LMFDB - Embedded newform 552.2.q.a.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.3
Character	$\chi$	$=$	552.49
Dual form			552.2.q.a.169.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{3} +(0.531006 - 0.612813i) q^{5} +(0.0574024 - 0.0368903i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{3} +(0.531006 - 0.612813i) q^{5} +(0.0574024 - 0.0368903i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.604094 - 4.20157i) q^{11} +(-4.84866 - 3.11605i) q^{13} +(-0.336847 - 0.737592i) q^{15} +(0.227256 + 0.0667283i) q^{17} +(4.34857 - 1.27686i) q^{19} +(-0.00971076 - 0.0675398i) q^{21} +(4.39397 + 1.92172i) q^{23} +(0.618001 + 4.29829i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(1.20944 + 0.355123i) q^{29} +(-3.60253 - 7.88845i) q^{31} +(-3.57093 - 2.29490i) q^{33} +(0.00787415 - 0.0547659i) q^{35} +(-6.18949 - 7.14305i) q^{37} +(-4.84866 + 3.11605i) q^{39} +(2.67058 - 3.08202i) q^{41} +(1.20563 - 2.63996i) q^{43} -0.810868 q^{45} +6.56845 q^{47} +(-2.90597 + 6.36319i) q^{49} +(0.155104 - 0.178999i) q^{51} +(-4.88076 + 3.13667i) q^{53} +(-2.25400 - 2.60125i) q^{55} +(0.644993 - 4.48603i) q^{57} +(6.49470 + 4.17389i) q^{59} +(3.75708 + 8.22685i) q^{61} +(-0.0654704 - 0.0192238i) q^{63} +(-4.48422 + 1.31669i) q^{65} +(-1.11537 - 7.75760i) q^{67} +(3.57338 - 3.19858i) q^{69} +(1.03683 + 7.21130i) q^{71} +(-2.50603 + 0.735838i) q^{73} +(4.16659 + 1.22342i) q^{75} +(-0.120320 - 0.263465i) q^{77} +(5.66620 + 3.64145i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(6.83818 + 7.89168i) q^{83} +(0.161566 - 0.103832i) q^{85} +(0.825449 - 0.952619i) q^{87} +(6.06487 - 13.2802i) q^{89} -0.393277 q^{91} -8.67213 q^{93} +(1.52664 - 3.34288i) q^{95} +(-6.91552 + 7.98094i) q^{97} +(-3.57093 + 2.29490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	$ 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{8}{11}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$3$	0.415415	−	0.909632i	0.239840	−	0.525176i
$4$		0			0
$5$	0.531006	−	0.612813i	0.237473	−	0.274058i	−0.624486	−	0.781036i	$-0.714692\pi$
$5$	0.531006	−	0.612813i	0.237473	−	0.274058i	0.861960	+	0.506977i	$0.169237\pi$
$6$		0			0
$7$	0.0574024	−	0.0368903i	0.0216961	−	0.0139432i	−0.529748	−	0.848155i	$-0.677713\pi$
$7$	0.0574024	−	0.0368903i	0.0216961	−	0.0139432i	0.551444	+	0.834212i	$0.314077\pi$
$8$		0			0
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$		0			0
$11$	0.604094	−	4.20157i	0.182141	−	1.26682i	−0.669546	−	0.742770i	$-0.733511\pi$
$11$	0.604094	−	4.20157i	0.182141	−	1.26682i	0.851688	−	0.524050i	$-0.175579\pi$
$12$		0			0
$13$	−4.84866	−	3.11605i	−1.34478	−	0.864236i	−0.347479	−	0.937688i	$-0.612962\pi$
$13$	−4.84866	−	3.11605i	−1.34478	−	0.864236i	−0.997299	+	0.0734520i	$0.976598\pi$
$14$		0			0
$15$	−0.336847	−	0.737592i	−0.0869735	−	0.190445i
$16$		0			0
$17$	0.227256	+	0.0667283i	0.0551176	+	0.0161840i	0.309175	−	0.951005i	$-0.399947\pi$
$17$	0.227256	+	0.0667283i	0.0551176	+	0.0161840i	−0.254058	+	0.967189i	$0.581765\pi$
$18$		0			0
$19$	4.34857	−	1.27686i	0.997631	−	0.292931i	0.258147	−	0.966106i	$-0.416888\pi$
$19$	4.34857	−	1.27686i	0.997631	−	0.292931i	0.739484	+	0.673175i	$0.235070\pi$
$20$		0			0
$21$	−0.00971076	−	0.0675398i	−0.00211906	−	0.0147384i
$22$		0			0
$23$	4.39397	+	1.92172i	0.916206	+	0.400707i
$23$	4.39397	+	1.92172i	0.916206	+	0.400707i
$24$		0			0
$25$	0.618001	+	4.29829i	0.123600	+	0.859658i
$26$		0			0
$27$	−0.959493	+	0.281733i	−0.184655	+	0.0542195i
$28$		0			0
$29$	1.20944	+	0.355123i	0.224587	+	0.0659446i	0.392090	−	0.919927i	$-0.371752\pi$
$29$	1.20944	+	0.355123i	0.224587	+	0.0659446i	−0.167503	+	0.985872i	$0.553570\pi$
$30$		0			0
$31$	−3.60253	−	7.88845i	−0.647034	−	1.41681i	−0.894126	−	0.447815i	$-0.852202\pi$
$31$	−3.60253	−	7.88845i	−0.647034	−	1.41681i	0.247092	−	0.968992i	$-0.420525\pi$
$32$		0			0
$33$	−3.57093	−	2.29490i	−0.621619	−	0.399490i
$34$		0			0
$35$	0.00787415	−	0.0547659i	0.00133097	−	0.00925712i
$36$		0			0
$37$	−6.18949	−	7.14305i	−1.01755	−	1.17431i	−0.984594	−	0.174853i	$-0.944055\pi$
$37$	−6.18949	−	7.14305i	−1.01755	−	1.17431i	−0.0329513	−	0.999457i	$-0.510491\pi$
$38$		0			0
$39$	−4.84866	+	3.11605i	−0.776408	+	0.498967i
$40$		0			0
$41$	2.67058	−	3.08202i	0.417075	−	0.481330i	−0.507868	−	0.861435i	$-0.669566\pi$
$41$	2.67058	−	3.08202i	0.417075	−	0.481330i	0.924944	+	0.380104i	$0.124112\pi$
$42$		0			0
$43$	1.20563	−	2.63996i	0.183857	−	0.402590i	−0.795151	−	0.606411i	$-0.792609\pi$
$43$	1.20563	−	2.63996i	0.183857	−	0.402590i	0.979008	+	0.203821i	$0.0653360\pi$
$44$		0			0
$45$	−0.810868			−0.120877
$46$		0			0
$47$	6.56845			0.958108			0.479054	−	0.877786i	$-0.340980\pi$
$47$	6.56845			0.958108			0.479054	+	0.877786i	$0.340980\pi$
$48$		0			0
$49$	−2.90597	+	6.36319i	−0.415139	+	0.909027i
$50$		0			0
$51$	0.155104	−	0.178999i	0.0217189	−	0.0250649i
$52$		0			0
$53$	−4.88076	+	3.13667i	−0.670424	+	0.430855i	−0.831078	−	0.556155i	$-0.812276\pi$
$53$	−4.88076	+	3.13667i	−0.670424	+	0.430855i	0.160654	+	0.987011i	$0.448640\pi$
$54$		0			0
$55$	−2.25400	−	2.60125i	−0.303929	−	0.350753i
$56$		0			0
$57$	0.644993	−	4.48603i	0.0854314	−	0.594189i
$58$		0			0
$59$	6.49470	+	4.17389i	0.845538	+	0.543394i	0.890180	−	0.455609i	$-0.150578\pi$
$59$	6.49470	+	4.17389i	0.845538	+	0.543394i	−0.0446419	+	0.999003i	$0.514215\pi$
$60$		0			0
$61$	3.75708	+	8.22685i	0.481045	+	1.05334i	0.982175	+	0.187969i	$0.0601904\pi$
$61$	3.75708	+	8.22685i	0.481045	+	1.05334i	−0.501130	+	0.865372i	$0.667082\pi$
$62$		0			0
$63$	−0.0654704	−	0.0192238i	−0.00824849	−	0.00242197i
$64$		0			0
$65$	−4.48422	+	1.31669i	−0.556200	+	0.163315i
$66$		0			0
$67$	−1.11537	−	7.75760i	−0.136265	−	0.947742i	−0.937151	−	0.348925i	$-0.886547\pi$
$67$	−1.11537	−	7.75760i	−0.136265	−	0.947742i	0.800886	−	0.598817i	$-0.204362\pi$
$68$		0			0
$69$	3.57338	−	3.19858i	0.430185	−	0.385064i
$70$		0			0
$71$	1.03683	+	7.21130i	0.123049	+	0.855823i	0.954070	+	0.299583i	$0.0968475\pi$
$71$	1.03683	+	7.21130i	0.123049	+	0.855823i	−0.831021	+	0.556240i	$0.812243\pi$
$72$		0			0
$73$	−2.50603	+	0.735838i	−0.293309	+	0.0861233i	−0.425077	−	0.905157i	$-0.639753\pi$
$73$	−2.50603	+	0.735838i	−0.293309	+	0.0861233i	0.131768	+	0.991281i	$0.457935\pi$
$74$		0			0
$75$	4.16659	+	1.22342i	0.481116	+	0.141269i
$76$		0			0
$77$	−0.120320	−	0.263465i	−0.0137118	−	0.0300246i
$78$		0			0
$79$	5.66620	+	3.64145i	0.637497	+	0.409695i	0.819079	−	0.573681i	$-0.194485\pi$
$79$	5.66620	+	3.64145i	0.637497	+	0.409695i	−0.181581	+	0.983376i	$0.558122\pi$
$80$		0			0
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$		0			0
$83$	6.83818	+	7.89168i	0.750588	+	0.866224i	0.994625	−	0.103541i	$-0.0330174\pi$
$83$	6.83818	+	7.89168i	0.750588	+	0.866224i	−0.244037	+	0.969766i	$0.578472\pi$
$84$		0			0
$85$	0.161566	−	0.103832i	0.0175243	−	0.0112622i
