LMFDB - Embedded newform 504.2.t.c.193.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.2
Character	$\chi$	$=$	504.193
Dual form			504.2.t.c.457.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72608 - 0.143720i) q^{3} +2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +(2.95869 + 0.496145i) q^{9} +O(q^{10})$	\(q+(-1.72608 - 0.143720i) q^{3} +2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +(2.95869 + 0.496145i) q^{9} -3.43944 q^{11} +(-0.429164 + 0.743335i) q^{13} +(-4.78434 - 0.398364i) q^{15} +(-0.405132 + 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} +(-1.11726 - 4.44429i) q^{21} +7.64930 q^{23} +2.68286 q^{25} +(-5.03562 - 1.28161i) q^{27} +(3.99696 + 6.92294i) q^{29} +(3.60578 + 6.24540i) q^{31} +(5.93674 + 0.494317i) q^{33} +(2.37193 + 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(0.847604 - 1.22137i) q^{39} +(1.67577 - 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +(8.20089 + 1.37521i) q^{45} +(0.307520 - 0.532640i) q^{47} +(-5.53543 + 4.28474i) q^{49} +(0.800140 - 1.15298i) q^{51} +(6.31646 - 10.9404i) q^{53} -9.53342 q^{55} +(-1.10818 - 2.35070i) q^{57} +(-0.734690 - 1.27252i) q^{59} +(-5.71635 + 9.90101i) q^{61} +(1.28974 + 7.83177i) q^{63} +(-1.18956 + 2.06037i) q^{65} +(-8.10061 - 14.0307i) q^{67} +(-13.2033 - 1.09936i) q^{69} +14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(-4.63083 - 0.385582i) q^{75} +(-2.94325 - 8.61077i) q^{77} +(1.37586 - 2.38305i) q^{79} +(8.50768 + 2.93588i) q^{81} +(-5.75814 - 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(-5.90410 - 12.5240i) q^{87} +(-5.11395 - 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-5.32627 - 11.2983i) q^{93} +(2.07944 + 3.60170i) q^{95} +(3.82852 + 6.63119i) q^{97} +(-10.1762 - 1.70646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72608	−	0.143720i	−0.996551	−	0.0829771i
$3$	−1.72608	−	0.143720i	−0.996551	−	0.0829771i
$4$		0			0
$5$	2.77180			1.23959			0.619793	−	0.784766i	$-0.287217\pi$
$5$	2.77180			1.23959			0.619793	+	0.784766i	$0.287217\pi$
$6$		0			0
$7$	0.855737	+	2.50354i	0.323438	+	0.946249i
$7$	0.855737	+	2.50354i	0.323438	+	0.946249i
$8$		0			0
$9$	2.95869	+	0.496145i	0.986230	+	0.165382i
$10$		0			0
$11$	−3.43944			−1.03703			−0.518515	−	0.855069i	$-0.673515\pi$
$11$	−3.43944			−1.03703			−0.518515	+	0.855069i	$0.673515\pi$
$12$		0			0
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	−0.919383	−	0.393363i	$-0.871311\pi$
$13$	−0.429164	+	0.743335i	−0.119029	+	0.206164i	0.800354	+	0.599527i	$0.204645\pi$
$14$		0			0
$15$	−4.78434	−	0.398364i	−1.23531	−	0.102857i
$16$		0			0
$17$	−0.405132	+	0.701710i	−0.0982590	+	0.170190i	−0.910964	−	0.412486i	$-0.864661\pi$
$17$	−0.405132	+	0.701710i	−0.0982590	+	0.170190i	0.812705	+	0.582675i	$0.197994\pi$
$18$		0			0
$19$	0.750215	+	1.29941i	0.172111	+	0.298105i	0.939158	−	0.343486i	$-0.111608\pi$
$19$	0.750215	+	1.29941i	0.172111	+	0.298105i	−0.767047	+	0.641591i	$0.778275\pi$
$20$		0			0
$21$	−1.11726	−	4.44429i	−0.243806	−	0.969824i
$22$		0			0
$23$	7.64930			1.59499			0.797495	−	0.603326i	$-0.206158\pi$
$23$	7.64930			1.59499			0.797495	+	0.603326i	$0.206158\pi$
$24$		0			0
$25$	2.68286			0.536572
$26$		0			0
$27$	−5.03562	−	1.28161i	−0.969106	−	0.246646i
$28$		0			0
$29$	3.99696	+	6.92294i	0.742217	+	1.28556i	0.951484	+	0.307700i	$0.0995592\pi$
$29$	3.99696	+	6.92294i	0.742217	+	1.28556i	−0.209266	+	0.977859i	$0.567107\pi$
$30$		0			0
$31$	3.60578	+	6.24540i	0.647618	+	1.12171i	0.983690	+	0.179871i	$0.0575679\pi$
$31$	3.60578	+	6.24540i	0.647618	+	1.12171i	−0.336073	+	0.941836i	$0.609099\pi$
$32$		0			0
$33$	5.93674	+	0.494317i	1.03345	+	0.0860496i
$34$		0			0
$35$	2.37193	+	6.93931i	0.400929	+	1.17296i
$36$		0			0
$37$	0.458211	+	0.793644i	0.0753294	+	0.130474i	0.901229	−	0.433342i	$-0.142666\pi$
$37$	0.458211	+	0.793644i	0.0753294	+	0.130474i	−0.825900	+	0.563817i	$0.809333\pi$
$38$		0			0
$39$	0.847604	−	1.22137i	0.135725	−	0.195576i
$40$		0			0
$41$	1.67577	−	2.90251i	0.261711	−	0.453297i	−0.704986	−	0.709221i	$-0.749047\pi$
$41$	1.67577	−	2.90251i	0.261711	−	0.453297i	0.966697	+	0.255925i	$0.0823800\pi$
$42$		0			0
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	0.943140	−	0.332395i	$-0.107857\pi$
$43$	1.20465	+	2.08652i	0.183708	+	0.318191i	−0.759433	+	0.650586i	$0.774523\pi$
$44$		0			0
$45$	8.20089	+	1.37521i	1.22252	+	0.205005i
$46$		0			0
$47$	0.307520	−	0.532640i	0.0448564	−	0.0776935i	−0.842726	−	0.538343i	$-0.819050\pi$
$47$	0.307520	−	0.532640i	0.0448564	−	0.0776935i	0.887582	+	0.460650i	$0.152384\pi$
$48$		0			0
$49$	−5.53543	+	4.28474i	−0.790775	+	0.612106i
$50$		0			0
$51$	0.800140	−	1.15298i	0.112042	−	0.161449i
$52$		0			0
$53$	6.31646	−	10.9404i	0.867633	−	1.50278i	0.00322332	−	0.999995i	$-0.498974\pi$
$53$	6.31646	−	10.9404i	0.867633	−	1.50278i	0.864409	−	0.502789i	$-0.167693\pi$
$54$		0			0
$55$	−9.53342			−1.28549
$56$		0			0
$57$	−1.10818	−	2.35070i	−0.146782	−	0.311358i
$58$		0			0
$59$	−0.734690	−	1.27252i	−0.0956485	−	0.165668i	0.814231	−	0.580542i	$-0.197159\pi$
$59$	−0.734690	−	1.27252i	−0.0956485	−	0.165668i	−0.909879	+	0.414874i	$0.863826\pi$
$60$		0			0
$61$	−5.71635	+	9.90101i	−0.731904	+	1.26769i	0.224165	+	0.974551i	$0.428035\pi$
$61$	−5.71635	+	9.90101i	−0.731904	+	1.26769i	−0.956069	+	0.293143i	$0.905299\pi$
$62$		0			0
$63$	1.28974	+	7.83177i	0.162492	+	0.986710i
$64$		0			0
$65$	−1.18956	+	2.06037i	−0.147546	+	0.255558i
$66$		0			0
$67$	−8.10061	−	14.0307i	−0.989647	−	1.71412i	−0.619117	−	0.785299i	$-0.712509\pi$
$67$	−8.10061	−	14.0307i	−0.989647	−	1.71412i	−0.370530	−	0.928820i	$-0.620824\pi$
$68$		0			0
$69$	−13.2033	−	1.09936i	−1.58949	−	0.132348i
$70$		0			0
$71$	14.4177			1.71106			0.855532	−	0.517749i	$-0.173230\pi$
$71$	14.4177			1.71106			0.855532	+	0.517749i	$0.173230\pi$
$72$		0			0
$73$	−4.16893	+	7.22079i	−0.487936	+	0.845130i	−0.999904	−	0.0138749i	$-0.995583\pi$
$73$	−4.16893	+	7.22079i	−0.487936	+	0.845130i	0.511968	+	0.859005i	$0.328917\pi$
$74$		0			0
$75$	−4.63083	−	0.385582i	−0.534722	−	0.0445232i
$76$		0			0
$77$	−2.94325	−	8.61077i	−0.335415	−	0.981288i
$78$		0			0
$79$	1.37586	−	2.38305i	0.154796	−	0.268115i	−0.778189	−	0.628031i	$-0.783861\pi$
$79$	1.37586	−	2.38305i	0.154796	−	0.268115i	0.932985	+	0.359916i	$0.117195\pi$
$80$		0			0
$81$	8.50768	+	2.93588i	0.945298	+	0.326209i
$82$		0			0
$83$	−5.75814	−	9.97340i	−0.632038	−	1.09472i	−0.987134	−	0.159893i	$-0.948885\pi$
$83$	−5.75814	−	9.97340i	−0.632038	−	1.09472i	0.355096	−	0.934830i	$-0.384448\pi$
