LMFDB - Embedded newform 504.2.q.c.25.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (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			25.8
Character	$\chi$	$=$	504.25
Dual form			504.2.q.c.121.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.987504 + 1.42297i) q^{3} +(-1.38590 + 2.40045i) q^{5} +(1.74026 - 1.99286i) q^{7} +(-1.04967 + 2.81037i) q^{9} +O(q^{10})$	\(q+(0.987504 + 1.42297i) q^{3} +(-1.38590 + 2.40045i) q^{5} +(1.74026 - 1.99286i) q^{7} +(-1.04967 + 2.81037i) q^{9} +(1.71972 + 2.97864i) q^{11} +(-0.429164 - 0.743335i) q^{13} +(-4.78434 + 0.398364i) q^{15} +(-0.405132 + 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} +(4.55429 + 0.508376i) q^{21} +(-3.82465 + 6.62449i) q^{23} +(-1.34143 - 2.32343i) q^{25} +(-5.03562 + 1.28161i) q^{27} +(3.99696 - 6.92294i) q^{29} -7.21156 q^{31} +(-2.54028 + 5.38852i) q^{33} +(2.37193 + 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(0.633939 - 1.34473i) q^{39} +(1.67577 + 2.90251i) q^{41} +(1.20465 - 2.08652i) q^{43} +(-5.29141 - 6.41457i) q^{45} -0.615039 q^{47} +(-0.942983 - 6.93619i) q^{49} +(-1.39858 + 0.116452i) q^{51} +(6.31646 - 10.9404i) q^{53} -9.53342 q^{55} +(-1.10818 + 2.35070i) q^{57} +1.46938 q^{59} +11.4327 q^{61} +(3.77398 + 6.98263i) q^{63} +2.37911 q^{65} +16.2012 q^{67} +(-13.2033 + 1.09936i) q^{69} +14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(1.98149 - 4.20320i) q^{75} +(8.92877 + 1.75645i) q^{77} -2.75171 q^{79} +(-6.79639 - 5.89993i) q^{81} +(-5.75814 + 9.97340i) q^{83} +(-1.12294 - 1.94500i) q^{85} +(13.7981 - 1.14889i) q^{87} +(-5.11395 - 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-7.12145 - 10.2618i) q^{93} -4.15889 q^{95} +(3.82852 - 6.63119i) q^{97} +(-10.1762 + 1.70646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	$ 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	0.987504	+	1.42297i	0.570136	+	0.821550i
$3$	0.987504	+	1.42297i	0.570136	+	0.821550i
$4$		0			0
$5$	−1.38590	+	2.40045i	−0.619793	+	1.07351i	0.369731	+	0.929139i	$0.379450\pi$
$5$	−1.38590	+	2.40045i	−0.619793	+	1.07351i	−0.989523	+	0.144373i	$0.953883\pi$
$6$		0			0
$7$	1.74026	−	1.99286i	0.657757	−	0.753230i
$7$	1.74026	−	1.99286i	0.657757	−	0.753230i
$8$		0			0
$9$	−1.04967	+	2.81037i	−0.349890	+	0.936791i
$10$		0			0
$11$	1.71972	+	2.97864i	0.518515	+	0.898094i	0.999769	+	0.0215124i	$0.00684814\pi$
$11$	1.71972	+	2.97864i	0.518515	+	0.898094i	−0.481254	+	0.876581i	$0.659819\pi$
$12$		0			0
$13$	−0.429164	−	0.743335i	−0.119029	−	0.206164i	0.800354	−	0.599527i	$-0.204645\pi$
$13$	−0.429164	−	0.743335i	−0.119029	−	0.206164i	−0.919383	+	0.393363i	$0.871311\pi$
$14$		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
$21$	4.55429	+	0.508376i	0.993827	+	0.110937i
$22$		0			0
$23$	−3.82465	+	6.62449i	−0.797495	+	1.38130i	0.123748	+	0.992314i	$0.460508\pi$
$23$	−3.82465	+	6.62449i	−0.797495	+	1.38130i	−0.921243	+	0.388988i	$0.872825\pi$
$24$		0			0
$25$	−1.34143	−	2.32343i	−0.268286	−	0.464685i
$26$		0			0
$27$	−5.03562	+	1.28161i	−0.969106	+	0.246646i
$28$		0			0
$29$	3.99696	−	6.92294i	0.742217	−	1.28556i	−0.209266	−	0.977859i	$-0.567107\pi$
$29$	3.99696	−	6.92294i	0.742217	−	1.28556i	0.951484	−	0.307700i	$-0.0995592\pi$
$30$		0			0
$31$	−7.21156			−1.29524			−0.647618	−	0.761965i	$-0.724235\pi$
$31$	−7.21156			−1.29524			−0.647618	+	0.761965i	$0.724235\pi$
$32$		0			0
$33$	−2.54028	+	5.38852i	−0.442205	+	0.938021i
$34$		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
$39$	0.633939	−	1.34473i	0.101511	−	0.215330i
$40$		0			0
$41$	1.67577	+	2.90251i	0.261711	+	0.453297i	0.966697	−	0.255925i	$-0.0823800\pi$
$41$	1.67577	+	2.90251i	0.261711	+	0.453297i	−0.704986	+	0.709221i	$0.749047\pi$
$42$		0			0
$43$	1.20465	−	2.08652i	0.183708	−	0.318191i	−0.759433	−	0.650586i	$-0.774523\pi$
$43$	1.20465	−	2.08652i	0.183708	−	0.318191i	0.943140	+	0.332395i	$0.107857\pi$
$44$		0			0
$45$	−5.29141	−	6.41457i	−0.788797	−	0.956227i
$46$		0			0
$47$	−0.615039			−0.0897127			−0.0448564	−	0.998993i	$-0.514283\pi$
$47$	−0.615039			−0.0897127			−0.0448564	+	0.998993i	$0.514283\pi$
$48$		0			0
$49$	−0.942983	−	6.93619i	−0.134712	−	0.990885i
$50$		0			0
$51$	−1.39858	+	0.116452i	−0.195840	+	0.0163065i
$52$		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
$59$	1.46938			0.191297			0.0956485	−	0.995415i	$-0.469508\pi$
$59$	1.46938			0.191297			0.0956485	+	0.995415i	$0.469508\pi$
$60$		0			0
$61$	11.4327			1.46381			0.731904	−	0.681408i	$-0.238632\pi$
$61$	11.4327			1.46381			0.731904	+	0.681408i	$0.238632\pi$
$62$		0			0
$63$	3.77398	+	6.98263i	0.475477	+	0.879728i
$64$		0			0
$65$	2.37911			0.295093
$66$		0			0
$67$	16.2012			1.97929			0.989647	−	0.143522i	$-0.0458427\pi$
$67$	16.2012			1.97929			0.989647	+	0.143522i	$0.0458427\pi$
$68$		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
$75$	1.98149	−	4.20320i	0.228803	−	0.485344i
$76$		0			0
$77$	8.92877	+	1.75645i	1.01753	+	0.200166i
$78$		0			0
$79$	−2.75171			−0.309592			−0.154796	−	0.987946i	$-0.549472\pi$
