LMFDB - Embedded newform 242.2.c.a.9.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [242,2,Mod(3,242)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("242.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(242, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 242 = 2 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	242.c (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.93237972891$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			9.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	242.9
Dual form			242.2.c.a.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.224514i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.00000 + 3.07768i) q^{5} +(0.118034 + 0.363271i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +3.23607 q^{10} +0.381966 q^{12} +(0.381966 - 1.17557i) q^{13} +(1.61803 - 1.17557i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.190983 - 0.587785i) q^{17} +(2.30902 + 1.67760i) q^{18} +(4.73607 - 3.44095i) q^{19} +(1.00000 - 3.07768i) q^{20} -0.763932 q^{21} +1.23607 q^{23} +(0.118034 - 0.363271i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-0.690983 - 2.12663i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-1.00000 + 0.726543i) q^{30} +(0.618034 - 1.90211i) q^{31} +1.00000 q^{32} -0.618034 q^{34} +(-2.00000 + 6.15537i) q^{35} +(2.30902 - 1.67760i) q^{36} +(3.00000 + 2.17963i) q^{37} +(-1.80902 - 5.56758i) q^{38} +(0.145898 + 0.449028i) q^{39} +(-2.61803 - 1.90211i) q^{40} +(-4.54508 + 3.30220i) q^{41} +(-0.236068 + 0.726543i) q^{42} -8.56231 q^{43} -9.23607 q^{45} +(0.381966 - 1.17557i) q^{46} +(5.23607 - 3.80423i) q^{47} +(-0.309017 - 0.224514i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.69098 + 5.20431i) q^{50} +(0.190983 + 0.138757i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(-0.472136 + 1.45309i) q^{53} -2.23607 q^{54} -2.00000 q^{56} +(-0.690983 + 2.12663i) q^{57} +(-3.61803 + 2.62866i) q^{58} +(6.97214 + 5.06555i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-0.763932 - 2.35114i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(-4.61803 + 3.35520i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +11.0902 q^{67} +(-0.190983 + 0.587785i) q^{68} +(-0.381966 + 0.277515i) q^{69} +(5.23607 + 3.80423i) q^{70} +(-1.61803 - 4.97980i) q^{71} +(-0.881966 - 2.71441i) q^{72} +(-8.39919 - 6.10237i) q^{73} +(3.00000 - 2.17963i) q^{74} +(0.645898 - 1.98787i) q^{75} -5.85410 q^{76} +0.472136 q^{78} +(4.14590 - 12.7598i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(-6.23607 - 4.53077i) q^{81} +(1.73607 + 5.34307i) q^{82} +(2.88197 + 8.86978i) q^{83} +(0.618034 + 0.449028i) q^{84} +(1.61803 - 1.17557i) q^{85} +(-2.64590 + 8.14324i) q^{86} +1.70820 q^{87} -8.09017 q^{89} +(-2.85410 + 8.78402i) q^{90} +(2.00000 - 1.45309i) q^{91} +(-1.00000 - 0.726543i) q^{92} +(0.236068 + 0.726543i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(15.3262 + 11.1352i) q^{95} +(-0.309017 + 0.224514i) q^{96} +(2.20820 - 6.79615i) q^{97} -3.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{3} - q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{7} - q^{8} - 8 q^{9} + 4 q^{10} + 6 q^{12} + 6 q^{13} + 2 q^{14} - 4 q^{15} - q^{16} - 3 q^{17} + 7 q^{18} + 10 q^{19} + 4 q^{20} - 12 q^{21}+ \cdots - 12 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^3 - q^4 + 4 * q^5 - 4 * q^6 + 2 * q^7 - q^8 - 8 * q^9 + 4 * q^10 + 6 * q^12 + 6 * q^13 + 2 * q^14 - 4 * q^15 - q^16 - 3 * q^17 + 7 * q^18 + 10 * q^19 + 4 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^24 - 11 * q^25 - 4 * q^26 - 5 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^34 - 8 * q^35 + 7 * q^36 + 12 * q^37 - 5 * q^38 + 14 * q^39 - 6 * q^40 - 7 * q^41 + 8 * q^42 + 6 * q^43 - 28 * q^45 + 6 * q^46 + 12 * q^47 + q^48 + 3 * q^49 + 9 * q^50 + 3 * q^51 - 4 * q^52 + 16 * q^53 - 8 * q^56 - 5 * q^57 - 10 * q^58 + 10 * q^59 + 6 * q^60 - 12 * q^61 - 2 * q^62 - 14 * q^63 - q^64 + 16 * q^65 + 22 * q^67 - 3 * q^68 - 6 * q^69 + 12 * q^70 - 2 * q^71 - 8 * q^72 - 9 * q^73 + 12 * q^74 + 16 * q^75 - 10 * q^76 - 16 * q^78 + 30 * q^79 - 6 * q^80 - 16 * q^81 - 2 * q^82 + 16 * q^83 - 2 * q^84 + 2 * q^85 - 24 * q^86 - 20 * q^87 - 10 * q^89 + 2 * q^90 + 8 * q^91 - 4 * q^92 - 8 * q^93 - 8 * q^94 + 30 * q^95 + q^96 - 18 * q^97 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/242\mathbb{Z}\right)^\times$.

$n$	$123$
$\chi(n)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	−0.309017	+	0.224514i	−0.178411	+	0.129623i	−0.673407	−	0.739272i	$-0.735170\pi$
$3$	−0.309017	+	0.224514i	−0.178411	+	0.129623i	0.494996	+	0.868895i	$0.335170\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	1.00000	+	3.07768i	0.447214	+	1.37638i	0.880038	+	0.474904i	$0.157517\pi$
$5$	1.00000	+	3.07768i	0.447214	+	1.37638i	−0.432824	+	0.901478i	$0.642483\pi$
$6$	0.118034	+	0.363271i	0.0481872	+	0.148305i
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	0.849963	−	0.526842i	$-0.176624\pi$
$7$	1.61803	+	1.17557i	0.611559	+	0.444324i	−0.238404	+	0.971166i	$0.576624\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.881966	+	2.71441i	−0.293989	+	0.904804i
$10$	3.23607			1.02333
$11$		0			0
$11$		0			0
$12$	0.381966			0.110264
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	−0.884011	−	0.467466i	$-0.845167\pi$
$13$	0.381966	−	1.17557i	0.105938	−	0.326045i	0.989950	+	0.141421i	$0.0451671\pi$
$14$	1.61803	−	1.17557i	0.432438	−	0.314184i
$15$	−1.00000	−	0.726543i	−0.258199	−	0.187592i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.190983	−	0.587785i	−0.0463202	−	0.142559i	0.925222	−	0.379427i	$-0.123879\pi$
$17$	−0.190983	−	0.587785i	−0.0463202	−	0.142559i	−0.971542	+	0.236868i	$0.923879\pi$
$18$	2.30902	+	1.67760i	0.544241	+	0.395414i
$19$	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	$0.0656454\pi$
$20$	1.00000	−	3.07768i	0.223607	−	0.688191i
$21$	−0.763932			−0.166704
$22$		0			0
$23$	1.23607			0.257738			0.128869	−	0.991662i	$-0.458865\pi$
$23$	1.23607			0.257738			0.128869	+	0.991662i	$0.458865\pi$
$24$	0.118034	−	0.363271i	0.0240936	−	0.0741524i
$25$	−4.42705	+	3.21644i	−0.885410	+	0.643288i
$26$	−1.00000	−	0.726543i	−0.196116	−	0.142487i
$27$	−0.690983	−	2.12663i	−0.132980	−	0.409270i
$28$	−0.618034	−	1.90211i	−0.116797	−	0.359466i
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	0.198793	−	0.980042i	$-0.436298\pi$
$29$	−3.61803	−	2.62866i	−0.671852	−	0.488129i	−0.870645	+	0.491912i	$0.836298\pi$
$30$	−1.00000	+	0.726543i	−0.182574	+	0.132648i
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	−0.880090	−	0.474807i	$-0.842518\pi$
