LMFDB - Embedded newform 925.2.bc.e.49.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, not 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:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.460177 - 0.548417i) q^{2} +(-0.215129 + 0.256381i) q^{3} +(0.258298 - 1.46488i) q^{4} +0.239601 q^{6} +(0.0206430 + 0.0567163i) q^{7} +(-2.16222 + 1.24836i) q^{8} +(0.501494 + 2.84411i) q^{9} +O(q^{10})$	\(q+(-0.460177 - 0.548417i) q^{2} +(-0.215129 + 0.256381i) q^{3} +(0.258298 - 1.46488i) q^{4} +0.239601 q^{6} +(0.0206430 + 0.0567163i) q^{7} +(-2.16222 + 1.24836i) q^{8} +(0.501494 + 2.84411i) q^{9} +(1.73809 + 3.01046i) q^{11} +(0.319999 + 0.381360i) q^{12} +(-3.02686 - 0.533718i) q^{13} +(0.0216047 - 0.0374205i) q^{14} +(-1.11592 - 0.406162i) q^{16} +(-3.48582 + 0.614644i) q^{17} +(1.32898 - 1.58382i) q^{18} +(-5.83847 - 4.89905i) q^{19} +(-0.0189819 - 0.00690884i) q^{21} +(0.851159 - 2.33854i) q^{22} +(-5.84284 - 3.37337i) q^{23} +(0.145101 - 0.822908i) q^{24} +(1.10019 + 1.90559i) q^{26} +(-1.70659 - 0.985300i) q^{27} +(0.0884145 - 0.0155899i) q^{28} +(-1.24236 - 2.15183i) q^{29} +1.50902 q^{31} +(1.99863 + 5.49118i) q^{32} +(-1.14574 - 0.202024i) q^{33} +(1.94117 + 1.62884i) q^{34} +4.29581 q^{36} +(-3.10210 + 5.23230i) q^{37} +5.45634i q^{38} +(0.788001 - 0.661211i) q^{39} +(-1.64311 + 9.31852i) q^{41} +(0.00494609 + 0.0135893i) q^{42} +5.05642i q^{43} +(4.85890 - 1.76849i) q^{44} +(0.838727 + 4.75666i) q^{46} +(-4.33077 - 2.50037i) q^{47} +(0.344199 - 0.198723i) q^{48} +(5.35952 - 4.49717i) q^{49} +(0.592318 - 1.02592i) q^{51} +(-1.56366 + 4.29613i) q^{52} +(-2.74519 + 7.54236i) q^{53} +(0.244977 + 1.38933i) q^{54} +(-0.115437 - 0.0968630i) q^{56} +(2.51205 - 0.442942i) q^{57} +(-0.608395 + 1.67155i) q^{58} +(-5.83358 - 2.12325i) q^{59} +(0.496944 - 2.81831i) q^{61} +(-0.694417 - 0.827574i) q^{62} +(-0.150955 + 0.0871540i) q^{63} +(0.904198 - 1.56612i) q^{64} +(0.416448 + 0.721309i) q^{66} +(1.59441 + 4.38060i) q^{67} +5.26506i q^{68} +(2.12183 - 0.772283i) q^{69} +(6.80358 + 5.70888i) q^{71} +(-4.63480 - 5.52354i) q^{72} -15.3830i q^{73} +(4.29700 - 0.706537i) q^{74} +(-8.68458 + 7.28723i) q^{76} +(-0.134863 + 0.160723i) q^{77} +(-0.725239 - 0.127879i) q^{78} +(-12.1576 + 4.42500i) q^{79} +(-7.52172 + 2.73768i) q^{81} +(5.86655 - 3.38706i) q^{82} +(15.7395 - 2.77529i) q^{83} +(-0.0150236 + 0.0260216i) q^{84} +(2.77303 - 2.32685i) q^{86} +(0.818955 + 0.144404i) q^{87} +(-7.51625 - 4.33951i) q^{88} +(0.826615 + 0.300863i) q^{89} +(-0.0322132 - 0.182690i) q^{91} +(-6.45076 + 7.68772i) q^{92} +(-0.324635 + 0.386884i) q^{93} +(0.621672 + 3.52568i) q^{94} +(-1.83779 - 0.668903i) q^{96} +(-10.5174 - 6.07223i) q^{97} +(-4.93265 - 0.869760i) q^{98} +(-7.69045 + 6.45305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

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 $

$2$	−0.460177	−	0.548417i	−0.325394	−	0.387789i	0.578403	−	0.815751i	$-0.303676\pi$
$2$	−0.460177	−	0.548417i	−0.325394	−	0.387789i	−0.903797	+	0.427962i	$0.859232\pi$
$3$	−0.215129	+	0.256381i	−0.124205	+	0.148021i	−0.824563	−	0.565770i	$-0.808579\pi$
$3$	−0.215129	+	0.256381i	−0.124205	+	0.148021i	0.700358	+	0.713791i	$0.253024\pi$
$4$	0.258298	−	1.46488i	0.129149	−	0.732439i
$5$		0			0
$5$		0			0
$6$	0.239601			0.0978167
$7$	0.0206430	+	0.0567163i	0.00780234	+	0.0214367i	0.943533	−	0.331280i	$-0.107480\pi$
$7$	0.0206430	+	0.0567163i	0.00780234	+	0.0214367i	−0.935730	+	0.352716i	$0.885258\pi$
$8$	−2.16222	+	1.24836i	−0.764459	+	0.441360i
$9$	0.501494	+	2.84411i	0.167165	+	0.948038i
$10$		0			0
$11$	1.73809	+	3.01046i	0.524054	+	0.907688i	0.999608	+	0.0280011i	$0.00891420\pi$
$11$	1.73809	+	3.01046i	0.524054	+	0.907688i	−0.475554	+	0.879686i	$0.657752\pi$
$12$	0.319999	+	0.381360i	0.0923758	+	0.110089i
$13$	−3.02686	−	0.533718i	−0.839501	−	0.148027i	−0.262665	−	0.964887i	$-0.584601\pi$
$13$	−3.02686	−	0.533718i	−0.839501	−	0.148027i	−0.576835	+	0.816860i	$0.695713\pi$
$14$	0.0216047	−	0.0374205i	0.00577411	−	0.0100011i
$15$		0			0
$16$	−1.11592	−	0.406162i	−0.278980	−	0.101540i
$17$	−3.48582	+	0.614644i	−0.845435	+	0.149073i	−0.579555	−	0.814933i	$-0.696774\pi$
$17$	−3.48582	+	0.614644i	−0.845435	+	0.149073i	−0.265880	+	0.964006i	$0.585662\pi$
$18$	1.32898	−	1.58382i	0.313245	−	0.373311i
$19$	−5.83847	−	4.89905i	−1.33944	−	1.12392i	−0.981770	−	0.190070i	$-0.939128\pi$
$19$	−5.83847	−	4.89905i	−1.33944	−	1.12392i	−0.357665	−	0.933850i	$-0.616427\pi$
$20$		0			0
$21$	−0.0189819	−	0.00690884i	−0.00414219	−	0.00150763i
$22$	0.851159	−	2.33854i	0.181468	−	0.498579i
$23$	−5.84284	−	3.37337i	−1.21832	−	0.703395i	−0.253759	−	0.967268i	$-0.581667\pi$
$23$	−5.84284	−	3.37337i	−1.21832	−	0.703395i	−0.964558	+	0.263872i	$0.915000\pi$
$24$	0.145101	−	0.822908i	0.0296186	−	0.167975i
$25$		0			0
$26$	1.10019	+	1.90559i	0.215765	+	0.373716i
$27$	−1.70659	−	0.985300i	−0.328433	−	0.189621i
$28$	0.0884145	−	0.0155899i	0.0167088	−	0.00294621i
$29$	−1.24236	−	2.15183i	−0.230700	−	0.399585i	0.727314	−	0.686305i	$-0.240768\pi$
$29$	−1.24236	−	2.15183i	−0.230700	−	0.399585i	−0.958014	+	0.286720i	$0.907435\pi$
$30$		0			0
$31$	1.50902			0.271028			0.135514	−	0.990775i	$-0.456731\pi$
$31$	1.50902			0.271028			0.135514	+	0.990775i	$0.456731\pi$
$32$	1.99863	+	5.49118i	0.353310	+	0.970712i
$33$	−1.14574	−	0.202024i	−0.199447	−	0.0351679i
$34$	1.94117	+	1.62884i	0.332908	+	0.279343i
$35$		0			0
$36$	4.29581			0.715969
$37$	−3.10210	+	5.23230i	−0.509982	+	0.860185i
$37$	−3.10210	+	5.23230i	−0.509982	+	0.860185i
$38$			5.45634i			0.885136i
$39$	0.788001	−	0.661211i	0.126181	−	0.105879i
$40$		0			0
$41$	−1.64311	+	9.31852i	−0.256610	+	1.45531i	0.535296	+	0.844665i	$0.320200\pi$
$41$	−1.64311	+	9.31852i	−0.256610	+	1.45531i	−0.791906	+	0.610643i	$0.790911\pi$
$42$	0.00494609	+	0.0135893i	0.000763199	+	0.00209687i
$43$			5.05642i			0.771097i	0.922688	+	0.385548i	$0.125988\pi$
$43$			5.05642i			0.771097i	−0.922688	+	0.385548i	$0.874012\pi$
$44$	4.85890	−	1.76849i	0.732507	−	0.266611i
$45$		0			0
$46$	0.838727	+	4.75666i	0.123664	+	0.701331i
$47$	−4.33077	−	2.50037i	−0.631707	−	0.364716i	0.149706	−	0.988731i	$-0.452167\pi$
$47$	−4.33077	−	2.50037i	−0.631707	−	0.364716i	−0.781413	+	0.624014i	$0.785501\pi$
$48$	0.344199	−	0.198723i	0.0496808	−	0.0286832i
$49$	5.35952	−	4.49717i	0.765646	−	0.642453i
$50$		0			0
$51$	0.592318	−	1.02592i	0.0829410	−	0.143658i
$52$	−1.56366	+	4.29613i	−0.216841	+	0.595766i
$53$	−2.74519	+	7.54236i	−0.377081	+	1.03602i	0.595479	+	0.803371i	$0.296962\pi$
$53$	−2.74519	+	7.54236i	−0.377081	+	1.03602i	−0.972560	+	0.232651i	$0.925260\pi$
$54$	0.244977	+	1.38933i	0.0333372	+	0.189065i
$55$		0			0
$56$	−0.115437	−	0.0968630i	−0.0154259	−	0.0129439i
$57$	2.51205	−	0.442942i	0.332729	−	0.0586690i
$58$	−0.608395	+	1.67155i	−0.0798862	+	0.219486i
$59$	−5.83358	−	2.12325i	−0.759467	−	0.276423i	−0.0668831	−	0.997761i	$-0.521305\pi$
$59$	−5.83358	−	2.12325i	−0.759467	−	0.276423i	−0.692584	+	0.721337i	$0.743528\pi$
$60$		0			0
$61$	0.496944	−	2.81831i	0.0636272	−	0.360848i	−0.936326	−	0.351133i	$-0.885797\pi$
$61$	0.496944	−	2.81831i	0.0636272	−	0.360848i	0.999953	−	0.00971480i	$-0.00309237\pi$
$62$	−0.694417	−	0.827574i	−0.0881910	−	0.105102i
$63$	−0.150955	+	0.0871540i	−0.0190186	+	0.0109804i
$64$	0.904198	−	1.56612i	0.113025	−	0.195765i
$65$		0			0
$66$	0.416448	+	0.721309i	0.0512612	+	0.0887870i
$67$	1.59441	+	4.38060i	0.194788	+	0.535175i	0.998182	−	0.0602725i	$-0.0191970\pi$
$67$	1.59441	+	4.38060i	0.194788	+	0.535175i	−0.803394	+	0.595448i	$0.796975\pi$
$68$			5.26506i			0.638482i
$69$	2.12183	−	0.772283i	0.255438	−	0.0929720i
$70$		0			0
$71$	6.80358	+	5.70888i	0.807436	+	0.677520i	0.949994	−	0.312267i	$-0.101088\pi$
$71$	6.80358	+	5.70888i	0.807436	+	0.677520i	−0.142558	+	0.989786i	$0.545533\pi$
$72$	−4.63480	−	5.52354i	−0.546217	−	0.650956i
$73$		−	15.3830i		−	1.80044i	−0.435433	−	0.900221i	$-0.643405\pi$
$73$		−	15.3830i		−	1.80044i	0.435433	−	0.900221i	$-0.356595\pi$
$74$	4.29700	−	0.706537i	0.499516	−	0.0821332i
$75$		0			0
$76$	−8.68458	+	7.28723i	−0.996189	+	0.835902i
$77$	−0.134863	+	0.160723i	−0.0153690	+	0.0183161i
$78$	−0.725239	−	0.127879i	−0.0821172	−	0.0144795i
$79$	−12.1576	+	4.42500i	−1.36784	+	0.497851i	−0.918468	−	0.395495i	$-0.870573\pi$
