LMFDB - Embedded newform 1148.2.i.d.165.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(165,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("1148.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.i (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:	$9.16682615204$
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} + 14 x^{14} - 8 x^{13} + 136 x^{12} - 87 x^{11} + 706 x^{10} - 568 x^{9} + 2685 x^{8} + \cdots + 121 $ x^16 + 14x^14 - 8x^13 + 136x^12 - 87x^11 + 706x^10 - 568x^9 + 2685x^8 - 2100x^7 + 5529x^6 - 4919x^5 + 8145x^4 - 5182x^3 + 2775x^2 - 660x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			165.3
Root			$0.666692 - 1.15474i$ of defining polynomial
Character	$\chi$	$=$	1148.165
Dual form			1148.2.i.d.821.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.666692 + 1.15474i) q^{3} +(-0.883435 - 1.53015i) q^{5} +(2.62366 - 0.341202i) q^{7} +(0.611043 + 1.05836i) q^{9} +O(q^{10})$	\(q+(-0.666692 + 1.15474i) q^{3} +(-0.883435 - 1.53015i) q^{5} +(2.62366 - 0.341202i) q^{7} +(0.611043 + 1.05836i) q^{9} +(1.24363 - 2.15404i) q^{11} -2.30214 q^{13} +2.35592 q^{15} +(0.702066 - 1.21601i) q^{17} +(-1.97804 - 3.42606i) q^{19} +(-1.35517 + 3.25713i) q^{21} +(0.0202760 + 0.0351191i) q^{23} +(0.939085 - 1.62654i) q^{25} -5.62966 q^{27} +6.20359 q^{29} +(1.49287 - 2.58572i) q^{31} +(1.65824 + 2.87216i) q^{33} +(-2.83992 - 3.71317i) q^{35} +(-0.0975626 - 0.168983i) q^{37} +(1.53482 - 2.65838i) q^{39} +1.00000 q^{41} -1.19665 q^{43} +(1.07963 - 1.86998i) q^{45} +(3.71964 + 6.44260i) q^{47} +(6.76716 - 1.79040i) q^{49} +(0.936124 + 1.62141i) q^{51} +(5.89997 - 10.2191i) q^{53} -4.39468 q^{55} +5.27497 q^{57} +(2.75423 - 4.77047i) q^{59} +(-1.95728 - 3.39011i) q^{61} +(1.96428 + 2.56828i) q^{63} +(2.03379 + 3.52262i) q^{65} +(-2.89923 + 5.02161i) q^{67} -0.0540714 q^{69} +10.2887 q^{71} +(6.14921 - 10.6507i) q^{73} +(1.25216 + 2.16881i) q^{75} +(2.52791 - 6.07578i) q^{77} +(0.679701 + 1.17728i) q^{79} +(1.92013 - 3.32575i) q^{81} +6.02722 q^{83} -2.48092 q^{85} +(-4.13589 + 7.16357i) q^{87} +(0.113032 + 0.195777i) q^{89} +(-6.04002 + 0.785495i) q^{91} +(1.99056 + 3.44776i) q^{93} +(-3.49493 + 6.05340i) q^{95} +1.43170 q^{97} +3.03965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^9	$ 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) $ 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.666692	+	1.15474i	−0.384915	+	0.666692i	−0.991757	−	0.128130i	$-0.959103\pi$
$3$	−0.666692	+	1.15474i	−0.384915	+	0.666692i	0.606842	+	0.794822i	$0.292436\pi$
$4$		0			0
$5$	−0.883435	−	1.53015i	−0.395084	−	0.684306i	0.598028	−	0.801475i	$-0.295951\pi$
$5$	−0.883435	−	1.53015i	−0.395084	−	0.684306i	−0.993112	+	0.117169i	$0.962618\pi$
$6$		0			0
$7$	2.62366	−	0.341202i	0.991649	−	0.128962i
$7$	2.62366	−	0.341202i	0.991649	−	0.128962i
$8$		0			0
$9$	0.611043	+	1.05836i	0.203681	+	0.352786i
$10$		0			0
$11$	1.24363	−	2.15404i	0.374970	−	0.649466i	−0.615353	−	0.788252i	$-0.710986\pi$
$11$	1.24363	−	2.15404i	0.374970	−	0.649466i	0.990322	+	0.138785i	$0.0443198\pi$
$12$		0			0
$13$	−2.30214			−0.638498			−0.319249	−	0.947671i	$-0.603431\pi$
$13$	−2.30214			−0.638498			−0.319249	+	0.947671i	$0.603431\pi$
$14$		0			0
$15$	2.35592			0.608295
$16$		0			0
$17$	0.702066	−	1.21601i	0.170276	−	0.294927i	−0.768240	−	0.640162i	$-0.778867\pi$
$17$	0.702066	−	1.21601i	0.170276	−	0.294927i	0.938516	+	0.345235i	$0.112201\pi$
$18$		0			0
$19$	−1.97804	−	3.42606i	−0.453793	−	0.785992i	0.544825	−	0.838550i	$-0.316596\pi$
$19$	−1.97804	−	3.42606i	−0.453793	−	0.785992i	−0.998618	+	0.0525576i	$0.983263\pi$
$20$		0			0
$21$	−1.35517	+	3.25713i	−0.295722	+	0.710765i
$22$		0			0
$23$	0.0202760	+	0.0351191i	0.00422784	+	0.00732283i	0.868132	−	0.496334i	$-0.165321\pi$
$23$	0.0202760	+	0.0351191i	0.00422784	+	0.00732283i	−0.863904	+	0.503657i	$0.831988\pi$
$24$		0			0
$25$	0.939085	−	1.62654i	0.187817	−	0.325308i
$26$		0			0
$27$	−5.62966			−1.08343
$28$		0			0
$29$	6.20359			1.15198			0.575989	−	0.817457i	$-0.304617\pi$
$29$	6.20359			1.15198			0.575989	+	0.817457i	$0.304617\pi$
$30$		0			0
$31$	1.49287	−	2.58572i	0.268127	−	0.464409i	−0.700251	−	0.713896i	$-0.746929\pi$
$31$	1.49287	−	2.58572i	0.268127	−	0.464409i	0.968378	+	0.249487i	$0.0802621\pi$
$32$		0			0
$33$	1.65824	+	2.87216i	0.288663	+	0.499979i
$34$		0			0
$35$	−2.83992	−	3.71317i	−0.480035	−	0.627641i
$36$		0			0
$37$	−0.0975626	−	0.168983i	−0.0160392	−	0.0277807i	0.857894	−	0.513826i	$-0.171772\pi$
$37$	−0.0975626	−	0.168983i	−0.0160392	−	0.0277807i	−0.873934	+	0.486045i	$0.838439\pi$
$38$		0			0
$39$	1.53482	−	2.65838i	0.245767	−	0.425682i
$40$		0			0
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$		0			0
$43$	−1.19665			−0.182488			−0.0912438	−	0.995829i	$-0.529084\pi$
$43$	−1.19665			−0.182488			−0.0912438	+	0.995829i	$0.529084\pi$
$44$		0			0
$45$	1.07963	−	1.86998i	0.160942	−	0.278760i
$46$		0			0
$47$	3.71964	+	6.44260i	0.542565	+	0.939749i	0.998756	+	0.0498677i	$0.0158800\pi$
$47$	3.71964	+	6.44260i	0.542565	+	0.939749i	−0.456191	+	0.889882i	$0.650787\pi$
$48$		0			0
$49$	6.76716	−	1.79040i	0.966737	−	0.255771i
$50$		0			0
$51$	0.936124	+	1.62141i	0.131084	+	0.227043i
$52$		0			0
$53$	5.89997	−	10.2191i	0.810424	−	1.40370i	−0.102144	−	0.994770i	$-0.532570\pi$
$53$	5.89997	−	10.2191i	0.810424	−	1.40370i	0.912568	−	0.408926i	$-0.134096\pi$
$54$		0			0
$55$	−4.39468			−0.592578
$56$		0			0
$57$	5.27497			0.698686
$58$		0			0
$59$	2.75423	−	4.77047i	0.358570	−	0.621062i	−0.629152	−	0.777282i	$-0.716598\pi$
$59$	2.75423	−	4.77047i	0.358570	−	0.621062i	0.987722	+	0.156221i	$0.0499310\pi$
$60$		0			0
$61$	−1.95728	−	3.39011i	−0.250604	−	0.434059i	0.713088	−	0.701074i	$-0.247296\pi$
$61$	−1.95728	−	3.39011i	−0.250604	−	0.434059i	−0.963692	+	0.267016i	$0.913962\pi$
$62$		0			0
$63$	1.96428	+	2.56828i	0.247476	+	0.323573i
$64$		0			0
$65$	2.03379	+	3.52262i	0.252260	+	0.436928i
$66$		0			0
$67$	−2.89923	+	5.02161i	−0.354197	+	0.613487i	−0.986980	−	0.160842i	$-0.948579\pi$
$67$	−2.89923	+	5.02161i	−0.354197	+	0.613487i	0.632783	+	0.774329i	$0.281912\pi$
$68$		0			0
$69$	−0.0540714			−0.00650943
$70$		0			0
$71$	10.2887			1.22105			0.610524	−	0.791997i	$-0.290959\pi$
$71$	10.2887			1.22105			0.610524	+	0.791997i	$0.290959\pi$
$72$		0			0
$73$	6.14921	−	10.6507i	0.719710	−	1.24657i	−0.241404	−	0.970425i	$-0.577608\pi$
$73$	6.14921	−	10.6507i	0.719710	−	1.24657i	0.961115	−	0.276150i	$-0.0890587\pi$
$74$		0			0
$75$	1.25216	+	2.16881i	0.144587	+	0.250432i
