LMFDB - Embedded newform 44.2.e.a.37.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [44,2,Mod(5,44)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("44.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(44, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 44 = 2^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	44.e (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.351341768894$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 + 0.587785i$ of defining polynomial
Character	$\chi$	$=$	44.37
Dual form			44.2.e.a.25.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 2.48990i) q^{3} +(1.30902 - 0.951057i) q^{5} +(-1.19098 - 3.66547i) q^{7} +(-3.11803 - 2.26538i) q^{9} +(1.23607 + 3.07768i) q^{11} +(-1.92705 - 1.40008i) q^{13} +(1.30902 + 4.02874i) q^{15} +(-1.92705 + 1.40008i) q^{17} +(1.19098 - 3.66547i) q^{19} +10.0902 q^{21} -2.47214 q^{23} +(-0.736068 + 2.26538i) q^{25} +(1.80902 - 1.31433i) q^{27} +(2.66312 + 8.19624i) q^{29} +(-0.690983 - 0.502029i) q^{31} +(-8.66312 + 0.587785i) q^{33} +(-5.04508 - 3.66547i) q^{35} +(-0.572949 - 1.76336i) q^{37} +(5.04508 - 3.66547i) q^{39} +(2.66312 - 8.19624i) q^{41} -6.23607 q^{45} +(0.427051 - 1.31433i) q^{47} +(-6.35410 + 4.61653i) q^{49} +(-1.92705 - 5.93085i) q^{51} +(3.30902 + 2.40414i) q^{53} +(4.54508 + 2.85317i) q^{55} +(8.16312 + 5.93085i) q^{57} +(0.336881 + 1.03681i) q^{59} +(-1.92705 + 1.40008i) q^{61} +(-4.59017 + 14.1271i) q^{63} -3.85410 q^{65} +12.9443 q^{67} +(2.00000 - 6.15537i) q^{69} +(5.16312 - 3.75123i) q^{71} +(-0.281153 - 0.865300i) q^{73} +(-5.04508 - 3.66547i) q^{75} +(9.80902 - 8.19624i) q^{77} +(5.78115 + 4.20025i) q^{79} +(-1.76393 - 5.42882i) q^{81} +(-10.5451 + 7.66145i) q^{83} +(-1.19098 + 3.66547i) q^{85} -22.5623 q^{87} +0.472136 q^{89} +(-2.83688 + 8.73102i) q^{91} +(1.80902 - 1.31433i) q^{93} +(-1.92705 - 5.93085i) q^{95} +(11.7812 + 8.55951i) q^{97} +(3.11803 - 12.3965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} - 4 q^{11} - q^{13} + 3 q^{15} - q^{17} + 7 q^{19} + 18 q^{21} + 8 q^{23} + 6 q^{25} + 5 q^{27} - 5 q^{29} - 5 q^{31} - 19 q^{33} - 9 q^{35} - 9 q^{37} + 9 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) $ 4 * q - q^3 + 3 * q^5 - 7 * q^7 - 8 * q^9 - 4 * q^11 - q^13 + 3 * q^15 - q^17 + 7 * q^19 + 18 * q^21 + 8 * q^23 + 6 * q^25 + 5 * q^27 - 5 * q^29 - 5 * q^31 - 19 * q^33 - 9 * q^35 - 9 * q^37 + 9 * q^39 - 5 * q^41 - 16 * q^45 - 5 * q^47 - 12 * q^49 - q^51 + 11 * q^53 + 7 * q^55 + 17 * q^57 + 17 * q^59 - q^61 + 4 * q^63 - 2 * q^65 + 16 * q^67 + 8 * q^69 + 5 * q^71 + 19 * q^73 - 9 * q^75 + 37 * q^77 + 3 * q^79 - 16 * q^81 - 31 * q^83 - 7 * q^85 - 50 * q^87 - 16 * q^89 - 27 * q^91 + 5 * q^93 - q^95 + 27 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/44\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	0.389254	+	0.921131i	$0.372733\pi$
$3$	−0.809017	+	2.48990i	−0.467086	+	1.43754i	−0.856340	+	0.516413i	$0.827267\pi$
$4$		0			0
$5$	1.30902	−	0.951057i	0.585410	−	0.425325i	−0.255260	−	0.966872i	$-0.582161\pi$
$5$	1.30902	−	0.951057i	0.585410	−	0.425325i	0.840670	+	0.541547i	$0.182161\pi$
$6$		0			0
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	−0.876737	−	0.480971i	$-0.840284\pi$
$7$	−1.19098	−	3.66547i	−0.450149	−	1.38542i	0.426587	−	0.904446i	$-0.359716\pi$
$8$		0			0
$9$	−3.11803	−	2.26538i	−1.03934	−	0.755128i
$10$		0			0
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$11$	1.23607	+	3.07768i	0.372689	+	0.927957i
$12$		0			0
$13$	−1.92705	−	1.40008i	−0.534468	−	0.388314i	0.287559	−	0.957763i	$-0.407156\pi$
$13$	−1.92705	−	1.40008i	−0.534468	−	0.388314i	−0.822026	+	0.569449i	$0.807156\pi$
$14$		0			0
$15$	1.30902	+	4.02874i	0.337987	+	1.04022i
$16$		0			0
$17$	−1.92705	+	1.40008i	−0.467379	+	0.339570i	−0.796419	−	0.604746i	$-0.793275\pi$
$17$	−1.92705	+	1.40008i	−0.467379	+	0.339570i	0.329040	+	0.944316i	$0.393275\pi$
$18$		0			0
$19$	1.19098	−	3.66547i	0.273230	−	0.840916i	−0.716452	−	0.697636i	$-0.754235\pi$
$19$	1.19098	−	3.66547i	0.273230	−	0.840916i	0.989682	−	0.143280i	$-0.0457649\pi$
$20$		0			0
$21$	10.0902			2.20186
$22$		0			0
$23$	−2.47214			−0.515476			−0.257738	−	0.966215i	$-0.582977\pi$
$23$	−2.47214			−0.515476			−0.257738	+	0.966215i	$0.582977\pi$
$24$		0			0
$25$	−0.736068	+	2.26538i	−0.147214	+	0.453077i
$26$		0			0
$27$	1.80902	−	1.31433i	0.348145	−	0.252942i
$28$		0			0
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	0.817690	+	0.575659i	$0.195254\pi$
$29$	2.66312	+	8.19624i	0.494529	+	1.52200i	−0.323161	+	0.946344i	$0.604746\pi$
$30$		0			0
$31$	−0.690983	−	0.502029i	−0.124104	−	0.0901670i	0.524002	−	0.851717i	$-0.324439\pi$
$31$	−0.690983	−	0.502029i	−0.124104	−	0.0901670i	−0.648106	+	0.761550i	$0.724439\pi$
$32$		0			0
$33$	−8.66312	+	0.587785i	−1.50806	+	0.102320i
$34$		0			0
$35$	−5.04508	−	3.66547i	−0.852775	−	0.619577i
$36$		0			0
$37$	−0.572949	−	1.76336i	−0.0941922	−	0.289894i	0.892850	−	0.450354i	$-0.148702\pi$
$37$	−0.572949	−	1.76336i	−0.0941922	−	0.289894i	−0.987042	+	0.160460i	$0.948702\pi$
$38$		0			0
$39$	5.04508	−	3.66547i	0.807860	−	0.586945i
$40$		0			0
$41$	2.66312	−	8.19624i	0.415909	−	1.28004i	−0.495526	−	0.868593i	$-0.665025\pi$
$41$	2.66312	−	8.19624i	0.415909	−	1.28004i	0.911435	−	0.411444i	$-0.134975\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−6.23607			−0.929618
$46$		0			0
$47$	0.427051	−	1.31433i	0.0622918	−	0.191714i	−0.915068	−	0.403301i	$-0.867863\pi$
$47$	0.427051	−	1.31433i	0.0622918	−	0.191714i	0.977359	+	0.211586i	$0.0678629\pi$
$48$		0			0
$49$	−6.35410	+	4.61653i	−0.907729	+	0.659504i
$50$		0			0
$51$	−1.92705	−	5.93085i	−0.269841	−	0.830486i
$52$		0			0
$53$	3.30902	+	2.40414i	0.454528	+	0.330234i	0.791381	−	0.611323i	$-0.209362\pi$
$53$	3.30902	+	2.40414i	0.454528	+	0.330234i	−0.336853	+	0.941557i	$0.609362\pi$
$54$		0			0
$55$	4.54508	+	2.85317i	0.612859	+	0.384721i
$56$		0			0
$57$	8.16312	+	5.93085i	1.08123	+	0.785561i
$58$		0			0
$59$	0.336881	+	1.03681i	0.0438582	+	0.134982i	0.970588	−	0.240747i	$-0.0773924\pi$
$59$	0.336881	+	1.03681i	0.0438582	+	0.134982i	−0.926730	+	0.375729i	$0.877392\pi$
$60$		0			0
$61$	−1.92705	+	1.40008i	−0.246734	+	0.179262i	−0.704278	−	0.709924i	$-0.748729\pi$
$61$	−1.92705	+	1.40008i	−0.246734	+	0.179262i	0.457544	+	0.889187i	$0.348729\pi$
$62$		0			0
$63$	−4.59017	+	14.1271i	−0.578307	+	1.77985i
$64$		0			0
$65$	−3.85410			−0.478043
$66$		0			0
$67$	12.9443			1.58139			0.790697	−	0.612207i	$-0.209718\pi$
$67$	12.9443			1.58139			0.790697	+	0.612207i	$0.209718\pi$
$68$		0			0
$69$	2.00000	−	6.15537i	0.240772	−	0.741019i
$70$		0			0
$71$	5.16312	−	3.75123i	0.612749	−	0.445189i	−0.237632	−	0.971355i	$-0.576371\pi$
$71$	5.16312	−	3.75123i	0.612749	−	0.445189i	0.850381	+	0.526167i	$0.176371\pi$
$72$		0			0
$73$	−0.281153	−	0.865300i	−0.0329065	−	0.101276i	0.933254	−	0.359217i	$-0.116956\pi$
