LMFDB - Embedded newform 260.2.z.a.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(49,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("260.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.z (of order $6$, degree $2$, 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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 21x^{12} - 22x^{10} - 26x^{8} - 198x^{6} + 1701x^{4} - 5103x^{2} + 6561 $ x^16 - 7x^14 + 21x^12 - 22x^10 - 26x^8 - 198x^6 + 1701x^4 - 5103*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			69.2
Root			$1.42836 + 0.979681i$ of defining polynomial
Character	$\chi$	$=$	260.69
Dual form			260.2.z.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.69686 - 0.979681i) q^{3} +(-2.16188 + 0.571200i) q^{5} +(1.42836 + 2.47400i) q^{7} +(0.419550 + 0.726682i) q^{9} +O(q^{10})$	\(q+(-1.69686 - 0.979681i) q^{3} +(-2.16188 + 0.571200i) q^{5} +(1.42836 + 2.47400i) q^{7} +(0.419550 + 0.726682i) q^{9} +(4.84746 + 2.79868i) q^{11} +(2.08253 + 2.94331i) q^{13} +(4.22800 + 1.14871i) q^{15} +(3.40111 - 1.96363i) q^{17} +(-7.09546 + 4.09657i) q^{19} -5.59737i q^{21} +(0.309177 + 0.178504i) q^{23} +(4.34746 - 2.46973i) q^{25} +4.23399i q^{27} +(1.90890 - 3.30631i) q^{29} +8.47182i q^{31} +(-5.48363 - 9.49793i) q^{33} +(-4.50110 - 4.53261i) q^{35} +(-3.77939 + 6.54609i) q^{37} +(-0.650247 - 7.03459i) q^{39} +(-6.85811 - 3.95953i) q^{41} +(-2.89741 + 1.67282i) q^{43} +(-1.32210 - 1.33135i) q^{45} +8.64753 q^{47} +(-0.580450 + 1.00537i) q^{49} -7.69492 q^{51} +0.581615i q^{53} +(-12.0782 - 3.28155i) q^{55} +16.0533 q^{57} +(-0.510653 + 0.294826i) q^{59} +(-2.90890 - 5.03836i) q^{61} +(-1.19854 + 2.07593i) q^{63} +(-6.18340 - 5.17355i) q^{65} +(6.09997 - 10.5655i) q^{67} +(-0.349753 - 0.605790i) q^{69} +(2.11676 - 1.22211i) q^{71} +4.16506 q^{73} +(-9.79657 - 0.0683422i) q^{75} +15.9902i q^{77} +9.85582 q^{79} +(5.40661 - 9.36452i) q^{81} -6.09174 q^{83} +(-6.23116 + 6.18785i) q^{85} +(-6.47825 + 3.74022i) q^{87} +(0.510653 + 0.294826i) q^{89} +(-4.30714 + 9.35629i) q^{91} +(8.29968 - 14.3755i) q^{93} +(12.9996 - 12.9092i) q^{95} +(2.35841 + 4.08489i) q^{97} +4.69675i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) $ 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.69686	−	0.979681i	−0.979681	−	0.565619i	−0.0775072	−	0.996992i	$-0.524696\pi$
$3$	−1.69686	−	0.979681i	−0.979681	−	0.565619i	−0.902174	+	0.431373i	$0.858029\pi$
$4$		0			0
$5$	−2.16188	+	0.571200i	−0.966823	+	0.255448i
$5$	−2.16188	+	0.571200i	−0.966823	+	0.255448i
$6$		0			0
$7$	1.42836	+	2.47400i	0.539871	+	0.935084i	0.998910	+	0.0466681i	$0.0148603\pi$
$7$	1.42836	+	2.47400i	0.539871	+	0.935084i	−0.459039	+	0.888416i	$0.651806\pi$
$8$		0			0
$9$	0.419550	+	0.726682i	0.139850	+	0.242227i
$10$		0			0
$11$	4.84746	+	2.79868i	1.46156	+	0.843835i	0.999084	−	0.0427946i	$-0.0136261\pi$
$11$	4.84746	+	2.79868i	1.46156	+	0.843835i	0.462481	+	0.886629i	$0.346959\pi$
$12$		0			0
$13$	2.08253	+	2.94331i	0.577589	+	0.816328i
$13$	2.08253	+	2.94331i	0.577589	+	0.816328i
$14$		0			0
$15$	4.22800	+	1.14871i	1.09166	+	0.296596i
$16$		0			0
$17$	3.40111	−	1.96363i	0.824889	−	0.476250i	−0.0272102	−	0.999630i	$-0.508662\pi$
$17$	3.40111	−	1.96363i	0.824889	−	0.476250i	0.852100	+	0.523380i	$0.175329\pi$
$18$		0			0
$19$	−7.09546	+	4.09657i	−1.62781	+	0.939816i	−0.643065	+	0.765811i	$0.722338\pi$
$19$	−7.09546	+	4.09657i	−1.62781	+	0.939816i	−0.984745	+	0.174005i	$0.944329\pi$
$20$		0			0
$21$		−	5.59737i		−	1.22145i
$22$		0			0
$23$	0.309177	+	0.178504i	0.0644679	+	0.0372206i	0.531887	−	0.846815i	$-0.321483\pi$
$23$	0.309177	+	0.178504i	0.0644679	+	0.0372206i	−0.467420	+	0.884036i	$0.654816\pi$
$24$		0			0
$25$	4.34746	−	2.46973i	0.869492	−	0.493946i
$26$		0			0
$27$			4.23399i			0.814831i
$28$		0			0
$29$	1.90890	−	3.30631i	0.354473	−	0.613966i	−0.632554	−	0.774516i	$-0.717994\pi$
$29$	1.90890	−	3.30631i	0.354473	−	0.613966i	0.987028	+	0.160550i	$0.0513268\pi$
$30$		0			0
$31$			8.47182i			1.52158i	0.648996	+	0.760792i	$0.275189\pi$
$31$			8.47182i			1.52158i	−0.648996	+	0.760792i	$0.724811\pi$
$32$		0			0
$33$	−5.48363	−	9.49793i	−0.954578	−	1.65338i
$34$		0			0
$35$	−4.50110	−	4.53261i	−0.760825	−	0.766151i
$36$		0			0
$37$	−3.77939	+	6.54609i	−0.621327	+	1.07617i	0.367912	+	0.929861i	$0.380073\pi$
$37$	−3.77939	+	6.54609i	−0.621327	+	1.07617i	−0.989239	+	0.146309i	$0.953260\pi$
$38$		0			0
$39$	−0.650247	−	7.03459i	−0.104123	−	1.12644i
$40$		0			0
$41$	−6.85811	−	3.95953i	−1.07106	−	0.618375i	−0.142587	−	0.989782i	$-0.545542\pi$
$41$	−6.85811	−	3.95953i	−1.07106	−	0.618375i	−0.928470	+	0.371407i	$0.878876\pi$
$42$		0			0
$43$	−2.89741	+	1.67282i	−0.441851	+	0.255103i	−0.704383	−	0.709820i	$-0.748776\pi$
$43$	−2.89741	+	1.67282i	−0.441851	+	0.255103i	0.262531	+	0.964923i	$0.415443\pi$
$44$		0			0
$45$	−1.32210	−	1.33135i	−0.197087	−	0.198466i
$46$		0			0
$47$	8.64753			1.26137			0.630686	−	0.776038i	$-0.282774\pi$
$47$	8.64753			1.26137			0.630686	+	0.776038i	$0.282774\pi$
$48$		0			0
$49$	−0.580450	+	1.00537i	−0.0829214	+	0.143624i
$50$		0			0
$51$	−7.69492			−1.07750
$52$		0			0
$53$			0.581615i			0.0798909i	0.999202	+	0.0399455i	$0.0127184\pi$
$53$			0.581615i			0.0798909i	−0.999202	+	0.0399455i	$0.987282\pi$
$54$		0			0
$55$	−12.0782	−	3.28155i	−1.62863	−	0.442484i
$56$		0			0
$57$	16.0533			2.12631
$58$		0			0
$59$	−0.510653	+	0.294826i	−0.0664813	+	0.0383830i	−0.532872	−	0.846196i	$-0.678887\pi$
$59$	−0.510653	+	0.294826i	−0.0664813	+	0.0383830i	0.466391	+	0.884579i	$0.345554\pi$
$60$		0			0
$61$	−2.90890	−	5.03836i	−0.372446	−	0.645096i	0.617495	−	0.786575i	$-0.288148\pi$
$61$	−2.90890	−	5.03836i	−0.372446	−	0.645096i	−0.989941	+	0.141479i	$0.954814\pi$
$62$		0			0
$63$	−1.19854	+	2.07593i	−0.151002	+	0.261543i
$64$		0			0
$65$	−6.18340	−	5.17355i	−0.766956	−	0.641700i
$66$		0			0
$67$	6.09997	−	10.5655i	0.745230	−	1.29078i	−0.204857	−	0.978792i	$-0.565673\pi$
$67$	6.09997	−	10.5655i	0.745230	−	1.29078i	0.950087	−	0.311985i	$-0.100994\pi$
$68$		0			0
$69$	−0.349753	−	0.605790i	−0.0421053	−	0.0729286i
$70$		0			0
$71$	2.11676	−	1.22211i	0.251214	−	0.145038i	−0.369106	−	0.929387i	$-0.620336\pi$
$71$	2.11676	−	1.22211i	0.251214	−	0.145038i	0.620320	+	0.784349i	$0.287003\pi$
$72$		0			0
$73$	4.16506			0.487483			0.243741	−	0.969840i	$-0.421625\pi$
$73$	4.16506			0.487483			0.243741	+	0.969840i	$0.421625\pi$
$74$		0			0
$75$	−9.79657	−	0.0683422i	−1.13121	−	0.00789148i
$76$		0			0
$77$			15.9902i			1.82225i
$78$		0			0
$79$	9.85582			1.10887			0.554433	−	0.832228i	$-0.312935\pi$
$79$	9.85582			1.10887			0.554433	+	0.832228i	$0.312935\pi$
$80$		0			0
$81$	5.40661	−	9.36452i	0.600734	−	1.04050i
