LMFDB - Embedded newform 363.2.e.f.130.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(124,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("363.124");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, 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:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			130.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	363.130
Dual form			363.2.e.f.148.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 - 2.48990i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.92705 - 2.85317i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.809017 - 2.48990i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.61803 q^{10} -4.85410 q^{12} +(-0.0729490 + 0.224514i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(3.04508 + 9.37181i) q^{16} +(0.354102 + 1.08981i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(4.73607 - 3.44095i) q^{19} +(-0.927051 + 2.85317i) q^{20} -1.00000 q^{21} +0.236068 q^{23} +(-2.30902 + 7.10642i) q^{24} +(3.73607 - 2.71441i) q^{25} +(0.500000 + 0.363271i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-1.30902 + 0.951057i) q^{30} +(-1.88197 + 5.79210i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(-0.190983 + 0.587785i) q^{35} +(-3.92705 + 2.85317i) q^{36} +(5.04508 + 3.66547i) q^{37} +(-4.73607 - 14.5761i) q^{38} +(0.0729490 + 0.224514i) q^{39} +(3.73607 + 2.71441i) q^{40} +(0.190983 - 0.138757i) q^{41} +(-0.809017 + 2.48990i) q^{42} +6.70820 q^{43} -0.618034 q^{45} +(0.190983 - 0.587785i) q^{46} +(8.16312 - 5.93085i) q^{47} +(7.97214 + 5.79210i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(-3.73607 - 11.4984i) q^{50} +(0.927051 + 0.673542i) q^{51} +(0.927051 - 0.673542i) q^{52} +(-0.118034 + 0.363271i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(1.80902 - 5.56758i) q^{57} +(-12.7082 + 9.23305i) q^{58} +(-5.97214 - 4.33901i) q^{59} +(0.927051 + 2.85317i) q^{60} +(3.57295 + 10.9964i) q^{61} +(12.8992 + 9.37181i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(2.69098 - 8.28199i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(1.71885 - 5.29007i) q^{68} +(0.190983 - 0.138757i) q^{69} +(1.30902 + 0.951057i) q^{70} +(3.19098 + 9.82084i) q^{71} +(2.30902 + 7.10642i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(13.2082 - 9.59632i) q^{74} +(1.42705 - 4.39201i) q^{75} -28.4164 q^{76} +0.618034 q^{78} +(-3.39919 + 10.4616i) q^{79} +(4.92705 - 3.57971i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.190983 - 0.587785i) q^{82} +(-0.454915 - 1.40008i) q^{83} +(3.92705 + 2.85317i) q^{84} +(0.572949 - 0.416272i) q^{85} +(5.42705 - 16.7027i) q^{86} -6.00000 q^{87} -8.23607 q^{89} +(-0.500000 + 1.53884i) q^{90} +(0.190983 - 0.138757i) q^{91} +(-0.927051 - 0.673542i) q^{92} +(1.88197 + 5.79210i) q^{93} +(-8.16312 - 25.1235i) q^{94} +(-2.92705 - 2.12663i) q^{95} +(8.78115 - 6.37988i) q^{96} +(2.42705 - 7.46969i) q^{97} -15.7082 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} - 9 q^{4} - 3 q^{5} - q^{6} - q^{7} - 13 q^{8} - q^{9} - 2 q^{10} - 6 q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} + 3 q^{20} - 4 q^{21}+ \cdots - 36 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^3 - 9 * q^4 - 3 * q^5 - q^6 - q^7 - 13 * q^8 - q^9 - 2 * q^10 - 6 * q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^23 - 7 * q^24 + 6 * q^25 + 2 * q^26 + q^27 + 6 * q^28 - 6 * q^29 - 3 * q^30 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 - 9 * q^36 + 9 * q^37 - 10 * q^38 + 7 * q^39 + 6 * q^40 + 3 * q^41 - q^42 + 2 * q^45 + 3 * q^46 + 17 * q^47 + 14 * q^48 + 6 * q^49 - 6 * q^50 - 3 * q^51 - 3 * q^52 + 4 * q^53 - 6 * q^54 + 12 * q^56 + 5 * q^57 - 24 * q^58 - 6 * q^59 - 3 * q^60 + 21 * q^61 + 27 * q^62 - q^63 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^69 + 3 * q^70 + 15 * q^71 + 7 * q^72 - 14 * q^73 + 26 * q^74 - q^75 - 60 * q^76 - 2 * q^78 + 11 * q^79 + 13 * q^80 - q^81 - 3 * q^82 - 13 * q^83 + 9 * q^84 + 9 * q^85 + 15 * q^86 - 24 * q^87 - 24 * q^89 - 2 * q^90 + 3 * q^91 + 3 * q^92 + 12 * q^93 - 17 * q^94 - 5 * q^95 + 15 * q^96 + 3 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.809017	−	2.48990i	0.572061	−	1.76062i	−0.0739128	−	0.997265i	$-0.523549\pi$
$2$	0.809017	−	2.48990i	0.572061	−	1.76062i	0.645974	−	0.763359i	$-0.276451\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	−3.92705	−	2.85317i	−1.96353	−	1.42658i
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	0.899226	−	0.437485i	$-0.144131\pi$
$5$	−0.190983	−	0.587785i	−0.0854102	−	0.262866i	−0.984636	+	0.174619i	$0.944131\pi$
$6$	−0.809017	−	2.48990i	−0.330280	−	1.01650i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i	0.424304	−	0.905520i	$-0.360519\pi$
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i	−0.730084	+	0.683358i	$0.760519\pi$
$8$	−6.04508	+	4.39201i	−2.13726	+	1.55281i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$	−1.61803			−0.511667
$11$		0			0
$11$		0			0
$12$	−4.85410			−1.40126
$13$	−0.0729490	+	0.224514i	−0.0202324	+	0.0622690i	−0.960663	−	0.277717i	$-0.910422\pi$
$13$	−0.0729490	+	0.224514i	−0.0202324	+	0.0622690i	0.940431	+	0.339986i	$0.110422\pi$
$14$	−2.11803	+	1.53884i	−0.566068	+	0.411273i
$15$	−0.500000	−	0.363271i	−0.129099	−	0.0937962i
$16$	3.04508	+	9.37181i	0.761271	+	2.34295i
$17$	0.354102	+	1.08981i	0.0858823	+	0.264319i	0.984770	−	0.173860i	$-0.0556239\pi$
$17$	0.354102	+	1.08981i	0.0858823	+	0.264319i	−0.898888	+	0.438178i	$0.855624\pi$
$18$	−2.11803	−	1.53884i	−0.499225	−	0.362708i
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$	−0.927051	+	2.85317i	−0.207295	+	0.637988i
$21$	−1.00000			−0.218218
$22$		0			0
$23$	0.236068			0.0492236			0.0246118	−	0.999697i	$-0.492165\pi$
$23$	0.236068			0.0492236			0.0246118	+	0.999697i	$0.492165\pi$
$24$	−2.30902	+	7.10642i	−0.471326	+	1.45059i
$25$	3.73607	−	2.71441i	0.747214	−	0.542882i
$26$	0.500000	+	0.363271i	0.0980581	+	0.0712434i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	1.50000	+	4.61653i	0.283473	+	0.872441i
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	0.0374370	−	0.999299i	$-0.488081\pi$
$29$	−4.85410	−	3.52671i	−0.901384	−	0.654894i	−0.938821	+	0.344405i	$0.888081\pi$
$30$	−1.30902	+	0.951057i	−0.238993	+	0.173638i
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	0.627209	+	0.778851i	$0.284197\pi$
$31$	−1.88197	+	5.79210i	−0.338011	+	1.04029i	−0.965220	+	0.261440i	$0.915803\pi$
$32$	10.8541			1.91875
$33$		0			0
$34$	3.00000			0.514496
$35$	−0.190983	+	0.587785i	−0.0322820	+	0.0993538i
$36$	−3.92705	+	2.85317i	−0.654508	+	0.475528i
$37$	5.04508	+	3.66547i	0.829407	+	0.602599i	0.919391	−	0.393344i	$-0.128682\pi$
$37$	5.04508	+	3.66547i	0.829407	+	0.602599i	−0.0899846	+	0.995943i	$0.528682\pi$
$38$	−4.73607	−	14.5761i	−0.768292	−	2.36456i
$39$	0.0729490	+	0.224514i	0.0116812	+	0.0359510i
$40$	3.73607	+	2.71441i	0.590724	+	0.429186i
$41$	0.190983	−	0.138757i	0.0298265	−	0.0216702i	−0.572772	−	0.819715i	$-0.694132\pi$
$41$	0.190983	−	0.138757i	0.0298265	−	0.0216702i	0.602599	+	0.798044i	$0.294132\pi$
$42$	−0.809017	+	2.48990i	−0.124834	+	0.384200i
$43$	6.70820			1.02299			0.511496	−	0.859286i	$-0.329092\pi$
$43$	6.70820			1.02299			0.511496	+	0.859286i	$0.329092\pi$
$44$		0			0
$45$	−0.618034			−0.0921311
$46$	0.190983	−	0.587785i	0.0281589	−	0.0866642i
$47$	8.16312	−	5.93085i	1.19071	−	0.865104i	0.197374	−	0.980328i	$-0.436759\pi$
$47$	8.16312	−	5.93085i	1.19071	−	0.865104i	0.993339	+	0.115224i	$0.0367587\pi$
$48$	7.97214	+	5.79210i	1.15068	+	0.836017i
$49$	−1.85410	−	5.70634i	−0.264872	−	0.815191i
$50$	−3.73607	−	11.4984i	−0.528360	−	1.62612i
$51$	0.927051	+	0.673542i	0.129813	+	0.0943147i
$52$	0.927051	−	0.673542i	0.128559	−	0.0934035i
$53$	−0.118034	+	0.363271i	−0.0162132	+	0.0498991i	−0.958836	−	0.283961i	$-0.908351\pi$
$53$	−0.118034	+	0.363271i	−0.0162132	+	0.0498991i	0.942623	+	0.333860i	$0.108351\pi$
$54$	−2.61803			−0.356269
$55$		0			0
$56$	7.47214			0.998506
$57$	1.80902	−	5.56758i	0.239610	−	0.737444i
$58$	−12.7082	+	9.23305i	−1.66867	+	1.21236i
$59$	−5.97214	−	4.33901i	−0.777506	−	0.564891i	0.126724	−	0.991938i	$-0.459554\pi$
$59$	−5.97214	−	4.33901i	−0.777506	−	0.564891i	−0.904229	+	0.427047i	$0.859554\pi$
$60$	0.927051	+	2.85317i	0.119682	+	0.368343i
$61$	3.57295	+	10.9964i	0.457469	+	1.40795i	0.868212	+	0.496194i	$0.165270\pi$
$61$	3.57295	+	10.9964i	0.457469	+	1.40795i	−0.410742	+	0.911751i	$0.634730\pi$
$62$	12.8992	+	9.37181i	1.63820	+	1.19022i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	2.69098	−	8.28199i	0.336373	−	1.03525i
$65$	0.145898			0.0180964
$66$		0			0
$67$	1.85410			0.226515			0.113257	−	0.993566i	$-0.463872\pi$
$67$	1.85410			0.226515			0.113257	+	0.993566i	$0.463872\pi$
$68$	1.71885	−	5.29007i	0.208441	−	0.641515i
$69$	0.190983	−	0.138757i	0.0229917	−	0.0167044i
$70$	1.30902	+	0.951057i	0.156457	+	0.113673i
