LMFDB - Embedded newform 800.2.bq.d.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [800,2,Mod(63,800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(800, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 19]))

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

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

chi := DirichletCharacter("800.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.bq (of order $20$, degree $8$, 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			223.1
Character	$\chi$	$=$	800.223
Dual form			800.2.bq.d.287.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.46455 - 2.87435i) q^{3} +(-1.81895 + 1.30054i) q^{5} +(-2.79469 - 2.79469i) q^{7} +(-4.35362 + 5.99224i) q^{9} +(-1.60428 - 2.20810i) q^{11} +(-0.689899 - 4.35585i) q^{13} +(6.40217 + 3.32360i) q^{15} +(4.55876 + 2.32280i) q^{17} +(0.743109 + 2.28705i) q^{19} +(-3.93994 + 12.1259i) q^{21} +(-0.877961 + 5.54323i) q^{23} +(1.61719 - 4.73125i) q^{25} +(14.0412 + 2.22390i) q^{27} +(-6.14797 - 1.99760i) q^{29} +(-3.04391 + 0.989025i) q^{31} +(-3.99731 + 7.84515i) q^{33} +(8.71801 + 1.44881i) q^{35} +(6.09192 - 0.964866i) q^{37} +(-11.5098 + 8.36239i) q^{39} +(5.32289 + 3.86731i) q^{41} +(2.82738 - 2.82738i) q^{43} +(0.125886 - 16.5617i) q^{45} +(1.10121 - 0.561093i) q^{47} +8.62056i q^{49} -16.5054i q^{51} +(-4.64134 + 2.36488i) q^{53} +(5.78984 + 1.93001i) q^{55} +(5.48547 - 5.48547i) q^{57} +(-0.214752 - 0.156027i) q^{59} +(0.418495 - 0.304055i) q^{61} +(28.9134 - 4.57944i) q^{63} +(6.91985 + 7.02585i) q^{65} +(-2.64400 + 5.18915i) q^{67} +(17.2190 - 5.59479i) q^{69} +(-2.21412 - 0.719412i) q^{71} +(-10.4754 - 1.65914i) q^{73} +(-15.9677 + 2.28079i) q^{75} +(-1.68749 + 10.6544i) q^{77} +(-3.73675 + 11.5005i) q^{79} +(-7.30530 - 22.4834i) q^{81} +(5.80791 + 2.95928i) q^{83} +(-11.3131 + 1.70377i) q^{85} +(3.26225 + 20.5970i) q^{87} +(7.20569 + 9.91778i) q^{89} +(-10.2452 + 14.1013i) q^{91} +(7.30077 + 7.30077i) q^{93} +(-4.32609 - 3.19361i) q^{95} +(-4.94401 - 9.70316i) q^{97} +20.2159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43}+ \cdots + 132 q^{99}+O(q^{100}) $ 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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
$3$	−1.46455	−	2.87435i	−0.845561	−	1.65951i	−0.747437	−	0.664333i	$-0.768716\pi$
$3$	−1.46455	−	2.87435i	−0.845561	−	1.65951i	−0.0981245	−	0.995174i	$-0.531284\pi$
$4$		0			0
$5$	−1.81895	+	1.30054i	−0.813461	+	0.581619i
$5$	−1.81895	+	1.30054i	−0.813461	+	0.581619i
$6$		0			0
$7$	−2.79469	−	2.79469i	−1.05629	−	1.05629i	−0.998318	−	0.0579747i	$-0.981536\pi$
$7$	−2.79469	−	2.79469i	−1.05629	−	1.05629i	−0.0579747	−	0.998318i	$-0.518464\pi$
$8$		0			0
$9$	−4.35362	+	5.99224i	−1.45121	+	1.99741i
$10$		0			0
$11$	−1.60428	−	2.20810i	−0.483709	−	0.665768i	0.495504	−	0.868606i	$-0.334984\pi$
$11$	−1.60428	−	2.20810i	−0.483709	−	0.665768i	−0.979212	+	0.202838i	$0.934984\pi$
$12$		0			0
$13$	−0.689899	−	4.35585i	−0.191343	−	1.20809i	−0.877116	−	0.480279i	$-0.840535\pi$
$13$	−0.689899	−	4.35585i	−0.191343	−	1.20809i	0.685772	−	0.727816i	$-0.259465\pi$
$14$		0			0
$15$	6.40217	+	3.32360i	1.65303	+	0.858150i
$16$		0			0
$17$	4.55876	+	2.32280i	1.10566	+	0.563363i	0.908869	−	0.417082i	$-0.136947\pi$
$17$	4.55876	+	2.32280i	1.10566	+	0.563363i	0.196793	+	0.980445i	$0.436947\pi$
$18$		0			0
$19$	0.743109	+	2.28705i	0.170481	+	0.524686i	0.999398	−	0.0346847i	$-0.0110427\pi$
$19$	0.743109	+	2.28705i	0.170481	+	0.524686i	−0.828917	+	0.559371i	$0.811043\pi$
$20$		0			0
$21$	−3.93994	+	12.1259i	−0.859765	+	2.64609i
$22$		0			0
$23$	−0.877961	+	5.54323i	−0.183067	+	1.15584i	0.709425	+	0.704781i	$0.248955\pi$
$23$	−0.877961	+	5.54323i	−0.183067	+	1.15584i	−0.892493	+	0.451062i	$0.851045\pi$
$24$		0			0
$25$	1.61719	−	4.73125i	0.323438	−	0.946249i
$26$		0			0
$27$	14.0412	+	2.22390i	2.70223	+	0.427990i
$28$		0			0
$29$	−6.14797	−	1.99760i	−1.14165	−	0.370944i	−0.323658	−	0.946174i	$-0.604913\pi$
$29$	−6.14797	−	1.99760i	−1.14165	−	0.370944i	−0.817992	+	0.575230i	$0.804913\pi$
$30$		0			0
$31$	−3.04391	+	0.989025i	−0.546702	+	0.177634i	−0.569329	−	0.822110i	$-0.692797\pi$
$31$	−3.04391	+	0.989025i	−0.546702	+	0.177634i	0.0226272	+	0.999744i	$0.492797\pi$
$32$		0			0
$33$	−3.99731	+	7.84515i	−0.695842	+	1.36567i
$34$		0			0
$35$	8.71801	+	1.44881i	1.47361	+	0.244893i
$36$		0			0
$37$	6.09192	−	0.964866i	1.00151	−	0.158623i	0.365914	−	0.930649i	$-0.380756\pi$
$37$	6.09192	−	0.964866i	1.00151	−	0.158623i	0.635591	+	0.772026i	$0.280756\pi$
$38$		0			0
$39$	−11.5098	+	8.36239i	−1.84305	+	1.33905i
$40$		0			0
$41$	5.32289	+	3.86731i	0.831296	+	0.603972i	0.919926	−	0.392093i	$-0.128249\pi$
$41$	5.32289	+	3.86731i	0.831296	+	0.603972i	−0.0886296	+	0.996065i	$0.528249\pi$
$42$		0			0
$43$	2.82738	−	2.82738i	0.431172	−	0.431172i	−0.457855	−	0.889027i	$-0.651382\pi$
$43$	2.82738	−	2.82738i	0.431172	−	0.431172i	0.889027	+	0.457855i	$0.151382\pi$
$44$		0			0
$45$	0.125886	−	16.5617i	0.0187659	−	2.46887i
$46$		0			0
$47$	1.10121	−	0.561093i	0.160628	−	0.0818439i	−0.371829	−	0.928301i	$-0.621269\pi$
$47$	1.10121	−	0.561093i	0.160628	−	0.0818439i	0.532456	+	0.846458i	$0.321269\pi$
$48$		0			0
$49$			8.62056i			1.23151i
$50$		0			0
$51$		−	16.5054i		−	2.31121i
$52$		0			0
$53$	−4.64134	+	2.36488i	−0.637537	+	0.324842i	−0.742711	−	0.669612i	$-0.766460\pi$
$53$	−4.64134	+	2.36488i	−0.637537	+	0.324842i	0.105173	+	0.994454i	$0.466460\pi$
$54$		0			0
$55$	5.78984	+	1.93001i	0.780702	+	0.260242i
$56$		0			0
$57$	5.48547	−	5.48547i	0.726569	−	0.726569i
$58$		0			0
$59$	−0.214752	−	0.156027i	−0.0279584	−	0.0203129i	0.573718	−	0.819053i	$-0.305500\pi$
$59$	−0.214752	−	0.156027i	−0.0279584	−	0.0203129i	−0.601677	+	0.798740i	$0.705500\pi$
$60$		0			0
$61$	0.418495	−	0.304055i	0.0535828	−	0.0389302i	−0.560671	−	0.828038i	$-0.689457\pi$
$61$	0.418495	−	0.304055i	0.0535828	−	0.0389302i	0.614254	+	0.789108i	$0.289457\pi$
$62$		0			0
$63$	28.9134	−	4.57944i	3.64275	−	0.576955i
$64$		0			0
$65$	6.91985	+	7.02585i	0.858301	+	0.871449i
$66$		0			0
$67$	−2.64400	+	5.18915i	−0.323017	+	0.633956i	−0.994225	−	0.107313i	$-0.965775\pi$
$67$	−2.64400	+	5.18915i	−0.323017	+	0.633956i	0.671209	+	0.741268i	$0.265775\pi$
$68$		0			0
$69$	17.2190	−	5.59479i	2.07292	−	0.673534i
$70$		0			0
$71$	−2.21412	−	0.719412i	−0.262768	−	0.0853785i	0.174670	−	0.984627i	$-0.444114\pi$
$71$	−2.21412	−	0.719412i	−0.262768	−	0.0853785i	−0.437438	+	0.899249i	$0.644114\pi$
$72$		0			0
$73$	−10.4754	−	1.65914i	−1.22605	−	0.194188i	−0.490371	−	0.871514i	$-0.663139\pi$
$73$	−10.4754	−	1.65914i	−1.22605	−	0.194188i	−0.735683	+	0.677326i	$0.763139\pi$
$74$		0			0
$75$	−15.9677	+	2.28079i	−1.84379	+	0.263363i
$76$		0			0
$77$	−1.68749	+	10.6544i	−0.192308	+	1.21418i
$78$		0			0