$76$		0			0
$77$	2.52791	−	6.07578i	0.288082	−	0.692400i
$78$		0			0
$79$	0.679701	+	1.17728i	0.0764723	+	0.132454i	0.901726	−	0.432309i	$-0.142301\pi$
$79$	0.679701	+	1.17728i	0.0764723	+	0.132454i	−0.825253	+	0.564763i	$0.808968\pi$
$80$		0			0
$81$	1.92013	−	3.32575i	0.213347	−	0.369528i
$82$		0			0
$83$	6.02722			0.661573			0.330787	−	0.943706i	$-0.392686\pi$
$83$	6.02722			0.661573			0.330787	+	0.943706i	$0.392686\pi$
$84$		0			0
$85$	−2.48092			−0.269093
$86$		0			0
$87$	−4.13589	+	7.16357i	−0.443414	+	0.768015i
$88$		0			0
$89$	0.113032	+	0.195777i	0.0119813	+	0.0207523i	0.871954	−	0.489588i	$-0.162853\pi$
$89$	0.113032	+	0.195777i	0.0119813	+	0.0207523i	−0.859973	+	0.510340i	$0.829519\pi$
$90$		0			0
$91$	−6.04002	+	0.785495i	−0.633166	+	0.0823422i
$92$		0			0
$93$	1.99056	+	3.44776i	0.206412	+	0.357516i
$94$		0			0
$95$	−3.49493	+	6.05340i	−0.358573	+	0.621066i
$96$		0			0
$97$	1.43170			0.145367			0.0726836	−	0.997355i	$-0.476844\pi$
$97$	1.43170			0.145367			0.0726836	+	0.997355i	$0.476844\pi$
$98$		0			0
$99$	3.03965			0.305497
$100$		0			0
$101$	3.36789	−	5.83335i	0.335117	−	0.580440i	−0.648390	−	0.761308i	$-0.724557\pi$
$101$	3.36789	−	5.83335i	0.335117	−	0.580440i	0.983507	+	0.180868i	$0.0578907\pi$
$102$		0			0
$103$	3.46632	+	6.00384i	0.341547	+	0.591576i	0.984720	−	0.174144i	$-0.0557159\pi$
$103$	3.46632	+	6.00384i	0.341547	+	0.591576i	−0.643173	+	0.765721i	$0.722383\pi$
$104$		0			0
$105$	6.18112	−	0.803845i	0.603216	−	0.0784472i
$106$		0			0
$107$	5.83693	+	10.1099i	0.564278	+	0.977358i	0.997116	+	0.0758863i	$0.0241786\pi$
$107$	5.83693	+	10.1099i	0.564278	+	0.977358i	−0.432839	+	0.901471i	$0.642488\pi$
$108$		0			0
$109$	1.10031	−	1.90580i	0.105391	−	0.182543i	−0.808507	−	0.588487i	$-0.799724\pi$
$109$	1.10031	−	1.90580i	0.105391	−	0.182543i	0.913898	+	0.405944i	$0.133057\pi$
$110$		0			0
$111$	0.260177			0.0246949
$112$		0			0
$113$	9.83479			0.925180			0.462590	−	0.886572i	$-0.346920\pi$
$113$	9.83479			0.925180			0.462590	+	0.886572i	$0.346920\pi$
$114$		0			0
$115$	0.0358251	−	0.0620508i	0.00334070	−	0.00578627i
$116$		0			0
$117$	−1.40670	−	2.43648i	−0.130050	−	0.225253i
$118$		0			0
$119$	1.42707	−	3.42995i	0.130820	−	0.314423i
$120$		0			0
$121$	2.40675	+	4.16862i	0.218796	+	0.378965i
$122$		0			0
$123$	−0.666692	+	1.15474i	−0.0601136	+	0.104120i
$124$		0			0
$125$	−12.1528			−1.08698
$126$		0			0
$127$	−20.5602			−1.82443			−0.912213	−	0.409716i	$-0.865628\pi$
$127$	−20.5602			−1.82443			−0.912213	+	0.409716i	$0.865628\pi$
$128$		0			0
$129$	0.797798	−	1.38183i	0.0702422	−	0.121663i
$130$		0			0
$131$	4.13220	+	7.15718i	0.361032	+	0.625325i	0.988131	−	0.153614i	$-0.0490912\pi$
$131$	4.13220	+	7.15718i	0.361032	+	0.625325i	−0.627099	+	0.778939i	$0.715758\pi$
$132$		0			0
$133$	−6.35867	−	8.31390i	−0.551367	−	0.720906i
$134$		0			0
$135$	4.97344	+	8.61426i	0.428046	+	0.741397i
$136$		0			0
$137$	0.340556	−	0.589860i	0.0290956	−	0.0503951i	−0.851111	−	0.524986i	$-0.824071\pi$
$137$	0.340556	−	0.589860i	0.0290956	−	0.0503951i	0.880207	+	0.474591i	$0.157404\pi$
$138$		0			0
$139$	−13.1700			−1.11706			−0.558531	−	0.829484i	$-0.688635\pi$
$139$	−13.1700			−1.11706			−0.558531	+	0.829484i	$0.688635\pi$
$140$		0			0
$141$	−9.91941			−0.835365
$142$		0			0
$143$	−2.86301	+	4.95889i	−0.239417	+	0.414683i
$144$		0			0
$145$	−5.48047	−	9.49246i	−0.455129	−	0.788306i
$146$		0			0
$147$	−2.44416	+	9.00799i	−0.201591	+	0.742966i
$148$		0			0
$149$	7.64804	+	13.2468i	0.626551	+	1.08522i	0.988239	+	0.152919i	$0.0488675\pi$
$149$	7.64804	+	13.2468i	0.626551	+	1.08522i	−0.361687	+	0.932300i	$0.617799\pi$
$150$		0			0
$151$	1.99157	−	3.44951i	0.162072	−	0.280717i	−0.773540	−	0.633748i	$-0.781516\pi$
$151$	1.99157	−	3.44951i	0.162072	−	0.280717i	0.935612	+	0.353031i	$0.114849\pi$
$152$		0			0
$153$	1.71597			0.138728
$154$		0			0
$155$	−5.27540			−0.423730
$156$		0			0
$157$	−7.25701	+	12.5695i	−0.579173	+	1.00316i	0.416402	+	0.909181i	$0.363291\pi$
$157$	−7.25701	+	12.5695i	−0.579173	+	1.00316i	−0.995574	+	0.0939756i	$0.970042\pi$
$158$		0			0
$159$	7.86693	+	13.6259i	0.623889	+	1.08061i
$160$		0			0
$161$	0.0651800	+	0.0852222i	0.00513690	+	0.00671645i
$162$		0			0
$163$	−7.64431	−	13.2403i	−0.598749	−	1.03706i	−0.993006	−	0.118063i	$-0.962332\pi$
$163$	−7.64431	−	13.2403i	−0.598749	−	1.03706i	0.394258	−	0.919000i	$-0.371002\pi$
$164$		0			0
$165$	2.92990	−	5.07473i	0.228092	−	0.395067i
$166$		0			0
$167$	−13.7533			−1.06426			−0.532130	−	0.846663i	$-0.678608\pi$
$167$	−13.7533			−1.06426			−0.532130	+	0.846663i	$0.678608\pi$
$168$		0			0
$169$	−7.70017			−0.592321
$170$		0			0
$171$	2.41733	−	4.18694i	0.184858	−	0.320183i
$172$		0			0
$173$	−7.85466	−	13.6047i	−0.597179	−	1.03434i	−0.993235	−	0.116118i	$-0.962955\pi$
$173$	−7.85466	−	13.6047i	−0.597179	−	1.03434i	0.396057	−	0.918226i	$-0.370378\pi$
$174$		0			0
$175$	1.90886	−	4.58791i	0.144296	−	0.346813i
$176$		0			0
$177$	3.67245	+	6.36087i	0.276038	+	0.478112i
$178$		0			0
$179$	3.10753	−	5.38240i	0.232268	−	0.402299i	−0.726207	−	0.687476i	$-0.758719\pi$
$179$	3.10753	−	5.38240i	0.232268	−	0.402299i	0.958475	+	0.285176i	$0.0920522\pi$
$180$		0			0
$181$	−15.6181			−1.16088			−0.580441	−	0.814302i	$-0.697120\pi$
$181$	−15.6181			−1.16088			−0.580441	+	0.814302i	$0.697120\pi$
$182$		0			0
$183$	5.21961			0.385845
$184$		0			0
$185$	−0.172380	+	0.298572i	−0.0126737	+	0.0219514i
$186$		0			0
$187$	−1.74622	−	3.02455i	−0.127697	−	0.221177i
$188$		0			0
$189$	−14.7703	+	1.92086i	−1.07438	+	0.139722i
$190$		0			0
$191$	2.18174	+	3.77888i	0.157865	+	0.273430i	0.934099	−	0.357015i	$-0.116206\pi$
$191$	2.18174	+	3.77888i	0.157865	+	0.273430i	−0.776233	+	0.630446i	$0.782872\pi$
$192$		0			0
$193$	7.58370	−	13.1354i	0.545887	−	0.945503i	−0.452664	−	0.891681i	$-0.649526\pi$
$193$	7.58370	−	13.1354i	0.545887	−	0.945503i	0.998551	−	0.0538222i	$-0.0171404\pi$
$194$		0			0
$195$	−5.42364			−0.388395
$196$		0			0
$197$	−4.34032			−0.309235			−0.154618	−	0.987974i	$-0.549415\pi$
$197$	−4.34032			−0.309235			−0.154618	+	0.987974i	$0.549415\pi$
$198$		0			0
$199$	−1.53724	+	2.66258i	−0.108972	+	0.188745i	−0.915354	−	0.402650i	$-0.868089\pi$
$199$	−1.53724	+	2.66258i	−0.108972	+	0.188745i	0.806382	+	0.591395i	$0.201423\pi$
$200$		0			0
$201$	−3.86578	−	6.69574i	−0.272671	−	0.472281i
$202$		0			0
$203$	16.2761	−	2.11668i	1.14236	−	0.148562i
$204$		0			0
$205$	−0.883435	−	1.53015i	−0.0617018	−	0.106871i
$206$		0			0