$86$		0			0
$87$	0.825449	−	0.952619i	0.0884975	−	0.102132i
$88$		0			0
$89$	6.06487	−	13.2802i	0.642875	−	1.40770i	−0.254779	−	0.966999i	$-0.582003\pi$
$89$	6.06487	−	13.2802i	0.642875	−	1.40770i	0.897654	−	0.440701i	$-0.145270\pi$
$90$		0			0
$91$	−0.393277			−0.0412266
$92$		0			0
$93$	−8.67213			−0.899258
$94$		0			0
$95$	1.52664	−	3.34288i	0.156630	−	0.342972i
$96$		0			0
$97$	−6.91552	+	7.98094i	−0.702165	+	0.810341i	−0.989043	−	0.147626i	$-0.952837\pi$
$97$	−6.91552	+	7.98094i	−0.702165	+	0.810341i	0.286879	+	0.957967i	$0.407382\pi$
$98$		0			0
$99$	−3.57093	+	2.29490i	−0.358892	+	0.230646i
$100$		0			0
$101$	2.77244	+	3.19957i	0.275868	+	0.318369i	0.876729	−	0.480985i	$-0.159721\pi$
$101$	2.77244	+	3.19957i	0.275868	+	0.318369i	−0.600861	+	0.799354i	$0.705175\pi$
$102$		0			0
$103$	−1.17108	+	8.14502i	−0.115390	+	0.802553i	0.847139	+	0.531372i	$0.178323\pi$
$103$	−1.17108	+	8.14502i	−0.115390	+	0.802553i	−0.962528	+	0.271181i	$0.912586\pi$
$104$		0			0
$105$	−0.0465458	−	0.0299131i	−0.00454240	−	0.00291922i
$106$		0			0
$107$	3.32096	+	7.27188i	0.321049	+	0.702999i	0.999499	−	0.0316473i	$-0.0100753\pi$
$107$	3.32096	+	7.27188i	0.321049	+	0.702999i	−0.678450	+	0.734646i	$0.737348\pi$
$108$		0			0
$109$	−5.43564	−	1.59605i	−0.520640	−	0.152874i	0.0108453	−	0.999941i	$-0.496548\pi$
$109$	−5.43564	−	1.59605i	−0.520640	−	0.152874i	−0.531485	+	0.847067i	$0.678366\pi$
$110$		0			0
$111$	−9.06875	+	2.66283i	−0.860768	+	0.252744i
$112$		0			0
$113$	2.37570	+	16.5234i	0.223487	+	1.55439i	0.724701	+	0.689064i	$0.241978\pi$
$113$	2.37570	+	16.5234i	0.223487	+	1.55439i	−0.501213	+	0.865324i	$0.667113\pi$
$114$		0			0
$115$	3.51088	−	1.67224i	0.327391	−	0.155937i
$116$		0			0
$117$	0.820248	+	5.70495i	0.0758320	+	0.527423i
$118$		0			0
$119$	0.0155066	−	0.00455316i	0.00142149	−	0.000417388i
$120$		0			0
$121$	−6.73382	−	1.97723i	−0.612165	−	0.179748i
$122$		0			0
$123$	−1.69410	−	3.70957i	−0.152752	−	0.334480i
$124$		0			0
$125$	6.37294	+	4.09564i	0.570013	+	0.366325i
$126$		0			0
$127$	−1.43794	+	10.0011i	−0.127596	+	0.887452i	0.820992	+	0.570940i	$0.193421\pi$
$127$	−1.43794	+	10.0011i	−0.127596	+	0.887452i	−0.948588	+	0.316512i	$0.897488\pi$
$128$		0			0
$129$	−1.90056	−	2.19336i	−0.167335	−	0.193114i
$130$		0			0
$131$	5.38364	−	3.45986i	0.470371	−	0.302289i	−0.283898	−	0.958854i	$-0.591628\pi$
$131$	5.38364	−	3.45986i	0.470371	−	0.302289i	0.754269	+	0.656565i	$0.227991\pi$
$132$		0			0
$133$	0.202515	−	0.233715i	0.0175603	−	0.0202656i
$134$		0			0
$135$	−0.336847	+	0.737592i	−0.0289912	+	0.0634818i
$136$		0			0
$137$	18.5207			1.58233			0.791165	−	0.611603i	$-0.209475\pi$
$137$	18.5207			1.58233			0.791165	+	0.611603i	$0.209475\pi$
$138$		0			0
$139$	16.8196			1.42662			0.713310	−	0.700849i	$-0.247195\pi$
$139$	16.8196			1.42662			0.713310	+	0.700849i	$0.247195\pi$
$140$		0			0
$141$	2.72863	−	5.97488i	0.229792	−	0.503175i
$142$		0			0
$143$	−16.0213	+	18.4896i	−1.33977	+	1.54618i
$144$		0			0
$145$	0.859842	−	0.552587i	0.0714060	−	0.0458899i
$146$		0			0
$147$	4.58098	+	5.28673i	0.377833	+	0.436042i
$148$		0			0
$149$	−0.793048	+	5.51577i	−0.0649691	+	0.451870i	0.931206	+	0.364493i	$0.118758\pi$
$149$	−0.793048	+	5.51577i	−0.0649691	+	0.451870i	−0.996175	+	0.0873771i	$0.972152\pi$
$150$		0			0
$151$	−17.7556	−	11.4108i	−1.44493	−	0.928601i	−0.999445	−	0.0333130i	$-0.989394\pi$
$151$	−17.7556	−	11.4108i	−1.44493	−	0.928601i	−0.445487	−	0.895288i	$-0.646969\pi$
$152$		0			0
$153$	−0.0983910	−	0.215446i	−0.00795444	−	0.0174178i
$154$		0			0
$155$	−6.74711	−	1.98113i	−0.541941	−	0.159128i
$156$		0			0
$157$	3.58552	−	1.05280i	0.286156	−	0.0840229i	−0.135505	−	0.990777i	$-0.543266\pi$
$157$	3.58552	−	1.05280i	0.286156	−	0.0840229i	0.421660	+	0.906754i	$0.361447\pi$
$158$		0			0
$159$	0.825678	+	5.74272i	0.0654805	+	0.455427i
$160$		0			0
$161$	0.323117	−	0.0517832i	0.0254652	−	0.00408109i
$162$		0			0
$163$	−2.32343	−	16.1598i	−0.181985	−	1.26573i	−0.852061	−	0.523442i	$-0.824648\pi$
$163$	−2.32343	−	16.1598i	−0.181985	−	1.26573i	0.670076	−	0.742292i	$-0.266261\pi$
$164$		0			0
$165$	−3.30253	+	0.969710i	−0.257102	+	0.0754918i
$166$		0			0
$167$	−16.2271	−	4.76471i	−1.25569	−	0.368705i	−0.414803	−	0.909911i	$-0.636149\pi$
$167$	−16.2271	−	4.76471i	−1.25569	−	0.368705i	−0.840889	+	0.541207i	$0.817968\pi$
$168$		0			0
$169$	8.39940	+	18.3921i	0.646107	+	1.41478i
$170$		0			0
$171$	−3.81269	−	2.45027i	−0.291564	−	0.187377i
$172$		0			0
$173$	1.46839	−	10.2129i	0.111640	−	0.776472i	−0.854685	−	0.519147i	$-0.826250\pi$
$173$	1.46839	−	10.2129i	0.111640	−	0.776472i	0.966325	−	0.257325i	$-0.0828411\pi$
$174$		0			0
$175$	0.194040	+	0.223934i	0.0146680	+	0.0169278i
$176$		0			0
$177$	6.49470	−	4.17389i	0.488172	−	0.313729i
$178$		0			0
$179$	7.23756	−	8.35259i	0.540960	−	0.624302i	−0.417792	−	0.908543i	$-0.637196\pi$
$179$	7.23756	−	8.35259i	0.540960	−	0.624302i	0.958753	+	0.284241i	$0.0917415\pi$
$180$		0			0
$181$	−6.78299	+	14.8527i	−0.504176	+	1.10399i	0.470914	+	0.882179i	$0.343924\pi$
$181$	−6.78299	+	14.8527i	−0.504176	+	1.10399i	−0.975090	+	0.221812i	$0.928803\pi$
$182$		0			0
$183$	9.04416			0.668563
$184$		0			0
$185$	−7.66401			−0.563469
$186$		0			0
$187$	0.417647	−	0.914520i	0.0305414	−	0.0668763i
$188$		0			0
$189$	−0.0446840	+	0.0515681i	−0.00325028	+	0.00375102i
$190$		0			0
$191$	−15.7832	+	10.1432i	−1.14203	+	0.733937i	−0.968036	−	0.250810i	$-0.919303\pi$
$191$	−15.7832	+	10.1432i	−1.14203	+	0.733937i	−0.173993	+	0.984747i	$0.555667\pi$
$192$		0			0
$193$	10.7066	+	12.3561i	0.770681	+	0.889413i	0.996400	−	0.0847791i	$-0.0270184\pi$
$193$	10.7066	+	12.3561i	0.770681	+	0.889413i	−0.225719	+	0.974193i	$0.572473\pi$
$194$		0			0
$195$	−0.665113	+	4.62597i	−0.0476298	+	0.331272i
$196$		0			0
$197$	−0.451689	−	0.290283i	−0.0321815	−	0.0206818i	0.524451	−	0.851441i	$-0.324271\pi$
$197$	−0.451689	−	0.290283i	−0.0321815	−	0.0206818i	−0.556633	+	0.830759i	$0.687907\pi$
$198$		0			0
$199$	0.222341	+	0.486859i	0.0157613	+	0.0345125i	0.917349	−	0.398084i	$-0.130325\pi$
$199$	0.222341	+	0.486859i	0.0157613	+	0.0345125i	−0.901588	+	0.432597i	$0.857597\pi$
$200$		0			0
$201$	−7.51990	−	2.20804i	−0.530413	−	0.155743i
$202$		0			0
$203$	0.0825251	−	0.0242316i	0.00579213	−	0.00170072i
$204$		0			0
$205$	−0.470606	−	3.27314i	−0.0328686	−	0.228606i
$206$		0			0
$207$	−1.42510	−	4.57920i	−0.0990511	−	0.318277i
$208$		0			0
$209$	−2.73785	−	19.0422i	−0.189381	−	1.31717i
$210$		0			0
$211$	2.04685	−	0.601010i	0.140911	−	0.0413752i	−0.210516	−	0.977590i	$-0.567515\pi$
$211$	2.04685	−	0.601010i	0.140911	−	0.0413752i	0.351428	+	0.936215i	$0.385696\pi$
$212$		0			0
$213$	6.99034	+	2.05255i	0.478970	+	0.140638i
$214$		0			0
$215$	−0.977607	−	2.14066i	−0.0666722	−	0.145992i
$216$		0			0
$217$	−0.497801	−	0.319917i	−0.0337929	−	0.0217174i
