LMFDB - Embedded newform 693.2.m.k.64.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			64.7
Character	$\chi$	$=$	693.64
Dual form			693.2.m.k.379.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.643412 - 1.98022i) q^{2} +(-1.88925 - 1.37262i) q^{4} +(0.411680 + 1.26702i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.564713 + 0.410288i) q^{8} +O(q^{10})$	\(q+(0.643412 - 1.98022i) q^{2} +(-1.88925 - 1.37262i) q^{4} +(0.411680 + 1.26702i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.564713 + 0.410288i) q^{8} +2.77386 q^{10} +(-1.44342 - 2.98606i) q^{11} +(1.77589 - 5.46564i) q^{13} +(-1.68447 + 1.22384i) q^{14} +(-0.994144 - 3.05966i) q^{16} +(1.32024 + 4.06329i) q^{17} +(-0.131508 + 0.0955461i) q^{19} +(0.961374 - 2.95880i) q^{20} +(-6.84176 + 0.937014i) q^{22} +1.12680 q^{23} +(2.60922 - 1.89571i) q^{25} +(-9.68052 - 7.03331i) q^{26} +(0.721631 + 2.22095i) q^{28} +(-7.95706 - 5.78115i) q^{29} +(2.81045 - 8.64967i) q^{31} -8.09449 q^{32} +8.89567 q^{34} +(0.411680 - 1.26702i) q^{35} +(6.81773 + 4.95337i) q^{37} +(0.104588 + 0.321890i) q^{38} +(-0.752324 - 0.546596i) q^{40} +(-3.64634 + 2.64922i) q^{41} -8.02855 q^{43} +(-1.37175 + 7.62269i) q^{44} +(0.724995 - 2.23131i) q^{46} +(2.26019 - 1.64212i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-2.07512 - 6.38656i) q^{50} +(-10.8574 + 7.88834i) q^{52} +(-3.24105 + 9.97492i) q^{53} +(3.18917 - 3.05814i) q^{55} +0.698024 q^{56} +(-16.5676 + 12.0371i) q^{58} +(11.0127 + 8.00123i) q^{59} +(2.49310 + 7.67299i) q^{61} +(-15.3200 - 11.1306i) q^{62} +(-3.21981 + 9.90954i) q^{64} +7.65617 q^{65} +9.10333 q^{67} +(3.08309 - 9.48879i) q^{68} +(-2.24410 - 1.63043i) q^{70} +(0.314901 + 0.969164i) q^{71} +(6.18756 + 4.49552i) q^{73} +(14.1954 - 10.3135i) q^{74} +0.379601 q^{76} +(-0.587413 + 3.26419i) q^{77} +(-0.00169116 + 0.00520485i) q^{79} +(3.46738 - 2.51920i) q^{80} +(2.89993 + 8.92508i) q^{82} +(0.875237 + 2.69370i) q^{83} +(-4.60476 + 3.34555i) q^{85} +(-5.16567 + 15.8983i) q^{86} +(2.04026 + 1.09405i) q^{88} +10.5254 q^{89} +(-4.64935 + 3.37795i) q^{91} +(-2.12881 - 1.54667i) q^{92} +(-1.79753 - 5.53223i) q^{94} +(-0.175198 - 0.127289i) q^{95} +(3.75805 - 11.5661i) q^{97} +2.08213 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) $ 32 * q - 10 * q^4 - 8 * q^7	$ 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) $ 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	0.643412	−	1.98022i	0.454961	−	1.40023i	−0.416220	−	0.909264i	$-0.636645\pi$
$2$	0.643412	−	1.98022i	0.454961	−	1.40023i	0.871181	−	0.490962i	$-0.163355\pi$
$3$		0			0
$3$		0			0
$4$	−1.88925	−	1.37262i	−0.944627	−	0.686312i
$5$	0.411680	+	1.26702i	0.184109	+	0.566629i	0.999932	−	0.0116729i	$-0.00371569\pi$
$5$	0.411680	+	1.26702i	0.184109	+	0.566629i	−0.815823	+	0.578302i	$0.803716\pi$
$6$		0			0
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−0.564713	+	0.410288i	−0.199656	+	0.145059i
$9$		0			0
$10$	2.77386			0.877171
$11$	−1.44342	−	2.98606i	−0.435206	−	0.900331i
$11$	−1.44342	−	2.98606i	−0.435206	−	0.900331i
$12$		0			0
$13$	1.77589	−	5.46564i	0.492544	−	1.51589i	−0.328206	−	0.944606i	$-0.606444\pi$
$13$	1.77589	−	5.46564i	0.492544	−	1.51589i	0.820750	−	0.571288i	$-0.193556\pi$
$14$	−1.68447	+	1.22384i	−0.450195	+	0.327086i
$15$		0			0
$16$	−0.994144	−	3.05966i	−0.248536	−	0.764915i
$17$	1.32024	+	4.06329i	0.320206	+	0.985493i	0.973558	+	0.228439i	$0.0733622\pi$
$17$	1.32024	+	4.06329i	0.320206	+	0.985493i	−0.653352	+	0.757054i	$0.726638\pi$
$18$		0			0
$19$	−0.131508	+	0.0955461i	−0.0301700	+	0.0219198i	−0.602768	−	0.797916i	$-0.705936\pi$
$19$	−0.131508	+	0.0955461i	−0.0301700	+	0.0219198i	0.572598	+	0.819836i	$0.305936\pi$
$20$	0.961374	−	2.95880i	0.214970	−	0.661609i
$21$		0			0
$22$	−6.84176	+	0.937014i	−1.45867	+	0.199772i
$23$	1.12680			0.234954			0.117477	−	0.993076i	$-0.462519\pi$
$23$	1.12680			0.234954			0.117477	+	0.993076i	$0.462519\pi$
$24$		0			0
$25$	2.60922	−	1.89571i	0.521845	−	0.379143i
$26$	−9.68052	−	7.03331i	−1.89851	−	1.37935i
$27$		0			0
$28$	0.721631	+	2.22095i	0.136375	+	0.419720i
$29$	−7.95706	−	5.78115i	−1.47759	−	1.07353i	−0.978323	−	0.207083i	$-0.933603\pi$
$29$	−7.95706	−	5.78115i	−1.47759	−	1.07353i	−0.499266	−	0.866449i	$-0.666397\pi$
$30$		0			0
$31$	2.81045	−	8.64967i	0.504772	−	1.55353i	−0.296383	−	0.955069i	$-0.595780\pi$
$31$	2.81045	−	8.64967i	0.504772	−	1.55353i	0.801154	−	0.598458i	$-0.204220\pi$
$32$	−8.09449			−1.43092
$33$		0			0
$34$	8.89567			1.52559
$35$	0.411680	−	1.26702i	0.0695866	−	0.214166i
$36$		0			0
$37$	6.81773	+	4.95337i	1.12083	+	0.814329i	0.984334	−	0.176312i	$-0.0564168\pi$
$37$	6.81773	+	4.95337i	1.12083	+	0.814329i	0.136493	+	0.990641i	$0.456417\pi$
$38$	0.104588	+	0.321890i	0.0169665	+	0.0522175i
$39$		0			0
$40$	−0.752324	−	0.546596i	−0.118953	−	0.0864244i
$41$	−3.64634	+	2.64922i	−0.569462	+	0.413738i	−0.834910	−	0.550387i	$-0.814480\pi$
$41$	−3.64634	+	2.64922i	−0.569462	+	0.413738i	0.265448	+	0.964125i	$0.414480\pi$
$42$		0			0
$43$	−8.02855			−1.22434			−0.612172	−	0.790725i	$-0.709704\pi$
$43$	−8.02855			−1.22434			−0.612172	+	0.790725i	$0.709704\pi$
$44$	−1.37175	+	7.62269i	−0.206800	+	1.14916i
$45$		0			0
$46$	0.724995	−	2.23131i	0.106895	−	0.328988i
$47$	2.26019	−	1.64212i	0.329682	−	0.239528i	−0.410614	−	0.911809i	$-0.634685\pi$
$47$	2.26019	−	1.64212i	0.329682	−	0.239528i	0.740296	+	0.672281i	$0.234685\pi$
$48$		0			0
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−2.07512	−	6.38656i	−0.293466	−	0.903196i
$51$		0			0
$52$	−10.8574	+	7.88834i	−1.50565	+	1.09392i
$53$	−3.24105	+	9.97492i	−0.445192	+	1.37016i	0.437080	+	0.899422i	$0.356013\pi$
$53$	−3.24105	+	9.97492i	−0.445192	+	1.37016i	−0.882273	+	0.470739i	$0.843987\pi$
$54$		0			0
$55$	3.18917	−	3.05814i	0.430028	−	0.412359i
$56$	0.698024			0.0932774
$57$		0			0
$58$	−16.5676	+	12.0371i	−2.17543	+	1.58054i
$59$	11.0127	+	8.00123i	1.43374	+	1.04167i	0.989305	+	0.145859i	$0.0465945\pi$
$59$	11.0127	+	8.00123i	1.43374	+	1.04167i	0.444432	+	0.895812i	$0.353405\pi$
$60$		0			0
$61$	2.49310	+	7.67299i	0.319209	+	0.982425i	0.973987	+	0.226604i	$0.0727622\pi$
$61$	2.49310	+	7.67299i	0.319209	+	0.982425i	−0.654778	+	0.755822i	$0.727238\pi$
$62$	−15.3200	−	11.1306i	−1.94564	−	1.41359i
$63$		0			0
$64$	−3.21981	+	9.90954i	−0.402476	+	1.23869i
$65$	7.65617			0.949631
$66$		0			0
$67$	9.10333			1.11215			0.556074	−	0.831133i	$-0.312307\pi$
$67$	9.10333			1.11215			0.556074	+	0.831133i	$0.312307\pi$
$68$	3.08309	−	9.48879i	0.373880	−	1.15068i
$69$		0			0
$70$	−2.24410	−	1.63043i	−0.268221	−	0.194874i
$71$	0.314901	+	0.969164i	0.0373718	+	0.115019i	0.968002	−	0.250942i	$-0.0807404\pi$
$71$	0.314901	+	0.969164i	0.0373718	+	0.115019i	−0.930630	+	0.365961i	$0.880740\pi$
$72$		0			0
$73$	6.18756	+	4.49552i	0.724199	+	0.526161i	0.887723	−	0.460378i	$-0.152286\pi$
$73$	6.18756	+	4.49552i	0.724199	+	0.526161i	−0.163524	+	0.986539i	$0.552286\pi$
$74$	14.1954	−	10.3135i	1.65018	−	1.19892i
$75$		0			0
$76$	0.379601			0.0435432
$77$	−0.587413	+	3.26419i	−0.0669419	+	0.371989i
$78$		0			0
$79$	−0.00169116	+	0.00520485i	−0.000190270	+	0.000585592i	−0.951152	−	0.308724i	$-0.900098\pi$
$79$	−0.00169116	+	0.00520485i	−0.000190270	+	0.000585592i	0.950961	+	0.309310i	$0.100098\pi$
$80$	3.46738	−	2.51920i	0.387665	−	0.281655i
$81$		0			0
$82$	2.89993	+	8.92508i	0.320244	+	0.985610i
