LMFDB - Embedded newform 441.2.g.c.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (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			79.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	441.79
Dual form			441.2.g.c.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26604 - 2.19285i) q^{2} +(1.70574 + 0.300767i) q^{3} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} +(-1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})$	\(q+(-1.26604 - 2.19285i) q^{2} +(1.70574 + 0.300767i) q^{3} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} +(-1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 + 1.02606i) q^{9} +(1.11334 + 1.92836i) q^{10} +3.87939 q^{11} +(-4.91147 + 5.85327i) q^{12} +(2.72668 + 4.72275i) q^{13} +(-1.50000 - 0.264490i) q^{15} +(-3.31908 - 5.74881i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(-1.31908 - 7.48086i) q^{18} +(-1.20574 + 2.08840i) q^{19} +(1.93969 - 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +3.16250 q^{23} +(10.4153 + 1.83651i) q^{24} -4.22668 q^{25} +(6.90420 - 11.9584i) q^{26} +(4.50000 + 2.59808i) q^{27} +(3.02481 - 5.23913i) q^{29} +(1.31908 + 3.62414i) q^{30} +(2.27719 - 3.94421i) q^{31} +(-2.29813 + 3.98048i) q^{32} +(6.61721 + 1.16679i) q^{33} +(-2.09240 + 3.62414i) q^{34} +(-10.1382 + 8.50692i) q^{36} +(2.27719 - 3.94421i) q^{37} +6.10607 q^{38} +(3.23055 + 8.87587i) q^{39} -5.36959 q^{40} +(0.592396 + 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(-8.55690 + 14.8210i) q^{44} +(-2.47906 - 0.902302i) q^{45} +(-4.00387 - 6.93491i) q^{46} +(0.511144 + 0.885328i) q^{47} +(-3.93242 - 10.8042i) q^{48} +(5.35117 + 9.26849i) q^{50} +(-0.979055 - 2.68993i) q^{51} -24.0574 q^{52} +(-3.64543 - 6.31407i) q^{53} -13.1571i q^{54} -3.41147 q^{55} +(-2.68479 + 3.19961i) q^{57} -15.3182 q^{58} +(-3.33022 + 5.76811i) q^{59} +(4.31908 - 5.14728i) q^{60} +(1.29813 + 2.24843i) q^{61} -11.5321 q^{62} -1.63816 q^{64} +(-2.39780 - 4.15312i) q^{65} +(-5.81908 - 15.9878i) q^{66} +(1.47906 - 2.56180i) q^{67} +7.29086 q^{68} +(5.39440 + 0.951178i) q^{69} -3.68004 q^{71} +(17.2135 + 6.26519i) q^{72} +(6.39053 + 11.0687i) q^{73} -11.5321 q^{74} +(-7.20961 - 1.27125i) q^{75} +(-5.31908 - 9.21291i) q^{76} +(15.3735 - 18.3214i) q^{78} +(2.97906 + 5.15988i) q^{79} +(2.91875 + 5.05542i) q^{80} +(6.89440 + 5.78509i) q^{81} +(1.50000 - 2.59808i) q^{82} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +0.467911 q^{86} +(6.73530 - 8.02682i) q^{87} +23.6878 q^{88} +(-5.51367 + 9.54996i) q^{89} +(1.15998 + 6.57856i) q^{90} +(-6.97565 + 12.0822i) q^{92} +(5.07057 - 6.04288i) q^{93} +(1.29426 - 2.24173i) q^{94} +(1.06031 - 1.83651i) q^{95} +(-5.11721 + 6.09845i) q^{96} +(-6.25150 + 10.8279i) q^{97} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8} + 12 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} - 3 q^{16} - 6 q^{17} + 9 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 24 q^{23} + 18 q^{24} - 12 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} + 12 q^{38} - 18 q^{39} - 18 q^{40} + 3 q^{43} - 15 q^{44} - 18 q^{45} - 3 q^{47} + 6 q^{50} - 9 q^{51} - 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} + 3 q^{59} + 9 q^{60} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} - 18 q^{66} + 12 q^{67} + 12 q^{68} - 9 q^{69} + 18 q^{71} + 45 q^{72} + 21 q^{73} - 60 q^{74} - 9 q^{75} - 15 q^{76} + 54 q^{78} + 21 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} + 12 q^{86} + 36 q^{87} + 54 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 3 q^{97} + 18 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8 + 12 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 - 3 * q^16 - 6 * q^17 + 9 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 24 * q^23 + 18 * q^24 - 12 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 + 12 * q^38 - 18 * q^39 - 18 * q^40 + 3 * q^43 - 15 * q^44 - 18 * q^45 - 3 * q^47 + 6 * q^50 - 9 * q^51 - 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 + 3 * q^59 + 9 * q^60 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 - 18 * q^66 + 12 * q^67 + 12 * q^68 - 9 * q^69 + 18 * q^71 + 45 * q^72 + 21 * q^73 - 60 * q^74 - 9 * q^75 - 15 * q^76 + 54 * q^78 + 21 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 + 12 * q^86 + 36 * q^87 + 54 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 3 * q^97 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.833521	−	0.552487i	$-0.813679\pi$
$2$	−1.26604	−	2.19285i	−0.895229	−	1.55058i	−0.0617072	−	0.998094i	$-0.519654\pi$
$3$	1.70574	+	0.300767i	0.984808	+	0.173648i
$3$	1.70574	+	0.300767i	0.984808	+	0.173648i
$4$	−2.20574	+	3.82045i	−1.10287	+	1.91022i
$5$	−0.879385			−0.393273			−0.196637	−	0.980476i	$-0.563002\pi$
$5$	−0.879385			−0.393273			−0.196637	+	0.980476i	$0.563002\pi$
$6$	−1.50000	−	4.12122i	−0.612372	−	1.68248i
$7$		0			0
$7$		0			0
$8$	6.10607			2.15882
$9$	2.81908	+	1.02606i	0.939693	+	0.342020i
$10$	1.11334	+	1.92836i	0.352069	+	0.609802i
$11$	3.87939			1.16968			0.584839	−	0.811149i	$-0.301158\pi$
$11$	3.87939			1.16968			0.584839	+	0.811149i	$0.301158\pi$
$12$	−4.91147	+	5.85327i	−1.41782	+	1.68969i
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	0.944753	+	0.327784i	$0.106302\pi$
$13$	2.72668	+	4.72275i	0.756245	+	1.30986i	−0.188507	+	0.982072i	$0.560365\pi$
$14$		0			0
$15$	−1.50000	−	0.264490i	−0.387298	−	0.0682911i
$16$	−3.31908	−	5.74881i	−0.829769	−	1.43720i
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	0.748244	−	0.663424i	$-0.230897\pi$
$17$	−0.826352	−	1.43128i	−0.200420	−	0.347137i	−0.948664	+	0.316286i	$0.897564\pi$
$18$	−1.31908	−	7.48086i	−0.310910	−	1.76326i
$19$	−1.20574	+	2.08840i	−0.276615	+	0.479111i	−0.970541	−	0.240935i	$-0.922546\pi$
$19$	−1.20574	+	2.08840i	−0.276615	+	0.479111i	0.693926	+	0.720046i	$0.255879\pi$
$20$	1.93969	−	3.35965i	0.433728	−	0.751240i
$21$		0			0
$22$	−4.91147	−	8.50692i	−1.04713	−	1.81368i
$23$	3.16250			0.659428			0.329714	−	0.944081i	$-0.393048\pi$
$23$	3.16250			0.659428			0.329714	+	0.944081i	$0.393048\pi$
$24$	10.4153	+	1.83651i	2.12602	+	0.374875i
$25$	−4.22668			−0.845336
$26$	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	$-0.0231835\pi$
$30$	1.31908	+	3.62414i	0.240830	+	0.661674i
$31$	2.27719	−	3.94421i	0.408995	−	0.708400i	−0.585782	−	0.810468i	$-0.699213\pi$
$31$	2.27719	−	3.94421i	0.408995	−	0.708400i	0.994777	+	0.102068i	$0.0325459\pi$
$32$	−2.29813	+	3.98048i	−0.406256	+	0.703657i
$33$	6.61721	+	1.16679i	1.15191	+	0.203113i
$34$	−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	−0.615865	−	0.787852i	$-0.711193\pi$
$37$	2.27719	−	3.94421i	0.374368	−	0.648424i	0.990232	+	0.139428i	$0.0445265\pi$
$38$	6.10607			0.990535
$39$	3.23055	+	8.87587i	0.517302	+	1.42128i
$40$	−5.36959			−0.849006
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	0.908570	−	0.417734i	$-0.137175\pi$
$41$	0.592396	+	1.02606i	0.0925168	+	0.160244i	−0.816053	+	0.577977i	$0.803842\pi$
$42$		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
$45$	−2.47906	−	0.902302i	−0.369556	−	0.134507i
$46$	−4.00387	−	6.93491i	−0.590338	−	1.02250i
$47$	0.511144	+	0.885328i	0.0745581	+	0.129138i	0.900894	−	0.434039i	$-0.142912\pi$
$47$	0.511144	+	0.885328i	0.0745581	+	0.129138i	−0.826336	+	0.563178i	$0.809579\pi$
$48$	−3.93242	−	10.8042i	−0.567596	−	1.55946i
$49$		0			0
$50$	5.35117	+	9.26849i	0.756769	+	1.31076i
$51$	−0.979055	−	2.68993i	−0.137095	−	0.376666i
$52$	−24.0574			−3.33616
$53$	−3.64543	−	6.31407i	−0.500738	−	0.867304i	−1.00000		0.000852699i	$-0.999729\pi$
