LMFDB - Embedded newform 360.2.bm.b.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31577 - 0.518408i) q^{2} +(0.424591 + 1.67920i) q^{3} +(1.46251 + 1.36421i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.311848 - 2.42956i) q^{6} +(3.88456 + 2.24275i) q^{7} +(-1.21710 - 2.55317i) q^{8} +(-2.63944 + 1.42595i) q^{9} +O(q^{10})$	\(q+(-1.31577 - 0.518408i) q^{2} +(0.424591 + 1.67920i) q^{3} +(1.46251 + 1.36421i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.311848 - 2.42956i) q^{6} +(3.88456 + 2.24275i) q^{7} +(-1.21710 - 2.55317i) q^{8} +(-2.63944 + 1.42595i) q^{9} +(-0.208931 - 1.39870i) q^{10} +(1.05081 + 0.606687i) q^{11} +(-1.66982 + 3.03508i) q^{12} +(1.71090 - 0.987790i) q^{13} +(-3.94853 - 4.96473i) q^{14} +(-1.24194 + 1.20731i) q^{15} +(0.277844 + 3.99034i) q^{16} -5.28743i q^{17} +(4.21213 - 0.507913i) q^{18} -4.86627 q^{19} +(-0.450191 + 1.94867i) q^{20} +(-2.11668 + 7.47521i) q^{21} +(-1.06812 - 1.34301i) q^{22} +(1.40767 + 2.43816i) q^{23} +(3.77051 - 3.12781i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.76323 + 0.412759i) q^{26} +(-3.51514 - 3.82672i) q^{27} +(2.62160 + 8.57940i) q^{28} +(-4.20865 + 7.28960i) q^{29} +(2.25998 - 0.944711i) q^{30} +(6.04943 - 3.49264i) q^{31} +(1.70305 - 5.39441i) q^{32} +(-0.572584 + 2.02212i) q^{33} +(-2.74105 + 6.95704i) q^{34} +4.48550i q^{35} +(-5.80550 - 1.51531i) q^{36} +4.71412i q^{37} +(6.40290 + 2.52272i) q^{38} +(2.38513 + 2.45355i) q^{39} +(1.60256 - 2.33063i) q^{40} +(-5.30898 + 3.06514i) q^{41} +(6.66028 - 8.73836i) q^{42} +(1.17866 - 2.04150i) q^{43} +(0.709169 + 2.32082i) q^{44} +(-2.55463 - 1.57285i) q^{45} +(-0.588212 - 3.93781i) q^{46} +(5.97373 - 10.3468i) q^{47} +(-6.58262 + 2.16082i) q^{48} +(6.55985 + 11.3620i) q^{49} +(1.10684 - 0.880287i) q^{50} +(8.87867 - 2.24500i) q^{51} +(3.84976 + 0.889388i) q^{52} +0.739256 q^{53} +(2.64132 + 6.85736i) q^{54} +1.21337i q^{55} +(0.998212 - 12.6476i) q^{56} +(-2.06618 - 8.17146i) q^{57} +(9.31661 - 7.40964i) q^{58} +(1.70932 - 0.986877i) q^{59} +(-3.46337 + 0.0714286i) q^{60} +(-4.81044 - 2.77731i) q^{61} +(-9.77027 + 1.45944i) q^{62} +(-13.4511 - 0.380430i) q^{63} +(-5.03732 + 6.21493i) q^{64} +(1.71090 + 0.987790i) q^{65} +(1.80167 - 2.36382i) q^{66} +(1.58725 + 2.74920i) q^{67} +(7.21318 - 7.73289i) q^{68} +(-3.49648 + 3.39899i) q^{69} +(2.32532 - 5.90189i) q^{70} +3.40951 q^{71} +(6.85316 + 5.00342i) q^{72} -6.69774 q^{73} +(2.44384 - 6.20271i) q^{74} +(-1.66653 - 0.471895i) q^{75} +(-7.11695 - 6.63863i) q^{76} +(2.72129 + 4.71342i) q^{77} +(-1.86635 - 4.46478i) q^{78} +(-11.2535 - 6.49720i) q^{79} +(-3.31681 + 2.23579i) q^{80} +(4.93333 - 7.52743i) q^{81} +(8.57439 - 1.28080i) q^{82} +(-5.00954 - 2.89226i) q^{83} +(-13.2934 + 8.04493i) q^{84} +(4.57905 - 2.64371i) q^{85} +(-2.60918 + 2.07512i) q^{86} +(-14.0277 - 3.97208i) q^{87} +(0.270027 - 3.42130i) q^{88} -2.71936i q^{89} +(2.54593 + 3.39385i) q^{90} +8.86146 q^{91} +(-1.26744 + 5.48619i) q^{92} +(8.43338 + 8.67527i) q^{93} +(-13.2239 + 10.5172i) q^{94} +(-2.43314 - 4.21431i) q^{95} +(9.78140 + 0.569340i) q^{96} +(8.61075 - 14.9143i) q^{97} +(-2.74111 - 18.3505i) q^{98} +(-3.63867 - 0.102910i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.31577	−	0.518408i	−0.930390	−	0.366570i
$2$	−1.31577	−	0.518408i	−0.930390	−	0.366570i
$3$	0.424591	+	1.67920i	0.245138	+	0.969488i
$3$	0.424591	+	1.67920i	0.245138	+	0.969488i
$4$	1.46251	+	1.36421i	0.731253	+	0.682107i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.311848	−	2.42956i	0.127311	−	0.991863i
$7$	3.88456	+	2.24275i	1.46822	+	0.847680i	0.999366	−	0.0355937i	$-0.0113322\pi$
$7$	3.88456	+	2.24275i	1.46822	+	0.847680i	0.468858	+	0.883273i	$0.344666\pi$
$8$	−1.21710	−	2.55317i	−0.430311	−	0.902681i
$9$	−2.63944	+	1.42595i	−0.879815	+	0.475317i
$10$	−0.208931	−	1.39870i	−0.0660696	−	0.442306i
$11$	1.05081	+	0.606687i	0.316832	+	0.182923i	0.649980	−	0.759952i	$-0.274777\pi$
$11$	1.05081	+	0.606687i	0.316832	+	0.182923i	−0.333148	+	0.942875i	$0.608111\pi$
$12$	−1.66982	+	3.03508i	−0.482037	+	0.876151i
$13$	1.71090	−	0.987790i	0.474519	−	0.273964i	−0.243611	−	0.969873i	$-0.578332\pi$
$13$	1.71090	−	0.987790i	0.474519	−	0.273964i	0.718130	+	0.695909i	$0.244999\pi$
$14$	−3.94853	−	4.96473i	−1.05529	−	1.32688i
$15$	−1.24194	+	1.20731i	−0.320667	+	0.311726i
$16$	0.277844	+	3.99034i	0.0694611	+	0.997585i
$17$		−	5.28743i		−	1.28239i	−0.767378	−	0.641195i	$-0.778439\pi$
$17$		−	5.28743i		−	1.28239i	0.767378	−	0.641195i	$-0.221561\pi$
$18$	4.21213	−	0.507913i	0.992808	−	0.119716i
$19$	−4.86627			−1.11640			−0.558200	−	0.829707i	$-0.688508\pi$
$19$	−4.86627			−1.11640			−0.558200	+	0.829707i	$0.688508\pi$
$20$	−0.450191	+	1.94867i	−0.100666	+	0.435737i
$21$	−2.11668	+	7.47521i	−0.461898	+	1.63122i
$22$	−1.06812	−	1.34301i	−0.227723	−	0.286331i
$23$	1.40767	+	2.43816i	0.293520	+	0.508392i	0.974640	−	0.223781i	$-0.0718399\pi$
$23$	1.40767	+	2.43816i	0.293520	+	0.508392i	−0.681119	+	0.732172i	$0.738507\pi$
$24$	3.77051	−	3.12781i	0.769653	−	0.638462i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.76323	+	0.412759i	−0.541915	+	0.0809487i
$27$	−3.51514	−	3.82672i	−0.676490	−	0.736452i
$28$	2.62160	+	8.57940i	0.495435	+	1.62135i
$29$	−4.20865	+	7.28960i	−0.781527	+	1.35364i	0.149525	+	0.988758i	$0.452225\pi$
$29$	−4.20865	+	7.28960i	−0.781527	+	1.35364i	−0.931052	+	0.364886i	$0.881108\pi$
$30$	2.25998	−	0.944711i	0.412615	−	0.172480i
$31$	6.04943	−	3.49264i	1.08651	−	0.627296i	0.153864	−	0.988092i	$-0.450828\pi$
$31$	6.04943	−	3.49264i	1.08651	−	0.627296i	0.932645	+	0.360796i	$0.117495\pi$
$32$	1.70305	−	5.39441i	0.301059	−	0.953606i
$33$	−0.572584	+	2.02212i	−0.0996742	+	0.352006i
$34$	−2.74105	+	6.95704i	−0.470086	+	1.19312i
$35$			4.48550i			0.758188i
$36$	−5.80550	−	1.51531i	−0.967584	−	0.252551i
$37$			4.71412i			0.774997i	0.921870	+	0.387499i	$0.126661\pi$
$37$			4.71412i			0.774997i	−0.921870	+	0.387499i	$0.873339\pi$
$38$	6.40290	+	2.52272i	1.03869	+	0.409239i
$39$	2.38513	+	2.45355i	0.381927	+	0.392882i
$40$	1.60256	−	2.33063i	0.253386	−	0.368504i
$41$	−5.30898	+	3.06514i	−0.829123	+	0.478695i	−0.853552	−	0.521007i	$-0.825557\pi$
$41$	−5.30898	+	3.06514i	−0.829123	+	0.478695i	0.0244291	+	0.999702i	$0.492223\pi$
$42$	6.66028	−	8.73836i	1.02770	−	1.34836i
$43$	1.17866	−	2.04150i	0.179744	−	0.311326i	−0.762049	−	0.647520i	$-0.775806\pi$
$43$	1.17866	−	2.04150i	0.179744	−	0.311326i	0.941793	+	0.336194i	$0.109140\pi$
$44$	0.709169	+	2.32082i	0.106911	+	0.349876i
$45$	−2.55463	−	1.57285i	−0.380822	−	0.234467i
$46$	−0.588212	−	3.93781i	−0.0867271	−	0.580599i
$47$	5.97373	−	10.3468i	0.871358	−	1.50924i	0.0107652	−	0.999942i	$-0.496573\pi$
$47$	5.97373	−	10.3468i	0.871358	−	1.50924i	0.860593	−	0.509294i	$-0.170093\pi$
$48$	−6.58262	+	2.16082i	−0.950119	+	0.311888i
$49$	6.55985	+	11.3620i	0.937122	+	1.62314i
$50$	1.10684	−	0.880287i	0.156531	−	0.124491i
$51$	8.87867	−	2.24500i	1.24326	−	0.314362i
$52$	3.84976	+	0.889388i	0.533866	+	0.123336i
$53$	0.739256			0.101545			0.0507723	−	0.998710i	$-0.483832\pi$
$53$	0.739256			0.101545			0.0507723	+	0.998710i	$0.483832\pi$
$54$	2.64132	+	6.85736i	0.359438	+	0.933169i
$55$			1.21337i			0.163611i
$56$	0.998212	−	12.6476i	0.133392	−	1.69010i
$57$	−2.06618	−	8.17146i	−0.273672	−	1.08234i
$58$	9.31661	−	7.40964i	1.22333	−	0.972933i
$59$	1.70932	−	0.986877i	0.222535	−	0.128480i	−0.384589	−	0.923088i	$-0.625657\pi$
$59$	1.70932	−	0.986877i	0.222535	−	0.128480i	0.607123	+	0.794608i	$0.292323\pi$
$60$	−3.46337	+	0.0714286i	−0.447119	+	0.00922140i
$61$	−4.81044	−	2.77731i	−0.615914	−	0.355598i	0.159362	−	0.987220i	$-0.449056\pi$
$61$	−4.81044	−	2.77731i	−0.615914	−	0.355598i	−0.775277	+	0.631622i	$0.782389\pi$
$62$	−9.77027	+	1.45944i	−1.24083	+	0.185349i
$63$	−13.4511	−	0.380430i	−1.69468	−	0.0479296i
$64$	−5.03732	+	6.21493i	−0.629665	+	0.776866i
$65$	1.71090	+	0.987790i	0.212211	+	0.122520i
$66$	1.80167	−	2.36382i	0.221771	−	0.290966i
$67$	1.58725	+	2.74920i	0.193913	+	0.335868i	0.946544	−	0.322576i	$-0.104549\pi$
$67$	1.58725	+	2.74920i	0.193913	+	0.335868i	−0.752630	+	0.658443i	$0.771215\pi$
$68$	7.21318	−	7.73289i	0.874727	−	0.937751i
$69$	−3.49648	+	3.39899i	−0.420927	+	0.409190i
$70$	2.32532	−	5.90189i	0.277929	−	0.705411i
$71$	3.40951			0.404635			0.202317	−	0.979320i	$-0.435153\pi$
$71$	3.40951			0.404635			0.202317	+	0.979320i	$0.435153\pi$
$72$	6.85316	+	5.00342i	0.807653	+	0.589658i
$73$	−6.69774			−0.783911			−0.391956	−	0.919984i	$-0.628201\pi$
$73$	−6.69774			−0.783911			−0.391956	+	0.919984i	$0.628201\pi$
$74$	2.44384	−	6.20271i	0.284091	−	0.721050i
$75$	−1.66653	−	0.471895i	−0.192434	−	0.0544897i
$76$	−7.11695	−	6.63863i	−0.816370	−	0.761503i
$77$	2.72129	+	4.71342i	0.310120	+	0.537144i
$78$	−1.86635	−	4.46478i	−0.211323	−	0.505536i
$79$	−11.2535	−	6.49720i	−1.26612	−	0.730992i	−0.291865	−	0.956459i	$-0.594276\pi$
$79$	−11.2535	−	6.49720i	−1.26612	−	0.730992i	−0.974251	+	0.225467i	$0.927609\pi$
$80$	−3.31681	+	2.23579i	−0.370831	+	0.249969i
$81$	4.93333	−	7.52743i	0.548148	−	0.836381i