$83$	0.875237	+	2.69370i	0.0960698	+	0.295672i	0.987531	−	0.157425i	$-0.0503191\pi$
$83$	0.875237	+	2.69370i	0.0960698	+	0.295672i	−0.891461	+	0.453097i	$0.850319\pi$
$84$		0			0
$85$	−4.60476	+	3.34555i	−0.499456	+	0.362876i
$86$	−5.16567	+	15.8983i	−0.557028	+	1.71436i
$87$		0			0
$88$	2.04026	+	1.09405i	0.217493	+	0.116626i
$89$	10.5254			1.11569			0.557845	−	0.829945i	$-0.311628\pi$
$89$	10.5254			1.11569			0.557845	+	0.829945i	$0.311628\pi$
$90$		0			0
$91$	−4.64935	+	3.37795i	−0.487384	+	0.354105i
$92$	−2.12881	−	1.54667i	−0.221943	−	0.161251i
$93$		0			0
$94$	−1.79753	−	5.53223i	−0.185401	−	0.570606i
$95$	−0.175198	−	0.127289i	−0.0179749	−	0.0130596i
$96$		0			0
$97$	3.75805	−	11.5661i	0.381572	−	1.17436i	−0.557365	−	0.830268i	$-0.688188\pi$
$97$	3.75805	−	11.5661i	0.381572	−	1.17436i	0.938937	−	0.344090i	$-0.111812\pi$
$98$	2.08213			0.210326
$99$		0			0
$100$	−7.53159			−0.753159
$101$	0.470287	−	1.44739i	0.0467953	−	0.144021i	−0.924929	−	0.380140i	$-0.875876\pi$
$101$	0.470287	−	1.44739i	0.0467953	−	0.144021i	0.971724	+	0.236119i	$0.0758756\pi$
$102$		0			0
$103$	−12.5126	−	9.09097i	−1.23291	−	0.895760i	−0.235803	−	0.971801i	$-0.575772\pi$
$103$	−12.5126	−	9.09097i	−1.23291	−	0.895760i	−0.997105	+	0.0760414i	$0.975772\pi$
$104$	1.23962	+	3.81514i	0.121554	+	0.374106i
$105$		0			0
$106$	17.6672	+	12.8360i	1.71599	+	1.24674i
$107$	6.67473	−	4.84948i	0.645271	−	0.468817i	−0.216386	−	0.976308i	$-0.569427\pi$
$107$	6.67473	−	4.84948i	0.645271	−	0.468817i	0.861657	+	0.507491i	$0.169427\pi$
$108$		0			0
$109$	0.305943			0.0293040			0.0146520	−	0.999893i	$-0.495336\pi$
$109$	0.305943			0.0293040			0.0146520	+	0.999893i	$0.495336\pi$
$110$	−4.00383	−	8.28290i	−0.381750	−	0.789744i
$111$		0			0
$112$	−0.994144	+	3.05966i	−0.0939378	+	0.289111i
$113$	−8.21174	+	5.96618i	−0.772495	+	0.561251i	−0.902717	−	0.430234i	$-0.858431\pi$
$113$	−8.21174	+	5.96618i	−0.772495	+	0.561251i	0.130222	+	0.991485i	$0.458431\pi$
$114$		0			0
$115$	0.463880	+	1.42768i	0.0432570	+	0.133131i
$116$	7.09758	+	21.8441i	0.658994	+	2.02817i
$117$		0			0
$118$	22.9299	−	16.6596i	2.11087	−	1.53364i
$119$	1.32024	−	4.06329i	0.121027	−	0.372481i
$120$		0			0
$121$	−6.83310	+	8.62025i	−0.621191	+	0.783659i
$122$	16.7983			1.52085
$123$		0			0
$124$	−17.1824	+	12.4837i	−1.54302	+	1.12107i
$125$	8.86503	+	6.44082i	0.792912	+	0.576085i
$126$		0			0
$127$	1.17666	+	3.62138i	0.104411	+	0.321345i	0.989592	−	0.143903i	$-0.0459652\pi$
$127$	1.17666	+	3.62138i	0.104411	+	0.321345i	−0.885180	+	0.465248i	$0.845965\pi$
$128$	4.45424	+	3.23619i	0.393703	+	0.286042i
$129$		0			0
$130$	4.92607	−	15.1609i	0.432045	−	1.32970i
$131$	−14.6612			−1.28096			−0.640479	−	0.767976i	$-0.721264\pi$
$131$	−14.6612			−1.28096			−0.640479	+	0.767976i	$0.721264\pi$
$132$		0			0
$133$	0.162553			0.0140951
$134$	5.85719	−	18.0266i	0.505984	−	1.55726i
$135$		0			0
$136$	−2.41268	−	1.75291i	−0.206886	−	0.150311i
$137$	5.20094	+	16.0069i	0.444347	+	1.36756i	0.883199	+	0.468999i	$0.155385\pi$
$137$	5.20094	+	16.0069i	0.444347	+	1.36756i	−0.438852	+	0.898559i	$0.644615\pi$
$138$		0			0
$139$	6.30602	+	4.58159i	0.534870	+	0.388606i	0.822176	−	0.569233i	$-0.192760\pi$
$139$	6.30602	+	4.58159i	0.534870	+	0.388606i	−0.287306	+	0.957839i	$0.592760\pi$
$140$	−2.51691	+	1.82864i	−0.212718	+	0.154548i
$141$		0			0
$142$	2.12177			0.178055
$143$	−18.8841	+	2.58627i	−1.57916	+	0.216275i
$144$		0			0
$145$	4.04907	−	12.4617i	0.336257	−	1.03489i
$146$	12.8833	−	9.36024i	1.06623	−	0.774659i
$147$		0			0
$148$	−6.08131	−	18.7163i	−0.499880	−	1.53847i
$149$	3.00361	+	9.24416i	0.246065	+	0.757311i	0.995459	+	0.0951870i	$0.0303449\pi$
$149$	3.00361	+	9.24416i	0.246065	+	0.757311i	−0.749394	+	0.662124i	$0.769655\pi$
$150$		0			0
$151$	−8.17231	+	5.93753i	−0.665053	+	0.483190i	−0.868366	−	0.495924i	$-0.834829\pi$
$151$	−8.17231	+	5.93753i	−0.665053	+	0.483190i	0.203312	+	0.979114i	$0.434829\pi$
$152$	0.0350628	−	0.107912i	0.00284397	−	0.00875284i
$153$		0			0
$154$	6.08586	+	3.26343i	0.490413	+	0.262974i
$155$	12.1163			0.973206
$156$		0			0
$157$	4.00395	−	2.90904i	0.319550	−	0.232166i	−0.416434	−	0.909166i	$-0.636720\pi$
$157$	4.00395	−	2.90904i	0.319550	−	0.232166i	0.735983	+	0.677000i	$0.236720\pi$
$158$	0.00921864	+	0.00669773i	0.000733395	+	0.000532843i
$159$		0			0
$160$	−3.33234	−	10.2559i	−0.263445	−	0.810799i
$161$	−0.911599	−	0.662315i	−0.0718440	−	0.0521978i
$162$		0			0
$163$	2.08060	−	6.40343i	0.162965	−	0.501556i	−0.835915	−	0.548858i	$-0.815063\pi$
$163$	2.08060	−	6.40343i	0.162965	−	0.501556i	0.998881	+	0.0473029i	$0.0150626\pi$
$164$	10.5252			0.821882
$165$		0			0
$166$	5.89726			0.457716
$167$	4.32234	−	13.3028i	0.334473	−	1.02940i	−0.632509	−	0.774553i	$-0.717975\pi$
$167$	4.32234	−	13.3028i	0.334473	−	1.02940i	0.966981	−	0.254847i	$-0.0820252\pi$
$168$		0			0
$169$	−16.2022	−	11.7716i	−1.24632	−	0.905504i
$170$	3.66217	+	11.2710i	0.280875	+	0.864446i
$171$		0			0
$172$	15.1680	+	11.0202i	1.15655	+	0.840281i
$173$	2.83865	−	2.06240i	0.215819	−	0.156802i	−0.474624	−	0.880189i	$-0.657416\pi$
$173$	2.83865	−	2.06240i	0.215819	−	0.156802i	0.690443	+	0.723387i	$0.257416\pi$
$174$		0			0
$175$	−3.22518			−0.243801
$176$	−7.70137	+	7.38494i	−0.580512	+	0.556661i
$177$		0			0
$178$	6.77217	−	20.8426i	0.507595	−	1.56222i
$179$	−1.80196	+	1.30920i	−0.134685	+	0.0978544i	−0.653088	−	0.757282i	$-0.726527\pi$
$179$	−1.80196	+	1.30920i	−0.134685	+	0.0978544i	0.518403	+	0.855137i	$0.326527\pi$
$180$		0			0
$181$	0.344343	+	1.05978i	0.0255948	+	0.0787727i	0.963038	−	0.269366i	$-0.0868140\pi$
$181$	0.344343	+	1.05978i	0.0255948	+	0.0787727i	−0.937443	+	0.348138i	$0.886814\pi$
$182$	3.69763	+	11.3801i	0.274087	+	0.843552i
$183$		0			0
$184$	−0.636318	+	0.462312i	−0.0469100	+	0.0340821i
$185$	−3.46930	+	10.6774i	−0.255068	+	0.785018i
$186$		0			0
$187$	10.2276	−	9.80735i	0.747914	−	0.717185i
$188$	−6.52408			−0.475818
$189$		0			0
$190$	−0.364784	+	0.265031i	−0.0264642	+	0.0192274i
$191$	−8.27740	−	6.01388i	−0.598932	−	0.435149i	0.246568	−	0.969126i	$-0.420697\pi$
$191$	−8.27740	−	6.01388i	−0.598932	−	0.435149i	−0.845500	+	0.533976i	$0.820697\pi$
$192$		0			0
$193$	−5.54178	−	17.0558i	−0.398906	−	1.22771i	−0.925878	−	0.377823i	$-0.876673\pi$
$193$	−5.54178	−	17.0558i	−0.398906	−	1.22771i	0.526972	−	0.849883i	$-0.323327\pi$
$194$	−20.4854	−	14.8835i	−1.47077	−	1.06857i
$195$		0			0
$196$	0.721631	−	2.22095i	0.0515450	−	0.158639i
$197$	4.30284			0.306564			0.153282	−	0.988182i	$-0.451016\pi$
$197$	4.30284			0.306564			0.153282	+	0.988182i	$0.451016\pi$
$198$		0			0
$199$	22.0560			1.56351			0.781753	−	0.623588i	$-0.214326\pi$
$199$	22.0560			1.56351			0.781753	+	0.623588i	$0.214326\pi$
$200$	−0.695675	+	2.14107i	−0.0491917	+	0.151396i
$201$		0			0
$202$	−2.56357	−	1.86254i	−0.180372	−	0.131048i
$203$	3.03933	+	9.35409i	0.213319	+	0.656528i
$204$		0			0
$205$	−4.85774	−	3.52935i	−0.339279	−	0.246501i
$206$	−26.0529	+	18.9285i	−1.81519	+	1.31881i
$207$		0			0
$208$	−18.4885			−1.28195
$209$	0.475127	+	0.254778i	0.0328652	+	0.0176233i
$210$		0			0
$211$	−4.58968	+	14.1256i	−0.315966	+	0.972444i	0.659389	+	0.751802i	$0.270815\pi$
$211$	−4.58968	+	14.1256i	−0.315966	+	0.972444i	−0.975355	+	0.220642i	$0.929185\pi$
$212$	19.8150	−	14.3964i	1.36090	−	0.988750i
$213$		0			0
$214$	−5.30842	−	16.3376i	−0.362876	−	1.11682i
$215$	−3.30519	−	10.1723i	−0.225412	−	0.693748i
$216$		0			0