$71$	3.19098	+	9.82084i	0.378700	+	1.16552i	0.940948	+	0.338550i	$0.109937\pi$
$71$	3.19098	+	9.82084i	0.378700	+	1.16552i	−0.562248	+	0.826968i	$0.690063\pi$
$72$	2.30902	+	7.10642i	0.272120	+	0.837500i
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	0.283771	−	0.958892i	$-0.408415\pi$
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	−0.824271	+	0.566196i	$0.808415\pi$
$74$	13.2082	−	9.59632i	1.53542	−	1.11555i
$75$	1.42705	−	4.39201i	0.164782	−	0.507146i
$76$	−28.4164			−3.25959
$77$		0			0
$78$	0.618034			0.0699786
$79$	−3.39919	+	10.4616i	−0.382438	+	1.17702i	0.555883	+	0.831260i	$0.312380\pi$
$79$	−3.39919	+	10.4616i	−0.382438	+	1.17702i	−0.938322	+	0.345764i	$0.887620\pi$
$80$	4.92705	−	3.57971i	0.550861	−	0.400224i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−0.190983	−	0.587785i	−0.0210905	−	0.0649100i
$83$	−0.454915	−	1.40008i	−0.0499334	−	0.153679i	0.922981	−	0.384846i	$-0.125746\pi$
$83$	−0.454915	−	1.40008i	−0.0499334	−	0.153679i	−0.972914	+	0.231167i	$0.925746\pi$
$84$	3.92705	+	2.85317i	0.428476	+	0.311306i
$85$	0.572949	−	0.416272i	0.0621450	−	0.0451510i
$86$	5.42705	−	16.7027i	0.585214	−	1.80110i
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−8.23607			−0.873021			−0.436511	−	0.899699i	$-0.643786\pi$
$89$	−8.23607			−0.873021			−0.436511	+	0.899699i	$0.643786\pi$
$90$	−0.500000	+	1.53884i	−0.0527046	+	0.162208i
$91$	0.190983	−	0.138757i	0.0200205	−	0.0145457i
$92$	−0.927051	−	0.673542i	−0.0966517	−	0.0702216i
$93$	1.88197	+	5.79210i	0.195151	+	0.600612i
$94$	−8.16312	−	25.1235i	−0.841961	−	2.59129i
$95$	−2.92705	−	2.12663i	−0.300309	−	0.218187i
$96$	8.78115	−	6.37988i	0.896223	−	0.651144i
$97$	2.42705	−	7.46969i	0.246430	−	0.758433i	−0.748968	−	0.662606i	$-0.769451\pi$
$97$	2.42705	−	7.46969i	0.246430	−	0.758433i	0.995398	−	0.0958268i	$-0.0305495\pi$
$98$	−15.7082			−1.58677
$99$		0			0
$100$	−22.4164			−2.24164
$101$	3.16312	−	9.73508i	0.314742	−	0.968677i	−0.661118	−	0.750282i	$-0.729918\pi$
$101$	3.16312	−	9.73508i	0.314742	−	0.968677i	0.975860	−	0.218395i	$-0.0700821\pi$
$102$	2.42705	−	1.76336i	0.240314	−	0.174598i
$103$	8.85410	+	6.43288i	0.872421	+	0.633851i	0.931235	−	0.364418i	$-0.118732\pi$
$103$	8.85410	+	6.43288i	0.872421	+	0.633851i	−0.0588148	+	0.998269i	$0.518732\pi$
$104$	−0.545085	−	1.67760i	−0.0534500	−	0.164502i
$105$	0.190983	+	0.587785i	0.0186380	+	0.0573620i
$106$	0.809017	+	0.587785i	0.0785787	+	0.0570908i
$107$	−9.28115	+	6.74315i	−0.897243	+	0.651885i	−0.937756	−	0.347294i	$-0.887101\pi$
$107$	−9.28115	+	6.74315i	−0.897243	+	0.651885i	0.0405134	+	0.999179i	$0.487101\pi$
$108$	−1.50000	+	4.61653i	−0.144338	+	0.444225i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$		0			0
$111$	6.23607			0.591901
$112$	3.04508	−	9.37181i	0.287733	−	0.885553i
$113$	−10.8992	+	7.91872i	−1.02531	+	0.744931i	−0.967364	−	0.253389i	$-0.918455\pi$
$113$	−10.8992	+	7.91872i	−1.02531	+	0.744931i	−0.0579448	+	0.998320i	$0.518455\pi$
$114$	−12.3992	−	9.00854i	−1.16129	−	0.843727i
$115$	−0.0450850	−	0.138757i	−0.00420420	−	0.0129392i
$116$	9.00000	+	27.6992i	0.835629	+	2.57180i
$117$	0.190983	+	0.138757i	0.0176564	+	0.0128281i
$118$	−15.6353	+	11.3597i	−1.43934	+	1.04574i
$119$	0.354102	−	1.08981i	0.0324605	−	0.0999031i
$120$	4.61803			0.421567
$121$		0			0
$122$	30.2705			2.74056
$123$	0.0729490	−	0.224514i	0.00657759	−	0.0202437i
$124$	23.9164	−	17.3763i	2.14776	−	1.56044i
$125$	−4.80902	−	3.49396i	−0.430132	−	0.312509i
$126$	0.809017	+	2.48990i	0.0720730	+	0.221818i
$127$	−2.38197	−	7.33094i	−0.211365	−	0.650516i	−0.999392	−	0.0348741i	$-0.988897\pi$
$127$	−2.38197	−	7.33094i	−0.211365	−	0.650516i	0.788026	−	0.615641i	$-0.211103\pi$
$128$	−0.881966	−	0.640786i	−0.0779555	−	0.0566380i
$129$	5.42705	−	3.94298i	0.477825	−	0.347160i
$130$	0.118034	−	0.363271i	0.0103523	−	0.0318610i
$131$	11.7984			1.03083			0.515414	−	0.856941i	$-0.327638\pi$
$131$	11.7984			1.03083			0.515414	+	0.856941i	$0.327638\pi$
$132$		0			0
$133$	−5.85410			−0.507615
$134$	1.50000	−	4.61653i	0.129580	−	0.398807i
$135$	−0.500000	+	0.363271i	−0.0430331	+	0.0312654i
$136$	−6.92705	−	5.03280i	−0.593990	−	0.431559i
$137$	3.01722	+	9.28605i	0.257779	+	0.793361i	0.993269	+	0.115826i	$0.0369516\pi$
$137$	3.01722	+	9.28605i	0.257779	+	0.793361i	−0.735491	+	0.677535i	$0.763048\pi$
$138$	−0.190983	−	0.587785i	−0.0162576	−	0.0500356i
$139$	11.7812	+	8.55951i	0.999264	+	0.726008i	0.961930	−	0.273295i	$-0.0881134\pi$
$139$	11.7812	+	8.55951i	0.999264	+	0.726008i	0.0373340	+	0.999303i	$0.488113\pi$
$140$	2.42705	−	1.76336i	0.205123	−	0.149031i
$141$	3.11803	−	9.59632i	0.262586	−	0.808156i
$142$	27.0344			2.26868
$143$		0			0
$144$	9.85410			0.821175
$145$	−1.14590	+	3.52671i	−0.0951617	+	0.292877i
$146$	−12.0902	+	8.78402i	−1.00059	+	0.726971i
$147$	−4.85410	−	3.52671i	−0.400360	−	0.290878i
$148$	−9.35410	−	28.7890i	−0.768902	−	2.36644i
$149$	1.30902	+	4.02874i	0.107239	+	0.330047i	0.990249	−	0.139306i	$-0.0444871\pi$
$149$	1.30902	+	4.02874i	0.107239	+	0.330047i	−0.883011	+	0.469353i	$0.844487\pi$
$150$	−9.78115	−	7.10642i	−0.798628	−	0.580237i
$151$	0.854102	−	0.620541i	0.0695058	−	0.0504989i	−0.552490	−	0.833520i	$-0.686322\pi$
$151$	0.854102	−	0.620541i	0.0695058	−	0.0504989i	0.621996	+	0.783021i	$0.286322\pi$
$152$	−13.5172	+	41.6017i	−1.09639	+	3.37435i
$153$	1.14590			0.0926404
$154$		0			0
$155$	3.76393			0.302326
$156$	0.354102	−	1.08981i	0.0283508	−	0.0872549i
$157$	−12.7082	+	9.23305i	−1.01423	+	0.736878i	−0.965091	−	0.261915i	$-0.915646\pi$
$157$	−12.7082	+	9.23305i	−1.01423	+	0.736878i	−0.0491340	+	0.998792i	$0.515646\pi$
$158$	23.2984	+	16.9273i	1.85352	+	1.34666i
$159$	0.118034	+	0.363271i	0.00936070	+	0.0288093i
$160$	−2.07295	−	6.37988i	−0.163881	−	0.504374i
$161$	−0.190983	−	0.138757i	−0.0150516	−	0.0109356i
$162$	−2.11803	+	1.53884i	−0.166408	+	0.120903i
$163$	−1.59017	+	4.89404i	−0.124552	+	0.383331i	−0.993819	−	0.111011i	$-0.964591\pi$
$163$	−1.59017	+	4.89404i	−0.124552	+	0.383331i	0.869267	+	0.494342i	$0.164591\pi$
$164$	−1.14590			−0.0894796
$165$		0			0
$166$	−3.85410			−0.299136
$167$	−3.71885	+	11.4454i	−0.287773	+	0.885674i	0.697781	+	0.716311i	$0.254171\pi$
$167$	−3.71885	+	11.4454i	−0.287773	+	0.885674i	−0.985554	+	0.169363i	$0.945829\pi$
$168$	6.04508	−	4.39201i	0.466388	−	0.338851i
$169$	10.4721	+	7.60845i	0.805549	+	0.585266i
$170$	−0.572949	−	1.76336i	−0.0439432	−	0.135243i
$171$	−1.80902	−	5.56758i	−0.138339	−	0.425764i
$172$	−26.3435	−	19.1396i	−2.00867	−	1.45938i
$173$	−14.5902	+	10.6004i	−1.10927	+	0.805932i	−0.982549	−	0.186006i	$-0.940445\pi$
$173$	−14.5902	+	10.6004i	−1.10927	+	0.805932i	−0.126722	+	0.991938i	$0.540445\pi$
$174$	−4.85410	+	14.9394i	−0.367989	+	1.13255i
$175$	−4.61803			−0.349091
$176$		0			0
$177$	−7.38197			−0.554863
$178$	−6.66312	+	20.5070i	−0.499422	+	1.53706i
$179$	6.89919	−	5.01255i	0.515669	−	0.374656i	−0.299301	−	0.954159i	$-0.596753\pi$
$179$	6.89919	−	5.01255i	0.515669	−	0.374656i	0.814970	+	0.579503i	$0.196753\pi$
$180$	2.42705	+	1.76336i	0.180902	+	0.131433i
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	0.975881	−	0.218301i	$-0.0700515\pi$
$181$	0.781153	+	2.40414i	0.0580626	+	0.178698i	−0.917819	+	0.396999i	$0.870051\pi$
$182$	−0.190983	−	0.587785i	−0.0141566	−	0.0435695i
$183$	9.35410	+	6.79615i	0.691475	+	0.502386i
$184$	−1.42705	+	1.03681i	−0.105204	+	0.0764349i
$185$	1.19098	−	3.66547i	0.0875628	−	0.269491i
$186$	15.9443			1.16909
$187$		0			0
$188$	−48.9787			−3.57214
$189$	−0.309017	+	0.951057i	−0.0224777	+	0.0691792i
$190$	−7.66312	+	5.56758i	−0.555941	+	0.403915i
$191$	0.663119	+	0.481784i	0.0479816	+	0.0348607i	0.611518	−	0.791231i	$-0.290559\pi$
$191$	0.663119	+	0.481784i	0.0479816	+	0.0348607i	−0.563536	+	0.826092i	$0.690559\pi$
$192$	−2.69098	−	8.28199i	−0.194205	−	0.597701i
$193$	0.972136	+	2.99193i	0.0699759	+	0.215364i	0.979929	−	0.199348i	$-0.0638824\pi$
$193$	0.972136	+	2.99193i	0.0699759	+	0.215364i	−0.909953	+	0.414712i	$0.863882\pi$
$194$	−16.6353	−	12.0862i	−1.19434	−	0.867740i
$195$	0.118034	−	0.0857567i	0.00845259	−	0.00614117i
$196$	−9.00000	+	27.6992i	−0.642857	+	1.97851i
$197$	−13.0344			−0.928666			−0.464333	−	0.885661i	$-0.653706\pi$
$197$	−13.0344			−0.928666			−0.464333	+	0.885661i	$0.653706\pi$
$198$		0			0
$199$	6.70820			0.475532			0.237766	−	0.971322i	$-0.423585\pi$
$199$	6.70820			0.475532			0.237766	+	0.971322i	$0.423585\pi$
$200$	−10.6631	+	32.8177i	−0.753996	+	2.32056i
$201$	1.50000	−	1.08981i	0.105802	−	0.0768695i
$202$	−21.6803	−	15.7517i	−1.52542	−	1.10828i
$203$	1.85410	+	5.70634i	0.130132	+	0.400506i
$204$	−1.71885	−	5.29007i	−0.120343	−	0.370379i
$205$	−0.118034	−	0.0857567i	−0.00824385	−	0.00598951i
$206$	23.1803	−	16.8415i	1.61505	−	1.17340i
$207$	0.0729490	−	0.224514i	0.00507031	−	0.0156048i
$208$	−2.32624			−0.161296
$209$		0			0