$79$	−2.75171			−0.309592			−0.154796	+	0.987946i	$0.549472\pi$
$80$		0			0
$81$	−6.79639	−	5.89993i	−0.755154	−	0.655547i
$82$		0			0
$83$	−5.75814	+	9.97340i	−0.632038	+	1.09472i	0.355096	+	0.934830i	$0.384448\pi$
$83$	−5.75814	+	9.97340i	−0.632038	+	1.09472i	−0.987134	+	0.159893i	$0.948885\pi$
$84$		0			0
$85$	−1.12294	−	1.94500i	−0.121800	−	0.210965i
$86$		0			0
$87$	13.7981	−	1.14889i	1.47932	−	0.123174i
$88$		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
$93$	−7.12145	−	10.2618i	−0.738460	−	1.06410i
$94$		0			0
$95$	−4.15889			−0.426693
$96$		0			0
$97$	3.82852	−	6.63119i	0.388727	−	0.673296i	−0.603551	−	0.797324i	$-0.706248\pi$
$97$	3.82852	−	6.63119i	0.388727	−	0.673296i	0.992279	+	0.124029i	$0.0395814\pi$
$98$		0			0
$99$	−10.1762	+	1.70646i	−1.02275	+	0.171506i
$100$		0			0
$101$	1.84302	+	3.19220i	0.183387	+	0.317635i	0.943032	−	0.332703i	$-0.107961\pi$
$101$	1.84302	+	3.19220i	0.183387	+	0.317635i	−0.759645	+	0.650338i	$0.774627\pi$
$102$		0			0
$103$	8.06026	−	13.9608i	0.794201	−	1.37560i	−0.129145	−	0.991626i	$-0.541223\pi$
$103$	8.06026	−	13.9608i	0.794201	−	1.37560i	0.923346	−	0.383970i	$-0.125443\pi$
$104$		0			0
$105$	−7.53211	+	10.2278i	−0.735059	+	0.998128i
$106$		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	0.991467	−	0.130360i	$-0.0416132\pi$
$113$	4.06963	+	7.04881i	0.382839	+	0.663096i	−0.608628	+	0.793456i	$0.708280\pi$
$114$		0			0
$115$	−10.6012	−	18.3617i	−0.988563	−	1.71224i
$116$		0			0
$117$	2.53953	−	0.425856i	0.234779	−	0.0393704i
$118$		0			0
$119$	0.693374	+	2.02853i	0.0635615	+	0.185955i
$120$		0			0
$121$	−0.414862	+	0.718563i	−0.0377148	+	0.0653239i
$122$		0			0
$123$	−2.47535	+	5.25081i	−0.223195	+	0.473449i
$124$		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
$129$	4.15864	−	0.346266i	0.366148	−	0.0304870i
$130$		0			0
$131$	−0.792752	+	1.37309i	−0.0692631	+	0.119967i	−0.898577	−	0.438816i	$-0.855398\pi$
$131$	−0.792752	+	1.37309i	−0.0692631	+	0.119967i	0.829314	+	0.558783i	$0.188731\pi$
$132$		0			0
$133$	3.89511	+	0.766240i	0.337749	+	0.0664414i
$134$		0			0
$135$	3.90242	−	13.8639i	0.335867	−	1.19322i
$136$		0			0
$137$	−2.46394	−	4.26767i	−0.210508	−	0.364611i	0.741365	−	0.671102i	$-0.234179\pi$
$137$	−2.46394	−	4.26767i	−0.210508	−	0.364611i	−0.951874	+	0.306490i	$0.900845\pi$
$138$		0			0
$139$	4.12999	+	7.15336i	0.350301	+	0.606740i	0.986302	−	0.164949i	$-0.0527458\pi$
$139$	4.12999	+	7.15336i	0.350301	+	0.606740i	−0.636001	+	0.771688i	$0.719412\pi$
$140$		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
$147$	8.93877	−	8.19136i	0.737258	−	0.675612i
$148$		0			0
$149$	6.95698	−	12.0498i	0.569938	−	0.987161i	−0.426634	−	0.904425i	$-0.640301\pi$
$149$	6.95698	−	12.0498i	0.569938	−	0.987161i	0.996571	−	0.0827368i	$-0.0263661\pi$
$150$		0			0
$151$	−11.4964	−	19.9123i	−0.935561	−	1.62044i	−0.773631	−	0.633637i	$-0.781561\pi$
$151$	−11.4964	−	19.9123i	−0.935561	−	1.62044i	−0.161930	−	0.986802i	$-0.551772\pi$
$152$		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
$157$	18.5804			1.48288			0.741441	−	0.671019i	$-0.234143\pi$
$157$	18.5804			1.48288			0.741441	+	0.671019i	$0.234143\pi$
$158$		0			0
$159$	21.8054	−	1.81561i	1.72928	−	0.143987i
$160$		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
$165$	−9.41430	−	13.5657i	−0.732902	−	1.05609i
$166$		0			0
$167$	−5.47493	−	9.48286i	−0.423663	−	0.733805i	0.572632	−	0.819813i	$-0.305923\pi$
$167$	−5.47493	−	9.48286i	−0.423663	−	0.733805i	−0.996295	+	0.0860073i	$0.972589\pi$
$168$		0			0
$169$	6.13164	−	10.6203i	0.471664	−	0.816947i
$170$		0			0
$171$	−4.43931	+	0.744432i	−0.339482	+	0.0569281i
$172$		0			0
$173$	−13.4054			−1.01920			−0.509598	−	0.860413i	$-0.670206\pi$
$173$	−13.4054			−1.01920			−0.509598	+	0.860413i	$0.670206\pi$
$174$		0			0
$175$	−6.96470	−	1.37008i	−0.526482	−	0.103569i
$176$		0			0
$177$	1.45102	+	2.09088i	0.109065	+	0.157160i
$178$		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
$185$	−2.54013			−0.186754
$186$		0			0
$187$	−2.78685			−0.203795
$188$		0			0
$189$	−6.20923	+	12.2656i	−0.451655	+	0.892193i
$190$		0			0
$191$	−18.6111			−1.34665			−0.673325	−	0.739347i	$-0.735134\pi$
$191$	−18.6111			−1.34665			−0.673325	+	0.739347i	$0.735134\pi$
$192$		0			0
$193$	2.92940			0.210863			0.105431	−	0.994427i	$-0.466378\pi$
$193$	2.92940			0.210863			0.105431	+	0.994427i	$0.466378\pi$
$194$		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
$201$	15.9988	+	23.0538i	1.12847	+	1.62609i
$202$		0			0
$203$	−6.84070	−	20.0131i	−0.480123	−	1.40465i
$204$		0			0
$205$	−9.28977			−0.648826
$206$		0			0
$207$	−14.6027	−	17.7022i	−1.01495	−	1.23039i
$208$		0			0
$209$	−2.58032	+	4.46924i	−0.178484	+	0.309144i
$210$		0			0
$211$	12.3436	+	21.3798i	0.849770	+	1.47184i	0.881414	+	0.472345i	$0.156592\pi$
$211$	12.3436	+	21.3798i	0.849770	+	1.47184i	−0.0316443	+	0.999499i	$0.510074\pi$
$212$		0			0
$213$	14.2375	+	20.5159i	0.975539	+	1.40573i
$214$		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
$219$	−14.3918	+	1.19832i	−0.972506	+	0.0809750i
