$	−6.76507	−	20.8207i	−0.573806	−	1.76599i	−0.640210	−	0.768200i	$-0.721153\pi$
$139$	−6.76507	−	20.8207i	−0.573806	−	1.76599i	0.0664040	−	0.997793i	$-0.478847\pi$
$140$	−4.51780	−	6.68657i	−0.381824	−	0.565118i
$141$	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
$145$	−6.17097	−	0.210636i	−0.512471	−	0.0174924i
$146$	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	0.981031	−	0.193849i	$-0.0620972\pi$
$151$	13.5149	+	9.81914i	1.09983	+	0.799070i	0.118794	+	0.992919i	$0.462097\pi$
$152$	1.76807	−	0.574481i	0.143409	−	0.0465965i
$153$	−6.67975	−	2.17038i	−0.540026	−	0.175465i
$154$	−17.1706			−1.38365
$155$	−7.14149	−	10.1980i	−0.573619	−	0.819123i
$156$	1.45994			0.116888
$157$	3.03062	+	0.984708i	0.241870	+	0.0785883i	0.427443	−	0.904042i	$-0.359414\pi$
$157$	3.03062	+	0.984708i	0.241870	+	0.0785883i	−0.185574	+	0.982630i	$0.559414\pi$
$158$	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	$-0.0537224\pi$
$163$	6.65695	+	9.16250i	0.521412	+	0.717663i	−0.464379	+	0.885637i	$0.653722\pi$
$164$	−0.0493617	+	0.0358634i	−0.00385450	+	0.00280046i
$165$	0.362931	−	10.6327i	0.0282541	−	0.827755i
$166$	12.8990	+	9.37164i	1.00115	+	0.727381i
$167$	14.3567	+	4.66478i	1.11095	+	0.360971i	0.806309	−	0.591495i	$-0.201462\pi$
$167$	14.3567	+	4.66478i	1.11095	+	0.360971i	0.304646	+	0.952466i	$0.401462\pi$
$168$	3.43226	−	1.11521i	0.264805	−	0.0860403i
$169$	−8.79287	+	6.38840i	−0.676375	+	0.491415i
$170$	13.0132	−	8.79238i	0.998064	−	0.674345i
$171$	−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	$-0.692643\pi$
$173$	−7.17916	+	2.33265i	−0.545821	+	0.177348i	0.0231102	+	0.999733i	$0.492643\pi$
$174$	0.853303	−	2.62620i	0.0646888	−	0.199092i
$175$	1.23041	−	18.0025i	0.0930100	−	1.36086i
$176$	−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	0.994800	+	0.101848i	$0.0324754\pi$
$179$	18.7183	+	13.5997i	1.39907	+	1.01649i	0.404273	+	0.914638i	$0.367525\pi$
$180$	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
$190$	3.90740	+	1.41870i	0.283473	+	0.102923i
$191$	−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	0.412880	−	0.910785i	$-0.364523\pi$
$193$	15.9972	−	22.0182i	1.15150	−	1.58491i	0.738622	−	0.674120i	$-0.235477\pi$
$194$	6.67382	−	4.84881i	0.479152	−	0.348125i
$195$	2.57405	+	2.00781i	0.184332	+	0.143782i
$196$	1.86156	−	5.72929i	0.132969	−	0.409235i
$197$	0.902462	−	1.24213i	0.0642978	−	0.0884983i	−0.775657	−	0.631155i	$-0.782581\pi$
$197$	0.902462	−	1.24213i	0.0642978	−	0.0884983i	0.839955	+	0.542656i	$0.182581\pi$
$198$	4.52499	+	1.47026i	0.321577	+	0.104487i
$199$	0.937390	+	2.88499i	0.0664498	+	0.204511i	0.978768	−	0.204970i	$-0.0657097\pi$
$199$	0.937390	+	2.88499i	0.0664498	+	0.204511i	−0.912318	+	0.409481i	$0.865710\pi$
$200$	−4.63886	−	1.86574i	−0.328017	−	0.131928i
$201$	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
$205$	−0.136353	−	0.00465420i	−0.00952331	−	0.000325063i
$206$	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
$210$	7.58524	+	2.75405i	0.523431	+	0.190047i
$211$	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
$215$	−0.808330	+	23.6815i	−0.0551277	+	1.61506i
$216$	−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
$220$	−8.81536	+	5.95613i	−0.594332	+	0.401562i
$221$	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
$225$	−1.86574	+	4.63886i	−0.124383	+	0.309257i
$226$	−14.6553	+	10.6477i	−0.974856	+	0.708275i
$227$	−4.35350	−	1.41454i	−0.288952	−	0.0938861i	0.160955	−	0.986962i	$-0.448543\pi$
$227$	−4.35350	−	1.41454i	−0.288952	−	0.0938861i	−0.449906	+	0.893076i	$0.648543\pi$
$228$	−1.09273	+	1.50401i	−0.0723676	+	0.0996055i
$229$	−1.53614	+	4.72776i	−0.101511	+	0.312419i	−0.988896	−	0.148611i	$-0.952520\pi$
$229$	−1.53614	+	4.72776i	−0.101511	+	0.312419i	0.887385	+	0.461030i	$0.152520\pi$
$230$	2.72074	−	1.83828i	0.179400	−	0.121212i
$231$	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	$-0.358114\pi$
$233$	20.0005	−	6.49857i	1.31028	−	0.425735i	0.879146	+	0.476553i	$0.158114\pi$
$234$	−1.18111	+	0.858129i	−0.0772117	+	0.0560976i
$235$	−4.72654	−	6.99551i	−0.308325	−	0.456337i
$236$	−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	−0.994328	−	0.106354i	$-0.966082\pi$
$239$	−18.5584	+	13.4835i	−1.20044	+	0.872174i	−0.206116	+	0.978528i	$0.566082\pi$
$240$	1.37527	−	1.76313i	0.0887736	−	0.113809i
$241$	−1.36289	−	0.990198i	−0.0877915	−	0.0637842i	0.543024	−	0.839717i	$-0.317279\pi$
$241$	−1.36289	−	0.990198i	−0.0877915	−	0.0637842i	−0.630815	+	0.775933i	$0.717279\pi$