$82$	8.57439	−	1.28080i	0.946883	−	0.141441i
$83$	−5.00954	−	2.89226i	−0.549868	−	0.317467i	0.199201	−	0.979959i	$-0.436165\pi$
$83$	−5.00954	−	2.89226i	−0.549868	−	0.317467i	−0.749069	+	0.662492i	$0.769499\pi$
$84$	−13.2934	+	8.04493i	−1.45043	+	0.877774i
$85$	4.57905	−	2.64371i	0.496667	−	0.286751i
$86$	−2.60918	+	2.07512i	−0.281355	+	0.223766i
$87$	−14.0277	−	3.97208i	−1.50392	−	0.425851i
$88$	0.270027	−	3.42130i	0.0287849	−	0.364712i
$89$		−	2.71936i		−	0.288252i	−0.989559	−	0.144126i	$-0.953963\pi$
$89$		−	2.71936i		−	0.288252i	0.989559	−	0.144126i	$-0.0460370\pi$
$90$	2.54593	+	3.39385i	0.268365	+	0.357744i
$91$	8.86146			0.928934
$92$	−1.26744	+	5.48619i	−0.132140	+	0.571975i
$93$	8.43338	+	8.67527i	0.874501	+	0.899584i
$94$	−13.2239	+	10.5172i	−1.36394	+	1.08477i
$95$	−2.43314	−	4.21431i	−0.249634	−	0.432380i
$96$	9.78140	+	0.569340i	0.998310	+	0.0581080i
$97$	8.61075	−	14.9143i	0.874289	−	1.51431i	0.0167712	−	0.999859i	$-0.494661\pi$
$97$	8.61075	−	14.9143i	0.874289	−	1.51431i	0.857518	−	0.514454i	$-0.172005\pi$
$98$	−2.74111	−	18.3505i	−0.276894	−	1.85368i
$99$	−3.63867	−	0.102910i	−0.365700	−	0.0103429i
$100$	−1.91270	+	0.584460i	−0.191270	+	0.0584460i
$101$	−2.65852	+	4.60469i	−0.264532	+	0.458183i	−0.967441	−	0.253097i	$-0.918551\pi$
$101$	−2.65852	+	4.60469i	−0.264532	+	0.458183i	0.702909	+	0.711280i	$0.251884\pi$
$102$	−12.8461	−	1.64887i	−1.27195	−	0.163263i
$103$	13.2519	−	7.65097i	1.30575	−	0.753873i	0.324363	−	0.945933i	$-0.394850\pi$
$103$	13.2519	−	7.65097i	1.30575	−	0.753873i	0.981383	+	0.192060i	$0.0615169\pi$
$104$	−4.60434	−	3.16598i	−0.451492	−	0.310450i
$105$	−7.53206	+	1.90450i	−0.735054	+	0.185861i
$106$	−0.972691	−	0.383236i	−0.0944761	−	0.0372232i
$107$			7.25445i			0.701314i	0.936504	+	0.350657i	$0.114042\pi$
$107$			7.25445i			0.701314i	−0.936504	+	0.350657i	$0.885958\pi$
$108$	0.0795388	−	10.3920i	0.00765363	−	0.999971i
$109$		−	18.6200i		−	1.78347i	−0.452558	−	0.891735i	$-0.649488\pi$
$109$		−	18.6200i		−	1.78347i	0.452558	−	0.891735i	$-0.350512\pi$
$110$	0.629023	−	1.59652i	0.0599750	−	0.152222i
$111$	−7.91597	+	2.00158i	−0.751351	+	0.189981i
$112$	−7.87003	+	16.1238i	−0.743648	+	1.52356i
$113$	−5.19909	+	3.00170i	−0.489090	+	0.282376i	−0.724197	−	0.689593i	$-0.757789\pi$
$113$	−5.19909	+	3.00170i	−0.489090	+	0.282376i	0.235107	+	0.971969i	$0.424456\pi$
$114$	−1.51754	+	11.8229i	−0.142130	+	1.10731i
$115$	−1.40767	+	2.43816i	−0.131266	+	0.227360i
$116$	−16.0997	+	4.91958i	−1.49482	+	0.456771i
$117$	−3.10729	+	5.04688i	−0.287269	+	0.466584i
$118$	−2.76068	+	0.412378i	−0.254141	+	0.0379624i
$119$	11.8584	−	20.5393i	1.08706	−	1.88284i
$120$	4.59402	+	1.70145i	0.419375	+	0.155321i
$121$	−4.76386	−	8.25125i	−0.433078	−	0.750114i
$122$	4.88966	+	6.14808i	0.442689	+	0.556621i
$123$	−7.40114	−	7.61342i	−0.667338	−	0.686479i
$124$	13.6120	+	3.14471i	1.22240	+	0.282403i
$125$	−1.00000			−0.0894427
$126$	17.5014	+	7.47373i	1.55915	+	0.665813i
$127$			0.151104i			0.0134083i	0.999978	+	0.00670414i	$0.00213401\pi$
$127$			0.151104i			0.0134083i	−0.999978	+	0.00670414i	$0.997866\pi$
$128$	9.84984	−	5.56603i	0.870611	−	0.491973i
$129$	3.92854	+	1.11241i	0.345889	+	0.0979420i
$130$	−1.73908	−	2.18665i	−0.152527	−	0.191782i
$131$	14.8788	−	8.59027i	1.29997	−	0.750536i	0.319568	−	0.947563i	$-0.396462\pi$
$131$	14.8788	−	8.59027i	1.29997	−	0.750536i	0.980398	+	0.197028i	$0.0631289\pi$
$132$	−3.59601	+	2.17624i	−0.312993	+	0.189417i
$133$	−18.9033	−	10.9138i	−1.63912	−	0.946349i
$134$	−0.663249	−	4.44015i	−0.0572960	−	0.383571i
$135$	1.55646	−	4.95756i	0.133959	−	0.426679i
$136$	−13.4997	+	6.43534i	−1.15759	+	0.551826i
$137$	14.1817	+	8.18778i	1.21162	+	0.699529i	0.963112	−	0.269100i	$-0.0867264\pi$
$137$	14.1817	+	8.18778i	1.21162	+	0.699529i	0.248508	+	0.968630i	$0.420060\pi$
$138$	6.36263	−	2.65969i	0.541623	−	0.226408i
$139$	6.13746	+	10.6304i	0.520573	+	0.901658i	0.999714	+	0.0239203i	$0.00761480\pi$
$139$	6.13746	+	10.6304i	0.520573	+	0.901658i	−0.479141	+	0.877738i	$0.659052\pi$
$140$	−6.11918	+	6.56007i	−0.517165	+	0.554427i
$141$	19.9108	+	5.63794i	1.67679	+	0.474800i
$142$	−4.48614	−	1.76752i	−0.376468	−	0.148327i
$143$	2.39712			0.200457
$144$	−6.42338	−	10.1361i	−0.535282	−	0.844674i
$145$	−8.41730			−0.699019
$146$	8.81269	+	3.47217i	0.729344	+	0.287358i
$147$	−16.2938	+	15.8395i	−1.34389	+	1.30642i
$148$	−6.43107	+	6.89443i	−0.528631	+	0.566719i
$149$	10.4468	+	18.0944i	0.855836	+	1.48235i	0.875868	+	0.482552i	$0.160290\pi$
$149$	10.4468	+	18.0944i	0.855836	+	1.48235i	−0.0200319	+	0.999799i	$0.506377\pi$
$150$	1.94813	+	1.48485i	0.159065	+	0.121237i
$151$	2.72496	+	1.57326i	0.221754	+	0.128030i	0.606762	−	0.794883i	$-0.292468\pi$
$151$	2.72496	+	1.57326i	0.221754	+	0.128030i	−0.385008	+	0.922913i	$0.625801\pi$
$152$	5.92275	+	12.4244i	0.480398	+	1.00775i
$153$	7.53961	+	13.9559i	0.609541	+	1.12827i
$154$	−1.13712	−	7.61252i	−0.0916320	−	0.613434i
$155$	6.04943	+	3.49264i	0.485902	+	0.280535i
$156$	0.141113	+	6.84216i	0.0112981	+	0.547811i
$157$	9.64516	−	5.56863i	0.769767	−	0.444425i	−0.0630243	−	0.998012i	$-0.520075\pi$
$157$	9.64516	−	5.56863i	0.769767	−	0.444425i	0.832792	+	0.553587i	$0.186741\pi$
$158$	11.4388	+	14.3827i	0.910022	+	1.14423i
$159$	0.313882	+	1.24136i	0.0248924	+	0.0984463i
$160$	5.52322	−	1.22232i	0.436649	−	0.0966331i
$161$			12.6282i			0.995244i
$162$	−10.3934	+	7.34689i	−0.816584	+	0.577226i
$163$	−0.567815			−0.0444747			−0.0222373	−	0.999753i	$-0.507079\pi$
$163$	−0.567815			−0.0444747			−0.0222373	+	0.999753i	$0.507079\pi$
$164$	−11.9459	−	2.75980i	−0.932819	−	0.215504i
$165$	−2.03750	+	0.515188i	−0.158619	+	0.0401073i
$166$	5.09203	+	6.40254i	0.395218	+	0.496933i
$167$	9.59132	+	16.6127i	0.742199	+	1.28553i	0.951492	+	0.307673i	$0.0995503\pi$
$167$	9.59132	+	16.6127i	0.742199	+	1.28553i	−0.209293	+	0.977853i	$0.567116\pi$
$168$	21.6617	−	3.69385i	1.67124	−	0.284987i
$169$	−4.54854	+	7.87831i	−0.349888	+	0.606023i
$170$	−7.39550	+	1.10471i	−0.567209	+	0.0847270i
$171$	12.8443	−	6.93906i	0.982224	−	0.530643i
$172$	4.50884	−	1.37776i	0.343796	−	0.105053i
$173$	−0.727868	+	1.26070i	−0.0553388	+	0.0958496i	−0.892368	−	0.451309i	$-0.850957\pi$
$173$	−0.727868	+	1.26070i	−0.0553388	+	0.0958496i	0.837029	+	0.547159i	$0.184291\pi$
$174$	16.3980	+	12.4984i	1.24313	+	0.947502i
$175$	−3.88456	+	2.24275i	−0.293645	+	0.169536i
$176$	−2.12892	+	4.36166i	−0.160474	+	0.328773i
$177$	2.38293	+	2.45128i	0.179112	+	0.184249i
$178$	−1.40974	+	3.57806i	−0.105665	+	0.268187i
$179$		−	21.1074i		−	1.57764i	−0.614623	−	0.788821i	$-0.710692\pi$
$179$		−	21.1074i		−	1.57764i	0.614623	−	0.788821i	$-0.289308\pi$
$180$	−1.59046	−	5.78536i	−0.118546	−	0.431216i
$181$		−	8.53010i		−	0.634037i	−0.948419	−	0.317019i	$-0.897318\pi$
$181$		−	8.53010i		−	0.634037i	0.948419	−	0.317019i	$-0.102682\pi$
$182$	−11.6597	−	4.59386i	−0.864271	−	0.340519i
$183$	2.62120	−	9.25693i	0.193764	−	0.684292i
$184$	4.51175	−	6.56152i	0.332611	−	0.483721i
$185$	−4.08255	+	2.35706i	−0.300155	+	0.173295i
$186$	−6.59906	−	15.7866i	−0.483867	−	1.15753i
$187$	3.20781	−	5.55610i	0.234579	−	0.406302i
$188$	22.8519	−	6.98281i	1.66664	−	0.509274i
$189$	−5.07241	−	22.7487i	−0.368964	−	1.65472i
$190$	1.01671	+	6.80643i	0.0737601	+	0.493790i
$191$	0.214023	−	0.370698i	0.0154861	−	0.0268228i	−0.858178	−	0.513351i	$-0.828404\pi$
$191$	0.214023	−	0.370698i	0.0154861	−	0.0268228i	0.873665	+	0.486529i	$0.161737\pi$
$192$	−12.5749	−	5.81988i	−0.907518	−	0.420014i
$193$	−4.74084	−	8.21138i	−0.341253	−	0.591068i	0.643412	−	0.765520i	$-0.277518\pi$
$193$	−4.74084	−	8.21138i	−0.341253	−	0.591068i	−0.984666	+	0.174452i	$0.944185\pi$
$194$	−19.0614	+	15.1599i	−1.36853	+	1.08841i
$195$	−0.932265	+	3.29236i	−0.0667609	+	0.235771i
$196$	−5.90637	+	25.5660i	−0.421884	+	1.82615i
$197$	−4.16402			−0.296674			−0.148337	−	0.988937i	$-0.547392\pi$
$197$	−4.16402			−0.296674			−0.148337	+	0.988937i	$0.547392\pi$
$198$	4.73430	+	2.02172i	0.336452	+	0.143677i
$199$			20.4857i			1.45219i	0.687594	+	0.726095i	$0.258667\pi$
$199$			20.4857i			1.45219i	−0.687594	+	0.726095i	$0.741333\pi$
$200$	2.81966	+	0.222542i	0.199380	+	0.0157361i
$201$	−3.94252	+	3.83260i	−0.278084	+	0.270331i
$202$	5.88511	−	4.68051i	0.414075	−	0.329320i
$203$	−32.6975	+	18.8779i	−2.29491	+	1.32497i
$204$	16.0478	+	8.82907i	1.12357	+	0.618159i
$205$	−5.30898	−	3.06514i	−0.370795	−	0.214079i
$206$	−21.4028	+	3.19704i	−1.49120	+	0.222749i
$207$	−7.19217	−	4.42812i	−0.499890	−	0.307776i
$208$	4.41698	+	6.55263i	0.306263	+	0.454343i
$209$	−5.11354	−	2.95230i	−0.353711	−	0.204215i
$210$	10.8978	+	1.39879i	0.752018	+	0.0965260i
$211$	−12.8150	−	22.1963i	−0.882222	−	1.52805i	−0.848865	−	0.528610i	$-0.822713\pi$
$211$	−12.8150	−	22.1963i	−0.882222	−	1.52805i	−0.0333576	−	0.999443i	$-0.510620\pi$
$212$	1.08117	+	1.00850i	0.0742548	+	0.0692642i
$213$	1.44765	+	5.72527i	0.0991914	+	0.392289i
$214$	3.76077	−	9.54520i	0.257081	−	0.652496i
$215$	2.35732			0.160768
$216$	−5.49196	+	13.6323i	−0.373680	+	0.927558i
