LMFDB - Embedded newform 441.2.h.e.214.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(214,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("441.214");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.h (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			214.3
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	441.214
Dual form			441.2.h.e.373.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.53209 q^{2} +(0.592396 + 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 + 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})$	\(q+2.53209 q^{2} +(0.592396 + 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 + 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 + 1.92836i) q^{9} +(-1.11334 + 1.92836i) q^{10} +(-1.93969 - 3.35965i) q^{11} +(2.61334 + 7.18009i) q^{12} +(-2.72668 - 4.72275i) q^{13} +(-1.50000 - 0.264490i) q^{15} +6.63816 q^{16} +(0.826352 - 1.43128i) q^{17} +(-5.81908 + 4.88279i) q^{18} +(1.20574 + 2.08840i) q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(-1.58125 + 2.73881i) q^{23} +(3.61721 + 9.93821i) q^{24} +(2.11334 + 3.66041i) q^{25} +(-6.90420 - 11.9584i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(3.02481 - 5.23913i) q^{29} +(-3.79813 - 0.669713i) q^{30} +4.55438 q^{31} +4.59627 q^{32} +(4.31908 - 5.14728i) q^{33} +(2.09240 - 3.62414i) q^{34} +(-10.1382 + 8.50692i) q^{36} +(2.27719 + 3.94421i) q^{37} +(3.05303 + 5.28801i) q^{38} +(6.07145 - 7.23567i) q^{39} +(-2.68479 + 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(-8.55690 - 14.8210i) q^{44} +(-0.458111 - 2.59808i) q^{45} +(-4.00387 + 6.93491i) q^{46} +1.02229 q^{47} +(3.93242 + 10.8042i) q^{48} +(5.35117 + 9.26849i) q^{50} +(2.81908 + 0.497079i) q^{51} +(-12.0287 - 20.8343i) q^{52} +(-3.64543 + 6.31407i) q^{53} +(-11.3944 - 6.57856i) q^{54} +3.41147 q^{55} +(-2.68479 + 3.19961i) q^{57} +(7.65910 - 13.2660i) q^{58} -6.66044 q^{59} +(-6.61721 - 1.16679i) q^{60} +2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} +4.79561 q^{65} +(10.9363 - 13.0334i) q^{66} -2.95811 q^{67} +(3.64543 - 6.31407i) q^{68} +(-5.39440 - 0.951178i) q^{69} -3.68004 q^{71} +(-14.0326 + 11.7747i) q^{72} +(-6.39053 + 11.0687i) q^{73} +(5.76604 + 9.98708i) q^{74} +(-4.70574 + 5.60808i) q^{75} +(5.31908 + 9.21291i) q^{76} +(15.3735 - 18.3214i) q^{78} -5.95811 q^{79} +(-2.91875 + 5.05542i) q^{80} +(1.56283 - 8.86327i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(-0.233956 + 0.405223i) q^{86} +(10.3191 + 1.81953i) q^{87} +(-11.8439 - 20.5142i) q^{88} +(5.51367 + 9.54996i) q^{89} +(-1.15998 - 6.57856i) q^{90} +(-6.97565 + 12.0822i) q^{92} +(2.69800 + 7.41268i) q^{93} +2.58853 q^{94} -2.12061 q^{95} +(2.72281 + 7.48086i) q^{96} +(6.25150 - 10.8279i) q^{97} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} - 9 q^{24} + 6 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} + 6 q^{31} + 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} + 6 q^{38} + 36 q^{39} - 9 q^{40} + 3 q^{43} - 15 q^{44} - 9 q^{45} - 6 q^{47} + 6 q^{50} - 21 q^{52} - 6 q^{53} - 27 q^{54} - 9 q^{57} + 9 q^{58} + 6 q^{59} - 9 q^{60} - 12 q^{61} + 60 q^{62} + 24 q^{64} + 30 q^{65} + 18 q^{66} - 24 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 9 q^{72} - 21 q^{73} + 30 q^{74} - 18 q^{75} + 15 q^{76} + 54 q^{78} - 42 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} + 45 q^{87} - 27 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} + 54 q^{93} + 36 q^{94} - 24 q^{95} + 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 - 9 * q^24 + 6 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 + 6 * q^31 + 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 + 6 * q^38 + 36 * q^39 - 9 * q^40 + 3 * q^43 - 15 * q^44 - 9 * q^45 - 6 * q^47 + 6 * q^50 - 21 * q^52 - 6 * q^53 - 27 * q^54 - 9 * q^57 + 9 * q^58 + 6 * q^59 - 9 * q^60 - 12 * q^61 + 60 * q^62 + 24 * q^64 + 30 * q^65 + 18 * q^66 - 24 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 9 * q^72 - 21 * q^73 + 30 * q^74 - 18 * q^75 + 15 * q^76 + 54 * q^78 - 42 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 + 45 * q^87 - 27 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 + 54 * q^93 + 36 * q^94 - 24 * q^95 + 27 * q^96 - 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	2.53209			1.79046			0.895229	−	0.445607i	$-0.147012\pi$
$2$	2.53209			1.79046			0.895229	+	0.445607i	$0.147012\pi$
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$3$	0.592396	+	1.62760i	0.342020	+	0.939693i
$4$	4.41147			2.20574
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	−0.947436	−	0.319946i	$-0.896335\pi$
$5$	−0.439693	+	0.761570i	−0.196637	+	0.340584i	0.750799	+	0.660530i	$0.229669\pi$
$6$	1.50000	+	4.12122i	0.612372	+	1.68248i
$7$		0			0
$7$		0			0
$8$	6.10607			2.15882
$9$	−2.29813	+	1.92836i	−0.766044	+	0.642788i
$10$	−1.11334	+	1.92836i	−0.352069	+	0.609802i
$11$	−1.93969	−	3.35965i	−0.584839	−	1.01297i	−0.994895	−	0.100911i	$-0.967824\pi$
$11$	−1.93969	−	3.35965i	−0.584839	−	1.01297i	0.410056	−	0.912060i	$-0.365509\pi$
$12$	2.61334	+	7.18009i	0.754407	+	2.07271i
$13$	−2.72668	−	4.72275i	−0.756245	−	1.30986i	−0.944753	−	0.327784i	$-0.893698\pi$
$13$	−2.72668	−	4.72275i	−0.756245	−	1.30986i	0.188507	−	0.982072i	$-0.439635\pi$
$14$		0			0
$15$	−1.50000	−	0.264490i	−0.387298	−	0.0682911i
$16$	6.63816			1.65954
$17$	0.826352	−	1.43128i	0.200420	−	0.347137i	−0.748244	−	0.663424i	$-0.769103\pi$
$17$	0.826352	−	1.43128i	0.200420	−	0.347137i	0.948664	+	0.316286i	$0.102436\pi$
$18$	−5.81908	+	4.88279i	−1.37157	+	1.15088i
$19$	1.20574	+	2.08840i	0.276615	+	0.479111i	0.970541	−	0.240935i	$-0.0774540\pi$
$19$	1.20574	+	2.08840i	0.276615	+	0.479111i	−0.693926	+	0.720046i	$0.744121\pi$
$20$	−1.93969	+	3.35965i	−0.433728	+	0.751240i
$21$		0			0
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	−1.58125	+	2.73881i	−0.329714	+	0.571081i	−0.982455	−	0.186500i	$-0.940286\pi$
$23$	−1.58125	+	2.73881i	−0.329714	+	0.571081i	0.652741	+	0.757581i	$0.273619\pi$
$24$	3.61721	+	9.93821i	0.738360	+	2.02863i
$25$	2.11334	+	3.66041i	0.422668	+	0.732083i
$26$	−6.90420	−	11.9584i	−1.35403	−	2.34524i
$27$	−4.50000	−	2.59808i	−0.866025	−	0.500000i
$28$		0			0
$29$	3.02481	−	5.23913i	0.561694	−	0.972883i	−0.435655	−	0.900114i	$-0.643483\pi$
$29$	3.02481	−	5.23913i	0.561694	−	0.972883i	0.997349	−	0.0727688i	$-0.0231835\pi$
$30$	−3.79813	−	0.669713i	−0.693441	−	0.122272i
$31$	4.55438			0.817990			0.408995	−	0.912537i	$-0.365879\pi$
$31$	4.55438			0.817990			0.408995	+	0.912537i	$0.365879\pi$
$32$	4.59627			0.812513
$33$	4.31908	−	5.14728i	0.751855	−	0.896026i
$34$	2.09240	−	3.62414i	0.358843	−	0.621534i
$35$		0			0
$36$	−10.1382	+	8.50692i	−1.68969	+	1.41782i
$37$	2.27719	+	3.94421i	0.374368	+	0.648424i	0.990232	−	0.139428i	$-0.0445265\pi$
$37$	2.27719	+	3.94421i	0.374368	+	0.648424i	−0.615865	+	0.787852i	$0.711193\pi$
$38$	3.05303	+	5.28801i	0.495267	+	0.857828i
$39$	6.07145	−	7.23567i	0.972210	−	1.15864i
$40$	−2.68479	+	4.65020i	−0.424503	+	0.735261i
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	0.816053	−	0.577977i	$-0.196158\pi$
$41$	−0.592396	−	1.02606i	−0.0925168	−	0.160244i	−0.908570	+	0.417734i	$0.862825\pi$
$42$		0			0
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	−0.872985	−	0.487748i	$-0.837819\pi$
$43$	−0.0923963	+	0.160035i	−0.0140903	+	0.0244051i	0.858894	+	0.512153i	$0.171152\pi$
$44$	−8.55690	−	14.8210i	−1.29000	−	2.23435i
$45$	−0.458111	−	2.59808i	−0.0682911	−	0.387298i
$46$	−4.00387	+	6.93491i	−0.590338	+	1.02250i
$47$	1.02229			0.149116			0.0745581	−	0.997217i	$-0.476245\pi$
$47$	1.02229			0.149116			0.0745581	+	0.997217i	$0.476245\pi$
$48$	3.93242	+	10.8042i	0.567596	+	1.55946i
$49$		0			0
$50$	5.35117	+	9.26849i	0.756769	+	1.31076i
$51$	2.81908	+	0.497079i	0.394750	+	0.0696051i
$52$	−12.0287	−	20.8343i	−1.66808	−	2.88920i
$53$	−3.64543	+	6.31407i	−0.500738	+	0.867304i	0.499261	+	0.866451i	$0.333605\pi$
$53$	−3.64543	+	6.31407i	−0.500738	+	0.867304i	−1.00000		0.000852699i	$0.999729\pi$
$54$	−11.3944	−	6.57856i	−1.55058	−	0.895229i
$55$	3.41147			0.460003
$56$		0			0
$57$	−2.68479	+	3.19961i	−0.355609	+	0.423799i
$58$	7.65910	−	13.2660i	1.00569	−	1.74190i
$59$	−6.66044			−0.867116			−0.433558	−	0.901126i	$-0.642742\pi$
$59$	−6.66044			−0.867116			−0.433558	+	0.901126i	$0.642742\pi$
$60$	−6.61721	−	1.16679i	−0.854278	−	0.150632i
$61$	2.59627			0.332418			0.166209	−	0.986091i	$-0.446847\pi$
$61$	2.59627			0.332418			0.166209	+	0.986091i	$0.446847\pi$
$62$	11.5321			1.46458
$63$		0			0
$64$	−1.63816			−0.204769
$65$	4.79561			0.594822