$79$	−3.73675	+	11.5005i	−0.420418	+	1.29391i	0.486897	+	0.873459i	$0.338129\pi$
$79$	−3.73675	+	11.5005i	−0.420418	+	1.29391i	−0.907314	+	0.420453i	$0.861871\pi$
$80$		0			0
$81$	−7.30530	−	22.4834i	−0.811700	−	2.49816i
$82$		0			0
$83$	5.80791	+	2.95928i	0.637501	+	0.324823i	0.742696	−	0.669629i	$-0.233547\pi$
$83$	5.80791	+	2.95928i	0.637501	+	0.324823i	−0.105195	+	0.994452i	$0.533547\pi$
$84$		0			0
$85$	−11.3131	+	1.70377i	−1.22708	+	0.184800i
$86$		0			0
$87$	3.26225	+	20.5970i	0.349750	+	2.20823i
$88$		0			0
$89$	7.20569	+	9.91778i	0.763802	+	1.05128i	0.996888	+	0.0788270i	$0.0251175\pi$
$89$	7.20569	+	9.91778i	0.763802	+	1.05128i	−0.233086	+	0.972456i	$0.574883\pi$
$90$		0			0
$91$	−10.2452	+	14.1013i	−1.07399	+	1.47822i
$92$		0			0
$93$	7.30077	+	7.30077i	0.757055	+	0.757055i
$94$		0			0
$95$	−4.32609	−	3.19361i	−0.443847	−	0.327657i
$96$		0			0
$97$	−4.94401	−	9.70316i	−0.501988	−	0.985206i	−0.993446	−	0.114305i	$-0.963536\pi$
$97$	−4.94401	−	9.70316i	−0.501988	−	0.985206i	0.491458	−	0.870901i	$-0.336464\pi$
$98$		0			0
$99$	20.2159			2.03177
$100$		0			0
$101$	−5.20311			−0.517729			−0.258864	−	0.965914i	$-0.583348\pi$
$101$	−5.20311			−0.517729			−0.258864	+	0.965914i	$0.583348\pi$
$102$		0			0
$103$	−3.77970	−	7.41808i	−0.372425	−	0.730925i	0.626394	−	0.779506i	$-0.284530\pi$
$103$	−3.77970	−	7.41808i	−0.372425	−	0.730925i	−0.998819	+	0.0485812i	$0.984530\pi$
$104$		0			0
$105$	−8.60363	−	27.1805i	−0.839628	−	2.65254i
$106$		0			0
$107$	−12.3186	−	12.3186i	−1.19088	−	1.19088i	−0.976819	−	0.214065i	$-0.931330\pi$
$107$	−12.3186	−	12.3186i	−1.19088	−	1.19088i	−0.214065	−	0.976819i	$-0.568670\pi$
$108$		0			0
$109$	−3.85539	+	5.30648i	−0.369279	+	0.508269i	−0.952705	−	0.303898i	$-0.901712\pi$
$109$	−3.85539	+	5.30648i	−0.369279	+	0.508269i	0.583426	+	0.812166i	$0.301712\pi$
$110$		0			0
$111$	−11.6953	−	16.0972i	−1.11007	−	1.52788i
$112$		0			0
$113$	0.987363	+	6.23396i	0.0928833	+	0.586442i	0.989601	+	0.143839i	$0.0459448\pi$
$113$	0.987363	+	6.23396i	0.0928833	+	0.586442i	−0.896718	+	0.442603i	$0.854055\pi$
$114$		0			0
$115$	−5.61222	−	11.2247i	−0.523342	−	1.04671i
$116$		0			0
$117$	29.1048	+	14.8297i	2.69074	+	1.37100i
$118$		0			0
$119$	−6.24880	−	19.2318i	−0.572827	−	1.76298i
$120$		0			0
$121$	1.09718	−	3.37679i	0.0997441	−	0.306981i
$122$		0			0
$123$	3.32033	−	20.9637i	0.299384	−	1.89024i
$124$		0			0
$125$	3.21157	+	10.7091i	0.287252	+	0.957855i
$126$		0			0
$127$	2.85861	+	0.452759i	0.253660	+	0.0401758i	0.281970	−	0.959423i	$-0.409012\pi$
$127$	2.85861	+	0.452759i	0.253660	+	0.0401758i	−0.0283092	+	0.999599i	$0.509012\pi$
$128$		0			0
$129$	−12.2677	−	3.98603i	−1.08012	−	0.350951i
$130$		0			0
$131$	2.76968	−	0.899925i	0.241988	−	0.0786268i	−0.185512	−	0.982642i	$-0.559394\pi$
$131$	2.76968	−	0.899925i	0.241988	−	0.0786268i	0.427500	+	0.904015i	$0.359394\pi$
$132$		0			0
$133$	4.31485	−	8.46836i	0.374145	−	0.734300i
$134$		0			0
$135$	−28.4325	+	14.2159i	−2.44708	+	1.22351i
$136$		0			0
$137$	−3.12844	+	0.495496i	−0.267280	+	0.0423331i	−0.288636	−	0.957439i	$-0.593202\pi$
$137$	−3.12844	+	0.495496i	−0.267280	+	0.0423331i	0.0213557	+	0.999772i	$0.493202\pi$
$138$		0			0
$139$	−18.4701	+	13.4193i	−1.56661	+	1.13821i	−0.636298	+	0.771444i	$0.719535\pi$
$139$	−18.4701	+	13.4193i	−1.56661	+	1.13821i	−0.930313	+	0.366766i	$0.880465\pi$
$140$		0			0
$141$	−3.22556	−	2.34350i	−0.271641	−	0.197359i
$142$		0			0
$143$	−8.51137	+	8.51137i	−0.711756	+	0.711756i
$144$		0			0
$145$	13.7808	−	4.36214i	1.14444	−	0.362256i
$146$		0			0
$147$	24.7785	−	12.6253i	2.04370	−	1.04132i
$148$		0			0
$149$			7.69000i			0.629989i	0.949094	+	0.314994i	$0.102003\pi$
$149$			7.69000i			0.629989i	−0.949094	+	0.314994i	$0.897997\pi$
$150$		0			0
$151$		−	7.50362i		−	0.610636i	−0.952250	−	0.305318i	$-0.901237\pi$
$151$		−	7.50362i		−	0.610636i	0.952250	−	0.305318i	$-0.0987627\pi$
$152$		0			0
$153$	−33.7659	+	17.2046i	−2.72981	+	1.39091i
$154$		0			0
$155$	4.25046	−	5.75771i	0.341405	−	0.462471i
$156$		0			0
$157$	−12.3164	+	12.3164i	−0.982952	+	0.982952i	−0.999857	−	0.0169050i	$-0.994619\pi$
$157$	−12.3164	+	12.3164i	−0.982952	+	0.982952i	0.0169050	+	0.999857i	$0.494619\pi$
$158$		0			0
$159$	13.5950	+	9.87735i	1.07815	+	0.783324i
$160$		0			0
$161$	17.9452	−	13.0380i	1.41428	−	1.02754i
$162$		0			0
$163$	−13.1012	+	2.07502i	−1.02616	+	0.162529i	−0.646753	−	0.762700i	$-0.723874\pi$
$163$	−13.1012	+	2.07502i	−1.02616	+	0.162529i	−0.379412	+	0.925228i	$0.623874\pi$
$164$		0			0
$165$	−2.93202	−	19.4686i	−0.228257	−	1.51563i
$166$		0			0
$167$	−2.99484	+	5.87769i	−0.231747	+	0.454830i	−0.977370	−	0.211539i	$-0.932152\pi$
$167$	−2.99484	+	5.87769i	−0.231747	+	0.454830i	0.745622	+	0.666369i	$0.232152\pi$
$168$		0			0
$169$	−6.13372	+	1.99297i	−0.471824	+	0.153305i
$170$		0			0
$171$	−16.9398	−	5.50407i	−1.29542	−	0.420907i
$172$		0			0
$173$	9.68291	+	1.53362i	0.736178	+	0.116599i	0.513254	−	0.858237i	$-0.328440\pi$
$173$	9.68291	+	1.53362i	0.736178	+	0.116599i	0.222924	+	0.974836i	$0.428440\pi$
$174$		0			0
$175$	−17.7419	+	8.70281i	−1.34116	+	0.657870i
$176$		0			0
$177$	−0.133959	+	0.845783i	−0.0100690	+	0.0635729i
$178$		0			0
$179$	−4.31387	+	13.2767i	−0.322433	+	0.992348i	0.650152	+	0.759804i	$0.274705\pi$
$179$	−4.31387	+	13.2767i	−0.322433	+	0.992348i	−0.972586	+	0.232544i	$0.925295\pi$
$180$		0			0
$181$	3.79297	+	11.6736i	0.281929	+	0.867688i	0.987302	+	0.158852i	$0.0507794\pi$
$181$	3.79297	+	11.6736i	0.281929	+	0.867688i	−0.705373	+	0.708836i	$0.749221\pi$
$182$		0			0
$183$	−1.48687	−	0.757598i	−0.109913	−	0.0560032i
$184$		0			0
$185$	−9.82608	+	9.67783i	−0.722428	+	0.711528i
$186$		0			0
$187$	−2.18454	−	13.7926i	−0.159749	−	1.00862i
$188$		0			0
$189$	−33.0256	−	45.4558i	−2.40226	−	3.30642i
$190$		0			0
$191$	5.62078	−	7.73634i	0.406705	−	0.559782i	−0.555706	−	0.831379i	$-0.687552\pi$
$191$	5.62078	−	7.73634i	0.406705	−	0.559782i	0.962411	+	0.271597i	$0.0875518\pi$
$192$		0			0
$193$	−5.15678	−	5.15678i	−0.371193	−	0.371193i	0.496719	−	0.867912i	$-0.334538\pi$
$193$	−5.15678	−	5.15678i	−0.371193	−	0.371193i	−0.867912	+	0.496719i	$0.834538\pi$
$194$		0			0
$195$	10.0603	−	30.1798i	0.720430	−	2.16122i
$196$		0			0
$197$	−1.57698	−	3.09500i	−0.112355	−	0.220510i	0.827981	−	0.560756i	$-0.189490\pi$
$197$	−1.57698	−	3.09500i	−0.112355	−	0.220510i	−0.940336	+	0.340246i	$0.889490\pi$
$198$		0			0
$199$	−7.93232			−0.562307			−0.281154	−	0.959663i	$-0.590717\pi$
$199$	−7.93232			−0.562307			−0.281154	+	0.959663i	$0.590717\pi$
$200$		0			0
$201$	18.7877			1.32518
$202$		0			0
$203$	11.5990	+	22.7643i	0.814090	+	1.59774i
$204$		0			0
$205$	−14.7117	−	0.111824i	−1.02751	−	0.00781012i
$206$		0			0
$207$	−29.3940	−	29.3940i	−2.04303	−	2.04303i
$208$		0			0
$209$	3.85790	−	5.30994i	0.266856	−	0.367296i