$217$	−7.35785	+	5.34579i	−0.499483	+	0.362896i
$218$	0.196847	−	0.605833i	0.0133322	−	0.0410322i
$219$		0			0
$220$	−10.2228	+	1.40007i	−0.689223	+	0.0943925i
$221$	24.5531			1.65162
$222$		0			0
$223$	−4.52873	+	3.29031i	−0.303266	+	0.220336i	−0.729002	−	0.684512i	$-0.760015\pi$
$223$	−4.52873	+	3.29031i	−0.303266	+	0.220336i	0.425736	+	0.904848i	$0.360015\pi$
$224$	6.54858	+	4.75782i	0.437545	+	0.317895i
$225$		0			0
$226$	6.53081	+	20.0998i	0.434423	+	1.33702i
$227$	6.09093	+	4.42532i	0.404269	+	0.293719i	0.771278	−	0.636499i	$-0.219618\pi$
$227$	6.09093	+	4.42532i	0.404269	+	0.293719i	−0.367009	+	0.930218i	$0.619618\pi$
$228$		0			0
$229$	−8.41547	+	25.9002i	−0.556110	+	1.71153i	0.136883	+	0.990587i	$0.456292\pi$
$229$	−8.41547	+	25.9002i	−0.556110	+	1.71153i	−0.692993	+	0.720944i	$0.743708\pi$
$230$	3.12558			0.206094
$231$		0			0
$232$	6.86539			0.450735
$233$	−1.69646	+	5.22117i	−0.111139	+	0.342050i	−0.991122	−	0.132954i	$-0.957554\pi$
$233$	−1.69646	+	5.22117i	−0.111139	+	0.342050i	0.879983	+	0.475005i	$0.157554\pi$
$234$		0			0
$235$	3.01108	+	2.18767i	0.196421	+	0.142708i
$236$	−9.82320	−	30.2327i	−0.639436	−	1.96798i
$237$		0			0
$238$	−7.19675	−	5.22874i	−0.466496	−	0.338929i
$239$	20.0971	−	14.6014i	1.29997	−	0.944484i	0.300015	−	0.953934i	$-0.403008\pi$
$239$	20.0971	−	14.6014i	1.29997	−	0.944484i	0.999955	+	0.00945057i	$0.00300825\pi$
$240$		0			0
$241$	17.3238			1.11592			0.557961	−	0.829867i	$-0.311584\pi$
$241$	17.3238			1.11592			0.557961	+	0.829867i	$0.311584\pi$
$242$	12.6735	+	19.0774i	0.814683	+	1.22634i
$243$		0			0
$244$	5.82201	−	17.9183i	0.372716	−	1.14710i
$245$	−1.07779	+	0.783062i	−0.0688576	+	0.0500280i
$246$		0			0
$247$	0.288676	+	0.888454i	0.0183680	+	0.0565310i
$248$	1.96176	+	6.03768i	0.124572	+	0.383393i
$249$		0			0
$250$	18.4581	−	13.4106i	1.16739	−	0.848161i
$251$	−7.62206	+	23.4583i	−0.481100	+	1.48067i	0.356451	+	0.934314i	$0.383987\pi$
$251$	−7.62206	+	23.4583i	−0.481100	+	1.48067i	−0.837551	+	0.546360i	$0.816013\pi$
$252$		0			0
$253$	−1.62644	−	3.36469i	−0.102253	−	0.211536i
$254$	7.92819			0.497459
$255$		0			0
$256$	−7.58484	+	5.51071i	−0.474052	+	0.344419i
$257$	−3.13815	−	2.28000i	−0.195753	−	0.142223i	0.485591	−	0.874186i	$-0.338604\pi$
$257$	−3.13815	−	2.28000i	−0.195753	−	0.142223i	−0.681344	+	0.731963i	$0.738604\pi$
$258$		0			0
$259$	−2.60414	−	8.01472i	−0.161813	−	0.498010i
$260$	−14.4644	−	10.5090i	−0.897047	−	0.651743i
$261$		0			0
$262$	−9.43321	+	29.0324i	−0.582786	+	1.79363i
$263$	−5.19075			−0.320075			−0.160038	−	0.987111i	$-0.551162\pi$
$263$	−5.19075			−0.320075			−0.160038	+	0.987111i	$0.551162\pi$
$264$		0			0
$265$	−13.9727			−0.858336
$266$	0.104588	−	0.321890i	0.00641273	−	0.0197363i
$267$		0			0
$268$	−17.1985	−	12.4954i	−1.05057	−	0.763280i
$269$	−5.20374	−	16.0155i	−0.317278	−	0.976481i	−0.974807	−	0.223052i	$-0.928398\pi$
$269$	−5.20374	−	16.0155i	−0.317278	−	0.976481i	0.657529	−	0.753429i	$-0.271602\pi$
$270$		0			0
$271$	11.3436	+	8.24157i	0.689072	+	0.500640i	0.876355	−	0.481666i	$-0.159968\pi$
$271$	11.3436	+	8.24157i	0.689072	+	0.500640i	−0.187283	+	0.982306i	$0.559968\pi$
$272$	11.1198	−	8.07900i	0.674236	−	0.489861i
$273$		0			0
$274$	35.0434			2.11705
$275$	−9.42691	−	5.05500i	−0.568464	−	0.304828i
$276$		0			0
$277$	0.292122	−	0.899060i	0.0175519	−	0.0540193i	−0.941897	−	0.335902i	$-0.890959\pi$
$277$	0.292122	−	0.899060i	0.0175519	−	0.0540193i	0.959449	+	0.281883i	$0.0909589\pi$
$278$	13.1299	−	9.53945i	0.787481	−	0.572138i
$279$		0			0
$280$	0.287362	+	0.884410i	0.0171732	+	0.0528536i
$281$	1.24700	+	3.83789i	0.0743901	+	0.228949i	0.981337	−	0.192296i	$-0.0615933\pi$
$281$	1.24700	+	3.83789i	0.0743901	+	0.228949i	−0.906947	+	0.421245i	$0.861593\pi$
$282$		0			0
$283$	−3.88814	+	2.82490i	−0.231126	+	0.167923i	−0.697321	−	0.716759i	$-0.745625\pi$
$283$	−3.88814	+	2.82490i	−0.231126	+	0.167923i	0.466195	+	0.884682i	$0.345625\pi$
$284$	0.735370	−	2.26324i	0.0436362	−	0.134298i
$285$		0			0
$286$	−7.02886	+	39.0586i	−0.415625	+	2.30958i
$287$	4.50712			0.266047
$288$		0			0
$289$	−1.01402	+	0.736728i	−0.0596482	+	0.0433370i
$290$	−22.0718	−	16.0361i	−1.29610	−	0.941671i
$291$		0			0
$292$	−5.51920	−	16.9864i	−0.322987	−	0.994052i
$293$	0.846778	+	0.615220i	0.0494693	+	0.0359415i	0.612245	−	0.790668i	$-0.290267\pi$
$293$	0.846778	+	0.615220i	0.0494693	+	0.0359415i	−0.562776	+	0.826610i	$0.690267\pi$
$294$		0			0
$295$	−5.60399	+	17.2473i	−0.326277	+	1.00418i
$296$	−5.88237			−0.341906
$297$		0			0
$298$	20.2380			1.17236
$299$	2.00107	−	6.15867i	0.115725	−	0.356165i
$300$		0			0
$301$	6.49524	+	4.71907i	0.374379	+	0.272002i
$302$	6.49945	+	20.0032i	0.374001	+	1.15106i
$303$		0			0
$304$	0.423077	+	0.307383i	0.0242651	+	0.0176296i
$305$	−8.69547	+	6.31763i	−0.497901	+	0.361746i
$306$		0			0
$307$	−26.1929			−1.49491			−0.747455	−	0.664313i	$-0.768724\pi$
$307$	−26.1929			−1.49491			−0.747455	+	0.664313i	$0.768724\pi$
$308$	5.59028	−	5.36059i	0.318536	−	0.305448i
$309$		0			0
$310$	7.79578	−	23.9930i	0.442771	−	1.36271i
$311$	17.8241	−	12.9500i	1.01071	−	0.734325i	0.0463539	−	0.998925i	$-0.485240\pi$
$311$	17.8241	−	12.9500i	1.01071	−	0.734325i	0.964358	+	0.264600i	$0.0852398\pi$
$312$		0			0
$313$	9.39779	+	28.9234i	0.531194	+	1.63485i	0.751731	+	0.659470i	$0.229219\pi$
$313$	9.39779	+	28.9234i	0.531194	+	1.63485i	−0.220537	+	0.975379i	$0.570781\pi$
$314$	−3.18434	−	9.80040i	−0.179703	−	0.553068i
$315$		0			0
$316$	0.0103393	−	0.00751196i	0.000581633	−	0.000422581i
$317$	−5.89531	+	18.1439i	−0.331114	+	1.01906i	0.637491	+	0.770458i	$0.279972\pi$
$317$	−5.89531	+	18.1439i	−0.331114	+	1.01906i	−0.968605	+	0.248606i	$0.920028\pi$
$318$		0			0
$319$	−5.77748	+	32.1049i	−0.323477	+	1.79753i
$320$	−13.8811			−0.775978
$321$		0			0
$322$	−1.89806	+	1.37902i	−0.105775	+	0.0768500i
$323$	−0.561855	−	0.408211i	−0.0312624	−	0.0227135i
$324$		0			0
$325$	−5.72757	−	17.6277i	−0.317709	−	0.977806i
$326$	−11.3415	−	8.24009i	−0.628148	−	0.456377i
$327$		0			0
$328$	0.972191	−	2.99210i	0.0536803	−	0.165211i
$329$	−2.79374			−0.154024
$330$		0			0
$331$	3.61239			0.198555			0.0992774	−	0.995060i	$-0.468347\pi$
$331$	3.61239			0.198555			0.0992774	+	0.995060i	$0.468347\pi$
$332$	2.04389	−	6.29046i	0.112173	−	0.345234i
$333$		0			0
$334$	−23.5614	−	17.1183i	−1.28922	−	0.936674i
$335$	3.74766	+	11.5341i	0.204756	+	0.630175i
$336$		0			0
$337$	2.16686	+	1.57432i	0.118037	+	0.0857586i	0.645237	−	0.763982i	$-0.276758\pi$
$337$	2.16686	+	1.57432i	0.118037	+	0.0857586i	−0.527201	+	0.849741i	$0.676758\pi$
$338$	−33.7349	+	24.5099i	−1.83494	+	1.33316i
$339$		0			0
$340$	13.2917			0.720846
$341$	−29.8851	+	4.09291i	−1.61837	+	0.221644i
$342$		0			0
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	4.53383	−	3.29402i	0.244448	−	0.177602i
$345$		0			0
$346$	−2.25759	−	6.94813i	−0.121369	−	0.373534i
$347$	−5.70279	−	17.5514i	−0.306142	−	0.942208i	−0.979249	−	0.202663i	$-0.935041\pi$
$347$	−5.70279	−	17.5514i	−0.306142	−	0.942208i	0.673107	−	0.739545i	$-0.264959\pi$
$348$		0			0
$349$	−16.4243	+	11.9329i	−0.879171	+	0.638755i	−0.933032	−	0.359793i	$-0.882847\pi$
$349$	−16.4243	+	11.9329i	−0.879171	+	0.638755i	0.0538608	+	0.998548i	$0.482847\pi$
$350$	−2.07512	+	6.38656i	−0.110920	+	0.341376i
$351$		0			0
$352$	11.6837	+	24.1706i	0.622745	+	1.28830i
$353$	−12.7771			−0.680054			−0.340027	−	0.940416i	$-0.610436\pi$