$210$	1.61803			0.111655
$211$	−1.11803	+	3.44095i	−0.0769686	+	0.236885i	−0.982137	−	0.188169i	$-0.939745\pi$
$211$	−1.11803	+	3.44095i	−0.0769686	+	0.236885i	0.905168	+	0.425054i	$0.139745\pi$
$212$	1.50000	−	1.08981i	0.103020	−	0.0748487i
$213$	8.35410	+	6.06961i	0.572414	+	0.415883i
$214$	9.28115	+	28.5645i	0.634447	+	1.95263i
$215$	−1.28115	−	3.94298i	−0.0873739	−	0.268909i
$216$	6.04508	+	4.39201i	0.411316	+	0.298839i
$217$	4.92705	−	3.57971i	0.334470	−	0.243007i
$218$	9.70820	−	29.8788i	0.657523	−	2.02365i
$219$	−5.70820			−0.385725
$220$		0			0
$221$	−0.270510			−0.0181965
$222$	5.04508	−	15.5272i	0.338604	−	1.04212i
$223$	−5.80902	+	4.22050i	−0.389001	+	0.282625i	−0.765046	−	0.643976i	$-0.777284\pi$
$223$	−5.80902	+	4.22050i	−0.389001	+	0.282625i	0.376045	+	0.926601i	$0.377284\pi$
$224$	−8.78115	−	6.37988i	−0.586715	−	0.426274i
$225$	−1.42705	−	4.39201i	−0.0951367	−	0.292801i
$226$	10.8992	+	33.5442i	0.725003	+	2.23133i
$227$	10.6631	+	7.74721i	0.707736	+	0.514200i	0.882443	−	0.470420i	$-0.155898\pi$
$227$	10.6631	+	7.74721i	0.707736	+	0.514200i	−0.174706	+	0.984621i	$0.555898\pi$
$228$	−22.9894	+	16.7027i	−1.52251	+	1.10617i
$229$	0.145898	−	0.449028i	0.00964121	−	0.0296726i	−0.946120	−	0.323816i	$-0.895034\pi$
$229$	0.145898	−	0.449028i	0.00964121	−	0.0296726i	0.955761	+	0.294143i	$0.0950342\pi$
$230$	−0.381966			−0.0251861
$231$		0			0
$232$	44.8328			2.94342
$233$	1.28115	−	3.94298i	0.0839311	−	0.258313i	−0.900280	−	0.435311i	$-0.856638\pi$
$233$	1.28115	−	3.94298i	0.0839311	−	0.258313i	0.984211	+	0.176997i	$0.0566384\pi$
$234$	0.500000	−	0.363271i	0.0326860	−	0.0237478i
$235$	−5.04508	−	3.66547i	−0.329105	−	0.239109i
$236$	11.0729	+	34.0790i	0.720788	+	2.21836i
$237$	3.39919	+	10.4616i	0.220801	+	0.679555i
$238$	−2.42705	−	1.76336i	−0.157322	−	0.114301i
$239$	0.309017	−	0.224514i	0.0199886	−	0.0145226i	−0.577746	−	0.816217i	$-0.696068\pi$
$239$	0.309017	−	0.224514i	0.0199886	−	0.0145226i	0.597735	+	0.801694i	$0.296068\pi$
$240$	1.88197	−	5.79210i	0.121480	−	0.373878i
$241$	−8.29180			−0.534122			−0.267061	−	0.963680i	$-0.586052\pi$
$241$	−8.29180			−0.534122			−0.267061	+	0.963680i	$0.586052\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	17.3435	−	53.3777i	1.11030	−	3.41716i
$245$	−3.00000	+	2.17963i	−0.191663	+	0.139251i
$246$	−0.500000	−	0.363271i	−0.0318788	−	0.0231613i
$247$	0.427051	+	1.31433i	0.0271726	+	0.0836287i
$248$	−14.0623	−	43.2793i	−0.892957	−	2.74824i
$249$	−1.19098	−	0.865300i	−0.0754755	−	0.0548361i
$250$	−12.5902	+	9.14729i	−0.796272	+	0.578526i
$251$	−6.79180	+	20.9030i	−0.428694	+	1.31939i	0.470718	+	0.882284i	$0.343995\pi$
$251$	−6.79180	+	20.9030i	−0.428694	+	1.31939i	−0.899412	+	0.437102i	$0.856005\pi$
$252$	4.85410			0.305780
$253$		0			0
$254$	−20.1803			−1.26623
$255$	0.218847	−	0.673542i	0.0137047	−	0.0421788i
$256$	11.7812	−	8.55951i	0.736322	−	0.534969i
$257$	−24.0623	−	17.4823i	−1.50097	−	1.09052i	−0.969995	−	0.243125i	$-0.921828\pi$
$257$	−24.0623	−	17.4823i	−1.50097	−	1.09052i	−0.530970	−	0.847390i	$-0.678172\pi$
$258$	−5.42705	−	16.7027i	−0.337873	−	1.03987i
$259$	−1.92705	−	5.93085i	−0.119741	−	0.368525i
$260$	−0.572949	−	0.416272i	−0.0355328	−	0.0258161i
$261$	−4.85410	+	3.52671i	−0.300461	+	0.218298i
$262$	9.54508	−	29.3768i	0.589697	−	1.81490i
$263$	15.2705			0.941620			0.470810	−	0.882235i	$-0.343962\pi$
$263$	15.2705			0.941620			0.470810	+	0.882235i	$0.343962\pi$
$264$		0			0
$265$	0.236068			0.0145015
$266$	−4.73607	+	14.5761i	−0.290387	+	0.893719i
$267$	−6.66312	+	4.84104i	−0.407776	+	0.296267i
$268$	−7.28115	−	5.29007i	−0.444767	−	0.323142i
$269$	−7.85410	−	24.1724i	−0.478873	−	1.47382i	−0.840662	−	0.541560i	$-0.817834\pi$
$269$	−7.85410	−	24.1724i	−0.478873	−	1.47382i	0.361789	−	0.932260i	$-0.382166\pi$
$270$	0.500000	+	1.53884i	0.0304290	+	0.0936509i
$271$	15.0623	+	10.9434i	0.914970	+	0.664765i	0.942267	−	0.334863i	$-0.108690\pi$
$271$	15.0623	+	10.9434i	0.914970	+	0.664765i	−0.0272970	+	0.999627i	$0.508690\pi$
$272$	−9.13525	+	6.63715i	−0.553906	+	0.402436i
$273$	0.0729490	−	0.224514i	0.00441508	−	0.0135882i
$274$	25.5623			1.54428
$275$		0			0
$276$	−1.14590			−0.0689750
$277$	9.02786	−	27.7849i	0.542432	−	1.66943i	−0.184587	−	0.982816i	$-0.559095\pi$
$277$	9.02786	−	27.7849i	0.542432	−	1.66943i	0.727019	−	0.686617i	$-0.240905\pi$
$278$	30.8435	−	22.4091i	1.84987	−	1.34401i
$279$	4.92705	+	3.57971i	0.294975	+	0.214312i
$280$	−1.42705	−	4.39201i	−0.0852826	−	0.262473i
$281$	−7.65248	−	23.5519i	−0.456508	−	1.40499i	−0.869355	−	0.494188i	$-0.835465\pi$
$281$	−7.65248	−	23.5519i	−0.456508	−	1.40499i	0.412847	−	0.910801i	$-0.364535\pi$
$282$	−21.3713	−	15.5272i	−1.27264	−	0.924630i
$283$	−4.61803	+	3.35520i	−0.274514	+	0.199446i	−0.716521	−	0.697566i	$-0.754267\pi$
$283$	−4.61803	+	3.35520i	−0.274514	+	0.199446i	0.442007	+	0.897011i	$0.354267\pi$
$284$	15.4894	−	47.6713i	0.919124	−	2.82877i
$285$	−3.61803			−0.214314
$286$		0			0
$287$	−0.236068			−0.0139347
$288$	3.35410	−	10.3229i	0.197642	−	0.608281i
$289$	12.6910	−	9.22054i	0.746528	−	0.542385i
$290$	7.85410	+	5.70634i	0.461209	+	0.335088i
$291$	−2.42705	−	7.46969i	−0.142276	−	0.437881i
$292$	8.56231	+	26.3521i	0.501071	+	1.54214i
$293$	−17.5172	−	12.7270i	−1.02337	−	0.743520i	−0.0563966	−	0.998408i	$-0.517961\pi$
$293$	−17.5172	−	12.7270i	−1.02337	−	0.743520i	−0.966970	+	0.254889i	$0.917961\pi$
$294$	−12.7082	+	9.23305i	−0.741158	+	0.538482i
$295$	−1.40983	+	4.33901i	−0.0820835	+	0.252627i
$296$	−46.5967			−2.70838
$297$		0			0
$298$	11.0902			0.642436
$299$	−0.0172209	+	0.0530006i	−0.000995912	+	0.00306510i
$300$	−18.1353	+	13.1760i	−1.04704	+	0.760719i
$301$	−5.42705	−	3.94298i	−0.312810	−	0.227270i
$302$	−0.854102	−	2.62866i	−0.0491480	−	0.151262i
$303$	−3.16312	−	9.73508i	−0.181716	−	0.559266i
$304$	46.6697	+	33.9075i	2.67669	+	1.94473i
$305$	5.78115	−	4.20025i	0.331028	−	0.240506i
$306$	0.927051	−	2.85317i	0.0529960	−	0.163105i
$307$	−27.9787			−1.59683			−0.798415	−	0.602108i	$-0.794328\pi$
$307$	−27.9787			−1.59683			−0.798415	+	0.602108i	$0.794328\pi$
$308$		0			0
$309$	10.9443			0.622598
$310$	3.04508	−	9.37181i	0.172949	−	0.532283i
$311$	−9.42705	+	6.84915i	−0.534559	+	0.388380i	−0.822060	−	0.569400i	$-0.807175\pi$
$311$	−9.42705	+	6.84915i	−0.534559	+	0.388380i	0.287501	+	0.957780i	$0.407175\pi$
$312$	−1.42705	−	1.03681i	−0.0807909	−	0.0586980i
$313$	−0.781153	−	2.40414i	−0.0441534	−	0.135890i	0.926550	−	0.376172i	$-0.122760\pi$
$313$	−0.781153	−	2.40414i	−0.0441534	−	0.135890i	−0.970703	+	0.240282i	$0.922760\pi$
$314$	12.7082	+	39.1118i	0.717165	+	2.20721i
$315$	0.500000	+	0.363271i	0.0281718	+	0.0204680i
$316$	43.1976	−	31.3849i	2.43005	−	1.76554i
$317$	−2.10739	+	6.48588i	−0.118363	+	0.364283i	−0.992634	−	0.121155i	$-0.961340\pi$
$317$	−2.10739	+	6.48588i	−0.118363	+	0.364283i	0.874271	+	0.485439i	$0.161340\pi$
$318$	1.00000			0.0560772
$319$		0			0
$320$	−5.38197			−0.300861
$321$	−3.54508	+	10.9106i	−0.197867	+	0.608973i
$322$	−0.500000	+	0.363271i	−0.0278639	+	0.0202443i
$323$	5.42705	+	3.94298i	0.301969	+	0.219393i
$324$	1.50000	+	4.61653i	0.0833333	+	0.256474i
$325$	0.336881	+	1.03681i	0.0186868	+	0.0575121i
$326$	10.8992	+	7.91872i	0.603650	+	0.438577i
$327$	9.70820	−	7.05342i	0.536865	−	0.390055i
$328$	−0.545085	+	1.67760i	−0.0300973	+	0.0926299i
$329$	−10.0902			−0.556289
$330$		0			0
$331$	16.7082			0.918366			0.459183	−	0.888342i	$-0.348142\pi$
$331$	16.7082			0.918366			0.459183	+	0.888342i	$0.348142\pi$
$332$	−2.20820	+	6.79615i	−0.121191	+	0.372987i
$333$	5.04508	−	3.66547i	0.276469	−	0.200866i
$334$	25.4894	+	18.5191i	1.39472	+	1.01332i
$335$	−0.354102	−	1.08981i	−0.0193467	−	0.0595429i
$336$	−3.04508	−	9.37181i	−0.166123	−	0.511274i
$337$	−14.7082	−	10.6861i	−0.801207	−	0.582111i	0.110061	−	0.993925i	$-0.464895\pi$
$337$	−14.7082	−	10.6861i	−0.801207	−	0.582111i	−0.911268	+	0.411814i	$0.864895\pi$
$338$	27.4164	−	19.9192i	1.49126	−	1.08346i
$339$	−4.16312	+	12.8128i	−0.226110	+	0.695894i
$340$	−3.43769			−0.186435
$341$		0			0
$342$	−15.3262			−0.828748
$343$	−4.01722	+	12.3637i	−0.216910	+	0.667579i
$344$	−40.5517	+	29.4625i	−2.18640	+	1.58851i
$345$	−0.118034	−	0.0857567i	−0.00635474	−	0.00461699i
$346$	14.5902	+	44.9039i	0.784372	+	2.41405i
$347$	0.472136	+	1.45309i	0.0253456	+	0.0780057i	0.962929	−	0.269754i	$-0.0869424\pi$
$347$	0.472136	+	1.45309i	0.0253456	+	0.0780057i	−0.937584	+	0.347760i	$0.886942\pi$
$348$	23.5623	+	17.1190i	1.26307	+	0.917676i
$349$	10.2812	−	7.46969i	0.550337	−	0.399844i	−0.277572	−	0.960705i	$-0.589530\pi$
$349$	10.2812	−	7.46969i	0.550337	−	0.399844i	0.827910	+	0.560861i	$0.189530\pi$
$350$	−3.73607	+	11.4984i	−0.199701	+	0.614617i
$351$	0.236068			0.0126004
$352$		0			0
$353$	−12.0000			−0.638696			−0.319348	−	0.947638i	$-0.603464\pi$
$353$	−12.0000			−0.638696			−0.319348	+	0.947638i	$0.603464\pi$