$79$	−12.1576	+	4.42500i	−1.36784	+	0.497851i	−0.449368	+	0.893347i	$0.648351\pi$
$80$		0			0
$81$	−7.52172	+	2.73768i	−0.835746	+	0.304187i
$82$	5.86655	−	3.38706i	0.647852	−	0.374038i
$83$	15.7395	−	2.77529i	1.72763	−	0.304628i	0.780423	−	0.625252i	$-0.215004\pi$
$83$	15.7395	−	2.77529i	1.72763	−	0.304628i	0.947207	+	0.320624i	$0.103893\pi$
$84$	−0.0150236	+	0.0260216i	−0.00163921	+	0.00283919i
$85$		0			0
$86$	2.77303	−	2.32685i	0.299023	−	0.250910i
$87$	0.818955	+	0.144404i	0.0878012	+	0.0154817i
$88$	−7.51625	−	4.33951i	−0.801235	−	0.462593i
$89$	0.826615	+	0.300863i	0.0876210	+	0.0318914i	0.385459	−	0.922725i	$-0.374043\pi$
$89$	0.826615	+	0.300863i	0.0876210	+	0.0318914i	−0.297838	+	0.954617i	$0.596265\pi$
$90$		0			0
$91$	−0.0322132	−	0.182690i	−0.00337686	−	0.0191511i
$92$	−6.45076	+	7.68772i	−0.672538	+	0.801500i
$93$	−0.324635	+	0.386884i	−0.0336630	+	0.0401180i
$94$	0.621672	+	3.52568i	0.0641206	+	0.363646i
$95$		0			0
$96$	−1.83779	−	0.668903i	−0.187569	−	0.0682696i
$97$	−10.5174	−	6.07223i	−1.06788	−	0.616542i	−0.140280	−	0.990112i	$-0.544800\pi$
$97$	−10.5174	−	6.07223i	−1.06788	−	0.616542i	−0.927602	+	0.373570i	$0.878133\pi$
$98$	−4.93265	−	0.869760i	−0.498273	−	0.0878590i
$99$	−7.69045	+	6.45305i	−0.772919	+	0.648556i
$100$		0			0
$101$	4.85139	−	8.40286i	0.482732	−	0.836116i	−0.517072	−	0.855942i	$-0.672978\pi$
$101$	4.85139	−	8.40286i	0.482732	−	0.836116i	0.999803	+	0.0198263i	$0.00631131\pi$
$102$	−0.835205	+	0.147269i	−0.0826976	+	0.0145818i
$103$	1.41712	−	0.818177i	0.139633	−	0.0806174i	−0.428556	−	0.903515i	$-0.640977\pi$
$103$	1.41712	−	0.818177i	0.139633	−	0.0806174i	0.568189	+	0.822898i	$0.307644\pi$
$104$	7.21100	−	2.62459i	0.707096	−	0.257362i
$105$		0			0
$106$	5.39963	−	1.96531i	0.524459	−	0.190887i
$107$	7.32061	+	1.29082i	0.707710	+	0.124788i	0.515907	−	0.856645i	$-0.327455\pi$
$107$	7.32061	+	1.29082i	0.707710	+	0.124788i	0.191804	+	0.981433i	$0.438566\pi$
$108$	−1.88415	+	2.24544i	−0.181303	+	0.216068i
$109$	−10.8390	+	9.09498i	−1.03819	+	0.871141i	−0.991802	−	0.127783i	$-0.959214\pi$
$109$	−10.8390	+	9.09498i	−1.03819	+	0.871141i	−0.0463834	+	0.998924i	$0.514770\pi$
$110$		0			0
$111$	−0.674109	−	1.92094i	−0.0639836	−	0.182327i
$112$		−	0.0716753i		−	0.00677268i
$113$	8.32103	+	9.91662i	0.782777	+	0.932877i	0.999055	−	0.0434548i	$-0.0138364\pi$
$113$	8.32103	+	9.91662i	0.782777	+	0.932877i	−0.216279	+	0.976332i	$0.569392\pi$
$114$	−1.39890	−	1.17382i	−0.131019	−	0.109938i
$115$		0			0
$116$	−3.47306	+	1.26409i	−0.322466	+	0.117368i
$117$		−	8.87640i		−	0.820623i
$118$	1.52005	+	4.17630i	0.139932	+	0.384460i
$119$	−0.106818	−	0.185015i	−0.00979201	−	0.0169603i
$120$		0			0
$121$	−0.541909	+	0.938614i	−0.0492644	+	0.0853285i
$122$	−1.77429	+	1.02439i	−0.160637	+	0.0927437i
$123$	−2.03561	−	2.42594i	−0.183545	−	0.218740i
$124$	0.389777	−	2.21053i	0.0350030	−	0.198512i
$125$		0			0
$126$	0.117263	+	0.0426802i	0.0104466	+	0.00380225i
$127$	0.0139160	−	0.0382339i	0.00123484	−	0.00339271i	−0.939074	−	0.343716i	$-0.888314\pi$
$127$	0.0139160	−	0.0382339i	0.00123484	−	0.00339271i	0.940309	+	0.340323i	$0.110536\pi$
$128$	10.2346	−	1.80464i	0.904624	−	0.159510i
$129$	−1.29637	−	1.08778i	−0.114139	−	0.0957739i
$130$		0			0
$131$	−0.361771	−	2.05171i	−0.0316081	−	0.179258i	0.964917	−	0.262557i	$-0.0845657\pi$
$131$	−0.361771	−	2.05171i	−0.0316081	−	0.179258i	−0.996525	+	0.0832983i	$0.973455\pi$
$132$	−0.591882	+	1.62618i	−0.0515167	+	0.141541i
$133$	0.157333	−	0.432268i	0.0136425	−	0.0374824i
$134$	1.66869	−	2.89025i	0.144153	−	0.249679i
$135$		0			0
$136$	6.76979	−	5.68053i	0.580505	−	0.487102i
$137$	−2.41242	+	1.39281i	−0.206107	+	0.118996i	−0.599501	−	0.800374i	$-0.704634\pi$
$137$	−2.41242	+	1.39281i	−0.206107	+	0.118996i	0.393394	+	0.919370i	$0.371301\pi$
$138$	−1.39995	−	0.808262i	−0.119172	−	0.0688038i
$139$	2.95426	+	16.7544i	0.250577	+	1.42109i	0.807176	+	0.590311i	$0.200995\pi$
$139$	2.95426	+	16.7544i	0.250577	+	1.42109i	−0.556599	+	0.830781i	$0.687894\pi$
$140$		0			0
$141$	1.57272	−	0.572423i	0.132447	−	0.0482067i
$142$		−	6.35829i		−	0.533576i
$143$	−3.65422	−	10.0399i	−0.305581	−	0.839578i
$144$	0.595543	−	3.37749i	0.0496286	−	0.281458i
$145$		0			0
$146$	−8.43629	+	7.07889i	−0.698192	+	0.585853i
$147$			2.34155i			0.193128i
$148$	6.86342	+	5.89569i	0.564169	+	0.484623i
$149$	−8.52537			−0.698425			−0.349213	−	0.937044i	$-0.613551\pi$
$149$	−8.52537			−0.698425			−0.349213	+	0.937044i	$0.613551\pi$
$150$		0			0
$151$	−8.18915	−	6.87151i	−0.666424	−	0.559196i	0.245581	−	0.969376i	$-0.421021\pi$
$151$	−8.18915	−	6.87151i	−0.666424	−	0.559196i	−0.912004	+	0.410180i	$0.865466\pi$
$152$	18.7398	+	3.30433i	1.52000	+	0.268016i
$153$	−3.49623	−	9.60582i	−0.282654	−	0.776584i
$154$	0.150204			0.0121038
$155$		0			0
$156$	−0.765055	−	1.32511i	−0.0612534	−	0.106094i
$157$	5.22063	−	0.920537i	0.416651	−	0.0734669i	0.0386072	−	0.999254i	$-0.487708\pi$
$157$	5.22063	−	0.920537i	0.416651	−	0.0734669i	0.378044	+	0.925788i	$0.376597\pi$
$158$	8.02138	+	4.63115i	0.638147	+	0.368434i
$159$	−1.34314	−	2.32639i	−0.106518	−	0.184495i
$160$		0			0
$161$	0.0707108	−	0.401021i	0.00557279	−	0.0316049i
$162$	4.96271	+	2.86522i	0.389907	+	0.225113i
$163$	2.55533	−	7.02070i	0.200149	−	0.549904i	−0.798493	−	0.602004i	$-0.794369\pi$
$163$	2.55533	−	7.02070i	0.200149	−	0.549904i	0.998642	+	0.0520999i	$0.0165914\pi$
$164$	13.2261	+	4.81390i	1.03278	+	0.375902i
$165$		0			0
$166$	−8.76495	−	7.35466i	−0.680292	−	0.570833i
$167$	7.57376	−	9.02606i	0.586075	−	0.698457i	−0.388771	−	0.921334i	$-0.627100\pi$
$167$	7.57376	−	9.02606i	0.586075	−	0.698457i	0.974847	+	0.222877i	$0.0715448\pi$
$168$	0.0496676	−	0.00875774i	0.00383194	−	0.000675674i
$169$	−3.33896	−	1.21528i	−0.256843	−	0.0934833i
$170$		0			0
$171$	11.0055	−	19.0621i	0.841612	−	1.45772i
$172$	7.40704	+	1.30606i	0.564781	+	0.0995862i
$173$	−0.394661	−	0.470339i	−0.0300055	−	0.0357592i	0.750833	−	0.660492i	$-0.229652\pi$
$173$	−0.394661	−	0.470339i	−0.0300055	−	0.0357592i	−0.780839	+	0.624733i	$0.785208\pi$
$174$	−0.297670	−	0.515580i	−0.0225663	−	0.0390860i
$175$		0			0
$176$	−0.716836	−	4.06538i	−0.0540335	−	0.306439i
$177$	1.79933	−	1.03884i	0.135246	−	0.0780843i
$178$	−0.215390	−	0.591780i	−0.0161442	−	0.0443558i
$179$	25.4162			1.89970			0.949849	−	0.312708i	$-0.101236\pi$
$179$	25.4162			1.89970			0.949849	+	0.312708i	$0.101236\pi$
$180$		0			0
$181$	−1.38666	+	7.86416i	−0.103070	+	0.584538i	0.888904	+	0.458094i	$0.151468\pi$
$181$	−1.38666	+	7.86416i	−0.103070	+	0.584538i	−0.991974	+	0.126444i	$0.959643\pi$
$182$	−0.0853666	+	0.101736i	−0.00632779	+	0.00754117i
$183$	0.615654	+	0.733707i	0.0455104	+	0.0542372i
$184$	16.8446			1.24180
$185$		0			0
$186$	0.361563			0.0265111
$187$	−7.90902	−	9.42560i	−0.578365	−	0.689268i
$188$	−4.78136	+	5.69821i	−0.348717	+	0.415584i
$189$	0.0206534	−	0.117131i	0.00150231	−	0.00852003i
$190$		0			0
$191$	−8.95234			−0.647769			−0.323884	−	0.946097i	$-0.604989\pi$
$191$	−8.95234			−0.647769			−0.323884	+	0.946097i	$0.604989\pi$
$192$	0.207003	+	0.568736i	0.0149392	+	0.0410450i
$193$	0.0531650	−	0.0306948i	0.00382690	−	0.00220946i	−0.498085	−	0.867128i	$-0.665963\pi$
$193$	0.0531650	−	0.0306948i	0.00382690	−	0.00220946i	0.501912	+	0.864919i	$0.332630\pi$
$194$	1.50975	+	8.56223i	0.108394	+	0.614732i
$195$		0			0
$196$	−5.20346	−	9.01265i	−0.371676	−	0.643761i
$197$	−4.32846	−	5.15846i	−0.308390	−	0.367525i	0.589482	−	0.807782i	$-0.299332\pi$
$197$	−4.32846	−	5.15846i	−0.308390	−	0.367525i	−0.897872	+	0.440256i	$0.854888\pi$
$198$	7.07793	+	1.24803i	0.503006	+	0.0886936i
$199$	−5.14245	+	8.90699i	−0.364539	+	0.631400i	−0.988702	−	0.149894i	$-0.952107\pi$
$199$	−5.14245	+	8.90699i	−0.364539	+	0.631400i	0.624163	+	0.781294i	$0.285440\pi$
$200$		0			0
$201$	−1.46610	−	0.533618i	−0.103411	−	0.0376385i
$202$	−6.84077	+	1.20621i	−0.481315	+	0.0848688i
$203$	0.0963977	−	0.114882i	0.00676579	−	0.00806316i
$204$	−1.34986	−	1.13267i	−0.0945091	−	0.0793025i
$205$		0			0
$206$	−1.10083	−	0.400669i	−0.0766985	−	0.0279160i
$207$	6.66409	−	18.3094i	0.463186	−	1.27259i
$208$	3.16096	+	1.82498i	0.219173	+	0.126540i
$209$	4.60063	−	26.0915i	0.318232	−	1.80478i
$210$		0			0
$211$	−13.2615	−	22.9696i	−0.912960	−	1.58129i	−0.809861	−	0.586622i	$-0.800457\pi$
