LMFDB - Embedded newform 1064.2.q.n.457.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.8
Root			$1.29764 + 2.24758i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.n.305.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29764 + 2.24758i) q^{3} +(-0.833107 + 1.44298i) q^{5} +(2.29509 - 1.31627i) q^{7} +(-1.86773 + 3.23500i) q^{9} +O(q^{10})$	\(q+(1.29764 + 2.24758i) q^{3} +(-0.833107 + 1.44298i) q^{5} +(2.29509 - 1.31627i) q^{7} +(-1.86773 + 3.23500i) q^{9} +(-0.0726443 - 0.125824i) q^{11} -1.47949 q^{13} -4.32429 q^{15} +(2.95447 + 5.11729i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(5.93662 + 3.45033i) q^{21} +(-3.11003 + 5.38673i) q^{23} +(1.11187 + 1.92581i) q^{25} -1.90873 q^{27} -3.13688 q^{29} +(0.441263 + 0.764290i) q^{31} +(0.188532 - 0.326547i) q^{33} +(-0.0126906 + 4.40837i) q^{35} +(0.981199 - 1.69949i) q^{37} +(-1.91984 - 3.32527i) q^{39} -2.00000 q^{41} -2.05954 q^{43} +(-3.11204 - 5.39021i) q^{45} +(0.0872023 - 0.151039i) q^{47} +(3.53484 - 6.04193i) q^{49} +(-7.66767 + 13.2808i) q^{51} +(-4.21921 - 7.30789i) q^{53} +0.242082 q^{55} -2.59528 q^{57} +(0.790938 + 1.36994i) q^{59} +(4.27622 - 7.40663i) q^{61} +(-0.0284509 + 9.88306i) q^{63} +(1.23257 - 2.13488i) q^{65} +(-0.669653 - 1.15987i) q^{67} -16.1428 q^{69} +7.37135 q^{71} +(-2.36212 - 4.09132i) q^{73} +(-2.88560 + 4.99801i) q^{75} +(-0.332343 - 0.193156i) q^{77} +(-5.74929 + 9.95806i) q^{79} +(3.12636 + 5.41501i) q^{81} +4.37769 q^{83} -9.84555 q^{85} +(-4.07054 - 7.05038i) q^{87} +(0.696489 - 1.20635i) q^{89} +(-3.39556 + 1.94742i) q^{91} +(-1.14520 + 1.98354i) q^{93} +(-0.833107 - 1.44298i) q^{95} +10.6777 q^{97} +0.542720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	1.29764	+	2.24758i	0.749192	+	1.29764i	0.948210	+	0.317643i	$0.102891\pi$
$3$	1.29764	+	2.24758i	0.749192	+	1.29764i	−0.199019	+	0.979996i	$0.563775\pi$
$4$		0			0
$5$	−0.833107	+	1.44298i	−0.372577	+	0.645322i	−0.989961	−	0.141340i	$-0.954859\pi$
$5$	−0.833107	+	1.44298i	−0.372577	+	0.645322i	0.617384	+	0.786662i	$0.288192\pi$
$6$		0			0
$7$	2.29509	−	1.31627i	0.867461	−	0.497505i
$7$	2.29509	−	1.31627i	0.867461	−	0.497505i
$8$		0			0
$9$	−1.86773	+	3.23500i	−0.622577	+	1.07833i
$10$		0			0
$11$	−0.0726443	−	0.125824i	−0.0219031	−	0.0379372i	0.854866	−	0.518849i	$-0.173639\pi$
$11$	−0.0726443	−	0.125824i	−0.0219031	−	0.0379372i	−0.876769	+	0.480911i	$0.840306\pi$
$12$		0			0
$13$	−1.47949			−0.410337			−0.205169	−	0.978727i	$-0.565774\pi$
$13$	−1.47949			−0.410337			−0.205169	+	0.978727i	$0.565774\pi$
$14$		0			0
$15$	−4.32429			−1.11653
$16$		0			0
$17$	2.95447	+	5.11729i	0.716564	+	1.24113i	0.962353	+	0.271802i	$0.0876196\pi$
$17$	2.95447	+	5.11729i	0.716564	+	1.24113i	−0.245789	+	0.969323i	$0.579047\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	5.93662	+	3.45033i	1.29548	+	0.752924i
$22$		0			0
$23$	−3.11003	+	5.38673i	−0.648486	+	1.12321i	0.334999	+	0.942219i	$0.391264\pi$
$23$	−3.11003	+	5.38673i	−0.648486	+	1.12321i	−0.983485	+	0.180992i	$0.942069\pi$
$24$		0			0
$25$	1.11187	+	1.92581i	0.222373	+	0.385162i
$26$		0			0
$27$	−1.90873			−0.367335
$28$		0			0
$29$	−3.13688			−0.582504			−0.291252	−	0.956646i	$-0.594072\pi$
$29$	−3.13688			−0.582504			−0.291252	+	0.956646i	$0.594072\pi$
$30$		0			0
$31$	0.441263	+	0.764290i	0.0792532	+	0.137271i	0.902928	−	0.429792i	$-0.141413\pi$
$31$	0.441263	+	0.764290i	0.0792532	+	0.137271i	−0.823675	+	0.567063i	$0.808080\pi$
$32$		0			0
$33$	0.188532	−	0.326547i	0.0328192	−	0.0568446i
$34$		0			0
$35$	−0.0126906	+	4.40837i	−0.00214511	+	0.745150i
$36$		0			0
$37$	0.981199	−	1.69949i	0.161308	−	0.279394i	−0.774030	−	0.633149i	$-0.781762\pi$
$37$	0.981199	−	1.69949i	0.161308	−	0.279394i	0.935338	+	0.353755i	$0.115095\pi$
$38$		0			0
$39$	−1.91984	−	3.32527i	−0.307421	−	0.532469i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	−2.05954			−0.314076			−0.157038	−	0.987593i	$-0.550195\pi$
$43$	−2.05954			−0.314076			−0.157038	+	0.987593i	$0.550195\pi$
$44$		0			0
$45$	−3.11204	−	5.39021i	−0.463915	−	0.803525i
$46$		0			0
$47$	0.0872023	−	0.151039i	0.0127198	−	0.0220313i	−0.859595	−	0.510975i	$-0.829284\pi$
$47$	0.0872023	−	0.151039i	0.0127198	−	0.0220313i	0.872315	+	0.488944i	$0.162618\pi$
$48$		0			0
$49$	3.53484	−	6.04193i	0.504978	−	0.863132i
$50$		0			0
$51$	−7.66767	+	13.2808i	−1.07369	+	1.85968i
$52$		0			0
$53$	−4.21921	−	7.30789i	−0.579553	−	1.00382i	−0.995530	−	0.0944409i	$-0.969894\pi$
$53$	−4.21921	−	7.30789i	−0.579553	−	1.00382i	0.415977	−	0.909375i	$-0.363440\pi$
$54$		0			0
$55$	0.242082			0.0326423
$56$		0			0
$57$	−2.59528			−0.343753
$58$		0			0
$59$	0.790938	+	1.36994i	0.102971	+	0.178352i	0.912908	−	0.408166i	$-0.133832\pi$
$59$	0.790938	+	1.36994i	0.102971	+	0.178352i	−0.809936	+	0.586518i	$0.800498\pi$
$60$		0			0
$61$	4.27622	−	7.40663i	0.547514	−	0.948322i	−0.450930	−	0.892559i	$-0.648908\pi$
$61$	4.27622	−	7.40663i	0.547514	−	0.948322i	0.998444	−	0.0557626i	$-0.0177590\pi$
$62$		0			0
$63$	−0.0284509	+	9.88306i	−0.00358448	+	1.24515i
$64$		0			0
$65$	1.23257	−	2.13488i	0.152882	−	0.264799i
$66$		0			0
$67$	−0.669653	−	1.15987i	−0.0818112	−	0.141701i	0.822217	−	0.569174i	$-0.192737\pi$
$67$	−0.669653	−	1.15987i	−0.0818112	−	0.141701i	−0.904028	+	0.427473i	$0.859404\pi$
$68$		0			0
$69$	−16.1428			−1.94336
$70$		0			0
$71$	7.37135			0.874819			0.437409	−	0.899263i	$-0.355896\pi$
$71$	7.37135			0.874819			0.437409	+	0.899263i	$0.355896\pi$
$72$		0			0
$73$	−2.36212	−	4.09132i	−0.276466	−	0.478853i	0.694038	−	0.719938i	$-0.255830\pi$
$73$	−2.36212	−	4.09132i	−0.276466	−	0.478853i	−0.970504	+	0.241086i	$0.922497\pi$
$74$		0			0
$75$	−2.88560	+	4.99801i	−0.333201	+	0.577120i
$76$		0			0
$77$	−0.332343	−	0.193156i	−0.0378740	−	0.0220122i
$78$		0			0
$79$	−5.74929	+	9.95806i	−0.646846	+	1.12037i	0.337026	+	0.941495i	$0.390579\pi$
$79$	−5.74929	+	9.95806i	−0.646846	+	1.12037i	−0.983872	+	0.178874i	$0.942754\pi$
$80$		0			0
$81$	3.12636	+	5.41501i	0.347373	+	0.601667i
$82$		0			0
$83$	4.37769			0.480514			0.240257	−	0.970709i	$-0.422768\pi$
$83$	4.37769			0.480514			0.240257	+	0.970709i	$0.422768\pi$
$84$		0			0
$85$	−9.84555			−1.06790
$86$		0			0
$87$	−4.07054	−	7.05038i	−0.436408	−	0.755880i
$88$		0			0