$210$		0			0
$211$	12.3726	+	17.0295i	0.851768	+	1.17236i	0.983471	+	0.181068i	$0.0579555\pi$
$211$	12.3726	+	17.0295i	0.851768	+	1.17236i	−0.131703	+	0.991289i	$0.542045\pi$
$212$		0			0
$213$	1.17486	+	7.41778i	0.0805002	+	0.508258i
$214$		0			0
$215$	−1.46576	+	8.82001i	−0.0999638	+	0.601519i
$216$		0			0
$217$	11.2708	+	5.74275i	0.765111	+	0.389843i
$218$		0			0
$219$	10.5729	+	32.5399i	0.714448	+	2.19884i
$220$		0			0
$221$	6.97270	−	21.4598i	0.469035	−	1.44354i
$222$		0			0
$223$	−1.07738	+	6.80229i	−0.0721465	+	0.455515i	0.924996	+	0.379976i	$0.124068\pi$
$223$	−1.07738	+	6.80229i	−0.0721465	+	0.455515i	−0.997143	+	0.0755389i	$0.975932\pi$
$224$		0			0
$225$	21.3101	+	30.2886i	1.42067	+	2.01924i
$226$		0			0
$227$	−16.2657	−	2.57623i	−1.07959	−	0.170991i	−0.408791	−	0.912628i	$-0.634050\pi$
$227$	−16.2657	−	2.57623i	−1.07959	−	0.170991i	−0.670801	+	0.741637i	$0.734050\pi$
$228$		0			0
$229$	−11.5696	−	3.75919i	−0.764541	−	0.248414i	−0.0993145	−	0.995056i	$-0.531665\pi$
$229$	−11.5696	−	3.75919i	−0.764541	−	0.248414i	−0.665226	+	0.746642i	$0.731665\pi$
$230$		0			0
$231$	33.0960	−	10.7535i	2.17756	−	0.707531i
$232$		0			0
$233$	12.0215	−	23.5935i	0.787552	−	1.54566i	−0.0496507	−	0.998767i	$-0.515811\pi$
$233$	12.0215	−	23.5935i	0.787552	−	1.54566i	0.837203	−	0.546892i	$-0.184189\pi$
$234$		0			0
$235$	−1.27332	+	2.45277i	−0.0830624	+	0.160001i
$236$		0			0
$237$	38.5293	−	6.10244i	2.50275	−	0.396396i
$238$		0			0
$239$	17.2941	−	12.5649i	1.11866	−	0.812758i	0.134659	−	0.990892i	$-0.457006\pi$
$239$	17.2941	−	12.5649i	1.11866	−	0.812758i	0.984006	+	0.178134i	$0.0570062\pi$
$240$		0			0
$241$	11.6753	+	8.48263i	0.752075	+	0.546414i	0.896469	−	0.443106i	$-0.146123\pi$
$241$	11.6753	+	8.48263i	0.752075	+	0.546414i	−0.144394	+	0.989520i	$0.546123\pi$
$242$		0			0
$243$	−23.7690	+	23.7690i	−1.52479	+	1.52479i
$244$		0			0
$245$	−11.2114	−	15.6804i	−0.716269	−	1.00178i
$246$		0			0
$247$	9.44939	−	4.81471i	0.601250	−	0.306352i
$248$		0			0
$249$		−	21.0280i		−	1.33260i
$250$		0			0
$251$			8.72581i			0.550768i	0.961334	+	0.275384i	$0.0888050\pi$
$251$			8.72581i			0.550768i	−0.961334	+	0.275384i	$0.911195\pi$
$252$		0			0
$253$	13.6485	−	6.95426i	0.858074	−	0.437211i
$254$		0			0
$255$	21.4659	+	30.0225i	1.34424	+	1.88008i
$256$		0			0
$257$	−11.5328	+	11.5328i	−0.719397	+	0.719397i	−0.968482	−	0.249084i	$-0.919870\pi$
$257$	−11.5328	+	11.5328i	−0.719397	+	0.719397i	0.249084	+	0.968482i	$0.419870\pi$
$258$		0			0
$259$	−19.7215	−	14.3285i	−1.22544	−	0.890331i
$260$		0			0
$261$	38.7360	−	28.1433i	2.39770	−	1.74203i
$262$		0			0
$263$	18.1552	−	2.87549i	1.11949	−	0.177311i	0.430860	−	0.902419i	$-0.358210\pi$
$263$	18.1552	−	2.87549i	1.11949	−	0.177311i	0.688635	+	0.725108i	$0.258210\pi$
$264$		0			0
$265$	5.36677	−	10.3379i	0.329678	−	0.635050i
$266$		0			0
$267$	17.9541	−	35.2368i	1.09877	−	2.15646i
$268$		0			0
$269$	−11.0677	+	3.59613i	−0.674812	+	0.219260i	−0.626323	−	0.779564i	$-0.715441\pi$
$269$	−11.0677	+	3.59613i	−0.674812	+	0.219260i	−0.0484895	+	0.998824i	$0.515441\pi$
$270$		0			0
$271$	−7.19982	−	2.33936i	−0.437358	−	0.142106i	0.0820585	−	0.996628i	$-0.473851\pi$
$271$	−7.19982	−	2.33936i	−0.437358	−	0.142106i	−0.519416	+	0.854521i	$0.673851\pi$
$272$		0			0
$273$	55.5367	+	8.79615i	3.36123	+	0.532367i
$274$		0			0
$275$	−13.0415	+	4.01932i	−0.786433	+	0.242374i
$276$		0			0
$277$	3.99596	−	25.2295i	0.240094	−	1.51589i	−0.513234	−	0.858249i	$-0.671553\pi$
$277$	3.99596	−	25.2295i	0.240094	−	1.51589i	0.753328	−	0.657645i	$-0.228447\pi$
$278$		0			0
$279$	7.32552	−	22.5456i	0.438568	−	1.34977i
$280$		0			0
$281$	−4.41297	−	13.5817i	−0.263256	−	0.810217i	−0.992090	−	0.125527i	$-0.959938\pi$
$281$	−4.41297	−	13.5817i	−0.263256	−	0.810217i	0.728835	−	0.684690i	$-0.240062\pi$
$282$		0			0
$283$	1.41981	+	0.723431i	0.0843991	+	0.0430035i	0.495681	−	0.868505i	$-0.334919\pi$
$283$	1.41981	+	0.723431i	0.0843991	+	0.0430035i	−0.411281	+	0.911508i	$0.634919\pi$
$284$		0			0
$285$	−2.84375	+	17.1119i	−0.168449	+	1.01362i
$286$		0			0
$287$	−4.06791	−	25.6837i	−0.240121	−	1.51606i
$288$		0			0
$289$	5.39453	+	7.42494i	0.317325	+	0.436761i
$290$		0			0
$291$	−20.6495	+	28.4216i	−1.21050	+	1.66610i
$292$		0			0
$293$	12.2420	+	12.2420i	0.715187	+	0.715187i	0.967615	−	0.252429i	$-0.0812294\pi$
$293$	12.2420	+	12.2420i	0.715187	+	0.715187i	−0.252429	+	0.967615i	$0.581229\pi$
$294$		0			0
$295$	0.593543	+	0.00451154i	0.0345574	+	0.000262672i
$296$		0			0
$297$	−17.6154	−	34.5721i	−1.02215	−	2.00608i
$298$		0			0
$299$	24.7512			1.43140
$300$		0			0
$301$	−15.8033			−0.910888
$302$		0			0
$303$	7.62024	+	14.9556i	0.437771	+	0.859175i
$304$		0			0
$305$	−0.365789	+	1.09733i	−0.0209450	+	0.0628330i
$306$		0			0
$307$	10.0589	+	10.0589i	0.574089	+	0.574089i	0.933269	−	0.359179i	$-0.116943\pi$
$307$	10.0589	+	10.0589i	0.574089	+	0.574089i	−0.359179	+	0.933269i	$0.616943\pi$
$308$		0			0
$309$	−15.7866	+	21.7284i	−0.898068	+	1.23608i
$310$		0			0
$311$	6.07301	+	8.35878i	0.344369	+	0.473983i	0.945711	−	0.325009i	$-0.105367\pi$
$311$	6.07301	+	8.35878i	0.344369	+	0.473983i	−0.601342	+	0.798991i	$0.705367\pi$
$312$		0			0
$313$	2.55644	+	16.1407i	0.144498	+	0.912326i	0.948288	+	0.317412i	$0.102814\pi$
$313$	2.55644	+	16.1407i	0.144498	+	0.912326i	−0.803789	+	0.594914i	$0.797186\pi$
$314$		0			0
$315$	−46.6365	+	45.9329i	−2.62767	+	2.58802i
$316$		0			0
$317$	−29.7982	−	15.1829i	−1.67363	−	0.852758i	−0.992727	−	0.120387i	$-0.961586\pi$
$317$	−29.7982	−	15.1829i	−1.67363	−	0.852758i	−0.680906	−	0.732371i	$-0.738414\pi$
$318$		0			0
$319$	5.45217	+	16.7801i	0.305263	+	0.939503i
$320$		0			0
$321$	−17.3667	+	53.4493i	−0.969316	+	2.98325i
$322$		0			0
$323$	−1.92472	+	12.1522i	−0.107095	+	0.676168i
$324$		0			0
$325$	−21.7243	−	3.78016i	−1.20505	−	0.209686i
$326$		0			0
$327$	20.8991	+	3.31009i	1.15572	+	0.183049i
$328$		0			0
$329$	−4.64561	−	1.50945i	−0.256121	−	0.0832187i
$330$		0			0
$331$	−3.88228	+	1.26143i	−0.213390	+	0.0693345i	−0.413761	−	0.910386i	$-0.635785\pi$
$331$	−3.88228	+	1.26143i	−0.213390	+	0.0693345i	0.200371	+	0.979720i	$0.435785\pi$
$332$		0			0
$333$	−20.7402	+	40.7049i	−1.13655	+	2.23061i
$334$		0			0
$335$	−1.93937	−	12.8775i	−0.105959	−	0.703571i
$336$		0			0
$337$	−28.5845	+	4.52734i	−1.55710	+	0.246620i	−0.874811	−	0.484465i	$-0.839014\pi$
$337$	−28.5845	+	4.52734i	−1.55710	+	0.246620i	−0.682286	+	0.731085i	$0.739014\pi$
$338$		0			0
$339$	16.4726	−	11.9680i	0.894666	−	0.650013i
$340$		0			0
$341$	7.06715	+	5.13458i	0.382708	+	0.278053i
$342$		0			0
$343$	4.52896	−	4.52896i	0.244541	−	0.244541i
$344$		0			0
$345$	−24.0443	+	32.5707i	−1.29450	+	1.75355i
$346$		0			0
$347$	23.8682	−	12.1615i	1.28131	−	0.652862i	0.325141	−	0.945666i	$-0.394588\pi$