$242$			11.6372i			0.748068i
$243$			1.00000i			0.0641500i
$244$	0.927103	+	0.673580i	0.0593517	+	0.0431215i
$245$	11.1615	−	7.54132i	0.713083	−	0.481797i
$246$	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
$250$	−5.61300	−	9.66924i	−0.354997	−	0.611537i
$251$	2.78675	+	8.57672i	0.175898	+	0.541358i	0.999673	−	0.0255582i	$-0.00813633\pi$
$251$	2.78675	+	8.57672i	0.175898	+	0.541358i	−0.823775	+	0.566916i	$0.808136\pi$
$252$	−2.12126	+	2.91966i	−0.133627	+	0.183921i
$253$		−	6.98666i		−	0.439248i
$254$	−9.60095			−0.602417
$255$	−5.35983	+	14.7621i	−0.335646	+	0.924441i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−11.7459	−	16.1669i	−0.732690	−	1.00846i	−0.999006	−	0.0445752i	$-0.985807\pi$
$257$	−11.7459	−	16.1669i	−0.732690	−	1.00846i	0.266316	−	0.963886i	$-0.414193\pi$
$258$	−10.0782	−	3.27461i	−0.627441	−	0.203868i
$259$	−9.97674	−	7.24853i	−0.619924	−	0.450401i
$260$	0.111364	−	3.26261i	0.00690652	−	0.202339i
$261$	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	$-0.782322\pi$
$263$	−16.7182	+	5.43209i	−1.03089	+	0.334957i	−0.255749	+	0.966743i	$0.582322\pi$
$264$	−1.47026	−	4.52499i	−0.0904882	−	0.278494i
$265$	−5.77956	+	7.40950i	−0.355035	+	0.455162i
$266$	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	−0.923375	−	0.383900i	$-0.874581\pi$
$269$	0.808606	−	2.48863i	0.0493016	−	0.151735i	0.972676	+	0.232165i	$0.0745809\pi$
$270$	−1.76313	−	1.37527i	−0.107301	−	0.0836966i
$271$	20.4486	−	14.8568i	1.24216	−	0.902485i	0.244424	−	0.969669i	$-0.421401\pi$
$271$	20.4486	−	14.8568i	1.24216	−	0.902485i	0.997741	+	0.0671835i	$0.0214013\pi$
$272$	4.12831	−	5.68214i	0.250316	−	0.344530i
$273$			5.26876i			0.318880i
$274$	20.5399			1.24086
$275$	−23.7339	−	1.62213i	−1.43121	−	0.0978181i
$276$	0.453775	+	1.39658i	0.0273140	+	0.0840640i
$277$	20.4670	+	6.65014i	1.22975	+	0.399568i	0.850622	−	0.525778i	$-0.176226\pi$
$277$	20.4670	+	6.65014i	1.22975	+	0.399568i	0.379123	+	0.925346i	$0.376226\pi$
$278$		−	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	−0.998035	−	0.0626553i	$-0.980043\pi$
$281$	−2.57782	+	7.93372i	−0.153780	+	0.473286i	0.844255	+	0.535941i	$0.180043\pi$
$282$	3.59085	−	1.16674i	0.213832	−	0.0694782i
$283$	14.8727	−	20.4706i	0.884093	−	1.21685i	−0.0911772	−	0.995835i	$-0.529063\pi$
$283$	14.8727	−	20.4706i	0.884093	−	1.21685i	0.975270	−	0.221015i	$-0.0709370\pi$
$284$	−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
$290$	−5.80385	−	2.10726i	−0.340814	−	0.123743i
$291$	−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	$-0.165224\pi$
$293$	2.19404	+	3.01984i	0.128177	+	0.176421i	−0.740105	+	0.672491i	$0.765224\pi$
$294$	1.86156	+	5.72929i	0.108568	+	0.334139i
$295$	−21.5152	+	14.5368i	−1.25266	+	0.846367i
$296$	−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
$300$	4.84957	−	1.21724i	0.279990	−	0.0702773i
$301$	−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	$-0.712750\pi$
$307$	−11.5598	+	3.75601i	−0.659752	+	0.214367i	−0.0400430	+	0.999198i	$0.512750\pi$
$308$	−16.3302	−	5.30601i	−0.930501	−	0.302338i
$309$	−11.4558			−0.651699
$310$	−3.64061	−	11.9057i	−0.206773	−	0.676199i
$311$	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	$-0.420062\pi$
$313$	18.0260	−	5.85702i	1.01889	−	0.331058i	0.770390	+	0.637573i	$0.220062\pi$
$314$	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	$-0.816860\pi$
$317$	−1.10814	+	1.52522i	−0.0622391	+	0.0856647i	0.776763	+	0.629793i	$0.216860\pi$
$318$	−2.47015	−	3.39987i	−0.138519	−	0.190655i
$319$	−10.6289	+	7.72238i	−0.595107	+	0.432370i
$320$	−2.23477	−	0.0762803i	−0.124927	−	0.00426420i
$321$	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
$325$	4.68334	−	5.59925i	0.259785	−	0.310591i
$326$	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
$330$	3.63085	−	10.0001i	0.199872	−	0.550490i
$331$	−0.622406	+	1.91557i	−0.0342105	+	0.105289i	−0.966704	−	0.255899i	$-0.917629\pi$
$331$	−0.622406	+	1.91557i	−0.0342105	+	0.105289i	0.932493	+	0.361188i	$0.117629\pi$
$332$	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	$-0.918543\pi$
$337$	−7.85244	+	10.8080i	−0.427750	+	0.588747i	0.539685	+	0.841867i	$0.318543\pi$
$338$	−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
$345$	−1.12061	+	3.08641i	−0.0603317	+	0.166167i
$346$	−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	−0.535091	−	0.844794i	$-0.679723\pi$
$349$	1.92426	−	1.39806i	0.103003	−	0.0748363i	0.638095	+	0.769958i	$0.279723\pi$
$350$	6.73326	−	16.7412i	0.359908	−	0.894853i