$220$		0			0
$221$	0.695474			0.0467826
$222$		0			0
$223$	−9.78468	+	16.9476i	−0.655231	+	1.13489i	0.326605	+	0.945161i	$0.394095\pi$
$223$	−9.78468	+	16.9476i	−0.655231	+	1.13489i	−0.981836	+	0.189732i	$0.939238\pi$
$224$		0			0
$225$	7.93775	−	1.33109i	0.529183	−	0.0887393i
$226$		0			0
$227$	−4.32404	−	7.48945i	−0.286996	−	0.497092i	0.686095	−	0.727512i	$-0.259323\pi$
$227$	−4.32404	−	7.48945i	−0.286996	−	0.497092i	−0.973091	+	0.230420i	$0.925990\pi$
$228$		0			0
$229$	−5.77136	+	9.99630i	−0.381382	+	0.660574i	−0.991260	−	0.131922i	$-0.957885\pi$
$229$	−5.77136	+	9.99630i	−0.381382	+	0.660574i	0.609878	+	0.792496i	$0.291219\pi$
$230$		0			0
$231$	6.31783	+	14.4398i	0.415683	+	0.950072i
$232$		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	0.916790	+	0.399371i	$0.130771\pi$
$239$	12.4336	+	21.5355i	0.804260	+	1.39302i	−0.112530	+	0.993648i	$0.535895\pi$
$240$		0			0
$241$	9.51814	+	16.4859i	0.613117	+	1.06195i	0.990712	+	0.135979i	$0.0434180\pi$
$241$	9.51814	+	16.4859i	0.613117	+	1.06195i	−0.377595	+	0.925971i	$0.623249\pi$
$242$		0			0
$243$	1.68394	−	15.4972i	0.108025	−	0.994148i
$244$		0			0
$245$	17.9568	+	7.34928i	1.14722	+	0.469528i
$246$		0			0
$247$	0.643931	−	1.11532i	0.0409724	−	0.0709662i
$248$		0			0
$249$	−19.8780	+	1.65513i	−1.25972	+	0.104889i
$250$		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
$255$	1.65875	−	3.51861i	0.103875	−	0.220344i
$256$		0			0
$257$	−2.18362	+	3.78215i	−0.136211	+	0.235924i	−0.926059	−	0.377378i	$-0.876826\pi$
$257$	−2.18362	+	3.78215i	−0.136211	+	0.235924i	0.789849	+	0.613302i	$0.210159\pi$
$258$		0			0
$259$	2.37903	+	0.467998i	0.147826	+	0.0290800i
$260$		0			0
$261$	15.2606	+	18.4998i	0.944605	+	1.14511i
$262$		0			0
$263$	6.24212	+	10.8117i	0.384905	+	0.666676i	0.991756	−	0.128140i	$-0.0409007\pi$
$263$	6.24212	+	10.8117i	0.384905	+	0.666676i	−0.606851	+	0.794816i	$0.707567\pi$
$264$		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
$273$	−1.57665	−	3.60354i	−0.0954230	−	0.218096i
$274$		0			0
$275$	4.61376	−	7.99127i	0.278220	−	0.481892i
$276$		0			0
$277$	0.980373	+	1.69806i	0.0589049	+	0.102026i	0.893974	−	0.448119i	$-0.147906\pi$
$277$	0.980373	+	1.69806i	0.0589049	+	0.102026i	−0.835069	+	0.550145i	$0.814572\pi$
$278$		0			0
$279$	7.56976	−	20.2672i	0.453190	−	1.21336i
$280$		0			0
$281$	9.42057	−	16.3169i	0.561984	−	0.973385i	−0.435339	−	0.900267i	$-0.643372\pi$
$281$	9.42057	−	16.3169i	0.561984	−	0.973385i	0.997323	−	0.0731185i	$-0.0232951\pi$
$282$		0			0
$283$	−23.4844			−1.39600			−0.698002	−	0.716095i	$-0.745928\pi$
$283$	−23.4844			−1.39600			−0.698002	+	0.716095i	$0.745928\pi$
$284$		0			0
$285$	−4.10692	−	5.91796i	−0.243273	−	0.350550i
$286$		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
$291$	13.2167	−	1.10047i	0.774774	−	0.0645109i
$292$		0			0
$293$	−1.00384	−	1.73871i	−0.0586452	−	0.101576i	0.835212	−	0.549928i	$-0.185345\pi$
$293$	−1.00384	−	1.73871i	−0.0586452	−	0.101576i	−0.893857	+	0.448351i	$0.852011\pi$
$294$		0			0
$295$	−2.03641	+	3.52717i	−0.118564	+	0.205360i
$296$		0			0
$297$	−12.4773	−	12.7953i	−0.724007	−	0.742458i
$298$		0			0
$299$	6.56561			0.379699
$300$		0			0
$301$	−2.06173	−	6.03179i	−0.118836	−	0.347666i
$302$		0			0
$303$	−2.72240	+	5.77486i	−0.156398	+	0.331757i
$304$		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
$311$	−14.0996			−0.799514			−0.399757	−	0.916621i	$-0.630906\pi$
$311$	−14.0996			−0.799514			−0.399757	+	0.916621i	$0.630906\pi$
$312$		0			0
$313$	−34.1539			−1.93049			−0.965245	−	0.261345i	$-0.915834\pi$
$313$	−34.1539			−1.93049			−0.965245	+	0.261345i	$0.915834\pi$
$314$		0			0
$315$	−21.9918	−	0.617975i	−1.23910	−	0.0348189i
$316$		0			0
$317$	−1.58117			−0.0888074			−0.0444037	−	0.999014i	$-0.514139\pi$
$317$	−1.58117			−0.0888074			−0.0444037	+	0.999014i	$0.514139\pi$
$318$		0			0
$319$	27.4946			1.53940
$320$		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
$327$	16.8975	−	1.40696i	0.934434	−	0.0778049i
$328$		0			0
$329$	−1.07033	+	1.22569i	−0.0590092	+	0.0675743i
$330$		0			0
$331$	13.7372			0.755067			0.377533	−	0.925996i	$-0.376772\pi$
$331$	13.7372			0.755067			0.377533	+	0.925996i	$0.376772\pi$
$332$		0			0
$333$	−2.71141	+	0.454678i	−0.148584	+	0.0249162i
$334$		0			0
$335$	−22.4533	+	38.8902i	−1.22675	+	2.12480i
$336$		0			0
$337$	−8.72318	−	15.1090i	−0.475182	−	0.823039i	0.524414	−	0.851463i	$-0.324284\pi$
$337$	−8.72318	−	15.1090i	−0.475182	−	0.823039i	−0.999596	+	0.0284243i	$0.990951\pi$
$338$		0			0
$339$	−6.01144	+	12.7517i	−0.326497	+	0.692576i
$340$		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
$345$	15.6595	−	33.2174i	0.843077	−	1.78836i
$346$		0			0
$347$	3.83104			0.205661			0.102830	−	0.994699i	$-0.467210\pi$
$347$	3.83104			0.205661			0.102830	+	0.994699i	$0.467210\pi$
$348$		0			0
$349$	1.69984	−	2.94421i	0.0909903	−	0.157600i	−0.816938	−	0.576726i	$-0.804330\pi$
$349$	1.69984	−	2.94421i	0.0909903	−	0.157600i	0.907928	+	0.419126i	$0.137663\pi$
$350$		0			0
$351$	3.11377	+	3.19313i	0.166201	+	0.170437i