$89$	0.696489	−	1.20635i	0.0738277	−	0.127873i	−0.826748	−	0.562572i	$-0.809812\pi$
$89$	0.696489	−	1.20635i	0.0738277	−	0.127873i	0.900576	+	0.434699i	$0.143145\pi$
$90$		0			0
$91$	−3.39556	+	1.94742i	−0.355952	+	0.204145i
$92$		0			0
$93$	−1.14520	+	1.98354i	−0.118752	+	0.205684i
$94$		0			0
$95$	−0.833107	−	1.44298i	−0.0854749	−	0.148047i
$96$		0			0
$97$	10.6777			1.08416			0.542080	−	0.840327i	$-0.317637\pi$
$97$	10.6777			1.08416			0.542080	+	0.840327i	$0.317637\pi$
$98$		0			0
$99$	0.542720			0.0545454
$100$		0			0
$101$	0.601227	+	1.04136i	0.0598244	+	0.103619i	0.894386	−	0.447295i	$-0.147613\pi$
$101$	0.601227	+	1.04136i	0.0598244	+	0.103619i	−0.834562	+	0.550914i	$0.814279\pi$
$102$		0			0
$103$	9.77362	−	16.9284i	0.963024	−	1.66801i	0.248190	−	0.968711i	$-0.420164\pi$
$103$	9.77362	−	16.9284i	0.963024	−	1.66801i	0.714834	−	0.699295i	$-0.246502\pi$
$104$		0			0
$105$	−9.92461	+	5.69194i	−0.968543	+	0.555477i
$106$		0			0
$107$	−4.01055	+	6.94647i	−0.387714	+	0.671541i	−0.992142	−	0.125119i	$-0.960069\pi$
$107$	−4.01055	+	6.94647i	−0.387714	+	0.671541i	0.604427	+	0.796660i	$0.293402\pi$
$108$		0			0
$109$	−10.1921	−	17.6532i	−0.976226	−	1.69087i	−0.675828	−	0.737059i	$-0.736214\pi$
$109$	−10.1921	−	17.6532i	−0.976226	−	1.69087i	−0.300398	−	0.953814i	$-0.597119\pi$
$110$		0			0
$111$	5.09297			0.483403
$112$		0			0
$113$	8.93908			0.840918			0.420459	−	0.907312i	$-0.361869\pi$
$113$	8.93908			0.840918			0.420459	+	0.907312i	$0.361869\pi$
$114$		0			0
$115$	−5.18197	−	8.97544i	−0.483221	−	0.836964i
$116$		0			0
$117$	2.76329	−	4.78616i	0.255466	−	0.442481i
$118$		0			0
$119$	13.5165	+	7.85573i	1.23906	+	0.720134i
$120$		0			0
$121$	5.48945	−	9.50800i	0.499041	−	0.864364i
$122$		0			0
$123$	−2.59528	−	4.49515i	−0.234008	−	0.405314i
$124$		0			0
$125$	−12.0363			−1.07656
$126$		0			0
$127$	1.76063			0.156231			0.0781154	−	0.996944i	$-0.475110\pi$
$127$	1.76063			0.156231			0.0781154	+	0.996944i	$0.475110\pi$
$128$		0			0
$129$	−2.67253	−	4.62896i	−0.235303	−	0.407557i
$130$		0			0
$131$	−2.02136	+	3.50109i	−0.176607	+	0.305892i	−0.940716	−	0.339195i	$-0.889845\pi$
$131$	−2.02136	+	3.50109i	−0.176607	+	0.305892i	0.764109	+	0.645087i	$0.223179\pi$
$132$		0			0
$133$	−0.00761644	+	2.64574i	−0.000660429	+	0.229415i
$134$		0			0
$135$	1.59017	−	2.75426i	0.136860	−	0.237049i
$136$		0			0
$137$	10.2042	+	17.6742i	0.871805	+	1.51001i	0.860127	+	0.510079i	$0.170384\pi$
$137$	10.2042	+	17.6742i	0.871805	+	1.51001i	0.0116777	+	0.999932i	$0.496283\pi$
$138$		0			0
$139$	11.2435			0.953662			0.476831	−	0.878995i	$-0.341785\pi$
$139$	11.2435			0.953662			0.476831	+	0.878995i	$0.341785\pi$
$140$		0			0
$141$	0.452628			0.0381182
$142$		0			0
$143$	0.107477	+	0.186155i	0.00898765	+	0.0155671i
$144$		0			0
$145$	2.61336	−	4.52647i	0.217028	−	0.375903i
$146$		0			0
$147$	18.1666	+	0.104595i	1.49836	+	0.00862689i
$148$		0			0
$149$	2.79348	−	4.83846i	0.228851	−	0.396382i	−0.728617	−	0.684922i	$-0.759836\pi$
$149$	2.79348	−	4.83846i	0.228851	−	0.396382i	0.957468	+	0.288540i	$0.0931697\pi$
$150$		0			0
$151$	9.67873	+	16.7641i	0.787644	+	1.36424i	0.927407	+	0.374054i	$0.122033\pi$
$151$	9.67873	+	16.7641i	0.787644	+	1.36424i	−0.139763	+	0.990185i	$0.544634\pi$
$152$		0			0
$153$	−22.0726			−1.78446
$154$		0			0
$155$	−1.47048			−0.118112
$156$		0			0
$157$	5.46176	+	9.46004i	0.435896	+	0.754994i	0.997368	−	0.0725017i	$-0.0230983\pi$
$157$	5.46176	+	9.46004i	0.435896	+	0.754994i	−0.561472	+	0.827495i	$0.689765\pi$
$158$		0			0
$159$	10.9500	−	18.9660i	0.868393	−	1.50410i
$160$		0			0
$161$	−0.0473747	+	16.4567i	−0.00373365	+	1.29697i
$162$		0			0
$163$	−8.14940	+	14.1152i	−0.638310	+	1.10559i	0.347493	+	0.937683i	$0.387033\pi$
$163$	−8.14940	+	14.1152i	−0.638310	+	1.10559i	−0.985803	+	0.167903i	$0.946300\pi$
$164$		0			0
$165$	0.314135	+	0.544097i	0.0244553	+	0.0423579i
$166$		0			0
$167$	16.7379			1.29522			0.647610	−	0.761972i	$-0.275769\pi$
$167$	16.7379			1.29522			0.647610	+	0.761972i	$0.275769\pi$
$168$		0			0
$169$	−10.8111			−0.831623
$170$		0			0
$171$	−1.86773	−	3.23500i	−0.142829	−	0.247387i
$172$		0			0
$173$	9.12010	−	15.7965i	0.693389	−	1.20098i	−0.277332	−	0.960774i	$-0.589450\pi$
$173$	9.12010	−	15.7965i	0.693389	−	1.20098i	0.970721	−	0.240210i	$-0.0772164\pi$
$174$		0			0
$175$	5.08672	+	2.95638i	0.384520	+	0.223481i
$176$		0			0
$177$	−2.05270	+	3.55538i	−0.154291	+	0.267239i
$178$		0			0
$179$	1.01913	+	1.76519i	0.0761737	+	0.131937i	0.901596	−	0.432579i	$-0.142396\pi$
$179$	1.01913	+	1.76519i	0.0761737	+	0.131937i	−0.825422	+	0.564516i	$0.809063\pi$
$180$		0			0
$181$	−8.70643			−0.647144			−0.323572	−	0.946204i	$-0.604884\pi$
$181$	−8.70643			−0.647144			−0.323572	+	0.946204i	$0.604884\pi$
$182$		0			0
$183$	22.1960			1.64077
$184$		0			0
$185$	1.63489	+	2.83171i	0.120199	+	0.208191i
$186$		0			0
$187$	0.429251	−	0.743484i	0.0313899	−	0.0543689i
$188$		0			0
$189$	−4.38069	+	2.51241i	−0.318649	+	0.182751i
$190$		0			0
$191$	−7.32901	+	12.6942i	−0.530309	+	0.918522i	0.469066	+	0.883163i	$0.344591\pi$
$191$	−7.32901	+	12.6942i	−0.530309	+	0.918522i	−0.999375	+	0.0353584i	$0.988743\pi$
$192$		0			0
$193$	−8.39024	−	14.5323i	−0.603943	−	1.04606i	−0.992218	−	0.124516i	$-0.960262\pi$
$193$	−8.39024	−	14.5323i	−0.603943	−	1.04606i	0.388275	−	0.921544i	$-0.373071\pi$
$194$		0			0
$195$	6.39774			0.458152
$196$		0			0
$197$	24.0559			1.71391			0.856955	−	0.515391i	$-0.172353\pi$
$197$	24.0559			1.71391			0.856955	+	0.515391i	$0.172353\pi$
$198$		0			0
$199$	−3.13214	−	5.42502i	−0.222031	−	0.384569i	0.733393	−	0.679804i	$-0.237935\pi$
$199$	−3.13214	−	5.42502i	−0.222031	−	0.384569i	−0.955425	+	0.295235i	$0.904602\pi$
$200$		0			0
$201$	1.73794	−	3.01019i	0.122585	−	0.212323i
$202$		0			0
$203$	−7.19942	+	4.12900i	−0.505300	+	0.289799i
$204$		0			0
$205$	1.66621	−	2.88597i	0.116373	−	0.201565i
$206$		0			0
$207$	−11.6174	−	20.1219i	−0.807465	−	1.39857i
$208$		0			0
$209$	0.145289			0.0100498
$210$		0			0
$211$	−4.39876			−0.302823			−0.151412	−	0.988471i	$-0.548382\pi$
$211$	−4.39876			−0.302823			−0.151412	+	0.988471i	$0.548382\pi$
$212$		0			0
$213$	9.56535	+	16.5677i	0.655407	+	1.13520i
$214$		0			0
$215$	1.71581	−	2.97187i	0.117017	−	0.202680i
$216$		0			0