$351$	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	$-0.618506\pi$
$353$	−22.6504	−	7.35956i	−1.20556	−	0.391710i	−0.841803	+	0.539785i	$0.818506\pi$
$354$	−3.58839	−	11.0439i	−0.190721	−	0.586978i
$355$	−1.22604	−	0.956335i	−0.0650714	−	0.0507570i
$356$	−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	0.978845	+	0.204605i	$0.0655909\pi$
$359$	5.82073	+	17.9144i	0.307206	+	0.945484i	−0.671638	+	0.740879i	$0.734409\pi$
$360$	−0.0762803	+	2.23477i	−0.00402032	+	0.117783i
$361$	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
$365$	0.231910	+	0.0842019i	0.0121387	+	0.00440733i
$366$	−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
$370$	−7.63640	−	0.260657i	−0.396998	−	0.0135509i
$371$	−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
$375$	10.2244	+	4.52335i	0.527988	+	0.233585i
$376$	−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	0.639272	−	0.768981i	$-0.279236\pi$
$379$	2.05336	+	1.49185i	0.105474	+	0.0766314i	−0.533798	+	0.845612i	$0.679236\pi$
$380$	3.27776	+	2.55672i	0.168145	+	0.131157i
$381$	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	0.266574	+	0.963814i	$0.414108\pi$
$383$	−14.3342	+	19.7293i	−0.732444	+	1.00812i	−0.999018	+	0.0443078i	$0.985892\pi$
$384$	0.309017	−	0.951057i	0.0157695	−	0.0485334i
$385$	−21.4950	−	31.8137i	−1.09549	−	1.62138i
$386$	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	−0.833885	−	0.551938i	$-0.813888\pi$
$389$	−11.1760	+	8.11983i	−0.566645	+	0.411692i	0.267240	+	0.963630i	$0.413888\pi$
$390$	1.82762	+	2.70497i	0.0925452	+	0.136971i
$391$	−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
$395$	22.2691	+	17.3703i	1.12048	+	0.873996i
$396$	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
$400$	−3.83527	−	3.20791i	−0.191764	−	0.160395i
$401$	8.40258	−	25.8605i	0.419605	−	1.29141i	−0.488462	−	0.872585i	$-0.662442\pi$
$401$	8.40258	−	25.8605i	0.419605	−	1.29141i	0.908067	−	0.418826i	$-0.137558\pi$
$402$			7.32216i			0.365196i
$403$	6.49536	−	4.88713i	0.323557	−	0.243445i
$404$	−10.0410			−0.499558
$405$	2.23477	+	0.0762803i	0.111046	+	0.00379040i
$406$	−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	$0.539234\pi$
$410$	−0.128241	−	0.0465618i	−0.00633338	−	0.00229952i
$411$	−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
$415$	−1.21621	+	35.6311i	−0.0597015	+	1.74906i
$416$	−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	−0.946108	−	0.323851i	$-0.895022\pi$
$419$	−7.59511	−	23.3753i	−0.371045	−	1.14196i	0.575063	−	0.818109i	$-0.304978\pi$
$420$	6.36295	+	4.96322i	0.310480	+	0.242181i
$421$	−9.02472	−	27.7752i	−0.439838	−	1.35368i	−0.888047	−	0.459753i	$-0.847938\pi$
$421$	−9.02472	−	27.7752i	−0.439838	−	1.35368i	0.448209	−	0.893929i	$-0.352062\pi$
$422$	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
$425$	32.5811	+	13.1040i	1.58041	+	0.635639i
$426$	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
$430$	−8.08675	+	22.2726i	−0.389977	+	1.07408i
$431$	−6.37766	−	19.6284i	−0.307201	−	0.945468i	−0.978847	−	0.204595i	$-0.934412\pi$
$431$	−6.37766	−	19.6284i	−0.307201	−	0.945468i	0.671645	−	0.740873i	$-0.265588\pi$
$432$	−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	$-0.217952\pi$
$443$	−1.39467	−	1.91960i	−0.0662629	−	0.0912031i	−0.840862	+	0.541249i	$0.817952\pi$
$444$	1.05594	−	3.24985i	0.0501127	−	0.154231i
$445$	10.5612	−	29.0879i	0.500650	−	1.37890i
$446$	−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	0.994133	−	0.108165i	$-0.0344975\pi$
$449$	2.67592	+	8.23565i	0.126285	+	0.388664i	−0.867848	+	0.496829i	$0.834497\pi$
$450$	−3.20791	+	3.83527i	−0.151222	+	0.180796i
$451$	−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
$455$	11.7744	+	0.401902i	0.551994	+	0.0188415i
$456$	−1.50401	+	1.09273i	−0.0704317	+	0.0511716i
$457$	−9.48548	−	13.0556i	−0.443712	−	0.610717i	0.527320	−	0.849667i	$-0.323197\pi$
$457$	−9.48548	−	13.0556i	−0.443712	−	0.610717i	−0.971032	+	0.238950i	$0.923197\pi$
$458$	−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	0.270354	−	0.962761i	$-0.412859\pi$
$461$	−12.0611	−	8.76292i	−0.561742	−	0.408130i	−0.832096	+	0.554631i	$0.812859\pi$
$462$	16.3302	−	5.30601i	0.759751	−	0.246858i
$463$	−34.5736	−	11.2336i	−1.60677	−	0.522072i	−0.638002	−	0.770035i	$-0.720239\pi$
$463$	−34.5736	−	11.2336i	−1.60677	−	0.522072i	−0.968769	+	0.247964i	$0.920239\pi$
$464$	−2.76135			−0.128192
$465$	9.94332	+	7.49203i	0.461110	+	0.347434i
$466$	21.0298			0.974187