$352$		0			0
$353$	−6.27841	−	10.8745i	−0.334166	−	0.578793i	0.649158	−	0.760653i	$-0.275121\pi$
$353$	−6.27841	−	10.8745i	−0.334166	−	0.578793i	−0.983324	+	0.181861i	$0.941788\pi$
$354$		0			0
$355$	−19.9815	+	34.6089i	−1.06051	+	1.83685i
$356$		0			0
$357$	−2.20182	+	2.98983i	−0.116533	+	0.158239i
$358$		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
$367$	1.01257	+	1.75382i	0.0528557	+	0.0915487i	0.891243	−	0.453527i	$-0.149834\pi$
$367$	1.01257	+	1.75382i	0.0528557	+	0.0915487i	−0.838387	+	0.545075i	$0.816501\pi$
$368$		0			0
$369$	−9.91615	+	1.66285i	−0.516214	+	0.0865644i
$370$		0			0
$371$	−10.8105	−	31.6270i	−0.561251	−	1.64199i
$372$		0			0
$373$	−10.8130	+	18.7286i	−0.559874	+	0.969731i	0.437632	+	0.899154i	$0.355817\pi$
$373$	−10.8130	+	18.7286i	−0.559874	+	0.969731i	−0.997506	+	0.0705766i	$0.977516\pi$
$374$		0			0
$375$	−6.34239	−	9.13921i	−0.327519	−	0.471947i
$376$		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
$381$	−12.4088	−	17.8807i	−0.635722	−	0.916058i
$382$		0			0
$383$	3.82822	−	6.63068i	0.195613	−	0.338812i	−0.751488	−	0.659747i	$-0.770664\pi$
$383$	3.82822	−	6.63068i	0.195613	−	0.338812i	0.947101	+	0.320935i	$0.103997\pi$
$384$		0			0
$385$	−16.5906	+	18.9988i	−0.845537	+	0.968267i
$386$		0			0
$387$	4.59941	+	5.57567i	0.233801	+	0.283427i
$388$		0			0
$389$	10.5781	+	18.3218i	0.536329	+	0.928950i	0.999098	+	0.0424705i	$0.0135228\pi$
$389$	10.5781	+	18.3218i	0.536329	+	0.928950i	−0.462768	+	0.886479i	$0.653144\pi$
$390$		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
$399$	2.75611	+	6.29928i	0.137978	+	0.315359i
$400$		0			0
$401$	3.88886	−	6.73571i	0.194201	−	0.336365i	−0.752438	−	0.658664i	$-0.771122\pi$
$401$	3.88886	−	6.73571i	0.194201	−	0.336365i	0.946638	+	0.322298i	$0.104455\pi$
$402$		0			0
$403$	3.09495	+	5.36061i	0.154170	+	0.267031i
$404$		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
$409$	19.5265			0.965526			0.482763	−	0.875751i	$-0.339633\pi$
$409$	19.5265			0.965526			0.482763	+	0.875751i	$0.339633\pi$
$410$		0			0
$411$	3.63960	−	7.72044i	0.179528	−	0.380821i
$412$		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
$417$	−6.10060	+	12.9408i	−0.298748	+	0.633714i
$418$		0			0
$419$	−12.5259	−	21.6955i	−0.611932	−	1.05990i	−0.990915	−	0.134493i	$-0.957059\pi$
$419$	−12.5259	−	21.6955i	−0.611932	−	1.05990i	0.378983	−	0.925404i	$-0.376274\pi$
$420$		0			0
$421$	18.0746	−	31.3061i	0.880902	−	1.52577i	0.0305620	−	0.999533i	$-0.490270\pi$
$421$	18.0746	−	31.3061i	0.880902	−	1.52577i	0.850340	−	0.526234i	$-0.176396\pi$
$422$		0			0
$423$	0.645588	−	1.72849i	0.0313896	−	0.0840421i
$424$		0			0
$425$	2.17383			0.105446
$426$		0			0
$427$	19.8959	−	22.7838i	0.962829	−	1.10258i
$428$		0			0
$429$	5.09567	−	0.424287i	0.246021	−	0.0204848i
$430$		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
$437$	−11.4772			−0.549031
$438$		0			0
$439$	−4.78469			−0.228361			−0.114180	−	0.993460i	$-0.536424\pi$
$439$	−4.78469			−0.228361			−0.114180	+	0.993460i	$0.536424\pi$
$440$		0			0
$441$	20.4831	+	4.63058i	0.975386	+	0.220504i
$442$		0			0
$443$	−8.26427			−0.392647			−0.196324	−	0.980539i	$-0.562900\pi$
$443$	−8.26427			−0.392647			−0.196324	+	0.980539i	$0.562900\pi$
$444$		0			0
$445$	28.3497			1.34390
$446$		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
$453$	16.9818	−	36.0224i	0.797875	−	1.69248i
$454$		0			0
$455$	4.14028	−	4.74124i	0.194099	−	0.222273i
$456$		0			0
$457$	−17.9644			−0.840339			−0.420170	−	0.907446i	$-0.638029\pi$
$457$	−17.9644			−0.840339			−0.420170	+	0.907446i	$0.638029\pi$
$458$		0			0
$459$	1.14077	−	4.05277i	0.0532468	−	0.189167i
$460$		0			0
$461$	4.03501	−	6.98885i	0.187929	−	0.325503i	−0.756630	−	0.653843i	$-0.773156\pi$
$461$	4.03501	−	6.98885i	0.187929	−	0.325503i	0.944560	+	0.328340i	$0.106489\pi$
$462$		0			0
$463$	−2.50704	−	4.34232i	−0.116512	−	0.201805i	0.801871	−	0.597497i	$-0.203838\pi$
$463$	−2.50704	−	4.34232i	−0.116512	−	0.201805i	−0.918383	+	0.395692i	$0.870505\pi$
$464$		0			0
$465$	34.5026	−	2.87283i	1.60002	−	0.133224i
$466$		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
$471$	18.3483	+	26.4394i	0.845444	+	1.21826i
$472$		0			0
$473$	8.28665			0.381020
$474$		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
$479$	12.6222	+	21.8623i	0.576724	+	0.998916i	0.995852	+	0.0909886i	$0.0290027\pi$
$479$	12.6222	+	21.8623i	0.576724	+	0.998916i	−0.419128	+	0.907927i	$0.637664\pi$
$480$		0			0
$481$	0.393295	−	0.681208i	0.0179327	−	0.0310604i
$482$		0			0
$483$	−20.7863	+	28.2255i	−0.945809	+	1.28430i
$484$		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	−0.963675	−	0.267078i	$-0.913942\pi$
$491$	−15.8020	−	27.3698i	−0.713134	−	1.23518i	0.250541	−	0.968106i	$-0.419391\pi$
$492$		0			0
$493$	3.23860	+	5.60942i	0.145859	+	0.252635i
$494$		0			0
$495$	10.0069	−	26.7925i	0.449779	−	1.20423i
$496$		0			0
$497$	25.0905	−	28.7324i	1.12546	−	1.28883i
$498$		0			0
$499$	−2.97445	+	5.15190i	−0.133155	+	0.230631i	−0.924891	−	0.380232i	$-0.875844\pi$