$207$	−0.0247790	+	0.0429185i	−0.00172226	+	0.00298304i
$208$		0			0
$209$	−9.83981			−0.680634
$210$		0			0
$211$	0.480367			0.0330698			0.0165349	−	0.999863i	$-0.494737\pi$
$211$	0.480367			0.0330698			0.0165349	+	0.999863i	$0.494737\pi$
$212$		0			0
$213$	−6.85942	+	11.8809i	−0.470000	+	0.814064i
$214$		0			0
$215$	1.05716	+	1.83106i	0.0720979	+	0.124877i
$216$		0			0
$217$	3.03451	−	7.29341i	0.205996	−	0.495109i
$218$		0			0
$219$	8.19926	+	14.2015i	0.554054	+	0.959650i
$220$		0			0
$221$	−1.61625	+	2.79943i	−0.108721	+	0.188310i
$222$		0			0
$223$	−7.20336			−0.482373			−0.241186	−	0.970479i	$-0.577537\pi$
$223$	−7.20336			−0.482373			−0.241186	+	0.970479i	$0.577537\pi$
$224$		0			0
$225$	2.29528			0.153019
$226$		0			0
$227$	−3.96266	+	6.86353i	−0.263011	+	0.455549i	−0.967041	−	0.254622i	$-0.918049\pi$
$227$	−3.96266	+	6.86353i	−0.263011	+	0.455549i	0.704030	+	0.710171i	$0.251382\pi$
$228$		0			0
$229$	−9.19899	−	15.9331i	−0.607886	−	1.05289i	−0.991588	−	0.129433i	$-0.958684\pi$
$229$	−9.19899	−	15.9331i	−0.607886	−	1.05289i	0.383702	−	0.923457i	$-0.374649\pi$
$230$		0			0
$231$	5.33065	+	6.96977i	0.350731	+	0.458577i
$232$		0			0
$233$	−7.39384	−	12.8065i	−0.484386	−	0.838982i	0.515453	−	0.856918i	$-0.327624\pi$
$233$	−7.39384	−	12.8065i	−0.484386	−	0.838982i	−0.999839	+	0.0179361i	$0.994290\pi$
$234$		0			0
$235$	6.57211	−	11.3832i	0.428717	−	0.742560i
$236$		0			0
$237$	−1.81260			−0.117741
$238$		0			0
$239$	−25.7876			−1.66806			−0.834031	−	0.551717i	$-0.813973\pi$
$239$	−25.7876			−1.66806			−0.834031	+	0.551717i	$0.813973\pi$
$240$		0			0
$241$	8.09571	−	14.0222i	0.521491	−	0.903249i	−0.478197	−	0.878253i	$-0.658709\pi$
$241$	8.09571	−	14.0222i	0.521491	−	0.903249i	0.999688	−	0.0249959i	$-0.00795726\pi$
$242$		0			0
$243$	−5.88423	−	10.1918i	−0.377474	−	0.653803i
$244$		0			0
$245$	−8.71793	−	8.77310i	−0.556968	−	0.560493i
$246$		0			0
$247$	4.55371	+	7.88726i	0.289746	+	0.501854i
$248$		0			0
$249$	−4.01830	+	6.95990i	−0.254650	+	0.441066i
$250$		0			0
$251$	1.47665			0.0932054			0.0466027	−	0.998914i	$-0.485161\pi$
$251$	1.47665			0.0932054			0.0466027	+	0.998914i	$0.485161\pi$
$252$		0			0
$253$	0.100864			0.00634124
$254$		0			0
$255$	1.65401	−	2.86483i	0.103578	−	0.179402i
$256$		0			0
$257$	3.18374	+	5.51440i	0.198596	+	0.343979i	0.948074	−	0.318051i	$-0.103028\pi$
$257$	3.18374	+	5.51440i	0.198596	+	0.343979i	−0.749477	+	0.662030i	$0.769695\pi$
$258$		0			0
$259$	−0.313628	−	0.410066i	−0.0194879	−	0.0254803i
$260$		0			0
$261$	3.79066	+	6.56562i	0.234636	+	0.406402i
$262$		0			0
$263$	−9.05654	+	15.6864i	−0.558450	+	0.967264i	0.439176	+	0.898401i	$0.355270\pi$
$263$	−9.05654	+	15.6864i	−0.558450	+	0.967264i	−0.997626	+	0.0688627i	$0.978063\pi$
$264$		0			0
$265$	−20.8490			−1.28074
$266$		0			0
$267$	−0.301430			−0.0184472
$268$		0			0
$269$	8.58730	−	14.8736i	0.523577	−	0.906862i	−0.476046	−	0.879420i	$-0.657931\pi$
$269$	8.58730	−	14.8736i	0.523577	−	0.906862i	0.999623	−	0.0274420i	$-0.00873617\pi$
$270$		0			0
$271$	7.87495	+	13.6398i	0.478369	+	0.828560i	0.999692	−	0.0247994i	$-0.00789470\pi$
$271$	7.87495	+	13.6398i	0.478369	+	0.828560i	−0.521323	+	0.853359i	$0.674561\pi$
$272$		0			0
$273$	3.11979	−	7.49836i	0.188818	−	0.453822i
$274$		0			0
$275$	−2.33575	−	4.04564i	−0.140851	−	0.243962i
$276$		0			0
$277$	−9.81348	+	16.9974i	−0.589635	+	1.02128i	0.404645	+	0.914474i	$0.367395\pi$
$277$	−9.81348	+	16.9974i	−0.589635	+	1.02128i	−0.994280	+	0.106804i	$0.965938\pi$
$278$		0			0
$279$	3.64882			0.218449
$280$		0			0
$281$	8.20950			0.489738			0.244869	−	0.969556i	$-0.421255\pi$
$281$	8.20950			0.489738			0.244869	+	0.969556i	$0.421255\pi$
$282$		0			0
$283$	−8.98529	+	15.5630i	−0.534120	+	0.925123i	0.465085	+	0.885266i	$0.346024\pi$
$283$	−8.98529	+	15.5630i	−0.534120	+	0.925123i	−0.999205	+	0.0398571i	$0.987310\pi$
$284$		0			0
$285$	−4.66009	−	8.07152i	−0.276040	−	0.478115i
$286$		0			0
$287$	2.62366	−	0.341202i	0.154870	−	0.0201405i
$288$		0			0
$289$	7.51421	+	13.0150i	0.442012	+	0.765588i
$290$		0			0
$291$	−0.954504	+	1.65325i	−0.0559540	+	0.0969152i
$292$		0			0
$293$	7.45654			0.435616			0.217808	−	0.975992i	$-0.430109\pi$
$293$	7.45654			0.435616			0.217808	+	0.975992i	$0.430109\pi$
$294$		0			0
$295$	−9.73273			−0.566662
$296$		0			0
$297$	−7.00124	+	12.1265i	−0.406253	+	0.703651i
$298$		0			0
$299$	−0.0466781	−	0.0808489i	−0.00269947	−	0.00467561i
$300$		0			0
$301$	−3.13960	+	0.408300i	−0.180964	+	0.0235340i
$302$		0			0
$303$	4.49069	+	7.77810i	0.257983	+	0.446840i
$304$		0			0
$305$	−3.45826	+	5.98988i	−0.198019	+	0.342979i
$306$		0			0
$307$	12.0440			0.687387			0.343693	−	0.939082i	$-0.388322\pi$
$307$	12.0440			0.687387			0.343693	+	0.939082i	$0.388322\pi$
$308$		0			0
$309$	−9.24388			−0.525866
$310$		0			0
$311$	−13.3846	+	23.1828i	−0.758970	+	1.31457i	0.184407	+	0.982850i	$0.440964\pi$
$311$	−13.3846	+	23.1828i	−0.758970	+	1.31457i	−0.943376	+	0.331724i	$0.892370\pi$
$312$		0			0
$313$	1.12169	+	1.94283i	0.0634018	+	0.109815i	0.895984	−	0.444087i	$-0.146472\pi$
$313$	1.12169	+	1.94283i	0.0634018	+	0.109815i	−0.832582	+	0.553902i	$0.813138\pi$
$314$		0			0
$315$	2.19455	−	5.27456i	0.123649	−	0.297188i
$316$		0			0
$317$	14.2313	+	24.6493i	0.799309	+	1.38444i	0.920067	+	0.391761i	$0.128134\pi$
$317$	14.2313	+	24.6493i	0.799309	+	1.38444i	−0.120758	+	0.992682i	$0.538533\pi$
$318$		0			0
$319$	7.71500	−	13.3628i	0.431957	−	0.748171i
$320$		0			0
$321$	−15.5658			−0.868796
$322$		0			0
$323$	−5.55485			−0.309080
$324$		0			0
$325$	−2.16190	+	3.74452i	−0.119921	+	0.207709i
$326$		0			0
$327$	1.46714	+	2.54116i	0.0811331	+	0.140527i
$328$		0			0
$329$	11.9573	+	15.6340i	0.659226	+	0.861932i
$330$		0			0
$331$	−2.11871	−	3.66971i	−0.116455	−	0.201705i	0.801906	−	0.597451i	$-0.203820\pi$
$331$	−2.11871	−	3.66971i	−0.116455	−	0.201705i	−0.918360	+	0.395745i	$0.870486\pi$
$332$		0			0
$333$	0.119230	−	0.206512i	0.00653375	−	0.0113168i
$334$		0			0
$335$	10.2451			0.559751
$336$		0			0
$337$	−9.10406			−0.495930			−0.247965	−	0.968769i	$-0.579762\pi$
$337$	−9.10406			−0.495930			−0.247965	+	0.968769i	$0.579762\pi$
$338$		0			0
$339$	−6.55678	+	11.3567i	−0.356115	+	0.616810i
$340$		0			0
$341$	−3.71315	−	6.43137i	−0.201079	−	0.348278i
$342$		0			0
$343$	17.1438	−	7.00636i	0.925680	−	0.378308i
$344$		0			0
$345$	0.0477686	+	0.0827376i	0.00257177	+	0.00445444i
$346$		0			0
$347$	−5.05966	+	8.76358i	−0.271617	+	0.470454i	−0.969276	−	0.245976i	$-0.920892\pi$