$467$	−35.3724	−	11.4932i	−1.63684	−	0.531841i	−0.661009	−	0.750378i	$-0.729872\pi$
$467$	−35.3724	−	11.4932i	−1.63684	−	0.531841i	−0.975829	+	0.218537i	$0.929872\pi$
$468$	−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
$475$	2.26292	+	9.01563i	0.103830	+	0.413666i
$476$	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	−0.0287223	−	0.999587i	$-0.509144\pi$
$479$	19.9834	−	14.5188i	0.913066	−	0.663381i	0.941788	+	0.336206i	$0.109144\pi$
$480$	1.85280	−	1.25185i	0.0845684	−	0.0571389i
$481$	−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
$485$	17.3385	+	6.29527i	0.787301	+	0.285853i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−7.56882	−	10.4176i	−0.342976	−	0.472066i	0.602332	−	0.798246i	$-0.294238\pi$
$487$	−7.56882	−	10.4176i	−0.342976	−	0.472066i	−0.945308	+	0.326180i	$0.894238\pi$
$488$	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	−0.996909	−	0.0785631i	$-0.974967\pi$
$499$	−5.28459	−	16.2643i	−0.236571	−	0.728091i	0.760338	−	0.649527i	$-0.225033\pi$
$500$	−2.35032	−	10.9305i	−0.105109	−	0.488827i
$501$	−15.0955			−0.674419
$502$			9.01810i			0.402498i
$503$	16.6478	−	22.9137i	0.742289	−	1.02167i	−0.256195	−	0.966625i	$-0.582469\pi$
$503$	16.6478	−	22.9137i	0.742289	−	1.02167i	0.998484	−	0.0550480i	$-0.0175312\pi$
$504$	−2.91966	+	2.12126i	−0.130052	+	0.0944883i
$505$	−17.7036	−	13.8091i	−0.787798	−	0.614498i
$506$	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	−0.990913	−	0.134502i	$-0.957056\pi$
$509$	−6.05326	−	18.6300i	−0.268306	−	0.825761i	0.722607	−	0.691259i	$-0.242944\pi$
$510$	−9.65925	+	12.3833i	−0.427719	+	0.548344i
$511$	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
$515$	−0.873853	+	25.6011i	−0.0385066	+	1.12812i
$516$	−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
$520$	1.11412	−	3.06852i	0.0488573	−	0.134563i
$521$	−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	$-0.898314\pi$
$523$	−8.17216	+	11.2480i	−0.357343	+	0.491841i	0.592063	+	0.805892i	$0.298314\pi$
$524$	2.72918	+	8.39956i	0.119225	+	0.366936i
$525$	4.39289	+	17.5016i	0.191721	+	0.763832i
$526$	−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
$530$	−7.78635	+	5.26087i	−0.338217	+	0.228518i
$531$	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
$535$	10.1153	−	12.9680i	0.437324	−	0.560657i
$536$	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
$540$	−1.25185	−	1.85280i	−0.0538711	−	0.0797318i
$541$	−9.90951	+	7.19968i	−0.426043	+	0.309538i	−0.780065	−	0.625699i	$-0.784814\pi$
$541$	−9.90951	+	7.19968i	−0.426043	+	0.309538i	0.354022	+	0.935237i	$0.384814\pi$
$542$	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
$545$	−3.92004	+	2.64859i	−0.167916	+	0.113453i
$546$	−1.62814	+	5.01088i	−0.0696778	+	0.214446i
$547$	−7.19840	+	9.90775i	−0.307782	+	0.423625i	−0.934688	−	0.355470i	$-0.884321\pi$
$547$	−7.19840	+	9.90775i	−0.307782	+	0.423625i	0.626906	+	0.779095i	$0.284321\pi$
$548$	19.5346	+	6.34719i	0.834478	+	0.271138i
$549$	0.927103	−	0.673580i	0.0395678	−	0.0287477i
$550$	−22.0710	−	8.87692i	−0.941112	−	0.378513i
$551$	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
$555$	6.33119	−	4.27769i	0.268744	−	0.181578i
$556$	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
$560$	0.275288	−	8.06504i	0.0116330	−	0.340810i
$561$	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
$565$	−38.0743	−	13.8240i	−1.60180	−	0.581581i
$566$	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	0.579421	−	0.815028i	$-0.303279\pi$
$569$	−0.397530	−	0.288822i	−0.0166653	−	0.0121081i	−0.596087	+	0.802920i	$0.703279\pi$
$570$	−4.15456	−	0.141809i	−0.174015	−	0.00593974i
$571$	2.21668	+	6.82223i	0.0927651	+	0.285502i	0.986665	−	0.162765i	$-0.0520414\pi$
$571$	2.21668	+	6.82223i	0.0927651	+	0.285502i	−0.893900	+	0.448267i	$0.852041\pi$
$572$	−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
$575$	6.81192	+	2.73974i	0.284077	+	0.114255i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−16.1432	−	5.24526i	−0.672052	−	0.218363i	−0.0469398	−	0.998898i	$-0.514947\pi$
$577$	−16.1432	−	5.24526i	−0.672052	−	0.218363i	−0.625112	+	0.780535i	$0.714947\pi$
$578$	−19.0029	+	26.1553i	−0.790417	+	1.08792i
$579$	−8.41021	+	25.8840i	−0.349516	+	1.07570i
$580$	−4.86861	−	3.79761i	−0.202158	−	0.157687i
$581$	−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
$585$	−3.06852	−	1.11412i	−0.126868	−	0.0460631i
$586$	1.15348	+	3.55004i	0.0476497	+	0.146651i
$587$	5.44686	+	1.76979i	0.224816	+	0.0730471i	0.419259	−	0.907867i	$-0.362290\pi$