$217$	31.3325			2.12699
$218$	−9.65275	+	24.4996i	−0.653767	+	1.65932i
$219$	−2.84380	−	11.2469i	−0.192166	−	0.759993i
$220$	−1.65530	+	1.77457i	−0.111600	+	0.119641i
$221$	−5.22287	−	9.04628i	−0.351328	−	0.608518i
$222$	11.4532	+	1.47009i	0.768691	+	0.0986660i
$223$	0.577728	+	0.333551i	0.0386875	+	0.0223363i	0.519219	−	0.854641i	$-0.326223\pi$
$223$	0.577728	+	0.333551i	0.0386875	+	0.0223363i	−0.480531	+	0.876977i	$0.659556\pi$
$224$	18.7139	−	17.1354i	1.25037	−	1.14491i
$225$	0.0848132	−	2.99880i	0.00565421	−	0.199920i
$226$	8.39692	−	1.25429i	0.558555	−	0.0834343i
$227$	3.21685	+	1.85725i	0.213510	+	0.123270i	0.602941	−	0.797785i	$-0.293995\pi$
$227$	3.21685	+	1.85725i	0.213510	+	0.123270i	−0.389432	+	0.921055i	$0.627329\pi$
$228$	8.12581	−	14.7695i	0.538145	−	0.978134i
$229$	−5.27024	+	3.04277i	−0.348267	+	0.201072i	−0.663922	−	0.747802i	$-0.731109\pi$
$229$	−5.27024	+	3.04277i	−0.348267	+	0.201072i	0.315655	+	0.948874i	$0.397776\pi$
$230$	3.11614	−	2.47831i	0.205472	−	0.163415i
$231$	−6.75935	+	6.57088i	−0.444733	+	0.432332i
$232$	23.7339	+	1.87320i	1.55821	+	0.122982i
$233$		−	11.4524i		−	0.750269i	−0.926970	−	0.375134i	$-0.877597\pi$
$233$		−	11.4524i		−	0.750269i	0.926970	−	0.375134i	$-0.122403\pi$
$234$	6.70483	−	5.02969i	0.438308	−	0.328801i
$235$	11.9475			0.779366
$236$	3.84620	+	0.888566i	0.250367	+	0.0578407i
$237$	6.13199	−	21.6555i	0.398315	−	1.40668i
$238$	−26.2507	+	20.8776i	−1.70158	+	1.35329i
$239$	5.82006	+	10.0806i	0.376468	+	0.652062i	0.990546	−	0.137184i	$-0.0438050\pi$
$239$	5.82006	+	10.0806i	0.376468	+	0.652062i	−0.614077	+	0.789246i	$0.710472\pi$
$240$	−5.16263	−	4.62030i	−0.333247	−	0.298239i
$241$	3.24695	−	5.62388i	0.209154	−	0.362266i	−0.742294	−	0.670074i	$-0.766262\pi$
$241$	3.24695	−	5.62388i	0.209154	−	0.362266i	0.951448	+	0.307808i	$0.0995955\pi$
$242$	1.99063	+	13.3264i	0.127963	+	0.856652i
$243$	14.7347	+	5.08798i	0.945234	+	0.326394i
$244$	−3.24646	−	10.6243i	−0.207833	−	0.680151i
$245$	−6.55985	+	11.3620i	−0.419094	+	0.725892i
$246$	5.79134	+	13.8543i	0.369242	+	0.883320i
$247$	−8.32572	+	4.80685i	−0.529753	+	0.305853i
$248$	−16.2801	−	11.1943i	−1.03378	−	0.710839i
$249$	2.72968	−	9.64006i	0.172987	−	0.610914i
$250$	1.31577	+	0.518408i	0.0832167	+	0.0327870i
$251$		−	3.49601i		−	0.220666i	−0.993895	−	0.110333i	$-0.964808\pi$
$251$		−	3.49601i		−	0.220666i	0.993895	−	0.110333i	$-0.0351917\pi$
$252$	−19.1534	−	18.9066i	−1.20655	−	1.19100i
$253$			3.41607i			0.214766i
$254$	0.0783334	−	0.198818i	0.00491507	−	0.0124749i
$255$	6.38356	+	6.56665i	0.399754	+	0.411220i
$256$	−15.8456	+	2.21739i	−0.990350	+	0.138587i
$257$	−2.88796	+	1.66737i	−0.180146	+	0.104007i	−0.587361	−	0.809325i	$-0.699833\pi$
$257$	−2.88796	+	1.66737i	−0.180146	+	0.104007i	0.407215	+	0.913332i	$0.366500\pi$
$258$	−4.59238	−	3.50026i	−0.285909	−	0.217917i
$259$	−10.5726	+	18.3123i	−0.656949	+	1.13787i
$260$	1.15465	+	3.77868i	0.0716082	+	0.234344i
$261$	0.713898	−	25.2418i	0.0441892	−	1.56243i
$262$	−24.0303	+	3.58954i	−1.48460	+	0.221763i
$263$	6.66510	−	11.5443i	0.410988	−	0.711852i	−0.584010	−	0.811746i	$-0.698517\pi$
$263$	6.66510	−	11.5443i	0.410988	−	0.711852i	0.994998	+	0.0998946i	$0.0318505\pi$
$264$	5.85971	−	0.999225i	0.360640	−	0.0614980i
$265$	0.369628	+	0.640214i	0.0227061	+	0.0393280i
$266$	19.2146	+	24.1597i	1.17812	+	1.48133i
$267$	4.56636	−	1.15462i	0.279457	−	0.0706615i
$268$	−1.42913	+	6.18606i	−0.0872979	+	0.377874i
$269$	−1.95866			−0.119421			−0.0597107	−	0.998216i	$-0.519018\pi$
$269$	−1.95866			−0.119421			−0.0597107	+	0.998216i	$0.519018\pi$
$270$	−4.61799	+	5.71613i	−0.281042	+	0.347873i
$271$			22.5736i			1.37125i	0.727955	+	0.685625i	$0.240471\pi$
$271$			22.5736i			1.37125i	−0.727955	+	0.685625i	$0.759529\pi$
$272$	21.0986	−	1.46908i	1.27929	−	0.0890762i
$273$	3.76250	+	14.8802i	0.227717	+	0.900590i
$274$	−14.4152	−	18.1251i	−0.870853	−	1.09498i
$275$	−1.05081	+	0.606687i	−0.0633664	+	0.0365846i
$276$	−9.75057	+	0.201096i	−0.586916	+	0.0121046i
$277$	−20.8634	−	12.0455i	−1.25356	−	0.723744i	−0.281746	−	0.959489i	$-0.590914\pi$
$277$	−20.8634	−	12.0455i	−1.25356	−	0.723744i	−0.971815	+	0.235745i	$0.924247\pi$
$278$	−2.56461	−	17.1689i	−0.153815	−	1.02972i
$279$	−10.9868	+	17.8448i	−0.657762	+	1.06834i
$280$	11.4522	−	5.45931i	0.684402	−	0.326256i
$281$	−26.4445	−	15.2677i	−1.57755	−	0.910796i	−0.995201	−	0.0978540i	$-0.968802\pi$
$281$	−26.4445	−	15.2677i	−1.57755	−	0.910796i	−0.582344	−	0.812942i	$-0.697864\pi$
$282$	−23.2753	−	17.7401i	−1.38602	−	1.05641i
$283$	3.84951	+	6.66756i	0.228830	+	0.396345i	0.957462	−	0.288561i	$-0.0931767\pi$
$283$	3.84951	+	6.66756i	0.228830	+	0.396345i	−0.728632	+	0.684906i	$0.759843\pi$
$284$	4.98643	+	4.65130i	0.295890	+	0.276004i
$285$	6.04360	−	5.87509i	0.357992	−	0.348010i
$286$	−3.15406	−	1.24269i	−0.186503	−	0.0734815i
$287$	−27.4974			−1.62312
$288$	3.19706	+	16.6667i	0.188389	+	0.982095i
$289$	−10.9569			−0.644524
$290$	11.0752	+	4.36360i	0.650360	+	0.256239i
$291$	28.7001	+	8.12673i	1.68243	+	0.476397i
$292$	−9.79548	−	9.13715i	−0.573237	−	0.534711i
$293$	−9.03781	−	15.6539i	−0.527994	−	0.914513i	−0.999467	−	0.0326326i	$-0.989611\pi$
$293$	−9.03781	−	15.6539i	−0.527994	−	0.914513i	0.471473	−	0.881880i	$-0.343722\pi$
$294$	29.6503	−	12.3943i	1.72924	−	0.722852i
$295$	1.70932	+	0.986877i	0.0995206	+	0.0574582i
$296$	12.0359	−	5.73757i	0.699575	−	0.333490i
$297$	−1.37214	−	6.15375i	−0.0796196	−	0.357077i
$298$	−4.36531	−	29.2238i	−0.252876	−	1.69289i
$299$	4.81678	+	2.78097i	0.278562	+	0.160828i
$300$	−1.79354	−	2.96365i	−0.103550	−	0.171106i
$301$	9.15715	−	5.28688i	0.527809	−	0.304731i
$302$	−2.76983	−	3.48269i	−0.159386	−	0.200406i
$303$	−8.86099	−	2.50908i	−0.509050	−	0.144143i
$304$	−1.35207	−	19.4181i	−0.0775463	−	1.11370i
$305$		−	5.55462i		−	0.318057i
$306$	−2.68556	−	22.2713i	−0.153523	−	1.27317i
$307$	−23.7235			−1.35397			−0.676986	−	0.735996i	$-0.736714\pi$
$307$	−23.7235			−1.35397			−0.676986	+	0.735996i	$0.736714\pi$
$308$	−2.45020	+	10.6058i	−0.139613	+	0.604323i
$309$	18.4742	+	19.0040i	1.05096	+	1.08110i
$310$	−6.14905	−	7.73158i	−0.349242	−	0.439124i
$311$	6.24004	+	10.8081i	0.353840	+	0.612869i	0.986919	−	0.161219i	$-0.0515424\pi$
$311$	6.24004	+	10.8081i	0.353840	+	0.612869i	−0.633079	+	0.774087i	$0.718209\pi$
$312$	3.36136	−	9.07586i	0.190299	−	0.513820i
$313$	−7.40717	+	12.8296i	−0.418678	+	0.725171i	−0.995807	−	0.0914817i	$-0.970840\pi$
$313$	−7.40717	+	12.8296i	−0.418678	+	0.725171i	0.577129	+	0.816653i	$0.304173\pi$
$314$	−15.5776	+	2.32692i	−0.879097	+	0.131315i
$315$	−6.39610	−	11.8392i	−0.360379	−	0.667065i
$316$	−7.59471	−	24.8543i	−0.427236	−	1.39817i
$317$	−11.5991	+	20.0903i	−0.651473	+	1.12838i	0.331292	+	0.943528i	$0.392515\pi$
$317$	−11.5991	+	20.0903i	−0.651473	+	1.12838i	−0.982766	+	0.184856i	$0.940818\pi$
$318$	0.230535	−	1.79606i	0.0129278	−	0.100718i
$319$	−8.84500	+	5.10667i	−0.495225	+	0.285918i
$320$	−7.90095	−	1.25498i	−0.441677	−	0.0701558i
$321$	−12.1817	+	3.08018i	−0.679916	+	0.171919i
$322$	6.54658	−	16.6159i	0.364827	−	0.925966i
$323$			25.7301i			1.43166i
$324$	17.4840	−	4.27879i	0.971336	−	0.237711i
$325$			1.97558i			0.109585i
$326$	0.747114	+	0.294360i	0.0413788	+	0.0163031i
$327$	31.2667	−	7.90588i	1.72905	−	0.437196i
$328$	14.2874	+	9.82412i	0.788889	+	0.542446i
$329$	46.4106	−	26.7952i	2.55870	−	1.47726i
$330$	2.94796	+	0.378388i	0.162280	+	0.0208296i
$331$	3.40861	−	5.90389i	0.187354	−	0.324507i	−0.757013	−	0.653400i	$-0.773342\pi$
$331$	3.40861	−	5.90389i	0.187354	−	0.324507i	0.944367	+	0.328893i	$0.106675\pi$
$332$	−3.38082	−	11.0640i	−0.185547	−	0.607217i
$333$	−6.72210	−	12.4427i	−0.368369	−	0.681854i
$334$	−4.00784	−	26.8307i	−0.219299	−	1.46811i
$335$	−1.58725	+	2.74920i	−0.0867207	+	0.150205i
$336$	−30.4167	−	6.36934i	−1.65937	−	0.347476i
$337$	4.18185	+	7.24318i	0.227800	+	0.394561i	0.957156	−	0.289573i	$-0.0935134\pi$
$337$	4.18185	+	7.24318i	0.227800	+	0.394561i	−0.729356	+	0.684135i	$0.760180\pi$
$338$	10.0690	−	8.00804i	0.547682	−	0.435580i
$339$	−7.24795	−	7.45584i	−0.393655	−	0.404945i
$340$	10.3035	+	2.38035i	0.558784	+	0.129093i
$341$	8.47575			0.458988
$342$	−20.4974	+	2.47164i	−1.10837	+	0.133651i
$343$			27.4500i			1.48216i
$344$	−6.64684	−	0.524603i	−0.358374	−	0.0282847i
$345$	−4.69185	−	1.32855i	−0.252601	−	0.0715265i
$346$	1.61127	−	1.28147i	0.0866223	−	0.0688920i
$347$	−12.4465	+	7.18596i	−0.668161	+	0.385763i	−0.795379	−	0.606112i	$-0.792728\pi$
$347$	−12.4465	+	7.18596i	−0.668161	+	0.385763i	0.127219	+	0.991875i	$0.459395\pi$
$348$	−15.0968	−	24.9459i	−0.809272	−	1.33724i
$349$	5.20288	+	3.00388i	0.278504	+	0.160794i	0.632746	−	0.774360i	$-0.281928\pi$
$349$	5.20288	+	3.00388i	0.278504	+	0.160794i	−0.354242	+	0.935154i	$0.615261\pi$
$350$	6.27385	−	0.937158i	0.335351	−	0.0500932i
$351$	−9.79406	−	3.07491i	−0.522768	−	0.164127i
$352$	5.06230	−	4.63530i	0.269821	−	0.247062i
$353$	−12.6839	−	7.32305i	−0.675096	−	0.389767i	0.122909	−	0.992418i	$-0.460778\pi$