$353$	−12.7771			−0.680054			−0.340027	+	0.940416i	$0.610436\pi$
$354$		0			0
$355$	−1.09831	+	0.797971i	−0.0582924	+	0.0423519i
$356$	−19.8851	−	14.4474i	−1.05391	−	0.765711i
$357$		0			0
$358$	1.43310	+	4.41064i	0.0757419	+	0.233109i
$359$	−8.33093	−	6.05277i	−0.439689	−	0.319453i	0.345822	−	0.938300i	$-0.387600\pi$
$359$	−8.33093	−	6.05277i	−0.439689	−	0.319453i	−0.785512	+	0.618847i	$0.787600\pi$
$360$		0			0
$361$	−5.86316	+	18.0449i	−0.308587	+	0.949734i
$362$	2.32015			0.121944
$363$		0			0
$364$	13.4204			0.703423
$365$	−3.14863	+	9.69047i	−0.164807	+	0.507223i
$366$		0			0
$367$	−2.14410	−	1.55778i	−0.111921	−	0.0813153i	0.530417	−	0.847737i	$-0.322035\pi$
$367$	−2.14410	−	1.55778i	−0.111921	−	0.0813153i	−0.642338	+	0.766422i	$0.722035\pi$
$368$	−1.12020	−	3.44762i	−0.0583944	−	0.179720i
$369$		0			0
$370$	18.9114	+	13.7399i	0.983157	+	0.714305i
$371$	8.48518	−	6.16484i	0.440528	−	0.320063i
$372$		0			0
$373$	32.9030			1.70365			0.851827	−	0.523824i	$-0.175495\pi$
$373$	32.9030			1.70365			0.851827	+	0.523824i	$0.175495\pi$
$374$	−12.8402	−	26.5630i	−0.663949	−	1.37354i
$375$		0			0
$376$	−0.602614	+	1.85466i	−0.0310775	+	0.0956466i
$377$	−45.7285	+	33.2237i	−2.35514	+	1.71111i
$378$		0			0
$379$	−6.87018	−	21.1442i	−0.352897	−	1.08611i	−0.957219	−	0.289366i	$-0.906556\pi$
$379$	−6.87018	−	21.1442i	−0.352897	−	1.08611i	0.604321	−	0.796741i	$-0.293444\pi$
$380$	0.156274	+	0.480962i	0.00801668	+	0.0246728i
$381$		0			0
$382$	−17.2346	+	12.5217i	−0.881798	+	0.640664i
$383$	7.76524	−	23.8990i	0.396785	−	1.22118i	−0.530777	−	0.847512i	$-0.678100\pi$
$383$	7.76524	−	23.8990i	0.396785	−	1.22118i	0.927562	−	0.373668i	$-0.121900\pi$
$384$		0			0
$385$	−4.37762	+	0.599538i	−0.223104	+	0.0305553i
$386$	−37.3399			−1.90055
$387$		0			0
$388$	−22.9758	+	16.6929i	−1.16642	+	0.847452i
$389$	18.6582	+	13.5560i	0.946007	+	0.687314i	0.949859	−	0.312678i	$-0.101226\pi$
$389$	18.6582	+	13.5560i	0.946007	+	0.687314i	−0.00385199	+	0.999993i	$0.501226\pi$
$390$		0			0
$391$	1.48765	+	4.57851i	0.0752336	+	0.231545i
$392$	−0.564713	−	0.410288i	−0.0285223	−	0.0207227i
$393$		0			0
$394$	2.76850	−	8.52056i	0.139475	−	0.429260i
$395$	−0.00729087			−0.000366844
$396$		0			0
$397$	−3.78504			−0.189966			−0.0949828	−	0.995479i	$-0.530280\pi$
$397$	−3.78504			−0.189966			−0.0949828	+	0.995479i	$0.530280\pi$
$398$	14.1911	−	43.6757i	0.711335	−	2.18926i
$399$		0			0
$400$	−8.39419	−	6.09873i	−0.419709	−	0.304937i
$401$	−12.0701	−	37.1479i	−0.602751	−	1.85508i	−0.511569	−	0.859242i	$-0.670936\pi$
$401$	−12.0701	−	37.1479i	−0.602751	−	1.85508i	−0.0911817	−	0.995834i	$-0.529064\pi$
$402$		0			0
$403$	−42.2849	−	30.7218i	−2.10636	−	1.53036i
$404$	−2.87522	+	2.08897i	−0.143047	+	0.103930i
$405$		0			0
$406$	20.4787			1.01634
$407$	4.95023	−	27.5079i	0.245374	−	1.36352i
$408$		0			0
$409$	−9.08614	+	27.9643i	−0.449281	+	1.38274i	0.428439	+	0.903571i	$0.359064\pi$
$409$	−9.08614	+	27.9643i	−0.449281	+	1.38274i	−0.877720	+	0.479174i	$0.840936\pi$
$410$	−10.1144	+	7.34855i	−0.499515	+	0.362919i
$411$		0			0
$412$	11.1611	+	34.3503i	0.549867	+	1.69232i
$413$	−4.20650	−	12.9463i	−0.206988	−	0.637044i
$414$		0			0
$415$	−3.05266	+	2.21789i	−0.149849	+	0.108872i
$416$	−14.3749	+	44.2415i	−0.704790	+	2.16912i
$417$		0			0
$418$	0.810218	−	0.776929i	0.0396291	−	0.0380008i
$419$	14.5510			0.710863			0.355431	−	0.934702i	$-0.384334\pi$
$419$	14.5510			0.710863			0.355431	+	0.934702i	$0.384334\pi$
$420$		0			0
$421$	−14.3660	+	10.4375i	−0.700158	+	0.508695i	−0.879984	−	0.475004i	$-0.842447\pi$
$421$	−14.3660	+	10.4375i	−0.700158	+	0.508695i	0.179825	+	0.983699i	$0.442447\pi$
$422$	25.0187	+	18.1771i	1.21789	+	0.884849i
$423$		0			0
$424$	−2.26233	−	6.96274i	−0.109868	−	0.338140i
$425$	11.1477	+	8.09924i	0.540741	+	0.392871i
$426$		0			0
$427$	2.49310	−	7.67299i	0.120650	−	0.371322i
$428$	−19.2668			−0.931295
$429$		0			0
$430$	−22.2701			−1.07396
$431$	−5.51229	+	16.9651i	−0.265518	+	0.817180i	0.726056	+	0.687636i	$0.241351\pi$
$431$	−5.51229	+	16.9651i	−0.265518	+	0.817180i	−0.991574	+	0.129544i	$0.958649\pi$
$432$		0			0
$433$	−10.0646	−	7.31233i	−0.483672	−	0.351408i	0.319074	−	0.947730i	$-0.396628\pi$
$433$	−10.0646	−	7.31233i	−0.483672	−	0.351408i	−0.802745	+	0.596322i	$0.796628\pi$
$434$	5.85171	+	18.0097i	0.280891	+	0.864493i
$435$		0			0
$436$	−0.578003	−	0.419944i	−0.0276813	−	0.0201117i
$437$	−0.148183	+	0.107661i	−0.00708855	+	0.00515013i
$438$		0			0
$439$	16.3740			0.781489			0.390744	−	0.920499i	$-0.372218\pi$
$439$	16.3740			0.781489			0.390744	+	0.920499i	$0.372218\pi$
$440$	−0.546250	+	3.03545i	−0.0260414	+	0.144709i
$441$		0			0
$442$	15.7978	−	48.6205i	0.751423	−	2.31264i
$443$	−1.80189	+	1.30915i	−0.0856102	+	0.0621994i	−0.629767	−	0.776784i	$-0.716850\pi$
$443$	−1.80189	+	1.30915i	−0.0856102	+	0.0621994i	0.544157	+	0.838984i	$0.316850\pi$
$444$		0			0
$445$	4.33309	+	13.3359i	0.205408	+	0.632182i
$446$	3.60170	+	11.0849i	0.170546	+	0.524885i
$447$		0			0
$448$	8.42956	−	6.12443i	0.398259	−	0.289352i
$449$	9.87291	−	30.3857i	0.465932	−	1.43399i	−0.391876	−	0.920018i	$-0.628174\pi$
$449$	9.87291	−	30.3857i	0.465932	−	1.43399i	0.857807	−	0.513972i	$-0.171826\pi$
$450$		0			0
$451$	13.1739	+	7.06425i	0.620335	+	0.332642i
$452$	23.7034			1.11491
$453$		0			0
$454$	12.6821	−	9.21407i	0.595199	−	0.432438i
$455$	−6.19397	−	4.50018i	−0.290378	−	0.210972i
$456$		0			0
$457$	−6.83984	−	21.0509i	−0.319954	−	0.984718i	−0.973667	−	0.227975i	$-0.926790\pi$
$457$	−6.83984	−	21.0509i	−0.319954	−	0.984718i	0.653713	−	0.756743i	$-0.273210\pi$
$458$	45.8734	+	33.3290i	2.14352	+	1.55736i
$459$		0			0
$460$	1.08327	−	3.33397i	0.0505079	−	0.155447i
$461$	−14.9408			−0.695865			−0.347932	−	0.937520i	$-0.613116\pi$
$461$	−14.9408			−0.695865			−0.347932	+	0.937520i	$0.613116\pi$
$462$		0			0
$463$	5.02953			0.233742			0.116871	−	0.993147i	$-0.462714\pi$
$463$	5.02953			0.233742			0.116871	+	0.993147i	$0.462714\pi$
$464$	−9.77788	+	30.0932i	−0.453927	+	1.39704i
$465$		0			0
$466$	9.24754	+	6.71873i	0.428384	+	0.311239i
$467$	−9.93111	−	30.5648i	−0.459557	−	1.41437i	−0.865701	−	0.500561i	$-0.833127\pi$
$467$	−9.93111	−	30.5648i	−0.459557	−	1.41437i	0.406144	−	0.913809i	$-0.366873\pi$
$468$		0			0
$469$	−7.36475	−	5.35080i	−0.340072	−	0.247077i
$470$	6.26944	−	4.55501i	0.289188	−	0.210107i
$471$		0			0
$472$	−9.50185			−0.437358
$473$	11.5885	+	23.9737i	0.532842	+	1.10231i
$474$		0			0
$475$	−0.162006	+	0.498603i	−0.00743334	+	0.0228775i
$476$	−8.07165	+	5.86439i	−0.369963	+	0.268794i
$477$		0			0
$478$	−15.9832	−	49.1913i	−0.731055	−	2.24996i
$479$	−4.06329	−	12.5055i	−0.185657	−	0.571392i	0.814302	−	0.580441i	$-0.197120\pi$
$479$	−4.06329	−	12.5055i	−0.185657	−	0.571392i	−0.999959	+	0.00904845i	$0.997120\pi$
$480$		0			0
$481$	39.1809	−	28.4666i	1.78649	−	1.29796i
$482$	11.1463	−	34.3049i	0.507701	−	1.56254i
$483$		0			0
$484$	24.7418	−	6.90658i	1.12463	−	0.313935i
$485$	16.2016			0.735675
$486$		0			0
$487$	−0.851290	+	0.618499i	−0.0385756	+	0.0280268i	−0.606906	−	0.794774i	$-0.707590\pi$
$487$	−0.851290	+	0.618499i	−0.0385756	+	0.0280268i	0.568330	+	0.822800i	$0.307590\pi$
$488$	−4.55602	−	3.31015i	−0.206242	−	0.149843i
$489$		0			0
$490$	0.857169	+	2.63809i	0.0387229	+	0.119177i
$491$	−22.1030	−	16.0588i	−0.997494	−	0.724722i	−0.0359444	−	0.999354i	$-0.511444\pi$