$499$	−2.97445	+	5.15190i	−0.133155	+	0.230631i	0.791736	+	0.610863i	$0.209177\pi$
$500$		0			0
$501$	8.08727	−	17.1550i	0.361313	−	0.766429i
$502$		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
$507$	21.1674	−	1.76248i	0.940075	−	0.0782746i
$508$		0			0
$509$	−18.6443	+	32.2928i	−0.826392	+	1.43135i	0.0744581	+	0.997224i	$0.476277\pi$
$509$	−18.6443	+	32.2928i	−0.826392	+	1.43135i	−0.900850	+	0.434129i	$0.857056\pi$
$510$		0			0
$511$	7.13501	+	20.8741i	0.315634	+	0.923418i
$512$		0			0
$513$	−5.44314	−	5.58186i	−0.240320	−	0.246445i
$514$		0			0
$515$	22.3414	+	38.6964i	0.984480	+	1.70517i
$516$		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
$525$	−4.92809	−	11.2635i	−0.215079	−	0.491580i
$526$		0			0
$527$	2.92164	−	5.06043i	0.127269	−	0.220436i
$528$		0			0
$529$	−17.7559	−	30.7541i	−0.771996	−	1.33714i
$530$		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
$535$	−17.5603			−0.759196
$536$		0			0
$537$	−22.9530	+	1.91116i	−0.990494	+	0.0824727i
$538$		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
$543$	−10.7825	−	15.5373i	−0.462723	−	0.666771i
$544$		0			0
$545$	13.5673	+	23.4993i	0.581159	+	1.00660i
$546$		0			0
$547$	−13.8412	+	23.9736i	−0.591805	+	1.02504i	0.402184	+	0.915559i	$0.368251\pi$
$547$	−13.8412	+	23.9736i	−0.591805	+	1.02504i	−0.993989	+	0.109478i	$0.965082\pi$
$548$		0			0
$549$	−12.0006	+	32.1301i	−0.512172	+	1.37128i
$550$		0			0
$551$	11.9943			0.510976
$552$		0			0
$553$	−4.78870	+	5.48378i	−0.203636	+	0.233194i
$554$		0			0
$555$	−2.50839	−	3.61453i	−0.106475	−	0.153428i
$556$		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
$563$	1.91343			0.0806414			0.0403207	−	0.999187i	$-0.487162\pi$
$563$	1.91343			0.0806414			0.0403207	+	0.999187i	$0.487162\pi$
$564$		0			0
$565$	−22.5604			−0.949122
$566$		0			0
$567$	−23.5852	+	3.27684i	−0.990486	+	0.137614i
$568$		0			0
$569$	−14.7628			−0.618887			−0.309444	−	0.950918i	$-0.600143\pi$
$569$	−14.7628			−0.618887			−0.309444	+	0.950918i	$0.600143\pi$
$570$		0			0
$571$	2.56417			0.107307			0.0536535	−	0.998560i	$-0.482913\pi$
$571$	2.56417			0.107307			0.0536535	+	0.998560i	$0.482913\pi$
$572$		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
$579$	2.89279	+	4.16844i	0.120220	+	0.173234i
$580$		0			0
$581$	9.85491	+	28.8315i	0.408851	+	1.19613i
$582$		0			0
$583$	43.4501			1.79952
$584$		0			0
$585$	−2.49728	+	6.68619i	−0.103250	+	0.276440i
$586$		0			0
$587$	15.7666	−	27.3085i	0.650756	−	1.12714i	−0.332183	−	0.943215i	$-0.607785\pi$
$587$	15.7666	−	27.3085i	0.650756	−	1.12714i	0.982940	−	0.183928i	$-0.0588813\pi$
$588$		0			0
$589$	−5.41022	−	9.37078i	−0.222924	−	0.386116i
$590$		0			0
$591$	−18.2738	−	26.3320i	−0.751683	−	1.08315i
$592$		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
$597$	2.74045	−	0.228181i	0.112159	−	0.00933883i
$598$		0			0
$599$	5.61368			0.229369			0.114684	−	0.993402i	$-0.463414\pi$
$599$	5.61368			0.229369			0.114684	+	0.993402i	$0.463414\pi$
$600$		0			0
$601$	19.2223	−	33.2940i	0.784094	−	1.35809i	−0.145444	−	0.989366i	$-0.546461\pi$
$601$	19.2223	−	33.2940i	0.784094	−	1.35809i	0.929539	−	0.368725i	$-0.120205\pi$
$602$		0			0
$603$	−17.0059	+	45.5315i	−0.692535	+	1.85418i
$604$		0			0
$605$	−1.14991	−	1.99171i	−0.0467507	−	0.0809745i
$606$		0			0
$607$	8.17187	−	14.1541i	0.331686	−	0.574497i	−0.651157	−	0.758943i	$-0.725716\pi$
$607$	8.17187	−	14.1541i	0.331686	−	0.574497i	0.982843	+	0.184446i	$0.0590492\pi$
$608$		0			0
$609$	21.7228	−	29.4971i	0.880252	−	1.19528i
$610$		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	0.885764	+	0.464136i	$0.153635\pi$
$617$	20.9853	+	36.3476i	0.844836	+	1.46330i	−0.0409280	+	0.999162i	$0.513031\pi$
$618$		0			0
$619$	17.9473	+	31.0856i	0.721361	+	1.24943i	0.960454	+	0.278438i	$0.0898166\pi$
$619$	17.9473	+	31.0856i	0.721361	+	1.24943i	−0.239093	+	0.970997i	$0.576850\pi$
$620$		0			0
$621$	10.7695	−	38.2601i	0.432164	−	1.53533i
$622$		0			0
$623$	−26.5516	−	5.22319i	−1.06377	−	0.209263i
$624$		0			0
$625$	15.6083	−	27.0343i	0.624331	−	1.08137i
$626$		0			0
$627$	−8.90766	+	0.741689i	−0.355737	+	0.0296202i
$628$		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
$633$	−18.2333	+	38.6772i	−0.724710	+	1.53728i
$634$		0			0
$635$	17.4149	−	30.1636i	0.691091	−	1.19700i
$636$		0			0
$637$	−4.75122	+	3.67772i	−0.188250	+	0.145717i
$638$		0			0
$639$	−15.1338	+	40.5191i	−0.598684	+	1.60291i
$640$		0			0
$641$	7.30132	+	12.6463i	0.288385	+	0.499497i	0.973424	−	0.229009i	$-0.0735485\pi$
$641$	7.30132	+	12.6463i	0.288385	+	0.499497i	−0.685040	+	0.728506i	$0.740215\pi$
$642$		0			0
$643$	−5.96942	−	10.3393i	−0.235411	−	0.407744i	0.723981	−	0.689820i	$-0.242310\pi$
$643$	−5.96942	−	10.3393i	−0.235411	−	0.407744i	−0.959392	+	0.282076i	$0.908977\pi$
$644$		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
$651$	−32.8436	−	3.66618i	−1.28724	−	0.143689i
$652$		0			0
$653$	−19.9959	+	34.6339i	−0.782501	+	1.35533i	0.147980	+	0.988990i	$0.452723\pi$
$653$	−19.9959	+	34.6339i	−0.782501	+	1.35533i	−0.930481	+	0.366340i	$0.880611\pi$