$353$	−12.6839	−	7.32305i	−0.675096	−	0.389767i	−0.798005	+	0.602651i	$0.794111\pi$
$354$	−1.86463	−	4.46065i	−0.0991038	−	0.237081i
$355$	1.70476	+	2.95273i	0.0904791	+	0.156714i
$356$	3.70979	−	3.97708i	0.196619	−	0.210785i
$357$	39.5246	+	11.1918i	2.09187	+	0.592333i
$358$	−10.9423	+	27.7725i	−0.578316	+	1.46782i
$359$	−0.983893			−0.0519279			−0.0259639	−	0.999663i	$-0.508266\pi$
$359$	−0.983893			−0.0519279			−0.0259639	+	0.999663i	$0.508266\pi$
$360$	−0.906503	+	8.43672i	−0.0477769	+	0.444654i
$361$	4.68059			0.246347
$362$	−4.42207	+	11.2237i	−0.232419	+	0.589902i
$363$	11.8328	−	11.5029i	0.621062	−	0.603746i
$364$	12.9599	+	12.0889i	0.679285	+	0.633632i
$365$	−3.34887	−	5.80041i	−0.175288	−	0.303608i
$366$	−8.24776	+	10.8211i	−0.431117	+	0.565631i
$367$	22.8347	+	13.1836i	1.19196	+	0.688180i	0.958751	−	0.284246i	$-0.0917433\pi$
$367$	22.8347	+	13.1836i	1.19196	+	0.688180i	0.233211	+	0.972426i	$0.425077\pi$
$368$	−9.33798	+	6.29452i	−0.486776	+	0.328125i
$369$	9.64202	−	15.6606i	0.501943	−	0.815259i
$370$	6.59362	−	0.984924i	0.342786	−	0.0512038i
$371$	2.87168	+	1.65797i	0.149090	+	0.0860773i
$372$	0.498949	+	24.1926i	0.0258693	+	1.25433i
$373$	−0.428139	+	0.247186i	−0.0221682	+	0.0127988i	−0.511043	−	0.859555i	$-0.670741\pi$
$373$	−0.428139	+	0.247186i	−0.0221682	+	0.0127988i	0.488875	+	0.872354i	$0.337407\pi$
$374$	−7.10107	+	5.64759i	−0.367188	+	0.292030i
$375$	−0.424591	−	1.67920i	−0.0219258	−	0.0867137i
$376$	−33.6877	−	2.65881i	−1.73731	−	0.137118i
$377$			16.6291i			0.856440i
$378$	−5.11898	+	32.5616i	−0.263292	+	1.67479i
$379$	−20.0342			−1.02909			−0.514544	−	0.857464i	$-0.672039\pi$
$379$	−20.0342			−1.02909			−0.514544	+	0.857464i	$0.672039\pi$
$380$	2.19075	−	9.48277i	0.112383	−	0.486456i
$381$	−0.253734	+	0.0641573i	−0.0129992	+	0.00328688i
$382$	−0.473778	+	0.376802i	−0.0242406	+	0.0192789i
$383$	−7.16431	−	12.4089i	−0.366079	−	0.634068i	0.622870	−	0.782326i	$-0.285967\pi$
$383$	−7.16431	−	12.4089i	−0.366079	−	0.634068i	−0.988949	+	0.148258i	$0.952633\pi$
$384$	13.5287	+	14.1766i	0.690381	+	0.723446i
$385$	−2.72129	+	4.71342i	−0.138690	+	0.240218i
$386$	1.98101	+	13.2620i	0.100831	+	0.675017i
$387$	−0.199932	+	7.06914i	−0.0101631	+	0.359345i
$388$	32.9395	−	10.0653i	1.67225	−	0.510987i
$389$	7.19727	−	12.4660i	0.364916	−	0.632053i	−0.623847	−	0.781547i	$-0.714431\pi$
$389$	7.19727	−	12.4660i	0.364916	−	0.632053i	0.988763	+	0.149494i	$0.0477643\pi$
$390$	2.93343	−	3.84870i	0.148540	−	0.194886i
$391$	12.8916	−	7.44297i	0.651957	−	0.376407i
$392$	21.0251	−	30.5771i	1.06193	−	1.54438i
$393$	20.7422	+	21.3371i	1.04631	+	1.07632i
$394$	5.47890	+	2.15866i	0.276023	+	0.108752i
$395$		−	12.9944i		−	0.653820i
$396$	−5.18118	−	5.11442i	−0.260364	−	0.257009i
$397$			12.1034i			0.607454i	0.952759	+	0.303727i	$0.0982311\pi$
$397$			12.1034i			0.607454i	−0.952759	+	0.303727i	$0.901769\pi$
$398$	10.6199	−	26.9544i	0.532330	−	1.35110i
$399$	10.3004	−	36.3764i	0.515663	−	1.82110i
$400$	−3.59466	−	1.75455i	−0.179733	−	0.0877274i
$401$	−14.6874	+	8.47977i	−0.733454	+	0.423460i	−0.819684	−	0.572816i	$-0.805851\pi$
$401$	−14.6874	+	8.47977i	−0.733454	+	0.423460i	0.0862307	+	0.996275i	$0.472518\pi$
$402$	7.17431	−	2.99898i	0.357822	−	0.149576i
$403$	6.89999	−	11.9511i	0.343713	−	0.595328i
$404$	−10.1699	+	3.10760i	−0.505970	+	0.154609i
$405$	8.98561	+	0.508676i	0.446499	+	0.0252763i
$406$	52.8089	−	7.88834i	2.62086	−	0.391492i
$407$	−2.86000	+	4.95366i	−0.141765	+	0.245544i
$408$	−16.5381	−	19.9363i	−0.818758	−	0.986995i
$409$	12.3239	+	21.3456i	0.609376	+	1.05547i	0.991343	+	0.131294i	$0.0419132\pi$
$409$	12.3239	+	21.3456i	0.609376	+	1.05547i	−0.381968	+	0.924176i	$0.624753\pi$
$410$	5.39641	+	6.78524i	0.266509	+	0.335099i
$411$	−7.72754	+	27.2903i	−0.381171	+	1.34613i
$412$	29.8185	+	6.88879i	1.46905	+	0.339386i
$413$	8.85328			0.435641
$414$	7.16767	+	9.55487i	0.352272	+	0.469596i
$415$		−	5.78452i		−	0.283951i
$416$	−2.41480	−	10.9116i	−0.118395	−	0.534983i
$417$	−15.2447	+	14.8196i	−0.746535	+	0.725720i
$418$	5.19775	+	6.53545i	0.254230	+	0.319660i
$419$	22.0686	−	12.7413i	1.07812	−	0.622455i	0.147734	−	0.989027i	$-0.452802\pi$
$419$	22.0686	−	12.7413i	1.07812	−	0.622455i	0.930390	+	0.366572i	$0.119469\pi$
$420$	−13.6138	−	7.48999i	−0.664287	−	0.365474i
$421$	−2.84113	−	1.64033i	−0.138468	−	0.0799446i	0.429166	−	0.903226i	$-0.358808\pi$
$421$	−2.84113	−	1.64033i	−0.138468	−	0.0799446i	−0.567634	+	0.823281i	$0.692141\pi$
$422$	5.35490	+	35.8486i	0.260672	+	1.74508i
$423$	−1.01330	+	35.8280i	−0.0492684	+	1.74202i
$424$	−0.899750	−	1.88744i	−0.0436957	−	0.0916624i
$425$	4.57905	+	2.64371i	0.222116	+	0.128239i
$426$	1.06325	−	8.28361i	0.0515146	−	0.401342i
$427$	−12.4576	−	21.5772i	−0.602867	−	1.04420i
$428$	−9.89662	+	10.6097i	−0.478371	+	0.512838i
$429$	1.01780	+	4.02525i	0.0491396	+	0.194341i
$430$	−3.10170	−	1.22206i	−0.149577	−	0.0589327i
$431$	−10.5731			−0.509290			−0.254645	−	0.967035i	$-0.581959\pi$
$431$	−10.5731			−0.509290			−0.254645	+	0.967035i	$0.581959\pi$
$432$	14.2932	−	15.0898i	0.687683	−	0.726011i
$433$	−10.9701			−0.527191			−0.263596	−	0.964633i	$-0.584908\pi$
$433$	−10.9701			−0.527191			−0.263596	+	0.964633i	$0.584908\pi$
$434$	−41.2263	−	16.2430i	−1.97893	−	0.779689i
$435$	−3.57391	−	14.1344i	−0.171356	−	0.677690i
$436$	25.4016	−	27.2318i	1.21652	−	1.30417i
$437$	−6.85012	−	11.8648i	−0.327686	−	0.567568i
$438$	−2.08868	+	16.2726i	−0.0998008	+	0.777533i
$439$	8.06638	+	4.65712i	0.384987	+	0.222272i	0.679986	−	0.733225i	$-0.261986\pi$
$439$	8.06638	+	4.65712i	0.384987	+	0.222272i	−0.294999	+	0.955498i	$0.595319\pi$
$440$	3.09795	−	1.47680i	0.147689	−	0.0704037i
$441$	−33.5160	−	20.6353i	−1.59600	−	0.982636i
$442$	2.18243	+	14.6104i	0.103808	+	0.694946i
$443$	−1.06647	−	0.615728i	−0.0506696	−	0.0292541i	0.474451	−	0.880282i	$-0.342647\pi$
$443$	−1.06647	−	0.615728i	−0.0506696	−	0.0292541i	−0.525121	+	0.851028i	$0.675980\pi$
$444$	−14.3077	−	7.87175i	−0.679015	−	0.373577i
$445$	2.35504	−	1.35968i	0.111639	−	0.0644551i
$446$	−0.587242	−	0.738376i	−0.0278067	−	0.0349631i
$447$	−25.9485	+	25.2250i	−1.22732	+	1.19310i
$448$	−33.5063	+	12.8448i	−1.58302	+	0.606860i
$449$			6.49670i			0.306598i	0.988180	+	0.153299i	$0.0489898\pi$
$449$			6.49670i			0.306598i	−0.988180	+	0.153299i	$0.951010\pi$
$450$	−1.66620	+	3.90177i	−0.0785453	+	0.183931i
$451$	−7.43832			−0.350257
$452$	−11.6987	−	2.70267i	−0.550259	−	0.127123i
$453$	−1.48482	+	5.24375i	−0.0697630	+	0.246373i
$454$	−3.26982	−	4.11136i	−0.153460	−	0.192955i
$455$	4.43073	+	7.67425i	0.207716	+	0.359775i
$456$	−18.3483	+	15.2208i	−0.859240	+	0.712779i
$457$	11.9191	−	20.6444i	0.557550	−	0.965706i	−0.440150	−	0.897924i	$-0.645075\pi$
$457$	11.9191	−	20.6444i	0.557550	−	0.965706i	0.997700	−	0.0677813i	$-0.0215920\pi$
$458$	8.51183	−	1.27146i	0.397731	−	0.0594113i
$459$	−20.2335	+	18.5861i	−0.944418	+	0.867524i
$460$	−5.38490	+	1.64546i	−0.251072	+	0.0767199i
$461$	−8.00659	+	13.8678i	−0.372904	+	0.645889i	−0.990011	−	0.140991i	$-0.954971\pi$
$461$	−8.00659	+	13.8678i	−0.372904	+	0.645889i	0.617107	+	0.786879i	$0.288305\pi$
$462$	12.3002	−	5.14167i	0.572255	−	0.239212i
$463$	−24.9383	+	14.3982i	−1.15898	+	0.669139i	−0.951060	−	0.309006i	$-0.900004\pi$
$463$	−24.9383	+	14.3982i	−1.15898	+	0.669139i	−0.207923	+	0.978145i	$0.566670\pi$
$464$	−30.2573	−	14.7686i	−1.40466	−	0.685613i
$465$	−3.29631	+	11.6412i	−0.152863	+	0.539846i
$466$	−5.93700	+	15.0687i	−0.275026	+	0.698043i
$467$		−	27.0588i		−	1.25213i	−0.779769	−	0.626067i	$-0.784664\pi$
$467$		−	27.0588i		−	1.25213i	0.779769	−	0.626067i	$-0.215336\pi$
$468$	−11.4295	+	3.14208i	−0.528327	+	0.145243i
$469$			14.2392i			0.657505i
$470$	−15.7201	−	6.19366i	−0.725115	−	0.285692i
$471$	13.4461	+	13.8318i	0.619564	+	0.637335i
$472$	−4.60008	−	3.16305i	−0.211736	−	0.145591i
$473$	2.47710	−	1.43016i	0.113897	−	0.0657587i
$474$	−19.2947	+	25.3149i	−0.886235	+	1.16275i
$475$	2.43314	−	4.21431i	0.111640	−	0.193366i
$476$	45.3630	−	13.8615i	2.07921	−	0.635341i
$477$	−1.95122	+	1.05414i	−0.0893404	+	0.0482658i
$478$	−2.43198	−	16.2810i	−0.111236	−	0.744675i
$479$	−5.93681	+	10.2829i	−0.271260	+	0.469836i	−0.969185	−	0.246335i	$-0.920774\pi$
$479$	−5.93681	+	10.2829i	−0.271260	+	0.469836i	0.697925	+	0.716171i	$0.254107\pi$
$480$	4.39764	+	8.75561i	0.200724	+	0.399637i
$481$	4.65656	+	8.06541i	0.212321	+	0.367751i
$482$	−7.18771	+	5.71649i	−0.327391	+	0.260379i
$483$	−21.2054	+	5.36184i	−0.964878	+	0.243972i
$484$	4.28929	−	18.5664i	0.194968	−	0.843928i
$485$	17.2215			0.781988
$486$	−16.7499	−	14.3332i	−0.759790	−	0.650169i
$487$		−	11.2361i		−	0.509158i	−0.967052	−	0.254579i	$-0.918063\pi$
$487$		−	11.2361i		−	0.509158i	0.967052	−	0.254579i	$-0.0819369\pi$
$488$	−1.23614	+	15.6621i	−0.0559573	+	0.708992i
$489$	−0.241089	−	0.953476i	−0.0109024	−	0.0431177i
$490$	14.5214	−	11.5491i	0.656011	−	0.521735i
$491$	26.2016	−	15.1275i	1.18246	−	0.682694i	0.225877	−	0.974156i	$-0.427475\pi$
$491$	26.2016	−	15.1275i	1.18246	−	0.682694i	0.956582	+	0.291462i	$0.0941418\pi$