$84$		0			0
$85$	−1.12294	+	1.94500i	−0.121800	+	0.210965i
$86$		0			0
$87$	−5.90410	−	12.5240i	−0.632986	−	1.34271i
$88$		0			0
$89$	−5.11395	−	8.85763i	−0.542078	−	0.938907i	−0.998785	−	0.0492892i	$-0.984304\pi$
$89$	−5.11395	−	8.85763i	−0.542078	−	0.938907i	0.456707	−	0.889617i	$-0.349029\pi$
$90$		0			0
$91$	−2.22822	−	0.438331i	−0.233581	−	0.0459496i
$92$		0			0
$93$	−5.32627	−	11.2983i	−0.552308	−	1.17158i
$94$		0			0
$95$	2.07944	+	3.60170i	0.213346	+	0.369527i
$96$		0			0
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	0.992279	−	0.124029i	$-0.0395814\pi$
$97$	3.82852	+	6.63119i	0.388727	+	0.673296i	−0.603551	+	0.797324i	$0.706248\pi$
$98$		0			0
$99$	−10.1762	−	1.70646i	−1.02275	−	0.171506i
$100$		0			0
$101$	−3.68603			−0.366774			−0.183387	−	0.983041i	$-0.558706\pi$
$101$	−3.68603			−0.366774			−0.183387	+	0.983041i	$0.558706\pi$
$102$		0			0
$103$	−16.1205			−1.58840			−0.794201	−	0.607656i	$-0.792110\pi$
$103$	−16.1205			−1.58840			−0.794201	+	0.607656i	$0.792110\pi$
$104$		0			0
$105$	−3.09681	−	12.3187i	−0.302218	−	1.20218i
$106$		0			0
$107$	3.16767	+	5.48656i	0.306230	+	0.530405i	0.977534	−	0.210776i	$-0.0675991\pi$
$107$	3.16767	+	5.48656i	0.306230	+	0.530405i	−0.671305	+	0.741182i	$0.734266\pi$
$108$		0			0
$109$	4.89477	−	8.47799i	0.468834	−	0.812044i	−0.530532	−	0.847665i	$-0.678008\pi$
$109$	4.89477	−	8.47799i	0.468834	−	0.812044i	0.999365	+	0.0356213i	$0.0113410\pi$
$110$		0			0
$111$	−0.676844	−	1.43575i	−0.0642432	−	0.136275i
$112$		0			0
$113$	4.06963	−	7.04881i	0.382839	−	0.663096i	−0.608628	−	0.793456i	$-0.708280\pi$
$113$	4.06963	−	7.04881i	0.382839	−	0.663096i	0.991467	+	0.130360i	$0.0416132\pi$
$114$		0			0
$115$	21.2023			1.97713
$116$		0			0
$117$	−1.63857	+	1.98637i	−0.151485	+	0.183640i
$118$		0			0
$119$	−2.10345	−	0.413786i	−0.192823	−	0.0379317i
$120$		0			0
$121$	0.829725			0.0754295
$122$		0			0
$123$	−3.30966	+	4.76912i	−0.298422	+	0.430017i
$124$		0			0
$125$	−6.42264			−0.574459
$126$		0			0
$127$	−12.5658			−1.11504			−0.557518	−	0.830165i	$-0.688246\pi$
$127$	−12.5658			−1.11504			−0.557518	+	0.830165i	$0.688246\pi$
$128$		0			0
$129$	−1.77945	−	3.77463i	−0.156672	−	0.332337i
$130$		0			0
$131$	1.58550			0.138526			0.0692631	−	0.997598i	$-0.477935\pi$
$131$	1.58550			0.138526			0.0692631	+	0.997598i	$0.477935\pi$
$132$		0			0
$133$	−2.61114	+	2.99015i	−0.226415	+	0.259279i
$134$		0			0
$135$	−13.9577	−	3.55236i	−1.20129	−	0.305739i
$136$		0			0
$137$	4.92788			0.421017			0.210508	−	0.977592i	$-0.432488\pi$
$137$	4.92788			0.421017			0.210508	+	0.977592i	$0.432488\pi$
$138$		0			0
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	−0.636001	−	0.771688i	$-0.719412\pi$
$139$	4.12999	−	7.15336i	0.350301	−	0.606740i	0.986302	+	0.164949i	$0.0527458\pi$
$140$		0			0
$141$	−0.607354	+	0.875181i	−0.0511485	+	0.0737035i
$142$		0			0
$143$	1.47608	−	2.55665i	0.123436	−	0.213798i
$144$		0			0
$145$	11.0788	+	19.1890i	0.920042	+	1.59356i
$146$		0			0
$147$	10.1704	−	6.60025i	0.838839	−	0.544379i
$148$		0			0
$149$	−13.9140			−1.13988			−0.569938	−	0.821688i	$-0.693033\pi$
$149$	−13.9140			−1.13988			−0.569938	+	0.821688i	$0.693033\pi$
$150$		0			0
$151$	22.9927			1.87112			0.935561	−	0.353166i	$-0.114895\pi$
$151$	22.9927			1.87112			0.935561	+	0.353166i	$0.114895\pi$
$152$		0			0
$153$	−1.54681	+	1.87514i	−0.125052	+	0.151596i
$154$		0			0
$155$	9.99450	+	17.3110i	0.802777	+	1.39045i
$156$		0			0
$157$	−9.29022	−	16.0911i	−0.741441	−	1.28421i	−0.951839	−	0.306597i	$-0.900810\pi$
$157$	−9.29022	−	16.0911i	−0.741441	−	1.28421i	0.210399	−	0.977616i	$-0.432524\pi$
$158$		0			0
$159$	−12.4751	+	17.9762i	−0.989337	+	1.42561i
$160$		0			0
$161$	6.54579	+	19.1503i	0.515880	+	1.50926i
$162$		0			0
$163$	−2.45194	−	4.24688i	−0.192050	−	0.332641i	0.753879	−	0.657013i	$-0.228180\pi$
$163$	−2.45194	−	4.24688i	−0.192050	−	0.332641i	−0.945930	+	0.324372i	$0.894847\pi$
$164$		0			0
$165$	16.4554	+	1.37015i	1.28105	+	0.106666i
$166$		0			0
$167$	−5.47493	+	9.48286i	−0.423663	+	0.733805i	−0.996295	−	0.0860073i	$-0.972589\pi$
$167$	−5.47493	+	9.48286i	−0.423663	+	0.733805i	0.572632	+	0.819813i	$0.305923\pi$
$168$		0			0
$169$	6.13164	+	10.6203i	0.471664	+	0.816947i
$170$		0			0
$171$	1.57496	+	4.21677i	0.120440	+	0.322464i
$172$		0			0
$173$	6.70271	−	11.6094i	0.509598	−	0.882649i	−0.490340	−	0.871531i	$-0.663127\pi$
$173$	6.70271	−	11.6094i	0.509598	−	0.882649i	0.999938	−	0.0111184i	$-0.00353917\pi$
$174$		0			0
$175$	2.29582	+	6.71665i	0.173548	+	0.507731i
$176$		0			0
$177$	1.08524	+	2.30206i	0.0815720	+	0.173033i
$178$		0			0
$179$	−6.64888	+	11.5162i	−0.496961	+	0.860761i	−0.999994	−	0.00350600i	$-0.998884\pi$
$179$	−6.64888	+	11.5162i	−0.496961	+	0.860761i	0.503033	+	0.864267i	$0.332217\pi$
$180$		0			0
$181$	−10.9190			−0.811601			−0.405801	−	0.913962i	$-0.633007\pi$
$181$	−10.9190			−0.811601			−0.405801	+	0.913962i	$0.633007\pi$
$182$		0			0
$183$	11.2898	−	16.2684i	0.834569	−	1.20259i
$184$		0			0
$185$	1.27007	+	2.19982i	0.0933772	+	0.161734i
$186$		0			0
$187$	1.39343	−	2.41349i	0.101897	−	0.176492i
$188$		0			0
$189$	−1.10061	−	13.7036i	−0.0800573	−	0.996790i
$190$		0			0
$191$	9.30553	−	16.1177i	0.673325	−	1.16623i	−0.303631	−	0.952790i	$-0.598199\pi$
$191$	9.30553	−	16.1177i	0.673325	−	1.16623i	0.976956	−	0.213443i	$-0.0684677\pi$
$192$		0			0
$193$	−1.46470	−	2.53693i	−0.105431	−	0.182613i	0.808483	−	0.588520i	$-0.200289\pi$
$193$	−1.46470	−	2.53693i	−0.105431	−	0.182613i	−0.913914	+	0.405907i	$0.866956\pi$
$194$		0			0
$195$	2.34939	−	3.38540i	0.168243	−	0.242434i
$196$		0			0
$197$	−18.5050			−1.31843			−0.659214	−	0.751956i	$-0.729111\pi$
$197$	−18.5050			−1.31843			−0.659214	+	0.751956i	$0.729111\pi$
$198$		0			0
$199$	0.793836	−	1.37496i	0.0562736	−	0.0974687i	−0.836516	−	0.547942i	$-0.815411\pi$
$199$	0.793836	−	1.37496i	0.0562736	−	0.0974687i	0.892790	+	0.450473i	$0.148745\pi$
$200$		0			0
$201$	11.9658	+	25.3823i	0.844002	+	1.79033i
$202$		0			0
$203$	−13.9115	+	15.9308i	−0.976397	+	1.11812i
$204$		0			0
$205$	4.64489	−	8.04518i	0.324413	−	0.561900i
$206$		0			0
$207$	22.6319	+	3.79517i	1.57303	+	0.263782i
$208$		0			0
$209$	−2.58032	−	4.46924i	−0.178484	−	0.309144i
$210$		0			0
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	−0.0316443	−	0.999499i	$-0.510074\pi$
$211$	12.3436	−	21.3798i	0.849770	−	1.47184i	0.881414	−	0.472345i	$-0.156592\pi$
$212$		0			0
$213$	−24.8860	−	2.07212i	−1.70516	−	0.141979i
$214$		0			0
$215$	3.33905	+	5.78340i	0.227721	+	0.394425i
