LMFDB - Embedded newform 925.2.bc.e.49.16

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			49.16
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.16

$q$-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	0.903797	−	0.427962i	$-0.140768\pi$
$2$	0.460177	+	0.548417i	0.325394	+	0.387789i	−0.578403	+	0.815751i	$0.696324\pi$
$3$	0.215129	−	0.256381i	0.124205	−	0.148021i	−0.700358	−	0.713791i	$-0.746976\pi$
$3$	0.215129	−	0.256381i	0.124205	−	0.148021i	0.824563	+	0.565770i	$0.191421\pi$
$4$	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	0.935730	−	0.352716i	$-0.114742\pi$
$7$	−0.0206430	−	0.0567163i	−0.00780234	−	0.0214367i	−0.943533	+	0.331280i	$0.892520\pi$
$8$	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	0.576835	−	0.816860i	$-0.304287\pi$
$13$	3.02686	+	0.533718i	0.839501	+	0.148027i	0.262665	+	0.964887i	$0.415399\pi$
$14$	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	0.265880	−	0.964006i	$-0.414338\pi$
$17$	3.48582	−	0.614644i	0.845435	−	0.149073i	0.579555	+	0.814933i	$0.303226\pi$
$18$	−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	0.964558	−	0.263872i	$-0.0849997\pi$
$23$	5.84284	+	3.37337i	1.21832	+	0.703395i	0.253759	+	0.967268i	$0.418333\pi$
$24$	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	$-0.874012\pi$
$43$		−	5.05642i		−	0.771097i	0.922688	−	0.385548i	$-0.125988\pi$
$44$	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	0.781413	−	0.624014i	$-0.214499\pi$
$47$	4.33077	+	2.50037i	0.631707	+	0.364716i	−0.149706	+	0.988731i	$0.547833\pi$
$48$	−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	$-0.703038\pi$
$53$	2.74519	−	7.54236i	0.377081	−	1.03602i	0.972560	−	0.232651i	$-0.0747401\pi$
$54$	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	0.803394	−	0.595448i	$-0.203025\pi$
$67$	−1.59441	−	4.38060i	−0.194788	−	0.535175i	−0.998182	+	0.0602725i	$0.980803\pi$
$68$		−	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	$0.356595\pi$
$73$			15.3830i			1.80044i	−0.435433	+	0.900221i	$0.643405\pi$
$74$	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	−0.947207	−	0.320624i	$-0.896107\pi$
$83$	−15.7395	+	2.77529i	−1.72763	+	0.304628i	−0.780423	+	0.625252i	$0.784996\pi$
$84$	−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	0.927602	−	0.373570i	$-0.121867\pi$
$97$	10.5174	+	6.07223i	1.06788	+	0.616542i	0.140280	+	0.990112i	$0.455200\pi$
$98$	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	−0.568189	−	0.822898i	$-0.692356\pi$
$103$	−1.41712	+	0.818177i	−0.139633	+	0.0806174i	0.428556	+	0.903515i	$0.359023\pi$
$104$	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	−0.191804	−	0.981433i	$-0.561434\pi$
$107$	−7.32061	−	1.29082i	−0.707710	−	0.124788i	−0.515907	+	0.856645i	$0.672545\pi$
$108$	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	0.216279	−	0.976332i	$-0.430608\pi$
$113$	−8.32103	−	9.91662i	−0.782777	−	0.932877i	−0.999055	+	0.0434548i	$0.986164\pi$
$114$	−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	−0.940309	−	0.340323i	$-0.889464\pi$
$127$	−0.0139160	+	0.0382339i	−0.00123484	+	0.00339271i	0.939074	+	0.343716i	$0.111686\pi$
$128$	−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	−0.393394	−	0.919370i	$-0.628699\pi$
$137$	2.41242	−	1.39281i	0.206107	−	0.118996i	0.599501	+	0.800374i	$0.295366\pi$
$138$	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	−0.378044	−	0.925788i	$-0.623403\pi$
$157$	−5.22063	+	0.920537i	−0.416651	+	0.0734669i	−0.0386072	+	0.999254i	$0.512292\pi$
$158$	−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	−0.998642	−	0.0520999i	$-0.983409\pi$
$163$	−2.55533	+	7.02070i	−0.200149	+	0.549904i	0.798493	+	0.602004i	$0.205631\pi$
$164$	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	−0.974847	−	0.222877i	$-0.928455\pi$
$167$	−7.57376	+	9.02606i	−0.586075	+	0.698457i	0.388771	+	0.921334i	$0.372900\pi$
$168$	−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	0.780839	−	0.624733i	$-0.214792\pi$