$492$	−0.437878	−	21.2314i	−0.0197410	−	0.957186i
$493$	38.5432	+	22.2529i	1.73590	+	1.00222i
$494$	13.4466	−	2.00860i	0.604993	−	0.0903711i
$495$	−1.73021	−	3.20263i	−0.0777672	−	0.143948i
$496$	15.6176	+	23.1688i	0.701251	+	1.04031i
$497$	13.2445	+	7.64669i	0.594095	+	0.343001i
$498$	−8.58912	+	11.2690i	−0.384888	+	0.504977i
$499$	4.81293	+	8.33624i	0.215456	+	0.373182i	0.953414	−	0.301666i	$-0.0975427\pi$
$499$	4.81293	+	8.33624i	0.215456	+	0.373182i	−0.737957	+	0.674847i	$0.764209\pi$
$500$	−1.46251	−	1.36421i	−0.0654052	−	0.0610095i
$501$	−23.8236	+	23.1594i	−1.06436	+	1.03468i
$502$	−1.81236	+	4.59994i	−0.0808896	+	0.205306i
$503$	−28.3463			−1.26390			−0.631950	−	0.775009i	$-0.717745\pi$
$503$	−28.3463			−1.26390			−0.631950	+	0.775009i	$0.717745\pi$
$504$	15.4001	+	34.8060i	0.685975	+	1.55038i
$505$	−5.31703			−0.236605
$506$	1.77092	−	4.49476i	0.0787269	−	0.199817i
$507$	−15.1605	−	4.29286i	−0.673303	−	0.190653i
$508$	−0.206137	+	0.220990i	−0.00914587	+	0.00980484i
$509$	−19.7957	−	34.2872i	−0.877431	−	1.51976i	−0.854150	−	0.520026i	$-0.825922\pi$
$509$	−19.7957	−	34.2872i	−0.877431	−	1.51976i	−0.0232807	−	0.999729i	$-0.507411\pi$
$510$	−4.99509	−	11.9495i	−0.221186	−	0.529133i
$511$	−26.0178	−	15.0214i	−1.15096	−	0.664506i
$512$	21.9987	+	5.29692i	0.972214	+	0.234093i
$513$	17.1056	+	18.6218i	0.755233	+	0.822174i
$514$	4.66427	−	0.696727i	0.205732	−	0.0307313i
$515$	13.2519	+	7.65097i	0.583947	+	0.337142i
$516$	4.22795	+	6.98627i	0.186125	+	0.307553i
$517$	12.5545	−	7.24837i	0.552148	−	0.318783i
$518$	23.4044	−	18.6138i	1.02833	−	0.817845i
$519$	−2.42603	−	0.686954i	−0.106491	−	0.0301539i
$520$	0.439649	−	5.57046i	0.0192799	−	0.244281i
$521$			35.6218i			1.56062i	0.625393	+	0.780310i	$0.284939\pi$
$521$			35.6218i			1.56062i	−0.625393	+	0.780310i	$0.715061\pi$
$522$	−14.0249	+	32.8423i	−0.613853	+	1.43747i
$523$	13.0675			0.571404			0.285702	−	0.958319i	$-0.407773\pi$
$523$	13.0675			0.571404			0.285702	+	0.958319i	$0.407773\pi$
$524$	33.4793	+	7.73452i	1.46255	+	0.337884i
$525$	−5.41538	−	5.57071i	−0.236347	−	0.243126i
$526$	−14.7544	+	11.7344i	−0.643323	+	0.511644i
$527$	−18.4671	−	31.9859i	−0.804438	−	1.39333i
$528$	−8.22804	−	1.72297i	−0.358079	−	0.0749827i
$529$	7.53691	−	13.0543i	0.327692	−	0.567579i
$530$	−0.154453	−	1.03399i	−0.00670901	−	0.0449138i
$531$	−3.10442	+	5.04222i	−0.134720	+	0.218814i
$532$	−12.7574	−	41.7497i	−0.553103	−	1.81008i
$533$	−6.05543	+	10.4883i	−0.262290	+	0.454299i
$534$	−6.60685	−	0.848028i	−0.285906	−	0.0366977i
$535$	−6.28254	+	3.62723i	−0.271618	+	0.156819i
$536$	5.08731	−	7.39856i	0.219738	−	0.319569i
$537$	35.4436	−	8.96203i	1.52951	−	0.386740i
$538$	2.57714	+	1.01538i	0.111108	+	0.0437763i
$539$			15.9191i			0.685685i
$540$	9.03951	−	5.12712i	0.388998	−	0.220636i
$541$			41.8805i			1.80059i	0.435285	+	0.900293i	$0.356647\pi$
$541$			41.8805i			1.80059i	−0.435285	+	0.900293i	$0.643353\pi$
$542$	11.7024	−	29.7017i	0.502659	−	1.27580i
$543$	14.3238	−	3.62181i	0.614692	−	0.155427i
$544$	−28.5225	−	9.00473i	−1.22289	−	0.386075i
$545$	16.1254	−	9.30999i	0.690735	−	0.398796i
$546$	2.76343	−	21.5294i	0.118264	−	0.921375i
$547$	8.32180	−	14.4138i	0.355814	−	0.616288i	−0.631443	−	0.775423i	$-0.717537\pi$
$547$	8.32180	−	14.4138i	0.355814	−	0.616288i	0.987257	+	0.159134i	$0.0508702\pi$
$548$	9.57087	+	31.3215i	0.408847	+	1.33799i
$549$	16.6572	+	0.471105i	0.710912	+	0.0201063i
$550$	1.69714	−	0.253511i	0.0723663	−	0.0108097i
$551$	20.4804	−	35.4732i	0.872496	−	1.51121i
$552$	12.9338	+	4.79018i	0.550498	+	0.203884i
$553$	−29.1432	−	50.4775i	−1.23930	−	2.14652i
$554$	21.2070	+	26.6649i	0.900998	+	1.13288i
$555$	−5.69140	−	5.85464i	−0.241587	−	0.248516i
$556$	−5.52605	+	23.9198i	−0.234357	+	1.01443i
$557$	−10.8296			−0.458863			−0.229431	−	0.973325i	$-0.573687\pi$
$557$	−10.8296			−0.458863			−0.229431	+	0.973325i	$0.573687\pi$
$558$	23.7070	−	17.7840i	1.00360	−	0.752858i
$559$		−	4.65708i		−	0.196973i
$560$	−17.8987	+	1.24627i	−0.756357	+	0.0526646i
$561$	10.6918	+	3.02750i	0.451409	+	0.127821i
$562$	26.8800	+	33.7979i	1.13386	+	1.42568i
$563$	−16.4450	+	9.49453i	−0.693074	+	0.400147i	−0.804763	−	0.593597i	$-0.797707\pi$
$563$	−16.4450	+	9.49453i	−0.693074	+	0.400147i	0.111688	+	0.993743i	$0.464374\pi$
$564$	21.4283	+	35.4081i	0.902293	+	1.49095i
$565$	−5.19909	−	3.00170i	−0.218727	−	0.126282i
$566$	−1.60856	−	10.7686i	−0.0676129	−	0.452638i
$567$	36.0460	−	18.1765i	1.51379	−	0.763341i
$568$	−4.14973	−	8.70506i	−0.174119	−	0.365256i
$569$	−7.51839	−	4.34075i	−0.315187	−	0.181974i	0.334058	−	0.942553i	$-0.391582\pi$
$569$	−7.51839	−	4.34075i	−0.315187	−	0.181974i	−0.649245	+	0.760579i	$0.724915\pi$
$570$	−10.9977	+	4.59722i	−0.460642	+	0.192556i
$571$	18.8435	+	32.6378i	0.788574	+	1.36585i	0.926840	+	0.375456i	$0.122514\pi$
$571$	18.8435	+	32.6378i	0.788574	+	1.36585i	−0.138266	+	0.990395i	$0.544153\pi$
$572$	3.50580	+	3.27018i	0.146585	+	0.136733i
$573$	0.713349	+	0.201992i	0.0298006	+	0.00843834i
$574$	36.1802	+	14.2549i	1.51013	+	0.594987i
$575$	−2.81535			−0.117408
$576$	4.43355	−	23.5869i	0.184731	−	0.982789i
$577$	−45.5995			−1.89833			−0.949166	−	0.314776i	$-0.898071\pi$
$577$	−45.5995			−1.89833			−0.949166	+	0.314776i	$0.898071\pi$
$578$	14.4168	+	5.68015i	0.599659	+	0.236263i
$579$	11.7757	−	11.4473i	0.489379	−	0.475734i
$580$	−12.3103	−	11.4830i	−0.511159	−	0.476805i
$581$	−12.9732	−	22.4703i	−0.538220	−	0.932225i
$582$	−33.5498	−	25.5713i	−1.39068	−	1.05996i
$583$	0.776819	+	0.448497i	0.0321726	+	0.0185748i
$584$	8.15184	+	17.1005i	0.337325	+	0.707622i
$585$	−5.92437	−	0.167555i	−0.244943	−	0.00692756i
$586$	3.77655	+	25.2823i	0.156008	+	1.04440i
$587$	8.14708	+	4.70372i	0.336266	+	0.194143i	0.658620	−	0.752476i	$-0.271141\pi$
$587$	8.14708	+	4.70372i	0.336266	+	0.194143i	−0.322354	+	0.946619i	$0.604474\pi$
$588$	−45.4383	+	0.937123i	−1.87385	+	0.0386463i
$589$	−29.4381	+	16.9961i	−1.21298	+	0.700313i
$590$	−1.73747	−	2.18463i	−0.0715305	−	0.0899398i
$591$	−1.76801	−	6.99224i	−0.0727261	−	0.287622i
$592$	−18.8109	+	1.30979i	−0.773125	+	0.0538322i
$593$		−	14.4808i		−	0.594657i	−0.954775	−	0.297328i	$-0.903904\pi$
$593$		−	14.4808i		−	0.594657i	0.954775	−	0.297328i	$-0.0960956\pi$
$594$	−1.38474	+	8.80826i	−0.0568164	+	0.361407i
$595$	23.7168			0.972292
$596$	−9.40611	+	40.7148i	−0.385289	+	1.66774i
$597$	−34.3996	+	8.69804i	−1.40788	+	0.355987i
$598$	−4.89610	−	6.15618i	−0.200217	−	0.251745i
$599$	2.00132	+	3.46639i	0.0817718	+	0.141633i	0.904011	−	0.427509i	$-0.140609\pi$
$599$	2.00132	+	3.46639i	0.0817718	+	0.141633i	−0.822239	+	0.569142i	$0.807275\pi$
$600$	0.823510	+	4.82927i	0.0336196	+	0.197154i
$601$	−21.9214	+	37.9690i	−0.894193	+	1.54879i	−0.0593924	+	0.998235i	$0.518916\pi$
$601$	−21.9214	+	37.9690i	−0.894193	+	1.54879i	−0.834800	+	0.550553i	$0.814417\pi$
$602$	−14.7895	+	2.20918i	−0.602774	+	0.0900396i
$603$	−8.10967	−	4.99301i	−0.330251	−	0.203331i
$604$	1.83901	+	6.01832i	0.0748283	+	0.244882i
$605$	4.76386	−	8.25125i	0.193679	−	0.335461i
$606$	10.3583	+	7.89498i	0.420777	+	0.320712i
$607$	5.60723	−	3.23734i	0.227591	−	0.131399i	−0.381869	−	0.924216i	$-0.624720\pi$
$607$	5.60723	−	3.23734i	0.227591	−	0.131399i	0.609460	+	0.792817i	$0.291386\pi$
$608$	−8.28748	+	26.2507i	−0.336102	+	1.06460i
$609$	−45.5829	−	46.8903i	−1.84711	−	1.90009i
$610$	−2.87956	+	7.30861i	−0.116590	+	0.295917i
$611$		−	23.6032i		−	0.954882i
$612$	−8.01207	+	30.6962i	−0.323869	+	1.24082i
$613$		−	40.2895i		−	1.62728i	−0.581370	−	0.813639i	$-0.697483\pi$
$613$		−	40.2895i		−	1.62728i	0.581370	−	0.813639i	$-0.302517\pi$
$614$	31.2147	+	12.2985i	1.25972	+	0.496325i
$615$	2.89285	−	10.2163i	0.116651	−	0.411960i
$616$	8.72205	−	12.6846i	0.351422	−	0.511078i
$617$	−13.7460	+	7.93629i	−0.553395	+	0.319503i	−0.750490	−	0.660882i	$-0.770183\pi$
$617$	−13.7460	+	7.93629i	−0.553395	+	0.319503i	0.197095	+	0.980384i	$0.436849\pi$
$618$	−14.4559	−	34.5821i	−0.581502	−	1.39110i
$619$	−20.1549	+	34.9094i	−0.810095	+	1.40313i	0.102702	+	0.994712i	$0.467251\pi$
$619$	−20.1549	+	34.9094i	−0.810095	+	1.40313i	−0.912797	+	0.408413i	$0.866082\pi$
$620$	4.08262	+	13.3607i	0.163962	+	0.536579i
$621$	4.38198	−	13.9573i	0.175843	−	0.560085i
$622$	−2.60747	−	17.4558i	−0.104550	−	0.699915i
$623$	6.09885	−	10.5635i	0.244345	−	0.423218i
$624$	−9.12778	+	10.1992i	−0.365404	+	0.408295i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	16.3971	−	13.0409i	0.655360	−	0.521218i
$627$	2.78635	−	9.84019i	0.111276	−	0.392979i
$628$	21.7029	+	5.01389i	0.866040	+	0.200076i
$629$	24.9256			0.993849
$630$	2.27825	+	18.8935i	0.0907675	+	0.752735i
$631$			9.05567i			0.360500i	0.983621	+	0.180250i	$0.0576908\pi$
$631$			9.05567i			0.360500i	−0.983621	+	0.180250i	$0.942309\pi$
$632$	−2.89180	+	36.6398i	−0.115030	+	1.45745i
$633$	31.8309	−	30.9434i	1.26516	−	1.22989i
$634$	25.6768	−	20.4212i	1.01976	−	0.811028i
$635$	−0.130860	+	0.0755518i	−0.00519300	+	0.00299818i
$636$	−1.23443	+	2.24370i	−0.0489482	+	0.0889684i
$637$	22.4465	+	12.9595i	0.889365	+	0.513475i