$66$	10.9363	−	13.0334i	1.34616	−	1.60430i
$67$	−2.95811			−0.361391			−0.180695	−	0.983539i	$-0.557835\pi$
$67$	−2.95811			−0.361391			−0.180695	+	0.983539i	$0.557835\pi$
$68$	3.64543	−	6.31407i	0.442073	−	0.765693i
$69$	−5.39440	−	0.951178i	−0.649409	−	0.114508i
$70$		0			0
$71$	−3.68004			−0.436741			−0.218370	−	0.975866i	$-0.570074\pi$
$71$	−3.68004			−0.436741			−0.218370	+	0.975866i	$0.570074\pi$
$72$	−14.0326	+	11.7747i	−1.65375	+	1.38766i
$73$	−6.39053	+	11.0687i	−0.747955	+	1.29550i	0.200847	+	0.979623i	$0.435631\pi$
$73$	−6.39053	+	11.0687i	−0.747955	+	1.29550i	−0.948801	+	0.315873i	$0.897703\pi$
$74$	5.76604	+	9.98708i	0.670289	+	1.16097i
$75$	−4.70574	+	5.60808i	−0.543372	+	0.647565i
$76$	5.31908	+	9.21291i	0.610140	+	1.05679i
$77$		0			0
$78$	15.3735	−	18.3214i	1.74070	−	2.07449i
$79$	−5.95811			−0.670340			−0.335170	−	0.942158i	$-0.608794\pi$
$79$	−5.95811			−0.670340			−0.335170	+	0.942158i	$0.608794\pi$
$80$	−2.91875	+	5.05542i	−0.326326	+	0.565213i
$81$	1.56283	−	8.86327i	0.173648	−	0.984808i
$82$	−1.50000	−	2.59808i	−0.165647	−	0.286910i
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	−0.871971	−	0.489558i	$-0.837158\pi$
$83$	−0.109470	+	0.189608i	−0.0120159	+	0.0208122i	0.859955	+	0.510370i	$0.170492\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	−0.233956	+	0.405223i	−0.0252281	+	0.0436963i
$87$	10.3191	+	1.81953i	1.10632	+	0.195074i
$88$	−11.8439	−	20.5142i	−1.26256	−	2.18682i
$89$	5.51367	+	9.54996i	0.584448	+	1.01229i	0.994944	+	0.100431i	$0.0320222\pi$
$89$	5.51367	+	9.54996i	0.584448	+	1.01229i	−0.410496	+	0.911862i	$0.634644\pi$
$90$	−1.15998	−	6.57856i	−0.122272	−	0.693441i
$91$		0			0
$92$	−6.97565	+	12.0822i	−0.727262	+	1.25965i
$93$	2.69800	+	7.41268i	0.279769	+	0.768660i
$94$	2.58853			0.266986
$95$	−2.12061			−0.217570
$96$	2.72281	+	7.48086i	0.277896	+	0.763512i
$97$	6.25150	−	10.8279i	0.634743	−	1.09941i	−0.351826	−	0.936065i	$-0.614439\pi$
$97$	6.25150	−	10.8279i	0.634743	−	1.09941i	0.986569	−	0.163342i	$-0.0522275\pi$
$98$		0			0
$99$	10.9363	+	3.98048i	1.09914	+	0.400054i
$100$	9.32295	+	16.1478i	0.932295	+	1.61478i
$101$	−4.85844	−	8.41507i	−0.483433	−	0.837330i	0.516386	−	0.856356i	$-0.327277\pi$
$101$	−4.85844	−	8.41507i	−0.483433	−	0.837330i	−0.999819	+	0.0190255i	$0.993944\pi$
$102$	7.13816	+	1.25865i	0.706783	+	0.124625i
$103$	3.29813	−	5.71253i	0.324975	−	0.562873i	−0.656533	−	0.754298i	$-0.727978\pi$
$103$	3.29813	−	5.71253i	0.324975	−	0.562873i	0.981507	+	0.191425i	$0.0613109\pi$
$104$	−16.6493	−	28.8374i	−1.63260	−	2.82774i
$105$		0			0
$106$	−9.23055	+	15.9878i	−0.896550	+	1.55287i
$107$	−1.19459	−	2.06910i	−0.115486	−	0.200027i	0.802488	−	0.596668i	$-0.203509\pi$
$107$	−1.19459	−	2.06910i	−0.115486	−	0.200027i	−0.917974	+	0.396641i	$0.870176\pi$
$108$	−19.8516	−	11.4613i	−1.91022	−	1.10287i
$109$	−1.97906	+	3.42782i	−0.189559	+	0.328326i	−0.945103	−	0.326772i	$-0.894039\pi$
$109$	−1.97906	+	3.42782i	−0.189559	+	0.328326i	0.755544	+	0.655098i	$0.227373\pi$
$110$	8.63816			0.823616
$111$	−5.07057	+	6.04288i	−0.481278	+	0.573564i
$112$		0			0
$113$	−8.22668	−	14.2490i	−0.773901	−	1.34044i	−0.935410	−	0.353565i	$-0.884969\pi$
$113$	−8.22668	−	14.2490i	−0.773901	−	1.34044i	0.161509	−	0.986871i	$-0.448364\pi$
$114$	−6.79813	+	8.10170i	−0.636704	+	0.758794i
$115$	−1.39053	−	2.40847i	−0.129668	−	0.224591i
$116$	13.3439	−	23.1123i	1.23895	−	2.14592i
$117$	15.3735	+	5.59548i	1.42128	+	0.517302i
$118$	−16.8648			−1.55253
$119$		0			0
$120$	−9.15910	−	1.61500i	−0.836108	−	0.147428i
$121$	−2.02481	+	3.50708i	−0.184074	+	0.318826i
$122$	6.57398			0.595180
$123$	1.31908	−	1.57202i	0.118937	−	0.141744i
$124$	20.0915			1.80427
$125$	−8.11381			−0.725721
$126$		0			0
$127$	17.6536			1.56651			0.783253	−	0.621702i	$-0.213559\pi$
$127$	17.6536			1.56651			0.783253	+	0.621702i	$0.213559\pi$
$128$	−13.3405			−1.17914
$129$	−0.315207	−	0.0555796i	−0.0277525	−	0.00489351i
$130$	12.1429			1.06500
$131$	−9.59879	+	16.6256i	−0.838650	+	1.45259i	0.0523729	+	0.998628i	$0.483322\pi$
$131$	−9.59879	+	16.6256i	−0.838650	+	1.45259i	−0.891023	+	0.453958i	$0.850012\pi$
$132$	19.0535	−	22.7071i	1.65839	−	1.97640i
$133$		0			0
$134$	−7.49020			−0.647055
$135$	3.95723	−	2.28471i	0.340584	−	0.196637i
$136$	5.04576	−	8.73951i	0.432670	−	0.749407i
$137$	−9.07785	−	15.7233i	−0.775573	−	1.34333i	−0.934472	−	0.356037i	$-0.884128\pi$
$137$	−9.07785	−	15.7233i	−0.775573	−	1.34333i	0.158899	−	0.987295i	$-0.449206\pi$
$138$	−13.6591	−	2.40847i	−1.16274	−	0.205022i
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.773846	+	0.633374i	$0.218330\pi$
$139$	11.0287	+	19.1022i	0.935441	+	1.62023i	0.161595	+	0.986857i	$0.448336\pi$
$140$		0			0
$141$	0.605600	+	1.66387i	0.0510007	+	0.140123i
$142$	−9.31820			−0.781966
$143$	−10.5778	+	18.3214i	−0.884564	+	1.53211i
$144$	−15.2554	+	12.8008i	−1.27128	+	1.06673i
$145$	2.65998	+	4.60722i	0.220899	+	0.382608i
$146$	−16.1814	+	28.0270i	−1.33918	+	2.31953i
$147$		0			0
$148$	10.0458	+	17.3998i	0.825756	+	1.43025i
$149$	7.57785	−	13.1252i	0.620802	−	1.07526i	−0.368535	−	0.929614i	$-0.620141\pi$
$149$	7.57785	−	13.1252i	0.620802	−	1.07526i	0.989337	−	0.145646i	$-0.0465261\pi$
$150$	−11.9153	+	14.2002i	−0.972884	+	1.15944i
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	0.936838	+	0.349764i	$0.113738\pi$
$151$	9.47818	+	16.4167i	0.771323	+	1.33597i	−0.165515	+	0.986207i	$0.552929\pi$
$152$	7.36231	+	12.7519i	0.597162	+	1.03432i
$153$	0.860967	+	4.88279i	0.0696051	+	0.394750i
$154$		0			0
$155$	−2.00253	+	3.46848i	−0.160847	+	0.278595i
$156$	26.7841	−	31.9200i	2.14444	−	2.55564i
$157$	18.0574			1.44114			0.720568	−	0.693385i	$-0.243881\pi$
$157$	18.0574			1.44114			0.720568	+	0.693385i	$0.243881\pi$
$158$	−15.0865			−1.20021
$159$	−12.4363	−	2.19285i	−0.986262	−	0.173905i
$160$	−2.02094	+	3.50038i	−0.159770	+	0.276729i
$161$		0			0
$162$	3.95723	−	22.4426i	0.310910	−	1.76326i
$163$	−0.479055	−	0.829748i	−0.0375225	−	0.0649909i	0.846654	−	0.532143i	$-0.178613\pi$
$163$	−0.479055	−	0.829748i	−0.0375225	−	0.0649909i	−0.884177	+	0.467152i	$0.845280\pi$
$164$	−2.61334	−	4.52644i	−0.204068	−	0.353456i
$165$	2.02094	+	5.55250i	0.157330	+	0.432261i
$166$	−0.277189	+	0.480105i	−0.0215140	+	0.0372634i
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	0.938876	+	0.344255i	$0.111869\pi$
$167$	9.91921	+	17.1806i	0.767572	+	1.32947i	−0.171304	+	0.985218i	$0.554798\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	1.84002	+	3.18701i	0.141123	+	0.244433i
$171$	−6.79813	−	2.47432i	−0.519866	−	0.189216i
$172$	−0.407604	+	0.705990i	−0.0310795	+	0.0538313i
$173$	−22.6827			−1.72454			−0.862268	−	0.506452i	$-0.830957\pi$
$173$	−22.6827			−1.72454			−0.862268	+	0.506452i	$0.830957\pi$
$174$	26.1288	+	4.60722i	1.98082	+	0.349272i
$175$		0			0
$176$	−12.8760	−	22.3019i	−0.970564	−	1.68107i
$177$	−3.94562	−	10.8405i	−0.296571	−	0.814823i
$178$	13.9611	+	24.1813i	1.04643	+	1.81247i
$179$	3.67365	−	6.36295i	0.274581	−	0.475589i	−0.695448	−	0.718576i	$-0.744794\pi$
$179$	3.67365	−	6.36295i	0.274581	−	0.475589i	0.970029	+	0.242988i	$0.0781274\pi$
$180$	−2.02094	−	11.4613i	−0.150632	−	0.854278i
$181$	3.44562			0.256111			0.128056	−	0.991767i	$-0.459126\pi$
$181$	3.44562			0.256111			0.128056	+	0.991767i	$0.459126\pi$
$182$		0			0
$183$	1.53802	+	4.22567i	0.113694	+	0.312371i
$184$	−9.65523	+	16.7233i	−0.711793	+	1.23286i
$185$	−4.00505			−0.294457
$186$	6.83157	+	18.7696i	0.500915	+	1.37625i
$187$	−6.41147			−0.468853
$188$	4.50980			0.328911
$189$		0			0
$190$	−5.36959			−0.389551
$191$	5.65776			0.409381			0.204690	−	0.978827i	$-0.434381\pi$
$191$	5.65776			0.409381			0.204690	+	0.978827i	$0.434381\pi$
$192$	−0.970437	−	2.66625i	−0.0700353	−	0.192420i
$193$	9.59627			0.690754			0.345377	−	0.938464i	$-0.387751\pi$
$193$	9.59627			0.690754			0.345377	+	0.938464i	$0.387751\pi$
$194$	15.8293	−	27.4172i	1.13648	−	1.96844i
$195$	2.84090	+	7.80531i	0.203441	+	0.558950i
$196$		0			0
$197$	8.31996			0.592772			0.296386	−	0.955068i	$-0.404218\pi$
$197$	8.31996			0.592772			0.296386	+	0.955068i	$0.404218\pi$
$198$	27.6917	+	10.0789i	1.96796	+	0.716279i
$199$	3.29813	−	5.71253i	0.233798	−	0.404951i	−0.725124	−	0.688618i	$-0.758218\pi$
$199$	3.29813	−	5.71253i	0.233798	−	0.404951i	0.958923	+	0.283667i	$0.0915511\pi$
$200$	12.9042	+	22.3507i	0.912465	+	1.58044i
$201$	−1.75237	−	4.81461i	−0.123603	−	0.339596i
$202$	−12.3020	−	21.3077i	−0.865566	−	1.49920i
$203$		0			0
$204$	12.4363	+	2.19285i	0.870714	+	0.153530i
$205$	1.04189			0.0727687