$53$	−3.64543	−	6.31407i	−0.500738	−	0.867304i	0.499261	−	0.866451i	$-0.333605\pi$
$54$		−	13.1571i		−	1.79046i
$55$	−3.41147			−0.460003
$56$		0			0
$57$	−2.68479	+	3.19961i	−0.355609	+	0.423799i
$58$	−15.3182			−2.01138
$59$	−3.33022	+	5.76811i	−0.433558	+	0.750944i	−0.997177	−	0.0750906i	$-0.976075\pi$
$59$	−3.33022	+	5.76811i	−0.433558	+	0.750944i	0.563619	+	0.826035i	$0.309409\pi$
$60$	4.31908	−	5.14728i	0.557591	−	0.664511i
$61$	1.29813	+	2.24843i	0.166209	+	0.287882i	0.937084	−	0.349104i	$-0.113514\pi$
$61$	1.29813	+	2.24843i	0.166209	+	0.287882i	−0.770875	+	0.636986i	$0.780181\pi$
$62$	−11.5321			−1.46458
$63$		0			0
$64$	−1.63816			−0.204769
$65$	−2.39780	−	4.15312i	−0.297411	−	0.515131i
$66$	−5.81908	−	15.9878i	−0.716279	−	1.96796i
$67$	1.47906	−	2.56180i	0.180695	−	0.312974i	−0.761422	−	0.648256i	$-0.775499\pi$
$67$	1.47906	−	2.56180i	0.180695	−	0.312974i	0.942118	+	0.335283i	$0.108832\pi$
$68$	7.29086			0.884147
$69$	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	$0.570074\pi$
$72$	17.2135	+	6.26519i	2.02863	+	0.738360i
$73$	6.39053	+	11.0687i	0.747955	+	1.29550i	0.948801	+	0.315873i	$0.102297\pi$
$73$	6.39053	+	11.0687i	0.747955	+	1.29550i	−0.200847	+	0.979623i	$0.564369\pi$
$74$	−11.5321			−1.34058
$75$	−7.20961	−	1.27125i	−0.832494	−	0.146791i
$76$	−5.31908	−	9.21291i	−0.610140	−	1.05679i
$77$		0			0
$78$	15.3735	−	18.3214i	1.74070	−	2.07449i
$79$	2.97906	+	5.15988i	0.335170	+	0.580531i	0.983517	−	0.180813i	$-0.0578729\pi$
$79$	2.97906	+	5.15988i	0.335170	+	0.580531i	−0.648348	+	0.761345i	$0.724540\pi$
$80$	2.91875	+	5.05542i	0.326326	+	0.565213i
$81$	6.89440	+	5.78509i	0.766044	+	0.642788i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	−0.859955	−	0.510370i	$-0.829508\pi$
$83$	0.109470	−	0.189608i	0.0120159	−	0.0208122i	0.871971	+	0.489558i	$0.162842\pi$
$84$		0			0
$85$	0.726682	+	1.25865i	0.0788197	+	0.136520i
$86$	0.467911			0.0504562
$87$	6.73530	−	8.02682i	0.722100	−	0.860565i
$88$	23.6878			2.52513
$89$	−5.51367	+	9.54996i	−0.584448	+	1.01229i	0.410496	+	0.911862i	$0.365356\pi$
$89$	−5.51367	+	9.54996i	−0.584448	+	1.01229i	−0.994944	+	0.100431i	$0.967978\pi$
$90$	1.15998	+	6.57856i	0.122272	+	0.693441i
$91$		0			0
$92$	−6.97565	+	12.0822i	−0.727262	+	1.25965i
$93$	5.07057	−	6.04288i	0.525794	−	0.626617i
$94$	1.29426	−	2.24173i	0.133493	−	0.231217i
$95$	1.06031	−	1.83651i	0.108785	−	0.188422i
$96$	−5.11721	+	6.09845i	−0.522273	+	0.622421i
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	0.351826	+	0.936065i	$0.385561\pi$
$97$	−6.25150	+	10.8279i	−0.634743	+	1.09941i	−0.986569	+	0.163342i	$0.947773\pi$
$98$		0			0
$99$	10.9363	+	3.98048i	1.09914	+	0.400054i
$100$	9.32295	−	16.1478i	0.932295	−	1.61478i
$101$	−9.71688			−0.966866			−0.483433	−	0.875381i	$-0.660610\pi$
$101$	−9.71688			−0.966866			−0.483433	+	0.875381i	$0.660610\pi$
$102$	−4.65910	+	5.55250i	−0.461320	+	0.549779i
$103$	6.59627			0.649949			0.324975	−	0.945723i	$-0.394644\pi$
$103$	6.59627			0.649949			0.324975	+	0.945723i	$0.394644\pi$
$104$	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	−0.917974	−	0.396641i	$-0.870176\pi$
$107$	−1.19459	+	2.06910i	−0.115486	+	0.200027i	0.802488	+	0.596668i	$0.203509\pi$
$108$	−19.8516	+	11.4613i	−1.91022	+	1.10287i
$109$	−1.97906	−	3.42782i	−0.189559	−	0.328326i	0.755544	−	0.655098i	$-0.227373\pi$
$109$	−1.97906	−	3.42782i	−0.189559	−	0.328326i	−0.945103	+	0.326772i	$0.894039\pi$
$110$	4.31908	+	7.48086i	0.411808	+	0.713272i
$111$	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	$-0.448364\pi$
$114$	10.4153	+	1.83651i	0.975486	+	0.172005i
$115$	−2.78106			−0.259335
$116$	13.3439	+	23.1123i	1.23895	+	2.14592i
$117$	2.84090	+	16.1115i	0.262641	+	1.48951i
$118$	16.8648			1.55253
$119$		0			0
$120$	−9.15910	−	1.61500i	−0.836108	−	0.147428i
$121$	4.04963			0.368148
$122$	3.28699	−	5.69323i	0.297590	−	0.515441i
$123$	0.701867	+	1.92836i	0.0632852	+	0.173875i
$124$	10.0458	+	17.3998i	0.902136	+	1.56255i
$125$	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	$0.213559\pi$
$128$	6.67024	+	11.5532i	0.589572	+	1.02117i
$129$	−0.205737	+	0.245188i	−0.0181141	+	0.0215876i
$130$	−6.07145	+	10.5161i	−0.532502	+	0.922320i
$131$	−19.1976			−1.67730			−0.838650	−	0.544670i	$-0.816655\pi$
$131$	−19.1976			−1.67730			−0.838650	+	0.544670i	$0.816655\pi$
$132$	−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
$137$	18.1557			1.55115			0.775573	−	0.631258i	$-0.217461\pi$
$137$	18.1557			1.55115			0.775573	+	0.631258i	$0.217461\pi$
$138$	−4.74376	−	13.0334i	−0.403815	−	1.10947i
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.773846	−	0.633374i	$-0.781670\pi$
$139$	−11.0287	−	19.1022i	−0.935441	−	1.62023i	−0.161595	−	0.986857i	$-0.551664\pi$
$140$		0			0
$141$	0.605600	+	1.66387i	0.0510007	+	0.140123i
$142$	4.65910	+	8.06980i	0.390983	+	0.677202i
$143$	10.5778	+	18.3214i	0.884564	+	1.53211i
$144$	−3.45811	−	19.6119i	−0.288176	−	1.63433i
$145$	−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
$149$	−15.1557			−1.24160			−0.620802	−	0.783968i	$-0.713193\pi$
$149$	−15.1557			−1.24160			−0.620802	+	0.783968i	$0.713193\pi$
$150$	6.34002	+	17.4191i	0.517661	+	1.42226i
$151$	−18.9564			−1.54265			−0.771323	−	0.636444i	$-0.780405\pi$
$151$	−18.9564			−1.54265			−0.771323	+	0.636444i	$0.780405\pi$
$152$	−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
$156$	−41.0355	−	7.23567i	−3.28547	−	0.579318i
$157$	9.02869	−	15.6381i	0.720568	−	1.24806i	−0.240205	−	0.970722i	$-0.577215\pi$
$157$	9.02869	−	15.6381i	0.720568	−	1.24806i	0.960773	−	0.277337i	$-0.0894520\pi$
$158$	7.54323	−	13.0653i	0.600107	−	1.03942i
$159$	−4.31908	−	11.8666i	−0.342525	−	0.941080i
$160$	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	−0.884177	−	0.467152i	$-0.845280\pi$
$163$	−0.479055	+	0.829748i	−0.0375225	+	0.0649909i	0.846654	+	0.532143i	$0.178613\pi$
$164$	−5.22668			−0.408135
$165$	−5.81908	−	1.02606i	−0.453015	−	0.0798787i
$166$	−0.554378			−0.0430280
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	−0.938876	−	0.344255i	$-0.888131\pi$
$167$	−9.91921	−	17.1806i	−0.767572	−	1.32947i	0.171304	−	0.985218i	$-0.445202\pi$
$168$		0			0
$169$	−8.36959	+	14.4965i	−0.643814	+	1.11512i
$170$	1.84002	−	3.18701i	0.141123	−	0.244433i
$171$	−5.54189	+	4.65020i	−0.423799	+	0.355609i
$172$	−0.407604	−	0.705990i	−0.0310795	−	0.0538313i
$173$	−11.3414	−	19.6438i	−0.862268	−	1.49349i	−0.869734	−	0.493520i	$-0.835710\pi$
$173$	−11.3414	−	19.6438i	−0.862268	−	1.49349i	0.00746626	−	0.999972i	$-0.497623\pi$
$174$	−26.1288	−	4.60722i	−1.98082	−	0.349272i
$175$		0			0
$176$	−12.8760	−	22.3019i	−0.970564	−	1.68107i
$177$	−7.41534	+	8.83726i	−0.557371	+	0.664249i
$178$	27.9222			2.09286
$179$	3.67365	+	6.36295i	0.274581	+	0.475589i	0.970029	−	0.242988i	$-0.0781274\pi$
$179$	3.67365	+	6.36295i	0.274581	+	0.475589i	−0.695448	+	0.718576i	$0.744794\pi$
$180$	8.91534	−	7.48086i	0.664511	−	0.557591i
$181$	−3.44562			−0.256111			−0.128056	−	0.991767i	$-0.540874\pi$
$181$	−3.44562			−0.256111			−0.128056	+	0.991767i	$0.540874\pi$
$182$		0			0
$183$	1.53802	+	4.22567i	0.113694	+	0.312371i
$184$	19.3105			1.42359
$185$	−2.00253	+	3.46848i	−0.147229	+	0.255008i
$186$	−19.6707	−	3.46848i	−1.44233	−	0.254321i
$187$	−3.20574	−	5.55250i	−0.234427	−	0.406039i
$188$	−4.50980			−0.328911
$189$		0			0
$190$	−5.36959			−0.389551
$191$	−2.82888	−	4.89976i	−0.204690	−	0.354534i	0.745344	−	0.666680i	$-0.232285\pi$
$191$	−2.82888	−	4.89976i	−0.204690	−	0.354534i	−0.950034	+	0.312146i	$0.898952\pi$
