LMFDB - Embedded newform 392.2.y.a.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(9,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("392.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.y (of order $21$, degree $12$, 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$7$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			65.4
Character	$\chi$	$=$	392.65
Dual form			392.2.y.a.193.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0247290 - 0.329985i) q^{3} +(-1.09829 + 0.748802i) q^{5} +(-2.39796 - 1.11795i) q^{7} +(2.85821 - 0.430806i) q^{9} +(3.93140 + 0.592563i) q^{11} +(2.53251 - 3.17567i) q^{13} +(0.274253 + 0.343903i) q^{15} +(5.78695 - 1.78504i) q^{17} +(2.43803 - 4.22279i) q^{19} +(-0.309607 + 0.818935i) q^{21} +(-2.69032 - 0.829855i) q^{23} +(-1.18117 + 3.00956i) q^{25} +(-0.433744 - 1.90036i) q^{27} +(-1.04067 + 4.55949i) q^{29} +(-1.29611 - 2.24492i) q^{31} +(0.0983175 - 1.31196i) q^{33} +(3.47078 - 0.567761i) q^{35} +(4.15258 + 3.85303i) q^{37} +(-1.11055 - 0.757161i) q^{39} +(-5.14698 - 2.47865i) q^{41} +(-8.70663 + 4.19289i) q^{43} +(-2.81656 + 2.61339i) q^{45} +(-2.96130 - 7.54527i) q^{47} +(4.50038 + 5.36158i) q^{49} +(-0.732141 - 1.86546i) q^{51} +(9.90956 - 9.19473i) q^{53} +(-4.76153 + 2.29303i) q^{55} +(-1.45375 - 0.700088i) q^{57} +(10.9531 + 7.46772i) q^{59} +(2.06626 + 1.91721i) q^{61} +(-7.33549 - 2.16228i) q^{63} +(-0.403488 + 5.38417i) q^{65} +(-4.76846 - 8.25921i) q^{67} +(-0.207311 + 0.908288i) q^{69} +(0.702213 + 3.07659i) q^{71} +(-3.48349 + 8.87578i) q^{73} +(1.02232 + 0.315344i) q^{75} +(-8.76486 - 5.81604i) q^{77} +(-7.30122 + 12.6461i) q^{79} +(7.66988 - 2.36585i) q^{81} +(1.50601 + 1.88848i) q^{83} +(-5.01912 + 6.29377i) q^{85} +(1.53030 + 0.230655i) q^{87} +(-11.5242 + 1.73700i) q^{89} +(-9.62310 + 4.78390i) q^{91} +(-0.708740 + 0.483211i) q^{93} +(0.484370 + 6.46346i) q^{95} -15.5042 q^{97} +11.4921 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{3} - q^{5} + 4 q^{7} + 41 q^{9} + q^{11} - 2 q^{13} + q^{15} - 5 q^{17} - 13 q^{19} + 12 q^{21} - 5 q^{23} + 2 q^{25} + 4 q^{27} - 21 q^{29} + 23 q^{31} - 17 q^{33} - 22 q^{35} - 60 q^{37}+ \cdots - 94 q^{99}+O(q^{100}) $ 84 * q - 8 * q^3 - q^5 + 4 * q^7 + 41 * q^9 + q^11 - 2 * q^13 + q^15 - 5 * q^17 - 13 * q^19 + 12 * q^21 - 5 * q^23 + 2 * q^25 + 4 * q^27 - 21 * q^29 + 23 * q^31 - 17 * q^33 - 22 * q^35 - 60 * q^37 - 61 * q^39 + 4 * q^41 + 22 * q^43 + 30 * q^45 + 82 * q^47 - 2 * q^49 + 3 * q^51 + 38 * q^53 + 69 * q^55 - 2 * q^57 - 6 * q^59 - 26 * q^61 - 37 * q^63 + 2 * q^65 + 43 * q^67 + 7 * q^69 - 21 * q^71 - 7 * q^73 - 80 * q^75 - 85 * q^77 - 25 * q^79 - 10 * q^81 - 17 * q^83 + 23 * q^85 + 47 * q^87 + 7 * q^89 - 3 * q^91 - 50 * q^93 - 129 * q^95 - 150 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{21}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.0247290	−	0.329985i	−0.0142773	−	0.190517i	−0.999782	−	0.0208701i	$-0.993356\pi$
$3$	−0.0247290	−	0.329985i	−0.0142773	−	0.190517i	0.985505	−	0.169647i	$-0.0542627\pi$
$4$		0			0
$5$	−1.09829	+	0.748802i	−0.491171	+	0.334875i	−0.783446	−	0.621460i	$-0.786540\pi$
$5$	−1.09829	+	0.748802i	−0.491171	+	0.334875i	0.292275	+	0.956334i	$0.405588\pi$
$6$		0			0
$7$	−2.39796	−	1.11795i	−0.906342	−	0.422545i
$7$	−2.39796	−	1.11795i	−0.906342	−	0.422545i
$8$		0			0
$9$	2.85821	−	0.430806i	0.952738	−	0.143602i
$10$		0			0
$11$	3.93140	+	0.592563i	1.18536	+	0.178664i	0.711984	−	0.702196i	$-0.247797\pi$
$11$	3.93140	+	0.592563i	1.18536	+	0.178664i	0.473377	+	0.880860i	$0.343035\pi$
$12$		0			0
$13$	2.53251	−	3.17567i	0.702393	−	0.880773i	−0.294807	−	0.955557i	$-0.595255\pi$
$13$	2.53251	−	3.17567i	0.702393	−	0.880773i	0.997200	+	0.0747837i	$0.0238266\pi$
$14$		0			0
$15$	0.274253	+	0.343903i	0.0708119	+	0.0887953i
$16$		0			0
$17$	5.78695	−	1.78504i	1.40354	−	0.432935i	0.501715	−	0.865033i	$-0.332703\pi$
$17$	5.78695	−	1.78504i	1.40354	−	0.432935i	0.901827	+	0.432098i	$0.142227\pi$
$18$		0			0
$19$	2.43803	−	4.22279i	0.559323	−	0.968776i	−0.438230	−	0.898863i	$-0.644395\pi$
$19$	2.43803	−	4.22279i	0.559323	−	0.968776i	0.997553	−	0.0699128i	$-0.0222721\pi$
$20$		0			0
$21$	−0.309607	+	0.818935i	−0.0675619	+	0.178706i
$22$		0			0
$23$	−2.69032	−	0.829855i	−0.560971	−	0.173037i	0.00128589	−	0.999999i	$-0.499591\pi$
$23$	−2.69032	−	0.829855i	−0.560971	−	0.173037i	−0.562257	+	0.826962i	$0.690067\pi$
$24$		0			0
$25$	−1.18117	+	3.00956i	−0.236233	+	0.601912i
$26$		0			0
$27$	−0.433744	−	1.90036i	−0.0834740	−	0.365724i
$28$		0			0
$29$	−1.04067	+	4.55949i	−0.193248	+	0.846676i	0.781595	+	0.623786i	$0.214406\pi$
$29$	−1.04067	+	4.55949i	−0.193248	+	0.846676i	−0.974844	+	0.222890i	$0.928451\pi$
$30$		0			0
$31$	−1.29611	−	2.24492i	−0.232788	−	0.403200i	0.725840	−	0.687864i	$-0.241451\pi$
$31$	−1.29611	−	2.24492i	−0.232788	−	0.403200i	−0.958627	+	0.284664i	$0.908118\pi$
$32$		0			0
$33$	0.0983175	−	1.31196i	0.0171149	−	0.228382i
$34$		0			0
$35$	3.47078	−	0.567761i	0.586668	−	0.0959691i
$36$		0			0
$37$	4.15258	+	3.85303i	0.682679	+	0.633434i	0.943274	−	0.332014i	$-0.107728\pi$
$37$	4.15258	+	3.85303i	0.682679	+	0.633434i	−0.260595	+	0.965448i	$0.583919\pi$
$38$		0			0
$39$	−1.11055	−	0.757161i	−0.177830	−	0.121243i
$40$		0			0
$41$	−5.14698	−	2.47865i	−0.803823	−	0.387101i	−0.0135902	−	0.999908i	$-0.504326\pi$
$41$	−5.14698	−	2.47865i	−0.803823	−	0.387101i	−0.790233	+	0.612807i	$0.790040\pi$
$42$		0			0
$43$	−8.70663	+	4.19289i	−1.32775	+	0.639410i	−0.957206	−	0.289406i	$-0.906542\pi$
$43$	−8.70663	+	4.19289i	−1.32775	+	0.639410i	−0.370542	+	0.928816i	$0.620828\pi$
$44$		0			0
$45$	−2.81656	+	2.61339i	−0.419868	+	0.389581i
$46$		0			0
$47$	−2.96130	−	7.54527i	−0.431950	−	1.10059i	−0.966775	−	0.255628i	$-0.917718\pi$
$47$	−2.96130	−	7.54527i	−0.431950	−	1.10059i	0.534825	−	0.844963i	$-0.320378\pi$
$48$		0			0
$49$	4.50038	+	5.36158i	0.642911	+	0.765941i
$50$		0			0
$51$	−0.732141	−	1.86546i	−0.102520	−	0.261217i
$52$		0			0
$53$	9.90956	−	9.19473i	1.36118	−	1.26299i	0.427913	−	0.903820i	$-0.359249\pi$
$53$	9.90956	−	9.19473i	1.36118	−	1.26299i	0.933271	−	0.359174i	$-0.116941\pi$
$54$		0			0
$55$	−4.76153	+	2.29303i	−0.642045	+	0.309193i
$56$		0			0
$57$	−1.45375	−	0.700088i	−0.192554	−	0.0927290i
$58$		0			0
$59$	10.9531	+	7.46772i	1.42598	+	0.972215i	0.997645	+	0.0685939i	$0.0218513\pi$
$59$	10.9531	+	7.46772i	1.42598	+	0.972215i	0.428333	+	0.903621i	$0.359101\pi$
$60$		0			0
$61$	2.06626	+	1.91721i	0.264558	+	0.245474i	0.801286	−	0.598282i	$-0.204150\pi$
$61$	2.06626	+	1.91721i	0.264558	+	0.245474i	−0.536728	+	0.843755i	$0.680340\pi$
$62$		0			0
$63$	−7.33549	−	2.16228i	−0.924185	−	0.272422i
$64$		0			0
$65$	−0.403488	+	5.38417i	−0.0500465	+	0.667824i
$66$		0			0
$67$	−4.76846	−	8.25921i	−0.582560	−	1.00902i	−0.995175	−	0.0981178i	$-0.968718\pi$
$67$	−4.76846	−	8.25921i	−0.582560	−	1.00902i	0.412615	−	0.910906i	$-0.364616\pi$
$68$		0			0
$69$	−0.207311	+	0.908288i	−0.0249573	+	0.109345i
$70$		0			0