$217$	2.01875	+	1.17329i	0.137042	+	0.0796480i
$218$		0			0
$219$	6.13037	−	10.6181i	0.414252	−	0.717505i
$220$		0			0
$221$	−4.37111	−	7.57099i	−0.294033	−	0.509280i
$222$		0			0
$223$	19.7309			1.32128			0.660639	−	0.750703i	$-0.270285\pi$
$223$	19.7309			1.32128			0.660639	+	0.750703i	$0.270285\pi$
$224$		0			0
$225$	−8.30667			−0.553778
$226$		0			0
$227$	4.07360	+	7.05568i	0.270374	+	0.468302i	0.968958	−	0.247227i	$-0.0795192\pi$
$227$	4.07360	+	7.05568i	0.270374	+	0.468302i	−0.698583	+	0.715529i	$0.746186\pi$
$228$		0			0
$229$	8.48851	−	14.7025i	0.560937	−	0.971571i	−0.436478	−	0.899715i	$-0.643774\pi$
$229$	8.48851	−	14.7025i	0.560937	−	0.971571i	0.997415	−	0.0718559i	$-0.0228922\pi$
$230$		0			0
$231$	0.00287189	−	0.997614i	0.000188956	−	0.0656382i
$232$		0			0
$233$	1.59596	−	2.76428i	0.104555	−	0.181094i	−0.809002	−	0.587807i	$-0.799992\pi$
$233$	1.59596	−	2.76428i	0.104555	−	0.181094i	0.913556	+	0.406713i	$0.133325\pi$
$234$		0			0
$235$	0.145298	+	0.251663i	0.00947817	+	0.0164167i
$236$		0			0
$237$	−29.8420			−1.93845
$238$		0			0
$239$	−19.9212			−1.28859			−0.644297	−	0.764775i	$-0.722850\pi$
$239$	−19.9212			−1.28859			−0.644297	+	0.764775i	$0.722850\pi$
$240$		0			0
$241$	4.14573	+	7.18061i	0.267050	+	0.462544i	0.968099	−	0.250570i	$-0.0806179\pi$
$241$	4.14573	+	7.18061i	0.267050	+	0.462544i	−0.701049	+	0.713113i	$0.747285\pi$
$242$		0			0
$243$	−10.9768	+	19.0125i	−0.704165	+	1.21965i
$244$		0			0
$245$	5.77349	+	10.1343i	0.368855	+	0.647456i
$246$		0			0
$247$	0.739746	−	1.28128i	0.0470689	−	0.0815257i
$248$		0			0
$249$	5.68066	+	9.83919i	0.359997	+	0.623534i
$250$		0			0
$251$	−10.2504			−0.647002			−0.323501	−	0.946228i	$-0.604860\pi$
$251$	−10.2504			−0.647002			−0.323501	+	0.946228i	$0.604860\pi$
$252$		0			0
$253$	0.903703			0.0568153
$254$		0			0
$255$	−12.7760	−	22.1286i	−0.800062	−	1.38575i
$256$		0			0
$257$	4.57142	−	7.91793i	0.285157	−	0.493907i	−0.687490	−	0.726194i	$-0.741287\pi$
$257$	4.57142	−	7.91793i	0.285157	−	0.493907i	0.972647	+	0.232287i	$0.0746208\pi$
$258$		0			0
$259$	0.0149465	−	5.19200i	0.000928730	−	0.322615i
$260$		0			0
$261$	5.85885	−	10.1478i	0.362654	−	0.628135i
$262$		0			0
$263$	−1.33961	−	2.32026i	−0.0826036	−	0.143074i	0.821764	−	0.569828i	$-0.192990\pi$
$263$	−1.33961	−	2.32026i	−0.0826036	−	0.143074i	−0.904368	+	0.426754i	$0.859657\pi$
$264$		0			0
$265$	14.0602			0.863712
$266$		0			0
$267$	3.61516			0.221244
$268$		0			0
$269$	−12.6031	−	21.8293i	−0.768426	−	1.33095i	−0.938416	−	0.345508i	$-0.887707\pi$
$269$	−12.6031	−	21.8293i	−0.768426	−	1.33095i	0.169990	−	0.985446i	$-0.445627\pi$
$270$		0			0
$271$	6.33513	−	10.9728i	0.384831	−	0.666548i	−0.606914	−	0.794767i	$-0.707593\pi$
$271$	6.33513	−	10.9728i	0.384831	−	0.666548i	0.991746	+	0.128220i	$0.0409262\pi$
$272$		0			0
$273$	−8.78318	−	5.10474i	−0.531582	−	0.308953i
$274$		0			0
$275$	0.161542	−	0.279798i	0.00974132	−	0.0168725i
$276$		0			0
$277$	−11.0243	−	19.0946i	−0.662386	−	1.14729i	−0.979987	−	0.199061i	$-0.936211\pi$
$277$	−11.0243	−	19.0946i	−0.662386	−	1.14729i	0.317601	−	0.948224i	$-0.397123\pi$
$278$		0			0
$279$	−3.29664			−0.197365
$280$		0			0
$281$	10.9385			0.652539			0.326270	−	0.945277i	$-0.394208\pi$
$281$	10.9385			0.652539			0.326270	+	0.945277i	$0.394208\pi$
$282$		0			0
$283$	−10.3108	−	17.8589i	−0.612916	−	1.06160i	−0.990746	−	0.135727i	$-0.956663\pi$
$283$	−10.3108	−	17.8589i	−0.612916	−	1.06160i	0.377830	−	0.925875i	$-0.376670\pi$
$284$		0			0
$285$	2.16214	−	3.74494i	0.128074	−	0.221831i
$286$		0			0
$287$	−4.59017	+	2.63255i	−0.270949	+	0.155394i
$288$		0			0
$289$	−8.95778	+	15.5153i	−0.526928	+	0.912666i
$290$		0			0
$291$	13.8558	+	23.9990i	0.812244	+	1.40685i
$292$		0			0
$293$	23.8496			1.39331			0.696654	−	0.717407i	$-0.254671\pi$
$293$	23.8496			1.39331			0.696654	+	0.717407i	$0.254671\pi$
$294$		0			0
$295$	−2.63574			−0.153459
$296$		0			0
$297$	0.138658	+	0.240163i	0.00804576	+	0.0139357i
$298$		0			0
$299$	4.60126	−	7.96962i	0.266098	−	0.460895i
$300$		0			0
$301$	−4.72681	+	2.71091i	−0.272449	+	0.156254i
$302$		0			0
$303$	−1.56035	+	2.70261i	−0.0896398	+	0.155261i
$304$		0			0
$305$	7.12510	+	12.3410i	0.407982	+	0.706645i
$306$		0			0
$307$	−14.6943			−0.838647			−0.419323	−	0.907837i	$-0.637733\pi$
$307$	−14.6943			−0.838647			−0.419323	+	0.907837i	$0.637733\pi$
$308$		0			0
$309$	50.7305			2.88596
$310$		0			0
$311$	−2.95754	−	5.12260i	−0.167706	−	0.290476i	0.769907	−	0.638157i	$-0.220303\pi$
$311$	−2.95754	−	5.12260i	−0.167706	−	0.290476i	−0.937613	+	0.347680i	$0.886969\pi$
$312$		0			0
$313$	−0.455326	+	0.788648i	−0.0257365	+	0.0445770i	−0.878607	−	0.477546i	$-0.841526\pi$
$313$	−0.455326	+	0.788648i	−0.0257365	+	0.0445770i	0.852870	+	0.522123i	$0.174860\pi$
$314$		0			0
$315$	−14.2374	−	8.27470i	−0.802186	−	0.466227i
$316$		0			0
$317$	12.7054	−	22.0064i	0.713607	−	1.23600i	−0.249887	−	0.968275i	$-0.580393\pi$
$317$	12.7054	−	22.0064i	0.713607	−	1.23600i	0.963494	−	0.267729i	$-0.0862733\pi$
$318$		0			0
$319$	0.227877	+	0.394694i	0.0127586	+	0.0220986i
$320$		0			0
$321$	−20.8170			−1.16189
$322$		0			0
$323$	−5.90894			−0.328782
$324$		0			0
$325$	−1.64500	−	2.84922i	−0.0912480	−	0.158046i
$326$		0			0
$327$	26.4513	−	45.8150i	1.46276	−	2.53358i
$328$		0			0
$329$	0.00132834	−	0.461429i	7.32339e−5	−	0.0254394i
$330$		0			0
$331$	−4.89762	+	8.48293i	−0.269198	+	0.466264i	−0.968655	−	0.248410i	$-0.920092\pi$
$331$	−4.89762	+	8.48293i	−0.269198	+	0.466264i	0.699457	+	0.714675i	$0.253425\pi$
$332$		0			0
$333$	3.66523	+	6.34837i	0.200853	+	0.347888i
$334$		0			0
$335$	2.23157			0.121924
$336$		0			0
$337$	23.8358			1.29842			0.649210	−	0.760609i	$-0.275100\pi$
$337$	23.8358			1.29842			0.649210	+	0.760609i	$0.275100\pi$
$338$		0			0
$339$	11.5997	+	20.0913i	0.630009	+	1.09121i
$340$		0			0
$341$	0.0641105	−	0.111043i	0.00347178	−	0.00601330i
$342$		0			0
$343$	0.159943	−	18.5196i	0.00863614	−	0.999963i
$344$		0			0
$345$	13.4486	−	23.2937i	0.724051	−	1.25409i
$346$		0			0
$347$	−13.3196	−	23.0703i	−0.715035	−	1.23848i	−0.962946	−	0.269694i	$-0.913077\pi$
$347$	−13.3196	−	23.0703i	−0.715035	−	1.23848i	0.247911	−	0.968783i	$-0.420256\pi$
$348$		0			0
$349$	−6.31857			−0.338225			−0.169113	−	0.985597i	$-0.554090\pi$