$347$	23.8682	−	12.1615i	1.28131	−	0.652862i	0.956173	+	0.292804i	$0.0945883\pi$
$348$		0			0
$349$		−	9.07661i		−	0.485860i	−0.970044	−	0.242930i	$-0.921892\pi$
$349$		−	9.07661i		−	0.485860i	0.970044	−	0.242930i	$-0.0781085\pi$
$350$		0			0
$351$		−	62.6955i		−	3.34644i
$352$		0			0
$353$	−2.80378	+	1.42860i	−0.149230	+	0.0760364i	−0.527011	−	0.849859i	$-0.676687\pi$
$353$	−2.80378	+	1.42860i	−0.149230	+	0.0760364i	0.377781	+	0.925895i	$0.376687\pi$
$354$		0			0
$355$	4.96301	−	1.57098i	0.263409	−	0.0833788i
$356$		0			0
$357$	−46.1273	+	46.1273i	−2.44132	+	2.44132i
$358$		0			0
$359$	−16.3120	−	11.8514i	−0.860914	−	0.625490i	0.0672196	−	0.997738i	$-0.478587\pi$
$359$	−16.3120	−	11.8514i	−0.860914	−	0.625490i	−0.928133	+	0.372248i	$0.878587\pi$
$360$		0			0
$361$	10.6929	−	7.76886i	0.562785	−	0.408887i
$362$		0			0
$363$	−11.3130	+	1.79180i	−0.593776	+	0.0940449i
$364$		0			0
$365$	21.2121	−	10.6058i	1.11029	−	0.555132i
$366$		0			0
$367$	−15.3915	+	30.2076i	−0.803431	+	1.57682i	0.0133758	+	0.999911i	$0.495742\pi$
$367$	−15.3915	+	30.2076i	−0.803431	+	1.57682i	−0.816807	+	0.576911i	$0.804258\pi$
$368$		0			0
$369$	−46.3477	+	15.0593i	−2.41276	+	0.783954i
$370$		0			0
$371$	19.5802	+	6.36200i	1.01655	+	0.330298i
$372$		0			0
$373$	−0.0157471	−	0.00249409i	−0.000815354	−	0.000129139i	0.156027	−	0.987753i	$-0.450131\pi$
$373$	−0.0157471	−	0.00249409i	−0.000815354	−	0.000129139i	−0.156842	+	0.987624i	$0.550131\pi$
$374$		0			0
$375$	26.0783	−	24.9153i	1.34668	−	1.28662i
$376$		0			0
$377$	−4.45975	+	28.1578i	−0.229689	+	1.45020i
$378$		0			0
$379$	9.53680	−	29.3513i	0.489873	−	1.50767i	−0.334925	−	0.942245i	$-0.608711\pi$
$379$	9.53680	−	29.3513i	0.489873	−	1.50767i	0.824798	−	0.565428i	$-0.191289\pi$
$380$		0			0
$381$	−2.88520	−	8.87973i	−0.147813	−	0.454922i
$382$		0			0
$383$	18.6404	+	9.49776i	0.952480	+	0.485313i	0.859939	−	0.510396i	$-0.170501\pi$
$383$	18.6404	+	9.49776i	0.952480	+	0.485313i	0.0925405	+	0.995709i	$0.470501\pi$
$384$		0			0
$385$	−10.7870	−	21.5746i	−0.549758	−	1.09954i
$386$		0			0
$387$	4.63301	+	29.2517i	0.235509	+	1.48695i
$388$		0			0
$389$	20.0307	+	27.5699i	1.01560	+	1.39785i	0.915245	+	0.402898i	$0.131997\pi$
$389$	20.0307	+	27.5699i	1.01560	+	1.39785i	0.100353	+	0.994952i	$0.468003\pi$
$390$		0			0
$391$	−16.8782	+	23.2309i	−0.853570	+	1.17484i
$392$		0			0
$393$	−6.64305	−	6.64305i	−0.335098	−	0.335098i
$394$		0			0
$395$	−8.15993	−	25.7788i	−0.410571	−	1.29707i
$396$		0			0
$397$	0.451213	+	0.885556i	0.0226457	+	0.0444448i	0.902052	−	0.431627i	$-0.142060\pi$
$397$	0.451213	+	0.885556i	0.0226457	+	0.0444448i	−0.879406	+	0.476072i	$0.842060\pi$
$398$		0			0
$399$	−30.6604			−1.53494
$400$		0			0
$401$	18.8940			0.943521			0.471761	−	0.881727i	$-0.343619\pi$
$401$	18.8940			0.943521			0.471761	+	0.881727i	$0.343619\pi$
$402$		0			0
$403$	6.40803	+	12.5765i	0.319207	+	0.626478i
$404$		0			0
$405$	42.5286	+	31.3955i	2.11326	+	1.56005i
$406$		0			0
$407$	−11.9037	−	11.9037i	−0.590043	−	0.590043i
$408$		0			0
$409$	22.9396	−	31.5737i	1.13429	−	1.56122i	0.354638	−	0.935004i	$-0.384604\pi$
$409$	22.9396	−	31.5737i	1.13429	−	1.56122i	0.779652	−	0.626213i	$-0.215396\pi$
$410$		0			0
$411$	6.00600	+	8.26654i	0.296254	+	0.407759i
$412$		0			0
$413$	0.164120	+	1.03621i	0.00807580	+	0.0509886i
$414$		0			0
$415$	−14.4130	+	2.17063i	−0.707506	+	0.106552i
$416$		0			0
$417$	65.6222	+	33.4362i	3.21353	+	1.63738i
$418$		0			0
$419$	4.82220	+	14.8412i	0.235580	+	0.725041i	0.997044	+	0.0768334i	$0.0244810\pi$
$419$	4.82220	+	14.8412i	0.235580	+	0.725041i	−0.761464	+	0.648207i	$0.775519\pi$
$420$		0			0
$421$	−4.85470	+	14.9412i	−0.236604	+	0.728192i	0.760301	+	0.649571i	$0.225052\pi$
$421$	−4.85470	+	14.9412i	−0.236604	+	0.728192i	−0.996905	+	0.0786205i	$0.974948\pi$
$422$		0			0
$423$	−1.43203	+	9.04148i	−0.0696277	+	0.439612i
$424$		0			0
$425$	18.3622	−	17.8122i	0.890695	−	0.864019i
$426$		0			0
$427$	−2.01930	−	0.319826i	−0.0977209	−	0.0154775i
$428$		0			0
$429$	36.9300	+	11.9993i	1.78300	+	0.579331i
$430$		0			0
$431$	−34.4523	+	11.1942i	−1.65951	+	0.539207i	−0.980769	−	0.195173i	$-0.937473\pi$
$431$	−34.4523	+	11.1942i	−1.65951	+	0.539207i	−0.678738	+	0.734380i	$0.737473\pi$
$432$		0			0
$433$	−4.66192	+	9.14954i	−0.224038	+	0.439699i	−0.975476	−	0.220104i	$-0.929360\pi$
$433$	−4.66192	+	9.14954i	−0.224038	+	0.439699i	0.751439	+	0.659803i	$0.229360\pi$
$434$		0			0
$435$	−32.7211	−	33.2223i	−1.56886	−	1.59289i
$436$		0			0
$437$	−13.3301	+	2.11128i	−0.637664	+	0.100996i
$438$		0			0
$439$	5.27551	−	3.83288i	0.251786	−	0.182933i	−0.454732	−	0.890628i	$-0.650265\pi$
$439$	5.27551	−	3.83288i	0.251786	−	0.182933i	0.706518	+	0.707695i	$0.250265\pi$
$440$		0			0
$441$	−51.6565	−	37.5306i	−2.45983	−	1.78717i
$442$		0			0
$443$	21.4275	−	21.4275i	1.01805	−	1.01805i	0.0182176	−	0.999834i	$-0.494201\pi$
$443$	21.4275	−	21.4275i	1.01805	−	1.01805i	0.999834	−	0.0182176i	$-0.00579917\pi$
$444$		0			0
$445$	−26.0053	−	8.66871i	−1.23277	−	0.410936i
$446$		0			0
$447$	22.1037	−	11.2624i	1.04547	−	0.532694i
$448$		0			0
$449$		−	26.5999i		−	1.25533i	−0.778485	−	0.627663i	$-0.784012\pi$
$449$		−	26.5999i		−	1.25533i	0.778485	−	0.627663i	$-0.215988\pi$
$450$		0			0
$451$		−	17.9577i		−	0.845597i
$452$		0			0
$453$	−21.5680	+	10.9895i	−1.01335	+	0.516330i
$454$		0			0
$455$	0.296241	−	38.9739i	0.0138880	−	1.82712i
$456$		0			0
$457$	−28.1522	+	28.1522i	−1.31690	+	1.31690i	−0.400687	+	0.916215i	$0.631229\pi$
$457$	−28.1522	+	28.1522i	−1.31690	+	1.31690i	−0.916215	+	0.400687i	$0.868771\pi$
$458$		0			0
$459$	58.8447	+	42.7532i	2.74663	+	1.99555i
$460$		0			0
$461$	−1.83986	+	1.33674i	−0.0856908	+	0.0622580i	−0.629806	−	0.776753i	$-0.716866\pi$
$461$	−1.83986	+	1.33674i	−0.0856908	+	0.0622580i	0.544115	+	0.839011i	$0.316866\pi$
$462$		0			0
$463$	32.0023	−	5.06867i	1.48728	−	0.235561i	0.640684	−	0.767805i	$-0.278651\pi$
$463$	32.0023	−	5.06867i	1.48728	−	0.235561i	0.846591	+	0.532244i	$0.178651\pi$
$464$		0			0
$465$	−22.7747	−	3.78483i	−1.05615	−	0.175517i
$466$		0			0
$467$	−11.7289	+	23.0192i	−0.542747	+	1.06520i	0.442929	+	0.896556i	$0.353939\pi$
$467$	−11.7289	+	23.0192i	−0.542747	+	1.06520i	−0.985677	+	0.168645i	$0.946061\pi$
$468$		0			0
$469$	21.8912	−	7.11289i	1.01084	−	0.328443i
$470$		0			0
$471$	53.4395	+	17.3635i	2.46236	+	0.800070i
$472$		0			0
$473$	−10.7791	−	1.70724i	−0.495622	−	0.0784988i
$474$		0			0
$475$	12.0224	+	0.182775i	0.551624	+	0.00838630i
$476$		0			0
$477$	6.03568	−	38.1078i	0.276355	−	1.74484i
$478$		0			0
$479$	−2.02478	+	6.23165i	−0.0925148	+	0.284731i	−0.986598	−	0.163170i	$-0.947828\pi$
$479$	−2.02478	+	6.23165i	−0.0925148	+	0.284731i	0.894083	+	0.447901i	$0.147828\pi$
$480$		0			0
$481$	−8.40562	−	25.8698i	−0.383263	−	1.17956i
$482$		0			0
