LMFDB - Embedded newform 441.2.w.a.62.16

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			62.16
Character	$\chi$	$=$	441.62
Dual form			441.2.w.a.377.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.79728 - 0.410217i) q^{2} +(1.26000 - 0.606784i) q^{4} +(2.31994 + 2.90911i) q^{5} +(-1.91410 - 1.82654i) q^{7} +(-0.866954 + 0.691373i) q^{8} +O(q^{10})$	\(q+(1.79728 - 0.410217i) q^{2} +(1.26000 - 0.606784i) q^{4} +(2.31994 + 2.90911i) q^{5} +(-1.91410 - 1.82654i) q^{7} +(-0.866954 + 0.691373i) q^{8} +(5.36294 + 4.27680i) q^{10} +(4.35372 - 0.993708i) q^{11} +(3.23505 - 0.738379i) q^{13} +(-4.18945 - 2.49760i) q^{14} +(-3.01844 + 3.78500i) q^{16} +(0.255335 + 0.122963i) q^{17} +4.23595i q^{19} +(4.68832 + 2.25777i) q^{20} +(7.41722 - 3.57194i) q^{22} +(-3.40372 - 7.06790i) q^{23} +(-1.96820 + 8.62324i) q^{25} +(5.51140 - 2.65415i) q^{26} +(-3.52007 - 1.13999i) q^{28} +(-1.41433 + 2.93688i) q^{29} -5.34738i q^{31} +(-2.91006 + 6.04280i) q^{32} +(0.509349 + 0.116256i) q^{34} +(0.873006 - 9.80576i) q^{35} +(-9.73410 - 4.68770i) q^{37} +(1.73766 + 7.61320i) q^{38} +(-4.02256 - 0.918122i) q^{40} +(-2.99446 - 3.75494i) q^{41} +(-2.53762 + 3.18207i) q^{43} +(4.88272 - 3.89384i) q^{44} +(-9.01681 - 11.3067i) q^{46} +(-1.41800 - 6.21269i) q^{47} +(0.327535 + 6.99233i) q^{49} +16.3058i q^{50} +(3.62813 - 2.89333i) q^{52} +(-3.06021 - 6.35459i) q^{53} +(12.9912 + 10.3601i) q^{55} +(2.92225 + 0.260168i) q^{56} +(-1.33718 + 5.85857i) q^{58} +(8.01966 - 10.0563i) q^{59} +(1.20103 - 2.49397i) q^{61} +(-2.19359 - 9.61074i) q^{62} +(-0.596794 + 2.61472i) q^{64} +(9.65313 + 7.69811i) q^{65} -4.33299 q^{67} +0.396333 q^{68} +(-2.45346 - 17.9818i) q^{70} +(5.11483 + 10.6211i) q^{71} +(4.82984 + 1.10238i) q^{73} +(-19.4179 - 4.43201i) q^{74} +(2.57031 + 5.33730i) q^{76} +(-10.1485 - 6.05017i) q^{77} -4.76385 q^{79} -18.0136 q^{80} +(-6.92223 - 5.52030i) q^{82} +(0.882792 - 3.86776i) q^{83} +(0.234648 + 1.02806i) q^{85} +(-3.25547 + 6.76005i) q^{86} +(-3.08745 + 3.87154i) q^{88} +(-3.23059 + 14.1541i) q^{89} +(-7.54088 - 4.49561i) q^{91} +(-8.57737 - 6.84023i) q^{92} +(-5.09710 - 10.5842i) q^{94} +(-12.3228 + 9.82714i) q^{95} +17.3956i q^{97} +(3.45705 + 12.4328i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{11}{14}\right)$	$-1$

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	$-0.345453\pi$
$2$	1.79728	−	0.410217i	1.27087	−	0.290068i	0.804197	+	0.594363i	$0.202596\pi$
$3$		0			0
$3$		0			0
$4$	1.26000	−	0.606784i	0.630000	−	0.303392i
$5$	2.31994	+	2.90911i	1.03751	+	1.30099i	0.952476	+	0.304614i	$0.0985274\pi$
$5$	2.31994	+	2.90911i	1.03751	+	1.30099i	0.0850305	+	0.996378i	$0.472901\pi$
$6$		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	$-0.336336\pi$
$11$	4.35372	−	0.993708i	1.31270	−	0.299614i	0.820888	+	0.571089i	$0.193479\pi$
$12$		0			0
$13$	3.23505	−	0.738379i	0.897242	−	0.204790i	0.251058	−	0.967972i	$-0.419221\pi$
$13$	3.23505	−	0.738379i	0.897242	−	0.204790i	0.646183	+	0.763182i	$0.276364\pi$
$14$	−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	$-0.346201\pi$
$17$	0.255335	+	0.122963i	0.0619277	+	0.0298228i	−0.402664	+	0.915348i	$0.631916\pi$
$18$		0			0
$19$			4.23595i			0.971794i	0.874016	+	0.485897i	$0.161507\pi$
$19$			4.23595i			0.971794i	−0.874016	+	0.485897i	$0.838493\pi$
$20$	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	−0.873277	−	0.487224i	$-0.838010\pi$
$23$	−3.40372	−	7.06790i	−0.709725	−	1.47376i	0.163553	−	0.986535i	$-0.447705\pi$
$24$		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	$-0.955016\pi$
$29$	−1.41433	+	2.93688i	−0.262634	+	0.545364i	0.727397	+	0.686217i	$0.240730\pi$
$30$		0			0
$31$		−	5.34738i		−	0.960418i	−0.877154	−	0.480209i	$-0.840561\pi$