$654$		0			0
$655$	−2.19735	−	3.80592i	−0.0858575	−	0.148710i
$656$		0			0
$657$	−15.9171	−	19.2957i	−0.620986	−	0.752796i
$658$		0			0
$659$	1.60101	−	2.77303i	0.0623665	−	0.108022i	−0.833156	−	0.553038i	$-0.813469\pi$
$659$	1.60101	−	2.77303i	0.0623665	−	0.108022i	0.895523	+	0.445016i	$0.146802\pi$
$660$		0			0
$661$	−43.3030			−1.68429			−0.842146	−	0.539250i	$-0.818708\pi$
$661$	−43.3030			−1.68429			−0.842146	+	0.539250i	$0.818708\pi$
$662$		0			0
$663$	0.686783	+	0.989636i	0.0266725	+	0.0384343i
$664$		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
$669$	−33.7782	+	2.81252i	−1.30594	+	0.108738i
$670$		0			0
$671$	19.6610	+	34.0539i	0.759006	+	1.31464i
$672$		0			0
$673$	12.2936	−	21.2931i	0.473883	−	0.820790i	−0.525670	−	0.850689i	$-0.676185\pi$
$673$	12.2936	−	21.2931i	0.473883	−	0.820790i	0.999553	+	0.0298991i	$0.00951859\pi$
$674$		0			0
$675$	9.73266	+	9.98070i	0.374610	+	0.384157i
$676$		0			0
$677$	−38.4188			−1.47655			−0.738276	−	0.674498i	$-0.764360\pi$
$677$	−38.4188			−1.47655			−0.738276	+	0.674498i	$0.764360\pi$
$678$		0			0
$679$	−6.55242	−	19.1697i	−0.251459	−	0.735666i
$680$		0			0
$681$	6.38724	−	13.5488i	0.244759	−	0.519192i
$682$		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
$689$	−10.8432			−0.413093
$690$		0			0
$691$	−7.30292			−0.277816			−0.138908	−	0.990305i	$-0.544359\pi$
$691$	−7.30292			−0.277816			−0.138908	+	0.990305i	$0.544359\pi$
$692$		0			0
$693$	−14.3085	+	23.2495i	−0.543537	+	0.883175i
$694$		0			0
$695$	−22.8950			−0.868457
$696$		0			0
$697$	−2.71563			−0.102862
$698$		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
$705$	2.94256	−	0.245010i	0.110823	−	0.00922760i
$706$		0			0
$707$	9.56893	+	1.88238i	0.359877	+	0.0707943i
$708$		0			0
$709$	2.92274			0.109766			0.0548828	−	0.998493i	$-0.482521\pi$
$709$	2.92274			0.109766			0.0548828	+	0.998493i	$0.482521\pi$
$710$		0			0
$711$	2.88839	−	7.73334i	0.108323	−	0.290023i
$712$		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
$717$	−18.3662	+	38.9590i	−0.685898	+	1.45495i
$718$		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
$723$	−14.0597	+	29.8239i	−0.522885	+	1.10916i
$724$		0			0
$725$	−21.4466			−0.796506
$726$		0			0
$727$	20.0486	−	34.7252i	0.743561	−	1.28789i	−0.207303	−	0.978277i	$-0.566469\pi$
$727$	20.0486	−	34.7252i	0.743561	−	1.28789i	0.950864	−	0.309609i	$-0.100198\pi$
$728$		0			0
$729$	23.7150	−	12.9074i	0.878332	−	0.478052i
$730$		0			0
$731$	0.976087	+	1.69063i	0.0361019	+	0.0625303i
$732$		0			0
$733$	3.56234	−	6.17016i	0.131578	−	0.227900i	−0.792707	−	0.609603i	$-0.791329\pi$
$733$	3.56234	−	6.17016i	0.131578	−	0.227900i	0.924285	+	0.381703i	$0.124662\pi$
$734$		0			0
$735$	7.27468	+	32.8094i	0.268331	+	1.21019i
$736$		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	0.868004	−	0.496557i	$-0.165402\pi$
$743$	0.108257	+	0.187507i	0.00397157	+	0.00687896i	−0.864033	+	0.503436i	$0.832069\pi$
$744$		0			0
$745$	19.2833	+	33.3997i	0.706487	+	1.22367i
$746$		0			0
$747$	−21.9848	−	26.6513i	−0.804382	−	0.975120i
$748$		0			0
$749$	16.4465	+	3.23533i	0.600942	+	0.118216i
$750$		0			0
$751$	−11.7920	+	20.4244i	−0.430297	+	0.745296i	−0.996899	−	0.0786955i	$-0.974925\pi$
$751$	−11.7920	+	20.4244i	−0.430297	+	0.745296i	0.566602	+	0.823992i	$0.308258\pi$
$752$		0			0
$753$	−0.968182	−	1.39512i	−0.0352825	−	0.0508412i
$754$		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
$759$	−25.9805	−	37.4372i	−0.943034	−	1.35889i
$760$		0			0
$761$	9.05699	−	15.6872i	0.328316	−	0.568659i	−0.653862	−	0.756614i	$-0.726852\pi$
$761$	9.05699	−	15.6872i	0.328316	−	0.568659i	0.982178	+	0.187954i	$0.0601857\pi$
$762$		0			0
$763$	−8.37727	−	24.5085i	−0.303277	−	0.887267i
$764$		0			0
$765$	6.64489	−	1.11429i	0.240246	−	0.0402872i
$766$		0			0
$767$	−0.630606	−	1.09224i	−0.0227699	−	0.0394385i
$768$		0			0
$769$	3.16710	+	5.48558i	0.114209	+	0.197815i	0.917463	−	0.397821i	$-0.130233\pi$
$769$	3.16710	+	5.48558i	0.114209	+	0.197815i	−0.803255	+	0.595636i	$0.796900\pi$
$770$		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
$777$	1.68336	+	3.84743i	0.0603900	+	0.138026i
$778$		0			0
$779$	−2.51437	+	4.35502i	−0.0900867	+	0.156035i
$780$		0			0
$781$	24.7944	+	42.9451i	0.887212	+	1.53670i
$782$		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
$787$	−19.3183			−0.688624			−0.344312	−	0.938855i	$-0.611888\pi$
$787$	−19.3183			−0.688624			−0.344312	+	0.938855i	$0.611888\pi$
$788$		0			0
$789$	−9.22052	+	19.5589i	−0.328259	+	0.696315i
$790$		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
$795$	−25.8618	+	54.8590i	−0.917224	+	1.94565i
$796$		0			0
$797$	−5.09519	−	8.82513i	−0.180481	−	0.312602i	0.761563	−	0.648090i	$-0.224432\pi$
$797$	−5.09519	−	8.82513i	−0.180481	−	0.312602i	−0.942044	+	0.335488i	$0.891099\pi$
$798$		0			0
$799$	0.249172	−	0.431579i	0.00881509	−	0.0152682i
$800$		0			0
$801$	30.2612	−	5.07453i	1.06923	−	0.179300i
$802$		0			0
$803$	−28.6775			−1.01201
$804$		0			0
$805$	−55.0412	−	10.8276i	−1.93995	−	0.381623i