$71$	0.702213	+	3.07659i	0.0833373	+	0.365125i	0.999351	−	0.0360224i	$-0.0114688\pi$
$71$	0.702213	+	3.07659i	0.0833373	+	0.365125i	−0.916014	+	0.401147i	$0.868612\pi$
$72$		0			0
$73$	−3.48349	+	8.87578i	−0.407711	+	1.03883i	0.568630	+	0.822594i	$0.307474\pi$
$73$	−3.48349	+	8.87578i	−0.407711	+	1.03883i	−0.976341	+	0.216238i	$0.930621\pi$
$74$		0			0
$75$	1.02232	+	0.315344i	0.118047	+	0.0364128i
$76$		0			0
$77$	−8.76486	−	5.81604i	−0.998849	−	0.662800i
$78$		0			0
$79$	−7.30122	+	12.6461i	−0.821452	+	1.42280i	0.0831492	+	0.996537i	$0.473502\pi$
$79$	−7.30122	+	12.6461i	−0.821452	+	1.42280i	−0.904601	+	0.426259i	$0.859831\pi$
$80$		0			0
$81$	7.66988	−	2.36585i	0.852209	−	0.262872i
$82$		0			0
$83$	1.50601	+	1.88848i	0.165306	+	0.207288i	0.857584	−	0.514343i	$-0.171964\pi$
$83$	1.50601	+	1.88848i	0.165306	+	0.207288i	−0.692278	+	0.721631i	$0.743393\pi$
$84$		0			0
$85$	−5.01912	+	6.29377i	−0.544400	+	0.682656i
$86$		0			0
$87$	1.53030	+	0.230655i	0.164065	+	0.0247288i
$88$		0			0
$89$	−11.5242	+	1.73700i	−1.22156	+	0.184121i	−0.727993	−	0.685584i	$-0.759547\pi$
$89$	−11.5242	+	1.73700i	−1.22156	+	0.184121i	−0.493571	+	0.869706i	$0.664309\pi$
$90$		0			0
$91$	−9.62310	+	4.78390i	−1.00877	+	0.501489i
$92$		0			0
$93$	−0.708740	+	0.483211i	−0.0734929	+	0.0501066i
$94$		0			0
$95$	0.484370	+	6.46346i	0.0496953	+	0.663137i
$96$		0			0
$97$	−15.5042			−1.57421			−0.787105	−	0.616819i	$-0.788421\pi$
$97$	−15.5042			−1.57421			−0.787105	+	0.616819i	$0.788421\pi$
$98$		0			0
$99$	11.4921			1.15500
$100$		0			0
$101$	−0.106289	−	1.41833i	−0.0105762	−	0.141129i	0.989416	−	0.145107i	$-0.0463528\pi$
$101$	−0.106289	−	1.41833i	−0.0105762	−	0.141129i	−0.999992	+	0.00397807i	$0.998734\pi$
$102$		0			0
$103$	4.65161	−	3.17141i	0.458336	−	0.312489i	−0.312050	−	0.950066i	$-0.601016\pi$
$103$	4.65161	−	3.17141i	0.458336	−	0.312489i	0.770387	+	0.637577i	$0.220063\pi$
$104$		0			0
$105$	−0.273181	−	1.13126i	−0.0266598	−	0.110400i
$106$		0			0
$107$	8.92492	−	1.34522i	0.862805	−	0.130047i	0.297292	−	0.954787i	$-0.403916\pi$
$107$	8.92492	−	1.34522i	0.862805	−	0.130047i	0.565513	+	0.824740i	$0.308678\pi$
$108$		0			0
$109$	1.36894	+	0.206334i	0.131121	+	0.0197632i	0.214275	−	0.976773i	$-0.431261\pi$
$109$	1.36894	+	0.206334i	0.131121	+	0.0197632i	−0.0831541	+	0.996537i	$0.526499\pi$
$110$		0			0
$111$	1.16875	−	1.46557i	0.110933	−	0.139106i
$112$		0			0
$113$	−8.08063	−	10.1328i	−0.760162	−	0.953213i	0.239682	−	0.970851i	$-0.422957\pi$
$113$	−8.08063	−	10.1328i	−0.760162	−	0.953213i	−0.999844	+	0.0176383i	$0.994385\pi$
$114$		0			0
$115$	3.57616	−	1.10310i	0.333478	−	0.102864i
$116$		0			0
$117$	5.87037	−	10.1678i	0.542716	−	0.940011i
$118$		0			0
$119$	−15.8724	−	2.18908i	−1.45502	−	0.200672i
$120$		0			0
$121$	4.59346	+	1.41689i	0.417587	+	0.128809i
$122$		0			0
$123$	−0.690639	+	1.75972i	−0.0622728	+	0.158669i
$124$		0			0
$125$	−2.43525	−	10.6695i	−0.217815	−	0.954312i
$126$		0			0
$127$	−2.74707	+	12.0357i	−0.243763	+	1.06799i	0.693797	+	0.720171i	$0.255936\pi$
$127$	−2.74707	+	12.0357i	−0.243763	+	1.06799i	−0.937560	+	0.347824i	$0.886921\pi$
$128$		0			0
$129$	1.59890	+	2.76937i	0.140775	+	0.243829i
$130$		0			0
$131$	0.247732	−	3.30576i	0.0216445	−	0.288826i	−0.975869	−	0.218355i	$-0.929931\pi$
$131$	0.247732	−	3.30576i	0.0216445	−	0.288826i	0.997514	−	0.0704705i	$-0.0224501\pi$
$132$		0			0
$133$	−10.5672	+	7.40048i	−0.916289	+	0.641703i
$134$		0			0
$135$	1.89937	+	1.76236i	0.163472	+	0.151679i
$136$		0			0
$137$	4.89427	+	3.33686i	0.418146	+	0.285087i	0.754060	−	0.656806i	$-0.228093\pi$
$137$	4.89427	+	3.33686i	0.418146	+	0.285087i	−0.335914	+	0.941893i	$0.609045\pi$
$138$		0			0
$139$	−4.61054	−	2.22032i	−0.391061	−	0.188325i	0.228012	−	0.973658i	$-0.426777\pi$
$139$	−4.61054	−	2.22032i	−0.391061	−	0.188325i	−0.619073	+	0.785333i	$0.712492\pi$
$140$		0			0
$141$	−2.41660	+	1.16377i	−0.203514	+	0.0980073i
$142$		0			0
$143$	11.8381	−	10.9842i	0.989952	−	0.918542i
$144$		0			0
$145$	−2.27119	−	5.78691i	−0.188612	−	0.480576i
$146$		0			0
$147$	1.65795	−	1.61764i	0.136746	−	0.133421i
$148$		0			0
$149$	5.96562	+	15.2002i	0.488723	+	1.24525i	0.936363	+	0.351032i	$0.114169\pi$
$149$	5.96562	+	15.2002i	0.488723	+	1.24525i	−0.447641	+	0.894214i	$0.647736\pi$
$150$		0			0
$151$	0.634167	−	0.588421i	0.0516078	−	0.0478850i	−0.653947	−	0.756540i	$-0.726888\pi$
$151$	0.634167	−	0.588421i	0.0516078	−	0.0478850i	0.705555	+	0.708655i	$0.250698\pi$
$152$		0			0
$153$	15.7713	−	7.59507i	1.27504	−	0.614025i
$154$		0			0
$155$	3.10451	+	1.49505i	0.249360	+	0.120086i
$156$		0			0
$157$	−0.654478	−	0.446216i	−0.0522330	−	0.0356119i	0.536922	−	0.843632i	$-0.319587\pi$
$157$	−0.654478	−	0.446216i	−0.0522330	−	0.0356119i	−0.589155	+	0.808020i	$0.700539\pi$
$158$		0			0
$159$	−3.27918	−	3.04263i	−0.260056	−	0.241296i
$160$		0			0
$161$	5.52354	+	4.99760i	0.435316	+	0.393866i
$162$		0			0
$163$	−0.761747	+	10.1648i	−0.0596646	+	0.796169i	0.884467	+	0.466602i	$0.154522\pi$
$163$	−0.761747	+	10.1648i	−0.0596646	+	0.796169i	−0.944132	+	0.329567i	$0.893097\pi$
$164$		0			0
$165$	0.874414	+	1.51453i	0.0680731	+	0.117906i
$166$		0			0
$167$	−3.91027	+	17.1320i	−0.302586	+	1.32571i	0.563623	+	0.826032i	$0.309407\pi$
$167$	−3.91027	+	17.1320i	−0.302586	+	1.32571i	−0.866209	+	0.499682i	$0.833450\pi$
$168$		0			0
$169$	−0.778496	−	3.41081i	−0.0598843	−	0.262370i
$170$		0			0
$171$	5.14921	−	13.1200i	0.393770	−	1.00331i
$172$		0			0
$173$	7.05609	+	2.17652i	0.536465	+	0.165477i	0.551137	−	0.834415i	$-0.314194\pi$
$173$	7.05609	+	2.17652i	0.536465	+	0.165477i	−0.0146721	+	0.999892i	$0.504670\pi$
$174$		0			0
$175$	6.19692	−	5.89631i	0.468443	−	0.445719i
$176$		0			0
$177$	2.19338	−	3.79904i	0.164864	−	0.285553i
$178$		0			0
$179$	6.59849	−	2.03536i	0.493194	−	0.152130i	−0.0381743	−	0.999271i	$-0.512154\pi$
$179$	6.59849	−	2.03536i	0.493194	−	0.152130i	0.531368	+	0.847141i	$0.321678\pi$
$180$		0			0
$181$	−13.8911	−	17.4189i	−1.03252	−	1.29474i	−0.954635	−	0.297778i	$-0.903754\pi$
$181$	−13.8911	−	17.4189i	−1.03252	−	1.29474i	−0.0778858	−	0.996962i	$-0.524817\pi$
$182$		0			0
$183$	0.581554	−	0.729245i	0.0429897	−	0.0539074i
$184$		0			0
$185$	−7.44589	−	1.12229i	−0.547433	−	0.0825123i
$186$		0			0
$187$	23.8085	−	3.58856i	1.74105	−	0.262422i
$188$		0			0
$189$	−1.08440	+	5.04187i	−0.0788787	+	0.366742i
$190$		0			0
$191$	−0.446308	+	0.304288i	−0.0322937	+	0.0220175i	−0.579359	−	0.815072i	$-0.696697\pi$
$191$	−0.446308	+	0.304288i	−0.0322937	+	0.0220175i	0.547066	+	0.837090i	$0.315745\pi$
$192$		0			0
$193$	−1.17545	−	15.6853i	−0.0846109	−	1.12905i	−0.864330	−	0.502925i	$-0.832257\pi$
$193$	−1.17545	−	15.6853i	−0.0846109	−	1.12905i	0.779719	−	0.626129i	$-0.215362\pi$
$194$		0			0
$195$	1.78667			0.127946
$196$		0			0
$197$	−8.85459			−0.630863			−0.315432	−	0.948948i	$-0.602149\pi$
$197$	−8.85459			−0.630863			−0.315432	+	0.948948i	$0.602149\pi$
$198$		0			0
$199$	1.42731	+	19.0461i	0.101179	+	1.35014i	0.784547	+	0.620069i	$0.212896\pi$