$491$	−22.1030	−	16.0588i	−0.997494	−	0.724722i	−0.961549	+	0.274632i	$0.911444\pi$
$492$		0			0
$493$	12.9852	−	39.9644i	0.584825	−	1.79991i
$494$	1.94507			0.0875129
$495$		0			0
$496$	−29.2591			−1.31377
$497$	0.314901	−	0.969164i	0.0141252	−	0.0434730i
$498$		0			0
$499$	18.9783	+	13.7885i	0.849586	+	0.617260i	0.925032	−	0.379890i	$-0.124038\pi$
$499$	18.9783	+	13.7885i	0.849586	+	0.617260i	−0.0754460	+	0.997150i	$0.524038\pi$
$500$	−7.90747	−	24.3367i	−0.353633	−	1.08837i
$501$		0			0
$502$	41.5484	+	30.1867i	1.85440	+	1.34730i
$503$	9.28711	−	6.74748i	0.414092	−	0.300855i	−0.361164	−	0.932502i	$-0.617621\pi$
$503$	9.28711	−	6.74748i	0.414092	−	0.300855i	0.775256	+	0.631647i	$0.217621\pi$
$504$		0			0
$505$	2.02749			0.0902219
$506$	−7.70928	+	1.05583i	−0.342719	+	0.0469372i
$507$		0			0
$508$	2.74778	−	8.45680i	0.121913	−	0.375210i
$509$	−1.13793	+	0.826754i	−0.0504378	+	0.0366452i	−0.612719	−	0.790301i	$-0.709924\pi$
$509$	−1.13793	+	0.826754i	−0.0504378	+	0.0366452i	0.562281	+	0.826946i	$0.309924\pi$
$510$		0			0
$511$	−2.36344	−	7.27391i	−0.104552	−	0.321779i
$512$	9.43497	+	29.0378i	0.416971	+	1.28330i
$513$		0			0
$514$	−6.53403	+	4.74725i	−0.288204	+	0.209392i
$515$	6.36724	−	19.5963i	0.280574	−	0.863518i
$516$		0			0
$517$	−8.16586	−	4.37879i	−0.359134	−	0.192579i
$518$	−17.5464			−0.770946
$519$		0			0
$520$	−4.32354	+	3.14124i	−0.189600	+	0.137752i
$521$	14.9953	+	10.8947i	0.656955	+	0.477305i	0.865633	−	0.500679i	$-0.166916\pi$
$521$	14.9953	+	10.8947i	0.656955	+	0.477305i	−0.208679	+	0.977984i	$0.566916\pi$
$522$		0			0
$523$	−11.2689	−	34.6822i	−0.492756	−	1.51655i	−0.820425	−	0.571754i	$-0.806263\pi$
$523$	−11.2689	−	34.6822i	−0.492756	−	1.51655i	0.327670	−	0.944792i	$-0.393737\pi$
$524$	27.6988	+	20.1243i	1.21003	+	0.879136i
$525$		0			0
$526$	−3.33979	+	10.2788i	−0.145622	+	0.448177i
$527$	38.8566			1.69262
$528$		0			0
$529$	−21.7303			−0.944797
$530$	−8.99021	+	27.6690i	−0.390510	+	1.20187i
$531$		0			0
$532$	−0.307103	−	0.223124i	−0.0133146	−	0.00967364i
$533$	8.00416	+	24.6343i	0.346699	+	1.06703i
$534$		0			0
$535$	8.89224	+	6.46059i	0.384445	+	0.279316i
$536$	−5.14077	+	3.73499i	−0.222047	+	0.161327i
$537$		0			0
$538$	−35.0623			−1.51164
$539$	2.39387	−	2.29551i	0.103111	−	0.0988748i
$540$		0			0
$541$	6.84909	−	21.0793i	0.294465	−	0.906271i	−0.688935	−	0.724823i	$-0.741921\pi$
$541$	6.84909	−	21.0793i	0.294465	−	0.906271i	0.983400	−	0.181448i	$-0.0580785\pi$
$542$	23.6187	−	17.1600i	1.01451	−	0.737085i
$543$		0			0
$544$	−10.6867	−	32.8903i	−0.458189	−	1.41016i
$545$	0.125950	+	0.387636i	0.00539512	+	0.0166045i
$546$		0			0
$547$	32.8440	−	23.8625i	1.40431	−	1.02029i	0.410187	−	0.912001i	$-0.365463\pi$
$547$	32.8440	−	23.8625i	1.40431	−	1.02029i	0.994120	−	0.108287i	$-0.0345366\pi$
$548$	12.1455	−	37.3799i	0.518829	−	1.59679i
$549$		0			0
$550$	−16.0754	+	15.4149i	−0.685457	+	0.657293i
$551$	1.59878			0.0681105
$552$		0			0
$553$	0.00442751	−	0.00321678i	0.000188277	−	0.000136791i
$554$	−1.59238	−	1.15693i	−0.0676538	−	0.0491533i
$555$		0			0
$556$	−5.62487	−	17.3116i	−0.238548	−	0.734175i
$557$	−32.3429	−	23.4985i	−1.37041	−	0.995663i	−0.997705	−	0.0677138i	$-0.978430\pi$
$557$	−32.3429	−	23.4985i	−1.37041	−	0.995663i	−0.372707	−	0.927949i	$-0.621570\pi$
$558$		0			0
$559$	−14.2579	+	43.8812i	−0.603043	+	1.85598i
$560$	−4.28592			−0.181113
$561$		0			0
$562$	8.40219			0.354425
$563$	−8.90935	+	27.4202i	−0.375484	+	1.15562i	0.567667	+	0.823258i	$0.307846\pi$
$563$	−8.90935	+	27.4202i	−0.375484	+	1.15562i	−0.943151	+	0.332364i	$0.892154\pi$
$564$		0			0
$565$	−10.9399	−	7.94829i	−0.460244	−	0.334387i
$566$	3.09224	+	9.51695i	0.129977	+	0.400027i
$567$		0			0
$568$	−0.575465	−	0.418100i	−0.0241460	−	0.0175431i
$569$	14.5771	−	10.5909i	0.611103	−	0.443993i	−0.238699	−	0.971094i	$-0.576721\pi$
$569$	14.5771	−	10.5909i	0.611103	−	0.443993i	0.849803	+	0.527101i	$0.176721\pi$
$570$		0			0
$571$	18.2208			0.762515			0.381258	−	0.924469i	$-0.375491\pi$
$571$	18.2208			0.762515			0.381258	+	0.924469i	$0.375491\pi$
$572$	39.2268	+	21.0346i	1.64015	+	0.879500i
$573$		0			0
$574$	2.89993	−	8.92508i	0.121041	−	0.372526i
$575$	2.94007	−	2.13609i	0.122609	−	0.0890809i
$576$		0			0
$577$	3.25391	+	10.0145i	0.135462	+	0.416909i	0.995662	−	0.0930483i	$-0.0296611\pi$
$577$	3.25391	+	10.0145i	0.135462	+	0.416909i	−0.860200	+	0.509958i	$0.829661\pi$
$578$	0.806451	+	2.48200i	0.0335439	+	0.103238i
$579$		0			0
$580$	−24.7550	+	17.9856i	−1.02789	+	0.746809i
$581$	0.875237	−	2.69370i	0.0363110	−	0.111754i
$582$		0			0
$583$	34.4639	−	4.72001i	1.42735	−	0.195483i
$584$	−5.33865			−0.220915
$585$		0			0
$586$	1.76310	−	1.28097i	0.0728329	−	0.0529162i
$587$	1.98322	+	1.44090i	0.0818564	+	0.0594722i	0.627961	−	0.778245i	$-0.283890\pi$
$587$	1.98322	+	1.44090i	0.0818564	+	0.0594722i	−0.546104	+	0.837717i	$0.683890\pi$
$588$		0			0
$589$	0.456846	+	1.40603i	0.0188240	+	0.0579344i
$590$	30.5478	+	22.1943i	1.25763	+	0.913724i
$591$		0			0
$592$	8.37783	−	25.7843i	0.344327	−	1.05973i
$593$	27.7941			1.14137			0.570684	−	0.821170i	$-0.306678\pi$
$593$	27.7941			1.14137			0.570684	+	0.821170i	$0.306678\pi$
$594$		0			0
$595$	5.69179			0.233341
$596$	7.01417	−	21.5874i	0.287312	−	0.884254i
$597$		0			0
$598$	−10.9080	−	7.92512i	−0.446061	−	0.324082i
$599$	0.230847	+	0.710474i	0.00943216	+	0.0290292i	0.955662	−	0.294466i	$-0.0951419\pi$
$599$	0.230847	+	0.710474i	0.00943216	+	0.0290292i	−0.946230	+	0.323496i	$0.895142\pi$
$600$		0			0
$601$	12.1995	+	8.86347i	0.497629	+	0.361548i	0.808110	−	0.589031i	$-0.200490\pi$
$601$	12.1995	+	8.86347i	0.497629	+	0.361548i	−0.310482	+	0.950579i	$0.600490\pi$
$602$	13.5239	−	9.82569i	0.551193	−	0.400465i
$603$		0			0
$604$	23.5896			0.959846
$605$	−13.7351	−	5.10889i	−0.558411	−	0.207706i
$606$		0			0
$607$	−1.28739	+	3.96218i	−0.0522536	+	0.160820i	−0.973778	−	0.227501i	$-0.926945\pi$
$607$	−1.28739	+	3.96218i	−0.0522536	+	0.160820i	0.921524	+	0.388321i	$0.126945\pi$
$608$	1.06449	−	0.773397i	0.0431708	−	0.0313654i
$609$		0			0
$610$	6.91552	+	21.2838i	0.280001	+	0.861755i
$611$	−4.96139	−	15.2696i	−0.200716	−	0.617742i
$612$		0			0
$613$	−29.6936	+	21.5737i	−1.19931	+	0.871352i	−0.994217	−	0.107390i	$-0.965751\pi$
$613$	−29.6936	+	21.5737i	−1.19931	+	0.871352i	−0.205096	+	0.978742i	$0.565751\pi$
$614$	−16.8528	+	51.8677i	−0.680126	+	2.09321i
$615$		0			0
$616$	−1.00754	−	2.08434i	−0.0405949	−	0.0839805i
$617$	−22.8780			−0.921035			−0.460518	−	0.887651i	$-0.652336\pi$
$617$	−22.8780			−0.921035			−0.460518	+	0.887651i	$0.652336\pi$
$618$		0			0
$619$	2.09893	−	1.52496i	0.0843631	−	0.0612934i	−0.544804	−	0.838563i	$-0.683396\pi$
$619$	2.09893	−	1.52496i	0.0843631	−	0.0612934i	0.629167	+	0.777270i	$0.283396\pi$
$620$	−22.8908	−	16.6311i	−0.919316	−	0.667922i
$621$		0			0
$622$	−14.1755	−	43.6278i	−0.568387	−	1.74932i
$623$	−8.51522	−	6.18667i	−0.341155	−	0.247864i
$624$		0			0
$625$	0.472079	−	1.45291i	0.0188831	−	0.0581163i
$626$	63.3214			2.53083
$627$		0			0
$628$	−11.5575			−0.461194
$629$	−11.1259	+	34.2421i	−0.443620	+	1.36532i
$630$		0			0
$631$	−24.1037	−	17.5123i	−0.959552	−	0.697155i	−0.00650533	−	0.999979i	$-0.502071\pi$
$631$	−24.1037	−	17.5123i	−0.959552	−	0.697155i	−0.953047	+	0.302824i	$0.902071\pi$
$632$	−0.00118047	−	0.00363311i	−4.69566e−5	−	0.000144517i
$633$		0			0
$634$	32.1358	+	23.3480i	1.27628	+	0.927269i
$635$	−4.10395	+	2.98169i	−0.162860	+	0.118325i