$206$	8.35117	−	14.4646i	0.581853	−	1.00780i
$207$	−1.64749	−	9.34337i	−0.114508	−	0.649409i
$208$	−18.1001	−	31.3504i	−1.25502	−	2.17376i
$209$	4.67752	−	8.10170i	0.323551	−	0.560406i
$210$		0			0
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	0.918173	−	0.396179i	$-0.129664\pi$
$211$	1.68479	+	2.91815i	0.115986	+	0.200893i	−0.802188	+	0.597072i	$0.796331\pi$
$212$	−16.0817	+	27.8544i	−1.10450	+	1.91304i
$213$	−2.18004	−	5.98962i	−0.149374	−	0.410402i
$214$	−3.02481	−	5.23913i	−0.206772	−	0.358140i
$215$	−0.0812519	−	0.140732i	−0.00554133	−	0.00959787i
$216$	−27.4773	−	15.8640i	−1.86959	−	1.07941i
$217$		0			0
$218$	−5.01114	+	8.67956i	−0.339398	+	0.587854i
$219$	−21.8011	−	3.84413i	−1.47318	−	0.259762i
$220$	15.0496			1.01465
$221$	−9.01279			−0.606266
$222$	−12.8391	+	15.3011i	−0.861707	+	1.02694i
$223$	−3.13816	+	5.43545i	−0.210146	+	0.363984i	−0.951760	−	0.306843i	$-0.900727\pi$
$223$	−3.13816	+	5.43545i	−0.210146	+	0.363984i	0.741614	+	0.670827i	$0.234061\pi$
$224$		0			0
$225$	−11.9153	−	4.33683i	−0.794356	−	0.289122i
$226$	−20.8307	−	36.0798i	−1.38564	−	2.39999i
$227$	−3.08125	−	5.33688i	−0.204510	−	0.354221i	0.745467	−	0.666543i	$-0.232227\pi$
$227$	−3.08125	−	5.33688i	−0.204510	−	0.354221i	−0.949976	+	0.312322i	$0.898893\pi$
$228$	−11.8439	+	14.1150i	−0.784381	+	0.934789i
$229$	11.6925	−	20.2521i	0.772664	−	1.33829i	−0.163434	−	0.986554i	$-0.552257\pi$
$229$	11.6925	−	20.2521i	0.772664	−	1.33829i	0.936098	−	0.351740i	$-0.114410\pi$
$230$	−3.52094	−	6.09845i	−0.232164	−	0.402120i
$231$		0			0
$232$	18.4697	−	31.9905i	1.21260	−	2.10028i
$233$	4.26264	+	7.38311i	0.279255	+	0.483684i	0.971200	−	0.238267i	$-0.0765792\pi$
$233$	4.26264	+	7.38311i	0.279255	+	0.483684i	−0.691945	+	0.721950i	$0.743246\pi$
$234$	38.9270	+	14.1683i	2.54473	+	0.926208i
$235$	−0.449493	+	0.778544i	−0.0293217	+	0.0507866i
$236$	−29.3824			−1.91263
$237$	−3.52956	−	9.69739i	−0.229270	−	0.629913i
$238$		0			0
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	0.528476	−	0.848948i	$-0.322764\pi$
$239$	−7.28106	−	12.6112i	−0.470973	−	0.815748i	−0.999449	+	0.0331997i	$0.989430\pi$
$240$	−9.95723	−	1.75573i	−0.642737	−	0.113332i
$241$	−2.70187	−	4.67977i	−0.174043	−	0.301451i	0.765787	−	0.643094i	$-0.222350\pi$
$241$	−2.70187	−	4.67977i	−0.174043	−	0.301451i	−0.939830	+	0.341644i	$0.889016\pi$
$242$	−5.12701	+	8.88024i	−0.329577	+	0.570844i
$243$	15.3516	−	2.70691i	0.984808	−	0.173648i
$244$	11.4534			0.733226
$245$		0			0
$246$	3.34002	−	3.98048i	0.212952	−	0.253786i
$247$	6.57532	−	11.3888i	0.418378	−	0.724651i
$248$	27.8093			1.76589
$249$	−0.373455	−	0.0658503i	−0.0236668	−	0.00417309i
$250$	−20.5449			−1.29937
$251$	12.0669			0.761654			0.380827	−	0.924646i	$-0.375639\pi$
$251$	12.0669			0.761654			0.380827	+	0.924646i	$0.375639\pi$
$252$		0			0
$253$	12.2686			0.771318
$254$	44.7006			2.80476
$255$	−1.61809	+	1.92836i	−0.101329	+	0.120759i
$256$	−30.5030			−1.90644
$257$	5.28312	−	9.15063i	0.329552	−	0.570801i	−0.652871	−	0.757469i	$-0.726436\pi$
$257$	5.28312	−	9.15063i	0.329552	−	0.570801i	0.982423	+	0.186668i	$0.0597690\pi$
$258$	−0.798133	−	0.140732i	−0.0496896	−	0.00876162i
$259$		0			0
$260$	21.1557			1.31202
$261$	3.15152	+	17.8732i	0.195074	+	1.10632i
$262$	−24.3050	+	42.0975i	−1.50157	+	2.60079i
$263$	14.1766	+	24.5547i	0.874169	+	1.51411i	0.857645	+	0.514242i	$0.171927\pi$
$263$	14.1766	+	24.5547i	0.874169	+	1.51411i	0.0165240	+	0.999863i	$0.494740\pi$
$264$	26.3726	−	31.4296i	1.62312	−	1.93436i
$265$	−3.20574	−	5.55250i	−0.196927	−	0.341087i
$266$		0			0
$267$	−12.2772	+	14.6314i	−0.751352	+	0.895426i
$268$	−13.0496			−0.797133
$269$	3.74170	−	6.48081i	0.228135	−	0.395142i	−0.729120	−	0.684386i	$-0.760070\pi$
$269$	3.74170	−	6.48081i	0.228135	−	0.395142i	0.957255	+	0.289244i	$0.0934038\pi$
$270$	10.0201	−	5.78509i	0.609802	−	0.352069i
$271$	6.81908	+	11.8110i	0.414229	+	0.717467i	0.995347	−	0.0963530i	$-0.0307178\pi$
$271$	6.81908	+	11.8110i	0.414229	+	0.717467i	−0.581118	+	0.813819i	$0.697384\pi$
$272$	5.48545	−	9.50108i	0.332604	−	0.576088i
$273$		0			0
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	8.19846	−	14.2002i	0.494386	−	0.856302i
$276$	−23.7973	−	4.19610i	−1.43243	−	0.252575i
$277$	3.07532	+	5.32661i	0.184778	+	0.320045i	0.943502	−	0.331368i	$-0.107510\pi$
$277$	3.07532	+	5.32661i	0.184778	+	0.320045i	−0.758724	+	0.651413i	$0.774177\pi$
$278$	27.9256	+	48.3686i	1.67487	+	2.90095i
$279$	−10.4666	+	8.78249i	−0.626617	+	0.525794i
$280$		0			0
$281$	−1.65611	+	2.86846i	−0.0987951	+	0.171118i	−0.911186	−	0.411995i	$-0.864832\pi$
$281$	−1.65611	+	2.86846i	−0.0987951	+	0.171118i	0.812391	+	0.583113i	$0.198165\pi$
$282$	1.53343	+	4.21307i	0.0913146	+	0.250885i
$283$	−29.0232			−1.72525			−0.862626	−	0.505843i	$-0.831182\pi$
$283$	−29.0232			−1.72525			−0.862626	+	0.505843i	$0.831182\pi$
$284$	−16.2344			−0.963336
$285$	−1.25624	−	3.45150i	−0.0744135	−	0.204449i
$286$	−26.7841	+	46.3913i	−1.58377	+	2.74318i
$287$		0			0
$288$	−10.5628	+	8.86327i	−0.622421	+	0.522273i
$289$	7.13429	+	12.3569i	0.419664	+	0.726879i
$290$	6.73530	+	11.6659i	0.395510	+	0.685044i
$291$	21.3268	+	3.76049i	1.25020	+	0.220444i
$292$	−28.1917	+	48.8294i	−1.64979	+	2.85752i
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	0.716464	−	0.697624i	$-0.245759\pi$
$293$	−4.20961	−	7.29125i	−0.245928	−	0.425960i	−0.962392	+	0.271664i	$0.912426\pi$
$294$		0			0
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	13.9047	+	24.0836i	0.808192	+	1.39983i
$297$			20.1579i			1.16968i
$298$	19.1878	−	33.2342i	1.11152	−	1.92521i
$299$	17.2463			0.997378
$300$	−20.7592	+	24.7399i	−1.19854	+	1.42836i
$301$		0			0
$302$	23.9996	+	41.5685i	1.38102	+	2.39200i
$303$	10.8182	−	12.8926i	0.621489	−	0.740662i
$304$	8.00387	+	13.8631i	0.459053	+	0.795104i
$305$	−1.14156	+	1.97724i	−0.0653655	+	0.113216i
$306$	2.18004	+	12.3636i	0.124625	+	0.706783i
$307$	12.6878			0.724130			0.362065	−	0.932153i	$-0.382072\pi$
$307$	12.6878			0.724130			0.362065	+	0.932153i	$0.382072\pi$
$308$		0			0
$309$	11.2515	+	1.98394i	0.640075	+	0.112863i
$310$	−5.07057	+	8.78249i	−0.287989	+	0.498812i
$311$	16.4902			0.935073			0.467537	−	0.883974i	$-0.345142\pi$
$311$	16.4902			0.935073			0.467537	+	0.883974i	$0.345142\pi$
$312$	37.0727	−	44.1815i	2.09883	−	2.50129i
$313$	−28.5185			−1.61196			−0.805980	−	0.591943i	$-0.798361\pi$
$313$	−28.5185			−1.61196			−0.805980	+	0.591943i	$0.798361\pi$
$314$	45.7229			2.58029
$315$		0			0
$316$	−26.2841			−1.47859
$317$	−25.8949			−1.45440			−0.727200	−	0.686425i	$-0.759179\pi$
$317$	−25.8949			−1.45440			−0.727200	+	0.686425i	$0.759179\pi$
$318$	−31.4898	−	5.55250i	−1.76586	−	0.311369i
$319$	−23.4688			−1.31400
$320$	0.720285	−	1.24757i	0.0402652	−	0.0697413i
$321$	2.65998	−	3.17004i	0.148465	−	0.176934i
$322$		0			0
$323$	3.98545			0.221756
$324$	6.89440	−	39.1001i	0.383022	−	2.17223i
$325$	11.5248	−	19.9616i	0.639282	−	1.10727i
$326$	−1.21301	−	2.10100i	−0.0671825	−	0.116363i
$327$	−6.75150	−	1.19047i	−0.373359	−	0.0658332i
$328$	−3.61721	−	6.26519i	−0.199727	−	0.345937i
$329$		0			0
$330$	5.11721	+	14.0594i	0.281693	+	0.773946i
$331$	8.21894			0.451754			0.225877	−	0.974156i	$-0.427475\pi$
$331$	8.21894			0.451754			0.225877	+	0.974156i	$0.427475\pi$
$332$	−0.482926	+	0.836452i	−0.0265040	+	0.0459063i
$333$	−12.8391	−	4.67307i	−0.703581	−	0.256082i
$334$	25.1163	+	43.5028i	1.37430	+	2.38037i
$335$	1.30066	−	2.25281i	0.0710626	−	0.123084i
$336$		0			0
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	0.797033	−	0.603936i	$-0.206402\pi$
$337$	−2.28564	−	3.95885i	−0.124507	−	0.215652i	−0.921540	+	0.388283i	$0.873068\pi$
$338$	−21.1925	+	36.7065i	−1.15272	+	1.99657i
$339$	18.3182	−	21.8308i	0.994908	−	1.18569i
$340$	3.20574	+	5.55250i	0.173856	+	0.301127i
$341$	−8.83409	−	15.3011i	−0.478393	−	0.828601i
$342$	−17.2135	−	6.26519i	−0.930798	−	0.338783i
$343$		0			0
$344$	−0.564178	+	0.977185i	−0.0304184	+	0.0526863i
$345$	3.09627	−	3.68999i	0.166697	−	0.198662i
$346$	−57.4347			−3.08771
$347$	22.4662			1.20605			0.603023	−	0.797724i	$-0.293963\pi$
$347$	22.4662			1.20605			0.603023	+	0.797724i	$0.293963\pi$
$348$	45.5223	+	8.02682i	2.44025	+	0.430283i
$349$	13.0496	−	22.6026i	0.698531	−	1.20989i	−0.270445	−	0.962735i	$-0.587171\pi$
$349$	13.0496	−	22.6026i	0.698531	−	1.20989i	0.968976	−	0.247155i	$-0.0794958\pi$
$350$		0			0
$351$			28.3365i			1.51249i
$352$	−8.91534	−	15.4418i	−0.475189	−	0.823052i
$353$	−0.177519	−	0.307471i	−0.00944836	−	0.0163650i	0.861263	−	0.508160i	$-0.169674\pi$
