LMFDB - Embedded newform 441.2.w.a.377.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(62,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 11]))

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

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

chi := DirichletCharacter("441.62");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.w (of order $14$, degree $6$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			377.5
Character	$\chi$	$=$	441.377
Dual form			441.2.w.a.62.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79728 - 0.410217i) q^{2} +(1.26000 + 0.606784i) q^{4} +(-2.31994 + 2.90911i) q^{5} +(-1.91410 + 1.82654i) q^{7} +(0.866954 + 0.691373i) q^{8} +O(q^{10})$	\(q+(-1.79728 - 0.410217i) q^{2} +(1.26000 + 0.606784i) q^{4} +(-2.31994 + 2.90911i) q^{5} +(-1.91410 + 1.82654i) q^{7} +(0.866954 + 0.691373i) q^{8} +(5.36294 - 4.27680i) q^{10} +(-4.35372 - 0.993708i) q^{11} +(3.23505 + 0.738379i) q^{13} +(4.18945 - 2.49760i) q^{14} +(-3.01844 - 3.78500i) q^{16} +(-0.255335 + 0.122963i) q^{17} -4.23595i q^{19} +(-4.68832 + 2.25777i) q^{20} +(7.41722 + 3.57194i) q^{22} +(3.40372 - 7.06790i) q^{23} +(-1.96820 - 8.62324i) q^{25} +(-5.51140 - 2.65415i) q^{26} +(-3.52007 + 1.13999i) q^{28} +(1.41433 + 2.93688i) q^{29} +5.34738i q^{31} +(2.91006 + 6.04280i) q^{32} +(0.509349 - 0.116256i) q^{34} +(-0.873006 - 9.80576i) q^{35} +(-9.73410 + 4.68770i) q^{37} +(-1.73766 + 7.61320i) q^{38} +(-4.02256 + 0.918122i) q^{40} +(2.99446 - 3.75494i) q^{41} +(-2.53762 - 3.18207i) q^{43} +(-4.88272 - 3.89384i) q^{44} +(-9.01681 + 11.3067i) q^{46} +(1.41800 - 6.21269i) q^{47} +(0.327535 - 6.99233i) q^{49} +16.3058i q^{50} +(3.62813 + 2.89333i) q^{52} +(3.06021 - 6.35459i) q^{53} +(12.9912 - 10.3601i) q^{55} +(-2.92225 + 0.260168i) q^{56} +(-1.33718 - 5.85857i) q^{58} +(-8.01966 - 10.0563i) q^{59} +(1.20103 + 2.49397i) q^{61} +(2.19359 - 9.61074i) q^{62} +(-0.596794 - 2.61472i) q^{64} +(-9.65313 + 7.69811i) q^{65} -4.33299 q^{67} -0.396333 q^{68} +(-2.45346 + 17.9818i) q^{70} +(-5.11483 + 10.6211i) q^{71} +(4.82984 - 1.10238i) q^{73} +(19.4179 - 4.43201i) q^{74} +(2.57031 - 5.33730i) q^{76} +(10.1485 - 6.05017i) q^{77} -4.76385 q^{79} +18.0136 q^{80} +(-6.92223 + 5.52030i) q^{82} +(-0.882792 - 3.86776i) q^{83} +(0.234648 - 1.02806i) q^{85} +(3.25547 + 6.76005i) q^{86} +(-3.08745 - 3.87154i) q^{88} +(3.23059 + 14.1541i) q^{89} +(-7.54088 + 4.49561i) q^{91} +(8.57737 - 6.84023i) q^{92} +(-5.09710 + 10.5842i) q^{94} +(12.3228 + 9.82714i) q^{95} -17.3956i q^{97} +(-3.45705 + 12.4328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 24 q^{4}+O(q^{10}) $ 120 * q + 24 * q^4	$ 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) $ 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{3}{14}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.79728	−	0.410217i	−1.27087	−	0.290068i	−0.466672	−	0.884430i	$-0.654547\pi$
$2$	−1.79728	−	0.410217i	−1.27087	−	0.290068i	−0.804197	+	0.594363i	$0.797404\pi$
$3$		0			0
$3$		0			0
$4$	1.26000	+	0.606784i	0.630000	+	0.303392i
$5$	−2.31994	+	2.90911i	−1.03751	+	1.30099i	−0.0850305	+	0.996378i	$0.527099\pi$
$5$	−2.31994	+	2.90911i	−1.03751	+	1.30099i	−0.952476	+	0.304614i	$0.901473\pi$
$6$		0			0
$7$	−1.91410	+	1.82654i	−0.723461	+	0.690366i
$7$	−1.91410	+	1.82654i	−0.723461	+	0.690366i
$8$	0.866954	+	0.691373i	0.306515	+	0.244437i
$9$		0			0
$10$	5.36294	−	4.27680i	1.69591	−	1.35244i
$11$	−4.35372	−	0.993708i	−1.31270	−	0.299614i	−0.491808	−	0.870704i	$-0.663664\pi$
$11$	−4.35372	−	0.993708i	−1.31270	−	0.299614i	−0.820888	+	0.571089i	$0.806521\pi$
$12$		0			0
$13$	3.23505	+	0.738379i	0.897242	+	0.204790i	0.646183	−	0.763182i	$-0.276364\pi$
$13$	3.23505	+	0.738379i	0.897242	+	0.204790i	0.251058	+	0.967972i	$0.419221\pi$
$14$	4.18945	−	2.49760i	1.11968	−	0.667512i
$15$		0			0
$16$	−3.01844	−	3.78500i	−0.754610	−	0.946251i
$17$	−0.255335	+	0.122963i	−0.0619277	+	0.0298228i	−0.464591	−	0.885525i	$-0.653799\pi$
$17$	−0.255335	+	0.122963i	−0.0619277	+	0.0298228i	0.402664	+	0.915348i	$0.368084\pi$
$18$		0			0
$19$		−	4.23595i		−	0.971794i	−0.874016	−	0.485897i	$-0.838493\pi$
$19$		−	4.23595i		−	0.971794i	0.874016	−	0.485897i	$-0.161507\pi$
$20$	−4.68832	+	2.25777i	−1.04834	+	0.504854i
$21$		0			0
$22$	7.41722	+	3.57194i	1.58136	+	0.761541i
$23$	3.40372	−	7.06790i	0.709725	−	1.47376i	−0.163553	−	0.986535i	$-0.552295\pi$
$23$	3.40372	−	7.06790i	0.709725	−	1.47376i	0.873277	−	0.487224i	$-0.161990\pi$
$24$		0			0
$25$	−1.96820	−	8.62324i	−0.393640	−	1.72465i
$26$	−5.51140	−	2.65415i	−1.08087	−	0.520521i
$27$		0			0
$28$	−3.52007	+	1.13999i	−0.665232	+	0.215438i
$29$	1.41433	+	2.93688i	0.262634	+	0.545364i	0.990031	−	0.140853i	$-0.0449844\pi$
$29$	1.41433	+	2.93688i	0.262634	+	0.545364i	−0.727397	+	0.686217i	$0.759270\pi$
$30$		0			0
$31$			5.34738i			0.960418i	0.877154	+	0.480209i	$0.159439\pi$
$31$			5.34738i			0.960418i	−0.877154	+	0.480209i	$0.840561\pi$
$32$	2.91006	+	6.04280i	0.514431	+	1.06823i
$33$		0			0
$34$	0.509349	−	0.116256i	0.0873526	−	0.0199377i
$35$	−0.873006	−	9.80576i	−0.147565	−	1.65748i
$36$		0			0
$37$	−9.73410	+	4.68770i	−1.60028	+	0.770653i	−0.999584	−	0.0288274i	$-0.990823\pi$
$37$	−9.73410	+	4.68770i	−1.60028	+	0.770653i	−0.600693	+	0.799480i	$0.705108\pi$
$38$	−1.73766	+	7.61320i	−0.281886	+	1.23502i
$39$		0			0
$40$	−4.02256	+	0.918122i	−0.636022	+	0.145168i
$41$	2.99446	−	3.75494i	0.467657	−	0.586423i	−0.490939	−	0.871194i	$-0.663346\pi$
$41$	2.99446	−	3.75494i	0.467657	−	0.586423i	0.958596	+	0.284771i	$0.0919176\pi$
$42$		0			0
$43$	−2.53762	−	3.18207i	−0.386983	−	0.485262i	0.549738	−	0.835337i	$-0.314727\pi$
$43$	−2.53762	−	3.18207i	−0.386983	−	0.485262i	−0.936722	+	0.350075i	$0.886156\pi$
$44$	−4.88272	−	3.89384i	−0.736098	−	0.587018i
$45$		0			0
$46$	−9.01681	+	11.3067i	−1.32946	+	1.66709i
$47$	1.41800	−	6.21269i	0.206837	−	0.906213i	−0.759819	−	0.650135i	$-0.774712\pi$
$47$	1.41800	−	6.21269i	0.206837	−	0.906213i	0.966656	−	0.256078i	$-0.0824305\pi$
$48$		0			0
$49$	0.327535	−	6.99233i	0.0467908	−	0.998905i
$50$			16.3058i			2.30598i
$51$		0			0
$52$	3.62813	+	2.89333i	0.503131	+	0.401233i
$53$	3.06021	−	6.35459i	0.420352	−	0.872870i	−0.578030	−	0.816015i	$-0.696179\pi$
$53$	3.06021	−	6.35459i	0.420352	−	0.872870i	0.998382	−	0.0568548i	$-0.0181072\pi$
$54$		0			0
$55$	12.9912	−	10.3601i	1.75173	−	1.39696i
$56$	−2.92225	+	0.260168i	−0.390502	+	0.0347664i
$57$		0			0
$58$	−1.33718	−	5.85857i	−0.175580	−	0.769268i
$59$	−8.01966	−	10.0563i	−1.04407	−	1.30922i	−0.949521	−	0.313704i	$-0.898430\pi$
$59$	−8.01966	−	10.0563i	−1.04407	−	1.30922i	−0.0945502	−	0.995520i	$-0.530141\pi$
$60$		0			0
$61$	1.20103	+	2.49397i	0.153776	+	0.319320i	0.963598	−	0.267357i	$-0.0861502\pi$
$61$	1.20103	+	2.49397i	0.153776	+	0.319320i	−0.809821	+	0.586677i	$0.800436\pi$
$62$	2.19359	−	9.61074i	0.278586	−	1.22056i
$63$		0			0
$64$	−0.596794	−	2.61472i	−0.0745992	−	0.326840i
$65$	−9.65313	+	7.69811i	−1.19732	+	0.954834i
$66$		0			0
$67$	−4.33299			−0.529359			−0.264679	−	0.964336i	$-0.585266\pi$
$67$	−4.33299			−0.529359			−0.264679	+	0.964336i	$0.585266\pi$
$68$	−0.396333			−0.0480625
$69$		0			0
$70$	−2.45346	+	17.9818i	−0.293244	+	2.14924i
$71$	−5.11483	+	10.6211i	−0.607019	+	1.26049i	0.340337	+	0.940304i	$0.389459\pi$
$71$	−5.11483	+	10.6211i	−0.607019	+	1.26049i	−0.947355	+	0.320184i	$0.896255\pi$
$72$		0			0
$73$	4.82984	−	1.10238i	0.565291	−	0.129024i	0.0696810	−	0.997569i	$-0.477802\pi$
$73$	4.82984	−	1.10238i	0.565291	−	0.129024i	0.495610	+	0.868545i	$0.334945\pi$