$199$	1.42731	+	19.0461i	0.101179	+	1.35014i	−0.683368	+	0.730074i	$0.739485\pi$
$200$		0			0
$201$	−2.60750	+	1.77776i	−0.183919	+	0.125394i
$202$		0			0
$203$	7.59277	−	9.77003i	0.532908	−	0.685722i
$204$		0			0
$205$	7.50890	−	1.13179i	0.524445	−	0.0790473i
$206$		0			0
$207$	−8.04703	−	1.21289i	−0.559307	−	0.0843020i
$208$		0			0
$209$	12.0871	−	15.1568i	0.836085	−	1.04842i
$210$		0			0
$211$	13.3127	+	16.6936i	0.916484	+	1.14923i	0.988407	+	0.151825i	$0.0485149\pi$
$211$	13.3127	+	16.6936i	0.916484	+	1.14923i	−0.0719233	+	0.997410i	$0.522914\pi$
$212$		0			0
$213$	0.997865	−	0.307801i	0.0683726	−	0.0210901i
$214$		0			0
$215$	6.42277	−	11.1246i	0.438029	−	0.758689i
$216$		0			0
$217$	0.598297	+	6.83221i	0.0406150	+	0.463801i
$218$		0			0
$219$	3.01502	+	0.930009i	0.203736	+	0.0628442i
$220$		0			0
$221$	8.98684	−	22.8981i	0.604520	−	1.54029i
$222$		0			0
$223$	−0.981286	−	4.29930i	−0.0657118	−	0.287902i	0.931386	−	0.364033i	$-0.118600\pi$
$223$	−0.981286	−	4.29930i	−0.0657118	−	0.287902i	−0.997098	+	0.0761309i	$0.975743\pi$
$224$		0			0
$225$	−2.07949	+	9.11083i	−0.138632	+	0.607388i
$226$		0			0
$227$	7.40903	+	12.8328i	0.491755	+	0.851744i	0.999955	−	0.00949463i	$-0.00302228\pi$
$227$	7.40903	+	12.8328i	0.491755	+	0.851744i	−0.508200	+	0.861239i	$0.669689\pi$
$228$		0			0
$229$	−0.798026	+	10.6489i	−0.0527350	+	0.703700i	0.906701	+	0.421774i	$0.138592\pi$
$229$	−0.798026	+	10.6489i	−0.0527350	+	0.703700i	−0.959436	+	0.281926i	$0.909027\pi$
$230$		0			0
$231$	−1.70246	+	3.03610i	−0.112014	+	0.199761i
$232$		0			0
$233$	−15.8433	−	14.7004i	−1.03793	−	0.963058i	−0.0385848	−	0.999255i	$-0.512285\pi$
$233$	−15.8433	−	14.7004i	−1.03793	−	0.963058i	−0.999345	+	0.0361975i	$0.988475\pi$
$234$		0			0
$235$	8.90229	+	6.06948i	0.580721	+	0.395929i
$236$		0			0
$237$	4.35357	+	2.09657i	0.282795	+	0.136187i
$238$		0			0
$239$	9.76927	−	4.70463i	0.631921	−	0.304317i	−0.0903678	−	0.995908i	$-0.528804\pi$
$239$	9.76927	−	4.70463i	0.631921	−	0.304317i	0.722289	+	0.691591i	$0.243090\pi$
$240$		0			0
$241$	6.58829	−	6.11304i	0.424389	−	0.393776i	−0.438859	−	0.898556i	$-0.644617\pi$
$241$	6.58829	−	6.11304i	0.424389	−	0.393776i	0.863248	+	0.504781i	$0.168427\pi$
$242$		0			0
$243$	−3.10676	−	7.91589i	−0.199299	−	0.507805i
$244$		0			0
$245$	−8.95750	−	2.51869i	−0.572273	−	0.160913i
$246$		0			0
$247$	−7.23586	−	18.4367i	−0.460407	−	1.17310i
$248$		0			0
$249$	0.585928	−	0.543662i	0.0371317	−	0.0344532i
$250$		0			0
$251$	−1.40751	+	0.677822i	−0.0888414	+	0.0427838i	−0.477777	−	0.878481i	$-0.658557\pi$
$251$	−1.40751	+	0.677822i	−0.0888414	+	0.0427838i	0.388935	+	0.921265i	$0.372843\pi$
$252$		0			0
$253$	−10.0850	−	4.85668i	−0.634038	−	0.305337i
$254$		0			0
$255$	2.20097	+	1.50059i	0.137830	+	0.0939709i
$256$		0			0
$257$	7.89389	+	7.32446i	0.492407	+	0.456887i	0.886866	−	0.462026i	$-0.152877\pi$
$257$	7.89389	+	7.32446i	0.492407	+	0.456887i	−0.394459	+	0.918914i	$0.629068\pi$
$258$		0			0
$259$	−5.65020	−	13.8818i	−0.351086	−	0.862570i
$260$		0			0
$261$	−1.01021	+	13.4803i	−0.0625305	+	0.834411i
$262$		0			0
$263$	1.69904	+	2.94283i	0.104767	+	0.181463i	0.913643	−	0.406517i	$-0.133257\pi$
$263$	1.69904	+	2.94283i	0.104767	+	0.181463i	−0.808876	+	0.587980i	$0.799924\pi$
$264$		0			0
$265$	−3.99855	+	17.5188i	−0.245629	+	1.07617i
$266$		0			0
$267$	0.858164	+	3.75986i	0.0525188	+	0.230100i
$268$		0			0
$269$	−0.523532	+	1.33394i	−0.0319203	+	0.0813317i	−0.945945	−	0.324326i	$-0.894862\pi$
$269$	−0.523532	+	1.33394i	−0.0319203	+	0.0813317i	0.914025	+	0.405658i	$0.132958\pi$
$270$		0			0
$271$	−30.4868	−	9.40393i	−1.85194	−	0.571248i	−0.998768	−	0.0496185i	$-0.984199\pi$
$271$	−30.4868	−	9.40393i	−1.85194	−	0.571248i	−0.853172	−	0.521629i	$-0.825324\pi$
$272$		0			0
$273$	1.81658	+	3.05718i	0.109945	+	0.185029i
$274$		0			0
$275$	−6.42699	+	11.1319i	−0.387562	+	0.671277i
$276$		0			0
$277$	−3.56738	+	1.10039i	−0.214343	+	0.0661160i	−0.400067	−	0.916486i	$-0.631013\pi$
$277$	−3.56738	+	1.10039i	−0.214343	+	0.0661160i	0.185724	+	0.982602i	$0.440537\pi$
$278$		0			0
$279$	−4.67168	−	5.85810i	−0.279686	−	0.350715i
$280$		0			0
$281$	−1.44123	+	1.80725i	−0.0859767	+	0.107811i	−0.822959	−	0.568100i	$-0.807679\pi$
$281$	−1.44123	+	1.80725i	−0.0859767	+	0.107811i	0.736983	+	0.675912i	$0.236250\pi$
$282$		0			0
$283$	9.38213	+	1.41413i	0.557710	+	0.0840613i	0.421848	−	0.906667i	$-0.361382\pi$
$283$	9.38213	+	1.41413i	0.557710	+	0.0840613i	0.135862	+	0.990728i	$0.456620\pi$
$284$		0			0
$285$	2.12087	−	0.319669i	0.125629	−	0.0189356i
$286$		0			0
$287$	9.57121	+	11.6978i	0.564971	+	0.690497i
$288$		0			0
$289$	16.2564	−	11.0834i	0.956257	−	0.651965i
$290$		0			0
$291$	0.383402	+	5.11615i	0.0224754	+	0.299914i
$292$		0			0
$293$	−16.6942			−0.975287			−0.487644	−	0.873043i	$-0.662143\pi$
$293$	−16.6942			−0.975287			−0.487644	+	0.873043i	$0.662143\pi$
$294$		0			0
$295$	−17.6216			−1.02597
$296$		0			0
$297$	−0.579139	−	7.72807i	−0.0336051	−	0.448428i
$298$		0			0
$299$	−9.44863	+	6.44197i	−0.546428	+	0.372549i
$300$		0			0
$301$	25.5655	−	0.320798i	1.47357	−	0.0184905i
$302$		0			0
$303$	−0.465400	+	0.0701478i	−0.0267365	+	0.00402988i
$304$		0			0
$305$	−3.70497	−	0.558434i	−0.212146	−	0.0319758i
$306$		0			0
$307$	−0.726351	+	0.910815i	−0.0414550	+	0.0519830i	−0.802127	−	0.597154i	$-0.796298\pi$
$307$	−0.726351	+	0.910815i	−0.0414550	+	0.0519830i	0.760672	+	0.649137i	$0.224870\pi$
$308$		0			0
$309$	−1.16155	−	1.45653i	−0.0660781	−	0.0828594i
$310$		0			0
$311$	7.07320	−	2.18179i	0.401084	−	0.123718i	−0.0876488	−	0.996151i	$-0.527935\pi$
$311$	7.07320	−	2.18179i	0.401084	−	0.123718i	0.488733	+	0.872433i	$0.337459\pi$
$312$		0			0
$313$	−14.3138	+	24.7922i	−0.809063	+	1.40134i	0.104450	+	0.994530i	$0.466692\pi$
$313$	−14.3138	+	24.7922i	−0.809063	+	1.40134i	−0.913513	+	0.406809i	$0.866642\pi$
$314$		0			0
$315$	9.67563	−	3.11801i	0.545160	−	0.175680i
$316$		0			0
$317$	14.2206	+	4.38646i	0.798706	+	0.246368i	0.667133	−	0.744938i	$-0.267521\pi$
$317$	14.2206	+	4.38646i	0.798706	+	0.246368i	0.131573	+	0.991307i	$0.457997\pi$
$318$		0			0
$319$	−6.79309	+	17.3085i	−0.380340	+	0.969090i
$320$		0			0
$321$	−0.664605	−	2.91182i	−0.0370946	−	0.162522i
$322$		0			0
$323$	6.57092	−	28.7891i	0.365616	−	1.60187i
$324$		0			0
$325$	6.56607	+	11.3728i	0.364220	+	0.630847i
$326$		0			0
$327$	0.0342348	−	0.456832i	0.00189319	−	0.0252628i
$328$		0			0
$329$	−1.33416	+	21.4038i	−0.0735548	+	1.18003i
$330$		0			0
$331$	−23.1305	−	21.4620i	−1.27137	−	1.17966i	−0.974413	−	0.224766i	$-0.927838\pi$
$331$	−23.1305	−	21.4620i	−1.27137	−	1.17966i	−0.296956	−	0.954891i	$-0.595971\pi$
$332$		0			0
$333$	13.5289	+	9.22382i	0.741377	+	0.505462i
$334$		0			0
$335$	11.4217	+	5.50039i	0.624033	+	0.300518i
$336$		0			0
$337$	5.13756	−	2.47412i	0.279861	−	0.134774i	−0.288688	−	0.957423i	$-0.593219\pi$
$337$	5.13756	−	2.47412i	0.279861	−	0.134774i	0.568549	+	0.822649i	$0.307505\pi$
$338$		0			0