$211$	−13.2615	−	22.9696i	−0.912960	−	1.58129i	−0.103099	−	0.994671i	$-0.532876\pi$
$212$	10.3396	+	5.96955i	0.710124	+	0.409990i
$213$	−2.92729	+	0.516161i	−0.200575	+	0.0353668i
$214$	−2.66087	−	4.60875i	−0.181893	−	0.315048i
$215$		0			0
$216$	4.92002			0.334765
$217$	0.0311508	+	0.0855862i	0.00211466	+	0.00580997i
$218$	9.97569	+	1.75898i	0.675639	+	0.119133i
$219$	3.94390	+	3.30933i	0.266504	+	0.223623i
$220$		0			0
$221$	10.8791			0.731810
$222$	−0.743266	+	1.25366i	−0.0498848	+	0.0841404i
$223$			2.64503i			0.177124i	0.996071	+	0.0885620i	$0.0282272\pi$
$223$			2.64503i			0.177124i	−0.996071	+	0.0885620i	$0.971773\pi$
$224$	−0.270182	+	0.226709i	−0.0180523	+	0.0151477i
$225$		0			0
$226$	1.60930	−	9.12679i	0.107049	−	0.607105i
$227$	1.31337	+	3.60845i	0.0871713	+	0.239501i	0.975617	−	0.219481i	$-0.0704364\pi$
$227$	1.31337	+	3.60845i	0.0871713	+	0.239501i	−0.888446	+	0.458982i	$0.848214\pi$
$228$		−	3.79425i		−	0.251280i
$229$	−24.8064	+	9.02880i	−1.63925	+	0.596640i	−0.986909	−	0.161281i	$-0.948437\pi$
$229$	−24.8064	+	9.02880i	−1.63925	+	0.596640i	−0.652346	+	0.757921i	$0.726215\pi$
$230$		0			0
$231$	−0.0121934	−	0.0691524i	−0.000802269	−	0.00454989i
$232$	5.37249	+	3.10181i	0.352722	+	0.203644i
$233$	0.969331	−	0.559644i	0.0635030	−	0.0366635i	−0.467912	−	0.883775i	$-0.654994\pi$
$233$	0.969331	−	0.559644i	0.0635030	−	0.0366635i	0.531415	+	0.847111i	$0.321660\pi$
$234$	−4.86797	+	4.08471i	−0.318229	+	0.267026i
$235$		0			0
$236$	−4.61710	+	7.99705i	−0.300547	+	0.520563i
$237$	1.48096	−	4.06892i	0.0961990	−	0.264305i
$238$	−0.0523099	+	0.143720i	−0.00339075	+	0.00931600i
$239$	−1.86059	−	10.5519i	−0.120352	−	0.682548i	−0.983961	−	0.178386i	$-0.942913\pi$
$239$	−1.86059	−	10.5519i	−0.120352	−	0.682548i	0.863609	−	0.504162i	$-0.168199\pi$
$240$		0			0
$241$	7.16375	+	6.01110i	0.461458	+	0.387209i	0.843667	−	0.536867i	$-0.180392\pi$
$241$	7.16375	+	6.01110i	0.461458	+	0.387209i	−0.382209	+	0.924076i	$0.624837\pi$
$242$	0.764126	−	0.134736i	0.0491198	−	0.00866115i
$243$	2.93820	−	8.07265i	0.188486	−	0.517861i
$244$	−4.00012	−	1.45593i	−0.256082	−	0.0932061i
$245$		0			0
$246$	−0.393690	+	2.23273i	−0.0251007	+	0.142353i
$247$	15.0575	+	17.9449i	0.958087	+	1.14180i
$248$	−3.26283	+	1.88380i	−0.207190	+	0.119621i
$249$	−2.67448	+	4.63234i	−0.169488	+	0.293563i
$250$		0			0
$251$	−0.965819	−	1.67285i	−0.0609619	−	0.105589i	0.833934	−	0.551865i	$-0.186083\pi$
$251$	−0.965819	−	1.67285i	−0.0609619	−	0.105589i	−0.894896	+	0.446275i	$0.852750\pi$
$252$	0.0886787	+	0.243643i	0.00558623	+	0.0153480i
$253$		−	23.4528i		−	1.47447i
$254$	−0.0273719	+	0.00996256i	−0.00171747	+	0.000625107i
$255$		0			0
$256$	−8.47007	−	7.10723i	−0.529379	−	0.444202i
$257$	12.3880	+	14.7635i	0.772745	+	0.920921i	0.998582	−	0.0532437i	$-0.0169560\pi$
$257$	12.3880	+	14.7635i	0.772745	+	0.920921i	−0.225837	+	0.974165i	$0.572512\pi$
$258$			1.21152i			0.0754261i
$259$	−0.360794	−	0.0679291i	−0.0224186	−	0.00422091i
$260$		0			0
$261$	5.49701	−	4.61254i	0.340256	−	0.285509i
$262$	−0.958712	+	1.14255i	−0.0592294	+	0.0705869i
$263$	−20.3861	−	3.59462i	−1.25706	−	0.221654i	−0.494848	−	0.868980i	$-0.664776\pi$
$263$	−20.3861	−	3.59462i	−1.25706	−	0.221654i	−0.762213	+	0.647326i	$0.775887\pi$
$264$	2.72953	−	0.993467i	0.167991	−	0.0611437i
$265$		0			0
$266$	−0.309464	+	0.112636i	−0.0189744	+	0.00690613i
$267$	−0.254964	+	0.147204i	−0.0156036	+	0.00900873i
$268$	6.82887	−	1.20411i	0.417140	−	0.0735530i
$269$	4.95821	−	8.58787i	0.302307	−	0.523612i	−0.674351	−	0.738411i	$-0.735576\pi$
$269$	4.95821	−	8.58787i	0.302307	−	0.523612i	0.976658	+	0.214799i	$0.0689098\pi$
$270$		0			0
$271$	6.41261	−	5.38082i	0.389539	−	0.326862i	−0.426895	−	0.904301i	$-0.640393\pi$
$271$	6.41261	−	5.38082i	0.389539	−	0.326862i	0.816433	+	0.577440i	$0.195948\pi$
$272$	4.13954	+	0.729912i	0.250996	+	0.0442574i
$273$	0.0537682	+	0.0310431i	0.00325420	+	0.00187881i
$274$	1.87398	+	0.682073i	0.113211	+	0.0412055i
$275$		0			0
$276$	−0.583237	−	3.30770i	−0.0351067	−	0.199100i
$277$	−16.1915	+	19.2963i	−0.972853	+	1.15940i	0.0143449	+	0.999897i	$0.495434\pi$
$277$	−16.1915	+	19.2963i	−0.972853	+	1.15940i	−0.987197	+	0.159503i	$0.949011\pi$
$278$	7.82894	−	9.33017i	0.469549	−	0.559586i
$279$	0.756766	+	4.29183i	0.0453064	+	0.256945i
$280$		0			0
$281$	−17.3621	−	6.31928i	−1.03573	−	0.376976i	−0.232473	−	0.972603i	$-0.574682\pi$
$281$	−17.3621	−	6.31928i	−1.03573	−	0.376976i	−0.803262	+	0.595626i	$0.796904\pi$
$282$	−1.03766	−	0.599091i	−0.0617915	−	0.0356753i
$283$	11.9564	+	2.10824i	0.710737	+	0.125322i	0.517317	−	0.855794i	$-0.326931\pi$
$283$	11.9564	+	2.10824i	0.710737	+	0.125322i	0.193420	+	0.981116i	$0.438042\pi$
$284$	10.1202	−	8.49182i	0.600521	−	0.503897i
$285$		0			0
$286$	−3.82446	+	6.62416i	−0.226145	+	0.391695i
$287$	−0.562431	+	0.0991717i	−0.0331992	+	0.00585392i
$288$	−14.6152	+	8.43811i	−0.861211	+	0.497220i
$289$	−4.20164	+	1.52927i	−0.247155	+	0.0899572i
$290$		0			0
$291$	3.81940	−	1.39015i	0.223897	−	0.0814920i
$292$	−22.5342	−	3.97339i	−1.31871	−	0.232525i
$293$	−16.3459	+	19.4803i	−0.954937	+	1.13805i	0.0354002	+	0.999373i	$0.488729\pi$
$293$	−16.3459	+	19.4803i	−0.954937	+	1.13805i	−0.990338	+	0.138677i	$0.955715\pi$
$294$	1.28415	−	1.07753i	0.0748929	−	0.0628426i
$295$		0			0
$296$	0.175640	−	15.1859i	0.0102089	−	0.882662i
$297$		−	6.85016i		−	0.397486i
$298$	3.92317	+	4.67546i	0.227263	+	0.270842i
$299$	15.8851	+	13.3291i	0.918656	+	0.770844i
$300$		0			0
$301$	−0.286781	+	0.104380i	−0.0165298	+	0.00601636i
$302$			7.65318i			0.440391i
$303$	1.11066	+	3.05150i	0.0638055	+	0.175304i
$304$	4.52545	+	7.83831i	0.259553	+	0.449558i
$305$		0			0
$306$	−3.65911	+	6.33777i	−0.209177	+	0.362306i
$307$	23.0738	−	13.3217i	1.31689	−	0.760308i	0.333665	−	0.942692i	$-0.391714\pi$
$307$	23.0738	−	13.3217i	1.31689	−	0.760308i	0.983228	+	0.182383i	$0.0583812\pi$
$308$	0.200605	+	0.239072i	0.0114305	+	0.0136224i
$309$	−0.0950997	+	0.539337i	−0.00541003	+	0.0306818i
$310$		0			0
$311$	−13.8569	−	5.04349i	−0.785751	−	0.285990i	−0.0821821	−	0.996617i	$-0.526189\pi$
$311$	−13.8569	−	5.04349i	−0.785751	−	0.285990i	−0.703568	+	0.710628i	$0.748411\pi$
$312$	−0.878401	+	2.41339i	−0.0497296	+	0.136631i
$313$	9.49869	−	1.67487i	0.536898	−	0.0946695i	0.101377	−	0.994848i	$-0.467675\pi$
$313$	9.49869	−	1.67487i	0.536898	−	0.0946695i	0.435521	+	0.900179i	$0.356564\pi$
$314$	−2.90725	−	2.43947i	−0.164065	−	0.137667i
$315$		0			0
$316$	3.34181	+	18.9524i	0.187992	+	1.06615i
$317$	5.83984	−	16.0448i	0.327998	−	0.901167i	−0.660620	−	0.750720i	$-0.729707\pi$
$317$	5.83984	−	16.0448i	0.327998	−	0.901167i	0.988618	−	0.150447i	$-0.0480712\pi$
$318$	−0.657751	+	1.80716i	−0.0368848	+	0.101340i
$319$	4.31866	−	7.48014i	0.241799	−	0.418807i
$320$		0			0
$321$	−1.90582	+	1.59917i	−0.106372	+	0.0892570i
$322$	−0.252466	+	0.145761i	−0.0140694	+	0.00812297i
$323$	23.3630	+	13.4886i	1.29995	+	0.750528i
$324$	2.06753	+	11.7255i	0.114863	+	0.651418i
$325$		0			0
$326$	−5.02617	+	1.82938i	−0.278374	+	0.101320i
$327$		−	4.73550i		−	0.261874i
$328$	−8.08007	−	22.1998i	−0.446147	−	1.22578i
$329$	0.0524115	−	0.297240i	0.00288954	−	0.0163874i
$330$		0			0
$331$	19.6375	−	16.4778i	1.07937	−	0.905701i	0.0835036	−	0.996507i	$-0.473389\pi$
$331$	19.6375	−	16.4778i	1.07937	−	0.905701i	0.995869	+	0.0908067i	$0.0289446\pi$
$332$		−	23.7732i		−	1.30473i
$333$	−16.4369	−	6.19876i	−0.900739	−	0.339690i
$334$	−8.43531			−0.461560
$335$		0			0
$336$	0.0183762	+	0.0154194i	0.00100250	+	0.000841199i
$337$	−5.70530	−	1.00600i	−0.310787	−	0.0548002i	0.0160792	−	0.999871i	$-0.494882\pi$
$337$	−5.70530	−	1.00600i	−0.310787	−	0.0548002i	−0.326866	+	0.945071i	$0.605993\pi$
$338$	0.870030	+	2.39039i	0.0473234	+	0.130020i
$339$	−4.33252			−0.235310
$340$		0			0
$341$	2.62282	+	4.54285i	0.142033	+	0.246009i
$342$	−15.5185	+	2.73632i	−0.839142	+	0.147963i
$343$	0.731590	+	0.422384i	0.0395021	+	0.0228066i
$344$	−6.31221	−	10.9331i	−0.340331	−	0.589471i
$345$		0			0
$346$	−0.0763281	+	0.432878i	−0.00410342	+	0.0232717i
$347$	−11.4125	−	6.58898i	−0.612653	−	0.353715i	0.161350	−	0.986897i	$-0.448415\pi$
$347$	−11.4125	−	6.58898i	−0.612653	−	0.353715i	−0.774003	+	0.633182i	$0.781748\pi$