$192$	−2.79426	−	0.492704i	−0.201659	−	0.0355578i
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	−0.985422	−	0.170127i	$-0.945582\pi$
$193$	−4.79813	+	8.31061i	−0.345377	+	0.598211i	0.640045	+	0.768337i	$0.278916\pi$
$194$	31.6587			2.27296
$195$	−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	$0.404218\pi$
$198$	−5.11721	−	29.0211i	−0.363664	−	2.06244i
$199$	−3.29813	−	5.71253i	−0.233798	−	0.404951i	0.725124	−	0.688618i	$-0.241782\pi$
$199$	−3.29813	−	5.71253i	−0.233798	−	0.404951i	−0.958923	+	0.283667i	$0.908449\pi$
$200$	−25.8084			−1.82493
$201$	3.29339	−	3.92490i	0.232298	−	0.276841i
$202$	12.3020	+	21.3077i	0.865566	+	1.49920i
$203$		0			0
$204$	12.4363	+	2.19285i	0.870714	+	0.153530i
$205$	−0.520945	−	0.902302i	−0.0363843	−	0.0630195i
$206$	−8.35117	−	14.4646i	−0.581853	−	1.00780i
$207$	8.91534	+	3.24492i	0.619659	+	0.225538i
$208$	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	$0.796331\pi$
$212$	32.1634			2.20899
$213$	−6.27719	−	1.10684i	−0.430106	−	0.0758393i
$214$	6.04963			0.413544
$215$	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
$219$	7.57145	+	20.8024i	0.511631	+	1.40570i
$220$	7.52481	−	13.0334i	0.507323	−	0.878709i
$221$	4.50640	−	7.80531i	0.303133	−	0.525042i
$222$	−19.6707	−	3.46848i	−1.32021	−	0.232789i
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	−0.741614	−	0.670827i	$-0.765939\pi$
$223$	3.13816	−	5.43545i	0.210146	−	0.363984i	0.951760	+	0.306843i	$0.0992726\pi$
$224$		0			0
$225$	−11.9153	−	4.33683i	−0.794356	−	0.289122i
$226$	−20.8307	+	36.0798i	−1.38564	+	2.39999i
$227$	−6.16250			−0.409020			−0.204510	−	0.978865i	$-0.565560\pi$
$227$	−6.16250			−0.409020			−0.204510	+	0.978865i	$0.565560\pi$
$228$	−6.30200	−	17.3146i	−0.417360	−	1.14669i
$229$	23.3851			1.54533			0.772664	−	0.634815i	$-0.218924\pi$
$229$	23.3851			1.54533			0.772664	+	0.634815i	$0.218924\pi$
$230$	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	−0.691945	−	0.721950i	$-0.743246\pi$
$233$	4.26264	−	7.38311i	0.279255	−	0.483684i	0.971200	+	0.238267i	$0.0765792\pi$
$234$	31.7335	−	26.6276i	2.07449	−	1.74070i
$235$	−0.449493	−	0.778544i	−0.0293217	−	0.0507866i
$236$	−14.6912	−	25.4459i	−0.956315	−	1.65639i
$237$	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	$0.989430\pi$
$240$	3.45811	+	9.50108i	0.223220	+	0.613292i
$241$	−5.40373			−0.348085			−0.174043	−	0.984738i	$-0.555683\pi$
$241$	−5.40373			−0.348085			−0.174043	+	0.984738i	$0.555683\pi$
$242$	−5.12701	−	8.88024i	−0.329577	−	0.570844i
$243$	10.0201	+	11.9415i	0.642788	+	0.766044i
$244$	−11.4534			−0.733226
$245$		0			0
$246$	3.34002	−	3.98048i	0.212952	−	0.253786i
$247$	−13.1506			−0.836755
$248$	13.9047	−	24.0836i	0.882947	−	1.52931i
$249$	0.243756	−	0.290497i	0.0154474	−	0.0184095i
$250$	−10.2724	−	17.7924i	−0.649686	−	1.12529i
$251$	−12.0669			−0.761654			−0.380827	−	0.924646i	$-0.624361\pi$
$251$	−12.0669			−0.761654			−0.380827	+	0.924646i	$0.624361\pi$
$252$		0			0
$253$	12.2686			0.771318
$254$	−22.3503	−	38.7118i	−1.40238	−	2.42900i
$255$	0.860967	+	2.36549i	0.0539158	+	0.148133i
$256$	15.2515	−	26.4164i	0.953219	−	1.65102i
$257$	10.5662			0.659104			0.329552	−	0.944137i	$-0.393102\pi$
$257$	10.5662			0.659104			0.329552	+	0.944137i	$0.393102\pi$
$258$	0.798133	+	0.140732i	0.0496896	+	0.00876162i
$259$		0			0
$260$	21.1557			1.31202
$261$	13.9029	−	11.6659i	0.860565	−	0.722100i
$262$	24.3050	+	42.0975i	1.50157	+	2.60079i
$263$	−28.3533			−1.74834			−0.874169	−	0.485622i	$-0.838593\pi$
$263$	−28.3533			−1.74834			−0.874169	+	0.485622i	$0.838593\pi$
$264$	40.4051	+	7.12452i	2.48676	+	0.438484i
$265$	3.20574	+	5.55250i	0.196927	+	0.341087i
$266$		0			0
$267$	−12.2772	+	14.6314i	−0.751352	+	0.895426i
$268$	6.52481	+	11.3013i	0.398567	+	0.690337i
$269$	−3.74170	−	6.48081i	−0.228135	−	0.395142i	0.729120	−	0.684386i	$-0.239930\pi$
$269$	−3.74170	−	6.48081i	−0.228135	−	0.395142i	−0.957255	+	0.289244i	$0.906596\pi$
$270$			11.5702i			0.704139i
$271$	−6.81908	+	11.8110i	−0.414229	+	0.717467i	−0.995347	−	0.0963530i	$-0.969282\pi$
$271$	−6.81908	+	11.8110i	−0.414229	+	0.717467i	0.581118	+	0.813819i	$0.302616\pi$
$272$	−5.48545	+	9.50108i	−0.332604	+	0.576088i
$273$		0			0
$274$	−22.9859	−	39.8128i	−1.38863	−	2.40518i
$275$	−16.3969			−0.988772
$276$	−15.5326	+	18.5110i	−0.934950	+	1.11423i
$277$	−6.15064			−0.369556			−0.184778	−	0.982780i	$-0.559157\pi$
$277$	−6.15064			−0.369556			−0.184778	+	0.982780i	$0.559157\pi$
$278$	−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	$0.198165\pi$
$282$	2.88191	−	3.43453i	0.171615	−	0.204523i
$283$	−14.5116	+	25.1348i	−0.862626	+	1.49411i	0.00675974	+	0.999977i	$0.497848\pi$
$283$	−14.5116	+	25.1348i	−0.862626	+	1.49411i	−0.869385	+	0.494134i	$0.835485\pi$
$284$	8.11721	−	14.0594i	0.481668	−	0.834273i
$285$	2.36097	−	2.81369i	0.139852	−	0.166669i
$286$	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
$290$	13.4706			0.791021
$291$	−13.9201	+	16.5893i	−0.816010	+	0.972483i
$292$	−56.3833			−3.29958
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	0.962392	−	0.271664i	$-0.0875740\pi$
$293$	4.20961	+	7.29125i	0.245928	+	0.425960i	−0.716464	+	0.697624i	$0.754241\pi$
$294$		0			0
$295$	2.92855	−	5.07239i	0.170507	−	0.295326i
$296$	13.9047	−	24.0836i	0.808192	−	1.39983i
$297$	17.4572	+	10.0789i	1.01297	+	0.584839i
$298$	19.1878	+	33.2342i	1.11152	+	1.92521i
$299$	8.62314	+	14.9357i	0.498689	+	0.863755i
$300$	20.7592	−	24.7399i	1.19854	−	1.42836i
$301$		0			0
$302$	23.9996	+	41.5685i	1.38102	+	2.39200i
$303$	−16.5744	−	2.92252i	−0.952177	−	0.167894i
$304$	16.0077			0.918107
$305$	−1.14156	−	1.97724i	−0.0653655	−	0.113216i
$306$	−9.61721	+	8.06980i	−0.549779	+	0.461320i
$307$	−12.6878			−0.724130			−0.362065	−	0.932153i	$-0.617928\pi$
$307$	−12.6878			−0.724130			−0.362065	+	0.932153i	$0.617928\pi$
$308$		0			0
$309$	11.2515	+	1.98394i	0.640075	+	0.112863i
$310$	10.1411			0.575979
$311$	8.24510	−	14.2809i	0.467537	−	0.809797i	−0.531775	−	0.846886i	$-0.678475\pi$
$311$	8.24510	−	14.2809i	0.467537	−	0.809797i	0.999312	+	0.0370881i	$0.0118082\pi$
$312$	19.7260	+	54.1966i	1.11676	+	3.06828i
$313$	−14.2592	−	24.6977i	−0.805980	−	1.39600i	−0.915628	−	0.402027i	$-0.868306\pi$
$313$	−14.2592	−	24.6977i	−0.805980	−	1.39600i	0.109648	−	0.993970i	$-0.465028\pi$
$314$	−45.7229			−2.58029
$315$		0			0
$316$	−26.2841			−1.47859
$317$	12.9474	+	22.4256i	0.727200	+	1.25955i	0.958062	+	0.286561i	$0.0925122\pi$
$317$	12.9474	+	22.4256i	0.727200	+	1.25955i	−0.230862	+	0.972987i	$0.574154\pi$
$318$	−20.5535	+	24.4947i	−1.15258	+	1.37360i
$319$	11.7344	−	20.3246i	0.657002	−	1.13796i
$320$	1.44057			0.0805303
$321$	−2.65998	+	3.17004i	−0.148465	+	0.176934i
$322$		0			0
$323$	3.98545			0.221756
$324$	−37.3089	+	13.5793i	−2.07271	+	0.754407i
$325$	−11.5248	−	19.9616i	−0.639282	−	1.10727i
$326$	2.42602			0.134365
$327$	−2.34477	−	6.44220i	−0.129666	−	0.356255i
$328$	3.61721	+	6.26519i	0.199727	+	0.345937i
$329$		0			0
$330$	5.11721	+	14.0594i	0.281693	+	0.773946i
$331$	−4.10947	−	7.11781i	−0.225877	−	0.391230i	0.730705	−	0.682693i	$-0.239191\pi$
$331$	−4.10947	−	7.11781i	−0.225877	−	0.391230i	−0.956582	+	0.291463i	$0.905858\pi$
$332$	0.482926	+	0.836452i	0.0265040	+	0.0459063i
$333$	10.4666	−	8.78249i	0.573564	−	0.481278i
$334$	−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	$0.873068\pi$
$338$	42.3851			2.30544
$339$	−9.74691	−	26.7794i	−0.529380	−	1.45446i
$340$	−6.41147			−0.347711