$339$	−3.14384	+	2.91706i	−0.170750	+	0.158433i
$340$		0			0
$341$	−3.76526	−	9.59372i	−0.203900	−	0.519529i
$342$		0			0
$343$	−4.79773	−	17.8880i	−0.259053	−	0.965863i
$344$		0			0
$345$	−0.452440	−	1.15280i	−0.0243586	−	0.0620646i
$346$		0			0
$347$	−18.2224	+	16.9079i	−0.978231	+	0.907666i	−0.995742	−	0.0921808i	$-0.970616\pi$
$347$	−18.2224	+	16.9079i	−0.978231	+	0.907666i	0.0175111	+	0.999847i	$0.494426\pi$
$348$		0			0
$349$	8.32432	−	4.00878i	0.445591	−	0.214585i	−0.197613	−	0.980280i	$-0.563319\pi$
$349$	8.32432	−	4.00878i	0.445591	−	0.214585i	0.643204	+	0.765695i	$0.277605\pi$
$350$		0			0
$351$	−7.13337	−	3.43525i	−0.380751	−	0.183360i
$352$		0			0
$353$	−24.5375	−	16.7294i	−1.30600	−	0.890416i	−0.307863	−	0.951431i	$-0.599614\pi$
$353$	−24.5375	−	16.7294i	−1.30600	−	0.890416i	−0.998137	+	0.0610152i	$0.980566\pi$
$354$		0			0
$355$	−3.07500	−	2.85318i	−0.163204	−	0.151431i
$356$		0			0
$357$	−0.329853	+	5.29180i	−0.0174577	+	0.280072i
$358$		0			0
$359$	−0.207560	+	2.76969i	−0.0109546	+	0.146179i	−0.999999	−	0.00143979i	$-0.999542\pi$
$359$	−0.207560	+	2.76969i	−0.0109546	+	0.146179i	0.989044	+	0.147618i	$0.0471607\pi$
$360$		0			0
$361$	−2.38800	−	4.13613i	−0.125684	−	0.217691i
$362$		0			0
$363$	0.353962	−	1.55081i	0.0185782	−	0.0813964i
$364$		0			0
$365$	−2.82032	−	12.3566i	−0.147622	−	0.646776i
$366$		0			0
$367$	−1.99885	+	5.09299i	−0.104339	+	0.265852i	−0.973504	−	0.228671i	$-0.926562\pi$
$367$	−1.99885	+	5.09299i	−0.104339	+	0.265852i	0.869164	+	0.494523i	$0.164657\pi$
$368$		0			0
$369$	−15.7790	−	4.86717i	−0.821421	−	0.253375i
$370$		0			0
$371$	−34.0419	+	10.9702i	−1.76737	+	0.569543i
$372$		0			0
$373$	−14.3447	+	24.8458i	−0.742743	+	1.28647i	0.208500	+	0.978022i	$0.433142\pi$
$373$	−14.3447	+	24.8458i	−0.742743	+	1.28647i	−0.951242	+	0.308445i	$0.900191\pi$
$374$		0			0
$375$	−3.46056	+	1.06744i	−0.178703	+	0.0551225i
$376$		0			0
$377$	11.8439	+	14.8518i	0.609993	+	0.764907i
$378$		0			0
$379$	−6.25401	+	7.84228i	−0.321247	+	0.402831i	−0.916065	−	0.401029i	$-0.868653\pi$
$379$	−6.25401	+	7.84228i	−0.321247	+	0.402831i	0.594818	+	0.803860i	$0.297224\pi$
$380$		0			0
$381$	4.03953	+	0.608861i	0.206951	+	0.0311929i
$382$		0			0
$383$	27.8754	−	4.20154i	1.42436	−	0.214688i	0.608786	−	0.793334i	$-0.291657\pi$
$383$	27.8754	−	4.20154i	1.42436	−	0.214688i	0.815579	+	0.578646i	$0.196419\pi$
$384$		0			0
$385$	13.9814	−	0.175440i	0.712560	−	0.00894124i
$386$		0			0
$387$	−23.0791	+	15.7351i	−1.17318	+	0.799858i
$388$		0			0
$389$	1.65608	+	22.0989i	0.0839668	+	1.12046i	0.866943	+	0.498408i	$0.166082\pi$
$389$	1.65608	+	22.0989i	0.0839668	+	1.12046i	−0.782976	+	0.622052i	$0.786299\pi$
$390$		0			0
$391$	−17.0501			−0.862260
$392$		0			0
$393$	−1.09698			−0.0553352
$394$		0			0
$395$	−1.45055	−	19.3563i	−0.0729852	−	0.973919i
$396$		0			0
$397$	−2.66260	+	1.81533i	−0.133632	+	0.0911088i	−0.628291	−	0.777978i	$-0.716245\pi$
$397$	−2.66260	+	1.81533i	−0.133632	+	0.0911088i	0.494659	+	0.869087i	$0.335293\pi$
$398$		0			0
$399$	2.70336	+	3.30400i	0.135337	+	0.165407i
$400$		0			0
$401$	24.3170	−	3.66520i	1.21433	−	0.183031i	0.489530	−	0.871987i	$-0.337168\pi$
$401$	24.3170	−	3.66520i	1.21433	−	0.183031i	0.724804	+	0.688955i	$0.241930\pi$
$402$		0			0
$403$	−10.4116	−	1.56929i	−0.518637	−	0.0781719i
$404$		0			0
$405$	−6.65222	+	8.34161i	−0.330551	+	0.414498i
$406$		0			0
$407$	14.0423	+	17.6084i	0.696049	+	0.872818i
$408$		0			0
$409$	−33.5586	+	10.3514i	−1.65936	+	0.511846i	−0.975915	−	0.218152i	$-0.929997\pi$
$409$	−33.5586	+	10.3514i	−1.65936	+	0.511846i	−0.683450	+	0.729998i	$0.739521\pi$
$410$		0			0
$411$	0.980082	−	1.69755i	0.0483439	−	0.0837341i
$412$		0			0
$413$	−17.9166	−	30.1523i	−0.881618	−	1.48370i
$414$		0			0
$415$	−3.06814	−	0.946396i	−0.150609	−	0.0464567i
$416$		0			0
$417$	−0.618658	+	1.57631i	−0.0302958	+	0.0771925i
$418$		0			0
$419$	4.15641	+	18.2104i	0.203054	+	0.889637i	0.969064	+	0.246809i	$0.0793819\pi$
$419$	4.15641	+	18.2104i	0.203054	+	0.889637i	−0.766010	+	0.642828i	$0.777761\pi$
$420$		0			0
$421$	−0.405376	+	1.77607i	−0.0197568	+	0.0865603i	−0.983845	−	0.179021i	$-0.942707\pi$
$421$	−0.405376	+	1.77607i	−0.0197568	+	0.0865603i	0.964088	+	0.265582i	$0.0855640\pi$
$422$		0			0
$423$	−11.7146	−	20.2903i	−0.569583	−	0.986546i
$424$		0			0
$425$	−1.46317	+	19.5246i	−0.0709740	+	0.947083i
$426$		0			0
$427$	−2.81146	−	6.90736i	−0.136056	−	0.334270i
$428$		0			0
$429$	−3.91735	−	3.63477i	−0.189132	−	0.175488i
$430$		0			0
$431$	−4.82277	−	3.28811i	−0.232304	−	0.158382i	0.441574	−	0.897225i	$-0.354420\pi$
$431$	−4.82277	−	3.28811i	−0.232304	−	0.158382i	−0.673878	+	0.738842i	$0.735373\pi$
$432$		0			0
$433$	25.6397	+	12.3474i	1.23217	+	0.593380i	0.932675	−	0.360719i	$-0.117469\pi$
$433$	25.6397	+	12.3474i	1.23217	+	0.593380i	0.299492	+	0.954099i	$0.403183\pi$
$434$		0			0
$435$	−1.85343	+	0.892564i	−0.0888651	+	0.0427952i
$436$		0			0
$437$	−10.0634	+	9.33747i	−0.481398	+	0.446672i
$438$		0			0
$439$	14.5231	+	37.0043i	0.693151	+	1.76612i	0.641077	+	0.767477i	$0.278488\pi$
$439$	14.5231	+	37.0043i	0.693151	+	1.76612i	0.0520740	+	0.998643i	$0.483417\pi$
$440$		0			0
$441$	15.1729	+	13.3858i	0.722517	+	0.637417i
$442$		0			0
$443$	−5.78442	−	14.7385i	−0.274826	−	0.700246i	−0.999933	−	0.0116090i	$-0.996305\pi$
$443$	−5.78442	−	14.7385i	−0.274826	−	0.700246i	0.725106	−	0.688637i	$-0.241791\pi$
$444$		0			0
$445$	11.3563	−	10.5371i	0.538339	−	0.499506i
$446$		0			0
$447$	4.86830	−	2.34445i	0.230263	−	0.110889i
$448$		0			0
$449$	20.1211	+	9.68983i	0.949576	+	0.457292i	0.843537	−	0.537070i	$-0.180469\pi$
$449$	20.1211	+	9.68983i	0.949576	+	0.457292i	0.106038	+	0.994362i	$0.466183\pi$
$450$		0			0
$451$	−18.7661	−	12.7945i	−0.883659	−	0.602469i
$452$		0			0
$453$	−0.209852	−	0.194714i	−0.00985972	−	0.00914848i
$454$		0			0
$455$	6.98677	−	12.4599i	0.327545	−	0.584130i
$456$		0			0
$457$	1.99644	−	26.6406i	0.0933894	−	1.24619i	−0.731871	−	0.681443i	$-0.761353\pi$
$457$	1.99644	−	26.6406i	0.0933894	−	1.24619i	0.825261	−	0.564752i	$-0.191028\pi$
$458$		0			0
$459$	−5.90226	−	10.2230i	−0.275494	−	0.477169i
$460$		0			0
$461$	0.389263	−	1.70547i	0.0181298	−	0.0794317i	−0.965054	−	0.262052i	$-0.915601\pi$
$461$	0.389263	−	1.70547i	0.0181298	−	0.0794317i	0.983184	+	0.182620i	$0.0584579\pi$
$462$		0			0
$463$	0.439409	+	1.92518i	0.0204211	+	0.0894705i	0.984112	−	0.177551i	$-0.0568176\pi$
$463$	0.439409	+	1.92518i	0.0204211	+	0.0894705i	−0.963690	+	0.267022i	$0.913960\pi$
$464$		0			0
$465$	0.416574	−	1.06141i	0.0193181	−	0.0492218i
$466$		0			0
$467$	−10.9636	−	3.38183i	−0.507336	−	0.156492i	0.0305118	−	0.999534i	$-0.490286\pi$
$467$	−10.9636	−	3.38183i	−0.507336	−	0.156492i	−0.537848	+	0.843042i	$0.680762\pi$
$468$		0			0
$469$	2.20117	+	25.1361i	0.101641	+	1.16068i
$470$		0			0
$471$	−0.131060	+	0.227002i	−0.00603892	+	0.0104597i
$472$		0			0
$473$	−36.7138	+	11.3247i	−1.68810	+	0.520710i
$474$		0			0
$475$	9.82904	+	12.3252i	0.450987	+	0.565520i