$348$	0.423068	−	1.16237i	0.0226788	−	0.0623096i
$349$	−5.64573	−	2.05488i	−0.302209	−	0.109995i	0.186465	−	0.982462i	$-0.440297\pi$
$349$	−5.64573	−	2.05488i	−0.302209	−	0.109995i	−0.488674	+	0.872466i	$0.662519\pi$
$350$		0			0
$351$	4.63974	+	3.89320i	0.247651	+	0.207804i
$352$	−13.0572	+	15.5609i	−0.695950	+	0.829401i
$353$	−20.8335	+	3.67350i	−1.10885	+	0.195521i	−0.697942	−	0.716155i	$-0.745901\pi$
$353$	−20.8335	+	3.67350i	−1.10885	+	0.195521i	−0.410911	+	0.911675i	$0.634789\pi$
$354$	−1.39773	−	0.508732i	−0.0742885	−	0.0270388i
$355$		0			0
$356$	0.654241	−	1.13318i	0.0346747	−	0.0600583i
$357$	0.0704139	+	0.0124159i	0.00372670	+	0.000657117i
$358$	−11.6960	−	13.9387i	−0.618151	−	0.736683i
$359$	−2.10079	−	3.63867i	−0.110875	−	0.192042i	0.805248	−	0.592938i	$-0.202032\pi$
$359$	−2.10079	−	3.63867i	−0.110875	−	0.192042i	−0.916123	+	0.400896i	$0.868699\pi$
$360$		0			0
$361$	6.78763	+	38.4946i	0.357244	+	2.02603i
$362$	4.95095	−	2.85843i	0.260216	−	0.150236i
$363$	−0.124062	−	0.340858i	−0.00651157	−	0.0178904i
$364$	−0.275939			−0.0144631
$365$		0			0
$366$	0.119068	−	0.675270i	0.00622380	−	0.0352969i
$367$	19.4898	−	23.2271i	1.01736	−	1.21244i	0.0403641	−	0.999185i	$-0.487148\pi$
$367$	19.4898	−	23.2271i	1.01736	−	1.21244i	0.976996	−	0.213258i	$-0.0684073\pi$
$368$	5.15001	+	6.13755i	0.268463	+	0.319942i
$369$	−27.3269			−1.42258
$370$		0			0
$371$	−0.484444			−0.0251511
$372$	0.482886	+	0.575481i	0.0250365	+	0.0298373i
$373$	7.32238	−	8.72647i	0.379138	−	0.451840i	−0.542404	−	0.840118i	$-0.682486\pi$
$373$	7.32238	−	8.72647i	0.379138	−	0.451840i	0.921542	+	0.388278i	$0.126930\pi$
$374$	−1.52962	+	8.67489i	−0.0790946	+	0.448568i
$375$		0			0
$376$	12.4854			0.643885
$377$	2.61198	+	7.17636i	0.134524	+	0.369601i
$378$	−0.0737409	+	0.0425743i	−0.00379282	+	0.00218979i
$379$	−0.838617	−	4.75603i	−0.0430769	−	0.244301i	0.955664	−	0.294458i	$-0.0951390\pi$
$379$	−0.838617	−	4.75603i	−0.0430769	−	0.244301i	−0.998741	+	0.0501567i	$0.984028\pi$
$380$		0			0
$381$	0.00680869	+	0.0117930i	0.000348820	+	0.000604174i
$382$	4.11966	+	4.90962i	0.210780	+	0.251198i
$383$	27.2549	+	4.80578i	1.39266	+	0.245564i	0.819125	−	0.573615i	$-0.194460\pi$
$383$	27.2549	+	4.80578i	1.39266	+	0.245564i	0.573538	+	0.819179i	$0.305571\pi$
$384$	−1.73909	+	3.01220i	−0.0887477	+	0.153716i
$385$		0			0
$386$	−0.0412988	−	0.0150315i	−0.00210205	−	0.000765085i
$387$	−14.3810	+	2.53576i	−0.731029	+	0.128900i
$388$	−11.6117	+	13.8383i	−0.589495	+	0.702532i
$389$	20.9451	+	17.5750i	1.06196	+	0.891087i	0.994300	−	0.106622i	$-0.0340033\pi$
$389$	20.9451	+	17.5750i	1.06196	+	0.891087i	0.0676566	+	0.997709i	$0.478448\pi$
$390$		0			0
$391$	22.4405	+	8.16767i	1.13486	+	0.413057i
$392$	−5.97437	+	16.4144i	−0.301751	+	0.829054i
$393$	0.603845	+	0.348630i	0.0304600	+	0.0175861i
$394$	−0.837131	+	4.74761i	−0.0421741	+	0.239181i
$395$		0			0
$396$	7.46651	+	12.9324i	0.375206	+	0.649876i
$397$	−21.7258	−	12.5434i	−1.09038	−	0.629534i	−0.156706	−	0.987645i	$-0.550087\pi$
$397$	−21.7258	−	12.5434i	−1.09038	−	0.629534i	−0.933679	+	0.358111i	$0.883421\pi$
$398$	7.25118	−	1.27858i	0.363469	−	0.0640894i
$399$	0.0769783	+	0.133330i	0.00385373	+	0.00667486i
$400$		0			0
$401$	3.44550			0.172060			0.0860301	−	0.996293i	$-0.472582\pi$
$401$	3.44550			0.172060			0.0860301	+	0.996293i	$0.472582\pi$
$402$	0.382021	+	1.04960i	0.0190535	+	0.0523491i
$403$	−4.56760	−	0.805392i	−0.227529	−	0.0401194i
$404$	−11.0561	−	9.27714i	−0.550060	−	0.461555i
$405$		0			0
$406$	−0.107363			−0.00532836
$407$	−21.1434	−	0.244544i	−1.04804	−	0.0121216i
$408$			2.95769i			0.146428i
$409$	0.999556	−	0.838727i	0.0494249	−	0.0414724i	−0.617741	−	0.786382i	$-0.711952\pi$
$409$	0.999556	−	0.838727i	0.0494249	−	0.0414724i	0.667165	+	0.744910i	$0.267507\pi$
$410$		0			0
$411$	0.161891	−	0.918132i	0.00798551	−	0.0452881i
$412$	−0.832490	−	2.28725i	−0.0410138	−	0.112685i
$413$		−	0.374689i		−	0.0184372i
$414$	−13.1079	+	4.77087i	−0.644216	+	0.234475i
$415$		0			0
$416$	−3.11883	−	17.6877i	−0.152913	−	0.867213i
$417$	−4.93106	−	2.84695i	−0.241475	−	0.139416i
$418$	−16.4261	+	9.48361i	−0.803427	+	0.463859i
$419$	−4.52329	+	3.79549i	−0.220977	+	0.185422i	−0.746555	−	0.665324i	$-0.768294\pi$
$419$	−4.52329	+	3.79549i	−0.220977	+	0.185422i	0.525578	+	0.850746i	$0.323849\pi$
$420$		0			0
$421$	−14.8327	+	25.6909i	−0.722900	+	1.25210i	0.236933	+	0.971526i	$0.423858\pi$
$421$	−14.8327	+	25.6909i	−0.722900	+	1.25210i	−0.959833	+	0.280573i	$0.909476\pi$
$422$	−6.49429	+	17.8429i	−0.316137	+	0.868580i
$423$	4.93948	−	13.5711i	0.240166	−	0.659850i
$424$	−3.47984	−	19.7352i	−0.168996	−	0.958425i
$425$		0			0
$426$	1.63014	+	1.36785i	0.0789807	+	0.0662727i
$427$	0.170103	−	0.0299937i	0.00823184	−	0.00145150i
$428$	3.78179	−	10.3904i	0.182800	−	0.502238i
$429$	3.36016	+	1.22300i	0.162230	+	0.0590470i
$430$		0			0
$431$	1.59947	−	9.07106i	0.0770439	−	0.436937i	−0.921748	−	0.387790i	$-0.873239\pi$
$431$	1.59947	−	9.07106i	0.0770439	−	0.436937i	0.998792	−	0.0491473i	$-0.0156504\pi$
$432$	1.50423	+	1.79267i	0.0723721	+	0.0862497i
$433$	−27.8154	+	16.0592i	−1.33672	+	0.771756i	−0.986320	−	0.164843i	$-0.947288\pi$
$433$	−27.8154	+	16.0592i	−1.33672	+	0.771756i	−0.350402	+	0.936600i	$0.613955\pi$
$434$	0.0326020	−	0.0564684i	0.00156495	−	0.00271057i
$435$		0			0
$436$	10.5234	+	18.2270i	0.503977	+	0.872914i
$437$	17.5869	+	48.3197i	0.841297	+	2.31144i
$438$		−	3.68578i		−	0.176113i
$439$	−10.7255	+	3.90376i	−0.511900	+	0.186316i	−0.585038	−	0.811006i	$-0.698921\pi$
$439$	−10.7255	+	3.90376i	−0.511900	+	0.186316i	0.0731389	+	0.997322i	$0.476698\pi$
$440$		0			0
$441$	15.4782	+	12.9878i	0.737059	+	0.618466i
$442$	−5.00632	−	5.96630i	−0.238127	−	0.283788i
$443$			22.0611i			1.04815i	0.851671	+	0.524077i	$0.175589\pi$
$443$			22.0611i			1.04815i	−0.851671	+	0.524077i	$0.824411\pi$
$444$	−2.98806	+	0.491314i	−0.141807	+	0.0233167i
$445$		0			0
$446$	1.45058	−	1.21718i	0.0686868	−	0.0576351i
$447$	1.83405	−	2.18574i	0.0867477	−	0.103382i
$448$	0.107490	+	0.0189533i	0.00507841	+	0.000895461i
$449$	22.7416	−	8.27726i	1.07324	−	0.390628i	0.255854	−	0.966716i	$-0.417644\pi$
$449$	22.7416	−	8.27726i	1.07324	−	0.390628i	0.817388	+	0.576088i	$0.195421\pi$
$450$		0			0
$451$	−30.9089	+	11.2499i	−1.45544	+	0.529738i
$452$	16.6759	−	9.62786i	0.784370	−	0.452856i
$453$	3.52345	−	0.621279i	0.165546	−	0.0291902i
$454$	1.37455	−	2.38080i	0.0645110	−	0.111736i
$455$		0			0
$456$	−4.87864	+	4.09366i	−0.228463	+	0.191703i
$457$	−34.2916	−	6.04653i	−1.60409	−	0.282845i	−0.701283	−	0.712883i	$-0.747389\pi$
$457$	−34.2916	−	6.04653i	−1.60409	−	0.282845i	−0.902811	+	0.430039i	$0.858500\pi$
$458$	16.3669	+	9.44943i	0.764774	+	0.441543i
$459$	6.55447	+	2.38563i	0.305936	+	0.111352i
$460$		0			0
$461$	6.05689	+	34.3503i	0.282097	+	1.59985i	0.715473	+	0.698640i	$0.246211\pi$
$461$	6.05689	+	34.3503i	0.282097	+	1.59985i	−0.433376	+	0.901213i	$0.642678\pi$
$462$	−0.0323132	+	0.0385094i	−0.00150335	+	0.00179162i
$463$	1.53910	−	1.83423i	0.0715281	−	0.0852438i	−0.729094	−	0.684414i	$-0.760058\pi$
$463$	1.53910	−	1.83423i	0.0715281	−	0.0852438i	0.800622	+	0.599170i	$0.204503\pi$
$464$	0.512383	+	2.90587i	0.0237868	+	0.134902i
$465$		0			0
$466$	−0.752982	−	0.274063i	−0.0348812	−	0.0126957i
$467$	18.0342	+	10.4120i	0.834523	+	0.481812i	0.855399	−	0.517970i	$-0.173312\pi$
$467$	18.0342	+	10.4120i	0.834523	+	0.481812i	−0.0208761	+	0.999782i	$0.506646\pi$
$468$	−13.0028	−	2.29275i	−0.601056	−	0.105982i
$469$	−0.215538	+	0.180858i	−0.00995261	+	0.00835123i
$470$		0			0
$471$	−0.887100	+	1.53650i	−0.0408754	+	0.0707983i
$472$	15.2640	−	2.69146i	0.702583	−	0.123884i
$473$	−15.2221	+	8.78851i	−0.699915	+	0.404096i
$474$	−2.91297	+	1.06023i	−0.133797	+	0.0486982i
$475$		0			0
$476$	−0.298615	+	0.108687i	−0.0136870	+	0.00498165i
$477$	−22.8280	−	4.02519i	−1.04522	−	0.184301i
$478$	−4.93066	+	5.87613i	−0.225523	+	0.268768i
$479$	5.12322	−	4.29890i	0.234086	−	0.196422i	−0.518197	−	0.855261i	$-0.673397\pi$
$479$	5.12322	−	4.29890i	0.234086	−	0.196422i	0.752284	+	0.658839i	$0.228952\pi$
$480$		0			0
$481$	12.1822	−	14.1818i	0.555461	−	0.646635i
$482$		−	6.69489i		−	0.304944i
$483$	0.0876021	+	0.104400i	0.00398603	+	0.00475037i
$484$	1.23498	+	1.03627i	0.0561355	+	0.0471033i