$347$	−5.05966	+	8.76358i	−0.271617	+	0.470454i	0.697659	+	0.716430i	$0.254225\pi$
$348$		0			0
$349$	7.60171			0.406910			0.203455	−	0.979084i	$-0.434783\pi$
$349$	7.60171			0.406910			0.203455	+	0.979084i	$0.434783\pi$
$350$		0			0
$351$	12.9603			0.691767
$352$		0			0
$353$	−4.67113	+	8.09064i	−0.248619	+	0.430621i	−0.963143	−	0.268990i	$-0.913310\pi$
$353$	−4.67113	+	8.09064i	−0.248619	+	0.430621i	0.714524	+	0.699611i	$0.246643\pi$
$354$		0			0
$355$	−9.08944	−	15.7434i	−0.482417	−	0.835571i
$356$		0			0
$357$	3.00930	+	3.93463i	0.159269	+	0.208243i
$358$		0			0
$359$	2.28526	+	3.95819i	0.120611	+	0.208905i	0.920009	−	0.391897i	$-0.128181\pi$
$359$	2.28526	+	3.95819i	0.120611	+	0.208905i	−0.799398	+	0.600802i	$0.794848\pi$
$360$		0			0
$361$	1.67474	−	2.90074i	0.0881443	−	0.152670i
$362$		0			0
$363$	−6.41825			−0.336871
$364$		0			0
$365$	−21.7297			−1.13738
$366$		0			0
$367$	−16.3082	+	28.2467i	−0.851283	+	1.47447i	0.0287679	+	0.999586i	$0.490842\pi$
$367$	−16.3082	+	28.2467i	−0.851283	+	1.47447i	−0.880051	+	0.474879i	$0.842492\pi$
$368$		0			0
$369$	0.611043	+	1.05836i	0.0318096	+	0.0550959i
$370$		0			0
$371$	11.9927	−	28.8244i	0.622632	−	1.49649i
$372$		0			0
$373$	12.7860	+	22.1460i	0.662034	+	1.14668i	0.980080	+	0.198601i	$0.0636398\pi$
$373$	12.7860	+	22.1460i	0.662034	+	1.14668i	−0.318047	+	0.948075i	$0.603027\pi$
$374$		0			0
$375$	8.10220	−	14.0334i	0.418396	−	0.724683i
$376$		0			0
$377$	−14.2815			−0.735536
$378$		0			0
$379$	32.0887			1.64828			0.824142	−	0.566383i	$-0.191658\pi$
$379$	32.0887			1.64828			0.824142	+	0.566383i	$0.191658\pi$
$380$		0			0
$381$	13.7074	−	23.7418i	0.702249	−	1.21633i
$382$		0			0
$383$	−0.235080	−	0.407170i	−0.0120120	−	0.0208054i	0.859957	−	0.510367i	$-0.170490\pi$
$383$	−0.235080	−	0.407170i	−0.0120120	−	0.0208054i	−0.871969	+	0.489561i	$0.837157\pi$
$384$		0			0
$385$	−11.5301	+	1.49947i	−0.587630	+	0.0764203i
$386$		0			0
$387$	−0.731205	−	1.26648i	−0.0371692	−	0.0643790i
$388$		0			0
$389$	7.73845	−	13.4034i	0.392355	−	0.679579i	−0.600405	−	0.799696i	$-0.704994\pi$
$389$	7.73845	−	13.4034i	0.392355	−	0.679579i	0.992760	+	0.120118i	$0.0383271\pi$
$390$		0			0
$391$	0.0569403			0.00287960
$392$		0			0
$393$	−11.0196			−0.555866
$394$		0			0
$395$	1.20094	−	2.08009i	0.0604260	−	0.104661i
$396$		0			0
$397$	−14.1882	−	24.5747i	−0.712086	−	1.23337i	−0.964073	−	0.265639i	$-0.914417\pi$
$397$	−14.1882	−	24.5747i	−0.712086	−	1.23337i	0.251986	−	0.967731i	$-0.418916\pi$
$398$		0			0
$399$	13.8397	−	1.79983i	0.692852	−	0.0901043i
$400$		0			0
$401$	12.5153	+	21.6771i	0.624982	+	1.08250i	0.988544	+	0.150931i	$0.0482270\pi$
$401$	12.5153	+	21.6771i	0.624982	+	1.08250i	−0.363563	+	0.931570i	$0.618440\pi$
$402$		0			0
$403$	−3.43678	+	5.95268i	−0.171198	+	0.296524i
$404$		0			0
$405$	−6.78522			−0.337160
$406$		0			0
$407$	−0.485328			−0.0240568
$408$		0			0
$409$	−12.5780	+	21.7857i	−0.621940	+	1.07723i	0.367184	+	0.930148i	$0.380322\pi$
$409$	−12.5780	+	21.7857i	−0.621940	+	1.07723i	−0.989124	+	0.147084i	$0.953011\pi$
$410$		0			0
$411$	0.454092	+	0.786510i	0.0223987	+	0.0387957i
$412$		0			0
$413$	5.59846	−	13.4558i	0.275482	−	0.662118i
$414$		0			0
$415$	−5.32466	−	9.22258i	−0.261377	−	0.452719i
$416$		0			0
$417$	8.78031	−	15.2079i	0.429974	−	0.744736i
$418$		0			0
$419$	−3.32306			−0.162342			−0.0811710	−	0.996700i	$-0.525866\pi$
$419$	−3.32306			−0.162342			−0.0811710	+	0.996700i	$0.525866\pi$
$420$		0			0
$421$	−3.67892			−0.179300			−0.0896498	−	0.995973i	$-0.528575\pi$
$421$	−3.67892			−0.179300			−0.0896498	+	0.995973i	$0.528575\pi$
$422$		0			0
$423$	−4.54571	+	7.87341i	−0.221020	+	0.382818i
$424$		0			0
$425$	−1.31860	−	2.28388i	−0.0639614	−	0.110784i
$426$		0			0
$427$	−6.29194	−	8.22665i	−0.304488	−	0.398116i
$428$		0			0
$429$	−3.81750	−	6.61210i	−0.184311	−	0.319235i
$430$		0			0
$431$	−12.4301	+	21.5296i	−0.598737	+	1.03704i	0.394271	+	0.918994i	$0.370997\pi$
$431$	−12.4301	+	21.5296i	−0.598737	+	1.03704i	−0.993008	+	0.118048i	$0.962336\pi$
$432$		0			0
$433$	38.5625			1.85320			0.926599	−	0.376052i	$-0.122719\pi$
$433$	38.5625			1.85320			0.926599	+	0.376052i	$0.122719\pi$
$434$		0			0
$435$	14.6152			0.700743
$436$		0			0
$437$	0.0802133	−	0.138934i	0.00383712	−	0.00664609i
$438$		0			0
$439$	−12.7220	−	22.0351i	−0.607187	−	1.05168i	−0.991702	−	0.128560i	$-0.958964\pi$
$439$	−12.7220	−	22.0351i	−0.607187	−	1.05168i	0.384515	−	0.923119i	$-0.374369\pi$
$440$		0			0
$441$	6.02991	+	6.06806i	0.287138	+	0.288955i
$442$		0			0
$443$	−1.88136	−	3.25861i	−0.0893860	−	0.154821i	0.817866	−	0.575409i	$-0.195157\pi$
$443$	−1.88136	−	3.25861i	−0.0893860	−	0.154821i	−0.907252	+	0.420588i	$0.861824\pi$
$444$		0			0
$445$	0.199712	−	0.345912i	0.00946728	−	0.0163978i
$446$		0			0
$447$	−20.3955			−0.964676
$448$		0			0
$449$	29.9012			1.41113			0.705563	−	0.708647i	$-0.250694\pi$
$449$	29.9012			1.41113			0.705563	+	0.708647i	$0.250694\pi$
$450$		0			0
$451$	1.24363	−	2.15404i	0.0585604	−	0.101430i
$452$		0			0
$453$	2.65553	+	4.59952i	0.124768	+	0.216104i
$454$		0			0
$455$	6.53789	+	8.54823i	0.306501	+	0.400747i
$456$		0			0
$457$	6.05429	+	10.4863i	0.283208	+	0.490530i	0.972173	−	0.234264i	$-0.0752681\pi$
$457$	6.05429	+	10.4863i	0.283208	+	0.490530i	−0.688965	+	0.724794i	$0.741935\pi$
$458$		0			0
$459$	−3.95239	+	6.84575i	−0.184482	+	0.319532i
$460$		0			0
$461$	−3.92540			−0.182824			−0.0914120	−	0.995813i	$-0.529138\pi$
$461$	−3.92540			−0.182824			−0.0914120	+	0.995813i	$0.529138\pi$
$462$		0			0
$463$	−13.6329			−0.633575			−0.316788	−	0.948496i	$-0.602604\pi$
$463$	−13.6329			−0.633575			−0.316788	+	0.948496i	$0.602604\pi$
$464$		0			0
$465$	3.51707	−	6.09174i	0.163100	−	0.282498i
$466$		0			0
$467$	−5.96064	−	10.3241i	−0.275826	−	0.477744i	0.694517	−	0.719476i	$-0.255618\pi$
$467$	−5.96064	−	10.3241i	−0.275826	−	0.477744i	−0.970343	+	0.241732i	$0.922285\pi$
$468$		0			0
$469$	−5.89319	+	14.1642i	−0.272122	+	0.654042i
$470$		0			0
$471$	−9.67639	−	16.7600i	−0.445864	−	0.772260i
$472$		0			0
$473$	−1.48819	+	2.57763i	−0.0684273	+	0.118520i
$474$		0			0
$475$	−7.43018			−0.340920
$476$		0			0
$477$	14.4205			0.660272
$478$		0			0
$479$	−1.27937	+	2.21593i	−0.0584558	+	0.101248i	−0.893772	−	0.448521i	$-0.851951\pi$
$479$	−1.27937	+	2.21593i	−0.0584558	+	0.101248i	0.835317	+	0.549769i	$0.185284\pi$
$480$		0			0
$481$	0.224602	+	0.389023i	0.0102410	+	0.0177379i
$482$		0			0
$483$	−0.141865	+	0.0184493i	−0.00645507	+	0.000839472i
$484$		0			0