$476$		0			0
$477$	24.3625	−	30.5496i	1.11548	−	1.39877i
$478$		0			0
$479$	−15.3307	−	2.31073i	−0.700476	−	0.105580i	−0.210858	−	0.977517i	$-0.567626\pi$
$479$	−15.3307	−	2.31073i	−0.700476	−	0.105580i	−0.489618	+	0.871937i	$0.662864\pi$
$480$		0			0
$481$	22.7524	−	3.42937i	1.03742	−	0.156366i
$482$		0			0
$483$	1.51254	−	1.94627i	0.0688230	−	0.0885584i
$484$		0			0
$485$	17.0281	−	11.6096i	0.773206	−	0.527163i
$486$		0			0
$487$	−2.83768	−	37.8661i	−0.128587	−	1.71588i	−0.572580	−	0.819849i	$-0.694058\pi$
$487$	−2.83768	−	37.8661i	−0.128587	−	1.71588i	0.443993	−	0.896030i	$-0.353561\pi$
$488$		0			0
$489$	3.37307			0.152536
$490$		0			0
$491$	24.4091			1.10157			0.550784	−	0.834648i	$-0.314329\pi$
$491$	24.4091			1.10157			0.550784	+	0.834648i	$0.314329\pi$
$492$		0			0
$493$	2.11653	+	28.2432i	0.0953239	+	1.27201i
$494$		0			0
$495$	−12.6216	+	8.60528i	−0.567300	+	0.386779i
$496$		0			0
$497$	1.75560	−	8.16257i	0.0787495	−	0.366142i
$498$		0			0
$499$	32.0079	−	4.82441i	1.43287	−	0.215970i	0.613708	−	0.789533i	$-0.289677\pi$
$499$	32.0079	−	4.82441i	1.43287	−	0.215970i	0.819161	+	0.573563i	$0.194439\pi$
$500$		0			0
$501$	5.75000	+	0.866673i	0.256891	+	0.0387201i
$502$		0			0
$503$	17.3441	−	21.7488i	0.773335	−	0.969731i	−0.226656	−	0.973975i	$-0.572779\pi$
$503$	17.3441	−	21.7488i	0.773335	−	0.969731i	0.999991	+	0.00424376i	$0.00135084\pi$
$504$		0			0
$505$	1.17879	+	1.47815i	0.0524554	+	0.0657769i
$506$		0			0
$507$	−1.10627	+	0.341238i	−0.0491310	+	0.0151549i
$508$		0			0
$509$	5.69883	−	9.87066i	0.252596	−	0.437509i	−0.711644	−	0.702540i	$-0.752049\pi$
$509$	5.69883	−	9.87066i	0.252596	−	0.437509i	0.964240	+	0.265031i	$0.0853823\pi$
$510$		0			0
$511$	18.2759	−	17.3894i	0.808479	−	0.769260i
$512$		0			0
$513$	−9.08229	−	2.80152i	−0.400993	−	0.123690i
$514$		0			0
$515$	−2.73406	+	6.96627i	−0.120477	+	0.306970i
$516$		0			0
$517$	−7.17101	−	31.4182i	−0.315381	−	1.38177i
$518$		0			0
$519$	0.543728	−	2.38223i	0.0238670	−	0.104568i
$520$		0			0
$521$	−5.19371	−	8.99577i	−0.227541	−	0.394112i	0.729538	−	0.683940i	$-0.239735\pi$
$521$	−5.19371	−	8.99577i	−0.227541	−	0.394112i	−0.957079	+	0.289828i	$0.906402\pi$
$522$		0			0
$523$	−0.874759	+	11.6728i	−0.0382505	+	0.510418i	0.944868	+	0.327450i	$0.106189\pi$
$523$	−0.874759	+	11.6728i	−0.0382505	+	0.510418i	−0.983119	+	0.182968i	$0.941430\pi$
$524$		0			0
$525$	−2.09894	−	1.89908i	−0.0916051	−	0.0828827i
$526$		0			0
$527$	−11.5078	−	10.6777i	−0.501287	−	0.465126i
$528$		0			0
$529$	−12.4543	−	8.49120i	−0.541492	−	0.369183i
$530$		0			0
$531$	34.5236	+	16.6257i	1.49820	+	0.721493i
$532$		0			0
$533$	−20.9062	+	10.0679i	−0.905548	+	0.436089i
$534$		0			0
$535$	−8.79487	+	8.16044i	−0.380235	+	0.352807i
$536$		0			0
$537$	−0.834813	−	2.12707i	−0.0360248	−	0.0917898i
$538$		0			0
$539$	14.5157	+	23.7453i	0.625236	+	1.02278i
$540$		0			0
$541$	−12.2189	−	31.1333i	−0.525332	−	1.33852i	−0.909670	−	0.415332i	$-0.863665\pi$
$541$	−12.2189	−	31.1333i	−0.525332	−	1.33852i	0.384338	−	0.923193i	$-0.374430\pi$
$542$		0			0
$543$	−5.40448	+	5.01462i	−0.231928	+	0.215198i
$544$		0			0
$545$	−1.65800	+	0.798449i	−0.0710208	+	0.0342018i
$546$		0			0
$547$	−7.70942	−	3.71266i	−0.329631	−	0.158742i	0.261747	−	0.965137i	$-0.415701\pi$
$547$	−7.70942	−	3.71266i	−0.329631	−	0.158742i	−0.591378	+	0.806395i	$0.701416\pi$
$548$		0			0
$549$	6.73176	+	4.58964i	0.287305	+	0.195881i
$550$		0			0
$551$	16.7166	+	15.5107i	0.712151	+	0.660779i
$552$		0			0
$553$	31.6457	−	22.1624i	1.34571	−	0.942440i
$554$		0			0
$555$	−0.186209	+	2.48479i	−0.00790413	+	0.105473i
$556$		0			0
$557$	14.0384	+	24.3153i	0.594827	+	1.03027i	0.993571	+	0.113209i	$0.0361129\pi$
$557$	14.0384	+	24.3153i	0.594827	+	1.03027i	−0.398744	+	0.917062i	$0.630554\pi$
$558$		0			0
$559$	−8.73441	+	38.2680i	−0.369426	+	1.61856i
$560$		0			0
$561$	−1.77293	−	7.76772i	−0.0748532	−	0.327953i
$562$		0			0
$563$	4.13546	−	10.5370i	0.174289	−	0.444081i	−0.816860	−	0.576836i	$-0.804287\pi$
$563$	4.13546	−	10.5370i	0.174289	−	0.444081i	0.991149	+	0.132755i	$0.0423824\pi$
$564$		0			0
$565$	16.4624	+	5.07796i	0.692576	+	0.213632i
$566$		0			0
$567$	−21.0369	−	2.90135i	−0.883468	−	0.121845i
$568$		0			0
$569$	−12.1236	+	20.9988i	−0.508249	+	0.880313i	0.491705	+	0.870762i	$0.336374\pi$
$569$	−12.1236	+	20.9988i	−0.508249	+	0.880313i	−0.999954	+	0.00955172i	$0.996960\pi$
$570$		0			0
$571$	−19.3429	+	5.96648i	−0.809473	+	0.249689i	−0.671747	−	0.740781i	$-0.734456\pi$
$571$	−19.3429	+	5.96648i	−0.809473	+	0.249689i	−0.137726	+	0.990470i	$0.543979\pi$
$572$		0			0
$573$	0.111447	+	0.139750i	0.00465577	+	0.00583815i
$574$		0			0
$575$	5.67522	−	7.11650i	0.236673	−	0.296779i
$576$		0			0
$577$	12.2409	+	1.84502i	0.509595	+	0.0768091i	0.398807	−	0.917035i	$-0.369424\pi$
$577$	12.2409	+	1.84502i	0.509595	+	0.0768091i	0.110788	+	0.993844i	$0.464662\pi$
$578$		0			0
$579$	−5.14685	+	0.775763i	−0.213896	+	0.0322396i
$580$		0			0
$581$	−1.50013	−	6.21214i	−0.0622357	−	0.257723i
$582$		0			0
$583$	44.4069	−	30.2761i	1.83915	−	1.25391i
$584$		0			0
$585$	1.16628	+	15.5629i	0.0482198	+	0.643448i
$586$		0			0
$587$	−45.5194			−1.87879			−0.939393	−	0.342842i	$-0.888610\pi$
$587$	−45.5194			−1.87879			−0.939393	+	0.342842i	$0.888610\pi$
$588$		0			0
$589$	−12.6398			−0.520814
$590$		0			0
$591$	0.218965	+	2.92188i	0.00900700	+	0.120190i
$592$		0			0
$593$	−22.1788	+	15.1212i	−0.910772	+	0.620954i	−0.925422	−	0.378939i	$-0.876289\pi$
$593$	−22.1788	+	15.1212i	−0.910772	+	0.620954i	0.0146495	+	0.999893i	$0.495337\pi$
$594$		0			0
$595$	19.0717	−	9.48107i	0.781865	−	0.388686i
$596$		0			0
$597$	6.24964	−	0.941981i	0.255781	−	0.0385527i
$598$		0			0
$599$	31.7505	+	4.78562i	1.29729	+	0.195535i	0.761141	−	0.648587i	$-0.224640\pi$
$599$	31.7505	+	4.78562i	1.29729	+	0.195535i	0.536151	+	0.844122i	$0.319878\pi$
$600$		0			0
$601$	−5.60195	+	7.02462i	−0.228508	+	0.286540i	−0.882846	−	0.469662i	$-0.844376\pi$
$601$	−5.60195	+	7.02462i	−0.228508	+	0.286540i	0.654338	+	0.756202i	$0.272947\pi$
$602$		0			0
$603$	−17.1874	−	21.5523i	−0.699925	−	0.877678i
$604$		0			0
$605$	−6.10593	+	1.88343i	−0.248241	+	0.0765723i
$606$		0			0
$607$	8.33069	−	14.4292i	0.338132	−	0.585662i	−0.645949	−	0.763380i	$-0.723538\pi$
$607$	8.33069	−	14.4292i	0.338132	−	0.585662i	0.984081	+	0.177718i	$0.0568716\pi$
$608$		0			0
$609$	−3.41172	−	2.26390i	−0.138250	−	0.0917377i
$610$		0			0
$611$	−31.4609	−	9.70439i	−1.27277	−	0.392598i
$612$		0			0
$613$	15.8001	−	40.2579i	0.638158	−	1.62600i	−0.134304	−	0.990940i	$-0.542880\pi$
$613$	15.8001	−	40.2579i	0.638158	−	1.62600i	0.772462	−	0.635061i	$-0.219025\pi$
$614$		0			0
$615$	−0.559159	−	2.44984i	−0.0225475	−	0.0987870i
$616$		0			0
$617$	10.0283	−	43.9370i	0.403726	−	1.76884i	−0.208366	−	0.978051i	$-0.566815\pi$
$617$	10.0283	−	43.9370i	0.403726	−	1.76884i	0.612092	−	0.790787i	$-0.290328\pi$
$618$		0			0
$619$	−6.71948	−	11.6385i	−0.270079	−	0.467790i	0.698803	−	0.715314i	$-0.253716\pi$