$82$		0			0
$83$	−6.09174			−0.668655			−0.334327	−	0.942457i	$-0.608509\pi$
$83$	−6.09174			−0.668655			−0.334327	+	0.942457i	$0.608509\pi$
$84$		0			0
$85$	−6.23116	+	6.18785i	−0.675865	+	0.671166i
$86$		0			0
$87$	−6.47825	+	3.74022i	−0.694542	+	0.400994i
$88$		0			0
$89$	0.510653	+	0.294826i	0.0541291	+	0.0312515i	0.526820	−	0.849977i	$-0.323384\pi$
$89$	0.510653	+	0.294826i	0.0541291	+	0.0312515i	−0.472691	+	0.881228i	$0.656717\pi$
$90$		0			0
$91$	−4.30714	+	9.35629i	−0.451511	+	0.980806i
$92$		0			0
$93$	8.29968	−	14.3755i	0.860637	−	1.49067i
$94$		0			0
$95$	12.9996	−	12.9092i	1.33373	−	1.32446i
$96$		0			0
$97$	2.35841	+	4.08489i	0.239460	+	0.414758i	0.960560	−	0.278074i	$-0.0896961\pi$
$97$	2.35841	+	4.08489i	0.239460	+	0.414758i	−0.721099	+	0.692832i	$0.756363\pi$
$98$		0			0
$99$			4.69675i			0.472041i
$100$		0			0
$101$	−1.26701	+	2.19453i	−0.126072	+	0.218364i	−0.922152	−	0.386829i	$-0.873570\pi$
$101$	−1.26701	+	2.19453i	−0.126072	+	0.218364i	0.796079	+	0.605192i	$0.206904\pi$
$102$		0			0
$103$		−	0.930087i		−	0.0916442i	−0.998950	−	0.0458221i	$-0.985409\pi$
$103$		−	0.930087i		−	0.0916442i	0.998950	−	0.0458221i	$-0.0145907\pi$
$104$		0			0
$105$	3.19721	+	12.1008i	0.312016	+	1.18092i
$106$		0			0
$107$	−0.511085	−	0.295075i	−0.0494084	−	0.0285260i	0.475092	−	0.879936i	$-0.342415\pi$
$107$	−0.511085	−	0.295075i	−0.0494084	−	0.0285260i	−0.524501	+	0.851410i	$0.675748\pi$
$108$		0			0
$109$			4.88056i			0.467473i	0.972300	+	0.233737i	$0.0750953\pi$
$109$			4.88056i			0.467473i	−0.972300	+	0.233737i	$0.924905\pi$
$110$		0			0
$111$	12.8262	−	7.40518i	1.21740	−	0.702869i
$112$		0			0
$113$	−6.79482	+	3.92299i	−0.639203	+	0.369044i	−0.784307	−	0.620372i	$-0.786982\pi$
$113$	−6.79482	+	3.92299i	−0.639203	+	0.369044i	0.145104	+	0.989416i	$0.453648\pi$
$114$		0			0
$115$	−0.770365	−	0.209301i	−0.0718370	−	0.0195175i
$116$		0			0
$117$	−1.26513	+	2.74820i	−0.116961	+	0.254071i
$118$		0			0
$119$	9.71604	+	5.60956i	0.890668	+	0.514227i
$120$		0			0
$121$	10.1653	+	17.6067i	0.924114	+	1.60061i
$122$		0			0
$123$	7.75816	+	13.4375i	0.699530	+	1.21162i
$124$		0			0
$125$	−7.98799	+	7.82254i	−0.714467	+	0.699669i
$126$		0			0
$127$	−6.47825	−	3.74022i	−0.574852	−	0.331891i	0.184233	−	0.982883i	$-0.441020\pi$
$127$	−6.47825	−	3.74022i	−0.574852	−	0.331891i	−0.759085	+	0.650992i	$0.774353\pi$
$128$		0			0
$129$	6.55533			0.577165
$130$		0			0
$131$	2.86041			0.249915			0.124957	−	0.992162i	$-0.460121\pi$
$131$	2.86041			0.249915			0.124957	+	0.992162i	$0.460121\pi$
$132$		0			0
$133$	−20.2698	−	11.7028i	−1.75761	−	1.01476i
$134$		0			0
$135$	−2.41845	−	9.15337i	−0.208147	−	0.787797i
$136$		0			0
$137$	−8.18250	−	14.1725i	−0.699078	−	1.21084i	−0.968786	−	0.247897i	$-0.920261\pi$
$137$	−8.18250	−	14.1725i	−0.699078	−	1.21084i	0.269708	−	0.962942i	$-0.413073\pi$
$138$		0			0
$139$	−0.898244	−	1.55580i	−0.0761881	−	0.131962i	0.825414	−	0.564528i	$-0.190942\pi$
$139$	−0.898244	−	1.55580i	−0.0761881	−	0.131962i	−0.901602	+	0.432566i	$0.857608\pi$
$140$		0			0
$141$	−14.6736	−	8.47182i	−1.23574	−	0.713456i
$142$		0			0
$143$	1.85758	+	20.0959i	0.155339	+	1.68051i
$144$		0			0
$145$	−2.23825	+	8.23820i	−0.185876	+	0.684146i
$146$		0			0
$147$	1.96988	−	1.13731i	0.162473	−	0.0938039i
$148$		0			0
$149$	18.5317	−	10.6993i	1.51818	−	0.876521i	0.518407	−	0.855134i	$-0.326525\pi$
$149$	18.5317	−	10.6993i	1.51818	−	0.876521i	0.999771	−	0.0213870i	$-0.00680822\pi$
$150$		0			0
$151$			8.34466i			0.679079i	0.940592	+	0.339540i	$0.110271\pi$
$151$			8.34466i			0.679079i	−0.940592	+	0.339540i	$0.889729\pi$
$152$		0			0
$153$	2.85387	+	1.64768i	0.230722	+	0.133207i
$154$		0			0
$155$	−4.83910	−	18.3151i	−0.388686	−	1.47110i
$156$		0			0
$157$			2.68191i			0.214040i	0.994257	+	0.107020i	$0.0341309\pi$
$157$			2.68191i			0.214040i	−0.994257	+	0.107020i	$0.965869\pi$
$158$		0			0
$159$	0.569797	−	0.986917i	0.0451878	−	0.0782676i
$160$		0			0
$161$			1.01987i			0.0803772i
$162$		0			0
$163$	−3.62354	−	6.27615i	−0.283817	−	0.491586i	0.688504	−	0.725232i	$-0.258268\pi$
$163$	−3.62354	−	6.27615i	−0.283817	−	0.491586i	−0.972322	+	0.233646i	$0.924934\pi$
$164$		0			0
$165$	17.2802	+	17.4012i	1.34526	+	1.35468i
$166$		0			0
$167$	−6.36847	+	11.0305i	−0.492807	+	0.853566i	−0.999966	−	0.00828625i	$-0.997362\pi$
$167$	−6.36847	+	11.0305i	−0.492807	+	0.853566i	0.507159	+	0.861853i	$0.330696\pi$
$168$		0			0
$169$	−4.32616	+	12.2591i	−0.332781	+	0.943004i
$170$		0			0
$171$	−5.95380	−	3.43743i	−0.455298	−	0.262867i
$172$		0			0
$173$	10.1100	−	5.83703i	0.768651	−	0.443781i	−0.0637421	−	0.997966i	$-0.520303\pi$
$173$	10.1100	−	5.83703i	0.768651	−	0.443781i	0.832393	+	0.554185i	$0.186970\pi$
$174$		0			0
$175$	12.3199	+	7.22794i	0.931295	+	0.546381i
$176$		0			0
$177$	1.15534			0.0868407
$178$		0			0
$179$	−0.510653	+	0.884477i	−0.0381680	+	0.0661089i	−0.884478	−	0.466581i	$-0.845486\pi$
$179$	−0.510653	+	0.884477i	−0.0381680	+	0.0661089i	0.846310	+	0.532690i	$0.178819\pi$
$180$		0			0
$181$	13.8771			1.03148			0.515739	−	0.856745i	$-0.327517\pi$
$181$	13.8771			1.03148			0.515739	+	0.856745i	$0.327517\pi$
$182$		0			0
$183$			11.3992i			0.842651i
$184$		0			0
$185$	4.43146	−	16.3106i	0.325807	−	1.19918i
$186$		0			0
$187$	21.9823			1.60751
$188$		0			0
$189$	−10.4749	+	6.04767i	−0.761935	+	0.439904i
$190$		0			0
$191$	−3.24135	−	5.61418i	−0.234536	−	0.406228i	0.724602	−	0.689168i	$-0.242024\pi$
$191$	−3.24135	−	5.61418i	−0.234536	−	0.406228i	−0.959138	+	0.282940i	$0.908690\pi$
$192$		0			0
$193$	10.9599	−	18.9831i	0.788909	−	1.36643i	−0.137726	−	0.990470i	$-0.543979\pi$
$193$	10.9599	−	18.9831i	0.788909	−	1.36643i	0.926636	−	0.375961i	$-0.122687\pi$
$194$		0			0
$195$	5.42391	+	14.8365i	0.388415	+	1.06247i
$196$		0			0
$197$	9.52412	−	16.4963i	0.678566	−	1.17531i	−0.296847	−	0.954925i	$-0.595935\pi$
$197$	9.52412	−	16.4963i	0.678566	−	1.17531i	0.975413	−	0.220385i	$-0.0707314\pi$
$198$		0			0
$199$	−5.84746	−	10.1281i	−0.414516	−	0.717962i	0.580862	−	0.814002i	$-0.302716\pi$
$199$	−5.84746	−	10.1281i	−0.414516	−	0.717962i	−0.995377	+	0.0960401i	$0.969382\pi$
$200$		0			0
$201$	−20.7016	+	11.9521i	−1.46018	+	0.843033i
$202$		0			0
$203$	10.9064			0.765479
$204$		0			0
$205$	17.0881	+	4.64269i	1.19349	+	0.324259i
$206$		0			0
$207$			0.299565i			0.0208212i
$208$		0			0
$209$	−45.8600			−3.17220
$210$		0			0
$211$	−6.59946	+	11.4306i	−0.454326	+	0.786915i	−0.998649	−	0.0519600i	$-0.983453\pi$
$211$	−6.59946	+	11.4306i	−0.454326	+	0.786915i	0.544323	+	0.838876i	$0.316786\pi$
$212$		0			0
$213$	−4.78913			−0.328146
$214$		0			0
$215$	5.30835	−	5.27144i	0.362026	−	0.359510i