$354$	−5.97214	+	18.3803i	−0.317415	+	0.976904i
$355$	5.16312	−	3.75123i	0.274030	−	0.199094i
$356$	32.3435	+	23.4989i	1.71420	+	1.24544i
$357$	−0.354102	−	1.08981i	−0.0187411	−	0.0576791i
$358$	−6.89919	−	21.2335i	−0.364633	−	1.12223i
$359$	−7.85410	−	5.70634i	−0.414524	−	0.301169i	0.360907	−	0.932602i	$-0.382467\pi$
$359$	−7.85410	−	5.70634i	−0.414524	−	0.301169i	−0.775431	+	0.631433i	$0.782467\pi$
$360$	3.73607	−	2.71441i	0.196908	−	0.143062i
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	6.61803			0.347836
$363$		0			0
$364$	−1.14590			−0.0600614
$365$	−1.09017	+	3.35520i	−0.0570621	+	0.175619i
$366$	24.4894	−	17.7926i	1.28008	−	0.930032i
$367$	−17.9164	−	13.0170i	−0.935229	−	0.679484i	0.0120386	−	0.999928i	$-0.496168\pi$
$367$	−17.9164	−	13.0170i	−0.935229	−	0.679484i	−0.947267	+	0.320444i	$0.896168\pi$
$368$	0.718847	+	2.21238i	0.0374725	+	0.115328i
$369$	−0.0729490	−	0.224514i	−0.00379757	−	0.0116877i
$370$	−8.16312	−	5.93085i	−0.424380	−	0.308330i
$371$	0.309017	−	0.224514i	0.0160434	−	0.0116562i
$372$	9.13525	−	28.1154i	0.473641	−	1.45772i
$373$	−0.888544			−0.0460071			−0.0230035	−	0.999735i	$-0.507323\pi$
$373$	−0.888544			−0.0460071			−0.0230035	+	0.999735i	$0.507323\pi$
$374$		0			0
$375$	−5.94427			−0.306961
$376$	−23.2984	+	71.7050i	−1.20152	+	3.69790i
$377$	1.14590	−	0.832544i	0.0590168	−	0.0428782i
$378$	2.11803	+	1.53884i	0.108940	+	0.0791495i
$379$	−7.69098	−	23.6704i	−0.395059	−	1.21587i	−0.928915	−	0.370292i	$-0.879258\pi$
$379$	−7.69098	−	23.6704i	−0.395059	−	1.21587i	0.533856	−	0.845575i	$-0.320742\pi$
$380$	5.42705	+	16.7027i	0.278402	+	0.856833i
$381$	−6.23607	−	4.53077i	−0.319483	−	0.232118i
$382$	1.73607	−	1.26133i	0.0888250	−	0.0645351i
$383$	−3.92705	+	12.0862i	−0.200663	+	0.617577i	0.799201	+	0.601064i	$0.205256\pi$
$383$	−3.92705	+	12.0862i	−0.200663	+	0.617577i	−0.999864	+	0.0165128i	$0.994744\pi$
$384$	−1.09017			−0.0556325
$385$		0			0
$386$	8.23607			0.419205
$387$	2.07295	−	6.37988i	0.105374	−	0.324308i
$388$	−30.8435	+	22.4091i	−1.56584	+	1.13765i
$389$	29.7254	+	21.5968i	1.50714	+	1.09500i	0.967427	+	0.253151i	$0.0814669\pi$
$389$	29.7254	+	21.5968i	1.50714	+	1.09500i	0.539712	+	0.841850i	$0.318533\pi$
$390$	−0.118034	−	0.363271i	−0.00597688	−	0.0183950i
$391$	0.0835921	+	0.257270i	0.00422744	+	0.0130107i
$392$	36.2705	+	26.3521i	1.83194	+	1.33098i
$393$	9.54508	−	6.93491i	0.481486	−	0.349820i
$394$	−10.5451	+	32.4544i	−0.531254	+	1.63503i
$395$	6.79837			0.342063
$396$		0			0
$397$	−18.7082			−0.938938			−0.469469	−	0.882949i	$-0.655555\pi$
$397$	−18.7082			−0.938938			−0.469469	+	0.882949i	$0.655555\pi$
$398$	5.42705	−	16.7027i	0.272033	−	0.837233i
$399$	−4.73607	+	3.44095i	−0.237100	+	0.172263i
$400$	36.8156	+	26.7481i	1.84078	+	1.33740i
$401$	−9.79180	−	30.1360i	−0.488979	−	1.50492i	−0.826134	−	0.563473i	$-0.809465\pi$
$401$	−9.79180	−	30.1360i	−0.488979	−	1.50492i	0.337155	−	0.941449i	$-0.390535\pi$
$402$	−1.50000	−	4.61653i	−0.0748132	−	0.230251i
$403$	−1.16312	−	0.845055i	−0.0579391	−	0.0420952i
$404$	−40.1976	+	29.2052i	−1.99990	+	1.45301i
$405$	−0.190983	+	0.587785i	−0.00949002	+	0.0292073i
$406$	15.7082			0.779585
$407$		0			0
$408$	−8.56231			−0.423897
$409$	2.00000	−	6.15537i	0.0988936	−	0.304363i	−0.889355	−	0.457217i	$-0.848846\pi$
$409$	2.00000	−	6.15537i	0.0988936	−	0.304363i	0.988249	+	0.152854i	$0.0488463\pi$
$410$	−0.309017	+	0.224514i	−0.0152613	+	0.0110880i
$411$	7.89919	+	5.73910i	0.389638	+	0.283089i
$412$	−16.4164	−	50.5245i	−0.808778	−	2.48916i
$413$	2.28115	+	7.02067i	0.112248	+	0.345464i
$414$	−0.500000	−	0.363271i	−0.0245737	−	0.0178538i
$415$	−0.736068	+	0.534785i	−0.0361322	+	0.0262515i
$416$	−0.791796	+	2.43690i	−0.0388210	+	0.119479i
$417$	14.5623			0.713119
$418$		0			0
$419$	31.4508			1.53647			0.768237	−	0.640165i	$-0.221134\pi$
$419$	31.4508			1.53647			0.768237	+	0.640165i	$0.221134\pi$
$420$	0.927051	−	2.85317i	0.0452355	−	0.139220i
$421$	−8.50000	+	6.17561i	−0.414265	+	0.300981i	−0.775326	−	0.631561i	$-0.782414\pi$
$421$	−8.50000	+	6.17561i	−0.414265	+	0.300981i	0.361061	+	0.932542i	$0.382414\pi$
$422$	7.66312	+	5.56758i	0.373035	+	0.271026i
$423$	−3.11803	−	9.59632i	−0.151604	−	0.466589i
$424$	−0.881966	−	2.71441i	−0.0428321	−	0.131824i
$425$	4.28115	+	3.11044i	0.207666	+	0.150878i
$426$	21.8713	−	15.8904i	1.05967	−	0.769895i
$427$	3.57295	−	10.9964i	0.172907	−	0.532153i
$428$	55.6869			2.69173
$429$		0			0
$430$	−10.8541			−0.523431
$431$	1.82624	−	5.62058i	0.0879668	−	0.270734i	−0.897390	−	0.441238i	$-0.854540\pi$
$431$	1.82624	−	5.62058i	0.0879668	−	0.270734i	0.985357	+	0.170504i	$0.0545395\pi$
$432$	7.97214	−	5.79210i	0.383560	−	0.278672i
$433$	−28.5623	−	20.7517i	−1.37262	−	0.997264i	−0.997528	−	0.0702758i	$-0.977612\pi$
$433$	−28.5623	−	20.7517i	−1.37262	−	0.997264i	−0.375089	−	0.926989i	$-0.622388\pi$
$434$	−4.92705	−	15.1639i	−0.236506	−	0.727891i
$435$	1.14590	+	3.52671i	0.0549416	+	0.169093i
$436$	−47.1246	−	34.2380i	−2.25686	−	1.63970i
$437$	1.11803	−	0.812299i	0.0534828	−	0.0388575i
$438$	−4.61803	+	14.2128i	−0.220658	+	0.679116i
$439$	−23.2918			−1.11166			−0.555828	−	0.831297i	$-0.687599\pi$
$439$	−23.2918			−1.11166			−0.555828	+	0.831297i	$0.687599\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	−0.218847	+	0.673542i	−0.0104095	+	0.0320371i
$443$	25.5623	−	18.5721i	1.21450	−	0.882387i	0.218870	−	0.975754i	$-0.429763\pi$
$443$	25.5623	−	18.5721i	1.21450	−	0.882387i	0.995632	+	0.0933668i	$0.0297629\pi$
$444$	−24.4894	−	17.7926i	−1.16221	−	0.844397i
$445$	1.57295	+	4.84104i	0.0745649	+	0.229487i
$446$	5.80902	+	17.8783i	0.275065	+	0.846563i
$447$	3.42705	+	2.48990i	0.162094	+	0.117768i
$448$	−7.04508	+	5.11855i	−0.332849	+	0.241829i
$449$	−2.79837	+	8.61251i	−0.132063	+	0.406449i	−0.995122	−	0.0986549i	$-0.968546\pi$
$449$	−2.79837	+	8.61251i	−0.132063	+	0.406449i	0.863058	+	0.505104i	$0.168546\pi$
$450$	−12.0902			−0.569936
$451$		0			0
$452$	65.3951			3.07593
$453$	0.326238	−	1.00406i	0.0153280	−	0.0471747i
$454$	27.9164	−	20.2825i	1.31018	−	0.951903i
$455$	−0.118034	−	0.0857567i	−0.00553352	−	0.00402034i
$456$	13.5172	+	41.6017i	0.633002	+	1.94818i
$457$	−7.40983	−	22.8051i	−0.346617	−	1.06678i	−0.960712	−	0.277546i	$-0.910479\pi$
$457$	−7.40983	−	22.8051i	−0.346617	−	1.06678i	0.614095	−	0.789232i	$-0.289521\pi$
$458$	−1.00000	−	0.726543i	−0.0467269	−	0.0339491i
$459$	0.927051	−	0.673542i	0.0432710	−	0.0314382i
$460$	−0.218847	+	0.673542i	−0.0102038	+	0.0314041i
$461$	−9.27051			−0.431771			−0.215885	−	0.976419i	$-0.569264\pi$
$461$	−9.27051			−0.431771			−0.215885	+	0.976419i	$0.569264\pi$
$462$		0			0
$463$	1.72949			0.0803762			0.0401881	−	0.999192i	$-0.487204\pi$
$463$	1.72949			0.0803762			0.0401881	+	0.999192i	$0.487204\pi$
$464$	18.2705	−	56.2308i	0.848187	−	2.61045i
$465$	3.04508	−	2.21238i	0.141212	−	0.102597i
$466$	−8.78115	−	6.37988i	−0.406779	−	0.295542i
$467$	6.45492	+	19.8662i	0.298698	+	0.919297i	0.981954	+	0.189119i	$0.0605631\pi$
$467$	6.45492	+	19.8662i	0.298698	+	0.919297i	−0.683256	+	0.730179i	$0.739437\pi$
$468$	−0.354102	−	1.08981i	−0.0163684	−	0.0503767i
$469$	−1.50000	−	1.08981i	−0.0692636	−	0.0503229i
$470$	−13.2082	+	9.59632i	−0.609249	+	0.442645i
$471$	−4.85410	+	14.9394i	−0.223665	+	0.688371i
$472$	55.1591			2.53890
$473$		0			0
$474$	28.7984			1.32275
$475$	8.35410	−	25.7113i	0.383312	−	1.17971i
$476$	−4.50000	+	3.26944i	−0.206257	+	0.149855i
$477$	0.309017	+	0.224514i	0.0141489	+	0.0102798i
$478$	−0.309017	−	0.951057i	−0.0141341	−	0.0435003i
$479$	8.77051	+	26.9929i	0.400735	+	1.23333i	0.924405	+	0.381414i	$0.124563\pi$
$479$	8.77051	+	26.9929i	0.400735	+	1.23333i	−0.523670	+	0.851921i	$0.675437\pi$
$480$	−5.42705	−	3.94298i	−0.247710	−	0.179972i
$481$	−1.19098	+	0.865300i	−0.0543042	+	0.0394543i
$482$	−6.70820	+	20.6457i	−0.305550	+	0.940387i
$483$	−0.236068			−0.0107415
$484$		0			0
$485$	−4.85410			−0.220413
$486$	−0.809017	+	2.48990i	−0.0366978	+	0.112944i
$487$	10.2812	−	7.46969i	0.465884	−	0.338484i	−0.329951	−	0.943998i	$-0.607032\pi$
$487$	10.2812	−	7.46969i	0.465884	−	0.338484i	0.795835	+	0.605514i	$0.207032\pi$
$488$	−69.8951	−	50.7818i	−3.16400	−	2.29878i
$489$	1.59017	+	4.89404i	0.0719100	+	0.221316i
$490$	3.00000	+	9.23305i	0.135526	+	0.417107i
$491$	−14.4894	−	10.5271i	−0.653896	−	0.475083i	0.210700	−	0.977551i	$-0.432426\pi$
$491$	−14.4894	−	10.5271i	−0.653896	−	0.475083i	−0.864596	+	0.502468i	$0.832426\pi$
$492$	−0.927051	+	0.673542i	−0.0417947	+	0.0303656i
$493$	2.12461	−	6.53888i	0.0956877	−	0.294496i
$494$	3.61803			0.162783
$495$		0			0
$496$	−60.0132			−2.69467
$497$	3.19098	−	9.82084i	0.143135	−	0.440525i
$498$	−3.11803	+	2.26538i	−0.139722	+	0.101514i
$499$	14.6803	+	10.6659i	0.657182	+	0.477471i	0.865710	−	0.500546i	$-0.166867\pi$
$499$	14.6803	+	10.6659i	0.657182	+	0.477471i	−0.208528	+	0.978016i	$0.566867\pi$