$485$		0			0
$486$	−5.77927	+	2.10348i	−0.262153	+	0.0954159i
$487$			40.4363i			1.83235i	0.400784	+	0.916173i	$0.368738\pi$
$487$			40.4363i			1.83235i	−0.400784	+	0.916173i	$0.631262\pi$
$488$	2.44375	+	6.71416i	0.110624	+	0.303936i
$489$	1.25025	+	2.16549i	0.0565382	+	0.0979270i
$490$		0			0
$491$	−11.9543	+	20.7055i	−0.539491	+	0.934425i	0.459441	+	0.888208i	$0.348050\pi$
$491$	−11.9543	+	20.7055i	−0.539491	+	0.934425i	−0.998931	+	0.0462167i	$0.985284\pi$
$492$	−4.07950	+	2.35530i	−0.183918	+	0.106185i
$493$	5.65324	+	6.73727i	0.254609	+	0.303432i
$494$	2.91215	−	16.5156i	0.131024	−	0.743072i
$495$		0			0
$496$	−1.68395	−	0.612907i	−0.0756115	−	0.0275203i
$497$	−0.183340	+	0.503723i	−0.00822392	+	0.0225950i
$498$	3.77119	−	0.664962i	0.168991	−	0.0297977i
$499$	−6.66733	−	5.59456i	−0.298471	−	0.250447i	0.481237	−	0.876591i	$-0.340188\pi$
$499$	−6.66733	−	5.59456i	−0.298471	−	0.250447i	−0.779707	+	0.626144i	$0.784632\pi$
$500$		0			0
$501$	0.684772	+	3.88353i	0.0305933	+	0.173504i
$502$	−0.472971	+	1.29948i	−0.0211097	+	0.0579985i
$503$	5.35736	−	14.7192i	0.238873	−	0.656298i	−0.761098	−	0.648637i	$-0.775339\pi$
$503$	5.35736	−	14.7192i	0.238873	−	0.656298i	0.999971	−	0.00766089i	$-0.00243856\pi$
$504$	0.217598	−	0.376892i	0.00969261	−	0.0167881i
$505$		0			0
$506$	−12.8619	+	10.7925i	−0.571783	+	0.479783i
$507$	1.02988	−	0.594603i	0.0457387	−	0.0264072i
$508$	−0.0524135	−	0.0302609i	−0.00232547	−	0.00134261i
$509$	−2.86745	−	16.2621i	−0.127097	−	0.720805i	−0.980040	−	0.198800i	$-0.936295\pi$
$509$	−2.86745	−	16.2621i	−0.127097	−	0.720805i	0.852943	−	0.522005i	$-0.174816\pi$
$510$		0			0
$511$	0.872466	−	0.317552i	0.0385956	−	0.0140477i
$512$		−	12.8694i		−	0.568751i
$513$	5.13683	+	14.1133i	0.226796	+	0.623118i
$514$	2.39587	−	13.5876i	0.105677	−	0.599325i
$515$		0			0
$516$	−1.92832	+	1.61805i	−0.0848894	+	0.0712307i
$517$		−	17.3835i		−	0.764524i
$518$	0.128775	+	0.229125i	0.00565806	+	0.0100672i
$519$	0.205489			0.00901996
$520$		0			0
$521$	24.1898	+	20.2977i	1.05977	+	0.889257i	0.994087	−	0.108584i	$-0.0346315\pi$
$521$	24.1898	+	20.2977i	1.05977	+	0.889257i	0.0656875	+	0.997840i	$0.479076\pi$
$522$	−5.05919	−	0.892072i	−0.221435	−	0.0390449i
$523$	8.50398	+	23.3645i	0.371853	+	1.02166i	0.974645	+	0.223759i	$0.0718328\pi$
$523$	8.50398	+	23.3645i	0.371853	+	1.02166i	−0.602792	+	0.797899i	$0.705945\pi$
$524$	−3.09894			−0.135378
$525$		0			0
$526$	7.40986	+	12.8342i	0.323085	+	0.559600i
$527$	−5.26018	+	0.927511i	−0.229137	+	0.0404030i
$528$	1.19650	+	0.690798i	0.0520708	+	0.0300631i
$529$	11.2592	+	19.5015i	0.489530	+	0.847891i
$530$		0			0
$531$	3.11325	−	17.6561i	0.135104	−	0.766211i
$532$	−0.592581	−	0.342127i	−0.0256916	−	0.0148331i
$533$	9.94691	−	27.3289i	0.430849	−	1.18375i
$534$	0.198058	+	0.0720871i	0.00857080	+	0.00311952i
$535$		0			0
$536$	−8.91599	−	7.48141i	−0.385112	−	0.323148i
$537$	−5.46777	+	6.51623i	−0.235952	+	0.281196i
$538$	−6.99139	+	1.23277i	−0.301420	+	0.0531485i
$539$	22.8539	+	8.31813i	0.984386	+	0.358287i
$540$		0			0
$541$	2.47693	−	4.29017i	0.106492	−	0.184449i	−0.807855	−	0.589381i	$-0.799372\pi$
$541$	2.47693	−	4.29017i	0.106492	−	0.184449i	0.914347	+	0.404932i	$0.132705\pi$
$542$	−5.90187	−	1.04066i	−0.253507	−	0.0447001i
$543$	−1.71791	−	2.04732i	−0.0737225	−	0.0878590i
$544$	−10.3420	−	17.9128i	−0.443408	−	0.768005i
$545$		0			0
$546$	−0.00771831	−	0.0437727i	−0.000330313	−	0.00187330i
$547$	19.1488	−	11.0555i	0.818742	−	0.472701i	−0.0312406	−	0.999512i	$-0.509946\pi$
$547$	19.1488	−	11.0555i	0.818742	−	0.472701i	0.849982	+	0.526811i	$0.176612\pi$
$548$	1.41718	+	3.89366i	0.0605388	+	0.166329i
$549$	8.26481			0.352734
$550$		0			0
$551$	−3.28846	+	18.6498i	−0.140093	+	0.794507i
$552$	−3.62377	+	4.31864i	−0.154238	+	0.183814i
$553$	−0.501939	−	0.598188i	−0.0213446	−	0.0254375i
$554$	18.0334			0.766164
$555$		0			0
$556$	25.3063			1.07323
$557$	−29.9180	−	35.6548i	−1.26766	−	1.51074i	−0.761258	−	0.648449i	$-0.775418\pi$
$557$	−29.9180	−	35.6548i	−1.26766	−	1.51074i	−0.506407	−	0.862295i	$-0.669027\pi$
$558$	2.00547	−	2.39002i	0.0848982	−	0.101178i
$559$	2.69870	−	15.3051i	0.114143	−	0.647336i
$560$		0			0
$561$	4.11800			0.173862
$562$	4.52402	+	12.4296i	0.190834	+	0.524313i
$563$	−16.4474	+	9.49594i	−0.693177	+	0.400206i	−0.804801	−	0.593544i	$-0.797728\pi$
$563$	−16.4474	+	9.49594i	−0.693177	+	0.400206i	0.111624	+	0.993751i	$0.464395\pi$
$564$	−0.432301	−	2.45170i	−0.0182031	−	0.103235i
$565$		0			0
$566$	−4.34588	−	7.52728i	−0.182671	−	0.316395i
$567$	−0.310542	−	0.370090i	−0.0130415	−	0.0155423i
$568$	−21.8375	−	3.85054i	−0.916282	−	0.161565i
$569$	12.9877	−	22.4954i	0.544474	−	0.943057i	−0.454166	−	0.890917i	$-0.650063\pi$
$569$	12.9877	−	22.4954i	0.544474	−	0.943057i	0.998640	−	0.0521397i	$-0.0166041\pi$
$570$		0			0
$571$	−19.9992	−	7.27913i	−0.836942	−	0.304622i	−0.112237	−	0.993681i	$-0.535802\pi$
$571$	−19.9992	−	7.27913i	−0.836942	−	0.304622i	−0.724705	+	0.689059i	$0.758024\pi$
$572$	−15.6511	+	2.75971i	−0.654405	+	0.115389i
$573$	1.92591	−	2.29521i	0.0804560	−	0.0958837i
$574$	0.313205	+	0.262810i	0.0130729	+	0.0109695i
$575$		0			0
$576$	4.90766	+	1.78624i	0.204486	+	0.0744268i
$577$	−1.21015	+	3.32487i	−0.0503794	+	0.138416i	−0.962330	−	0.271883i	$-0.912354\pi$
$577$	−1.21015	+	3.32487i	−0.0503794	+	0.138416i	0.911951	+	0.410299i	$0.134576\pi$
$578$	2.77218	+	1.60052i	0.115307	+	0.0665727i
$579$	−0.00356777	+	0.0202338i	−0.000148271	+	0.000840889i
$580$		0			0
$581$	0.482315	+	0.835393i	0.0200098	+	0.0346580i
$582$	−2.51998	−	1.45491i	−0.104457	−	0.0603081i
$583$	−27.4773	+	4.84500i	−1.13800	+	0.200659i
$584$	19.2034	+	33.2613i	0.794644	+	1.37636i
$585$		0			0
$586$	18.2053			0.752055
$587$	13.7794	+	37.8587i	0.568738	+	1.56259i	0.806477	+	0.591265i	$0.201371\pi$
$587$	13.7794	+	37.8587i	0.568738	+	1.56259i	−0.237739	+	0.971329i	$0.576406\pi$
$588$	3.43008	+	0.604817i	0.141454	+	0.0249422i
$589$	−8.81038	−	7.39278i	−0.363025	−	0.304614i
$590$		0			0
$591$	2.25371			0.0927052
$592$	5.58686	−	4.57887i	0.229618	−	0.188191i
$593$			17.7814i			0.730193i	0.930970	+	0.365096i	$0.118964\pi$
$593$			17.7814i			0.730193i	−0.930970	+	0.365096i	$0.881036\pi$
$594$	−3.75674	+	3.15228i	−0.154141	+	0.129340i
$595$		0			0
$596$	−2.20208	+	12.4886i	−0.0902007	+	0.511554i
$597$	−1.17729	−	3.23458i	−0.0481833	−	0.132382i
$598$		−	14.8454i		−	0.607073i
$599$	−14.6759	+	5.34161i	−0.599643	+	0.218252i	−0.623965	−	0.781452i	$-0.714479\pi$
$599$	−14.6759	+	5.34161i	−0.599643	+	0.218252i	0.0243225	+	0.999704i	$0.492257\pi$
$600$		0			0
$601$	−5.78343	−	32.7995i	−0.235911	−	1.33792i	−0.840687	−	0.541522i	$-0.817848\pi$
$601$	−5.78343	−	32.7995i	−0.235911	−	1.33792i	0.604776	−	0.796396i	$-0.293263\pi$
$602$	0.189214	+	0.109243i	0.00771178	+	0.00445240i
$603$	−11.6593	+	6.73152i	−0.474805	+	0.274129i
$604$	−12.1812	+	10.2212i	−0.495645	+	0.415895i
$605$		0			0
$606$	1.16240	−	2.01333i	0.0472192	−	0.0817861i
$607$	13.9731	−	38.3909i	0.567153	−	1.55824i	−0.241776	−	0.970332i	$-0.577730\pi$
$607$	13.9731	−	38.3909i	0.567153	−	1.55824i	0.808929	−	0.587907i	$-0.200048\pi$
$608$	15.2327	−	41.8514i	0.617766	−	1.69730i
$609$	0.00871567	+	0.0494290i	0.000353177	+	0.00200297i
$610$		0			0
$611$	11.7741	+	9.87968i	0.476331	+	0.399689i
$612$	−14.9744	+	2.64039i	−0.605305	+	0.106732i
$613$	−16.3616	+	44.9530i	−0.660837	+	1.81564i	−0.0877481	+	0.996143i	$0.527967\pi$
$613$	−16.3616	+	44.9530i	−0.660837	+	1.81564i	−0.573089	+	0.819493i	$0.694255\pi$
$614$	−17.9239	−	6.52376i	−0.723349	−	0.263277i
$615$		0			0
$616$	0.0909626	−	0.515874i	0.00366499	−	0.0207852i
$617$	20.0008	+	23.8360i	0.805202	+	0.959603i	0.999773	−	0.0212858i	$-0.00677600\pi$
$617$	20.0008	+	23.8360i	0.805202	+	0.959603i	−0.194571	+	0.980888i	$0.562332\pi$
$618$	0.339544	−	0.196036i	0.0136585	−	0.00788573i
$619$	−8.66083	+	15.0010i	−0.348108	+	0.602941i	−0.985913	−	0.167257i	$-0.946509\pi$
$619$	−8.66083	+	15.0010i	−0.348108	+	0.602941i	0.637805	+	0.770198i	$0.279842\pi$
$620$		0			0
$621$	6.64755	+	11.5139i	0.266757	+	0.462037i
$622$	3.61067	+	9.92023i	0.144775	+	0.397765i
$623$			0.0530933i			0.00212714i
$624$	−1.14790	+	0.417803i	−0.0459530	+	0.0167255i
$625$		0			0
$626$	−5.28960	−	4.43850i	−0.211415	−	0.177398i