$638$	14.2853	−	2.13388i	0.565562	−	0.0844810i
$639$	−8.99922	+	4.86180i	−0.356004	+	0.192330i
$640$	9.74524	+	5.74719i	0.385215	+	0.227178i
$641$	−7.53980	−	4.35311i	−0.297804	−	0.171937i	0.343652	−	0.939097i	$-0.388336\pi$
$641$	−7.53980	−	4.35311i	−0.297804	−	0.171937i	−0.641456	+	0.767160i	$0.721669\pi$
$642$	17.6251	+	2.26229i	0.695608	+	0.0892853i
$643$	10.5478	+	18.2693i	0.415963	+	0.720469i	0.995529	−	0.0944562i	$-0.0301112\pi$
$643$	10.5478	+	18.2693i	0.415963	+	0.720469i	−0.579566	+	0.814925i	$0.696778\pi$
$644$	−17.2276	+	18.4689i	−0.678863	+	0.727775i
$645$	1.00090	+	3.95842i	0.0394103	+	0.155863i
$646$	13.3387	−	33.8549i	0.524803	−	1.33200i
$647$	36.6479			1.44078			0.720388	−	0.693571i	$-0.243964\pi$
$647$	36.6479			1.44078			0.720388	+	0.693571i	$0.243964\pi$
$648$	−25.2232	−	3.43397i	−0.990859	−	0.134899i
$649$	2.39490			0.0940081
$650$	1.02416	−	2.59941i	0.0401708	−	0.101957i
$651$	13.3035	+	52.6135i	0.521405	+	2.06209i
$652$	−0.830432	−	0.774621i	−0.0325222	−	0.0303365i
$653$	0.680992	+	1.17951i	0.0266493	+	0.0461579i	0.879042	−	0.476743i	$-0.158183\pi$
$653$	0.680992	+	1.17951i	0.0266493	+	0.0461579i	−0.852393	+	0.522901i	$0.824850\pi$
$654$	−45.2383	−	5.80660i	−1.76896	−	0.227056i
$655$	14.8788	+	8.59027i	0.581362	+	0.335650i
$656$	−13.7060	−	20.3330i	−0.535130	−	0.793870i
$657$	17.6783	−	9.55065i	0.689697	−	0.372606i
$658$	−74.9565	+	11.1967i	−2.92211	+	0.436491i
$659$	−17.5744	−	10.1466i	−0.684600	−	0.395254i	0.116986	−	0.993134i	$-0.462677\pi$
$659$	−17.5744	−	10.1466i	−0.684600	−	0.395254i	−0.801586	+	0.597879i	$0.796010\pi$
$660$	−3.68268	−	2.02612i	−0.143348	−	0.0788666i
$661$	−6.63502	+	3.83073i	−0.258073	+	0.148998i	−0.623455	−	0.781859i	$-0.714272\pi$
$661$	−6.63502	+	3.83073i	−0.258073	+	0.148998i	0.365382	+	0.930857i	$0.380938\pi$
$662$	−7.54558	+	6.00111i	−0.293267	+	0.233240i
$663$	12.9729	−	12.6112i	0.503828	−	0.489780i
$664$	−1.28730	+	16.3104i	−0.0499568	+	0.632965i
$665$		−	21.8277i		−	0.846440i
$666$	2.39437	+	19.8565i	0.0927798	+	0.769423i
$667$	−23.6976			−0.917575
$668$	−8.63585	+	37.3807i	−0.334131	+	1.44630i
$669$	−0.314802	+	1.11175i	−0.0121710	+	0.0429826i
$670$	3.51366	−	2.79447i	0.135745	−	0.107960i
$671$	−3.36992	−	5.83686i	−0.130094	−	0.225330i
$672$	36.7195	+	24.1489i	1.41649	+	0.931563i
$673$	9.53849	−	16.5212i	0.367682	−	0.636844i	−0.621521	−	0.783398i	$-0.713485\pi$
$673$	9.53849	−	16.5212i	0.367682	−	0.636844i	0.989203	+	0.146554i	$0.0468182\pi$
$674$	−1.74743	−	11.6983i	−0.0673086	−	0.450601i
$675$	5.07161	−	1.13085i	0.195206	−	0.0435263i
$676$	−17.4000	+	5.31688i	−0.669229	+	0.204496i
$677$	9.09868	−	15.7594i	0.349690	−	0.605682i	−0.636504	−	0.771273i	$-0.719620\pi$
$677$	9.09868	−	15.7594i	0.349690	−	0.605682i	0.986194	+	0.165592i	$0.0529534\pi$
$678$	5.67147	+	13.5676i	0.217812	+	0.521059i
$679$	66.8979	−	38.6235i	2.56731	−	1.48223i
$680$	−12.3230	−	8.47340i	−0.472566	−	0.324940i
$681$	−1.75285	+	6.19031i	−0.0671694	+	0.237213i
$682$	−11.1521	−	4.39390i	−0.427038	−	0.168251i
$683$		−	4.17953i		−	0.159925i	−0.996798	−	0.0799626i	$-0.974520\pi$
$683$		−	4.17953i		−	0.159925i	0.996798	−	0.0799626i	$-0.0254801\pi$
$684$	28.2511	+	7.37389i	1.08021	+	0.281948i
$685$			16.3756i			0.625678i
$686$	14.2303	−	36.1179i	0.543315	−	1.37899i
$687$	−7.34713	−	7.55786i	−0.280311	−	0.288351i
$688$	8.47376	+	4.13604i	0.323059	+	0.157685i
$689$	1.26479	−	0.730229i	0.0481848	−	0.0278195i
$690$	5.48467	+	4.18036i	0.208798	+	0.159144i
$691$	−2.99450	+	5.18663i	−0.113916	+	0.197309i	−0.917346	−	0.398091i	$-0.869673\pi$
$691$	−2.99450	+	5.18663i	−0.113916	+	0.197309i	0.803430	+	0.595400i	$0.203006\pi$
$692$	−2.78438	+	0.850820i	−0.105846	+	0.0323433i
$693$	−13.9038	−	8.56038i	−0.528162	−	0.325182i
$694$	20.1019	−	3.00273i	0.763059	−	0.113982i
$695$	−6.13746	+	10.6304i	−0.232807	+	0.403234i
$696$	6.93173	+	40.6494i	0.262746	+	1.54081i
$697$	16.2067	+	28.0709i	0.613873	+	1.06326i
$698$	−5.28856	−	6.64964i	−0.200175	−	0.251692i
$699$	19.2308	−	4.86257i	0.727377	−	0.183919i
$700$	−8.74077	−	2.01933i	−0.330370	−	0.0763235i
$701$	−18.5227			−0.699592			−0.349796	−	0.936826i	$-0.613749\pi$
$701$	−18.5227			−0.699592			−0.349796	+	0.936826i	$0.613749\pi$
$702$	11.2927	+	9.12321i	0.426215	+	0.344333i
$703$		−	22.9402i		−	0.865206i
$704$	−9.06380	+	3.47465i	−0.341605	+	0.130956i
$705$	5.07279	+	20.0622i	0.191052	+	0.755586i
$706$	12.8928	+	16.2109i	0.485226	+	0.610105i
$707$	−20.6543	+	11.9248i	−0.776786	+	0.448477i
$708$	0.140983	+	6.83583i	0.00529845	+	0.256906i
$709$	−17.4280	−	10.0621i	−0.654522	−	0.377888i	0.135665	−	0.990755i	$-0.456683\pi$
$709$	−17.4280	−	10.0621i	−0.654522	−	0.377888i	−0.790187	+	0.612866i	$0.790016\pi$
$710$	−0.712352	−	4.76887i	−0.0267341	−	0.178973i
$711$	38.9676	+	1.10210i	1.46140	+	0.0413319i
$712$	−6.94299	+	3.30974i	−0.260199	+	0.124038i
$713$	17.0312	+	9.83299i	0.637825	+	0.368248i
$714$	−46.2034	−	35.2158i	−1.72912	−	1.31792i
$715$	1.19856	+	2.07596i	0.0448235	+	0.0776367i
$716$	28.7950	−	30.8697i	1.07612	−	1.15366i
$717$	−14.4563	+	14.0532i	−0.539880	+	0.524827i
$718$	1.29458	+	0.510058i	0.0483132	+	0.0190352i
$719$	−26.2181			−0.977768			−0.488884	−	0.872349i	$-0.662596\pi$
$719$	−26.2181			−0.977768			−0.488884	+	0.872349i	$0.662596\pi$
$720$	5.56642	−	10.6309i	0.207448	−	0.396188i
$721$	68.6369			2.55617
$722$	−6.15859	−	2.42646i	−0.229199	−	0.0903035i
$723$	10.8223	+	3.06444i	0.402484	+	0.113968i
$724$	11.6369	−	12.4753i	0.432481	−	0.463641i
$725$	−4.20865	−	7.28960i	−0.156305	−	0.270729i
$726$	−21.5325	+	9.00094i	−0.799146	+	0.334056i
$727$	−20.5836	−	11.8839i	−0.763402	−	0.440750i	0.0671138	−	0.997745i	$-0.478621\pi$
$727$	−20.5836	−	11.8839i	−0.763402	−	0.440750i	−0.830516	+	0.556995i	$0.811954\pi$
$728$	−10.7853	−	22.6248i	−0.399730	−	0.838531i
$729$	−2.28752	+	26.9029i	−0.0847228	+	0.996405i
$730$	1.39936	+	9.36810i	0.0517927	+	0.346729i
$731$	−10.7943	−	6.23209i	−0.399241	−	0.230502i
$732$	16.4619	−	9.96244i	0.608451	−	0.368222i
$733$	17.5140	−	10.1117i	0.646894	−	0.373485i	−0.140371	−	0.990099i	$-0.544830\pi$
$733$	17.5140	−	10.1117i	0.646894	−	0.373485i	0.787265	+	0.616614i	$0.211496\pi$
$734$	−23.2107	−	29.1843i	−0.856724	−	1.07721i
$735$	−21.8644	−	6.19112i	−0.806479	−	0.228363i
$736$	15.5498	−	3.44126i	0.573172	−	0.126847i
$737$			3.85185i			0.141885i
$738$	−20.8053	+	15.6073i	−0.765853	+	0.574511i
$739$	25.0224			0.920463			0.460232	−	0.887799i	$-0.347766\pi$
$739$	25.0224			0.920463			0.460232	+	0.887799i	$0.347766\pi$
$740$	−9.18629	−	2.12225i	−0.337695	−	0.0780156i
$741$	−11.6067	−	11.9396i	−0.426383	−	0.438613i
$742$	−2.91897	−	3.67021i	−0.107159	−	0.134738i
$743$	−0.871379	−	1.50927i	−0.0319678	−	0.0553699i	0.849599	−	0.527429i	$-0.176844\pi$
$743$	−0.871379	−	1.50927i	−0.0319678	−	0.0553699i	−0.881567	+	0.472060i	$0.843511\pi$
$744$	11.8851	−	32.0905i	0.435730	−	1.17650i
$745$	−10.4468	+	18.0944i	−0.382741	+	0.662927i
$746$	0.691476	−	0.103289i	0.0253167	−	0.00378169i
$747$	17.3466	+	0.490603i	0.634680	+	0.0179502i
$748$	12.2711	−	3.74968i	0.448678	−	0.137102i
$749$	−16.2699	+	28.1803i	−0.594490	+	1.02969i
$750$	−0.311848	+	2.42956i	−0.0113871	+	0.0887149i
$751$	−14.6053	+	8.43240i	−0.532957	+	0.307703i	−0.742220	−	0.670157i	$-0.766227\pi$
$751$	−14.6053	+	8.43240i	−0.532957	+	0.307703i	0.209263	+	0.977859i	$0.432894\pi$
$752$	42.9470	+	20.9624i	1.56612	+	0.764420i
$753$	5.87050	−	1.48437i	0.213933	−	0.0540936i
$754$	8.62064	−	21.8800i	0.313945	−	0.796823i
$755$			3.14651i			0.114513i
$756$	23.6156	−	40.1899i	0.858892	−	1.46169i
$757$			25.4545i			0.925160i	0.886577	+	0.462580i	$0.153076\pi$
$757$			25.4545i			0.925160i	−0.886577	+	0.462580i	$0.846924\pi$
$758$	26.3604	+	10.3859i	0.957453	+	0.377233i
$759$	−5.73627	+	1.45043i	−0.208213	+	0.0526474i
$760$	−7.79847	+	11.3415i	−0.282880	+	0.411398i
$761$	−39.3748	+	22.7331i	−1.42734	+	0.824073i	−0.996910	−	0.0785520i	$-0.974970\pi$
$761$	−39.3748	+	22.7331i	−1.42734	+	0.824073i	−0.430427	+	0.902625i	$0.641637\pi$
$762$	0.367115	+	0.0471213i	0.0132992	+	0.00170703i
$763$	41.7600	−	72.3304i	1.51181	−	2.61853i
$764$	0.818720	−	0.250175i	0.0296203	−	0.00905103i
$765$	−8.31634	+	13.5074i	−0.300678	+	0.488362i
$766$	2.99369	+	20.0414i	0.108166	+	0.724124i
$767$	1.94966	−	3.37690i	0.0703980	−	0.121933i
$768$	−10.4513	−	25.6665i	−0.377131	−	0.926160i
$769$	6.11507	+	10.5916i	0.220515	+	0.381943i	0.954965	−	0.296720i	$-0.0958928\pi$
$769$	6.11507	+	10.5916i	0.220515	+	0.381943i	−0.734449	+	0.678663i	$0.762559\pi$
$770$	6.02408	−	4.79104i	0.217093	−	0.172657i
$771$	−4.02605	−	4.14153i	−0.144995	−	0.149153i
$772$	4.26857	−	18.4767i	0.153629	−	0.664991i
$773$	23.0762			0.829992			0.414996	−	0.909823i	$-0.363783\pi$
$773$	23.0762			0.829992			0.414996	+	0.909823i	$0.363783\pi$
$774$	3.92777	−	9.19772i	0.141181	−	0.330605i
$775$			6.98528i			0.250919i
$776$	−48.5588	−	3.83251i	−1.74316	−	0.137579i
$777$	−35.2391	−	9.97830i	−1.26419	−	0.357970i
$778$	−15.9325	+	12.6713i	−0.571206	+	0.454289i
$779$	25.8349	−	14.9158i	0.925633	−	0.534414i