$500$	8.91641	+	27.4419i	0.398754	+	1.22724i
$501$	3.71885	+	11.4454i	0.166146	+	0.511344i
$502$	46.5517	+	33.8218i	2.07770	+	1.50954i
$503$	7.00000	−	5.08580i	0.312115	−	0.226765i	−0.420689	−	0.907205i	$-0.638212\pi$
$503$	7.00000	−	5.08580i	0.312115	−	0.226765i	0.732803	+	0.680441i	$0.238212\pi$
$504$	2.30902	−	7.10642i	0.102852	−	0.316545i
$505$	−6.32624			−0.281514
$506$		0			0
$507$	12.9443			0.574875
$508$	−11.5623	+	35.5851i	−0.512994	+	1.57883i
$509$	−31.3435	+	22.7724i	−1.38927	+	1.00937i	−0.393330	+	0.919397i	$0.628677\pi$
$509$	−31.3435	+	22.7724i	−1.38927	+	1.00937i	−0.995945	+	0.0899695i	$0.971323\pi$
$510$	−1.50000	−	1.08981i	−0.0664211	−	0.0482578i
$511$	1.76393	+	5.42882i	0.0780318	+	0.240157i
$512$	−12.4549	−	38.3323i	−0.550435	−	1.69406i
$513$	−4.73607	−	3.44095i	−0.209103	−	0.151922i
$514$	−62.9959	+	45.7692i	−2.77863	+	2.01879i
$515$	2.09017	−	6.43288i	0.0921039	−	0.283467i
$516$	−32.5623			−1.43348
$517$		0			0
$518$	−16.3262			−0.717334
$519$	−5.57295	+	17.1518i	−0.244625	+	0.752879i
$520$	−0.881966	+	0.640786i	−0.0386768	+	0.0281003i
$521$	−7.23607	−	5.25731i	−0.317018	−	0.230327i	0.417884	−	0.908500i	$-0.362772\pi$
$521$	−7.23607	−	5.25731i	−0.317018	−	0.230327i	−0.734902	+	0.678173i	$0.762772\pi$
$522$	4.85410	+	14.9394i	0.212458	+	0.653879i
$523$	−5.64590	−	17.3763i	−0.246878	−	0.759812i	−0.995322	−	0.0966140i	$-0.969199\pi$
$523$	−5.64590	−	17.3763i	−0.246878	−	0.759812i	0.748444	−	0.663198i	$-0.230801\pi$
$524$	−46.3328	−	33.6628i	−2.02406	−	1.47056i
$525$	−3.73607	+	2.71441i	−0.163055	+	0.118467i
$526$	12.3541	−	38.0220i	0.538664	−	1.65784i
$527$	−6.97871			−0.303998
$528$		0			0
$529$	−22.9443			−0.997577
$530$	0.190983	−	0.587785i	0.00829577	−	0.0255318i
$531$	−5.97214	+	4.33901i	−0.259169	+	0.188297i
$532$	22.9894	+	16.7027i	0.996715	+	0.724156i
$533$	0.0172209	+	0.0530006i	0.000745921	+	0.00229571i
$534$	6.66312	+	20.5070i	0.288341	+	0.887423i
$535$	5.73607	+	4.16750i	0.247992	+	0.180177i
$536$	−11.2082	+	8.14324i	−0.484121	+	0.351734i
$537$	2.63525	−	8.11048i	0.113720	−	0.349993i
$538$	−66.5410			−2.86879
$539$		0			0
$540$	3.00000			0.129099
$541$	2.31559	−	7.12667i	0.0995552	−	0.306399i	−0.888859	−	0.458181i	$-0.848501\pi$
$541$	2.31559	−	7.12667i	0.0995552	−	0.306399i	0.988414	+	0.151782i	$0.0485011\pi$
$542$	39.4336	−	28.6502i	1.69382	−	1.23063i
$543$	2.04508	+	1.48584i	0.0877630	+	0.0637635i
$544$	3.84346	+	11.8290i	0.164787	+	0.507162i
$545$	−2.29180	−	7.05342i	−0.0981698	−	0.302135i
$546$	−0.500000	−	0.363271i	−0.0213980	−	0.0155466i
$547$	−24.8713	+	18.0701i	−1.06342	+	0.772621i	−0.974718	−	0.223438i	$-0.928272\pi$
$547$	−24.8713	+	18.0701i	−1.06342	+	0.772621i	−0.0887027	+	0.996058i	$0.528272\pi$
$548$	14.6459	−	45.0754i	0.625642	−	1.92553i
$549$	11.5623			0.493467
$550$		0			0
$551$	−35.1246			−1.49636
$552$	−0.545085	+	1.67760i	−0.0232004	+	0.0714034i
$553$	8.89919	−	6.46564i	0.378432	−	0.274947i
$554$	−61.8779	−	44.9569i	−2.62894	−	1.91004i
$555$	−1.19098	−	3.66547i	−0.0505544	−	0.155590i
$556$	−21.8435	−	67.2273i	−0.926369	−	2.85107i
$557$	30.4443	+	22.1191i	1.28997	+	0.937215i	0.999805	−	0.0197634i	$-0.00629130\pi$
$557$	30.4443	+	22.1191i	1.28997	+	0.937215i	0.290161	+	0.956978i	$0.406291\pi$
$558$	12.8992	−	9.37181i	0.546066	−	0.396740i
$559$	−0.489357	+	1.50609i	−0.0206976	+	0.0637006i
$560$	−6.09017			−0.257357
$561$		0			0
$562$	−64.8328			−2.73481
$563$	−12.5451	+	38.6098i	−0.528712	+	1.62721i	0.228144	+	0.973627i	$0.426734\pi$
$563$	−12.5451	+	38.6098i	−0.528712	+	1.62721i	−0.756856	+	0.653582i	$0.773266\pi$
$564$	−39.6246	+	28.7890i	−1.66850	+	1.21223i
$565$	6.73607	+	4.89404i	0.283389	+	0.205894i
$566$	4.61803	+	14.2128i	0.194110	+	0.597411i
$567$	0.309017	+	0.951057i	0.0129775	+	0.0399406i
$568$	−62.4230	−	45.3530i	−2.61921	−	1.90297i
$569$	27.6525	−	20.0907i	1.15925	−	0.842246i	0.169569	−	0.985518i	$-0.445763\pi$
$569$	27.6525	−	20.0907i	1.15925	−	0.842246i	0.989683	+	0.143272i	$0.0457625\pi$
$570$	−2.92705	+	9.00854i	−0.122601	+	0.377326i
$571$	9.09017			0.380412			0.190206	−	0.981744i	$-0.439084\pi$
$571$	9.09017			0.380412			0.190206	+	0.981744i	$0.439084\pi$
$572$		0			0
$573$	0.819660			0.0342418
$574$	−0.190983	+	0.587785i	−0.00797148	+	0.0245337i
$575$	0.881966	−	0.640786i	0.0367805	−	0.0267226i
$576$	−7.04508	−	5.11855i	−0.293545	−	0.213273i
$577$	9.79837	+	30.1563i	0.407912	+	1.25542i	0.918439	+	0.395562i	$0.129450\pi$
$577$	9.79837	+	30.1563i	0.407912	+	1.25542i	−0.510528	+	0.859861i	$0.670550\pi$
$578$	−12.6910	−	39.0588i	−0.527875	−	1.62463i
$579$	2.54508	+	1.84911i	0.105770	+	0.0768465i
$580$	14.5623	−	10.5801i	0.604667	−	0.439316i
$581$	−0.454915	+	1.40008i	−0.0188731	+	0.0580853i
$582$	−20.5623			−0.852335
$583$		0			0
$584$	42.6525			1.76497
$585$	0.0450850	−	0.138757i	0.00186403	−	0.00573691i
$586$	−45.8607	+	33.3197i	−1.89449	+	1.37643i
$587$	1.71885	+	1.24882i	0.0709444	+	0.0515441i	0.622692	−	0.782467i	$-0.286039\pi$
$587$	1.71885	+	1.24882i	0.0709444	+	0.0515441i	−0.551748	+	0.834011i	$0.686039\pi$
$588$	9.00000	+	27.6992i	0.371154	+	1.14229i
$589$	11.0172	+	33.9075i	0.453957	+	1.39714i
$590$	9.66312	+	7.02067i	0.397824	+	0.289036i
$591$	−10.5451	+	7.66145i	−0.433767	+	0.315150i
$592$	−18.9894	+	58.4432i	−0.780458	+	2.40200i
$593$	14.0344			0.576325			0.288163	−	0.957581i	$-0.406956\pi$
$593$	14.0344			0.576325			0.288163	+	0.957581i	$0.406956\pi$
$594$		0			0
$595$	−0.708204			−0.0290335
$596$	6.35410	−	19.5559i	0.260274	−	0.801041i
$597$	5.42705	−	3.94298i	0.222114	−	0.161376i
$598$	0.118034	+	0.0857567i	0.00482677	+	0.00350685i
$599$	3.90983	+	12.0332i	0.159751	+	0.491664i	0.998611	−	0.0526833i	$-0.0167774\pi$
$599$	3.90983	+	12.0332i	0.159751	+	0.491664i	−0.838860	+	0.544347i	$0.816777\pi$
$600$	10.6631	+	32.8177i	0.435320	+	1.33978i
$601$	−5.57295	−	4.04898i	−0.227325	−	0.165162i	0.468293	−	0.883573i	$-0.344869\pi$
$601$	−5.57295	−	4.04898i	−0.227325	−	0.165162i	−0.695618	+	0.718412i	$0.744869\pi$
$602$	−14.2082	+	10.3229i	−0.579083	+	0.420729i
$603$	0.572949	−	1.76336i	0.0233323	−	0.0718094i
$604$	−5.12461			−0.208517
$605$		0			0
$606$	−26.7984			−1.08861
$607$	5.11803	−	15.7517i	0.207735	−	0.639341i	−0.791855	−	0.610709i	$-0.790885\pi$
$607$	5.11803	−	15.7517i	0.207735	−	0.639341i	0.999590	−	0.0286327i	$-0.00911532\pi$
$608$	51.4058	−	37.3485i	2.08478	−	1.51468i
$609$	4.85410	+	3.52671i	0.196698	+	0.142910i
$610$	−5.78115	−	17.7926i	−0.234072	−	0.720400i
$611$	0.736068	+	2.26538i	0.0297781	+	0.0916476i
$612$	−4.50000	−	3.26944i	−0.181902	−	0.132159i
$613$	−11.5623	+	8.40051i	−0.466997	+	0.339293i	−0.796270	−	0.604942i	$-0.793196\pi$
$613$	−11.5623	+	8.40051i	−0.466997	+	0.339293i	0.329273	+	0.944235i	$0.393196\pi$
$614$	−22.6353	+	69.6642i	−0.913485	+	2.81142i
$615$	−0.145898			−0.00588318
$616$		0			0
$617$	11.1803			0.450104			0.225052	−	0.974347i	$-0.427745\pi$
$617$	11.1803			0.450104			0.225052	+	0.974347i	$0.427745\pi$
$618$	8.85410	−	27.2501i	0.356164	−	1.09616i
$619$	−19.5172	+	14.1801i	−0.784463	+	0.569946i	−0.906315	−	0.422602i	$-0.861117\pi$
$619$	−19.5172	+	14.1801i	−0.784463	+	0.569946i	0.121852	+	0.992548i	$0.461117\pi$
$620$	−14.7812	−	10.7391i	−0.593625	−	0.431294i
$621$	−0.0729490	−	0.224514i	−0.00292734	−	0.00900944i
$622$	9.42705	+	29.0135i	0.377990	+	1.16333i
$623$	6.66312	+	4.84104i	0.266952	+	0.193952i
$624$	−1.88197	+	1.36733i	−0.0753389	+	0.0547369i
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$	−6.61803			−0.264510
$627$		0			0
$628$	76.2492			3.04268
$629$	−2.20820	+	6.79615i	−0.0880469	+	0.270980i
$630$	1.30902	−	0.951057i	0.0521525	−	0.0378910i
$631$	−15.5451	−	11.2942i	−0.618840	−	0.449614i	0.233676	−	0.972314i	$-0.424924\pi$
$631$	−15.5451	−	11.2942i	−0.618840	−	0.449614i	−0.852516	+	0.522701i	$0.824924\pi$
$632$	−25.3992	−	78.1707i	−1.01033	−	3.10946i
$633$	1.11803	+	3.44095i	0.0444379	+	0.136766i
$634$	14.4443	+	10.4944i	0.573655	+	0.416785i
$635$	−3.85410	+	2.80017i	−0.152945	+	0.111121i
$636$	0.572949	−	1.76336i	0.0227189	−	0.0699216i
$637$	1.41641			0.0561201
$638$		0			0
$639$	10.3262			0.408500
$640$	−0.208204	+	0.640786i	−0.00822998	+	0.0253293i
$641$	20.2984	−	14.7476i	0.801738	−	0.582496i	−0.109686	−	0.993966i	$-0.534984\pi$
$641$	20.2984	−	14.7476i	0.801738	−	0.582496i	0.911423	+	0.411470i	$0.134984\pi$
$642$	24.2984	+	17.6538i	0.958980	+	0.696740i
$643$	6.44427	+	19.8334i	0.254137	+	0.782154i	0.993998	+	0.109394i	$0.0348912\pi$
$643$	6.44427	+	19.8334i	0.254137	+	0.782154i	−0.739861	+	0.672760i	$0.765109\pi$
$644$	0.354102	+	1.08981i	0.0139536	+	0.0429447i
$645$	−3.35410	−	2.43690i	−0.132068	−	0.0959528i
$646$	14.2082	−	10.3229i	0.559014	−	0.406148i
$647$	13.9164	−	42.8303i	0.547110	−	1.68383i	−0.168808	−	0.985649i	$-0.553992\pi$
$647$	13.9164	−	42.8303i	0.547110	−	1.68383i	0.715918	−	0.698184i	$-0.246008\pi$