$74$	19.4179	−	4.43201i	2.25728	−	0.515210i
$75$		0			0
$76$	2.57031	−	5.33730i	0.294835	−	0.612230i
$77$	10.1485	−	6.05017i	1.15653	−	0.689481i
$78$		0			0
$79$	−4.76385			−0.535975			−0.267987	−	0.963422i	$-0.586359\pi$
$79$	−4.76385			−0.535975			−0.267987	+	0.963422i	$0.586359\pi$
$80$	18.0136			2.01398
$81$		0			0
$82$	−6.92223	+	5.52030i	−0.764433	+	0.609615i
$83$	−0.882792	−	3.86776i	−0.0968990	−	0.424542i	0.903089	−	0.429453i	$-0.141294\pi$
$83$	−0.882792	−	3.86776i	−0.0968990	−	0.424542i	−0.999988	+	0.00491141i	$0.998437\pi$
$84$		0			0
$85$	0.234648	−	1.02806i	0.0254512	−	0.111509i
$86$	3.25547	+	6.76005i	0.351046	+	0.728955i
$87$		0			0
$88$	−3.08745	−	3.87154i	−0.329124	−	0.412708i
$89$	3.23059	+	14.1541i	0.342442	+	1.50033i	0.793903	+	0.608044i	$0.208046\pi$
$89$	3.23059	+	14.1541i	0.342442	+	1.50033i	−0.451462	+	0.892291i	$0.649097\pi$
$90$		0			0
$91$	−7.54088	+	4.49561i	−0.790499	+	0.471267i
$92$	8.57737	−	6.84023i	0.894253	−	0.713143i
$93$		0			0
$94$	−5.09710	+	10.5842i	−0.525726	+	1.09168i
$95$	12.3228	+	9.82714i	1.26430	+	1.00824i
$96$		0			0
$97$		−	17.3956i		−	1.76625i	−0.469136	−	0.883126i	$-0.655435\pi$
$97$		−	17.3956i		−	1.76625i	0.469136	−	0.883126i	$-0.344565\pi$
$98$	−3.45705	+	12.4328i	−0.349215	+	1.25590i
$99$		0			0
$100$	2.75251	−	12.0595i	0.275251	−	1.20595i
$101$	−3.05585	+	3.83192i	−0.304069	+	0.381290i	−0.910266	−	0.414024i	$-0.864123\pi$
$101$	−3.05585	+	3.83192i	−0.304069	+	0.381290i	0.606197	+	0.795314i	$0.292694\pi$
$102$		0			0
$103$	6.59938	+	5.26283i	0.650257	+	0.518562i	0.892149	−	0.451741i	$-0.149197\pi$
$103$	6.59938	+	5.26283i	0.650257	+	0.518562i	−0.241893	+	0.970303i	$0.577768\pi$
$104$	2.29415	+	2.87677i	0.224959	+	0.282090i
$105$		0			0
$106$	−8.10682	+	10.1656i	−0.787404	+	0.987373i
$107$	7.43039	−	1.69594i	0.718323	−	0.163952i	0.152291	−	0.988336i	$-0.451335\pi$
$107$	7.43039	−	1.69594i	0.718323	−	0.163952i	0.566032	+	0.824383i	$0.308478\pi$
$108$		0			0
$109$	0.245552	−	1.07583i	0.0235196	−	0.103046i	−0.961806	−	0.273733i	$-0.911742\pi$
$109$	0.245552	−	1.07583i	0.0235196	−	0.103046i	0.985325	+	0.170687i	$0.0545986\pi$
$110$	−27.5986	+	13.2908i	−2.63143	+	1.26723i
$111$		0			0
$112$	12.6910	+	1.73158i	1.19919	+	0.163619i
$113$	0.211655	−	0.0483089i	0.0199108	−	0.00454452i	−0.212554	−	0.977149i	$-0.568178\pi$
$113$	0.211655	−	0.0483089i	0.0199108	−	0.00454452i	0.232465	+	0.972605i	$0.425321\pi$
$114$		0			0
$115$	12.6649	+	26.2988i	1.18100	+	2.45238i
$116$			4.55865i			0.423260i
$117$		0			0
$118$	10.2883	+	21.3639i	0.947114	+	1.96670i
$119$	0.264139	−	0.701740i	0.0242136	−	0.0643284i
$120$		0			0
$121$	8.05677	+	3.87993i	0.732433	+	0.352721i
$122$	−1.13552	−	4.97504i	−0.102805	−	0.450419i
$123$		0			0
$124$	−3.24470	+	6.73770i	−0.291383	+	0.605063i
$125$	12.8900	+	6.20749i	1.15292	+	0.555215i
$126$		0			0
$127$	7.27670	−	3.50428i	0.645703	−	0.310954i	−0.0822188	−	0.996614i	$-0.526201\pi$
$127$	7.27670	−	3.50428i	0.645703	−	0.310954i	0.727922	+	0.685660i	$0.240486\pi$
$128$		−	8.46981i		−	0.748632i
$129$		0			0
$130$	20.5073	−	9.87579i	1.79861	−	0.866164i
$131$	−0.684134	−	0.857877i	−0.0597730	−	0.0749530i	0.751046	−	0.660250i	$-0.229550\pi$
$131$	−0.684134	−	0.857877i	−0.0597730	−	0.0749530i	−0.810819	+	0.585297i	$0.800978\pi$
$132$		0			0
$133$	7.73712	+	8.10803i	0.670893	+	0.703055i
$134$	7.78759	+	1.77747i	0.672745	+	0.153550i
$135$		0			0
$136$	−0.306376	−	0.0699284i	−0.0262716	−	0.00599631i
$137$	−6.00235	+	4.78671i	−0.512815	+	0.408957i	−0.845414	−	0.534112i	$-0.820646\pi$
$137$	−6.00235	+	4.78671i	−0.512815	+	0.408957i	0.332598	+	0.943069i	$0.392075\pi$
$138$		0			0
$139$	−5.88646	−	4.69430i	−0.499283	−	0.398165i	0.341210	−	0.939987i	$-0.389163\pi$
$139$	−5.88646	−	4.69430i	−0.499283	−	0.398165i	−0.840493	+	0.541822i	$0.817735\pi$
$140$	4.84999	−	12.8850i	0.409899	−	1.08898i
$141$		0			0
$142$	13.5497	−	16.9908i	1.13707	−	1.42584i
$143$	−13.3508	−	6.42939i	−1.11645	−	0.537653i
$144$		0			0
$145$	−11.8248	−	2.69894i	−0.981999	−	0.224135i
$146$	−9.13280			−0.755836
$147$		0			0
$148$	−15.1094			−1.24198
$149$	−15.4365	−	3.52328i	−1.26461	−	0.288638i	−0.462930	−	0.886395i	$-0.653202\pi$
$149$	−15.4365	−	3.52328i	−1.26461	−	0.288638i	−0.801678	+	0.597756i	$0.796059\pi$
$150$		0			0
$151$	−1.65202	−	0.795573i	−0.134440	−	0.0647428i	0.365455	−	0.930829i	$-0.380914\pi$
$151$	−1.65202	−	0.795573i	−0.134440	−	0.0647428i	−0.499894	+	0.866086i	$0.666628\pi$
$152$	2.92862	−	3.67238i	0.237543	−	0.297869i
$153$		0			0
$154$	−20.7216	+	6.71077i	−1.66979	+	0.540769i
$155$	−15.5561	−	12.4056i	−1.24950	−	0.996440i
$156$		0			0
$157$	8.19749	−	6.53728i	0.654231	−	0.521731i	−0.239178	−	0.970976i	$-0.576878\pi$
$157$	8.19749	−	6.53728i	0.654231	−	0.521731i	0.893409	+	0.449244i	$0.148307\pi$
$158$	8.56197	+	1.95421i	0.681153	+	0.155469i
$159$		0			0
$160$	−24.3303	−	5.55324i	−1.92348	−	0.439022i
$161$	6.39471	+	19.7457i	0.503974	+	1.55618i
$162$		0			0
$163$	−4.58703	−	5.75196i	−0.359284	−	0.450528i	0.569035	−	0.822314i	$-0.307317\pi$
$163$	−4.58703	−	5.75196i	−0.359284	−	0.450528i	−0.928319	+	0.371786i	$0.878746\pi$
$164$	6.05146	−	2.91423i	0.472540	−	0.227563i
$165$		0			0
$166$			7.31359i			0.567645i
$167$	−8.66950	+	4.17501i	−0.670866	+	0.323072i	−0.738126	−	0.674663i	$-0.764289\pi$
$167$	−8.66950	+	4.17501i	−0.670866	+	0.323072i	0.0672592	+	0.997736i	$0.478575\pi$
$168$		0			0
$169$	−1.79225	−	0.863102i	−0.137865	−	0.0663924i
$170$	−0.843457	+	1.75146i	−0.0646902	+	0.134331i
$171$		0			0
$172$	−1.26657	−	5.54920i	−0.0965749	−	0.423122i
$173$	−11.3157	−	5.44937i	−0.860319	−	0.414308i	−0.0489218	−	0.998803i	$-0.515578\pi$
$173$	−11.3157	−	5.44937i	−0.860319	−	0.414308i	−0.811398	+	0.584495i	$0.801293\pi$
$174$		0			0
$175$	19.5180	+	12.9107i	1.47542	+	0.975960i
$176$	9.38025	+	19.4783i	0.707063	+	1.46823i
$177$		0			0
$178$		−	26.7642i		−	2.00606i
$179$	5.88085	+	12.2117i	0.439555	+	0.912746i	0.996610	+	0.0822700i	$0.0262170\pi$
$179$	5.88085	+	12.2117i	0.439555	+	0.912746i	−0.557055	+	0.830476i	$0.688069\pi$
$180$		0			0
$181$	−8.65895	+	1.97635i	−0.643615	+	0.146901i	−0.531857	−	0.846834i	$-0.678505\pi$
$181$	−8.65895	+	1.97635i	−0.643615	+	0.146901i	−0.111758	+	0.993735i	$0.535648\pi$
$182$	15.3972	−	4.98646i	1.14132	−	0.369621i
$183$		0			0
$184$	7.83742	−	3.77430i	0.577782	−	0.278245i
$185$	8.94548	−	39.1927i	0.657685	−	2.88150i
$186$		0			0
$187$	1.23384	−	0.281617i	0.0902276	−	0.0205939i
$188$	5.55644	−	6.96756i	0.405245	−	0.508161i
$189$		0			0
$190$	−18.1163	−	22.7172i	−1.31430	−	1.64808i
$191$	−18.8571	−	15.0381i	−1.36446	−	1.08812i	−0.986760	−	0.162186i	$-0.948145\pi$
$191$	−18.8571	−	15.0381i	−1.36446	−	1.08812i	−0.377695	−	0.925930i	$-0.623283\pi$
$192$		0			0
$193$	−10.4245	+	13.0720i	−0.750374	+	0.940940i	−0.999622	−	0.0275000i	$-0.991245\pi$
$193$	−10.4245	+	13.0720i	−0.750374	+	0.940940i	0.249247	+	0.968440i	$0.419817\pi$
$194$	−7.13596	+	31.2647i	−0.512332	+	2.24467i
$195$		0			0
$196$	4.65553	−	8.61159i	0.332538	−	0.615114i
$197$		−	8.60653i		−	0.613190i	−0.951840	−	0.306595i	$-0.900810\pi$
$197$		−	8.60653i		−	0.613190i	0.951840	−	0.306595i	$-0.0991897\pi$
$198$		0			0
$199$	−11.1524	−	8.89376i	−0.790574	−	0.630462i	0.142643	−	0.989774i	$-0.454440\pi$
$199$	−11.1524	−	8.89376i	−0.790574	−	0.630462i	−0.933217	+	0.359312i	$0.883011\pi$
$200$	4.25554	−	8.83671i	0.300912	−	0.624850i
$201$		0			0
$202$	7.06414	−	5.63347i	0.497031	−	0.396369i
$203$	−8.07147	−	3.03815i	−0.566506	−	0.213236i
$204$		0			0