$587$	5.44686	+	1.76979i	0.224816	+	0.0730471i	−0.194443	+	0.980914i	$0.562290\pi$
$588$			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	$-0.882653\pi$
$593$	−7.35011	+	10.1166i	−0.301833	+	0.415437i	0.630980	+	0.775799i	$0.282653\pi$
$594$	−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	−0.822105	−	0.569336i	$-0.807200\pi$
$599$	4.34762	−	13.3806i	0.177639	−	0.546717i	0.999744	+	0.0226190i	$0.00720047\pi$
$600$	4.98836	+	0.340937i	0.203649	+	0.0139187i
$601$	4.53166	−	13.9470i	0.184850	−	0.568910i	−0.815096	−	0.579326i	$-0.803316\pi$
$601$	4.53166	−	13.9470i	0.184850	−	0.568910i	0.999946	+	0.0104163i	$0.00331567\pi$
$602$	−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
$605$	−21.5614	+	14.5681i	−0.876597	+	0.592275i
$606$	8.12334	−	5.90195i	0.329988	−	0.239750i
$607$	−41.1077	+	13.3567i	−1.66851	+	0.542132i	−0.982629	−	0.185582i	$-0.940583\pi$
$607$	−41.1077	+	13.3567i	−1.66851	+	0.542132i	−0.685881	+	0.727714i	$0.740583\pi$
$608$	1.76807	+	0.574481i	0.0717047	+	0.0232983i
$609$	8.06219	+	5.85753i	0.326697	+	0.237359i
$610$	−0.0874143	+	2.56096i	−0.00353930	+	0.103690i
$611$	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	−0.194130	−	0.980976i	$-0.562188\pi$
$613$	19.7779	−	27.2220i	0.798823	−	1.09949i	0.992953	−	0.118509i	$-0.0378116\pi$
$614$	−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	$-0.327628\pi$
$617$	35.6727	−	11.5908i	1.43613	−	0.466626i	0.920688	+	0.390299i	$0.127628\pi$
$618$	−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	$0.475578\pi$
$620$	0.216641	−	12.4480i	0.00870051	−	0.499924i
$621$	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
$630$	−8.06504	−	0.275288i	−0.321319	−	0.0109677i
$631$	35.6539	+	25.9041i	1.41936	+	1.03122i	0.991877	+	0.127200i	$0.0405990\pi$
$631$	35.6539	+	25.9041i	1.41936	+	1.03122i	0.427481	+	0.904024i	$0.359401\pi$
$632$	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
$635$	−12.0190	−	17.7887i	−0.476958	−	0.705921i
$636$	−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
$640$	−2.10182	−	0.763128i	−0.0830816	−	0.0301653i
$641$	6.84597	−	21.0697i	0.270400	−	0.832204i	−0.720001	−	0.693974i	$-0.755858\pi$
$641$	6.84597	−	21.0697i	0.270400	−	0.832204i	0.990400	−	0.138231i	$-0.0441415\pi$
$642$	4.32324	+	5.95042i	0.170625	+	0.234845i
$643$	−1.46975	−	2.02294i	−0.0579614	−	0.0797770i	0.779052	−	0.626959i	$-0.215701\pi$
$643$	−1.46975	−	2.02294i	−0.0579614	−	0.0797770i	−0.837014	+	0.547182i	$0.815701\pi$
$644$	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	0.106398	+	0.994324i	$0.466068\pi$
$647$	−22.1839	+	30.5335i	−0.872138	+	1.20040i	−0.978537	+	0.206072i	$0.933932\pi$
$648$	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	$-0.380818\pi$
$653$	2.92742	+	0.951175i	0.114559	+	0.0372224i	−0.251177	+	0.967941i	$0.580818\pi$
$654$	−0.653799	−	2.01219i	−0.0255655	−	0.0786827i
$655$	−6.73980	+	18.5629i	−0.263346	+	0.725311i
$656$	−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	−0.868019	−	0.496531i	$-0.834607\pi$
$659$	−17.0461	+	12.3847i	−0.664023	+	0.482441i	0.203996	+	0.978972i	$0.434607\pi$
$660$	6.54336	−	8.38871i	0.254700	−	0.326530i
$661$	−7.18228	+	22.1048i	−0.279358	+	0.859777i	0.708675	+	0.705535i	$0.249293\pi$
$661$	−7.18228	+	22.1048i	−0.279358	+	0.859777i	−0.988033	+	0.154241i	$0.950707\pi$
$662$	−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
$665$	−9.22692	+	11.8291i	−0.357805	+	0.458712i
$666$	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
$670$	16.3633	+	0.558536i	0.632170	+	0.0215781i
$671$	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	0.806730	+	0.590920i	$0.201235\pi$
$673$	29.0407	+	39.9710i	1.11944	+	1.54077i	0.312705	+	0.949850i	$0.398765\pi$
$674$	−10.8080	+	7.85244i	−0.416307	+	0.302465i
$675$	0.340937	−	4.98836i	0.0131227	−	0.192002i
$676$	−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
$680$	15.6959	+	0.535755i	0.601910	+	0.0205453i
$681$	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
$685$	25.7129	+	38.0564i	0.982440	+	1.45406i
$686$	−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
$690$	−2.01952	+	2.58906i	−0.0768817	+	0.0985638i
$691$	15.6437	−	11.3658i	0.595116	−	0.432377i	−0.249026	−	0.968497i	$-0.580110\pi$
$691$	15.6437	−	11.3658i	0.595116	−	0.432377i	0.844142	+	0.536120i	$0.180110\pi$
$692$	−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
$695$	40.5619	−	27.4058i	1.53860	−	1.03956i
$696$	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