$341$	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
$345$	−4.74376	−	0.836452i	−0.255395	−	0.0450331i
$346$	−28.7173	+	49.7399i	−1.54385	+	2.67403i
$347$	−11.2331	+	19.4563i	−0.603023	+	1.04447i	0.389337	+	0.921095i	$0.372704\pi$
$347$	−11.2331	+	19.4563i	−0.603023	+	1.04447i	−0.992361	+	0.123372i	$0.960629\pi$
$348$	15.8097	+	43.4369i	0.847491	+	2.32846i
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	0.270445	+	0.962735i	$0.412829\pi$
$349$	−13.0496	+	22.6026i	−0.698531	+	1.20989i	−0.968976	+	0.247155i	$0.920504\pi$
$350$		0			0
$351$			28.3365i			1.51249i
$352$	−8.91534	+	15.4418i	−0.475189	+	0.823052i
$353$	−0.355037			−0.0188967			−0.00944836	−	0.999955i	$-0.503008\pi$
$353$	−0.355037			−0.0188967			−0.00944836	+	0.999955i	$0.503008\pi$
$354$	28.7670	+	5.07239i	1.52895	+	0.269595i
$355$	3.23618			0.171758
$356$	−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	−0.928992	−	0.370100i	$-0.879323\pi$
$359$	−2.72803	+	4.72508i	−0.143980	+	0.249380i	0.785012	+	0.619480i	$0.212657\pi$
$360$	−15.1373	−	5.50952i	−0.797805	−	0.290377i
$361$	6.59240	+	11.4184i	0.346968	+	0.600967i
$362$	4.36231	+	7.55574i	0.229278	+	0.397121i
$363$	6.90760	+	1.21800i	0.362555	+	0.0639283i
$364$		0			0
$365$	−5.61974	−	9.73367i	−0.294150	−	0.509484i
$366$	7.31908	−	8.72254i	0.382574	−	0.455934i
$367$	10.9240			0.570226			0.285113	−	0.958494i	$-0.407969\pi$
$367$	10.9240			0.570226			0.285113	+	0.958494i	$0.407969\pi$
$368$	−10.4966	−	18.1806i	−0.547173	−	0.947731i
$369$	0.617211	+	3.50038i	0.0321307	+	0.182222i
$370$	10.1411			0.527213
$371$		0			0
$372$	11.9021	+	32.7009i	0.617097	+	1.69546i
$373$	1.73143			0.0896500			0.0448250	−	0.998995i	$-0.485727\pi$
$373$	1.73143			0.0896500			0.0448250	+	0.998995i	$0.485727\pi$
$374$	−8.11721	+	14.0594i	−0.419731	+	0.726995i
$375$	13.8400	+	2.44037i	0.714696	+	0.126020i
$376$	3.12108	+	5.40587i	0.160957	+	0.278787i
$377$	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	$0.600873\pi$
$380$	4.67752	+	8.10170i	0.239952	+	0.415608i
$381$	30.1125	+	5.30964i	1.54271	+	0.272021i
$382$	−7.16297	+	12.4066i	−0.366489	+	0.634778i
$383$	−8.71183			−0.445154			−0.222577	−	0.974915i	$-0.571447\pi$
$383$	−8.71183			−0.445154			−0.222577	+	0.974915i	$0.571447\pi$
$384$	7.90286	+	21.7129i	0.403291	+	1.10803i
$385$		0			0
$386$	24.2986			1.23677
$387$	−0.424678	+	0.356347i	−0.0215876	+	0.0181141i
$388$	−27.5783	−	47.7670i	−1.40008	−	2.42500i
$389$	3.64321			0.184718			0.0923590	−	0.995726i	$-0.470559\pi$
$389$	3.64321			0.184718			0.0923590	+	0.995726i	$0.470559\pi$
$390$	−13.5192	+	16.1115i	−0.684571	+	0.815840i
$391$	−2.61334	−	4.52644i	−0.132162	−	0.228912i
$392$		0			0
$393$	−32.7460	−	5.77401i	−1.65182	−	0.291260i
$394$	−10.5334	−	18.2444i	−0.530667	−	0.919142i
$395$	−2.61974	−	4.53752i	−0.131813	−	0.228307i
$396$	−39.3298	+	33.0016i	−1.97640	+	1.65839i
$397$	7.72281	−	13.3763i	0.387597	−	0.671337i	−0.604529	−	0.796583i	$-0.706639\pi$
$397$	7.72281	−	13.3763i	0.387597	−	0.671337i	0.992126	+	0.125246i	$0.0399720\pi$
$398$	−8.35117	+	14.4646i	−0.418606	+	0.725047i
$399$		0			0
$400$	14.0287	+	24.2984i	0.701434	+	1.21492i
$401$	18.4219			0.919946			0.459973	−	0.887933i	$-0.347859\pi$
$401$	18.4219			0.919946			0.459973	+	0.887933i	$0.347859\pi$
$402$	−12.7763	−	2.25281i	−0.637224	−	0.112360i
$403$	24.8367			1.23720
$404$	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
$408$	−5.97818	−	16.4249i	−0.295964	−	0.813154i
$409$	14.3182	−	24.7999i	0.707989	−	1.22627i	−0.257612	−	0.966248i	$-0.582936\pi$
$409$	14.3182	−	24.7999i	0.707989	−	1.22627i	0.965602	−	0.260025i	$-0.0837309\pi$
$410$	−1.31908	+	2.28471i	−0.0651446	+	0.112834i
$411$	30.9688	+	5.46064i	1.52758	+	0.269354i
$412$	−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
$416$	−25.0651			−1.22892
$417$	−13.0667	−	35.9005i	−0.639879	−	1.75805i
$418$	23.6878			1.15861
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	0.883438	+	0.468548i	$0.155223\pi$
$419$	17.3478	+	30.0472i	0.847494	+	1.46790i	−0.0359442	+	0.999354i	$0.511444\pi$
$420$		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
$423$	0.532556	+	3.02027i	0.0258937	+	0.146851i
$424$	−22.2592	−	38.5541i	−1.08100	−	1.87235i
$425$	3.49273	+	6.04958i	0.169422	+	0.293448i
$426$	5.52007	+	15.1663i	0.267448	+	0.734808i
$427$		0			0
$428$	−5.26991	−	9.12776i	−0.254731	−	0.441207i
$429$	12.5326	+	34.4329i	0.605077	+	1.66244i
$430$	−0.411474			−0.0198430
$431$	−13.2961	−	23.0295i	−0.640449	−	1.10929i	−0.985333	−	0.170645i	$-0.945415\pi$
$431$	−13.2961	−	23.0295i	−0.640449	−	1.10929i	0.344883	−	0.938646i	$-0.387919\pi$
$432$		−	34.4929i		−	1.65954i
$433$	37.1830			1.78690			0.893451	−	0.449160i	$-0.148277\pi$
$433$	37.1830			1.78690			0.893451	+	0.449160i	$0.148277\pi$
$434$		0			0
$435$	−5.92292	+	7.05866i	−0.283982	+	0.338437i
$436$	17.4611			0.836235
$437$	−3.81315	+	6.60457i	−0.182408	+	0.315939i
$438$	36.0308	−	42.9398i	1.72162	−	2.05174i
$439$	−12.5373	−	21.7152i	−0.598373	−	1.03641i	−0.993061	−	0.117597i	$-0.962481\pi$
$439$	−12.5373	−	21.7152i	−0.598373	−	1.03641i	0.394689	−	0.918815i	$-0.370853\pi$
$440$	−20.8307			−0.993064
$441$		0			0
$442$	−22.8212			−1.08549
$443$	−1.02229	−	1.77066i	−0.0485704	−	0.0841264i	0.840718	−	0.541473i	$-0.182133\pi$
$443$	−1.02229	−	1.77066i	−0.0485704	−	0.0841264i	−0.889288	+	0.457347i	$0.848800\pi$
$444$	11.9021	+	32.7009i	0.564851	+	1.55191i
$445$	4.84864	−	8.39809i	0.229848	−	0.398108i
$446$	−15.8922			−0.752516
$447$	−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	$0.577638\pi$
$450$	5.57532	+	31.6192i	0.262823	+	1.49054i
$451$	2.29813	+	3.98048i	0.108215	+	0.187434i
$452$	72.5836			3.41404
$453$	−32.3346	−	5.70146i	−1.51921	−	0.267878i
$454$	7.80200	+	13.5135i	0.366166	+	0.634218i
$455$		0			0
$456$	−16.3935	+	19.5370i	−0.767697	+	0.914906i
$457$	21.2973	+	36.8879i	0.996244	+	1.72554i	0.573115	+	0.819475i	$0.305735\pi$
$457$	21.2973	+	36.8879i	0.996244	+	1.72554i	0.423129	+	0.906070i	$0.360932\pi$
$458$	−29.6065	−	51.2800i	−1.38342	−	2.39616i
$459$		−	8.58770i		−	0.400840i
$460$	6.13429	−	10.6249i	0.286013	−	0.495388i
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	−0.871843	−	0.489786i	$-0.837075\pi$
$461$	−0.252374	+	0.437124i	−0.0117542	+	0.0203589i	0.860088	+	0.510145i	$0.170408\pi$
$462$		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	$0.853169\pi$
$464$	−40.1584			−1.86431
$465$	−4.45899	+	5.31402i	−0.206781	+	0.246432i
$466$	−21.5868			−0.999988
$467$	15.7083	−	27.2075i	0.726892	−	1.25901i	−0.231299	−	0.972883i	$-0.574298\pi$
$467$	15.7083	−	27.2075i	0.726892	−	1.25901i	0.958191	−	0.286131i	$-0.0923691\pi$
$468$	−67.8196	−	24.6843i	−3.13496	−	1.14103i
$469$		0			0
$470$	−1.13816	+	1.97134i	−0.0524992	+	0.0909313i
$471$	20.1040	−	23.9590i	0.926344	−	1.10397i
$472$	−20.3346	+	35.2205i	−0.935974	+	1.62115i
$473$	−0.358441	+	0.620838i	−0.0164811	+	0.0285461i
$474$	16.7964	−	20.0171i	0.771483	−	0.919418i
$475$	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
$479$	−16.4406			−0.751189			−0.375594	−	0.926784i	$-0.622561\pi$
$479$	−16.4406			−0.751189			−0.375594	+	0.926784i	$0.622561\pi$
$480$	4.50000	−	5.36289i	0.205396	−	0.244781i
$481$	24.8367			1.13245
$482$	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
$486$	13.5000	−	37.0909i	0.612372	−	1.68248i
$487$	1.48767	+	2.57673i	0.0674129	+	0.116763i	0.897762	−	0.440481i	$-0.145192\pi$
$487$	1.48767	+	2.57673i	0.0674129	+	0.116763i	−0.830349	+	0.557244i	$0.811859\pi$
$488$	7.92649	+	13.7291i	0.358815	+	0.621486i