$483$	−63.7574	−	32.4860i	−2.90106	−	1.47817i
$484$		0			0
$485$	21.6123	+	11.2197i	0.981362	+	0.509462i
$486$		0			0
$487$	−3.57636	−	22.5803i	−0.162061	−	1.02321i	−0.925890	−	0.377792i	$-0.876683\pi$
$487$	−3.57636	−	22.5803i	−0.162061	−	1.02321i	0.763830	−	0.645418i	$-0.223317\pi$
$488$		0			0
$489$	25.1518	+	34.6184i	1.13740	+	1.56550i
$490$		0			0
$491$	−10.8187	+	14.8906i	−0.488239	+	0.672004i	−0.980062	−	0.198692i	$-0.936331\pi$
$491$	−10.8187	+	14.8906i	−0.488239	+	0.672004i	0.491823	+	0.870695i	$0.336331\pi$
$492$		0			0
$493$	−23.3871	−	23.3871i	−1.05330	−	1.05330i
$494$		0			0
$495$	−36.7718	+	26.2916i	−1.65277	+	1.18172i
$496$		0			0
$497$	4.17725	+	8.19831i	0.187375	+	0.367745i
$498$		0			0
$499$	−26.3658			−1.18030			−0.590148	−	0.807295i	$-0.700931\pi$
$499$	−26.3658			−1.18030			−0.590148	+	0.807295i	$0.700931\pi$
$500$		0			0
$501$	21.2807			0.950750
$502$		0			0
$503$	3.47288	+	6.81591i	0.154848	+	0.303907i	0.955378	−	0.295387i	$-0.0954484\pi$
$503$	3.47288	+	6.81591i	0.154848	+	0.303907i	−0.800530	+	0.599293i	$0.795448\pi$
$504$		0			0
$505$	9.46422	−	6.76685i	0.421152	−	0.301121i
$506$		0			0
$507$	14.7116	+	14.7116i	0.653367	+	0.653367i
$508$		0			0
$509$	−15.3150	+	21.0793i	−0.678824	+	0.934321i	−0.999919	−	0.0127257i	$-0.995949\pi$
$509$	−15.3150	+	21.0793i	−0.678824	+	0.934321i	0.321095	+	0.947047i	$0.395949\pi$
$510$		0			0
$511$	24.6387	+	33.9123i	1.08995	+	1.50019i
$512$		0			0
$513$	5.34794	+	33.7655i	0.236117	+	1.49079i
$514$		0			0
$515$	16.5226	+	8.57750i	0.728073	+	0.377970i
$516$		0			0
$517$	−3.00560	−	1.53143i	−0.132186	−	0.0673521i
$518$		0			0
$519$	−9.77299	−	30.0782i	−0.428987	−	1.32028i
$520$		0			0
$521$	−6.19545	+	19.0676i	−0.271428	+	0.835368i	0.718715	+	0.695305i	$0.244731\pi$
$521$	−6.19545	+	19.0676i	−0.271428	+	0.835368i	−0.990143	+	0.140063i	$0.955269\pi$
$522$		0			0
$523$	1.37408	−	8.67559i	0.0600843	−	0.379357i	−0.939262	−	0.343201i	$-0.888489\pi$
$523$	1.37408	−	8.67559i	0.0600843	−	0.379357i	0.999346	−	0.0361559i	$-0.0115113\pi$
$524$		0			0
$525$	50.9989	+	38.2507i	2.22578	+	1.66940i
$526$		0			0
$527$	−16.1738	−	2.56167i	−0.704540	−	0.111588i
$528$		0			0
$529$	−8.08224	−	2.62608i	−0.351402	−	0.114177i
$530$		0			0
$531$	1.86990	−	0.607566i	0.0811466	−	0.0263661i
$532$		0			0
$533$	13.1731	−	25.8538i	0.570592	−	1.11985i
$534$		0			0
$535$	38.4278	+	6.38615i	1.66138	+	0.276097i
$536$		0			0
$537$	44.4798	−	7.04491i	1.91945	−	0.304010i
$538$		0			0
$539$	19.0351	−	13.8298i	0.819899	−	0.595692i
$540$		0			0
$541$	−17.8972	−	13.0031i	−0.769461	−	0.559046i	0.132336	−	0.991205i	$-0.457752\pi$
$541$	−17.8972	−	13.0031i	−0.769461	−	0.559046i	−0.901798	+	0.432159i	$0.857752\pi$
$542$		0			0
$543$	27.9989	−	27.9989i	1.20155	−	1.20155i
$544$		0			0
$545$	0.111479	−	14.6663i	0.00477524	−	0.628237i
$546$		0			0
$547$	2.19922	−	1.12056i	0.0940320	−	0.0479117i	−0.406342	−	0.913721i	$-0.633196\pi$
$547$	2.19922	−	1.12056i	0.0940320	−	0.0479117i	0.500374	+	0.865809i	$0.333196\pi$
$548$		0			0
$549$			3.83146i			0.163523i
$550$		0			0
$551$		−	15.5452i		−	0.662247i
$552$		0			0
$553$	42.5835	−	21.6974i	1.81083	−	0.922666i
$554$		0			0
$555$	42.2083	+	14.0699i	1.79164	+	0.597234i
$556$		0			0
$557$	7.90748	−	7.90748i	0.335051	−	0.335051i	−0.519450	−	0.854501i	$-0.673863\pi$
$557$	7.90748	−	7.90748i	0.335051	−	0.335051i	0.854501	+	0.519450i	$0.173863\pi$
$558$		0			0
$559$	−14.2663	−	10.3650i	−0.603398	−	0.438395i
$560$		0			0
$561$	−36.4455	+	26.4792i	−1.53873	+	1.11795i
$562$		0			0
$563$	−15.7185	+	2.48957i	−0.662457	+	0.104923i	−0.478604	−	0.878031i	$-0.658857\pi$
$563$	−15.7185	+	2.48957i	−0.662457	+	0.104923i	−0.183853	+	0.982954i	$0.558857\pi$
$564$		0			0
$565$	−9.90349	−	10.0552i	−0.416643	−	0.423025i
$566$		0			0
$567$	−42.4181	+	83.2501i	−1.78139	+	3.49618i
$568$		0			0
$569$	−40.4687	+	13.1491i	−1.69654	+	0.551238i	−0.988002	−	0.154439i	$-0.950643\pi$
$569$	−40.4687	+	13.1491i	−1.69654	+	0.551238i	−0.708533	+	0.705677i	$0.750643\pi$
$570$		0			0
$571$	−16.6012	−	5.39406i	−0.694739	−	0.225734i	−0.0597020	−	0.998216i	$-0.519015\pi$
$571$	−16.6012	−	5.39406i	−0.694739	−	0.225734i	−0.635037	+	0.772482i	$0.719015\pi$
$572$		0			0
$573$	−30.4689	−	4.82580i	−1.27286	−	0.201601i
$574$		0			0
$575$	24.8065	+	13.1183i	1.03450	+	0.547071i
$576$		0			0
$577$	5.79961	−	36.6173i	0.241441	−	1.52440i	−0.507437	−	0.861689i	$-0.669407\pi$
$577$	5.79961	−	36.6173i	0.241441	−	1.52440i	0.748877	−	0.662709i	$-0.230593\pi$
$578$		0			0
$579$	−7.27001	+	22.3748i	−0.302131	+	0.929864i
$580$		0			0
$581$	−7.96104	−	24.5016i	−0.330280	−	1.01650i
$582$		0			0
$583$	12.6679	+	6.45463i	0.524652	+	0.267323i
$584$		0			0
$585$	−72.2269	+	10.8775i	−2.98622	+	0.449730i
$586$		0			0
$587$	3.95971	+	25.0006i	0.163435	+	1.03189i	0.923935	+	0.382549i	$0.124954\pi$
$587$	3.95971	+	25.0006i	0.163435	+	1.03189i	−0.760501	+	0.649337i	$0.775046\pi$
$588$		0			0
$589$	−4.52391	−	6.22663i	−0.186404	−	0.256564i
$590$		0			0
$591$	−6.58655	+	9.06560i	−0.270934	+	0.372909i
$592$		0			0
$593$	−16.2733	−	16.2733i	−0.668266	−	0.668266i	0.289049	−	0.957314i	$-0.406661\pi$
$593$	−16.2733	−	16.2733i	−0.668266	−	0.668266i	−0.957314	+	0.289049i	$0.906661\pi$
$594$		0			0
$595$	36.3780	+	26.8550i	1.49135	+	1.10095i
$596$		0			0
$597$	11.6173	+	22.8003i	0.475465	+	0.933153i
$598$		0			0
$599$	−12.7517			−0.521019			−0.260509	−	0.965471i	$-0.583890\pi$
$599$	−12.7517			−0.521019			−0.260509	+	0.965471i	$0.583890\pi$
$600$		0			0
$601$	5.60928			0.228807			0.114404	−	0.993434i	$-0.463504\pi$
$601$	5.60928			0.228807			0.114404	+	0.993434i	$0.463504\pi$
$602$		0			0
$603$	−19.5836	−	38.4351i	−0.797508	−	1.56520i
$604$		0			0
$605$	2.39592	+	7.56916i	0.0974079	+	0.307730i
$606$		0			0
$607$	−8.41059	−	8.41059i	−0.341375	−	0.341375i	0.515509	−	0.856884i	$-0.327603\pi$
$607$	−8.41059	−	8.41059i	−0.341375	−	0.341375i	−0.856884	+	0.515509i	$0.827603\pi$
$608$		0			0
$609$	48.4453	−	66.6792i	1.96310	−	2.70198i
$610$		0			0
$611$	−3.20376	−	4.40959i	−0.129610	−	0.178393i
$612$		0			0
$613$	2.17512	+	13.7332i	0.0878523	+	0.554677i	0.991877	+	0.127198i	$0.0405984\pi$
$613$	2.17512	+	13.7332i	0.0878523	+	0.554677i	−0.904025	+	0.427479i	$0.859402\pi$
$614$		0			0
$615$	21.2247	+	42.4503i	0.855861	+	1.71176i
$616$		0			0
$617$	−30.4274	−	15.5035i	−1.22496	−	0.624149i	−0.282758	−	0.959191i	$-0.591249\pi$
$617$	−30.4274	−	15.5035i	−1.22496	−	0.624149i	−0.942203	+	0.335042i	$0.891249\pi$
$618$		0			0
$619$	3.44153	+	10.5920i	0.138327	+	0.425727i	0.996093	−	0.0883143i	$-0.0281480\pi$
$619$	3.44153	+	10.5920i	0.138327	+	0.425727i	−0.857766	+	0.514041i	$0.828148\pi$
$620$		0			0
$621$	−24.6552	+	75.8809i	−0.989379	+	3.04500i
$622$		0			0
$623$	7.57945	−	47.8548i	0.303664	−	1.91726i
$624$		0			0