$700$	11.5770	−	13.8411i	0.437570	−	0.523144i
$701$	−6.09569	+	18.7606i	−0.230231	+	0.708578i	0.767487	+	0.641064i	$0.221507\pi$
$701$	−6.09569	+	18.7606i	−0.230231	+	0.708578i	−0.997718	+	0.0675138i	$0.978493\pi$
$702$	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
$705$	6.65694	+	5.19254i	0.250715	+	0.195563i
$706$	−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	−0.266789	−	0.963755i	$-0.585963\pi$
$709$	−33.7050	−	24.4881i	−1.26582	−	0.919669i	−0.999028	+	0.0440857i	$0.985963\pi$
$710$	−0.870508	−	1.28840i	−0.0326696	−	0.0483526i
$711$	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
$715$	0.529855	−	15.5231i	0.0198155	−	0.580529i
$716$	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	$0.188016\pi$
$720$	−0.763128	+	2.10182i	−0.0284401	+	0.0783301i
$721$	−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
$725$	−3.36122	−	13.3914i	−0.124833	−	0.497342i
$726$	−3.59610	−	11.0676i	−0.133464	−	0.410759i
$727$	−4.36308	−	6.00526i	−0.161818	−	0.222723i	0.720407	−	0.693551i	$-0.243955\pi$
$727$	−4.36308	−	6.00526i	−0.161818	−	0.222723i	−0.882225	+	0.470829i	$0.843955\pi$
$728$	5.01088	−	1.62814i	0.185716	−	0.0603427i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	0.194540	+	0.151745i	0.00720024	+	0.00561633i
$731$	−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	0.119049	+	0.992888i	$0.462015\pi$
$733$	−23.3386	+	32.1229i	−0.862032	+	1.18649i	−0.981081	+	0.193597i	$0.937985\pi$
$734$	1.07775	−	3.31697i	0.0397804	−	0.122432i
$735$	−8.28484	+	10.6213i	−0.305591	+	0.391773i
$736$	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	$0.711522\pi$
$740$	−7.18210	−	2.60768i	−0.264019	−	0.0958601i
$741$	−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	0.612572	−	0.790415i	$-0.290135\pi$
$751$	1.37401	+	0.998277i	0.0501383	+	0.0364276i	−0.562434	+	0.826842i	$0.690135\pi$
$752$	−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
$755$	−12.7483	+	35.1115i	−0.463958	+	1.27784i
$756$	1.11521	−	3.43226i	0.0405598	−	0.124830i
$757$	8.10615	−	2.63385i	0.294623	−	0.0957288i	−0.157976	−	0.987443i	$-0.550497\pi$
$757$	8.10615	−	2.63385i	0.294623	−	0.0957288i	0.452599	+	0.891714i	$0.350497\pi$
$758$	1.49185	+	2.05336i	0.0541866	+	0.0745814i
$759$	2.15900	+	6.64471i	0.0783666	+	0.241188i
$760$	2.32726	+	3.44446i	0.0844187	+	0.124944i
$761$	−4.88155	+	3.54666i	−0.176956	+	0.128566i	−0.672738	−	0.739881i	$-0.734882\pi$
$761$	−4.88155	+	3.54666i	−0.176956	+	0.128566i	0.495781	+	0.868447i	$0.334882\pi$
$762$	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
$765$	0.535755	−	15.6959i	0.0193703	−	0.567486i
$766$	−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	$-0.675301\pi$
$773$	−40.2459	−	13.0767i	−1.44754	−	0.470336i	−0.924241	+	0.381810i	$0.875301\pi$
$774$	10.5968			0.380896
$775$	17.5014	−	21.6495i	0.628669	−	0.777673i
$776$	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
$785$	−0.243073	+	7.12127i	−0.00867566	+	0.254169i
$786$	−7.14509	−	5.19121i	−0.254857	−	0.185164i
$787$	22.0525	+	7.16529i	0.786087	+	0.255415i	0.674437	−	0.738332i	$-0.264386\pi$
$787$	22.0525	+	7.16529i	0.786087	+	0.255415i	0.111650	+	0.993748i	$0.464386\pi$
$788$	1.46021	−	0.474453i	0.0520180	−	0.0169017i
$789$	14.2214	−	10.3324i	0.506295	−	0.367845i
$790$	15.8114	+	23.4017i	0.562546	+	0.832595i
$791$	−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
$795$	3.20702	−	8.83283i	0.113741	−	0.313268i
$796$	−0.937390	+	2.88499i	−0.0332249	+	0.102256i
$797$	22.1383	+	30.4707i	0.784178	+	1.07933i	0.994809	+	0.101763i	$0.0324483\pi$
$797$	22.1383	+	30.4707i	0.784178	+	1.07933i	−0.210631	+	0.977566i	$0.567552\pi$
$798$	−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	0.883952	−	0.467578i	$-0.154873\pi$
$809$	−3.01539	−	9.28042i	−0.106015	−	0.326282i	−0.989967	+	0.141296i	$0.954873\pi$
$810$	2.10182	+	0.763128i	0.0738503	+	0.0268136i
$811$	−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
$815$	−15.5756	+	19.9683i	−0.545591	+	0.699458i
$816$	−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
$820$	−0.107576	−	0.0839117i	−0.00375673	−	0.00293032i
$821$	−2.49192	−	7.66935i	−0.0869688	−	0.267662i	0.898109	−	0.439773i	$-0.144941\pi$
$821$	−2.49192	−	7.66935i	−0.0869688	−	0.267662i	−0.985078	+	0.172111i	$0.944941\pi$
$822$	−19.5346	+	6.34719i	−0.681348	+	0.221384i
$823$	−8.23342	−	11.3323i	−0.286999	−	0.395020i	0.641037	−	0.767510i	$-0.278504\pi$
$823$	−8.23342	−	11.3323i	−0.286999	−	0.395020i	−0.928036	+	0.372489i	$0.878504\pi$