$216$		0			0
$217$	−20.9593	+	12.1008i	−1.42281	+	0.821459i
$218$		0			0
$219$	−7.06751	−	4.08043i	−0.477578	−	0.275730i
$220$		0			0
$221$	12.8625	+	5.92120i	0.865223	+	0.398303i
$222$		0			0
$223$	1.31858	−	2.28384i	0.0882985	−	0.152938i	−0.818493	−	0.574516i	$-0.805190\pi$
$223$	1.31858	−	2.28384i	0.0882985	−	0.152938i	0.906792	+	0.421578i	$0.138524\pi$
$224$		0			0
$225$	3.61869	+	2.12305i	0.241246	+	0.141536i
$226$		0			0
$227$	−10.6149	−	18.3855i	−0.704535	−	1.22029i	−0.966859	−	0.255311i	$-0.917822\pi$
$227$	−10.6149	−	18.3855i	−0.704535	−	1.22029i	0.262324	−	0.964980i	$-0.415511\pi$
$228$		0			0
$229$		−	10.0154i		−	0.661838i	−0.943659	−	0.330919i	$-0.892641\pi$
$229$		−	10.0154i		−	0.661838i	0.943659	−	0.330919i	$-0.107359\pi$
$230$		0			0
$231$	15.6653	−	27.1330i	1.03070	−	1.78522i
$232$		0			0
$233$			17.9666i			1.17703i	0.808486	+	0.588515i	$0.200287\pi$
$233$			17.9666i			1.17703i	−0.808486	+	0.588515i	$0.799713\pi$
$234$		0			0
$235$	−18.6949	+	4.93946i	−1.21952	+	0.322215i
$236$		0			0
$237$	−16.7239	−	9.65556i	−1.08634	−	0.627196i
$238$		0			0
$239$		−	12.6771i		−	0.820014i	−0.912082	−	0.410007i	$-0.865526\pi$
$239$		−	12.6771i		−	0.820014i	0.912082	−	0.410007i	$-0.134474\pi$
$240$		0			0
$241$	7.38988	−	4.26655i	0.476024	−	0.274833i	−0.242734	−	0.970093i	$-0.578044\pi$
$241$	7.38988	−	4.26655i	0.476024	−	0.274833i	0.718758	+	0.695260i	$0.244711\pi$
$242$		0			0
$243$	−7.34826	+	4.24252i	−0.471391	+	0.272158i
$244$		0			0
$245$	0.680597	−	2.50504i	0.0434818	−	0.160041i
$246$		0			0
$247$	−26.8340	−	12.3529i	−1.70740	−	0.785998i
$248$		0			0
$249$	10.3368	+	5.96796i	0.655069	+	0.378204i
$250$		0			0
$251$	−9.86247	−	17.0823i	−0.622514	−	1.07823i	−0.989016	−	0.147808i	$-0.952778\pi$
$251$	−9.86247	−	17.0823i	−0.622514	−	1.07823i	0.366502	−	0.930417i	$-0.380555\pi$
$252$		0			0
$253$	0.999150	+	1.73058i	0.0628160	+	0.108800i
$254$		0			0
$255$	16.6355	−	4.39534i	1.04176	−	0.275247i
$256$		0			0
$257$	−20.7648	−	11.9885i	−1.29527	−	0.747824i	−0.315687	−	0.948863i	$-0.602235\pi$
$257$	−20.7648	−	11.9885i	−1.29527	−	0.747824i	−0.979583	+	0.201039i	$0.935568\pi$
$258$		0			0
$259$	−21.5934			−1.34175
$260$		0			0
$261$	3.20351			0.198292
$262$		0			0
$263$	0.547238	+	0.315948i	0.0337441	+	0.0194822i	0.516777	−	0.856120i	$-0.327132\pi$
$263$	0.547238	+	0.315948i	0.0337441	+	0.0194822i	−0.483033	+	0.875602i	$0.660465\pi$
$264$		0			0
$265$	−0.332218	−	1.25738i	−0.0204080	−	0.0772404i
$266$		0			0
$267$	−0.577670	−	1.00055i	−0.0353528	−	0.0612329i
$268$		0			0
$269$	−3.68656	−	6.38531i	−0.224774	−	0.389319i	0.731478	−	0.681865i	$-0.238831\pi$
$269$	−3.68656	−	6.38531i	−0.224774	−	0.389319i	−0.956252	+	0.292546i	$0.905498\pi$
$270$		0			0
$271$	−10.0955	−	5.82862i	−0.613255	−	0.354063i	0.160983	−	0.986957i	$-0.448534\pi$
$271$	−10.0955	−	5.82862i	−0.613255	−	0.354063i	−0.774238	+	0.632894i	$0.781867\pi$
$272$		0			0
$273$	16.4748	−	11.6567i	0.997100	−	0.705494i
$274$		0			0
$275$	27.9862	+	0.195235i	1.68763	+	0.0117731i
$276$		0			0
$277$	−0.798087	+	0.460776i	−0.0479524	+	0.0276853i	−0.523785	−	0.851851i	$-0.675480\pi$
$277$	−0.798087	+	0.460776i	−0.0479524	+	0.0276853i	0.475832	+	0.879536i	$0.342147\pi$
$278$		0			0
$279$	−6.15632	+	3.55435i	−0.368569	+	0.212793i
$280$		0			0
$281$			13.3326i			0.795358i	0.917525	+	0.397679i	$0.130184\pi$
$281$			13.3326i			0.795358i	−0.917525	+	0.397679i	$0.869816\pi$
$282$		0			0
$283$	4.50837	+	2.60291i	0.267995	+	0.154727i	0.627976	−	0.778233i	$-0.283884\pi$
$283$	4.50837	+	2.60291i	0.267995	+	0.154727i	−0.359981	+	0.932960i	$0.617217\pi$
$284$		0			0
$285$	−34.7053	+	9.16965i	−2.05577	+	0.543163i
$286$		0			0
$287$		−	22.6226i		−	1.33537i
$288$		0			0
$289$	−0.788317	+	1.36541i	−0.0463716	+	0.0803180i
$290$		0			0
$291$		−	9.24197i		−	0.541774i
$292$		0			0
$293$	7.52296	+	13.0302i	0.439496	+	0.761230i	0.997651	−	0.0685075i	$-0.0218237\pi$
$293$	7.52296	+	13.0302i	0.439496	+	0.761230i	−0.558155	+	0.829737i	$0.688490\pi$
$294$		0			0
$295$	0.935567	−	0.929063i	0.0544708	−	0.0540921i
$296$		0			0
$297$	−11.8496	+	20.5241i	−0.687583	+	1.19093i
$298$		0			0
$299$	0.118479	+	1.28174i	0.00685180	+	0.0741251i
$300$		0			0
$301$	−8.27712	−	4.77880i	−0.477085	−	0.275445i
$302$		0			0
$303$	4.29988	−	2.48253i	0.247021	−	0.142618i
$304$		0			0
$305$	9.16660	+	9.23077i	0.524878	+	0.528552i
$306$		0			0
$307$	−4.41991			−0.252258			−0.126129	−	0.992014i	$-0.540255\pi$
$307$	−4.41991			−0.252258			−0.126129	+	0.992014i	$0.540255\pi$
$308$		0			0
$309$	−0.911189	+	1.57822i	−0.0518357	+	0.0897821i
$310$		0			0
$311$	32.2076			1.82633			0.913164	−	0.407593i	$-0.133632\pi$
$311$	32.2076			1.82633			0.913164	+	0.407593i	$0.133632\pi$
$312$		0			0
$313$		−	18.8549i		−	1.06574i	−0.846196	−	0.532872i	$-0.821113\pi$
$313$		−	18.8549i		−	1.06574i	0.846196	−	0.532872i	$-0.178887\pi$
$314$		0			0
$315$	1.40533	−	5.17253i	0.0791814	−	0.291439i
$316$		0			0
$317$	23.9904			1.34743			0.673716	−	0.738990i	$-0.264697\pi$
$317$	23.9904			1.34743			0.673716	+	0.738990i	$0.264697\pi$
$318$		0			0
$319$	18.5066	−	10.6848i	1.03617	−	0.598234i
$320$		0			0
$321$	0.578158	+	1.00140i	0.0322697	+	0.0558927i
$322$		0			0
$323$	−16.0883	+	27.8657i	−0.895175	+	1.55049i
$324$		0			0
$325$	16.3229	+	7.65264i	0.905432	+	0.424492i
$326$		0			0
$327$	4.78140	−	8.28162i	0.264412	−	0.457975i
$328$		0			0
$329$	12.3518	+	21.3940i	0.680978	+	1.17949i
$330$		0			0
$331$	−6.24135	+	3.60345i	−0.343056	+	0.198063i	−0.661622	−	0.749837i	$-0.730132\pi$
$331$	−6.24135	+	3.60345i	−0.343056	+	0.198063i	0.318567	+	0.947900i	$0.396798\pi$
$332$		0			0
$333$	−6.34257			−0.347570
$334$		0			0
$335$	−7.15243	+	26.3256i	−0.390779	+	1.43832i
$336$		0			0
$337$			20.1923i			1.09995i	0.835183	+	0.549973i	$0.185362\pi$
$337$			20.1923i			1.09995i	−0.835183	+	0.549973i	$0.814638\pi$
$338$		0			0
$339$	15.3731			0.834953
$340$		0			0
$341$	−23.7099	+	41.0668i	−1.28396	+	2.22389i
$342$		0			0
$343$	16.6807			0.900675
$344$		0			0
$345$	1.10215	+	1.10987i	0.0593379	+	0.0597532i
$346$		0			0
$347$	7.21747	−	4.16701i	0.387454	−	0.223697i	−0.293602	−	0.955928i	$-0.594854\pi$
$347$	7.21747	−	4.16701i	0.387454	−	0.223697i	0.681056	+	0.732231i	$0.261521\pi$
$348$		0			0
$349$	19.2518	+	11.1150i	1.03052	+	0.594973i	0.917135	−	0.398577i	$-0.130496\pi$
$349$	19.2518	+	11.1150i	1.03052	+	0.594973i	0.113389	+	0.993551i	$0.463829\pi$
$350$		0			0
$351$	−12.4619	+	8.81739i	−0.665169	+	0.470638i
$352$		0			0
$353$	−11.8106	+	20.4565i	−0.628613	+	1.08879i	0.359217	+	0.933254i	$0.383044\pi$
$353$	−11.8106	+	20.4565i	−0.628613	+	1.08879i	−0.987830	+	0.155536i	$0.950290\pi$
$354$		0			0