$625$	−19.7694	−	15.3027i	−0.790775	−	0.612107i
$626$		0			0
$627$	−20.9127	−	3.31225i	−0.835174	−	0.132279i
$628$		0			0
$629$	30.0128	+	9.75175i	1.19669	+	0.388828i
$630$		0			0
$631$	30.9083	−	10.0427i	1.23044	−	0.399794i	0.379565	−	0.925165i	$-0.376074\pi$
$631$	30.9083	−	10.0427i	1.23044	−	0.399794i	0.850873	+	0.525371i	$0.176074\pi$
$632$		0			0
$633$	30.8283	−	60.5039i	1.22531	−	2.40481i
$634$		0			0
$635$	−5.78851	+	2.89418i	−0.229710	+	0.114852i
$636$		0			0
$637$	37.5499	−	5.94731i	1.48778	−	0.235641i
$638$		0			0
$639$	13.9503	−	10.1355i	0.551866	−	0.400954i
$640$		0			0
$641$	27.5141	+	19.9901i	1.08674	+	0.789563i	0.978846	−	0.204599i	$-0.0655890\pi$
$641$	27.5141	+	19.9901i	1.08674	+	0.789563i	0.107895	+	0.994162i	$0.465589\pi$
$642$		0			0
$643$	−20.5380	+	20.5380i	−0.809941	+	0.809941i	−0.984625	−	0.174684i	$-0.944110\pi$
$643$	−20.5380	+	20.5380i	−0.809941	+	0.809941i	0.174684	+	0.984625i	$0.444110\pi$
$644$		0			0
$645$	27.4985	−	8.70428i	1.08275	−	0.342731i
$646$		0			0
$647$	−2.67176	+	1.36133i	−0.105038	+	0.0535193i	−0.505720	−	0.862698i	$-0.668773\pi$
$647$	−2.67176	+	1.36133i	−0.105038	+	0.0535193i	0.400682	+	0.916217i	$0.368773\pi$
$648$		0			0
$649$			0.724506i			0.0284393i
$650$		0			0
$651$		−	40.8068i		−	1.59934i
$652$		0			0
$653$	−14.3147	+	7.29369i	−0.560177	+	0.285424i	−0.711065	−	0.703127i	$-0.751787\pi$
$653$	−14.3147	+	7.29369i	−0.560177	+	0.285424i	0.150888	+	0.988551i	$0.451787\pi$
$654$		0			0
$655$	−3.86754	+	5.23901i	−0.151117	+	0.204705i
$656$		0			0
$657$	55.5479	−	55.5479i	2.16713	−	2.16713i
$658$		0			0
$659$	1.06188	+	0.771504i	0.0413651	+	0.0300535i	0.608276	−	0.793726i	$-0.291862\pi$
$659$	1.06188	+	0.771504i	0.0413651	+	0.0300535i	−0.566911	+	0.823779i	$0.691862\pi$
$660$		0			0
$661$	34.8370	−	25.3105i	1.35500	−	0.984466i	0.356256	−	0.934388i	$-0.384053\pi$
$661$	34.8370	−	25.3105i	1.35500	−	0.984466i	0.998745	−	0.0500779i	$-0.0159469\pi$
$662$		0			0
$663$	−71.8948	+	11.3870i	−2.79216	+	0.442235i
$664$		0			0
$665$	3.16493	+	21.0152i	0.122731	+	0.814934i
$666$		0			0
$667$	16.4708	−	32.3258i	0.637752	−	1.25166i
$668$		0			0
$669$	21.1300	−	6.86556i	0.816934	−	0.265438i
$670$		0			0
$671$	−1.34277	−	0.436292i	−0.0518370	−	0.0168429i
$672$		0			0
$673$	−46.9047	−	7.42897i	−1.80804	−	0.286366i	−0.841010	−	0.541019i	$-0.818039\pi$
$673$	−46.9047	−	7.42897i	−1.80804	−	0.286366i	−0.967032	+	0.254653i	$0.918039\pi$
$674$		0			0
$675$	33.2291	−	62.8358i	1.27899	−	2.41855i
$676$		0			0
$677$	5.40918	−	34.1522i	0.207892	−	1.31258i	−0.634170	−	0.773194i	$-0.718658\pi$
$677$	5.40918	−	34.1522i	0.207892	−	1.31258i	0.842061	−	0.539382i	$-0.181342\pi$
$678$		0			0
$679$	−13.3003	+	40.9342i	−0.510420	+	1.57091i
$680$		0			0
$681$	16.4170	+	50.5264i	0.629101	+	1.93617i
$682$		0			0
$683$	24.9863	+	12.7312i	0.956074	+	0.487144i	0.861156	−	0.508341i	$-0.169741\pi$
$683$	24.9863	+	12.7312i	0.956074	+	0.487144i	0.0949182	+	0.995485i	$0.469741\pi$
$684$		0			0
$685$	5.04607	−	4.96994i	0.192801	−	0.189892i
$686$		0			0
$687$	6.13908	+	38.7606i	0.234221	+	1.47881i
$688$		0			0
$689$	13.5031	+	18.5855i	0.514428	+	0.708049i
$690$		0			0
$691$	−8.46130	+	11.6460i	−0.321883	+	0.443034i	−0.939041	−	0.343805i	$-0.888284\pi$
$691$	−8.46130	+	11.6460i	−0.321883	+	0.443034i	0.617158	+	0.786839i	$0.288284\pi$
$692$		0			0
$693$	−56.4971	−	56.4971i	−2.14615	−	2.14615i
$694$		0			0
$695$	16.1439	−	48.4301i	0.612373	−	1.83706i
$696$		0			0
$697$	15.2828	+	29.9942i	0.578877	+	1.13611i
$698$		0			0
$699$	−85.4220			−3.23096
$700$		0			0
$701$	23.6691			0.893968			0.446984	−	0.894542i	$-0.352498\pi$
$701$	23.6691			0.893968			0.446984	+	0.894542i	$0.352498\pi$
$702$		0			0
$703$	6.73366	+	13.2156i	0.253965	+	0.498434i
$704$		0			0
$705$	8.91496	+	0.0677629i	0.335757	+	0.00255210i
$706$		0			0
$707$	14.5411	+	14.5411i	0.546873	+	0.546873i
$708$		0			0
$709$	−10.7394	+	14.7815i	−0.403326	+	0.555131i	−0.961575	−	0.274543i	$-0.911474\pi$
$709$	−10.7394	+	14.7815i	−0.403326	+	0.555131i	0.558249	+	0.829674i	$0.311474\pi$
$710$		0			0
$711$	−52.6456	−	72.4605i	−1.97436	−	2.71748i
$712$		0			0
$713$	−2.80996	−	17.7414i	−0.105234	−	0.664420i
$714$		0			0
$715$	4.41242	−	26.5512i	0.165015	−	0.992958i
$716$		0			0
$717$	−61.4442	−	31.3074i	−2.29468	−	1.16920i
$718$		0			0
$719$	8.20814	+	25.2621i	0.306112	+	0.942116i	0.979260	+	0.202608i	$0.0649417\pi$
$719$	8.20814	+	25.2621i	0.306112	+	0.942116i	−0.673148	+	0.739508i	$0.735058\pi$
$720$		0			0
$721$	−10.1681	+	31.2943i	−0.378681	+	1.16546i
$722$		0			0
$723$	7.28288	−	45.9823i	0.270853	−	1.71010i
$724$		0			0
$725$	−19.3936	+	25.8571i	−0.720259	+	0.960307i
$726$		0			0
$727$	−14.2659	−	2.25950i	−0.529094	−	0.0838002i	−0.113828	−	0.993500i	$-0.536311\pi$
$727$	−14.2659	−	2.25950i	−0.529094	−	0.0838002i	−0.415266	+	0.909700i	$0.636311\pi$
$728$		0			0
$729$	35.6815	+	11.5936i	1.32154	+	0.429393i
$730$		0			0
$731$	19.4568	−	6.32191i	0.719637	−	0.233824i
$732$		0			0
$733$	20.1391	−	39.5251i	0.743853	−	1.45989i	−0.139024	−	0.990289i	$-0.544396\pi$
$733$	20.1391	−	39.5251i	0.743853	−	1.45989i	0.882877	−	0.469605i	$-0.155604\pi$
$734$		0			0
$735$	−28.6513	+	55.1903i	−1.05682	+	2.03572i
$736$		0			0
$737$	15.6999	−	2.48662i	0.578313	−	0.0915959i
$738$		0			0
$739$	−18.5363	+	13.4674i	−0.681870	+	0.495408i	−0.873978	−	0.485966i	$-0.838468\pi$
$739$	−18.5363	+	13.4674i	−0.681870	+	0.495408i	0.192108	+	0.981374i	$0.438468\pi$
$740$		0			0
$741$	−27.6783	−	20.1095i	−1.01679	−	0.738740i
$742$		0			0
$743$	−16.8830	+	16.8830i	−0.619377	+	0.619377i	−0.945372	−	0.325994i	$-0.894301\pi$
$743$	−16.8830	+	16.8830i	−0.619377	+	0.619377i	0.325994	+	0.945372i	$0.394301\pi$
$744$		0			0
$745$	−10.0011	−	13.9878i	−0.366414	−	0.512472i
$746$		0			0
$747$	−43.0181	+	21.9188i	−1.57395	+	0.801968i
$748$		0			0
$749$			68.8533i			2.51585i
$750$		0			0
$751$			14.8477i			0.541801i	0.962607	+	0.270900i	$0.0873214\pi$
$751$			14.8477i			0.541801i	−0.962607	+	0.270900i	$0.912679\pi$
$752$		0			0
$753$	25.0810	−	12.7794i	0.914003	−	0.465708i
$754$		0			0
$755$	9.75876	+	13.6487i	0.355158	+	0.496729i
$756$		0			0
$757$	−6.81120	+	6.81120i	−0.247557	+	0.247557i	−0.819967	−	0.572410i	$-0.806009\pi$
$757$	−6.81120	+	6.81120i	−0.247557	+	0.247557i	0.572410	+	0.819967i	$0.306009\pi$
$758$		0			0
$759$	−39.9780	−	29.0457i	−1.45111	−	1.05429i
$760$		0			0
$761$	0.259631	−	0.188633i	0.00941163	−	0.00683795i	−0.583069	−	0.812422i	$-0.698148\pi$
$761$	0.259631	−	0.188633i	0.00941163	−	0.00683795i	0.592481	+	0.805584i	$0.298148\pi$
$762$		0			0
$763$	25.6046	−	4.05536i	0.926947	−	0.146814i
$764$		0			0
$765$	39.0434	−	75.2082i	1.41162	−	2.71916i
$766$		0			0
$767$	−0.531471	+	1.04307i	−0.0191903	+	0.0376631i
$768$		0			0
$769$	6.96700	−	2.26371i	0.251236	−	0.0816316i	−0.180691	−	0.983540i	$-0.557834\pi$