$218$		0			0
$219$	−0.371702	+	2.58525i	−0.0251173	+	0.174695i
$220$		0			0
$221$	−0.893958	−	1.03168i	−0.0601341	−	0.0693985i
$222$		0			0
$223$	−6.84271	+	4.39754i	−0.458222	+	0.294481i	−0.749315	−	0.662213i	$-0.769617\pi$
$223$	−6.84271	+	4.39754i	−0.458222	+	0.294481i	0.291094	+	0.956695i	$0.405981\pi$
$224$		0			0
$225$	2.84373	−	3.28184i	0.189582	−	0.218789i
$226$		0			0
$227$	−4.06694	+	8.90536i	−0.269932	+	0.591070i	−0.995251	−	0.0973440i	$-0.968965\pi$
$227$	−4.06694	+	8.90536i	−0.269932	+	0.591070i	0.725318	+	0.688414i	$0.241693\pi$
$228$		0			0
$229$	16.2817			1.07592			0.537962	−	0.842969i	$-0.319194\pi$
$229$	16.2817			1.07592			0.537962	+	0.842969i	$0.319194\pi$
$230$		0			0
$231$	−0.289639			−0.0190569
$232$		0			0
$233$	7.62935	−	16.7060i	0.499816	−	1.09444i	−0.476714	−	0.879059i	$-0.658172\pi$
$233$	7.62935	−	16.7060i	0.499816	−	1.09444i	0.976529	−	0.215385i	$-0.0691006\pi$
$234$		0			0
$235$	3.48789	−	4.02524i	0.227525	−	0.262578i
$236$		0			0
$237$	5.66620	−	3.64145i	0.368059	−	0.236537i
$238$		0			0
$239$	−10.2291	−	11.8050i	−0.661665	−	0.763602i	0.321383	−	0.946949i	$-0.395852\pi$
$239$	−10.2291	−	11.8050i	−0.661665	−	0.763602i	−0.983048	+	0.183347i	$0.941307\pi$
$240$		0			0
$241$	0.806286	−	5.60784i	0.0519375	−	0.361233i	−0.947234	−	0.320542i	$-0.896135\pi$
$241$	0.806286	−	5.60784i	0.0519375	−	0.361233i	0.999172	−	0.0406911i	$-0.0129559\pi$
$242$		0			0
$243$	0.841254	+	0.540641i	0.0539664	+	0.0346821i
$244$		0			0
$245$	2.35636	+	5.15971i	0.150542	+	0.329642i
$246$		0			0
$247$	−25.0635	−	7.35931i	−1.59475	−	0.468262i
$248$		0			0
$249$	10.0192	−	2.94190i	0.634941	−	0.186436i
$250$		0			0
$251$	−1.61324	−	11.2203i	−0.101827	−	0.708220i	−0.975225	−	0.221214i	$-0.928998\pi$
$251$	−1.61324	−	11.2203i	−0.101827	−	0.708220i	0.873399	−	0.487006i	$-0.161911\pi$
$252$		0			0
$253$	10.7286	−	17.3007i	0.674503	−	1.08768i
$254$		0			0
$255$	−0.0273321	−	0.190099i	−0.00171161	−	0.0119045i
$256$		0			0
$257$	−14.4757	+	4.25045i	−0.902970	+	0.265136i	−0.700079	−	0.714066i	$-0.746852\pi$
$257$	−14.4757	+	4.25045i	−0.902970	+	0.265136i	−0.202891	+	0.979201i	$0.565034\pi$
$258$		0			0
$259$	−0.618800	−	0.181696i	−0.0384504	−	0.0112901i
$260$		0			0
$261$	−0.523629	−	1.14659i	−0.0324118	−	0.0709720i
$262$		0			0
$263$	4.73729	+	3.04447i	0.292114	+	0.187730i	0.678487	−	0.734612i	$-0.262636\pi$
$263$	4.73729	+	3.04447i	0.292114	+	0.187730i	−0.386373	+	0.922343i	$0.626272\pi$
$264$		0			0
$265$	−0.669516	+	4.65659i	−0.0411281	+	0.286052i
$266$		0			0
$267$	−9.56067	−	11.0336i	−0.585103	−	0.675245i
$268$		0			0
$269$	21.9979	−	14.1372i	1.34124	−	0.861960i	0.344200	−	0.938896i	$-0.388150\pi$
$269$	21.9979	−	14.1372i	1.34124	−	0.861960i	0.997036	+	0.0769366i	$0.0245139\pi$
$270$		0			0
$271$	13.1559	−	15.1827i	0.799164	−	0.922285i	−0.199171	−	0.979965i	$-0.563825\pi$
$271$	13.1559	−	15.1827i	0.799164	−	0.922285i	0.998335	+	0.0576802i	$0.0183704\pi$
$272$		0			0
$273$	−0.163373	+	0.357737i	−0.00988778	+	0.0216512i
$274$		0			0
$275$	18.4329			1.11155
$276$		0			0
$277$	8.13559			0.488820			0.244410	−	0.969672i	$-0.421406\pi$
$277$	8.13559			0.488820			0.244410	+	0.969672i	$0.421406\pi$
$278$		0			0
$279$	−3.60253	+	7.88845i	−0.215678	+	0.472269i
$280$		0			0
$281$	−0.363722	+	0.419758i	−0.0216979	+	0.0250407i	−0.766495	−	0.642251i	$-0.778001\pi$
$281$	−0.363722	+	0.419758i	−0.0216979	+	0.0250407i	0.744797	+	0.667291i	$0.232546\pi$
$282$		0			0
$283$	−5.82661	+	3.74453i	−0.346356	+	0.222589i	−0.702239	−	0.711941i	$-0.747816\pi$
$283$	−5.82661	+	3.74453i	−0.346356	+	0.222589i	0.355884	+	0.934530i	$0.384180\pi$
$284$		0			0
$285$	−2.40660	−	2.77737i	−0.142555	−	0.164517i
$286$		0			0
$287$	0.0396014	−	0.275434i	0.00233760	−	0.0162583i
$288$		0			0
$289$	−14.2541	−	9.16057i	−0.838478	−	0.538857i
$290$		0			0
$291$	4.38690	+	9.60598i	0.257165	+	0.563113i
$292$		0			0
$293$	−21.8013	−	6.40144i	−1.27365	−	0.373976i	−0.426089	−	0.904681i	$-0.640109\pi$
$293$	−21.8013	−	6.40144i	−1.27365	−	0.373976i	−0.847557	+	0.530705i	$0.821927\pi$
$294$		0			0
$295$	6.00654	−	1.76368i	0.349714	−	0.102685i
$296$		0			0
$297$	0.604094	+	4.20157i	0.0350531	+	0.243800i
$298$		0			0
$299$	−15.3167	−	23.0096i	−0.885788	−	1.33068i
$300$		0			0
$301$	−0.0281828	−	0.196016i	−0.00162443	−	0.0112982i
$302$		0			0
$303$	4.06214	−	1.19275i	0.233364	−	0.0685218i
$304$		0			0
$305$	7.03656	+	2.06612i	0.402912	+	0.118306i
$306$		0			0
$307$	−5.00314	−	10.9553i	−0.285544	−	0.625254i	0.711450	−	0.702737i	$-0.248039\pi$
$307$	−5.00314	−	10.9553i	−0.285544	−	0.625254i	−0.996994	+	0.0774829i	$0.975312\pi$
$308$		0			0
$309$	6.92249	+	4.44881i	0.393807	+	0.253084i
$310$		0			0
$311$	−0.403531	+	2.80662i	−0.0228821	+	0.159149i	−0.998059	−	0.0622798i	$-0.980163\pi$
$311$	−0.403531	+	2.80662i	−0.0228821	+	0.159149i	0.975177	+	0.221429i	$0.0710720\pi$
$312$		0			0
$313$	10.4287	+	12.0354i	0.589467	+	0.680281i	0.969613	−	0.244646i	$-0.0786717\pi$
$313$	10.4287	+	12.0354i	0.589467	+	0.680281i	−0.380146	+	0.924927i	$0.624126\pi$
$314$		0			0
$315$	−0.0465458	+	0.0299131i	−0.00262256	+	0.00168541i
$316$		0			0
$317$	1.39640	−	1.61153i	0.0784297	−	0.0905127i	−0.715178	−	0.698942i	$-0.753655\pi$
$317$	1.39640	−	1.61153i	0.0784297	−	0.0905127i	0.793608	+	0.608429i	$0.208200\pi$
$318$		0			0
$319$	2.22269	−	4.86700i	0.124447	−	0.272500i
$320$		0			0
$321$	7.99431			0.446199
$322$		0			0
$323$	1.07344			0.0597278
$324$		0			0
$325$	10.3972	−	22.7667i	0.576733	−	1.26287i
$326$		0			0
$327$	−3.70986	+	4.28141i	−0.205156	+	0.236763i
$328$		0			0
$329$	0.377045	−	0.242312i	0.0207872	−	0.0133591i
$330$		0			0
$331$	8.24263	+	9.51250i	0.453056	+	0.522854i	0.935621	−	0.353006i	$-0.114840\pi$
$331$	8.24263	+	9.51250i	0.453056	+	0.522854i	−0.482565	+	0.875860i	$0.660295\pi$
$332$		0			0
$333$	−1.34510	+	9.35541i	−0.0737113	+	0.512673i
$334$		0			0
$335$	−5.34623	−	3.43581i	−0.292096	−	0.187719i
$336$		0			0
$337$	−4.19558	−	9.18704i	−0.228548	−	0.500450i	0.760265	−	0.649613i	$-0.225069\pi$
$337$	−4.19558	−	9.18704i	−0.228548	−	0.500450i	−0.988813	+	0.149163i	$0.952342\pi$
$338$		0			0
$339$	16.0171	+	4.70304i	0.869929	+	0.255434i
$340$		0			0
$341$	−35.3201	+	10.3709i	−1.91269	+	0.561617i
$342$		0			0
$343$	0.135905	+	0.945243i	0.00733820	+	0.0510383i
$344$		0			0
$345$	−0.0626474	−	3.88828i	−0.00337282	−	0.209338i
$346$		0			0
$347$	1.21585	+	8.45639i	0.0652700	+	0.453963i	0.996080	+	0.0884590i	$0.0281942\pi$
$347$	1.21585	+	8.45639i	0.0652700	+	0.453963i	−0.930810	+	0.365504i	$0.880897\pi$
$348$		0			0
$349$	11.0563	−	3.24643i	0.591831	−	0.173777i	0.0279163	−	0.999610i	$-0.491113\pi$
$349$	11.0563	−	3.24643i	0.591831	−	0.173777i	0.563915	+	0.825833i	$0.309295\pi$
$350$		0			0
$351$	5.53015	+	1.62380i	0.295178	+	0.0866720i
$352$		0			0
$353$	−13.3189	−	29.1642i	−0.708891	−	1.55226i	−0.828847	−	0.559476i	$-0.811002\pi$