$355$	−3.87812	+	3.85116i	−0.205829	+	0.204398i
$356$		0			0
$357$	−10.9912	−	19.0372i	−0.581714	−	1.00756i
$358$		0			0
$359$		−	2.91598i		−	0.153899i	−0.997035	−	0.0769497i	$-0.975482\pi$
$359$		−	2.91598i		−	0.153899i	0.997035	−	0.0769497i	$-0.0245181\pi$
$360$		0			0
$361$	24.0637	−	41.6795i	1.26651	−	2.19366i
$362$		0			0
$363$		−	39.8348i		−	2.09079i
$364$		0			0
$365$	−9.00436	+	2.37908i	−0.471310	+	0.124527i
$366$		0			0
$367$	13.0933	+	7.55944i	0.683467	+	0.394600i	0.801160	−	0.598450i	$-0.204217\pi$
$367$	13.0933	+	7.55944i	0.683467	+	0.394600i	−0.117693	+	0.993050i	$0.537550\pi$
$368$		0			0
$369$		−	6.64489i		−	0.345919i
$370$		0			0
$371$	−1.43891	+	0.830758i	−0.0747047	+	0.0431308i
$372$		0			0
$373$	9.15978	−	5.28840i	0.474275	−	0.273823i	−0.243752	−	0.969838i	$-0.578378\pi$
$373$	9.15978	−	5.28840i	0.474275	−	0.273823i	0.718028	+	0.696014i	$0.245045\pi$
$374$		0			0
$375$	21.2181	−	5.44805i	1.09570	−	0.281336i
$376$		0			0
$377$	13.7068	−	1.26700i	0.705937	−	0.0652537i
$378$		0			0
$379$	5.38724	+	3.11032i	0.276724	+	0.159767i	0.631939	−	0.775018i	$-0.282259\pi$
$379$	5.38724	+	3.11032i	0.276724	+	0.159767i	−0.355215	+	0.934784i	$0.615592\pi$
$380$		0			0
$381$	7.32845	+	12.6932i	0.375448	+	0.650295i
$382$		0			0
$383$	6.49304	+	11.2463i	0.331779	+	0.574657i	0.982861	−	0.184350i	$-0.0590180\pi$
$383$	6.49304	+	11.2463i	0.331779	+	0.574657i	−0.651082	+	0.759007i	$0.725685\pi$
$384$		0			0
$385$	−9.13358	−	34.5688i	−0.465490	−	1.76179i
$386$		0			0
$387$	−2.43122	−	1.40367i	−0.123586	−	0.0713523i
$388$		0			0
$389$	−0.474689			−0.0240677			−0.0120338	−	0.999928i	$-0.503831\pi$
$389$	−0.474689			−0.0240677			−0.0120338	+	0.999928i	$0.503831\pi$
$390$		0			0
$391$	1.40206			0.0709052
$392$		0			0
$393$	−4.85370	−	2.80229i	−0.244837	−	0.141357i
$394$		0			0
$395$	−21.3071	+	5.62964i	−1.07208	+	0.283258i
$396$		0			0
$397$	−12.5054	−	21.6600i	−0.627629	−	1.08709i	−0.988026	−	0.154286i	$-0.950692\pi$
$397$	−12.5054	−	21.6600i	−0.627629	−	1.08709i	0.360397	−	0.932799i	$-0.382641\pi$
$398$		0			0
$399$	22.9300	+	39.7159i	1.14793	+	1.98828i
$400$		0			0
$401$	11.2970	+	6.52234i	0.564147	+	0.325710i	0.754808	−	0.655946i	$-0.227730\pi$
$401$	11.2970	+	6.52234i	0.564147	+	0.325710i	−0.190661	+	0.981656i	$0.561063\pi$
$402$		0			0
$403$	−24.9352	+	17.6428i	−1.24211	+	0.878850i
$404$		0			0
$405$	−6.33943	+	23.3332i	−0.315009	+	1.15944i
$406$		0			0
$407$	−36.6408	+	21.1546i	−1.81622	+	1.04859i
$408$		0			0
$409$	10.0173	−	5.78349i	0.495324	−	0.285975i	−0.231457	−	0.972845i	$-0.574349\pi$
$409$	10.0173	−	5.78349i	0.495324	−	0.285975i	0.726780	+	0.686870i	$0.241016\pi$
$410$		0			0
$411$			32.0650i			1.58165i
$412$		0			0
$413$	−1.45880	−	0.842237i	−0.0717827	−	0.0414438i
$414$		0			0
$415$	13.1696	−	3.47960i	0.646471	−	0.170807i
$416$		0			0
$417$			3.51997i			0.172374i
$418$		0			0
$419$	8.22688	−	14.2494i	0.401909	−	0.696128i	−0.592047	−	0.805904i	$-0.701680\pi$
$419$	8.22688	−	14.2494i	0.401909	−	0.696128i	0.993956	+	0.109776i	$0.0350133\pi$
$420$		0			0
$421$			22.2913i			1.08641i	0.839599	+	0.543206i	$0.182790\pi$
$421$			22.2913i			1.08641i	−0.839599	+	0.543206i	$0.817210\pi$
$422$		0			0
$423$	3.62807	+	6.28400i	0.176403	+	0.305539i
$424$		0			0
$425$	9.93654	−	16.9366i	0.481993	−	0.821547i
$426$		0			0
$427$	8.30993	−	14.3932i	0.402146	−	0.696537i
$428$		0			0
$429$	16.5355	−	35.9197i	0.798344	−	1.73422i
$430$		0			0
$431$	−23.4893	−	13.5616i	−1.13144	−	0.653238i	−0.187145	−	0.982332i	$-0.559923\pi$
$431$	−23.4893	−	13.5616i	−1.13144	−	0.653238i	−0.944297	+	0.329094i	$0.893257\pi$
$432$		0			0
$433$	19.0881	−	11.0205i	0.917315	−	0.529612i	0.0345372	−	0.999403i	$-0.489004\pi$
$433$	19.0881	−	11.0205i	0.917315	−	0.529612i	0.882777	+	0.469792i	$0.155671\pi$
$434$		0			0
$435$	11.8688	−	11.7863i	0.569065	−	0.565109i
$436$		0			0
$437$	−2.92501			−0.139922
$438$		0			0
$439$	−13.1843	+	22.8358i	−0.629251	+	1.08989i	0.358451	+	0.933548i	$0.383305\pi$
$439$	−13.1843	+	22.8358i	−0.629251	+	1.08989i	−0.987702	+	0.156346i	$0.950028\pi$
$440$		0			0
$441$	−0.974111			−0.0463862
$442$		0			0
$443$			40.3081i			1.91510i	0.288274	+	0.957548i	$0.406918\pi$
$443$			40.3081i			1.91510i	−0.288274	+	0.957548i	$0.593082\pi$
$444$		0			0
$445$	−1.27238	−	0.345693i	−0.0603164	−	0.0163874i
$446$		0			0
$447$	−41.9276			−1.98311
$448$		0			0
$449$	−0.993353	+	0.573512i	−0.0468792	+	0.0270657i	−0.523256	−	0.852175i	$-0.675283\pi$
$449$	−0.993353	+	0.573512i	−0.0468792	+	0.0270657i	0.476377	+	0.879241i	$0.341950\pi$
$450$		0			0
$451$	−22.1630	−	38.3874i	−1.04361	−	1.80759i
$452$		0			0
$453$	8.17511	−	14.1597i	0.384100	−	0.665281i
$454$		0			0
$455$	3.96722	−	22.6874i	0.185986	−	1.06360i
$456$		0			0
$457$	−5.24440	+	9.08357i	−0.245323	+	0.424912i	−0.962222	−	0.272265i	$-0.912227\pi$
$457$	−5.24440	+	9.08357i	−0.245323	+	0.424912i	0.716899	+	0.697177i	$0.245561\pi$
$458$		0			0
$459$	8.31398	+	14.4002i	0.388063	+	0.672145i
$460$		0			0
$461$	−2.20580	+	1.27352i	−0.102734	+	0.0593138i	−0.550487	−	0.834844i	$-0.685558\pi$
$461$	−2.20580	+	1.27352i	−0.102734	+	0.0593138i	0.447752	+	0.894158i	$0.352225\pi$
$462$		0			0
$463$	−3.25551			−0.151296			−0.0756482	−	0.997135i	$-0.524103\pi$
$463$	−3.25551			−0.151296			−0.0756482	+	0.997135i	$0.524103\pi$
$464$		0			0
$465$	−9.73166	+	35.8188i	−0.451295	+	1.66106i
$466$		0			0
$467$			0.164237i			0.00759998i	0.999993	+	0.00379999i	$0.00120958\pi$
$467$			0.164237i			0.00759998i	−0.999993	+	0.00379999i	$0.998790\pi$
$468$		0			0
$469$	34.8519			1.60931
$470$		0			0
$471$	2.62742	−	4.55082i	0.121065	−	0.209691i
$472$		0			0
$473$	−18.7268			−0.861059
$474$		0			0
$475$	−20.7298	+	35.3335i	−0.951149	+	1.62121i
$476$		0			0
$477$	−0.422649	+	0.244017i	−0.0193518	+	0.0111727i
$478$		0			0
$479$	−6.34346	−	3.66240i	−0.289840	−	0.167339i	0.348030	−	0.937483i	$-0.386851\pi$
$479$	−6.34346	−	3.66240i	−0.289840	−	0.167339i	−0.637870	+	0.770144i	$0.720184\pi$
$480$		0			0
$481$	−27.1378	+	2.50850i	−1.23738	+	0.114378i
$482$		0			0
$483$	0.999150	−	1.73058i	0.0454629	−	0.0787440i
$484$		0			0
$485$	−7.43190	−	7.48392i	−0.337465	−	0.339827i
$486$		0			0
$487$	15.9481	+	27.6228i	0.722675	+	1.25171i	0.959924	+	0.280261i	$0.0904211\pi$
$487$	15.9481	+	27.6228i	0.722675	+	1.25171i	−0.237248	+	0.971449i	$0.576246\pi$
$488$		0			0
$489$			14.1996i			0.642130i
$490$		0			0
$491$	3.47434	−	6.01773i	0.156795	−	0.271576i	−0.776916	−	0.629604i	$-0.783217\pi$
$491$	3.47434	−	6.01773i	0.156795	−	0.271576i	0.933711	+	0.358027i	$0.116551\pi$
$492$		0			0
$493$		−	14.9935i		−	0.675272i
$494$		0			0
$495$	−2.68278	−	10.1538i	−0.120582	−	0.456380i
$496$		0			0