$485$	−1.26482	−	2.19072i	−0.0574323	−	0.0994757i
$486$		0			0
$487$	−0.998738	+	1.72987i	−0.0452572	+	0.0783877i	−0.887767	−	0.460294i	$-0.847744\pi$
$487$	−0.998738	+	1.72987i	−0.0452572	+	0.0783877i	0.842509	+	0.538682i	$0.181077\pi$
$488$		0			0
$489$	20.3856			0.921869
$490$		0			0
$491$	8.72991			0.393975			0.196988	−	0.980406i	$-0.436884\pi$
$491$	8.72991			0.393975			0.196988	+	0.980406i	$0.436884\pi$
$492$		0			0
$493$	4.35533	−	7.54365i	0.196154	−	0.339749i
$494$		0			0
$495$	−2.68534	−	4.65114i	−0.120697	−	0.209053i
$496$		0			0
$497$	26.9941	−	3.51054i	1.21085	−	0.157469i
$498$		0			0
$499$	4.91138	+	8.50675i	0.219863	+	0.380815i	0.954766	−	0.297358i	$-0.0961055\pi$
$499$	4.91138	+	8.50675i	0.219863	+	0.380815i	−0.734903	+	0.678173i	$0.762772\pi$
$500$		0			0
$501$	9.16920	−	15.8815i	0.409650	−	0.709534i
$502$		0			0
$503$	16.7626			0.747407			0.373703	−	0.927548i	$-0.378088\pi$
$503$	16.7626			0.747407			0.373703	+	0.927548i	$0.378088\pi$
$504$		0			0
$505$	−11.9012			−0.529598
$506$		0			0
$507$	5.13364	−	8.89173i	0.227993	−	0.394896i
$508$		0			0
$509$	−4.10837	−	7.11590i	−0.182100	−	0.315407i	0.760495	−	0.649343i	$-0.224956\pi$
$509$	−4.10837	−	7.11590i	−0.182100	−	0.315407i	−0.942596	+	0.333937i	$0.891623\pi$
$510$		0			0
$511$	12.4994	−	30.0420i	0.552939	−	1.32898i
$512$		0			0
$513$	11.1357	+	19.2876i	0.491652	+	0.851567i
$514$		0			0
$515$	6.12454	−	10.6080i	0.269879	−	0.467445i
$516$		0			0
$517$	18.5035			0.813781
$518$		0			0
$519$	20.9466			0.919452
$520$		0			0
$521$	11.2279	−	19.4473i	0.491903	−	0.852000i	−0.508054	−	0.861325i	$-0.669635\pi$
$521$	11.2279	−	19.4473i	0.491903	−	0.852000i	0.999957	+	0.00932485i	$0.00296824\pi$
$522$		0			0
$523$	15.2420	+	26.4000i	0.666488	+	1.15439i	0.978880	+	0.204438i	$0.0655367\pi$
$523$	15.2420	+	26.4000i	0.666488	+	1.15439i	−0.312391	+	0.949954i	$0.601130\pi$
$524$		0			0
$525$	4.02524	+	5.26297i	0.175676	+	0.229695i
$526$		0			0
$527$	−2.09618	−	3.63069i	−0.0913110	−	0.158155i
$528$		0			0
$529$	11.4992	−	19.9172i	0.499964	−	0.865963i
$530$		0			0
$531$	6.73181			0.292136
$532$		0			0
$533$	−2.30214			−0.0997166
$534$		0			0
$535$	10.3131	−	17.8628i	0.445874	−	0.772277i
$536$		0			0
$537$	4.14353	+	7.17681i	0.178807	+	0.309702i
$538$		0			0
$539$	4.55929	−	16.8033i	0.196382	−	0.723770i
$540$		0			0
$541$	−9.23538	−	15.9961i	−0.397060	−	0.687728i	0.596302	−	0.802760i	$-0.296636\pi$
$541$	−9.23538	−	15.9961i	−0.397060	−	0.687728i	−0.993362	+	0.115033i	$0.963303\pi$
$542$		0			0
$543$	10.4124	−	18.0349i	0.446841	−	0.773951i
$544$		0			0
$545$	−3.88823			−0.166553
$546$		0			0
$547$	−26.1709			−1.11899			−0.559494	−	0.828834i	$-0.689005\pi$
$547$	−26.1709			−1.11899			−0.559494	+	0.828834i	$0.689005\pi$
$548$		0			0
$549$	2.39196	−	4.14300i	0.102086	−	0.176819i
$550$		0			0
$551$	−12.2709	−	21.2539i	−0.522759	−	0.905446i
$552$		0			0
$553$	2.18499	+	2.85685i	0.0929153	+	0.121486i
$554$		0			0
$555$	−0.229849	−	0.398111i	−0.00975656	−	0.0168989i
$556$		0			0
$557$	−6.11016	+	10.5831i	−0.258896	+	0.448420i	−0.965946	−	0.258742i	$-0.916692\pi$
$557$	−6.11016	+	10.5831i	−0.258896	+	0.448420i	0.707051	+	0.707163i	$0.250025\pi$
$558$		0			0
$559$	2.75485			0.116518
$560$		0			0
$561$	4.65678			0.196609
$562$		0			0
$563$	−14.6049	+	25.2964i	−0.615524	+	1.06612i	0.374769	+	0.927118i	$0.377722\pi$
$563$	−14.6049	+	25.2964i	−0.615524	+	1.06612i	−0.990292	+	0.139000i	$0.955611\pi$
$564$		0			0
$565$	−8.68840	−	15.0488i	−0.365524	−	0.633106i
$566$		0			0
$567$	3.90300	−	9.38079i	0.163910	−	0.393956i
$568$		0			0
$569$	−15.6937	−	27.1823i	−0.657916	−	1.13954i	−0.981154	−	0.193226i	$-0.938105\pi$
$569$	−15.6937	−	27.1823i	−0.657916	−	1.13954i	0.323239	−	0.946317i	$-0.395228\pi$
$570$		0			0
$571$	19.3513	−	33.5174i	0.809826	−	1.40266i	−0.103158	−	0.994665i	$-0.532895\pi$
$571$	19.3513	−	33.5174i	0.809826	−	1.40266i	0.912984	−	0.407995i	$-0.133772\pi$
$572$		0			0
$573$	−5.81820			−0.243059
$574$		0			0
$575$	0.0761635			0.00317624
$576$		0			0
$577$	−15.6761	+	27.1517i	−0.652603	+	1.13034i	0.329886	+	0.944021i	$0.392990\pi$
$577$	−15.6761	+	27.1517i	−0.652603	+	1.13034i	−0.982489	+	0.186320i	$0.940344\pi$
$578$		0			0
$579$	10.1120	+	17.5145i	0.420240	+	0.727877i
$580$		0			0
$581$	15.8134	−	2.05650i	0.656049	−	0.0853181i
$582$		0			0
$583$	−14.6748	−	25.4175i	−0.607769	−	1.05269i
$584$		0			0
$585$	−2.48546	+	4.30495i	−0.102761	+	0.177988i
$586$		0			0
$587$	−7.78318			−0.321246			−0.160623	−	0.987016i	$-0.551350\pi$
$587$	−7.78318			−0.321246			−0.160623	+	0.987016i	$0.551350\pi$
$588$		0			0
$589$	−11.8118			−0.486696
$590$		0			0
$591$	2.89366	−	5.01197i	0.119029	−	0.206165i
$592$		0			0
$593$	18.7553	+	32.4852i	0.770190	+	1.33401i	0.937459	+	0.348096i	$0.113172\pi$
$593$	18.7553	+	32.4852i	0.770190	+	1.33401i	−0.167269	+	0.985911i	$0.553495\pi$
$594$		0			0
$595$	−6.50908	+	0.846495i	−0.266846	+	0.0347029i
$596$		0			0
$597$	−2.04973	−	3.55024i	−0.0838899	−	0.145302i
$598$		0			0
$599$	−10.9618	+	18.9864i	−0.447887	+	0.775763i	−0.998248	−	0.0591633i	$-0.981157\pi$
$599$	−10.9618	+	18.9864i	−0.447887	+	0.775763i	0.550361	+	0.834927i	$0.314490\pi$
$600$		0			0
$601$	−25.9765			−1.05960			−0.529802	−	0.848122i	$-0.677734\pi$
$601$	−25.9765			−1.05960			−0.529802	+	0.848122i	$0.677734\pi$
$602$		0			0
$603$	−7.08621			−0.288573
$604$		0			0
$605$	4.25242	−	7.36541i	0.172885	−	0.299446i
$606$		0			0
$607$	9.31755	+	16.1385i	0.378188	+	0.655040i	0.990799	−	0.135344i	$-0.0432141\pi$
$607$	9.31755	+	16.1385i	0.378188	+	0.655040i	−0.612611	+	0.790385i	$0.709881\pi$
$608$		0			0
$609$	−8.40693	+	20.2059i	−0.340666	+	0.818786i
$610$		0			0
$611$	−8.56311	−	14.8317i	−0.346426	−	0.600028i
$612$		0			0
$613$	13.3701	−	23.1577i	0.540013	−	0.935330i	−0.458890	−	0.888493i	$-0.651753\pi$
$613$	13.3701	−	23.1577i	0.540013	−	0.935330i	0.998903	−	0.0468366i	$-0.0149140\pi$
$614$		0			0
$615$	2.35592			0.0949998
$616$		0			0
$617$	3.57592			0.143961			0.0719805	−	0.997406i	$-0.477068\pi$
$617$	3.57592			0.143961			0.0719805	+	0.997406i	$0.477068\pi$
$618$		0			0
$619$	−1.65838	+	2.87241i	−0.0666561	+	0.115452i	−0.897427	−	0.441162i	$-0.854566\pi$
$619$	−1.65838	+	2.87241i	−0.0666561	+	0.115452i	0.830771	+	0.556614i	$0.187900\pi$
$620$		0			0
$621$	−0.114147	−	0.197708i	−0.00458056	−	0.00793377i
$622$		0			0
$623$	0.363356	+	0.475084i	0.0145576	+	0.0190339i
$624$		0			0
$625$	6.04082	+	10.4630i	0.241633	+	0.418520i
$626$		0			0