$353$	−13.3189	−	29.1642i	−0.708891	−	1.55226i	0.119955	−	0.992779i	$-0.461725\pi$
$354$		0			0
$355$	4.96974	+	3.19386i	0.263766	+	0.169512i
$356$		0			0
$357$	0.00229999	−	0.0159968i	0.000121728	−	0.000846640i
$358$		0			0
$359$	−23.2211	−	26.7986i	−1.22556	−	1.41438i	−0.879320	−	0.476231i	$-0.842003\pi$
$359$	−23.2211	−	26.7986i	−1.22556	−	1.41438i	−0.346243	−	0.938145i	$-0.612543\pi$
$360$		0			0
$361$	1.29591	−	0.832829i	0.0682057	−	0.0438331i
$362$		0			0
$363$	−4.59588	+	5.30393i	−0.241221	+	0.278384i
$364$		0			0
$365$	−0.879788	+	1.92647i	−0.0460502	+	0.100836i
$366$		0			0
$367$	16.2132			0.846321			0.423160	−	0.906055i	$-0.360921\pi$
$367$	16.2132			0.846321			0.423160	+	0.906055i	$0.360921\pi$
$368$		0			0
$369$	−4.07810			−0.212297
$370$		0			0
$371$	−0.164454	+	0.360105i	−0.00853805	+	0.0186957i
$372$		0			0
$373$	−6.50919	+	7.51201i	−0.337033	+	0.388957i	−0.898815	−	0.438328i	$-0.855571\pi$
$373$	−6.50919	+	7.51201i	−0.337033	+	0.388957i	0.561782	+	0.827286i	$0.310116\pi$
$374$		0			0
$375$	6.37294	−	4.09564i	0.329097	−	0.211498i
$376$		0			0
$377$	−4.75757	−	5.49053i	−0.245028	−	0.282777i
$378$		0			0
$379$	1.56527	−	10.8867i	0.0804024	−	0.559211i	−0.909308	−	0.416124i	$-0.863388\pi$
$379$	1.56527	−	10.8867i	0.0804024	−	0.559211i	0.989710	−	0.143087i	$-0.0457027\pi$
$380$		0			0
$381$	8.49996	+	5.46259i	0.435466	+	0.279857i
$382$		0			0
$383$	8.58725	+	18.8034i	0.438788	+	0.960811i	0.991819	+	0.127651i	$0.0407437\pi$
$383$	8.58725	+	18.8034i	0.438788	+	0.960811i	−0.553031	+	0.833160i	$0.686529\pi$
$384$		0			0
$385$	−0.225346	−	0.0661675i	−0.0114847	−	0.00337221i
$386$		0			0
$387$	−2.78467	+	0.817652i	−0.141553	+	0.0415636i
$388$		0			0
$389$	3.22743	+	22.4473i	0.163637	+	1.13812i	0.891705	+	0.452618i	$0.149510\pi$
$389$	3.22743	+	22.4473i	0.163637	+	1.13812i	−0.728067	+	0.685506i	$0.759581\pi$
$390$		0			0
$391$	0.870322	+	0.729925i	0.0440141	+	0.0369139i
$392$		0			0
$393$	−0.910751	−	6.33441i	−0.0459413	−	0.319529i
$394$		0			0
$395$	5.24031	−	1.53869i	0.263669	−	0.0774201i
$396$		0			0
$397$	−6.10952	−	1.79392i	−0.306628	−	0.0900342i	0.124799	−	0.992182i	$-0.460172\pi$
$397$	−6.10952	−	1.79392i	−0.306628	−	0.0900342i	−0.431427	+	0.902148i	$0.641990\pi$
$398$		0			0
$399$	−0.128467	−	0.281302i	−0.00643137	−	0.0140827i
$400$		0			0
$401$	−25.8845	−	16.6349i	−1.29261	−	0.830709i	−0.300222	−	0.953869i	$-0.597061\pi$
$401$	−25.8845	−	16.6349i	−1.29261	−	0.830709i	−0.992387	+	0.123160i	$0.960697\pi$
$402$		0			0
$403$	−7.11330	+	49.4741i	−0.354339	+	2.46448i
$404$		0			0
$405$	0.531006	+	0.612813i	0.0263859	+	0.0304509i
$406$		0			0
$407$	−33.7510	+	21.6905i	−1.67298	+	1.07516i
$408$		0			0
$409$	24.7471	−	28.5597i	1.22367	−	1.41219i	0.342410	−	0.939551i	$-0.388757\pi$
$409$	24.7471	−	28.5597i	1.22367	−	1.41219i	0.881257	−	0.472637i	$-0.156698\pi$
$410$		0			0
$411$	7.69378	−	16.8470i	0.379506	−	0.831002i
$412$		0			0
$413$	0.526787			0.0259215
$414$		0			0
$415$	8.46724			0.415640
$416$		0			0
$417$	6.98711	−	15.2996i	0.342160	−	0.749227i
$418$		0			0
$419$	−0.205553	+	0.237221i	−0.0100419	+	0.0115890i	−0.760748	−	0.649047i	$-0.775168\pi$
$419$	−0.205553	+	0.237221i	−0.0100419	+	0.0115890i	0.750706	+	0.660636i	$0.229713\pi$
$420$		0			0
$421$	−21.5836	+	13.8709i	−1.05192	+	0.676028i	−0.947907	−	0.318548i	$-0.896805\pi$
$421$	−21.5836	+	13.8709i	−1.05192	+	0.676028i	−0.104013	+	0.994576i	$0.533168\pi$
$422$		0			0
$423$	−4.30142	−	4.96411i	−0.209142	−	0.241363i
$424$		0			0
$425$	−0.146373	+	1.01805i	−0.00710016	+	0.0493827i
$426$		0			0
$427$	0.519156	+	0.333641i	0.0251237	+	0.0161460i
$428$		0			0
$429$	10.1632	+	22.2544i	0.490685	+	1.07445i
$430$		0			0
$431$	8.96748	+	2.63309i	0.431948	+	0.126831i	0.490477	−	0.871454i	$-0.336823\pi$
$431$	8.96748	+	2.63309i	0.431948	+	0.126831i	−0.0585284	+	0.998286i	$0.518641\pi$
$432$		0			0
$433$	−19.4573	+	5.71318i	−0.935059	+	0.274558i	−0.713553	−	0.700601i	$-0.752915\pi$
$433$	−19.4573	+	5.71318i	−0.935059	+	0.274558i	−0.221505	+	0.975159i	$0.571097\pi$
$434$		0			0
$435$	−0.145459	−	1.01169i	−0.00697425	−	0.0485070i
$436$		0			0
$437$	21.5613	+	2.74629i	1.03142	+	0.131373i
$438$		0			0
$439$	4.49160	+	31.2397i	0.214372	+	1.49099i	0.758326	+	0.651876i	$0.226018\pi$
$439$	4.49160	+	31.2397i	0.214372	+	1.49099i	−0.543954	+	0.839115i	$0.683073\pi$
$440$		0			0
$441$	6.71198	−	1.97082i	0.319618	−	0.0938484i
$442$		0			0
$443$	−30.0487	−	8.82308i	−1.42765	−	0.419197i	−0.525568	−	0.850752i	$-0.676147\pi$
$443$	−30.0487	−	8.82308i	−1.42765	−	0.419197i	−0.902087	+	0.431555i	$0.857965\pi$
$444$		0			0
$445$	−4.91781	−	10.7685i	−0.233127	−	0.510476i
$446$		0			0
$447$	4.68788	+	3.01272i	0.221729	+	0.142497i
$448$		0			0
$449$	−5.66105	+	39.3735i	−0.267162	+	1.85815i	0.207837	+	0.978163i	$0.433358\pi$
$449$	−5.66105	+	39.3735i	−0.267162	+	1.85815i	−0.474999	+	0.879986i	$0.657552\pi$
$450$		0			0
$451$	−11.3360	−	13.0825i	−0.533793	−	0.616029i
$452$		0			0
$453$	−17.7556	+	11.4108i	−0.834232	+	0.536128i
$454$		0			0
$455$	−0.208832	+	0.241005i	−0.00979020	+	0.0112985i
$456$		0			0
$457$	−12.9981	+	28.4618i	−0.608025	+	1.33139i	0.315892	+	0.948795i	$0.397696\pi$
$457$	−12.9981	+	28.4618i	−0.608025	+	1.33139i	−0.923917	+	0.382594i	$0.875031\pi$
$458$		0			0
$459$	−0.236850			−0.0110552
$460$		0			0
$461$	25.1742			1.17248			0.586239	−	0.810138i	$-0.300608\pi$
$461$	25.1742			1.17248			0.586239	+	0.810138i	$0.300608\pi$
$462$		0			0
$463$	−8.83473	+	19.3454i	−0.410585	+	0.899056i	0.585502	+	0.810671i	$0.300898\pi$
$463$	−8.83473	+	19.3454i	−0.410585	+	0.899056i	−0.996086	+	0.0883843i	$0.971830\pi$
$464$		0			0
$465$	−4.60495	+	5.31440i	−0.213550	+	0.246449i
$466$		0			0
$467$	9.03603	−	5.80710i	0.418137	−	0.268721i	−0.314610	−	0.949221i	$-0.601874\pi$
$467$	9.03603	−	5.80710i	0.418137	−	0.268721i	0.732748	+	0.680500i	$0.238237\pi$
$468$		0			0
$469$	−0.350205	−	0.404158i	−0.0161710	−	0.0186623i
$470$		0			0
$471$	0.531815	−	3.69885i	0.0245047	−	0.170434i
$472$		0			0
$473$	−10.3637	−	6.66032i	−0.476522	−	0.306242i
$474$		0			0
$475$	8.17572	+	17.9023i	0.375128	+	0.821416i
$476$		0			0
$477$	5.56676	+	1.63455i	0.254884	+	0.0748408i
$478$		0			0
$479$	31.9105	−	9.36977i	1.45803	−	0.428116i	0.545840	−	0.837889i	$-0.316210\pi$
$479$	31.9105	−	9.36977i	1.45803	−	0.428116i	0.912187	+	0.409774i	$0.134392\pi$
$480$		0			0
$481$	7.75267	+	53.9210i	0.353491	+	2.45859i
$482$		0			0
$483$	0.0871241	−	0.315429i	0.00396428	−	0.0143525i
$484$		0			0
$485$	1.21864	+	8.47585i	0.0553357	+	0.384868i
$486$		0			0
$487$	8.50548	−	2.49743i	0.385420	−	0.113170i	−0.0832817	−	0.996526i	$-0.526540\pi$
$487$	8.50548	−	2.49743i	0.385420	−	0.113170i	0.468702	+	0.883357i	$0.344722\pi$
$488$		0			0
$489$	−15.6647	−	4.59956i	−0.708381	−	0.207999i
$490$		0			0