$349$	−6.31857			−0.338225			−0.169113	+	0.985597i	$0.554090\pi$
$350$		0			0
$351$	2.82395			0.150731
$352$		0			0
$353$	−1.56235	−	2.70608i	−0.0831557	−	0.144030i	0.821448	−	0.570283i	$-0.193167\pi$
$353$	−1.56235	−	2.70608i	−0.0831557	−	0.144030i	−0.904604	+	0.426253i	$0.859833\pi$
$354$		0			0
$355$	−6.14112	+	10.6367i	−0.325937	+	0.564539i
$356$		0			0
$357$	−0.116801	+	40.5733i	−0.00618175	+	2.14737i
$358$		0			0
$359$	7.56219	−	13.0981i	0.399117	−	0.691291i	−0.594500	−	0.804096i	$-0.702650\pi$
$359$	7.56219	−	13.0981i	0.399117	−	0.691291i	0.993617	+	0.112804i	$0.0359833\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	28.4933			1.49551
$364$		0			0
$365$	7.87161			0.412019
$366$		0			0
$367$	−2.22586	−	3.85531i	−0.116189	−	0.201246i	0.802065	−	0.597236i	$-0.203735\pi$
$367$	−2.22586	−	3.85531i	−0.116189	−	0.201246i	−0.918254	+	0.395991i	$0.870401\pi$
$368$		0			0
$369$	3.73546	−	6.47001i	0.194460	−	0.336815i
$370$		0			0
$371$	−19.3026	−	11.2186i	−1.00214	−	0.582441i
$372$		0			0
$373$	−5.83058	+	10.0989i	−0.301896	+	0.522899i	−0.976565	−	0.215221i	$-0.930953\pi$
$373$	−5.83058	+	10.0989i	−0.301896	+	0.522899i	0.674669	+	0.738120i	$0.264286\pi$
$374$		0			0
$375$	−15.6187	−	27.0525i	−0.806548	−	1.39698i
$376$		0			0
$377$	4.64099			0.239023
$378$		0			0
$379$	36.0926			1.85395			0.926976	−	0.375122i	$-0.122399\pi$
$379$	36.0926			1.85395			0.926976	+	0.375122i	$0.122399\pi$
$380$		0			0
$381$	2.28466	+	3.95715i	0.117047	+	0.202731i
$382$		0			0
$383$	−7.29960	+	12.6433i	−0.372992	+	0.646041i	−0.990024	−	0.140897i	$-0.955002\pi$
$383$	−7.29960	+	12.6433i	−0.372992	+	0.646041i	0.617032	+	0.786938i	$0.288335\pi$
$384$		0			0
$385$	0.555599	−	0.318646i	0.0283159	−	0.0162397i
$386$		0			0
$387$	3.84666	−	6.66261i	0.195537	−	0.338679i
$388$		0			0
$389$	−2.26994	−	3.93165i	−0.115090	−	0.199342i	0.802726	−	0.596349i	$-0.203382\pi$
$389$	−2.26994	−	3.93165i	−0.115090	−	0.199342i	−0.917816	+	0.397006i	$0.870049\pi$
$390$		0			0
$391$	−36.7539			−1.85873
$392$		0			0
$393$	−10.4920			−0.529249
$394$		0			0
$395$	−9.57955	−	16.5923i	−0.481999	−	0.834847i
$396$		0			0
$397$	−10.9422	+	18.9525i	−0.549175	+	0.951198i	0.449157	+	0.893453i	$0.351724\pi$
$397$	−10.9422	+	18.9525i	−0.549175	+	0.951198i	−0.998331	+	0.0577452i	$0.981609\pi$
$398$		0			0
$399$	−5.95638	+	3.41610i	−0.298192	+	0.171019i
$400$		0			0
$401$	−4.03673	+	6.99182i	−0.201585	+	0.349155i	−0.949039	−	0.315158i	$-0.897942\pi$
$401$	−4.03673	+	6.99182i	−0.201585	+	0.349155i	0.747455	+	0.664313i	$0.231276\pi$
$402$		0			0
$403$	−0.652845	−	1.13076i	−0.0325205	−	0.0563272i
$404$		0			0
$405$	−10.4184			−0.517692
$406$		0			0
$407$	−0.285114			−0.0141326
$408$		0			0
$409$	−18.7633	−	32.4989i	−0.927784	−	1.60697i	−0.787022	−	0.616925i	$-0.788378\pi$
$409$	−18.7633	−	32.4989i	−0.927784	−	1.60697i	−0.140762	−	0.990043i	$-0.544955\pi$
$410$		0			0
$411$	−26.4828	+	45.8695i	−1.30630	+	2.26258i
$412$		0			0
$413$	3.61849	+	2.10305i	0.178054	+	0.103484i
$414$		0			0
$415$	−3.64708	+	6.31694i	−0.179028	+	0.310086i
$416$		0			0
$417$	14.5900	+	25.2706i	0.714476	+	1.23751i
$418$		0			0
$419$	−24.9638			−1.21956			−0.609782	−	0.792569i	$-0.708743\pi$
$419$	−24.9638			−1.21956			−0.609782	+	0.792569i	$0.708743\pi$
$420$		0			0
$421$	17.4710			0.851485			0.425743	−	0.904844i	$-0.360013\pi$
$421$	17.4710			0.851485			0.425743	+	0.904844i	$0.360013\pi$
$422$		0			0
$423$	0.325741	+	0.564200i	0.0158381	+	0.0274323i
$424$		0			0
$425$	−6.56995	+	11.3795i	−0.318689	+	0.551986i
$426$		0			0
$427$	0.0651392	−	22.6275i	0.00315230	−	1.09502i
$428$		0			0
$429$	−0.278932	+	0.483124i	−0.0134669	+	0.0233254i
$430$		0			0
$431$	−12.7879	−	22.1494i	−0.615973	−	1.06690i	−0.990213	−	0.139565i	$-0.955430\pi$
$431$	−12.7879	−	22.1494i	−0.615973	−	1.06690i	0.374240	−	0.927332i	$-0.377904\pi$
$432$		0			0
$433$	−21.5603			−1.03612			−0.518060	−	0.855344i	$-0.673346\pi$
$433$	−21.5603			−1.03612			−0.518060	+	0.855344i	$0.673346\pi$
$434$		0			0
$435$	13.5648			0.650381
$436$		0			0
$437$	−3.11003	−	5.38673i	−0.148773	−	0.257682i
$438$		0			0
$439$	−12.9215	+	22.3807i	−0.616710	+	1.06817i	0.373372	+	0.927682i	$0.378202\pi$
$439$	−12.9215	+	22.3807i	−0.616710	+	1.06817i	−0.990082	+	0.140491i	$0.955132\pi$
$440$		0			0
$441$	12.9435	+	22.7199i	0.616358	+	1.08190i
$442$		0			0
$443$	−14.5285	+	25.1641i	−0.690270	+	1.19558i	0.281479	+	0.959567i	$0.409175\pi$
$443$	−14.5285	+	25.1641i	−0.690270	+	1.19558i	−0.971749	+	0.236016i	$0.924158\pi$
$444$		0			0
$445$	1.16050	+	2.01004i	0.0550129	+	0.0952852i
$446$		0			0
$447$	14.4997			0.685814
$448$		0			0
$449$	29.6266			1.39817			0.699083	−	0.715040i	$-0.253592\pi$
$449$	29.6266			1.39817			0.699083	+	0.715040i	$0.253592\pi$
$450$		0			0
$451$	0.145289	+	0.251647i	0.00684137	+	0.0118496i
$452$		0			0
$453$	−25.1190	+	43.5074i	−1.18019	+	2.04415i
$454$		0			0
$455$	0.0187757	−	6.52214i	0.000880216	−	0.305763i
$456$		0			0
$457$	2.01616	−	3.49209i	0.0943119	−	0.163353i	−0.815009	−	0.579448i	$-0.803268\pi$
$457$	2.01616	−	3.49209i	0.0943119	−	0.163353i	0.909321	+	0.416095i	$0.136602\pi$
$458$		0			0
$459$	−5.63927	−	9.76751i	−0.263219	−	0.455908i
$460$		0			0
$461$	17.6181			0.820555			0.410277	−	0.911961i	$-0.365432\pi$
$461$	17.6181			0.820555			0.410277	+	0.911961i	$0.365432\pi$
$462$		0			0
$463$	−26.2595			−1.22038			−0.610192	−	0.792253i	$-0.708908\pi$
$463$	−26.2595			−1.22038			−0.610192	+	0.792253i	$0.708908\pi$
$464$		0			0
$465$	−1.90815	−	3.30501i	−0.0884882	−	0.153266i
$466$		0			0
$467$	−17.4759	+	30.2691i	−0.808688	+	1.40069i	0.105085	+	0.994463i	$0.466489\pi$
$467$	−17.4759	+	30.2691i	−0.808688	+	1.40069i	−0.913773	+	0.406226i	$0.866845\pi$
$468$		0			0
$469$	−3.06362	−	1.78056i	−0.141465	−	0.0822188i
$470$		0			0
$471$	−14.1748	+	24.5514i	−0.653139	+	1.13127i
$472$		0			0
$473$	0.149614	+	0.259138i	0.00687924	+	0.0119152i
$474$		0			0
$475$	−2.22373			−0.102032
$476$		0			0
$477$	31.5214			1.44327
$478$		0			0
$479$	13.5239	+	23.4242i	0.617925	+	1.07028i	0.989864	+	0.142020i	$0.0453597\pi$
$479$	13.5239	+	23.4242i	0.617925	+	1.07028i	−0.371939	+	0.928257i	$0.621307\pi$
$480$		0			0
$481$	−1.45168	+	2.51438i	−0.0661907	+	0.114646i