$173$	0.394661	+	0.470339i	0.0300055	+	0.0357592i	−0.750833	+	0.660492i	$0.770348\pi$
$174$	−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	−0.501912	−	0.864919i	$-0.667370\pi$
$193$	−0.0531650	+	0.0306948i	−0.00382690	+	0.00220946i	0.498085	+	0.867128i	$0.334037\pi$
$194$	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	0.897872	−	0.440256i	$-0.145112\pi$
$197$	4.32846	+	5.15846i	0.308390	+	0.367525i	−0.589482	+	0.807782i	$0.700668\pi$
$198$	−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	$-0.971773\pi$
$223$		−	2.64503i		−	0.177124i	0.996071	−	0.0885620i	$-0.0282272\pi$
$224$	−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	0.888446	−	0.458982i	$-0.151786\pi$
$227$	−1.31337	−	3.60845i	−0.0871713	−	0.239501i	−0.975617	+	0.219481i	$0.929564\pi$
$228$			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	−0.531415	−	0.847111i	$-0.678340\pi$
$233$	−0.969331	+	0.559644i	−0.0635030	+	0.0366635i	0.467912	+	0.883775i	$0.345006\pi$
$234$	−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	0.225837	−	0.974165i	$-0.427488\pi$
$257$	−12.3880	−	14.7635i	−0.772745	−	0.920921i	−0.998582	+	0.0532437i	$0.983044\pi$
$258$		−	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	0.762213	−	0.647326i	$-0.224113\pi$
$263$	20.3861	+	3.59462i	1.25706	+	0.221654i	0.494848	+	0.868980i	$0.335224\pi$
$264$	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	$-0.504566\pi$
$277$	16.1915	−	19.2963i	0.972853	−	1.15940i	0.987197	−	0.159503i	$-0.0509893\pi$
$278$	−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	−0.193420	−	0.981116i	$-0.561958\pi$
$283$	−11.9564	−	2.10824i	−0.710737	−	0.125322i	−0.517317	+	0.855794i	$0.673069\pi$
$284$	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	$-0.511271\pi$
$293$	16.3459	−	19.4803i	0.954937	−	1.13805i	0.990338	−	0.138677i	$-0.0442850\pi$
$294$	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	−0.983228	−	0.182383i	$-0.941619\pi$
$307$	−23.0738	+	13.3217i	−1.31689	+	0.760308i	−0.333665	+	0.942692i	$0.608286\pi$
$308$	−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	−0.435521	−	0.900179i	$-0.643436\pi$
$313$	−9.49869	+	1.67487i	−0.536898	+	0.0946695i	−0.101377	+	0.994848i	$0.532325\pi$
$314$	−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	$0.270293\pi$
$317$	−5.83984	+	16.0448i	−0.327998	+	0.901167i	−0.988618	+	0.150447i	$0.951929\pi$
$318$	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	0.326866	−	0.945071i	$-0.394007\pi$
$337$	5.70530	+	1.00600i	0.310787	+	0.0548002i	−0.0160792	+	0.999871i	$0.505118\pi$
$338$	−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	0.774003	−	0.633182i	$-0.218252\pi$
$347$	11.4125	+	6.58898i	0.612653	+	0.353715i	−0.161350	+	0.986897i	$0.551585\pi$
$348$	−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	0.410911	−	0.911675i	$-0.365211\pi$
$353$	20.8335	−	3.67350i	1.10885	−	0.195521i	0.697942	+	0.716155i	$0.254099\pi$
$354$	−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	$0.512852\pi$
$367$	−19.4898	+	23.2271i	−1.01736	+	1.21244i	−0.976996	+	0.213258i	$0.931593\pi$
$368$	−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	−0.921542	−	0.388278i	$-0.873070\pi$
$373$	−7.32238	+	8.72647i	−0.379138	+	0.451840i	0.542404	+	0.840118i	$0.317514\pi$
$374$	−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	−0.573538	−	0.819179i	$-0.694429\pi$
$383$	−27.2549	−	4.80578i	−1.39266	−	0.245564i	−0.819125	+	0.573615i	$0.805540\pi$
$384$	−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	0.933679	−	0.358111i	$-0.116579\pi$
$397$	21.7258	+	12.5434i	1.09038	+	0.629534i	0.156706	+	0.987645i	$0.449913\pi$
$398$	−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	0.350402	−	0.936600i	$-0.386045\pi$
$433$	27.8154	−	16.0592i	1.33672	−	0.771756i	0.986320	+	0.164843i	$0.0527118\pi$
$434$	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	$-0.824411\pi$
$443$		−	22.0611i		−	1.04815i	0.851671	−	0.524077i	$-0.175589\pi$
$444$	−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	0.902811	−	0.430039i	$-0.141500\pi$