$491$	−8.71092	−	19.0743i	−0.393118	−	0.860809i	−0.997922	−	0.0644345i	$-0.979476\pi$
$491$	−8.71092	−	19.0743i	−0.393118	−	0.860809i	0.604804	−	0.796375i	$-0.293252\pi$
$492$		0			0
$493$	0.251155	+	0.161407i	0.0113114	+	0.00726942i
$494$		0			0
$495$	−0.489841	+	3.40692i	−0.0220167	+	0.153130i
$496$		0			0
$497$	0.325543	+	0.375697i	0.0146026	+	0.0168523i
$498$		0			0
$499$	27.0929	−	17.4115i	1.21284	−	0.779447i	0.231711	−	0.972785i	$-0.425567\pi$
$499$	27.0929	−	17.4115i	1.21284	−	0.779447i	0.981132	+	0.193337i	$0.0619311\pi$
$500$		0			0
$501$	−11.0751	+	12.7814i	−0.494800	+	0.571030i
$502$		0			0
$503$	9.67442	−	21.1840i	0.431361	−	0.944549i	−0.561743	−	0.827312i	$-0.689869\pi$
$503$	9.67442	−	21.1840i	0.431361	−	0.944549i	0.993104	−	0.117237i	$-0.0374037\pi$
$504$		0			0
$505$	3.43292			0.152763
$506$		0			0
$507$	20.2193			0.897970
$508$		0			0
$509$	1.64060	−	3.59242i	0.0727185	−	0.159231i	−0.869782	−	0.493436i	$-0.835741\pi$
$509$	1.64060	−	3.59242i	0.0727185	−	0.159231i	0.942500	+	0.334205i	$0.108468\pi$
$510$		0			0
$511$	−0.116707	+	0.134687i	−0.00516282	+	0.00595821i
$512$		0			0
$513$	−3.81269	+	2.45027i	−0.168335	+	0.108182i
$514$		0			0
$515$	4.36953	+	5.04271i	0.192545	+	0.222208i
$516$		0			0
$517$	3.96797	−	27.5978i	0.174511	−	1.21375i
$518$		0			0
$519$	−8.67998	−	5.57829i	−0.381009	−	0.244860i
$520$		0			0
$521$	−2.96027	−	6.48210i	−0.129692	−	0.283986i	0.833635	−	0.552315i	$-0.186256\pi$
$521$	−2.96027	−	6.48210i	−0.129692	−	0.283986i	−0.963327	+	0.268330i	$0.913528\pi$
$522$		0			0
$523$	−27.2477	−	8.00064i	−1.19146	−	0.349844i	−0.374877	−	0.927074i	$-0.622315\pi$
$523$	−27.2477	−	8.00064i	−1.19146	−	0.349844i	−0.816581	+	0.577231i	$0.804133\pi$
$524$		0			0
$525$	0.284305	−	0.0834793i	0.0124081	−	0.00364334i
$526$		0			0
$527$	−0.292314	−	2.03309i	−0.0127334	−	0.0885626i
$528$		0			0
$529$	15.6140	+	16.8880i	0.678868	+	0.734261i
$530$		0			0
$531$	−1.09871	−	7.64169i	−0.0476799	−	0.331621i
$532$		0			0
$533$	−22.5525	+	6.62201i	−0.976856	+	0.286831i
$534$		0			0
$535$	6.21975	+	1.82628i	0.268903	+	0.0789572i
$536$		0			0
$537$	−4.59119	−	10.0533i	−0.198124	−	0.433832i
$538$		0			0
$539$	24.9799	+	16.0536i	1.07596	+	0.691477i
$540$		0			0
$541$	3.55721	−	24.7409i	0.152936	−	1.06370i	−0.758328	−	0.651874i	$-0.773983\pi$
$541$	3.55721	−	24.7409i	0.152936	−	1.06370i	0.911264	−	0.411822i	$-0.135108\pi$
$542$		0			0
$543$	10.6927	+	12.3401i	0.458868	+	0.529562i
$544$		0			0
$545$	−3.86444	+	2.48352i	−0.165534	+	0.106382i
$546$		0			0
$547$	17.0241	−	19.6469i	0.727898	−	0.840039i	−0.264335	−	0.964431i	$-0.585152\pi$
$547$	17.0241	−	19.6469i	0.727898	−	0.840039i	0.992233	+	0.124392i	$0.0396979\pi$
$548$		0			0
$549$	3.75708	−	8.22685i	0.160348	−	0.351114i
$550$		0			0
$551$	5.71277			0.243372
$552$		0			0
$553$	0.459587			0.0195436
$554$		0			0
$555$	−3.18375	+	6.97143i	−0.135142	+	0.295921i
$556$		0			0
$557$	−29.7456	+	34.3283i	−1.26036	+	1.45453i	−0.424658	+	0.905354i	$0.639606\pi$
$557$	−29.7456	+	34.3283i	−1.26036	+	1.45453i	−0.835703	+	0.549181i	$0.814940\pi$
$558$		0			0
$559$	−14.0719	+	9.04348i	−0.595179	+	0.382499i
$560$		0			0
$561$	−0.658380	−	0.759811i	−0.0277968	−	0.0320792i
$562$		0			0
$563$	−0.118610	+	0.824950i	−0.00499881	+	0.0347675i	−0.992168	−	0.124909i	$-0.960136\pi$
$563$	−0.118610	+	0.824950i	−0.00499881	+	0.0347675i	0.987169	+	0.159677i	$0.0510452\pi$
$564$		0			0
$565$	11.3873	+	7.31814i	0.479065	+	0.307877i
$566$		0			0
$567$	0.0283456	+	0.0620681i	0.00119040	+	0.00260662i
$568$		0			0
$569$	27.7297	+	8.14217i	1.16249	+	0.341338i	0.805399	−	0.592732i	$-0.201951\pi$
$569$	27.7297	+	8.14217i	1.16249	+	0.341338i	0.357090	+	0.934070i	$0.383769\pi$
$570$		0			0
$571$	14.3574	−	4.21571i	0.600838	−	0.176422i	0.0328523	−	0.999460i	$-0.489541\pi$
$571$	14.3574	−	4.21571i	0.600838	−	0.176422i	0.567986	+	0.823038i	$0.307723\pi$
$572$		0			0
$573$	2.67004	+	18.5705i	0.111542	+	0.775794i
$574$		0			0
$575$	−5.54465	+	20.0742i	−0.231228	+	0.837152i
$576$		0			0
$577$	6.58866	+	45.8251i	0.274290	+	1.90773i	0.401516	+	0.915852i	$0.368483\pi$
$577$	6.58866	+	45.8251i	0.274290	+	1.90773i	−0.127226	+	0.991874i	$0.540607\pi$
$578$		0			0
$579$	15.6872	−	4.60619i	0.651939	−	0.191427i
$580$		0			0
$581$	0.683654	+	0.200739i	0.0283627	+	0.00832805i
$582$		0			0
$583$	10.2305	+	22.4017i	0.423704	+	0.927783i
$584$		0			0
$585$	3.93163	+	2.52670i	0.162553	+	0.104466i
$586$		0			0
$587$	−3.32069	+	23.0959i	−0.137060	+	0.953271i	0.798975	+	0.601364i	$0.205376\pi$
$587$	−3.32069	+	23.0959i	−0.137060	+	0.953271i	−0.936035	+	0.351907i	$0.885533\pi$
$588$		0			0
$589$	−25.7383	−	29.7036i	−1.06053	−	1.22391i
$590$		0			0
$591$	−0.451689	+	0.290283i	−0.0185800	+	0.0119407i
$592$		0			0
$593$	3.62562	−	4.18419i	0.148886	−	0.171824i	−0.676407	−	0.736528i	$-0.736464\pi$
$593$	3.62562	−	4.18419i	0.148886	−	0.171824i	0.825294	+	0.564704i	$0.191010\pi$
$594$		0			0
$595$	0.00544388	−	0.0119204i	0.000223177	−	0.000488690i
$596$		0			0
$597$	0.535226			0.0219054
$598$		0			0
$599$	28.1457			1.15000			0.575001	−	0.818153i	$-0.305002\pi$
$599$	28.1457			1.15000			0.575001	+	0.818153i	$0.305002\pi$
$600$		0			0
$601$	3.01242	−	6.59628i	0.122879	−	0.269068i	−0.838189	−	0.545380i	$-0.816385\pi$
$601$	3.01242	−	6.59628i	0.122879	−	0.269068i	0.961068	+	0.276313i	$0.0891125\pi$
$602$		0			0
$603$	−5.13239	+	5.92309i	−0.209007	+	0.241207i
$604$		0			0
$605$	−4.78737	+	3.07665i	−0.194634	+	0.125084i
$606$		0			0
$607$	−15.1133	−	17.4417i	−0.613430	−	0.707936i	0.361015	−	0.932560i	$-0.382430\pi$
$607$	−15.1133	−	17.4417i	−0.613430	−	0.707936i	−0.974446	+	0.224624i	$0.927885\pi$
$608$		0			0
$609$	0.0122404	−	0.0851336i	0.000496005	−	0.00344979i
$610$		0			0
$611$	−31.8482	−	20.4676i	−1.28844	−	0.828031i
$612$		0			0
$613$	−8.95011	−	19.5980i	−0.361491	−	0.791556i	−0.999764	−	0.0217450i	$-0.993078\pi$
$613$	−8.95011	−	19.5980i	−0.361491	−	0.791556i	0.638272	−	0.769811i	$-0.279649\pi$
$614$		0			0
$615$	−3.17285	−	0.931633i	−0.127942	−	0.0375671i
$616$		0			0
$617$	−20.7847	+	6.10293i	−0.836759	+	0.245695i	−0.671918	−	0.740625i	$-0.734529\pi$
$617$	−20.7847	+	6.10293i	−0.836759	+	0.245695i	−0.164841	+	0.986320i	$0.552711\pi$
$618$		0			0
$619$	4.90539	+	34.1178i	0.197164	+	1.37131i	0.812462	+	0.583014i	$0.198127\pi$
$619$	4.90539	+	34.1178i	0.197164	+	1.37131i	−0.615298	+	0.788295i	$0.710964\pi$
$620$		0			0
$621$	−4.75740	−	0.605956i	−0.190908	−	0.0243162i
$622$		0			0
$623$	−0.141773	−	0.986050i	−0.00568000	−	0.0395053i
$624$		0			0
$625$	−14.9390	+	4.38649i	−0.597561	+	0.175460i
$626$		0			0
$627$	−18.4587	−	5.41997i	−0.737170	−	0.216453i
$628$		0			0
$629$	−0.929953	−	2.03631i	−0.0370797	−	0.0811931i
$630$		0			0
$631$	17.0080	+	10.9304i	0.677079	+	0.435132i	0.833471	−	0.552563i	$-0.186350\pi$
$631$	17.0080	+	10.9304i	0.677079	+	0.435132i	−0.156392	+	0.987695i	$0.549986\pi$