$806$		0			0
$807$	28.6277	−	2.38366i	1.00774	−	0.0839088i
$808$		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
$815$	13.5925			0.476126
$816$		0			0
$817$	3.61499			0.126473
$818$		0			0
$819$	3.57077	−	5.80202i	0.124773	−	0.202739i
$820$		0			0
$821$	53.6353			1.87189			0.935943	−	0.352152i	$-0.114550\pi$
$821$	53.6353			1.87189			0.935943	+	0.352152i	$0.114550\pi$
$822$		0			0
$823$	−0.950384			−0.0331283			−0.0165641	−	0.999863i	$-0.505273\pi$
$823$	−0.950384			−0.0331283			−0.0165641	+	0.999863i	$0.505273\pi$
$824$		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
$831$	−1.44815	+	3.07187i	−0.0502359	+	0.106562i
$832$		0			0
$833$	5.24923	+	2.14838i	0.181875	+	0.0744368i
$834$		0			0
$835$	30.3508			1.05033
$836$		0			0
$837$	36.3147	−	9.24241i	1.25522	−	0.319464i
$838$		0			0
$839$	−15.7367	+	27.2567i	−0.543290	+	0.941006i	0.455422	+	0.890276i	$0.349488\pi$
$839$	−15.7367	+	27.2567i	−0.543290	+	0.941006i	−0.998712	+	0.0507305i	$0.983845\pi$
$840$		0			0
$841$	−17.4514	−	30.2268i	−0.601774	−	1.04230i
$842$		0			0
$843$	32.5213	−	2.70786i	1.12009	−	0.0932636i
$844$		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
$849$	−23.1910	−	33.4176i	−0.795913	−	1.14689i
$850$		0			0
$851$	−7.00998			−0.240299
$852$		0			0
$853$	−26.6959	+	46.2386i	−0.914049	+	1.58318i	−0.105762	+	0.994391i	$0.533728\pi$
$853$	−26.6959	+	46.2386i	−0.914049	+	1.58318i	−0.808287	+	0.588788i	$0.799605\pi$
$854$		0			0
$855$	4.36546	−	11.6880i	0.149296	−	0.399722i
$856$		0			0
$857$	−10.8149	−	18.7319i	−0.369428	−	0.639869i	0.620048	−	0.784564i	$-0.287113\pi$
$857$	−10.8149	−	18.7319i	−0.369428	−	0.639869i	−0.989476	+	0.144695i	$0.953780\pi$
$858$		0			0
$859$	17.2144	−	29.8162i	0.587348	−	1.01732i	−0.407230	−	0.913326i	$-0.633505\pi$
$859$	17.2144	−	29.8162i	0.587348	−	1.01732i	0.994578	−	0.103991i	$-0.0331614\pi$
$860$		0			0
$861$	6.15636	+	14.0708i	0.209808	+	0.479532i
$862$		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
$871$	−6.95299	−	12.0429i	−0.235593	−	0.408059i
$872$		0			0
$873$	14.6174	+	17.7201i	0.494725	+	0.599736i
$874$		0			0
$875$	−11.1771	+	12.7994i	−0.377854	+	0.432700i
$876$		0			0
$877$	−16.2034	+	28.0651i	−0.547150	+	0.947692i	0.451318	+	0.892363i	$0.350954\pi$
$877$	−16.2034	+	28.0651i	−0.547150	+	0.947692i	−0.998468	+	0.0553291i	$0.982379\pi$
$878$		0			0
$879$	1.48282	−	3.14542i	0.0500144	−	0.106092i
$880$		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
$885$	−7.03001	+	0.585348i	−0.236311	+	0.0196763i
$886$		0			0
$887$	−11.9778	+	20.7461i	−0.402174	+	0.696586i	−0.993988	−	0.109489i	$-0.965079\pi$
$887$	−11.9778	+	20.7461i	−0.402174	+	0.696586i	0.591814	+	0.806074i	$0.298412\pi$
$888$		0			0
$889$	−21.8678	+	25.0419i	−0.733422	+	0.839879i
$890$		0			0
$891$	5.88588	−	30.3902i	0.197185	−	1.01811i
$892$		0			0
$893$	−0.461412	−	0.799189i	−0.0154406	−	0.0267438i
$894$		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
$903$	6.54707	−	8.89019i	0.217873	−	0.295847i
$904$		0			0
$905$	15.1326	−	26.2104i	0.503025	−	0.871264i
$906$		0			0
$907$	−2.35064	−	4.07143i	−0.0780517	−	0.135190i	0.824358	−	0.566069i	$-0.191537\pi$
$907$	−2.35064	−	4.07143i	−0.0780517	−	0.135190i	−0.902409	+	0.430880i	$0.858203\pi$
$908$		0			0
$909$	−10.9058	+	1.82881i	−0.361723	+	0.0606577i
$910$		0			0
$911$	21.0884	−	36.5262i	0.698689	−	1.21017i	−0.270232	−	0.962795i	$-0.587100\pi$
$911$	21.0884	−	36.5262i	0.698689	−	1.21017i	0.968921	−	0.247370i	$-0.0795663\pi$
$912$		0			0
$913$	−39.6095			−1.31088
$914$		0			0
$915$	−54.6979	+	4.55438i	−1.80826	+	0.150563i
$916$		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
$921$	32.3539	+	46.6211i	1.06610	+	1.53622i
$922$		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
$927$	30.7744	+	37.3065i	1.01076	+	1.22531i
$928$		0			0
$929$	−30.1424			−0.988938			−0.494469	−	0.869195i	$-0.664638\pi$
$929$	−30.1424			−0.988938			−0.494469	+	0.869195i	$0.664638\pi$
$930$		0			0
$931$	8.30552	−	6.42896i	0.272203	−	0.210701i
$932$		0			0
$933$	−13.9234	−	20.0632i	−0.455832	−	0.656841i
$934$		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
$941$	−3.04326			−0.0992075			−0.0496038	−	0.998769i	$-0.515796\pi$
$941$	−3.04326			−0.0992075			−0.0496038	+	0.998769i	$0.515796\pi$
$942$		0			0
$943$	−25.6369			−0.834852
$944$		0			0
$945$	−20.8376	−	31.9038i	−0.677848	−	1.03783i
$946$		0			0
$947$	12.6781			0.411983			0.205991	−	0.978554i	$-0.433958\pi$
$947$	12.6781			0.411983			0.205991	+	0.978554i	$0.433958\pi$
$948$		0			0
$949$	7.15662			0.232314
$950$		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
$957$	27.1510	+	39.1239i	0.877669	+	1.26470i
$958$		0			0
$959$	−12.7928	−	2.51657i	−0.413100	−	0.0812642i
$960$		0			0
$961$	21.0067			0.677634
$962$		0			0
$963$	−18.7443	+	3.14325i	−0.604026	+	0.101290i
$964$		0			0
$965$	−4.05985	+	7.03187i	−0.130691	+	0.226364i
$966$		0			0
$967$	−0.617767	−	1.07000i	−0.0198660	−	0.0344090i	0.855921	−	0.517106i	$-0.172991\pi$