$31$		−	5.34738i		−	0.960418i	0.877154	−	0.480209i	$-0.159439\pi$
$32$	−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	−0.600693	−	0.799480i	$-0.705108\pi$
$37$	−9.73410	−	4.68770i	−1.60028	−	0.770653i	−0.999584	+	0.0288274i	$0.990823\pi$
$38$	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	$-0.336654\pi$
$41$	−2.99446	−	3.75494i	−0.467657	−	0.586423i	−0.958596	+	0.284771i	$0.908082\pi$
$42$		0			0
$43$	−2.53762	+	3.18207i	−0.386983	+	0.485262i	−0.936722	−	0.350075i	$-0.886156\pi$
$43$	−2.53762	+	3.18207i	−0.386983	+	0.485262i	0.549738	+	0.835337i	$0.314727\pi$
$44$	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	−0.966656	−	0.256078i	$-0.917570\pi$
$47$	−1.41800	−	6.21269i	−0.206837	−	0.906213i	0.759819	−	0.650135i	$-0.225288\pi$
$48$		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	−0.998382	−	0.0568548i	$-0.981893\pi$
$53$	−3.06021	−	6.35459i	−0.420352	−	0.872870i	0.578030	−	0.816015i	$-0.303821\pi$
$54$		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	0.0945502	−	0.995520i	$-0.469859\pi$
$59$	8.01966	−	10.0563i	1.04407	−	1.30922i	0.949521	−	0.313704i	$-0.101570\pi$
$60$		0			0
$61$	1.20103	−	2.49397i	0.153776	−	0.319320i	−0.809821	−	0.586677i	$-0.800436\pi$
$61$	1.20103	−	2.49397i	0.153776	−	0.319320i	0.963598	+	0.267357i	$0.0861502\pi$
$62$	−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	0.947355	+	0.320184i	$0.103745\pi$
$71$	5.11483	+	10.6211i	0.607019	+	1.26049i	−0.340337	+	0.940304i	$0.610541\pi$
$72$		0			0
$73$	4.82984	+	1.10238i	0.565291	+	0.129024i	0.495610	−	0.868545i	$-0.334945\pi$
$73$	4.82984	+	1.10238i	0.565291	+	0.129024i	0.0696810	+	0.997569i	$0.477802\pi$
$74$	−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	$-0.858706\pi$
$83$	0.882792	−	3.86776i	0.0968990	−	0.424542i	0.999988	+	0.00491141i	$0.00156336\pi$
$84$		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	0.451462	+	0.892291i	$0.350903\pi$
$89$	−3.23059	+	14.1541i	−0.342442	+	1.50033i	−0.793903	+	0.608044i	$0.791954\pi$
$90$		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	$0.344565\pi$
$97$			17.3956i			1.76625i	−0.469136	+	0.883126i	$0.655435\pi$
$98$	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	$-0.135877\pi$
$101$	3.05585	+	3.83192i	0.304069	+	0.381290i	−0.606197	+	0.795314i	$0.707306\pi$
$102$		0			0
$103$	6.59938	−	5.26283i	0.650257	−	0.518562i	−0.241893	−	0.970303i	$-0.577768\pi$
$103$	6.59938	−	5.26283i	0.650257	−	0.518562i	0.892149	+	0.451741i	$0.149197\pi$
$104$	−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	$-0.548665\pi$
$107$	−7.43039	−	1.69594i	−0.718323	−	0.163952i	−0.566032	+	0.824383i	$0.691522\pi$
$108$		0			0
$109$	0.245552	+	1.07583i	0.0235196	+	0.103046i	0.985325	−	0.170687i	$-0.0545986\pi$
$109$	0.245552	+	1.07583i	0.0235196	+	0.103046i	−0.961806	+	0.273733i	$0.911742\pi$
$110$	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	$-0.431822\pi$
$113$	−0.211655	−	0.0483089i	−0.0199108	−	0.00454452i	−0.232465	+	0.972605i	$0.574679\pi$
$114$		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	0.727922	−	0.685660i	$-0.240486\pi$
$127$	7.27670	+	3.50428i	0.645703	+	0.310954i	−0.0822188	+	0.996614i	$0.526201\pi$
$128$		−	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	$-0.770450\pi$
$131$	0.684134	−	0.857877i	0.0597730	−	0.0749530i	0.810819	+	0.585297i	$0.199022\pi$
$132$		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	$-0.179354\pi$
$137$	6.00235	+	4.78671i	0.512815	+	0.408957i	−0.332598	+	0.943069i	$0.607925\pi$
$138$		0			0
$139$	−5.88646	+	4.69430i	−0.499283	+	0.398165i	−0.840493	−	0.541822i	$-0.817735\pi$
$139$	−5.88646	+	4.69430i	−0.499283	+	0.398165i	0.341210	+	0.939987i	$0.389163\pi$