$205$	3.97656	+	17.4224i	0.277735	+	1.21684i
$206$	−9.70204	−	12.1660i	−0.675973	−	0.847643i
$207$		0			0
$208$	−6.97004	−	14.4734i	−0.483285	−	1.00355i
$209$	−4.20930	+	18.4422i	−0.291164	+	1.27567i
$210$		0			0
$211$	1.50444	+	6.59138i	0.103570	+	0.453769i	0.999945	+	0.0104731i	$0.00333376\pi$
$211$	1.50444	+	6.59138i	0.103570	+	0.453769i	−0.896375	+	0.443296i	$0.853809\pi$
$212$	7.71173	−	6.14990i	0.529643	−	0.422377i
$213$		0			0
$214$	−14.0502			−0.960451
$215$	15.1441			1.03282
$216$		0			0
$217$	−9.76718	−	10.2354i	−0.663039	−	0.694824i
$218$	−0.882652	+	1.83285i	−0.0597807	+	0.124136i
$219$		0			0
$220$	22.6552	−	5.17090i	1.52741	−	0.348622i
$221$	−0.916813	+	0.209257i	−0.0616715	+	0.0140761i
$222$		0			0
$223$	9.21117	−	19.1272i	0.616826	−	1.28085i	−0.325306	−	0.945609i	$-0.605467\pi$
$223$	9.21117	−	19.1272i	0.616826	−	1.28085i	0.942132	−	0.335243i	$-0.108818\pi$
$224$	−16.6075	−	6.25118i	−1.10964	−	0.417675i
$225$		0			0
$226$	−0.400220			−0.0266223
$227$	1.88947			0.125409			0.0627044	−	0.998032i	$-0.480027\pi$
$227$	1.88947			0.125409			0.0627044	+	0.998032i	$0.480027\pi$
$228$		0			0
$229$	12.4770	−	9.95007i	0.824503	−	0.657519i	−0.117519	−	0.993071i	$-0.537494\pi$
$229$	12.4770	−	9.95007i	0.824503	−	0.657519i	0.942022	+	0.335552i	$0.108923\pi$
$230$	−11.9740	−	52.4617i	−0.789545	−	3.45922i
$231$		0			0
$232$	−0.804322	+	3.52396i	−0.0528063	+	0.231360i
$233$	−0.103180	−	0.214255i	−0.00675953	−	0.0140363i	0.897562	−	0.440889i	$-0.145337\pi$
$233$	−0.103180	−	0.214255i	−0.00675953	−	0.0140363i	−0.904321	+	0.426852i	$0.859622\pi$
$234$		0			0
$235$	14.7837	+	18.5382i	0.964381	+	1.20930i
$236$	−4.00275	−	17.5372i	−0.260557	−	1.14157i
$237$		0			0
$238$	−0.762599	+	1.15287i	−0.0494319	+	0.0747294i
$239$	−4.13746	+	3.29952i	−0.267630	+	0.213428i	−0.748105	−	0.663581i	$-0.769036\pi$
$239$	−4.13746	+	3.29952i	−0.267630	+	0.213428i	0.480475	+	0.877009i	$0.340464\pi$
$240$		0			0
$241$	−7.84318	+	16.2865i	−0.505223	+	1.04911i	0.479910	+	0.877318i	$0.340669\pi$
$241$	−7.84318	+	16.2865i	−0.505223	+	1.04911i	−0.985134	+	0.171790i	$0.945045\pi$
$242$	−12.8886	−	10.2784i	−0.828514	−	0.660718i
$243$		0			0
$244$			3.87117i			0.247826i
$245$	19.5816	+	17.1746i	1.25102	+	1.09724i
$246$		0			0
$247$	3.12774	−	13.7035i	0.199013	−	0.871934i
$248$	−3.69703	+	4.63593i	−0.234762	+	0.294382i
$249$		0			0
$250$	−20.6205	−	16.4443i	−1.30416	−	1.04003i
$251$	−5.22808	−	6.55581i	−0.329994	−	0.413799i	0.588962	−	0.808161i	$-0.299537\pi$
$251$	−5.22808	−	6.55581i	−0.329994	−	0.413799i	−0.918955	+	0.394362i	$0.870966\pi$
$252$		0			0
$253$	−21.8423	+	27.3893i	−1.37321	+	1.72195i
$254$	−14.5158	+	3.31313i	−0.910802	+	0.207885i
$255$		0			0
$256$	−4.66805	+	20.4521i	−0.291753	+	1.27825i
$257$	10.2661	−	4.94389i	0.640382	−	0.308392i	−0.0853689	−	0.996349i	$-0.527207\pi$
$257$	10.2661	−	4.94389i	0.640382	−	0.308392i	0.725751	+	0.687958i	$0.241493\pi$
$258$		0			0
$259$	10.0698	−	26.7524i	0.625705	−	1.66231i
$260$	−16.8340	+	3.84226i	−1.04400	+	0.238287i
$261$		0			0
$262$	0.877664	+	1.82249i	0.0542223	+	0.112594i
$263$		−	7.64758i		−	0.471570i	−0.971805	−	0.235785i	$-0.924234\pi$
$263$		−	7.64758i		−	0.471570i	0.971805	−	0.235785i	$-0.0757661\pi$
$264$		0			0
$265$	11.3867	+	23.6447i	0.699479	+	1.45248i
$266$	−10.5797	−	17.7463i	−0.648684	−	1.08810i
$267$		0			0
$268$	−5.45956	−	2.62919i	−0.333496	−	0.160603i
$269$	6.14266	+	26.9127i	0.374524	+	1.64090i	0.713900	+	0.700247i	$0.246927\pi$
$269$	6.14266	+	26.9127i	0.374524	+	1.64090i	−0.339376	+	0.940651i	$0.610216\pi$
$270$		0			0
$271$	8.32357	−	17.2841i	0.505621	−	1.04993i	−0.479416	−	0.877588i	$-0.659151\pi$
$271$	8.32357	−	17.2841i	0.505621	−	1.04993i	0.985037	−	0.172345i	$-0.0551343\pi$
$272$	1.23613	+	0.595287i	0.0749512	+	0.0360946i
$273$		0			0
$274$	12.7515	−	6.14080i	0.770346	−	0.370979i
$275$			39.4990i			2.38188i
$276$		0			0
$277$	−19.3217	+	9.30482i	−1.16093	+	0.559073i	−0.912298	−	0.409527i	$-0.865694\pi$
$277$	−19.3217	+	9.30482i	−1.16093	+	0.559073i	−0.248628	+	0.968599i	$0.579980\pi$
$278$	8.65394	+	10.8517i	0.519029	+	0.650842i
$279$		0			0
$280$	6.02258	−	9.10472i	0.359918	−	0.544111i
$281$	−9.98810	−	2.27972i	−0.595840	−	0.135997i	−0.0860431	−	0.996291i	$-0.527422\pi$
$281$	−9.98810	−	2.27972i	−0.595840	−	0.135997i	−0.509797	+	0.860295i	$0.670279\pi$
$282$		0			0
$283$	−28.0125	−	6.39366i	−1.66517	−	0.380064i	−0.716811	−	0.697268i	$-0.754399\pi$
$283$	−28.0125	−	6.39366i	−1.66517	−	0.380064i	−0.948357	+	0.317204i	$0.897256\pi$
$284$	−12.8894	+	10.2789i	−0.764843	+	0.609942i
$285$		0			0
$286$	21.3576	+	17.0321i	1.26290	+	1.00713i
$287$	1.12684	+	12.6568i	0.0665150	+	0.747108i
$288$		0			0
$289$	−10.5493	+	13.2283i	−0.620544	+	0.778138i
$290$	20.1454	+	9.70150i	1.18298	+	0.569692i
$291$		0			0
$292$	6.75451	+	1.54167i	0.395278	+	0.0902196i
$293$	−20.7358			−1.21140			−0.605699	−	0.795694i	$-0.707107\pi$
$293$	−20.7358			−1.21140			−0.605699	+	0.795694i	$0.707107\pi$
$294$		0			0
$295$	47.8601			2.78652
$296$	−11.6800	−	2.66588i	−0.678885	−	0.154951i
$297$		0			0
$298$	26.2984	+	12.6646i	1.52343	+	0.733643i
$299$	16.2300	−	20.3518i	0.938605	−	1.17697i
$300$		0			0
$301$	10.6694	+	1.45575i	0.614975	+	0.0839078i
$302$	2.64279	+	2.10756i	0.152076	+	0.121276i
$303$		0			0
$304$	−16.0331	+	12.7860i	−0.919562	+	0.733326i
$305$	−10.0415	−	2.29191i	−0.574976	−	0.131235i
$306$		0			0
$307$	−8.47487	−	1.93433i	−0.483686	−	0.110398i	−0.0262773	−	0.999655i	$-0.508365\pi$
$307$	−8.47487	−	1.93433i	−0.483686	−	0.110398i	−0.457409	+	0.889256i	$0.651222\pi$
$308$	16.4582	−	1.46528i	0.937795	−	0.0834918i
$309$		0			0
$310$	22.8697	+	28.6777i	1.29891	+	1.62878i
$311$	9.60300	−	4.62456i	0.544536	−	0.262235i	−0.141330	−	0.989963i	$-0.545138\pi$
$311$	9.60300	−	4.62456i	0.544536	−	0.262235i	0.685866	+	0.727728i	$0.259424\pi$
$312$		0			0
$313$			3.13860i			0.177404i	0.996058	+	0.0887022i	$0.0282719\pi$
$313$			3.13860i			0.177404i	−0.996058	+	0.0887022i	$0.971728\pi$
$314$	−17.4149	+	8.38657i	−0.982779	+	0.473281i
$315$		0			0
$316$	−6.00244	−	2.89062i	−0.337664	−	0.162610i
$317$	−5.61929	+	11.6686i	−0.315611	+	0.655372i	−0.997071	−	0.0764829i	$-0.975631\pi$
$317$	−5.61929	+	11.6686i	−0.315611	+	0.655372i	0.681460	+	0.731855i	$0.261345\pi$
$318$		0			0
$319$	−3.23918	−	14.1918i	−0.181359	−	0.794586i
$320$	8.99103	+	4.32985i	0.502614	+	0.242046i
$321$		0			0
$322$	−3.39308	−	38.1117i	−0.189089	−	2.12388i
$323$	0.520864	+	1.08159i	0.0289816	+	0.0601810i
$324$		0			0
$325$		−	29.3499i		−	1.62804i
$326$	5.88463	+	12.2196i	0.325919	+	0.676779i
$327$		0			0
$328$	5.19213	−	1.18507i	0.286687	−	0.0654345i
$329$	8.63349	+	14.4817i	0.475980	+	0.798403i
$330$		0			0
$331$	−13.7782	+	6.63521i	−0.757316	+	0.364704i	−0.772362	−	0.635183i	$-0.780925\pi$
$331$	−13.7782	+	6.63521i	−0.757316	+	0.364704i	0.0150462	+	0.999887i	$0.495210\pi$
$332$	1.23458	−	5.40904i	0.0677563	−	0.296860i
$333$		0			0
$334$	17.2942	−	3.94729i	0.946296	−	0.215986i
$335$	10.0522	−	12.6051i	0.549213	−	0.688691i
$336$		0			0
$337$	−16.7723	−	21.0318i	−0.913647	−	1.14568i	−0.988910	−	0.148514i	$-0.952551\pi$
$337$	−16.7723	−	21.0318i	−0.913647	−	1.14568i	0.0752630	−	0.997164i	$-0.476020\pi$
$338$	2.86711	+	2.28645i	0.155950	+	0.124366i
$339$		0			0
$340$	0.919467	−	1.15298i	0.0498651	−	0.0625289i
$341$	5.31373	−	23.2810i	0.287755	−	1.26074i
$342$		0			0
$343$	12.1448	+	13.9823i	0.655758	+	0.754971i
$344$		−	4.51315i		−	0.243333i
$345$		0			0
$346$	18.1021	+	14.4360i	0.973176	+	0.776082i