$482$		0			0
$483$	−37.0491	+	21.2483i	−1.68579	+	0.966832i
$484$		0			0
$485$	−8.89569	+	15.4078i	−0.403933	+	0.699632i
$486$		0			0
$487$	−9.60833	−	16.6421i	−0.435395	−	0.754126i	0.561933	−	0.827183i	$-0.310058\pi$
$487$	−9.60833	−	16.6421i	−0.435395	−	0.754126i	−0.997328	+	0.0730565i	$0.976725\pi$
$488$		0			0
$489$	−42.2999			−1.91287
$490$		0			0
$491$	31.6972			1.43048			0.715238	−	0.698881i	$-0.246318\pi$
$491$	31.6972			1.43048			0.715238	+	0.698881i	$0.246318\pi$
$492$		0			0
$493$	−9.26782	−	16.0523i	−0.417402	−	0.722961i
$494$		0			0
$495$	−0.452144	+	0.783136i	−0.0203223	+	0.0351993i
$496$		0			0
$497$	16.9179	−	9.70272i	0.758871	−	0.435227i
$498$		0			0
$499$	−10.7795	+	18.6706i	−0.482556	+	0.835812i	−0.999799	−	0.0200267i	$-0.993625\pi$
$499$	−10.7795	+	18.6706i	−0.482556	+	0.835812i	0.517243	+	0.855838i	$0.326958\pi$
$500$		0			0
$501$	21.7198	+	37.6198i	0.970368	+	1.68073i
$502$		0			0
$503$	−7.27173			−0.324230			−0.162115	−	0.986772i	$-0.551832\pi$
$503$	−7.27173			−0.324230			−0.162115	+	0.986772i	$0.551832\pi$
$504$		0			0
$505$	−2.00355			−0.0891566
$506$		0			0
$507$	−14.0289	−	24.2988i	−0.623046	−	1.07915i
$508$		0			0
$509$	−20.3403	+	35.2304i	−0.901567	+	1.56156i	−0.0761058	+	0.997100i	$0.524249\pi$
$509$	−20.3403	+	35.2304i	−0.901567	+	1.56156i	−0.825461	+	0.564459i	$0.809085\pi$
$510$		0			0
$511$	−10.8066	−	6.28073i	−0.478055	−	0.277843i
$512$		0			0
$513$	0.954363	−	1.65301i	0.0421362	−	0.0729820i
$514$		0			0
$515$	16.2849	+	28.2063i	0.717600	+	1.24292i
$516$		0			0
$517$	−0.0253390			−0.00111441
$518$		0			0
$519$	47.3384			2.07792
$520$		0			0
$521$	1.01935	+	1.76556i	0.0446583	+	0.0773505i	0.887491	−	0.460826i	$-0.152447\pi$
$521$	1.01935	+	1.76556i	0.0446583	+	0.0773505i	−0.842832	+	0.538176i	$0.819113\pi$
$522$		0			0
$523$	18.7965	−	32.5565i	0.821914	−	1.42360i	−0.0823405	−	0.996604i	$-0.526239\pi$
$523$	18.7965	−	32.5565i	0.821914	−	1.42360i	0.904255	−	0.426993i	$-0.140427\pi$
$524$		0			0
$525$	−0.0439560	+	15.2691i	−0.00191840	+	0.666398i
$526$		0			0
$527$	−2.60740	+	4.51614i	−0.113580	+	0.196726i
$528$		0			0
$529$	−7.84455	−	13.5872i	−0.341068	−	0.590746i
$530$		0			0
$531$	−5.90904			−0.256430
$532$		0			0
$533$	2.95898			0.128168
$534$		0			0
$535$	−6.68243	−	11.5743i	−0.288907	−	0.500401i
$536$		0			0
$537$	−2.64493	+	4.58116i	−0.114137	+	0.197692i
$538$		0			0
$539$	−1.01700	−	0.00585546i	−0.0438054	−	0.000252212i
$540$		0			0
$541$	−16.1595	+	27.9891i	−0.694751	+	1.20334i	0.275513	+	0.961297i	$0.411152\pi$
$541$	−16.1595	+	27.9891i	−0.694751	+	1.20334i	−0.970264	+	0.242047i	$0.922181\pi$
$542$		0			0
$543$	−11.2978	−	19.5684i	−0.484835	−	0.839759i
$544$		0			0
$545$	33.9644			1.45488
$546$		0			0
$547$	5.52462			0.236216			0.118108	−	0.993001i	$-0.462317\pi$
$547$	5.52462			0.236216			0.118108	+	0.993001i	$0.462317\pi$
$548$		0			0
$549$	15.9737	+	27.6672i	0.681739	+	1.18081i
$550$		0			0
$551$	1.56844	−	2.71662i	0.0668178	−	0.115732i
$552$		0			0
$553$	−0.0875783	+	30.4223i	−0.00372421	+	1.29369i
$554$		0			0
$555$	−4.24298	+	7.34907i	−0.180105	+	0.311950i
$556$		0			0
$557$	15.8530	+	27.4582i	0.671712	+	1.16344i	0.977418	+	0.211314i	$0.0677741\pi$
$557$	15.8530	+	27.4582i	0.671712	+	1.16344i	−0.305706	+	0.952126i	$0.598893\pi$
$558$		0			0
$559$	3.04707			0.128877
$560$		0			0
$561$	2.22805			0.0940683
$562$		0			0
$563$	−17.3777	−	30.0991i	−0.732383	−	1.26852i	−0.955862	−	0.293816i	$-0.905075\pi$
$563$	−17.3777	−	30.0991i	−0.732383	−	1.26852i	0.223479	−	0.974709i	$-0.428259\pi$
$564$		0			0
$565$	−7.44721	+	12.8989i	−0.313306	+	0.542663i
$566$		0			0
$567$	14.3029	+	8.31277i	0.600665	+	0.349103i
$568$		0			0
$569$	17.9493	−	31.0891i	0.752473	−	1.30332i	−0.194148	−	0.980972i	$-0.562194\pi$
$569$	17.9493	−	31.0891i	0.752473	−	1.30332i	0.946621	−	0.322349i	$-0.104472\pi$
$570$		0			0
$571$	21.5441	+	37.3154i	0.901592	+	1.56160i	0.825428	+	0.564507i	$0.190934\pi$
$571$	21.5441	+	37.3154i	0.901592	+	1.56160i	0.0761632	+	0.997095i	$0.475733\pi$
$572$		0			0
$573$	−38.0416			−1.58921
$574$		0			0
$575$	−13.8317			−0.576824
$576$		0			0
$577$	−23.3082	−	40.3711i	−0.970335	−	1.68067i	−0.694543	−	0.719452i	$-0.744393\pi$
$577$	−23.3082	−	40.3711i	−0.970335	−	1.68067i	−0.275792	−	0.961217i	$-0.588940\pi$
$578$		0			0
$579$	21.7750	−	37.7154i	0.904938	−	1.56740i
$580$		0			0
$581$	10.0472	−	5.76224i	0.416827	−	0.239058i
$582$		0			0
$583$	−0.613003	+	1.06175i	−0.0253880	+	0.0439733i
$584$		0			0
$585$	4.60423	+	7.97477i	0.190362	+	0.329716i
$586$		0			0
$587$	46.4370			1.91666			0.958331	−	0.285661i	$-0.0922132\pi$
$587$	46.4370			1.91666			0.958331	+	0.285661i	$0.0922132\pi$
$588$		0			0
$589$	−0.882526			−0.0363639
$590$		0			0
$591$	31.2158	+	54.0674i	1.28405	+	2.22404i
$592$		0			0
$593$	−20.1502	+	34.9011i	−0.827468	+	1.43322i	0.0725505	+	0.997365i	$0.476886\pi$
$593$	−20.1502	+	34.9011i	−0.827468	+	1.43322i	−0.900018	+	0.435852i	$0.856447\pi$
$594$		0			0
$595$	−22.5964	+	12.9594i	−0.926362	+	0.531285i
$596$		0			0
$597$	8.12876	−	14.0794i	0.332688	−	0.576233i
$598$		0			0
$599$	9.89620	+	17.1407i	0.404348	+	0.700351i	0.994245	−	0.107127i	$-0.0341653\pi$
$599$	9.89620	+	17.1407i	0.404348	+	0.700351i	−0.589898	+	0.807478i	$0.700832\pi$
$600$		0			0
$601$	39.2064			1.59926			0.799631	−	0.600492i	$-0.205029\pi$
$601$	39.2064			1.59926			0.799631	+	0.600492i	$0.205029\pi$
$602$		0			0
$603$	5.00293			0.203735
$604$		0			0
$605$	9.14659	+	15.8424i	0.371862	+	0.644083i
$606$		0			0
$607$	8.61466	−	14.9210i	0.349658	−	0.605626i	−0.636531	−	0.771252i	$-0.719631\pi$
$607$	8.61466	−	14.9210i	0.349658	−	0.605626i	0.986189	+	0.165626i	$0.0529644\pi$
$608$		0			0
$609$	−18.6225	−	10.8233i	−0.754621	−	0.438582i
$610$		0			0
$611$	−0.129015	+	0.223461i	−0.00521939	+	0.00904025i
$612$		0			0
$613$	−12.0565	−	20.8825i	−0.486959	−	0.843437i	0.512929	−	0.858431i	$-0.328560\pi$
$613$	−12.0565	−	20.8825i	−0.486959	−	0.843437i	−0.999888	+	0.0149940i	$0.995227\pi$
$614$		0			0
$615$	8.64857			0.348744
$616$		0			0
$617$	−44.6161			−1.79618			−0.898089	−	0.439814i	$-0.855044\pi$
$617$	−44.6161			−1.79618			−0.898089	+	0.439814i	$0.855044\pi$
$618$		0			0
$619$	10.2775	+	17.8011i	0.413086	+	0.715486i	0.995225	−	0.0976031i	$-0.0311176\pi$