$353$	−0.177519	−	0.307471i	−0.00944836	−	0.0163650i	−0.870711	+	0.491795i	$0.836341\pi$
$354$	−9.99067	−	27.4491i	−0.530998	−	1.45890i
$355$	1.61809	−	2.80261i	0.0858792	−	0.148747i
$356$	24.3234	+	42.1294i	1.28914	+	2.23285i
$357$		0			0
$358$	9.30200	−	16.1115i	0.491626	−	0.851522i
$359$	−2.72803	−	4.72508i	−0.143980	−	0.249380i	0.785012	−	0.619480i	$-0.212657\pi$
$359$	−2.72803	−	4.72508i	−0.143980	−	0.249380i	−0.928992	+	0.370100i	$0.879323\pi$
$360$	−2.79726	−	15.8640i	−0.147428	−	0.836108i
$361$	6.59240	−	11.4184i	0.346968	−	0.600967i
$362$	8.72462			0.458556
$363$	−6.90760	−	1.21800i	−0.362555	−	0.0639283i
$364$		0			0
$365$	−5.61974	−	9.73367i	−0.294150	−	0.509484i
$366$	3.89440	+	10.6998i	0.203564	+	0.559286i
$367$	5.46198	+	9.46043i	0.285113	+	0.493830i	0.972637	−	0.232332i	$-0.0746355\pi$
$367$	5.46198	+	9.46043i	0.285113	+	0.493830i	−0.687523	+	0.726162i	$0.741302\pi$
$368$	−10.4966	+	18.1806i	−0.547173	+	0.947731i
$369$	3.34002	+	1.21567i	0.173875	+	0.0632852i
$370$	−10.1411			−0.527213
$371$		0			0
$372$	11.9021	+	32.7009i	0.617097	+	1.69546i
$373$	−0.865715	+	1.49946i	−0.0448250	+	0.0776392i	−0.887567	−	0.460678i	$-0.847606\pi$
$373$	−0.865715	+	1.49946i	−0.0448250	+	0.0776392i	0.842742	+	0.538317i	$0.180940\pi$
$374$	−16.2344			−0.839462
$375$	−4.80659	−	13.2060i	−0.248211	−	0.681955i
$376$	6.24216			0.321915
$377$	−32.9908			−1.69911
$378$		0			0
$379$	−12.1334			−0.623251			−0.311626	−	0.950205i	$-0.600873\pi$
$379$	−12.1334			−0.623251			−0.311626	+	0.950205i	$0.600873\pi$
$380$	−9.35504			−0.479903
$381$	10.4579	+	28.7330i	0.535777	+	1.47204i
$382$	14.3259			0.732979
$383$	−4.35591	+	7.54467i	−0.222577	+	0.385514i	−0.955590	−	0.294700i	$-0.904780\pi$
$383$	−4.35591	+	7.54467i	−0.222577	+	0.385514i	0.733013	+	0.680215i	$0.238113\pi$
$384$	−7.90286	−	21.7129i	−0.403291	−	1.10803i
$385$		0			0
$386$	24.2986			1.23677
$387$	−0.0962667	−	0.545955i	−0.00489351	−	0.0277525i
$388$	27.5783	−	47.7670i	1.40008	−	2.42500i
$389$	−1.82160	−	3.15511i	−0.0923590	−	0.159970i	0.816144	−	0.577848i	$-0.196107\pi$
$389$	−1.82160	−	3.15511i	−0.0923590	−	0.159970i	−0.908503	+	0.417878i	$0.862774\pi$
$390$	7.19341	+	19.7637i	0.364253	+	1.00078i
$391$	2.61334	+	4.52644i	0.132162	+	0.228912i
$392$		0			0
$393$	−32.7460	−	5.77401i	−1.65182	−	0.291260i
$394$	21.0669			1.06133
$395$	2.61974	−	4.53752i	0.131813	−	0.228307i
$396$	48.2452	+	17.5598i	2.42441	+	0.882413i
$397$	−7.72281	−	13.3763i	−0.387597	−	0.671337i	0.604529	−	0.796583i	$-0.293361\pi$
$397$	−7.72281	−	13.3763i	−0.387597	−	0.671337i	−0.992126	+	0.125246i	$0.960028\pi$
$398$	8.35117	−	14.4646i	0.418606	−	0.725047i
$399$		0			0
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	−9.21095	+	15.9538i	−0.459973	+	0.796697i	−0.998959	−	0.0456182i	$-0.985474\pi$
$401$	−9.21095	+	15.9538i	−0.459973	+	0.796697i	0.538986	+	0.842315i	$0.318808\pi$
$402$	−4.43717	−	12.1910i	−0.221306	−	0.608033i
$403$	−12.4183	−	21.5092i	−0.618601	−	1.07145i
$404$	−21.4329	−	37.1228i	−1.06633	−	1.84693i
$405$	6.06283	+	5.08732i	0.301265	+	0.252791i
$406$		0			0
$407$	8.83409	−	15.3011i	0.437890	−	0.758447i
$408$	17.2135	+	3.03520i	0.852194	+	0.150265i
$409$	28.6364			1.41598			0.707989	−	0.706223i	$-0.249602\pi$
$409$	28.6364			1.41598			0.707989	+	0.706223i	$0.249602\pi$
$410$	2.63816			0.130289
$411$	20.2135	−	24.0895i	0.997057	−	1.18825i
$412$	14.5496	−	25.2007i	0.716809	−	1.24155i
$413$		0			0
$414$	−4.17159	−	23.6583i	−0.205022	−	1.16274i
$415$	−0.0962667	−	0.166739i	−0.00472554	−	0.00818488i
$416$	−12.5326	−	21.7070i	−0.614459	−	1.06427i
$417$	−24.5574	+	29.2663i	−1.20258	+	1.43318i
$418$	11.8439	−	20.5142i	0.579304	−	1.00338i
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	−0.883438	−	0.468548i	$-0.844777\pi$
$419$	−17.3478	−	30.0472i	−0.847494	−	1.46790i	0.0359442	−	0.999354i	$-0.488556\pi$
$420$		0			0
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	−0.310788	−	0.950479i	$-0.600593\pi$
$421$	13.7010	−	23.7308i	0.667745	−	1.15657i	0.978533	−	0.206090i	$-0.0660738\pi$
$422$	4.26604	+	7.38901i	0.207668	+	0.359691i
$423$	−2.34936	+	1.97134i	−0.114230	+	0.0958500i
$424$	−22.2592	+	38.5541i	−1.08100	+	1.87235i
$425$	6.98545			0.338844
$426$	−5.52007	−	15.1663i	−0.267448	−	0.734808i
$427$		0			0
$428$	−5.26991	−	9.12776i	−0.254731	−	0.441207i
$429$	−36.0861	−	6.36295i	−1.74225	−	0.307206i
$430$	−0.205737	−	0.356347i	−0.00992152	−	0.0171846i
$431$	−13.2961	+	23.0295i	−0.640449	+	1.10929i	0.344883	+	0.938646i	$0.387919\pi$
$431$	−13.2961	+	23.0295i	−0.640449	+	1.10929i	−0.985333	+	0.170645i	$0.945415\pi$
$432$	−29.8717	−	17.2464i	−1.43720	−	0.829769i
$433$	−37.1830			−1.78690			−0.893451	−	0.449160i	$-0.851723\pi$
$433$	−37.1830			−1.78690			−0.893451	+	0.449160i	$0.851723\pi$
$434$		0			0
$435$	−5.92292	+	7.05866i	−0.283982	+	0.338437i
$436$	−8.73055	+	15.1218i	−0.418118	+	0.724201i
$437$	−7.62630			−0.364815
$438$	−55.2024	−	9.73367i	−2.63767	−	0.465093i
$439$	−25.0746			−1.19675			−0.598373	−	0.801218i	$-0.704186\pi$
$439$	−25.0746			−1.19675			−0.598373	+	0.801218i	$0.704186\pi$
$440$	20.8307			0.993064
$441$		0			0
$442$	−22.8212			−1.08549
$443$	2.04458			0.0971408			0.0485704	−	0.998820i	$-0.484533\pi$
$443$	2.04458			0.0971408			0.0485704	+	0.998820i	$0.484533\pi$
$444$	−22.3687	+	26.6580i	−1.06157	+	1.26513i
$445$	−9.69728			−0.459695
$446$	−7.94609	+	13.7630i	−0.376258	+	0.651698i
$447$	25.8516	+	4.55834i	1.22274	+	0.215602i
$448$		0			0
$449$	−10.2344			−0.482992			−0.241496	−	0.970402i	$-0.577638\pi$
$449$	−10.2344			−0.482992			−0.241496	+	0.970402i	$0.577638\pi$
$450$	−30.1707	−	10.9812i	−1.42226	−	0.517661i
$451$	−2.29813	+	3.98048i	−0.108215	+	0.187434i
$452$	−36.2918	−	62.8592i	−1.70702	−	2.95665i
$453$	−21.1049	+	25.1518i	−0.991594	+	1.18174i
$454$	−7.80200	−	13.5135i	−0.366166	−	0.634218i
$455$		0			0
$456$	−16.3935	+	19.5370i	−0.767697	+	0.914906i
$457$	−42.5945			−1.99249			−0.996244	−	0.0865948i	$-0.972401\pi$
$457$	−42.5945			−1.99249			−0.996244	+	0.0865948i	$0.972401\pi$
$458$	29.6065	−	51.2800i	1.38342	−	2.39616i
$459$	−7.43717	+	4.29385i	−0.347137	+	0.200420i
$460$	−6.13429	−	10.6249i	−0.286013	−	0.495388i
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	−0.860088	−	0.510145i	$-0.829592\pi$
$461$	0.252374	−	0.437124i	0.0117542	−	0.0203589i	0.871843	+	0.489786i	$0.162925\pi$
$462$		0			0
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	0.833206	−	0.552962i	$-0.186503\pi$
$463$	−1.34002	−	2.32099i	−0.0622761	−	0.107865i	−0.895482	+	0.445097i	$0.853169\pi$
$464$	20.0792	−	34.7782i	0.932153	−	1.61454i
$465$	−6.83157	−	1.20459i	−0.316806	−	0.0558615i
$466$	10.7934	+	18.6947i	0.499994	+	0.866015i
$467$	−15.7083	−	27.2075i	−0.726892	−	1.25901i	−0.958191	−	0.286131i	$-0.907631\pi$
$467$	−15.7083	−	27.2075i	−0.726892	−	1.25901i	0.231299	−	0.972883i	$-0.425702\pi$
$468$	67.8196	+	24.6843i	3.13496	+	1.14103i
$469$		0			0
$470$	−1.13816	+	1.97134i	−0.0524992	+	0.0909313i
$471$	10.6971	+	29.3901i	0.492897	+	1.35422i
$472$	−40.6691			−1.87195
$473$	0.716881			0.0329622
$474$	−8.93717	−	24.5547i	−0.410498	−	1.12783i
$475$	−5.09627	+	8.82699i	−0.233833	+	0.405010i
$476$		0			0
$477$	−3.79813	−	21.5403i	−0.173905	−	0.986262i
$478$	−18.4363	−	31.9326i	−0.843256	−	1.46056i
$479$	−8.22028	−	14.2380i	−0.375594	−	0.650549i	0.614821	−	0.788666i	$-0.289228\pi$
$479$	−8.22028	−	14.2380i	−0.375594	−	0.650549i	−0.990416	+	0.138118i	$0.955895\pi$
$480$	−6.89440	−	1.21567i	−0.314685	−	0.0554874i
$481$	12.4183	−	21.5092i	0.566227	−	0.980735i
$482$	−6.84137	−	11.8496i	−0.311616	−	0.539734i
$483$		0			0
$484$	−8.93242	+	15.4714i	−0.406019	+	0.703246i
$485$	5.49747	+	9.52190i	0.249627	+	0.432367i
$486$	38.8717	−	6.85413i	1.76326	−	0.310910i
$487$	1.48767	−	2.57673i	0.0674129	−	0.116763i	−0.830349	−	0.557244i	$-0.811859\pi$
$487$	1.48767	−	2.57673i	0.0674129	−	0.116763i	0.897762	+	0.440481i	$0.145192\pi$
$488$	15.8530			0.717631
$489$	1.06670	−	1.27125i	0.0482380	−	0.0574878i
$490$		0			0
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	0.993167	+	0.116702i	$0.0372321\pi$
$491$	13.2430	+	22.9376i	0.597650	+	1.03516i	−0.395517	+	0.918459i	$0.629435\pi$
$492$	5.81908	−	6.93491i	0.262344	−	0.312650i
$493$	−4.99912	−	8.65873i	−0.225149	−	0.389970i
$494$	16.6493	−	28.8374i	0.749087	−	1.29746i
$495$	−7.84002	+	6.57856i	−0.352383	+	0.295684i
$496$	30.2327			1.35749
$497$		0			0
$498$	−0.945622	−	0.166739i	−0.0423744	−	0.00747174i
$499$	6.72193	−	11.6427i	0.300915	−	0.521200i	−0.675428	−	0.737426i	$-0.736041\pi$