$216$		0			0
$217$	−12.5500	+	14.3716i	−0.851950	+	0.975611i
$218$		0			0
$219$	8.23367	−	11.8645i	0.556380	−	0.801728i
$220$		0			0
$221$	−0.347737	−	0.602298i	−0.0233913	−	0.0405149i
$222$		0			0
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	−0.981836	−	0.189732i	$-0.939238\pi$
$223$	−9.78468	−	16.9476i	−0.655231	−	1.13489i	0.326605	−	0.945161i	$-0.394095\pi$
$224$		0			0
$225$	7.93775	+	1.33109i	0.529183	+	0.0887393i
$226$		0			0
$227$	8.64808			0.573993			0.286996	−	0.957932i	$-0.407343\pi$
$227$	8.64808			0.573993			0.286996	+	0.957932i	$0.407343\pi$
$228$		0			0
$229$	11.5427			0.762765			0.381382	−	0.924417i	$-0.375448\pi$
$229$	11.5427			0.762765			0.381382	+	0.924417i	$0.375448\pi$
$230$		0			0
$231$	3.84274	+	15.2859i	0.252834	+	1.00574i
$232$		0			0
$233$	−8.12745	−	14.0772i	−0.532447	−	0.922225i	−0.999282	−	0.0378811i	$-0.987939\pi$
$233$	−8.12745	−	14.0772i	−0.532447	−	0.922225i	0.466835	−	0.884344i	$-0.345394\pi$
$234$		0			0
$235$	0.852382	−	1.47637i	0.0556033	−	0.0963077i
$236$		0			0
$237$	−2.71733	+	3.91560i	−0.176510	+	0.254345i
$238$		0			0
$239$	12.4336	−	21.5355i	0.804260	−	1.39302i	−0.112530	−	0.993648i	$-0.535895\pi$
$239$	12.4336	−	21.5355i	0.804260	−	1.39302i	0.916790	−	0.399371i	$-0.130771\pi$
$240$		0			0
$241$	−19.0363			−1.22623			−0.613117	−	0.789992i	$-0.710085\pi$
$241$	−19.0363			−1.22623			−0.613117	+	0.789992i	$0.710085\pi$
$242$		0			0
$243$	−14.2630	−	6.29028i	−0.914970	−	0.403522i
$244$		0			0
$245$	−15.3431	+	11.8764i	−0.980234	+	0.758758i
$246$		0			0
$247$	−1.28786			−0.0819447
$248$		0			0
$249$	8.50562	+	18.0424i	0.539022	+	1.14339i
$250$		0			0
$251$	−0.980433			−0.0618844			−0.0309422	−	0.999521i	$-0.509851\pi$
$251$	−0.980433			−0.0618844			−0.0309422	+	0.999521i	$0.509851\pi$
$252$		0			0
$253$	−26.3093			−1.65405
$254$		0			0
$255$	2.21783	−	3.19583i	0.138886	−	0.200130i
$256$		0			0
$257$	4.36725			0.272421			0.136211	−	0.990680i	$-0.456508\pi$
$257$	4.36725			0.272421			0.136211	+	0.990680i	$0.456508\pi$
$258$		0			0
$259$	−1.59481	+	1.82630i	−0.0990968	+	0.113481i
$260$		0			0
$261$	8.39098	+	22.4659i	0.519389	+	1.39060i
$262$		0			0
$263$	−12.4842			−0.769811			−0.384905	−	0.922956i	$-0.625766\pi$
$263$	−12.4842			−0.769811			−0.384905	+	0.922956i	$0.625766\pi$
$264$		0			0
$265$	17.5079	−	30.3247i	1.07550	−	1.86283i
$266$		0			0
$267$	7.55406	+	16.0239i	0.462301	+	0.980649i
$268$		0			0
$269$	8.29270	−	14.3634i	0.505615	−	0.875750i	−0.494364	−	0.869255i	$-0.664599\pi$
$269$	8.29270	−	14.3634i	0.505615	−	0.875750i	0.999979	−	0.00649532i	$-0.00206754\pi$
$270$		0			0
$271$	12.9814	+	22.4845i	0.788566	+	1.36584i	0.926845	+	0.375444i	$0.122510\pi$
$271$	12.9814	+	22.4845i	0.788566	+	1.36584i	−0.138279	+	0.990393i	$0.544157\pi$
$272$		0			0
$273$	3.78308	+	1.07684i	0.228963	+	0.0651730i
$274$		0			0
$275$	−9.22753			−0.556441
$276$		0			0
$277$	−1.96075			−0.117810			−0.0589049	−	0.998264i	$-0.518761\pi$
$277$	−1.96075			−0.117810			−0.0589049	+	0.998264i	$0.518761\pi$
$278$		0			0
$279$	7.56976	+	20.2672i	0.453190	+	1.21336i
$280$		0			0
$281$	9.42057	+	16.3169i	0.561984	+	0.973385i	0.997323	+	0.0731185i	$0.0232951\pi$
$281$	9.42057	+	16.3169i	0.561984	+	0.973385i	−0.435339	+	0.900267i	$0.643372\pi$
$282$		0			0
$283$	11.7422	+	20.3381i	0.698002	+	1.20898i	0.969158	+	0.246440i	$0.0792608\pi$
$283$	11.7422	+	20.3381i	0.698002	+	1.20898i	−0.271156	+	0.962536i	$0.587406\pi$
$284$		0			0
$285$	−3.07164	−	6.51568i	−0.181948	−	0.385955i
$286$		0			0
$287$	8.70058	+	1.71156i	0.513579	+	0.101030i
$288$		0			0
$289$	8.17174	+	14.1539i	0.480690	+	0.832580i
$290$		0			0
$291$	−5.65529	−	11.9962i	−0.331519	−	0.703229i
$292$		0			0
$293$	−1.00384	+	1.73871i	−0.0586452	+	0.101576i	−0.893857	−	0.448351i	$-0.852011\pi$
$293$	−1.00384	+	1.73871i	−0.0586452	+	0.101576i	0.835212	+	0.549928i	$0.185345\pi$
$294$		0			0
$295$	−2.03641	−	3.52717i	−0.118564	−	0.205360i
$296$		0			0
$297$	17.3197	+	4.40802i	1.00499	+	0.255779i
$298$		0			0
$299$	−3.28281	+	5.68599i	−0.189850	+	0.328829i
$300$		0			0
$301$	−4.19282	+	4.80140i	−0.241670	+	0.276748i
$302$		0			0
$303$	6.36237	+	0.529758i	0.365509	+	0.0304338i
$304$		0			0
$305$	−15.8446	+	27.4436i	−0.907257	+	1.57142i
$306$		0			0
$307$	32.7633			1.86990			0.934951	−	0.354777i	$-0.115443\pi$
$307$	32.7633			1.86990			0.934951	+	0.354777i	$0.115443\pi$
$308$		0			0
$309$	27.8253	+	2.31685i	1.58292	+	0.131801i
$310$		0			0
$311$	7.04979	+	12.2106i	0.399757	+	0.692400i	0.993696	−	0.112111i	$-0.0357611\pi$
$311$	7.04979	+	12.2106i	0.399757	+	0.692400i	−0.593939	+	0.804510i	$0.702428\pi$
$312$		0			0
$313$	17.0769	−	29.5781i	0.965245	−	1.67185i	0.256291	−	0.966600i	$-0.417499\pi$
$313$	17.0769	−	29.5781i	0.965245	−	1.67185i	0.708954	−	0.705255i	$-0.249167\pi$
$314$		0			0
$315$	3.57490	+	21.7081i	0.201423	+	1.22311i
$316$		0			0
$317$	0.790586	−	1.36933i	0.0444037	−	0.0769095i	−0.842969	−	0.537962i	$-0.819195\pi$
$317$	0.790586	−	1.36933i	0.0444037	−	0.0769095i	0.887373	+	0.461052i	$0.152528\pi$
$318$		0			0
$319$	−13.7473	−	23.8110i	−0.769701	−	1.33316i
$320$		0			0
$321$	−4.67911	−	9.92548i	−0.261162	−	0.553986i
$322$		0			0
$323$	−1.21575			−0.0676459
$324$		0			0
$325$	−1.15139	+	1.99426i	−0.0638675	+	0.110622i
$326$		0			0
$327$	−9.66721	+	13.9302i	−0.534598	+	0.770341i
$328$		0			0
$329$	1.59664	+	0.314088i	0.0880257	+	0.0173163i
$330$		0			0
$331$	−6.86862	+	11.8968i	−0.377533	+	0.653907i	−0.990703	−	0.136044i	$-0.956561\pi$
$331$	−6.86862	+	11.8968i	−0.377533	+	0.653907i	0.613169	+	0.789951i	$0.289894\pi$
$332$		0			0
$333$	0.961940	+	2.57549i	0.0527140	+	0.141136i
$334$		0			0
$335$	−22.4533	−	38.8902i	−1.22675	−	2.12480i
$336$		0			0
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	−0.999596	−	0.0284243i	$-0.990951\pi$
$337$	−8.72318	+	15.1090i	−0.475182	+	0.823039i	0.524414	+	0.851463i	$0.324284\pi$
$338$		0			0
$339$	−8.03756	+	11.5819i	−0.436540	+	0.629042i
$340$		0			0
$341$	−12.4019	−	21.4807i	−0.671598	−	1.16324i
$342$		0			0
$343$	−15.4639	−	10.1916i	−0.834972	−	0.550292i
$344$		0			0
$345$	−36.5968	−	3.04721i	−1.97031	−	0.164056i
$346$		0			0
$347$	−1.91552	−	3.31778i	−0.102830	−	0.178108i	0.810019	−	0.586403i	$-0.199457\pi$
$347$	−1.91552	−	3.31778i	−0.102830	−	0.178108i	−0.912850	+	0.408296i	$0.866123\pi$
$348$		0			0
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	0.907928	−	0.419126i	$-0.137663\pi$
$349$	1.69984	+	2.94421i	0.0909903	+	0.157600i	−0.816938	+	0.576726i	$0.804330\pi$
$350$		0			0