$73$	−0.281153	−	0.865300i	−0.0329065	−	0.101276i	−0.966161	+	0.257941i	$0.916956\pi$
$74$		0			0
$75$	−5.04508	−	3.66547i	−0.582556	−	0.423252i
$76$		0			0
$77$	9.80902	−	8.19624i	1.11784	−	0.934048i
$78$		0			0
$79$	5.78115	+	4.20025i	0.650431	+	0.472565i	0.863418	−	0.504490i	$-0.168319\pi$
$79$	5.78115	+	4.20025i	0.650431	+	0.472565i	−0.212987	+	0.977055i	$0.568319\pi$
$80$		0			0
$81$	−1.76393	−	5.42882i	−0.195992	−	0.603203i
$82$		0			0
$83$	−10.5451	+	7.66145i	−1.15747	+	0.840954i	−0.989456	−	0.144830i	$-0.953736\pi$
$83$	−10.5451	+	7.66145i	−1.15747	+	0.840954i	−0.168017	+	0.985784i	$0.553736\pi$
$84$		0			0
$85$	−1.19098	+	3.66547i	−0.129180	+	0.397576i
$86$		0			0
$87$	−22.5623			−2.41893
$88$		0			0
$89$	0.472136			0.0500463			0.0250232	−	0.999687i	$-0.492034\pi$
$89$	0.472136			0.0500463			0.0250232	+	0.999687i	$0.492034\pi$
$90$		0			0
$91$	−2.83688	+	8.73102i	−0.297386	+	0.915260i
$92$		0			0
$93$	1.80902	−	1.31433i	0.187586	−	0.136289i
$94$		0			0
$95$	−1.92705	−	5.93085i	−0.197711	−	0.608493i
$96$		0			0
$97$	11.7812	+	8.55951i	1.19619	+	0.869086i	0.993905	−	0.110239i	$-0.0351617\pi$
$97$	11.7812	+	8.55951i	1.19619	+	0.869086i	0.202290	+	0.979326i	$0.435162\pi$
$98$		0			0
$99$	3.11803	−	12.3965i	0.313374	−	1.24589i
$100$		0			0
$101$	−14.3992	−	10.4616i	−1.43277	−	1.04097i	−0.989492	−	0.144587i	$-0.953815\pi$
$101$	−14.3992	−	10.4616i	−1.43277	−	1.04097i	−0.443281	−	0.896383i	$-0.646185\pi$
$102$		0			0
$103$	−2.42705	−	7.46969i	−0.239144	−	0.736011i	−0.996545	−	0.0830599i	$-0.973531\pi$
$103$	−2.42705	−	7.46969i	−0.239144	−	0.736011i	0.757400	−	0.652951i	$-0.226469\pi$
$104$		0			0
$105$	13.2082	−	9.59632i	1.28899	−	0.936505i
$106$		0			0
$107$	−3.57295	+	10.9964i	−0.345410	+	1.06306i	0.615954	+	0.787782i	$0.288771\pi$
$107$	−3.57295	+	10.9964i	−0.345410	+	1.06306i	−0.961364	+	0.275281i	$0.911229\pi$
$108$		0			0
$109$	−12.4721			−1.19461			−0.597307	−	0.802013i	$-0.703763\pi$
$109$	−12.4721			−1.19461			−0.597307	+	0.802013i	$0.703763\pi$
$110$		0			0
$111$	4.85410			0.460731
$112$		0			0
$113$	5.42705	−	16.7027i	0.510534	−	1.57126i	−0.280730	−	0.959787i	$-0.590576\pi$
$113$	5.42705	−	16.7027i	0.510534	−	1.57126i	0.791264	−	0.611475i	$-0.209424\pi$
$114$		0			0
$115$	−3.23607	+	2.35114i	−0.301765	+	0.219245i
$116$		0			0
$117$	2.83688	+	8.73102i	0.262270	+	0.807183i
$118$		0			0
$119$	7.42705	+	5.39607i	0.680837	+	0.494657i
$120$		0			0
$121$	−7.94427	+	7.60845i	−0.722207	+	0.691677i
$122$		0			0
$123$	18.2533	+	13.2618i	1.64584	+	1.19578i
$124$		0			0
$125$	3.69098	+	11.3597i	0.330132	+	1.01604i
$126$		0			0
$127$	1.92705	−	1.40008i	0.170998	−	0.124237i	−0.498995	−	0.866605i	$-0.666297\pi$
$127$	1.92705	−	1.40008i	0.170998	−	0.124237i	0.669993	+	0.742368i	$0.266297\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	9.52786			0.832453			0.416227	−	0.909261i	$-0.363352\pi$
$131$	9.52786			0.832453			0.416227	+	0.909261i	$0.363352\pi$
$132$		0			0
$133$	−14.8541			−1.28801
$134$		0			0
$135$	1.11803	−	3.44095i	0.0962250	−	0.296150i
$136$		0			0
$137$	−11.1631	+	8.11048i	−0.953730	+	0.692925i	−0.951686	−	0.307073i	$-0.900650\pi$
$137$	−11.1631	+	8.11048i	−0.953730	+	0.692925i	−0.00204358	+	0.999998i	$0.500650\pi$
$138$		0			0
$139$	3.57295	+	10.9964i	0.303054	+	0.932703i	0.980396	+	0.197035i	$0.0631314\pi$
$139$	3.57295	+	10.9964i	0.303054	+	0.932703i	−0.677343	+	0.735668i	$0.736869\pi$
$140$		0			0
$141$	2.92705	+	2.12663i	0.246502	+	0.179094i
$142$		0			0
$143$	1.92705	−	7.66145i	0.161148	−	0.640683i
$144$		0			0
$145$	11.2812	+	8.19624i	0.936849	+	0.680660i
$146$		0			0
$147$	−6.35410	−	19.5559i	−0.524077	−	1.61294i
$148$		0			0
$149$	−1.92705	+	1.40008i	−0.157870	+	0.114699i	−0.663916	−	0.747807i	$-0.731107\pi$
$149$	−1.92705	+	1.40008i	−0.157870	+	0.114699i	0.506046	+	0.862507i	$0.331107\pi$
$150$		0			0
$151$	5.95492	−	18.3273i	0.484604	−	1.49146i	−0.347949	−	0.937513i	$-0.613122\pi$
$151$	5.95492	−	18.3273i	0.484604	−	1.49146i	0.832553	−	0.553945i	$-0.186878\pi$
$152$		0			0
$153$	9.18034			0.742186
$154$		0			0
$155$	−1.38197			−0.111002
$156$		0			0
$157$	5.42705	−	16.7027i	0.433126	−	1.33302i	−0.461869	−	0.886948i	$-0.652821\pi$
$157$	5.42705	−	16.7027i	0.433126	−	1.33302i	0.894995	−	0.446076i	$-0.147179\pi$
$158$		0			0
$159$	−8.66312	+	6.29412i	−0.687030	+	0.499157i
$160$		0			0
$161$	2.94427	+	9.06154i	0.232041	+	0.714149i
$162$		0			0
$163$	−9.16312	−	6.65740i	−0.717711	−	0.521447i	0.167941	−	0.985797i	$-0.446288\pi$
$163$	−9.16312	−	6.65740i	−0.717711	−	0.521447i	−0.885652	+	0.464350i	$0.846288\pi$
$164$		0			0
$165$	−10.7812	+	9.00854i	−0.839312	+	0.701314i
$166$		0			0
$167$	−14.3992	−	10.4616i	−1.11424	−	0.809545i	−0.130916	−	0.991393i	$-0.541792\pi$
$167$	−14.3992	−	10.4616i	−1.11424	−	0.809545i	−0.983326	+	0.181849i	$0.941792\pi$
$168$		0			0
$169$	−2.26393	−	6.96767i	−0.174149	−	0.535974i
$170$		0			0
$171$	−12.0172	+	8.73102i	−0.918980	+	0.667678i
$172$		0			0
$173$	−2.10081	+	6.46564i	−0.159722	+	0.491573i	−0.998609	−	0.0527326i	$-0.983207\pi$
$173$	−2.10081	+	6.46564i	−0.159722	+	0.491573i	0.838887	+	0.544306i	$0.183207\pi$
$174$		0			0
$175$	9.18034			0.693968
$176$		0			0
$177$	−2.85410			−0.214527
$178$		0			0
$179$	−0.809017	+	2.48990i	−0.0604688	+	0.186104i	−0.976728	−	0.214482i	$-0.931194\pi$
$179$	−0.809017	+	2.48990i	−0.0604688	+	0.186104i	0.916259	+	0.400586i	$0.131194\pi$
$180$		0			0
$181$	1.30902	−	0.951057i	0.0972985	−	0.0706915i	−0.538072	−	0.842899i	$-0.680847\pi$
$181$	1.30902	−	0.951057i	0.0972985	−	0.0706915i	0.635371	+	0.772207i	$0.280847\pi$
$182$		0			0
$183$	−1.92705	−	5.93085i	−0.142452	−	0.438421i
$184$		0			0
$185$	−2.42705	−	1.76336i	−0.178440	−	0.129644i
$186$		0			0
$187$	−6.69098	−	4.20025i	−0.489293	−	0.307153i
$188$		0			0
$189$	−6.97214	−	5.06555i	−0.507148	−	0.368465i
$190$		0			0
$191$	8.04508	+	24.7602i	0.582122	+	1.79159i	0.610533	+	0.791991i	$0.290955\pi$
$191$	8.04508	+	24.7602i	0.582122	+	1.79159i	−0.0284112	+	0.999596i	$0.509045\pi$
$192$		0			0
$193$	18.2533	−	13.2618i	1.31390	−	0.954605i	0.313914	−	0.949451i	$-0.398360\pi$
$193$	18.2533	−	13.2618i	1.31390	−	0.954605i	0.999987	−	0.00515308i	$-0.00164028\pi$
$194$		0			0
$195$	3.11803	−	9.59632i	0.223287	−	0.687207i
$196$		0			0
$197$	−2.94427			−0.209771			−0.104885	−	0.994484i	$-0.533448\pi$
$197$	−2.94427			−0.209771			−0.104885	+	0.994484i	$0.533448\pi$
$198$		0			0
$199$	−0.944272			−0.0669377			−0.0334688	−	0.999440i	$-0.510655\pi$
$199$	−0.944272			−0.0669377			−0.0334688	+	0.999440i	$0.510655\pi$
$200$		0			0
$201$	−10.4721	+	32.2299i	−0.738648	+	2.27332i
$202$		0			0
$203$	26.8713	−	19.5232i	1.88600	−	1.37026i
$204$		0			0
$205$	−4.30902	−	13.2618i	−0.300955	−	0.926244i
$206$		0			0
$207$	7.70820	+	5.60034i	0.535757	+	0.389250i