$31$	0.618034	−	1.90211i	0.111002	−	0.341630i	0.991092	+	0.133177i	$0.0425179\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.618034			−0.105992
$35$	−2.00000	+	6.15537i	−0.338062	+	1.04045i
$36$	2.30902	−	1.67760i	0.384836	−	0.279600i
$37$	3.00000	+	2.17963i	0.493197	+	0.358329i	0.806412	−	0.591354i	$-0.201406\pi$
$37$	3.00000	+	2.17963i	0.493197	+	0.358329i	−0.313215	+	0.949682i	$0.601406\pi$
$38$	−1.80902	−	5.56758i	−0.293461	−	0.903181i
$39$	0.145898	+	0.449028i	0.0233624	+	0.0719020i
$40$	−2.61803	−	1.90211i	−0.413948	−	0.300750i
$41$	−4.54508	+	3.30220i	−0.709823	+	0.515717i	−0.883117	−	0.469154i	$-0.844559\pi$
$41$	−4.54508	+	3.30220i	−0.709823	+	0.515717i	0.173294	+	0.984870i	$0.444559\pi$
$42$	−0.236068	+	0.726543i	−0.0364261	+	0.112108i
$43$	−8.56231			−1.30574			−0.652870	−	0.757470i	$-0.726435\pi$
$43$	−8.56231			−1.30574			−0.652870	+	0.757470i	$0.726435\pi$
$44$		0			0
$45$	−9.23607			−1.37683
$46$	0.381966	−	1.17557i	0.0563178	−	0.173328i
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	−0.136302	−	0.990667i	$-0.543522\pi$
$47$	5.23607	−	3.80423i	0.763759	−	0.554903i	0.900061	+	0.435764i	$0.143522\pi$
$48$	−0.309017	−	0.224514i	−0.0446028	−	0.0324058i
$49$	−0.927051	−	2.85317i	−0.132436	−	0.407596i
$50$	1.69098	+	5.20431i	0.239141	+	0.736001i
$51$	0.190983	+	0.138757i	0.0267430	+	0.0194299i
$52$	−1.00000	+	0.726543i	−0.138675	+	0.100753i
$53$	−0.472136	+	1.45309i	−0.0648529	+	0.199597i	−0.978232	−	0.207513i	$-0.933463\pi$
$53$	−0.472136	+	1.45309i	−0.0648529	+	0.199597i	0.913379	+	0.407109i	$0.133463\pi$
$54$	−2.23607			−0.304290
$55$		0			0
$56$	−2.00000			−0.267261
$57$	−0.690983	+	2.12663i	−0.0915229	+	0.281679i
$58$	−3.61803	+	2.62866i	−0.475071	+	0.345159i
$59$	6.97214	+	5.06555i	0.907695	+	0.659479i	0.940431	−	0.339985i	$-0.110422\pi$
$59$	6.97214	+	5.06555i	0.907695	+	0.659479i	−0.0327360	+	0.999464i	$0.510422\pi$
$60$	0.381966	+	1.17557i	0.0493116	+	0.151765i
$61$	−0.763932	−	2.35114i	−0.0978115	−	0.301033i	0.890165	−	0.455639i	$-0.150589\pi$
$61$	−0.763932	−	2.35114i	−0.0978115	−	0.301033i	−0.987976	+	0.154606i	$0.950589\pi$
$62$	−1.61803	−	1.17557i	−0.205491	−	0.149298i
$63$	−4.61803	+	3.35520i	−0.581818	+	0.422715i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	4.00000			0.496139
$66$		0			0
$67$	11.0902			1.35488			0.677440	−	0.735578i	$-0.263089\pi$
$67$	11.0902			1.35488			0.677440	+	0.735578i	$0.263089\pi$
$68$	−0.190983	+	0.587785i	−0.0231601	+	0.0712794i
$69$	−0.381966	+	0.277515i	−0.0459833	+	0.0334088i
$70$	5.23607	+	3.80423i	0.625830	+	0.454692i
$71$	−1.61803	−	4.97980i	−0.192025	−	0.590993i	−0.999998	−	0.00177378i	$-0.999435\pi$
$71$	−1.61803	−	4.97980i	−0.192025	−	0.590993i	0.807973	−	0.589219i	$-0.200565\pi$
$72$	−0.881966	−	2.71441i	−0.103941	−	0.319897i
$73$	−8.39919	−	6.10237i	−0.983050	−	0.714228i	−0.0246622	−	0.999696i	$-0.507851\pi$
$73$	−8.39919	−	6.10237i	−0.983050	−	0.714228i	−0.958388	+	0.285468i	$0.907851\pi$
$74$	3.00000	−	2.17963i	0.348743	−	0.253377i
$75$	0.645898	−	1.98787i	0.0745819	−	0.229539i
$76$	−5.85410			−0.671512
$77$		0			0
$78$	0.472136			0.0534589
$79$	4.14590	−	12.7598i	0.466450	−	1.43559i	−0.390700	−	0.920518i	$-0.627767\pi$
$79$	4.14590	−	12.7598i	0.466450	−	1.43559i	0.857150	−	0.515067i	$-0.172233\pi$
$80$	−2.61803	+	1.90211i	−0.292705	+	0.212663i
$81$	−6.23607	−	4.53077i	−0.692896	−	0.503419i
$82$	1.73607	+	5.34307i	0.191717	+	0.590043i
$83$	2.88197	+	8.86978i	0.316337	+	0.973585i	0.975201	+	0.221323i	$0.0710373\pi$
$83$	2.88197	+	8.86978i	0.316337	+	0.973585i	−0.658864	+	0.752262i	$0.728963\pi$
$84$	0.618034	+	0.449028i	0.0674330	+	0.0489930i
$85$	1.61803	−	1.17557i	0.175500	−	0.127509i
$86$	−2.64590	+	8.14324i	−0.285315	+	0.878108i
$87$	1.70820			0.183139
$88$		0			0
$89$	−8.09017			−0.857556			−0.428778	−	0.903410i	$-0.641056\pi$
$89$	−8.09017			−0.857556			−0.428778	+	0.903410i	$0.641056\pi$
$90$	−2.85410	+	8.78402i	−0.300849	+	0.925917i
$91$	2.00000	−	1.45309i	0.209657	−	0.152325i
$92$	−1.00000	−	0.726543i	−0.104257	−	0.0757473i
$93$	0.236068	+	0.726543i	0.0244791	+	0.0753390i
$94$	−2.00000	−	6.15537i	−0.206284	−	0.634878i
$95$	15.3262	+	11.1352i	1.57244	+	1.14244i
$96$	−0.309017	+	0.224514i	−0.0315389	+	0.0229144i
$97$	2.20820	−	6.79615i	0.224209	−	0.690045i	−0.774162	−	0.632988i	$-0.781828\pi$
$97$	2.20820	−	6.79615i	0.224209	−	0.690045i	0.998371	−	0.0570570i	$-0.0181717\pi$
$98$	−3.00000			−0.303046
$99$		0			0
$100$	5.47214			0.547214
$101$	−1.29180	+	3.97574i	−0.128539	+	0.395601i	−0.994529	−	0.104459i	$-0.966689\pi$
$101$	−1.29180	+	3.97574i	−0.128539	+	0.395601i	0.865991	+	0.500060i	$0.166689\pi$
$102$	0.190983	−	0.138757i	0.0189101	−	0.0137390i
$103$	−12.7082	−	9.23305i	−1.25218	−	0.909760i	−0.253830	−	0.967249i	$-0.581691\pi$
$103$	−12.7082	−	9.23305i	−1.25218	−	0.909760i	−0.998346	+	0.0574892i	$0.981691\pi$
$104$	0.381966	+	1.17557i	0.0374548	+	0.115274i
$105$	−0.763932	−	2.35114i	−0.0745521	−	0.229448i
$106$	1.23607	+	0.898056i	0.120058	+	0.0872269i
$107$	0.927051	−	0.673542i	0.0896214	−	0.0651138i	−0.542072	−	0.840332i	$-0.682360\pi$
$107$	0.927051	−	0.673542i	0.0896214	−	0.0651138i	0.631694	+	0.775218i	$0.282360\pi$
$108$	−0.690983	+	2.12663i	−0.0664899	+	0.204635i
$109$	18.9443			1.81453			0.907266	−	0.420557i	$-0.138165\pi$
$109$	18.9443			1.81453			0.907266	+	0.420557i	$0.138165\pi$
$110$		0			0
$111$	−1.41641			−0.134439
$112$	−0.618034	+	1.90211i	−0.0583987	+	0.179733i
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	−0.514992	−	0.857195i	$-0.672205\pi$
$113$	1.50000	−	1.08981i	0.141108	−	0.102521i	0.656100	+	0.754674i	$0.272205\pi$
$114$	1.80902	+	1.31433i	0.169430	+	0.123098i
$115$	1.23607	+	3.80423i	0.115264	+	0.354746i
$116$	1.38197	+	4.25325i	0.128312	+	0.394905i
$117$	2.85410	+	2.07363i	0.263862	+	0.191707i
$118$	6.97214	−	5.06555i	0.641837	−	0.466322i
$119$	0.381966	−	1.17557i	0.0350148	−	0.107764i
$120$	1.23607			0.112837
$121$		0			0
$122$	−2.47214			−0.223817
$123$	0.663119	−	2.04087i	0.0597914	−	0.184019i
$124$	−1.61803	+	1.17557i	−0.145304	+	0.105569i
$125$	−1.23607	−	0.898056i	−0.110557	−	0.0803246i
$126$	1.76393	+	5.42882i	0.157144	+	0.483638i
$127$	−3.38197	−	10.4086i	−0.300101	−	0.923616i	−0.981460	−	0.191667i	$-0.938611\pi$
$127$	−3.38197	−	10.4086i	−0.300101	−	0.923616i	0.681359	−	0.731949i	$-0.261389\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	2.64590	−	1.92236i	0.232958	−	0.169254i
$130$	1.23607	−	3.80423i	0.108410	−	0.333653i
$131$	6.79837			0.593977			0.296988	−	0.954881i	$-0.404018\pi$
$131$	6.79837			0.593977			0.296988	+	0.954881i	$0.404018\pi$
$132$		0			0
$133$	11.7082			1.01523
$134$	3.42705	−	10.5474i	0.296052	−	0.911155i
$135$	5.85410	−	4.25325i	0.503841	−	0.366062i