$351$	3.11377	−	3.19313i	0.166201	−	0.170437i
$352$		0			0
$353$	12.5568			0.668332			0.334166	−	0.942514i	$-0.391545\pi$
$353$	12.5568			0.668332			0.334166	+	0.942514i	$0.391545\pi$
$354$		0			0
$355$	39.9629			2.12101
$356$		0			0
$357$	3.57124	+	1.01654i	0.189010	+	0.0538008i
$358$		0			0
$359$	−6.02209	−	10.4306i	−0.317834	−	0.550504i	0.662202	−	0.749325i	$-0.269622\pi$
$359$	−6.02209	−	10.4306i	−0.317834	−	0.550504i	−0.980036	+	0.198821i	$0.936289\pi$
$360$		0			0
$361$	8.37435	−	14.5048i	0.440756	−	0.763411i
$362$		0			0
$363$	−1.43217	−	0.119248i	−0.0751694	−	0.00625892i
$364$		0			0
$365$	−11.5554	+	20.0146i	−0.604838	+	1.04761i
$366$		0			0
$367$	−2.02514			−0.105711			−0.0528557	−	0.998602i	$-0.516832\pi$
$367$	−2.02514			−0.105711			−0.0528557	+	0.998602i	$0.516832\pi$
$368$		0			0
$369$	6.39814	−	7.75621i	0.333074	−	0.403772i
$370$		0			0
$371$	32.7950	+	6.45138i	1.70263	+	0.334939i
$372$		0			0
$373$	21.6259			1.11975			0.559874	−	0.828578i	$-0.310849\pi$
$373$	21.6259			1.11975			0.559874	+	0.828578i	$0.310849\pi$
$374$		0			0
$375$	11.0860	+	0.923065i	0.572477	+	0.0476669i
$376$		0			0
$377$	−6.86142			−0.353381
$378$		0			0
$379$	−6.76701			−0.347598			−0.173799	−	0.984781i	$-0.555604\pi$
$379$	−6.76701			−0.347598			−0.173799	+	0.984781i	$0.555604\pi$
$380$		0			0
$381$	21.6896	+	1.80597i	1.11119	+	0.0925224i
$382$		0			0
$383$	−7.65645			−0.391226			−0.195613	−	0.980681i	$-0.562670\pi$
$383$	−7.65645			−0.391226			−0.195613	+	0.980681i	$0.562670\pi$
$384$		0			0
$385$	−8.15810	−	23.8673i	−0.415775	−	1.21639i
$386$		0			0
$387$	2.52897	+	6.77104i	0.128555	+	0.344191i
$388$		0			0
$389$	−21.1561			−1.07266			−0.536329	−	0.844009i	$-0.680189\pi$
$389$	−21.1561			−1.07266			−0.536329	+	0.844009i	$0.680189\pi$
$390$		0			0
$391$	−3.09898	+	5.36759i	−0.156722	+	0.271451i
$392$		0			0
$393$	−2.73670	−	0.227869i	−0.138048	−	0.0114945i
$394$		0			0
$395$	3.81360	−	6.60534i	0.191883	−	0.332351i
$396$		0			0
$397$	4.02642	+	6.97396i	0.202080	+	0.350013i	0.949199	−	0.314678i	$-0.101896\pi$
$397$	4.02642	+	6.97396i	0.202080	+	0.350013i	−0.747118	+	0.664691i	$0.768563\pi$
$398$		0			0
$399$	4.93678	−	4.78595i	0.247148	−	0.239597i
$400$		0			0
$401$	−7.77773			−0.388401			−0.194201	−	0.980962i	$-0.562211\pi$
$401$	−7.77773			−0.388401			−0.194201	+	0.980962i	$0.562211\pi$
$402$		0			0
$403$	−6.18989			−0.308341
$404$		0			0
$405$	23.5816	+	8.13766i	1.17178	+	0.404364i
$406$		0			0
$407$	−1.57599	−	2.72969i	−0.0781188	−	0.135306i
$408$		0			0
$409$	−9.76327	−	16.9105i	−0.482763	−	0.836170i	0.517041	−	0.855960i	$-0.327033\pi$
$409$	−9.76327	−	16.9105i	−0.482763	−	0.836170i	−0.999804	+	0.0197907i	$0.993700\pi$
$410$		0			0
$411$	−8.50590	−	0.708237i	−0.419565	−	0.0349347i
$412$		0			0
$413$	2.55710	−	2.92827i	0.125827	−	0.144091i
$414$		0			0
$415$	−15.9604	−	27.6442i	−0.783466	−	1.35700i
$416$		0			0
$417$	−8.15677	+	11.7537i	−0.399439	+	0.575580i
$418$		0			0
$419$	−12.5259	+	21.6955i	−0.611932	+	1.05990i	0.378983	+	0.925404i	$0.376274\pi$
$419$	−12.5259	+	21.6955i	−0.611932	+	1.05990i	−0.990915	+	0.134493i	$0.957059\pi$
$420$		0			0
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.850340	+	0.526234i	$0.176396\pi$
$421$	18.0746	+	31.3061i	0.880902	+	1.52577i	0.0305620	+	0.999533i	$0.490270\pi$
$422$		0			0
$423$	1.17412	−	1.42334i	0.0570878	−	0.0692052i
$424$		0			0
$425$	−1.08691	+	1.88259i	−0.0527231	+	0.0913190i
$426$		0			0
$427$	−29.6793	−	5.83845i	−1.43628	−	0.282543i
$428$		0			0
$429$	−2.91528	+	4.20084i	−0.140751	+	0.202818i
$430$		0			0
$431$	−1.95636	+	3.38852i	−0.0942346	+	0.163219i	−0.909289	−	0.416165i	$-0.863374\pi$
$431$	−1.95636	+	3.38852i	−0.0942346	+	0.163219i	0.815054	+	0.579385i	$0.196707\pi$
$432$		0			0
$433$	−14.2929			−0.686872			−0.343436	−	0.939176i	$-0.611591\pi$
$433$	−14.2929			−0.686872			−0.343436	+	0.939176i	$0.611591\pi$
$434$		0			0
$435$	−16.3650	−	34.7139i	−0.784640	−	1.66441i
$436$		0			0
$437$	5.73862	+	9.93958i	0.274515	+	0.475475i
$438$		0			0
$439$	2.39235	−	4.14367i	0.114180	−	0.197766i	−0.803271	−	0.595613i	$-0.796909\pi$
$439$	2.39235	−	4.14367i	0.114180	−	0.197766i	0.917452	+	0.397847i	$0.130242\pi$
$440$		0			0
$441$	−18.5035	+	9.93085i	−0.881117	+	0.472898i
$442$		0			0
$443$	4.13213	−	7.15707i	0.196324	−	0.340042i	−0.751010	−	0.660291i	$-0.770433\pi$
$443$	4.13213	−	7.15707i	0.196324	−	0.340042i	0.947334	+	0.320248i	$0.103766\pi$
$444$		0			0
$445$	−14.1748	−	24.5515i	−0.671952	−	1.16385i
$446$		0			0
$447$	24.0166	+	1.99972i	1.13594	+	0.0945835i
$448$		0			0
$449$	−20.6036			−0.972346			−0.486173	−	0.873863i	$-0.661608\pi$
$449$	−20.6036			−0.972346			−0.486173	+	0.873863i	$0.661608\pi$
$450$		0			0
$451$	−5.76370	+	9.98301i	−0.271402	+	0.470082i
$452$		0			0
$453$	−39.6872	−	3.30453i	−1.86467	−	0.155260i
$454$		0			0
$455$	−6.17617	−	1.21497i	−0.289543	−	0.0569585i
$456$		0			0
$457$	8.98220	−	15.5576i	0.420170	−	0.727755i	−0.575786	−	0.817600i	$-0.695304\pi$
$457$	8.98220	−	15.5576i	0.420170	−	0.727755i	0.995956	+	0.0898451i	$0.0286372\pi$
$458$		0			0
$459$	2.93941	−	3.01432i	0.137200	−	0.140697i
$460$		0			0
$461$	4.03501	+	6.98885i	0.187929	+	0.325503i	0.944560	−	0.328340i	$-0.106489\pi$
$461$	4.03501	+	6.98885i	0.187929	+	0.325503i	−0.756630	+	0.653843i	$0.773156\pi$
$462$		0			0
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	−0.918383	−	0.395692i	$-0.870505\pi$
$463$	−2.50704	+	4.34232i	−0.116512	+	0.201805i	0.801871	+	0.597497i	$0.203838\pi$
$464$		0			0
$465$	−14.7633	−	31.3165i	−0.684633	−	1.45227i
$466$		0			0
$467$	−13.1673	−	22.8063i	−0.609308	−	1.05535i	−0.991355	−	0.131209i	$-0.958114\pi$
$467$	−13.1673	−	22.8063i	−0.609308	−	1.05535i	0.382047	−	0.924143i	$-0.375219\pi$
$468$		0			0
$469$	28.1944	−	32.2868i	1.30189	−	1.49086i
$470$		0			0
$471$	13.7230	+	29.1098i	0.632323	+	1.34131i
$472$		0			0
$473$	−4.14332	−	7.17645i	−0.190510	−	0.329973i
$474$		0			0
$475$	2.01272	+	3.48614i	0.0923500	+	0.159955i
$476$		0			0
$477$	24.1165	−	29.2354i	1.10422	−	1.33860i
$478$		0			0
$479$	−25.2445			−1.15345			−0.576724	−	0.816939i	$-0.695669\pi$
$479$	−25.2445			−1.15345			−0.576724	+	0.816939i	$0.695669\pi$
$480$		0			0
$481$	−0.786591			−0.0358655
$482$		0			0
$483$	−8.54625	−	33.9957i	−0.388868	−	1.54686i
$484$		0			0
$485$	10.6119	+	18.3803i	0.481861	+	0.834608i
$486$		0			0
$487$	1.36124	−	2.35774i	0.0616837	−	0.106839i	−0.833534	−	0.552468i	$-0.813686\pi$
$487$	1.36124	−	2.35774i	0.0616837	−	0.106839i	0.895218	+	0.445628i	$0.147020\pi$
$488$		0			0