$632$		0			0
$633$	0.303595	−	2.11155i	0.0120668	−	0.0839266i
$634$		0			0
$635$	5.36524	+	6.19182i	0.212913	+	0.245715i
$636$		0			0
$637$	33.9181	−	21.7978i	1.34388	−	0.863661i
$638$		0			0
$639$	4.77096	−	5.50598i	0.188736	−	0.217813i
$640$		0			0
$641$	−8.64466	+	18.9292i	−0.341444	+	0.747657i	−0.999988	−	0.00488475i	$-0.998445\pi$
$641$	−8.64466	+	18.9292i	−0.341444	+	0.747657i	0.658545	+	0.752542i	$0.271172\pi$
$642$		0			0
$643$	−37.2866			−1.47044			−0.735220	−	0.677828i	$-0.762921\pi$
$643$	−37.2866			−1.47044			−0.735220	+	0.677828i	$0.762921\pi$
$644$		0			0
$645$	−2.35333			−0.0926621
$646$		0			0
$647$	8.86762	−	19.4174i	0.348622	−	0.763376i	−0.651367	−	0.758763i	$-0.725804\pi$
$647$	8.86762	−	19.4174i	0.348622	−	0.763376i	0.999989	−	0.00461342i	$-0.00146850\pi$
$648$		0			0
$649$	21.4603	−	24.7665i	0.842391	−	0.972170i
$650$		0			0
$651$	−0.497801	+	0.319917i	−0.0195103	+	0.0125385i
$652$		0			0
$653$	−14.0956	−	16.2671i	−0.551602	−	0.636582i	0.409654	−	0.912241i	$-0.365650\pi$
$653$	−14.0956	−	16.2671i	−0.551602	−	0.636582i	−0.961256	+	0.275659i	$0.911104\pi$
$654$		0			0
$655$	0.738499	−	5.13637i	0.0288555	−	0.200695i
$656$		0			0
$657$	2.19721	+	1.41206i	0.0857214	+	0.0550898i
$658$		0			0
$659$	13.8962	+	30.4285i	0.541321	+	1.18533i	0.960719	+	0.277524i	$0.0895140\pi$
$659$	13.8962	+	30.4285i	0.541321	+	1.18533i	−0.419398	+	0.907803i	$0.637759\pi$
$660$		0			0
$661$	−44.3105	−	13.0107i	−1.72348	−	0.506059i	−0.737846	−	0.674969i	$-0.764157\pi$
$661$	−44.3105	−	13.0107i	−1.72348	−	0.506059i	−0.985631	+	0.168910i	$0.945975\pi$
$662$		0			0
$663$	−1.30982	+	0.384596i	−0.0508690	+	0.0149365i
$664$		0			0
$665$	−0.0356869	−	0.248208i	−0.00138388	−	0.00962508i
$666$		0			0
$667$	4.63178	+	3.88460i	0.179343	+	0.150412i
$668$		0			0
$669$	1.15758	+	8.05115i	0.0447547	+	0.311275i
$670$		0			0
$671$	36.8353	−	10.8158i	1.42201	−	0.417540i
$672$		0			0
$673$	−25.0119	−	7.34416i	−0.964138	−	0.283096i	−0.238476	−	0.971148i	$-0.576648\pi$
$673$	−25.0119	−	7.34416i	−0.964138	−	0.283096i	−0.725662	+	0.688052i	$0.758466\pi$
$674$		0			0
$675$	−1.80394	−	3.95007i	−0.0694336	−	0.152038i
$676$		0			0
$677$	22.9021	+	14.7183i	0.880201	+	0.565671i	0.900857	−	0.434116i	$-0.142939\pi$
$677$	22.9021	+	14.7183i	0.880201	+	0.565671i	−0.0206560	+	0.999787i	$0.506575\pi$
$678$		0			0
$679$	−0.102548	+	0.713240i	−0.00393545	+	0.0273716i
$680$		0			0
$681$	6.41113	+	7.39884i	0.245675	+	0.283524i
$682$		0			0
$683$	−26.3019	+	16.9032i	−1.00641	+	0.646782i	−0.936462	−	0.350768i	$-0.885920\pi$
$683$	−26.3019	+	16.9032i	−1.00641	+	0.646782i	−0.0699502	+	0.997550i	$0.522284\pi$
$684$		0			0
$685$	9.83460	−	11.3497i	0.375761	−	0.433651i
$686$		0			0
$687$	6.76366	−	14.8103i	0.258050	−	0.565050i
$688$		0			0
$689$	33.4392			1.27393
$690$		0			0
$691$	21.6410			0.823264			0.411632	−	0.911350i	$-0.364959\pi$
$691$	21.6410			0.823264			0.411632	+	0.911350i	$0.364959\pi$
$692$		0			0
$693$	−0.120320	+	0.263465i	−0.00457060	+	0.0100082i
$694$		0			0
$695$	8.93130	−	10.3073i	0.338784	−	0.390977i
$696$		0			0
$697$	0.812564	−	0.522203i	0.0307780	−	0.0197798i
$698$		0			0
$699$	−12.0269	−	13.8798i	−0.454900	−	0.524983i
$700$		0			0
$701$	0.708137	−	4.92520i	0.0267460	−	0.186022i	−0.972069	−	0.234696i	$-0.924590\pi$
$701$	0.708137	−	4.92520i	0.0267460	−	0.186022i	0.998815	+	0.0486740i	$0.0154995\pi$
$702$		0			0
$703$	−36.0361	−	23.1590i	−1.35913	−	0.873458i
$704$		0			0
$705$	−2.21256	−	4.84484i	−0.0833300	−	0.182467i
$706$		0			0
$707$	0.277177	+	0.0813866i	0.0104243	+	0.00306086i
$708$		0			0
$709$	−48.1869	+	14.1489i	−1.80970	+	0.531375i	−0.998568	−	0.0534933i	$-0.982964\pi$
$709$	−48.1869	+	14.1489i	−1.80970	+	0.531375i	−0.811128	+	0.584868i	$0.801146\pi$
$710$		0			0
$711$	−0.958551	−	6.66687i	−0.0359485	−	0.250027i
$712$		0			0
$713$	−0.670006	−	41.5847i	−0.0250919	−	1.55736i
$714$		0			0
$715$	2.82326	+	19.6362i	0.105584	+	0.734351i
$716$		0			0
$717$	−14.9875	+	4.40073i	−0.559719	+	0.164348i
$718$		0			0
$719$	24.2145	+	7.11003i	0.903050	+	0.265159i	0.700113	−	0.714032i	$-0.253133\pi$
$719$	24.2145	+	7.11003i	0.903050	+	0.265159i	0.202937	+	0.979192i	$0.434951\pi$
$720$		0			0
$721$	0.233249	+	0.510745i	0.00868666	+	0.0190211i
$722$		0			0
$723$	−4.76613	−	3.06301i	−0.177254	−	0.113914i
$724$		0			0
$725$	−0.778988	+	5.41798i	−0.0289309	+	0.201219i
$726$		0			0
$727$	14.7543	+	17.0274i	0.547206	+	0.631510i	0.960230	−	0.279211i	$-0.0900728\pi$
$727$	14.7543	+	17.0274i	0.547206	+	0.631510i	−0.413024	+	0.910720i	$0.635527\pi$
$728$		0			0
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$		0			0
$731$	0.450146	−	0.519497i	0.0166493	−	0.0192143i
$732$		0			0
$733$	−5.61233	+	12.2893i	−0.207296	+	0.453915i	−0.984512	−	0.175319i	$-0.943904\pi$
$733$	−5.61233	+	12.2893i	−0.207296	+	0.453915i	0.777215	+	0.629235i	$0.216632\pi$
$734$		0			0
$735$	5.67230			0.209226
$736$		0			0
$737$	−33.2679			−1.22544
$738$		0			0
$739$	−11.4489	+	25.0695i	−0.421154	+	0.922198i	0.573527	+	0.819187i	$0.305575\pi$
$739$	−11.4489	+	25.0695i	−0.421154	+	0.922198i	−0.994680	+	0.103011i	$0.967152\pi$
$740$		0			0
$741$	−17.1060	+	19.7414i	−0.628405	+	0.725219i
$742$		0			0
$743$	40.0823	−	25.7593i	1.47048	−	0.945019i	0.472508	−	0.881326i	$-0.343349\pi$
$743$	40.0823	−	25.7593i	1.47048	−	0.945019i	0.997970	−	0.0636921i	$-0.0202876\pi$
$744$		0			0
$745$	2.95903	+	3.41490i	0.108410	+	0.125112i
$746$		0			0
$747$	1.48608	−	10.3359i	0.0543728	−	0.378171i
$748$		0			0
$749$	0.458892	+	0.294912i	0.0167676	+	0.0107759i
$750$		0			0
$751$	−12.1906	−	26.6937i	−0.444842	−	0.974068i	−0.990684	−	0.136180i	$-0.956517\pi$
$751$	−12.1906	−	26.6937i	−0.444842	−	0.974068i	0.545842	−	0.837888i	$-0.316210\pi$
$752$		0			0
$753$	−10.8765	−	3.19363i	−0.396362	−	0.116383i
$754$		0			0
$755$	−16.4211	+	4.82166i	−0.597623	+	0.175478i
$756$		0			0
$757$	−2.14939	−	14.9493i	−0.0781208	−	0.543342i	−0.990870	−	0.134821i	$-0.956954\pi$
$757$	−2.14939	−	14.9493i	−0.0781208	−	0.543342i	0.912749	−	0.408520i	$-0.133955\pi$
$758$		0			0
$759$	−11.2804	−	16.9461i	−0.409453	−	0.615103i
$760$		0			0
$761$	5.79089	+	40.2765i	0.209919	+	1.46002i	0.773414	+	0.633902i	$0.218548\pi$
$761$	5.79089	+	40.2765i	0.209919	+	1.46002i	−0.563494	+	0.826120i	$0.690543\pi$
$762$		0			0
$763$	−0.370897	+	0.108905i	−0.0134274	+	0.00394264i
$764$		0			0
$765$	−0.184275	−	0.0541079i	−0.00666246	−	0.00195627i
$766$		0			0
$767$	−18.4846	−	40.4756i	−0.667440	−	1.46149i
$768$		0			0
$769$	5.99330	+	3.85166i	0.216124	+	0.138894i	0.644224	−	0.764837i	$-0.277181\pi$
$769$	5.99330	+	3.85166i	0.216124	+	0.138894i	−0.428100	+	0.903731i	$0.640817\pi$
$770$		0			0
$771$	−2.14708	+	14.9333i	−0.0773252	+	0.537808i
$772$		0			0
$773$	4.26567	+	4.92285i	0.153426	+	0.177063i	0.827259	−	0.561821i	$-0.189899\pi$