$497$	6.04702	+	3.49125i	0.271246	+	0.156604i
$498$		0			0
$499$		−	14.5396i		−	0.650881i	−0.945563	−	0.325440i	$-0.894487\pi$
$499$		−	14.5396i		−	0.650881i	0.945563	−	0.325440i	$-0.105513\pi$
$500$		0			0
$501$	21.6128	−	12.4781i	0.965587	−	0.557482i
$502$		0			0
$503$	25.8715	−	14.9369i	1.15355	−	0.666003i	0.203801	−	0.979012i	$-0.434670\pi$
$503$	25.8715	−	14.9369i	1.15355	−	0.666003i	0.949750	+	0.313009i	$0.101337\pi$
$504$		0			0
$505$	1.48561	−	5.46803i	0.0661090	−	0.243324i
$506$		0			0
$507$	19.3508	−	16.5636i	0.859401	−	0.735616i
$508$		0			0
$509$	−19.6483	−	11.3440i	−0.870896	−	0.502812i	−0.00325001	−	0.999995i	$-0.501035\pi$
$509$	−19.6483	−	11.3440i	−0.870896	−	0.502812i	−0.867646	+	0.497183i	$0.834368\pi$
$510$		0			0
$511$	5.94922	+	10.3043i	0.263178	+	0.455837i
$512$		0			0
$513$	−17.3448	−	30.0421i	−0.765791	−	1.32639i
$514$		0			0
$515$	0.531265	+	2.01074i	0.0234104	+	0.0886037i
$516$		0			0
$517$	41.9185	+	24.2017i	1.84358	+	1.06439i
$518$		0			0
$519$	−22.8737			−1.00404
$520$		0			0
$521$	27.0167			1.18362			0.591812	−	0.806076i	$-0.298413\pi$
$521$	27.0167			1.18362			0.591812	+	0.806076i	$0.298413\pi$
$522$		0			0
$523$	19.6728	+	11.3581i	0.860232	+	0.496655i	0.864090	−	0.503337i	$-0.167895\pi$
$523$	19.6728	+	11.3581i	0.860232	+	0.496655i	−0.00385780	+	0.999993i	$0.501228\pi$
$524$		0			0
$525$	−13.8240	−	24.3343i	−0.603329	−	1.06204i
$526$		0			0
$527$	16.6355	+	28.8135i	0.724654	+	1.25514i
$528$		0			0
$529$	−11.4363	−	19.8082i	−0.497229	−	0.861226i
$530$		0			0
$531$	−0.428489	−	0.247388i	−0.0185948	−	0.0107357i
$532$		0			0
$533$	−2.62807	−	28.4314i	−0.113835	−	1.23150i
$534$		0			0
$535$	1.27345	+	0.345985i	0.0550561	+	0.0149583i
$536$		0			0
$537$	1.73301	−	1.00055i	0.0747849	−	0.0431771i
$538$		0			0
$539$	−5.62742	+	3.24899i	−0.242390	+	0.139944i
$540$		0			0
$541$		−	25.2514i		−	1.08564i	−0.839848	−	0.542821i	$-0.817356\pi$
$541$		−	25.2514i		−	1.08564i	0.839848	−	0.542821i	$-0.182644\pi$
$542$		0			0
$543$	−23.5475	−	13.5952i	−1.01052	−	0.583424i
$544$		0			0
$545$	−2.78778	−	10.5512i	−0.119415	−	0.451964i
$546$		0			0
$547$		−	36.9221i		−	1.57867i	−0.613960	−	0.789337i	$-0.710424\pi$
$547$		−	36.9221i		−	1.57867i	0.613960	−	0.789337i	$-0.289576\pi$
$548$		0			0
$549$	2.44086	−	4.22769i	0.104173	−	0.180433i
$550$		0			0
$551$			31.2797i			1.33256i
$552$		0			0
$553$	14.0777	+	24.3833i	0.598645	+	1.03688i
$554$		0			0
$555$	−23.4988	+	23.3354i	−0.997468	+	0.990534i
$556$		0			0
$557$	13.3951	−	23.2010i	0.567570	−	0.983060i	−0.429236	−	0.903192i	$-0.641217\pi$
$557$	13.3951	−	23.2010i	0.567570	−	0.983060i	0.996806	−	0.0798671i	$-0.0254496\pi$
$558$		0			0
$559$	−10.9576	−	5.04429i	−0.463456	−	0.213351i
$560$		0			0
$561$	−37.3008	−	21.5357i	−1.57484	−	0.909236i
$562$		0			0
$563$	−12.4689	+	7.19895i	−0.525503	+	0.303399i	−0.739183	−	0.673504i	$-0.764788\pi$
$563$	−12.4689	+	7.19895i	−0.525503	+	0.303399i	0.213680	+	0.976904i	$0.431455\pi$
$564$		0			0
$565$	12.4488	−	12.3622i	0.523724	−	0.520083i
$566$		0			0
$567$	30.8904			1.29728
$568$		0			0
$569$	−15.4173	+	26.7035i	−0.646325	+	1.11947i	0.337669	+	0.941265i	$0.390362\pi$
$569$	−15.4173	+	26.7035i	−0.646325	+	1.11947i	−0.983994	+	0.178203i	$0.942972\pi$
$570$		0			0
$571$	36.5884			1.53118			0.765588	−	0.643331i	$-0.222448\pi$
$571$	36.5884			1.53118			0.765588	+	0.643331i	$0.222448\pi$
$572$		0			0
$573$			12.7020i			0.530632i
$574$		0			0
$575$	1.78499	+	0.0124523i	0.0744393	+	0.000519299i
$576$		0			0
$577$	17.3008			0.720241			0.360120	−	0.932906i	$-0.382736\pi$
$577$	17.3008			0.720241			0.360120	+	0.932906i	$0.382736\pi$
$578$		0			0
$579$	−37.1947	+	21.4744i	−1.54576	+	0.892444i
$580$		0			0
$581$	−8.70122	−	15.0710i	−0.360987	−	0.625249i
$582$		0			0
$583$	−1.62776	+	2.81936i	−0.0674147	+	0.116766i
$584$		0			0
$585$	1.16528	−	6.66393i	0.0481784	−	0.275519i
$586$		0			0
$587$	−3.93725	+	6.81951i	−0.162508	+	0.281471i	−0.935767	−	0.352618i	$-0.885292\pi$
$587$	−3.93725	+	6.81951i	−0.162508	+	0.281471i	0.773260	+	0.634089i	$0.218625\pi$
$588$		0			0
$589$	−34.7053	−	60.1114i	−1.43001	−	2.47685i
$590$		0			0
$591$	−32.3222	+	18.6612i	−1.32956	+	0.767619i
$592$		0			0
$593$	−43.2400			−1.77565			−0.887826	−	0.460179i	$-0.847785\pi$
$593$	−43.2400			−1.77565			−0.887826	+	0.460179i	$0.847785\pi$
$594$		0			0
$595$	−24.2091	−	6.57740i	−0.992476	−	0.269647i
$596$		0			0
$597$			22.9146i			0.937832i
$598$		0			0
$599$	2.10157			0.0858676			0.0429338	−	0.999078i	$-0.486330\pi$
$599$	2.10157			0.0858676			0.0429338	+	0.999078i	$0.486330\pi$
$600$		0			0
$601$	17.2987	−	29.9623i	0.705630	−	1.22219i	−0.260833	−	0.965384i	$-0.583997\pi$
$601$	17.2987	−	29.9623i	0.705630	−	1.22219i	0.966464	−	0.256804i	$-0.0826694\pi$
$602$		0			0
$603$	10.2370			0.416882
$604$		0			0
$605$	−32.0330	−	32.2573i	−1.30233	−	1.31145i
$606$		0			0
$607$	−8.67746	+	5.00993i	−0.352207	+	0.203347i	−0.665657	−	0.746258i	$-0.731849\pi$
$607$	−8.67746	+	5.00993i	−0.352207	+	0.203347i	0.313450	+	0.949605i	$0.398515\pi$
$608$		0			0
$609$	−18.5066	−	10.6848i	−0.749926	−	0.432970i
$610$		0			0
$611$	18.0087	+	25.4524i	0.728555	+	1.02969i
$612$		0			0
$613$	−20.5432	+	35.5818i	−0.829731	+	1.43714i	0.0685186	+	0.997650i	$0.478173\pi$
$613$	−20.5432	+	35.5818i	−0.829731	+	1.43714i	−0.898249	+	0.439486i	$0.855161\pi$
$614$		0			0
$615$	−24.4477	−	24.6189i	−0.985828	−	0.992729i
$616$		0			0
$617$	−1.17550	−	2.03603i	−0.0473238	−	0.0819673i	0.841393	−	0.540423i	$-0.181736\pi$
$617$	−1.17550	−	2.03603i	−0.0473238	−	0.0819673i	−0.888717	+	0.458456i	$0.848403\pi$
$618$		0			0
$619$		−	14.1595i		−	0.569117i	−0.958659	−	0.284559i	$-0.908153\pi$
$619$		−	14.1595i		−	0.569117i	0.958659	−	0.284559i	$-0.0918471\pi$
$620$		0			0
$621$	−0.755781	+	1.30905i	−0.0303285	+	0.0525304i
$622$		0			0
$623$			1.68447i			0.0674870i
$624$		0			0
$625$	12.8008	−	21.4741i	0.512034	−	0.858965i
$626$		0			0
$627$	77.8178	+	44.9281i	3.10774	+	1.79426i
$628$		0			0
$629$			29.6853i			1.18363i
$630$		0			0
$631$	−5.36835	+	3.09942i	−0.213711	+	0.123386i	−0.603035	−	0.797715i	$-0.706042\pi$
$631$	−5.36835	+	3.09942i	−0.213711	+	0.123386i	0.389324	+	0.921101i	$0.372709\pi$
$632$		0			0
$633$	22.3967	−	12.9307i	0.890189	−	0.513951i
$634$		0			0
$635$	16.1416	+	4.38554i	0.640561	+	0.174035i
$636$		0			0
$637$	−4.16792	+	0.385264i	−0.165139	+	0.0152647i
$638$		0			0
$639$	1.77618	+	1.02548i	0.0702645	+	0.0405672i
$640$		0			0
$641$	−7.85182	−	13.5997i	−0.310128	−	0.537158i	0.668262	−	0.743926i	$-0.267039\pi$
$641$	−7.85182	−	13.5997i	−0.310128	−	0.537158i	−0.978390	+	0.206769i	$0.933705\pi$
$642$		0			0
$643$	−21.1891	−	36.7006i	−0.835616	−	1.44733i	−0.893528	−	0.449008i	$-0.851777\pi$