$636$		0			0
$637$	5.74691			0.227701
$638$	59.8574	+	32.0973i	2.36978	+	1.27075i
$639$		0			0
$640$	−2.26660	+	6.97588i	−0.0895953	+	0.275746i
$641$	−26.6729	+	19.3790i	−1.05351	+	0.765423i	−0.972878	−	0.231320i	$-0.925695\pi$
$641$	−26.6729	+	19.3790i	−1.05351	+	0.765423i	−0.0806369	+	0.996744i	$0.525695\pi$
$642$		0			0
$643$	6.46639	+	19.9015i	0.255010	+	0.784839i	0.993828	+	0.110934i	$0.0353843\pi$
$643$	6.46639	+	19.9015i	0.255010	+	0.784839i	−0.738818	+	0.673905i	$0.764616\pi$
$644$	0.813132	+	2.50256i	0.0320419	+	0.0986148i
$645$		0			0
$646$	−1.16985	+	0.849947i	−0.0460272	+	0.0334407i
$647$	−4.00652	+	12.3308i	−0.157513	+	0.484774i	−0.998407	−	0.0564255i	$-0.982030\pi$
$647$	−4.00652	+	12.3308i	−0.157513	+	0.484774i	0.840894	+	0.541200i	$0.182030\pi$
$648$		0			0
$649$	7.99616	−	44.4338i	0.313877	−	1.74418i
$650$	−38.5918			−1.51370
$651$		0			0
$652$	−12.7203	+	9.24183i	−0.498165	+	0.361938i
$653$	−3.71990	−	2.70266i	−0.145571	−	0.105763i	0.512616	−	0.858618i	$-0.328676\pi$
$653$	−3.71990	−	2.70266i	−0.145571	−	0.105763i	−0.658187	+	0.752854i	$0.728676\pi$
$654$		0			0
$655$	−6.03573	−	18.5761i	−0.235836	−	0.725827i
$656$	11.7307	+	8.52285i	0.458007	+	0.332761i
$657$		0			0
$658$	−1.79753	+	5.53223i	−0.0700750	+	0.215669i
$659$	−27.8639			−1.08542			−0.542712	−	0.839919i	$-0.682602\pi$
$659$	−27.8639			−1.08542			−0.542712	+	0.839919i	$0.682602\pi$
$660$		0			0
$661$	36.2151			1.40861			0.704303	−	0.709900i	$-0.251260\pi$
$661$	36.2151			1.40861			0.704303	+	0.709900i	$0.251260\pi$
$662$	2.32425	−	7.15332i	0.0903347	−	0.278022i
$663$		0			0
$664$	−1.59945	−	1.16207i	−0.0620708	−	0.0450971i
$665$	0.0669197	+	0.205958i	0.00259503	+	0.00798670i
$666$		0			0
$667$	−8.96600	−	6.51418i	−0.347165	−	0.252230i
$668$	−26.4257	+	19.1994i	−1.02244	+	0.742847i
$669$		0			0
$670$	25.2513			0.975544
$671$	19.3134	−	18.5199i	0.745586	−	0.714952i
$672$		0			0
$673$	−2.15470	+	6.63150i	−0.0830578	+	0.255625i	−0.983958	−	0.178401i	$-0.942908\pi$
$673$	−2.15470	+	6.63150i	−0.0830578	+	0.255625i	0.900900	+	0.434026i	$0.142908\pi$
$674$	4.51168	−	3.27793i	0.173784	−	0.126261i
$675$		0			0
$676$	14.4521	+	44.4789i	0.555849	+	1.71073i
$677$	−6.76966	−	20.8349i	−0.260179	−	0.800749i	−0.992765	−	0.120075i	$-0.961687\pi$
$677$	−6.76966	−	20.8349i	−0.260179	−	0.800749i	0.732586	−	0.680675i	$-0.238313\pi$
$678$		0			0
$679$	−9.83870	+	7.14823i	−0.377574	+	0.274324i
$680$	1.22773	−	3.77855i	0.0470812	−	0.144901i
$681$		0			0
$682$	−11.1236	+	61.8124i	−0.425943	+	2.36692i
$683$	−48.9585			−1.87334			−0.936672	−	0.350208i	$-0.886111\pi$
$683$	−48.9585			−1.87334			−0.936672	+	0.350208i	$0.886111\pi$
$684$		0			0
$685$	−18.1399	+	13.1794i	−0.693090	+	0.503559i
$686$	−1.68447	−	1.22384i	−0.0643135	−	0.0467265i
$687$		0			0
$688$	7.98154	+	24.5647i	0.304293	+	0.936519i
$689$	48.7635	+	35.4288i	1.85774	+	1.34973i
$690$		0			0
$691$	−14.7942	+	45.5320i	−0.562799	+	1.73212i	0.111603	+	0.993753i	$0.464402\pi$
$691$	−14.7942	+	45.5320i	−0.562799	+	1.73212i	−0.674402	+	0.738364i	$0.735598\pi$
$692$	−8.19384			−0.311483
$693$		0			0
$694$	−38.4248			−1.45859
$695$	−3.20891	+	9.87601i	−0.121721	+	0.374618i
$696$		0			0
$697$	−15.5786	−	11.3185i	−0.590082	−	0.428719i
$698$	13.0622	+	40.2015i	0.494413	+	1.52165i
$699$		0			0
$700$	6.09318	+	4.42696i	0.230301	+	0.167323i
$701$	−5.62920	+	4.08985i	−0.212612	+	0.154472i	−0.688995	−	0.724766i	$-0.741948\pi$
$701$	−5.62920	+	4.08985i	−0.212612	+	0.154472i	0.476383	+	0.879238i	$0.341948\pi$
$702$		0			0
$703$	−1.36986			−0.0516653
$704$	34.2380	−	4.68907i	1.29039	−	0.176726i
$705$		0			0
$706$	−8.22091	+	25.3014i	−0.309398	+	0.952229i
$707$	−1.23123	+	0.894539i	−0.0463051	+	0.0336426i
$708$		0			0
$709$	−6.29895	−	19.3862i	−0.236562	−	0.728064i	−0.996910	−	0.0785479i	$-0.974972\pi$
$709$	−6.29895	−	19.3862i	−0.236562	−	0.728064i	0.760348	−	0.649516i	$-0.225028\pi$
$710$	0.873489	+	2.68832i	0.0327815	+	0.100891i
$711$		0			0
$712$	−5.94383	+	4.31844i	−0.222754	+	0.161841i
$713$	3.16681	−	9.74643i	0.118598	−	0.365007i
$714$		0			0
$715$	−11.0510	−	22.8618i	−0.413286	−	0.854982i
$716$	5.20141			0.194386
$717$		0			0
$718$	−17.3460	+	12.6026i	−0.647348	+	0.470326i
$719$	29.8961	+	21.7208i	1.11494	+	0.810048i	0.983434	−	0.181268i	$-0.0580200\pi$
$719$	29.8961	+	21.7208i	1.11494	+	0.810048i	0.131502	+	0.991316i	$0.458020\pi$
$720$		0			0
$721$	4.77940	+	14.7095i	0.177994	+	0.547810i
$722$	31.9605	+	23.2207i	1.18945	+	0.864184i
$723$		0			0
$724$	0.804125	−	2.47484i	0.0298851	−	0.0919768i
$725$	−31.7212			−1.17809
$726$		0			0
$727$	40.8565			1.51528			0.757641	−	0.652671i	$-0.226352\pi$
$727$	40.8565			1.51528			0.757641	+	0.652671i	$0.226352\pi$
$728$	1.23962	−	3.81514i	0.0459432	−	0.141399i
$729$		0			0
$730$	17.1634	+	12.4699i	0.635246	+	0.461533i
$731$	−10.5997	−	32.6224i	−0.392042	−	1.20658i
$732$		0			0
$733$	14.5403	+	10.5641i	0.537057	+	0.390195i	0.822991	−	0.568054i	$-0.192304\pi$
$733$	14.5403	+	10.5641i	0.537057	+	0.390195i	−0.285934	+	0.958249i	$0.592304\pi$
$734$	−4.46428	+	3.24349i	−0.164780	+	0.119719i
$735$		0			0
$736$	−9.12086			−0.336199
$737$	−13.1399	−	27.1831i	−0.484014	−	1.00130i
$738$		0			0
$739$	−0.725856	+	2.23395i	−0.0267010	+	0.0821773i	−0.963519	−	0.267640i	$-0.913756\pi$
$739$	−0.725856	+	2.23395i	−0.0267010	+	0.0821773i	0.936818	+	0.349817i	$0.113756\pi$
$740$	21.2104	−	15.4103i	0.779711	−	0.566493i
$741$		0			0
$742$	−6.74827	−	20.7690i	−0.247737	−	0.762456i
$743$	−11.8268	−	36.3991i	−0.433882	−	1.33535i	−0.894228	−	0.447612i	$-0.852274\pi$
$743$	−11.8268	−	36.3991i	−0.433882	−	1.33535i	0.460346	−	0.887740i	$-0.347726\pi$
$744$		0			0
$745$	−10.4760	+	7.61127i	−0.383812	+	0.278855i
$746$	21.1702	−	65.1552i	0.775096	−	2.38550i
$747$		0			0
$748$	−32.7843	+	4.48997i	−1.19871	+	0.164170i
$749$	−8.25043			−0.301464
$750$		0			0
$751$	2.33871	−	1.69917i	0.0853406	−	0.0620036i	−0.544297	−	0.838893i	$-0.683203\pi$
$751$	2.33871	−	1.69917i	0.0853406	−	0.0620036i	0.629637	+	0.776889i	$0.283203\pi$
$752$	−7.27129	−	5.28290i	−0.265157	−	0.192648i
$753$		0			0
$754$	36.3679	+	111.929i	1.32444	+	4.07622i
$755$	−10.8873	−	7.91012i	−0.396231	−	0.287879i
$756$		0			0
$757$	7.46959	−	22.9890i	0.271487	−	0.835551i	−0.718641	−	0.695382i	$-0.755235\pi$
$757$	7.46959	−	22.9890i	0.271487	−	0.835551i	0.990128	−	0.140169i	$-0.0447647\pi$
$758$	−46.2906			−1.68135
$759$		0			0
$760$	0.151162			0.00548321
$761$	−7.63407	+	23.4953i	−0.276735	+	0.851702i	0.712020	+	0.702159i	$0.247780\pi$
$761$	−7.63407	+	23.4953i	−0.276735	+	0.851702i	−0.988755	+	0.149543i	$0.952220\pi$
$762$		0			0
$763$	−0.247513	−	0.179829i	−0.00896057	−	0.00651023i
$764$	7.38331	+	22.7235i	0.267119	+	0.822107i
$765$		0			0
$766$	−42.3289	−	30.7538i	−1.52941	−	1.11118i
$767$	63.2893	−	45.9823i	2.28524	−	1.66033i
$768$		0			0
$769$	−12.8939			−0.464967			−0.232483	−	0.972600i	$-0.574685\pi$
$769$	−12.8939			−0.464967			−0.232483	+	0.972600i	$0.574685\pi$
$770$	−1.62940	+	9.05440i	−0.0587195	+	0.326298i
$771$		0			0
$772$	−12.9414	+	39.8296i	−0.465772	+	1.43350i
$773$	26.2619	−	19.0804i	0.944577	−	0.686275i	−0.00494139	−	0.999988i	$-0.501573\pi$
$773$	26.2619	−	19.0804i	0.944577	−	0.686275i	0.949518	+	0.313713i	$0.101573\pi$
$774$		0			0
$775$	−9.06420	−	27.8967i	−0.325596	−	1.00208i
$776$	2.62321	+	8.07340i	0.0941676	+	0.289818i
$777$		0			0