$773$	4.26567	+	4.92285i	0.153426	+	0.177063i	−0.673833	+	0.738883i	$0.735353\pi$
$774$		0			0
$775$	31.6805	−	20.3598i	1.13800	−	0.731346i
$776$		0			0
$777$	−0.422336	+	0.487401i	−0.0151512	+	0.0174854i
$778$		0			0
$779$	7.67794	−	16.8123i	0.275091	−	0.602364i
$780$		0			0
$781$	30.9251			1.10659
$782$		0			0
$783$	−1.26050			−0.0450465
$784$		0			0
$785$	1.25876	−	2.75630i	0.0449271	−	0.0983765i
$786$		0			0
$787$	−6.58133	+	7.59526i	−0.234599	+	0.270742i	−0.860826	−	0.508899i	$-0.830053\pi$
$787$	−6.58133	+	7.59526i	−0.234599	+	0.270742i	0.626227	+	0.779641i	$0.284598\pi$
$788$		0			0
$789$	4.73729	−	3.04447i	0.168652	−	0.108386i
$790$		0			0
$791$	0.745922	+	0.860840i	0.0265219	+	0.0306079i
$792$		0			0
$793$	7.41845	−	51.5965i	0.263437	−	1.83224i
$794$		0			0
$795$	3.95765	+	2.54343i	0.140364	+	0.0902062i
$796$		0			0
$797$	0.647807	+	1.41850i	0.0229465	+	0.0502458i	0.920758	−	0.390134i	$-0.127571\pi$
$797$	0.647807	+	1.41850i	0.0229465	+	0.0502458i	−0.897812	+	0.440379i	$0.854844\pi$
$798$		0			0
$799$	1.49272	+	0.438302i	0.0528086	+	0.0155060i
$800$		0			0
$801$	−14.0082	+	4.11317i	−0.494954	+	0.145332i
$802$		0			0
$803$	1.57779	+	10.9738i	0.0556791	+	0.387257i
$804$		0			0
$805$	0.139844	−	0.225508i	0.00492884	−	0.00794810i
$806$		0			0
$807$	−3.72138	−	25.8828i	−0.130999	−	0.911118i
$808$		0			0
$809$	41.3137	−	12.1308i	1.45251	−	0.426496i	0.542140	−	0.840288i	$-0.317614\pi$
$809$	41.3137	−	12.1308i	1.45251	−	0.426496i	0.910371	+	0.413793i	$0.135796\pi$
$810$		0			0
$811$	−49.8837	−	14.6472i	−1.75165	−	0.514332i	−0.760766	−	0.649026i	$-0.775177\pi$
$811$	−49.8837	−	14.6472i	−1.75165	−	0.514332i	−0.990887	+	0.134694i	$0.956995\pi$
$812$		0			0
$813$	−8.34553	−	18.2742i	−0.292690	−	0.640903i
$814$		0			0
$815$	−11.1367	−	7.15712i	−0.390102	−	0.250703i
$816$		0			0
$817$	1.87192	−	13.0195i	0.0654901	−	0.455494i
$818$		0			0
$819$	0.257541	+	0.297219i	0.00899922	+	0.0103857i
$820$		0			0
$821$	0.649313	−	0.417288i	0.0226612	−	0.0145634i	−0.529261	−	0.848459i	$-0.677531\pi$
$821$	0.649313	−	0.417288i	0.0226612	−	0.0145634i	0.551922	+	0.833896i	$0.313894\pi$
$822$		0			0
$823$	−5.97656	+	6.89732i	−0.208330	+	0.240426i	−0.850293	−	0.526310i	$-0.823575\pi$
$823$	−5.97656	+	6.89732i	−0.208330	+	0.240426i	0.641963	+	0.766736i	$0.278120\pi$
$824$		0			0
$825$	7.65730	−	16.7672i	0.266593	−	0.583757i
$826$		0			0
$827$	39.4642			1.37230			0.686152	−	0.727458i	$-0.259298\pi$
$827$	39.4642			1.37230			0.686152	+	0.727458i	$0.259298\pi$
$828$		0			0
$829$	−15.2676			−0.530265			−0.265133	−	0.964212i	$-0.585416\pi$
$829$	−15.2676			−0.530265			−0.265133	+	0.964212i	$0.585416\pi$
$830$		0			0
$831$	3.37964	−	7.40039i	0.117239	−	0.256717i
$832$		0			0
$833$	−1.08500	+	1.25216i	−0.0375931	+	0.0433848i
$834$		0			0
$835$	−11.5366	+	7.41411i	−0.399240	+	0.256576i
$836$		0			0
$837$	5.67904	+	6.55396i	0.196296	+	0.226538i
$838$		0			0
$839$	−0.770249	+	5.35720i	−0.0265919	+	0.184951i	−0.998788	−	0.0492169i	$-0.984327\pi$
$839$	−0.770249	+	5.35720i	−0.0265919	+	0.184951i	0.972196	+	0.234168i	$0.0752365\pi$
$840$		0			0
$841$	−23.0597	−	14.8196i	−0.795163	−	0.511020i
$842$		0			0
$843$	0.230730	+	0.505227i	0.00794675	+	0.0174010i
$844$		0			0
$845$	15.7311	+	4.61906i	0.541165	+	0.158900i
$846$		0			0
$847$	−0.459477	+	0.134915i	−0.0157878	+	0.00463573i
$848$		0			0
$849$	0.985687	+	6.85560i	0.0338287	+	0.235284i
$850$		0			0
$851$	−13.4695	−	43.2808i	−0.461727	−	1.48365i
$852$		0			0
$853$	−4.89867	−	34.0710i	−0.167727	−	1.16657i	−0.883567	−	0.468304i	$-0.844865\pi$
$853$	−4.89867	−	34.0710i	−0.167727	−	1.16657i	0.715840	−	0.698264i	$-0.246044\pi$
$854$		0			0
$855$	−3.52612	+	1.03536i	−0.120591	+	0.0354086i
$856$		0			0
$857$	16.3490	+	4.80050i	0.558471	+	0.163982i	0.548774	−	0.835971i	$-0.315095\pi$
$857$	16.3490	+	4.80050i	0.558471	+	0.163982i	0.00969775	+	0.999953i	$0.496913\pi$
$858$		0			0
$859$	−6.54074	−	14.3222i	−0.223167	−	0.488668i	0.764619	−	0.644482i	$-0.222927\pi$
$859$	−6.54074	−	14.3222i	−0.223167	−	0.488668i	−0.987786	+	0.155814i	$0.950200\pi$
$860$		0			0
$861$	−0.234092	−	0.150442i	−0.00797784	−	0.00512705i
$862$		0			0
$863$	−5.87023	+	40.8284i	−0.199825	+	1.38981i	0.604964	+	0.796253i	$0.293188\pi$
$863$	−5.87023	+	40.8284i	−0.199825	+	1.38981i	−0.804789	+	0.593561i	$0.797722\pi$
$864$		0			0
$865$	−5.47887	−	6.32296i	−0.186287	−	0.214987i
$866$		0			0
$867$	−14.2541	+	9.16057i	−0.484095	+	0.311109i
$868$		0			0
$869$	18.7227	−	21.6072i	0.635124	−	0.732972i
$870$		0			0
$871$	−18.7650	+	41.0896i	−0.635827	+	1.39227i
$872$		0			0
$873$	10.5603			0.357412
$874$		0			0
$875$	0.516911			0.0174748
$876$		0			0
$877$	20.2684	−	44.3816i	0.684416	−	1.49866i	−0.173480	−	0.984837i	$-0.555501\pi$
$877$	20.2684	−	44.3816i	0.684416	−	1.49866i	0.857896	−	0.513824i	$-0.171772\pi$
$878$		0			0
$879$	−14.8795	+	17.1719i	−0.501875	+	0.579194i
$880$		0			0
$881$	28.6520	−	18.4135i	0.965310	−	0.620367i	0.0398475	−	0.999206i	$-0.487313\pi$
$881$	28.6520	−	18.4135i	0.965310	−	0.620367i	0.925463	+	0.378838i	$0.123676\pi$
$882$		0			0
$883$	−0.473530	−	0.546483i	−0.0159356	−	0.0183906i	0.747726	−	0.664008i	$-0.231146\pi$
$883$	−0.473530	−	0.546483i	−0.0159356	−	0.0183906i	−0.763661	+	0.645617i	$0.776600\pi$
$884$		0			0
$885$	0.890908	−	6.19640i	0.0299475	−	0.208290i
$886$		0			0
$887$	23.7219	+	15.2452i	0.796504	+	0.511882i	0.874473	−	0.485074i	$-0.161207\pi$
$887$	23.7219	+	15.2452i	0.796504	+	0.511882i	−0.0779690	+	0.996956i	$0.524844\pi$
$888$		0			0
$889$	0.286401	+	0.627131i	0.00960559	+	0.0210333i
$890$		0			0
$891$	4.07283	+	1.19589i	0.136445	+	0.0400639i
$892$		0			0
$893$	28.5634	−	8.38697i	0.955838	−	0.280659i
$894$		0			0
$895$	−1.27539	−	8.87055i	−0.0426316	−	0.296510i
$896$		0			0
$897$	−27.2931	+	4.37402i	−0.911289	+	0.146044i
$898$		0			0
$899$	−1.55567	−	10.8199i	−0.0518845	−	0.360865i
$900$		0			0
$901$	−1.31849	+	0.387142i	−0.0439251	+	0.0128976i
$902$		0			0
$903$	−0.190010	−	0.0557920i	−0.00632314	−	0.00185664i
$904$		0			0
$905$	5.50011	+	12.0436i	0.182830	+	0.400342i
$906$		0			0
$907$	6.35404	+	4.08350i	0.210983	+	0.135590i	0.641865	−	0.766818i	$-0.278161\pi$
$907$	6.35404	+	4.08350i	0.210983	+	0.135590i	−0.430882	+	0.902408i	$0.641797\pi$
$908$		0			0
$909$	0.602509	−	4.19054i	0.0199839	−	0.138991i
$910$		0			0
$911$	3.19136	+	3.68302i	0.105734	+	0.122024i	0.806150	−	0.591711i	$-0.201547\pi$
$911$	3.19136	+	3.68302i	0.105734	+	0.122024i	−0.700416	+	0.713735i	$0.747002\pi$
$912$		0			0
$913$	37.2883	−	23.9638i	1.23406	−	0.793084i
$914$		0			0
$915$	4.80250	−	5.54238i	0.158766	−	0.183225i
$916$		0			0
$917$	0.181399	−	0.397208i	0.00599031	−	0.0131170i
$918$		0			0
$919$	24.7591			0.816727			0.408363	−	0.912819i	$-0.366100\pi$
$919$	24.7591			0.816727			0.408363	+	0.912819i	$0.366100\pi$
$920$		0			0