$499$	6.72193	−	11.6427i	0.300915	−	0.521200i	0.976343	+	0.216225i	$0.0693746\pi$
$500$	−35.7939			−1.60075
$501$	−22.0869	+	26.3222i	−0.986771	+	1.17599i
$502$	30.5544			1.36371
$503$	22.6631			1.01050			0.505250	−	0.862973i	$-0.331400\pi$
$503$	22.6631			1.01050			0.505250	+	0.862973i	$0.331400\pi$
$504$		0			0
$505$	8.54488			0.380242
$506$	31.0651			1.38101
$507$	−28.5526	−	5.03460i	−1.26807	−	0.223594i
$508$	77.8786			3.45530
$509$	4.77379	−	8.26844i	0.211594	−	0.366492i	−0.740619	−	0.671925i	$-0.765468\pi$
$509$	4.77379	−	8.26844i	0.211594	−	0.366492i	0.952214	+	0.305433i	$0.0988011\pi$
$510$	−4.09714	+	4.88279i	−0.181425	+	0.216213i
$511$		0			0
$512$	−50.5553			−2.23425
$513$		−	12.5304i		−	0.553230i
$514$	13.3773	−	23.1702i	0.590049	−	1.02199i
$515$	2.90033	+	5.02352i	0.127804	+	0.221363i
$516$	−1.39053	−	0.245188i	−0.0612147	−	0.0107938i
$517$	−1.98293	−	3.43453i	−0.0872090	−	0.151050i
$518$		0			0
$519$	−13.4372	−	36.9183i	−0.589826	−	1.62053i
$520$	29.2823			1.28411
$521$	−1.55644	+	2.69583i	−0.0681887	+	0.118106i	−0.898104	−	0.439783i	$-0.855055\pi$
$521$	−1.55644	+	2.69583i	−0.0681887	+	0.118106i	0.829915	+	0.557889i	$0.188389\pi$
$522$	7.97993	+	45.2564i	0.349272	+	1.98082i
$523$	−8.07444	−	13.9853i	−0.353071	−	0.611537i	0.633715	−	0.773567i	$-0.281529\pi$
$523$	−8.07444	−	13.9853i	−0.353071	−	0.611537i	−0.986786	+	0.162030i	$0.948196\pi$
$524$	−42.3448	+	73.3434i	−1.84984	+	3.20402i
$525$		0			0
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	3.76352	−	6.51860i	0.163941	−	0.283955i
$528$	28.6707	−	34.1684i	1.24773	−	1.48699i
$529$	6.49928	+	11.2571i	0.282578	+	0.489439i
$530$	−8.11721	−	14.0594i	−0.352589	−	0.610702i
$531$	15.3066	−	12.8438i	0.664249	−	0.557371i
$532$		0			0
$533$	−3.23055	+	5.59548i	−0.139931	+	0.242367i
$534$	−31.0869	+	37.0480i	−1.34526	+	1.60322i
$535$	2.10101			0.0908348
$536$	−18.0624			−0.780178
$537$	12.5326	+	2.20983i	0.540820	+	0.0953611i
$538$	9.47431	−	16.4100i	0.408466	−	0.707485i
$539$		0			0
$540$	17.4572	−	10.0789i	0.751240	−	0.433728i
$541$	2.50774	+	4.34353i	0.107816	+	0.186743i	0.914885	−	0.403714i	$-0.132281\pi$
$541$	2.50774	+	4.34353i	0.107816	+	0.186743i	−0.807069	+	0.590457i	$0.798948\pi$
$542$	17.2665	+	29.9065i	0.741660	+	1.28459i
$543$	2.04117	+	5.60808i	0.0875952	+	0.240666i
$544$	3.79813	−	6.57856i	0.162844	−	0.282053i
$545$	−1.74035	−	3.01438i	−0.0745485	−	0.129122i
$546$		0			0
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	−0.986648	−	0.162870i	$-0.947925\pi$
$547$	−8.23901	+	14.2704i	−0.352275	+	0.610157i	0.634373	+	0.773027i	$0.281258\pi$
$548$	−40.0467	−	69.3629i	−1.71071	−	2.96304i
$549$	−5.96657	+	5.00654i	−0.254647	+	0.213674i
$550$	20.7592	−	35.9561i	0.885177	−	1.53317i
$551$	14.5885			0.621492
$552$	−32.9386	−	5.80796i	−1.40196	−	0.247203i
$553$		0			0
$554$	7.78699	+	13.4875i	0.330837	+	0.573027i
$555$	−2.37258	−	6.51860i	−0.100710	−	0.276699i
$556$	48.6528	+	84.2691i	2.06334	+	3.57380i
$557$	17.2815	−	29.9325i	0.732242	−	1.26828i	−0.223681	−	0.974662i	$-0.571807\pi$
$557$	17.2815	−	29.9325i	0.732242	−	1.26828i	0.955923	−	0.293618i	$-0.0948592\pi$
$558$	−26.5023	+	22.2381i	−1.12193	+	0.941412i
$559$	1.00774			0.0426229
$560$		0			0
$561$	−3.79813	−	10.4353i	−0.160357	−	0.440578i
$562$	−4.19341	+	7.26320i	−0.176888	+	0.306380i
$563$	37.2104			1.56823			0.784115	−	0.620615i	$-0.213117\pi$
$563$	37.2104			1.56823			0.784115	+	0.620615i	$0.213117\pi$
$564$	2.67159	+	7.34013i	0.112494	+	0.309075i
$565$	14.4688			0.608709
$566$	−73.4894			−3.08899
$567$		0			0
$568$	−22.4706			−0.942845
$569$	0.404667			0.0169645			0.00848226	−	0.999964i	$-0.497300\pi$
$569$	0.404667			0.0169645			0.00848226	+	0.999964i	$0.497300\pi$
$570$	−3.18092	−	8.73951i	−0.133234	−	0.366058i
$571$	−37.7793			−1.58101			−0.790507	−	0.612453i	$-0.790183\pi$
$571$	−37.7793			−1.58101			−0.790507	+	0.612453i	$0.790183\pi$
$572$	−46.6639	+	80.8243i	−1.95112	+	3.37943i
$573$	3.35163	+	9.20854i	0.140017	+	0.384692i
$574$		0			0
$575$	−13.3669			−0.557438
$576$	3.76470	−	3.15896i	0.156863	−	0.131623i
$577$	−1.10560	+	1.91496i	−0.0460267	+	0.0797206i	−0.888121	−	0.459610i	$-0.847989\pi$
$577$	−1.10560	+	1.91496i	−0.0460267	+	0.0797206i	0.842094	+	0.539330i	$0.181323\pi$
$578$	18.0646	+	31.2889i	0.751390	+	1.30145i
$579$	5.68479	+	15.6188i	0.236252	+	0.649097i
$580$	11.7344	+	20.3246i	0.487245	+	0.843934i
$581$		0			0
$582$	54.0014	+	9.52190i	2.23843	+	0.394696i
$583$	28.2841			1.17141
$584$	−39.0210	+	67.5864i	−1.61470	+	2.79674i
$585$	−11.0209	+	9.24767i	−0.455660	+	0.382344i
$586$	−10.6591	−	18.4621i	−0.440323	−	0.762662i
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	−0.500378	−	0.865807i	$-0.666806\pi$
$587$	12.1049	−	20.9663i	0.499622	−	0.865371i	1.00000		0.000436347i	$0.000138894\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	7.41534	−	12.8438i	0.305285	−	0.528769i
$591$	4.92871	+	13.5415i	0.202740	+	0.557024i
$592$	15.1163	+	26.1823i	0.621277	+	1.07608i
$593$	6.11927	+	10.5989i	0.251288	+	0.435244i	0.963881	−	0.266334i	$-0.0858124\pi$
$593$	6.11927	+	10.5989i	0.251288	+	0.435244i	−0.712592	+	0.701578i	$0.752479\pi$
$594$			51.0415i			2.09426i
$595$		0			0
$596$	33.4295	−	57.9016i	1.36932	−	2.37174i
$597$	11.2515	+	1.98394i	0.460493	+	0.0811974i
$598$	43.6691			1.78576
$599$	39.6168			1.61870			0.809349	−	0.587328i	$-0.199820\pi$
$599$	39.6168			1.61870			0.809349	+	0.587328i	$0.199820\pi$
$600$	−28.7335	+	34.2433i	−1.17304	+	1.39798i
$601$	−15.0039	+	25.9875i	−0.612021	+	1.06005i	0.378879	+	0.925446i	$0.376310\pi$
$601$	−15.0039	+	25.9875i	−0.612021	+	1.06005i	−0.990899	+	0.134605i	$0.957024\pi$
$602$		0			0
$603$	6.79813	−	5.70431i	0.276841	−	0.232298i
$604$	41.8127	+	72.4218i	1.70134	+	2.94680i
$605$	−1.78059	−	3.08408i	−0.0723914	−	0.125386i
$606$	27.3926	−	32.6453i	1.11275	−	1.32612i
$607$	−9.74216	+	16.8739i	−0.395422	+	0.684891i	−0.993155	−	0.116804i	$-0.962735\pi$
$607$	−9.74216	+	16.8739i	−0.395422	+	0.684891i	0.597733	+	0.801695i	$0.296068\pi$
$608$	5.54189	+	9.59883i	0.224753	+	0.389284i
$609$		0			0
$610$	−2.89053	+	5.00654i	−0.117034	+	0.202709i
$611$	−2.78746	−	4.82802i	−0.112768	−	0.195321i
$612$	3.79813	+	21.5403i	0.153530	+	0.870714i
$613$	9.26382	−	16.0454i	0.374162	−	0.648068i	−0.616039	−	0.787716i	$-0.711264\pi$
$613$	9.26382	−	16.0454i	0.374162	−	0.648068i	0.990201	+	0.139648i	$0.0445970\pi$
$614$	32.1266			1.29652
$615$	0.617211	+	1.69577i	0.0248884	+	0.0683802i
$616$		0			0
$617$	−13.9201	−	24.1103i	−0.560402	−	0.970644i	−0.997461	−	0.0712118i	$-0.977313\pi$
$617$	−13.9201	−	24.1103i	−0.560402	−	0.970644i	0.437059	−	0.899433i	$-0.356020\pi$
$618$	28.4898	+	5.02352i	1.14603	+	0.202076i
$619$	−22.4907	−	38.9550i	−0.903976	−	1.56573i	−0.822286	−	0.569075i	$-0.807301\pi$
$619$	−22.4907	−	38.9550i	−0.903976	−	1.56573i	−0.0816906	−	0.996658i	$-0.526032\pi$
$620$	−8.83409	+	15.3011i	−0.354786	+	0.614507i
$621$	14.2313	−	8.21643i	0.571081	−	0.329714i
$622$	41.7547			1.67421
$623$		0			0
$624$	40.3032	−	48.0315i	1.61342	−	1.92280i
$625$	−6.99912	+	12.1228i	−0.279965	+	0.484913i
$626$	−72.2113			−2.88614
$627$	15.9572	+	2.81369i	0.637271	+	0.112368i
$628$	79.6596			3.17877
$629$	7.52704			0.300123
$630$		0			0
$631$	9.43613			0.375646			0.187823	−	0.982203i	$-0.439857\pi$
$631$	9.43613			0.375646			0.187823	+	0.982203i	$0.439857\pi$
$632$	−36.3806			−1.44714
$633$	−3.75150	+	4.47086i	−0.149109	+	0.177701i
$634$	−65.5681			−2.60404
$635$	−7.76217	+	13.4445i	−0.308032	+	0.533528i
$636$	−54.8624	−	9.67372i	−2.17543	−	0.383588i
$637$		0			0
$638$	−59.4252			−2.35267
$639$	8.45723	−	7.09646i	0.334563	−	0.280732i
$640$	5.86571	−	10.1597i	0.231863	−	0.401598i
$641$	−18.6951	−	32.3808i	−0.738410	−	1.27896i	−0.953211	−	0.302306i	$-0.902243\pi$
$641$	−18.6951	−	32.3808i	−0.738410	−	1.27896i	0.214800	−	0.976658i	$-0.431090\pi$
$642$	6.73530	−	8.02682i	0.265821	−	0.316793i
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	0.881478	−	0.472225i	$-0.156549\pi$
$643$	0.805874	+	1.39581i	0.0317806	+	0.0550456i	−0.849698	+	0.527270i	$0.823216\pi$
$644$		0			0
$645$	0.180922	−	0.215615i	0.00712380	−	0.00848982i
$646$	10.0915			0.397046
$647$	−20.5881	+	35.6597i	−0.809402	+	1.40193i	0.103876	+	0.994590i	$0.466875\pi$
$647$	−20.5881	+	35.6597i	−0.809402	+	1.40193i	−0.913278	+	0.407336i	$0.866458\pi$
$648$	9.54277	−	54.1197i	0.374875	−	2.12602i
$649$	12.9192	+	22.3767i	0.507124	+	0.878364i
$650$	29.1819	−	50.5445i	1.14461	−	1.98252i
$651$		0			0
$652$	−2.11334	−	3.66041i	−0.0827648	−	0.143353i
$653$	−1.52600	+	2.64310i	−0.0597169	+	0.103433i	−0.894338	−	0.447391i	$-0.852353\pi$