$619$	−6.71948	−	11.6385i	−0.270079	−	0.467790i	−0.968882	+	0.247524i	$0.920383\pi$
$620$		0			0
$621$	−0.410108	+	5.47251i	−0.0164571	+	0.219604i
$622$		0			0
$623$	29.5764	+	8.71825i	1.18495	+	0.349289i
$624$		0			0
$625$	−1.18599	−	1.10043i	−0.0474394	−	0.0440173i
$626$		0			0
$627$	−5.30042	−	3.61376i	−0.211678	−	0.144320i
$628$		0			0
$629$	30.9085	+	14.8848i	1.23240	+	0.593495i
$630$		0			0
$631$	32.2345	−	15.5233i	1.28323	−	0.617973i	0.337015	−	0.941499i	$-0.390583\pi$
$631$	32.2345	−	15.5233i	1.28323	−	0.617973i	0.946219	+	0.323527i	$0.104869\pi$
$632$		0			0
$633$	5.17943	−	4.80581i	0.205864	−	0.191014i
$634$		0			0
$635$	−5.99527	−	15.2757i	−0.237915	−	0.606198i
$636$		0			0
$637$	28.4239	−	0.713442i	1.12620	−	0.0282676i
$638$		0			0
$639$	3.33249	+	8.49105i	0.131831	+	0.335901i
$640$		0			0
$641$	−20.2357	+	18.7759i	−0.799261	+	0.741605i	−0.969841	−	0.243738i	$-0.921626\pi$
$641$	−20.2357	+	18.7759i	−0.799261	+	0.741605i	0.170580	+	0.985344i	$0.445436\pi$
$642$		0			0
$643$	22.1695	−	10.6763i	0.874280	−	0.421031i	0.0577480	−	0.998331i	$-0.481608\pi$
$643$	22.1695	−	10.6763i	0.874280	−	0.421031i	0.816532	+	0.577300i	$0.195894\pi$
$644$		0			0
$645$	−3.82977	−	1.84432i	−0.150797	−	0.0726200i
$646$		0			0
$647$	−0.787172	−	0.536685i	−0.0309469	−	0.0210993i	0.547748	−	0.836644i	$-0.315485\pi$
$647$	−0.787172	−	0.536685i	−0.0309469	−	0.0210993i	−0.578695	+	0.815544i	$0.696438\pi$
$648$		0			0
$649$	38.6361	+	35.8490i	1.51660	+	1.40720i
$650$		0			0
$651$	2.23973	−	0.366382i	0.0877820	−	0.0143597i
$652$		0			0
$653$	−1.96890	+	26.2731i	−0.0770488	+	1.02815i	0.815961	+	0.578107i	$0.196209\pi$
$653$	−1.96890	+	26.2731i	−0.0770488	+	1.02815i	−0.893010	+	0.450038i	$0.851411\pi$
$654$		0			0
$655$	2.20328	+	3.81619i	0.0860892	+	0.149111i
$656$		0			0
$657$	−6.13281	+	26.8696i	−0.239264	+	1.04828i
$658$		0			0
$659$	−2.36990	−	10.3832i	−0.0923182	−	0.404472i	0.907563	−	0.419917i	$-0.137941\pi$
$659$	−2.36990	−	10.3832i	−0.0923182	−	0.404472i	−0.999881	+	0.0154446i	$0.995084\pi$
$660$		0			0
$661$	−3.95854	+	10.0862i	−0.153969	+	0.392307i	−0.986957	−	0.160984i	$-0.948533\pi$
$661$	−3.95854	+	10.0862i	−0.153969	+	0.392307i	0.832988	+	0.553291i	$0.186628\pi$
$662$		0			0
$663$	−7.77826	−	2.39928i	−0.302083	−	0.0931802i
$664$		0			0
$665$	6.06433	−	16.0406i	0.235164	−	0.622028i
$666$		0			0
$667$	6.58346	−	11.4029i	0.254913	−	0.441522i
$668$		0			0
$669$	−1.39444	+	0.430127i	−0.0539120	+	0.0166297i
$670$		0			0
$671$	6.98722	+	8.76170i	0.269739	+	0.338242i
$672$		0			0
$673$	21.2157	−	26.6037i	0.817806	−	1.02550i	−0.181308	−	0.983426i	$-0.558033\pi$
$673$	21.2157	−	26.6037i	0.817806	−	1.02550i	0.999115	−	0.0420703i	$-0.0133953\pi$
$674$		0			0
$675$	6.23156	+	0.939257i	0.239853	+	0.0361520i
$676$		0			0
$677$	−36.6409	+	5.52272i	−1.40822	+	0.212256i	−0.808756	−	0.588144i	$-0.799859\pi$
$677$	−36.6409	+	5.52272i	−1.40822	+	0.212256i	−0.599467	+	0.800399i	$0.704621\pi$
$678$		0			0
$679$	37.1783	+	17.3329i	1.42677	+	0.665175i
$680$		0			0
$681$	4.05142	−	2.76221i	0.155251	−	0.105848i
$682$		0			0
$683$	1.39095	+	18.5609i	0.0532230	+	0.710212i	0.958446	+	0.285275i	$0.0920849\pi$
$683$	1.39095	+	18.5609i	0.0532230	+	0.710212i	−0.905223	+	0.424937i	$0.860296\pi$
$684$		0			0
$685$	−7.87398			−0.300849
$686$		0			0
$687$	3.53372			0.134820
$688$		0			0
$689$	−4.10334	−	54.7553i	−0.156325	−	2.08601i
$690$		0			0
$691$	−15.0523	+	10.2625i	−0.572615	+	0.390402i	−0.814726	−	0.579846i	$-0.803113\pi$
$691$	−15.0523	+	10.2625i	−0.572615	+	0.390402i	0.242111	+	0.970249i	$0.422160\pi$
$692$		0			0
$693$	−27.5574	−	12.8475i	−1.04682	−	0.488037i
$694$		0			0
$695$	6.72630	−	1.01383i	0.255143	−	0.0384566i
$696$		0			0
$697$	−34.2098	−	5.15630i	−1.29579	−	0.195309i
$698$		0			0
$699$	−4.45914	+	5.59158i	−0.168660	+	0.211493i
$700$		0			0
$701$	7.47771	+	9.37676i	0.282429	+	0.354155i	0.902729	−	0.430210i	$-0.141560\pi$
$701$	7.47771	+	9.37676i	0.282429	+	0.354155i	−0.620300	+	0.784365i	$0.712989\pi$
$702$		0			0
$703$	26.3947	−	8.14167i	0.995493	−	0.307069i
$704$		0			0
$705$	1.78269	−	3.08771i	0.0671401	−	0.116290i
$706$		0			0
$707$	−1.33075	+	3.51992i	−0.0500479	+	0.132380i
$708$		0			0
$709$	−25.5636	−	7.88532i	−0.960060	−	0.296139i	−0.225165	−	0.974321i	$-0.572292\pi$
$709$	−25.5636	−	7.88532i	−0.960060	−	0.296139i	−0.734895	+	0.678181i	$0.762768\pi$
$710$		0			0
$711$	−15.4204	+	39.2906i	−0.578312	+	1.47351i
$712$		0			0
$713$	1.62399	+	7.11515i	0.0608188	+	0.266465i
$714$		0			0
$715$	−4.77673	+	20.9282i	−0.178640	+	0.782671i
$716$		0			0
$717$	−1.79404	−	3.10737i	−0.0669997	−	0.116047i
$718$		0			0
$719$	−0.210089	+	2.80345i	−0.00783501	+	0.104551i	−0.999750	−	0.0223519i	$-0.992885\pi$
$719$	−0.210089	+	2.80345i	−0.00783501	+	0.104551i	0.991915	+	0.126903i	$0.0405036\pi$
$720$		0			0
$721$	−14.6998	+	2.40464i	−0.547450	+	0.0895536i
$722$		0			0
$723$	−2.18013	−	2.02287i	−0.0810800	−	0.0752313i
$724$		0			0
$725$	−12.4929	−	8.51749i	−0.463973	−	0.316331i
$726$		0			0
$727$	33.8221	+	16.2879i	1.25439	+	0.604084i	0.938686	−	0.344773i	$-0.112044\pi$
$727$	33.8221	+	16.2879i	1.25439	+	0.604084i	0.315707	+	0.948857i	$0.397758\pi$
$728$		0			0
$729$	19.1595	−	9.22674i	0.709612	−	0.341731i
$730$		0			0
$731$	−42.9004	+	39.8057i	−1.58673	+	1.47227i
$732$		0			0
$733$	−15.9600	−	40.6654i	−0.589496	−	1.50201i	−0.844763	−	0.535141i	$-0.820258\pi$
$733$	−15.9600	−	40.6654i	−0.589496	−	1.50201i	0.255267	−	0.966871i	$-0.417837\pi$
$734$		0			0
$735$	−0.609619	+	3.01812i	−0.0224861	+	0.111325i
$736$		0			0
$737$	−13.8526	−	35.2959i	−0.510267	−	1.30014i
$738$		0			0
$739$	7.63564	−	7.08484i	0.280881	−	0.260620i	−0.527133	−	0.849783i	$-0.676733\pi$
$739$	7.63564	−	7.08484i	0.280881	−	0.260620i	0.808014	+	0.589163i	$0.200542\pi$
$740$		0			0
$741$	−5.90489	+	2.84365i	−0.216922	+	0.104464i
$742$		0			0
$743$	10.5523	+	5.08171i	0.387126	+	0.186430i	0.617315	−	0.786716i	$-0.288220\pi$
$743$	10.5523	+	5.08171i	0.387126	+	0.186430i	−0.230190	+	0.973146i	$0.573935\pi$
$744$		0			0
$745$	−17.9339	−	12.2271i	−0.657048	−	0.447967i
$746$		0			0
$747$	5.11808	+	4.74888i	0.187261	+	0.173752i
$748$		0			0
$749$	−22.9055	−	6.75184i	−0.836947	−	0.246707i
$750$		0			0
$751$	−1.40361	+	18.7299i	−0.0512186	+	0.683465i	0.911212	+	0.411938i	$0.135148\pi$
$751$	−1.40361	+	18.7299i	−0.0512186	+	0.683465i	−0.962431	+	0.271528i	$0.912471\pi$
$752$		0			0
$753$	0.258478	+	0.447696i	0.00941945	+	0.0163150i
$754$		0			0
$755$	−0.255889	+	1.12112i	−0.00931276	+	0.0408018i
$756$		0			0
$757$	6.53759	+	28.6431i	0.237613	+	1.04105i	0.943147	+	0.332375i	$0.107850\pi$
$757$	6.53759	+	28.6431i	0.237613	+	1.04105i	−0.705535	+	0.708675i	$0.749293\pi$
$758$		0			0
$759$	−1.35324	+	3.44800i	−0.0491195	+	0.125154i
$760$		0			0
$761$	−5.22663	−	1.61220i	−0.189465	−	0.0584423i	0.198571	−	0.980087i	$-0.436370\pi$
$761$	−5.22663	−	1.61220i	−0.189465	−	0.0584423i	−0.388036	+	0.921644i	$0.626846\pi$
$762$		0			0
$763$	−3.05198	−	2.02518i	−0.110489	−	0.0733166i