$140$	−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	$-0.346798\pi$
$149$	15.4365	−	3.52328i	1.26461	−	0.288638i	0.801678	+	0.597756i	$0.203941\pi$
$150$		0			0
$151$	−1.65202	+	0.795573i	−0.134440	+	0.0647428i	−0.499894	−	0.866086i	$-0.666628\pi$
$151$	−1.65202	+	0.795573i	−0.134440	+	0.0647428i	0.365455	+	0.930829i	$0.380914\pi$
$152$	−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	0.893409	−	0.449244i	$-0.148307\pi$
$157$	8.19749	+	6.53728i	0.654231	+	0.521731i	−0.239178	+	0.970976i	$0.576878\pi$
$158$	−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	−0.928319	−	0.371786i	$-0.878746\pi$
$163$	−4.58703	+	5.75196i	−0.359284	+	0.450528i	0.569035	+	0.822314i	$0.307317\pi$
$164$	−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	$-0.235711\pi$
$167$	8.66950	+	4.17501i	0.670866	+	0.323072i	−0.0672592	+	0.997736i	$0.521425\pi$
$168$		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	$-0.484422\pi$
$173$	11.3157	−	5.44937i	0.860319	−	0.414308i	0.811398	+	0.584495i	$0.198707\pi$
$174$		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	0.557055	+	0.830476i	$0.311931\pi$
$179$	−5.88085	+	12.2117i	−0.439555	+	0.912746i	−0.996610	+	0.0822700i	$0.973783\pi$
$180$		0			0
$181$	−8.65895	−	1.97635i	−0.643615	−	0.146901i	−0.111758	−	0.993735i	$-0.535648\pi$
$181$	−8.65895	−	1.97635i	−0.643615	−	0.146901i	−0.531857	+	0.846834i	$0.678505\pi$
$182$	−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	0.377695	−	0.925930i	$-0.376717\pi$
$191$	18.8571	−	15.0381i	1.36446	−	1.08812i	0.986760	−	0.162186i	$-0.0518546\pi$
$192$		0			0
$193$	−10.4245	−	13.0720i	−0.750374	−	0.940940i	0.249247	−	0.968440i	$-0.419817\pi$
$193$	−10.4245	−	13.0720i	−0.750374	−	0.940940i	−0.999622	+	0.0275000i	$0.991245\pi$
$194$	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	−0.933217	−	0.359312i	$-0.883011\pi$
$199$	−11.1524	+	8.89376i	−0.790574	+	0.630462i	0.142643	+	0.989774i	$0.454440\pi$
$200$	−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	−0.896375	−	0.443296i	$-0.853809\pi$
$211$	1.50444	−	6.59138i	0.103570	−	0.453769i	0.999945	−	0.0104731i	$-0.00333376\pi$
$212$	−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	0.942132	+	0.335243i	$0.108818\pi$
$223$	9.21117	+	19.1272i	0.616826	+	1.28085i	−0.325306	+	0.945609i	$0.605467\pi$
$224$	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	$-0.519973\pi$
$227$	−1.88947			−0.125409			−0.0627044	+	0.998032i	$0.519973\pi$
$228$		0			0
$229$	12.4770	+	9.95007i	0.824503	+	0.657519i	0.942022	−	0.335552i	$-0.108923\pi$
$229$	12.4770	+	9.95007i	0.824503	+	0.657519i	−0.117519	+	0.993071i	$0.537494\pi$
$230$	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	$-0.854663\pi$
$233$	0.103180	−	0.214255i	0.00675953	−	0.0140363i	0.904321	+	0.426852i	$0.140378\pi$
$234$		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	$-0.230964\pi$
$239$	4.13746	+	3.29952i	0.267630	+	0.213428i	−0.480475	+	0.877009i	$0.659536\pi$
$240$		0			0
$241$	−7.84318	−	16.2865i	−0.505223	−	1.04911i	−0.985134	−	0.171790i	$-0.945045\pi$
$241$	−7.84318	−	16.2865i	−0.505223	−	1.04911i	0.479910	−	0.877318i	$-0.340669\pi$
$242$	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	$-0.700463\pi$
$251$	5.22808	−	6.55581i	0.329994	−	0.413799i	0.918955	+	0.394362i	$0.129034\pi$
$252$		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	$-0.472793\pi$
$257$	−10.2661	−	4.94389i	−0.640382	−	0.308392i	−0.725751	+	0.687958i	$0.758507\pi$
$258$		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	0.339376	+	0.940651i	$0.389784\pi$
$269$	−6.14266	+	26.9127i	−0.374524	+	1.64090i	−0.713900	+	0.700247i	$0.753073\pi$
$270$		0			0
$271$	8.32357	+	17.2841i	0.505621	+	1.04993i	0.985037	+	0.172345i	$0.0551343\pi$