$653$	−1.52600	+	2.64310i	−0.0597169	+	0.103433i	0.834621	+	0.550824i	$0.185686\pi$
$654$	−17.0954	−	3.01438i	−0.668483	−	0.117872i
$655$	−8.44104	−	14.6203i	−0.329819	−	0.571263i
$656$	−3.93242	−	6.81115i	−0.153535	−	0.265931i
$657$	−6.65822	−	37.7607i	−0.259762	−	1.47318i
$658$		0			0
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	0.101277	+	0.994858i	$0.467707\pi$
$659$	−20.8175	+	36.0569i	−0.810934	+	1.40458i	−0.912211	+	0.409721i	$0.865626\pi$
$660$	8.91534	+	24.4947i	0.347029	+	0.953455i
$661$	−20.3010			−0.789616			−0.394808	−	0.918764i	$-0.629189\pi$
$661$	−20.3010			−0.789616			−0.394808	+	0.918764i	$0.629189\pi$
$662$	20.8111			0.808846
$663$	−5.33915	−	14.6692i	−0.207355	−	0.569704i
$664$	−0.668434	+	1.15776i	−0.0259403	+	0.0449298i
$665$		0			0
$666$	−32.5099	−	11.8326i	−1.25973	−	0.458505i
$667$	9.56599	+	16.5688i	0.370397	+	0.641546i
$668$	43.7584	+	75.7917i	1.69306	+	2.93247i
$669$	−10.7057	−	1.88771i	−0.413908	−	0.0729831i
$670$	3.29339	−	5.70431i	0.127235	−	0.220377i
$671$	−5.03596	−	8.72254i	−0.194411	−	0.336730i
$672$		0			0
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	−0.857909	−	0.513801i	$-0.828237\pi$
$673$	0.415345	−	0.719398i	0.0160104	−	0.0277307i	0.873920	+	0.486071i	$0.161570\pi$
$674$	−5.78746	−	10.0242i	−0.222924	−	0.386117i
$675$		−	21.9625i		−	0.845336i
$676$	−36.9222	+	63.9511i	−1.42008	+	2.45966i
$677$	−10.8672			−0.417660			−0.208830	−	0.977952i	$-0.566966\pi$
$677$	−10.8672			−0.417660			−0.208830	+	0.977952i	$0.566966\pi$
$678$	46.3833	−	55.2775i	1.78134	−	2.12292i
$679$		0			0
$680$	4.43717	+	7.68540i	0.170158	+	0.294722i
$681$	6.86097	−	8.17658i	0.262913	−	0.313327i
$682$	−22.3687	−	38.7437i	−0.856542	−	1.48357i
$683$	−16.3473	+	28.3143i	−0.625512	+	1.08342i	0.362930	+	0.931817i	$0.381777\pi$
$683$	−16.3473	+	28.3143i	−0.625512	+	1.08342i	−0.988442	+	0.151602i	$0.951557\pi$
$684$	−29.9898	−	10.9154i	−1.14669	−	0.417360i
$685$	15.9659			0.610024
$686$		0			0
$687$	39.8888	+	7.03347i	1.52185	+	0.268344i
$688$	−0.613341	+	1.06234i	−0.0233834	+	0.0405012i
$689$	39.7597			1.51472
$690$	7.84002	−	9.34337i	0.298465	−	0.355696i
$691$	−14.9982			−0.570560			−0.285280	−	0.958444i	$-0.592087\pi$
$691$	−14.9982			−0.570560			−0.285280	+	0.958444i	$0.592087\pi$
$692$	−100.064			−3.80387
$693$		0			0
$694$	56.8863			2.15937
$695$	−19.3969			−0.735767
$696$	63.0090	+	11.1102i	2.38835	+	0.421130i
$697$	−1.95811			−0.0741687
$698$	33.0428	−	57.2318i	1.25069	−	2.16626i
$699$	−9.49154	+	11.3116i	−0.359003	+	0.427843i
$700$		0			0
$701$	26.4688			0.999714			0.499857	−	0.866108i	$-0.333386\pi$
$701$	26.4688			0.999714			0.499857	+	0.866108i	$0.333386\pi$
$702$			71.7506i			2.70805i
$703$	−5.49138	+	9.51135i	−0.207111	+	0.358727i
$704$	3.17752	+	5.50362i	0.119757	+	0.207426i
$705$	−1.53343	−	0.270386i	−0.0577524	−	0.0101833i
$706$	−0.449493	−	0.778544i	−0.0169169	−	0.0293009i
$707$		0			0
$708$	−17.4060	−	47.8226i	−0.654158	−	1.79728i
$709$	15.3601			0.576860			0.288430	−	0.957501i	$-0.406867\pi$
$709$	15.3601			0.576860			0.288430	+	0.957501i	$0.406867\pi$
$710$	4.09714	−	7.09646i	0.153763	−	0.266325i
$711$	13.6925	−	11.4894i	0.513510	−	0.430886i
$712$	33.6668	+	58.3127i	1.26172	+	2.18536i
$713$	−7.20162	+	12.4736i	−0.269703	+	0.467139i
$714$		0			0
$715$	−9.30200	−	16.1115i	−0.347875	−	0.602538i
$716$	16.2062	−	28.0700i	0.605654	−	1.04902i
$717$	16.2126	−	19.3214i	0.605471	−	0.721572i
$718$	−6.90760	−	11.9643i	−0.257789	−	0.446504i
$719$	13.3653	+	23.1494i	0.498442	+	0.863326i	0.999998	−	0.00179839i	$-0.000572447\pi$
$719$	13.3653	+	23.1494i	0.498442	+	0.863326i	−0.501557	+	0.865125i	$0.667239\pi$
$720$	−3.04101	−	17.2464i	−0.113332	−	0.642737i
$721$		0			0
$722$	16.6925	−	28.9123i	0.621232	−	1.07600i
$723$	6.01620	−	7.16982i	0.223745	−	0.266649i
$724$	15.2003			0.564914
$725$	25.5699			0.949641
$726$	−17.4907	−	3.08408i	−0.649140	−	0.114461i
$727$	−22.8221	+	39.5290i	−0.846424	+	1.46605i	0.0379552	+	0.999279i	$0.487916\pi$
$727$	−22.8221	+	39.5290i	−0.846424	+	1.46605i	−0.884379	+	0.466770i	$0.845418\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−14.2297	−	24.6465i	−0.526664	−	0.912209i
$731$	0.152704	+	0.264490i	0.00564795	+	0.00978253i
$732$	6.78493	+	18.6414i	0.250778	+	0.689007i
$733$	2.98751	−	5.17452i	0.110346	−	0.191125i	−0.805564	−	0.592509i	$-0.798137\pi$
$733$	2.98751	−	5.17452i	0.110346	−	0.191125i	0.915910	+	0.401384i	$0.131471\pi$
$734$	13.8302	+	23.9546i	0.510483	+	0.884182i
$735$		0			0
$736$	−7.26786	+	12.5883i	−0.267897	+	0.464011i
$737$	5.73783	+	9.93821i	0.211356	+	0.366079i
$738$	8.45723	+	3.07818i	0.311315	+	0.113309i
$739$	17.7981	−	30.8273i	0.654715	−	1.13400i	−0.327250	−	0.944938i	$-0.606122\pi$
$739$	17.7981	−	30.8273i	0.654715	−	1.13400i	0.981965	−	0.189062i	$-0.0605447\pi$
$740$	−17.6682			−0.649495
$741$	22.4315	+	3.95529i	0.824043	+	0.145301i
$742$		0			0
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	0.999032	+	0.0439943i	$0.0140083\pi$
$743$	14.6544	+	25.3821i	0.537616	+	0.931178i	−0.461416	+	0.887184i	$0.652658\pi$
$744$	16.4741	+	45.2623i	0.603971	+	1.65940i
$745$	6.66385	+	11.5421i	0.244145	+	0.422871i
$746$	−2.19207	+	3.79677i	−0.0802573	+	0.139010i
$747$	−0.114056	−	0.646844i	−0.00417309	−	0.0236668i
$748$	−28.2841			−1.03417
$749$		0			0
$750$	−12.1707	−	33.4388i	−0.444412	−	1.22101i
$751$	8.66684	−	15.0114i	0.316258	−	0.547774i	−0.663446	−	0.748224i	$-0.730907\pi$
$751$	8.66684	−	15.0114i	0.316258	−	0.547774i	0.979704	+	0.200450i	$0.0642403\pi$
$752$	6.78611			0.247464
$753$	7.14837	+	19.6400i	0.260501	+	0.715720i
$754$	−83.5357			−3.04219
$755$	−16.6699			−0.606681
$756$		0			0
$757$	−2.77156			−0.100734			−0.0503671	−	0.998731i	$-0.516039\pi$
$757$	−2.77156			−0.100734			−0.0503671	+	0.998731i	$0.516039\pi$
$758$	−30.7229			−1.11590
$759$	7.26786	+	19.9683i	0.263806	+	0.724802i
$760$	−12.9486			−0.469696
$761$	3.75372	−	6.50163i	0.136072	−	0.235684i	−0.789934	−	0.613191i	$-0.789885\pi$
$761$	3.75372	−	6.50163i	0.136072	−	0.235684i	0.926007	+	0.377508i	$0.123219\pi$
$762$	26.4805	+	72.7545i	0.959286	+	2.63562i
$763$		0			0
$764$	24.9590			0.902987
$765$	−4.09714	−	1.49124i	−0.148133	−	0.0539158i
$766$	−11.0296	+	19.1038i	−0.398514	+	0.690247i
$767$	18.1609	+	31.4556i	0.655752	+	1.13580i
$768$	−18.0699	−	49.6465i	−0.652040	−	1.79146i
$769$	1.02182	+	1.76985i	0.0368478	+	0.0638223i	0.883861	−	0.467749i	$-0.154935\pi$
$769$	1.02182	+	1.76985i	0.0368478	+	0.0638223i	−0.847013	+	0.531572i	$0.821602\pi$
$770$		0			0
$771$	18.0232	+	3.17798i	0.649090	+	0.114452i
$772$	42.3337			1.52362
$773$	−12.4709	+	21.6002i	−0.448547	+	0.776907i	−0.998292	−	0.0584263i	$-0.981392\pi$
$773$	−12.4709	+	21.6002i	−0.448547	+	0.776907i	0.549744	+	0.835333i	$0.314725\pi$
$774$	−0.243756	−	1.38241i	−0.00876162	−	0.0496896i
$775$	9.62495	+	16.6709i	0.345738	+	0.598837i
$776$	38.1721	−	66.1159i	1.37030	−	2.37342i
$777$		0			0
$778$	−4.61246	−	7.98902i	−0.165365	−	0.286420i
$779$	1.42855	−	2.47432i	0.0511831	−	0.0886516i
$780$	12.5326	+	34.4329i	0.448737	+	1.23290i
$781$	7.13816	+	12.3636i	0.255423	+	0.442406i
$782$	6.61721	+	11.4613i	0.236631	+	0.409857i
$783$	−27.2233	+	15.7174i	−0.972883	+	0.561694i
$784$		0			0
$785$	−7.93969	+	13.7520i	−0.283380	+	0.490828i
$786$	−82.9159	−	14.6203i	−2.95751	−	0.521489i
$787$	−7.10700			−0.253337			−0.126669	−	0.991945i	$-0.540428\pi$
$787$	−7.10700			−0.253337			−0.126669	+	0.991945i	$0.540428\pi$
$788$	36.7033			1.30750
$789$	−31.5669	+	37.6199i	−1.12381	+	1.33930i
$790$	6.63341	−	11.4894i	0.236006	−	0.408774i
$791$		0			0
$792$	66.7777	+	24.3051i	2.37284	+	0.863644i
$793$	−7.07919	−	12.2615i	−0.251389	−	0.435419i
$794$	−19.5548	−	33.8700i	−0.693975	−	1.20200i
$795$	7.13816	−	8.50692i	0.253164	−	0.301709i
$796$	14.5496	−	25.2007i	0.515698	−	0.893215i
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	0.993376	+	0.114905i	$0.0366564\pi$
$797$	16.8314	+	29.1528i	0.596199	+	1.03265i	−0.397178	+	0.917742i	$0.630010\pi$
$798$		0			0
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	9.71348	+	16.8242i	0.343423	+	0.594827i
$801$	−31.0869	−	11.3147i	−1.09840	−	0.399786i
$802$	−23.3229	+	40.3965i	−0.823562	+	1.42645i
$803$	49.5827			1.74973
$804$	−7.73055	−	21.2395i	−0.272636	−	0.749060i
$805$		0			0
$806$	−31.4443	−	54.4632i	−1.10758	−	1.91838i
$807$	12.7647	+	2.25076i	0.449339	+	0.0792305i
$808$	−29.6660	−	51.3830i	−1.04364	−	1.80765i
$809$	6.40807	−	11.0991i	0.225296	−	0.390224i	−0.731112	−	0.682257i	$-0.760998\pi$