$643$	−21.1891	−	36.7006i	−0.835616	−	1.44733i	0.0579112	−	0.998322i	$-0.481556\pi$
$644$		0			0
$645$	−14.1718	+	3.74440i	−0.558016	+	0.147436i
$646$		0			0
$647$	−32.3398	−	18.6714i	−1.27141	−	0.734048i	−0.296155	−	0.955140i	$-0.595705\pi$
$647$	−32.3398	−	18.6714i	−1.27141	−	0.734048i	−0.975253	+	0.221092i	$0.929038\pi$
$648$		0			0
$649$	−3.30049			−0.129556
$650$		0			0
$651$	47.4199			1.85853
$652$		0			0
$653$	30.8970	+	17.8384i	1.20909	+	0.698069i	0.962561	−	0.271066i	$-0.0873761\pi$
$653$	30.8970	+	17.8384i	1.20909	+	0.698069i	0.246531	+	0.969135i	$0.420709\pi$
$654$		0			0
$655$	−6.18386	+	1.63386i	−0.241623	+	0.0638403i
$656$		0			0
$657$	1.74745	+	3.02667i	0.0681745	+	0.118082i
$658$		0			0
$659$	6.51065	+	11.2768i	0.253619	+	0.439281i	0.964520	−	0.264012i	$-0.0850457\pi$
$659$	6.51065	+	11.2768i	0.253619	+	0.439281i	−0.710900	+	0.703293i	$0.751712\pi$
$660$		0			0
$661$	−3.12096	−	1.80189i	−0.121391	−	0.0700853i	0.438075	−	0.898938i	$-0.355660\pi$
$661$	−3.12096	−	1.80189i	−0.121391	−	0.0700853i	−0.559466	+	0.828853i	$0.688994\pi$
$662$		0			0
$663$	−16.0249	−	22.6485i	−0.622355	−	0.879597i
$664$		0			0
$665$	50.5055	+	13.7219i	1.95852	+	0.532113i
$666$		0			0
$667$	1.18037	−	0.681490i	0.0457043	−	0.0263874i
$668$		0			0
$669$	−4.47488	+	2.58357i	−0.173009	+	0.0998867i
$670$		0			0
$671$		−	32.5643i		−	1.25713i
$672$		0			0
$673$	17.1417	+	9.89678i	0.660765	+	0.381493i	0.792568	−	0.609783i	$-0.208743\pi$
$673$	17.1417	+	9.89678i	0.660765	+	0.381493i	−0.131804	+	0.991276i	$0.542077\pi$
$674$		0			0
$675$	10.4568	+	18.4071i	0.402483	+	0.708489i
$676$		0			0
$677$			42.2737i			1.62471i	0.583163	+	0.812355i	$0.301815\pi$
$677$			42.2737i			1.62471i	−0.583163	+	0.812355i	$0.698185\pi$
$678$		0			0
$679$	−6.73734	+	11.6694i	−0.258556	+	0.447831i
$680$		0			0
$681$			41.5968i			1.59399i
$682$		0			0
$683$	−8.70386	−	15.0755i	−0.333044	−	0.576849i	0.650063	−	0.759880i	$-0.274742\pi$
$683$	−8.70386	−	15.0755i	−0.333044	−	0.576849i	−0.983107	+	0.183031i	$0.941409\pi$
$684$		0			0
$685$	25.7849	+	25.9654i	0.985192	+	0.992088i
$686$		0			0
$687$	−9.81193	+	16.9948i	−0.374348	+	0.648390i
$688$		0			0
$689$	−1.71187	+	1.21123i	−0.0652172	+	0.0461441i
$690$		0			0
$691$	−39.3977	−	22.7463i	−1.49876	−	0.865308i	−0.498759	−	0.866741i	$-0.666211\pi$
$691$	−39.3977	−	22.7463i	−1.49876	−	0.865308i	−0.999999	+	0.00143250i	$0.999544\pi$
$692$		0			0
$693$	−11.6198	+	6.70867i	−0.441398	+	0.254841i
$694$		0			0
$695$	2.83057	+	2.85039i	0.107370	+	0.108121i
$696$		0			0
$697$	−31.1002			−1.17801
$698$		0			0
$699$	17.6015	−	30.4867i	0.665751	−	1.15311i
$700$		0			0
$701$	−18.7036			−0.706427			−0.353213	−	0.935543i	$-0.614911\pi$
$701$	−18.7036			−0.706427			−0.353213	+	0.935543i	$0.614911\pi$
$702$		0			0
$703$		−	61.9300i		−	2.33573i
$704$		0			0
$705$	36.5617	+	9.93350i	1.37699	+	0.374117i
$706$		0			0
$707$	−7.23902			−0.272251
$708$		0			0
$709$	−6.95338	+	4.01454i	−0.261140	+	0.150769i	−0.624854	−	0.780741i	$-0.714842\pi$
$709$	−6.95338	+	4.01454i	−0.261140	+	0.150769i	0.363715	+	0.931510i	$0.381508\pi$
$710$		0			0
$711$	4.13501	+	7.16205i	0.155075	+	0.268598i
$712$		0			0
$713$	−1.51225	+	2.61929i	−0.0566342	+	0.0980933i
$714$		0			0
$715$	−15.4947	−	42.3839i	−0.579467	−	1.58507i
$716$		0			0
$717$	−12.4195	+	21.5112i	−0.463815	+	0.803352i
$718$		0			0
$719$	2.01466	+	3.48949i	0.0751341	+	0.130136i	0.901145	−	0.433519i	$-0.142728\pi$
$719$	2.01466	+	3.48949i	0.0751341	+	0.130136i	−0.826010	+	0.563655i	$0.809395\pi$
$720$		0			0
$721$	2.30103	−	1.32850i	0.0856950	−	0.0494760i
$722$		0			0
$723$	−16.7194			−0.621803
$724$		0			0
$725$	0.133164	−	19.0885i	0.00494559	−	0.708929i
$726$		0			0
$727$		−	20.5996i		−	0.763997i	−0.924163	−	0.381998i	$-0.875236\pi$
$727$		−	20.5996i		−	0.763997i	0.924163	−	0.381998i	$-0.124764\pi$
$728$		0			0
$729$	−15.8144			−0.585717
$730$		0			0
$731$	−6.56961	+	11.3789i	−0.242986	+	0.420864i
$732$		0			0
$733$	−5.93875			−0.219353			−0.109676	−	0.993967i	$-0.534981\pi$
$733$	−5.93875			−0.219353			−0.109676	+	0.993967i	$0.534981\pi$
$734$		0			0
$735$	−3.60902	+	3.58393i	−0.133121	+	0.132195i
$736$		0			0
$737$	59.1388	−	34.1438i	2.17840	−	1.25770i
$738$		0			0
$739$	20.8499	+	12.0377i	0.766975	+	0.442813i	0.831794	−	0.555084i	$-0.187314\pi$
$739$	20.8499	+	12.0377i	0.766975	+	0.442813i	−0.0648194	+	0.997897i	$0.520647\pi$
$740$		0			0
$741$	33.4315	+	47.2499i	1.22814	+	1.73577i
$742$		0			0
$743$	−0.496302	+	0.859620i	−0.0182075	+	0.0315364i	−0.874986	−	0.484149i	$-0.839129\pi$
$743$	−0.496302	+	0.859620i	−0.0182075	+	0.0315364i	0.856778	+	0.515685i	$0.172463\pi$
$744$		0			0
$745$	−33.9520	+	33.7159i	−1.24390	+	1.23526i
$746$		0			0
$747$	−2.55579	−	4.42676i	−0.0935114	−	0.161967i
$748$		0			0
$749$		−	1.68590i		−	0.0616014i
$750$		0			0
$751$	−13.8054	+	23.9116i	−0.503766	+	0.872548i	0.496225	+	0.868194i	$0.334719\pi$
$751$	−13.8054	+	23.9116i	−0.503766	+	0.872548i	−0.999991	+	0.00435392i	$0.998614\pi$
$752$		0			0
$753$			38.6483i			1.40842i
$754$		0			0
$755$	−4.76647	−	18.0402i	−0.173470	−	0.656549i
$756$		0			0
$757$	−9.01555	−	5.20513i	−0.327676	−	0.189184i	0.327133	−	0.944978i	$-0.393918\pi$
$757$	−9.01555	−	5.20513i	−0.327676	−	0.189184i	−0.654809	+	0.755795i	$0.727251\pi$
$758$		0			0
$759$		−	3.91539i		−	0.142120i
$760$		0			0
$761$	26.7558	−	15.4475i	0.969896	−	0.559970i	0.0706917	−	0.997498i	$-0.477479\pi$
$761$	26.7558	−	15.4475i	0.969896	−	0.559970i	0.899205	+	0.437528i	$0.144146\pi$
$762$		0			0
$763$	−12.0745	+	6.97122i	−0.437127	+	0.252375i
$764$		0			0
$765$	−7.11088	−	1.93196i	−0.257094	−	0.0698503i
$766$		0			0
$767$	−1.93121	−	0.889028i	−0.0697320	−	0.0321009i
$768$		0			0
$769$	46.0983	+	26.6148i	1.66235	+	0.959756i	0.971591	+	0.236666i	$0.0760549\pi$
$769$	46.0983	+	26.6148i	1.66235	+	0.959756i	0.690755	+	0.723089i	$0.257278\pi$
$770$		0			0
$771$	23.4899	+	40.6857i	0.845968	+	1.46526i
$772$		0			0
$773$	9.00393	+	15.5953i	0.323849	+	0.560923i	0.981279	−	0.192593i	$-0.0616897\pi$
$773$	9.00393	+	15.5953i	0.323849	+	0.560923i	−0.657430	+	0.753516i	$0.728356\pi$
$774$		0			0
$775$	20.9231	+	36.8309i	0.751581	+	1.32300i
$776$		0			0
$777$	36.6408	+	21.1546i	1.31448	+	0.758917i
$778$		0			0
$779$	64.8820			2.32464
$780$		0			0
$781$	13.6812			0.489554
$782$		0			0
$783$	13.9989	+	8.08224i	0.500278	+	0.288836i
$784$		0			0
$785$	−1.53191	−	5.79797i	−0.0546761	−	0.206939i
$786$		0			0
$787$	27.0083	+	46.7798i	0.962742	+	1.66752i	0.715562	+	0.698549i	$0.246171\pi$
$787$	27.0083	+	46.7798i	0.962742	+	1.66752i	0.247180	+	0.968970i	$0.420496\pi$
$788$		0			0
$789$	−0.619056	−	1.07224i	−0.0220390	−	0.0381726i