$769$	6.96700	−	2.26371i	0.251236	−	0.0816316i	0.431928	+	0.901908i	$0.357834\pi$
$770$		0			0
$771$	50.0398	+	16.2589i	1.80214	+	0.585551i
$772$		0			0
$773$	−22.7703	−	3.60646i	−0.818991	−	0.129715i	−0.267140	−	0.963658i	$-0.586078\pi$
$773$	−22.7703	−	3.60646i	−0.818991	−	0.129715i	−0.551851	+	0.833942i	$0.686078\pi$
$774$		0			0
$775$	−0.243261	+	16.0009i	−0.00873818	+	0.574770i
$776$		0			0
$777$	−12.3020	+	77.6715i	−0.441330	+	2.78645i
$778$		0			0
$779$	−4.88925	+	15.0476i	−0.175176	+	0.539135i
$780$		0			0
$781$	1.96354	+	6.04315i	0.0702609	+	0.216241i
$782$		0			0
$783$	−81.8823	−	41.7211i	−2.92623	−	1.49099i
$784$		0			0
$785$	6.38498	−	38.4208i	0.227890	−	1.37130i
$786$		0			0
$787$	−5.09483	−	32.1675i	−0.181611	−	1.14665i	−0.895062	−	0.445942i	$-0.852869\pi$
$787$	−5.09483	−	32.1675i	−0.181611	−	1.14665i	0.713451	−	0.700705i	$-0.247131\pi$
$788$		0			0
$789$	−34.8544	−	47.9730i	−1.24085	−	1.70788i
$790$		0			0
$791$	14.6626	−	20.1814i	0.521342	−	0.717566i
$792$		0			0
$793$	−1.61314	−	1.61314i	−0.0572841	−	0.0572841i
$794$		0			0
$795$	−37.5746	−	0.285605i	−1.33263	−	0.0101294i
$796$		0			0
$797$	−24.3883	−	47.8648i	−0.863879	−	1.69546i	−0.706255	−	0.707958i	$-0.749617\pi$
$797$	−24.3883	−	47.8648i	−0.863879	−	1.69546i	−0.157624	−	0.987499i	$-0.550383\pi$
$798$		0			0
$799$	6.32345			0.223708
$800$		0			0
$801$	−90.8005			−3.20828
$802$		0			0
$803$	13.1419	+	25.7925i	0.463769	+	0.910198i
$804$		0			0
$805$	−15.6851	+	47.0539i	−0.552829	+	1.65843i
$806$		0			0
$807$	26.5458	+	26.5458i	0.934458	+	0.934458i
$808$		0			0
$809$	−22.6777	+	31.2132i	−0.797307	+	1.09740i	0.195852	+	0.980633i	$0.437253\pi$
$809$	−22.6777	+	31.2132i	−0.797307	+	1.09740i	−0.993159	+	0.116766i	$0.962747\pi$
$810$		0			0
$811$	−20.6446	−	28.4149i	−0.724931	−	0.997782i	−0.999346	−	0.0361702i	$-0.988484\pi$
$811$	−20.6446	−	28.4149i	−0.724931	−	0.997782i	0.274415	−	0.961611i	$-0.411516\pi$
$812$		0			0
$813$	3.82038	+	24.1209i	0.133987	+	0.845958i
$814$		0			0
$815$	21.1318	−	20.8130i	0.740215	−	0.729048i
$816$		0			0
$817$	8.56743	+	4.36533i	0.299737	+	0.152723i
$818$		0			0
$819$	−39.8947	−	122.783i	−1.39403	−	4.29039i
$820$		0			0
$821$	1.41608	−	4.35825i	0.0494216	−	0.152104i	−0.923300	−	0.384079i	$-0.874519\pi$
$821$	1.41608	−	4.35825i	0.0494216	−	0.152104i	0.972722	+	0.231975i	$0.0745189\pi$
$822$		0			0
$823$	5.97979	−	37.7549i	0.208442	−	1.31605i	−0.632345	−	0.774687i	$-0.717907\pi$
$823$	5.97979	−	37.7549i	0.208442	−	1.31605i	0.840787	−	0.541366i	$-0.182093\pi$
$824$		0			0
$825$	30.6529	+	31.5994i	1.06720	+	1.10015i
$826$		0			0
$827$	6.05062	+	0.958323i	0.210401	+	0.0333242i	0.260745	−	0.965408i	$-0.416032\pi$
$827$	6.05062	+	0.958323i	0.210401	+	0.0333242i	−0.0503443	+	0.998732i	$0.516032\pi$
$828$		0			0
$829$	6.18322	+	2.00905i	0.214752	+	0.0697772i	0.414417	−	0.910087i	$-0.363985\pi$
$829$	6.18322	+	2.00905i	0.214752	+	0.0697772i	−0.199665	+	0.979864i	$0.563985\pi$
$830$		0			0
$831$	−78.3707	+	25.4642i	−2.71865	+	0.883343i
$832$		0			0
$833$	−20.0239	+	39.2991i	−0.693786	+	1.36163i
$834$		0			0
$835$	−2.19671	−	14.5862i	−0.0760202	−	0.504775i
$836$		0			0
$837$	−44.9395	+	7.11772i	−1.55334	+	0.246024i
$838$		0			0
$839$	−9.69717	+	7.04541i	−0.334783	+	0.243234i	−0.742458	−	0.669893i	$-0.766340\pi$
$839$	−9.69717	+	7.04541i	−0.334783	+	0.243234i	0.407674	+	0.913127i	$0.366340\pi$
$840$		0			0
$841$	10.3456	+	7.51655i	0.356747	+	0.259192i
$842$		0			0
$843$	−32.5756	+	32.5756i	−1.12196	+	1.12196i
$844$		0			0
$845$	8.56502	−	11.6023i	0.294646	−	0.399130i
$846$		0			0
$847$	−12.5034	+	6.37078i	−0.429620	+	0.218903i
$848$		0			0
$849$		−	5.14055i		−	0.176423i
$850$		0			0
$851$			34.6160i			1.18662i
$852$		0			0
$853$	39.4367	−	20.0940i	1.35029	−	0.688006i	0.378884	−	0.925444i	$-0.376308\pi$
$853$	39.4367	−	20.0940i	1.35029	−	0.688006i	0.971403	+	0.237438i	$0.0763078\pi$
$854$		0			0
$855$	37.9710	−	12.0192i	1.29858	−	0.411048i
$856$		0			0
$857$	12.1177	−	12.1177i	0.413934	−	0.413934i	−0.469173	−	0.883106i	$-0.655448\pi$
$857$	12.1177	−	12.1177i	0.413934	−	0.413934i	0.883106	+	0.469173i	$0.155448\pi$
$858$		0			0
$859$	−16.2646	−	11.8169i	−0.554941	−	0.403188i	0.274663	−	0.961541i	$-0.411434\pi$
$859$	−16.2646	−	11.8169i	−0.554941	−	0.403188i	−0.829604	+	0.558352i	$0.811434\pi$
$860$		0			0
$861$	−67.8664	+	49.3078i	−2.31288	+	1.68041i
$862$		0			0
$863$	−8.81063	+	1.39547i	−0.299917	+	0.0475023i	−0.304580	−	0.952487i	$-0.598516\pi$
$863$	−8.81063	+	1.39547i	−0.299917	+	0.0475023i	0.00466216	+	0.999989i	$0.498516\pi$
$864$		0			0
$865$	−19.6073	+	9.80342i	−0.666669	+	0.333326i
$866$		0			0
$867$	13.4413	−	26.3800i	0.456490	−	0.895912i
$868$		0			0
$869$	31.3892	−	10.1990i	1.06481	−	0.345976i
$870$		0			0
$871$	24.4272	+	7.93689i	0.827686	+	0.268931i
$872$		0			0
$873$	79.6679	+	12.6182i	2.69635	+	0.427060i
$874$		0			0
$875$	20.9534	−	38.9041i	0.708353	−	1.31520i
$876$		0			0
$877$	0.402784	−	2.54308i	0.0136011	−	0.0858737i	−0.979954	−	0.199223i	$-0.936158\pi$
$877$	0.402784	−	2.54308i	0.0136011	−	0.0858737i	0.993555	+	0.113350i	$0.0361580\pi$
$878$		0			0
$879$	17.2588	−	53.1170i	0.582123	−	1.79159i
$880$		0			0
$881$	10.1043	+	31.0979i	0.340423	+	1.04771i	0.963989	+	0.265944i	$0.0856835\pi$
$881$	10.1043	+	31.0979i	0.340423	+	1.04771i	−0.623565	+	0.781771i	$0.714316\pi$
$882$		0			0
$883$	−32.7812	−	16.7029i	−1.10317	−	0.562096i	−0.195049	−	0.980793i	$-0.562487\pi$
$883$	−32.7812	−	16.7029i	−1.10317	−	0.562096i	−0.908126	+	0.418698i	$0.862487\pi$
$884$		0			0
$885$	−0.856309	−	1.71266i	−0.0287845	−	0.0575704i
$886$		0			0
$887$	3.43852	+	21.7100i	0.115454	+	0.728949i	0.975707	+	0.219081i	$0.0703058\pi$
$887$	3.43852	+	21.7100i	0.115454	+	0.728949i	−0.860253	+	0.509868i	$0.829694\pi$
$888$		0			0
$889$	−6.72359	−	9.25423i	−0.225502	−	0.310377i
$890$		0			0
$891$	−37.9259	+	52.2005i	−1.27057	+	1.74878i
$892$		0			0
$893$	2.10157	+	2.10157i	0.0703263	+	0.0703263i
$894$		0			0
$895$	−9.42017	−	29.7601i	−0.314882	−	0.994770i
$896$		0			0
$897$	−36.2494	−	71.1435i	−1.21033	−	2.37541i
$898$		0			0
$899$	20.6895			0.690034
$900$		0			0
$901$	−26.6519			−0.887905
$902$		0			0
$903$	23.1448	+	45.4242i	0.770211	+	1.51162i
$904$		0			0
$905$	−22.0812	−	16.3008i	−0.734002	−	0.541856i
$906$		0			0
$907$	−37.9456	−	37.9456i	−1.25996	−	1.25996i	−0.951109	−	0.308854i	$-0.900054\pi$
$907$	−37.9456	−	37.9456i	−1.25996	−	1.25996i	−0.308854	−	0.951109i	$-0.599946\pi$
$908$		0			0
$909$	22.6523	−	31.1783i	0.751331	−	1.03412i
$910$		0			0
$911$	−33.3609	−	45.9174i	−1.10530	−	1.52131i	−0.828170	−	0.560478i	$-0.810618\pi$
$911$	−33.3609	−	45.9174i	−1.10530	−	1.52131i	−0.277127	−	0.960833i	$-0.589382\pi$
$912$		0			0
$913$	−2.78313	−	17.5720i	−0.0921081	−	0.581548i
$914$		0			0