$271$	8.32357	+	17.2841i	0.505621	+	1.04993i	−0.479416	+	0.877588i	$0.659151\pi$
$272$	−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	−0.248628	−	0.968599i	$-0.579980\pi$
$277$	−19.3217	−	9.30482i	−1.16093	−	0.559073i	−0.912298	+	0.409527i	$0.865694\pi$
$278$	−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	$-0.472578\pi$
$281$	9.98810	−	2.27972i	0.595840	−	0.135997i	0.509797	+	0.860295i	$0.329721\pi$
$282$		0			0
$283$	−28.0125	+	6.39366i	−1.66517	+	0.380064i	−0.948357	−	0.317204i	$-0.897256\pi$
$283$	−28.0125	+	6.39366i	−1.66517	+	0.380064i	−0.716811	+	0.697268i	$0.754399\pi$
$284$	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	$-0.292893\pi$
$293$	20.7358			1.21140			0.605699	+	0.795694i	$0.292893\pi$
$294$		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	−0.457409	−	0.889256i	$-0.651222\pi$
$307$	−8.47487	+	1.93433i	−0.483686	+	0.110398i	−0.0262773	+	0.999655i	$0.508365\pi$
$308$	−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	$-0.454862\pi$
$311$	−9.60300	−	4.62456i	−0.544536	−	0.262235i	−0.685866	+	0.727728i	$0.740576\pi$
$312$		0			0
$313$		−	3.13860i		−	0.177404i	−0.996058	−	0.0887022i	$-0.971728\pi$
$313$		−	3.13860i		−	0.177404i	0.996058	−	0.0887022i	$-0.0282719\pi$
$314$	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	$-0.0243690\pi$
$317$	5.61929	+	11.6686i	0.315611	+	0.655372i	−0.681460	+	0.731855i	$0.738655\pi$
$318$		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	0.0150462	−	0.999887i	$-0.495210\pi$
$331$	−13.7782	−	6.63521i	−0.757316	−	0.364704i	−0.772362	+	0.635183i	$0.780925\pi$
$332$	−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	0.0752630	+	0.997164i	$0.476020\pi$
$337$	−16.7723	+	21.0318i	−0.913647	+	1.14568i	−0.988910	+	0.148514i	$0.952551\pi$
$338$	−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	$-0.150045\pi$
$347$	−0.364992	−	0.757914i	−0.0195938	−	0.0406870i	−0.910536	+	0.413430i	$0.864331\pi$
$348$		0			0
$349$	8.51882	+	6.79353i	0.456002	+	0.363650i	0.824390	−	0.566023i	$-0.191519\pi$
$349$	8.51882	+	6.79353i	0.456002	+	0.363650i	−0.368387	+	0.929672i	$0.620090\pi$
$350$	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	0.0110210	+	0.999939i	$0.496492\pi$
$353$	−18.1551	+	22.7658i	−0.966300	+	1.21170i	−0.977321	+	0.211763i	$0.932080\pi$
$354$		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	−0.999866	−	0.0163430i	$-0.994798\pi$
$359$	−23.4623	−	18.7105i	−1.23829	−	0.987504i	−0.238424	−	0.971161i	$-0.576631\pi$
$360$		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	0.653902	−	0.756580i	$-0.273131\pi$
$367$	17.5246	+	3.99989i	0.914779	+	0.208792i	0.260877	+	0.965372i	$0.415988\pi$
$368$	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	−0.981960	−	0.189087i	$-0.939447\pi$
$379$	−3.49034	−	15.2922i	−0.179287	−	0.785506i	0.802674	−	0.596418i	$-0.203410\pi$
$380$	−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	0.762588	+	0.646884i	$0.223928\pi$
$383$	−4.01492	+	17.5905i	−0.205153	+	0.898832i	−0.967741	+	0.251948i	$0.918929\pi$
$384$		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	$-0.732177\pi$
$389$	−1.73250	+	1.38162i	−0.0878413	+	0.0700511i	0.578585	+	0.815622i	$0.303605\pi$
$390$		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	0.110063	−	0.993925i	$-0.464895\pi$
$397$	21.9883	−	17.5350i	1.10356	−	0.880059i	0.993496	+	0.113866i	$0.0363234\pi$
$398$	−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	$-0.238046\pi$
$401$	22.0002	+	5.02141i	1.09864	+	0.250757i	0.365484	+	0.930818i	$0.380904\pi$
$402$		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	0.412937	+	0.910760i	$0.364503\pi$
$409$	−11.2563	+	23.3738i	−0.556586	+	1.15576i	−0.969522	+	0.245003i	$0.921211\pi$