$778$	38.8487	−	28.2252i	1.39279	−	1.01192i
$779$	0.226400	−	0.696786i	0.00811161	−	0.0249650i
$780$		0			0
$781$	2.43945	−	2.33922i	0.0872903	−	0.0837038i
$782$	10.0236			0.358444
$783$		0			0
$784$	2.60270	−	1.89097i	0.0929537	−	0.0675348i
$785$	5.33415	+	3.87549i	0.190384	+	0.138322i
$786$		0			0
$787$	8.71146	+	26.8111i	0.310530	+	0.955713i	0.977555	+	0.210678i	$0.0675672\pi$
$787$	8.71146	+	26.8111i	0.310530	+	0.955713i	−0.667026	+	0.745035i	$0.732433\pi$
$788$	−8.12915	−	5.90617i	−0.289589	−	0.210399i
$789$		0			0
$790$	−0.00469103	+	0.0144375i	−0.000166900	+	0.000513664i
$791$	10.1503			0.360902
$792$		0			0
$793$	46.3652			1.64648
$794$	−2.43534	+	7.49521i	−0.0864270	+	0.265995i
$795$		0			0
$796$	−41.6693	−	30.2745i	−1.47693	−	1.07305i
$797$	13.1556	+	40.4887i	0.465994	+	1.43418i	0.857728	+	0.514104i	$0.171876\pi$
$797$	13.1556	+	40.4887i	0.465994	+	1.43418i	−0.391733	+	0.920079i	$0.628124\pi$
$798$		0			0
$799$	9.65642	+	7.01580i	0.341620	+	0.248201i
$800$	−21.1203	+	15.3448i	−0.746717	+	0.542522i
$801$		0			0
$802$	−81.3270			−2.87175
$803$	4.49268	−	24.9653i	0.158543	−	0.881007i
$804$		0			0
$805$	0.463880	−	1.42768i	0.0163496	−	0.0503190i
$806$	−88.0425	+	63.9666i	−3.10116	+	2.25313i
$807$		0			0
$808$	0.328271	+	1.01032i	0.0115485	+	0.0355428i
$809$	−4.38477	−	13.4949i	−0.154160	−	0.474456i	0.843915	−	0.536478i	$-0.180245\pi$
$809$	−4.38477	−	13.4949i	−0.154160	−	0.474456i	−0.998075	+	0.0620211i	$0.980245\pi$
$810$		0			0
$811$	−2.08963	+	1.51820i	−0.0733768	+	0.0533114i	−0.623869	−	0.781529i	$-0.714440\pi$
$811$	−2.08963	+	1.51820i	−0.0733768	+	0.0533114i	0.550492	+	0.834840i	$0.314440\pi$
$812$	7.09758	−	21.8441i	0.249076	−	0.766578i
$813$		0			0
$814$	−51.2867	−	27.5015i	−1.79760	−	0.963926i
$815$	8.96982			0.314199
$816$		0			0
$817$	1.05582	−	0.767097i	0.0369384	−	0.0268373i
$818$	49.5293	+	35.9851i	1.73175	+	1.25819i
$819$		0			0
$820$	4.33302	+	13.3357i	0.151316	+	0.465702i
$821$	42.5157	+	30.8894i	1.48381	+	1.07805i	0.976305	+	0.216399i	$0.0694311\pi$
$821$	42.5157	+	30.8894i	1.48381	+	1.07805i	0.507502	+	0.861650i	$0.330569\pi$
$822$		0			0
$823$	4.52738	−	13.9338i	0.157815	−	0.485703i	−0.840621	−	0.541624i	$-0.817809\pi$
$823$	4.52738	−	13.9338i	0.157815	−	0.485703i	0.998435	+	0.0559210i	$0.0178095\pi$
$824$	10.7960			0.376095
$825$		0			0
$826$	−28.3429			−0.986177
$827$	4.69482	−	14.4492i	0.163255	−	0.502447i	−0.835649	−	0.549265i	$-0.814908\pi$
$827$	4.69482	−	14.4492i	0.163255	−	0.502447i	0.998903	+	0.0468175i	$0.0149079\pi$
$828$		0			0
$829$	33.6682	+	24.4614i	1.16935	+	0.849579i	0.990930	−	0.134376i	$-0.0429030\pi$
$829$	33.6682	+	24.4614i	1.16935	+	0.849579i	0.178415	+	0.983955i	$0.442903\pi$
$830$	2.42778	+	7.47195i	0.0842696	+	0.259355i
$831$		0			0
$832$	48.4439	+	35.1966i	1.67949	+	1.22022i
$833$	−3.45644	+	2.51125i	−0.119759	+	0.0870098i
$834$		0			0
$835$	18.6343			0.644867
$836$	−0.547922	−	1.13351i	−0.0189503	−	0.0392033i
$837$		0			0
$838$	9.36229	−	28.8142i	0.323415	−	0.995369i
$839$	−17.7041	+	12.8628i	−0.611215	+	0.444074i	−0.849842	−	0.527038i	$-0.823303\pi$
$839$	−17.7041	+	12.8628i	−0.611215	+	0.444074i	0.238627	+	0.971111i	$0.423303\pi$
$840$		0			0
$841$	20.9317	+	64.4213i	0.721784	+	2.22142i
$842$	11.4253	+	35.1636i	0.393743	+	1.21182i
$843$		0			0
$844$	28.0601	−	20.3869i	0.965870	−	0.701746i
$845$	8.24470	−	25.3746i	0.283626	−	0.872912i
$846$		0			0
$847$	10.5950	−	2.95754i	0.364047	−	0.101622i
$848$	33.7420			1.15870
$849$		0			0
$850$	23.2108	−	16.8636i	0.796124	−	0.578418i
$851$	7.68220	+	5.58145i	0.263342	+	0.191330i
$852$		0			0
$853$	−6.86185	−	21.1186i	−0.234945	−	0.723087i	−0.997129	−	0.0757259i	$-0.975873\pi$
$853$	−6.86185	−	21.1186i	−0.234945	−	0.723087i	0.762183	−	0.647361i	$-0.224127\pi$
$854$	−13.5901	−	9.87379i	−0.465044	−	0.337874i
$855$		0			0
$856$	−1.77963	+	5.47713i	−0.0608264	+	0.187204i
$857$	24.6876			0.843311			0.421656	−	0.906756i	$-0.361449\pi$
$857$	24.6876			0.843311			0.421656	+	0.906756i	$0.361449\pi$
$858$		0			0
$859$	10.3940			0.354639			0.177320	−	0.984153i	$-0.443257\pi$
$859$	10.3940			0.354639			0.177320	+	0.984153i	$0.443257\pi$
$860$	−7.71844	+	23.7549i	−0.263197	+	0.810036i
$861$		0			0
$862$	30.0479	+	21.8311i	1.02344	+	0.743570i
$863$	−14.1894	−	43.6705i	−0.483013	−	1.48656i	−0.834838	−	0.550496i	$-0.814439\pi$
$863$	−14.1894	−	43.6705i	−0.483013	−	1.48656i	0.351825	−	0.936066i	$-0.385561\pi$
$864$		0			0
$865$	3.78172	+	2.74758i	0.128582	+	0.0934206i
$866$	−20.9557	+	15.2252i	−0.712102	+	0.517373i
$867$		0			0
$868$	21.2386			0.720885
$869$	0.0179830	−	0.00246287i	0.000610033	−	8.35471e-5i
$870$		0			0
$871$	16.1665	−	49.7555i	0.547782	−	1.68590i
$872$	−0.172770	+	0.125525i	−0.00585073	+	0.00425080i
$873$		0			0
$874$	0.117850	+	0.362705i	0.00398634	+	0.0122687i
$875$	−3.38614	−	10.4215i	−0.114472	−	0.352310i
$876$		0			0
$877$	−28.2244	+	20.5062i	−0.953069	+	0.692445i	−0.951531	−	0.307553i	$-0.900490\pi$
$877$	−28.2244	+	20.5062i	−0.953069	+	0.692445i	−0.00153852	+	0.999999i	$0.500490\pi$
$878$	10.5352	−	32.4241i	0.355547	−	1.09426i
$879$		0			0
$880$	−12.5274	−	6.71756i	−0.422297	−	0.226449i
$881$	−8.85305			−0.298267			−0.149133	−	0.988817i	$-0.547648\pi$
$881$	−8.85305			−0.298267			−0.149133	+	0.988817i	$0.547648\pi$
$882$		0			0
$883$	−14.0373	+	10.1987i	−0.472393	+	0.343214i	−0.798373	−	0.602163i	$-0.794306\pi$
$883$	−14.0373	+	10.1987i	−0.472393	+	0.343214i	0.325980	+	0.945377i	$0.394306\pi$
$884$	−46.3870	−	33.7021i	−1.56016	−	1.13353i
$885$		0			0
$886$	1.43304	+	4.41045i	0.0481440	+	0.148172i
$887$	30.7835	+	22.3655i	1.03361	+	0.750962i	0.969028	−	0.246951i	$-0.0794286\pi$
$887$	30.7835	+	22.3655i	1.03361	+	0.750962i	0.0645819	+	0.997912i	$0.479429\pi$
$888$		0			0
$889$	1.17666	−	3.62138i	0.0394638	−	0.121457i
$890$	29.1959			0.978650
$891$		0			0
$892$	13.0723			0.437692
$893$	−0.140334	+	0.431904i	−0.00469610	+	0.0144531i
$894$		0			0
$895$	−2.40062	−	1.74415i	−0.0802438	−	0.0583006i
$896$	−1.70137	−	5.23627i	−0.0568387	−	0.174932i
$897$		0			0
$898$	−53.8180	−	39.1011i	−1.79593	−	1.30482i
$899$	−72.3679	+	52.5784i	−2.41361	+	1.75359i
$900$		0			0
$901$	−44.8100			−1.49284
$902$	22.4650	−	21.5420i	0.748003	−	0.717270i
$903$		0			0
$904$	2.18943	−	6.73836i	0.0728192	−	0.224114i
$905$	−1.20100	+	0.872578i	−0.0399226	+	0.0290055i
$906$		0			0
$907$	−4.35967	−	13.4177i	−0.144761	−	0.445527i	0.852220	−	0.523184i	$-0.175256\pi$
$907$	−4.35967	−	13.4177i	−0.144761	−	0.445527i	−0.996980	+	0.0776572i	$0.975256\pi$
$908$	−5.43301	−	16.7211i	−0.180301	−	0.554909i
$909$		0			0
$910$	−12.8966	+	9.36995i	−0.427519	+	0.310611i
$911$	9.01413	−	27.7426i	0.298652	−	0.919155i	−0.683319	−	0.730120i	$-0.739464\pi$
$911$	9.01413	−	27.7426i	0.298652	−	0.919155i	0.981970	−	0.189035i	$-0.0605359\pi$
$912$		0			0
$913$	6.78022	−	6.50165i	0.224393	−	0.215173i
$914$	−46.0861			−1.52439
$915$		0			0
$916$	51.4501	−	37.3807i	1.69996	−	1.23509i
$917$	11.8612	+	8.61765i	0.391691	+	0.284580i
$918$		0			0
$919$	1.18739	+	3.65441i	0.0391683	+	0.120548i	0.968729	−	0.248122i	$-0.0798134\pi$
$919$	1.18739	+	3.65441i	0.0391683	+	0.120548i	−0.929560	+	0.368670i	$0.879813\pi$
$920$	−0.847718	−	0.615903i	−0.0279484	−	0.0203057i
$921$		0			0
$922$	−9.61312	+	29.5861i	−0.316591	+	0.974368i
$923$	5.85633			0.192763
$924$		0			0
$925$	27.1792			0.893645
$926$	3.23606	−	9.95956i	0.106343	−	0.327292i