$347$	0.364992	−	0.757914i	0.0195938	−	0.0406870i	−0.890942	−	0.454117i	$-0.849955\pi$
$347$	0.364992	−	0.757914i	0.0195938	−	0.0406870i	0.910536	+	0.413430i	$0.135669\pi$
$348$		0			0
$349$	8.51882	−	6.79353i	0.456002	−	0.363650i	−0.368387	−	0.929672i	$-0.620090\pi$
$349$	8.51882	−	6.79353i	0.456002	−	0.363650i	0.824390	+	0.566023i	$0.191519\pi$
$350$	−29.7831	−	31.2108i	−1.59197	−	1.66829i
$351$		0			0
$352$	−6.66481	−	29.2004i	−0.355235	−	1.55639i
$353$	18.1551	+	22.7658i	0.966300	+	1.21170i	0.977321	+	0.211763i	$0.0679204\pi$
$353$	18.1551	+	22.7658i	0.966300	+	1.21170i	−0.0110210	+	0.999939i	$0.503508\pi$
$354$		0			0
$355$	−19.0317	−	39.5197i	−1.01010	−	2.09749i
$356$	−4.51796	+	19.7945i	−0.239451	+	1.04910i
$357$		0			0
$358$	−5.56007	−	24.3603i	−0.293859	−	1.28748i
$359$	23.4623	−	18.7105i	1.23829	−	0.987504i	0.238424	−	0.971161i	$-0.423369\pi$
$359$	23.4623	−	18.7105i	1.23829	−	0.987504i	0.999866	−	0.0163430i	$-0.00520237\pi$
$360$		0			0
$361$	1.05670			0.0556157
$362$	16.3733			0.860562
$363$		0			0
$364$	−12.2294	+	1.08878i	−0.640993	+	0.0570675i
$365$	−7.99798	+	16.6080i	−0.418634	+	0.869302i
$366$		0			0
$367$	17.5246	−	3.99989i	0.914779	−	0.208792i	0.260877	−	0.965372i	$-0.415988\pi$
$367$	17.5246	−	3.99989i	0.914779	−	0.208792i	0.653902	+	0.756580i	$0.273131\pi$
$368$	−37.0259	+	8.45093i	−1.93011	+	0.440535i
$369$		0			0
$370$	−32.1551	+	66.7707i	−1.67166	+	3.47124i
$371$	5.74935	+	17.7529i	0.298491	+	0.921684i
$372$		0			0
$373$	−5.66319			−0.293229			−0.146614	−	0.989194i	$-0.546838\pi$
$373$	−5.66319			−0.293229			−0.146614	+	0.989194i	$0.546838\pi$
$374$	−2.33309			−0.120641
$375$		0			0
$376$	5.52463	−	4.40574i	0.284911	−	0.227209i
$377$	2.40688	+	10.5453i	0.123961	+	0.543108i
$378$		0			0
$379$	−3.49034	+	15.2922i	−0.179287	+	0.785506i	0.802674	+	0.596418i	$0.203410\pi$
$379$	−3.49034	+	15.2922i	−0.179287	+	0.785506i	−0.981960	+	0.189087i	$0.939447\pi$
$380$	9.56383	+	19.8595i	0.490614	+	1.01877i
$381$		0			0
$382$	27.7227	+	34.7632i	1.41842	+	1.77864i
$383$	4.01492	+	17.5905i	0.205153	+	0.898832i	0.967741	+	0.251948i	$0.0810712\pi$
$383$	4.01492	+	17.5905i	0.205153	+	0.898832i	−0.762588	+	0.646884i	$0.776072\pi$
$384$		0			0
$385$	−5.94324	+	43.5590i	−0.302895	+	2.21997i
$386$	24.0982	−	19.2176i	1.22656	−	0.978152i
$387$		0			0
$388$	10.5553	−	21.9184i	0.535867	−	1.11274i
$389$	1.73250	+	1.38162i	0.0878413	+	0.0700511i	0.666426	−	0.745571i	$-0.267823\pi$
$389$	1.73250	+	1.38162i	0.0878413	+	0.0700511i	−0.578585	+	0.815622i	$0.696395\pi$
$390$		0			0
$391$			2.22321i			0.112432i
$392$	5.11827	−	5.83558i	0.258512	−	0.294742i
$393$		0			0
$394$	−3.53055	+	15.4683i	−0.177867	+	0.779284i
$395$	11.0518	−	13.8585i	0.556077	−	0.697299i
$396$		0			0
$397$	21.9883	+	17.5350i	1.10356	+	0.880059i	0.993496	−	0.113866i	$-0.0363234\pi$
$397$	21.9883	+	17.5350i	1.10356	+	0.880059i	0.110063	+	0.993925i	$0.464895\pi$
$398$	16.3957	+	20.5595i	0.821840	+	1.03055i
$399$		0			0
$400$	−26.6981	+	33.4784i	−1.33491	+	1.67392i
$401$	−22.0002	+	5.02141i	−1.09864	+	0.250757i	−0.733156	−	0.680060i	$-0.761954\pi$
$401$	−22.0002	+	5.02141i	−1.09864	+	0.250757i	−0.365484	+	0.930818i	$0.619096\pi$
$402$		0			0
$403$	−3.94839	+	17.2990i	−0.196683	+	0.861727i
$404$	−6.17552	+	2.97397i	−0.307244	+	0.147961i
$405$		0			0
$406$	13.2604	+	8.77147i	0.658102	+	0.435321i
$407$	47.0378	−	10.7361i	2.33158	−	0.532167i
$408$		0			0
$409$	−11.2563	−	23.3738i	−0.556586	−	1.15576i	−0.969522	−	0.245003i	$-0.921211\pi$
$409$	−11.2563	−	23.3738i	−0.556586	−	1.15576i	0.412937	−	0.910760i	$-0.364503\pi$
$410$		−	32.9442i		−	1.62700i
$411$		0			0
$412$	5.12182	+	10.6356i	0.252334	+	0.523977i
$413$	33.7187	+	4.60061i	1.65919	+	0.226381i
$414$		0			0
$415$	13.2998	+	6.40482i	0.652859	+	0.314400i
$416$	4.95231	+	21.6975i	0.242807	+	1.06381i
$417$		0			0
$418$	15.1306	−	31.4190i	0.740061	−	1.53675i
$419$	−21.3874	−	10.2996i	−1.04484	−	0.503170i	−0.168924	−	0.985629i	$-0.554029\pi$
$419$	−21.3874	−	10.2996i	−1.04484	−	0.503170i	−0.875918	+	0.482459i	$0.839744\pi$
$420$		0			0
$421$	−24.6286	+	11.8605i	−1.20032	+	0.578046i	−0.923768	−	0.382952i	$-0.874907\pi$
$421$	−24.6286	+	11.8605i	−1.20032	+	0.578046i	−0.276556	+	0.960998i	$0.589193\pi$
$422$		−	12.4637i		−	0.606723i
$423$		0			0
$424$	7.04645	−	3.39339i	0.342206	−	0.164798i
$425$	1.56288	+	1.95980i	0.0758110	+	0.0950640i
$426$		0			0
$427$	−6.85421	−	2.57997i	−0.331699	−	0.124853i
$428$	10.3914	+	2.37176i	0.502285	+	0.114643i
$429$		0			0
$430$	−27.2182	−	6.21238i	−1.31258	−	0.299587i
$431$	−5.67341	+	4.52439i	−0.273279	+	0.217932i	−0.750533	−	0.660833i	$-0.770203\pi$
$431$	−5.67341	+	4.52439i	−0.273279	+	0.217932i	0.477255	+	0.878765i	$0.341632\pi$
$432$		0			0
$433$	−20.7687	−	16.5625i	−0.998078	−	0.795941i	−0.0190816	−	0.999818i	$-0.506074\pi$
$433$	−20.7687	−	16.5625i	−0.998078	−	0.795941i	−0.978996	+	0.203877i	$0.934646\pi$
$434$	13.3556	+	22.4026i	0.641090	+	1.07536i
$435$		0			0
$436$	0.962195	−	1.20655i	0.0460808	−	0.0577835i
$437$	−29.9393	−	14.4180i	−1.43219	−	0.689706i
$438$		0			0
$439$	−3.94857	−	0.901236i	−0.188455	−	0.0430136i	0.127252	−	0.991870i	$-0.459384\pi$
$439$	−3.94857	−	0.901236i	−0.188455	−	0.0430136i	−0.315707	+	0.948857i	$0.602242\pi$
$440$	18.4254			0.878398
$441$		0			0
$442$	1.73361			0.0824594
$443$	17.9367	+	4.09394i	0.852200	+	0.194509i	0.626243	−	0.779628i	$-0.284592\pi$
$443$	17.9367	+	4.09394i	0.852200	+	0.194509i	0.225957	+	0.974137i	$0.427449\pi$
$444$		0			0
$445$	−48.6706	−	23.4385i	−2.30721	−	1.11109i
$446$	−24.4014	+	30.5984i	−1.15544	+	1.44887i
$447$		0			0
$448$	5.91821	+	3.91477i	0.279609	+	0.184955i
$449$	−19.3541	−	15.4344i	−0.913375	−	0.728393i	0.0493761	−	0.998780i	$-0.484277\pi$
$449$	−19.3541	−	15.4344i	−0.913375	−	0.728393i	−0.962752	+	0.270388i	$0.912848\pi$
$450$		0			0
$451$	−16.7684	+	13.3723i	−0.789592	+	0.629678i
$452$	0.295998	+	0.0675597i	0.0139226	+	0.00317774i
$453$		0			0
$454$	−3.39591	−	0.775095i	−0.159378	−	0.0363770i
$455$	4.41615	−	32.3667i	0.207032	−	1.51738i
$456$		0			0
$457$	25.0379	+	31.3965i	1.17122	+	1.46867i	0.853968	+	0.520325i	$0.174189\pi$
$457$	25.0379	+	31.3965i	1.17122	+	1.46867i	0.317254	+	0.948341i	$0.397239\pi$
$458$	−26.5063	+	12.7648i	−1.23856	+	0.596459i
$459$		0			0
$460$			40.8214i			1.90331i
$461$	−6.45644	+	3.10926i	−0.300706	+	0.144813i	−0.578153	−	0.815929i	$-0.696226\pi$
$461$	−6.45644	+	3.10926i	−0.300706	+	0.144813i	0.277446	+	0.960741i	$0.410512\pi$
$462$		0			0
$463$	25.8416	+	12.4447i	1.20096	+	0.578352i	0.923949	−	0.382514i	$-0.124942\pi$
$463$	25.8416	+	12.4447i	1.20096	+	0.578352i	0.277011	+	0.960867i	$0.410656\pi$
$464$	6.84703	−	14.2180i	0.317866	−	0.660055i
$465$		0			0
$466$	0.0975518	+	0.427402i	0.00451900	+	0.0197990i
$467$	−10.9626	−	5.27932i	−0.507290	−	0.244298i	0.162690	−	0.986677i	$-0.447983\pi$
$467$	−10.9626	−	5.27932i	−0.507290	−	0.244298i	−0.669980	+	0.742379i	$0.733697\pi$
$468$		0			0
$469$	8.29376	−	7.91435i	0.382970	−	0.365451i
$470$	−18.9657	−	39.3828i	−0.874825	−	1.81659i
$471$		0			0
$472$		−	14.2630i		−	0.656506i
$473$	7.88603	+	16.3755i	0.362600	+	0.752947i
$474$		0			0
$475$	−36.5276	+	8.33719i	−1.67600	+	0.382537i
$476$	0.758620	−	0.723917i	0.0347713	−	0.0331807i
$477$		0			0
$478$	8.78970	−	4.23289i	0.402031	−	0.193608i
$479$	7.10221	−	31.1168i	0.324508	−	1.42176i	−0.504927	−	0.863162i	$-0.668481\pi$
$479$	7.10221	−	31.1168i	0.324508	−	1.42176i	0.829436	−	0.558602i	$-0.188662\pi$
$480$		0			0
$481$	−34.9516	+	7.97748i	−1.59366	+	0.363742i
$482$	20.7774	−	26.0540i	0.946385	−	1.18673i