$648$	7.47214			0.293533
$649$		0			0
$650$	2.85410			0.111947
$651$	1.88197	−	5.79210i	0.0737601	−	0.227010i
$652$	20.2082	−	14.6821i	0.791414	−	0.574996i
$653$	4.54508	+	3.30220i	0.177863	+	0.129225i	0.673155	−	0.739502i	$-0.264939\pi$
$653$	4.54508	+	3.30220i	0.177863	+	0.129225i	−0.495292	+	0.868727i	$0.664939\pi$
$654$	−9.70820	−	29.8788i	−0.379621	−	1.16835i
$655$	−2.25329	−	6.93491i	−0.0880433	−	0.270969i
$656$	1.88197	+	1.36733i	0.0734784	+	0.0533852i
$657$	−4.61803	+	3.35520i	−0.180167	+	0.130899i
$658$	−8.16312	+	25.1235i	−0.318232	+	0.979416i
$659$	41.1246			1.60199			0.800994	−	0.598673i	$-0.204305\pi$
$659$	41.1246			1.60199			0.800994	+	0.598673i	$0.204305\pi$
$660$		0			0
$661$	36.5623			1.42211			0.711054	−	0.703137i	$-0.248218\pi$
$661$	36.5623			1.42211			0.711054	+	0.703137i	$0.248218\pi$
$662$	13.5172	−	41.6017i	0.525362	−	1.61690i
$663$	−0.218847	+	0.159002i	−0.00849932	+	0.00617511i
$664$	8.89919	+	6.46564i	0.345355	+	0.250915i
$665$	1.11803	+	3.44095i	0.0433555	+	0.133435i
$666$	−5.04508	−	15.5272i	−0.195493	−	0.601666i
$667$	−1.14590	−	0.832544i	−0.0443693	−	0.0322362i
$668$	47.2599	−	34.3363i	1.82854	−	1.32851i
$669$	−2.21885	+	6.82891i	−0.0857856	+	0.264021i
$670$	−3.00000			−0.115900
$671$		0			0
$672$	−10.8541			−0.418706
$673$	−11.0729	+	34.0790i	−0.426831	+	1.31365i	0.474399	+	0.880310i	$0.342665\pi$
$673$	−11.0729	+	34.0790i	−0.426831	+	1.31365i	−0.901230	+	0.433340i	$0.857335\pi$
$674$	−38.5066	+	27.9767i	−1.48322	+	1.07762i
$675$	−3.73607	−	2.71441i	−0.143801	−	0.104478i
$676$	−19.4164	−	59.7576i	−0.746785	−	2.29837i
$677$	−4.18034	−	12.8658i	−0.160664	−	0.494471i	0.838027	−	0.545629i	$-0.183709\pi$
$677$	−4.18034	−	12.8658i	−0.160664	−	0.494471i	−0.998691	+	0.0511572i	$0.983709\pi$
$678$	28.5344	+	20.7315i	1.09586	+	0.796188i
$679$	−6.35410	+	4.61653i	−0.243848	+	0.177166i
$680$	−1.63525	+	5.03280i	−0.0627092	+	0.192999i
$681$	13.1803			0.505072
$682$		0			0
$683$	9.06888			0.347011			0.173506	−	0.984833i	$-0.444491\pi$
$683$	9.06888			0.347011			0.173506	+	0.984833i	$0.444491\pi$
$684$	−8.78115	+	27.0256i	−0.335756	+	1.03335i
$685$	4.88197	−	3.54696i	0.186530	−	0.135522i
$686$	27.5344	+	20.0049i	1.05127	+	0.763792i
$687$	−0.145898	−	0.449028i	−0.00556636	−	0.0171315i
$688$	20.4271	+	62.8680i	0.778774	+	2.39682i
$689$	−0.0729490	−	0.0530006i	−0.00277914	−	0.00201916i
$690$	−0.309017	+	0.224514i	−0.0117641	+	0.00854710i
$691$	0.416408	−	1.28157i	0.0158409	−	0.0487533i	−0.942824	−	0.333292i	$-0.891840\pi$
$691$	0.416408	−	1.28157i	0.0158409	−	0.0487533i	0.958665	+	0.284539i	$0.0918405\pi$
$692$	87.5410			3.32781
$693$		0			0
$694$	4.00000			0.151838
$695$	2.78115	−	8.55951i	0.105495	−	0.324681i
$696$	36.2705	−	26.3521i	1.37483	−	0.998873i
$697$	0.218847	+	0.159002i	0.00828942	+	0.00602262i
$698$	−10.2812	−	31.6421i	−0.389147	−	1.19767i
$699$	−1.28115	−	3.94298i	−0.0484577	−	0.149137i
$700$	18.1353	+	13.1760i	0.685448	+	0.498007i
$701$	−28.1525	+	20.4540i	−1.06330	+	0.772536i	−0.974697	−	0.223531i	$-0.928242\pi$
$701$	−28.1525	+	20.4540i	−1.06330	+	0.772536i	−0.0886075	+	0.996067i	$0.528242\pi$
$702$	0.190983	−	0.587785i	0.00720819	−	0.0221845i
$703$	36.5066			1.37687
$704$		0			0
$705$	−6.23607			−0.234864
$706$	−9.70820	+	29.8788i	−0.365373	+	1.12450i
$707$	−8.28115	+	6.01661i	−0.311445	+	0.226278i
$708$	28.9894	+	21.0620i	1.08949	+	0.791558i
$709$	3.46556	+	10.6659i	0.130152	+	0.400566i	0.994804	−	0.101804i	$-0.0324615\pi$
$709$	3.46556	+	10.6659i	0.130152	+	0.400566i	−0.864653	+	0.502370i	$0.832462\pi$
$710$	−5.16312	−	15.8904i	−0.193768	−	0.596358i
$711$	8.89919	+	6.46564i	0.333746	+	0.242480i
$712$	49.7877	−	36.1729i	1.86587	−	1.35564i
$713$	−0.444272	+	1.36733i	−0.0166381	+	0.0512068i
$714$	−3.00000			−0.112272
$715$		0			0
$716$	−41.3951			−1.54701
$717$	0.118034	−	0.363271i	0.00440806	−	0.0135666i
$718$	−20.5623	+	14.9394i	−0.767378	+	0.557533i
$719$	31.1353	+	22.6211i	1.16115	+	0.843624i	0.989923	−	0.141608i	$-0.0452271\pi$
$719$	31.1353	+	22.6211i	1.16115	+	0.843624i	0.171226	+	0.985232i	$0.445227\pi$
$720$	−1.88197	−	5.79210i	−0.0701367	−	0.215859i
$721$	−3.38197	−	10.4086i	−0.125951	−	0.387637i
$722$	−32.3435	−	23.4989i	−1.20370	−	0.874538i
$723$	−6.70820	+	4.87380i	−0.249481	+	0.181258i
$724$	3.79180	−	11.6699i	0.140921	−	0.433710i
$725$	−27.7082			−1.02906
$726$		0			0
$727$	−9.14590			−0.339203			−0.169601	−	0.985513i	$-0.554248\pi$
$727$	−9.14590			−0.339203			−0.169601	+	0.985513i	$0.554248\pi$
$728$	−0.545085	+	1.67760i	−0.0202022	+	0.0621760i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	7.47214	+	5.42882i	0.276556	+	0.200930i
$731$	2.37539	+	7.31069i	0.0878569	+	0.270396i
$732$	−17.3435	−	53.3777i	−0.641033	−	1.97290i
$733$	−0.326238	−	0.237026i	−0.0120499	−	0.00875474i	0.581744	−	0.813372i	$-0.302371\pi$
$733$	−0.326238	−	0.237026i	−0.0120499	−	0.00875474i	−0.593794	+	0.804617i	$0.702371\pi$
$734$	−46.9058	+	34.0790i	−1.73132	+	1.25788i
$735$	−1.14590	+	3.52671i	−0.0422671	+	0.130085i
$736$	2.56231			0.0944478
$737$		0			0
$738$	−0.618034			−0.0227501
$739$	−0.927051	+	2.85317i	−0.0341021	+	0.104956i	−0.966659	−	0.256068i	$-0.917573\pi$
$739$	−0.927051	+	2.85317i	−0.0341021	+	0.104956i	0.932557	+	0.361024i	$0.117573\pi$
$740$	−15.1353	+	10.9964i	−0.556383	+	0.404236i
$741$	1.11803	+	0.812299i	0.0410720	+	0.0298406i
$742$	−0.309017	−	0.951057i	−0.0113444	−	0.0349144i
$743$	13.2533	+	40.7894i	0.486216	+	1.49642i	0.830212	+	0.557448i	$0.188219\pi$
$743$	13.2533	+	40.7894i	0.486216	+	1.49642i	−0.343996	+	0.938971i	$0.611781\pi$
$744$	−36.8156	−	26.7481i	−1.34973	−	0.980633i
$745$	2.11803	−	1.53884i	0.0775988	−	0.0563788i
$746$	−0.718847	+	2.21238i	−0.0263189	+	0.0810011i
$747$	−1.47214			−0.0538626
$748$		0			0
$749$	11.4721			0.419183
$750$	−4.80902	+	14.8006i	−0.175600	+	0.540443i
$751$	−13.0623	+	9.49032i	−0.476650	+	0.346307i	−0.800027	−	0.599963i	$-0.795182\pi$
$751$	−13.0623	+	9.49032i	−0.476650	+	0.346307i	0.323377	+	0.946270i	$0.395182\pi$
$752$	80.4402	+	58.4432i	2.93335	+	2.13121i
$753$	6.79180	+	20.9030i	0.247507	+	0.761748i
$754$	−1.14590	−	3.52671i	−0.0417311	−	0.128435i
$755$	−0.527864	−	0.383516i	−0.0192109	−	0.0139576i
$756$	3.92705	−	2.85317i	0.142825	−	0.103769i
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	−0.919044	−	0.394156i	$-0.871037\pi$
$757$	1.54508	−	4.75528i	0.0561571	−	0.172834i	0.975201	+	0.221322i	$0.0710371\pi$
$758$	−65.1591			−2.36668
$759$		0			0
$760$	27.0344			0.980642
$761$	−9.05166	+	27.8582i	−0.328123	+	1.00986i	0.641889	+	0.766798i	$0.278151\pi$
$761$	−9.05166	+	27.8582i	−0.328123	+	1.00986i	−0.970011	+	0.243060i	$0.921849\pi$
$762$	−16.3262	+	11.8617i	−0.591437	+	0.429704i
$763$	−9.70820	−	7.05342i	−0.351461	−	0.255351i
$764$	−1.22949	−	3.78398i	−0.0444814	−	0.136900i
$765$	−0.218847	−	0.673542i	−0.00791243	−	0.0243520i
$766$	26.9164	+	19.5559i	0.972529	+	0.706584i
$767$	1.40983	−	1.02430i	0.0509060	−	0.0369854i
$768$	4.50000	−	13.8496i	0.162380	−	0.499754i
$769$	34.5066			1.24434			0.622170	−	0.782883i	$-0.286251\pi$
$769$	34.5066			1.24434			0.622170	+	0.782883i	$0.286251\pi$
$770$		0			0
$771$	−29.7426			−1.07116
$772$	4.71885	−	14.5231i	0.169835	−	0.522698i
$773$	−21.9894	+	15.9762i	−0.790902	+	0.574624i	−0.908231	−	0.418469i	$-0.862567\pi$
$773$	−21.9894	+	15.9762i	−0.790902	+	0.574624i	0.117329	+	0.993093i	$0.462567\pi$
$774$	−14.2082	−	10.3229i	−0.510703	−	0.371048i
$775$	8.69098	+	26.7481i	0.312189	+	0.960820i
$776$	18.1353	+	55.8146i	0.651018	+	2.00363i
$777$	−5.04508	−	3.66547i	−0.180991	−	0.131498i
$778$	77.8222	−	56.5411i	2.79006	−	2.02710i
$779$	0.427051	−	1.31433i	0.0153007	−	0.0470907i
$780$	−0.708204			−0.0253578
$781$		0			0
$782$	0.708204			0.0253253
$783$	−1.85410	+	5.70634i	−0.0662602	+	0.203928i
$784$	47.8328	−	34.7526i	1.70831	−	1.24116i
$785$	7.85410	+	5.70634i	0.280325	+	0.203668i
$786$	−9.54508	−	29.3768i	−0.340462	−	1.04783i
$787$	3.00000	+	9.23305i	0.106938	+	0.329123i	0.990181	−	0.139795i	$-0.0446442\pi$
$787$	3.00000	+	9.23305i	0.106938	+	0.329123i	−0.883242	+	0.468917i	$0.844644\pi$
$788$	51.1869	+	37.1895i	1.82346	+	1.32482i
$789$	12.3541	−	8.97578i	0.439818	−	0.319546i
$790$	5.50000	−	16.9273i	0.195681	−	0.602245i
$791$	13.4721			0.479014
$792$		0			0
$793$	−2.72949			−0.0969270
$794$	−15.1353	+	46.5815i	−0.537130	+	1.65312i
$795$	0.190983	−	0.138757i	0.00677347	−	0.00492121i
$796$	−26.3435	−	19.1396i	−0.933719	−	0.678387i
$797$	5.72949	+	17.6336i	0.202949	+	0.624613i	0.999791	+	0.0204255i	$0.00650208\pi$
$797$	5.72949	+	17.6336i	0.202949	+	0.624613i	−0.796842	+	0.604187i	$0.793498\pi$
$798$	4.73607	+	14.5761i	0.167655	+	0.515989i
$799$	9.35410	+	6.79615i	0.330924	+	0.240431i
$800$	40.5517	−	29.4625i	1.43372	−	1.04166i
$801$	−2.54508	+	7.83297i	−0.0899262	+	0.276764i
$802$	−82.9574			−2.92933
$803$		0			0
$804$	−9.00000			−0.317406