$136$	0.500000	+	0.363271i	0.0428746	+	0.0311503i
$137$	4.97214	+	15.3027i	0.424798	+	1.30739i	0.903187	+	0.429247i	$0.141221\pi$
$137$	4.97214	+	15.3027i	0.424798	+	1.30739i	−0.478389	+	0.878148i	$0.658779\pi$
$138$	0.145898	+	0.449028i	0.0124197	+	0.0382238i
$139$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$139$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$140$	5.23607	−	3.80423i	0.442529	−	0.321516i
$141$	−0.763932	+	2.35114i	−0.0643347	+	0.198002i
$142$	−5.23607			−0.439401
$143$		0			0
$144$	−2.85410			−0.237842
$145$	4.47214	−	13.7638i	0.371391	−	1.14302i
$146$	−8.39919	+	6.10237i	−0.695122	+	0.505035i
$147$	0.927051	+	0.673542i	0.0764619	+	0.0555528i
$148$	−1.14590	−	3.52671i	−0.0941922	−	0.289894i
$149$	−1.90983	−	5.87785i	−0.156459	−	0.481532i	0.841846	−	0.539717i	$-0.181469\pi$
$149$	−1.90983	−	5.87785i	−0.156459	−	0.481532i	−0.998306	+	0.0581846i	$0.981469\pi$
$150$	−1.69098	−	1.22857i	−0.138068	−	0.100312i
$151$	6.47214	−	4.70228i	0.526695	−	0.382666i	−0.292425	−	0.956288i	$-0.594462\pi$
$151$	6.47214	−	4.70228i	0.526695	−	0.382666i	0.819120	+	0.573622i	$0.194462\pi$
$152$	−1.80902	+	5.56758i	−0.146731	+	0.451591i
$153$	1.76393			0.142605
$154$		0			0
$155$	6.47214			0.519854
$156$	0.145898	−	0.449028i	0.0116812	−	0.0359510i
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	−0.855299	−	0.518135i	$-0.826627\pi$
$157$	−7.85410	+	5.70634i	−0.626826	+	0.455415i	0.228473	+	0.973550i	$0.426627\pi$
$158$	−10.8541	−	7.88597i	−0.863506	−	0.627374i
$159$	−0.180340	−	0.555029i	−0.0143019	−	0.0440167i
$160$	1.00000	+	3.07768i	0.0790569	+	0.243312i
$161$	2.00000	+	1.45309i	0.157622	+	0.114519i
$162$	−6.23607	+	4.53077i	−0.489952	+	0.355971i
$163$	0.281153	−	0.865300i	0.0220216	−	0.0677755i	−0.939442	−	0.342709i	$-0.888656\pi$
$163$	0.281153	−	0.865300i	0.0220216	−	0.0677755i	0.961463	+	0.274933i	$0.0886557\pi$
$164$	5.61803			0.438695
$165$		0			0
$166$	9.32624			0.723856
$167$	−4.56231	+	14.0413i	−0.353042	+	1.08655i	0.604094	+	0.796913i	$0.293535\pi$
$167$	−4.56231	+	14.0413i	−0.353042	+	1.08655i	−0.957136	+	0.289638i	$0.906465\pi$
$168$	0.618034	−	0.449028i	0.0476824	−	0.0346433i
$169$	9.28115	+	6.74315i	0.713935	+	0.518704i
$170$	−0.618034	−	1.90211i	−0.0474010	−	0.145885i
$171$	5.16312	+	15.8904i	0.394834	+	1.21517i
$172$	6.92705	+	5.03280i	0.528183	+	0.383747i
$173$	−17.7082	+	12.8658i	−1.34633	+	0.978166i	−0.347144	+	0.937812i	$0.612849\pi$
$173$	−17.7082	+	12.8658i	−1.34633	+	0.978166i	−0.999185	+	0.0403542i	$0.987151\pi$
$174$	0.527864	−	1.62460i	0.0400173	−	0.123160i
$175$	−10.9443			−0.827309
$176$		0			0
$177$	−3.29180			−0.247427
$178$	−2.50000	+	7.69421i	−0.187383	+	0.576705i
$179$	6.97214	−	5.06555i	0.521122	−	0.378617i	−0.295904	−	0.955218i	$-0.595621\pi$
$179$	6.97214	−	5.06555i	0.521122	−	0.378617i	0.817026	+	0.576600i	$0.195621\pi$
$180$	7.47214	+	5.42882i	0.556940	+	0.404641i
$181$	−1.29180	−	3.97574i	−0.0960184	−	0.295514i	0.891499	−	0.453022i	$-0.149654\pi$
$181$	−1.29180	−	3.97574i	−0.0960184	−	0.295514i	−0.987518	+	0.157508i	$0.949654\pi$
$182$	−0.763932	−	2.35114i	−0.0566264	−	0.174278i
$183$	0.763932	+	0.555029i	0.0564715	+	0.0410289i
$184$	−1.00000	+	0.726543i	−0.0737210	+	0.0535614i
$185$	−3.70820	+	11.4127i	−0.272633	+	0.839077i
$186$	0.763932			0.0560142
$187$		0			0
$188$	−6.47214			−0.472029
$189$	1.38197	−	4.25325i	0.100523	−	0.309379i
$190$	15.3262	−	11.1352i	1.11188	−	0.807830i
$191$	−3.85410	−	2.80017i	−0.278873	−	0.202613i	0.439553	−	0.898217i	$-0.355137\pi$
$191$	−3.85410	−	2.80017i	−0.278873	−	0.202613i	−0.718426	+	0.695604i	$0.755137\pi$
$192$	0.118034	+	0.363271i	0.00851837	+	0.0262168i
$193$	5.38197	+	16.5640i	0.387402	+	1.19230i	0.934722	+	0.355379i	$0.115648\pi$
$193$	5.38197	+	16.5640i	0.387402	+	1.19230i	−0.547320	+	0.836923i	$0.684352\pi$
$194$	−5.78115	−	4.20025i	−0.415063	−	0.301561i
$195$	−1.23607	+	0.898056i	−0.0885167	+	0.0643111i
$196$	−0.927051	+	2.85317i	−0.0662179	+	0.203798i
$197$	−20.9443			−1.49222			−0.746109	−	0.665824i	$-0.768080\pi$
$197$	−20.9443			−1.49222			−0.746109	+	0.665824i	$0.768080\pi$
$198$		0			0
$199$	−18.9443			−1.34292			−0.671462	−	0.741039i	$-0.734333\pi$
$199$	−18.9443			−1.34292			−0.671462	+	0.741039i	$0.734333\pi$
$200$	1.69098	−	5.20431i	0.119571	−	0.368000i
$201$	−3.42705	+	2.48990i	−0.241726	+	0.175624i
$202$	3.38197	+	2.45714i	0.237954	+	0.172884i
$203$	−2.76393	−	8.50651i	−0.193990	−	0.597040i
$204$	−0.0729490	−	0.224514i	−0.00510745	−	0.0157191i
$205$	−14.7082	−	10.6861i	−1.02727	−	0.746352i
$206$	−12.7082	+	9.23305i	−0.885423	+	0.643297i
$207$	−1.09017	+	3.35520i	−0.0757720	+	0.233202i
$208$	1.23607			0.0857059
$209$		0			0
$210$	−2.47214			−0.170594
$211$	−1.88197	+	5.79210i	−0.129560	+	0.398744i	−0.994704	−	0.102779i	$-0.967227\pi$
$211$	−1.88197	+	5.79210i	−0.129560	+	0.398744i	0.865144	+	0.501523i	$0.167227\pi$
$212$	1.23607	−	0.898056i	0.0848935	−	0.0616787i
$213$	1.61803	+	1.17557i	0.110866	+	0.0805488i
$214$	−0.354102	−	1.08981i	−0.0242059	−	0.0744981i
$215$	−8.56231	−	26.3521i	−0.583944	−	1.79720i
$216$	1.80902	+	1.31433i	0.123088	+	0.0894287i
$217$	3.23607	−	2.35114i	0.219679	−	0.159606i
$218$	5.85410	−	18.0171i	0.396490	−	1.22027i
$219$	3.96556			0.267968
$220$		0			0
$221$	−0.763932			−0.0513876
$222$	−0.437694	+	1.34708i	−0.0293761	+	0.0904104i
$223$	−20.7984	+	15.1109i	−1.39276	+	1.01190i	−0.397206	+	0.917729i	$0.630020\pi$
$223$	−20.7984	+	15.1109i	−1.39276	+	1.01190i	−0.995556	+	0.0941715i	$0.969980\pi$
$224$	1.61803	+	1.17557i	0.108109	+	0.0785461i
$225$	−4.82624	−	14.8536i	−0.321749	−	0.990242i
$226$	−0.572949	−	1.76336i	−0.0381120	−	0.117297i
$227$	−11.7361	−	8.52675i	−0.778950	−	0.565940i	0.125714	−	0.992067i	$-0.459878\pi$
$227$	−11.7361	−	8.52675i	−0.778950	−	0.565940i	−0.904664	+	0.426126i	$0.859878\pi$
$228$	1.80902	−	1.31433i	0.119805	−	0.0870435i
$229$	0.527864	−	1.62460i	0.0348822	−	0.107356i	−0.932099	−	0.362203i	$-0.882025\pi$
$229$	0.527864	−	1.62460i	0.0348822	−	0.107356i	0.966982	+	0.254846i	$0.0820248\pi$
$230$	4.00000			0.263752
$231$		0			0
$232$	4.47214			0.293610
$233$	−2.97214	+	9.14729i	−0.194711	+	0.599259i	0.805269	+	0.592910i	$0.202021\pi$
$233$	−2.97214	+	9.14729i	−0.194711	+	0.599259i	−0.999980	+	0.00634916i	$0.997979\pi$
$234$	2.85410	−	2.07363i	0.186578	−	0.135557i
$235$	16.9443	+	12.3107i	1.10532	+	0.803064i
$236$	−2.66312	−	8.19624i	−0.173354	−	0.533530i
$237$	1.58359	+	4.87380i	0.102865	+	0.316587i
$238$	−1.00000	−	0.726543i	−0.0648204	−	0.0470948i
$239$	17.5623	−	12.7598i	1.13601	−	0.825360i	0.149453	−	0.988769i	$-0.452249\pi$
$239$	17.5623	−	12.7598i	1.13601	−	0.825360i	0.986558	+	0.163408i	$0.0522488\pi$