$483$		0			0
$484$	7.79724	+	9.77743i	0.354420	+	0.444429i
$485$	50.6056	+	40.3566i	2.29788	+	1.83250i
$486$		0			0
$487$	15.4159	−	19.3309i	0.698560	−	0.875967i	−0.298355	−	0.954455i	$-0.596438\pi$
$487$	15.4159	−	19.3309i	0.698560	−	0.875967i	0.996915	+	0.0784883i	$0.0250093\pi$
$488$	−0.683022	+	2.99252i	−0.0309190	+	0.135465i
$489$		0			0
$490$	−28.1483	−	38.9003i	−1.27161	−	1.75733i
$491$			13.6976i			0.618163i	0.951036	+	0.309082i	$0.100022\pi$
$491$			13.6976i			0.618163i	−0.951036	+	0.309082i	$0.899978\pi$
$492$		0			0
$493$	−0.722252	−	0.575977i	−0.0325286	−	0.0259407i
$494$	−11.2428	+	23.3460i	−0.505840	+	1.05039i
$495$		0			0
$496$	20.2399	−	16.1407i	0.908796	−	0.724741i
$497$	−9.60945	−	29.6722i	−0.431043	−	1.33098i
$498$		0			0
$499$	0.434245	+	1.90255i	0.0194395	+	0.0851699i	0.983717	−	0.179724i	$-0.0575203\pi$
$499$	0.434245	+	1.90255i	0.0194395	+	0.0851699i	−0.964278	+	0.264894i	$0.914663\pi$
$500$	12.4748	+	15.6429i	0.557889	+	0.699571i
$501$		0			0
$502$	6.70702	+	13.9273i	0.299349	+	0.621604i
$503$	−3.00977	+	13.1867i	−0.134199	+	0.587964i	0.862448	+	0.506145i	$0.168930\pi$
$503$	−3.00977	+	13.1867i	−0.134199	+	0.587964i	−0.996647	+	0.0818187i	$0.973927\pi$
$504$		0			0
$505$	−4.05808	−	17.7796i	−0.180582	−	0.791182i
$506$	50.4923	−	40.2662i	2.24465	−	1.79005i
$507$		0			0
$508$	11.2950			0.501134
$509$	29.0511			1.28767			0.643833	−	0.765166i	$-0.277343\pi$
$509$	29.0511			1.28767			0.643833	+	0.765166i	$0.277343\pi$
$510$		0			0
$511$	−7.23125	+	10.9319i	−0.319892	+	0.483601i
$512$	9.42976	−	19.5811i	0.416741	−	0.865371i
$513$		0			0
$514$	−20.4791	+	4.67423i	−0.903296	+	0.206171i
$515$	−30.6203	+	6.98888i	−1.34929	+	0.307967i
$516$		0			0
$517$	−12.3472	+	25.6392i	−0.543029	+	1.12761i
$518$	−29.0725	+	43.9508i	−1.27737	+	1.93109i
$519$		0			0
$520$	−13.6911			−0.600394
$521$	−9.50180			−0.416281			−0.208141	−	0.978099i	$-0.566741\pi$
$521$	−9.50180			−0.416281			−0.208141	+	0.978099i	$0.566741\pi$
$522$		0			0
$523$	−15.0575	+	12.0079i	−0.658417	+	0.525070i	−0.894730	−	0.446607i	$-0.852632\pi$
$523$	−15.0575	+	12.0079i	−0.658417	+	0.525070i	0.236313	+	0.971677i	$0.424061\pi$
$524$	−0.341463	−	1.49605i	−0.0149169	−	0.0653551i
$525$		0			0
$526$	−3.13717	+	13.7448i	−0.136787	+	0.599303i
$527$	−0.657528	−	1.36537i	−0.0286424	−	0.0594765i
$528$		0			0
$529$	−24.0296	−	30.1321i	−1.04476	−	1.31009i
$530$	−10.7656	−	47.1672i	−0.467628	−	2.04881i
$531$		0			0
$532$	4.82895	+	14.9109i	0.209362	+	0.646468i
$533$	12.4598	−	9.93637i	0.539694	−	0.430392i
$534$		0			0
$535$	−12.3044	+	25.5503i	−0.531964	+	1.10463i
$536$	−3.75650	−	2.99571i	−0.162256	−	0.129395i
$537$		0			0
$538$		−	50.8895i		−	2.19400i
$539$	−8.37434	+	30.1172i	−0.360708	+	1.29724i
$540$		0			0
$541$	6.95489	−	30.4714i	0.299014	−	1.31007i	−0.572584	−	0.819846i	$-0.694059\pi$
$541$	6.95489	−	30.4714i	0.299014	−	1.31007i	0.871598	−	0.490221i	$-0.163084\pi$
$542$	−22.0500	+	27.6498i	−0.947129	+	1.18766i
$543$		0			0
$544$	−1.48608	−	1.18511i	−0.0637151	−	0.0508111i
$545$	2.56005	+	3.21020i	0.109661	+	0.137510i
$546$		0			0
$547$	24.6894	−	30.9595i	1.05564	−	1.32373i	0.111654	−	0.993747i	$-0.464385\pi$
$547$	24.6894	−	30.9595i	1.05564	−	1.32373i	0.943986	−	0.329985i	$-0.107044\pi$
$548$	−10.4675	+	2.38913i	−0.447148	+	0.102059i
$549$		0			0
$550$	16.2032	−	70.9907i	0.690906	−	3.02705i
$551$	12.4405	−	5.99102i	0.529982	−	0.255226i
$552$		0			0
$553$	9.11846	−	8.70133i	0.387756	−	0.370018i
$554$	38.5434	−	8.79729i	1.63755	−	0.373761i
$555$		0			0
$556$	−4.56852	−	9.48663i	−0.193748	−	0.402323i
$557$		−	26.9169i		−	1.14051i	−0.821469	−	0.570253i	$-0.806845\pi$
$557$		−	26.9169i		−	1.14051i	0.821469	−	0.570253i	$-0.193155\pi$
$558$		0			0
$559$	−5.85975	−	12.1679i	−0.247841	−	0.514647i
$560$	−34.4797	+	32.9024i	−1.45703	+	1.39038i
$561$		0			0
$562$	17.0162	+	8.19458i	0.717786	+	0.345668i
$563$	−3.97437	−	17.4129i	−0.167500	−	0.733864i	−0.986991	−	0.160773i	$-0.948601\pi$
$563$	−3.97437	−	17.4129i	−0.167500	−	0.733864i	0.819492	−	0.573091i	$-0.194256\pi$
$564$		0			0
$565$	−0.350490	+	0.727800i	−0.0147452	+	0.0306188i
$566$	47.7234	+	22.9824i	2.00597	+	0.966022i
$567$		0			0
$568$	−11.7774	+	5.67171i	−0.494170	+	0.237980i
$569$			37.7904i			1.58426i	0.610355	+	0.792128i	$0.291027\pi$
$569$			37.7904i			1.58426i	−0.610355	+	0.792128i	$0.708973\pi$
$570$		0			0
$571$	5.68188	−	2.73625i	0.237779	−	0.114509i	−0.311200	−	0.950344i	$-0.600731\pi$
$571$	5.68188	−	2.73625i	0.237779	−	0.114509i	0.548979	+	0.835836i	$0.315017\pi$
$572$	−12.9207	−	16.2021i	−0.540242	−	0.677442i
$573$		0			0
$574$	3.16681	−	23.2101i	0.132180	−	0.968770i
$575$	−67.6473	−	15.4401i	−2.82109	−	0.643895i
$576$		0			0
$577$	13.7644	+	3.14163i	0.573018	+	0.130788i	0.499204	−	0.866484i	$-0.333626\pi$
$577$	13.7644	+	3.14163i	0.573018	+	0.130788i	0.0738141	+	0.997272i	$0.476483\pi$
$578$	24.3865	−	19.4475i	1.01434	−	0.808911i
$579$		0			0
$580$	−13.2616	−	10.5758i	−0.550658	−	0.439135i
$581$	8.75435	+	5.79082i	0.363192	+	0.240244i
$582$		0			0
$583$	−19.6379	+	24.6252i	−0.813319	+	1.01987i
$584$	4.94941	+	2.38351i	0.204808	+	0.0986304i
$585$		0			0
$586$	37.2680	+	8.50619i	1.53953	+	0.351387i
$587$	−6.70403			−0.276705			−0.138352	−	0.990383i	$-0.544181\pi$
$587$	−6.70403			−0.276705			−0.138352	+	0.990383i	$0.544181\pi$
$588$		0			0
$589$	22.6512			0.933328
$590$	−86.0179	−	19.6330i	−3.54130	−	0.808279i
$591$		0			0
$592$	47.1248	+	22.6941i	1.93682	+	0.932721i
$593$	23.2839	−	29.1971i	0.956156	−	1.19898i	−0.0237892	−	0.999717i	$-0.507573\pi$
$593$	23.2839	−	29.1971i	0.956156	−	1.19898i	0.979946	−	0.199265i	$-0.0638555\pi$
$594$		0			0
$595$	1.42865	+	2.39640i	0.0585689	+	0.0982429i
$596$	−17.3121	−	13.8060i	−0.709132	−	0.565514i
$597$		0			0
$598$	−37.5185	+	29.9200i	−1.53425	+	1.22352i
$599$	−0.480066	−	0.109572i	−0.0196150	−	0.00447699i	0.212702	−	0.977117i	$-0.431774\pi$
$599$	−0.480066	−	0.109572i	−0.0196150	−	0.00447699i	−0.232317	+	0.972640i	$0.574631\pi$
$600$		0			0
$601$	43.8941	+	10.0185i	1.79048	+	0.408665i	0.983352	−	0.181713i	$-0.0581643\pi$
$601$	43.8941	+	10.0185i	1.79048	+	0.408665i	0.807127	+	0.590378i	$0.201021\pi$
$602$	−18.5788	−	6.99317i	−0.757214	−	0.285020i
$603$		0			0
$604$	−1.59881	−	2.00484i	−0.0650546	−	0.0815759i
$605$	−29.9783	+	14.4368i	−1.21879	+	0.586939i
$606$		0			0
$607$			14.1156i			0.572933i	0.958090	+	0.286466i	$0.0924806\pi$
$607$			14.1156i			0.572933i	−0.958090	+	0.286466i	$0.907519\pi$
$608$	25.5970	−	12.3269i	1.03810	−	0.499921i
$609$		0			0
$610$	17.1073	+	8.23842i	0.692653	+	0.333564i
$611$	9.17463	−	19.0513i	0.371166	−	0.770734i
$612$		0			0
$613$	0.815822	+	3.57435i	0.0329507	+	0.144367i	0.988727	−	0.149727i	$-0.0478395\pi$
$613$	0.815822	+	3.57435i	0.0329507	+	0.144367i	−0.955777	+	0.294093i	$0.904982\pi$
$614$	14.4382	+	6.95308i	0.582679	+	0.280603i
$615$		0			0
$616$	12.9812	+	1.77117i	0.523027	+	0.0713624i
$617$	10.3189	+	21.4275i	0.415425	+	0.862638i	0.998730	+	0.0503851i	$0.0160449\pi$
$617$	10.3189	+	21.4275i	0.415425	+	0.862638i	−0.583305	+	0.812253i	$0.698241\pi$
$618$		0			0
$619$		−	14.0962i		−	0.566573i	−0.959035	−	0.283286i	$-0.908575\pi$
$619$		−	14.0962i		−	0.566573i	0.959035	−	0.283286i	$-0.0914247\pi$
$620$	−12.0732	−	25.0702i	−0.484870	−	1.00684i
$621$		0			0
$622$	−19.1564	+	4.37231i	−0.768100	+	0.175314i
$623$	−32.0367	−	21.1916i	−1.28352	−	0.849023i
$624$		0			0
$625$	−8.11685	+	3.90887i	−0.324674	+	0.156355i
$626$	1.28751	−	5.64095i	0.0514593	−	0.225458i
$627$		0			0
$628$	14.2955	−	3.26286i	0.570454	−	0.130202i