$790$		0			0
$791$	−19.4110	−	11.2069i	−0.690174	−	0.398472i
$792$		0			0
$793$	8.77159	−	19.0543i	0.311488	−	0.676638i
$794$		0			0
$795$	−0.668107	+	2.45907i	−0.0236953	+	0.0872141i
$796$		0			0
$797$	14.3939	−	8.31034i	0.509859	−	0.294367i	−0.222917	−	0.974838i	$-0.571558\pi$
$797$	14.3939	−	8.31034i	0.509859	−	0.294367i	0.732776	+	0.680470i	$0.238224\pi$
$798$		0			0
$799$	29.4112	−	16.9805i	1.04049	−	0.600728i
$800$		0			0
$801$			0.494776i			0.0174821i
$802$		0			0
$803$	20.1899	+	11.6567i	0.712488	+	0.411355i
$804$		0			0
$805$	−0.582551	−	2.20484i	−0.0205322	−	0.0777105i
$806$		0			0
$807$			14.4466i			0.508545i
$808$		0			0
$809$	8.52131	−	14.7593i	0.299593	−	0.518911i	−0.676450	−	0.736489i	$-0.736482\pi$
$809$	8.52131	−	14.7593i	0.299593	−	0.518911i	0.976043	+	0.217578i	$0.0698157\pi$
$810$		0			0
$811$		−	2.60366i		−	0.0914268i	−0.998955	−	0.0457134i	$-0.985444\pi$
$811$		−	2.60366i		−	0.0914268i	0.998955	−	0.0457134i	$-0.0145561\pi$
$812$		0			0
$813$	11.4204	+	19.7807i	0.400530	+	0.693738i
$814$		0			0
$815$	11.4186	+	11.4985i	0.399976	+	0.402776i
$816$		0			0
$817$	13.7057	−	23.7389i	0.479500	−	0.830518i
$818$		0			0
$819$	−8.60611	+	0.795511i	−0.300722	+	0.0277974i
$820$		0			0
$821$	−40.7265	−	23.5134i	−1.42136	−	0.820625i	−0.424948	−	0.905218i	$-0.639708\pi$
$821$	−40.7265	−	23.5134i	−1.42136	−	0.820625i	−0.996416	+	0.0845933i	$0.973041\pi$
$822$		0			0
$823$	−9.26840	+	5.35111i	−0.323076	+	0.186528i	−0.652763	−	0.757562i	$-0.726390\pi$
$823$	−9.26840	+	5.35111i	−0.323076	+	0.186528i	0.329687	+	0.944090i	$0.393057\pi$
$824$		0			0
$825$	−47.2972	−	27.7488i	−1.64668	−	0.966089i
$826$		0			0
$827$	13.8240			0.480707			0.240354	−	0.970685i	$-0.422737\pi$
$827$	13.8240			0.480707			0.240354	+	0.970685i	$0.422737\pi$
$828$		0			0
$829$	−24.1310	+	41.7961i	−0.838104	+	1.45164i	0.0533731	+	0.998575i	$0.483003\pi$
$829$	−24.1310	+	41.7961i	−0.838104	+	1.45164i	−0.891478	+	0.453065i	$0.850331\pi$
$830$		0			0
$831$	1.80565			0.0626375
$832$		0			0
$833$			4.55915i			0.157965i
$834$		0			0
$835$	7.46724	−	27.4843i	0.258415	−	0.951134i
$836$		0			0
$837$	−35.8695			−1.23983
$838$		0			0
$839$	−44.3752	+	25.6200i	−1.53200	+	0.884502i	−0.532732	+	0.846284i	$0.678835\pi$
$839$	−44.3752	+	25.6200i	−1.53200	+	0.884502i	−0.999269	+	0.0382177i	$0.987832\pi$
$840$		0			0
$841$	7.21222	+	12.4919i	0.248697	+	0.430756i
$842$		0			0
$843$	13.0617	−	22.6236i	0.449869	−	0.779197i
$844$		0			0
$845$	2.35027	−	28.9737i	0.0808516	−	0.996726i
$846$		0			0
$847$	−29.0394	+	50.2977i	−0.997805	+	1.72825i
$848$		0			0
$849$	−5.10004	−	8.83353i	−0.175033	−	0.303166i
$850$		0			0
$851$	−2.33700	+	1.34927i	−0.0801113	+	0.0462523i
$852$		0			0
$853$	21.3777			0.731960			0.365980	−	0.930623i	$-0.380734\pi$
$853$	21.3777			0.731960			0.365980	+	0.930623i	$0.380734\pi$
$854$		0			0
$855$	14.8349	+	4.03050i	0.507342	+	0.137840i
$856$		0			0
$857$		−	36.9615i		−	1.26258i	−0.775546	−	0.631291i	$-0.782525\pi$
$857$		−	36.9615i		−	1.26258i	0.775546	−	0.631291i	$-0.217475\pi$
$858$		0			0
$859$	−36.3529			−1.24034			−0.620172	−	0.784465i	$-0.712937\pi$
$859$	−36.3529			−1.24034			−0.620172	+	0.784465i	$0.712937\pi$
$860$		0			0
$861$	−22.1630	+	38.3874i	−0.755312	+	1.30824i
$862$		0			0
$863$	−41.0328			−1.39677			−0.698387	−	0.715720i	$-0.746099\pi$
$863$	−41.0328			−1.39677			−0.698387	+	0.715720i	$0.746099\pi$
$864$		0			0
$865$	−18.5226	+	18.3938i	−0.629786	+	0.625408i
$866$		0			0
$867$	2.67532	−	1.54460i	0.0908588	−	0.0524573i
$868$		0			0
$869$	47.7757	+	27.5833i	1.62068	+	0.935700i
$870$		0			0
$871$	43.8008	−	4.04876i	1.48413	−	0.137187i
$872$		0			0
$873$	−1.97894	+	3.42763i	−0.0669771	+	0.116008i
$874$		0			0
$875$	−30.7627	−	8.58884i	−1.03997	−	0.290356i
$876$		0			0
$877$	8.37164	+	14.5001i	0.282690	+	0.489634i	0.972046	−	0.234789i	$-0.0754398\pi$
$877$	8.37164	+	14.5001i	0.282690	+	0.489634i	−0.689356	+	0.724423i	$0.742106\pi$
$878$		0			0
$879$		−	29.4804i		−	0.994350i
$880$		0			0
$881$	26.3345	−	45.6127i	0.887232	−	1.53673i	0.0440990	−	0.999027i	$-0.485958\pi$
$881$	26.3345	−	45.6127i	0.887232	−	1.53673i	0.843133	−	0.537704i	$-0.180708\pi$
$882$		0			0
$883$		−	45.5891i		−	1.53419i	−0.641531	−	0.767097i	$-0.721700\pi$
$883$		−	45.5891i		−	1.53419i	0.641531	−	0.767097i	$-0.278300\pi$
$884$		0			0
$885$	−2.49771	+	0.659930i	−0.0839596	+	0.0221833i
$886$		0			0
$887$	−17.3838	−	10.0366i	−0.583692	−	0.336995i	0.178907	−	0.983866i	$-0.442744\pi$
$887$	−17.3838	−	10.0366i	−0.583692	−	0.336995i	−0.762599	+	0.646871i	$0.776077\pi$
$888$		0			0
$889$		−	21.3696i		−	0.716713i
$890$		0			0
$891$	52.4166	−	30.2628i	1.75602	−	1.01384i
$892$		0			0
$893$	−61.3582	+	35.4251i	−2.05327	+	1.18546i
$894$		0			0
$895$	0.598758	−	2.20382i	0.0200143	−	0.0736655i
$896$		0			0
$897$	1.05466	−	2.29101i	0.0352140	−	0.0764945i
$898$		0			0
$899$	28.0104	+	16.1718i	0.934200	+	0.539361i
$900$		0			0
$901$	1.14208	+	1.97813i	0.0380481	+	0.0659012i
$902$		0			0
$903$	9.36340	+	16.2179i	0.311594	+	0.539697i
$904$		0			0
$905$	−30.0007	+	7.92661i	−0.997257	+	0.263490i
$906$		0			0
$907$	33.0943	+	19.1070i	1.09888	+	0.634438i	0.935926	−	0.352196i	$-0.114565\pi$
$907$	33.0943	+	19.1070i	1.09888	+	0.634438i	0.162953	+	0.986634i	$0.447898\pi$
$908$		0			0
$909$	−2.12630			−0.0705249
$910$		0			0
$911$	−36.3853			−1.20550			−0.602749	−	0.797931i	$-0.705928\pi$
$911$	−36.3853			−1.20550			−0.602749	+	0.797931i	$0.705928\pi$
$912$		0			0
$913$	−29.5295	−	17.0488i	−0.977282	−	0.564234i
$914$		0			0
$915$	−6.51120	−	24.6436i	−0.215254	−	0.814694i
$916$		0			0
$917$	4.08570	+	7.07664i	0.134922	+	0.233691i
$918$		0			0
$919$	−11.6508	−	20.1798i	−0.384324	−	0.665669i	0.607351	−	0.794434i	$-0.292232\pi$
$919$	−11.6508	−	20.1798i	−0.384324	−	0.665669i	−0.991675	+	0.128765i	$0.958899\pi$
$920$		0			0
$921$	7.49996	+	4.33011i	0.247132	+	0.142682i
$922$		0			0
$923$	8.00528	+	3.68521i	0.263497	+	0.121300i
$924$		0			0
$925$	−0.263649	+	37.7929i	−0.00866872	+	1.24262i
$926$		0			0
$927$	0.675877	−	0.390218i	0.0221987	−	0.0128164i
$928$		0			0
$929$	−3.17003	+	1.83022i	−0.104005	+	0.0600475i	−0.551100	−	0.834439i	$-0.685792\pi$
$929$	−3.17003	+	1.83022i	−0.104005	+	0.0600475i	0.447095	+	0.894486i	$0.352459\pi$
$930$		0			0
$931$		−	9.51140i		−	0.311724i
$932$		0			0
$933$	−54.6518	−	31.5532i	−1.78922	−	1.03301i
$934$		0			0
$935$	−47.5231	+	12.5563i	−1.55417	+	0.410635i
$936$		0			0
$937$		−	41.7022i		−	1.36235i	−0.732120	−	0.681175i	$-0.761469\pi$
$937$		−	41.7022i		−	1.36235i	0.732120	−	0.681175i	$-0.238531\pi$
$938$		0			0
$939$	−18.4718	+	31.9941i	−0.602805	+	1.04409i
$940$		0			0