$410$		−	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	$-0.445971\pi$
$419$	21.3874	−	10.2996i	1.04484	−	0.503170i	0.875918	+	0.482459i	$0.160256\pi$
$420$		0			0
$421$	−24.6286	−	11.8605i	−1.20032	−	0.578046i	−0.276556	−	0.960998i	$-0.589193\pi$
$421$	−24.6286	−	11.8605i	−1.20032	−	0.578046i	−0.923768	+	0.382952i	$0.874907\pi$
$422$		−	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	$-0.229797\pi$
$431$	5.67341	+	4.52439i	0.273279	+	0.217932i	−0.477255	+	0.878765i	$0.658368\pi$
$432$		0			0
$433$	−20.7687	+	16.5625i	−0.998078	+	0.795941i	−0.978996	−	0.203877i	$-0.934646\pi$
$433$	−20.7687	+	16.5625i	−0.998078	+	0.795941i	−0.0190816	+	0.999818i	$0.506074\pi$
$434$	−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	−0.315707	−	0.948857i	$-0.602242\pi$
$439$	−3.94857	+	0.901236i	−0.188455	+	0.0430136i	0.127252	+	0.991870i	$0.459384\pi$
$440$	−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	$-0.715408\pi$
$443$	−17.9367	+	4.09394i	−0.852200	+	0.194509i	−0.225957	+	0.974137i	$0.572551\pi$
$444$		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	$-0.515723\pi$
$449$	19.3541	−	15.4344i	0.913375	−	0.728393i	0.962752	+	0.270388i	$0.0871519\pi$
$450$		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	0.317254	−	0.948341i	$-0.397239\pi$
$457$	25.0379	−	31.3965i	1.17122	−	1.46867i	0.853968	−	0.520325i	$-0.174189\pi$
$458$	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	$-0.303774\pi$
$461$	6.45644	+	3.10926i	0.300706	+	0.144813i	−0.277446	+	0.960741i	$0.589488\pi$
$462$		0			0
$463$	25.8416	−	12.4447i	1.20096	−	0.578352i	0.277011	−	0.960867i	$-0.410656\pi$
$463$	25.8416	−	12.4447i	1.20096	−	0.578352i	0.923949	+	0.382514i	$0.124942\pi$
$464$	−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	$-0.552017\pi$
$467$	10.9626	−	5.27932i	0.507290	−	0.244298i	0.669980	+	0.742379i	$0.266303\pi$
$468$		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	−0.829436	−	0.558602i	$-0.811338\pi$
$479$	−7.10221	−	31.1168i	−0.324508	−	1.42176i	0.504927	−	0.863162i	$-0.331519\pi$
$480$		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	0.996915	−	0.0784883i	$-0.0250093\pi$
$487$	15.4159	+	19.3309i	0.698560	+	0.875967i	−0.298355	+	0.954455i	$0.596438\pi$
$488$	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	−0.964278	−	0.264894i	$-0.914663\pi$
$499$	0.434245	−	1.90255i	0.0194395	−	0.0851699i	0.983717	+	0.179724i	$0.0575203\pi$
$500$	−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	0.996647	+	0.0818187i	$0.0260728\pi$
$503$	3.00977	+	13.1867i	0.134199	+	0.587964i	−0.862448	+	0.506145i	$0.831070\pi$
$504$		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	$-0.722657\pi$
$509$	−29.0511			−1.28767			−0.643833	+	0.765166i	$0.722657\pi$
$510$		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	$-0.433259\pi$
$521$	9.50180			0.416281			0.208141	+	0.978099i	$0.433259\pi$
$522$		0			0
$523$	−15.0575	−	12.0079i	−0.658417	−	0.525070i	0.236313	−	0.971677i	$-0.424061\pi$
$523$	−15.0575	−	12.0079i	−0.658417	−	0.525070i	−0.894730	+	0.446607i	$0.852632\pi$
$524$	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	0.871598	+	0.490221i	$0.163084\pi$
$541$	6.95489	+	30.4714i	0.299014	+	1.31007i	−0.572584	+	0.819846i	$0.694059\pi$
$542$	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	0.943986	+	0.329985i	$0.107044\pi$
$547$	24.6894	+	30.9595i	1.05564	+	1.32373i	0.111654	+	0.993747i	$0.464385\pi$
$548$	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	−0.819492	−	0.573091i	$-0.805744\pi$
$563$	3.97437	−	17.4129i	0.167500	−	0.733864i	0.986991	−	0.160773i	$-0.0513987\pi$
$564$		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	0.548979	−	0.835836i	$-0.315017\pi$