$629$	1.90904	−	2.39386i	0.0761185	−	0.0954495i
$630$		0			0
$631$	−19.9819	−	25.0565i	−0.795467	−	0.997484i	−0.999827	−	0.0185879i	$-0.994083\pi$
$631$	−19.9819	−	25.0565i	−0.795467	−	0.997484i	0.204361	−	0.978896i	$-0.434488\pi$
$632$	−4.13004	−	3.29359i	−0.164284	−	0.131012i
$633$		0			0
$634$	14.8861	−	18.6666i	0.591202	−	0.741344i
$635$	−6.68717	+	29.2984i	−0.265372	+	1.16267i
$636$		0			0
$637$	6.22259	−	22.3787i	0.246548	−	0.886677i
$638$			26.8353i			1.06242i
$639$		0			0
$640$	24.6396	+	19.6494i	0.973965	+	0.776711i
$641$	3.51463	−	7.29821i	0.138820	−	0.288262i	−0.819956	−	0.572427i	$-0.806002\pi$
$641$	3.51463	−	7.29821i	0.138820	−	0.288262i	0.958775	+	0.284165i	$0.0917163\pi$
$642$		0			0
$643$	−3.49123	+	2.78416i	−0.137681	+	0.109797i	−0.689909	−	0.723897i	$-0.742349\pi$
$643$	−3.49123	+	2.78416i	−0.137681	+	0.109797i	0.552228	+	0.833693i	$0.313778\pi$
$644$	−3.92401	+	28.7597i	−0.154628	+	1.13329i
$645$		0			0
$646$	−0.492453	−	2.15758i	−0.0193753	−	0.0848888i
$647$	7.25040	+	9.09171i	0.285043	+	0.357432i	0.903653	−	0.428266i	$-0.140875\pi$
$647$	7.25040	+	9.09171i	0.285043	+	0.357432i	−0.618610	+	0.785698i	$0.712304\pi$
$648$		0			0
$649$	24.9223	+	51.7517i	0.978286	+	2.03143i
$650$	−12.0398	+	52.7500i	−0.472241	+	2.06902i
$651$		0			0
$652$	−2.28946	−	10.0308i	−0.0896624	−	0.392836i
$653$	−7.59489	+	6.05672i	−0.297211	+	0.237018i	−0.760729	−	0.649070i	$-0.775158\pi$
$653$	−7.59489	+	6.05672i	−0.297211	+	0.237018i	0.463518	+	0.886087i	$0.346587\pi$
$654$		0			0
$655$	4.08280			0.159528
$656$	−23.2511			−0.907802
$657$		0			0
$658$	−9.57615	−	29.5693i	−0.373317	−	1.15273i
$659$	−5.18433	+	10.7654i	−0.201953	+	0.419359i	−0.977207	−	0.212291i	$-0.931908\pi$
$659$	−5.18433	+	10.7654i	−0.201953	+	0.419359i	0.775254	+	0.631650i	$0.217622\pi$
$660$		0			0
$661$	14.3058	−	3.26521i	0.556432	−	0.127002i	0.0649481	−	0.997889i	$-0.479312\pi$
$661$	14.3058	−	3.26521i	0.556432	−	0.127002i	0.491484	+	0.870887i	$0.336455\pi$
$662$	27.4851	−	6.27329i	1.06824	−	0.243818i
$663$		0			0
$664$	1.90873	−	3.96351i	0.0740730	−	0.153814i
$665$	−41.5367	+	3.69801i	−1.61073	+	0.143403i
$666$		0			0
$667$	25.5715			0.990133
$668$	−13.4569			−0.520663
$669$		0			0
$670$	−23.2375	+	18.5313i	−0.897745	+	0.715928i
$671$	−2.75068	−	12.0515i	−0.106189	−	0.465243i
$672$		0			0
$673$	3.14704	−	13.7881i	0.121310	−	0.531492i	−0.877356	−	0.479841i	$-0.840694\pi$
$673$	3.14704	−	13.7881i	0.121310	−	0.531492i	0.998665	−	0.0516514i	$-0.0164485\pi$
$674$	21.5170	+	44.6804i	0.828802	+	1.72103i
$675$		0			0
$676$	−1.73452	−	2.17502i	−0.0667122	−	0.0836544i
$677$	−6.16536	−	27.0122i	−0.236954	−	1.03816i	−0.943728	−	0.330724i	$-0.892707\pi$
$677$	−6.16536	−	27.0122i	−0.236954	−	1.03816i	0.706774	−	0.707440i	$-0.250150\pi$
$678$		0			0
$679$	31.7736	+	33.2968i	1.21936	+	1.27781i
$680$	0.914203	−	0.729052i	0.0350581	−	0.0279579i
$681$		0			0
$682$	−19.1005	+	39.6627i	−0.731397	+	1.51876i
$683$	12.8119	+	10.2172i	0.490235	+	0.390949i	0.837173	−	0.546939i	$-0.184207\pi$
$683$	12.8119	+	10.2172i	0.490235	+	0.390949i	−0.346938	+	0.937888i	$0.612778\pi$
$684$		0			0
$685$		−	28.5663i		−	1.09146i
$686$	−16.0919	−	30.1121i	−0.614390	−	1.14968i
$687$		0			0
$688$	−4.38451	+	19.2098i	−0.167158	+	0.732367i
$689$	14.5920	−	18.2978i	0.555912	−	0.697092i
$690$		0			0
$691$	23.6998	+	18.8999i	0.901581	+	0.718987i	0.960206	−	0.279293i	$-0.0901001\pi$
$691$	23.6998	+	18.8999i	0.901581	+	0.718987i	−0.0586248	+	0.998280i	$0.518672\pi$
$692$	−10.9512	−	13.7324i	−0.416303	−	0.522028i
$693$		0			0
$694$	−0.966903	+	1.21246i	−0.0367031	+	0.0460243i
$695$	27.3124	−	6.23388i	1.03602	−	0.236465i
$696$		0			0
$697$	−0.302873	+	1.32697i	−0.0114721	+	0.0502627i
$698$	−18.0975	+	8.71531i	−0.685002	+	0.329879i
$699$		0			0
$700$	16.7586	+	28.1107i	0.633416	+	1.06248i
$701$	−31.9755	+	7.29819i	−1.20770	+	0.275649i	−0.778548	−	0.627585i	$-0.784043\pi$
$701$	−31.9755	+	7.29819i	−1.20770	+	0.275649i	−0.429148	+	0.903234i	$0.641186\pi$
$702$		0			0
$703$	19.8569	+	41.2332i	0.748916	+	1.55514i
$704$			11.9768i			0.451393i
$705$		0			0
$706$	−23.2909	−	48.3641i	−0.876565	−	1.82021i
$707$	−1.14994	−	12.9163i	−0.0432478	−	0.485767i
$708$		0			0
$709$	−38.3482	−	18.4675i	−1.44020	−	0.693563i	−0.459336	−	0.888263i	$-0.651912\pi$
$709$	−38.3482	−	18.4675i	−1.44020	−	0.693563i	−0.980863	+	0.194700i	$0.937627\pi$
$710$	17.9936	+	78.8352i	0.675289	+	2.95863i
$711$		0			0
$712$	−6.98501	+	14.5045i	−0.261774	+	0.543580i
$713$	37.7947	+	18.2010i	1.41542	+	0.681632i
$714$		0			0
$715$	49.6767	−	23.9230i	1.85780	−	0.894671i
$716$			18.9551i			0.708387i
$717$		0			0
$718$	−49.8436	+	24.0034i	−1.86015	+	0.895800i
$719$	16.0273	+	20.0976i	0.597717	+	0.749513i	0.985020	−	0.172439i	$-0.0551648\pi$
$719$	16.0273	+	20.0976i	0.597717	+	0.749513i	−0.387303	+	0.921952i	$0.626593\pi$
$720$		0			0
$721$	−22.2446	+	1.98044i	−0.828433	+	0.0737553i
$722$	−1.89918	−	0.433476i	−0.0706802	−	0.0161323i
$723$		0			0
$724$	−12.1095	−	2.76391i	−0.450046	−	0.102720i
$725$	22.5417	−	17.9764i	0.837178	−	0.667627i
$726$		0			0
$727$	1.21825	+	0.971521i	0.0451824	+	0.0360317i	0.645821	−	0.763489i	$-0.276515\pi$
$727$	1.21825	+	0.971521i	0.0451824	+	0.0360317i	−0.600638	+	0.799521i	$0.705087\pi$
$728$	−9.64574	−	1.31607i	−0.357495	−	0.0487769i
$729$		0			0
$730$	21.1875	−	26.5683i	0.784185	−	0.983336i
$731$	1.03922	+	0.500461i	0.0384369	+	0.0185102i
$732$		0			0
$733$	−14.6389	−	3.34123i	−0.540700	−	0.123411i	−0.0565557	−	0.998399i	$-0.518012\pi$
$733$	−14.6389	−	3.34123i	−0.540700	−	0.123411i	−0.484144	+	0.874988i	$0.660869\pi$
$734$	−33.1375			−1.22313
$735$		0			0
$736$	52.6149			1.93941
$737$	18.8646	+	4.30572i	0.694887	+	0.158603i
$738$		0			0
$739$	−40.3302	−	19.4220i	−1.48357	−	0.714450i	−0.495523	−	0.868595i	$-0.665024\pi$
$739$	−40.3302	−	19.4220i	−1.48357	−	0.714450i	−0.988048	+	0.154144i	$0.950738\pi$
$740$	35.0528	−	43.9548i	1.28857	−	1.61581i
$741$		0			0
$742$	−3.05064	−	34.2654i	−0.111993	−	1.25792i
$743$	−36.5137	−	29.1187i	−1.33956	−	1.06826i	−0.991406	−	0.130822i	$-0.958238\pi$
$743$	−36.5137	−	29.1187i	−1.33956	−	1.06826i	−0.348151	−	0.937439i	$-0.613190\pi$
$744$		0			0
$745$	46.0613	−	36.7327i	1.68756	−	1.34578i
$746$	10.1783	+	2.32314i	0.372656	+	0.0850562i
$747$		0			0
$748$	1.72552	+	0.393840i	0.0630914	+	0.0144002i
$749$	−11.1248	+	16.8181i	−0.406491	+	0.614518i
$750$		0			0
$751$	−2.75494	−	3.45459i	−0.100529	−	0.126060i	0.729022	−	0.684490i	$-0.239975\pi$
$751$	−2.75494	−	3.45459i	−0.100529	−	0.126060i	−0.829551	+	0.558430i	$0.811404\pi$
$752$	−27.7952	+	13.3855i	−1.01359	+	0.488118i
$753$		0			0
$754$		−	19.9401i		−	0.726176i
$755$	6.14699	−	2.96024i	0.223712	−	0.107734i
$756$		0			0
$757$	−3.90413	−	1.88013i	−0.141898	−	0.0683344i	0.361587	−	0.932338i	$-0.382235\pi$
$757$	−3.90413	−	1.88013i	−0.141898	−	0.0683344i	−0.503485	+	0.864004i	$0.667949\pi$
$758$	12.5462	−	26.0525i	0.455699	−	0.946270i
$759$		0			0
$760$	3.88912	+	17.0394i	0.141073	+	0.618083i
$761$	−33.5202	−	16.1425i	−1.21510	−	0.585164i	−0.287160	−	0.957883i	$-0.592711\pi$
$761$	−33.5202	−	16.1425i	−1.21510	−	0.585164i	−0.927944	+	0.372719i	$0.878426\pi$
$762$		0			0
$763$	1.49504	+	2.50776i	0.0541240	+	0.0907870i
$764$	−14.6351	−	30.3902i	−0.529481	−	1.09948i
$765$		0			0
$766$		−	33.2620i		−	1.20181i
$767$	−18.5186	−	38.4543i	−0.668669	−	1.38850i
$768$		0			0
$769$	51.8772	−	11.8406i	1.87074	−	0.426984i	0.872626	−	0.488389i	$-0.162415\pi$
$769$	51.8772	−	11.8406i	1.87074	−	0.426984i	0.998113	+	0.0614052i	$0.0195582\pi$