$805$	−0.0450850	+	0.138757i	−0.00158904	+	0.00489055i
$806$	−3.04508	+	2.21238i	−0.107259	+	0.0779279i
$807$	−20.5623	−	14.9394i	−0.723827	−	0.525891i
$808$	23.6353	+	72.7418i	0.831485	+	2.55905i
$809$	−8.37132	−	25.7643i	−0.294320	−	0.905824i	−0.983449	−	0.181185i	$-0.942007\pi$
$809$	−8.37132	−	25.7643i	−0.294320	−	0.905824i	0.689129	−	0.724639i	$-0.257993\pi$
$810$	1.30902	+	0.951057i	0.0459942	+	0.0334167i
$811$	29.5795	−	21.4908i	1.03868	−	0.754644i	0.0686507	−	0.997641i	$-0.478131\pi$
$811$	29.5795	−	21.4908i	1.03868	−	0.754644i	0.970027	+	0.242997i	$0.0781306\pi$
$812$	9.00000	−	27.6992i	0.315838	−	0.972050i
$813$	18.6180			0.652963
$814$		0			0
$815$	3.18034			0.111402
$816$	−3.48936	+	10.7391i	−0.122152	+	0.375945i
$817$	31.7705	−	23.0826i	1.11151	−	0.807559i
$818$	−13.7082	−	9.95959i	−0.479296	−	0.348229i
$819$	−0.0729490	−	0.224514i	−0.00254904	−	0.00784515i
$820$	0.218847	+	0.673542i	0.00764247	+	0.0235211i
$821$	32.8435	+	23.8622i	1.14624	+	0.832795i	0.987977	−	0.154601i	$-0.0494091\pi$
$821$	32.8435	+	23.8622i	1.14624	+	0.832795i	0.158268	+	0.987396i	$0.449409\pi$
$822$	20.6803	−	15.0251i	0.721310	−	0.524062i
$823$	−8.60081	+	26.4706i	−0.299805	+	0.922706i	0.681759	+	0.731577i	$0.261215\pi$
$823$	−8.60081	+	26.4706i	−0.299805	+	0.922706i	−0.981565	+	0.191130i	$0.938785\pi$
$824$	−81.7771			−2.84884
$825$		0			0
$826$	19.3262			0.672446
$827$	3.29180	−	10.1311i	0.114467	−	0.352293i	−0.877369	−	0.479817i	$-0.840703\pi$
$827$	3.29180	−	10.1311i	0.114467	−	0.352293i	0.991835	+	0.127524i	$0.0407030\pi$
$828$	−0.927051	+	0.673542i	−0.0322172	+	0.0234072i
$829$	25.3992	+	18.4536i	0.882150	+	0.640920i	0.933819	−	0.357745i	$-0.116454\pi$
$829$	25.3992	+	18.4536i	0.882150	+	0.640920i	−0.0516692	+	0.998664i	$0.516454\pi$
$830$	0.736068	+	2.26538i	0.0255493	+	0.0786326i
$831$	−9.02786	−	27.7849i	−0.313173	−	0.963848i
$832$	1.66312	+	1.20833i	0.0576583	+	0.0418912i
$833$	5.56231	−	4.04125i	0.192722	−	0.140021i
$834$	11.7812	−	36.2587i	0.407948	−	1.25553i
$835$	7.43769			0.257392
$836$		0			0
$837$	6.09017			0.210507
$838$	25.4443	−	78.3094i	0.878958	−	2.70515i
$839$	14.4271	−	10.4819i	0.498077	−	0.361874i	−0.310205	−	0.950670i	$-0.600398\pi$
$839$	14.4271	−	10.4819i	0.498077	−	0.361874i	0.808282	+	0.588796i	$0.200398\pi$
$840$	−3.73607	−	2.71441i	−0.128907	−	0.0936561i
$841$	2.16312	+	6.65740i	0.0745903	+	0.229565i
$842$	8.50000	+	26.1603i	0.292929	+	0.901544i
$843$	−20.0344	−	14.5559i	−0.690023	−	0.501331i
$844$	14.2082	−	10.3229i	0.489067	−	0.355328i
$845$	2.47214	−	7.60845i	0.0850441	−	0.261739i
$846$	−26.4164			−0.908215
$847$		0			0
$848$	−3.76393			−0.129254
$849$	−1.76393	+	5.42882i	−0.0605380	+	0.186317i
$850$	11.2082	−	8.14324i	0.384438	−	0.279311i
$851$	1.19098	+	0.865300i	0.0408264	+	0.0296621i
$852$	−15.4894	−	47.6713i	−0.530657	−	1.63319i
$853$	17.2533	+	53.1002i	0.590741	+	1.81811i	0.574876	+	0.818241i	$0.305050\pi$
$853$	17.2533	+	53.1002i	0.590741	+	1.81811i	0.0158658	+	0.999874i	$0.494950\pi$
$854$	−24.4894	−	17.7926i	−0.838009	−	0.608849i
$855$	−2.92705	+	2.12663i	−0.100103	+	0.0727291i
$856$	26.4894	−	81.5259i	0.905388	−	2.78650i
$857$	−27.7639			−0.948398			−0.474199	−	0.880418i	$-0.657262\pi$
$857$	−27.7639			−0.948398			−0.474199	+	0.880418i	$0.657262\pi$
$858$		0			0
$859$	−34.4164			−1.17427			−0.587136	−	0.809488i	$-0.699745\pi$
$859$	−34.4164			−1.17427			−0.587136	+	0.809488i	$0.699745\pi$
$860$	−6.21885	+	19.1396i	−0.212061	+	0.652656i
$861$	−0.190983	+	0.138757i	−0.00650868	+	0.00472884i
$862$	−12.5172	−	9.09429i	−0.426338	−	0.309753i
$863$	0.0344419	+	0.106001i	0.00117241	+	0.00360832i	0.951641	−	0.307212i	$-0.0993962\pi$
$863$	0.0344419	+	0.106001i	0.00117241	+	0.00360832i	−0.950469	+	0.310821i	$0.899396\pi$
$864$	−3.35410	−	10.3229i	−0.114109	−	0.351191i
$865$	9.01722	+	6.55139i	0.306595	+	0.222754i
$866$	−74.7771	+	54.3287i	−2.54103	+	1.84617i
$867$	4.84752	−	14.9191i	0.164631	−	0.506681i
$868$	−29.5623			−1.00341
$869$		0			0
$870$	9.70820			0.329139
$871$	−0.135255	+	0.416272i	−0.00458294	+	0.0141048i
$872$	−72.5410	+	52.7041i	−2.45655	+	1.78479i
$873$	−6.35410	−	4.61653i	−0.215054	−	0.156246i
$874$	−1.11803	−	3.44095i	−0.0378181	−	0.116392i
$875$	1.83688	+	5.65334i	0.0620979	+	0.191118i
$876$	22.4164	+	16.2865i	0.757380	+	0.550269i
$877$	−46.8779	+	34.0588i	−1.58295	+	1.15008i	−0.669746	+	0.742590i	$0.733597\pi$
$877$	−46.8779	+	34.0588i	−1.58295	+	1.15008i	−0.913208	+	0.407493i	$0.866403\pi$
$878$	−18.8435	+	57.9942i	−0.635936	+	1.95721i
$879$	−21.6525			−0.730320
$880$		0			0
$881$	6.20163			0.208938			0.104469	−	0.994528i	$-0.466686\pi$
$881$	6.20163			0.208938			0.104469	+	0.994528i	$0.466686\pi$
$882$	−4.85410	+	14.9394i	−0.163446	+	0.503035i
$883$	−0.854102	+	0.620541i	−0.0287428	+	0.0208829i	−0.602064	−	0.798448i	$-0.705655\pi$
$883$	−0.854102	+	0.620541i	−0.0287428	+	0.0208829i	0.573321	+	0.819331i	$0.305655\pi$
$884$	1.06231	+	0.771810i	0.0357292	+	0.0259588i
$885$	1.40983	+	4.33901i	0.0473909	+	0.145854i
$886$	−25.5623	−	78.6727i	−0.858782	−	2.64306i
$887$	−44.0795	−	32.0257i	−1.48005	−	1.07532i	−0.977542	−	0.210741i	$-0.932412\pi$
$887$	−44.0795	−	32.0257i	−1.48005	−	1.07532i	−0.502504	−	0.864575i	$-0.667588\pi$
$888$	−37.6976	+	27.3889i	−1.26505	+	0.919111i
$889$	−2.38197	+	7.33094i	−0.0798886	+	0.245872i
$890$	13.3262			0.446697
$891$		0			0
$892$	34.8541			1.16700
$893$	18.2533	−	56.1778i	0.610823	−	1.87992i
$894$	8.97214	−	6.51864i	0.300073	−	0.218016i
$895$	−4.26393	−	3.09793i	−0.142528	−	0.103552i
$896$	0.336881	+	1.03681i	0.0112544	+	0.0346375i
$897$	0.0172209	+	0.0530006i	0.000574990	+	0.00176964i
$898$	19.1803	+	13.9353i	0.640056	+	0.465028i
$899$	29.5623	−	21.4783i	0.985958	−	0.716340i
$900$	−6.92705	+	21.3193i	−0.230902	+	0.710642i
$901$	−0.437694			−0.0145817
$902$		0			0
$903$	−6.70820			−0.223235
$904$	31.1074	−	95.7387i	1.03462	−	3.18422i
$905$	1.26393	−	0.918300i	0.0420145	−	0.0305253i
$906$	−2.23607	−	1.62460i	−0.0742884	−	0.0539737i
$907$	−13.1008	−	40.3202i	−0.435005	−	1.33881i	−0.893081	−	0.449896i	$-0.851461\pi$
$907$	−13.1008	−	40.3202i	−0.435005	−	1.33881i	0.458076	−	0.888913i	$-0.348539\pi$
$908$	−19.7705	−	60.8474i	−0.656107	−	2.01929i
$909$	−8.28115	−	6.01661i	−0.274669	−	0.199558i
$910$	−0.309017	+	0.224514i	−0.0102438	+	0.00744257i
$911$	11.9271	−	36.7077i	0.395161	−	1.21618i	−0.533675	−	0.845689i	$-0.679190\pi$
$911$	11.9271	−	36.7077i	0.395161	−	1.21618i	0.928836	−	0.370491i	$-0.120810\pi$
$912$	57.6869			1.91020
$913$		0			0
$914$	−62.7771			−2.07648
$915$	2.20820	−	6.79615i	0.0730010	−	0.224674i
$916$	−1.85410	+	1.34708i	−0.0612613	+	0.0445089i
$917$	−9.54508	−	6.93491i	−0.315206	−	0.229011i
$918$	−0.927051	−	2.85317i	−0.0305972	−	0.0941686i
$919$	−7.92705	−	24.3970i	−0.261489	−	0.804781i	−0.992481	−	0.122395i	$-0.960942\pi$
$919$	−7.92705	−	24.3970i	−0.261489	−	0.804781i	0.730992	−	0.682386i	$-0.239058\pi$
$920$	0.881966	+	0.640786i	0.0290776	+	0.0211261i
$921$	−22.6353	+	16.4455i	−0.745857	+	0.541897i
$922$	−7.50000	+	23.0826i	−0.246999	+	0.760186i
$923$	−2.43769			−0.0802377
$924$		0			0
$925$	28.7984			0.946885
$926$	1.39919	−	4.30625i	0.0459801	−	0.141512i
$927$	8.85410	−	6.43288i	0.290807	−	0.211284i
$928$	−52.6869	−	38.2793i	−1.72953	−	1.25658i
$929$	−3.92705	−	12.0862i	−0.128842	−	0.396536i	0.865739	−	0.500495i	$-0.166849\pi$
$929$	−3.92705	−	12.0862i	−0.128842	−	0.396536i	−0.994582	+	0.103959i	$0.966849\pi$
$930$	−3.04508	−	9.37181i	−0.0998523	−	0.307314i
$931$	−28.4164	−	20.6457i	−0.931310	−	0.676636i
$932$	−16.2812	+	11.8290i	−0.533307	+	0.387470i
$933$	−3.60081	+	11.0822i	−0.117885	+	0.362814i
$934$	54.6869			1.78941
$935$		0			0
$936$	−1.76393			−0.0576559
$937$	−12.8713	+	39.6139i	−0.420488	+	1.29413i	0.486761	+	0.873535i	$0.338178\pi$
$937$	−12.8713	+	39.6139i	−0.420488	+	1.29413i	−0.907249	+	0.420593i	$0.861822\pi$
$938$	−3.92705	+	2.85317i	−0.128223	+	0.0931593i
$939$	−2.04508	−	1.48584i	−0.0667388	−	0.0484886i
$940$	9.35410	+	28.7890i	0.305097	+	0.938993i
$941$	4.46556	+	13.7436i	0.145573	+	0.448028i	0.997084	−	0.0763087i	$-0.0243134\pi$
$941$	4.46556	+	13.7436i	0.145573	+	0.448028i	−0.851511	+	0.524336i	$0.824313\pi$
$942$	33.2705	+	24.1724i	1.08401	+	0.787581i
$943$	0.0450850	−	0.0327561i	0.00146817	−	0.00106669i
$944$	22.4787	−	69.1824i	0.731620	−	2.25169i
$945$	0.618034			0.0201046
$946$		0			0
$947$	−32.3951			−1.05270			−0.526350	−	0.850268i	$-0.676440\pi$
$947$	−32.3951			−1.05270			−0.526350	+	0.850268i	$0.676440\pi$
$948$	16.5000	−	50.7818i	0.535895	−	1.64932i
$949$	1.09017	−	0.792055i	0.0353884	−	0.0257112i
$950$	−57.2599	−	41.6017i	−1.85776	−	1.34974i
$951$	2.10739	+	6.48588i	0.0683368	+	0.210319i
$952$	2.64590	+	8.14324i	0.0857540	+	0.263924i
$953$	9.18034	+	6.66991i	0.297380	+	0.216059i	0.726463	−	0.687206i	$-0.241163\pi$