$240$	0.381966	−	1.17557i	0.0246558	−	0.0758827i
$241$	−11.0902			−0.714381			−0.357190	−	0.934032i	$-0.616265\pi$
$241$	−11.0902			−0.714381			−0.357190	+	0.934032i	$0.616265\pi$
$242$		0			0
$243$	9.65248			0.619207
$244$	−0.763932	+	2.35114i	−0.0489057	+	0.150516i
$245$	7.85410	−	5.70634i	0.501780	−	0.364565i
$246$	−1.73607	−	1.26133i	−0.110688	−	0.0804193i
$247$	−2.23607	−	6.88191i	−0.142278	−	0.437885i
$248$	0.618034	+	1.90211i	0.0392452	+	0.120784i
$249$	−2.88197	−	2.09387i	−0.182637	−	0.132694i
$250$	−1.23607	+	0.898056i	−0.0781758	+	0.0567980i
$251$	6.47214	−	19.9192i	0.408518	−	1.25729i	−0.509404	−	0.860527i	$-0.670134\pi$
$251$	6.47214	−	19.9192i	0.408518	−	1.25729i	0.917922	−	0.396761i	$-0.129866\pi$
$252$	5.70820			0.359583
$253$		0			0
$254$	−10.9443			−0.686705
$255$	−0.236068	+	0.726543i	−0.0147832	+	0.0454979i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.54508	+	3.30220i	0.283515	+	0.205985i	0.720449	−	0.693508i	$-0.243936\pi$
$257$	4.54508	+	3.30220i	0.283515	+	0.205985i	−0.436934	+	0.899493i	$0.643936\pi$
$258$	−1.01064	−	3.11044i	−0.0629199	−	0.193648i
$259$	2.29180	+	7.05342i	0.142405	+	0.438278i
$260$	−3.23607	−	2.35114i	−0.200692	−	0.145812i
$261$	10.3262	−	7.50245i	0.639178	−	0.464390i
$262$	2.10081	−	6.46564i	0.129789	−	0.399448i
$263$	−23.2361			−1.43280			−0.716399	−	0.697691i	$-0.754211\pi$
$263$	−23.2361			−1.43280			−0.716399	+	0.697691i	$0.754211\pi$
$264$		0			0
$265$	−4.94427			−0.303724
$266$	3.61803	−	11.1352i	0.221836	−	0.682741i
$267$	2.50000	−	1.81636i	0.152998	−	0.111159i
$268$	−8.97214	−	6.51864i	−0.548060	−	0.398189i
$269$	1.90983	+	5.87785i	0.116444	+	0.358379i	0.992246	−	0.124293i	$-0.0396663\pi$
$269$	1.90983	+	5.87785i	0.116444	+	0.358379i	−0.875801	+	0.482672i	$0.839666\pi$
$270$	−2.23607	−	6.88191i	−0.136083	−	0.418820i
$271$	−1.61803	−	1.17557i	−0.0982886	−	0.0714108i	0.537555	−	0.843228i	$-0.319348\pi$
$271$	−1.61803	−	1.17557i	−0.0982886	−	0.0714108i	−0.635844	+	0.771818i	$0.719348\pi$
$272$	0.500000	−	0.363271i	0.0303170	−	0.0220266i
$273$	−0.291796	+	0.898056i	−0.0176603	+	0.0543528i
$274$	16.0902			0.972043
$275$		0			0
$276$	0.472136			0.0284192
$277$	−7.32624	+	22.5478i	−0.440191	+	1.35477i	0.447482	+	0.894293i	$0.352321\pi$
$277$	−7.32624	+	22.5478i	−0.440191	+	1.35477i	−0.887672	+	0.460475i	$0.847679\pi$
$278$		0			0
$279$	4.61803	+	3.35520i	0.276474	+	0.200870i
$280$	−2.00000	−	6.15537i	−0.119523	−	0.367854i
$281$	−4.97214	−	15.3027i	−0.296613	−	0.912880i	−0.982675	−	0.185337i	$-0.940662\pi$
$281$	−4.97214	−	15.3027i	−0.296613	−	0.912880i	0.686062	−	0.727543i	$-0.259338\pi$
$282$	2.00000	+	1.45309i	0.119098	+	0.0865300i
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.989032	−	0.147703i	$-0.952812\pi$
$283$	−19.4164	+	14.1068i	−1.15419	+	0.838565i	−0.165154	+	0.986268i	$0.552812\pi$
$284$	−1.61803	+	4.97980i	−0.0960127	+	0.295497i
$285$	−7.23607			−0.428628
$286$		0			0
$287$	−11.2361			−0.663244
$288$	−0.881966	+	2.71441i	−0.0519703	+	0.159948i
$289$	13.4443	−	9.76784i	0.790840	−	0.574579i
$290$	−11.7082	−	8.50651i	−0.687529	−	0.499519i
$291$	0.843459	+	2.59590i	0.0494444	+	0.152174i
$292$	3.20820	+	9.87384i	0.187746	+	0.577823i
$293$	22.9443	+	16.6700i	1.34042	+	0.973871i	0.999428	+	0.0338043i	$0.0107623\pi$
$293$	22.9443	+	16.6700i	1.34042	+	0.973871i	0.340990	+	0.940067i	$0.389238\pi$
$294$	0.927051	−	0.673542i	0.0540667	−	0.0392818i
$295$	−8.61803	+	26.5236i	−0.501761	+	1.54426i
$296$	−3.70820			−0.215535
$297$		0			0
$298$	−6.18034			−0.358017
$299$	0.472136	−	1.45309i	0.0273043	−	0.0840341i
$300$	−1.69098	+	1.22857i	−0.0976289	+	0.0709316i
$301$	−13.8541	−	10.0656i	−0.798537	−	0.580171i
$302$	−2.47214	−	7.60845i	−0.142255	−	0.437817i
$303$	−0.493422	−	1.51860i	−0.0283464	−	0.0872411i
$304$	4.73607	+	3.44095i	0.271632	+	0.197352i
$305$	6.47214	−	4.70228i	0.370593	−	0.269252i
$306$	0.545085	−	1.67760i	0.0311604	−	0.0959020i
$307$	27.7984			1.58654			0.793268	−	0.608872i	$-0.208378\pi$
$307$	27.7984			1.58654			0.793268	+	0.608872i	$0.208378\pi$
$308$		0			0
$309$	6.00000			0.341328
$310$	2.00000	−	6.15537i	0.113592	−	0.349601i
$311$	−21.0902	+	15.3229i	−1.19591	+	0.868882i	−0.993877	−	0.110496i	$-0.964756\pi$
$311$	−21.0902	+	15.3229i	−1.19591	+	0.868882i	−0.202037	+	0.979378i	$0.564756\pi$
$312$	−0.381966	−	0.277515i	−0.0216246	−	0.0157112i
$313$	1.33688	+	4.11450i	0.0755650	+	0.232565i	0.981703	−	0.190416i	$-0.0609837\pi$
$313$	1.33688	+	4.11450i	0.0755650	+	0.232565i	−0.906139	+	0.422981i	$0.860984\pi$
$314$	3.00000	+	9.23305i	0.169300	+	0.521051i
$315$	−14.9443	−	10.8576i	−0.842014	−	0.611759i
$316$	−10.8541	+	7.88597i	−0.610591	+	0.443620i
$317$	−1.14590	+	3.52671i	−0.0643600	+	0.198080i	−0.978066	−	0.208297i	$-0.933208\pi$
$317$	−1.14590	+	3.52671i	−0.0643600	+	0.198080i	0.913706	+	0.406377i	$0.133208\pi$
$318$	−0.583592			−0.0327262
$319$		0			0
$320$	3.23607			0.180902
$321$	−0.135255	+	0.416272i	−0.00754919	+	0.0232340i
$322$	2.00000	−	1.45309i	0.111456	−	0.0809773i
$323$	−2.92705	−	2.12663i	−0.162865	−	0.118329i
$324$	2.38197	+	7.33094i	0.132331	+	0.407274i
$325$	2.09017	+	6.43288i	0.115942	+	0.356832i
$326$	−0.736068	−	0.534785i	−0.0407670	−	0.0296190i
$327$	−5.85410	+	4.25325i	−0.323733	+	0.235205i
$328$	1.73607	−	5.34307i	0.0958583	−	0.295022i
$329$	12.9443			0.713641
$330$		0			0
$331$	6.27051			0.344658			0.172329	−	0.985039i	$-0.444871\pi$
$331$	6.27051			0.344658			0.172329	+	0.985039i	$0.444871\pi$
$332$	2.88197	−	8.86978i	0.158168	−	0.486792i
$333$	−8.56231	+	6.22088i	−0.469211	+	0.340902i
$334$	11.9443	+	8.67802i	0.653561	+	0.474840i
$335$	11.0902	+	34.1320i	0.605921	+	1.86483i
$336$	−0.236068	−	0.726543i	−0.0128786	−	0.0396361i
$337$	21.6803	+	15.7517i	1.18100	+	0.858049i	0.992284	−	0.123982i	$-0.0395665\pi$
$337$	21.6803	+	15.7517i	1.18100	+	0.858049i	0.188719	+	0.982031i	$0.439567\pi$
$338$	9.28115	−	6.74315i	0.504828	−	0.366779i
$339$	−0.218847	+	0.673542i	−0.0118861	+	0.0365818i
$340$	−2.00000			−0.108465
$341$		0			0
$342$	16.7082			0.903476
$343$	6.18034	−	19.0211i	0.333707	−	1.02704i
$344$	6.92705	−	5.03280i	0.373482	−	0.271350i
$345$	−1.23607	−	0.898056i	−0.0665477	−	0.0483497i
$346$	6.76393	+	20.8172i	0.363631	+	1.11914i
$347$	5.13525	+	15.8047i	0.275675	+	0.848440i	0.989040	+	0.147648i	$0.0471701\pi$
$347$	5.13525	+	15.8047i	0.275675	+	0.848440i	−0.713365	+	0.700793i	$0.752830\pi$
$348$	−1.38197	−	1.00406i	−0.0740812	−	0.0538231i
$349$	15.8541	−	11.5187i	0.848651	−	0.616581i	−0.0761230	−	0.997098i	$-0.524254\pi$
$349$	15.8541	−	11.5187i	0.848651	−	0.616581i	0.924774	+	0.380518i	$0.124254\pi$
$350$	−3.38197	+	10.4086i	−0.180774	+	0.556364i