$915$	3.68983	−	0.555697i	0.121982	−	0.0183708i
$916$		0			0
$917$	−10.2554	−	5.22539i	−0.338664	−	0.172558i
$918$		0			0
$919$	1.38497	+	4.26249i	0.0456859	+	0.140607i	0.971297	−	0.237868i	$-0.0764486\pi$
$919$	1.38497	+	4.26249i	0.0456859	+	0.140607i	−0.925612	+	0.378475i	$0.876449\pi$
$920$		0			0
$921$	14.1809	−	43.6444i	0.467278	−	1.43813i
$922$		0			0
$923$	−1.60613	+	10.1407i	−0.0528664	+	0.333785i
$924$		0			0
$925$	5.28679	−	30.3828i	0.173829	−	0.998979i
$926$		0			0
$927$	60.9063	+	9.64661i	2.00042	+	0.316836i
$928$		0			0
$929$	19.4161	+	6.30868i	0.637022	+	0.206981i	0.609683	−	0.792645i	$-0.291297\pi$
$929$	19.4161	+	6.30868i	0.637022	+	0.206981i	0.0273390	+	0.999626i	$0.491297\pi$
$930$		0			0
$931$	−19.7157	+	6.40602i	−0.646156	+	0.209949i
$932$		0			0
$933$	15.1318	−	29.6978i	0.495393	−	0.972263i
$934$		0			0
$935$	21.9115	+	22.2471i	0.716582	+	0.727558i
$936$		0			0
$937$	−48.4276	+	7.67018i	−1.58206	+	0.250574i	−0.884705	−	0.466151i	$-0.845640\pi$
$937$	−48.4276	+	7.67018i	−1.58206	+	0.250574i	−0.697356	+	0.716725i	$0.745640\pi$
$938$		0			0
$939$	42.6500	−	30.9870i	1.39183	−	1.01122i
$940$		0			0
$941$	−21.1187	−	15.3436i	−0.688450	−	0.500189i	0.187700	−	0.982226i	$-0.439897\pi$
$941$	−21.1187	−	15.3436i	−0.688450	−	0.500189i	−0.876150	+	0.482038i	$0.839897\pi$
$942$		0			0
$943$	−26.1107	+	26.1107i	−0.850280	+	0.850280i
$944$		0			0
$945$	119.189	+	39.7310i	3.87722	+	1.29245i
$946$		0			0
$947$	−35.0327	+	17.8501i	−1.13841	+	0.580049i	−0.918480	−	0.395467i	$-0.870583\pi$
$947$	−35.0327	+	17.8501i	−1.13841	+	0.580049i	−0.219930	+	0.975516i	$0.570583\pi$
$948$		0			0
$949$			46.7740i			1.51835i
$950$		0			0
$951$			107.887i			3.49846i
$952$		0			0
$953$	−28.6513	+	14.5986i	−0.928106	+	0.472894i	−0.851610	−	0.524176i	$-0.824373\pi$
$953$	−28.6513	+	14.5986i	−0.928106	+	0.472894i	−0.0764965	+	0.997070i	$0.524373\pi$
$954$		0			0
$955$	−0.162526	+	21.3821i	−0.00525921	+	0.691909i
$956$		0			0
$957$	40.2468	−	40.2468i	1.30099	−	1.30099i
$958$		0			0
$959$	10.1278	+	7.35825i	0.327042	+	0.237610i
$960$		0			0
$961$	−16.7923	+	12.2003i	−0.541688	+	0.393559i
$962$		0			0
$963$	127.446	−	20.1855i	4.10691	−	0.650470i
$964$		0			0
$965$	16.0865	+	2.67335i	0.517844	+	0.0860582i
$966$		0			0
$967$	−11.7698	+	23.0996i	−0.378492	+	0.742832i	−0.999149	−	0.0412505i	$-0.986866\pi$
$967$	−11.7698	+	23.0996i	−0.378492	+	0.742832i	0.620657	+	0.784082i	$0.286866\pi$
$968$		0			0
$969$	37.7486	−	12.2653i	1.21266	−	0.394018i
$970$		0			0
$971$	−41.7528	−	13.5663i	−1.33991	−	0.435364i	−0.450625	−	0.892714i	$-0.648799\pi$
$971$	−41.7528	−	13.5663i	−1.33991	−	0.435364i	−0.889287	+	0.457350i	$0.848799\pi$
$972$		0			0
$973$	89.1208	+	14.1154i	2.85708	+	0.452517i
$974$		0			0
$975$	20.9509	+	67.9795i	0.670966	+	2.17709i
$976$		0			0
$977$	1.09435	−	6.90944i	0.0350113	−	0.221052i	−0.963979	−	0.265978i	$-0.914305\pi$
$977$	1.09435	−	6.90944i	0.0350113	−	0.221052i	0.998990	+	0.0449257i	$0.0143051\pi$
$978$		0			0
$979$	10.3395	−	31.8218i	0.330453	−	1.01703i
$980$		0			0
$981$	−15.0128	−	46.2048i	−0.479323	−	1.47520i
$982$		0			0
$983$	2.60540	+	1.32752i	0.0830993	+	0.0423412i	0.495046	−	0.868867i	$-0.335151\pi$
$983$	2.60540	+	1.32752i	0.0830993	+	0.0423412i	−0.411947	+	0.911208i	$0.635151\pi$
$984$		0			0
$985$	6.89363	+	3.57874i	0.219649	+	0.114028i
$986$		0			0
$987$	2.46506	+	15.5638i	0.0784638	+	0.495401i
$988$		0			0
$989$	13.1905	+	18.1552i	0.419433	+	0.577300i
$990$		0			0
$991$	11.1499	−	15.3466i	0.354189	−	0.487499i	−0.594329	−	0.804222i	$-0.702582\pi$
$991$	11.1499	−	15.3466i	0.354189	−	0.487499i	0.948518	+	0.316722i	$0.102582\pi$
$992$		0			0
$993$	9.31161	+	9.31161i	0.295495	+	0.295495i
$994$		0			0
$995$	14.4285	−	10.3163i	0.457415	−	0.327049i
$996$		0			0
$997$	27.4234	+	53.8214i	0.868508	+	1.70454i	0.694112	+	0.719867i	$0.255797\pi$
$997$	27.4234	+	53.8214i	0.868508	+	1.70454i	0.174395	+	0.984676i	$0.444203\pi$
$998$		0			0
$999$	87.6835			2.77418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.bq.d.223.1	yes	64
4.3	odd	2		800.2.bq.c.223.8	✓	64
25.12	odd	20		800.2.bq.c.287.8	yes	64
100.87	even	20	inner	800.2.bq.d.287.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
800.2.bq.c.223.8	✓	64	4.3	odd	2
800.2.bq.c.287.8	yes	64	25.12	odd	20
800.2.bq.d.223.1	yes	64	1.1	even	1	trivial
800.2.bq.d.287.1	yes	64	100.87	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.bq (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46455 - 2.87435i) q^{3} +(-1.81895 + 1.30054i) q^{5} +(-2.79469 - 2.79469i) q^{7} +(-4.35362 + 5.99224i) q^{9} +(-1.60428 - 2.20810i) q^{11} +(-0.689899 - 4.35585i) q^{13} +(6.40217 + 3.32360i) q^{15} +(4.55876 + 2.32280i) q^{17} +(0.743109 + 2.28705i) q^{19} +(-3.93994 + 12.1259i) q^{21} +(-0.877961 + 5.54323i) q^{23} +(1.61719 - 4.73125i) q^{25} +(14.0412 + 2.22390i) q^{27} +(-6.14797 - 1.99760i) q^{29} +(-3.04391 + 0.989025i) q^{31} +(-3.99731 + 7.84515i) q^{33} +(8.71801 + 1.44881i) q^{35} +(6.09192 - 0.964866i) q^{37} +(-11.5098 + 8.36239i) q^{39} +(5.32289 + 3.86731i) q^{41} +(2.82738 - 2.82738i) q^{43} +(0.125886 - 16.5617i) q^{45} +(1.10121 - 0.561093i) q^{47} +8.62056i q^{49} -16.5054i q^{51} +(-4.64134 + 2.36488i) q^{53} +(5.78984 + 1.93001i) q^{55} +(5.48547 - 5.48547i) q^{57} +(-0.214752 - 0.156027i) q^{59} +(0.418495 - 0.304055i) q^{61} +(28.9134 - 4.57944i) q^{63} +(6.91985 + 7.02585i) q^{65} +(-2.64400 + 5.18915i) q^{67} +(17.2190 - 5.59479i) q^{69} +(-2.21412 - 0.719412i) q^{71} +(-10.4754 - 1.65914i) q^{73} +(-15.9677 + 2.28079i) q^{75} +(-1.68749 + 10.6544i) q^{77} +(-3.73675 + 11.5005i) q^{79} +(-7.30530 - 22.4834i) q^{81} +(5.80791 + 2.95928i) q^{83} +(-11.3131 + 1.70377i) q^{85} +(3.26225 + 20.5970i) q^{87} +(7.20569 + 9.91778i) q^{89} +(-10.2452 + 14.1013i) q^{91} +(7.30077 + 7.30077i) q^{93} +(-4.32609 - 3.19361i) q^{95} +(-4.94401 - 9.70316i) q^{97} +20.2159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{5} + 4 q^{7} + 4 q^{13} + 22 q^{15} + 8 q^{17} - 18 q^{19} - 16 q^{21} + 8 q^{23} + 40 q^{25} + 18 q^{27} - 20 q^{31} + 44 q^{33} + 38 q^{35} - 10 q^{37} - 36 q^{39} - 16 q^{41} + 32 q^{43}+ \cdots + 132 q^{99}+O(q^{100}) \) 64 * q + 2 * q^5 + 4 * q^7 + 4 * q^13 + 22 * q^15 + 8 * q^17 - 18 * q^19 - 16 * q^21 + 8 * q^23 + 40 * q^25 + 18 * q^27 - 20 * q^31 + 44 * q^33 + 38 * q^35 - 10 * q^37 - 36 * q^39 - 16 * q^41 + 32 * q^43 + 14 * q^45 + 8 * q^47 - 22 * q^53 - 24 * q^55 - 8 * q^57 - 4 * q^59 - 36 * q^61 + 18 * q^63 - 24 * q^65 - 26 * q^67 + 60 * q^69 + 70 * q^71 - 12 * q^73 + 66 * q^75 + 48 * q^77 + 16 * q^79 - 24 * q^81 - 52 * q^83 - 46 * q^85 - 144 * q^87 - 60 * q^89 - 30 * q^91 + 20 * q^93 - 8 * q^95 - 56 * q^97 + 132 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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