$627$	6.56013	−	11.3625i	0.261986	−	0.453773i
$628$		0			0
$629$	−0.273981			−0.0109244
$630$		0			0
$631$	−41.9093			−1.66838			−0.834191	−	0.551475i	$-0.814065\pi$
$631$	−41.9093			−1.66838			−0.834191	+	0.551475i	$0.814065\pi$
$632$		0			0
$633$	−0.320257	+	0.554701i	−0.0127291	+	0.0220474i
$634$		0			0
$635$	18.1636	+	31.4603i	0.720802	+	1.24847i
$636$		0			0
$637$	−15.5789	+	4.12174i	−0.617260	+	0.163309i
$638$		0			0
$639$	6.28686	+	10.8892i	0.248704	+	0.430769i
$640$		0			0
$641$	12.1992	−	21.1297i	0.481840	−	0.834572i	−0.517942	−	0.855415i	$-0.673302\pi$
$641$	12.1992	−	21.1297i	0.481840	−	0.834572i	0.999783	+	0.0208436i	$0.00663519\pi$
$642$		0			0
$643$	−5.91248			−0.233166			−0.116583	−	0.993181i	$-0.537194\pi$
$643$	−5.91248			−0.233166			−0.116583	+	0.993181i	$0.537194\pi$
$644$		0			0
$645$	−2.81921			−0.111006
$646$		0			0
$647$	9.50944	−	16.4708i	0.373855	−	0.647535i	−0.616300	−	0.787511i	$-0.711369\pi$
$647$	9.50944	−	16.4708i	0.373855	−	0.647535i	0.990155	+	0.139976i	$0.0447026\pi$
$648$		0			0
$649$	−6.85050	−	11.8654i	−0.268906	−	0.465759i
$650$		0			0
$651$	6.39894	+	8.36655i	0.250794	+	0.327911i
$652$		0			0
$653$	−6.95107	−	12.0396i	−0.272016	−	0.471146i	0.697362	−	0.716719i	$-0.254357\pi$
$653$	−6.95107	−	12.0396i	−0.272016	−	0.471146i	−0.969378	+	0.245573i	$0.921024\pi$
$654$		0			0
$655$	7.30106	−	12.6458i	0.285276	−	0.494112i
$656$		0			0
$657$	15.0297			0.586365
$658$		0			0
$659$	20.2641			0.789379			0.394689	−	0.918815i	$-0.370852\pi$
$659$	20.2641			0.789379			0.394689	+	0.918815i	$0.370852\pi$
$660$		0			0
$661$	1.06664	−	1.84747i	0.0414875	−	0.0718584i	−0.844536	−	0.535499i	$-0.820124\pi$
$661$	1.06664	−	1.84747i	0.0414875	−	0.0718584i	0.886024	+	0.463640i	$0.153457\pi$
$662$		0			0
$663$	−2.15508	−	3.73272i	−0.0836966	−	0.144967i
$664$		0			0
$665$	−7.10408	+	17.0745i	−0.275484	+	0.662122i
$666$		0			0
$667$	0.125784	+	0.217864i	0.00487038	+	0.00843574i
$668$		0			0
$669$	4.80243	−	8.31805i	0.185673	−	0.321594i
$670$		0			0
$671$	−9.73655			−0.375875
$672$		0			0
$673$	−2.81059			−0.108340			−0.0541702	−	0.998532i	$-0.517251\pi$
$673$	−2.81059			−0.108340			−0.0541702	+	0.998532i	$0.517251\pi$
$674$		0			0
$675$	−5.28673	+	9.15689i	−0.203486	+	0.352449i
$676$		0			0
$677$	5.51694	+	9.55561i	0.212033	+	0.367252i	0.952351	−	0.305005i	$-0.0986582\pi$
$677$	5.51694	+	9.55561i	0.212033	+	0.367252i	−0.740318	+	0.672257i	$0.765325\pi$
$678$		0			0
$679$	3.75629	−	0.488500i	0.144153	−	0.0187469i
$680$		0			0
$681$	−5.28375	−	9.15173i	−0.202474	−	0.350695i
$682$		0			0
$683$	−13.3611	+	23.1421i	−0.511248	+	0.885507i	0.488667	+	0.872470i	$0.337483\pi$
$683$	−13.3611	+	23.1421i	−0.511248	+	0.885507i	−0.999915	+	0.0130369i	$0.995850\pi$
$684$		0			0
$685$	−1.20344			−0.0459809
$686$		0			0
$687$	24.5316			0.935938
$688$		0			0
$689$	−13.5825	+	23.5257i	−0.517454	+	0.896256i
$690$		0			0
$691$	−11.3864	−	19.7219i	−0.433160	−	0.750255i	0.563983	−	0.825786i	$-0.309268\pi$
$691$	−11.3864	−	19.7219i	−0.433160	−	0.750255i	−0.997143	+	0.0755307i	$0.975935\pi$
$692$		0			0
$693$	7.97501	−	1.03714i	0.302946	−	0.0393976i
$694$		0			0
$695$	11.6348	+	20.1521i	0.441333	+	0.764412i
$696$		0			0
$697$	0.702066	−	1.21601i	0.0265926	−	0.0460598i
$698$		0			0
$699$	19.7177			0.745790
$700$		0			0
$701$	−51.9521			−1.96220			−0.981102	−	0.193494i	$-0.938018\pi$
$701$	−51.9521			−1.96220			−0.981102	+	0.193494i	$0.938018\pi$
$702$		0			0
$703$	−0.385965	+	0.668510i	−0.0145569	+	0.0252133i
$704$		0			0
$705$	8.76315	+	15.1782i	0.330040	+	0.571645i
$706$		0			0
$707$	6.84583	−	16.4539i	0.257464	−	0.618811i
$708$		0			0
$709$	3.35239	+	5.80651i	0.125902	+	0.218068i	0.922085	−	0.386987i	$-0.126484\pi$
$709$	3.35239	+	5.80651i	0.125902	+	0.218068i	−0.796183	+	0.605055i	$0.793151\pi$
$710$		0			0
$711$	−0.830653	+	1.43873i	−0.0311519	+	0.0539567i
$712$		0			0
$713$	0.121077			0.00453438
$714$		0			0
$715$	10.1171			0.378360
$716$		0			0
$717$	17.1924	−	29.7781i	0.642062	−	1.11208i
$718$		0			0
$719$	14.5590	+	25.2169i	0.542959	+	0.940432i	0.998732	+	0.0503363i	$0.0160293\pi$
$719$	14.5590	+	25.2169i	0.542959	+	0.940432i	−0.455774	+	0.890096i	$0.650637\pi$
$720$		0			0
$721$	11.1430	+	14.5693i	0.414986	+	0.542590i
$722$		0			0
$723$	10.7947	+	18.6970i	0.401459	+	0.695348i
$724$		0			0
$725$	5.82570	−	10.0904i	0.216361	−	0.374748i
$726$		0			0
$727$	−30.2981			−1.12369			−0.561846	−	0.827242i	$-0.689909\pi$
$727$	−30.2981			−1.12369			−0.561846	+	0.827242i	$0.689909\pi$
$728$		0			0
$729$	27.2126			1.00788
$730$		0			0
$731$	−0.840128	+	1.45514i	−0.0310732	+	0.0538204i
$732$		0			0
$733$	−10.1530	−	17.5856i	−0.375011	−	0.649538i	0.615318	−	0.788279i	$-0.289028\pi$
$733$	−10.1530	−	17.5856i	−0.375011	−	0.649538i	−0.990329	+	0.138741i	$0.955694\pi$
$734$		0			0
$735$	15.9429	−	4.21803i	0.588062	−	0.155584i
$736$		0			0
$737$	7.21115	+	12.4901i	0.265626	+	0.460078i
$738$		0			0
$739$	3.87092	−	6.70464i	0.142394	−	0.246634i	−0.786003	−	0.618222i	$-0.787853\pi$
$739$	3.87092	−	6.70464i	0.142394	−	0.246634i	0.928398	+	0.371588i	$0.121187\pi$
$740$		0			0
$741$	−12.1437			−0.446110
$742$		0			0
$743$	31.5135			1.15612			0.578058	−	0.815995i	$-0.303811\pi$
$743$	31.5135			1.15612			0.578058	+	0.815995i	$0.303811\pi$
$744$		0			0
$745$	13.5131	−	23.4054i	0.495081	−	0.857506i
$746$		0			0
$747$	3.68289	+	6.37895i	0.134750	+	0.233394i
$748$		0			0
$749$	18.7636	+	24.5333i	0.685608	+	0.896426i
$750$		0			0
$751$	−12.5939	−	21.8132i	−0.459556	−	0.795975i	0.539381	−	0.842062i	$-0.318658\pi$
$751$	−12.5939	−	21.8132i	−0.459556	−	0.795975i	−0.998937	+	0.0460870i	$0.985325\pi$
$752$		0			0
$753$	−0.984472	+	1.70516i	−0.0358762	+	0.0621393i
$754$		0			0
$755$	−7.03771			−0.256128
$756$		0			0
$757$	−28.2989			−1.02854			−0.514270	−	0.857628i	$-0.671937\pi$
$757$	−28.2989			−1.02854			−0.514270	+	0.857628i	$0.671937\pi$
$758$		0			0
$759$	−0.0672450	+	0.116472i	−0.00244084	+	0.00422766i
$760$		0			0
$761$	4.55376	+	7.88734i	0.165074	+	0.285916i	0.936681	−	0.350183i	$-0.113881\pi$
$761$	4.55376	+	7.88734i	0.165074	+	0.285916i	−0.771608	+	0.636099i	$0.780547\pi$
$762$		0			0
$763$	2.23658	−	5.37560i	0.0809698	−	0.194610i
$764$		0			0
$765$	−1.51595	−	2.62570i	−0.0548092	−	0.0949323i
$766$		0			0
$767$	−6.34061	+	10.9823i	−0.228946	+	0.396547i
$768$		0			0
$769$	16.0188			0.577653			0.288826	−	0.957381i	$-0.406735\pi$
$769$	16.0188			0.577653			0.288826	+	0.957381i	$0.406735\pi$
$770$		0			0
$771$	−8.49031			−0.305771
$772$		0			0