$351$	−2.76393			−0.147528
$352$		0			0
$353$	32.6180			1.73608			0.868041	−	0.496492i	$-0.165379\pi$
$353$	32.6180			1.73608			0.868041	+	0.496492i	$0.165379\pi$
$354$	−1.01722	+	3.13068i	−0.0540647	+	0.166394i
$355$	13.7082	−	9.95959i	0.727556	−	0.528600i
$356$	6.54508	+	4.75528i	0.346889	+	0.252029i
$357$	0.145898	+	0.449028i	0.00772174	+	0.0237651i
$358$	−2.66312	−	8.19624i	−0.140750	−	0.433185i
$359$	−4.14590	−	3.01217i	−0.218812	−	0.158976i	0.472980	−	0.881073i	$-0.343178\pi$
$359$	−4.14590	−	3.01217i	−0.218812	−	0.158976i	−0.691792	+	0.722097i	$0.743178\pi$
$360$	7.47214	−	5.42882i	0.393816	−	0.286124i
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	−4.18034			−0.219714
$363$		0			0
$364$	−2.47214			−0.129575
$365$	10.3820	−	31.9524i	0.543417	−	1.67247i
$366$	0.763932	−	0.555029i	0.0399314	−	0.0290118i
$367$	−15.9443	−	11.5842i	−0.832284	−	0.604690i	0.0879204	−	0.996128i	$-0.471978\pi$
$367$	−15.9443	−	11.5842i	−0.832284	−	0.604690i	−0.920205	+	0.391438i	$0.871978\pi$
$368$	0.381966	+	1.17557i	0.0199114	+	0.0612808i
$369$	−4.95492	−	15.2497i	−0.257943	−	0.793866i
$370$	9.70820	+	7.05342i	0.504705	+	0.366690i
$371$	−2.47214	+	1.79611i	−0.128347	+	0.0932495i
$372$	0.236068	−	0.726543i	0.0122396	−	0.0376695i
$373$	−4.29180			−0.222221			−0.111110	−	0.993808i	$-0.535441\pi$
$373$	−4.29180			−0.222221			−0.111110	+	0.993808i	$0.535441\pi$
$374$		0			0
$375$	0.583592			0.0301366
$376$	−2.00000	+	6.15537i	−0.103142	+	0.317439i
$377$	−4.47214	+	3.24920i	−0.230327	+	0.167342i
$378$	−3.61803	−	2.62866i	−0.186092	−	0.135203i
$379$	4.40983	+	13.5721i	0.226518	+	0.697150i	0.998134	+	0.0610616i	$0.0194486\pi$
$379$	4.40983	+	13.5721i	0.226518	+	0.697150i	−0.771616	+	0.636088i	$0.780551\pi$
$380$	−5.85410	−	18.0171i	−0.300309	−	0.924256i
$381$	3.38197	+	2.45714i	0.173263	+	0.125883i
$382$	−3.85410	+	2.80017i	−0.197193	+	0.143269i
$383$	−8.76393	+	26.9726i	−0.447816	+	1.37824i	0.431550	+	0.902089i	$0.357967\pi$
$383$	−8.76393	+	26.9726i	−0.447816	+	1.37824i	−0.879366	+	0.476147i	$0.842033\pi$
$384$	0.381966			0.0194921
$385$		0			0
$386$	17.4164			0.886472
$387$	7.55166	−	23.2416i	0.383873	−	1.18144i
$388$	−5.78115	+	4.20025i	−0.293494	+	0.213236i
$389$	8.61803	+	6.26137i	0.436952	+	0.317464i	0.784423	−	0.620227i	$-0.212959\pi$
$389$	8.61803	+	6.26137i	0.436952	+	0.317464i	−0.347471	+	0.937691i	$0.612959\pi$
$390$	0.472136	+	1.45309i	0.0239075	+	0.0735798i
$391$	−0.236068	−	0.726543i	−0.0119385	−	0.0367428i
$392$	2.42705	+	1.76336i	0.122585	+	0.0890629i
$393$	−2.10081	+	1.52633i	−0.105972	+	0.0769932i
$394$	−6.47214	+	19.9192i	−0.326061	+	1.00351i
$395$	43.4164			2.18452
$396$		0			0
$397$	−17.1246			−0.859460			−0.429730	−	0.902958i	$-0.641391\pi$
$397$	−17.1246			−0.859460			−0.429730	+	0.902958i	$0.641391\pi$
$398$	−5.85410	+	18.0171i	−0.293440	+	0.903114i
$399$	−3.61803	+	2.62866i	−0.181128	+	0.131597i
$400$	−4.42705	−	3.21644i	−0.221353	−	0.160822i
$401$	−5.50000	−	16.9273i	−0.274657	−	0.845307i	−0.989310	−	0.145828i	$-0.953415\pi$
$401$	−5.50000	−	16.9273i	−0.274657	−	0.845307i	0.714653	−	0.699479i	$-0.246585\pi$
$402$	1.30902	+	4.02874i	0.0652878	+	0.200935i
$403$	−2.00000	−	1.45309i	−0.0996271	−	0.0723833i
$404$	3.38197	−	2.45714i	0.168259	−	0.122247i
$405$	7.70820	−	23.7234i	0.383024	−	1.17883i
$406$	−8.94427			−0.443897
$407$		0			0
$408$	−0.236068			−0.0116871
$409$	−4.14590	+	12.7598i	−0.205001	+	0.630930i	0.794712	+	0.606987i	$0.207622\pi$
$409$	−4.14590	+	12.7598i	−0.205001	+	0.630930i	−0.999713	+	0.0239428i	$0.992378\pi$
$410$	−14.7082	+	10.6861i	−0.726386	+	0.527751i
$411$	−4.97214	−	3.61247i	−0.245257	−	0.178190i
$412$	4.85410	+	14.9394i	0.239144	+	0.736011i
$413$	5.32624	+	16.3925i	0.262087	+	0.806621i
$414$	2.85410	+	2.07363i	0.140271	+	0.101913i
$415$	−24.4164	+	17.7396i	−1.19855	+	0.870801i
$416$	0.381966	−	1.17557i	0.0187274	−	0.0576371i
$417$		0			0
$418$		0			0
$419$	−10.8541			−0.530258			−0.265129	−	0.964213i	$-0.585414\pi$
$419$	−10.8541			−0.530258			−0.265129	+	0.964213i	$0.585414\pi$
$420$	−0.763932	+	2.35114i	−0.0372761	+	0.114724i
$421$	25.4164	−	18.4661i	1.23872	−	0.899983i	0.241207	−	0.970474i	$-0.422457\pi$
$421$	25.4164	−	18.4661i	1.23872	−	0.899983i	0.997512	+	0.0704909i	$0.0224566\pi$
$422$	4.92705	+	3.57971i	0.239845	+	0.174258i
$423$	5.70820	+	17.5680i	0.277542	+	0.854188i
$424$	−0.472136	−	1.45309i	−0.0229289	−	0.0705680i
$425$	2.73607	+	1.98787i	0.132719	+	0.0964258i
$426$	1.61803	−	1.17557i	0.0783940	−	0.0569566i
$427$	1.52786	−	4.70228i	0.0739385	−	0.227559i
$428$	−1.14590			−0.0553891
$429$		0			0
$430$	−27.7082			−1.33621
$431$	−5.23607	+	16.1150i	−0.252213	+	0.776230i	0.742154	+	0.670230i	$0.233804\pi$
$431$	−5.23607	+	16.1150i	−0.252213	+	0.776230i	−0.994366	+	0.106000i	$0.966196\pi$
$432$	1.80902	−	1.31433i	0.0870364	−	0.0632356i
$433$	−22.4443	−	16.3067i	−1.07860	−	0.783651i	−0.101164	−	0.994870i	$-0.532257\pi$
$433$	−22.4443	−	16.3067i	−1.07860	−	0.783651i	−0.977439	+	0.211219i	$0.932257\pi$
$434$	−1.23607	−	3.80423i	−0.0593332	−	0.182609i
$435$	1.70820	+	5.25731i	0.0819021	+	0.252069i
$436$	−15.3262	−	11.1352i	−0.733994	−	0.533278i
$437$	5.85410	−	4.25325i	0.280040	−	0.203461i
$438$	1.22542	−	3.77147i	0.0585531	−	0.180208i
$439$	−6.58359			−0.314218			−0.157109	−	0.987581i	$-0.550217\pi$
$439$	−6.58359			−0.314218			−0.157109	+	0.987581i	$0.550217\pi$
$440$		0			0
$441$	8.56231			0.407729
$442$	−0.236068	+	0.726543i	−0.0112286	+	0.0345581i
$443$	6.92705	−	5.03280i	0.329114	−	0.239115i	−0.410941	−	0.911662i	$-0.634800\pi$
$443$	6.92705	−	5.03280i	0.329114	−	0.239115i	0.740055	+	0.672547i	$0.234800\pi$
$444$	1.14590	+	0.832544i	0.0543819	+	0.0395108i
$445$	−8.09017	−	24.8990i	−0.383511	−	1.18032i
$446$	7.94427	+	24.4500i	0.376172	+	1.15774i
$447$	1.90983	+	1.38757i	0.0903319	+	0.0656299i
$448$	1.61803	−	1.17557i	0.0764449	−	0.0555405i
$449$	2.86475	−	8.81678i	0.135196	−	0.416090i	−0.860425	−	0.509578i	$-0.829802\pi$
$449$	2.86475	−	8.81678i	0.135196	−	0.416090i	0.995620	+	0.0934881i	$0.0298017\pi$
$450$	−15.6180			−0.736241
$451$		0			0
$452$	−1.85410			−0.0872096
$453$	−0.944272	+	2.90617i	−0.0443658	+	0.136544i
$454$	−11.7361	+	8.52675i	−0.550801	+	0.400180i
$455$	6.47214	+	4.70228i	0.303418	+	0.220446i
$456$	−0.690983	−	2.12663i	−0.0323582	−	0.0995884i
$457$	−2.91641	−	8.97578i	−0.136424	−	0.419869i	0.859385	−	0.511329i	$-0.170847\pi$
$457$	−2.91641	−	8.97578i	−0.136424	−	0.419869i	−0.995809	+	0.0914598i	$0.970847\pi$
$458$	−1.38197	−	1.00406i	−0.0645750	−	0.0469165i
$459$	−1.11803	+	0.812299i	−0.0521854	+	0.0379149i
$460$	1.23607	−	3.80423i	0.0576320	−	0.177373i