$489$	3.62187	+	7.68283i	0.163787	+	0.347430i
$490$		0			0
$491$	−15.8020	+	27.3698i	−0.713134	+	1.23518i	0.250541	+	0.968106i	$0.419391\pi$
$491$	−15.8020	+	27.3698i	−0.713134	+	1.23518i	−0.963675	+	0.267078i	$0.913942\pi$
$492$		0			0
$493$	−6.47720			−0.291718
$494$		0			0
$495$	−28.2064	−	4.72996i	−1.26778	−	0.212596i
$496$		0			0
$497$	12.3377	+	36.0953i	0.553424	+	1.61909i
$498$		0			0
$499$	5.94890			0.266309			0.133155	−	0.991095i	$-0.457489\pi$
$499$	5.94890			0.266309			0.133155	+	0.991095i	$0.457489\pi$
$500$		0			0
$501$	10.8130	−	15.5813i	0.483091	−	0.696121i
$502$		0			0
$503$	−27.6905			−1.23466			−0.617329	−	0.786705i	$-0.711785\pi$
$503$	−27.6905			−1.23466			−0.617329	+	0.786705i	$0.711785\pi$
$504$		0			0
$505$	−10.2169			−0.454647
$506$		0			0
$507$	−9.05732	−	19.2127i	−0.402250	−	0.853267i
$508$		0			0
$509$	37.2885			1.65278			0.826392	−	0.563095i	$-0.190389\pi$
$509$	37.2885			1.65278			0.826392	+	0.563095i	$0.190389\pi$
$510$		0			0
$511$	−21.6450	−	4.25798i	−0.957521	−	0.188362i
$512$		0			0
$513$	−2.11246	−	7.50482i	−0.0932674	−	0.331346i
$514$		0			0
$515$	−44.6828			−1.96896
$516$		0			0
$517$	−1.05769	+	1.83198i	−0.0465174	+	0.0805704i
$518$		0			0
$519$	−13.2379	+	19.0755i	−0.581080	+	0.837321i
$520$		0			0
$521$	18.1271	−	31.3971i	0.794163	−	1.37553i	−0.129207	−	0.991618i	$-0.541243\pi$
$521$	18.1271	−	31.3971i	0.794163	−	1.37553i	0.923370	−	0.383912i	$-0.125423\pi$
$522$		0			0
$523$	10.2931	+	17.8282i	0.450086	+	0.779572i	0.998391	−	0.0567068i	$-0.0180600\pi$
$523$	10.2931	+	17.8282i	0.450086	+	0.779572i	−0.548305	+	0.836278i	$0.684727\pi$
$524$		0			0
$525$	−2.99745	−	11.9234i	−0.130819	−	0.520380i
$526$		0			0
$527$	−5.84328			−0.254537
$528$		0			0
$529$	35.5118			1.54399
$530$		0			0
$531$	−1.54236	−	4.12951i	−0.0669329	−	0.179205i
$532$		0			0
$533$	1.43836	+	2.49131i	0.0623023	+	0.107911i
$534$		0			0
$535$	8.78013	+	15.2076i	0.379598	+	0.657483i
$536$		0			0
$537$	13.1316	−	18.9223i	0.566670	−	0.816556i
$538$		0			0
$539$	19.0388	−	14.7371i	0.820057	−	0.634772i
$540$		0			0
$541$	−0.649192	−	1.12443i	−0.0279109	−	0.0483432i	0.851733	−	0.523977i	$-0.175552\pi$
$541$	−0.649192	−	1.12443i	−0.0279109	−	0.0483432i	−0.879643	+	0.475634i	$0.842219\pi$
$542$		0			0
$543$	18.8470	+	1.56928i	0.808802	+	0.0673443i
$544$		0			0
$545$	13.5673	−	23.4993i	0.581159	−	1.00660i
$546$		0			0
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	−0.993989	−	0.109478i	$-0.965082\pi$
$547$	−13.8412	−	23.9736i	−0.591805	−	1.02504i	0.402184	−	0.915559i	$-0.368251\pi$
$548$		0			0
$549$	−21.8252	+	26.4579i	−0.931479	+	1.12919i
$550$		0			0
$551$	−5.99716	+	10.3874i	−0.255488	+	0.442518i
$552$		0			0
$553$	7.14344	+	1.40525i	0.303770	+	0.0597571i
$554$		0			0
$555$	−1.87608	−	3.97960i	−0.0796350	−	0.168924i
$556$		0			0
$557$	−7.72089	+	13.3730i	−0.327145	+	0.566631i	−0.981944	−	0.189172i	$-0.939420\pi$
$557$	−7.72089	+	13.3730i	−0.327145	+	0.566631i	0.654799	+	0.755803i	$0.272753\pi$
$558$		0			0
$559$	−2.06797			−0.0874660
$560$		0			0
$561$	−2.75203	+	3.96560i	−0.116191	+	0.167428i
$562$		0			0
$563$	−0.956715	−	1.65708i	−0.0403207	−	0.0698375i	0.845161	−	0.534512i	$-0.179505\pi$
$563$	−0.956715	−	1.65708i	−0.0403207	−	0.0698375i	−0.885482	+	0.464675i	$0.846171\pi$
$564$		0			0
$565$	11.2802	−	19.5379i	0.474561	−	0.821964i
$566$		0			0
$567$	−0.0697573	+	23.8117i	−0.00292953	+	0.999996i
$568$		0			0
$569$	7.38138	−	12.7849i	0.309444	−	0.535972i	−0.668797	−	0.743445i	$-0.733191\pi$
$569$	7.38138	−	12.7849i	0.309444	−	0.535972i	0.978241	+	0.207473i	$0.0665239\pi$
$570$		0			0
$571$	−1.28208	−	2.22063i	−0.0536535	−	0.0929306i	0.837951	−	0.545745i	$-0.183753\pi$
$571$	−1.28208	−	2.22063i	−0.0536535	−	0.0929306i	−0.891605	+	0.452814i	$0.850420\pi$
$572$		0			0
$573$	−18.3785	+	26.4829i	−0.767773	+	1.10634i
$574$		0			0
$575$	20.5220			0.855827
$576$		0			0
$577$	7.01283	−	12.1466i	0.291948	−	0.505669i	−0.682322	−	0.731052i	$-0.739030\pi$
$577$	7.01283	−	12.1466i	0.291948	−	0.505669i	0.974270	+	0.225383i	$0.0723632\pi$
$578$		0			0
$579$	2.16358	+	4.58945i	0.0899151	+	0.190731i
$580$		0			0
$581$	20.0413	−	22.9504i	0.831455	−	0.952141i
$582$		0			0
$583$	−21.7251	+	37.6289i	−0.899760	+	1.55843i
$584$		0			0
$585$	−4.54177	+	5.50581i	−0.187779	+	0.227637i
$586$		0			0
$587$	15.7666	+	27.3085i	0.650756	+	1.12714i	0.982940	+	0.183928i	$0.0588813\pi$
$587$	15.7666	+	27.3085i	0.650756	+	1.12714i	−0.332183	+	0.943215i	$0.607785\pi$
$588$		0			0
$589$	−5.41022	+	9.37078i	−0.222924	+	0.386116i
$590$		0			0
$591$	31.9411	+	2.65955i	1.31388	+	0.109399i
$592$		0			0
$593$	−5.72311	−	9.91272i	−0.235020	−	0.407067i	0.724258	−	0.689529i	$-0.242182\pi$
$593$	−5.72311	−	9.91272i	−0.235020	−	0.407067i	−0.959279	+	0.282462i	$0.908849\pi$
$594$		0			0
$595$	−5.83033	−	1.14693i	−0.239020	−	0.0470196i
$596$		0			0
$597$	−1.56783	+	2.25921i	−0.0641672	+	0.0924631i
$598$		0			0
$599$	−2.80684	−	4.86159i	−0.114684	−	0.198639i	0.802969	−	0.596021i	$-0.203252\pi$
$599$	−2.80684	−	4.86159i	−0.114684	−	0.198639i	−0.917654	+	0.397381i	$0.869919\pi$
$600$		0			0
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	0.929539	+	0.368725i	$0.120205\pi$
$601$	19.2223	+	33.2940i	0.784094	+	1.35809i	−0.145444	+	0.989366i	$0.546461\pi$
$602$		0			0
$603$	−17.0059	−	45.5315i	−0.692535	−	1.85418i
$604$		0			0
$605$	2.29983			0.0935013
$606$		0			0
$607$	−16.3437			−0.663372			−0.331686	−	0.943390i	$-0.607617\pi$
$607$	−16.3437			−0.663372			−0.331686	+	0.943390i	$0.607617\pi$
$608$		0			0
$609$	26.3019	−	25.4984i	1.06581	−	1.03325i
$610$		0			0
$611$	0.263953	+	0.457180i	0.0106784	+	0.0184955i
$612$		0			0
$613$	−6.19332	+	10.7272i	−0.250146	+	0.433266i	−0.963566	−	0.267471i	$-0.913812\pi$
$613$	−6.19332	+	10.7272i	−0.250146	+	0.433266i	0.713420	+	0.700737i	$0.247145\pi$
$614$		0			0
$615$	−9.17369	+	13.2190i	−0.369919	+	0.533043i
$616$		0			0
$617$	20.9853	−	36.3476i	0.844836	−	1.46330i	−0.0409280	−	0.999162i	$-0.513031\pi$
$617$	20.9853	−	36.3476i	0.844836	−	1.46330i	0.885764	−	0.464136i	$-0.153635\pi$
$618$		0			0
$619$	−35.8945			−1.44272			−0.721361	−	0.692559i	$-0.756483\pi$
$619$	−35.8945			−1.44272			−0.721361	+	0.692559i	$0.756483\pi$
$620$		0			0
$621$	−38.5190	−	9.80342i	−1.54571	−	0.393398i
$622$		0			0
$623$	17.7992	−	20.3828i	0.713111	−	0.816619i
$624$		0			0
$625$	−31.2166			−1.24866
$626$		0			0
$627$	3.81151	+	8.08510i	0.152217	+	0.322888i
$628$		0			0
$629$	−0.742544			−0.0296072
$630$		0			0
$631$	−19.5519			−0.778349			−0.389175	−	0.921164i	$-0.627240\pi$