$921$	−12.0437			−0.396854
$922$		0			0
$923$	17.4435	−	38.1959i	0.574160	−	1.25723i
$924$		0			0
$925$	26.8778	−	31.0186i	0.883737	−	1.01989i
$926$		0			0
$927$	6.92249	−	4.44881i	0.227364	−	0.146118i
$928$		0			0
$929$	−0.220788	−	0.254802i	−0.00724380	−	0.00835979i	0.752116	−	0.659031i	$-0.229033\pi$
$929$	−0.220788	−	0.254802i	−0.00724380	−	0.00835979i	−0.759360	+	0.650671i	$0.774488\pi$
$930$		0			0
$931$	−4.51195	+	31.3813i	−0.147873	+	1.02848i
$932$		0			0
$933$	2.38536	+	1.53298i	0.0780931	+	0.0501874i
$934$		0			0
$935$	−0.338657	−	0.741556i	−0.0110753	−	0.0242515i
$936$		0			0
$937$	−11.8880	−	3.49062i	−0.388363	−	0.114034i	0.0817213	−	0.996655i	$-0.473958\pi$
$937$	−11.8880	−	3.49062i	−0.388363	−	0.114034i	−0.470084	+	0.882622i	$0.655776\pi$
$938$		0			0
$939$	15.2800	−	4.48662i	0.498645	−	0.146415i
$940$		0			0
$941$	5.98166	+	41.6034i	0.194997	+	1.35623i	0.818543	+	0.574445i	$0.194782\pi$
$941$	5.98166	+	41.6034i	0.194997	+	1.35623i	−0.623547	+	0.781786i	$0.714309\pi$
$942$		0			0
$943$	17.6573	−	8.41017i	0.574999	−	0.273873i
$944$		0			0
$945$	0.00787415	+	0.0547659i	0.000256146	+	0.00178153i
$946$		0			0
$947$	−53.2433	+	15.6337i	−1.73018	+	0.508026i	−0.986952	−	0.161017i	$-0.948523\pi$
$947$	−53.2433	+	15.6337i	−1.73018	+	0.508026i	−0.743224	+	0.669042i	$0.766705\pi$
$948$		0			0
$949$	14.4438	+	4.24109i	0.468866	+	0.137672i
$950$		0			0
$951$	−0.885816	−	1.93967i	−0.0287246	−	0.0628980i
$952$		0			0
$953$	−26.8885	−	17.2802i	−0.871003	−	0.559760i	0.0270562	−	0.999634i	$-0.491387\pi$
$953$	−26.8885	−	17.2802i	−0.871003	−	0.559760i	−0.898059	+	0.439874i	$0.855023\pi$
$954$		0			0
$955$	−2.16505	+	15.0582i	−0.0700593	+	0.487273i
$956$		0			0
$957$	−3.50385	−	4.04365i	−0.113263	−	0.130713i
$958$		0			0
$959$	1.06313	−	0.683234i	0.0343303	−	0.0220628i
$960$		0			0
$961$	−28.9487	+	33.4085i	−0.933828	+	1.07769i
$962$		0			0
$963$	3.32096	−	7.27188i	0.107016	−	0.234333i
$964$		0			0
$965$	13.2573			0.426767
$966$		0			0
$967$	22.2116			0.714276			0.357138	−	0.934052i	$-0.383753\pi$
$967$	22.2116			0.714276			0.357138	+	0.934052i	$0.383753\pi$
$968$		0			0
$969$	0.445923	−	0.976436i	0.0143251	−	0.0313676i
$970$		0			0
$971$	−32.5060	+	37.5139i	−1.04317	+	1.20388i	−0.0646093	+	0.997911i	$0.520580\pi$
$971$	−32.5060	+	37.5139i	−1.04317	+	1.20388i	−0.978558	+	0.205969i	$0.933965\pi$
$972$		0			0
$973$	0.965484	−	0.620479i	0.0309520	−	0.0198916i
$974$		0			0
$975$	−16.3902	−	18.9153i	−0.524905	−	0.605773i
$976$		0			0
$977$	−5.11833	+	35.5988i	−0.163750	+	1.13891i	0.727736	+	0.685858i	$0.240573\pi$
$977$	−5.11833	+	35.5988i	−0.163750	+	1.13891i	−0.891486	+	0.453049i	$0.850336\pi$
$978$		0			0
$979$	−52.1340	−	33.5045i	−1.66621	−	1.07081i
$980$		0			0
$981$	2.35338	+	5.15317i	0.0751375	+	0.164528i
$982$		0			0
$983$	−9.68321	−	2.84325i	−0.308846	−	0.0906855i	0.123637	−	0.992328i	$-0.460544\pi$
$983$	−9.68321	−	2.84325i	−0.308846	−	0.0906855i	−0.432483	+	0.901642i	$0.642362\pi$
$984$		0			0
$985$	−0.417739	+	0.122659i	−0.0133103	+	0.00390825i
$986$		0			0
$987$	−0.0637847	−	0.443632i	−0.00203029	−	0.0141210i
$988$		0			0
$989$	10.3708	−	9.28302i	0.329771	−	0.295183i
$990$		0			0
$991$	−8.70948	−	60.5757i	−0.276666	−	1.92425i	−0.370842	−	0.928696i	$-0.620931\pi$
$991$	−8.70948	−	60.5757i	−0.276666	−	1.92425i	0.0941761	−	0.995556i	$-0.469978\pi$
$992$		0			0
$993$	12.0770	−	3.54612i	0.383252	−	0.112533i
$994$		0			0
$995$	0.416418	+	0.122271i	0.0132013	+	0.00387626i
$996$		0			0
$997$	22.6514	+	49.5996i	0.717376	+	1.57083i	0.817546	+	0.575864i	$0.195334\pi$
$997$	22.6514	+	49.5996i	0.717376	+	1.57083i	−0.100170	+	0.994970i	$0.531939\pi$
$998$		0			0
$999$	7.95120	+	5.10993i	0.251565	+	0.161671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.a.49.3	✓	30
23.8	even	11	inner	552.2.q.a.169.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.a.49.3	✓	30	1.1	even	1	trivial
552.2.q.a.169.3	yes	30	23.8	even	11	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:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{3} +(0.531006 - 0.612813i) q^{5} +(0.0574024 - 0.0368903i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{3} +(0.531006 - 0.612813i) q^{5} +(0.0574024 - 0.0368903i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(0.604094 - 4.20157i) q^{11} +(-4.84866 - 3.11605i) q^{13} +(-0.336847 - 0.737592i) q^{15} +(0.227256 + 0.0667283i) q^{17} +(4.34857 - 1.27686i) q^{19} +(-0.00971076 - 0.0675398i) q^{21} +(4.39397 + 1.92172i) q^{23} +(0.618001 + 4.29829i) q^{25} +(-0.959493 + 0.281733i) q^{27} +(1.20944 + 0.355123i) q^{29} +(-3.60253 - 7.88845i) q^{31} +(-3.57093 - 2.29490i) q^{33} +(0.00787415 - 0.0547659i) q^{35} +(-6.18949 - 7.14305i) q^{37} +(-4.84866 + 3.11605i) q^{39} +(2.67058 - 3.08202i) q^{41} +(1.20563 - 2.63996i) q^{43} -0.810868 q^{45} +6.56845 q^{47} +(-2.90597 + 6.36319i) q^{49} +(0.155104 - 0.178999i) q^{51} +(-4.88076 + 3.13667i) q^{53} +(-2.25400 - 2.60125i) q^{55} +(0.644993 - 4.48603i) q^{57} +(6.49470 + 4.17389i) q^{59} +(3.75708 + 8.22685i) q^{61} +(-0.0654704 - 0.0192238i) q^{63} +(-4.48422 + 1.31669i) q^{65} +(-1.11537 - 7.75760i) q^{67} +(3.57338 - 3.19858i) q^{69} +(1.03683 + 7.21130i) q^{71} +(-2.50603 + 0.735838i) q^{73} +(4.16659 + 1.22342i) q^{75} +(-0.120320 - 0.263465i) q^{77} +(5.66620 + 3.64145i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(6.83818 + 7.89168i) q^{83} +(0.161566 - 0.103832i) q^{85} +(0.825449 - 0.952619i) q^{87} +(6.06487 - 13.2802i) q^{89} -0.393277 q^{91} -8.67213 q^{93} +(1.52664 - 3.34288i) q^{95} +(-6.91552 + 7.98094i) q^{97} +(-3.57093 + 2.29490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9	\( 30 q - 3 q^{3} - 2 q^{7} - 3 q^{9} - 15 q^{11} + 5 q^{13} - 15 q^{17} + 5 q^{19} + 9 q^{21} + 14 q^{23} + 5 q^{25} - 3 q^{27} + 13 q^{29} - 29 q^{31} - 15 q^{33} + 8 q^{35} - 3 q^{37} + 5 q^{39} + 24 q^{41} + 2 q^{43} + 22 q^{45} + 38 q^{47} + 15 q^{49} + 7 q^{51} - 7 q^{53} + 46 q^{55} - 6 q^{57} - 43 q^{59} - 22 q^{61} - 2 q^{63} + 44 q^{65} + 31 q^{67} + 3 q^{69} + 19 q^{71} - 50 q^{73} + 5 q^{75} + 16 q^{77} - 84 q^{79} - 3 q^{81} - 73 q^{83} - 8 q^{85} + 2 q^{87} + 19 q^{89} + 18 q^{91} + 26 q^{93} - 67 q^{95} - 29 q^{97} - 15 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 2 * q^7 - 3 * q^9 - 15 * q^11 + 5 * q^13 - 15 * q^17 + 5 * q^19 + 9 * q^21 + 14 * q^23 + 5 * q^25 - 3 * q^27 + 13 * q^29 - 29 * q^31 - 15 * q^33 + 8 * q^35 - 3 * q^37 + 5 * q^39 + 24 * q^41 + 2 * q^43 + 22 * q^45 + 38 * q^47 + 15 * q^49 + 7 * q^51 - 7 * q^53 + 46 * q^55 - 6 * q^57 - 43 * q^59 - 22 * q^61 - 2 * q^63 + 44 * q^65 + 31 * q^67 + 3 * q^69 + 19 * q^71 - 50 * q^73 + 5 * q^75 + 16 * q^77 - 84 * q^79 - 3 * q^81 - 73 * q^83 - 8 * q^85 + 2 * q^87 + 19 * q^89 + 18 * q^91 + 26 * q^93 - 67 * q^95 - 29 * q^97 - 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more