$780$	−5.85492	+	3.54329i	−0.209640	+	0.126870i
$781$	3.58276	+	2.06851i	0.128201	+	0.0740170i
$782$	−20.8209	+	3.11013i	−0.744554	+	0.111218i
$783$	42.6892	−	9.51867i	1.52559	−	0.340170i
$784$	−43.5156	+	29.3329i	−1.55413	+	1.04760i
$785$	9.64516	+	5.56863i	0.344250	+	0.198753i
$786$	−16.2306	−	38.8277i	−0.578928	−	1.38494i
$787$	8.21382	+	14.2268i	0.292791	+	0.507129i	0.974469	−	0.224524i	$-0.0720826\pi$
$787$	8.21382	+	14.2268i	0.292791	+	0.507129i	−0.681678	+	0.731653i	$0.738749\pi$
$788$	−6.08990	−	5.68061i	−0.216944	−	0.202363i
$789$	22.2152	+	6.29045i	0.790881	+	0.223946i
$790$	−6.73641	+	17.0977i	−0.239671	+	0.608307i
$791$	−26.9282			−0.957458
$792$	4.16588	+	9.41537i	0.148028	+	0.334561i
$793$	−10.9736			−0.389684
$794$	6.27452	−	15.9253i	0.222674	−	0.565169i
$795$	−0.918109	+	0.892510i	−0.0325620	+	0.0316541i
$796$	−27.9468	+	29.9604i	−0.990549	+	1.06192i
$797$	−18.7569	−	32.4878i	−0.664402	−	1.15078i	−0.979447	−	0.201701i	$-0.935353\pi$
$797$	−18.7569	−	32.4878i	−0.664402	−	1.15078i	0.315045	−	0.949077i	$-0.397980\pi$
$798$	−32.4107	+	42.5232i	−1.14733	+	1.50531i
$799$	−54.7080	−	31.5857i	−1.93543	−	1.11742i
$800$	3.82017	+	4.17208i	0.135063	+	0.147505i
$801$	3.87768	+	7.17761i	0.137011	+	0.253608i
$802$	23.7212	−	3.54337i	0.837626	−	0.125121i
$803$	−7.03807	−	4.06343i	−0.248368	−	0.143395i
$804$	−10.9944	+	0.226750i	−0.387744	+	0.00799686i
$805$	−10.9364	+	6.31412i	−0.385457	+	0.222543i
$806$	−15.2744	+	12.1479i	−0.538017	+	0.427893i
$807$	−0.831628	−	3.28898i	−0.0292747	−	0.115778i
$808$	14.9922	+	1.18326i	0.527425	+	0.0416271i
$809$		−	13.7094i		−	0.481998i	−0.970525	−	0.240999i	$-0.922525\pi$
$809$		−	13.7094i		−	0.481998i	0.970525	−	0.240999i	$-0.0774751\pi$
$810$	−11.5593	−	5.32752i	−0.406153	−	0.187190i
$811$	−47.6781			−1.67420			−0.837102	−	0.547047i	$-0.815752\pi$
$811$	−47.6781			−1.67420			−0.837102	+	0.547047i	$0.815752\pi$
$812$	−73.5737	−	16.9973i	−2.58193	−	0.596489i
$813$	−37.9057	+	9.58457i	−1.32941	+	0.336146i
$814$	6.33112	−	5.03523i	0.221906	−	0.176485i
$815$	−0.283907	−	0.491742i	−0.00994484	−	0.0172250i
$816$	11.4252	+	34.8051i	0.399961	+	1.21842i
$817$	−5.73568	+	9.93450i	−0.200666	+	0.347564i
$818$	−5.14966	−	34.4747i	−0.180054	−	1.20538i
$819$	−23.3893	+	12.6360i	−0.817290	+	0.441538i
$820$	−3.58291	−	11.7254i	−0.125121	−	0.409468i
$821$	14.6238	−	25.3292i	0.510376	−	0.883997i	−0.489552	−	0.871974i	$-0.662840\pi$
$821$	14.6238	−	25.3292i	0.510376	−	0.883997i	0.999928	−	0.0120227i	$-0.00382702\pi$
$822$	24.3152	−	31.9018i	0.848090	−	1.11270i
$823$	29.6471	−	17.1168i	1.03343	−	0.596653i	0.115466	−	0.993311i	$-0.463164\pi$
$823$	29.6471	−	17.1168i	1.03343	−	0.596653i	0.917966	+	0.396659i	$0.129830\pi$
$824$	−35.6631	−	24.5222i	−1.24238	−	0.854272i
$825$	−1.46492	−	1.50693i	−0.0510018	−	0.0524647i
$826$	−11.6489	−	4.58961i	−0.405316	−	0.159693i
$827$		−	18.2917i		−	0.636065i	−0.948080	−	0.318032i	$-0.896978\pi$
$827$		−	18.2917i		−	0.636065i	0.948080	−	0.318032i	$-0.103022\pi$
$828$	−4.47769	−	16.2878i	−0.155611	−	0.566040i
$829$			11.0727i			0.384572i	0.981339	+	0.192286i	$0.0615902\pi$
$829$			11.0727i			0.384572i	−0.981339	+	0.192286i	$0.938410\pi$
$830$	−2.99874	+	7.61110i	−0.104088	+	0.264185i
$831$	11.3684	−	40.1483i	0.394366	−	1.39273i
$832$	−2.47932	+	15.6090i	−0.0859551	+	0.541143i
$833$	60.0758	−	34.6848i	2.08150	−	1.20176i
$834$	27.7411	−	11.5962i	0.960596	−	0.401545i
$835$	−9.59132	+	16.6127i	−0.331921	+	0.574905i
$836$	−3.45101	−	11.2937i	−0.119356	−	0.390601i
$837$	−34.6299	−	10.8723i	−1.19699	−	0.375802i
$838$	−35.6425	+	5.32411i	−1.23125	+	0.183918i
$839$	−21.6805	+	37.5517i	−0.748494	+	1.29643i	0.200051	+	0.979785i	$0.435889\pi$
$839$	−21.6805	+	37.5517i	−0.748494	+	1.29643i	−0.948545	+	0.316643i	$0.897444\pi$
$840$	14.0298	+	16.9126i	0.484074	+	0.583542i
$841$	−20.9255	−	36.2440i	−0.721568	−	1.24979i
$842$	2.88791	+	3.63116i	0.0995241	+	0.125138i
$843$	14.4095	−	50.8882i	0.496290	−	1.75268i
$844$	11.5384	−	49.9446i	0.397168	−	1.71916i
$845$	−9.09708			−0.312949
$846$	19.9068	−	46.6162i	0.684411	−	1.60270i
$847$		−	42.7366i		−	1.46845i
$848$	0.205398	+	2.94988i	0.00705340	+	0.101299i
$849$	−9.56171	+	9.29510i	−0.328157	+	0.319007i
$850$	−4.65445	−	5.85234i	−0.159646	−	0.200734i
$851$	−11.4938	+	6.63595i	−0.394002	+	0.227477i
$852$	−5.69329	+	10.3481i	−0.195049	+	0.354521i
$853$	18.7351	+	10.8167i	0.641479	+	0.370358i	0.785184	−	0.619263i	$-0.212568\pi$
$853$	18.7351	+	10.8167i	0.641479	+	0.370358i	−0.143705	+	0.989621i	$0.545902\pi$
$854$	5.20556	+	34.8488i	0.178130	+	1.19250i
$855$	12.4315	+	7.65392i	0.425149	+	0.261758i
$856$	18.5218	−	8.82941i	0.633063	−	0.301783i
$857$	−10.5218	−	6.07474i	−0.359417	−	0.207509i	0.309408	−	0.950929i	$-0.399869\pi$
$857$	−10.5218	−	6.07474i	−0.359417	−	0.207509i	−0.668825	+	0.743420i	$0.733202\pi$
$858$	0.747536	−	5.82393i	0.0255205	−	0.198826i
$859$	−16.1108	−	27.9048i	−0.549694	−	0.952098i	−0.998295	−	0.0583659i	$-0.981411\pi$
$859$	−16.1108	−	27.9048i	−0.549694	−	0.952098i	0.448601	−	0.893732i	$-0.351922\pi$
$860$	3.44760	+	3.21589i	0.117562	+	0.109661i
$861$	−11.6751	−	46.1737i	−0.397888	−	1.57359i
$862$	13.9118	+	5.48121i	0.473839	+	0.186691i
$863$	−7.86707			−0.267798			−0.133899	−	0.990995i	$-0.542750\pi$
$863$	−7.86707			−0.267798			−0.133899	+	0.990995i	$0.542750\pi$
$864$	−26.6293	+	12.4451i	−0.905948	+	0.423389i
$865$	−1.45574			−0.0494965
$866$	14.4342	+	5.68701i	0.490494	+	0.193253i
$867$	−4.65221	−	18.3989i	−0.157997	−	0.624858i
$868$	45.8239	+	42.7441i	1.55536	+	1.45083i
$869$	−7.88354	−	13.6547i	−0.267431	−	0.463203i
$870$	−2.62492	+	20.4503i	−0.0889931	+	0.693331i
$871$	5.43126	+	3.13574i	0.184031	+	0.106250i
$872$	−47.5399	+	22.6624i	−1.60990	+	0.767446i
$873$	−1.46061	+	51.6438i	−0.0494342	+	1.74788i
$874$	2.86240	+	19.1625i	0.0968221	+	0.648180i
$875$	−3.88456	−	2.24275i	−0.131322	−	0.0758188i
$876$	11.1840	−	20.3282i	0.377874	−	0.686825i
$877$	−9.62451	+	5.55672i	−0.324997	+	0.187637i	−0.653618	−	0.756825i	$-0.726750\pi$
$877$	−9.62451	+	5.55672i	−0.324997	+	0.187637i	0.328621	+	0.944462i	$0.393416\pi$
$878$	−8.19921	−	10.3094i	−0.276710	−	0.347925i
$879$	22.4488	−	21.8228i	0.757178	−	0.736066i
$880$	−4.84177	+	0.337129i	−0.163216	+	0.0113646i
$881$		−	1.03742i		−	0.0349514i	−0.999847	−	0.0174757i	$-0.994437\pi$
$881$		−	1.03742i		−	0.0349514i	0.999847	−	0.0174757i	$-0.00556298\pi$
$882$	33.4019	+	44.5264i	1.12470	+	1.49928i
$883$	47.3991			1.59511			0.797554	−	0.603248i	$-0.206127\pi$
$883$	47.3991			1.59511			0.797554	+	0.603248i	$0.206127\pi$
$884$	4.70257	−	20.3553i	0.158165	−	0.684624i
$885$	−0.931404	+	3.28932i	−0.0313088	+	0.110569i
$886$	1.08403	+	1.36303i	0.0364189	+	0.0457917i
$887$	7.80889	+	13.5254i	0.262197	+	0.454139i	0.966825	−	0.255438i	$-0.0822196\pi$
$887$	7.80889	+	13.5254i	0.262197	+	0.454139i	−0.704628	+	0.709576i	$0.748886\pi$
$888$	14.7449	+	17.7747i	0.494807	+	0.596479i
$889$	−0.338887	+	0.586970i	−0.0113659	+	0.0196864i
$890$	−3.80356	+	0.568158i	−0.127496	+	0.0190447i
$891$	9.75080	−	4.91693i	0.326664	−	0.164723i
$892$	0.389895	+	1.27597i	0.0130547	+	0.0427225i
$893$	−29.0698	+	50.3503i	−0.972783	+	1.68491i
$894$	47.2192	−	19.7384i	1.57925	−	0.660151i
$895$	18.2796	−	10.5537i	0.611018	−	0.352772i
$896$	50.7455	+	0.469144i	1.69529	+	0.0156730i
$897$	−2.62465	+	9.26913i	−0.0876345	+	0.309487i
$898$	3.36795	−	8.54817i	0.112390	−	0.285256i
$899$			58.7972i			1.96100i
$900$	4.21504	−	4.27006i	0.140501	−	0.142335i
$901$		−	3.90876i		−	0.130220i
$902$	9.78713	+	3.85609i	0.325876	+	0.128394i
$903$	12.7658	+	13.1319i	0.424819	+	0.437004i
$904$	13.9917	+	9.62078i	0.465356	+	0.319982i
$905$	7.38728	−	4.26505i	0.245562	−	0.141775i
$906$	4.67209	−	6.12983i	0.155220	−	0.203650i
$907$	−25.0385	+	43.3680i	−0.831390	+	1.44001i	0.0655459	+	0.997850i	$0.479121\pi$
$907$	−25.0385	+	43.3680i	−0.831390	+	1.44001i	−0.896936	+	0.442160i	$0.854212\pi$
$908$	2.17098	+	7.10470i	0.0720464	+	0.235778i
$909$	0.450955	−	15.9447i	0.0149572	−	0.528853i
$910$	−1.85143	−	12.3945i	−0.0613743	−	0.410873i
$911$	−10.7564	+	18.6307i	−0.356376	+	0.617262i	−0.987353	−	0.158540i	$-0.949321\pi$
$911$	−10.7564	+	18.6307i	−0.356376	+	0.617262i	0.630976	+	0.775802i	$0.282655\pi$
$912$	32.0328	−	10.5151i	1.06071	−	0.348191i
$913$	−3.50939	−	6.07844i	−0.116144	−	0.201167i
$914$	−26.3850	+	20.9844i	−0.872738	+	0.694102i
$915$	9.32733	−	2.35844i	0.308352	−	0.0779678i
$916$	−11.8587	−	2.73966i	−0.391824	−	0.0905208i
$917$	77.0633			2.54486
$918$	36.2578	−	13.9658i	1.19669	−	0.460940i
$919$		−	28.7522i		−	0.948448i	−0.880404	−	0.474224i	$-0.842729\pi$
$919$		−	28.7522i		−	0.948448i	0.880404	−	0.474224i	$-0.157271\pi$
$920$	7.93832	+	0.626533i	0.261719	+	0.0206562i
$921$	−10.0728	−	39.8366i	−0.331910	−	1.31266i
$922$	17.7240	−	14.0962i	0.583710	−	0.464233i
$923$	5.83335	−	3.36788i	0.192007	−	0.110855i
$924$	−18.8497	+	0.388757i	−0.620109	+	0.0127892i
$925$	−4.08255	−	2.35706i	−0.134233	−	0.0774997i
$926$	40.2773	−	6.01643i	1.32359	−	0.197712i
$927$	−24.0677	+	39.0908i	−0.790486	+	1.28391i