$631$	−19.5519			−0.778349			−0.389175	+	0.921164i	$0.627240\pi$
$632$		0			0
$633$	−24.3788	+	35.1291i	−0.968968	+	1.39626i
$634$		0			0
$635$	−34.8299			−1.38218
$636$		0			0
$637$	−0.809390	−	5.95353i	−0.0320692	−	0.235888i
$638$		0			0
$639$	42.6574	+	7.15327i	1.68750	+	0.282979i
$640$		0			0
$641$	−14.6026			−0.576769			−0.288385	−	0.957515i	$-0.593118\pi$
$641$	−14.6026			−0.576769			−0.288385	+	0.957515i	$0.593118\pi$
$642$		0			0
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	−0.959392	−	0.282076i	$-0.908977\pi$
$643$	−5.96942	+	10.3393i	−0.235411	+	0.407744i	0.723981	+	0.689820i	$0.242310\pi$
$644$		0			0
$645$	−4.93227	−	10.4625i	−0.194208	−	0.411960i
$646$		0			0
$647$	−1.92060	+	3.32658i	−0.0755067	+	0.130781i	−0.901306	−	0.433182i	$-0.857391\pi$
$647$	−1.92060	+	3.32658i	−0.0755067	+	0.130781i	0.825800	+	0.563963i	$0.190724\pi$
$648$		0			0
$649$	2.52692	+	4.37675i	0.0991903	+	0.171803i
$650$		0			0
$651$	23.7278	−	23.0029i	0.929965	−	0.901554i
$652$		0			0
$653$	39.9918			1.56500			0.782501	−	0.622650i	$-0.213944\pi$
$653$	39.9918			1.56500			0.782501	+	0.622650i	$0.213944\pi$
$654$		0			0
$655$	4.39469			0.171715
$656$		0			0
$657$	−15.9171	+	19.2957i	−0.620986	+	0.752796i
$658$		0			0
$659$	1.60101	+	2.77303i	0.0623665	+	0.108022i	0.895523	−	0.445016i	$-0.146802\pi$
$659$	1.60101	+	2.77303i	0.0623665	+	0.108022i	−0.833156	+	0.553038i	$0.813469\pi$
$660$		0			0
$661$	21.6515	+	37.5015i	0.842146	+	1.45864i	0.888077	+	0.459695i	$0.152041\pi$
$661$	21.6515	+	37.5015i	0.842146	+	1.45864i	−0.0459311	+	0.998945i	$0.514625\pi$
$662$		0			0
$663$	0.513658	+	1.08959i	0.0199488	+	0.0423162i
$664$		0			0
$665$	−7.23755	+	8.28808i	−0.280660	+	0.321398i
$666$		0			0
$667$	30.5740	+	52.9557i	1.18383	+	2.05045i
$668$		0			0
$669$	14.4534	+	30.6591i	0.558801	+	1.18535i
$670$		0			0
$671$	19.6610	−	34.0539i	0.759006	−	1.31464i
$672$		0			0
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	0.999553	−	0.0298991i	$-0.00951859\pi$
$673$	12.2936	+	21.2931i	0.473883	+	0.820790i	−0.525670	+	0.850689i	$0.676185\pi$
$674$		0			0
$675$	−13.5099	−	3.43838i	−0.519995	−	0.132343i
$676$		0			0
$677$	19.2094	−	33.2716i	0.738276	−	1.27873i	−0.214994	−	0.976615i	$-0.568973\pi$
$677$	19.2094	−	33.2716i	0.738276	−	1.27873i	0.953271	−	0.302117i	$-0.0976933\pi$
$678$		0			0
$679$	−13.3253	+	15.2594i	−0.511376	+	0.585603i
$680$		0			0
$681$	−14.9273	−	1.24291i	−0.572013	−	0.0476282i
$682$		0			0
$683$	−0.122464	+	0.212113i	−0.00468594	+	0.00811629i	−0.868359	−	0.495936i	$-0.834825\pi$
$683$	−0.122464	+	0.212113i	−0.00468594	+	0.00811629i	0.863673	+	0.504053i	$0.168158\pi$
$684$		0			0
$685$	13.6591			0.521886
$686$		0			0
$687$	−19.9236	−	1.65893i	−0.760135	−	0.0632920i
$688$		0			0
$689$	5.42160	+	9.39049i	0.206547	+	0.357749i
$690$		0			0
$691$	3.65146	−	6.32452i	0.138908	−	0.240596i	−0.788175	−	0.615451i	$-0.788974\pi$
$691$	3.65146	−	6.32452i	0.138908	−	0.240596i	0.927084	+	0.374855i	$0.122307\pi$
$692$		0			0
$693$	−4.43598	−	26.9369i	−0.168509	−	1.02325i
$694$		0			0
$695$	11.4475	−	19.8277i	0.434229	−	0.752106i
$696$		0			0
$697$	1.35782	+	2.35181i	0.0514309	+	0.0890810i
$698$		0			0
$699$	12.0054	+	25.4664i	0.454087	+	0.963226i
$700$		0			0
$701$	32.3889			1.22331			0.611656	−	0.791124i	$-0.290504\pi$
$701$	32.3889			1.22331			0.611656	+	0.791124i	$0.290504\pi$
$702$		0			0
$703$	−0.687513	+	1.19081i	−0.0259301	+	0.0449122i
$704$		0			0
$705$	−1.68346	+	2.42582i	−0.0634029	+	0.0913618i
$706$		0			0
$707$	−3.15427	−	9.22813i	−0.118629	−	0.347059i
$708$		0			0
$709$	−1.46137	+	2.53116i	−0.0548828	+	0.0950599i	−0.892162	−	0.451716i	$-0.850812\pi$
$709$	−1.46137	+	2.53116i	−0.0548828	+	0.0950599i	0.837279	+	0.546776i	$0.184145\pi$
$710$		0			0
$711$	5.25307	−	6.36809i	0.197006	−	0.238822i
$712$		0			0
$713$	27.5817	+	47.7729i	1.03294	+	1.78911i
$714$		0			0
$715$	4.09141	−	7.08652i	0.153010	−	0.265021i
$716$		0			0
$717$	−24.5564	+	35.3851i	−0.917075	+	1.32148i
$718$		0			0
$719$	8.78527	+	15.2165i	0.327635	+	0.567481i	0.982042	−	0.188662i	$-0.0604150\pi$
$719$	8.78527	+	15.2165i	0.327635	+	0.567481i	−0.654407	+	0.756143i	$0.727082\pi$
$720$		0			0
$721$	−13.7949	−	40.3584i	−0.513750	−	1.50302i
$722$		0			0
$723$	32.8581	+	2.73590i	1.22201	+	0.101749i
$724$		0			0
$725$	10.7233	+	18.5733i	0.398253	+	0.689795i
$726$		0			0
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	0.950864	+	0.309609i	$0.100198\pi$
$727$	20.0486	+	34.7252i	0.743561	+	1.28789i	−0.207303	+	0.978277i	$0.566469\pi$
$728$		0			0
$729$	23.7150	+	12.9074i	0.878332	+	0.478052i
$730$		0			0
$731$	−1.95217			−0.0722037
$732$		0			0
$733$	−7.12469			−0.263156			−0.131578	−	0.991306i	$-0.542004\pi$
$733$	−7.12469			−0.263156			−0.131578	+	0.991306i	$0.542004\pi$
$734$		0			0
$735$	28.1902	−	18.2945i	1.03981	−	0.674805i
$736$		0			0
$737$	27.8615	+	48.2576i	1.02629	+	1.77759i
$738$		0			0
$739$	−2.13570	+	3.69914i	−0.0785631	+	0.136075i	−0.902630	−	0.430417i	$-0.858367\pi$
$739$	−2.13570	+	3.69914i	−0.0785631	+	0.136075i	0.824067	+	0.566492i	$0.191700\pi$
$740$		0			0
$741$	2.22295	+	0.185092i	0.0816621	+	0.00679953i
$742$		0			0
$743$	0.108257	−	0.187507i	0.00397157	−	0.00687896i	−0.864033	−	0.503436i	$-0.832069\pi$
$743$	0.108257	−	0.187507i	0.00397157	−	0.00687896i	0.868004	+	0.496557i	$0.165402\pi$
$744$		0			0
$745$	−38.5667			−1.41297
$746$		0			0
$747$	−12.0883	−	32.3651i	−0.442288	−	1.18418i
$748$		0			0
$749$	−11.0251	+	12.6254i	−0.402849	+	0.461323i
$750$		0			0
$751$	23.5840			0.860594			0.430297	−	0.902687i	$-0.358409\pi$
$751$	23.5840			0.860594			0.430297	+	0.902687i	$0.358409\pi$
$752$		0			0
$753$	1.69230	+	0.140908i	0.0616710	+	0.00513499i
$754$		0			0
$755$	63.7312			2.31942
$756$		0			0
$757$	−22.0176			−0.800242			−0.400121	−	0.916462i	$-0.631032\pi$
$757$	−22.0176			−0.800242			−0.400121	+	0.916462i	$0.631032\pi$
$758$		0			0
$759$	45.4119	+	3.78118i	1.64835	+	0.137248i
$760$		0			0
$761$	−18.1140			−0.656631			−0.328316	−	0.944568i	$-0.606481\pi$
$761$	−18.1140			−0.656631			−0.328316	+	0.944568i	$0.606481\pi$
$762$		0			0
$763$	25.4136	+	4.99932i	0.920035	+	0.180988i
$764$		0			0
$765$	−4.28745	+	5.19750i	−0.155013	+	0.187916i
$766$		0			0
$767$	1.26121			0.0455397
$768$		0			0
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	−0.803255	−	0.595636i	$-0.796900\pi$
$769$	3.16710	−	5.48558i	0.114209	−	0.197815i	0.917463	+	0.397821i	$0.130233\pi$
$770$		0			0
$771$	−7.53821	−	0.627663i	−0.271482	−	0.0226047i