$619$	10.2775	+	17.8011i	0.413086	+	0.715486i	−0.582139	+	0.813089i	$0.697784\pi$
$620$		0			0
$621$	5.93619	−	10.2818i	0.238211	−	0.412594i
$622$		0			0
$623$	0.0106095	−	3.68546i	0.000425062	−	0.147655i
$624$		0			0
$625$	4.46817	−	7.73911i	0.178727	−	0.309564i
$626$		0			0
$627$	0.188532	+	0.326547i	0.00752925	+	0.0130410i
$628$		0			0
$629$	11.5957			0.462350
$630$		0			0
$631$	3.35794			0.133678			0.0668388	−	0.997764i	$-0.478709\pi$
$631$	3.35794			0.133678			0.0668388	+	0.997764i	$0.478709\pi$
$632$		0			0
$633$	−5.70800	−	9.88655i	−0.226873	−	0.392955i
$634$		0			0
$635$	−1.46679	+	2.54056i	−0.0582079	+	0.100819i
$636$		0			0
$637$	−5.22977	+	8.93898i	−0.207211	+	0.354175i
$638$		0			0
$639$	−13.7677	+	23.8464i	−0.544642	+	0.943347i
$640$		0			0
$641$	2.32930	+	4.03447i	0.0920020	+	0.159352i	0.908353	−	0.418203i	$-0.137340\pi$
$641$	2.32930	+	4.03447i	0.0920020	+	0.159352i	−0.816351	+	0.577555i	$0.804007\pi$
$642$		0			0
$643$	9.50546			0.374859			0.187429	−	0.982278i	$-0.439984\pi$
$643$	9.50546			0.374859			0.187429	+	0.982278i	$0.439984\pi$
$644$		0			0
$645$	8.90602			0.350674
$646$		0			0
$647$	−6.51540	−	11.2850i	−0.256147	−	0.443660i	0.709059	−	0.705149i	$-0.249120\pi$
$647$	−6.51540	−	11.2850i	−0.256147	−	0.443660i	−0.965206	+	0.261489i	$0.915786\pi$
$648$		0			0
$649$	0.114914	−	0.199037i	0.00451078	−	0.00781290i
$650$		0			0
$651$	−0.0174447	+	6.05980i	−0.000683712	+	0.237502i
$652$		0			0
$653$	−3.51227	+	6.08344i	−0.137446	+	0.238063i	−0.926529	−	0.376223i	$-0.877223\pi$
$653$	−3.51227	+	6.08344i	−0.137446	+	0.238063i	0.789083	+	0.614286i	$0.210556\pi$
$654$		0			0
$655$	−3.36801	−	5.83357i	−0.131599	−	0.227936i
$656$		0			0
$657$	17.6472			0.688485
$658$		0			0
$659$	−7.92031			−0.308532			−0.154266	−	0.988029i	$-0.549301\pi$
$659$	−7.92031			−0.308532			−0.154266	+	0.988029i	$0.549301\pi$
$660$		0			0
$661$	−5.37679	−	9.31287i	−0.209133	−	0.362228i	0.742309	−	0.670058i	$-0.233731\pi$
$661$	−5.37679	−	9.31287i	−0.209133	−	0.362228i	−0.951442	+	0.307829i	$0.900397\pi$
$662$		0			0
$663$	11.3442	−	19.6488i	0.440574	−	0.763097i
$664$		0			0
$665$	−3.81141	−	2.21517i	−0.147800	−	0.0859008i
$666$		0			0
$667$	9.75579	−	16.8975i	0.377746	−	0.654275i
$668$		0			0
$669$	25.6036	+	44.3467i	0.989891	+	1.71454i
$670$		0			0
$671$	−1.24257			−0.0479690
$672$		0			0
$673$	−32.6941			−1.26027			−0.630133	−	0.776487i	$-0.717000\pi$
$673$	−32.6941			−1.26027			−0.630133	+	0.776487i	$0.717000\pi$
$674$		0			0
$675$	−2.12225	−	3.67584i	−0.0816854	−	0.141483i
$676$		0			0
$677$	−18.2997	+	31.6960i	−0.703314	+	1.21818i	0.263983	+	0.964527i	$0.414964\pi$
$677$	−18.2997	+	31.6960i	−0.703314	+	1.21818i	−0.967297	+	0.253648i	$0.918370\pi$
$678$		0			0
$679$	24.5063	−	14.0548i	0.940466	−	0.539375i
$680$		0			0
$681$	−10.5721	+	18.3114i	−0.405124	+	0.701696i
$682$		0			0
$683$	−1.48720	−	2.57591i	−0.0569062	−	0.0985644i	0.836169	−	0.548472i	$-0.184790\pi$
$683$	−1.48720	−	2.57591i	−0.0569062	−	0.0985644i	−0.893075	+	0.449908i	$0.851457\pi$
$684$		0			0
$685$	−34.0048			−1.29926
$686$		0			0
$687$	44.0601			1.68100
$688$		0			0
$689$	6.24229	+	10.8120i	0.237812	+	0.411903i
$690$		0			0
$691$	0.911558	−	1.57886i	0.0346773	−	0.0600628i	−0.848166	−	0.529731i	$-0.822293\pi$
$691$	0.911558	−	1.57886i	0.0346773	−	0.0600628i	0.882843	+	0.469668i	$0.155626\pi$
$692$		0			0
$693$	1.24559	−	0.714368i	0.0473160	−	0.0271366i
$694$		0			0
$695$	−9.36705	+	16.2242i	−0.355312	+	0.615419i
$696$		0			0
$697$	−5.90894	−	10.2346i	−0.223817	−	0.387662i
$698$		0			0
$699$	8.28390			0.313326
$700$		0			0
$701$	−49.7699			−1.87978			−0.939891	−	0.341474i	$-0.889074\pi$
$701$	−49.7699			−1.87978			−0.939891	+	0.341474i	$0.889074\pi$
$702$		0			0
$703$	0.981199	+	1.69949i	0.0370066	+	0.0640974i
$704$		0			0
$705$	−0.377088	+	0.653135i	−0.0142019	+	0.0245985i
$706$		0			0
$707$	2.75058	+	1.59862i	0.103446	+	0.0601224i
$708$		0			0
$709$	7.47624	−	12.9492i	0.280776	−	0.486318i	−0.690800	−	0.723046i	$-0.742742\pi$
$709$	7.47624	−	12.9492i	0.280776	−	0.486318i	0.971576	+	0.236727i	$0.0760748\pi$
$710$		0			0
$711$	−21.4763	−	37.1980i	−0.805422	−	1.39503i
$712$		0			0
$713$	−5.48936			−0.205578
$714$		0			0
$715$	−0.358158			−0.0133943
$716$		0			0
$717$	−25.8505	−	44.7744i	−0.965404	−	1.67213i
$718$		0			0
$719$	−7.13480	+	12.3578i	−0.266083	+	0.460870i	−0.967847	−	0.251540i	$-0.919063\pi$
$719$	−7.13480	+	12.3578i	−0.266083	+	0.460870i	0.701764	+	0.712410i	$0.252396\pi$
$720$		0			0
$721$	0.148880	−	51.7169i	0.00554460	−	1.92604i
$722$		0			0
$723$	−10.7593	+	18.6357i	−0.400143	+	0.693068i
$724$		0			0
$725$	−3.48779	−	6.04104i	−0.129533	−	0.224358i
$726$		0			0
$727$	−2.40032			−0.0890231			−0.0445115	−	0.999009i	$-0.514173\pi$
$727$	−2.40032			−0.0890231			−0.0445115	+	0.999009i	$0.514173\pi$
$728$		0			0
$729$	−38.2178			−1.41547
$730$		0			0
$731$	−6.08483	−	10.5392i	−0.225056	−	0.389808i
$732$		0			0
$733$	6.20364	−	10.7450i	0.229137	−	0.396876i	−0.728416	−	0.685135i	$-0.759743\pi$
$733$	6.20364	−	10.7450i	0.229137	−	0.396876i	0.957552	+	0.288259i	$0.0930764\pi$
$734$		0			0
$735$	−15.2857	+	26.1270i	−0.563821	+	0.963709i
$736$		0			0
$737$	−0.0972930	+	0.168516i	−0.00358383	+	0.00620738i
$738$		0			0
$739$	0.0240469	+	0.0416505i	0.000884580	+	0.00153214i	0.866467	−	0.499234i	$-0.166385\pi$
$739$	0.0240469	+	0.0416505i	0.000884580	+	0.00153214i	−0.865583	+	0.500766i	$0.833052\pi$
$740$		0			0
$741$	3.83969			0.141055
$742$		0			0
$743$	−28.5507			−1.04742			−0.523712	−	0.851895i	$-0.675453\pi$
$743$	−28.5507			−1.04742			−0.523712	+	0.851895i	$0.675453\pi$
$744$		0			0
$745$	4.65454	+	8.06190i	0.170529	+	0.295365i
$746$		0			0
$747$	−8.17635	+	14.1619i	−0.299157	+	0.518155i
$748$		0			0
$749$	−0.0610922	+	21.2217i	−0.00223226	+	0.775425i
$750$		0			0
$751$	5.42782	−	9.40126i	0.198064	−	0.343057i	−0.749837	−	0.661623i	$-0.769868\pi$
$751$	5.42782	−	9.40126i	0.198064	−	0.343057i	0.947901	+	0.318566i	$0.103201\pi$
$752$		0			0
$753$	−13.3014	−	23.0386i	−0.484728	−	0.839574i
$754$		0			0
$755$	−32.2537			−1.17383
$756$		0			0
$757$	−20.1699			−0.733089			−0.366545	−	0.930400i	$-0.619459\pi$
$757$	−20.1699			−0.733089			−0.366545	+	0.930400i	$0.619459\pi$
$758$		0			0