$208$		0			0
$209$	12.7533	−	0.865300i	0.882163	−	0.0598540i
$210$		0			0
$211$	−9.63525	−	7.00042i	−0.663318	−	0.481929i	0.204464	−	0.978874i	$-0.434455\pi$
$211$	−9.63525	−	7.00042i	−0.663318	−	0.481929i	−0.867782	+	0.496945i	$0.834455\pi$
$212$		0			0
$213$	5.16312	+	15.8904i	0.353771	+	1.08880i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.01722	+	3.13068i	−0.0690535	+	0.212525i
$218$		0			0
$219$	2.38197			0.160958
$220$		0			0
$221$	5.67376			0.381659
$222$		0			0
$223$	−3.75329	+	11.5514i	−0.251339	+	0.773541i	0.743190	+	0.669080i	$0.233312\pi$
$223$	−3.75329	+	11.5514i	−0.251339	+	0.773541i	−0.994529	+	0.104461i	$0.966688\pi$
$224$		0			0
$225$	7.42705	−	5.39607i	0.495137	−	0.359738i
$226$		0			0
$227$	1.75329	+	5.39607i	0.116370	+	0.358150i	0.992230	−	0.124415i	$-0.0397054\pi$
$227$	1.75329	+	5.39607i	0.116370	+	0.358150i	−0.875860	+	0.482565i	$0.839705\pi$
$228$		0			0
$229$	−13.1631	−	9.56357i	−0.869843	−	0.631978i	0.0607015	−	0.998156i	$-0.480666\pi$
$229$	−13.1631	−	9.56357i	−0.869843	−	0.631978i	−0.930545	+	0.366178i	$0.880666\pi$
$230$		0			0
$231$	12.4721	+	31.0543i	0.820606	+	2.04323i
$232$		0			0
$233$	−1.92705	−	1.40008i	−0.126245	−	0.0917226i	0.522871	−	0.852412i	$-0.324861\pi$
$233$	−1.92705	−	1.40008i	−0.126245	−	0.0917226i	−0.649116	+	0.760689i	$0.724861\pi$
$234$		0			0
$235$	−0.690983	−	2.12663i	−0.0450748	−	0.138726i
$236$		0			0
$237$	−15.1353	+	10.9964i	−0.983140	+	0.714293i
$238$		0			0
$239$	−3.57295	+	10.9964i	−0.231115	+	0.711298i	0.766498	+	0.642246i	$0.221997\pi$
$239$	−3.57295	+	10.9964i	−0.231115	+	0.711298i	−0.997613	+	0.0690519i	$0.978003\pi$
$240$		0			0
$241$	12.4721			0.803401			0.401700	−	0.915771i	$-0.368419\pi$
$241$	12.4721			0.803401			0.401700	+	0.915771i	$0.368419\pi$
$242$		0			0
$243$	21.6525			1.38901
$244$		0			0
$245$	−3.92705	+	12.0862i	−0.250890	+	0.772160i
$246$		0			0
$247$	−7.42705	+	5.39607i	−0.472572	+	0.343344i
$248$		0			0
$249$	−10.5451	−	32.4544i	−0.668268	−	2.05672i
$250$		0			0
$251$	−20.8713	−	15.1639i	−1.31739	−	0.957137i	−0.999961	−	0.00885387i	$-0.997182\pi$
$251$	−20.8713	−	15.1639i	−1.31739	−	0.957137i	−0.317425	−	0.948283i	$-0.602818\pi$
$252$		0			0
$253$	−3.05573	−	7.60845i	−0.192112	−	0.478339i
$254$		0			0
$255$	−8.16312	−	5.93085i	−0.511194	−	0.371404i
$256$		0			0
$257$	−1.51722	−	4.66953i	−0.0946416	−	0.291277i	0.892518	−	0.451011i	$-0.148936\pi$
$257$	−1.51722	−	4.66953i	−0.0946416	−	0.291277i	−0.987160	+	0.159734i	$0.948936\pi$
$258$		0			0
$259$	−5.78115	+	4.20025i	−0.359223	+	0.260991i
$260$		0			0
$261$	10.2639	−	31.5891i	0.635321	−	1.95532i
$262$		0			0
$263$	5.88854			0.363103			0.181552	−	0.983381i	$-0.441888\pi$
$263$	5.88854			0.363103			0.181552	+	0.983381i	$0.441888\pi$
$264$		0			0
$265$	6.61803			0.406543
$266$		0			0
$267$	−0.381966	+	1.17557i	−0.0233759	+	0.0719437i
$268$		0			0
$269$	19.4894	−	14.1598i	1.18829	−	0.863341i	0.195205	−	0.980762i	$-0.437463\pi$
$269$	19.4894	−	14.1598i	1.18829	−	0.863341i	0.993082	+	0.117421i	$0.0374628\pi$
$270$		0			0
$271$	−5.95492	−	18.3273i	−0.361735	−	1.11331i	−0.952000	−	0.306097i	$-0.900977\pi$
$271$	−5.95492	−	18.3273i	−0.361735	−	1.11331i	0.590265	−	0.807210i	$-0.299023\pi$
$272$		0			0
$273$	−19.4443	−	14.1271i	−1.17682	−	0.855010i
$274$		0			0
$275$	−7.88197	+	0.534785i	−0.475300	+	0.0322487i
$276$		0			0
$277$	18.2533	+	13.2618i	1.09673	+	0.796824i	0.980524	−	0.196401i	$-0.0629254\pi$
$277$	18.2533	+	13.2618i	1.09673	+	0.796824i	0.116210	+	0.993225i	$0.462925\pi$
$278$		0			0
$279$	1.01722	+	3.13068i	0.0608994	+	0.187429i
$280$		0			0
$281$	−22.1074	+	16.0620i	−1.31882	+	0.958176i	−0.318870	+	0.947798i	$0.603303\pi$
$281$	−22.1074	+	16.0620i	−1.31882	+	0.958176i	−0.999946	+	0.0103778i	$0.996697\pi$
$282$		0			0
$283$	−3.57295	+	10.9964i	−0.212390	+	0.653669i	0.786939	+	0.617031i	$0.211665\pi$
$283$	−3.57295	+	10.9964i	−0.212390	+	0.653669i	−0.999329	+	0.0366375i	$0.988335\pi$
$284$		0			0
$285$	16.3262			0.967083
$286$		0			0
$287$	−33.2148			−1.96061
$288$		0			0
$289$	−3.50000	+	10.7719i	−0.205882	+	0.633641i
$290$		0			0
$291$	−30.8435	+	22.4091i	−1.80808	+	1.31364i
$292$		0			0
$293$	2.66312	+	8.19624i	0.155581	+	0.478829i	0.998219	−	0.0596508i	$-0.0189987\pi$
$293$	2.66312	+	8.19624i	0.155581	+	0.478829i	−0.842638	+	0.538480i	$0.818999\pi$
$294$		0			0
$295$	1.42705	+	1.03681i	0.0830861	+	0.0603656i
$296$		0			0
$297$	6.28115	+	3.94298i	0.364469	+	0.228795i
$298$		0			0
$299$	4.76393	+	3.46120i	0.275505	+	0.200166i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	37.6976	−	27.3889i	2.16567	−	1.57345i
$304$		0			0
$305$	−1.19098	+	3.66547i	−0.0681955	+	0.209884i
$306$		0			0
$307$	9.52786			0.543784			0.271892	−	0.962328i	$-0.412351\pi$
$307$	9.52786			0.543784			0.271892	+	0.962328i	$0.412351\pi$
$308$		0			0
$309$	20.5623			1.16975
$310$		0			0
$311$	5.19098	−	15.9762i	0.294354	−	0.905927i	−0.689084	−	0.724681i	$-0.741987\pi$
$311$	5.19098	−	15.9762i	0.294354	−	0.905927i	0.983438	−	0.181246i	$-0.0580130\pi$
$312$		0			0
$313$	6.07295	−	4.41226i	0.343263	−	0.249395i	−0.402774	−	0.915299i	$-0.631954\pi$
$313$	6.07295	−	4.41226i	0.343263	−	0.249395i	0.746037	+	0.665904i	$0.231954\pi$
$314$		0			0
$315$	7.42705	+	22.8581i	0.418467	+	1.28791i
$316$		0			0
$317$	11.7812	+	8.55951i	0.661695	+	0.480750i	0.867235	−	0.497899i	$-0.165895\pi$
$317$	11.7812	+	8.55951i	0.661695	+	0.480750i	−0.205540	+	0.978649i	$0.565895\pi$
$318$		0			0
$319$	−21.9336	+	18.3273i	−1.22805	+	1.02613i
$320$		0			0
$321$	−24.4894	−	17.7926i	−1.36686	−	0.993084i
$322$		0			0
$323$	2.83688	+	8.73102i	0.157848	+	0.485807i
$324$		0			0
$325$	4.59017	−	3.33495i	0.254617	−	0.184990i
$326$		0			0
$327$	10.0902	−	31.0543i	0.557988	−	1.71731i
$328$		0			0
$329$	−5.32624			−0.293645
$330$		0			0
$331$	−12.0000			−0.659580			−0.329790	−	0.944054i	$-0.606978\pi$
$331$	−12.0000			−0.659580			−0.329790	+	0.944054i	$0.606978\pi$
$332$		0			0
$333$	−2.20820	+	6.79615i	−0.121009	+	0.372427i
$334$		0			0
$335$	16.9443	−	12.3107i	0.925764	−	0.672607i
$336$		0			0
$337$	7.42705	+	22.8581i	0.404577	+	1.24516i	0.921248	+	0.388976i	$0.127171\pi$
$337$	7.42705	+	22.8581i	0.404577	+	1.24516i	−0.516670	+	0.856184i	$0.672829\pi$
$338$		0			0
$339$	37.1976	+	27.0256i	2.02029	+	1.46783i
$340$		0			0
$341$	0.690983	−	2.74717i	0.0374188	−	0.148768i
$342$		0			0
$343$	2.66312	+	1.93487i	0.143795	+	0.104473i
$344$		0			0
$345$	−3.23607	−	9.95959i	−0.174224	−	0.536206i
$346$		0			0
$347$	14.3992	−	10.4616i	0.772989	−	0.561609i	−0.129878	−	0.991530i	$-0.541458\pi$
$347$	14.3992	−	10.4616i	0.772989	−	0.561609i	0.902867	+	0.429921i	$0.141458\pi$
$348$		0			0
$349$	−5.04508	+	15.5272i	−0.270057	+	0.831151i	0.720428	+	0.693530i	$0.243945\pi$
$349$	−5.04508	+	15.5272i	−0.270057	+	0.831151i	−0.990485	+	0.137621i	$0.956055\pi$