$772$		0			0
$773$	3.10740	−	5.38218i	0.111765	−	0.193584i	−0.804717	−	0.593659i	$-0.797683\pi$
$773$	3.10740	−	5.38218i	0.111765	−	0.193584i	0.916482	+	0.400076i	$0.131016\pi$
$774$		0			0
$775$	9.67381	+	16.7555i	0.347494	+	0.601876i
$776$		0			0
$777$	3.01525	−	2.92313i	0.108171	−	0.104867i
$778$		0			0
$779$	5.02874			0.180173
$780$		0			0
$781$	−49.5887			−1.77442
$782$		0			0
$783$	−11.2547	−	39.9839i	−0.402209	−	1.42891i
$784$		0			0
$785$	−25.7506	−	44.6014i	−0.919079	−	1.59189i
$786$		0			0
$787$	9.65916	+	16.7302i	0.344312	+	0.596366i	0.985229	−	0.171245i	$-0.0547789\pi$
$787$	9.65916	+	16.7302i	0.344312	+	0.596366i	−0.640917	+	0.767611i	$0.721446\pi$
$788$		0			0
$789$	21.5488	+	1.79424i	0.767156	+	0.0638766i
$790$		0			0
$791$	21.1295	+	4.15656i	0.751279	+	0.147790i
$792$		0			0
$793$	−4.90651	−	8.49832i	−0.174235	−	0.301784i
$794$		0			0
$795$	−34.5784	+	49.8265i	−1.22637	+	1.76716i
$796$		0			0
$797$	−5.09519	+	8.82513i	−0.180481	+	0.312602i	−0.942044	−	0.335488i	$-0.891099\pi$
$797$	−5.09519	+	8.82513i	−0.180481	+	0.312602i	0.761563	+	0.648090i	$0.224432\pi$
$798$		0			0
$799$	0.249172	+	0.431579i	0.00881509	+	0.0152682i
$800$		0			0
$801$	−10.7359	−	28.7442i	−0.379335	−	1.01563i
$802$		0			0
$803$	14.3388	−	24.8355i	0.506004	−	0.876424i
$804$		0			0
$805$	18.1436	+	53.0808i	0.639478	+	1.87085i
$806$		0			0
$807$	−16.3781	+	23.6005i	−0.576538	+	0.830776i
$808$		0			0
$809$	−23.7068	+	41.0613i	−0.833485	+	1.44364i	0.0617729	+	0.998090i	$0.480325\pi$
$809$	−23.7068	+	41.0613i	−0.833485	+	1.44364i	−0.895258	+	0.445548i	$0.853009\pi$
$810$		0			0
$811$	47.4177			1.66506			0.832531	−	0.553979i	$-0.186891\pi$
$811$	47.4177			1.66506			0.832531	+	0.553979i	$0.186891\pi$
$812$		0			0
$813$	−19.1755	−	40.6757i	−0.672514	−	1.42656i
$814$		0			0
$815$	−6.79627	−	11.7715i	−0.238063	−	0.412337i
$816$		0			0
$817$	−1.80750	+	3.13067i	−0.0632363	+	0.109528i
$818$		0			0
$819$	−6.37513	−	2.40241i	−0.222765	−	0.0839469i
$820$		0			0
$821$	−26.8177	+	46.4495i	−0.935943	+	1.62110i	−0.162998	+	0.986626i	$0.552117\pi$
$821$	−26.8177	+	46.4495i	−0.935943	+	1.62110i	−0.772944	+	0.634474i	$0.781217\pi$
$822$		0			0
$823$	0.475192	+	0.823057i	0.0165641	+	0.0286899i	0.874189	−	0.485586i	$-0.161394\pi$
$823$	0.475192	+	0.823057i	0.0165641	+	0.0286899i	−0.857625	+	0.514276i	$0.828061\pi$
$824$		0			0
$825$	15.9274	+	1.32618i	0.554522	+	0.0461718i
$826$		0			0
$827$	20.7813			0.722636			0.361318	−	0.932443i	$-0.382327\pi$
$827$	20.7813			0.722636			0.361318	+	0.932443i	$0.382327\pi$
$828$		0			0
$829$	12.1615	−	21.0644i	0.422387	−	0.731596i	−0.573785	−	0.819006i	$-0.694526\pi$
$829$	12.1615	−	21.0644i	0.422387	−	0.731596i	0.996172	+	0.0874096i	$0.0278589\pi$
$830$		0			0
$831$	3.38440	+	0.281799i	0.117403	+	0.00977551i
$832$		0			0
$833$	−0.764066	−	5.62015i	−0.0264733	−	0.194727i
$834$		0			0
$835$	−15.1754	+	26.2846i	−0.525166	+	0.909615i
$836$		0			0
$837$	−10.1532	−	36.0707i	−0.350946	−	1.24678i
$838$		0			0
$839$	−15.7367	−	27.2567i	−0.543290	−	0.941006i	−0.998712	−	0.0507305i	$-0.983845\pi$
$839$	−15.7367	−	27.2567i	−0.543290	−	0.941006i	0.455422	−	0.890276i	$-0.349488\pi$
$840$		0			0
$841$	−17.4514	+	30.2268i	−0.601774	+	1.04230i
$842$		0			0
$843$	−13.9156	−	29.5182i	−0.479277	−	1.01666i
$844$		0			0
$845$	16.9957	+	29.4373i	0.584668	+	1.01268i
$846$		0			0
$847$	0.710026	+	2.07725i	0.0243968	+	0.0713751i
$848$		0			0
$849$	−17.3450	−	36.7928i	−0.595278	−	1.26272i
$850$		0			0
$851$	3.50499	+	6.07082i	0.120150	+	0.208105i
$852$		0			0
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.808287	−	0.588788i	$-0.799605\pi$
$853$	−26.6959	−	46.2386i	−0.914049	−	1.58318i	−0.105762	−	0.994391i	$-0.533728\pi$
$854$		0			0
$855$	4.36546	+	11.6880i	0.149296	+	0.399722i
$856$		0			0
$857$	21.6297			0.738857			0.369428	−	0.929259i	$-0.379554\pi$
$857$	21.6297			0.738857			0.369428	+	0.929259i	$0.379554\pi$
$858$		0			0
$859$	−34.4288			−1.17470			−0.587348	−	0.809334i	$-0.699828\pi$
$859$	−34.4288			−1.17470			−0.587348	+	0.809334i	$0.699828\pi$
$860$		0			0
$861$	−14.7719	−	4.20474i	−0.503425	−	0.143297i
$862$		0			0
$863$	−13.4262	−	23.2548i	−0.457033	−	0.791604i	0.541770	−	0.840527i	$-0.317754\pi$
$863$	−13.4262	−	23.2548i	−0.457033	−	0.791604i	−0.998803	+	0.0489229i	$0.984421\pi$
$864$		0			0
$865$	18.5786	−	32.1790i	0.631690	−	1.09412i
$866$		0			0
$867$	−12.0709	−	25.6051i	−0.409948	−	0.869595i
$868$		0			0
$869$	−4.73217	+	8.19636i	−0.160528	+	0.278043i
$870$		0			0
$871$	13.9060			0.471186
$872$		0			0
$873$	8.03737	+	21.5191i	0.272024	+	0.728313i
$874$		0			0
$875$	−5.49609	−	16.0793i	−0.185802	−	0.543581i
$876$		0			0
$877$	32.4068			1.09430			0.547150	−	0.837034i	$-0.315713\pi$
$877$	32.4068			1.09430			0.547150	+	0.837034i	$0.315713\pi$
$878$		0			0
$879$	1.98260	−	2.85687i	0.0668715	−	0.0963599i
$880$		0			0
$881$	−39.0404			−1.31530			−0.657652	−	0.753322i	$-0.728450\pi$
$881$	−39.0404			−1.31530			−0.657652	+	0.753322i	$0.728450\pi$
$882$		0			0
$883$	−13.8079			−0.464672			−0.232336	−	0.972636i	$-0.574637\pi$
$883$	−13.8079			−0.464672			−0.232336	+	0.972636i	$0.574637\pi$
$884$		0			0
$885$	3.00808	+	6.38084i	0.101115	+	0.214490i
$886$		0			0
$887$	23.9555			0.804348			0.402174	−	0.915563i	$-0.368255\pi$
$887$	23.9555			0.804348			0.402174	+	0.915563i	$0.368255\pi$
$888$		0			0
$889$	−10.7530	−	31.4590i	−0.360645	−	1.05510i
$890$		0			0
$891$	−29.2616	−	10.0978i	−0.980301	−	0.338288i
$892$		0			0
$893$	0.922824			0.0308811
$894$		0			0
$895$	−18.4293	+	31.9206i	−0.616025	+	1.06699i
$896$		0			0
$897$	6.48357	−	9.34265i	0.216480	−	0.311942i
$898$		0			0
$899$	−28.8244	+	49.9253i	−0.961346	+	1.66510i
$900$		0			0
$901$	5.11801	+	8.86465i	0.170505	+	0.295324i
$902$		0			0
$903$	7.92719	−	7.68500i	0.263800	−	0.255741i
$904$		0			0
$905$	−30.2652			−1.00605
$906$		0			0
$907$	4.70128			0.156103			0.0780517	−	0.996949i	$-0.475130\pi$
$907$	4.70128			0.156103			0.0780517	+	0.996949i	$0.475130\pi$
$908$		0			0
$909$	−10.9058	−	1.82881i	−0.361723	−	0.0606577i
$910$		0			0
$911$	21.0884	+	36.5262i	0.698689	+	1.21017i	0.968921	+	0.247370i	$0.0795663\pi$
$911$	21.0884	+	36.5262i	0.698689	+	1.21017i	−0.270232	+	0.962795i	$0.587100\pi$
$912$		0			0
$913$	19.8048	+	34.3029i	0.655442	+	1.13526i
$914$		0			0
$915$	31.2932	−	45.0926i	1.03452	−	1.49071i
$916$		0			0
$917$	1.35677	+	3.96937i	0.0448046	+	0.131080i
$918$		0			0
$919$	−20.1071	−	34.8265i	−0.663271	−	1.14882i	−0.979751	−	0.200220i	$-0.935834\pi$