$489$	−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	$0.629435\pi$
$492$	−8.91534	−	1.57202i	−0.401935	−	0.0708719i
$493$	−9.99825			−0.450298
$494$	16.6493	+	28.8374i	0.749087	+	1.29746i
$495$	−9.61721	−	3.50038i	−0.432261	−	0.157330i
$496$	−30.2327			−1.35749
$497$		0			0
$498$	−0.945622	−	0.166739i	−0.0423744	−	0.00747174i
$499$	−13.4439			−0.601830			−0.300915	−	0.953651i	$-0.597292\pi$
$499$	−13.4439			−0.601830			−0.300915	+	0.953651i	$0.597292\pi$
$500$	−17.8969	+	30.9984i	−0.800375	+	1.38629i
$501$	−11.7522	−	32.2889i	−0.525050	−	1.44256i
$502$	15.2772	+	26.4609i	0.681854	+	1.18101i
$503$	−22.6631			−1.01050			−0.505250	−	0.862973i	$-0.668600\pi$
$503$	−22.6631			−1.01050			−0.505250	+	0.862973i	$0.668600\pi$
$504$		0			0
$505$	8.54488			0.380242
$506$	−15.5326	−	26.9032i	−0.690506	−	1.19599i
$507$	−18.6364	+	22.2100i	−0.827672	+	0.986381i
$508$	−38.9393	+	67.4448i	−1.72765	+	2.99238i
$509$	9.54757			0.423189			0.211594	−	0.977358i	$-0.432134\pi$
$509$	9.54757			0.423189			0.211594	+	0.977358i	$0.432134\pi$
$510$	4.09714	−	4.88279i	0.181425	−	0.216213i
$511$		0			0
$512$	−50.5553			−2.23425
$513$	−10.8516	+	6.26519i	−0.479111	+	0.276615i
$514$	−13.3773	−	23.1702i	−0.590049	−	1.02199i
$515$	−5.80066			−0.255608
$516$	−0.482926	−	1.32683i	−0.0212596	−	0.0584103i
$517$	1.98293	+	3.43453i	0.0872090	+	0.151050i
$518$		0			0
$519$	−13.4372	−	36.9183i	−0.589826	−	1.62053i
$520$	−14.6411	−	25.3592i	−0.642057	−	1.11208i
$521$	1.55644	+	2.69583i	0.0681887	+	0.118106i	0.898104	−	0.439783i	$-0.144945\pi$
$521$	1.55644	+	2.69583i	0.0681887	+	0.118106i	−0.829915	+	0.557889i	$0.811611\pi$
$522$	−43.1832	−	15.7174i	−1.89008	−	0.687932i
$523$	8.07444	−	13.9853i	0.353071	−	0.611537i	−0.633715	−	0.773567i	$-0.718471\pi$
$523$	8.07444	−	13.9853i	0.353071	−	0.611537i	0.986786	+	0.162030i	$0.0518041\pi$
$524$	42.3448	−	73.3434i	1.84984	−	3.20402i
$525$		0			0
$526$	35.8965	+	62.1746i	1.56516	+	2.71094i
$527$	−7.52704			−0.327883
$528$	−15.2554	−	41.9138i	−0.663905	−	1.82406i
$529$	−12.9986			−0.565155
$530$	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
$534$	47.6279	+	8.39809i	2.06106	+	0.363421i
$535$	1.05051	−	1.81953i	0.0454174	−	0.0786652i
$536$	9.03121	−	15.6425i	0.390089	−	0.675654i
$537$	4.35251	+	11.9584i	0.187825	+	0.516044i
$538$	−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	−0.807069	−	0.590457i	$-0.798948\pi$
$541$	2.50774	−	4.34353i	0.107816	−	0.186743i	0.914885	+	0.403714i	$0.132281\pi$
$542$	34.5330			1.48332
$543$	−5.87733	−	1.03633i	−0.252220	−	0.0444732i
$544$	7.59627			0.325687
$545$	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
$549$	1.35251	+	7.67047i	0.0577238	+	0.327368i
$550$	20.7592	+	35.9561i	0.885177	+	1.53317i
$551$	7.29426	+	12.6340i	0.310746	+	0.538228i
$552$	32.9386	+	5.80796i	1.40196	+	0.247203i
$553$		0			0
$554$	7.78699	+	13.4875i	0.330837	+	0.573027i
$555$	−4.45899	+	5.31402i	−0.189274	+	0.225567i
$556$	97.3055			4.12667
$557$	17.2815	+	29.9325i	0.732242	+	1.26828i	0.955923	+	0.293618i	$0.0948592\pi$
$557$	17.2815	+	29.9325i	0.732242	+	1.26828i	−0.223681	+	0.974662i	$0.571807\pi$
$558$	−32.5099	−	11.8326i	−1.37625	−	0.500915i
$559$	−1.00774			−0.0426229
$560$		0			0
$561$	−3.79813	−	10.4353i	−0.160357	−	0.440578i
$562$	8.38682			0.353777
$563$	18.6052	−	32.2251i	0.784115	−	1.35813i	−0.145411	−	0.989371i	$-0.546450\pi$
$563$	18.6052	−	32.2251i	0.784115	−	1.35813i	0.929526	−	0.368756i	$-0.120216\pi$
$564$	−7.69253	−	1.35640i	−0.323914	−	0.0571148i
$565$	7.23442	+	12.5304i	0.304354	+	0.527157i
$566$	73.4894			3.08899
$567$		0			0
$568$	−22.4706			−0.942845
$569$	−0.202333	−	0.350452i	−0.00848226	−	0.0146917i	0.861753	−	0.507328i	$-0.169367\pi$
$569$	−0.202333	−	0.350452i	−0.00848226	−	0.0146917i	−0.870235	+	0.492636i	$0.836033\pi$
$570$	−9.15910	−	1.61500i	−0.383632	−	0.0676448i
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	−0.135146	−	0.990826i	$-0.543150\pi$
$571$	18.8897	−	32.7178i	0.790507	−	1.36920i	0.925653	−	0.378373i	$-0.123516\pi$
$572$	−93.3278			−3.90223
$573$	−3.35163	−	9.20854i	−0.140017	−	0.384692i
$574$		0			0
$575$	−13.3669			−0.557438
$576$	−4.61809	−	1.68085i	−0.192420	−	0.0700353i
$577$	1.10560	+	1.91496i	0.0460267	+	0.0797206i	0.888121	−	0.459610i	$-0.152011\pi$
$577$	1.10560	+	1.91496i	0.0460267	+	0.0797206i	−0.842094	+	0.539330i	$0.818677\pi$
$578$	−36.1293			−1.50278
$579$	−10.6839	+	12.7326i	−0.444008	+	0.529149i
$580$	−11.7344	−	20.3246i	−0.487245	−	0.843934i
$581$		0			0
$582$	54.0014	+	9.52190i	2.23843	+	0.394696i
$583$	−14.1420	−	24.4947i	−0.585703	−	1.01447i
$584$	39.0210	+	67.5864i	1.61470	+	2.79674i
$585$	−2.49825	−	14.1683i	−0.103290	−	0.585785i
$586$	10.6591	−	18.4621i	0.440323	−	0.762662i
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	−1.00000		0.000436347i	$-0.999861\pi$
$587$	−12.1049	+	20.9663i	−0.499622	+	0.865371i	0.500378	+	0.865807i	$0.333194\pi$
$588$		0			0
$589$	5.49138	+	9.51135i	0.226268	+	0.391908i
$590$	−14.8307			−0.610570
$591$	14.1917	+	2.50237i	0.583767	+	0.102934i
$592$	−30.2327			−1.24255
$593$	−6.11927	+	10.5989i	−0.251288	+	0.435244i	−0.963881	−	0.266334i	$-0.914188\pi$
$593$	−6.11927	+	10.5989i	−0.251288	+	0.435244i	0.712592	+	0.701578i	$0.247521\pi$
$594$		−	51.0415i		−	2.09426i
$595$		0			0
$596$	33.4295	−	57.9016i	1.36932	−	2.37174i
$597$	−3.90760	−	10.7361i	−0.159928	−	0.439397i
$598$	21.8346	−	37.8186i	0.892882	−	1.54652i
$599$	−19.8084	+	34.3092i	−0.809349	+	1.40183i	0.103966	+	0.994581i	$0.466847\pi$
$599$	−19.8084	+	34.3092i	−0.809349	+	1.40183i	−0.913315	+	0.407253i	$0.866487\pi$
$600$	−44.0223	−	7.76233i	−1.79720	−	0.316896i
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	−0.378879	−	0.925446i	$-0.623690\pi$
$601$	15.0039	−	25.9875i	0.612021	−	1.06005i	0.990899	−	0.134605i	$-0.0429764\pi$
$602$		0			0
$603$	6.79813	−	5.70431i	0.276841	−	0.232298i
$604$	41.8127	−	72.4218i	1.70134	−	2.94680i
$605$	−3.56118			−0.144783
$606$	14.5753	+	40.0454i	0.592082	+	1.62673i
$607$	−19.4843			−0.790844			−0.395422	−	0.918499i	$-0.629402\pi$
$607$	−19.4843			−0.790844			−0.395422	+	0.918499i	$0.629402\pi$
$608$	−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
$612$	20.5535	+	7.48086i	0.830826	+	0.302396i
$613$	9.26382	+	16.0454i	0.374162	+	0.648068i	0.990201	−	0.139648i	$-0.0445970\pi$
$613$	9.26382	+	16.0454i	0.374162	+	0.648068i	−0.616039	+	0.787716i	$0.711264\pi$
$614$	16.0633	+	27.8225i	0.648262	+	1.12282i
$615$	−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	$-0.356020\pi$
$618$	−9.89440	−	27.1846i	−0.398011	−	1.09353i
$619$	−44.9813			−1.80795			−0.903976	−	0.427583i	$-0.859365\pi$
$619$	−44.9813			−1.80795			−0.903976	+	0.427583i	$0.859365\pi$
$620$	−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
$625$	13.9982			0.559930
$626$	−36.1057	+	62.5368i	−1.44307	+	2.49947i
$627$	−10.4153	+	12.4125i	−0.415949	+	0.495708i
$628$	39.8298	+	68.9873i	1.58938	+	2.75289i
$629$	−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	$0.439857\pi$
$632$	18.1903	+	31.5065i	0.723572	+	1.25326i
$633$	1.99613	+	5.48432i	0.0793390	+	0.217982i
$634$	32.7841	−	56.7836i	1.30202	−	2.25517i
$635$	−15.5243			−0.616065
$636$	54.8624	+	9.67372i	2.17543	+	0.383588i
$637$		0			0
$638$	−59.4252			−2.35267
$639$	−10.3743	−	3.77595i	−0.410402	−	0.149374i
$640$	−5.86571	−	10.1597i	−0.231863	−	0.401598i
$641$	37.3901			1.47682			0.738410	−	0.674352i	$-0.235577\pi$
$641$	37.3901			1.47682			0.738410	+	0.674352i	$0.235577\pi$
$642$	10.3191	+	1.81953i	0.407262	+	0.0718112i