$350$		0			0
$351$	−5.32624			−0.284294
$352$		0			0
$353$	−14.9443			−0.795403			−0.397702	−	0.917515i	$-0.630192\pi$
$353$	−14.9443			−0.795403			−0.397702	+	0.917515i	$0.630192\pi$
$354$		0			0
$355$	3.19098	−	9.82084i	0.169360	−	0.521236i
$356$		0			0
$357$	−19.4443	+	14.1271i	−1.02910	+	0.747685i
$358$		0			0
$359$	3.57295	+	10.9964i	0.188573	+	0.580368i	0.999992	−	0.00409736i	$-0.00130423\pi$
$359$	3.57295	+	10.9964i	0.188573	+	0.580368i	−0.811419	+	0.584465i	$0.801304\pi$
$360$		0			0
$361$	3.35410	+	2.43690i	0.176532	+	0.128258i
$362$		0			0
$363$	−12.5172	−	25.9358i	−0.656984	−	1.36128i
$364$		0			0
$365$	−1.19098	−	0.865300i	−0.0623389	−	0.0452919i
$366$		0			0
$367$	6.22542	+	19.1599i	0.324965	+	1.00014i	0.971457	+	0.237217i	$0.0762353\pi$
$367$	6.22542	+	19.1599i	0.324965	+	1.00014i	−0.646492	+	0.762921i	$0.723765\pi$
$368$		0			0
$369$	−26.8713	+	19.5232i	−1.39887	+	1.01634i
$370$		0			0
$371$	4.87132	−	14.9924i	0.252906	−	0.778366i
$372$		0			0
$373$	−6.58359			−0.340885			−0.170443	−	0.985368i	$-0.554520\pi$
$373$	−6.58359			−0.340885			−0.170443	+	0.985368i	$0.554520\pi$
$374$		0			0
$375$	−31.2705			−1.61480
$376$		0			0
$377$	6.34346	−	19.5232i	0.326705	−	1.00549i
$378$		0			0
$379$	−2.54508	+	1.84911i	−0.130732	+	0.0949825i	−0.651230	−	0.758881i	$-0.725747\pi$
$379$	−2.54508	+	1.84911i	−0.130732	+	0.0949825i	0.520497	+	0.853863i	$0.325747\pi$
$380$		0			0
$381$	1.92705	+	5.93085i	0.0987258	+	0.303847i
$382$		0			0
$383$	−16.1074	−	11.7027i	−0.823049	−	0.597980i	0.0945351	−	0.995522i	$-0.469864\pi$
$383$	−16.1074	−	11.7027i	−0.823049	−	0.597980i	−0.917584	+	0.397541i	$0.869864\pi$
$384$		0			0
$385$	5.04508	−	20.0579i	0.257121	−	1.02225i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.28115	−	25.4868i	−0.419871	−	1.29223i	−0.907821	−	0.419359i	$-0.862255\pi$
$389$	−8.28115	−	25.4868i	−0.419871	−	1.29223i	0.487950	−	0.872872i	$-0.337745\pi$
$390$		0			0
$391$	4.76393	−	3.46120i	0.240922	−	0.175040i
$392$		0			0
$393$	−7.70820	+	23.7234i	−0.388827	+	1.19669i
$394$		0			0
$395$	11.5623			0.581763
$396$		0			0
$397$	32.8328			1.64783			0.823916	−	0.566712i	$-0.191785\pi$
$397$	32.8328			1.64783			0.823916	+	0.566712i	$0.191785\pi$
$398$		0			0
$399$	12.0172	−	36.9852i	0.601614	−	1.85158i
$400$		0			0
$401$	−5.45492	+	3.96323i	−0.272405	+	0.197914i	−0.715598	−	0.698512i	$-0.753846\pi$
$401$	−5.45492	+	3.96323i	−0.272405	+	0.197914i	0.443193	+	0.896426i	$0.353846\pi$
$402$		0			0
$403$	0.628677	+	1.93487i	0.0313166	+	0.0963827i
$404$		0			0
$405$	−7.47214	−	5.42882i	−0.371293	−	0.269760i
$406$		0			0
$407$	4.71885	−	3.94298i	0.233905	−	0.195446i
$408$		0			0
$409$	5.78115	+	4.20025i	0.285860	+	0.207689i	0.721469	−	0.692447i	$-0.243467\pi$
$409$	5.78115	+	4.20025i	0.285860	+	0.207689i	−0.435610	+	0.900136i	$0.643467\pi$
$410$		0			0
$411$	−11.1631	−	34.3565i	−0.550636	−	1.69468i
$412$		0			0
$413$	3.39919	−	2.46965i	0.167263	−	0.121524i
$414$		0			0
$415$	−6.51722	+	20.0579i	−0.319918	+	0.984606i
$416$		0			0
$417$	−30.2705			−1.48235
$418$		0			0
$419$	−4.58359			−0.223923			−0.111962	−	0.993713i	$-0.535713\pi$
$419$	−4.58359			−0.223923			−0.111962	+	0.993713i	$0.535713\pi$
$420$		0			0
$421$	−2.86475	+	8.81678i	−0.139619	+	0.429704i	−0.996280	−	0.0861767i	$-0.972535\pi$
$421$	−2.86475	+	8.81678i	−0.139619	+	0.429704i	0.856661	+	0.515880i	$0.172535\pi$
$422$		0			0
$423$	−4.30902	+	3.13068i	−0.209512	+	0.152219i
$424$		0			0
$425$	−1.75329	−	5.39607i	−0.0850470	−	0.261748i
$426$		0			0
$427$	7.42705	+	5.39607i	0.359420	+	0.261134i
$428$		0			0
$429$	17.5172	+	10.9964i	0.845739	+	0.530912i
$430$		0			0
$431$	13.4894	+	9.80059i	0.649759	+	0.472078i	0.863189	−	0.504881i	$-0.168463\pi$
$431$	13.4894	+	9.80059i	0.649759	+	0.472078i	−0.213430	+	0.976958i	$0.568463\pi$
$432$		0			0
$433$	6.01064	+	18.4989i	0.288853	+	0.888998i	0.985217	+	0.171310i	$0.0547999\pi$
$433$	6.01064	+	18.4989i	0.288853	+	0.888998i	−0.696364	+	0.717689i	$0.745200\pi$
$434$		0			0
$435$	−29.5344	+	21.4580i	−1.41607	+	1.02883i
$436$		0			0
$437$	−2.94427	+	9.06154i	−0.140844	+	0.433472i
$438$		0			0
$439$	−15.4164			−0.735785			−0.367893	−	0.929868i	$-0.619921\pi$
$439$	−15.4164			−0.735785			−0.367893	+	0.929868i	$0.619921\pi$
$440$		0			0
$441$	30.2705			1.44145
$442$		0			0
$443$	1.01064	−	3.11044i	0.0480171	−	0.147781i	−0.924173	−	0.381974i	$-0.875245\pi$
$443$	1.01064	−	3.11044i	0.0480171	−	0.147781i	0.972190	+	0.234192i	$0.0752445\pi$
$444$		0			0
$445$	0.618034	−	0.449028i	0.0292976	−	0.0212860i
$446$		0			0
$447$	−1.92705	−	5.93085i	−0.0911464	−	0.280520i
$448$		0			0
$449$	11.7812	+	8.55951i	0.555987	+	0.403948i	0.829988	−	0.557781i	$-0.188347\pi$
$449$	11.7812	+	8.55951i	0.555987	+	0.403948i	−0.274001	+	0.961729i	$0.588347\pi$
$450$		0			0
$451$	28.5172	−	1.93487i	1.34282	−	0.0911094i
$452$		0			0
$453$	40.8156	+	29.6543i	1.91768	+	1.39328i
$454$		0			0
$455$	4.59017	+	14.1271i	0.215190	+	0.662288i
$456$		0			0
$457$	5.78115	−	4.20025i	0.270431	−	0.196480i	−0.444302	−	0.895877i	$-0.646548\pi$
$457$	5.78115	−	4.20025i	0.270431	−	0.196480i	0.714733	+	0.699398i	$0.246548\pi$
$458$		0			0
$459$	−1.64590	+	5.06555i	−0.0768239	+	0.236440i
$460$		0			0
$461$	−33.7771			−1.57316			−0.786578	−	0.617491i	$-0.788149\pi$
$461$	−33.7771			−1.57316			−0.786578	+	0.617491i	$0.788149\pi$
$462$		0			0
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$		0			0
$465$	1.11803	−	3.44095i	0.0518476	−	0.159570i
$466$		0			0
$467$	−10.2533	+	7.44945i	−0.474466	+	0.344719i	−0.799179	−	0.601093i	$-0.794732\pi$
$467$	−10.2533	+	7.44945i	−0.474466	+	0.344719i	0.324713	+	0.945812i	$0.394732\pi$
$468$		0			0
$469$	−15.4164	−	47.4468i	−0.711864	−	2.19089i
$470$		0			0
$471$	37.1976	+	27.0256i	1.71397	+	1.24527i
$472$		0			0
$473$		0			0
$474$		0			0
$475$	7.42705	+	5.39607i	0.340776	+	0.247589i
$476$		0			0
$477$	−4.87132	−	14.9924i	−0.223043	−	0.686454i
$478$		0			0
$479$	22.1074	−	16.0620i	1.01011	−	0.733890i	0.0458798	−	0.998947i	$-0.485391\pi$
$479$	22.1074	−	16.0620i	1.01011	−	0.733890i	0.964233	+	0.265057i	$0.0853909\pi$
$480$		0			0
$481$	−1.36475	+	4.20025i	−0.0622270	+	0.191515i
$482$		0			0
$483$	−24.9443			−1.13500
$484$		0			0
$485$	23.5623			1.06991
$486$		0			0
$487$	−5.57295	+	17.1518i	−0.252534	+	0.777221i	0.741771	+	0.670653i	$0.233986\pi$
$487$	−5.57295	+	17.1518i	−0.252534	+	0.777221i	−0.994305	+	0.106568i	$0.966014\pi$
$488$		0			0
$489$	23.9894	−	17.4293i	1.08484	−	0.788180i
$490$		0			0
$491$	3.57295	+	10.9964i	0.161245	+	0.496261i	0.998740	−	0.0501840i	$-0.0159808\pi$
$491$	3.57295	+	10.9964i	0.161245	+	0.496261i	−0.837495	+	0.546445i	$0.815981\pi$
$492$		0			0
$493$	−16.6074	−	12.0660i	−0.747959	−	0.543424i
$494$		0			0
$495$	−7.70820	−	19.1926i	−0.346458	−	0.862645i
$496$		0			0
$497$	−19.8992	−	14.4576i	−0.892601	−	0.648512i