$461$	1.34752			0.0627605			0.0313802	−	0.999508i	$-0.490010\pi$
$461$	1.34752			0.0627605			0.0313802	+	0.999508i	$0.490010\pi$
$462$		0			0
$463$	−19.4164			−0.902357			−0.451178	−	0.892434i	$-0.648996\pi$
$463$	−19.4164			−0.902357			−0.451178	+	0.892434i	$0.648996\pi$
$464$	1.38197	−	4.25325i	0.0641562	−	0.197452i
$465$	−2.00000	+	1.45309i	−0.0927478	+	0.0673852i
$466$	7.78115	+	5.65334i	0.360455	+	0.261886i
$467$	−10.2918	−	31.6749i	−0.476248	−	1.46574i	−0.844268	−	0.535921i	$-0.819964\pi$
$467$	−10.2918	−	31.6749i	−0.476248	−	1.46574i	0.368020	−	0.929818i	$-0.380036\pi$
$468$	−1.09017	−	3.35520i	−0.0503931	−	0.155094i
$469$	17.9443	+	13.0373i	0.828589	+	0.602006i
$470$	16.9443	−	12.3107i	0.781581	−	0.567852i
$471$	1.14590	−	3.52671i	0.0528002	−	0.162502i
$472$	−8.61803			−0.396677
$473$		0			0
$474$	5.12461			0.235381
$475$	−9.89919	+	30.4666i	−0.454206	+	1.39790i
$476$	−1.00000	+	0.726543i	−0.0458349	+	0.0333010i
$477$	−3.52786	−	2.56314i	−0.161530	−	0.117358i
$478$	−6.70820	−	20.6457i	−0.306826	−	0.944314i
$479$	−10.6525	−	32.7849i	−0.486724	−	1.49798i	−0.829468	−	0.558554i	$-0.811356\pi$
$479$	−10.6525	−	32.7849i	−0.486724	−	1.49798i	0.342744	−	0.939429i	$-0.388644\pi$
$480$	−1.00000	−	0.726543i	−0.0456435	−	0.0331620i
$481$	3.70820	−	2.69417i	0.169080	−	0.122843i
$482$	−3.42705	+	10.5474i	−0.156098	+	0.480420i
$483$	−0.944272			−0.0429659
$484$		0			0
$485$	23.1246			1.05003
$486$	2.98278	−	9.18005i	0.135302	−	0.416416i
$487$	1.09017	−	0.792055i	0.0494003	−	0.0358914i	−0.562811	−	0.826586i	$-0.690280\pi$
$487$	1.09017	−	0.792055i	0.0494003	−	0.0358914i	0.612211	+	0.790694i	$0.290280\pi$
$488$	2.00000	+	1.45309i	0.0905357	+	0.0657781i
$489$	0.107391	+	0.330515i	0.00485638	+	0.0149464i
$490$	−3.00000	−	9.23305i	−0.135526	−	0.417107i
$491$	−18.4894	−	13.4333i	−0.834413	−	0.606237i	0.0863914	−	0.996261i	$-0.472466\pi$
$491$	−18.4894	−	13.4333i	−0.834413	−	0.606237i	−0.920804	+	0.390025i	$0.872466\pi$
$492$	−1.73607	+	1.26133i	−0.0782680	+	0.0568650i
$493$	−0.854102	+	2.62866i	−0.0384668	+	0.118389i
$494$	−7.23607			−0.325566
$495$		0			0
$496$	2.00000			0.0898027
$497$	3.23607	−	9.95959i	0.145157	−	0.446749i
$498$	−2.88197	+	2.09387i	−0.129144	+	0.0938286i
$499$	24.9615	+	18.1356i	1.11743	+	0.811860i	0.983818	−	0.179173i	$-0.0573423\pi$
$499$	24.9615	+	18.1356i	1.11743	+	0.811860i	0.133612	+	0.991034i	$0.457342\pi$
$500$	0.472136	+	1.45309i	0.0211146	+	0.0649839i
$501$	−1.74265	−	5.36331i	−0.0778557	−	0.239615i
$502$	−16.9443	−	12.3107i	−0.756260	−	0.549455i
$503$	2.61803	−	1.90211i	0.116732	−	0.0848110i	−0.527887	−	0.849314i	$-0.677016\pi$
$503$	2.61803	−	1.90211i	0.116732	−	0.0848110i	0.644620	+	0.764503i	$0.277016\pi$
$504$	1.76393	−	5.42882i	0.0785718	−	0.241819i
$505$	−13.5279			−0.601982
$506$		0			0
$507$	−4.38197			−0.194610
$508$	−3.38197	+	10.4086i	−0.150050	+	0.461808i
$509$	6.70820	−	4.87380i	0.297336	−	0.216027i	−0.429108	−	0.903253i	$-0.641172\pi$
$509$	6.70820	−	4.87380i	0.297336	−	0.216027i	0.726443	+	0.687226i	$0.241172\pi$
$510$	0.618034	+	0.449028i	0.0273670	+	0.0198833i
$511$	−6.41641	−	19.7477i	−0.283845	−	0.873586i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−10.5902	−	7.69421i	−0.467567	−	0.339708i
$514$	4.54508	−	3.30220i	0.200475	−	0.145654i
$515$	15.7082	−	48.3449i	0.692186	−	2.13033i
$516$	−3.27051			−0.143976
$517$		0			0
$518$	7.41641			0.325858
$519$	2.58359	−	7.95148i	0.113407	−	0.349031i
$520$	−3.23607	+	2.35114i	−0.141911	+	0.103104i
$521$	16.2082	+	11.7759i	0.710094	+	0.515914i	0.883204	−	0.468989i	$-0.155382\pi$
$521$	16.2082	+	11.7759i	0.710094	+	0.515914i	−0.173110	+	0.984903i	$0.555382\pi$
$522$	−3.94427	−	12.1392i	−0.172636	−	0.531319i
$523$	2.84346	+	8.75127i	0.124336	+	0.382666i	0.993779	−	0.111366i	$-0.0355225\pi$
$523$	2.84346	+	8.75127i	0.124336	+	0.382666i	−0.869444	+	0.494032i	$0.835523\pi$
$524$	−5.50000	−	3.99598i	−0.240269	−	0.174565i
$525$	3.38197	−	2.45714i	0.147601	−	0.107238i
$526$	−7.18034	+	22.0988i	−0.313078	+	0.963554i
$527$	−1.23607			−0.0538440
$528$		0			0
$529$	−21.4721			−0.933571
$530$	−1.52786	+	4.70228i	−0.0663662	+	0.204254i
$531$	−19.8992	+	14.4576i	−0.863551	+	0.627407i
$532$	−9.47214	−	6.88191i	−0.410669	−	0.298369i
$533$	2.14590	+	6.60440i	0.0929492	+	0.286068i
$534$	−0.954915	−	2.93893i	−0.0413232	−	0.127180i
$535$	3.00000	+	2.17963i	0.129701	+	0.0942335i
$536$	−8.97214	+	6.51864i	−0.387537	+	0.281562i
$537$	−1.01722	+	3.13068i	−0.0438963	+	0.135099i
$538$	6.18034			0.266453
$539$		0			0
$540$	−7.23607			−0.311391
$541$	−0.965558	+	2.97168i	−0.0415126	+	0.127763i	−0.969665	−	0.244438i	$-0.921397\pi$
$541$	−0.965558	+	2.97168i	−0.0415126	+	0.127763i	0.928152	+	0.372200i	$0.121397\pi$
$542$	−1.61803	+	1.17557i	−0.0695005	+	0.0504951i
$543$	1.29180	+	0.938545i	0.0554363	+	0.0402768i
$544$	−0.190983	−	0.587785i	−0.00818833	−	0.0252011i
$545$	18.9443	+	58.3045i	0.811483	+	2.49749i
$546$	0.763932	+	0.555029i	0.0326933	+	0.0237531i
$547$	−6.73607	+	4.89404i	−0.288013	+	0.209254i	−0.722405	−	0.691470i	$-0.756963\pi$
$547$	−6.73607	+	4.89404i	−0.288013	+	0.209254i	0.434392	+	0.900724i	$0.356963\pi$
$548$	4.97214	−	15.3027i	0.212399	−	0.653697i
$549$	7.05573			0.301131
$550$		0			0
$551$	−26.1803			−1.11532
$552$	0.145898	−	0.449028i	0.00620983	−	0.0191119i
$553$	21.7082	−	15.7719i	0.923127	−	0.670691i
$554$	19.1803	+	13.9353i	0.814895	+	0.592056i
$555$	−1.41641	−	4.35926i	−0.0601232	−	0.185040i
$556$		0			0
$557$	−28.5066	−	20.7112i	−1.20786	−	0.877563i	−0.212828	−	0.977090i	$-0.568267\pi$
$557$	−28.5066	−	20.7112i	−1.20786	−	0.877563i	−0.995035	+	0.0995263i	$0.968267\pi$
$558$	4.61803	−	3.35520i	0.195497	−	0.142037i
$559$	−3.27051	+	10.0656i	−0.138328	+	0.425729i
$560$	−6.47214			−0.273498
$561$		0			0
$562$	−16.0902			−0.678723
$563$	0.118034	−	0.363271i	0.00497454	−	0.0153101i	−0.948538	−	0.316662i	$-0.897438\pi$
$563$	0.118034	−	0.363271i	0.00497454	−	0.0153101i	0.953513	+	0.301352i	$0.0974379\pi$
$564$	2.00000	−	1.45309i	0.0842152	−	0.0611859i
$565$	4.85410	+	3.52671i	0.204214	+	0.148370i
$566$	7.41641	+	22.8254i	0.311735	+	0.959421i
$567$	−4.76393	−	14.6619i	−0.200066	−	0.615741i
$568$	4.23607	+	3.07768i	0.177741	+	0.129137i
$569$	−30.9164	+	22.4621i	−1.29608	+	0.941660i	−0.999909	−	0.0134744i	$-0.995711\pi$
$569$	−30.9164	+	22.4621i	−1.29608	+	0.941660i	−0.296174	+	0.955134i	$0.595711\pi$
$570$	−2.23607	+	6.88191i	−0.0936586	+	0.288251i
$571$	−2.47214			−0.103456			−0.0517278	−	0.998661i	$-0.516473\pi$
$571$	−2.47214			−0.103456			−0.0517278	+	0.998661i	$0.516473\pi$
$572$		0			0
$573$	1.81966			0.0760174
$574$	−3.47214	+	10.6861i	−0.144924	+	0.446031i
$575$	−5.47214	+	3.97574i	−0.228204	+	0.165800i