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	0.849698	−	0.527270i	$-0.176784\pi$
$643$	−0.805874	−	1.39581i	−0.0317806	−	0.0550456i	−0.881478	+	0.472225i	$0.843451\pi$
$644$		0			0
$645$	0.180922	−	0.215615i	0.00712380	−	0.00848982i
$646$	−5.04576	−	8.73951i	−0.198523	−	0.343851i
$647$	20.5881	+	35.6597i	0.809402	+	1.40193i	0.913278	+	0.407336i	$0.133542\pi$
$647$	20.5881	+	35.6597i	0.809402	+	1.40193i	−0.103876	+	0.994590i	$0.533125\pi$
$648$	42.0977	+	35.3241i	1.65375	+	1.38766i
$649$	−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
$653$	3.05199			0.119434			0.0597169	−	0.998215i	$-0.480980\pi$
$653$	3.05199			0.119434			0.0597169	+	0.998215i	$0.480980\pi$
$654$	−11.1582	+	13.2979i	−0.436321	+	0.519987i
$655$	16.8821			0.659637
$656$	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	$0.865626\pi$
$660$	16.7554	−	19.9683i	0.652202	−	0.777264i
$661$	−10.1505	+	17.5812i	−0.394808	+	0.683828i	−0.993077	−	0.117468i	$-0.962522\pi$
$661$	−10.1505	+	17.5812i	−0.394808	+	0.683828i	0.598269	+	0.801296i	$0.295856\pi$
$662$	−10.4055	+	18.0229i	−0.404423	+	0.700481i
$663$	10.0343	−	11.9584i	0.389700	−	0.464427i
$664$	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
$668$	87.5167			3.38612
$669$	6.98767	−	8.32759i	0.270159	−	0.321963i
$670$	6.58677			0.254469
$671$	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
$675$	−19.0201	−	10.9812i	−0.732083	−	0.422668i
$676$	−36.9222	−	63.9511i	−1.42008	−	2.45966i
$677$	−5.43360	−	9.41127i	−0.208830	−	0.361705i	0.742516	−	0.669828i	$-0.233632\pi$
$677$	−5.43360	−	9.41127i	−0.208830	−	0.361705i	−0.951346	+	0.308124i	$0.900299\pi$
$678$	−46.3833	+	55.2775i	−1.78134	+	2.12292i
$679$		0			0
$680$	4.43717	+	7.68540i	0.170158	+	0.294722i
$681$	−10.5116	−	1.85348i	−0.402806	−	0.0710255i
$682$	−44.7374			−1.71308
$683$	−16.3473	−	28.3143i	−0.625512	−	1.08342i	−0.988442	−	0.151602i	$-0.951557\pi$
$683$	−16.3473	−	28.3143i	−0.625512	−	1.08342i	0.362930	−	0.931817i	$-0.381777\pi$
$684$	−5.54189	−	31.4296i	−0.211899	−	1.20174i
$685$	−15.9659			−0.610024
$686$		0			0
$687$	39.8888	+	7.03347i	1.52185	+	0.268344i
$688$	1.22668			0.0467668
$689$	19.8799	−	34.4329i	0.757362	−	1.31179i
$690$	4.17159	+	11.4613i	0.158810	+	0.436326i
$691$	−7.49912	−	12.9889i	−0.285280	−	0.494120i	0.687397	−	0.726282i	$-0.258753\pi$
$691$	−7.49912	−	12.9889i	−0.285280	−	0.494120i	−0.972677	+	0.232162i	$0.925420\pi$
$692$	100.064			3.80387
$693$		0			0
$694$	56.8863			2.15937
$695$	9.69846	+	16.7982i	0.367884	+	0.637193i
$696$	41.1262	−	49.0123i	1.55888	−	1.85781i
$697$	0.979055	−	1.69577i	0.0370844	−	0.0642320i
$698$	66.0856			2.50138
$699$	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	$0.333386\pi$
$702$	62.1378	−	35.8753i	2.34524	−	1.35403i
$703$	5.49138	+	9.51135i	0.207111	+	0.358727i
$704$	−6.35504			−0.239514
$705$	−0.532556	−	1.46318i	−0.0200572	−	0.0551067i
$706$	0.449493	+	0.778544i	0.0169169	+	0.0293009i
$707$		0			0
$708$	−17.4060	−	47.8226i	−0.654158	−	1.79728i
$709$	−7.68004	−	13.3022i	−0.288430	−	0.499576i	0.685005	−	0.728538i	$-0.259800\pi$
$709$	−7.68004	−	13.3022i	−0.288430	−	0.499576i	−0.973435	+	0.228963i	$0.926467\pi$
$710$	−4.09714	−	7.09646i	−0.153763	−	0.266325i
$711$	3.10385	+	17.6028i	0.116403	+	0.660156i
$712$	−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
$716$	−32.4124			−1.21131
$717$	−8.62654	−	23.7012i	−0.322164	−	0.885139i
$718$	13.8152			0.515579
$719$	−13.3653	+	23.1494i	−0.498442	+	0.863326i	−0.999998	−	0.00179839i	$-0.999428\pi$
$719$	−13.3653	+	23.1494i	−0.498442	+	0.863326i	0.501557	+	0.865125i	$0.332761\pi$
$720$	3.04101	+	17.2464i	0.113332	+	0.642737i
$721$		0			0
$722$	16.6925	−	28.9123i	0.621232	−	1.07600i
$723$	−9.21735	−	1.62527i	−0.342797	−	0.0604443i
$724$	7.60014	−	13.1638i	0.282457	−	0.489230i
$725$	−12.7849	+	22.1441i	−0.474820	+	0.822413i
$726$	−6.07444	−	16.6894i	−0.225444	−	0.619402i
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	−0.0379552	−	0.999279i	$-0.512084\pi$
$727$	22.8221	−	39.5290i	0.846424	−	1.46605i	0.884379	−	0.466770i	$-0.154582\pi$
$728$		0			0
$729$	13.5000	+	23.3827i	0.500000	+	0.866025i
$730$	−14.2297	+	24.6465i	−0.526664	+	0.912209i
$731$	0.305407			0.0112959
$732$	−19.5364	−	3.44480i	−0.722087	−	0.127323i
$733$	5.97502			0.220693			0.110346	−	0.993893i	$-0.464804\pi$
$733$	5.97502			0.220693			0.110346	+	0.993893i	$0.464804\pi$
$734$	−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
$738$	6.89440	−	5.78509i	0.253786	−	0.212952i
$739$	17.7981	+	30.8273i	0.654715	+	1.13400i	0.981965	+	0.189062i	$0.0605447\pi$
$739$	17.7981	+	30.8273i	0.654715	+	1.13400i	−0.327250	+	0.944938i	$0.606122\pi$
$740$	−8.83409	−	15.3011i	−0.324748	−	0.562480i
$741$	−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	$0.652658\pi$
$744$	30.9613	−	36.8982i	1.13510	−	1.35275i
$745$	13.3277			0.488289
$746$	−2.19207	−	3.79677i	−0.0802573	−	0.139010i
$747$	0.503155	−	0.422197i	0.0184095	−	0.0154474i
$748$	28.2841			1.03417
$749$		0			0
$750$	−12.1707	−	33.4388i	−0.444412	−	1.22101i
$751$	−17.3337			−0.632515			−0.316258	−	0.948673i	$-0.602426\pi$
$751$	−17.3337			−0.632515			−0.316258	+	0.948673i	$0.602426\pi$
$752$	3.39306	−	5.87695i	0.123732	−	0.214310i
$753$	−20.5829	−	3.62932i	−0.750083	−	0.132260i
$754$	−41.7679	−	72.3440i	−1.52110	−	2.63461i
$755$	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	$0.516039\pi$
$758$	15.3614	+	26.6068i	0.557952	+	0.966402i
$759$	20.9270	+	3.68999i	0.759600	+	0.133938i
$760$	6.47431	−	11.2138i	0.234848	−	0.406768i
$761$	7.50744			0.272144			0.136072	−	0.990699i	$-0.456552\pi$
$761$	7.50744			0.272144			0.136072	+	0.990699i	$0.456552\pi$
$762$	−26.4805	−	72.7545i	−0.959286	−	2.63562i
$763$		0			0
$764$	24.9590			0.902987
$765$	0.757122	+	4.29385i	0.0273738	+	0.155244i
$766$	11.0296	+	19.1038i	0.398514	+	0.690247i
$767$	−36.3218			−1.31150
$768$	33.9602	−	40.4722i	1.22543	−	1.46042i
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	0.847013	−	0.531572i	$-0.178398\pi$
$769$	−1.02182	−	1.76985i	−0.0368478	−	0.0638223i	−0.883861	+	0.467749i	$0.845065\pi$
$770$		0			0
$771$	18.0232	+	3.17798i	0.649090	+	0.114452i
$772$	−21.1668	−	36.6620i	−0.761811	−	1.31950i
$773$	12.4709	+	21.6002i	0.448547	+	0.776907i	0.998292	−	0.0584263i	$-0.0186083\pi$
$773$	12.4709	+	21.6002i	0.448547	+	0.776907i	−0.549744	+	0.835333i	$0.685275\pi$
$774$	1.31908	+	0.480105i	0.0474133	+	0.0172570i
$775$	−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
$779$	−2.85710			−0.102366
$780$	36.0861	+	6.36295i	1.29209	+	0.227830i
$781$	−14.2763			−0.510847
$782$	−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
$786$	28.7964	+	79.1174i	1.02713	+	2.82202i
$787$	−3.55350	+	6.15484i	−0.126669	+	0.219396i	−0.922384	−	0.386274i	$-0.873762\pi$
$787$	−3.55350	+	6.15484i	−0.126669	+	0.219396i	0.795715	+	0.605671i	$0.207095\pi$
$788$	−18.3516	+	31.7860i	−0.653750	+	1.13233i
$789$	−48.3632	−	8.52774i	−1.72178	−	0.303596i
$790$	−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
$794$	−39.1097			−1.38795
$795$	3.79813	+	10.4353i	0.134706	+	0.370101i
$796$	29.0993			1.03140
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	−0.993376	−	0.114905i	$-0.963344\pi$
$797$	−16.8314	−	29.1528i	−0.596199	−	1.03265i	0.397178	−	0.917742i	$-0.369990\pi$
$798$		0			0
$799$	0.844770	−	1.46318i	0.0298858	−	0.0517638i
$800$	9.71348	−	16.8242i	0.343423	−	0.594827i
$801$	−25.3423	+	21.2647i	−0.895426	+	0.751352i
$802$	−23.3229	−	40.3965i	−0.823562	−	1.42645i