$809$	6.40807	−	11.0991i	0.225296	−	0.390224i	0.956408	+	0.292033i	$0.0943318\pi$
$810$	15.3516	+	12.8816i	0.539401	+	0.452612i
$811$	26.1239			0.917335			0.458667	−	0.888608i	$-0.348327\pi$
$811$	26.1239			0.917335			0.458667	+	0.888608i	$0.348327\pi$
$812$		0			0
$813$	−15.1839	+	18.0955i	−0.532523	+	0.634636i
$814$	22.3687	−	38.7437i	0.784023	−	1.35797i
$815$	0.842549			0.0295132
$816$	18.7135	+	3.29969i	0.655103	+	0.115512i
$817$	−0.445622			−0.0155904
$818$	72.5099			2.53525
$819$		0			0
$820$	4.59627			0.160509
$821$	27.6641			0.965483			0.482741	−	0.875763i	$-0.339641\pi$
$821$	27.6641			0.965483			0.482741	+	0.875763i	$0.339641\pi$
$822$	51.1823	−	60.9967i	1.78519	−	2.12750i
$823$	27.8324			0.970178			0.485089	−	0.874465i	$-0.338787\pi$
$823$	27.8324			0.970178			0.485089	+	0.874465i	$0.338787\pi$
$824$	20.1386	−	34.8811i	0.701562	−	1.21514i
$825$	27.9688	+	4.93166i	0.973750	+	0.171698i
$826$		0			0
$827$	4.65507			0.161873			0.0809363	−	0.996719i	$-0.474209\pi$
$827$	4.65507			0.161873			0.0809363	+	0.996719i	$0.474209\pi$
$828$	−7.26786	−	41.2181i	−0.252575	−	1.43243i
$829$	−4.98680	+	8.63738i	−0.173199	+	0.299989i	−0.939536	−	0.342449i	$-0.888744\pi$
$829$	−4.98680	+	8.63738i	−0.173199	+	0.299989i	0.766338	+	0.642438i	$0.222077\pi$
$830$	−0.243756	−	0.422197i	−0.00846089	−	0.0146547i
$831$	−6.84776	+	8.16085i	−0.237546	+	0.283097i
$832$	4.46673	+	7.73660i	0.154856	+	0.268218i
$833$		0			0
$834$	−62.1814	+	74.1050i	−2.15317	+	2.56604i
$835$	−17.4456			−0.603731
$836$	20.6348	−	35.7404i	0.713668	−	1.23611i
$837$	−20.4947	−	11.8326i	−0.708400	−	0.408995i
$838$	−43.9261	−	76.0822i	−1.51740	−	2.62822i
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	−0.918246	−	0.396011i	$-0.870394\pi$
$839$	−3.36484	+	5.82807i	−0.116167	+	0.201207i	0.802079	+	0.597218i	$0.203727\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	34.6921	−	60.0885i	1.19557	−	2.07079i
$843$	−5.64977	−	0.996206i	−0.194588	−	0.0343112i
$844$	7.43242	+	12.8733i	0.255834	+	0.443118i
$845$	−7.36009	−	12.7480i	−0.253195	−	0.438546i
$846$	−5.94878	+	4.99162i	−0.204523	+	0.171615i
$847$		0			0
$848$	−24.1989	+	41.9138i	−0.830995	+	1.43932i
$849$	−17.1932	−	47.2381i	−0.590071	−	1.62121i
$850$	17.6878			0.606686
$851$	−14.4032			−0.493737
$852$	−9.61721	−	26.4231i	−0.329480	−	0.905239i
$853$	2.89528	−	5.01477i	0.0991324	−	0.171702i	−0.812193	−	0.583388i	$-0.801727\pi$
$853$	2.89528	−	5.01477i	0.0991324	−	0.171702i	0.911326	+	0.411686i	$0.135060\pi$
$854$		0			0
$855$	4.87346	−	4.08931i	0.166669	−	0.139852i
$856$	−7.29426	−	12.6340i	−0.249313	−	0.431822i
$857$	−17.4538	−	30.2309i	−0.596211	−	1.03267i	−0.993375	−	0.114921i	$-0.963339\pi$
$857$	−17.4538	−	30.2309i	−0.596211	−	1.03267i	0.397163	−	0.917748i	$-0.369995\pi$
$858$	−91.3731	−	16.1115i	−3.11943	−	0.550039i
$859$	−6.30747	+	10.9249i	−0.215208	+	0.372751i	−0.953337	−	0.301909i	$-0.902376\pi$
$859$	−6.30747	+	10.9249i	−0.215208	+	0.372751i	0.738129	+	0.674660i	$0.235710\pi$
$860$	−0.358441	−	0.620838i	−0.0122227	−	0.0211704i
$861$		0			0
$862$	−33.6668	+	58.3127i	−1.14670	+	1.98614i
$863$	12.1027	+	20.9624i	0.411979	+	0.713569i	0.995106	−	0.0988119i	$-0.0315042\pi$
$863$	12.1027	+	20.9624i	0.411979	+	0.713569i	−0.583127	+	0.812381i	$0.698171\pi$
$864$	−20.6832	−	11.9415i	−0.703657	−	0.406256i
$865$	9.97343	−	17.2745i	0.339107	−	0.587350i
$866$	−94.1508			−3.19937
$867$	−15.8858	+	18.9319i	−0.539509	+	0.642962i
$868$		0			0
$869$	11.5569	+	20.0171i	0.392041	+	0.679035i
$870$	−14.9974	+	17.8732i	−0.508458	+	0.605957i
$871$	8.06583	+	13.9704i	0.273300	+	0.473370i
$872$	−12.0842	+	20.9305i	−0.409224	+	0.708797i
$873$	6.51337	+	36.9391i	0.220444	+	1.25020i
$874$	−19.3105			−0.653186
$875$		0			0
$876$	−96.1751	−	16.9583i	−3.24946	−	0.572967i
$877$	0.562834	−	0.974856i	0.0190055	−	0.0329186i	−0.856366	−	0.516369i	$-0.827283\pi$
$877$	0.562834	−	0.974856i	0.0190055	−	0.0329186i	0.875372	+	0.483450i	$0.160617\pi$
$878$	−63.4911			−2.14272
$879$	9.37346	−	11.1708i	0.316159	−	0.376783i
$880$	22.6459			0.763393
$881$	4.38331			0.147678			0.0738388	−	0.997270i	$-0.476475\pi$
$881$	4.38331			0.147678			0.0738388	+	0.997270i	$0.476475\pi$
$882$		0			0
$883$	−6.88949			−0.231850			−0.115925	−	0.993258i	$-0.536983\pi$
$883$	−6.88949			−0.231850			−0.115925	+	0.993258i	$0.536983\pi$
$884$	−39.7597			−1.33726
$885$	9.99067	+	1.76162i	0.335833	+	0.0592163i
$886$	5.17705			0.173926
$887$	19.5376	−	33.8401i	0.656009	−	1.13624i	−0.325631	−	0.945497i	$-0.605577\pi$
$887$	19.5376	−	33.8401i	0.656009	−	1.13624i	0.981640	−	0.190744i	$-0.0610899\pi$
$888$	−30.9613	+	36.8982i	−1.03899	+	1.23822i
$889$		0			0
$890$	−24.5544			−0.823065
$891$	−32.8089	+	11.9415i	−1.09914	+	0.400054i
$892$	−13.8439	+	23.9783i	−0.463528	+	0.802854i
$893$	1.23261	+	2.13495i	0.0412478	+	0.0714432i
$894$	65.4586	+	11.5421i	2.18926	+	0.386026i
$895$	3.23055	+	5.59548i	0.107985	+	0.187036i
$896$		0			0
$897$	10.2166	+	28.0700i	0.341123	+	0.937229i
$898$	−25.9145			−0.864777
$899$	13.7761	−	23.8610i	0.459460	−	0.795809i
$900$	−52.5642	−	19.1318i	−1.75214	−	0.637727i
$901$	6.02481	+	10.4353i	0.200716	+	0.347650i
$902$	−5.81908	+	10.0789i	−0.193754	+	0.335592i
$903$		0			0
$904$	−50.2327	−	87.0055i	−1.67071	−	2.89376i
$905$	−1.51501	+	2.62408i	−0.0503608	+	0.0872275i
$906$	−53.4394	+	63.6866i	−1.77541	+	2.11585i
$907$	−21.2469	−	36.8007i	−0.705492	−	1.22195i	−0.966514	−	0.256615i	$-0.917393\pi$
$907$	−21.2469	−	36.8007i	−0.705492	−	1.22195i	0.261022	−	0.965333i	$-0.415941\pi$
$908$	−13.5929	−	23.5435i	−0.451095	−	0.781319i
$909$	27.3926	+	9.97011i	0.908557	+	0.330688i
$910$		0			0
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	−0.708684	−	0.705526i	$-0.750711\pi$
$911$	7.74675	−	13.4178i	0.256661	−	0.444550i	0.965345	+	0.260976i	$0.0840442\pi$
$912$	−17.8221	+	21.2395i	−0.590148	+	0.703311i
$913$	0.849356			0.0281096
$914$	−107.853			−3.56746
$915$	−3.89440	−	0.686688i	−0.128745	−	0.0227012i
$916$	51.5813	−	89.3414i	1.70429	−	2.95192i
$917$		0			0
$918$	−18.8316	+	10.8724i	−0.621534	+	0.358843i
$919$	−3.26470	−	5.65463i	−0.107693	−	0.186529i	0.807143	−	0.590357i	$-0.201013\pi$
$919$	−3.26470	−	5.65463i	−0.107693	−	0.186529i	−0.914835	+	0.403828i	$0.867680\pi$
$920$	−8.49067	−	14.7063i	−0.279929	−	0.484851i
$921$	7.51620	+	20.6506i	0.247667	+	0.680460i
$922$	0.639033	−	1.10684i	0.0210454	−	0.0364518i
$923$	10.0343	+	17.3799i	0.330283	+	0.572068i
$924$		0			0
$925$	−9.62495	+	16.6709i	−0.316466	+	0.548136i
$926$	−3.39306	−	5.87695i	−0.111503	−	0.193128i
$927$	3.43629	+	19.4882i	0.112863	+	0.640075i
$928$	13.9029	−	24.0805i	0.456384	−	0.790480i
$929$	−58.2772			−1.91201			−0.956007	−	0.293343i	$-0.905232\pi$
$929$	−58.2772			−1.91201			−0.956007	+	0.293343i	$0.905232\pi$
$930$	−17.2981	−	3.05013i	−0.567228	−	0.100018i
$931$		0			0
$932$	18.8045	+	32.5704i	0.615963	+	1.06688i
$933$	9.76873	+	26.8394i	0.319814	+	0.878682i
$934$	−39.7747	−	68.8918i	−1.30147	−	2.25421i
$935$	2.81908	−	4.88279i	0.0921937	−	0.159684i
$936$	93.8713	+	34.1664i	3.06828	+	1.11676i
$937$	−32.4175			−1.05903			−0.529516	−	0.848300i	$-0.677626\pi$
$937$	−32.4175			−1.05903			−0.529516	+	0.848300i	$0.677626\pi$
$938$		0			0
$939$	−16.8942	−	46.4165i	−0.551323	−	1.51475i
$940$	−1.98293	+	3.43453i	−0.0646759	+	0.112022i
$941$	27.3226			0.890693			0.445346	−	0.895358i	$-0.353081\pi$
$941$	27.3226			0.890693			0.445346	+	0.895358i	$0.353081\pi$
$942$	27.0861	+	74.4183i	0.882511	+	2.42468i
$943$	3.74691			0.122016
$944$	−44.2131			−1.43901
$945$		0			0
$946$	1.81521			0.0590175
$947$	−38.2131			−1.24176			−0.620879	−	0.783906i	$-0.713224\pi$
$947$	−38.2131			−1.24176			−0.620879	+	0.783906i	$0.713224\pi$
$948$	−15.5706	−	42.7798i	−0.505709	−	1.38942i
$949$	69.6998			2.26255
$950$	−12.9042	+	22.3507i	−0.418668	+	0.725153i
$951$	−15.3400	−	42.1464i	−0.497434	−	1.36669i
$952$		0			0
$953$	58.9377			1.90918			0.954590	−	0.297924i	$-0.0962943\pi$
$953$	58.9377			1.90918			0.954590	+	0.297924i	$0.0962943\pi$
$954$	−9.61721	−	54.5419i	−0.311369	−	1.76586i
$955$	−2.48767	+	4.30878i	−0.0804992	+	0.139429i
$956$	−32.1202	−	55.6338i	−1.03884	−	1.79933i
$957$	−13.9029	−	38.1978i	−0.449416	−	1.23476i
$958$	−20.8145	−	36.0518i	−0.672486	−	1.16478i
$959$		0			0
$960$	2.45723	+	0.433277i	0.0793069	+	0.0139839i
$961$	−10.2576			−0.330892
$962$	31.4443	−	54.4632i	1.01381	−	1.75596i
$963$	6.73530	+	2.45145i	0.217042	+	0.0789968i
$964$	−11.9192	−	20.6447i	−0.383892	−	0.664921i
$965$	−4.21941	+	7.30823i	−0.135828	+	0.235260i
$966$		0			0
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	0.595960	−	0.803014i	$-0.296772\pi$