$571$	5.68188	+	2.73625i	0.237779	+	0.114509i	−0.311200	+	0.950344i	$0.600731\pi$
$572$	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	0.0738141	−	0.997272i	$-0.476483\pi$
$577$	13.7644	−	3.14163i	0.573018	−	0.130788i	0.499204	+	0.866484i	$0.333626\pi$
$578$	−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	$-0.455819\pi$
$587$	6.70403			0.276705			0.138352	+	0.990383i	$0.455819\pi$
$588$		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	−0.979946	−	0.199265i	$-0.936144\pi$
$593$	−23.2839	−	29.1971i	−0.956156	−	1.19898i	0.0237892	−	0.999717i	$-0.492427\pi$
$594$		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	$-0.568226\pi$
$599$	0.480066	−	0.109572i	0.0196150	−	0.00447699i	0.232317	+	0.972640i	$0.425369\pi$
$600$		0			0
$601$	43.8941	−	10.0185i	1.79048	−	0.408665i	0.807127	−	0.590378i	$-0.201021\pi$
$601$	43.8941	−	10.0185i	1.79048	−	0.408665i	0.983352	+	0.181713i	$0.0581643\pi$
$602$	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	$-0.907519\pi$
$607$		−	14.1156i		−	0.572933i	0.958090	−	0.286466i	$-0.0924806\pi$
$608$	−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	−0.955777	−	0.294093i	$-0.904982\pi$
$613$	0.815822	−	3.57435i	0.0329507	−	0.144367i	0.988727	+	0.149727i	$0.0478395\pi$
$614$	−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	0.583305	+	0.812253i	$0.301759\pi$
$617$	−10.3189	+	21.4275i	−0.415425	+	0.862638i	−0.998730	+	0.0503851i	$0.983955\pi$
$618$		0			0
$619$			14.0962i			0.566573i	0.959035	+	0.283286i	$0.0914247\pi$
$619$			14.0962i			0.566573i	−0.959035	+	0.283286i	$0.908575\pi$
$620$	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	0.204361	+	0.978896i	$0.434488\pi$
$631$	−19.9819	+	25.0565i	−0.795467	+	0.997484i	−0.999827	+	0.0185879i	$0.994083\pi$
$632$	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	$-0.193998\pi$
$641$	−3.51463	−	7.29821i	−0.138820	−	0.288262i	−0.958775	+	0.284165i	$0.908284\pi$
$642$		0			0
$643$	−3.49123	−	2.78416i	−0.137681	−	0.109797i	0.552228	−	0.833693i	$-0.313778\pi$
$643$	−3.49123	−	2.78416i	−0.137681	−	0.109797i	−0.689909	+	0.723897i	$0.742349\pi$
$644$	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	$-0.859125\pi$
$647$	−7.25040	+	9.09171i	−0.285043	+	0.357432i	0.618610	+	0.785698i	$0.287696\pi$
$648$		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	$-0.224842\pi$
$653$	7.59489	+	6.05672i	0.297211	+	0.237018i	−0.463518	+	0.886087i	$0.653413\pi$
$654$		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	$-0.0680924\pi$
$659$	5.18433	+	10.7654i	0.201953	+	0.419359i	−0.775254	+	0.631650i	$0.782378\pi$
$660$		0			0
$661$	14.3058	+	3.26521i	0.556432	+	0.127002i	0.491484	−	0.870887i	$-0.336455\pi$
$661$	14.3058	+	3.26521i	0.556432	+	0.127002i	0.0649481	+	0.997889i	$0.479312\pi$
$662$	−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	0.998665	+	0.0516514i	$0.0164485\pi$
$673$	3.14704	+	13.7881i	0.121310	+	0.531492i	−0.877356	+	0.479841i	$0.840694\pi$
$674$	−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	−0.706774	−	0.707440i	$-0.749850\pi$
$677$	6.16536	−	27.0122i	0.236954	−	1.03816i	0.943728	−	0.330724i	$-0.107293\pi$
$678$		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	$-0.815793\pi$
$683$	−12.8119	+	10.2172i	−0.490235	+	0.390949i	0.346938	+	0.937888i	$0.387222\pi$
$684$		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	−0.0586248	−	0.998280i	$-0.518672\pi$
$691$	23.6998	−	18.8999i	0.901581	−	0.718987i	0.960206	+	0.279293i	$0.0901001\pi$
$692$	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	$-0.215957\pi$
$701$	31.9755	+	7.29819i	1.20770	+	0.275649i	0.429148	+	0.903234i	$0.358814\pi$
$702$		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	−0.980863	−	0.194700i	$-0.937627\pi$