$498$		0			0
$499$	−7.19098	−	22.1316i	−0.321913	−	0.990745i	−0.972815	−	0.231584i	$-0.925609\pi$
$499$	−7.19098	−	22.1316i	−0.321913	−	0.990745i	0.650902	−	0.759161i	$-0.274391\pi$
$500$		0			0
$501$	37.6976	−	27.3889i	1.68420	−	1.22364i
$502$		0			0
$503$	−11.2812	+	34.7198i	−0.503002	+	1.54808i	0.301102	+	0.953592i	$0.402645\pi$
$503$	−11.2812	+	34.7198i	−0.503002	+	1.54808i	−0.804104	+	0.594488i	$0.797355\pi$
$504$		0			0
$505$	−28.7984			−1.28151
$506$		0			0
$507$	19.1803			0.851829
$508$		0			0
$509$	−8.86475	+	27.2829i	−0.392923	+	1.20929i	0.537644	+	0.843172i	$0.319314\pi$
$509$	−8.86475	+	27.2829i	−0.392923	+	1.20929i	−0.930567	+	0.366121i	$0.880686\pi$
$510$		0			0
$511$	−2.83688	+	2.06111i	−0.125496	+	0.0911783i
$512$		0			0
$513$	−2.66312	−	8.19624i	−0.117580	−	0.361873i
$514$		0			0
$515$	−10.2812	−	7.46969i	−0.453042	−	0.329154i
$516$		0			0
$517$	4.57295	−	0.310271i	0.201118	−	0.0136457i
$518$		0			0
$519$	−14.3992	−	10.4616i	−0.632054	−	0.459214i
$520$		0			0
$521$	2.37132	+	7.29818i	0.103890	+	0.319739i	0.989468	−	0.144750i	$-0.0462379\pi$
$521$	2.37132	+	7.29818i	0.103890	+	0.319739i	−0.885579	+	0.464489i	$0.846238\pi$
$522$		0			0
$523$	−23.0172	+	16.7230i	−1.00647	+	0.731245i	−0.963466	−	0.267830i	$-0.913694\pi$
$523$	−23.0172	+	16.7230i	−1.00647	+	0.731245i	−0.0430065	+	0.999075i	$0.513694\pi$
$524$		0			0
$525$	−7.42705	+	22.8581i	−0.324143	+	0.997610i
$526$		0			0
$527$	2.03444			0.0886217
$528$		0			0
$529$	−16.8885			−0.734285
$530$		0			0
$531$	1.29837	−	3.99598i	0.0563446	−	0.173411i
$532$		0			0
$533$	−16.6074	+	12.0660i	−0.719346	+	0.522635i
$534$		0			0
$535$	5.78115	+	17.7926i	0.249941	+	0.769239i
$536$		0			0
$537$	−5.54508	−	4.02874i	−0.239288	−	0.173853i
$538$		0			0
$539$	−22.0623	−	13.8496i	−0.950291	−	0.596543i
$540$		0			0
$541$	−6.69098	−	4.86128i	−0.287668	−	0.209003i	0.434587	−	0.900630i	$-0.356894\pi$
$541$	−6.69098	−	4.86128i	−0.287668	−	0.209003i	−0.722255	+	0.691627i	$0.756894\pi$
$542$		0			0
$543$	1.30902	+	4.02874i	0.0561753	+	0.172890i
$544$		0			0
$545$	−16.3262	+	11.8617i	−0.699339	+	0.508100i
$546$		0			0
$547$	11.8435	−	36.4504i	0.506390	−	1.55851i	−0.292032	−	0.956409i	$-0.594331\pi$
$547$	11.8435	−	36.4504i	0.506390	−	1.55851i	0.798422	−	0.602099i	$-0.205669\pi$
$548$		0			0
$549$	9.18034			0.391807
$550$		0			0
$551$	33.2148			1.41500
$552$		0			0
$553$	8.51064	−	26.1931i	0.361909	−	1.11384i
$554$		0			0
$555$	6.35410	−	4.61653i	0.269717	−	0.195961i
$556$		0			0
$557$	−9.80902	−	30.1891i	−0.415621	−	1.27915i	−0.911694	−	0.410870i	$-0.865225\pi$
$557$	−9.80902	−	30.1891i	−0.415621	−	1.27915i	0.496073	−	0.868281i	$-0.334775\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	15.8713	−	13.2618i	0.670088	−	0.559913i
$562$		0			0
$563$	10.5451	+	7.66145i	0.444422	+	0.322892i	0.787390	−	0.616456i	$-0.211432\pi$
$563$	10.5451	+	7.66145i	0.444422	+	0.322892i	−0.342967	+	0.939347i	$0.611432\pi$
$564$		0			0
$565$	−8.78115	−	27.0256i	−0.369426	−	1.13698i
$566$		0			0
$567$	−17.7984	+	12.9313i	−0.747461	+	0.543063i
$568$		0			0
$569$	9.24671	−	28.4585i	0.387642	−	1.19304i	−0.546903	−	0.837196i	$-0.684193\pi$
$569$	9.24671	−	28.4585i	0.387642	−	1.19304i	0.934545	−	0.355844i	$-0.115807\pi$
$570$		0			0
$571$	9.52786			0.398729			0.199364	−	0.979925i	$-0.436112\pi$
$571$	9.52786			0.398729			0.199364	+	0.979925i	$0.436112\pi$
$572$		0			0
$573$	−68.1591			−2.84739
$574$		0			0
$575$	1.81966	−	5.60034i	0.0758851	−	0.233550i
$576$		0			0
$577$	29.1976	−	21.2133i	1.21551	−	0.883120i	0.219791	−	0.975547i	$-0.429462\pi$
$577$	29.1976	−	21.2133i	1.21551	−	0.883120i	0.995719	+	0.0924270i	$0.0294625\pi$
$578$		0			0
$579$	18.2533	+	56.1778i	0.758581	+	2.33467i
$580$		0			0
$581$	40.6418	+	29.5280i	1.68611	+	1.22503i
$582$		0			0
$583$	−3.30902	+	13.1558i	−0.137045	+	0.544857i
$584$		0			0
$585$	12.0172	+	8.73102i	0.496851	+	0.360983i
$586$		0			0
$587$	−2.42705	−	7.46969i	−0.100175	−	0.308307i	0.888393	−	0.459084i	$-0.151822\pi$
$587$	−2.42705	−	7.46969i	−0.100175	−	0.308307i	−0.988568	+	0.150777i	$0.951822\pi$
$588$		0			0
$589$	−2.66312	+	1.93487i	−0.109732	+	0.0797249i
$590$		0			0
$591$	2.38197	−	7.33094i	0.0979810	−	0.301554i
$592$		0			0
$593$	37.4164			1.53651			0.768254	−	0.640145i	$-0.221126\pi$
$593$	37.4164			1.53651			0.768254	+	0.640145i	$0.221126\pi$
$594$		0			0
$595$	14.8541			0.608959
$596$		0			0
$597$	0.763932	−	2.35114i	0.0312657	−	0.0962258i
$598$		0			0
$599$	−37.1976	+	27.0256i	−1.51985	+	1.10424i	−0.558290	+	0.829646i	$0.688542\pi$
$599$	−37.1976	+	27.0256i	−1.51985	+	1.10424i	−0.961561	+	0.274591i	$0.911458\pi$
$600$		0			0
$601$	10.3713	+	31.9196i	0.423055	+	1.30203i	0.904844	+	0.425743i	$0.139987\pi$
$601$	10.3713	+	31.9196i	0.423055	+	1.30203i	−0.481789	+	0.876287i	$0.660013\pi$
$602$		0			0
$603$	−40.3607	−	29.3238i	−1.64361	−	1.19416i
$604$		0			0
$605$	−3.16312	+	17.5150i	−0.128599	+	0.712088i
$606$		0			0
$607$	−17.3435	−	12.6008i	−0.703949	−	0.511449i	0.177267	−	0.984163i	$-0.443274\pi$
$607$	−17.3435	−	12.6008i	−0.703949	−	0.511449i	−0.881216	+	0.472714i	$0.843274\pi$
$608$		0			0
$609$	26.8713	+	82.7014i	1.08888	+	3.35123i
$610$		0			0
$611$	−2.66312	+	1.93487i	−0.107738	+	0.0782764i
$612$		0			0
$613$	−3.22542	+	9.92684i	−0.130274	+	0.400941i	−0.994825	−	0.101603i	$-0.967603\pi$
$613$	−3.22542	+	9.92684i	−0.130274	+	0.400941i	0.864551	+	0.502545i	$0.167603\pi$
$614$		0			0
$615$	36.5066			1.47209
$616$		0			0
$617$	−7.52786			−0.303060			−0.151530	−	0.988453i	$-0.548420\pi$
$617$	−7.52786			−0.303060			−0.151530	+	0.988453i	$0.548420\pi$
$618$		0			0
$619$	6.89919	−	21.2335i	0.277302	−	0.853447i	−0.711299	−	0.702889i	$-0.751893\pi$
$619$	6.89919	−	21.2335i	0.277302	−	0.853447i	0.988601	−	0.150558i	$-0.0481070\pi$
$620$		0			0
$621$	−4.47214	+	3.24920i	−0.179461	+	0.130386i
$622$		0			0
$623$	−0.562306	−	1.73060i	−0.0225283	−	0.0693350i
$624$		0			0
$625$	6.00000	+	4.35926i	0.240000	+	0.174370i
$626$		0			0
$627$	−8.16312	+	32.4544i	−0.326004	+	1.29611i
$628$		0			0
$629$	3.57295	+	2.59590i	0.142463	+	0.103505i
$630$		0			0
$631$	−7.37132	−	22.6866i	−0.293448	−	0.903139i	−0.983738	−	0.179607i	$-0.942517\pi$
$631$	−7.37132	−	22.6866i	−0.293448	−	0.903139i	0.690291	−	0.723532i	$-0.257483\pi$
$632$		0			0
$633$	25.2254	−	18.3273i	1.00262	−	0.728447i
$634$		0			0
$635$	1.19098	−	3.66547i	0.0472627	−	0.145460i
$636$		0			0
$637$	18.7082			0.741246
$638$		0			0
$639$	−24.5967			−0.973032
$640$		0			0
$641$	8.37132	−	25.7643i	0.330647	−	1.01763i	−0.638179	−	0.769888i	$-0.720312\pi$
$641$	8.37132	−	25.7643i	0.330647	−	1.01763i	0.968827	−	0.247740i	$-0.0796879\pi$
$642$		0			0
$643$	9.92705	−	7.21242i	0.391485	−	0.284430i	−0.374579	−	0.927195i	$-0.622213\pi$