$759$	1.17268	+	2.03114i	0.0425656	+	0.0737258i
$760$		0			0
$761$	14.9613	−	25.9137i	0.542347	−	0.939373i	−0.456422	−	0.889764i	$-0.650869\pi$
$761$	14.9613	−	25.9137i	0.542347	−	0.939373i	0.998769	−	0.0496090i	$-0.0157975\pi$
$762$		0			0
$763$	−46.6282	−	27.1001i	−1.68806	−	0.981090i
$764$		0			0
$765$	18.3888	−	31.8504i	0.664850	−	1.15155i
$766$		0			0
$767$	−1.17019	−	2.02682i	−0.0422530	−	0.0731843i
$768$		0			0
$769$	−15.7701			−0.568685			−0.284343	−	0.958723i	$-0.591775\pi$
$769$	−15.7701			−0.568685			−0.284343	+	0.958723i	$0.591775\pi$
$770$		0			0
$771$	23.7282			0.854550
$772$		0			0
$773$	−17.6138	−	30.5081i	−0.633526	−	1.09730i	−0.986825	−	0.161789i	$-0.948274\pi$
$773$	−17.6138	−	30.5081i	−0.633526	−	1.09730i	0.353300	−	0.935510i	$-0.385060\pi$
$774$		0			0
$775$	−0.981251	+	1.69958i	−0.0352476	+	0.0610506i
$776$		0			0
$777$	11.6888	−	6.70374i	0.419333	−	0.240495i
$778$		0			0
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	−0.535487	−	0.927490i	−0.0191612	−	0.0331882i
$782$		0			0
$783$	5.98745			0.213974
$784$		0			0
$785$	−18.2009			−0.649618
$786$		0			0
$787$	−22.9558	−	39.7606i	−0.818286	−	1.41731i	−0.906944	−	0.421251i	$-0.861591\pi$
$787$	−22.9558	−	39.7606i	−0.818286	−	1.41731i	0.0886576	−	0.996062i	$-0.471742\pi$
$788$		0			0
$789$	3.47665	−	6.02173i	0.123772	−	0.214379i
$790$		0			0
$791$	20.5160	−	11.7663i	0.729464	−	0.418361i
$792$		0			0
$793$	−6.32663	+	10.9580i	−0.224665	+	0.389132i
$794$		0			0
$795$	18.2451	+	31.6014i	0.647086	+	1.12079i
$796$		0			0
$797$	−2.14407			−0.0759468			−0.0379734	−	0.999279i	$-0.512090\pi$
$797$	−2.14407			−0.0759468			−0.0379734	+	0.999279i	$0.512090\pi$
$798$		0			0
$799$	1.03055			0.0364581
$800$		0			0
$801$	2.60171	+	4.50629i	0.0919268	+	0.159222i
$802$		0			0
$803$	−0.343190	+	0.594422i	−0.0121109	+	0.0209767i
$804$		0			0
$805$	−23.7072	−	13.7785i	−0.835569	−	0.485629i
$806$		0			0
$807$	32.7086	−	56.6530i	1.15140	−	1.99428i
$808$		0			0
$809$	11.6682	+	20.2098i	0.410230	+	0.710540i	0.994915	−	0.100721i	$-0.0321149\pi$
$809$	11.6682	+	20.2098i	0.410230	+	0.710540i	−0.584684	+	0.811261i	$0.698782\pi$
$810$		0			0
$811$	41.5527			1.45911			0.729556	−	0.683921i	$-0.239727\pi$
$811$	41.5527			1.45911			0.729556	+	0.683921i	$0.239727\pi$
$812$		0			0
$813$	32.8828			1.15325
$814$		0			0
$815$	−13.5786	−	23.5189i	−0.475639	−	0.823831i
$816$		0			0
$817$	1.02977	−	1.78361i	0.0360270	−	0.0624006i
$818$		0			0
$819$	0.0420929	−	14.6219i	0.00147084	−	0.510931i
$820$		0			0
$821$	−15.5848	+	26.9936i	−0.543912	+	0.942083i	0.454762	+	0.890613i	$0.349724\pi$
$821$	−15.5848	+	26.9936i	−0.543912	+	0.942083i	−0.998675	+	0.0514705i	$0.983609\pi$
$822$		0			0
$823$	8.62864	+	14.9452i	0.300775	+	0.520958i	0.976312	−	0.216368i	$-0.0694212\pi$
$823$	8.62864	+	14.9452i	0.300775	+	0.520958i	−0.675536	+	0.737327i	$0.736088\pi$
$824$		0			0
$825$	0.838490			0.0291925
$826$		0			0
$827$	−35.1385			−1.22188			−0.610942	−	0.791675i	$-0.709209\pi$
$827$	−35.1385			−1.22188			−0.610942	+	0.791675i	$0.709209\pi$
$828$		0			0
$829$	14.6235	+	25.3287i	0.507897	+	0.879703i	0.999958	+	0.00914267i	$0.00291024\pi$
$829$	14.6235	+	25.3287i	0.507897	+	0.879703i	−0.492061	+	0.870561i	$0.663756\pi$
$830$		0			0
$831$	28.6111	−	49.5559i	0.992508	−	1.71907i
$832$		0			0
$833$	41.3619	+	0.238144i	1.43310	+	0.00825118i
$834$		0			0
$835$	−13.9445	+	24.1526i	−0.482569	+	0.835834i
$836$		0			0
$837$	−0.842251	−	1.45882i	−0.0291124	−	0.0504242i
$838$		0			0
$839$	−16.6637			−0.575294			−0.287647	−	0.957737i	$-0.592873\pi$
$839$	−16.6637			−0.575294			−0.287647	+	0.957737i	$0.592873\pi$
$840$		0			0
$841$	−19.1600			−0.660689
$842$		0			0
$843$	14.1943	+	24.5852i	0.488877	+	0.846760i
$844$		0			0
$845$	9.00680	−	15.6002i	0.309843	−	0.536665i
$846$		0			0
$847$	0.0836201	−	29.0473i	0.00287322	−	0.998077i
$848$		0			0
$849$	26.7595	−	46.3488i	0.918383	−	1.59069i
$850$		0			0
$851$	6.10311	+	10.5709i	0.209212	+	0.362366i
$852$		0			0
$853$	20.0759			0.687386			0.343693	−	0.939082i	$-0.388322\pi$
$853$	20.0759			0.687386			0.343693	+	0.939082i	$0.388322\pi$
$854$		0			0
$855$	6.22408			0.212859
$856$		0			0
$857$	−10.7412	−	18.6042i	−0.366911	−	0.635509i	0.622170	−	0.782882i	$-0.286251\pi$
$857$	−10.7412	−	18.6042i	−0.366911	−	0.635509i	−0.989081	+	0.147373i	$0.952918\pi$
$858$		0			0
$859$	−6.97298	+	12.0776i	−0.237915	+	0.412081i	−0.960116	−	0.279603i	$-0.909797\pi$
$859$	−6.97298	+	12.0776i	−0.237915	+	0.412081i	0.722201	+	0.691683i	$0.243131\pi$
$860$		0			0
$861$	−11.8732	−	6.90067i	−0.404639	−	0.235174i
$862$		0			0
$863$	5.01491	−	8.68608i	0.170709	−	0.295678i	−0.767959	−	0.640499i	$-0.778727\pi$
$863$	5.01491	−	8.68608i	0.170709	−	0.295678i	0.938668	+	0.344822i	$0.112061\pi$
$864$		0			0
$865$	15.1960	+	26.3203i	0.516681	+	0.894917i
$866$		0			0
$867$	−46.4958			−1.57908
$868$		0			0
$869$	1.67061			0.0566717
$870$		0			0
$871$	0.990746	+	1.71602i	0.0335702	+	0.0581452i
$872$		0			0
$873$	−19.9431	+	34.5425i	−0.674973	+	1.16909i
$874$		0			0
$875$	−27.6243	+	15.8430i	−0.933872	+	0.535593i
$876$		0			0
$877$	−7.13290	+	12.3546i	−0.240861	+	0.417184i	−0.960960	−	0.276688i	$-0.910763\pi$
$877$	−7.13290	+	12.3546i	−0.240861	+	0.417184i	0.720099	+	0.693872i	$0.244096\pi$
$878$		0			0
$879$	30.9482	+	53.6038i	1.04386	+	1.80801i
$880$		0			0
$881$	33.3253			1.12276			0.561379	−	0.827559i	$-0.310271\pi$
$881$	33.3253			1.12276			0.561379	+	0.827559i	$0.310271\pi$
$882$		0			0
$883$	40.1473			1.35107			0.675533	−	0.737330i	$-0.263914\pi$
$883$	40.1473			1.35107			0.675533	+	0.737330i	$0.263914\pi$
$884$		0			0
$885$	−3.42024	−	5.92403i	−0.114970	−	0.199134i
$886$		0			0
$887$	8.76916	−	15.1886i	0.294440	−	0.509985i	−0.680415	−	0.732827i	$-0.738200\pi$
$887$	8.76916	−	15.1886i	0.294440	−	0.509985i	0.974854	+	0.222843i	$0.0715336\pi$
$888$		0			0
$889$	4.04080	−	2.31747i	0.135524	−	0.0777256i
$890$		0			0
$891$	0.454224	−	0.786739i	0.0152171	−	0.0263567i
$892$		0			0
$893$	0.0872023	+	0.151039i	0.00291811	+	0.00505432i
$894$		0			0
$895$	−3.39619			−0.113522
$896$		0			0
$897$	23.8831			0.797433
$898$		0			0
$899$	−1.38419	−	2.39749i	−0.0461653	−	0.0799607i
$900$		0			0
$901$	24.9311	−	43.1819i	0.830574	−	1.43860i
$902$		0			0