$709$	−38.3482	+	18.4675i	−1.44020	+	0.693563i	−0.459336	+	0.888263i	$0.651912\pi$
$710$	−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	$-0.944835\pi$
$719$	−16.0273	+	20.0976i	−0.597717	+	0.749513i	0.387303	+	0.921952i	$0.373407\pi$
$720$		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	−0.600638	−	0.799521i	$-0.705087\pi$
$727$	1.21825	−	0.971521i	0.0451824	−	0.0360317i	0.645821	+	0.763489i	$0.276515\pi$
$728$	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	−0.484144	−	0.874988i	$-0.660869\pi$
$733$	−14.6389	+	3.34123i	−0.540700	+	0.123411i	−0.0565557	+	0.998399i	$0.518012\pi$
$734$	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	−0.988048	−	0.154144i	$-0.950738\pi$
$739$	−40.3302	+	19.4220i	−1.48357	+	0.714450i	−0.495523	+	0.868595i	$0.665024\pi$
$740$	−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	0.348151	−	0.937439i	$-0.386810\pi$
$743$	36.5137	−	29.1187i	1.33956	−	1.06826i	0.991406	−	0.130822i	$-0.0417616\pi$
$744$		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	−0.829551	−	0.558430i	$-0.811404\pi$
$751$	−2.75494	+	3.45459i	−0.100529	+	0.126060i	0.729022	+	0.684490i	$0.239975\pi$
$752$	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	−0.503485	−	0.864004i	$-0.667949\pi$
$757$	−3.90413	+	1.88013i	−0.141898	+	0.0683344i	0.361587	+	0.932338i	$0.382235\pi$
$758$	−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	$-0.407289\pi$
$761$	33.5202	−	16.1425i	1.21510	−	0.585164i	0.927944	+	0.372719i	$0.121574\pi$
$762$		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	0.998113	−	0.0614052i	$-0.0195582\pi$
$769$	51.8772	+	11.8406i	1.87074	+	0.426984i	0.872626	+	0.488389i	$0.162415\pi$
$770$	−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	0.995643	+	0.0932516i	$0.0297261\pi$
$773$	3.86627	+	16.9392i	0.139060	+	0.609261i	−0.856583	+	0.516010i	$0.827417\pi$
$774$		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	−0.853610	−	0.520913i	$-0.825592\pi$
$787$	−15.0284	+	11.9847i	−0.535704	+	0.427210i	0.317906	+	0.948122i	$0.397020\pi$
$788$	−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	0.699189	+	0.714937i	$0.253544\pi$
$797$	10.7121	+	46.9326i	0.379441	+	1.66244i	−0.319749	+	0.947502i	$0.603598\pi$
$798$		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	$-0.442613\pi$
$809$	−2.44570	−	0.558214i	−0.0859861	−	0.0196258i	−0.265298	+	0.964167i	$0.585470\pi$
$810$		0			0
$811$	−21.8734	−	45.4205i	−0.768078	−	1.59493i	−0.803317	−	0.595552i	$-0.796933\pi$
$811$	−21.8734	−	45.4205i	−0.768078	−	1.59493i	0.0352386	−	0.999379i	$-0.488781\pi$
$812$	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	$-0.739811\pi$
$821$	8.95903	−	18.6036i	0.312672	−	0.649271i	0.996787	+	0.0801040i	$0.0255252\pi$
$822$		0			0
$823$	−24.9293	+	31.2603i	−0.868979	+	1.08967i	0.126240	+	0.992000i	$0.459709\pi$
$823$	−24.9293	+	31.2603i	−0.868979	+	1.08967i	−0.995219	+	0.0976660i	$0.968862\pi$
$824$	−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	$-0.509912\pi$
$827$	−29.1176	−	23.2205i	−1.01252	−	0.807456i	−0.981383	+	0.192059i	$0.938484\pi$
$828$		0			0
$829$	−2.25627	−	4.68518i	−0.0783633	−	0.162723i	0.858106	−	0.513473i	$-0.171641\pi$
$829$	−2.25627	−	4.68518i	−0.0783633	−	0.162723i	−0.936469	+	0.350749i	$0.885927\pi$
$830$	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	$-0.913589\pi$
$839$	−14.1231	+	17.7098i	−0.487584	+	0.611411i	0.475794	+	0.879557i	$0.342161\pi$
$840$		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	−0.517239	−	0.855841i	$-0.673040\pi$
$853$	13.8547	−	28.7697i	0.474377	−	0.985055i	0.991617	−	0.129214i	$-0.0412454\pi$
$854$	−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	$-0.901432\pi$