$643$	9.92705	−	7.21242i	0.391485	−	0.284430i	0.766064	+	0.642765i	$0.222213\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.45492	−	3.96323i	−0.214455	−	0.155811i	0.475372	−	0.879785i	$-0.342313\pi$
$647$	−5.45492	−	3.96323i	−0.214455	−	0.155811i	−0.689827	+	0.723974i	$0.742313\pi$
$648$		0			0
$649$	−2.77458	+	2.31838i	−0.108912	+	0.0910046i
$650$		0			0
$651$	−6.97214	−	5.06555i	−0.273260	−	0.198535i
$652$		0			0
$653$	2.37132	+	7.29818i	0.0927970	+	0.285600i	0.986673	−	0.162714i	$-0.0520247\pi$
$653$	2.37132	+	7.29818i	0.0927970	+	0.285600i	−0.893876	+	0.448314i	$0.852025\pi$
$654$		0			0
$655$	12.4721	−	9.06154i	0.487327	−	0.354064i
$656$		0			0
$657$	−1.08359	+	3.33495i	−0.0422750	+	0.130109i
$658$		0			0
$659$	40.3607			1.57223			0.786114	−	0.618081i	$-0.212090\pi$
$659$	40.3607			1.57223			0.786114	+	0.618081i	$0.212090\pi$
$660$		0			0
$661$	−30.3607			−1.18089			−0.590447	−	0.807077i	$-0.701048\pi$
$661$	−30.3607			−1.18089			−0.590447	+	0.807077i	$0.701048\pi$
$662$		0			0
$663$	−4.59017	+	14.1271i	−0.178267	+	0.548651i
$664$		0			0
$665$	−19.4443	+	14.1271i	−0.754017	+	0.547825i
$666$		0			0
$667$	−6.58359	−	20.2622i	−0.254918	−	0.784556i
$668$		0			0
$669$	−25.7254	−	18.6906i	−0.994602	−	0.722621i
$670$		0			0
$671$	−6.69098	−	4.20025i	−0.258303	−	0.162149i
$672$		0			0
$673$	−29.8156	−	21.6623i	−1.14931	−	0.835020i	−0.160918	−	0.986968i	$-0.551446\pi$
$673$	−29.8156	−	21.6623i	−1.14931	−	0.835020i	−0.988389	+	0.151948i	$0.951446\pi$
$674$		0			0
$675$	1.64590	+	5.06555i	0.0633506	+	0.194973i
$676$		0			0
$677$	2.83688	−	2.06111i	0.109030	−	0.0792151i	−0.531934	−	0.846786i	$-0.678535\pi$
$677$	2.83688	−	2.06111i	0.109030	−	0.0792151i	0.640964	+	0.767571i	$0.278535\pi$
$678$		0			0
$679$	17.3435	−	53.3777i	0.665581	−	2.04845i
$680$		0			0
$681$	−14.8541			−0.569210
$682$		0			0
$683$	−0.944272			−0.0361316			−0.0180658	−	0.999837i	$-0.505751\pi$
$683$	−0.944272			−0.0361316			−0.0180658	+	0.999837i	$0.505751\pi$
$684$		0			0
$685$	−6.89919	+	21.2335i	−0.263604	+	0.811291i
$686$		0			0
$687$	34.4615	−	25.0377i	1.31479	−	0.955249i
$688$		0			0
$689$	−3.01064	−	9.26581i	−0.114696	−	0.352999i
$690$		0			0
$691$	19.4894	+	14.1598i	0.741410	+	0.538666i	0.893152	−	0.449754i	$-0.148488\pi$
$691$	19.4894	+	14.1598i	0.741410	+	0.538666i	−0.151742	+	0.988420i	$0.548488\pi$
$692$		0			0
$693$	−49.1525	+	3.33495i	−1.86715	+	0.126684i
$694$		0			0
$695$	15.1353	+	10.9964i	0.574113	+	0.417117i
$696$		0			0
$697$	6.34346	+	19.5232i	0.240276	+	0.739492i
$698$		0			0
$699$	5.04508	−	3.66547i	0.190823	−	0.138641i
$700$		0			0
$701$	15.1353	−	46.5815i	0.571651	−	1.75936i	−0.0756600	−	0.997134i	$-0.524106\pi$
$701$	15.1353	−	46.5815i	0.571651	−	1.75936i	0.647311	−	0.762226i	$-0.275894\pi$
$702$		0			0
$703$	−7.14590			−0.269513
$704$		0			0
$705$	5.85410			0.220478
$706$		0			0
$707$	−21.1976	+	65.2394i	−0.797216	+	2.45358i
$708$		0			0
$709$	−18.8713	+	13.7108i	−0.708727	+	0.514921i	−0.882763	−	0.469819i	$-0.844319\pi$
$709$	−18.8713	+	13.7108i	−0.708727	+	0.514921i	0.174035	+	0.984739i	$0.444319\pi$
$710$		0			0
$711$	−8.51064	−	26.1931i	−0.319174	−	0.982317i
$712$		0			0
$713$	1.70820	+	1.24108i	0.0639727	+	0.0464789i
$714$		0			0
$715$	−4.76393	−	11.8617i	−0.178161	−	0.443603i
$716$		0			0
$717$	−24.4894	−	17.7926i	−0.914572	−	0.664475i
$718$		0			0
$719$	−12.1353	−	37.3485i	−0.452569	−	1.39286i	−0.873966	−	0.485987i	$-0.838460\pi$
$719$	−12.1353	−	37.3485i	−0.452569	−	1.39286i	0.421397	−	0.906876i	$-0.361540\pi$
$720$		0			0
$721$	−24.4894	+	17.7926i	−0.912031	+	0.662630i
$722$		0			0
$723$	−10.0902	+	31.0543i	−0.375257	+	1.15492i
$724$		0			0
$725$	−20.5279			−0.762386
$726$		0			0
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$		0			0
$729$	−12.2254	+	37.6260i	−0.452794	+	1.39356i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	10.3713	+	31.9196i	0.383074	+	1.17898i	0.937868	+	0.346992i	$0.112797\pi$
$733$	10.3713	+	31.9196i	0.383074	+	1.17898i	−0.554795	+	0.831987i	$0.687203\pi$
$734$		0			0
$735$	−26.9164	−	19.5559i	−0.992827	−	0.721331i
$736$		0			0
$737$	16.0000	+	39.8384i	0.589368	+	1.46747i
$738$		0			0
$739$	−19.1631	−	13.9228i	−0.704927	−	0.512159i	0.176606	−	0.984282i	$-0.443488\pi$
$739$	−19.1631	−	13.9228i	−0.704927	−	0.512159i	−0.881533	+	0.472122i	$0.843488\pi$
$740$		0			0
$741$	−7.42705	−	22.8581i	−0.272840	−	0.839714i
$742$		0			0
$743$	−2.83688	+	2.06111i	−0.104075	+	0.0756150i	−0.638606	−	0.769534i	$-0.720488\pi$
$743$	−2.83688	+	2.06111i	−0.104075	+	0.0756150i	0.534531	+	0.845149i	$0.320488\pi$
$744$		0			0
$745$	−1.19098	+	3.66547i	−0.0436342	+	0.134292i
$746$		0			0
$747$	50.2361			1.83804
$748$		0			0
$749$	44.5623			1.62827
$750$		0			0
$751$	2.13525	−	6.57164i	0.0779166	−	0.239803i	−0.904510	−	0.426453i	$-0.859763\pi$
$751$	2.13525	−	6.57164i	0.0779166	−	0.239803i	0.982426	+	0.186650i	$0.0597631\pi$
$752$		0			0
$753$	54.6418	−	39.6996i	1.99126	−	1.44673i
$754$		0			0
$755$	−9.63525	−	29.6543i	−0.350663	−	1.07923i
$756$		0			0
$757$	−21.6353	−	15.7189i	−0.786347	−	0.571314i	0.120530	−	0.992710i	$-0.461540\pi$
$757$	−21.6353	−	15.7189i	−0.786347	−	0.571314i	−0.906877	+	0.421395i	$0.861540\pi$
$758$		0			0
$759$	21.4164	−	1.45309i	0.777366	−	0.0527436i
$760$		0			0
$761$	15.3090	+	11.1227i	0.554951	+	0.403196i	0.829608	−	0.558347i	$-0.188564\pi$
$761$	15.3090	+	11.1227i	0.554951	+	0.403196i	−0.274656	+	0.961542i	$0.588564\pi$
$762$		0			0
$763$	14.8541	+	45.7162i	0.537755	+	1.65504i
$764$		0			0
$765$	12.0172	−	8.73102i	0.434484	−	0.315671i
$766$		0			0
$767$	0.802439	−	2.46965i	0.0289744	−	0.0891740i
$768$		0			0
$769$	37.4164			1.34927			0.674635	−	0.738151i	$-0.264301\pi$
$769$	37.4164			1.34927			0.674635	+	0.738151i	$0.264301\pi$
$770$		0			0
$771$	12.8541			0.462929
$772$		0			0
$773$	−8.75329	+	26.9399i	−0.314834	+	0.968959i	0.660989	+	0.750396i	$0.270137\pi$
$773$	−8.75329	+	26.9399i	−0.314834	+	0.968959i	−0.975823	+	0.218563i	$0.929863\pi$
$774$		0			0
$775$	1.64590	−	1.19581i	0.0591224	−	0.0429549i
$776$		0			0
$777$	−5.78115	−	17.7926i	−0.207398	−	0.638305i
$778$		0			0
$779$	−26.8713	−	19.5232i	−0.962765	−	0.699490i
$780$		0			0
$781$	17.9271	+	11.2537i	0.641480	+	0.402688i
$782$		0			0
$783$	15.5902	+	11.3269i	0.557147	+	0.404791i
$784$		0			0
$785$	−8.78115	−	27.0256i	−0.313413	−	0.964585i
$786$		0			0
$787$	−13.4894	+	9.80059i	−0.480844	+	0.349353i	−0.801652	−	0.597791i	$-0.796045\pi$
$787$	−13.4894	+	9.80059i	−0.480844	+	0.349353i	0.320809	+	0.947144i	$0.396045\pi$
$788$		0			0
$789$	−4.76393	+	14.6619i	−0.169600	+	0.521977i
$790$		0			0
$791$	−67.6869			−2.40667
$792$		0			0
$793$	5.67376			0.201481
$794$		0			0
$795$	−5.35410	+	16.4782i	−0.189890	+	0.584423i
$796$		0			0
$797$	−11.1631	+	8.11048i	−0.395418	+	0.287288i	−0.767672	−	0.640843i	$-0.778585\pi$
$797$	−11.1631	+	8.11048i	−0.395418	+	0.287288i	0.372254	+	0.928131i	$0.378585\pi$