$803$	24.7913	+	42.9398i	0.874867	+	1.51531i
$804$	7.73055	+	21.2395i	0.272636	+	0.749060i
$805$		0			0
$806$	−31.4443	−	54.4632i	−1.10758	−	1.91838i
$807$	−4.43313	−	12.1799i	−0.156054	−	0.428754i
$808$	−59.3319			−2.08729
$809$	6.40807	+	11.0991i	0.225296	+	0.390224i	0.956408	−	0.292033i	$-0.0943318\pi$
$809$	6.40807	+	11.0991i	0.225296	+	0.390224i	−0.731112	+	0.682257i	$0.760998\pi$
$810$	−3.47993	+	19.7357i	−0.122272	+	0.693441i
$811$	−26.1239			−0.917335			−0.458667	−	0.888608i	$-0.651673\pi$
$811$	−26.1239			−0.917335			−0.458667	+	0.888608i	$0.651673\pi$
$812$		0			0
$813$	−15.1839	+	18.0955i	−0.532523	+	0.634636i
$814$	−44.7374			−1.56805
$815$	0.421274	−	0.729669i	0.0147566	−	0.0255592i
$816$	−12.2144	+	14.5565i	−0.427588	+	0.509579i
$817$	−0.222811	−	0.385920i	−0.00779518	−	0.0135016i
$818$	−72.5099			−2.53525
$819$		0			0
$820$	4.59627			0.160509
$821$	−13.8320	−	23.9578i	−0.482741	−	0.836132i	0.517062	−	0.855948i	$-0.327026\pi$
$821$	−13.8320	−	23.9578i	−0.482741	−	0.836132i	−0.999804	+	0.0198153i	$0.993692\pi$
$822$	−27.2335	−	74.8236i	−0.949879	−	2.60977i
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	−0.999853	−	0.0171330i	$-0.994546\pi$
$823$	−13.9162	+	24.1036i	−0.485089	+	0.840199i	0.514764	+	0.857332i	$0.327879\pi$
$824$	40.2772			1.40312
$825$	−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	$0.474209\pi$
$828$	−32.0620	+	26.9032i	−1.11423	+	0.934950i
$829$	4.98680	+	8.63738i	0.173199	+	0.299989i	0.939536	−	0.342449i	$-0.111256\pi$
$829$	4.98680	+	8.63738i	0.173199	+	0.299989i	−0.766338	+	0.642438i	$0.777923\pi$
$830$	0.487511			0.0169218
$831$	−10.4914	−	1.84991i	−0.363942	−	0.0641728i
$832$	−4.46673	−	7.73660i	−0.154856	−	0.268218i
$833$		0			0
$834$	−62.1814	+	74.1050i	−2.15317	+	2.56604i
$835$	8.72281	+	15.1084i	0.301865	+	0.522846i
$836$	−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	−0.802079	−	0.597218i	$-0.796273\pi$
$839$	3.36484	−	5.82807i	0.116167	−	0.201207i	0.918246	+	0.396011i	$0.129606\pi$
$840$		0			0
$841$	−3.79901	−	6.58008i	−0.131000	−	0.226899i
$842$	−69.3842			−2.39114
$843$	−3.68762	+	4.39474i	−0.127008	+	0.151363i
$844$	−14.8648			−0.511669
$845$	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
$849$	−32.3127	+	38.5088i	−1.10897	+	1.32162i
$850$	8.84389	−	15.3181i	0.303343	−	0.525406i
$851$	7.20162	−	12.4736i	0.246868	−	0.427588i
$852$	18.0744	−	21.5403i	0.619220	−	0.737958i
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	−0.911326	−	0.411686i	$-0.864940\pi$
$853$	−2.89528	+	5.01477i	−0.0991324	+	0.171702i	0.812193	+	0.583388i	$0.198273\pi$
$854$		0			0
$855$	4.87346	−	4.08931i	0.166669	−	0.139852i
$856$	−7.29426	+	12.6340i	−0.249313	+	0.431822i
$857$	−34.9077			−1.19242			−0.596211	−	0.802827i	$-0.703328\pi$
$857$	−34.9077			−1.19242			−0.596211	+	0.802827i	$0.703328\pi$
$858$	59.6396	−	71.0757i	2.03606	−	2.42648i
$859$	−12.6149			−0.430416			−0.215208	−	0.976568i	$-0.569043\pi$
$859$	−12.6149			−0.430416			−0.215208	+	0.976568i	$0.569043\pi$
$860$	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	−0.583127	−	0.812381i	$-0.698171\pi$
$863$	12.1027	−	20.9624i	0.411979	−	0.713569i	0.995106	+	0.0988119i	$0.0315042\pi$
$864$	−20.6832	+	11.9415i	−0.703657	+	0.406256i
$865$	9.97343	+	17.2745i	0.339107	+	0.587350i
$866$	−47.0754	−	81.5369i	−1.59969	−	2.77074i
$867$	15.8858	−	18.9319i	0.539509	−	0.642962i
$868$		0			0
$869$	11.5569	+	20.0171i	0.392041	+	0.679035i
$870$	22.9773	+	4.05152i	0.779003	+	0.137359i
$871$	16.1317			0.546600
$872$	−12.0842	−	20.9305i	−0.409224	−	0.708797i
$873$	−28.7335	+	24.1103i	−0.972483	+	0.816010i
$874$	19.3105			0.653186
$875$		0			0
$876$	−96.1751	−	16.9583i	−3.24946	−	0.572967i
$877$	−1.12567			−0.0380111			−0.0190055	−	0.999819i	$-0.506050\pi$
$877$	−1.12567			−0.0380111			−0.0190055	+	0.999819i	$0.506050\pi$
$878$	−31.7456	+	54.9849i	−1.07136	+	1.85565i
$879$	4.98751	+	13.7031i	0.168225	+	0.462193i
$880$	11.3229	+	19.6119i	0.381697	+	0.661118i
$881$	−4.38331			−0.147678			−0.0738388	−	0.997270i	$-0.523525\pi$
$881$	−4.38331			−0.147678			−0.0738388	+	0.997270i	$0.523525\pi$
$882$		0			0
$883$	−6.88949			−0.231850			−0.115925	−	0.993258i	$-0.536983\pi$
$883$	−6.88949			−0.231850			−0.115925	+	0.993258i	$0.536983\pi$
$884$	19.8799	+	34.4329i	0.668632	+	1.15810i
$885$	6.52094	−	7.77136i	0.219199	−	0.261231i
$886$	−2.58853	+	4.48346i	−0.0869632	+	0.150625i
$887$	39.0752			1.31202			0.656009	−	0.754753i	$-0.272243\pi$
$887$	39.0752			1.31202			0.656009	+	0.754753i	$0.272243\pi$
$888$	30.9613	−	36.8982i	1.03899	−	1.23822i
$889$		0			0
$890$	−24.5544			−0.823065
$891$	26.7460	+	22.4426i	0.896026	+	0.751855i
$892$	13.8439	+	23.9783i	0.463528	+	0.802854i
$893$	−2.46522			−0.0824955
$894$	22.7335	+	62.4599i	0.760323	+	2.08897i
$895$	−3.23055	−	5.59548i	−0.107985	−	0.187036i
$896$		0			0
$897$	10.2166	+	28.0700i	0.341123	+	0.937229i
$898$	12.9572	+	22.4426i	0.432388	+	0.748919i
$899$	−13.7761	−	23.8610i	−0.459460	−	0.795809i
$900$	42.8508	−	35.9561i	1.42836	−	1.19854i
$901$	−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
$905$	3.03003			0.100722
$906$	28.4345	+	78.1232i	0.944674	+	2.59547i
$907$	42.4938			1.41098			0.705492	−	0.708718i	$-0.250726\pi$
$907$	42.4938			1.41098			0.705492	+	0.708718i	$0.250726\pi$
$908$	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	$0.0840442\pi$
$912$	27.3050	+	4.81461i	0.904159	+	0.159428i
$913$	0.424678	−	0.735564i	0.0140548	−	0.0243436i
$914$	53.9265	−	93.4035i	1.78373	−	3.08951i
$915$	−1.35251	−	3.71599i	−0.0447126	−	0.122847i
$916$	−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	−0.914835	−	0.403828i	$-0.867680\pi$
$919$	−3.26470	+	5.65463i	−0.107693	+	0.186529i	0.807143	+	0.590357i	$0.201013\pi$
$920$	−16.9813			−0.559858
$921$	−21.6420	−	3.81607i	−0.713129	−	0.125744i
$922$	1.27807			0.0420909
$923$	−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
$927$	18.5954	+	6.76817i	0.610753	+	0.222296i
$928$	13.9029	+	24.0805i	0.456384	+	0.790480i
$929$	−29.1386	−	50.4696i	−0.956007	−	1.65585i	−0.732046	−	0.681255i	$-0.761435\pi$
$929$	−29.1386	−	50.4696i	−0.956007	−	1.65585i	−0.223961	−	0.974598i	$-0.571899\pi$
$930$	17.2981	+	3.05013i	0.567228	+	0.100018i
$931$		0			0
$932$	18.8045	+	32.5704i	0.615963	+	1.06688i
$933$	18.3592	−	21.8797i	0.601054	−	0.716308i
$934$	−79.5494			−2.60294
$935$	2.81908	+	4.88279i	0.0921937	+	0.159684i
$936$	17.3467	+	98.3782i	0.566995	+	3.21559i
$937$	32.4175			1.05903			0.529516	−	0.848300i	$-0.322374\pi$
$937$	32.4175			1.05903			0.529516	+	0.848300i	$0.322374\pi$
$938$		0			0
$939$	−16.8942	−	46.4165i	−0.551323	−	1.51475i
$940$	3.96585			0.129352
$941$	13.6613	−	23.6621i	0.445346	−	0.771363i	−0.552730	−	0.833360i	$-0.686414\pi$
$941$	13.6613	−	23.6621i	0.445346	−	0.771363i	0.998076	+	0.0619979i	$0.0197472\pi$
$942$	−77.9912	−	13.7520i	−2.54109	−	0.448063i
$943$	1.87346	+	3.24492i	0.0610081	+	0.105669i
$944$	44.2131			1.43901
$945$		0			0
$946$	1.81521			0.0590175
$947$	19.1065	+	33.0935i	0.620879	+	1.07539i	0.989322	+	0.145744i	$0.0465575\pi$
$947$	19.1065	+	33.0935i	0.620879	+	1.07539i	−0.368443	+	0.929650i	$0.620109\pi$
$948$	−44.8337	−	7.90539i	−1.45613	−	0.256755i
$949$	−34.8499	+	60.3618i	−1.13127	+	1.95943i
$950$	−25.8084			−0.837335
$951$	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	$0.0962943\pi$
$954$	−42.4261	+	35.5997i	−1.37360	+	1.15258i
$955$	2.48767	+	4.30878i	0.0804992	+	0.139429i
$956$	64.2404			2.07768
$957$	26.1288	−	31.1391i	0.844625	−	1.00658i