$764$		0			0
$765$	−11.6343	+	20.1512i	−0.420639	+	0.728569i
$766$		0			0
$767$	51.4540	−	15.8715i	1.85790	−	0.573086i
$768$		0			0
$769$	−8.42289	−	10.5620i	−0.303737	−	0.380874i	0.606415	−	0.795148i	$-0.292607\pi$
$769$	−8.42289	−	10.5620i	−0.303737	−	0.380874i	−0.910152	+	0.414274i	$0.864036\pi$
$770$		0			0
$771$	2.22175	−	2.78599i	0.0800145	−	0.100335i
$772$		0			0
$773$	9.12128	+	1.37481i	0.328070	+	0.0494485i	0.311012	−	0.950406i	$-0.399332\pi$
$773$	9.12128	+	1.37481i	0.328070	+	0.0494485i	0.0170576	+	0.999855i	$0.494570\pi$
$774$		0			0
$775$	8.28716	−	1.24909i	0.297683	−	0.0448686i
$776$		0			0
$777$	−4.44105	+	2.20776i	−0.159322	+	0.0792031i
$778$		0			0
$779$	−23.0153	+	15.6916i	−0.824610	+	0.562210i
$780$		0			0
$781$	0.937602	+	12.5114i	0.0335500	+	0.447694i
$782$		0			0
$783$	9.11603			0.325780
$784$		0			0
$785$	1.05293			0.0375809
$786$		0			0
$787$	1.88952	+	25.2139i	0.0673541	+	0.898779i	0.923882	+	0.382678i	$0.124998\pi$
$787$	1.88952	+	25.2139i	0.0673541	+	0.898779i	−0.856528	+	0.516101i	$0.827383\pi$
$788$		0			0
$789$	0.929073	−	0.633431i	0.0330759	−	0.0225508i
$790$		0			0
$791$	8.04905	+	33.3317i	0.286191	+	1.18514i
$792$		0			0
$793$	11.3213	−	1.70641i	0.402030	−	0.0605963i
$794$		0			0
$795$	5.87982	+	0.886240i	0.208536	+	0.0314317i
$796$		0			0
$797$	25.2505	−	31.6631i	0.894417	−	1.12156i	−0.0975702	−	0.995229i	$-0.531107\pi$
$797$	25.2505	−	31.6631i	0.894417	−	1.12156i	0.991988	−	0.126335i	$-0.0403215\pi$
$798$		0			0
$799$	−30.6055	−	38.3781i	−1.08274	−	1.35772i
$800$		0			0
$801$	−32.1904	+	9.92941i	−1.13739	+	0.350838i
$802$		0			0
$803$	−18.9544	+	32.8300i	−0.668887	+	1.15855i
$804$		0			0
$805$	−9.80867	−	1.35278i	−0.345710	−	0.0476793i
$806$		0			0
$807$	0.453126	+	0.139771i	0.0159508	+	0.00492017i
$808$		0			0
$809$	−10.4697	+	26.6764i	−0.368095	+	0.937891i	0.620077	+	0.784541i	$0.287101\pi$
$809$	−10.4697	+	26.6764i	−0.368095	+	0.937891i	−0.988172	+	0.153350i	$0.950994\pi$
$810$		0			0
$811$	−11.7296	−	51.3908i	−0.411883	−	1.80458i	−0.575213	−	0.818004i	$-0.695081\pi$
$811$	−11.7296	−	51.3908i	−0.411883	−	1.80458i	0.163330	−	0.986571i	$-0.447776\pi$
$812$		0			0
$813$	−2.34925	+	10.2927i	−0.0823917	+	0.360982i
$814$		0			0
$815$	−6.77481	−	11.7343i	−0.237311	−	0.411035i
$816$		0			0
$817$	−3.52132	+	46.9887i	−0.123195	+	1.64393i
$818$		0			0
$819$	−25.4439	+	17.8191i	−0.889083	+	0.622650i
$820$		0			0
$821$	−30.8245	−	28.6009i	−1.07578	−	0.998179i	−0.999999	−	0.00105425i	$-0.999664\pi$
$821$	−30.8245	−	28.6009i	−1.07578	−	0.998179i	−0.0757814	−	0.997124i	$-0.524145\pi$
$822$		0			0
$823$	−31.8450	−	21.7115i	−1.11005	−	0.756816i	−0.137726	−	0.990470i	$-0.543979\pi$
$823$	−31.8450	−	21.7115i	−1.11005	−	0.756816i	−0.972320	+	0.233654i	$0.924932\pi$
$824$		0			0
$825$	3.83228	+	1.84553i	0.133423	+	0.0642531i
$826$		0			0
$827$	−17.3821	+	8.37076i	−0.604434	+	0.291080i	−0.710963	−	0.703230i	$-0.751741\pi$
$827$	−17.3821	+	8.37076i	−0.604434	+	0.291080i	0.106529	+	0.994310i	$0.466026\pi$
$828$		0			0
$829$	28.7634	−	26.6885i	0.998993	−	0.926930i	0.00166604	−	0.999999i	$-0.499470\pi$
$829$	28.7634	−	26.6885i	0.998993	−	0.926930i	0.997327	+	0.0730686i	$0.0232792\pi$
$830$		0			0
$831$	0.451329	+	1.14997i	0.0156564	+	0.0398920i
$832$		0			0
$833$	35.6141	+	22.9939i	1.23396	+	0.796690i
$834$		0			0
$835$	−8.53387	−	21.7439i	−0.295327	−	0.752480i
$836$		0			0
$837$	−3.70397	+	3.43679i	−0.128028	+	0.118793i
$838$		0			0
$839$	7.30675	−	3.51875i	0.252257	−	0.121481i	−0.303483	−	0.952837i	$-0.598149\pi$
$839$	7.30675	−	3.51875i	0.252257	−	0.121481i	0.555740	+	0.831356i	$0.312435\pi$
$840$		0			0
$841$	6.42216	+	3.09275i	0.221454	+	0.106647i
$842$		0			0
$843$	0.632005	+	0.430894i	0.0217674	+	0.0148408i
$844$		0			0
$845$	3.40904	+	3.16313i	0.117275	+	0.108815i
$846$		0			0
$847$	−9.43089	−	8.53290i	−0.324049	−	0.293194i
$848$		0			0
$849$	0.234631	−	3.13093i	0.00805252	−	0.107453i
$850$		0			0
$851$	−7.97432	−	13.8119i	−0.273356	−	0.473467i
$852$		0			0
$853$	−5.05830	+	22.1619i	−0.173193	+	0.758808i	0.811478	+	0.584384i	$0.198664\pi$
$853$	−5.05830	+	22.1619i	−0.173193	+	0.758808i	−0.984671	+	0.174425i	$0.944193\pi$
$854$		0			0
$855$	4.16893	+	18.2653i	0.142575	+	0.624660i
$856$		0			0
$857$	2.18242	−	5.56071i	0.0745500	−	0.189950i	−0.888741	−	0.458410i	$-0.848419\pi$
$857$	2.18242	−	5.56071i	0.0745500	−	0.189950i	0.963291	+	0.268459i	$0.0865145\pi$
$858$		0			0
$859$	18.5037	+	5.70763i	0.631338	+	0.194742i	0.593877	−	0.804556i	$-0.297597\pi$
$859$	18.5037	+	5.70763i	0.631338	+	0.194742i	0.0374614	+	0.999298i	$0.488073\pi$
$860$		0			0
$861$	3.62340	−	3.44763i	0.123485	−	0.117495i
$862$		0			0
$863$	−8.99785	+	15.5847i	−0.306290	+	0.530510i	−0.977548	−	0.210714i	$-0.932421\pi$
$863$	−8.99785	+	15.5847i	−0.306290	+	0.530510i	0.671257	+	0.741224i	$0.265754\pi$
$864$		0			0
$865$	−9.37942	+	2.89317i	−0.318910	+	0.0983707i
$866$		0			0
$867$	−4.05936	−	5.09028i	−0.137863	−	0.172875i
$868$		0			0
$869$	−36.1976	+	45.3904i	−1.22792	+	1.53976i
$870$		0			0
$871$	−38.3047	−	5.77351i	−1.29791	−	0.195628i
$872$		0			0
$873$	−44.3143	+	6.67930i	−1.49981	+	0.226060i
$874$		0			0
$875$	−6.08837	+	28.3075i	−0.205824	+	0.956970i
$876$		0			0
$877$	−20.2836	+	13.8291i	−0.684928	+	0.466976i	−0.855117	−	0.518436i	$-0.826515\pi$
$877$	−20.2836	+	13.8291i	−0.684928	+	0.466976i	0.170189	+	0.985411i	$0.445562\pi$
$878$		0			0
$879$	0.412831	+	5.50884i	0.0139244	+	0.185809i
$880$		0			0
$881$	15.4666			0.521083			0.260541	−	0.965463i	$-0.416099\pi$
$881$	15.4666			0.521083			0.260541	+	0.965463i	$0.416099\pi$
$882$		0			0
$883$	−8.22258			−0.276712			−0.138356	−	0.990383i	$-0.544182\pi$
$883$	−8.22258			−0.276712			−0.138356	+	0.990383i	$0.544182\pi$
$884$		0			0
$885$	0.435763	+	5.81486i	0.0146480	+	0.195464i
$886$		0			0
$887$	−24.4317	+	16.6573i	−0.820336	+	0.559296i	−0.899174	−	0.437592i	$-0.855832\pi$
$887$	−24.4317	+	16.6573i	−0.820336	+	0.559296i	0.0788374	+	0.996887i	$0.474879\pi$
$888$		0			0
$889$	20.0426	−	25.7900i	0.672208	−	0.864967i
$890$		0			0
$891$	31.5553	−	4.75619i	1.05714	−	0.159338i
$892$		0			0
$893$	−39.0819	−	5.89065i	−1.30783	−	0.197123i
$894$		0			0
$895$	−5.72298	+	7.17638i	−0.191298	+	0.239880i
$896$		0			0
$897$	2.35941	+	2.95860i	0.0787783	+	0.0987849i
$898$		0			0
$899$	11.5845	−	3.57335i	0.386366	−	0.119178i
$900$		0			0
$901$	40.9332	−	70.8984i	1.36368	−	2.36197i
$902$		0			0
$903$	−0.738068	−	8.42831i	−0.0245614	−	0.280477i
$904$		0			0
$905$	28.2999	+	8.72936i	0.940720	+	0.290174i
$906$		0			0
$907$	−3.80095	+	9.68466i	−0.126208	+	0.321574i	−0.979987	−	0.199063i	$-0.936210\pi$
$907$	−3.80095	+	9.68466i	−0.126208	+	0.321574i	0.853778	+	0.520637i	$0.174305\pi$
$908$		0			0
$909$	−0.914825	−	4.00811i	−0.0303428	−	0.132941i
$910$		0			0
$911$	4.77731	−	20.9308i	0.158279	−	0.693467i	−0.832046	−	0.554706i	$-0.812831\pi$
$911$	4.77731	−	20.9308i	0.158279	−	0.693467i	0.990326	−	0.138761i	$-0.0443121\pi$
$912$		0			0