$798$		0			0
$799$	1.01722	+	3.13068i	0.0359867	+	0.110756i
$800$		0			0
$801$	−1.47214	−	1.06957i	−0.0520154	−	0.0377914i
$802$		0			0
$803$	2.31559	−	1.93487i	0.0817156	−	0.0682801i
$804$		0			0
$805$	12.4721	+	9.06154i	0.439585	+	0.319377i
$806$		0			0
$807$	19.4894	+	59.9821i	0.686058	+	2.11147i
$808$		0			0
$809$	15.3090	−	11.1227i	0.538236	−	0.391052i	−0.285193	−	0.958470i	$-0.592058\pi$
$809$	15.3090	−	11.1227i	0.538236	−	0.391052i	0.823430	+	0.567418i	$0.192058\pi$
$810$		0			0
$811$	−9.46149	+	29.1195i	−0.332238	+	1.02252i	0.635829	+	0.771830i	$0.280658\pi$
$811$	−9.46149	+	29.1195i	−0.332238	+	1.02252i	−0.968067	+	0.250693i	$0.919342\pi$
$812$		0			0
$813$	50.4508			1.76939
$814$		0			0
$815$	−18.3262			−0.641940
$816$		0			0
$817$		0			0
$818$		0			0
$819$	28.6246	−	20.7970i	1.00022	−	0.726706i
$820$		0			0
$821$	−7.98936	−	24.5887i	−0.278830	−	0.858152i	−0.988180	−	0.153295i	$-0.951011\pi$
$821$	−7.98936	−	24.5887i	−0.278830	−	0.858152i	0.709350	−	0.704857i	$-0.248989\pi$
$822$		0			0
$823$	31.9615	+	23.2214i	1.11411	+	0.809447i	0.983306	−	0.181962i	$-0.0582448\pi$
$823$	31.9615	+	23.2214i	1.11411	+	0.809447i	0.130802	+	0.991409i	$0.458245\pi$
$824$		0			0
$825$	5.04508	−	20.0579i	0.175647	−	0.698328i
$826$		0			0
$827$	10.5451	+	7.66145i	0.366689	+	0.266415i	0.755836	−	0.654760i	$-0.227231\pi$
$827$	10.5451	+	7.66145i	0.366689	+	0.266415i	−0.389148	+	0.921175i	$0.627231\pi$
$828$		0			0
$829$	10.7746	+	33.1607i	0.374216	+	1.15172i	0.944006	+	0.329929i	$0.107025\pi$
$829$	10.7746	+	33.1607i	0.374216	+	1.15172i	−0.569789	+	0.821791i	$0.692975\pi$
$830$		0			0
$831$	−47.7877	+	34.7198i	−1.65774	+	1.20442i
$832$		0			0
$833$	5.78115	−	17.7926i	0.200305	−	0.616476i
$834$		0			0
$835$	−28.7984			−0.996609
$836$		0			0
$837$	−1.90983			−0.0660134
$838$		0			0
$839$	−0.809017	+	2.48990i	−0.0279304	+	0.0859608i	−0.964050	−	0.265721i	$-0.914390\pi$
$839$	−0.809017	+	2.48990i	−0.0279304	+	0.0859608i	0.936120	+	0.351682i	$0.114390\pi$
$840$		0			0
$841$	−36.6246	+	26.6093i	−1.26292	+	0.917563i
$842$		0			0
$843$	−22.1074	−	68.0396i	−0.761419	−	2.34341i
$844$		0			0
$845$	−9.59017	−	6.96767i	−0.329912	−	0.239695i
$846$		0			0
$847$	37.3500	+	20.0579i	1.28336	+	0.689199i
$848$		0			0
$849$	−24.4894	−	17.7926i	−0.840473	−	0.610639i
$850$		0			0
$851$	1.41641	+	4.35926i	0.0485538	+	0.149433i
$852$		0			0
$853$	−14.3992	+	10.4616i	−0.493019	+	0.358199i	−0.806344	−	0.591447i	$-0.798557\pi$
$853$	−14.3992	+	10.4616i	−0.493019	+	0.358199i	0.313325	+	0.949646i	$0.398557\pi$
$854$		0			0
$855$	−7.42705	+	22.8581i	−0.254000	+	0.781731i
$856$		0			0
$857$	2.94427			0.100574			0.0502872	−	0.998735i	$-0.483986\pi$
$857$	2.94427			0.100574			0.0502872	+	0.998735i	$0.483986\pi$
$858$		0			0
$859$	−31.0557			−1.05961			−0.529804	−	0.848120i	$-0.677734\pi$
$859$	−31.0557			−1.05961			−0.529804	+	0.848120i	$0.677734\pi$
$860$		0			0
$861$	26.8713	−	82.7014i	0.915772	−	2.81846i
$862$		0			0
$863$	20.3992	−	14.8209i	0.694396	−	0.504509i	−0.183706	−	0.982981i	$-0.558809\pi$
$863$	20.3992	−	14.8209i	0.694396	−	0.504509i	0.878102	+	0.478473i	$0.158809\pi$
$864$		0			0
$865$	3.39919	+	10.4616i	0.115576	+	0.355706i
$866$		0			0
$867$	−23.9894	−	17.4293i	−0.814721	−	0.591930i
$868$		0			0
$869$	−5.78115	+	22.9844i	−0.196112	+	0.779691i
$870$		0			0
$871$	−24.9443	−	18.1231i	−0.845204	−	0.614077i
$872$		0			0
$873$	−17.3435	−	53.3777i	−0.586987	−	1.80656i
$874$		0			0
$875$	37.2426	−	27.0584i	1.25903	−	0.914740i
$876$		0			0
$877$	8.55166	−	26.3193i	0.288769	−	0.888740i	−0.696474	−	0.717582i	$-0.745249\pi$
$877$	8.55166	−	26.3193i	0.288769	−	0.888740i	0.985244	−	0.171158i	$-0.0547510\pi$
$878$		0			0
$879$	−22.5623			−0.761008
$880$		0			0
$881$	15.8885			0.535299			0.267649	−	0.963516i	$-0.413753\pi$
$881$	15.8885			0.535299			0.267649	+	0.963516i	$0.413753\pi$
$882$		0			0
$883$	1.55166	−	4.77553i	0.0522176	−	0.160709i	−0.921547	−	0.388267i	$-0.873074\pi$
$883$	1.55166	−	4.77553i	0.0522176	−	0.160709i	0.973765	+	0.227557i	$0.0730739\pi$
$884$		0			0
$885$	−3.73607	+	2.71441i	−0.125587	+	0.0912440i
$886$		0			0
$887$	0.628677	+	1.93487i	0.0211089	+	0.0649665i	0.961056	−	0.276353i	$-0.0891260\pi$
$887$	0.628677	+	1.93487i	0.0211089	+	0.0649665i	−0.939947	+	0.341320i	$0.889126\pi$
$888$		0			0
$889$	−7.42705	−	5.39607i	−0.249095	−	0.180978i
$890$		0			0
$891$	14.5279	−	12.1392i	0.486702	−	0.406679i
$892$		0			0
$893$	−4.30902	−	3.13068i	−0.144196	−	0.104764i
$894$		0			0
$895$	1.30902	+	4.02874i	0.0437556	+	0.134666i
$896$		0			0
$897$	−12.4721	+	9.06154i	−0.416432	+	0.302556i
$898$		0			0
$899$	2.27458	−	7.00042i	0.0758613	−	0.233477i
$900$		0			0
$901$	−9.74265			−0.324575
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.809017	−	2.48990i	0.0268926	−	0.0827670i
$906$		0			0
$907$	−1.60081	+	1.16306i	−0.0531541	+	0.0386187i	−0.614045	−	0.789271i	$-0.710459\pi$
$907$	−1.60081	+	1.16306i	−0.0531541	+	0.0386187i	0.560891	+	0.827890i	$0.310459\pi$
$908$		0			0
$909$	21.1976	+	65.2394i	0.703079	+	2.16385i
$910$		0			0
$911$	15.7812	+	11.4657i	0.522853	+	0.379875i	0.817678	−	0.575676i	$-0.195261\pi$
$911$	15.7812	+	11.4657i	0.522853	+	0.379875i	−0.294825	+	0.955551i	$0.595261\pi$
$912$		0			0
$913$	−36.6140	−	22.9844i	−1.21175	−	0.760671i
$914$		0			0
$915$	−8.16312	−	5.93085i	−0.269864	−	0.196068i
$916$		0			0
$917$	−11.3475	−	34.9241i	−0.374728	−	1.15330i
$918$		0			0
$919$	17.3435	−	12.6008i	0.572108	−	0.415661i	−0.263762	−	0.964588i	$-0.584963\pi$
$919$	17.3435	−	12.6008i	0.572108	−	0.415661i	0.835870	+	0.548927i	$0.184963\pi$
$920$		0			0
$921$	−7.70820	+	23.7234i	−0.253994	+	0.781713i
$922$		0			0
$923$	−15.2016			−0.500368
$924$		0			0
$925$	4.41641			0.145211
$926$		0			0
$927$	−9.35410	+	28.7890i	−0.307229	+	0.945554i
$928$		0			0
$929$	−16.1074	+	11.7027i	−0.528466	+	0.383953i	−0.819784	−	0.572673i	$-0.805906\pi$
$929$	−16.1074	+	11.7027i	−0.528466	+	0.383953i	0.291317	+	0.956626i	$0.405906\pi$
$930$		0			0
$931$	9.35410	+	28.7890i	0.306568	+	0.943520i
$932$		0			0
$933$	35.5795	+	25.8500i	1.16482	+	0.846292i
$934$		0			0
$935$	−12.7533	+	0.865300i	−0.417077	+	0.0282983i
$936$		0			0
$937$	5.78115	+	4.20025i	0.188862	+	0.137216i	0.678198	−	0.734879i	$-0.262761\pi$
$937$	5.78115	+	4.20025i	0.188862	+	0.137216i	−0.489336	+	0.872095i	$0.662761\pi$
$938$		0			0
$939$	6.07295	+	18.6906i	0.198183	+	0.609945i
$940$		0			0
$941$	−9.63525	+	7.00042i	−0.314100	+	0.228207i	−0.733654	−	0.679523i	$-0.762187\pi$
$941$	−9.63525	+	7.00042i	−0.314100	+	0.228207i	0.419554	+	0.907731i	$0.362187\pi$
$942$		0			0
$943$	−6.58359	+	20.2622i	−0.214391	+	0.659828i
$944$		0			0
$945$	−13.9443			−0.453607
$946$		0			0
$947$	−23.7771			−0.772652			−0.386326	−	0.922362i	$-0.626256\pi$
$947$	−23.7771			−0.772652			−0.386326	+	0.922362i	$0.626256\pi$