$941$		−	52.3086i		−	1.70521i	−0.522554	−	0.852606i	$-0.675021\pi$
$941$		−	52.3086i		−	1.70521i	0.522554	−	0.852606i	$-0.324979\pi$
$942$		0			0
$943$	−1.41358	−	2.44840i	−0.0460325	−	0.0797307i
$944$		0			0
$945$	19.1910	−	19.0576i	0.624284	−	0.619944i
$946$		0			0
$947$	18.5158	−	32.0703i	0.601682	−	1.04214i	−0.390884	−	0.920440i	$-0.627831\pi$
$947$	18.5158	−	32.0703i	0.601682	−	1.04214i	0.992566	−	0.121704i	$-0.0388360\pi$
$948$		0			0
$949$	8.67384	+	12.2591i	0.281565	+	0.397946i
$950$		0			0
$951$	−40.7082	−	23.5029i	−1.32005	−	0.762134i
$952$		0			0
$953$	12.5708	−	7.25776i	0.407209	−	0.235102i	−0.282381	−	0.959302i	$-0.591124\pi$
$953$	12.5708	−	7.25776i	0.407209	−	0.235102i	0.689590	+	0.724200i	$0.257791\pi$
$954$		0			0
$955$	10.2142	+	10.2857i	0.330525	+	0.332839i
$956$		0			0
$957$	−41.8708			−1.35349
$958$		0			0
$959$	23.3752	−	40.4870i	0.754824	−	1.30739i
$960$		0			0
$961$	−40.7717			−1.31522
$962$		0			0
$963$		−	0.495195i		−	0.0159574i
$964$		0			0
$965$	−12.8508	+	47.2994i	−0.413683	+	1.52262i
$966$		0			0
$967$	−24.2765			−0.780680			−0.390340	−	0.920671i	$-0.627643\pi$
$967$	−24.2765			−0.780680			−0.390340	+	0.920671i	$0.627643\pi$
$968$		0			0
$969$	54.5990	−	31.5228i	1.75397	−	1.01266i
$970$		0			0
$971$	−10.3284	−	17.8894i	−0.331456	−	0.574098i	0.651342	−	0.758784i	$-0.274206\pi$
$971$	−10.3284	−	17.8894i	−0.331456	−	0.574098i	−0.982798	+	0.184686i	$0.940873\pi$
$972$		0			0
$973$	2.56604	−	4.44451i	0.0822635	−	0.142485i
$974$		0			0
$975$	−20.2005	−	28.9767i	−0.646933	−	0.927996i
$976$		0			0
$977$	−12.6013	+	21.8260i	−0.403150	+	0.698277i	−0.994104	−	0.108429i	$-0.965418\pi$
$977$	−12.6013	+	21.8260i	−0.403150	+	0.698277i	0.590954	+	0.806705i	$0.298751\pi$
$978$		0			0
$979$	1.65025	+	2.85831i	0.0527421	+	0.0913520i
$980$		0			0
$981$	−3.54662	+	2.04764i	−0.113235	+	0.0653761i
$982$		0			0
$983$	43.9686			1.40238			0.701191	−	0.712973i	$-0.252652\pi$
$983$	43.9686			1.40238			0.701191	+	0.712973i	$0.252652\pi$
$984$		0			0
$985$	−11.1674	+	41.1031i	−0.355822	+	1.30965i
$986$		0			0
$987$		−	48.4034i		−	1.54070i
$988$		0			0
$989$	−1.19442			−0.0379803
$990$		0			0
$991$	−15.8117	+	27.3866i	−0.502275	+	0.869966i	0.497722	+	0.867337i	$0.334170\pi$
$991$	−15.8117	+	27.3866i	−0.502275	+	0.869966i	−0.999997	+	0.00262873i	$0.999163\pi$
$992$		0			0
$993$	14.1209			0.448113
$994$		0			0
$995$	18.4267	+	18.5557i	0.584165	+	0.588255i
$996$		0			0
$997$	16.5212	−	9.53853i	0.523232	−	0.302088i	−0.215024	−	0.976609i	$-0.568983\pi$
$997$	16.5212	−	9.53853i	0.523232	−	0.302088i	0.738256	+	0.674521i	$0.235650\pi$
$998$		0			0
$999$	−27.7160	−	16.0019i	−0.876897	−	0.506277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.z.a.69.2	yes	16
3.2	odd	2		2340.2.cr.a.1369.8		16
4.3	odd	2		1040.2.df.d.849.7		16
5.2	odd	4		1300.2.y.e.901.2		16
5.3	odd	4		1300.2.y.e.901.7		16
5.4	even	2	inner	260.2.z.a.69.7	yes	16
13.4	even	6		3380.2.d.d.1689.14		16
13.6	odd	12		3380.2.c.e.2029.14		16
13.7	odd	12		3380.2.c.e.2029.13		16
13.9	even	3		3380.2.d.d.1689.13		16
13.10	even	6	inner	260.2.z.a.49.7	yes	16
15.14	odd	2		2340.2.cr.a.1369.1		16
20.19	odd	2		1040.2.df.d.849.2		16
39.23	odd	6		2340.2.cr.a.829.1		16
52.23	odd	6		1040.2.df.d.49.2		16
65.4	even	6		3380.2.d.d.1689.3		16
65.9	even	6		3380.2.d.d.1689.4		16
65.19	odd	12		3380.2.c.e.2029.4		16
65.23	odd	12		1300.2.y.e.101.7		16
65.49	even	6	inner	260.2.z.a.49.2	✓	16
65.59	odd	12		3380.2.c.e.2029.3		16
65.62	odd	12		1300.2.y.e.101.2		16
195.179	odd	6		2340.2.cr.a.829.8		16
260.179	odd	6		1040.2.df.d.49.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.z.a.49.2	✓	16	65.49	even	6	inner
260.2.z.a.49.7	yes	16	13.10	even	6	inner
260.2.z.a.69.2	yes	16	1.1	even	1	trivial
260.2.z.a.69.7	yes	16	5.4	even	2	inner
1040.2.df.d.49.2		16	52.23	odd	6
1040.2.df.d.49.7		16	260.179	odd	6
1040.2.df.d.849.2		16	20.19	odd	2
1040.2.df.d.849.7		16	4.3	odd	2
1300.2.y.e.101.2		16	65.62	odd	12
1300.2.y.e.101.7		16	65.23	odd	12
1300.2.y.e.901.2		16	5.2	odd	4
1300.2.y.e.901.7		16	5.3	odd	4
2340.2.cr.a.829.1		16	39.23	odd	6
2340.2.cr.a.829.8		16	195.179	odd	6
2340.2.cr.a.1369.1		16	15.14	odd	2
2340.2.cr.a.1369.8		16	3.2	odd	2
3380.2.c.e.2029.3		16	65.59	odd	12
3380.2.c.e.2029.4		16	65.19	odd	12
3380.2.c.e.2029.13		16	13.7	odd	12
3380.2.c.e.2029.14		16	13.6	odd	12
3380.2.d.d.1689.3		16	65.4	even	6
3380.2.d.d.1689.4		16	65.9	even	6
3380.2.d.d.1689.13		16	13.9	even	3
3380.2.d.d.1689.14		16	13.4	even	6

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.69686 - 0.979681i) q^{3} +(-2.16188 + 0.571200i) q^{5} +(1.42836 + 2.47400i) q^{7} +(0.419550 + 0.726682i) q^{9} +O(q^{10})\)	\(q+(-1.69686 - 0.979681i) q^{3} +(-2.16188 + 0.571200i) q^{5} +(1.42836 + 2.47400i) q^{7} +(0.419550 + 0.726682i) q^{9} +(4.84746 + 2.79868i) q^{11} +(2.08253 + 2.94331i) q^{13} +(4.22800 + 1.14871i) q^{15} +(3.40111 - 1.96363i) q^{17} +(-7.09546 + 4.09657i) q^{19} -5.59737i q^{21} +(0.309177 + 0.178504i) q^{23} +(4.34746 - 2.46973i) q^{25} +4.23399i q^{27} +(1.90890 - 3.30631i) q^{29} +8.47182i q^{31} +(-5.48363 - 9.49793i) q^{33} +(-4.50110 - 4.53261i) q^{35} +(-3.77939 + 6.54609i) q^{37} +(-0.650247 - 7.03459i) q^{39} +(-6.85811 - 3.95953i) q^{41} +(-2.89741 + 1.67282i) q^{43} +(-1.32210 - 1.33135i) q^{45} +8.64753 q^{47} +(-0.580450 + 1.00537i) q^{49} -7.69492 q^{51} +0.581615i q^{53} +(-12.0782 - 3.28155i) q^{55} +16.0533 q^{57} +(-0.510653 + 0.294826i) q^{59} +(-2.90890 - 5.03836i) q^{61} +(-1.19854 + 2.07593i) q^{63} +(-6.18340 - 5.17355i) q^{65} +(6.09997 - 10.5655i) q^{67} +(-0.349753 - 0.605790i) q^{69} +(2.11676 - 1.22211i) q^{71} +4.16506 q^{73} +(-9.79657 - 0.0683422i) q^{75} +15.9902i q^{77} +9.85582 q^{79} +(5.40661 - 9.36452i) q^{81} -6.09174 q^{83} +(-6.23116 + 6.18785i) q^{85} +(-6.47825 + 3.74022i) q^{87} +(0.510653 + 0.294826i) q^{89} +(-4.30714 + 9.35629i) q^{91} +(8.29968 - 14.3755i) q^{93} +(12.9996 - 12.9092i) q^{95} +(2.35841 + 4.08489i) q^{97} +4.69675i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} - 6 q^{11} + 6 q^{15} - 18 q^{19} - 14 q^{25} + 12 q^{29} + 18 q^{39} - 48 q^{41} + 45 q^{45} - 6 q^{49} + 44 q^{51} + 2 q^{55} - 30 q^{59} - 28 q^{61} - 15 q^{65} - 34 q^{69} - 18 q^{71} - 42 q^{75} - 16 q^{79} - 44 q^{81} - 45 q^{85} + 30 q^{89} - 10 q^{91}+O(q^{100}) \) 16 * q + 10 * q^9 - 6 * q^11 + 6 * q^15 - 18 * q^19 - 14 * q^25 + 12 * q^29 + 18 * q^39 - 48 * q^41 + 45 * q^45 - 6 * q^49 + 44 * q^51 + 2 * q^55 - 30 * q^59 - 28 * q^61 - 15 * q^65 - 34 * q^69 - 18 * q^71 - 42 * q^75 - 16 * q^79 - 44 * q^81 - 45 * q^85 + 30 * q^89 - 10 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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