$576$	2.30902	+	1.67760i	0.0962090	+	0.0699000i
$577$	−2.10081	−	6.46564i	−0.0874580	−	0.269168i	0.897757	−	0.440491i	$-0.145196\pi$
$577$	−2.10081	−	6.46564i	−0.0874580	−	0.269168i	−0.985215	+	0.171323i	$0.945196\pi$
$578$	−5.13525	−	15.8047i	−0.213598	−	0.657388i
$579$	−5.38197	−	3.91023i	−0.223667	−	0.162503i
$580$	−11.7082	+	8.50651i	−0.486157	+	0.353214i
$581$	−5.76393	+	17.7396i	−0.239128	+	0.735961i
$582$	2.72949			0.113141
$583$		0			0
$584$	10.3820			0.429609
$585$	−3.52786	+	10.8576i	−0.145859	+	0.448909i
$586$	22.9443	−	16.6700i	0.947819	−	0.688631i
$587$	−17.9164	−	13.0170i	−0.739489	−	0.537270i	0.153062	−	0.988217i	$-0.451087\pi$
$587$	−17.9164	−	13.0170i	−0.739489	−	0.537270i	−0.892551	+	0.450946i	$0.851087\pi$
$588$	−0.354102	−	1.08981i	−0.0146029	−	0.0449432i
$589$	−3.61803	−	11.1352i	−0.149078	−	0.458816i
$590$	22.5623	+	16.3925i	0.928875	+	0.674868i
$591$	6.47214	−	4.70228i	0.266228	−	0.193426i
$592$	−1.14590	+	3.52671i	−0.0470961	+	0.144947i
$593$	−28.6869			−1.17803			−0.589015	−	0.808122i	$-0.700484\pi$
$593$	−28.6869			−1.17803			−0.589015	+	0.808122i	$0.700484\pi$
$594$		0			0
$595$	4.00000			0.163984
$596$	−1.90983	+	5.87785i	−0.0782297	+	0.240766i
$597$	5.85410	−	4.25325i	0.239592	−	0.174074i
$598$	−1.23607	−	0.898056i	−0.0505466	−	0.0367242i
$599$	−4.14590	−	12.7598i	−0.169397	−	0.521350i	0.829937	−	0.557858i	$-0.188377\pi$
$599$	−4.14590	−	12.7598i	−0.169397	−	0.521350i	−0.999333	+	0.0365080i	$0.988377\pi$
$600$	0.645898	+	1.98787i	0.0263687	+	0.0811544i
$601$	21.9615	+	15.9560i	0.895828	+	0.650857i	0.937391	−	0.348279i	$-0.113234\pi$
$601$	21.9615	+	15.9560i	0.895828	+	0.650857i	−0.0415630	+	0.999136i	$0.513234\pi$
$602$	−13.8541	+	10.0656i	−0.564651	+	0.410243i
$603$	−9.78115	+	30.1033i	−0.398319	+	1.22590i
$604$	−8.00000			−0.325515
$605$		0			0
$606$	−1.59675			−0.0648634
$607$	7.14590	−	21.9928i	0.290043	−	0.892661i	−0.694799	−	0.719204i	$-0.744506\pi$
$607$	7.14590	−	21.9928i	0.290043	−	0.892661i	0.984842	−	0.173456i	$-0.0554935\pi$
$608$	4.73607	−	3.44095i	0.192073	−	0.139549i
$609$	2.76393	+	2.00811i	0.112000	+	0.0813729i
$610$	−2.47214	−	7.60845i	−0.100094	−	0.308057i
$611$	−2.47214	−	7.60845i	−0.100012	−	0.307805i
$612$	−1.42705	−	1.03681i	−0.0576851	−	0.0419107i
$613$	−28.8885	+	20.9888i	−1.16680	+	0.847728i	−0.990622	−	0.136631i	$-0.956373\pi$
$613$	−28.8885	+	20.9888i	−1.16680	+	0.847728i	−0.176175	+	0.984359i	$0.556373\pi$
$614$	8.59017	−	26.4378i	0.346671	−	1.06694i
$615$	6.94427			0.280020
$616$		0			0
$617$	23.4508			0.944096			0.472048	−	0.881573i	$-0.343515\pi$
$617$	23.4508			0.944096			0.472048	+	0.881573i	$0.343515\pi$
$618$	1.85410	−	5.70634i	0.0745829	−	0.229543i
$619$	−4.20820	+	3.05744i	−0.169142	+	0.122889i	−0.669136	−	0.743140i	$-0.733336\pi$
$619$	−4.20820	+	3.05744i	−0.169142	+	0.122889i	0.499994	+	0.866029i	$0.333336\pi$
$620$	−5.23607	−	3.80423i	−0.210286	−	0.152781i
$621$	−0.854102	−	2.62866i	−0.0342739	−	0.105484i
$622$	8.05573	+	24.7930i	0.323005	+	0.994108i
$623$	−13.0902	−	9.51057i	−0.524447	−	0.381033i
$624$	−0.381966	+	0.277515i	−0.0152909	+	0.0111095i
$625$	−6.92705	+	21.3193i	−0.277082	+	0.852771i
$626$	4.32624			0.172911
$627$		0			0
$628$	9.70820			0.387400
$629$	0.708204	−	2.17963i	0.0282379	−	0.0869074i
$630$	−14.9443	+	10.8576i	−0.595394	+	0.432579i
$631$	−19.1803	−	13.9353i	−0.763557	−	0.554757i	0.136442	−	0.990648i	$-0.456433\pi$
$631$	−19.1803	−	13.9353i	−0.763557	−	0.554757i	−0.899999	+	0.435891i	$0.856433\pi$
$632$	4.14590	+	12.7598i	0.164915	+	0.507556i
$633$	−0.718847	−	2.21238i	−0.0285716	−	0.0879344i
$634$	3.00000	+	2.17963i	0.119145	+	0.0865641i
$635$	28.6525	−	20.8172i	1.13704	−	0.826107i
$636$	−0.180340	+	0.555029i	−0.00715094	+	0.0220083i
$637$	−3.70820			−0.146924
$638$		0			0
$639$	14.9443			0.591186
$640$	1.00000	−	3.07768i	0.0395285	−	0.121656i
$641$	−13.4894	+	9.80059i	−0.532798	+	0.387100i	−0.821403	−	0.570348i	$-0.806808\pi$
$641$	−13.4894	+	9.80059i	−0.532798	+	0.387100i	0.288606	+	0.957448i	$0.406808\pi$
$642$	0.354102	+	0.257270i	0.0139753	+	0.0101536i
$643$	12.3541	+	38.0220i	0.487198	+	1.49944i	0.828772	+	0.559587i	$0.189040\pi$
$643$	12.3541	+	38.0220i	0.487198	+	1.49944i	−0.341573	+	0.939855i	$0.610960\pi$
$644$	−0.763932	−	2.35114i	−0.0301031	−	0.0926479i
$645$	8.56231	+	6.22088i	0.337140	+	0.244947i
$646$	−2.92705	+	2.12663i	−0.115163	+	0.0836710i
$647$	8.97871	−	27.6336i	0.352990	−	1.08639i	−0.604176	−	0.796851i	$-0.706498\pi$
$647$	8.97871	−	27.6336i	0.352990	−	1.08639i	0.957166	−	0.289540i	$-0.0935023\pi$
$648$	7.70820			0.302807
$649$		0			0
$650$	6.76393			0.265303
$651$	−0.472136	+	1.45309i	−0.0185045	+	0.0569509i
$652$	−0.736068	+	0.534785i	−0.0288266	+	0.0209438i
$653$	12.4164	+	9.02105i	0.485892	+	0.353021i	0.803602	−	0.595167i	$-0.202914\pi$
$653$	12.4164	+	9.02105i	0.485892	+	0.353021i	−0.317711	+	0.948188i	$0.602914\pi$
$654$	2.23607	+	6.88191i	0.0874372	+	0.269104i
$655$	6.79837	+	20.9232i	0.265634	+	0.817539i
$656$	−4.54508	−	3.30220i	−0.177456	−	0.128929i
$657$	23.9721	−	17.4168i	0.935242	−	0.679493i
$658$	4.00000	−	12.3107i	0.155936	−	0.479922i
$659$	−16.9098			−0.658713			−0.329357	−	0.944206i	$-0.606832\pi$
$659$	−16.9098			−0.658713			−0.329357	+	0.944206i	$0.606832\pi$
$660$		0			0
$661$	−3.52786			−0.137218			−0.0686090	−	0.997644i	$-0.521856\pi$
$661$	−3.52786			−0.137218			−0.0686090	+	0.997644i	$0.521856\pi$
$662$	1.93769	−	5.96361i	0.0753106	−	0.231782i
$663$	0.236068	−	0.171513i	0.00916812	−	0.00666103i
$664$	−7.54508	−	5.48183i	−0.292806	−	0.212736i
$665$	11.7082	+	36.0341i	0.454025	+	1.39734i
$666$	3.27051	+	10.0656i	0.126730	+	0.390034i
$667$	−4.47214	−	3.24920i	−0.173162	−	0.125809i
$668$	11.9443	−	8.67802i	0.462138	−	0.335763i
$669$	3.03444	−	9.33905i	0.117318	−	0.361069i
$670$	35.8885			1.38650
$671$		0			0
$672$	−0.763932			−0.0294693
$673$	3.04508	−	9.37181i	0.117379	−	0.361257i	−0.875056	−	0.484021i	$-0.839176\pi$
$673$	3.04508	−	9.37181i	0.117379	−	0.361257i	0.992436	+	0.122764i	$0.0391759\pi$
$674$	21.6803	−	15.7517i	0.835095	−	0.606732i
$675$	9.89919	+	7.19218i	0.381020	+	0.276827i
$676$	−3.54508	−	10.9106i	−0.136349	−	0.419640i
$677$	−4.43769	−	13.6578i	−0.170554	−	0.524913i	0.828848	−	0.559474i	$-0.188997\pi$
$677$	−4.43769	−	13.6578i	−0.170554	−	0.524913i	−0.999403	+	0.0345610i	$0.988997\pi$
$678$	0.572949	+	0.416272i	0.0220040	+	0.0159868i
$679$	11.5623	−	8.40051i	0.443721	−	0.322382i
$680$	−0.618034	+	1.90211i	−0.0237005	+	0.0729427i
$681$	5.54102			0.212332
$682$		0			0
$683$	18.4721			0.706817			0.353408	−	0.935469i	$-0.385023\pi$
$683$	18.4721			0.706817			0.353408	+	0.935469i	$0.385023\pi$