$927$		0			0
$928$	64.4084	+	46.7954i	2.11431	+	1.53614i
$929$	3.46885	+	10.6760i	0.113809	+	0.350269i	0.991697	−	0.128598i	$-0.0410476\pi$
$929$	3.46885	+	10.6760i	0.113809	+	0.350269i	−0.877887	+	0.478867i	$0.841048\pi$
$930$		0			0
$931$	−0.131508	−	0.0955461i	−0.00431000	−	0.00313140i
$932$	10.3717	−	7.53551i	0.339738	−	0.246834i
$933$		0			0
$934$	−66.9148			−2.18952
$935$	16.6366	+	8.92105i	0.544075	+	0.291750i
$936$		0			0
$937$	3.38839	−	10.4284i	0.110694	−	0.340681i	−0.880331	−	0.474360i	$-0.842679\pi$
$937$	3.38839	−	10.4284i	0.110694	−	0.340681i	0.991025	+	0.133680i	$0.0426794\pi$
$938$	−15.3343	+	11.1410i	−0.500683	+	0.363768i
$939$		0			0
$940$	−2.68583	−	8.26614i	−0.0876022	−	0.269612i
$941$	−18.7663	−	57.7567i	−0.611764	−	1.88282i	−0.441011	−	0.897502i	$-0.645380\pi$
$941$	−18.7663	−	57.7567i	−0.611764	−	1.88282i	−0.170753	−	0.985314i	$-0.554620\pi$
$942$		0			0
$943$	−4.10868	+	2.98513i	−0.133797	+	0.0972093i
$944$	13.5328	−	41.6497i	0.440455	−	1.35558i
$945$		0			0
$946$	54.9295	−	7.52287i	1.78591	−	0.244590i
$947$	−45.2278			−1.46971			−0.734854	−	0.678226i	$-0.762749\pi$
$947$	−45.2278			−1.46971			−0.734854	+	0.678226i	$0.762749\pi$
$948$		0			0
$949$	35.5593	−	25.8354i	1.15430	−	0.838651i
$950$	0.883106	+	0.641614i	0.0286517	+	0.0208167i
$951$		0			0
$952$	0.921562	+	2.83628i	0.0298680	+	0.0919242i
$953$	1.19848	+	0.870745i	0.0388225	+	0.0282062i	0.607027	−	0.794681i	$-0.292362\pi$
$953$	1.19848	+	0.870745i	0.0388225	+	0.0282062i	−0.568205	+	0.822887i	$0.692362\pi$
$954$		0			0
$955$	4.21207	−	12.9634i	0.136299	−	0.419487i
$956$	−58.0106			−1.87620
$957$		0			0
$958$	−27.3781			−0.884545
$959$	5.20094	−	16.0069i	0.167947	−	0.516888i
$960$		0			0
$961$	−41.8387	−	30.3976i	−1.34963	−	0.980567i
$962$	−31.1606	−	95.9024i	−1.00466	−	3.09202i
$963$		0			0
$964$	−32.7290	−	23.7790i	−1.05413	−	0.765870i
$965$	19.3286	−	14.0431i	0.622211	−	0.452063i
$966$		0			0
$967$	−18.8504			−0.606187			−0.303094	−	0.952961i	$-0.598019\pi$
$967$	−18.8504			−0.606187			−0.303094	+	0.952961i	$0.598019\pi$
$968$	0.321952	−	7.67151i	0.0103479	−	0.246572i
$969$		0			0
$970$	10.4243	−	32.0827i	0.334704	−	1.03011i
$971$	−47.6687	+	34.6333i	−1.52976	+	1.11144i	−0.573389	+	0.819284i	$0.694371\pi$
$971$	−47.6687	+	34.6333i	−1.52976	+	1.11144i	−0.956372	+	0.292152i	$0.905629\pi$
$972$		0			0
$973$	−2.40869	−	7.41317i	−0.0772189	−	0.237655i
$974$	0.677032	+	2.08369i	0.0216935	+	0.0667658i
$975$		0			0
$976$	20.9982	−	15.2561i	0.672137	−	0.488336i
$977$	−13.3073	+	40.9556i	−0.425738	+	1.31029i	0.476548	+	0.879148i	$0.341888\pi$
$977$	−13.3073	+	40.9556i	−0.425738	+	1.31029i	−0.902286	+	0.431138i	$0.858112\pi$
$978$		0			0
$979$	−15.1925	−	31.4294i	−0.485555	−	1.00449i
$980$	3.11107			0.0993795
$981$		0			0
$982$	−46.0212	+	33.4363i	−1.46860	+	1.06700i
$983$	−10.7194	−	7.78808i	−0.341895	−	0.248401i	0.403566	−	0.914951i	$-0.367771\pi$
$983$	−10.7194	−	7.78808i	−0.341895	−	0.248401i	−0.745461	+	0.666549i	$0.767771\pi$
$984$		0			0
$985$	1.77139	+	5.45178i	0.0564412	+	0.173708i
$986$	−70.7834	−	51.4272i	−2.25420	−	1.63777i
$987$		0			0
$988$	0.674130	−	2.07476i	0.0214469	−	0.0660069i
$989$	−9.04656			−0.287664
$990$		0			0
$991$	14.1260			0.448728			0.224364	−	0.974505i	$-0.427970\pi$
$991$	14.1260			0.448728			0.224364	+	0.974505i	$0.427970\pi$
$992$	−22.7492	+	70.0147i	−0.722286	+	2.22297i
$993$		0			0
$994$	−1.71655	−	1.24714i	−0.0544455	−	0.0395570i
$995$	9.08000	+	27.9454i	0.287855	+	0.885928i
$996$		0			0
$997$	−10.8336	−	7.87108i	−0.343104	−	0.249280i	0.402866	−	0.915259i	$-0.368014\pi$
$997$	−10.8336	−	7.87108i	−0.343104	−	0.249280i	−0.745970	+	0.665979i	$0.768014\pi$
$998$	39.5152	−	28.7095i	1.25083	−	0.908783i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.k.64.7	yes	32
3.2	odd	2	inner	693.2.m.k.64.2	✓	32
11.4	even	5		7623.2.a.dc.1.13		16
11.5	even	5	inner	693.2.m.k.379.7	yes	32
11.7	odd	10		7623.2.a.db.1.4		16
33.5	odd	10	inner	693.2.m.k.379.2	yes	32
33.26	odd	10		7623.2.a.dc.1.4		16
33.29	even	10		7623.2.a.db.1.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.m.k.64.2	✓	32	3.2	odd	2	inner
693.2.m.k.64.7	yes	32	1.1	even	1	trivial
693.2.m.k.379.2	yes	32	33.5	odd	10	inner
693.2.m.k.379.7	yes	32	11.5	even	5	inner
7623.2.a.db.1.4		16	11.7	odd	10
7623.2.a.db.1.13		16	33.29	even	10
7623.2.a.dc.1.4		16	33.26	odd	10
7623.2.a.dc.1.13		16	11.4	even	5

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.643412 - 1.98022i) q^{2} +(-1.88925 - 1.37262i) q^{4} +(0.411680 + 1.26702i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.564713 + 0.410288i) q^{8} +O(q^{10})\)	\(q+(0.643412 - 1.98022i) q^{2} +(-1.88925 - 1.37262i) q^{4} +(0.411680 + 1.26702i) q^{5} +(-0.809017 - 0.587785i) q^{7} +(-0.564713 + 0.410288i) q^{8} +2.77386 q^{10} +(-1.44342 - 2.98606i) q^{11} +(1.77589 - 5.46564i) q^{13} +(-1.68447 + 1.22384i) q^{14} +(-0.994144 - 3.05966i) q^{16} +(1.32024 + 4.06329i) q^{17} +(-0.131508 + 0.0955461i) q^{19} +(0.961374 - 2.95880i) q^{20} +(-6.84176 + 0.937014i) q^{22} +1.12680 q^{23} +(2.60922 - 1.89571i) q^{25} +(-9.68052 - 7.03331i) q^{26} +(0.721631 + 2.22095i) q^{28} +(-7.95706 - 5.78115i) q^{29} +(2.81045 - 8.64967i) q^{31} -8.09449 q^{32} +8.89567 q^{34} +(0.411680 - 1.26702i) q^{35} +(6.81773 + 4.95337i) q^{37} +(0.104588 + 0.321890i) q^{38} +(-0.752324 - 0.546596i) q^{40} +(-3.64634 + 2.64922i) q^{41} -8.02855 q^{43} +(-1.37175 + 7.62269i) q^{44} +(0.724995 - 2.23131i) q^{46} +(2.26019 - 1.64212i) q^{47} +(0.309017 + 0.951057i) q^{49} +(-2.07512 - 6.38656i) q^{50} +(-10.8574 + 7.88834i) q^{52} +(-3.24105 + 9.97492i) q^{53} +(3.18917 - 3.05814i) q^{55} +0.698024 q^{56} +(-16.5676 + 12.0371i) q^{58} +(11.0127 + 8.00123i) q^{59} +(2.49310 + 7.67299i) q^{61} +(-15.3200 - 11.1306i) q^{62} +(-3.21981 + 9.90954i) q^{64} +7.65617 q^{65} +9.10333 q^{67} +(3.08309 - 9.48879i) q^{68} +(-2.24410 - 1.63043i) q^{70} +(0.314901 + 0.969164i) q^{71} +(6.18756 + 4.49552i) q^{73} +(14.1954 - 10.3135i) q^{74} +0.379601 q^{76} +(-0.587413 + 3.26419i) q^{77} +(-0.00169116 + 0.00520485i) q^{79} +(3.46738 - 2.51920i) q^{80} +(2.89993 + 8.92508i) q^{82} +(0.875237 + 2.69370i) q^{83} +(-4.60476 + 3.34555i) q^{85} +(-5.16567 + 15.8983i) q^{86} +(2.04026 + 1.09405i) q^{88} +10.5254 q^{89} +(-4.64935 + 3.37795i) q^{91} +(-2.12881 - 1.54667i) q^{92} +(-1.79753 - 5.53223i) q^{94} +(-0.175198 - 0.127289i) q^{95} +(3.75805 - 11.5661i) q^{97} +2.08213 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{4} - 8 q^{7}+O(q^{10}) \) 32 * q - 10 * q^4 - 8 * q^7	\( 32 q - 10 q^{4} - 8 q^{7} - 12 q^{10} + 10 q^{13} - 26 q^{16} - 10 q^{19} - 6 q^{22} - 52 q^{25} - 10 q^{28} - 20 q^{31} + 24 q^{34} - 4 q^{37} + 124 q^{40} + 32 q^{43} + 30 q^{46} - 8 q^{49} + 24 q^{52} - 12 q^{55} - 104 q^{58} + 34 q^{61} - 52 q^{64} + 104 q^{67} + 18 q^{70} + 2 q^{73} - 28 q^{76} - 42 q^{79} - 172 q^{82} - 30 q^{85} - 16 q^{88} - 10 q^{91} + 150 q^{94} - 74 q^{97}+O(q^{100}) \) 32 * q - 10 * q^4 - 8 * q^7 - 12 * q^10 + 10 * q^13 - 26 * q^16 - 10 * q^19 - 6 * q^22 - 52 * q^25 - 10 * q^28 - 20 * q^31 + 24 * q^34 - 4 * q^37 + 124 * q^40 + 32 * q^43 + 30 * q^46 - 8 * q^49 + 24 * q^52 - 12 * q^55 - 104 * q^58 + 34 * q^61 - 52 * q^64 + 104 * q^67 + 18 * q^70 + 2 * q^73 - 28 * q^76 - 42 * q^79 - 172 * q^82 - 30 * q^85 - 16 * q^88 - 10 * q^91 + 150 * q^94 - 74 * q^97

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