$627$	5.69962	+	6.79254i	0.227621	+	0.271268i
$628$		−	7.88535i		−	0.314660i
$629$	7.59736	−	20.1455i	0.302927	−	0.803255i
$630$		0			0
$631$	17.0191	−	14.2807i	0.677518	−	0.568505i	−0.237762	−	0.971324i	$-0.576414\pi$
$631$	17.0191	−	14.2807i	0.677518	−	0.568505i	0.915280	+	0.402818i	$0.131969\pi$
$632$	20.7633	−	24.7448i	0.825922	−	0.984295i
$633$	8.74190	+	1.54143i	0.347459	+	0.0612665i
$634$	−11.4866	+	4.18079i	−0.456192	+	0.166040i
$635$		0			0
$636$	−3.75481	+	1.36664i	−0.148888	+	0.0541908i
$637$	−18.6228	+	10.7519i	−0.737860	+	0.426004i
$638$	−6.08958	+	1.07376i	−0.241089	+	0.0425105i
$639$	−12.8248	+	22.2131i	−0.507339	+	0.878737i
$640$		0			0
$641$	−5.15227	+	4.32327i	−0.203502	+	0.170759i	−0.738843	−	0.673877i	$-0.764628\pi$
$641$	−5.15227	+	4.32327i	−0.203502	+	0.170759i	0.535341	+	0.844636i	$0.320183\pi$
$642$	1.75403	+	0.309282i	0.0692259	+	0.0122064i
$643$	−2.53298	−	1.46241i	−0.0998909	−	0.0576720i	0.449222	−	0.893420i	$-0.351701\pi$
$643$	−2.53298	−	1.46241i	−0.0998909	−	0.0576720i	−0.549113	+	0.835748i	$0.685034\pi$
$644$	−0.569182	−	0.207165i	−0.0224289	−	0.00816346i
$645$		0			0
$646$	−3.35371	−	19.0198i	−0.131950	−	0.748325i
$647$	−15.6949	+	18.7045i	−0.617030	+	0.735348i	−0.980557	−	0.196236i	$-0.937128\pi$
$647$	−15.6949	+	18.7045i	−0.617030	+	0.735348i	0.363526	+	0.931584i	$0.381573\pi$
$648$	12.8460	−	15.3092i	0.504637	−	0.601403i
$649$	−3.74732	−	21.2521i	−0.147095	−	0.834219i
$650$		0			0
$651$	−0.0286441	−	0.0104256i	−0.00112265	−	0.000408611i
$652$	−9.62444	−	5.55667i	−0.376922	−	0.217616i
$653$	1.33994	+	0.236268i	0.0524360	+	0.00924588i	0.199805	−	0.979836i	$-0.435969\pi$
$653$	1.33994	+	0.236268i	0.0524360	+	0.00924588i	−0.147369	+	0.989082i	$0.547080\pi$
$654$	−2.59703	+	2.17917i	−0.101552	+	0.0852121i
$655$		0			0
$656$	5.61840	−	9.73136i	0.219362	−	0.379946i
$657$	43.7509	−	7.71447i	1.70689	−	0.300970i
$658$	−0.187130	+	0.108040i	−0.00729510	+	0.00421183i
$659$	−24.1857	+	8.80287i	−0.942141	+	0.342911i	−0.767011	−	0.641634i	$-0.778257\pi$
$659$	−24.1857	+	8.80287i	−0.942141	+	0.342911i	−0.175130	+	0.984545i	$0.556035\pi$
$660$		0			0
$661$	−11.8792	+	4.32369i	−0.462049	+	0.168172i	−0.562547	−	0.826765i	$-0.690179\pi$
$661$	−11.8792	+	4.32369i	−0.462049	+	0.168172i	0.100498	+	0.994937i	$0.467956\pi$
$662$	−18.0734	−	3.18683i	−0.702442	−	0.123860i
$663$	−2.34042	+	2.78920i	−0.0908943	+	0.108324i
$664$	−30.5675	+	25.6492i	−1.18625	+	0.995382i
$665$		0			0
$666$	4.16439	+	11.8668i	0.161367	+	0.459830i
$667$			16.7637i			0.649094i
$668$	−11.2658	−	13.4260i	−0.435887	−	0.519469i
$669$	−0.678134	−	0.569022i	−0.0262182	−	0.0219997i
$670$		0			0
$671$	9.34814	−	3.40245i	0.360881	−	0.131350i
$672$		−	0.118041i		−	0.00455353i
$673$	−16.5389	−	45.4403i	−0.637529	−	1.75160i	−0.659353	−	0.751834i	$-0.729170\pi$
$673$	−16.5389	−	45.4403i	−0.637529	−	1.75160i	0.0218238	−	0.999762i	$-0.493053\pi$
$674$	2.07374	+	3.59182i	0.0798774	+	0.138352i
$675$		0			0
$676$	−2.64269	+	4.57727i	−0.101642	+	0.176049i
$677$	−9.03269	+	5.21503i	−0.347155	+	0.200430i	−0.663431	−	0.748237i	$-0.730901\pi$
$677$	−9.03269	+	5.21503i	−0.347155	+	0.200430i	0.316277	+	0.948667i	$0.397567\pi$
$678$	1.99373	+	2.37603i	0.0765686	+	0.0912509i
$679$	0.127283	−	0.721858i	0.00488468	−	0.0277024i
$680$		0			0
$681$	−1.20768	−	0.439559i	−0.0462784	−	0.0168440i
$682$	1.28442	−	3.52891i	0.0491829	−	0.135129i
$683$	−10.8177	+	1.90745i	−0.413927	+	0.0729866i	−0.376734	−	0.926322i	$-0.622953\pi$
$683$	−10.8177	+	1.90745i	−0.413927	+	0.0729866i	−0.0371935	+	0.999308i	$0.511842\pi$
$684$	−25.0810	−	21.0454i	−0.958994	−	0.804692i
$685$		0			0
$686$	−0.105018	−	0.595588i	−0.00400961	−	0.0227396i
$687$	3.02177	−	8.30225i	0.115288	−	0.316750i
$688$	2.05372	−	5.64256i	0.0782975	−	0.215121i
$689$	12.3348	−	21.3645i	0.469919	−	0.813923i
$690$		0			0
$691$	2.43470	−	2.04295i	0.0926203	−	0.0777176i	−0.595302	−	0.803502i	$-0.702968\pi$
$691$	2.43470	−	2.04295i	0.0926203	−	0.0777176i	0.687922	+	0.725785i	$0.258523\pi$
$692$	−0.790929	+	0.456643i	−0.0300666	+	0.0173590i
$693$	−0.524747	−	0.302963i	−0.0199335	−	0.0115086i
$694$	1.63823	+	9.29088i	0.0621865	+	0.352677i
$695$		0			0
$696$	−1.95102	+	0.710115i	−0.0739534	+	0.0269168i
$697$		−	33.4926i		−	1.26862i
$698$	1.47110	+	4.04182i	0.0556821	+	0.152985i
$699$	−0.0650494	+	0.368913i	−0.00246039	+	0.0139536i
$700$		0			0
$701$	−25.3946	+	21.3086i	−0.959140	+	0.804814i	−0.980813	−	0.194951i	$-0.937545\pi$
$701$	−25.3946	+	21.3086i	−0.959140	+	0.804814i	0.0216726	+	0.999765i	$0.493101\pi$
$702$		−	4.33607i		−	0.163655i
$703$	43.7448	−	15.3512i	1.64987	−	0.578983i
$704$	6.28631			0.236924
$705$		0			0
$706$	11.6017	+	9.73497i	0.436635	+	0.366380i
$707$	0.576727	+	0.101692i	0.0216900	+	0.00382454i
$708$	−1.05702	−	2.90413i	−0.0397251	−	0.109144i
$709$	25.3839			0.953314			0.476657	−	0.879089i	$-0.341848\pi$
$709$	25.3839			0.953314			0.476657	+	0.879089i	$0.341848\pi$
$710$		0			0
$711$	−18.6822	−	32.3585i	−0.700636	−	1.21354i
$712$	−2.16290	+	0.381378i	−0.0810583	+	0.0142928i
$713$	−8.81698	−	5.09049i	−0.330198	−	0.190640i
$714$	−0.0255937	−	0.0443297i	−0.000957822	−	0.00165900i
$715$		0			0
$716$	6.56495	−	37.2317i	0.245344	−	1.39141i
$717$	3.10558	+	1.79301i	0.115980	+	0.0669611i
$718$	−1.02878	+	2.82654i	−0.0383935	+	0.105485i
$719$	−11.9137	−	4.33623i	−0.444306	−	0.161714i	0.110172	−	0.993913i	$-0.464860\pi$
$719$	−11.9137	−	4.33623i	−0.444306	−	0.161714i	−0.554478	+	0.832198i	$0.687082\pi$
$720$		0			0
$721$	0.0756578	+	0.0634844i	0.00281764	+	0.00236428i
$722$	17.9876	−	21.4368i	0.669428	−	0.797793i
$723$	−3.08226	+	0.543486i	−0.114631	+	0.0202125i
$724$	11.1619	+	4.06259i	0.414827	+	0.150985i
$725$		0			0
$726$	−0.129842	+	0.224893i	−0.00481888	+	0.00834655i
$727$	−26.7067	−	4.70911i	−0.990495	−	0.174651i	−0.345155	−	0.938546i	$-0.612174\pi$
$727$	−26.7067	−	4.70911i	−0.990495	−	0.174651i	−0.645341	+	0.763895i	$0.723285\pi$
$728$	0.297714	+	0.354802i	0.0110340	+	0.0131498i
$729$	−10.5691	−	18.3062i	−0.391448	−	0.678007i
$730$		0			0
$731$	−3.10790	−	17.6257i	−0.114950	−	0.651912i
$732$	1.23381	−	0.712343i	0.0456031	−	0.0263289i
$733$	−8.45193	−	23.2215i	−0.312179	−	0.857705i	−0.992216	−	0.124527i	$-0.960259\pi$
$733$	−8.45193	−	23.2215i	−0.312179	−	0.857705i	0.680037	−	0.733178i	$-0.261964\pi$
$734$	−21.7069			−0.801215
$735$		0			0
$736$	6.84610	−	38.8262i	0.252351	−	1.43115i
$737$	−10.4164	+	12.4138i	−0.383693	+	0.457267i
$738$	12.5752	+	14.9866i	0.462900	+	0.551663i
$739$	43.6930			1.60727			0.803636	−	0.595121i	$-0.202896\pi$
$739$	43.6930			1.60727			0.803636	+	0.595121i	$0.202896\pi$
$740$		0			0
$741$	−7.84002			−0.288011
$742$	0.222930	+	0.265677i	0.00818401	+	0.00975332i
$743$	−10.6793	+	12.7271i	−0.391787	+	0.466914i	−0.925498	−	0.378754i	$-0.876353\pi$
$743$	−10.6793	+	12.7271i	−0.391787	+	0.466914i	0.533710	+	0.845667i	$0.320797\pi$
$744$	0.218960	−	1.24179i	0.00802748	−	0.0455261i
$745$		0			0
$746$	−8.15533			−0.298588
$747$	15.7865	+	43.3730i	0.577597	+	1.58694i
$748$	−15.8502	+	9.15114i	−0.579542	+	0.334599i
$749$	0.0779091	+	0.441845i	0.00284674	+	0.0161446i
$750$		0			0
$751$	−25.0371	−	43.3655i	−0.913616	−	1.58243i	−0.808915	−	0.587926i	$-0.799945\pi$
$751$	−25.0371	−	43.3655i	−0.913616	−	1.58243i	−0.104701	−	0.994504i	$-0.533389\pi$
$752$	3.81724	+	4.54920i	0.139200	+	0.165892i
$753$	0.636661	+	0.112261i	0.0232012	+	0.00409100i
$754$	2.73367	−	4.73485i	0.0995542	−	0.172433i
$755$		0			0
$756$	−0.166248	−	0.0605093i	−0.00604638	−	0.00220070i
$757$	−17.9965	+	3.17327i	−0.654094	+	0.115334i	−0.490840	−	0.871250i	$-0.663310\pi$
$757$	−17.9965	+	3.17327i	−0.654094	+	0.115334i	−0.163254	+	0.986584i	$0.552199\pi$
$758$	−2.22238	+	2.64853i	−0.0807204	+	0.0961988i
$759$	6.01286	+	5.04539i	0.218253	+	0.183136i
$760$		0			0
$761$	−34.9088	−	12.7058i	−1.26544	−	0.460584i	−0.379852	−	0.925047i	$-0.624025\pi$
$761$	−34.9088	−	12.7058i	−1.26544	−	0.460584i	−0.885592	+	0.464463i	$0.846247\pi$
$762$	0.00333428	−	0.00916087i	0.000120788	−	0.000331863i
$763$	−0.739583	−	0.426999i	−0.0267747	−	0.0154584i
$764$	−2.31237	+	13.1141i	−0.0836585	+	0.474451i
$765$		0			0
$766$	−9.90651	−	17.1586i	−0.357937	−	0.619965i
$767$	16.5242	+	9.54026i	0.596655	+	0.344479i
$768$	3.64431	−	0.642591i	0.131503	−	0.0231875i