$857$	1.10947	−	4.86089i	0.0378987	−	0.166045i	0.990336	+	0.138690i	$0.0442892\pi$
$858$		0			0
$859$	−19.4480	−	40.3843i	−0.663559	−	1.37789i	−0.912380	−	0.409344i	$-0.865757\pi$
$859$	−19.4480	−	40.3843i	−0.663559	−	1.37789i	0.248821	−	0.968549i	$-0.419957\pi$
$860$	−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	0.765045	−	0.643977i	$-0.222717\pi$
$877$	−0.977982	−	1.22635i	−0.0330241	−	0.0414109i	−0.798069	+	0.602566i	$0.794145\pi$
$878$	−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	$-0.524841\pi$
$881$	−4.62799			−0.155921			−0.0779605	+	0.996956i	$0.524841\pi$
$882$		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	$-0.200856\pi$
$887$	1.56645	+	1.96427i	0.0525963	+	0.0659536i	−0.754838	+	0.655912i	$0.772284\pi$
$888$		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	−0.385144	−	0.922856i	$-0.625848\pi$
$907$	10.9103	−	47.8012i	0.362271	−	1.58721i	0.747415	−	0.664357i	$-0.231295\pi$
$908$	−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	$-0.847445\pi$
$911$	0.797873	−	1.65680i	0.0264347	−	0.0548923i	0.913768	+	0.406236i	$0.133159\pi$
$912$		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	−0.485710	−	0.874120i	$-0.661439\pi$
$919$	−44.6225	−	21.4891i	−1.47196	−	0.708859i	−0.986250	+	0.165261i	$0.947153\pi$
$920$	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	$-0.116240\pi$
$929$	−1.90333	−	8.33902i	−0.0624461	−	0.273594i	−0.996506	+	0.0835223i	$0.973383\pi$
$930$		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	0.505987	−	0.862541i	$-0.331128\pi$
$937$	−6.80580	−	5.42745i	−0.222336	−	0.177307i	−0.728323	+	0.685234i	$0.759700\pi$
$938$	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	$-0.748035\pi$
$941$	4.51738	−	5.66462i	0.147263	−	0.184661i	0.849992	+	0.526796i	$0.176607\pi$
$942$		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	$-0.354703\pi$
$947$	−10.3476	−	8.25190i	−0.336251	−	0.268151i	−0.777029	+	0.629465i	$0.783274\pi$
$948$		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	−0.908657	−	0.417544i	$-0.862891\pi$
$953$	−20.6391	−	42.8576i	−0.668568	−	1.38829i	0.240089	−	0.970751i	$-0.422823\pi$
$954$		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	−0.999322	−	0.0368176i	$-0.988278\pi$
$967$	−3.57420	−	15.6596i	−0.114939	−	0.503579i	0.884383	−	0.466761i	$-0.154579\pi$
$968$	−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	$-0.921806\pi$
$971$	0.294729	−	1.29129i	0.00945830	−	0.0414395i	0.979437	+	0.201751i	$0.0646631\pi$
$972$		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	$-0.644771\pi$
$977$	10.5892	−	8.44458i	0.338778	−	0.270166i	0.778069	+	0.628178i	$0.216199\pi$
$978$		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	$-0.182154\pi$
$983$	3.93992	+	4.94050i	0.125664	+	0.157577i	−0.715020	+	0.699105i	$0.753582\pi$
$984$		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	−0.912857	−	0.408280i	$-0.866129\pi$
$991$	−8.42243	−	36.9011i	−0.267547	−	1.17220i	0.645309	−	0.763921i	$-0.276729\pi$
$992$	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	−0.124116	−	0.992268i	$-0.539610\pi$
$997$	23.0201	−	47.8018i	0.729055	−	1.51390i	0.853171	−	0.521631i	$-0.174676\pi$
$998$		−	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.62.16	yes	120
3.2	odd	2	inner	441.2.w.a.62.5	✓	120
49.34	odd	14	inner	441.2.w.a.377.5	yes	120
147.83	even	14	inner	441.2.w.a.377.16	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.w.a.62.5	✓	120	3.2	odd	2	inner
441.2.w.a.62.16	yes	120	1.1	even	1	trivial
441.2.w.a.377.5	yes	120	49.34	odd	14	inner
441.2.w.a.377.16	yes	120	147.83	even	14	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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