$457$	34.2916	+	6.04653i	1.60409	+	0.282845i	0.701283	+	0.712883i	$0.252611\pi$
$458$	−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	−0.800622	−	0.599170i	$-0.795497\pi$
$463$	−1.53910	+	1.83423i	−0.0715281	+	0.0852438i	0.729094	+	0.684414i	$0.239942\pi$
$464$	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	0.0208761	−	0.999782i	$-0.493354\pi$
$467$	−18.0342	−	10.4120i	−0.834523	−	0.481812i	−0.855399	+	0.517970i	$0.826688\pi$
$468$	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	$-0.631262\pi$
$487$		−	40.4363i		−	1.83235i	0.400784	−	0.916173i	$-0.368738\pi$
$488$	−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	$0.224661\pi$
$503$	−5.35736	+	14.7192i	−0.238873	+	0.656298i	−0.999971	+	0.00766089i	$0.997561\pi$
$504$	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	$-0.928167\pi$
$523$	−8.50398	−	23.3645i	−0.371853	−	1.02166i	0.602792	−	0.797899i	$-0.294055\pi$
$524$	−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	−0.849982	−	0.526811i	$-0.823388\pi$
$547$	−19.1488	+	11.0555i	−0.818742	+	0.472701i	0.0312406	+	0.999512i	$0.490054\pi$
$548$	−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	$0.224582\pi$
$557$	29.9180	+	35.6548i	1.26766	+	1.51074i	0.506407	+	0.862295i	$0.330973\pi$
$558$	−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	−0.111624	−	0.993751i	$-0.535605\pi$
$563$	16.4474	−	9.49594i	0.693177	−	0.400206i	0.804801	+	0.593544i	$0.202272\pi$
$564$	−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	−0.911951	−	0.410299i	$-0.865424\pi$
$577$	1.21015	−	3.32487i	0.0503794	−	0.138416i	0.962330	+	0.271883i	$0.0876464\pi$
$578$	−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	$-0.798629\pi$
$587$	−13.7794	−	37.8587i	−0.568738	−	1.56259i	0.237739	−	0.971329i	$-0.423594\pi$
$588$	−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	$-0.881036\pi$
$593$		−	17.7814i		−	0.730193i	0.930970	−	0.365096i	$-0.118964\pi$
$594$	−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	$0.422270\pi$
$607$	−13.9731	+	38.3909i	−0.567153	+	1.55824i	−0.808929	+	0.587907i	$0.799952\pi$
$608$	−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	$-0.472033\pi$
$613$	16.3616	−	44.9530i	0.660837	−	1.81564i	0.573089	−	0.819493i	$-0.305745\pi$
$614$	−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	0.194571	−	0.980888i	$-0.437668\pi$
$617$	−20.0008	−	23.8360i	−0.805202	−	0.959603i	−0.999773	+	0.0212858i	$0.993224\pi$
$618$	−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	0.549113	−	0.835748i	$-0.314966\pi$
$643$	2.53298	+	1.46241i	0.0998909	+	0.0576720i	−0.449222	+	0.893420i	$0.648299\pi$
$644$	−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	−0.363526	−	0.931584i	$-0.618427\pi$
$647$	15.6949	−	18.7045i	0.617030	−	0.735348i	0.980557	+	0.196236i	$0.0628718\pi$
$648$	−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	0.147369	−	0.989082i	$-0.452920\pi$
$653$	−1.33994	−	0.236268i	−0.0524360	−	0.00924588i	−0.199805	+	0.979836i	$0.564031\pi$
$654$	−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	$0.270830\pi$
$673$	16.5389	+	45.4403i	0.637529	+	1.75160i	−0.0218238	+	0.999762i	$0.506947\pi$
$674$	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	−0.316277	−	0.948667i	$-0.602433\pi$
$677$	9.03269	−	5.21503i	0.347155	−	0.200430i	0.663431	+	0.748237i	$0.269099\pi$
$678$	−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	0.0371935	−	0.999308i	$-0.488158\pi$
$683$	10.8177	−	1.90745i	0.413927	−	0.0729866i	0.376734	+	0.926322i	$0.377047\pi$
$684$	−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	0.645341	−	0.763895i	$-0.276715\pi$
$727$	26.7067	+	4.70911i	0.990495	+	0.174651i	0.345155	+	0.938546i	$0.387826\pi$
$728$	−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	$0.0397415\pi$
$733$	8.45193	+	23.2215i	0.312179	+	0.857705i	−0.680037	+	0.733178i	$0.738036\pi$
$734$	−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	−0.533710	−	0.845667i	$-0.679203\pi$