$769$	19.7287	+	34.1712i	0.711436	+	1.23224i	0.964318	+	0.264746i	$0.0852882\pi$
$769$	19.7287	+	34.1712i	0.711436	+	1.23224i	−0.252882	+	0.967497i	$0.581379\pi$
$770$		0			0
$771$	−6.45010			−0.232295
$772$	−0.0312318	−	0.0858086i	−0.00112406	−	0.00308832i
$773$	21.9405	+	3.86870i	0.789145	+	0.139148i	0.553674	−	0.832734i	$-0.313226\pi$
$773$	21.9405	+	3.86870i	0.789145	+	0.139148i	0.235471	+	0.971881i	$0.424337\pi$
$774$	8.00847	+	6.71990i	0.287858	+	0.241542i
$775$		0			0
$776$	30.3212			1.08847
$777$	0.0950329	−	0.0778870i	0.00340929	−	0.00279418i
$778$		−	19.5742i		−	0.701770i
$779$	55.2451	−	46.3562i	1.97936	−	1.66088i
$780$		0			0
$781$	−5.36112	+	30.4044i	−0.191836	+	1.08796i
$782$	−5.84730	−	16.0653i	−0.209099	−	0.574495i
$783$			4.89638i			0.174982i
$784$	−7.80738	+	2.84165i	−0.278835	+	0.101488i
$785$		0			0
$786$	−0.0866807	−	0.491591i	−0.00309180	−	0.0175345i
$787$	26.0542	+	15.0424i	0.928731	+	0.536203i	0.886410	−	0.462901i	$-0.153191\pi$
$787$	26.0542	+	15.0424i	0.928731	+	0.536203i	0.0423209	+	0.999104i	$0.486525\pi$
$788$	−8.67455	+	5.00825i	−0.309018	+	0.178412i
$789$	5.30723	−	4.45330i	0.188943	−	0.158542i
$790$		0			0
$791$	−0.390662	+	0.676647i	−0.0138904	+	0.0240588i
$792$	8.57270	−	23.5533i	0.304618	−	0.836930i
$793$	−3.00836	+	8.26541i	−0.106830	+	0.293513i
$794$	3.11869	+	17.6869i	0.110678	+	0.627686i
$795$		0			0
$796$	11.7194	+	9.83372i	0.415382	+	0.348547i
$797$	48.2250	−	8.50337i	1.70822	−	0.301205i	0.767665	−	0.640852i	$-0.221419\pi$
$797$	48.2250	−	8.50337i	1.70822	−	0.301205i	0.940553	+	0.339647i	$0.110308\pi$
$798$	0.0376970	−	0.103572i	0.00133446	−	0.00366640i
$799$	16.6331	+	6.05395i	0.588437	+	0.214173i
$800$		0			0
$801$	−0.441147	+	2.50187i	−0.0155872	+	0.0883992i
$802$	−1.58554	−	1.88957i	−0.0559873	−	0.0667231i
$803$	46.3098	−	26.7370i	1.63424	−	0.943528i
$804$	−1.16038	+	2.00983i	−0.0409233	+	0.0708813i
$805$		0			0
$806$	1.66021	+	2.87557i	0.0584785	+	0.101288i
$807$	1.13511	+	3.11869i	0.0399578	+	0.109783i
$808$			24.2251i			0.852234i
$809$	−5.74976	+	2.09274i	−0.202151	+	0.0735769i	−0.441111	−	0.897452i	$-0.645416\pi$
$809$	−5.74976	+	2.09274i	−0.202151	+	0.0735769i	0.238960	+	0.971029i	$0.423193\pi$
$810$		0			0
$811$	25.8545	+	21.6945i	0.907873	+	0.761796i	0.971713	−	0.236165i	$-0.0758905\pi$
$811$	25.8545	+	21.6945i	0.907873	+	0.761796i	−0.0638405	+	0.997960i	$0.520335\pi$
$812$	−0.143389	−	0.170885i	−0.00503198	−	0.00599688i
$813$			2.80164i			0.0982579i
$814$	9.59557	+	11.7079i	0.336324	+	0.410362i
$815$		0			0
$816$	−1.07767	+	0.904273i	−0.0377260	+	0.0316559i
$817$	24.7717	−	29.5217i	0.866651	−	1.03283i
$818$	−0.919944	−	0.162211i	−0.0321651	−	0.00567158i
$819$	0.503436	−	0.183236i	0.0175915	−	0.00640278i
$820$		0			0
$821$	−29.9060	+	10.8849i	−1.04373	+	0.379885i	−0.806292	−	0.591518i	$-0.798529\pi$
$821$	−29.9060	+	10.8849i	−1.04373	+	0.379885i	−0.237435	+	0.971403i	$0.576307\pi$
$822$	−0.578018	+	0.333719i	−0.0201607	+	0.0116398i
$823$	42.3584	−	7.46893i	1.47652	−	0.260351i	0.623335	−	0.781955i	$-0.285777\pi$
$823$	42.3584	−	7.46893i	1.47652	−	0.260351i	0.853187	+	0.521605i	$0.174666\pi$
$824$	−2.04275	+	3.53815i	−0.0711627	+	0.123257i
$825$		0			0
$826$	−0.205486	+	0.172423i	−0.00714977	+	0.00599937i
$827$	−21.1625	−	3.73152i	−0.735893	−	0.129758i	−0.206874	−	0.978368i	$-0.566329\pi$
$827$	−21.1625	−	3.73152i	−0.735893	−	0.129758i	−0.529019	+	0.848610i	$0.677440\pi$
$828$	−25.0998	−	14.4914i	−0.872277	−	0.503609i
$829$	21.1868	+	7.71135i	0.735847	+	0.267826i	0.682638	−	0.730757i	$-0.260833\pi$
$829$	21.1868	+	7.71135i	0.735847	+	0.267826i	0.0532093	+	0.998583i	$0.483055\pi$
$830$		0			0
$831$	−1.46393	−	8.30237i	−0.0507833	−	0.288006i
$832$	−3.57275	+	4.25783i	−0.123863	+	0.147614i
$833$	−15.9182	+	18.9705i	−0.551531	+	0.657289i
$834$	0.707843	+	4.01438i	0.0245106	+	0.139007i
$835$		0			0
$836$	−37.0325	−	13.4787i	−1.28079	−	0.466171i
$837$	−2.57528	−	1.48684i	−0.0890148	−	0.0513927i
$838$	4.16303	+	0.734054i	0.143809	+	0.0253575i
$839$	−43.0608	+	36.1323i	−1.48662	+	1.24742i	−0.587880	+	0.808948i	$0.700037\pi$
$839$	−43.0608	+	36.1323i	−1.48662	+	1.24742i	−0.898743	+	0.438476i	$0.855518\pi$
$840$		0			0
$841$	11.4131	−	19.7680i	0.393555	−	0.681657i
$842$	20.9150	−	3.68788i	0.720778	−	0.127093i
$843$	5.35523	−	3.09184i	0.184444	−	0.106489i
$844$	−37.0731	+	13.4935i	−1.27611	+	0.464465i
$845$		0			0
$846$	−9.71566	+	3.53621i	−0.334031	+	0.121577i
$847$	−0.0644213	−	0.0113592i	−0.00221354	−	0.000390307i
$848$	6.12683	−	7.30168i	0.210396	−	0.250741i
$849$	−3.11269	+	2.61186i	−0.106827	+	0.0896387i
$850$		0			0
$851$	35.7755	−	20.1070i	1.22637	−	0.689258i
$852$			4.42145i			0.151476i
$853$	11.3914	+	13.5757i	0.390033	+	0.464824i	0.924954	−	0.380078i	$-0.124103\pi$
$853$	11.3914	+	13.5757i	0.390033	+	0.464824i	−0.534921	+	0.844902i	$0.679659\pi$
$854$	−0.0947263	−	0.0794848i	−0.00324147	−	0.00271991i
$855$		0			0
$856$	−17.4401	+	6.34769i	−0.596092	+	0.216960i
$857$			37.2651i			1.27295i	0.771297	+	0.636475i	$0.219608\pi$
$857$			37.2651i			1.27295i	−0.771297	+	0.636475i	$0.780392\pi$
$858$	−0.875555	−	2.40557i	−0.0298910	−	0.0821247i
$859$	3.04374	+	5.27192i	0.103851	+	0.179876i	0.913268	−	0.407359i	$-0.133550\pi$
$859$	3.04374	+	5.27192i	0.103851	+	0.179876i	−0.809417	+	0.587234i	$0.800217\pi$
$860$		0			0
$861$	0.0955694	−	0.165531i	0.00325700	−	0.00564128i
$862$	−5.71076	+	3.29711i	−0.194509	+	0.112300i
$863$	5.65152	+	6.73522i	0.192380	+	0.229270i	0.853609	−	0.520915i	$-0.174409\pi$
$863$	5.65152	+	6.73522i	0.192380	+	0.229270i	−0.661229	+	0.750184i	$0.729965\pi$
$864$	1.99962	−	11.3404i	0.0680286	−	0.385809i
$865$		0			0
$866$	21.6071	+	7.86435i	0.734240	+	0.267242i
$867$	0.511819	−	1.40621i	0.0173823	−	0.0477574i
$868$	0.133419	−	0.0235255i	0.00452855	−	0.000798506i
$869$	−34.4523	−	28.9089i	−1.16871	−	0.980666i
$870$		0			0
$871$	−2.48805	−	14.1104i	−0.0843043	−	0.478114i
$872$	12.0824	−	33.1962i	0.409163	−	1.12417i
$873$	11.9957	−	32.9579i	0.405993	−	1.11546i
$874$	18.4062	−	31.8806i	0.622601	−	1.07838i
$875$		0			0
$876$	5.86646	−	4.92254i	0.198209	−	0.166317i
$877$	8.09389	−	4.67301i	0.273311	−	0.157796i	−0.357080	−	0.934074i	$-0.616228\pi$
$877$	8.09389	−	4.67301i	0.273311	−	0.157796i	0.630391	+	0.776277i	$0.282894\pi$
$878$	7.07651	+	4.08562i	0.238821	+	0.137883i
$879$	−1.47789	−	8.38155i	−0.0498481	−	0.282703i
$880$		0			0
$881$	12.2287	−	4.45087i	0.411994	−	0.149954i	−0.127704	−	0.991812i	$-0.540761\pi$
$881$	12.2287	−	4.45087i	0.411994	−	0.149954i	0.539698	+	0.841859i	$0.318538\pi$
$882$		−	14.4652i		−	0.487069i
$883$	4.80696	+	13.2070i	0.161767	+	0.444452i	0.993921	−	0.110093i	$-0.0351148\pi$
$883$	4.80696	+	13.2070i	0.161767	+	0.444452i	−0.832154	+	0.554544i	$0.812893\pi$
$884$	2.81005	−	15.9366i	0.0945123	−	0.536006i
$885$		0			0
$886$	12.0987	−	10.1520i	0.406463	−	0.341063i
$887$		−	35.2009i		−	1.18193i	−0.806697	−	0.590966i	$-0.798747\pi$
$887$		−	35.2009i		−	1.18193i	0.806697	−	0.590966i	$-0.201253\pi$
$888$	3.85558	+	3.31195i	0.129385	+	0.111142i
$889$	0.00245575			8.23633e−5
$890$		0			0
$891$	−21.3151	−	17.8855i	−0.714082	−	0.599186i
$892$	3.87464	+	0.683204i	0.129733	+	0.0228754i
$893$	13.0356	+	35.8150i	0.436219	+	1.19850i
$894$	−2.04269			−0.0683176
$895$		0			0
$896$	0.313627	+	0.543218i	0.0104775	+	0.0181476i
$897$	−6.83467	+	1.20514i	−0.228203	+	0.0402383i
$898$	−15.0045	−	8.66287i	−0.500708	−	0.289084i
$899$	−1.87475	−	3.24716i	−0.0625263	−	0.108299i
$900$		0			0
$901$	4.93338	−	27.9786i	0.164355	−	0.932102i
$902$	20.3932	+	11.7740i	0.679019	+	0.392032i
$903$	0.0349340	−	0.0959804i	0.00116253	−	0.00319403i
$904$	−30.3713	−	11.0543i	−1.01014	−	0.367659i
$905$		0			0
$906$	−1.96213	−	1.64642i	−0.0651873	−	0.0546987i
$907$	2.16868	−	2.58453i	0.0720097	−	0.0858179i	−0.728837	−	0.684687i	$-0.759939\pi$
$907$	2.16868	−	2.58453i	0.0720097	−	0.0858179i	0.800847	+	0.598870i	$0.204383\pi$
$908$	5.62517	−	0.991870i	0.186678	−	0.0329164i
$909$	26.3316	+	9.58393i	0.873365	+	0.317879i
$910$		0			0
$911$	21.8567	−	37.8570i	0.724146	−	1.25426i	−0.235179	−	0.971952i	$-0.575568\pi$
$911$	21.8567	−	37.8570i	0.724146	−	1.25426i	0.959325	−	0.282305i	$-0.0910991\pi$
$912$	−2.98315	−	0.526010i	−0.0987819	−	0.0174179i
$913$	35.7115	+	42.5593i	1.18188	+	1.40851i