$770$	28.5503	−	75.8498i	1.02888	−	2.73344i
$771$		0			0
$772$	−21.0668	+	10.1452i	−0.758209	+	0.365134i
$773$	−3.86627	+	16.9392i	−0.139060	+	0.609261i	0.856583	+	0.516010i	$0.172583\pi$
$773$	−3.86627	+	16.9392i	−0.139060	+	0.609261i	−0.995643	+	0.0932516i	$0.970274\pi$
$774$		0			0
$775$	46.1117	−	10.5247i	1.65638	−	0.378058i
$776$	12.0268	−	15.0812i	0.431738	−	0.541382i
$777$		0			0
$778$	−2.54702	−	3.19387i	−0.0913152	−	0.114506i
$779$	−15.9057	−	12.6844i	−0.569883	−	0.454466i
$780$		0			0
$781$	32.8228	−	41.1585i	1.17449	−	1.47277i
$782$	0.911999	−	3.99573i	0.0326130	−	0.142887i
$783$		0			0
$784$	−27.4547	+	19.8662i	−0.980523	+	0.709508i
$785$			39.0134i			1.39245i
$786$		0			0
$787$	−15.0284	−	11.9847i	−0.535704	−	0.427210i	0.317906	−	0.948122i	$-0.397020\pi$
$787$	−15.0284	−	11.9847i	−0.535704	−	0.427210i	−0.853610	+	0.520913i	$0.825592\pi$
$788$	5.22230	−	10.8442i	0.186037	−	0.386310i
$789$		0			0
$790$	−25.5482	+	20.3740i	−0.908965	+	0.724875i
$791$	−0.316890	+	0.479063i	−0.0112673	+	0.0170335i
$792$		0			0
$793$	2.04390	+	8.95493i	0.0725811	+	0.317999i
$794$	−32.3259	−	40.5354i	−1.14720	−	1.43855i
$795$		0			0
$796$	−8.65546	−	17.9732i	−0.306785	−	0.637045i
$797$	−10.7121	+	46.9326i	−0.379441	+	1.66244i	0.319749	+	0.947502i	$0.396402\pi$
$797$	−10.7121	+	46.9326i	−0.379441	+	1.66244i	−0.699189	+	0.714937i	$0.746456\pi$
$798$		0			0
$799$	0.401862	+	1.76067i	0.0142169	+	0.0622882i
$800$	46.3810	−	36.9876i	1.63981	−	1.30771i
$801$		0			0
$802$	41.6005			1.46896
$803$	−22.1232			−0.780712
$804$		0			0
$805$	−72.2775	−	27.2057i	−2.54745	−	0.958876i
$806$	14.1927	−	29.4715i	0.499918	−	1.03809i
$807$		0			0
$808$	−5.29857	+	1.20936i	−0.186403	+	0.0425453i
$809$	2.44570	−	0.558214i	0.0859861	−	0.0196258i	−0.179311	−	0.983792i	$-0.557387\pi$
$809$	2.44570	−	0.558214i	0.0859861	−	0.0196258i	0.265298	+	0.964167i	$0.414530\pi$
$810$		0			0
$811$	−21.8734	+	45.4205i	−0.768078	+	1.59493i	0.0352386	+	0.999379i	$0.488781\pi$
$811$	−21.8734	+	45.4205i	−0.768078	+	1.59493i	−0.803317	+	0.595552i	$0.796933\pi$
$812$	−8.32654	−	8.72571i	−0.292204	−	0.306212i
$813$		0			0
$814$	−88.9442			−3.11749
$815$	27.3747			0.958893
$816$		0			0
$817$	−13.4791	+	10.7492i	−0.471575	+	0.376068i
$818$	10.6423	+	46.6269i	0.372098	+	1.63027i
$819$		0			0
$820$	−5.56119	+	24.3652i	−0.194205	+	0.850869i
$821$	−8.95903	−	18.6036i	−0.312672	−	0.649271i	0.684114	−	0.729375i	$-0.260189\pi$
$821$	−8.95903	−	18.6036i	−0.312672	−	0.649271i	−0.996787	+	0.0801040i	$0.974475\pi$
$822$		0			0
$823$	−24.9293	−	31.2603i	−0.868979	−	1.08967i	−0.995219	−	0.0976660i	$-0.968862\pi$
$823$	−24.9293	−	31.2603i	−0.868979	−	1.08967i	0.126240	−	0.992000i	$-0.459709\pi$
$824$	2.08278	+	9.12527i	0.0725572	+	0.317894i
$825$		0			0
$826$	−58.7146	−	22.1006i	−2.04294	−	0.768977i
$827$	29.1176	−	23.2205i	1.01252	−	0.807456i	0.0311350	−	0.999515i	$-0.490088\pi$
$827$	29.1176	−	23.2205i	1.01252	−	0.807456i	0.981383	+	0.192059i	$0.0615164\pi$
$828$		0			0
$829$	−2.25627	+	4.68518i	−0.0783633	+	0.162723i	−0.936469	−	0.350749i	$-0.885927\pi$
$829$	−2.25627	+	4.68518i	−0.0783633	+	0.162723i	0.858106	+	0.513473i	$0.171641\pi$
$830$	−21.2760	−	16.9671i	−0.738501	−	0.588935i
$831$		0			0
$832$		−	8.89942i		−	0.308532i
$833$	0.776165	+	1.82566i	0.0268925	+	0.0632553i
$834$		0			0
$835$	7.96713	−	34.9063i	0.275714	−	1.20798i
$836$	−16.4941	+	20.6830i	−0.570461	+	0.715336i
$837$		0			0
$838$	34.2140	+	27.2848i	1.18190	+	0.942538i
$839$	14.1231	+	17.7098i	0.487584	+	0.611411i	0.963378	−	0.268146i	$-0.0864108\pi$
$839$	14.1231	+	17.7098i	0.487584	+	0.611411i	−0.475794	+	0.879557i	$0.657839\pi$
$840$		0			0
$841$	11.4563	−	14.3657i	0.395044	−	0.495370i
$842$	49.1299	−	11.2136i	1.69313	−	0.386445i
$843$		0			0
$844$	−2.10395	+	9.21800i	−0.0724209	+	0.317297i
$845$	6.66876	−	3.21150i	0.229412	−	0.110479i
$846$		0			0
$847$	−22.5083	+	7.28940i	−0.773393	+	0.250467i
$848$	−33.2892	+	7.59804i	−1.14316	+	0.260918i
$849$		0			0
$850$	−2.00500	−	4.16342i	−0.0687709	−	0.142804i
$851$			84.7553i			2.90537i
$852$		0			0
$853$	13.8547	+	28.7697i	0.474377	+	0.985055i	0.991617	+	0.129214i	$0.0412454\pi$
$853$	13.8547	+	28.7697i	0.474377	+	0.985055i	−0.517239	+	0.855841i	$0.673040\pi$
$854$	11.2606	+	7.44864i	0.385329	+	0.254887i
$855$		0			0
$856$	7.61433	+	3.66687i	0.260253	+	0.125331i
$857$	−1.10947	−	4.86089i	−0.0378987	−	0.166045i	0.952437	−	0.304735i	$-0.0985679\pi$
$857$	−1.10947	−	4.86089i	−0.0378987	−	0.166045i	−0.990336	+	0.138690i	$0.955711\pi$
$858$		0			0
$859$	−19.4480	+	40.3843i	−0.663559	+	1.37789i	0.248821	+	0.968549i	$0.419957\pi$
$859$	−19.4480	+	40.3843i	−0.663559	+	1.37789i	−0.912380	+	0.409344i	$0.865757\pi$
$860$	19.0816	+	9.18920i	0.650676	+	0.313349i
$861$		0			0
$862$	12.0527	−	5.80427i	0.410516	−	0.197694i
$863$		−	32.7848i		−	1.11601i	−0.829839	−	0.558004i	$-0.811568\pi$
$863$		−	32.7848i		−	1.11601i	0.829839	−	0.558004i	$-0.188432\pi$
$864$		0			0
$865$	42.1046	−	20.2765i	1.43160	−	0.689421i
$866$	30.5329	+	38.2870i	1.03755	+	1.30105i
$867$		0			0
$868$	−6.09596	−	18.8232i	−0.206911	−	0.638900i
$869$	20.7405	+	4.73387i	0.703572	+	0.160586i
$870$		0			0
$871$	−14.0174	−	3.19939i	−0.474962	−	0.108407i
$872$	0.956685	−	0.762931i	0.0323975	−	0.0258361i
$873$		0			0
$874$	47.8948	+	38.1948i	1.62006	+	1.29196i
$875$	−36.0109	+	11.6623i	−1.21739	+	0.394257i
$876$		0			0
$877$	−0.977982	+	1.22635i	−0.0330241	+	0.0414109i	−0.798069	−	0.602566i	$-0.794145\pi$
$877$	−0.977982	+	1.22635i	−0.0330241	+	0.0414109i	0.765045	+	0.643977i	$0.222717\pi$
$878$	6.72699	+	3.23955i	0.227025	+	0.109329i
$879$		0			0
$880$	−78.4260	−	17.9002i	−2.64374	−	0.603417i
$881$	4.62799			0.155921			0.0779605	−	0.996956i	$-0.475159\pi$
$881$	4.62799			0.155921			0.0779605	+	0.996956i	$0.475159\pi$
$882$		0			0
$883$	−10.0446			−0.338027			−0.169013	−	0.985614i	$-0.554058\pi$
$883$	−10.0446			−0.338027			−0.169013	+	0.985614i	$0.554058\pi$
$884$	−1.28216	−	0.292644i	−0.0431236	−	0.00984269i
$885$		0			0
$886$	−30.5579	−	14.7159i	−1.02661	−	0.494391i
$887$	−1.56645	+	1.96427i	−0.0525963	+	0.0659536i	−0.807434	−	0.589958i	$-0.799144\pi$
$887$	−1.56645	+	1.96427i	−0.0525963	+	0.0659536i	0.754838	+	0.655912i	$0.227716\pi$
$888$		0			0
$889$	−7.52763	+	19.9987i	−0.252469	+	0.670734i
$890$	77.8599	+	62.0912i	2.60987	+	2.08130i
$891$		0			0
$892$	23.2122	−	18.5111i	0.777200	−	0.619797i
$893$	−26.3166	−	6.00660i	−0.880653	−	0.201003i
$894$		0			0
$895$	−49.1683	−	11.2224i	−1.64352	−	0.375122i
$896$	15.4704	+	16.2120i	0.516830	+	0.541606i
$897$		0			0
$898$	28.4533	+	35.6793i	0.949497	+	1.19063i
$899$	−15.7046	+	7.56293i	−0.523777	+	0.252238i
$900$		0			0
$901$			1.99884i			0.0665909i
$902$	35.6230	−	17.1551i	1.18612	−	0.571204i
$903$		0			0
$904$	0.216895	+	0.104451i	0.00721381	+	0.00347399i
$905$	14.3388	−	29.7748i	0.476638	−	0.989749i
$906$		0			0
$907$	10.9103	+	47.8012i	0.362271	+	1.58721i	0.747415	+	0.664357i	$0.231295\pi$
$907$	10.9103	+	47.8012i	0.362271	+	1.58721i	−0.385144	+	0.922856i	$0.625848\pi$
$908$	2.38074	+	1.14650i	0.0790075	+	0.0380480i
$909$		0			0
$910$	−21.2145	+	56.3605i	−0.703252	+	1.86833i
$911$	−0.797873	−	1.65680i	−0.0264347	−	0.0548923i	0.887333	−	0.461129i	$-0.152555\pi$
$911$	−0.797873	−	1.65680i	−0.0264347	−	0.0548923i	−0.913768	+	0.406236i	$0.866841\pi$
$912$		0			0
$913$			17.7164i			0.586327i
$914$	−32.1207	−	66.6993i	−1.06246	−	2.20622i
$915$		0			0
$916$	21.7585	−	4.96624i	0.718922	−	0.164089i
$917$	2.87644	+	0.392464i	0.0949884	+	0.0129603i