$824$	3.54004	+	10.8951i	0.123323	+	0.379550i
$825$	23.0736	−	5.79145i	0.803318	−	0.201632i
$826$	−33.9039	−	24.6326i	−1.17967	−	0.857078i
$827$	33.7356	+	10.9614i	1.17310	+	0.381164i	0.829800	−	0.558061i	$-0.188455\pi$
$827$	33.7356	+	10.9614i	1.17310	+	0.381164i	0.343302	+	0.939225i	$0.388455\pi$
$828$	−0.863131	−	1.18800i	−0.0299959	−	0.0412858i
$829$	26.0371	−	18.9170i	0.904304	−	0.657015i	−0.0352637	−	0.999378i	$-0.511227\pi$
$829$	26.0371	−	18.9170i	0.904304	−	0.657015i	0.939568	+	0.342363i	$0.111227\pi$
$830$	−12.1673	+	33.5114i	−0.422333	+	1.16320i
$831$	−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
$835$	−1.15149	+	33.7350i	−0.0398490	+	1.16745i
$836$	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	−0.932010	−	0.362432i	$-0.881947\pi$
$839$	1.01478	−	3.12316i	0.0350340	−	0.107823i	0.967044	+	0.254608i	$0.0819466\pi$
$840$	4.51780	+	6.68657i	0.155879	+	0.230708i
$841$	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
$845$	−19.1627	−	14.9473i	−0.659217	−	0.514203i
$846$	−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
$850$	26.9371	+	22.5308i	0.923934	+	0.772799i
$851$	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	$-0.203182\pi$
$853$	52.6602	−	17.1103i	1.80305	−	0.585847i	0.999950	+	0.00999739i	$0.00318232\pi$
$854$	−3.34582	+	2.43088i	−0.114492	+	0.0831830i
$855$	3.44446	−	2.32726i	0.117798	−	0.0795907i
$856$	2.27286	−	6.99514i	0.0776848	−	0.239089i
$857$	−21.2293	+	29.2196i	−0.725179	+	0.998123i	0.274157	+	0.961685i	$0.411601\pi$
$857$	−21.2293	+	29.2196i	−0.725179	+	0.998123i	−0.999336	+	0.0364380i	$0.988399\pi$
$858$	6.60620	+	2.14648i	0.225532	+	0.0732797i
$859$	18.2241	−	13.2406i	0.621797	−	0.451762i	−0.231752	−	0.972775i	$-0.574446\pi$
$859$	18.2241	−	13.2406i	0.621797	−	0.451762i	0.853549	+	0.521013i	$0.174446\pi$
$860$	−14.5736	+	18.6836i	−0.496955	+	0.637105i
$861$	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
$865$	−9.44974	−	13.9861i	−0.321301	−	0.475541i
$866$	−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
$870$	6.17097	+	0.210636i	0.209215	+	0.00714124i
$871$	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
$875$	39.4471	−	8.48205i	1.33355	−	0.286746i
$876$	−0.0892652	+	0.0648550i	−0.00301599	+	0.00219125i
$877$	19.9736	+	27.4913i	0.674461	+	0.928316i	0.999851	−	0.0172637i	$-0.00549549\pi$
$877$	19.9736	+	27.4913i	0.674461	+	0.928316i	−0.325390	+	0.945580i	$0.605495\pi$
$878$	0.0846661	+	0.0275097i	0.00285734	+	0.000928407i
$879$	−3.01984	−	2.19404i	−0.101857	−	0.0740033i
$880$	−10.6327	−	0.362931i	−0.358428	−	0.0122344i
$881$	6.74982	+	20.7738i	0.227407	+	0.699888i	0.998038	+	0.0626061i	$0.0199412\pi$
$881$	6.74982	+	20.7738i	0.227407	+	0.699888i	−0.770631	+	0.637282i	$0.780059\pi$
$882$	−3.54090	−	4.87363i	−0.119228	−	0.164104i
$883$	−2.27348	+	0.738699i	−0.0765087	+	0.0248592i	−0.347021	−	0.937857i	$-0.612807\pi$
$883$	−2.27348	+	0.738699i	−0.0765087	+	0.0248592i	0.270513	+	0.962716i	$0.412807\pi$
$884$	3.16862	+	9.75201i	0.106572	+	0.327996i
$885$	15.9701	−	20.4739i	0.536828	−	0.688223i
$886$	−0.733223	−	2.25663i	−0.0246331	−	0.0758129i
$887$	18.2323	+	5.92403i	0.612180	+	0.198909i	0.598665	−	0.800999i	$-0.295698\pi$
$887$	18.2323	+	5.92403i	0.612180	+	0.198909i	0.0135148	+	0.999909i	$0.495698\pi$
$888$	2.00852	−	2.76448i	0.0674014	−	0.0927700i
$889$	10.7071	−	32.9530i	0.359104	−	1.10521i
$890$	19.0330	−	24.4006i	0.637986	−	0.817910i
$891$	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
$895$	−17.6566	+	48.6300i	−0.590194	+	1.62552i
$896$	−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	$-0.304737\pi$
$907$	−11.4403	−	15.7463i	−0.379870	−	0.522846i	−0.955550	+	0.294829i	$0.904737\pi$
$908$	−2.69061	−	3.70330i	−0.0892910	−	0.122898i
$909$	−3.10284	+	9.54955i	−0.102915	+	0.316739i
$910$	11.0740	+	4.02073i	0.367098	+	0.133286i
$911$	10.2766	−	31.6282i	0.340480	−	1.04789i	−0.623480	−	0.781840i	$-0.714282\pi$
$911$	10.2766	−	31.6282i	0.340480	−	1.04789i	0.963959	−	0.266049i	$-0.0857184\pi$
$912$	−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
$915$	−1.43457	−	2.12324i	−0.0474256	−	0.0701922i
$916$	−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	0.961958	−	0.273199i	$-0.0880818\pi$
$919$	30.2965	+	22.0117i	0.999391	+	0.726100i	0.0374334	+	0.999299i	$0.488082\pi$
$920$	3.28164	+	0.112013i	0.108192	+	0.00369298i
$921$	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	$0.699288\pi$
$930$	7.14149	+	10.1980i	0.234179	+	0.334405i