$948$		0			0
$949$	−0.669697	+	2.06111i	−0.0217393	+	0.0669066i
$950$		0			0
$951$	−30.8435	+	22.4091i	−1.00017	+	0.726664i
$952$		0			0
$953$	14.0106	+	43.1203i	0.453849	+	1.39680i	0.872481	+	0.488648i	$0.162510\pi$
$953$	14.0106	+	43.1203i	0.453849	+	1.39680i	−0.418632	+	0.908156i	$0.637490\pi$
$954$		0			0
$955$	34.0795	+	24.7602i	1.10279	+	0.801222i
$956$		0			0
$957$	−27.8885	−	69.4396i	−0.901509	−	2.24466i
$958$		0			0
$959$	43.0238	+	31.2586i	1.38931	+	1.00939i
$960$		0			0
$961$	−9.35410	−	28.7890i	−0.301745	−	0.928676i
$962$		0			0
$963$	36.0517	−	26.1931i	1.16175	−	0.844060i
$964$		0			0
$965$	11.2812	−	34.7198i	0.363153	−	1.11767i
$966$		0			0
$967$	44.0000			1.41494			0.707472	−	0.706741i	$-0.249835\pi$
$967$	44.0000			1.41494			0.707472	+	0.706741i	$0.249835\pi$
$968$		0			0
$969$	−24.0344			−0.772098
$970$		0			0
$971$	2.13525	−	6.57164i	0.0685236	−	0.210894i	−0.910931	−	0.412559i	$-0.864635\pi$
$971$	2.13525	−	6.57164i	0.0685236	−	0.210894i	0.979455	+	0.201665i	$0.0646352\pi$
$972$		0			0
$973$	36.0517	−	26.1931i	1.15576	−	0.839711i
$974$		0			0
$975$	4.59017	+	14.1271i	0.147003	+	0.452429i
$976$		0			0
$977$	16.5451	+	12.0207i	0.529324	+	0.384577i	0.820105	−	0.572213i	$-0.193915\pi$
$977$	16.5451	+	12.0207i	0.529324	+	0.384577i	−0.290781	+	0.956790i	$0.593915\pi$
$978$		0			0
$979$	0.583592	+	1.45309i	0.0186517	+	0.0464408i
$980$		0			0
$981$	38.8885	+	28.2542i	1.24162	+	0.902087i
$982$		0			0
$983$	−12.1353	−	37.3485i	−0.387055	−	1.19123i	−0.934979	−	0.354703i	$-0.884582\pi$
$983$	−12.1353	−	37.3485i	−0.387055	−	1.19123i	0.547924	−	0.836528i	$-0.315418\pi$
$984$		0			0
$985$	−3.85410	+	2.80017i	−0.122802	+	0.0892208i
$986$		0			0
$987$	4.30902	−	13.2618i	0.137158	−	0.422127i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	24.0000			0.762385			0.381193	−	0.924496i	$-0.375513\pi$
$991$	24.0000			0.762385			0.381193	+	0.924496i	$0.375513\pi$
$992$		0			0
$993$	9.70820	−	29.8788i	0.308081	−	0.948174i
$994$		0			0
$995$	−1.23607	+	0.898056i	−0.0391860	+	0.0284703i
$996$		0			0
$997$	9.24671	+	28.4585i	0.292846	+	0.901288i	0.983936	+	0.178520i	$0.0571308\pi$
$997$	9.24671	+	28.4585i	0.292846	+	0.901288i	−0.691090	+	0.722769i	$0.742869\pi$
$998$		0			0
$999$	−3.35410	−	2.43690i	−0.106119	−	0.0771000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	44.2.e.a.37.1	yes	4
3.2	odd	2		396.2.j.a.37.1		4
4.3	odd	2		176.2.m.b.81.1		4
5.2	odd	4		1100.2.cb.a.1049.2		8
5.3	odd	4		1100.2.cb.a.1049.1		8
5.4	even	2		1100.2.n.a.301.1		4
8.3	odd	2		704.2.m.d.257.1		4
8.5	even	2		704.2.m.e.257.1		4
11.2	odd	10		484.2.e.d.269.1		4
11.3	even	5	inner	44.2.e.a.25.1	✓	4
11.4	even	5		484.2.e.e.9.1		4
11.5	even	5		484.2.a.b.1.1		2
11.6	odd	10		484.2.a.c.1.1		2
11.7	odd	10		484.2.e.d.9.1		4
11.8	odd	10		484.2.e.c.245.1		4
11.9	even	5		484.2.e.e.269.1		4
11.10	odd	2		484.2.e.c.81.1		4
33.5	odd	10		4356.2.a.t.1.2		2
33.14	odd	10		396.2.j.a.289.1		4
33.17	even	10		4356.2.a.u.1.2		2
44.3	odd	10		176.2.m.b.113.1		4
44.27	odd	10		1936.2.a.ba.1.2		2
44.39	even	10		1936.2.a.z.1.2		2
55.3	odd	20		1100.2.cb.a.949.2		8
55.14	even	10		1100.2.n.a.201.1		4
55.47	odd	20		1100.2.cb.a.949.1		8
88.3	odd	10		704.2.m.d.641.1		4
88.5	even	10		7744.2.a.da.1.2		2
88.27	odd	10		7744.2.a.bp.1.1		2
88.61	odd	10		7744.2.a.db.1.2		2
88.69	even	10		704.2.m.e.641.1		4
88.83	even	10		7744.2.a.bo.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.e.a.25.1	✓	4	11.3	even	5	inner
44.2.e.a.37.1	yes	4	1.1	even	1	trivial
176.2.m.b.81.1		4	4.3	odd	2
176.2.m.b.113.1		4	44.3	odd	10
396.2.j.a.37.1		4	3.2	odd	2
396.2.j.a.289.1		4	33.14	odd	10
484.2.a.b.1.1		2	11.5	even	5
484.2.a.c.1.1		2	11.6	odd	10
484.2.e.c.81.1		4	11.10	odd	2
484.2.e.c.245.1		4	11.8	odd	10
484.2.e.d.9.1		4	11.7	odd	10
484.2.e.d.269.1		4	11.2	odd	10
484.2.e.e.9.1		4	11.4	even	5
484.2.e.e.269.1		4	11.9	even	5
704.2.m.d.257.1		4	8.3	odd	2
704.2.m.d.641.1		4	88.3	odd	10
704.2.m.e.257.1		4	8.5	even	2
704.2.m.e.641.1		4	88.69	even	10
1100.2.n.a.201.1		4	55.14	even	10
1100.2.n.a.301.1		4	5.4	even	2
1100.2.cb.a.949.1		8	55.47	odd	20
1100.2.cb.a.949.2		8	55.3	odd	20
1100.2.cb.a.1049.1		8	5.3	odd	4
1100.2.cb.a.1049.2		8	5.2	odd	4
1936.2.a.z.1.2		2	44.39	even	10
1936.2.a.ba.1.2		2	44.27	odd	10
4356.2.a.t.1.2		2	33.5	odd	10
4356.2.a.u.1.2		2	33.17	even	10
7744.2.a.bo.1.1		2	88.83	even	10
7744.2.a.bp.1.1		2	88.27	odd	10
7744.2.a.da.1.2		2	88.5	even	10
7744.2.a.db.1.2		2	88.61	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 44 = 2^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	44.e (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 2.48990i) q^{3} +(1.30902 - 0.951057i) q^{5} +(-1.19098 - 3.66547i) q^{7} +(-3.11803 - 2.26538i) q^{9} +(1.23607 + 3.07768i) q^{11} +(-1.92705 - 1.40008i) q^{13} +(1.30902 + 4.02874i) q^{15} +(-1.92705 + 1.40008i) q^{17} +(1.19098 - 3.66547i) q^{19} +10.0902 q^{21} -2.47214 q^{23} +(-0.736068 + 2.26538i) q^{25} +(1.80902 - 1.31433i) q^{27} +(2.66312 + 8.19624i) q^{29} +(-0.690983 - 0.502029i) q^{31} +(-8.66312 + 0.587785i) q^{33} +(-5.04508 - 3.66547i) q^{35} +(-0.572949 - 1.76336i) q^{37} +(5.04508 - 3.66547i) q^{39} +(2.66312 - 8.19624i) q^{41} -6.23607 q^{45} +(0.427051 - 1.31433i) q^{47} +(-6.35410 + 4.61653i) q^{49} +(-1.92705 - 5.93085i) q^{51} +(3.30902 + 2.40414i) q^{53} +(4.54508 + 2.85317i) q^{55} +(8.16312 + 5.93085i) q^{57} +(0.336881 + 1.03681i) q^{59} +(-1.92705 + 1.40008i) q^{61} +(-4.59017 + 14.1271i) q^{63} -3.85410 q^{65} +12.9443 q^{67} +(2.00000 - 6.15537i) q^{69} +(5.16312 - 3.75123i) q^{71} +(-0.281153 - 0.865300i) q^{73} +(-5.04508 - 3.66547i) q^{75} +(9.80902 - 8.19624i) q^{77} +(5.78115 + 4.20025i) q^{79} +(-1.76393 - 5.42882i) q^{81} +(-10.5451 + 7.66145i) q^{83} +(-1.19098 + 3.66547i) q^{85} -22.5623 q^{87} +0.472136 q^{89} +(-2.83688 + 8.73102i) q^{91} +(1.80902 - 1.31433i) q^{93} +(-1.92705 - 5.93085i) q^{95} +(11.7812 + 8.55951i) q^{97} +(3.11803 - 12.3965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{3} + 3 q^{5} - 7 q^{7} - 8 q^{9} - 4 q^{11} - q^{13} + 3 q^{15} - q^{17} + 7 q^{19} + 18 q^{21} + 8 q^{23} + 6 q^{25} + 5 q^{27} - 5 q^{29} - 5 q^{31} - 19 q^{33} - 9 q^{35} - 9 q^{37} + 9 q^{39}+ \cdots + 8 q^{99}+O(q^{100}) \) 4 * q - q^3 + 3 * q^5 - 7 * q^7 - 8 * q^9 - 4 * q^11 - q^13 + 3 * q^15 - q^17 + 7 * q^19 + 18 * q^21 + 8 * q^23 + 6 * q^25 + 5 * q^27 - 5 * q^29 - 5 * q^31 - 19 * q^33 - 9 * q^35 - 9 * q^37 + 9 * q^39 - 5 * q^41 - 16 * q^45 - 5 * q^47 - 12 * q^49 - q^51 + 11 * q^53 + 7 * q^55 + 17 * q^57 + 17 * q^59 - q^61 + 4 * q^63 - 2 * q^65 + 16 * q^67 + 8 * q^69 + 5 * q^71 + 19 * q^73 - 9 * q^75 + 37 * q^77 + 3 * q^79 - 16 * q^81 - 31 * q^83 - 7 * q^85 - 50 * q^87 - 16 * q^89 - 27 * q^91 + 5 * q^93 - q^95 + 27 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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