$773$	−15.1744	+	26.2828i	−0.545786	+	0.945328i	0.452771	+	0.891627i	$0.350435\pi$
$773$	−15.1744	+	26.2828i	−0.545786	+	0.945328i	−0.998557	+	0.0537017i	$0.982898\pi$
$774$		0			0
$775$	−2.80385	−	4.85642i	−0.100717	−	0.174448i
$776$		0			0
$777$	0.682615	−	0.0887730i	0.0244887	−	0.00318471i
$778$		0			0
$779$	−1.97804	−	3.42606i	−0.0708705	−	0.122751i
$780$		0			0
$781$	12.7954	−	22.1623i	0.457856	−	0.793030i
$782$		0			0
$783$	−34.9241			−1.24809
$784$		0			0
$785$	25.6444			0.915288
$786$		0			0
$787$	−16.9943	+	29.4350i	−0.605781	+	1.04924i	0.386147	+	0.922437i	$0.373806\pi$
$787$	−16.9943	+	29.4350i	−0.605781	+	1.04924i	−0.991928	+	0.126806i	$0.959527\pi$
$788$		0			0
$789$	−12.0758	−	20.9160i	−0.429911	−	0.744629i
$790$		0			0
$791$	25.8031	−	3.35566i	0.917454	−	0.119313i
$792$		0			0
$793$	4.50592	+	7.80449i	0.160010	+	0.277146i
$794$		0			0
$795$	13.8999	−	24.0753i	0.492977	−	0.853861i
$796$		0			0
$797$	44.5444			1.57784			0.788922	−	0.614494i	$-0.210640\pi$
$797$	44.5444			1.57784			0.788922	+	0.614494i	$0.210640\pi$
$798$		0			0
$799$	10.4457			0.369543
$800$		0			0
$801$	−0.138134	+	0.239256i	−0.00488074	+	0.00845369i
$802$		0			0
$803$	−15.2947	−	26.4912i	−0.539739	−	0.934855i
$804$		0			0
$805$	0.0728208	−	0.175024i	0.00256660	−	0.00616878i
$806$		0			0
$807$	11.4502	+	19.8323i	0.403065	+	0.698130i
$808$		0			0
$809$	13.4304	−	23.2622i	0.472188	−	0.817854i	−0.527305	−	0.849676i	$-0.676798\pi$
$809$	13.4304	−	23.2622i	0.472188	−	0.817854i	0.999494	+	0.0318219i	$0.0101309\pi$
$810$		0			0
$811$	38.5647			1.35419			0.677095	−	0.735896i	$-0.263239\pi$
$811$	38.5647			1.35419			0.677095	+	0.735896i	$0.263239\pi$
$812$		0			0
$813$	−21.0007			−0.736526
$814$		0			0
$815$	−13.5065	+	23.3940i	−0.473112	+	0.819454i
$816$		0			0
$817$	2.36702	+	4.09980i	0.0828115	+	0.143434i
$818$		0			0
$819$	−4.52204	−	5.91253i	−0.158013	−	0.206600i
$820$		0			0
$821$	13.9074	+	24.0883i	0.485370	+	0.840686i	0.999859	−	0.0168113i	$-0.00535145\pi$
$821$	13.9074	+	24.0883i	0.485370	+	0.840686i	−0.514488	+	0.857497i	$0.672018\pi$
$822$		0			0
$823$	11.3873	−	19.7234i	0.396936	−	0.687513i	−0.596410	−	0.802680i	$-0.703407\pi$
$823$	11.3873	−	19.7234i	0.396936	−	0.687513i	0.993346	+	0.115167i	$0.0367402\pi$
$824$		0			0
$825$	6.22892			0.216863
$826$		0			0
$827$	36.6139			1.27319			0.636595	−	0.771198i	$-0.280342\pi$
$827$	36.6139			1.27319			0.636595	+	0.771198i	$0.280342\pi$
$828$		0			0
$829$	−13.3228	+	23.0758i	−0.462720	+	0.801455i	−0.999095	−	0.0425248i	$-0.986460\pi$
$829$	−13.3228	+	23.0758i	−0.462720	+	0.801455i	0.536375	+	0.843980i	$0.319793\pi$
$830$		0			0
$831$	−13.0851	−	22.6641i	−0.453919	−	0.786210i
$832$		0			0
$833$	2.57385	−	9.48594i	0.0891785	−	0.328668i
$834$		0			0
$835$	12.1501	+	21.0446i	0.420472	+	0.728280i
$836$		0			0
$837$	−8.40433	+	14.5567i	−0.290496	+	0.503154i
$838$		0			0
$839$	14.1618			0.488920			0.244460	−	0.969659i	$-0.421389\pi$
$839$	14.1618			0.488920			0.244460	+	0.969659i	$0.421389\pi$
$840$		0			0
$841$	9.48458			0.327054
$842$		0			0
$843$	−5.47321	+	9.47987i	−0.188507	+	0.326504i
$844$		0			0
$845$	6.80260	+	11.7824i	0.234016	+	0.405328i
$846$		0			0
$847$	7.73684	+	10.1158i	0.265841	+	0.347584i
$848$		0			0
$849$	−11.9808	−	20.7514i	−0.411182	−	0.712187i
$850$		0			0
$851$	0.00395636	−	0.00685261i	0.000135622	−	0.000234904i
$852$		0			0
$853$	14.6813			0.502677			0.251338	−	0.967899i	$-0.419129\pi$
$853$	14.6813			0.502677			0.251338	+	0.967899i	$0.419129\pi$
$854$		0			0
$855$	−8.54222			−0.292138
$856$		0			0
$857$	1.80458	−	3.12563i	0.0616433	−	0.106769i	−0.833557	−	0.552434i	$-0.813699\pi$
$857$	1.80458	−	3.12563i	0.0616433	−	0.106769i	0.895200	+	0.445664i	$0.147033\pi$
$858$		0			0
$859$	22.4808	+	38.9378i	0.767033	+	1.32854i	0.939165	+	0.343467i	$0.111601\pi$
$859$	22.4808	+	38.9378i	0.767033	+	1.32854i	−0.172131	+	0.985074i	$0.555065\pi$
$860$		0			0
$861$	−1.35517	+	3.25713i	−0.0461841	+	0.111003i
$862$		0			0
$863$	4.26474	+	7.38675i	0.145173	+	0.251448i	0.929438	−	0.368979i	$-0.120293\pi$
$863$	4.26474	+	7.38675i	0.145173	+	0.251448i	−0.784264	+	0.620427i	$0.786959\pi$
$864$		0			0
$865$	−13.8782	+	24.0377i	−0.471872	+	0.817306i
$866$		0			0
$867$	−20.0387			−0.680548
$868$		0			0
$869$	3.38119			0.114699
$870$		0			0
$871$	6.67442	−	11.5604i	0.226154	−	0.391710i
$872$		0			0
$873$	0.874831	+	1.51525i	0.0296085	+	0.0512835i
$874$		0			0
$875$	−31.8849	+	4.14658i	−1.07791	+	0.140180i
$876$		0			0
$877$	4.05946	+	7.03120i	0.137078	+	0.237427i	0.926389	−	0.376567i	$-0.122895\pi$
$877$	4.05946	+	7.03120i	0.137078	+	0.237427i	−0.789311	+	0.613993i	$0.789562\pi$
$878$		0			0
$879$	−4.97122	+	8.61041i	−0.167675	+	0.290422i
$880$		0			0
$881$	38.5733			1.29957			0.649784	−	0.760119i	$-0.274859\pi$
$881$	38.5733			1.29957			0.649784	+	0.760119i	$0.274859\pi$
$882$		0			0
$883$	−37.4122			−1.25902			−0.629510	−	0.776992i	$-0.716744\pi$
$883$	−37.4122			−1.25902			−0.629510	+	0.776992i	$0.716744\pi$
$884$		0			0
$885$	6.48874	−	11.2388i	0.218117	−	0.377789i
$886$		0			0
$887$	−10.5629	−	18.2954i	−0.354667	−	0.614301i	0.632394	−	0.774647i	$-0.282072\pi$
$887$	−10.5629	−	18.2954i	−0.354667	−	0.614301i	−0.987061	+	0.160346i	$0.948739\pi$
$888$		0			0
$889$	−53.9430	+	7.01521i	−1.80919	+	0.235282i
$890$		0			0
$891$	−4.77586	−	8.27204i	−0.159997	−	0.277124i
$892$		0			0
$893$	14.7152	−	25.4874i	0.492424	−	0.852903i
$894$		0			0
$895$	−10.9812			−0.367061
$896$		0			0
$897$	0.124480			0.00415626
$898$		0			0
$899$	9.26113	−	16.0408i	0.308876	−	0.534989i
$900$		0			0
$901$	−8.28434	−	14.3489i	−0.275991	−	0.478031i
$902$		0			0
$903$	1.62167	−	3.89765i	0.0539657	−	0.129706i
$904$		0			0
$905$	13.7975	+	23.8981i	0.458646	+	0.794398i
$906$		0			0
$907$	9.83489	−	17.0345i	0.326562	−	0.565622i	−0.655265	−	0.755399i	$-0.727443\pi$
$907$	9.83489	−	17.0345i	0.326562	−	0.565622i	0.981827	+	0.189777i	$0.0607764\pi$
$908$		0			0
$909$	8.23169			0.273028
$910$		0			0
$911$	−32.5069			−1.07700			−0.538501	−	0.842625i	$-0.681009\pi$
$911$	−32.5069			−1.07700			−0.538501	+	0.842625i	$0.681009\pi$
$912$		0			0
$913$	7.49565	−	12.9829i	0.248070	−	0.429670i
$914$		0			0
$915$	−4.61119	−	7.98681i	−0.152441	−	0.264036i
$916$		0			0
$917$	13.2835	+	17.3681i	0.438660	+	0.573544i
$918$		0			0
$919$	−20.3653	−	35.2738i	−0.671791	−	1.16358i	−0.977396	−	0.211417i	$-0.932192\pi$
$919$	−20.3653	−	35.2738i	−0.671791	−	1.16358i	0.305605	−	0.952158i	$-0.401141\pi$
$920$		0			0