$931$	−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	$-0.686491\pi$
$937$	12.5618	−	17.2899i	0.410377	−	0.564836i	0.963310	+	0.268390i	$0.0864915\pi$
$938$	15.5322	+	21.3782i	0.507144	+	0.698023i
$939$	−15.3339	+	11.1407i	−0.500402	+	0.363563i
$940$	0.288007	−	8.43768i	0.00939375	−	0.275207i
$941$	29.9894	+	21.7886i	0.977628	+	0.710288i	0.957177	−	0.289503i	$-0.0934899\pi$
$941$	29.9894	+	21.7886i	0.977628	+	0.710288i	0.0204506	+	0.999791i	$0.493490\pi$
$942$	−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
$945$	6.68657	−	4.51780i	0.217514	−	0.146964i
$946$	15.5801	+	47.9506i	0.506553	+	1.55901i
$947$	−2.50403	−	3.44650i	−0.0813700	−	0.111996i	0.766392	−	0.642374i	$-0.222050\pi$
$947$	−2.50403	−	3.44650i	−0.0813700	−	0.111996i	−0.847762	+	0.530377i	$0.822050\pi$
$948$	−12.0123	+	3.90302i	−0.390140	+	0.126764i
$949$	−0.0497784	+	0.153202i	−0.00161587	+	0.00497315i
$950$	−0.633822	+	9.27366i	−0.0205639	+	0.300877i
$951$	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	$-0.265229\pi$
$953$	−7.38490	−	10.1644i	−0.239220	−	0.329258i	−0.911700	+	0.410857i	$0.865229\pi$
$954$	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
$965$	57.2031	+	20.7693i	1.84143	+	0.668587i
$966$	−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
$970$	14.5446	+	11.3450i	0.466998	+	0.364268i
$971$	0.725131	−	2.23172i	0.0232706	−	0.0716194i	−0.938747	−	0.344608i	$-0.888012\pi$
$971$	0.725131	−	2.23172i	0.0232706	−	0.0716194i	0.962017	+	0.272988i	$0.0880120\pi$
$972$	−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
$975$	−2.72386	+	6.77244i	−0.0872333	+	0.216892i
$976$	0.354122	+	1.08988i	0.0113352	+	0.0348861i
$977$	−19.6638	+	6.38915i	−0.629100	+	0.204407i	−0.606176	−	0.795330i	$-0.707297\pi$
$977$	−19.6638	+	6.38915i	−0.629100	+	0.204407i	−0.0229237	+	0.999737i	$0.507297\pi$
$978$	−6.65695	−	9.16250i	−0.212866	−	0.292985i
$979$	−20.3475	−	62.6231i	−0.650308	−	2.00144i
$980$	13.4625	+	0.459523i	0.430045	+	0.0146789i
$981$	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	$-0.388697\pi$
$983$	−20.5920	−	28.3425i	−0.656784	−	0.903985i	−0.999370	+	0.0355014i	$0.988697\pi$
$984$	0.0493617	−	0.0358634i	0.00157359	−	0.00114328i
$985$	3.22705	+	1.17168i	0.102822	+	0.0373327i
$986$	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
$990$	−0.362931	+	10.6327i	−0.0115347	+	0.337929i
$991$	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
$995$	−5.62039	+	3.79744i	−0.178178	+	0.120387i
$996$	−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.349.7	yes	32
5.4	even	2	inner	930.2.z.c.349.2	✓	32
31.4	even	5	inner	930.2.z.c.469.4	yes	32
155.4	even	10	inner	930.2.z.c.469.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.c.349.2	✓	32	5.4	even	2	inner
930.2.z.c.349.7	yes	32	1.1	even	1	trivial
930.2.z.c.469.4	yes	32	31.4	even	5	inner
930.2.z.c.469.5	yes	32	155.4	even	10	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} +(-0.0762803 + 2.23477i) 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} +(-1.25185 - 1.85280i) 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} +(-0.763128 + 2.10182i) 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} +(-7.58524 - 2.75405i) q^{35} +1.00000 q^{36} +3.41709i q^{37} +(1.09273 - 1.50401i) q^{38} +(1.18111 - 0.858129i) q^{39} +(-1.37527 + 1.76313i) 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} +(1.76313 + 1.37527i) 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} +(-4.84957 + 1.21724i) 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} +(-3.63085 + 10.0001i) q^{55} -3.60890 q^{56} +1.85906i q^{57} +(-1.62308 + 2.23398i) q^{58} +(3.58839 + 11.0439i) q^{59} +(0.0762803 - 2.23477i) q^{60} +1.14596 q^{61} +(-5.56699 + 0.0930792i) q^{62} +3.60890i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-1.82762 - 2.70497i) q^{65} +(-3.84919 - 2.79660i) q^{66} -7.32216i q^{67} -7.02351i q^{68} +(1.18800 + 0.863131i) q^{69} +(-6.36295 - 4.96322i) 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} +(3.20791 - 3.83527i) 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} +(-1.85280 + 1.25185i) 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} +(9.65925 - 12.3833i) q^{85} +(8.57303 + 6.22867i) q^{86} -2.76135i q^{87} +4.75786i q^{88} +(-11.1963 - 8.13458i) q^{89} +(1.25185 + 1.85280i) q^{90} +(1.62814 - 5.01088i) q^{91} -1.46845i q^{92} +(4.44908 - 3.34750i) q^{93} -3.77564 q^{94} +(4.15456 + 0.141809i) 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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