$919$	−20.1071	−	34.8265i	−0.663271	−	1.14882i	0.316480	−	0.948599i	$-0.397499\pi$
$920$		0			0
$921$	−56.5521	−	4.70876i	−1.86345	−	0.155159i
$922$		0			0
$923$	−6.18756	+	10.7172i	−0.203666	+	0.352760i
$924$		0			0
$925$	1.22932	+	2.12924i	0.0404196	+	0.0700089i
$926$		0			0
$927$	−47.6956	−	7.99812i	−1.56653	−	0.262693i
$928$		0			0
$929$	15.0712	−	26.1040i	0.494469	−	0.856446i	−0.505510	−	0.862820i	$-0.668696\pi$
$929$	15.0712	−	26.1040i	0.494469	−	0.856446i	0.999980	+	0.00637464i	$0.00202912\pi$
$930$		0			0
$931$	−9.72040	−	3.97831i	−0.318573	−	0.130384i
$932$		0			0
$933$	−10.4136	−	22.0896i	−0.340925	−	0.723183i
$934$		0			0
$935$	3.86230	−	6.68970i	0.126311	−	0.218776i
$936$		0			0
$937$	35.1550			1.14846			0.574231	−	0.818693i	$-0.305301\pi$
$937$	35.1550			1.14846			0.574231	+	0.818693i	$0.305301\pi$
$938$		0			0
$939$	−33.7271	+	48.5998i	−1.10064	+	1.58600i
$940$		0			0
$941$	1.52163	+	2.63554i	0.0496038	+	0.0859162i	0.889761	−	0.456426i	$-0.150871\pi$
$941$	1.52163	+	2.63554i	0.0496038	+	0.0859162i	−0.840157	+	0.542343i	$0.817537\pi$
$942$		0			0
$943$	12.8184	−	22.2022i	0.417426	−	0.723003i
$944$		0			0
$945$	−3.05066	−	37.9836i	−0.0992378	−	1.23561i
$946$		0			0
$947$	−6.33905	+	10.9796i	−0.205991	+	0.356788i	−0.950448	−	0.310883i	$-0.899375\pi$
$947$	−6.33905	+	10.9796i	−0.205991	+	0.356788i	0.744457	+	0.667671i	$0.232709\pi$
$948$		0			0
$949$	−3.57831	−	6.19781i	−0.116157	−	0.201190i
$950$		0			0
$951$	−1.56141	+	2.24996i	−0.0506323	+	0.0729598i
$952$		0			0
$953$	23.0052			0.745212			0.372606	−	0.927990i	$-0.378464\pi$
$953$	23.0052			0.745212			0.372606	+	0.927990i	$0.378464\pi$
$954$		0			0
$955$	25.7930	−	44.6749i	0.834643	−	1.44564i
$956$		0			0
$957$	20.3068	+	43.0755i	0.656425	+	1.39243i
$958$		0			0
$959$	4.21697	+	12.3371i	0.136173	+	0.398387i
$960$		0			0
$961$	−10.5033	+	18.1923i	−0.338817	+	0.586849i
$962$		0			0
$963$	6.65001	+	17.8046i	0.214293	+	0.573746i
$964$		0			0
$965$	−4.05985	−	7.03187i	−0.130691	−	0.226364i
$966$		0			0
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	−0.875788	−	0.482697i	$-0.839657\pi$
$967$	−0.617767	+	1.07000i	−0.0198660	+	0.0344090i	0.855921	+	0.517106i	$0.172991\pi$
$968$		0			0
$969$	2.09847	+	0.174728i	0.0674126	+	0.00561306i
$970$		0			0
$971$	−7.01657	−	12.1530i	−0.225172	−	0.390010i	0.731199	−	0.682164i	$-0.238961\pi$
$971$	−7.01657	−	12.1530i	−0.225172	−	0.390010i	−0.956371	+	0.292155i	$0.905628\pi$
$972$		0			0
$973$	21.4429	+	4.21821i	0.687428	+	0.135230i
$974$		0			0
$975$	2.27400	−	3.27677i	0.0728263	−	0.104941i
$976$		0			0
$977$	−11.1301	−	19.2780i	−0.356084	−	0.616756i	0.631218	−	0.775605i	$-0.282555\pi$
$977$	−11.1301	−	19.2780i	−0.356084	−	0.616756i	−0.987303	+	0.158849i	$0.949222\pi$
$978$		0			0
$979$	17.5891	+	30.4652i	0.562151	+	0.973673i
$980$		0			0
$981$	18.6884	−	22.6552i	0.596675	−	0.723325i
$982$		0			0
$983$	33.7341			1.07595			0.537976	−	0.842960i	$-0.319189\pi$
$983$	33.7341			1.07595			0.537976	+	0.842960i	$0.319189\pi$
$984$		0			0
$985$	−51.2921			−1.63430
$986$		0			0
$987$	−2.71079	−	0.771611i	−0.0862853	−	0.0245607i
$988$		0			0
$989$	9.21474	+	15.9604i	0.293012	+	0.507511i
$990$		0			0
$991$	6.87364	−	11.9055i	0.218348	−	0.378191i	−0.735955	−	0.677031i	$-0.763266\pi$
$991$	6.87364	−	11.9055i	0.218348	−	0.378191i	0.954303	+	0.298840i	$0.0965997\pi$
$992$		0			0
$993$	13.5656	−	19.5476i	0.430491	−	0.620325i
$994$		0			0
$995$	2.20035	−	3.81112i	0.0697559	−	0.120821i
$996$		0			0
$997$	37.2565			1.17993			0.589963	−	0.807430i	$-0.299142\pi$
$997$	37.2565			1.17993			0.589963	+	0.807430i	$0.299142\pi$
$998$		0			0
$999$	−1.29023	−	4.58374i	−0.0408212	−	0.145023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.193.2	yes	22
3.2	odd	2		1512.2.t.c.361.3		22
4.3	odd	2		1008.2.t.l.193.10		22
7.2	even	3		504.2.q.c.121.8	yes	22
9.2	odd	6		1512.2.q.d.1369.9		22
9.7	even	3		504.2.q.c.25.8	✓	22
12.11	even	2		3024.2.t.k.1873.3		22
21.2	odd	6		1512.2.q.d.793.9		22
28.23	odd	6		1008.2.q.l.625.4		22
36.7	odd	6		1008.2.q.l.529.4		22
36.11	even	6		3024.2.q.l.2881.9		22
63.2	odd	6		1512.2.t.c.289.3		22
63.16	even	3	inner	504.2.t.c.457.2	yes	22
84.23	even	6		3024.2.q.l.2305.9		22
252.79	odd	6		1008.2.t.l.961.10		22
252.191	even	6		3024.2.t.k.289.3		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.8	✓	22	9.7	even	3
504.2.q.c.121.8	yes	22	7.2	even	3
504.2.t.c.193.2	yes	22	1.1	even	1	trivial
504.2.t.c.457.2	yes	22	63.16	even	3	inner
1008.2.q.l.529.4		22	36.7	odd	6
1008.2.q.l.625.4		22	28.23	odd	6
1008.2.t.l.193.10		22	4.3	odd	2
1008.2.t.l.961.10		22	252.79	odd	6
1512.2.q.d.793.9		22	21.2	odd	6
1512.2.q.d.1369.9		22	9.2	odd	6
1512.2.t.c.289.3		22	63.2	odd	6
1512.2.t.c.361.3		22	3.2	odd	2
3024.2.q.l.2305.9		22	84.23	even	6
3024.2.q.l.2881.9		22	36.11	even	6
3024.2.t.k.289.3		22	252.191	even	6
3024.2.t.k.1873.3		22	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.72608 - 0.143720i) q^{3} +2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +(2.95869 + 0.496145i) q^{9} +O(q^{10})\)	\(q+(-1.72608 - 0.143720i) q^{3} +2.77180 q^{5} +(0.855737 + 2.50354i) q^{7} +(2.95869 + 0.496145i) q^{9} -3.43944 q^{11} +(-0.429164 + 0.743335i) q^{13} +(-4.78434 - 0.398364i) q^{15} +(-0.405132 + 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} +(-1.11726 - 4.44429i) q^{21} +7.64930 q^{23} +2.68286 q^{25} +(-5.03562 - 1.28161i) q^{27} +(3.99696 + 6.92294i) q^{29} +(3.60578 + 6.24540i) q^{31} +(5.93674 + 0.494317i) q^{33} +(2.37193 + 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(0.847604 - 1.22137i) q^{39} +(1.67577 - 2.90251i) q^{41} +(1.20465 + 2.08652i) q^{43} +(8.20089 + 1.37521i) q^{45} +(0.307520 - 0.532640i) q^{47} +(-5.53543 + 4.28474i) q^{49} +(0.800140 - 1.15298i) q^{51} +(6.31646 - 10.9404i) q^{53} -9.53342 q^{55} +(-1.10818 - 2.35070i) q^{57} +(-0.734690 - 1.27252i) q^{59} +(-5.71635 + 9.90101i) q^{61} +(1.28974 + 7.83177i) q^{63} +(-1.18956 + 2.06037i) q^{65} +(-8.10061 - 14.0307i) q^{67} +(-13.2033 - 1.09936i) q^{69} +14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(-4.63083 - 0.385582i) q^{75} +(-2.94325 - 8.61077i) q^{77} +(1.37586 - 2.38305i) q^{79} +(8.50768 + 2.93588i) q^{81} +(-5.75814 - 9.97340i) q^{83} +(-1.12294 + 1.94500i) q^{85} +(-5.90410 - 12.5240i) q^{87} +(-5.11395 - 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-5.32627 - 11.2983i) q^{93} +(2.07944 + 3.60170i) q^{95} +(3.82852 + 6.63119i) q^{97} +(-10.1762 - 1.70646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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