$967$	−0.617767	−	1.07000i	−0.0198660	−	0.0344090i	−0.875788	+	0.482697i	$0.839657\pi$
$968$		0			0
$969$	−1.20055	−	1.72997i	−0.0385674	−	0.0555745i
$970$		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
$975$	−3.97477	+	0.330956i	−0.127295	+	0.0105991i
$976$		0			0
$977$	22.2603			0.712169			0.356084	−	0.934454i	$-0.384112\pi$
$977$	22.2603			0.712169			0.356084	+	0.934454i	$0.384112\pi$
$978$		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
$983$	−16.8671	−	29.2146i	−0.537976	−	0.931801i	−0.999013	−	0.0444206i	$-0.985856\pi$
$983$	−16.8671	−	29.2146i	−0.537976	−	0.931801i	0.461037	−	0.887381i	$-0.347478\pi$
$984$		0			0
$985$	25.6461	−	44.4203i	0.817152	−	1.41535i
$986$		0			0
$987$	−2.80107	−	0.312671i	−0.0891590	−	0.00995243i
$988$		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
$997$	−18.6283	−	32.2651i	−0.589963	−	1.02185i	−0.994237	−	0.107208i	$-0.965809\pi$
$997$	−18.6283	−	32.2651i	−0.589963	−	1.02185i	0.404273	−	0.914638i	$-0.367524\pi$
$998$		0			0
$999$	−3.32452	−	3.40924i	−0.105183	−	0.107864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.c.25.8	✓	22
3.2	odd	2		1512.2.q.d.1369.9		22
4.3	odd	2		1008.2.q.l.529.4		22
7.2	even	3		504.2.t.c.457.2	yes	22
9.4	even	3		504.2.t.c.193.2	yes	22
9.5	odd	6		1512.2.t.c.361.3		22
12.11	even	2		3024.2.q.l.2881.9		22
21.2	odd	6		1512.2.t.c.289.3		22
28.23	odd	6		1008.2.t.l.961.10		22
36.23	even	6		3024.2.t.k.1873.3		22
36.31	odd	6		1008.2.t.l.193.10		22
63.23	odd	6		1512.2.q.d.793.9		22
63.58	even	3	inner	504.2.q.c.121.8	yes	22
84.23	even	6		3024.2.t.k.289.3		22
252.23	even	6		3024.2.q.l.2305.9		22
252.247	odd	6		1008.2.q.l.625.4		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.8	✓	22	1.1	even	1	trivial
504.2.q.c.121.8	yes	22	63.58	even	3	inner
504.2.t.c.193.2	yes	22	9.4	even	3
504.2.t.c.457.2	yes	22	7.2	even	3
1008.2.q.l.529.4		22	4.3	odd	2
1008.2.q.l.625.4		22	252.247	odd	6
1008.2.t.l.193.10		22	36.31	odd	6
1008.2.t.l.961.10		22	28.23	odd	6
1512.2.q.d.793.9		22	63.23	odd	6
1512.2.q.d.1369.9		22	3.2	odd	2
1512.2.t.c.289.3		22	21.2	odd	6
1512.2.t.c.361.3		22	9.5	odd	6
3024.2.q.l.2305.9		22	252.23	even	6
3024.2.q.l.2881.9		22	12.11	even	2
3024.2.t.k.289.3		22	84.23	even	6
3024.2.t.k.1873.3		22	36.23	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.987504 + 1.42297i) q^{3} +(-1.38590 + 2.40045i) q^{5} +(1.74026 - 1.99286i) q^{7} +(-1.04967 + 2.81037i) q^{9} +O(q^{10})\)	\(q+(0.987504 + 1.42297i) q^{3} +(-1.38590 + 2.40045i) q^{5} +(1.74026 - 1.99286i) q^{7} +(-1.04967 + 2.81037i) q^{9} +(1.71972 + 2.97864i) q^{11} +(-0.429164 - 0.743335i) q^{13} +(-4.78434 + 0.398364i) q^{15} +(-0.405132 + 0.701710i) q^{17} +(0.750215 + 1.29941i) q^{19} +(4.55429 + 0.508376i) q^{21} +(-3.82465 + 6.62449i) q^{23} +(-1.34143 - 2.32343i) q^{25} +(-5.03562 + 1.28161i) q^{27} +(3.99696 - 6.92294i) q^{29} -7.21156 q^{31} +(-2.54028 + 5.38852i) q^{33} +(2.37193 + 6.93931i) q^{35} +(0.458211 + 0.793644i) q^{37} +(0.633939 - 1.34473i) q^{39} +(1.67577 + 2.90251i) q^{41} +(1.20465 - 2.08652i) q^{43} +(-5.29141 - 6.41457i) q^{45} -0.615039 q^{47} +(-0.942983 - 6.93619i) q^{49} +(-1.39858 + 0.116452i) q^{51} +(6.31646 - 10.9404i) q^{53} -9.53342 q^{55} +(-1.10818 + 2.35070i) q^{57} +1.46938 q^{59} +11.4327 q^{61} +(3.77398 + 6.98263i) q^{63} +2.37911 q^{65} +16.2012 q^{67} +(-13.2033 + 1.09936i) q^{69} +14.4177 q^{71} +(-4.16893 + 7.22079i) q^{73} +(1.98149 - 4.20320i) q^{75} +(8.92877 + 1.75645i) q^{77} -2.75171 q^{79} +(-6.79639 - 5.89993i) q^{81} +(-5.75814 + 9.97340i) q^{83} +(-1.12294 - 1.94500i) q^{85} +(13.7981 - 1.14889i) q^{87} +(-5.11395 - 8.85763i) q^{89} +(-2.22822 - 0.438331i) q^{91} +(-7.12145 - 10.2618i) q^{93} -4.15889 q^{95} +(3.82852 - 6.63119i) q^{97} +(-10.1762 + 1.70646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9}+O(q^{10}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9	\( 22 q - 2 q^{3} + q^{5} + 5 q^{7} + 6 q^{9} + 3 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} - 22 q^{25} - 2 q^{27} - 7 q^{29} - 12 q^{31} - 3 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} - 3 q^{45} - 34 q^{47} - 25 q^{49} + 53 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} + 42 q^{59} - 62 q^{61} - 22 q^{63} + 6 q^{65} + 52 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} + 53 q^{75} - q^{77} + 32 q^{79} - 6 q^{81} - 36 q^{83} + 28 q^{85} - 5 q^{87} - 2 q^{89} + 15 q^{91} - 11 q^{93} + 48 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 + q^5 + 5 * q^7 + 6 * q^9 + 3 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 - 22 * q^25 - 2 * q^27 - 7 * q^29 - 12 * q^31 - 3 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 - 3 * q^45 - 34 * q^47 - 25 * q^49 + 53 * q^51 + q^53 + 2 * q^55 - 21 * q^57 + 42 * q^59 - 62 * q^61 - 22 * q^63 + 6 * q^65 + 52 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 + 53 * q^75 - q^77 + 32 * q^79 - 6 * q^81 - 36 * q^83 + 28 * q^85 - 5 * q^87 - 2 * q^89 + 15 * q^91 - 11 * q^93 + 48 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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