$953$	9.18034	+	6.66991i	0.297380	+	0.216059i	−0.429082	+	0.903265i	$0.641163\pi$
$954$	0.809017	−	0.587785i	0.0261929	−	0.0190303i
$955$	0.156541	−	0.481784i	0.00506555	−	0.0155902i
$956$	−1.85410			−0.0599659
$957$		0			0
$958$	74.3050			2.40068
$959$	3.01722	−	9.28605i	0.0974311	−	0.299862i
$960$	−4.35410	+	3.16344i	−0.140528	+	0.102100i
$961$	−4.92705	−	3.57971i	−0.158937	−	0.115475i
$962$	1.19098	+	3.66547i	0.0383988	+	0.118179i
$963$	3.54508	+	10.9106i	0.114239	+	0.351591i
$964$	32.5623	+	23.6579i	1.04876	+	0.761970i
$965$	1.57295	−	1.14281i	0.0506350	−	0.0367885i
$966$	−0.190983	+	0.587785i	−0.00614478	+	0.0189117i
$967$	−43.9230			−1.41247			−0.706234	−	0.707978i	$-0.749607\pi$
$967$	−43.9230			−1.41247			−0.706234	+	0.707978i	$0.749607\pi$
$968$		0			0
$969$	6.70820			0.215499
$970$	−3.92705	+	12.0862i	−0.126090	+	0.388065i
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.110957	−	0.993825i	$-0.464608\pi$
$971$	33.9787	−	24.6870i	1.09043	−	0.792243i	0.979472	+	0.201582i	$0.0646083\pi$
$972$	3.92705	+	2.85317i	0.125960	+	0.0915155i
$973$	−4.50000	−	13.8496i	−0.144263	−	0.443997i
$974$	−10.2812	−	31.6421i	−0.329429	−	1.01388i
$975$	0.881966	+	0.640786i	0.0282455	+	0.0205216i
$976$	−92.1763	+	66.9700i	−2.95049	+	2.14366i
$977$	−0.184405	+	0.567541i	−0.00589964	+	0.0181572i	−0.953963	−	0.299924i	$-0.903039\pi$
$977$	−0.184405	+	0.567541i	−0.00589964	+	0.0181572i	0.948063	+	0.318082i	$0.103039\pi$
$978$	13.4721			0.430791
$979$		0			0
$980$	18.0000			0.574989
$981$	3.70820	−	11.4127i	0.118394	−	0.364379i
$982$	−37.9336	+	27.5604i	−1.21051	+	0.879488i
$983$	6.56231	+	4.76779i	0.209305	+	0.152069i	0.687499	−	0.726185i	$-0.258708\pi$
$983$	6.56231	+	4.76779i	0.209305	+	0.152069i	−0.478194	+	0.878254i	$0.658708\pi$
$984$	0.545085	+	1.67760i	0.0173767	+	0.0534799i
$985$	2.48936	+	7.66145i	0.0793175	+	0.244114i
$986$	−14.5623	−	10.5801i	−0.463758	−	0.336940i
$987$	−8.16312	+	5.93085i	−0.259835	+	0.188781i
$988$	2.07295	−	6.37988i	0.0659493	−	0.202971i
$989$	1.58359			0.0503553
$990$		0			0
$991$	3.74265			0.118889			0.0594445	−	0.998232i	$-0.481067\pi$
$991$	3.74265			0.118889			0.0594445	+	0.998232i	$0.481067\pi$
$992$	−20.4271	+	62.8680i	−0.648560	+	1.99606i
$993$	13.5172	−	9.82084i	0.428956	−	0.311655i
$994$	−21.8713	−	15.8904i	−0.693716	−	0.504014i
$995$	−1.28115	−	3.94298i	−0.0406153	−	0.125001i
$996$	2.20820	+	6.79615i	0.0699696	+	0.215344i
$997$	−17.1525	−	12.4620i	−0.543224	−	0.394676i	0.282057	−	0.959398i	$-0.408983\pi$
$997$	−17.1525	−	12.4620i	−0.543224	−	0.394676i	−0.825281	+	0.564722i	$0.808983\pi$
$998$	38.4336	−	27.9237i	1.21660	−	0.883908i
$999$	1.92705	−	5.93085i	0.0609692	−	0.187644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.f.130.1		4
11.2	odd	10		363.2.e.k.124.1		4
11.3	even	5		363.2.e.b.202.1		4
11.4	even	5		363.2.a.i.1.2		2
11.5	even	5	inner	363.2.e.f.148.1		4
11.6	odd	10		33.2.e.b.16.1	✓	4
11.7	odd	10		363.2.a.d.1.1		2
11.8	odd	10		363.2.e.k.202.1		4
11.9	even	5		363.2.e.b.124.1		4
11.10	odd	2		33.2.e.b.31.1	yes	4
33.17	even	10		99.2.f.a.82.1		4
33.26	odd	10		1089.2.a.l.1.1		2
33.29	even	10		1089.2.a.t.1.2		2
33.32	even	2		99.2.f.a.64.1		4
44.7	even	10		5808.2.a.cj.1.1		2
44.15	odd	10		5808.2.a.ci.1.1		2
44.39	even	10		528.2.y.b.49.1		4
44.43	even	2		528.2.y.b.97.1		4
55.4	even	10		9075.2.a.u.1.1		2
55.17	even	20		825.2.bx.d.49.2		8
55.28	even	20		825.2.bx.d.49.1		8
55.29	odd	10		9075.2.a.cb.1.2		2
55.32	even	4		825.2.bx.d.724.1		8
55.39	odd	10		825.2.n.c.676.1		4
55.43	even	4		825.2.bx.d.724.2		8
55.54	odd	2		825.2.n.c.526.1		4
99.32	even	6		891.2.n.b.460.1		8
99.43	odd	6		891.2.n.c.757.1		8
99.50	even	30		891.2.n.b.379.1		8
99.61	odd	30		891.2.n.c.676.1		8
99.65	even	6		891.2.n.b.757.1		8
99.76	odd	6		891.2.n.c.460.1		8
99.83	even	30		891.2.n.b.676.1		8
99.94	odd	30		891.2.n.c.379.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.b.16.1	✓	4	11.6	odd	10
33.2.e.b.31.1	yes	4	11.10	odd	2
99.2.f.a.64.1		4	33.32	even	2
99.2.f.a.82.1		4	33.17	even	10
363.2.a.d.1.1		2	11.7	odd	10
363.2.a.i.1.2		2	11.4	even	5
363.2.e.b.124.1		4	11.9	even	5
363.2.e.b.202.1		4	11.3	even	5
363.2.e.f.130.1		4	1.1	even	1	trivial
363.2.e.f.148.1		4	11.5	even	5	inner
363.2.e.k.124.1		4	11.2	odd	10
363.2.e.k.202.1		4	11.8	odd	10
528.2.y.b.49.1		4	44.39	even	10
528.2.y.b.97.1		4	44.43	even	2
825.2.n.c.526.1		4	55.54	odd	2
825.2.n.c.676.1		4	55.39	odd	10
825.2.bx.d.49.1		8	55.28	even	20
825.2.bx.d.49.2		8	55.17	even	20
825.2.bx.d.724.1		8	55.32	even	4
825.2.bx.d.724.2		8	55.43	even	4
891.2.n.b.379.1		8	99.50	even	30
891.2.n.b.460.1		8	99.32	even	6
891.2.n.b.676.1		8	99.83	even	30
891.2.n.b.757.1		8	99.65	even	6
891.2.n.c.379.1		8	99.94	odd	30
891.2.n.c.460.1		8	99.76	odd	6
891.2.n.c.676.1		8	99.61	odd	30
891.2.n.c.757.1		8	99.43	odd	6
1089.2.a.l.1.1		2	33.26	odd	10
1089.2.a.t.1.2		2	33.29	even	10
5808.2.a.ci.1.1		2	44.15	odd	10
5808.2.a.cj.1.1		2	44.7	even	10
9075.2.a.u.1.1		2	55.4	even	10
9075.2.a.cb.1.2		2	55.29	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 - 2.48990i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-3.92705 - 2.85317i) q^{4} +(-0.190983 - 0.587785i) q^{5} +(-0.809017 - 2.48990i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-6.04508 + 4.39201i) q^{8} +(0.309017 - 0.951057i) q^{9} -1.61803 q^{10} -4.85410 q^{12} +(-0.0729490 + 0.224514i) q^{13} +(-2.11803 + 1.53884i) q^{14} +(-0.500000 - 0.363271i) q^{15} +(3.04508 + 9.37181i) q^{16} +(0.354102 + 1.08981i) q^{17} +(-2.11803 - 1.53884i) q^{18} +(4.73607 - 3.44095i) q^{19} +(-0.927051 + 2.85317i) q^{20} -1.00000 q^{21} +0.236068 q^{23} +(-2.30902 + 7.10642i) q^{24} +(3.73607 - 2.71441i) q^{25} +(0.500000 + 0.363271i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(1.50000 + 4.61653i) q^{28} +(-4.85410 - 3.52671i) q^{29} +(-1.30902 + 0.951057i) q^{30} +(-1.88197 + 5.79210i) q^{31} +10.8541 q^{32} +3.00000 q^{34} +(-0.190983 + 0.587785i) q^{35} +(-3.92705 + 2.85317i) q^{36} +(5.04508 + 3.66547i) q^{37} +(-4.73607 - 14.5761i) q^{38} +(0.0729490 + 0.224514i) q^{39} +(3.73607 + 2.71441i) q^{40} +(0.190983 - 0.138757i) q^{41} +(-0.809017 + 2.48990i) q^{42} +6.70820 q^{43} -0.618034 q^{45} +(0.190983 - 0.587785i) q^{46} +(8.16312 - 5.93085i) q^{47} +(7.97214 + 5.79210i) q^{48} +(-1.85410 - 5.70634i) q^{49} +(-3.73607 - 11.4984i) q^{50} +(0.927051 + 0.673542i) q^{51} +(0.927051 - 0.673542i) q^{52} +(-0.118034 + 0.363271i) q^{53} -2.61803 q^{54} +7.47214 q^{56} +(1.80902 - 5.56758i) q^{57} +(-12.7082 + 9.23305i) q^{58} +(-5.97214 - 4.33901i) q^{59} +(0.927051 + 2.85317i) q^{60} +(3.57295 + 10.9964i) q^{61} +(12.8992 + 9.37181i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(2.69098 - 8.28199i) q^{64} +0.145898 q^{65} +1.85410 q^{67} +(1.71885 - 5.29007i) q^{68} +(0.190983 - 0.138757i) q^{69} +(1.30902 + 0.951057i) q^{70} +(3.19098 + 9.82084i) q^{71} +(2.30902 + 7.10642i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(13.2082 - 9.59632i) q^{74} +(1.42705 - 4.39201i) q^{75} -28.4164 q^{76} +0.618034 q^{78} +(-3.39919 + 10.4616i) q^{79} +(4.92705 - 3.57971i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.190983 - 0.587785i) q^{82} +(-0.454915 - 1.40008i) q^{83} +(3.92705 + 2.85317i) q^{84} +(0.572949 - 0.416272i) q^{85} +(5.42705 - 16.7027i) q^{86} -6.00000 q^{87} -8.23607 q^{89} +(-0.500000 + 1.53884i) q^{90} +(0.190983 - 0.138757i) q^{91} +(-0.927051 - 0.673542i) q^{92} +(1.88197 + 5.79210i) q^{93} +(-8.16312 - 25.1235i) q^{94} +(-2.92705 - 2.12663i) q^{95} +(8.78115 - 6.37988i) q^{96} +(2.42705 - 7.46969i) q^{97} -15.7082 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} - 9 q^{4} - 3 q^{5} - q^{6} - q^{7} - 13 q^{8} - q^{9} - 2 q^{10} - 6 q^{12} - 7 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - 12 q^{17} - 4 q^{18} + 10 q^{19} + 3 q^{20} - 4 q^{21}+ \cdots - 36 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^3 - 9 * q^4 - 3 * q^5 - q^6 - q^7 - 13 * q^8 - q^9 - 2 * q^10 - 6 * q^12 - 7 * q^13 - 4 * q^14 - 2 * q^15 + q^16 - 12 * q^17 - 4 * q^18 + 10 * q^19 + 3 * q^20 - 4 * q^21 - 8 * q^23 - 7 * q^24 + 6 * q^25 + 2 * q^26 + q^27 + 6 * q^28 - 6 * q^29 - 3 * q^30 - 12 * q^31 + 30 * q^32 + 12 * q^34 - 3 * q^35 - 9 * q^36 + 9 * q^37 - 10 * q^38 + 7 * q^39 + 6 * q^40 + 3 * q^41 - q^42 + 2 * q^45 + 3 * q^46 + 17 * q^47 + 14 * q^48 + 6 * q^49 - 6 * q^50 - 3 * q^51 - 3 * q^52 + 4 * q^53 - 6 * q^54 + 12 * q^56 + 5 * q^57 - 24 * q^58 - 6 * q^59 - 3 * q^60 + 21 * q^61 + 27 * q^62 - q^63 + 13 * q^64 + 14 * q^65 - 6 * q^67 + 27 * q^68 + 3 * q^69 + 3 * q^70 + 15 * q^71 + 7 * q^72 - 14 * q^73 + 26 * q^74 - q^75 - 60 * q^76 - 2 * q^78 + 11 * q^79 + 13 * q^80 - q^81 - 3 * q^82 - 13 * q^83 + 9 * q^84 + 9 * q^85 + 15 * q^86 - 24 * q^87 - 24 * q^89 - 2 * q^90 + 3 * q^91 + 3 * q^92 + 12 * q^93 - 17 * q^94 - 5 * q^95 + 15 * q^96 + 3 * q^97 - 36 * q^98

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