$743$	10.6793	−	12.7271i	0.391787	−	0.466914i	0.925498	+	0.378754i	$0.123647\pi$
$744$	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	0.163254	−	0.986584i	$-0.447801\pi$
$757$	17.9965	−	3.17327i	0.654094	−	0.115334i	0.490840	+	0.871250i	$0.336690\pi$
$758$	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	−0.235471	−	0.971881i	$-0.575663\pi$
$773$	−21.9405	−	3.86870i	−0.789145	−	0.139148i	−0.553674	+	0.832734i	$0.686774\pi$
$774$	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	−0.0423209	−	0.999104i	$-0.513475\pi$
$787$	−26.0542	−	15.0424i	−0.928731	−	0.536203i	−0.886410	+	0.462901i	$0.846809\pi$
$788$	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	−0.940553	−	0.339647i	$-0.889692\pi$
$797$	−48.2250	+	8.50337i	−1.70822	+	0.301205i	−0.767665	+	0.640852i	$0.778581\pi$
$798$	−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	−0.853187	−	0.521605i	$-0.825334\pi$
$823$	−42.3584	+	7.46893i	−1.47652	+	0.260351i	−0.623335	+	0.781955i	$0.714223\pi$
$824$	−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	0.529019	−	0.848610i	$-0.322560\pi$
$827$	21.1625	+	3.73152i	0.735893	+	0.129758i	0.206874	+	0.978368i	$0.433671\pi$
$828$	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	0.534921	−	0.844902i	$-0.320341\pi$
$853$	−11.3914	−	13.5757i	−0.390033	−	0.464824i	−0.924954	+	0.380078i	$0.875897\pi$
$854$	−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	$-0.780392\pi$
$857$		−	37.2651i		−	1.27295i	0.771297	−	0.636475i	$-0.219608\pi$
$858$	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	0.661229	−	0.750184i	$-0.270035\pi$
$863$	−5.65152	−	6.73522i	−0.192380	−	0.229270i	−0.853609	+	0.520915i	$0.825591\pi$
$864$	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	−0.630391	−	0.776277i	$-0.717106\pi$
$877$	−8.09389	+	4.67301i	−0.273311	+	0.157796i	0.357080	+	0.934074i	$0.383772\pi$
$878$	−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	0.832154	−	0.554544i	$-0.187107\pi$
$883$	−4.80696	−	13.2070i	−0.161767	−	0.444452i	−0.993921	+	0.110093i	$0.964885\pi$
$884$	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	$0.201253\pi$
$887$			35.2009i			1.18193i	−0.806697	+	0.590966i	$0.798747\pi$
$888$	−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	−0.800847	−	0.598870i	$-0.795617\pi$
$907$	−2.16868	+	2.58453i	−0.0720097	+	0.0858179i	0.728837	+	0.684687i	$0.240061\pi$
$908$	−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	0.763735	−	0.645530i	$-0.223363\pi$
$937$	−0.141067	−	0.168117i	−0.00460847	−	0.00549216i	−0.768344	+	0.640037i	$0.778919\pi$
$938$	−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	$-0.724148\pi$
$947$	10.4147	−	28.6140i	0.338431	−	0.929831i	0.985840	−	0.167688i	$-0.0536303\pi$
$948$	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	−0.0218088	−	0.999762i	$-0.506942\pi$
$953$	9.24999	−	1.63102i	0.299637	−	0.0528340i	0.321445	+	0.946928i	$0.395831\pi$
$954$	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	$0.0221259\pi$
$967$	8.64596	+	23.7546i	0.278035	+	0.763895i	−0.719550	+	0.694441i	$0.755652\pi$
$968$			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	$-0.621513\pi$
$977$	15.9210	−	43.7427i	0.509359	−	1.39945i	0.881900	−	0.471437i	$-0.156265\pi$
$978$	−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	$-0.755905\pi$
$983$	8.70159	−	23.9074i	0.277538	−	0.762528i	0.997640	−	0.0686605i	$-0.0218725\pi$
$984$	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	0.605313	−	0.795988i	$-0.293048\pi$
$997$	−8.95771	−	10.6754i	−0.283694	−	0.338093i	−0.889006	+	0.457895i	$0.848604\pi$
$998$		−	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.49.16		156
5.2	odd	4		925.2.p.e.826.6	yes	78
5.3	odd	4		925.2.p.f.826.8	yes	78
5.4	even	2	inner	925.2.bc.e.49.11		156
37.34	even	9	inner	925.2.bc.e.774.11		156
185.34	even	18	inner	925.2.bc.e.774.16		156
185.108	odd	36		925.2.p.f.626.8	yes	78
185.182	odd	36		925.2.p.e.626.6	✓	78

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

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