$903$	−12.2267	−	7.10608i	−0.406878	−	0.236476i
$904$		0			0
$905$	7.25339	−	12.5632i	0.241111	−	0.417616i
$906$		0			0
$907$	−15.3986	−	26.6711i	−0.511301	−	0.885600i	−0.999914	−	0.0130993i	$-0.995830\pi$
$907$	−15.3986	−	26.6711i	−0.511301	−	0.885600i	0.488613	−	0.872501i	$-0.337503\pi$
$908$		0			0
$909$	−4.49172			−0.148981
$910$		0			0
$911$	−26.5837			−0.880758			−0.440379	−	0.897812i	$-0.645156\pi$
$911$	−26.5837			−0.880758			−0.440379	+	0.897812i	$0.645156\pi$
$912$		0			0
$913$	−0.318014	−	0.550817i	−0.0105247	−	0.0182294i
$914$		0			0
$915$	−18.4916	+	32.0284i	−0.611313	+	1.05883i
$916$		0			0
$917$	−0.0307911	+	10.6960i	−0.00101681	+	0.353212i
$918$		0			0
$919$	6.07346	−	10.5195i	0.200345	−	0.347008i	−0.748295	−	0.663367i	$-0.769127\pi$
$919$	6.07346	−	10.5195i	0.200345	−	0.347008i	0.948640	+	0.316359i	$0.102460\pi$
$920$		0			0
$921$	−19.0679	−	33.0265i	−0.628307	−	1.08826i
$922$		0			0
$923$	−10.9059			−0.358971
$924$		0			0
$925$	4.36385			0.143482
$926$		0			0
$927$	36.5090	+	63.2354i	1.19911	+	2.07692i
$928$		0			0
$929$	13.4092	−	23.2254i	0.439940	−	0.761999i	−0.557744	−	0.830013i	$-0.688333\pi$
$929$	13.4092	−	23.2254i	0.439940	−	0.761999i	0.997684	+	0.0680139i	$0.0216662\pi$
$930$		0			0
$931$	3.46504	+	6.08223i	0.113562	+	0.199337i
$932$		0			0
$933$	7.67562	−	13.2946i	0.251289	−	0.435245i
$934$		0			0
$935$	0.715223	+	1.23880i	0.0233903	+	0.0405132i
$936$		0			0
$937$	42.6816			1.39435			0.697174	−	0.716902i	$-0.254441\pi$
$937$	42.6816			1.39435			0.697174	+	0.716902i	$0.254441\pi$
$938$		0			0
$939$	−2.36339			−0.0771264
$940$		0			0
$941$	−13.2276	−	22.9109i	−0.431208	−	0.746874i	0.565770	−	0.824563i	$-0.308579\pi$
$941$	−13.2276	−	22.9109i	−0.431208	−	0.746874i	−0.996978	+	0.0776893i	$0.975246\pi$
$942$		0			0
$943$	6.22006	−	10.7735i	0.202553	−	0.350832i
$944$		0			0
$945$	0.0242229	−	8.41437i	0.000787972	−	0.273719i
$946$		0			0
$947$	3.62554	−	6.27962i	0.117814	−	0.204060i	−0.801087	−	0.598548i	$-0.795745\pi$
$947$	3.62554	−	6.27962i	0.117814	−	0.204060i	0.918901	+	0.394488i	$0.129078\pi$
$948$		0			0
$949$	3.49474	+	6.05307i	0.113444	+	0.196491i
$950$		0			0
$951$	65.9482			2.13852
$952$		0			0
$953$	−19.1832			−0.621404			−0.310702	−	0.950507i	$-0.600564\pi$
$953$	−19.1832			−0.621404			−0.310702	+	0.950507i	$0.600564\pi$
$954$		0			0
$955$	−12.2117	−	21.1513i	−0.395161	−	0.684439i
$956$		0			0
$957$	−0.591403	+	1.02434i	−0.0191173	+	0.0331122i
$958$		0			0
$959$	46.6837	+	27.1323i	1.50749	+	0.876149i
$960$		0			0
$961$	15.1106	−	26.1723i	0.487438	−	0.844267i
$962$		0			0
$963$	−14.9813	−	25.9483i	−0.482764	−	0.836172i
$964$		0			0
$965$	27.9599			0.900060
$966$		0			0
$967$	−25.6363			−0.824407			−0.412203	−	0.911092i	$-0.635241\pi$
$967$	−25.6363			−0.824407			−0.412203	+	0.911092i	$0.635241\pi$
$968$		0			0
$969$	−7.66767	−	13.2808i	−0.246321	−	0.426640i
$970$		0			0
$971$	−18.1446	+	31.4274i	−0.582289	+	1.00855i	0.412919	+	0.910768i	$0.364509\pi$
$971$	−18.1446	+	31.4274i	−0.582289	+	1.00855i	−0.995207	+	0.0977858i	$0.968824\pi$
$972$		0			0
$973$	25.8048	−	14.7995i	0.827265	−	0.474452i
$974$		0			0
$975$	4.26922	−	7.39451i	0.136725	−	0.236814i
$976$		0			0
$977$	−1.14552	−	1.98409i	−0.0366483	−	0.0634768i	0.847119	−	0.531403i	$-0.178335\pi$
$977$	−1.14552	−	1.98409i	−0.0366483	−	0.0634768i	−0.883768	+	0.467926i	$0.845001\pi$
$978$		0			0
$979$	−0.202384			−0.00646822
$980$		0			0
$981$	76.1444			2.43110
$982$		0			0
$983$	5.33524	+	9.24091i	0.170168	+	0.294739i	0.938478	−	0.345338i	$-0.112236\pi$
$983$	5.33524	+	9.24091i	0.170168	+	0.294739i	−0.768311	+	0.640077i	$0.778902\pi$
$984$		0			0
$985$	−20.0411	+	34.7122i	−0.638563	+	1.10602i
$986$		0			0
$987$	1.03882	−	0.595783i	0.0330660	−	0.0189640i
$988$		0			0
$989$	6.40521	−	11.0942i	0.203674	−	0.352774i
$990$		0			0
$991$	−9.36208	−	16.2156i	−0.297396	−	0.515105i	0.678143	−	0.734930i	$-0.262785\pi$
$991$	−9.36208	−	16.2156i	−0.297396	−	0.515105i	−0.975539	+	0.219824i	$0.929452\pi$
$992$		0			0
$993$	−25.4214			−0.806723
$994$		0			0
$995$	10.4376			0.330895
$996$		0			0
$997$	7.22465	+	12.5135i	0.228807	+	0.396305i	0.957455	−	0.288583i	$-0.0931842\pi$
$997$	7.22465	+	12.5135i	0.228807	+	0.396305i	−0.728648	+	0.684889i	$0.759851\pi$
$998$		0			0
$999$	−1.87284	+	3.24386i	−0.0592541	+	0.102631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.457.8	yes	16
7.2	even	3		7448.2.a.bq.1.1		8
7.4	even	3	inner	1064.2.q.n.305.8	✓	16
7.5	odd	6		7448.2.a.br.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.8	✓	16	7.4	even	3	inner
1064.2.q.n.457.8	yes	16	1.1	even	1	trivial
7448.2.a.bq.1.1		8	7.2	even	3
7448.2.a.br.1.8		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29764 + 2.24758i) q^{3} +(-0.833107 + 1.44298i) q^{5} +(2.29509 - 1.31627i) q^{7} +(-1.86773 + 3.23500i) q^{9} +O(q^{10})\)	\(q+(1.29764 + 2.24758i) q^{3} +(-0.833107 + 1.44298i) q^{5} +(2.29509 - 1.31627i) q^{7} +(-1.86773 + 3.23500i) q^{9} +(-0.0726443 - 0.125824i) q^{11} -1.47949 q^{13} -4.32429 q^{15} +(2.95447 + 5.11729i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(5.93662 + 3.45033i) q^{21} +(-3.11003 + 5.38673i) q^{23} +(1.11187 + 1.92581i) q^{25} -1.90873 q^{27} -3.13688 q^{29} +(0.441263 + 0.764290i) q^{31} +(0.188532 - 0.326547i) q^{33} +(-0.0126906 + 4.40837i) q^{35} +(0.981199 - 1.69949i) q^{37} +(-1.91984 - 3.32527i) q^{39} -2.00000 q^{41} -2.05954 q^{43} +(-3.11204 - 5.39021i) q^{45} +(0.0872023 - 0.151039i) q^{47} +(3.53484 - 6.04193i) q^{49} +(-7.66767 + 13.2808i) q^{51} +(-4.21921 - 7.30789i) q^{53} +0.242082 q^{55} -2.59528 q^{57} +(0.790938 + 1.36994i) q^{59} +(4.27622 - 7.40663i) q^{61} +(-0.0284509 + 9.88306i) q^{63} +(1.23257 - 2.13488i) q^{65} +(-0.669653 - 1.15987i) q^{67} -16.1428 q^{69} +7.37135 q^{71} +(-2.36212 - 4.09132i) q^{73} +(-2.88560 + 4.99801i) q^{75} +(-0.332343 - 0.193156i) q^{77} +(-5.74929 + 9.95806i) q^{79} +(3.12636 + 5.41501i) q^{81} +4.37769 q^{83} -9.84555 q^{85} +(-4.07054 - 7.05038i) q^{87} +(0.696489 - 1.20635i) q^{89} +(-3.39556 + 1.94742i) q^{91} +(-1.14520 + 1.98354i) q^{93} +(-0.833107 - 1.44298i) q^{95} +10.6777 q^{97} +0.542720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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