$967$	−12.3594	−	21.4071i	−0.397451	−	0.688405i	−0.993411	+	0.114609i	$0.963438\pi$
$968$	−12.3637	+	21.4145i	−0.397383	+	0.688287i
$969$	2.36097	+	6.48670i	0.0758452	+	0.208383i
$970$	13.9201	+	24.1103i	0.446947	+	0.774135i
$971$	4.08812	+	7.08082i	0.131194	+	0.227234i	0.924137	−	0.382061i	$-0.124786\pi$
$971$	4.08812	+	7.08082i	0.131194	+	0.227234i	−0.792943	+	0.609296i	$0.791452\pi$
$972$	67.7233	−	11.9415i	2.17223	−	0.383022i
$973$		0			0
$974$	3.76692	−	6.52450i	0.120700	−	0.209058i
$975$	39.3166	+	6.93258i	1.25914	+	0.222020i
$976$	17.2344			0.551660
$977$	−15.8485			−0.507040			−0.253520	−	0.967330i	$-0.581588\pi$
$977$	−15.8485			−0.507040			−0.253520	+	0.967330i	$0.581588\pi$
$978$	2.70099	−	3.21891i	0.0863681	−	0.102930i
$979$	21.3897	−	37.0480i	0.683616	−	1.18406i
$980$		0			0
$981$	−2.06196	−	11.6939i	−0.0658332	−	0.373359i
$982$	33.5326	+	58.0801i	1.07007	+	1.85341i
$983$	26.6532	+	46.1646i	0.850104	+	1.47242i	0.881114	+	0.472904i	$0.156794\pi$
$983$	26.6532	+	46.1646i	0.850104	+	1.47242i	−0.0310096	+	0.999519i	$0.509872\pi$
$984$	8.05438	−	9.59883i	0.256764	−	0.306000i
$985$	−3.65822	+	6.33623i	−0.116561	+	0.201889i
$986$	−12.6582	−	21.9247i	−0.403120	−	0.698224i
$987$		0			0
$988$	29.0069	−	50.2414i	0.922831	−	1.59839i
$989$	−0.292204	−	0.506111i	−0.00929153	−	0.0160934i
$990$	−19.8516	+	16.6575i	−0.630926	+	0.529410i
$991$	−20.1047	+	34.8224i	−0.638648	+	1.10617i	0.347082	+	0.937835i	$0.387172\pi$
$991$	−20.1047	+	34.8224i	−0.638648	+	1.10617i	−0.985730	+	0.168335i	$0.946161\pi$
$992$	20.9331			0.664628
$993$	4.86887	+	13.3771i	0.154509	+	0.424510i
$994$		0			0
$995$	2.90033	+	5.02352i	0.0919466	+	0.159256i
$996$	−1.64749	−	0.290497i	−0.0522027	−	0.00920474i
$997$	14.3601	+	24.8724i	0.454789	+	0.787717i	0.998676	−	0.0514412i	$-0.0163815\pi$
$997$	14.3601	+	24.8724i	0.454789	+	0.787717i	−0.543887	+	0.839158i	$0.683048\pi$
$998$	17.0205	−	29.4804i	0.538776	−	0.933187i
$999$		−	23.6652i		−	0.748735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.h.e.214.3		6
3.2	odd	2		1323.2.h.b.802.1		6
7.2	even	3		441.2.g.b.79.1		6
7.3	odd	6		63.2.f.a.43.1	yes	6
7.4	even	3		441.2.f.c.295.1		6
7.5	odd	6		441.2.g.c.79.1		6
7.6	odd	2		441.2.h.d.214.3		6
9.4	even	3		441.2.g.b.67.1		6
9.5	odd	6		1323.2.g.e.361.3		6
21.2	odd	6		1323.2.g.e.667.3		6
21.5	even	6		1323.2.g.d.667.3		6
21.11	odd	6		1323.2.f.d.883.3		6
21.17	even	6		189.2.f.b.127.3		6
21.20	even	2		1323.2.h.c.802.1		6
28.3	even	6		1008.2.r.h.673.3		6
63.4	even	3		441.2.f.c.148.1		6
63.5	even	6		1323.2.h.c.226.1		6
63.11	odd	6		3969.2.a.l.1.1		3
63.13	odd	6		441.2.g.c.67.1		6
63.23	odd	6		1323.2.h.b.226.1		6
63.25	even	3		3969.2.a.q.1.3		3
63.31	odd	6		63.2.f.a.22.1	✓	6
63.32	odd	6		1323.2.f.d.442.3		6
63.38	even	6		567.2.a.c.1.1		3
63.40	odd	6		441.2.h.d.373.3		6
63.41	even	6		1323.2.g.d.361.3		6
63.52	odd	6		567.2.a.h.1.3		3
63.58	even	3	inner	441.2.h.e.373.3		6
63.59	even	6		189.2.f.b.64.3		6
84.59	odd	6		3024.2.r.k.2017.1		6
252.31	even	6		1008.2.r.h.337.3		6
252.59	odd	6		3024.2.r.k.1009.1		6
252.115	even	6		9072.2.a.ca.1.1		3
252.227	odd	6		9072.2.a.bs.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	63.31	odd	6
63.2.f.a.43.1	yes	6	7.3	odd	6
189.2.f.b.64.3		6	63.59	even	6
189.2.f.b.127.3		6	21.17	even	6
441.2.f.c.148.1		6	63.4	even	3
441.2.f.c.295.1		6	7.4	even	3
441.2.g.b.67.1		6	9.4	even	3
441.2.g.b.79.1		6	7.2	even	3
441.2.g.c.67.1		6	63.13	odd	6
441.2.g.c.79.1		6	7.5	odd	6
441.2.h.d.214.3		6	7.6	odd	2
441.2.h.d.373.3		6	63.40	odd	6
441.2.h.e.214.3		6	1.1	even	1	trivial
441.2.h.e.373.3		6	63.58	even	3	inner
567.2.a.c.1.1		3	63.38	even	6
567.2.a.h.1.3		3	63.52	odd	6
1008.2.r.h.337.3		6	252.31	even	6
1008.2.r.h.673.3		6	28.3	even	6
1323.2.f.d.442.3		6	63.32	odd	6
1323.2.f.d.883.3		6	21.11	odd	6
1323.2.g.d.361.3		6	63.41	even	6
1323.2.g.d.667.3		6	21.5	even	6
1323.2.g.e.361.3		6	9.5	odd	6
1323.2.g.e.667.3		6	21.2	odd	6
1323.2.h.b.226.1		6	63.23	odd	6
1323.2.h.b.802.1		6	3.2	odd	2
1323.2.h.c.226.1		6	63.5	even	6
1323.2.h.c.802.1		6	21.20	even	2
3024.2.r.k.1009.1		6	252.59	odd	6
3024.2.r.k.2017.1		6	84.59	odd	6
3969.2.a.l.1.1		3	63.11	odd	6
3969.2.a.q.1.3		3	63.25	even	3
9072.2.a.bs.1.3		3	252.227	odd	6
9072.2.a.ca.1.1		3	252.115	even	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.53209 q^{2} +(0.592396 + 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 + 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 + 1.92836i) q^{9} +O(q^{10})\)	\(q+2.53209 q^{2} +(0.592396 + 1.62760i) q^{3} +4.41147 q^{4} +(-0.439693 + 0.761570i) q^{5} +(1.50000 + 4.12122i) q^{6} +6.10607 q^{8} +(-2.29813 + 1.92836i) q^{9} +(-1.11334 + 1.92836i) q^{10} +(-1.93969 - 3.35965i) q^{11} +(2.61334 + 7.18009i) q^{12} +(-2.72668 - 4.72275i) q^{13} +(-1.50000 - 0.264490i) q^{15} +6.63816 q^{16} +(0.826352 - 1.43128i) q^{17} +(-5.81908 + 4.88279i) q^{18} +(1.20574 + 2.08840i) q^{19} +(-1.93969 + 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +(-1.58125 + 2.73881i) q^{23} +(3.61721 + 9.93821i) q^{24} +(2.11334 + 3.66041i) q^{25} +(-6.90420 - 11.9584i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(3.02481 - 5.23913i) q^{29} +(-3.79813 - 0.669713i) q^{30} +4.55438 q^{31} +4.59627 q^{32} +(4.31908 - 5.14728i) q^{33} +(2.09240 - 3.62414i) q^{34} +(-10.1382 + 8.50692i) q^{36} +(2.27719 + 3.94421i) q^{37} +(3.05303 + 5.28801i) q^{38} +(6.07145 - 7.23567i) q^{39} +(-2.68479 + 4.65020i) q^{40} +(-0.592396 - 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(-8.55690 - 14.8210i) q^{44} +(-0.458111 - 2.59808i) q^{45} +(-4.00387 + 6.93491i) q^{46} +1.02229 q^{47} +(3.93242 + 10.8042i) q^{48} +(5.35117 + 9.26849i) q^{50} +(2.81908 + 0.497079i) q^{51} +(-12.0287 - 20.8343i) q^{52} +(-3.64543 + 6.31407i) q^{53} +(-11.3944 - 6.57856i) q^{54} +3.41147 q^{55} +(-2.68479 + 3.19961i) q^{57} +(7.65910 - 13.2660i) q^{58} -6.66044 q^{59} +(-6.61721 - 1.16679i) q^{60} +2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} +4.79561 q^{65} +(10.9363 - 13.0334i) q^{66} -2.95811 q^{67} +(3.64543 - 6.31407i) q^{68} +(-5.39440 - 0.951178i) q^{69} -3.68004 q^{71} +(-14.0326 + 11.7747i) q^{72} +(-6.39053 + 11.0687i) q^{73} +(5.76604 + 9.98708i) q^{74} +(-4.70574 + 5.60808i) q^{75} +(5.31908 + 9.21291i) q^{76} +(15.3735 - 18.3214i) q^{78} -5.95811 q^{79} +(-2.91875 + 5.05542i) q^{80} +(1.56283 - 8.86327i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(-0.233956 + 0.405223i) q^{86} +(10.3191 + 1.81953i) q^{87} +(-11.8439 - 20.5142i) q^{88} +(5.51367 + 9.54996i) q^{89} +(-1.15998 - 6.57856i) q^{90} +(-6.97565 + 12.0822i) q^{92} +(2.69800 + 7.41268i) q^{93} +2.58853 q^{94} -2.12061 q^{95} +(2.72281 + 7.48086i) q^{96} +(6.25150 - 10.8279i) q^{97} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} + 3 q^{5} + 9 q^{6} + 12 q^{8} - 6 q^{11} + 9 q^{12} - 3 q^{13} - 9 q^{15} + 6 q^{16} + 6 q^{17} - 18 q^{18} - 3 q^{19} - 6 q^{20} - 9 q^{22} - 12 q^{23} - 9 q^{24} + 6 q^{25} - 3 q^{26} - 27 q^{27} - 9 q^{29} - 9 q^{30} + 6 q^{31} + 9 q^{33} + 9 q^{34} - 27 q^{36} + 3 q^{37} + 6 q^{38} + 36 q^{39} - 9 q^{40} + 3 q^{43} - 15 q^{44} - 9 q^{45} - 6 q^{47} + 6 q^{50} - 21 q^{52} - 6 q^{53} - 27 q^{54} - 9 q^{57} + 9 q^{58} + 6 q^{59} - 9 q^{60} - 12 q^{61} + 60 q^{62} + 24 q^{64} + 30 q^{65} + 18 q^{66} - 24 q^{67} + 6 q^{68} + 9 q^{69} + 18 q^{71} - 9 q^{72} - 21 q^{73} + 30 q^{74} - 18 q^{75} + 15 q^{76} + 54 q^{78} - 42 q^{79} - 15 q^{80} - 9 q^{82} - 18 q^{83} - 9 q^{85} - 6 q^{86} + 45 q^{87} - 27 q^{88} + 12 q^{89} - 27 q^{90} - 3 q^{92} + 54 q^{93} + 36 q^{94} - 24 q^{95} + 27 q^{96} - 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 3 * q^5 + 9 * q^6 + 12 * q^8 - 6 * q^11 + 9 * q^12 - 3 * q^13 - 9 * q^15 + 6 * q^16 + 6 * q^17 - 18 * q^18 - 3 * q^19 - 6 * q^20 - 9 * q^22 - 12 * q^23 - 9 * q^24 + 6 * q^25 - 3 * q^26 - 27 * q^27 - 9 * q^29 - 9 * q^30 + 6 * q^31 + 9 * q^33 + 9 * q^34 - 27 * q^36 + 3 * q^37 + 6 * q^38 + 36 * q^39 - 9 * q^40 + 3 * q^43 - 15 * q^44 - 9 * q^45 - 6 * q^47 + 6 * q^50 - 21 * q^52 - 6 * q^53 - 27 * q^54 - 9 * q^57 + 9 * q^58 + 6 * q^59 - 9 * q^60 - 12 * q^61 + 60 * q^62 + 24 * q^64 + 30 * q^65 + 18 * q^66 - 24 * q^67 + 6 * q^68 + 9 * q^69 + 18 * q^71 - 9 * q^72 - 21 * q^73 + 30 * q^74 - 18 * q^75 + 15 * q^76 + 54 * q^78 - 42 * q^79 - 15 * q^80 - 9 * q^82 - 18 * q^83 - 9 * q^85 - 6 * q^86 + 45 * q^87 - 27 * q^88 + 12 * q^89 - 27 * q^90 - 3 * q^92 + 54 * q^93 + 36 * q^94 - 24 * q^95 + 27 * q^96 - 3 * q^97 + 18 * q^99

Introduction

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