$921$	−8.02963	+	13.9077i	−0.264585	+	0.458275i
$922$		0			0
$923$	−23.6861			−0.779637
$924$		0			0
$925$	−0.366478			−0.0120497
$926$		0			0
$927$	−4.23614	+	7.33721i	−0.139133	+	0.240986i
$928$		0			0
$929$	−6.14514	−	10.6437i	−0.201616	−	0.349208i	0.747434	−	0.664337i	$-0.231286\pi$
$929$	−6.14514	−	10.6437i	−0.201616	−	0.349208i	−0.949049	+	0.315128i	$0.897953\pi$
$930$		0			0
$931$	−19.5197	−	19.6432i	−0.639732	−	0.643781i
$932$		0			0
$933$	−17.8468	−	30.9115i	−0.584278	−	1.01200i
$934$		0			0
$935$	−3.08535	+	5.34399i	−0.100902	+	0.174767i
$936$		0			0
$937$	−57.2280			−1.86956			−0.934779	−	0.355229i	$-0.884403\pi$
$937$	−57.2280			−1.86956			−0.934779	+	0.355229i	$0.884403\pi$
$938$		0			0
$939$	−2.99129			−0.0976172
$940$		0			0
$941$	−1.48393	+	2.57025i	−0.0483748	+	0.0837876i	−0.889199	−	0.457521i	$-0.848738\pi$
$941$	−1.48393	+	2.57025i	−0.0483748	+	0.0837876i	0.840824	+	0.541308i	$0.182071\pi$
$942$		0			0
$943$	0.0202760	+	0.0351191i	0.000660277	+	0.00114363i
$944$		0			0
$945$	15.9878	+	20.9039i	0.520084	+	0.680004i
$946$		0			0
$947$	−4.83496	−	8.37439i	−0.157115	−	0.272131i	0.776712	−	0.629856i	$-0.216886\pi$
$947$	−4.83496	−	8.37439i	−0.157115	−	0.272131i	−0.933827	+	0.357725i	$0.883553\pi$
$948$		0			0
$949$	−14.1563	+	24.5195i	−0.459533	+	0.795935i
$950$		0			0
$951$	−37.9515			−1.23066
$952$		0			0
$953$	−14.5269			−0.470574			−0.235287	−	0.971926i	$-0.575603\pi$
$953$	−14.5269			−0.470574			−0.235287	+	0.971926i	$0.575603\pi$
$954$		0			0
$955$	3.85485	−	6.67680i	0.124740	−	0.216056i
$956$		0			0
$957$	10.2871	+	17.8177i	0.332533	+	0.575965i
$958$		0			0
$959$	0.692240	−	1.66379i	0.0223536	−	0.0537266i
$960$		0			0
$961$	11.0427	+	19.1265i	0.356216	+	0.616985i
$962$		0			0
$963$	−7.13323	+	12.3551i	−0.229865	+	0.398138i
$964$		0			0
$965$	−26.7988			−0.862685
$966$		0			0
$967$	43.5318			1.39989			0.699944	−	0.714198i	$-0.253208\pi$
$967$	43.5318			1.39989			0.699944	+	0.714198i	$0.253208\pi$
$968$		0			0
$969$	3.70337	−	6.41443i	0.118970	−	0.206061i
$970$		0			0
$971$	−10.9993	−	19.0514i	−0.352985	−	0.611387i	0.633786	−	0.773508i	$-0.281500\pi$
$971$	−10.9993	−	19.0514i	−0.352985	−	0.611387i	−0.986771	+	0.162121i	$0.948167\pi$
$972$		0			0
$973$	−34.5535	+	4.49362i	−1.10773	+	0.144059i
$974$		0			0
$975$	−2.88265	−	4.99289i	−0.0923185	−	0.159900i
$976$		0			0
$977$	−7.39652	+	12.8112i	−0.236636	+	0.409865i	−0.959747	−	0.280867i	$-0.909378\pi$
$977$	−7.39652	+	12.8112i	−0.236636	+	0.409865i	0.723111	+	0.690732i	$0.242711\pi$
$978$		0			0
$979$	0.562280			0.0179706
$980$		0			0
$981$	2.68936			0.0858646
$982$		0			0
$983$	22.2749	−	38.5813i	0.710460	−	1.23055i	−0.254225	−	0.967145i	$-0.581820\pi$
$983$	22.2749	−	38.5813i	0.710460	−	1.23055i	0.964685	−	0.263407i	$-0.0848464\pi$
$984$		0			0
$985$	3.83439	+	6.64137i	0.122174	+	0.211612i
$986$		0			0
$987$	−26.0251	+	3.38453i	−0.828389	+	0.107731i
$988$		0			0
$989$	−0.0242633	−	0.0420252i	−0.000771528	−	0.00133633i
$990$		0			0
$991$	8.82231	−	15.2807i	0.280250	−	0.485407i	−0.691196	−	0.722667i	$-0.742916\pi$
$991$	8.82231	−	15.2807i	0.280250	−	0.485407i	0.971446	+	0.237260i	$0.0762493\pi$
$992$		0			0
$993$	5.65010			0.179301
$994$		0			0
$995$	5.43220			0.172212
$996$		0			0
$997$	−27.8967	+	48.3185i	−0.883497	+	1.53026i	−0.0360698	+	0.999349i	$0.511484\pi$
$997$	−27.8967	+	48.3185i	−0.883497	+	1.53026i	−0.847427	+	0.530912i	$0.821849\pi$
$998$		0			0
$999$	0.549244	+	0.951319i	0.0173773	+	0.0300984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.i.d.165.3	✓	16
7.2	even	3	inner	1148.2.i.d.821.3	yes	16
7.3	odd	6		8036.2.a.n.1.3		8
7.4	even	3		8036.2.a.m.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.i.d.165.3	✓	16	1.1	even	1	trivial
1148.2.i.d.821.3	yes	16	7.2	even	3	inner
8036.2.a.m.1.6		8	7.4	even	3
8036.2.a.n.1.3		8	7.3	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.666692 + 1.15474i) q^{3} +(-0.883435 - 1.53015i) q^{5} +(2.62366 - 0.341202i) q^{7} +(0.611043 + 1.05836i) q^{9} +O(q^{10})\)	\(q+(-0.666692 + 1.15474i) q^{3} +(-0.883435 - 1.53015i) q^{5} +(2.62366 - 0.341202i) q^{7} +(0.611043 + 1.05836i) q^{9} +(1.24363 - 2.15404i) q^{11} -2.30214 q^{13} +2.35592 q^{15} +(0.702066 - 1.21601i) q^{17} +(-1.97804 - 3.42606i) q^{19} +(-1.35517 + 3.25713i) q^{21} +(0.0202760 + 0.0351191i) q^{23} +(0.939085 - 1.62654i) q^{25} -5.62966 q^{27} +6.20359 q^{29} +(1.49287 - 2.58572i) q^{31} +(1.65824 + 2.87216i) q^{33} +(-2.83992 - 3.71317i) q^{35} +(-0.0975626 - 0.168983i) q^{37} +(1.53482 - 2.65838i) q^{39} +1.00000 q^{41} -1.19665 q^{43} +(1.07963 - 1.86998i) q^{45} +(3.71964 + 6.44260i) q^{47} +(6.76716 - 1.79040i) q^{49} +(0.936124 + 1.62141i) q^{51} +(5.89997 - 10.2191i) q^{53} -4.39468 q^{55} +5.27497 q^{57} +(2.75423 - 4.77047i) q^{59} +(-1.95728 - 3.39011i) q^{61} +(1.96428 + 2.56828i) q^{63} +(2.03379 + 3.52262i) q^{65} +(-2.89923 + 5.02161i) q^{67} -0.0540714 q^{69} +10.2887 q^{71} +(6.14921 - 10.6507i) q^{73} +(1.25216 + 2.16881i) q^{75} +(2.52791 - 6.07578i) q^{77} +(0.679701 + 1.17728i) q^{79} +(1.92013 - 3.32575i) q^{81} +6.02722 q^{83} -2.48092 q^{85} +(-4.13589 + 7.16357i) q^{87} +(0.113032 + 0.195777i) q^{89} +(-6.04002 + 0.785495i) q^{91} +(1.99056 + 3.44776i) q^{93} +(-3.49493 + 6.05340i) q^{95} +1.43170 q^{97} +3.03965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^9	\( 16 q - 4 q^{9} + 8 q^{11} - 14 q^{13} - 2 q^{15} + q^{17} - 4 q^{19} + 13 q^{21} + 3 q^{23} + 4 q^{25} - 24 q^{27} - 8 q^{29} - 4 q^{31} - 23 q^{33} + 12 q^{35} + 31 q^{37} - 5 q^{39} + 16 q^{41} - 16 q^{43} - q^{45} - 24 q^{47} + 16 q^{49} + 23 q^{51} + q^{53} + 4 q^{55} - 30 q^{57} - 4 q^{59} + 4 q^{61} + 23 q^{63} + 24 q^{65} - 42 q^{69} + 16 q^{71} - 11 q^{73} + 15 q^{75} + 25 q^{77} - 14 q^{79} + 28 q^{81} - 84 q^{83} - 40 q^{85} - 25 q^{87} + 11 q^{89} + 7 q^{91} + 27 q^{93} + 15 q^{95} - 32 q^{97} - 16 q^{99}+O(q^{100}) \) 16 * q - 4 * q^9 + 8 * q^11 - 14 * q^13 - 2 * q^15 + q^17 - 4 * q^19 + 13 * q^21 + 3 * q^23 + 4 * q^25 - 24 * q^27 - 8 * q^29 - 4 * q^31 - 23 * q^33 + 12 * q^35 + 31 * q^37 - 5 * q^39 + 16 * q^41 - 16 * q^43 - q^45 - 24 * q^47 + 16 * q^49 + 23 * q^51 + q^53 + 4 * q^55 - 30 * q^57 - 4 * q^59 + 4 * q^61 + 23 * q^63 + 24 * q^65 - 42 * q^69 + 16 * q^71 - 11 * q^73 + 15 * q^75 + 25 * q^77 - 14 * q^79 + 28 * q^81 - 84 * q^83 - 40 * q^85 - 25 * q^87 + 11 * q^89 + 7 * q^91 + 27 * q^93 + 15 * q^95 - 32 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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