$913$	4.80169	+	8.31677i	0.158913	+	0.275245i
$914$		0			0
$915$	−0.0926548	+	1.23639i	−0.00306307	+	0.0408739i
$916$		0			0
$917$	−4.28972	+	7.65011i	−0.141659	+	0.252629i
$918$		0			0
$919$	−26.8030	−	24.8695i	−0.884148	−	0.820370i	0.100497	−	0.994937i	$-0.467957\pi$
$919$	−26.8030	−	24.8695i	−0.884148	−	0.820370i	−0.984645	+	0.174568i	$0.944147\pi$
$920$		0			0
$921$	0.318517	+	0.217161i	0.0104955	+	0.00715571i
$922$		0			0
$923$	11.5486	+	5.56152i	0.380128	+	0.183060i
$924$		0			0
$925$	−16.5008	+	7.94637i	−0.542543	+	0.261275i
$926$		0			0
$927$	11.9290	−	11.0685i	0.391801	−	0.363538i
$928$		0			0
$929$	−11.5326	−	29.3845i	−0.378372	−	0.964075i	−0.985531	−	0.169495i	$-0.945786\pi$
$929$	−11.5326	−	29.3845i	−0.378372	−	0.964075i	0.607160	−	0.794580i	$-0.292309\pi$
$930$		0			0
$931$	33.6129	−	5.93247i	1.10162	−	0.194429i
$932$		0			0
$933$	−0.894872	−	2.28010i	−0.0292968	−	0.0746470i
$934$		0			0
$935$	−23.4616	+	21.7692i	−0.767276	+	0.711928i
$936$		0			0
$937$	−30.8895	+	14.8756i	−1.00912	+	0.485964i	−0.864022	−	0.503454i	$-0.832062\pi$
$937$	−30.8895	+	14.8756i	−1.00912	+	0.485964i	−0.145093	+	0.989418i	$0.546348\pi$
$938$		0			0
$939$	8.53502	+	4.11025i	0.278530	+	0.134133i
$940$		0			0
$941$	25.9342	+	17.6816i	0.845431	+	0.576405i	0.906729	−	0.421714i	$-0.138571\pi$
$941$	25.9342	+	17.6816i	0.845431	+	0.576405i	−0.0612976	+	0.998120i	$0.519524\pi$
$942$		0			0
$943$	11.7901	+	10.9396i	0.383939	+	0.356243i
$944$		0			0
$945$	−2.58437	−	6.34945i	−0.0840697	−	0.206547i
$946$		0			0
$947$	−1.58126	+	21.1004i	−0.0513839	+	0.685671i	0.910726	+	0.413010i	$0.135523\pi$
$947$	−1.58126	+	21.1004i	−0.0513839	+	0.685671i	−0.962110	+	0.272661i	$0.912096\pi$
$948$		0			0
$949$	19.3646	+	33.5405i	0.628601	+	1.08877i
$950$		0			0
$951$	1.09581	−	4.80104i	0.0355340	−	0.155685i
$952$		0			0
$953$	5.34539	+	23.4197i	0.173154	+	0.758639i	0.984687	+	0.174332i	$0.0557765\pi$
$953$	5.34539	+	23.4197i	0.173154	+	0.758639i	−0.811533	+	0.584307i	$0.801366\pi$
$954$		0			0
$955$	0.262325	−	0.668393i	0.00848864	−	0.0216287i
$956$		0			0
$957$	5.87953	+	1.81360i	0.190058	+	0.0586252i
$958$		0			0
$959$	−8.00580	−	13.4732i	−0.258521	−	0.435071i
$960$		0			0
$961$	12.1402	−	21.0275i	0.391620	−	0.678305i
$962$		0			0
$963$	24.9298	−	7.68983i	0.803352	−	0.247801i
$964$		0			0
$965$	13.0362	+	16.3469i	0.419650	+	0.526224i
$966$		0			0
$967$	−8.13329	+	10.1988i	−0.261549	+	0.327972i	−0.895215	−	0.445635i	$-0.852978\pi$
$967$	−8.13329	+	10.1988i	−0.261549	+	0.327972i	0.633666	+	0.773607i	$0.281549\pi$
$968$		0			0
$969$	−9.66245	−	1.45638i	−0.310403	−	0.0467857i
$970$		0			0
$971$	24.5732	−	3.70381i	0.788591	−	0.118861i	0.257615	−	0.966248i	$-0.417063\pi$
$971$	24.5732	−	3.70381i	0.788591	−	0.118861i	0.530976	+	0.847387i	$0.321825\pi$
$972$		0			0
$973$	8.57366	+	10.4786i	0.274859	+	0.335928i
$974$		0			0
$975$	3.59047	−	2.44794i	0.114987	−	0.0783968i
$976$		0			0
$977$	−1.00039	−	13.3492i	−0.0320052	−	0.427080i	−0.990075	−	0.140543i	$-0.955115\pi$
$977$	−1.00039	−	13.3492i	−0.0320052	−	0.427080i	0.958069	−	0.286537i	$-0.0925040\pi$
$978$		0			0
$979$	−46.3355			−1.48089
$980$		0			0
$981$	4.00161			0.127762
$982$		0			0
$983$	1.02084	+	13.6222i	0.0325598	+	0.434480i	0.989533	+	0.144305i	$0.0460945\pi$
$983$	1.02084	+	13.6222i	0.0325598	+	0.434480i	−0.956974	+	0.290175i	$0.906286\pi$
$984$		0			0
$985$	9.72492	−	6.63034i	0.309862	−	0.211260i
$986$		0			0
$987$	7.09593	−	0.0890401i	0.225866	−	0.00283418i
$988$		0			0
$989$	26.9031	−	4.05500i	0.855470	−	0.128941i
$990$		0			0
$991$	16.6218	+	2.50533i	0.528008	+	0.0795844i	0.407636	−	0.913145i	$-0.366353\pi$
$991$	16.6218	+	2.50533i	0.528008	+	0.0795844i	0.120372	+	0.992729i	$0.461591\pi$
$992$		0			0
$993$	−6.51014	+	8.16346i	−0.206593	+	0.259059i
$994$		0			0
$995$	−15.8294	−	19.8494i	−0.501825	−	0.629269i
$996$		0			0
$997$	13.1735	−	4.06349i	0.417209	−	0.128692i	−0.0790415	−	0.996871i	$-0.525186\pi$
$997$	13.1735	−	4.06349i	0.417209	−	0.128692i	0.496250	+	0.868179i	$0.334710\pi$
$998$		0			0
$999$	5.52097	−	9.56259i	0.174676	−	0.302547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.y.a.65.4	✓	84
4.3	odd	2		784.2.bg.f.65.4		84
49.46	even	21	inner	392.2.y.a.193.4	yes	84
196.95	odd	42		784.2.bg.f.193.4		84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.y.a.65.4	✓	84	1.1	even	1	trivial
392.2.y.a.193.4	yes	84	49.46	even	21	inner
784.2.bg.f.65.4		84	4.3	odd	2
784.2.bg.f.193.4		84	196.95	odd	42

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.y (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0247290 - 0.329985i) q^{3} +(-1.09829 + 0.748802i) q^{5} +(-2.39796 - 1.11795i) q^{7} +(2.85821 - 0.430806i) q^{9} +(3.93140 + 0.592563i) q^{11} +(2.53251 - 3.17567i) q^{13} +(0.274253 + 0.343903i) q^{15} +(5.78695 - 1.78504i) q^{17} +(2.43803 - 4.22279i) q^{19} +(-0.309607 + 0.818935i) q^{21} +(-2.69032 - 0.829855i) q^{23} +(-1.18117 + 3.00956i) q^{25} +(-0.433744 - 1.90036i) q^{27} +(-1.04067 + 4.55949i) q^{29} +(-1.29611 - 2.24492i) q^{31} +(0.0983175 - 1.31196i) q^{33} +(3.47078 - 0.567761i) q^{35} +(4.15258 + 3.85303i) q^{37} +(-1.11055 - 0.757161i) q^{39} +(-5.14698 - 2.47865i) q^{41} +(-8.70663 + 4.19289i) q^{43} +(-2.81656 + 2.61339i) q^{45} +(-2.96130 - 7.54527i) q^{47} +(4.50038 + 5.36158i) q^{49} +(-0.732141 - 1.86546i) q^{51} +(9.90956 - 9.19473i) q^{53} +(-4.76153 + 2.29303i) q^{55} +(-1.45375 - 0.700088i) q^{57} +(10.9531 + 7.46772i) q^{59} +(2.06626 + 1.91721i) q^{61} +(-7.33549 - 2.16228i) q^{63} +(-0.403488 + 5.38417i) q^{65} +(-4.76846 - 8.25921i) q^{67} +(-0.207311 + 0.908288i) q^{69} +(0.702213 + 3.07659i) q^{71} +(-3.48349 + 8.87578i) q^{73} +(1.02232 + 0.315344i) q^{75} +(-8.76486 - 5.81604i) q^{77} +(-7.30122 + 12.6461i) q^{79} +(7.66988 - 2.36585i) q^{81} +(1.50601 + 1.88848i) q^{83} +(-5.01912 + 6.29377i) q^{85} +(1.53030 + 0.230655i) q^{87} +(-11.5242 + 1.73700i) q^{89} +(-9.62310 + 4.78390i) q^{91} +(-0.708740 + 0.483211i) q^{93} +(0.484370 + 6.46346i) q^{95} -15.5042 q^{97} +11.4921 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{3} - q^{5} + 4 q^{7} + 41 q^{9} + q^{11} - 2 q^{13} + q^{15} - 5 q^{17} - 13 q^{19} + 12 q^{21} - 5 q^{23} + 2 q^{25} + 4 q^{27} - 21 q^{29} + 23 q^{31} - 17 q^{33} - 22 q^{35} - 60 q^{37}+ \cdots - 94 q^{99}+O(q^{100}) \) 84 * q - 8 * q^3 - q^5 + 4 * q^7 + 41 * q^9 + q^11 - 2 * q^13 + q^15 - 5 * q^17 - 13 * q^19 + 12 * q^21 - 5 * q^23 + 2 * q^25 + 4 * q^27 - 21 * q^29 + 23 * q^31 - 17 * q^33 - 22 * q^35 - 60 * q^37 - 61 * q^39 + 4 * q^41 + 22 * q^43 + 30 * q^45 + 82 * q^47 - 2 * q^49 + 3 * q^51 + 38 * q^53 + 69 * q^55 - 2 * q^57 - 6 * q^59 - 26 * q^61 - 37 * q^63 + 2 * q^65 + 43 * q^67 + 7 * q^69 - 21 * q^71 - 7 * q^73 - 80 * q^75 - 85 * q^77 - 25 * q^79 - 10 * q^81 - 17 * q^83 + 23 * q^85 + 47 * q^87 + 7 * q^89 - 3 * q^91 - 50 * q^93 - 129 * q^95 - 150 * q^97 - 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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