$914$	12.4642	+	21.5886i	0.412278	+	0.714086i
$915$		0			0
$916$	6.81865	+	38.6705i	0.225295	+	1.27771i
$917$	0.108897	−	0.0628718i	0.00359610	−	0.00207621i
$918$	−1.70789	−	4.69239i	−0.0563688	−	0.154872i
$919$	44.0441			1.45288			0.726441	−	0.687229i	$-0.241173\pi$
$919$	44.0441			1.45288			0.726441	+	0.687229i	$0.241173\pi$
$920$		0			0
$921$	−1.54843	+	8.78156i	−0.0510224	+	0.289362i
$922$	16.0511	−	19.1289i	0.528614	−	0.629977i
$923$	−17.5466	−	20.9112i	−0.577552	−	0.688300i
$924$	−0.104449			−0.00343613
$925$		0			0
$926$	−1.71418			−0.0563315
$927$	3.03767	+	3.62015i	0.0997701	+	0.118901i
$928$	9.33306	−	11.1227i	0.306373	−	0.365121i
$929$	−7.32074	+	41.5180i	−0.240186	+	1.36216i	0.591227	+	0.806506i	$0.298644\pi$
$929$	−7.32074	+	41.5180i	−0.240186	+	1.36216i	−0.831412	+	0.555656i	$0.812467\pi$
$930$		0			0
$931$	−53.3233			−1.74760
$932$	−0.569434	−	1.56451i	−0.0186524	−	0.0512471i
$933$	4.27407	−	2.46763i	0.139927	−	0.0807867i
$934$	−2.58877	−	14.6816i	−0.0847071	−	0.480398i
$935$		0			0
$936$	11.0809	+	19.1927i	0.362191	+	0.627332i
$937$	0.141067	+	0.168117i	0.00460847	+	0.00549216i	0.768344	−	0.640037i	$-0.221081\pi$
$937$	0.141067	+	0.168117i	0.00460847	+	0.00549216i	−0.763735	+	0.645530i	$0.776637\pi$
$938$	0.198371	+	0.0349782i	0.00647704	+	0.00114208i
$939$	−1.61404	+	2.79559i	−0.0526721	+	0.0912308i
$940$		0			0
$941$	2.15188	+	0.783219i	0.0701492	+	0.0255322i	0.376856	−	0.926272i	$-0.377005\pi$
$941$	2.15188	+	0.783219i	0.0701492	+	0.0255322i	−0.306707	+	0.951804i	$0.599227\pi$
$942$	1.25087	−	0.220562i	0.0407554	−	0.00718628i
$943$	41.0352	−	48.9038i	1.33629	−	1.59253i
$944$	5.64742	+	4.73875i	0.183808	+	0.154233i
$945$		0			0
$946$	11.8246	+	4.30382i	0.384452	+	0.139929i
$947$	−10.4147	+	28.6140i	−0.338431	+	0.929831i	0.647409	+	0.762143i	$0.275852\pi$
$947$	−10.4147	+	28.6140i	−0.338431	+	0.929831i	−0.985840	+	0.167688i	$0.946370\pi$
$948$	−5.57794	−	3.22042i	−0.181163	−	0.104595i
$949$	−8.21017	+	46.5622i	−0.266513	+	1.51147i
$950$		0			0
$951$	2.85727	+	4.94893i	0.0926532	+	0.160480i
$952$	0.461928	+	0.266694i	0.0149712	+	0.00864361i
$953$	−9.24999	+	1.63102i	−0.299637	+	0.0528340i	−0.321445	−	0.946928i	$-0.604169\pi$
$953$	−9.24999	+	1.63102i	−0.299637	+	0.0528340i	0.0218088	+	0.999762i	$0.493058\pi$
$954$	8.29743	+	14.3716i	0.268639	+	0.465297i
$955$		0			0
$956$	−15.9379			−0.515468
$957$	0.988695	+	2.71642i	0.0319600	+	0.0878093i
$958$	−4.71518	−	0.831413i	−0.152340	−	0.0268617i
$959$	−0.128795	−	0.108072i	−0.00415900	−	0.00348981i
$960$		0			0
$961$	−28.7229			−0.926544
$962$	−13.3835	−	0.154794i	−0.431502	−	0.00499075i
$963$			21.4680i			0.691796i
$964$	10.6559	−	8.94137i	0.343204	−	0.287982i
$965$		0			0
$966$	0.0169424	−	0.0960850i	0.000545112	−	0.00309148i
$967$	−8.64596	−	23.7546i	−0.278035	−	0.763895i	−0.997585	−	0.0694547i	$-0.977874\pi$
$967$	−8.64596	−	23.7546i	−0.278035	−	0.763895i	0.719550	−	0.694441i	$-0.244348\pi$
$968$		−	2.70598i		−	0.0869735i
$969$	−8.48428	+	3.08803i	−0.272554	+	0.0992017i
$970$		0			0
$971$	−6.90577	−	39.1646i	−0.221617	−	1.25685i	−0.869048	−	0.494727i	$-0.835268\pi$
$971$	−6.90577	−	39.1646i	−0.221617	−	1.25685i	0.647432	−	0.762124i	$-0.275843\pi$
$972$	−11.0665	−	6.38926i	−0.354959	−	0.204936i
$973$	−0.889265	+	0.513417i	−0.0285085	+	0.0164594i
$974$	22.1760	−	18.6079i	0.710564	−	0.596234i
$975$		0			0
$976$	−1.69924	+	2.94317i	−0.0543914	+	0.0942086i
$977$	−15.9210	+	43.7427i	−0.509359	+	1.39945i	0.372541	+	0.928016i	$0.378487\pi$
$977$	−15.9210	+	43.7427i	−0.509359	+	1.39945i	−0.881900	+	0.471437i	$0.843735\pi$
$978$	0.612259	−	1.68217i	0.0195779	−	0.0537898i
$979$	0.530994	+	3.01142i	0.0169707	+	0.0962453i
$980$		0			0
$981$	−31.3028	−	26.2662i	−0.999423	−	0.838615i
$982$	16.8563	−	2.97223i	0.537907	−	0.0948476i
$983$	−8.70159	+	23.9074i	−0.277538	+	0.762528i	0.720103	+	0.693868i	$0.244095\pi$
$983$	−8.70159	+	23.9074i	−0.277538	+	0.762528i	−0.997640	+	0.0686605i	$0.978127\pi$
$984$	7.42987	+	2.70425i	0.236855	+	0.0862083i
$985$		0			0
$986$	1.09335	−	6.20067i	0.0348192	−	0.197470i
$987$	0.0649315	+	0.0773823i	0.00206679	+	0.00246311i
$988$	30.1763	−	17.4223i	0.960037	−	0.554278i
$989$	17.0571	−	29.5438i	0.542386	−	0.939440i
$990$		0			0
$991$	24.2883	+	42.0686i	0.771545	+	1.33635i	0.936716	+	0.350090i	$0.113849\pi$
$991$	24.2883	+	42.0686i	0.771545	+	1.33635i	−0.165172	+	0.986265i	$0.552818\pi$
$992$	3.01597	+	8.28631i	0.0957572	+	0.263091i
$993$			8.57951i			0.272263i
$994$	0.360619	−	0.131255i	0.0114381	−	0.00416314i
$995$		0			0
$996$	6.09500	+	5.11431i	0.193127	+	0.162053i
$997$	8.95771	+	10.6754i	0.283694	+	0.338093i	0.889006	−	0.457895i	$-0.151396\pi$
$997$	8.95771	+	10.6754i	0.283694	+	0.338093i	−0.605313	+	0.795988i	$0.706952\pi$
$998$			6.23096i			0.197238i
$999$	10.4494	−	5.87289i	0.330604	−	0.185810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.11		156
5.2	odd	4		925.2.p.f.826.8	yes	78
5.3	odd	4		925.2.p.e.826.6	yes	78
5.4	even	2	inner	925.2.bc.e.49.16		156
37.34	even	9	inner	925.2.bc.e.774.16		156
185.34	even	18	inner	925.2.bc.e.774.11		156
185.108	odd	36		925.2.p.e.626.6	✓	78
185.182	odd	36		925.2.p.f.626.8	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.6	✓	78	185.108	odd	36
925.2.p.e.826.6	yes	78	5.3	odd	4
925.2.p.f.626.8	yes	78	185.182	odd	36
925.2.p.f.826.8	yes	78	5.2	odd	4
925.2.bc.e.49.11		156	1.1	even	1	trivial
925.2.bc.e.49.16		156	5.4	even	2	inner
925.2.bc.e.774.11		156	185.34	even	18	inner
925.2.bc.e.774.16		156	37.34	even	9	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:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.460177 - 0.548417i) q^{2} +(-0.215129 + 0.256381i) q^{3} +(0.258298 - 1.46488i) q^{4} +0.239601 q^{6} +(0.0206430 + 0.0567163i) q^{7} +(-2.16222 + 1.24836i) q^{8} +(0.501494 + 2.84411i) q^{9} +O(q^{10})\)	\(q+(-0.460177 - 0.548417i) q^{2} +(-0.215129 + 0.256381i) q^{3} +(0.258298 - 1.46488i) q^{4} +0.239601 q^{6} +(0.0206430 + 0.0567163i) q^{7} +(-2.16222 + 1.24836i) q^{8} +(0.501494 + 2.84411i) q^{9} +(1.73809 + 3.01046i) q^{11} +(0.319999 + 0.381360i) q^{12} +(-3.02686 - 0.533718i) q^{13} +(0.0216047 - 0.0374205i) q^{14} +(-1.11592 - 0.406162i) q^{16} +(-3.48582 + 0.614644i) q^{17} +(1.32898 - 1.58382i) q^{18} +(-5.83847 - 4.89905i) q^{19} +(-0.0189819 - 0.00690884i) q^{21} +(0.851159 - 2.33854i) q^{22} +(-5.84284 - 3.37337i) q^{23} +(0.145101 - 0.822908i) q^{24} +(1.10019 + 1.90559i) q^{26} +(-1.70659 - 0.985300i) q^{27} +(0.0884145 - 0.0155899i) q^{28} +(-1.24236 - 2.15183i) q^{29} +1.50902 q^{31} +(1.99863 + 5.49118i) q^{32} +(-1.14574 - 0.202024i) q^{33} +(1.94117 + 1.62884i) q^{34} +4.29581 q^{36} +(-3.10210 + 5.23230i) q^{37} +5.45634i q^{38} +(0.788001 - 0.661211i) q^{39} +(-1.64311 + 9.31852i) q^{41} +(0.00494609 + 0.0135893i) q^{42} +5.05642i q^{43} +(4.85890 - 1.76849i) q^{44} +(0.838727 + 4.75666i) q^{46} +(-4.33077 - 2.50037i) q^{47} +(0.344199 - 0.198723i) q^{48} +(5.35952 - 4.49717i) q^{49} +(0.592318 - 1.02592i) q^{51} +(-1.56366 + 4.29613i) q^{52} +(-2.74519 + 7.54236i) q^{53} +(0.244977 + 1.38933i) q^{54} +(-0.115437 - 0.0968630i) q^{56} +(2.51205 - 0.442942i) q^{57} +(-0.608395 + 1.67155i) q^{58} +(-5.83358 - 2.12325i) q^{59} +(0.496944 - 2.81831i) q^{61} +(-0.694417 - 0.827574i) q^{62} +(-0.150955 + 0.0871540i) q^{63} +(0.904198 - 1.56612i) q^{64} +(0.416448 + 0.721309i) q^{66} +(1.59441 + 4.38060i) q^{67} +5.26506i q^{68} +(2.12183 - 0.772283i) q^{69} +(6.80358 + 5.70888i) q^{71} +(-4.63480 - 5.52354i) q^{72} -15.3830i q^{73} +(4.29700 - 0.706537i) q^{74} +(-8.68458 + 7.28723i) q^{76} +(-0.134863 + 0.160723i) q^{77} +(-0.725239 - 0.127879i) q^{78} +(-12.1576 + 4.42500i) q^{79} +(-7.52172 + 2.73768i) q^{81} +(5.86655 - 3.38706i) q^{82} +(15.7395 - 2.77529i) q^{83} +(-0.0150236 + 0.0260216i) q^{84} +(2.77303 - 2.32685i) q^{86} +(0.818955 + 0.144404i) q^{87} +(-7.51625 - 4.33951i) q^{88} +(0.826615 + 0.300863i) q^{89} +(-0.0322132 - 0.182690i) q^{91} +(-6.45076 + 7.68772i) q^{92} +(-0.324635 + 0.386884i) q^{93} +(0.621672 + 3.52568i) q^{94} +(-1.83779 - 0.668903i) q^{96} +(-10.5174 - 6.07223i) q^{97} +(-4.93265 - 0.869760i) q^{98} +(-7.69045 + 6.45305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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