$918$		0			0
$919$	−44.6225	+	21.4891i	−1.47196	+	0.708859i	−0.986250	−	0.165261i	$-0.947153\pi$
$919$	−44.6225	+	21.4891i	−1.47196	+	0.708859i	−0.485710	+	0.874120i	$0.661439\pi$
$920$	−7.20246	+	31.5560i	−0.237458	+	1.04037i
$921$		0			0
$922$	12.8795	−	2.93966i	0.424164	−	0.0968126i
$923$	−24.3891	+	30.5830i	−0.802777	+	1.00665i
$924$		0			0
$925$	59.5818	+	74.7132i	1.95904	+	2.45655i
$926$	−41.3396	−	32.9672i	−1.35850	−	1.08337i
$927$		0			0
$928$	−13.6312	+	17.0930i	−0.447466	+	0.561105i
$929$	1.90333	−	8.33902i	0.0624461	−	0.273594i	−0.934060	−	0.357117i	$-0.883760\pi$
$929$	1.90333	−	8.33902i	0.0624461	−	0.273594i	0.996506	+	0.0835223i	$0.0266170\pi$
$930$		0			0
$931$	−29.6192	−	1.38742i	−0.970730	−	0.0454710i
$932$		−	0.332569i		−	0.0108937i
$933$		0			0
$934$	17.5372	+	13.9855i	0.573836	+	0.457619i
$935$	−2.04318	+	4.24272i	−0.0668193	+	0.138752i
$936$		0			0
$937$	−6.80580	+	5.42745i	−0.222336	+	0.177307i	−0.728323	−	0.685234i	$-0.759700\pi$
$937$	−6.80580	+	5.42745i	−0.222336	+	0.177307i	0.505987	+	0.862541i	$0.331128\pi$
$938$	−18.1528	+	10.8221i	−0.592710	+	0.353353i
$939$		0			0
$940$	7.37879	+	32.3286i	0.240669	+	1.05444i
$941$	−4.51738	−	5.66462i	−0.147263	−	0.184661i	0.702729	−	0.711457i	$-0.251965\pi$
$941$	−4.51738	−	5.66462i	−0.147263	−	0.184661i	−0.849992	+	0.526796i	$0.823393\pi$
$942$		0			0
$943$	−16.3472	−	33.9453i	−0.532338	−	1.10541i
$944$	−13.8564	+	60.7089i	−0.450988	+	1.97591i
$945$		0			0
$946$	−7.45589	−	32.6664i	−0.242412	−	1.06208i
$947$	10.3476	−	8.25190i	0.336251	−	0.268151i	−0.440778	−	0.897616i	$-0.645297\pi$
$947$	10.3476	−	8.25190i	0.336251	−	0.268151i	0.777029	+	0.629465i	$0.216726\pi$
$948$		0			0
$949$	16.4388			0.533625
$950$	69.0705			2.24094
$951$		0			0
$952$	0.714161	−	0.425758i	0.0231461	−	0.0137989i
$953$	20.6391	−	42.8576i	0.668568	−	1.38829i	−0.240089	−	0.970751i	$-0.577177\pi$
$953$	20.6391	−	42.8576i	0.668568	−	1.38829i	0.908657	−	0.417544i	$-0.137109\pi$
$954$		0			0
$955$	87.4947	−	19.9701i	2.83126	−	0.646217i
$956$	−7.21529	+	1.64684i	−0.233359	+	0.0532627i
$957$		0			0
$958$	−25.5293	+	53.0122i	−0.824815	+	1.71275i
$959$	2.74598	−	20.1257i	0.0886722	−	0.649894i
$960$		0			0
$961$	2.40554			0.0775980
$962$	66.0903			2.13084
$963$		0			0
$964$	−19.7648	+	15.7619i	−0.636581	+	0.507657i
$965$	−13.8435	−	60.6522i	−0.445637	−	1.95246i
$966$		0			0
$967$	−3.57420	+	15.6596i	−0.114939	+	0.503579i	0.884383	+	0.466761i	$0.154579\pi$
$967$	−3.57420	+	15.6596i	−0.114939	+	0.503579i	−0.999322	+	0.0368176i	$0.988278\pi$
$968$	4.30237	+	8.93396i	0.138283	+	0.287148i
$969$		0			0
$970$	−74.3974	−	93.2914i	−2.38876	−	2.99541i
$971$	−0.294729	−	1.29129i	−0.00945830	−	0.0414395i	0.969979	−	0.243190i	$-0.0781940\pi$
$971$	−0.294729	−	1.29129i	−0.00945830	−	0.0414395i	−0.979437	+	0.201751i	$0.935337\pi$
$972$		0			0
$973$	19.8416	−	1.76649i	0.636091	−	0.0566312i
$974$	−35.6365	+	28.4192i	−1.14187	+	0.910609i
$975$		0			0
$976$	5.81444	−	12.0738i	0.186116	−	0.386473i
$977$	−10.5892	−	8.44458i	−0.338778	−	0.270166i	0.439292	−	0.898344i	$-0.355229\pi$
$977$	−10.5892	−	8.44458i	−0.338778	−	0.270166i	−0.778069	+	0.628178i	$0.783801\pi$
$978$		0			0
$979$		−	64.8334i		−	2.07208i
$980$	14.2515	+	33.5218i	0.455248	+	1.07081i
$981$		0			0
$982$	5.61899	−	24.6184i	0.179309	−	0.785604i
$983$	−3.93992	+	4.94050i	−0.125664	+	0.157577i	−0.840683	−	0.541527i	$-0.817846\pi$
$983$	−3.93992	+	4.94050i	−0.125664	+	0.157577i	0.715020	+	0.699105i	$0.246418\pi$
$984$		0			0
$985$	25.0373	+	19.9666i	0.797755	+	0.636189i
$986$	1.06181	+	1.33147i	0.0338150	+	0.0424027i
$987$		0			0
$988$	12.2560	−	15.3686i	0.389916	−	0.488939i
$989$	−31.1279	+	7.10474i	−0.989810	+	0.225918i
$990$		0			0
$991$	−8.42243	+	36.9011i	−0.267547	+	1.17220i	0.645309	+	0.763921i	$0.276729\pi$
$991$	−8.42243	+	36.9011i	−0.267547	+	1.17220i	−0.912857	+	0.408280i	$0.866129\pi$
$992$	−32.3132	+	15.5612i	−1.02594	+	0.494069i
$993$		0			0
$994$	5.09884	+	57.2711i	0.161726	+	1.81653i
$995$	51.7458	−	11.8106i	1.64045	−	0.374422i
$996$		0			0
$997$	23.0201	+	47.8018i	0.729055	+	1.51390i	0.853171	+	0.521631i	$0.174676\pi$
$997$	23.0201	+	47.8018i	0.729055	+	1.51390i	−0.124116	+	0.992268i	$0.539610\pi$
$998$		−	3.59755i		−	0.113879i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.w.a.377.5	yes	120
3.2	odd	2	inner	441.2.w.a.377.16	yes	120
49.13	odd	14	inner	441.2.w.a.62.16	yes	120
147.62	even	14	inner	441.2.w.a.62.5	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.5	✓	120	147.62	even	14	inner
441.2.w.a.62.16	yes	120	49.13	odd	14	inner
441.2.w.a.377.5	yes	120	1.1	even	1	trivial
441.2.w.a.377.16	yes	120	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.w (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.79728 - 0.410217i) q^{2} +(1.26000 + 0.606784i) q^{4} +(-2.31994 + 2.90911i) q^{5} +(-1.91410 + 1.82654i) q^{7} +(0.866954 + 0.691373i) q^{8} +O(q^{10})\)	\(q+(-1.79728 - 0.410217i) q^{2} +(1.26000 + 0.606784i) q^{4} +(-2.31994 + 2.90911i) q^{5} +(-1.91410 + 1.82654i) q^{7} +(0.866954 + 0.691373i) q^{8} +(5.36294 - 4.27680i) q^{10} +(-4.35372 - 0.993708i) q^{11} +(3.23505 + 0.738379i) q^{13} +(4.18945 - 2.49760i) q^{14} +(-3.01844 - 3.78500i) q^{16} +(-0.255335 + 0.122963i) q^{17} -4.23595i q^{19} +(-4.68832 + 2.25777i) q^{20} +(7.41722 + 3.57194i) q^{22} +(3.40372 - 7.06790i) q^{23} +(-1.96820 - 8.62324i) q^{25} +(-5.51140 - 2.65415i) q^{26} +(-3.52007 + 1.13999i) q^{28} +(1.41433 + 2.93688i) q^{29} +5.34738i q^{31} +(2.91006 + 6.04280i) q^{32} +(0.509349 - 0.116256i) q^{34} +(-0.873006 - 9.80576i) q^{35} +(-9.73410 + 4.68770i) q^{37} +(-1.73766 + 7.61320i) q^{38} +(-4.02256 + 0.918122i) q^{40} +(2.99446 - 3.75494i) q^{41} +(-2.53762 - 3.18207i) q^{43} +(-4.88272 - 3.89384i) q^{44} +(-9.01681 + 11.3067i) q^{46} +(1.41800 - 6.21269i) q^{47} +(0.327535 - 6.99233i) q^{49} +16.3058i q^{50} +(3.62813 + 2.89333i) q^{52} +(3.06021 - 6.35459i) q^{53} +(12.9912 - 10.3601i) q^{55} +(-2.92225 + 0.260168i) q^{56} +(-1.33718 - 5.85857i) q^{58} +(-8.01966 - 10.0563i) q^{59} +(1.20103 + 2.49397i) q^{61} +(2.19359 - 9.61074i) q^{62} +(-0.596794 - 2.61472i) q^{64} +(-9.65313 + 7.69811i) q^{65} -4.33299 q^{67} -0.396333 q^{68} +(-2.45346 + 17.9818i) q^{70} +(-5.11483 + 10.6211i) q^{71} +(4.82984 - 1.10238i) q^{73} +(19.4179 - 4.43201i) q^{74} +(2.57031 - 5.33730i) q^{76} +(10.1485 - 6.05017i) q^{77} -4.76385 q^{79} +18.0136 q^{80} +(-6.92223 + 5.52030i) q^{82} +(-0.882792 - 3.86776i) q^{83} +(0.234648 - 1.02806i) q^{85} +(3.25547 + 6.76005i) q^{86} +(-3.08745 - 3.87154i) q^{88} +(3.23059 + 14.1541i) q^{89} +(-7.54088 + 4.49561i) q^{91} +(8.57737 - 6.84023i) q^{92} +(-5.09710 + 10.5842i) q^{94} +(12.3228 + 9.82714i) q^{95} -17.3956i q^{97} +(-3.45705 + 12.4328i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 24 q^{4}+O(q^{10}) \) 120 * q + 24 * q^4	\( 120 q + 24 q^{4} - 32 q^{16} - 44 q^{22} - 4 q^{25} - 56 q^{28} + 112 q^{34} - 76 q^{37} + 28 q^{40} + 8 q^{43} - 40 q^{46} - 84 q^{49} - 140 q^{52} + 12 q^{58} - 84 q^{61} + 24 q^{64} + 16 q^{67} + 112 q^{70} - 84 q^{76} - 24 q^{79} + 140 q^{82} - 96 q^{85} - 24 q^{88} - 112 q^{91} - 112 q^{94}+O(q^{100}) \) 120 * q + 24 * q^4 - 32 * q^16 - 44 * q^22 - 4 * q^25 - 56 * q^28 + 112 * q^34 - 76 * q^37 + 28 * q^40 + 8 * q^43 - 40 * q^46 - 84 * q^49 - 140 * q^52 + 12 * q^58 - 84 * q^61 + 24 * q^64 + 16 * q^67 + 112 * q^70 - 84 * q^76 - 24 * q^79 + 140 * q^82 - 96 * q^85 - 24 * q^88 - 112 * q^91 - 112 * q^94

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