$928$	32.1555	+	35.1177i	1.05556	+	1.15279i
$929$	29.7995	+	17.2047i	0.977689	+	0.564469i	0.901572	−	0.432630i	$-0.142414\pi$
$929$	29.7995	+	17.2047i	0.977689	+	0.564469i	0.0761173	+	0.997099i	$0.475748\pi$
$930$	10.3721	−	13.6083i	0.340113	−	0.446232i
$931$	−31.9220	−	55.2906i	−1.04620	−	1.81208i
$932$	15.6235	−	16.7491i	0.511763	−	0.548636i
$933$	−15.4995	+	15.0673i	−0.507430	+	0.493281i
$934$	−14.0275	+	35.6032i	−0.458995	+	1.16497i
$935$	6.41563			0.209813
$936$	16.6674	+	1.79087i	0.544792	+	0.0585364i
$937$	9.52071			0.311028			0.155514	−	0.987834i	$-0.450297\pi$
$937$	9.52071			0.311028			0.155514	+	0.987834i	$0.450297\pi$
$938$	7.38172	−	18.7355i	0.241022	−	0.611737i
$939$	−24.6885	−	6.99080i	−0.805679	−	0.228136i
$940$	17.4732	+	16.2989i	0.569914	+	0.531611i
$941$	22.3517	+	38.7143i	0.728646	+	1.26205i	0.957456	+	0.288580i	$0.0931832\pi$
$941$	22.3517	+	38.7143i	0.728646	+	1.26205i	−0.228810	+	0.973471i	$0.573483\pi$
$942$	−10.5215	−	25.1700i	−0.342809	−	0.820084i
$943$	−14.9466	−	8.62943i	−0.486729	−	0.281013i
$944$	4.41290	+	6.54657i	0.143628	+	0.213073i
$945$	17.1647	−	15.7672i	0.558369	−	0.512906i
$946$	−4.00071	+	0.597607i	−0.130074	+	0.0194299i
$947$	7.64574	+	4.41427i	0.248453	+	0.143444i	0.619056	−	0.785347i	$-0.287515\pi$
$947$	7.64574	+	4.41427i	0.248453	+	0.143444i	−0.370603	+	0.928792i	$0.620849\pi$
$948$	38.5108	−	23.3060i	1.25077	−	0.756944i
$949$	−11.4592	+	6.61596i	−0.371981	+	0.214763i
$950$	−5.38618	+	4.28371i	−0.174751	+	0.138982i
$951$	−38.6606	−	10.9471i	−1.25366	−	0.354986i
$952$	−66.8732	−	5.27797i	−2.16737	−	0.171060i
$953$		−	25.0780i		−	0.812356i	−0.913794	−	0.406178i	$-0.866861\pi$
$953$		−	25.0780i		−	0.812356i	0.913794	−	0.406178i	$-0.133139\pi$
$954$	3.11384	−	0.375478i	0.100814	−	0.0121565i
$955$	0.428045			0.0138512
$956$	−5.24027	+	22.6828i	−0.169483	+	0.733614i
$957$	−12.3306	−	12.6843i	−0.398593	−	0.410026i
$958$	13.1422	−	10.4522i	0.424605	−	0.337695i
$959$	36.7263	+	63.6118i	1.18595	+	2.05413i
$960$	−1.24730	−	13.8002i	−0.0402565	−	0.445398i
$961$	8.89704	−	15.4101i	0.287001	−	0.497101i
$962$	−1.94580	−	13.0262i	−0.0627350	−	0.419982i
$963$	−10.3445	−	19.1477i	−0.333346	−	0.617027i
$964$	12.4209	−	3.79543i	0.400049	−	0.122242i
$965$	4.74084	−	8.21138i	0.152613	−	0.264334i
$966$	30.6810	+	3.93809i	0.987146	+	0.126706i
$967$	−46.2843	+	26.7222i	−1.48840	+	0.859329i	−0.999912	−	0.0132411i	$-0.995785\pi$
$967$	−46.2843	+	26.7222i	−1.48840	+	0.859329i	−0.488489	+	0.872570i	$0.662452\pi$
$968$	−15.2687	+	22.2056i	−0.490755	+	0.713713i
$969$	−43.2060	+	10.9248i	−1.38798	+	0.350954i
$970$	−22.6595	−	8.92777i	−0.727554	−	0.286653i
$971$			1.47479i			0.0473284i	0.999720	+	0.0236642i	$0.00753325\pi$
$971$			1.47479i			0.0473284i	−0.999720	+	0.0236642i	$0.992467\pi$
$972$	14.6085	+	27.5425i	0.468569	+	0.883427i
$973$			55.0592i			1.76512i
$974$	−5.82491	+	14.7842i	−0.186642	+	0.473716i
$975$	−3.31740	+	0.838814i	−0.106242	+	0.0268636i
$976$	9.74585	−	19.9670i	0.311957	−	0.639127i
$977$	−37.3937	+	21.5892i	−1.19633	+	0.690701i	−0.959735	−	0.280908i	$-0.909365\pi$
$977$	−37.3937	+	21.5892i	−1.19633	+	0.690701i	−0.236594	+	0.971609i	$0.576031\pi$
$978$	−0.177072	+	1.37954i	−0.00566213	+	0.0441128i
$979$	1.64980	−	2.85754i	0.0527279	−	0.0913274i
$980$	−25.0940	+	7.66795i	−0.801599	+	0.244944i
$981$	26.5512	+	49.1464i	0.847713	+	1.56912i
$982$	−42.3175	+	6.32118i	−1.35040	+	0.201717i
$983$	3.00102	−	5.19791i	0.0957175	−	0.165788i	−0.814190	−	0.580598i	$-0.802819\pi$
$983$	3.00102	−	5.19791i	0.0957175	−	0.165788i	0.909908	+	0.414810i	$0.136152\pi$
$984$	−10.4304	+	28.1627i	−0.332509	+	0.897793i
$985$	−2.08201	−	3.60615i	−0.0663384	−	0.114901i
$986$	−39.1779	−	49.2609i	−1.24768	−	1.56879i
$987$	64.7000	+	66.5558i	2.05942	+	2.11849i
$988$	−18.7340	−	4.32800i	−0.596007	−	0.137692i
$989$	6.63668			0.211034
$990$	0.616289	+	5.11089i	0.0195869	+	0.162435i
$991$		−	60.8130i		−	1.93179i	−0.258939	−	0.965894i	$-0.583373\pi$
$991$		−	60.8130i		−	1.93179i	0.258939	−	0.965894i	$-0.416627\pi$
$992$	−8.53827	−	38.5812i	−0.271090	−	1.22495i
$993$	11.3611	+	3.21701i	0.360533	+	0.102089i
$994$	−13.4626	−	16.9273i	−0.427006	−	0.536902i
$995$	−17.7411	+	10.2428i	−0.562431	+	0.324720i
$996$	17.1433	−	10.3748i	0.543205	−	0.328737i
$997$	−1.61374	−	0.931694i	−0.0511077	−	0.0295070i	0.474228	−	0.880402i	$-0.342727\pi$
$997$	−1.61374	−	0.931694i	−0.0511077	−	0.0295070i	−0.525336	+	0.850895i	$0.676060\pi$
$998$	−2.01114	−	13.4637i	−0.0636614	−	0.426184i
$999$	18.0396	−	16.5708i	0.570748	−	0.524278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.3	yes	48
3.2	odd	2		1080.2.bm.a.251.22		48
4.3	odd	2		1440.2.cc.b.911.10		48
8.3	odd	2		360.2.bm.a.11.6	✓	48
8.5	even	2		1440.2.cc.a.911.10		48
9.4	even	3		1080.2.bm.b.611.19		48
9.5	odd	6		360.2.bm.a.131.6	yes	48
12.11	even	2		4320.2.cc.a.1871.3		48
24.5	odd	2		4320.2.cc.b.1871.22		48
24.11	even	2		1080.2.bm.b.251.19		48
36.23	even	6		1440.2.cc.a.1391.10		48
36.31	odd	6		4320.2.cc.b.3311.22		48
72.5	odd	6		1440.2.cc.b.1391.10		48
72.13	even	6		4320.2.cc.a.3311.3		48
72.59	even	6	inner	360.2.bm.b.131.3	yes	48
72.67	odd	6		1080.2.bm.a.611.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.6	✓	48	8.3	odd	2
360.2.bm.a.131.6	yes	48	9.5	odd	6
360.2.bm.b.11.3	yes	48	1.1	even	1	trivial
360.2.bm.b.131.3	yes	48	72.59	even	6	inner
1080.2.bm.a.251.22		48	3.2	odd	2
1080.2.bm.a.611.22		48	72.67	odd	6
1080.2.bm.b.251.19		48	24.11	even	2
1080.2.bm.b.611.19		48	9.4	even	3
1440.2.cc.a.911.10		48	8.5	even	2
1440.2.cc.a.1391.10		48	36.23	even	6
1440.2.cc.b.911.10		48	4.3	odd	2
1440.2.cc.b.1391.10		48	72.5	odd	6
4320.2.cc.a.1871.3		48	12.11	even	2
4320.2.cc.a.3311.3		48	72.13	even	6
4320.2.cc.b.1871.22		48	24.5	odd	2
4320.2.cc.b.3311.22		48	36.31	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31577 - 0.518408i) q^{2} +(0.424591 + 1.67920i) q^{3} +(1.46251 + 1.36421i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.311848 - 2.42956i) q^{6} +(3.88456 + 2.24275i) q^{7} +(-1.21710 - 2.55317i) q^{8} +(-2.63944 + 1.42595i) q^{9} +O(q^{10})\)	\(q+(-1.31577 - 0.518408i) q^{2} +(0.424591 + 1.67920i) q^{3} +(1.46251 + 1.36421i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.311848 - 2.42956i) q^{6} +(3.88456 + 2.24275i) q^{7} +(-1.21710 - 2.55317i) q^{8} +(-2.63944 + 1.42595i) q^{9} +(-0.208931 - 1.39870i) q^{10} +(1.05081 + 0.606687i) q^{11} +(-1.66982 + 3.03508i) q^{12} +(1.71090 - 0.987790i) q^{13} +(-3.94853 - 4.96473i) q^{14} +(-1.24194 + 1.20731i) q^{15} +(0.277844 + 3.99034i) q^{16} -5.28743i q^{17} +(4.21213 - 0.507913i) q^{18} -4.86627 q^{19} +(-0.450191 + 1.94867i) q^{20} +(-2.11668 + 7.47521i) q^{21} +(-1.06812 - 1.34301i) q^{22} +(1.40767 + 2.43816i) q^{23} +(3.77051 - 3.12781i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.76323 + 0.412759i) q^{26} +(-3.51514 - 3.82672i) q^{27} +(2.62160 + 8.57940i) q^{28} +(-4.20865 + 7.28960i) q^{29} +(2.25998 - 0.944711i) q^{30} +(6.04943 - 3.49264i) q^{31} +(1.70305 - 5.39441i) q^{32} +(-0.572584 + 2.02212i) q^{33} +(-2.74105 + 6.95704i) q^{34} +4.48550i q^{35} +(-5.80550 - 1.51531i) q^{36} +4.71412i q^{37} +(6.40290 + 2.52272i) q^{38} +(2.38513 + 2.45355i) q^{39} +(1.60256 - 2.33063i) q^{40} +(-5.30898 + 3.06514i) q^{41} +(6.66028 - 8.73836i) q^{42} +(1.17866 - 2.04150i) q^{43} +(0.709169 + 2.32082i) q^{44} +(-2.55463 - 1.57285i) q^{45} +(-0.588212 - 3.93781i) q^{46} +(5.97373 - 10.3468i) q^{47} +(-6.58262 + 2.16082i) q^{48} +(6.55985 + 11.3620i) q^{49} +(1.10684 - 0.880287i) q^{50} +(8.87867 - 2.24500i) q^{51} +(3.84976 + 0.889388i) q^{52} +0.739256 q^{53} +(2.64132 + 6.85736i) q^{54} +1.21337i q^{55} +(0.998212 - 12.6476i) q^{56} +(-2.06618 - 8.17146i) q^{57} +(9.31661 - 7.40964i) q^{58} +(1.70932 - 0.986877i) q^{59} +(-3.46337 + 0.0714286i) q^{60} +(-4.81044 - 2.77731i) q^{61} +(-9.77027 + 1.45944i) q^{62} +(-13.4511 - 0.380430i) q^{63} +(-5.03732 + 6.21493i) q^{64} +(1.71090 + 0.987790i) q^{65} +(1.80167 - 2.36382i) q^{66} +(1.58725 + 2.74920i) q^{67} +(7.21318 - 7.73289i) q^{68} +(-3.49648 + 3.39899i) q^{69} +(2.32532 - 5.90189i) q^{70} +3.40951 q^{71} +(6.85316 + 5.00342i) q^{72} -6.69774 q^{73} +(2.44384 - 6.20271i) q^{74} +(-1.66653 - 0.471895i) q^{75} +(-7.11695 - 6.63863i) q^{76} +(2.72129 + 4.71342i) q^{77} +(-1.86635 - 4.46478i) q^{78} +(-11.2535 - 6.49720i) q^{79} +(-3.31681 + 2.23579i) q^{80} +(4.93333 - 7.52743i) q^{81} +(8.57439 - 1.28080i) q^{82} +(-5.00954 - 2.89226i) q^{83} +(-13.2934 + 8.04493i) q^{84} +(4.57905 - 2.64371i) q^{85} +(-2.60918 + 2.07512i) q^{86} +(-14.0277 - 3.97208i) q^{87} +(0.270027 - 3.42130i) q^{88} -2.71936i q^{89} +(2.54593 + 3.39385i) q^{90} +8.86146 q^{91} +(-1.26744 + 5.48619i) q^{92} +(8.43338 + 8.67527i) q^{93} +(-13.2239 + 10.5172i) q^{94} +(-2.43314 - 4.21431i) q^{95} +(9.78140 + 0.569340i) q^{96} +(8.61075 - 14.9143i) q^{97} +(-2.74111 - 18.3505i) q^{98} +(-3.63867 - 0.102910i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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