$958$	20.8145	+	36.0518i	0.672486	+	1.16478i
$959$		0			0
$960$	2.45723	+	0.433277i	0.0793069	+	0.0139839i
$961$	5.12882	+	8.88338i	0.165446	+	0.286561i
$962$	−31.4443	−	54.4632i	−1.01381	−	1.75596i
$963$	−5.49067	+	4.60722i	−0.176934	+	0.148465i
$964$	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	$0.963438\pi$
$968$	24.7273			0.794766
$969$	6.79813	+	1.19869i	0.218388	+	0.0385076i
$970$	−27.8402			−0.893894
$971$	−4.08812	+	7.08082i	−0.131194	+	0.227234i	−0.924137	−	0.382061i	$-0.875214\pi$
$971$	−4.08812	+	7.08082i	−0.131194	+	0.227234i	0.792943	+	0.609296i	$0.208548\pi$
$972$	−67.7233	+	11.9415i	−2.17223	+	0.383022i
$973$		0			0
$974$	3.76692	−	6.52450i	0.120700	−	0.209058i
$975$	−13.6545	−	37.5155i	−0.437294	−	1.20146i
$976$	8.61721	−	14.9254i	0.275830	−	0.477752i
$977$	7.92427	−	13.7252i	0.253520	−	0.439109i	−0.710973	−	0.703220i	$-0.751745\pi$
$977$	7.92427	−	13.7252i	0.253520	−	0.439109i	0.964492	+	0.264111i	$0.0850784\pi$
$978$	4.13816	+	0.729669i	0.132324	+	0.0233322i
$979$	−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
$983$	53.3063			1.70021			0.850104	−	0.526615i	$-0.176539\pi$
$983$	53.3063			1.70021			0.850104	+	0.526615i	$0.176539\pi$
$984$	4.28564	+	11.7747i	0.136621	+	0.375364i
$985$	−7.31645			−0.233121
$986$	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
$990$	4.50000	+	25.5208i	0.143019	+	0.811103i
$991$	−20.1047	−	34.8224i	−0.638648	−	1.10617i	−0.985730	−	0.168335i	$-0.946161\pi$
$991$	−20.1047	−	34.8224i	−0.638648	−	1.10617i	0.347082	−	0.937835i	$-0.387172\pi$
$992$	10.4666	+	18.1286i	0.332314	+	0.575584i
$993$	−4.86887	−	13.3771i	−0.154509	−	0.424510i
$994$		0			0
$995$	2.90033	+	5.02352i	0.0919466	+	0.159256i
$996$	0.572167	+	1.57202i	0.0181298	+	0.0498112i
$997$	28.7202			0.909577			0.454789	−	0.890599i	$-0.349715\pi$
$997$	28.7202			0.909577			0.454789	+	0.890599i	$0.349715\pi$
$998$	17.0205	+	29.4804i	0.538776	+	0.933187i
$999$	20.4947	−	11.8326i	0.648424	−	0.374368i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.f.a.22.1	✓	6	63.58	even	3
63.2.f.a.43.1	yes	6	7.2	even	3
189.2.f.b.64.3		6	63.23	odd	6
189.2.f.b.127.3		6	21.2	odd	6
441.2.f.c.148.1		6	63.40	odd	6
441.2.f.c.295.1		6	7.5	odd	6
441.2.g.b.67.1		6	63.31	odd	6
441.2.g.b.79.1		6	7.6	odd	2
441.2.g.c.67.1		6	63.4	even	3	inner
441.2.g.c.79.1		6	1.1	even	1	trivial
441.2.h.d.214.3		6	7.4	even	3
441.2.h.d.373.3		6	9.4	even	3
441.2.h.e.214.3		6	7.3	odd	6
441.2.h.e.373.3		6	63.13	odd	6
567.2.a.c.1.1		3	63.2	odd	6
567.2.a.h.1.3		3	63.16	even	3
1008.2.r.h.337.3		6	252.247	odd	6
1008.2.r.h.673.3		6	28.23	odd	6
1323.2.f.d.442.3		6	63.5	even	6
1323.2.f.d.883.3		6	21.5	even	6
1323.2.g.d.361.3		6	63.32	odd	6
1323.2.g.d.667.3		6	3.2	odd	2
1323.2.g.e.361.3		6	63.59	even	6
1323.2.g.e.667.3		6	21.20	even	2
1323.2.h.b.226.1		6	63.41	even	6
1323.2.h.b.802.1		6	21.17	even	6
1323.2.h.c.226.1		6	9.5	odd	6
1323.2.h.c.802.1		6	21.11	odd	6
3024.2.r.k.1009.1		6	252.23	even	6
3024.2.r.k.2017.1		6	84.23	even	6
3969.2.a.l.1.1		3	63.47	even	6
3969.2.a.q.1.3		3	63.61	odd	6
9072.2.a.bs.1.3		3	252.191	even	6
9072.2.a.ca.1.1		3	252.79	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:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26604 - 2.19285i) q^{2} +(1.70574 + 0.300767i) q^{3} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} +(-1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 + 1.02606i) q^{9} +O(q^{10})\)	\(q+(-1.26604 - 2.19285i) q^{2} +(1.70574 + 0.300767i) q^{3} +(-2.20574 + 3.82045i) q^{4} -0.879385 q^{5} +(-1.50000 - 4.12122i) q^{6} +6.10607 q^{8} +(2.81908 + 1.02606i) q^{9} +(1.11334 + 1.92836i) q^{10} +3.87939 q^{11} +(-4.91147 + 5.85327i) q^{12} +(2.72668 + 4.72275i) q^{13} +(-1.50000 - 0.264490i) q^{15} +(-3.31908 - 5.74881i) q^{16} +(-0.826352 - 1.43128i) q^{17} +(-1.31908 - 7.48086i) q^{18} +(-1.20574 + 2.08840i) q^{19} +(1.93969 - 3.35965i) q^{20} +(-4.91147 - 8.50692i) q^{22} +3.16250 q^{23} +(10.4153 + 1.83651i) q^{24} -4.22668 q^{25} +(6.90420 - 11.9584i) q^{26} +(4.50000 + 2.59808i) q^{27} +(3.02481 - 5.23913i) q^{29} +(1.31908 + 3.62414i) q^{30} +(2.27719 - 3.94421i) q^{31} +(-2.29813 + 3.98048i) q^{32} +(6.61721 + 1.16679i) q^{33} +(-2.09240 + 3.62414i) q^{34} +(-10.1382 + 8.50692i) q^{36} +(2.27719 - 3.94421i) q^{37} +6.10607 q^{38} +(3.23055 + 8.87587i) q^{39} -5.36959 q^{40} +(0.592396 + 1.02606i) q^{41} +(-0.0923963 + 0.160035i) q^{43} +(-8.55690 + 14.8210i) q^{44} +(-2.47906 - 0.902302i) q^{45} +(-4.00387 - 6.93491i) q^{46} +(0.511144 + 0.885328i) q^{47} +(-3.93242 - 10.8042i) q^{48} +(5.35117 + 9.26849i) q^{50} +(-0.979055 - 2.68993i) q^{51} -24.0574 q^{52} +(-3.64543 - 6.31407i) q^{53} -13.1571i q^{54} -3.41147 q^{55} +(-2.68479 + 3.19961i) q^{57} -15.3182 q^{58} +(-3.33022 + 5.76811i) q^{59} +(4.31908 - 5.14728i) q^{60} +(1.29813 + 2.24843i) q^{61} -11.5321 q^{62} -1.63816 q^{64} +(-2.39780 - 4.15312i) q^{65} +(-5.81908 - 15.9878i) q^{66} +(1.47906 - 2.56180i) q^{67} +7.29086 q^{68} +(5.39440 + 0.951178i) q^{69} -3.68004 q^{71} +(17.2135 + 6.26519i) q^{72} +(6.39053 + 11.0687i) q^{73} -11.5321 q^{74} +(-7.20961 - 1.27125i) q^{75} +(-5.31908 - 9.21291i) q^{76} +(15.3735 - 18.3214i) q^{78} +(2.97906 + 5.15988i) q^{79} +(2.91875 + 5.05542i) q^{80} +(6.89440 + 5.78509i) q^{81} +(1.50000 - 2.59808i) q^{82} +(0.109470 - 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +0.467911 q^{86} +(6.73530 - 8.02682i) q^{87} +23.6878 q^{88} +(-5.51367 + 9.54996i) q^{89} +(1.15998 + 6.57856i) q^{90} +(-6.97565 + 12.0822i) q^{92} +(5.07057 - 6.04288i) q^{93} +(1.29426 - 2.24173i) q^{94} +(1.06031 - 1.83651i) q^{95} +(-5.11721 + 6.09845i) q^{96} +(-6.25150 + 10.8279i) q^{97} +(10.9363 + 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} + 6 q^{5} - 9 q^{6} + 12 q^{8} + 12 q^{11} - 9 q^{12} + 3 q^{13} - 9 q^{15} - 3 q^{16} - 6 q^{17} + 9 q^{18} + 3 q^{19} + 6 q^{20} - 9 q^{22} + 24 q^{23} + 18 q^{24} - 12 q^{25} + 3 q^{26} + 27 q^{27} - 9 q^{29} - 9 q^{30} + 3 q^{31} + 9 q^{33} - 9 q^{34} - 27 q^{36} + 3 q^{37} + 12 q^{38} - 18 q^{39} - 18 q^{40} + 3 q^{43} - 15 q^{44} - 18 q^{45} - 3 q^{47} + 6 q^{50} - 9 q^{51} - 42 q^{52} - 6 q^{53} - 9 q^{57} - 18 q^{58} + 3 q^{59} + 9 q^{60} - 6 q^{61} - 60 q^{62} + 24 q^{64} - 15 q^{65} - 18 q^{66} + 12 q^{67} + 12 q^{68} - 9 q^{69} + 18 q^{71} + 45 q^{72} + 21 q^{73} - 60 q^{74} - 9 q^{75} - 15 q^{76} + 54 q^{78} + 21 q^{79} + 15 q^{80} + 9 q^{82} + 18 q^{83} - 9 q^{85} + 12 q^{86} + 36 q^{87} + 54 q^{88} - 12 q^{89} + 27 q^{90} - 3 q^{92} - 27 q^{93} + 18 q^{94} + 12 q^{95} + 3 q^{97} + 18 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 + 6 * q^5 - 9 * q^6 + 12 * q^8 + 12 * q^11 - 9 * q^12 + 3 * q^13 - 9 * q^15 - 3 * q^16 - 6 * q^17 + 9 * q^18 + 3 * q^19 + 6 * q^20 - 9 * q^22 + 24 * q^23 + 18 * q^24 - 12 * q^25 + 3 * q^26 + 27 * q^27 - 9 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^33 - 9 * q^34 - 27 * q^36 + 3 * q^37 + 12 * q^38 - 18 * q^39 - 18 * q^40 + 3 * q^43 - 15 * q^44 - 18 * q^45 - 3 * q^47 + 6 * q^50 - 9 * q^51 - 42 * q^52 - 6 * q^53 - 9 * q^57 - 18 * q^58 + 3 * q^59 + 9 * q^60 - 6 * q^61 - 60 * q^62 + 24 * q^64 - 15 * q^65 - 18 * q^66 + 12 * q^67 + 12 * q^68 - 9 * q^69 + 18 * q^71 + 45 * q^72 + 21 * q^73 - 60 * q^74 - 9 * q^75 - 15 * q^76 + 54 * q^78 + 21 * q^79 + 15 * q^80 + 9 * q^82 + 18 * q^83 - 9 * q^85 + 12 * q^86 + 36 * q^87 + 54 * q^88 - 12 * q^89 + 27 * q^90 - 3 * q^92 - 27 * q^93 + 18 * q^94 + 12 * q^95 + 3 * q^97 + 18 * q^99

Introduction

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