$684$	5.16312	−	15.8904i	0.197417	−	0.607586i
$685$	−42.1246	+	30.6053i	−1.60950	+	1.16937i
$686$	−16.1803	−	11.7557i	−0.617768	−	0.448835i
$687$	0.201626	+	0.620541i	0.00769252	+	0.0236751i
$688$	−2.64590	−	8.14324i	−0.100874	−	0.310458i
$689$	1.52786	+	1.11006i	0.0582070	+	0.0422898i
$690$	−1.23607	+	0.898056i	−0.0470563	+	0.0341884i
$691$	−8.10081	+	24.9317i	−0.308169	+	0.948448i	0.670306	+	0.742085i	$0.266163\pi$
$691$	−8.10081	+	24.9317i	−0.308169	+	0.948448i	−0.978475	+	0.206363i	$0.933837\pi$
$692$	21.8885			0.832078
$693$		0			0
$694$	16.6180			0.630812
$695$		0			0
$696$	−1.38197	+	1.00406i	−0.0523833	+	0.0380587i
$697$	2.80902	+	2.04087i	0.106399	+	0.0773035i
$698$	−6.05573	−	18.6376i	−0.229213	−	0.705444i
$699$	−1.13525	−	3.49396i	−0.0429393	−	0.132154i
$700$	8.85410	+	6.43288i	0.334654	+	0.243140i
$701$	12.0000	−	8.71851i	0.453234	−	0.329294i	−0.337637	−	0.941276i	$-0.609628\pi$
$701$	12.0000	−	8.71851i	0.453234	−	0.329294i	0.790871	+	0.611983i	$0.209628\pi$
$702$	−0.854102	+	2.62866i	−0.0322360	+	0.0992122i
$703$	21.7082			0.818740
$704$		0			0
$705$	−8.00000			−0.301297
$706$	10.0795	−	31.0216i	0.379348	−	1.16751i
$707$	−6.76393	+	4.91428i	−0.254384	+	0.184821i
$708$	2.66312	+	1.93487i	0.100086	+	0.0727168i
$709$	7.56231	+	23.2744i	0.284008	+	0.874088i	0.986694	+	0.162588i	$0.0519840\pi$
$709$	7.56231	+	23.2744i	0.284008	+	0.874088i	−0.702686	+	0.711500i	$0.748016\pi$
$710$	−5.23607	−	16.1150i	−0.196506	−	0.604784i
$711$	30.9787	+	22.5074i	1.16179	+	0.844092i
$712$	6.54508	−	4.75528i	0.245287	−	0.178212i
$713$	0.763932	−	2.35114i	0.0286095	−	0.0880509i
$714$	0.472136			0.0176692
$715$		0			0
$716$	−8.61803			−0.322071
$717$	−2.56231	+	7.88597i	−0.0956911	+	0.294507i
$718$	−4.14590	+	3.01217i	−0.154724	+	0.112413i
$719$	−21.7082	−	15.7719i	−0.809579	−	0.588194i	0.104129	−	0.994564i	$-0.466794\pi$
$719$	−21.7082	−	15.7719i	−0.809579	−	0.588194i	−0.913709	+	0.406370i	$0.866794\pi$
$720$	−2.85410	−	8.78402i	−0.106366	−	0.327361i
$721$	−9.70820	−	29.8788i	−0.361552	−	1.11274i
$722$	−12.3541	−	8.97578i	−0.459772	−	0.334044i
$723$	3.42705	−	2.48990i	0.127453	−	0.0926003i
$724$	−1.29180	+	3.97574i	−0.0480092	+	0.147757i
$725$	24.4721			0.908872
$726$		0			0
$727$	2.87539			0.106642			0.0533211	−	0.998577i	$-0.483019\pi$
$727$	2.87539			0.106642			0.0533211	+	0.998577i	$0.483019\pi$
$728$	−0.763932	+	2.35114i	−0.0283132	+	0.0871391i
$729$	15.7254	−	11.4252i	0.582423	−	0.423155i
$730$	−27.1803	−	19.7477i	−1.00599	−	0.730894i
$731$	1.63525	+	5.03280i	0.0604821	+	0.186145i
$732$	−0.291796	−	0.898056i	−0.0107851	−	0.0331931i
$733$	7.61803	+	5.53483i	0.281379	+	0.204433i	0.719518	−	0.694473i	$-0.244363\pi$
$733$	7.61803	+	5.53483i	0.281379	+	0.204433i	−0.438140	+	0.898907i	$0.644363\pi$
$734$	−15.9443	+	11.5842i	−0.588514	+	0.427580i
$735$	−1.14590	+	3.52671i	−0.0422671	+	0.130085i
$736$	1.23607			0.0455621
$737$		0			0
$738$	−16.0344			−0.590236
$739$	−11.6074	+	35.7239i	−0.426985	+	1.31412i	0.474096	+	0.880473i	$0.342775\pi$
$739$	−11.6074	+	35.7239i	−0.426985	+	1.31412i	−0.901081	+	0.433651i	$0.857225\pi$
$740$	9.70820	−	7.05342i	0.356881	−	0.259289i
$741$	2.23607	+	1.62460i	0.0821440	+	0.0596811i
$742$	0.944272	+	2.90617i	0.0346653	+	0.106689i
$743$	−2.70820	−	8.33499i	−0.0993544	−	0.305781i	0.889010	−	0.457888i	$-0.151394\pi$
$743$	−2.70820	−	8.33499i	−0.0993544	−	0.305781i	−0.988364	+	0.152107i	$0.951394\pi$
$744$	−0.618034	−	0.449028i	−0.0226582	−	0.0164622i
$745$	16.1803	−	11.7557i	0.592802	−	0.430696i
$746$	−1.32624	+	4.08174i	−0.0485570	+	0.149443i
$747$	−26.6180			−0.973903
$748$		0			0
$749$	2.29180			0.0837404
$750$	0.180340	−	0.555029i	0.00658508	−	0.0202668i
$751$	27.3262	−	19.8537i	0.997149	−	0.724471i	0.0356737	−	0.999363i	$-0.488642\pi$
$751$	27.3262	−	19.8537i	0.997149	−	0.724471i	0.961475	+	0.274893i	$0.0886423\pi$
$752$	5.23607	+	3.80423i	0.190940	+	0.138726i
$753$	2.47214	+	7.60845i	0.0900896	+	0.277267i
$754$	1.70820	+	5.25731i	0.0622091	+	0.191460i
$755$	20.9443	+	15.2169i	0.762240	+	0.553800i
$756$	−3.61803	+	2.62866i	−0.131587	+	0.0956033i
$757$	−0.819660	+	2.52265i	−0.0297911	+	0.0916874i	−0.964846	−	0.262814i	$-0.915349\pi$
$757$	−0.819660	+	2.52265i	−0.0297911	+	0.0916874i	0.935055	+	0.354501i	$0.115349\pi$
$758$	14.2705			0.518328
$759$		0			0
$760$	−18.9443			−0.687181
$761$	−1.31559	+	4.04898i	−0.0476903	+	0.146776i	−0.972066	−	0.234708i	$-0.924587\pi$
$761$	−1.31559	+	4.04898i	−0.0476903	+	0.146776i	0.924376	+	0.381483i	$0.124587\pi$
$762$	3.38197	−	2.45714i	0.122516	−	0.0890129i
$763$	30.6525	+	22.2703i	1.10969	+	0.806240i
$764$	1.47214	+	4.53077i	0.0532600	+	0.163917i
$765$	1.76393	+	5.42882i	0.0637751	+	0.196280i
$766$	22.9443	+	16.6700i	0.829010	+	0.602311i
$767$	8.61803	−	6.26137i	0.311179	−	0.226085i
$768$	0.118034	−	0.363271i	0.00425918	−	0.0131084i
$769$	13.4164			0.483808			0.241904	−	0.970300i	$-0.422228\pi$
$769$	13.4164			0.483808			0.241904	+	0.970300i	$0.422228\pi$
$770$		0			0
$771$	−2.14590			−0.0772826
$772$	5.38197	−	16.5640i	0.193701	−	0.596151i
$773$	3.14590	−	2.28563i	0.113150	−	0.0822084i	−0.529771	−	0.848141i	$-0.677722\pi$
$773$	3.14590	−	2.28563i	0.113150	−	0.0822084i	0.642921	+	0.765932i	$0.277722\pi$
$774$	−19.7705	−	14.3641i	−0.710636	−	0.516307i
$775$	3.38197	+	10.4086i	0.121484	+	0.373889i
$776$	2.20820	+	6.79615i	0.0792699	+	0.243968i
$777$	−2.29180	−	1.66509i	−0.0822177	−	0.0597347i
$778$	8.61803	−	6.26137i	0.308971	−	0.224481i
$779$	−10.1631	+	31.2789i	−0.364132	+	1.12068i
$780$	1.52786			0.0547063
$781$		0			0
$782$	−0.763932			−0.0273182
$783$	−3.09017	+	9.51057i	−0.110434	+	0.339880i
$784$	2.42705	−	1.76336i	0.0866804	−	0.0629770i
$785$	−25.4164	−	18.4661i	−0.907150	−	0.659083i
$786$	0.802439	+	2.46965i	0.0286221	+	0.0880896i
$787$	8.10081	+	24.9317i	0.288763	+	0.888721i	0.985246	+	0.171147i	$0.0547473\pi$
$787$	8.10081	+	24.9317i	0.288763	+	0.888721i	−0.696483	+	0.717574i	$0.745253\pi$
$788$	16.9443	+	12.3107i	0.603615	+	0.438552i
$789$	7.18034	−	5.21682i	0.255627	−	0.185724i
$790$	13.4164	−	41.2915i	0.477334	−	1.46908i
$791$	3.70820			0.131849
$792$		0			0
$793$	−3.05573			−0.108512
$794$	−5.29180	+	16.2865i	−0.187799	+	0.577985i
$795$	1.52786	−	1.11006i	0.0541878	−	0.0393697i
$796$	15.3262	+	11.1352i	0.543224	+	0.394675i
$797$	−7.65248	−	23.5519i	−0.271065	−	0.834251i	−0.990234	−	0.139416i	$-0.955477\pi$
$797$	−7.65248	−	23.5519i	−0.271065	−	0.834251i	0.719169	−	0.694835i	$-0.244523\pi$
$798$	1.38197	+	4.25325i	0.0489211	+	0.150564i
$799$	−3.23607	−	2.35114i	−0.114484	−	0.0831774i
$800$	−4.42705	+	3.21644i	−0.156520	+	0.113718i
$801$	7.13525	−	21.9601i	0.252112	−	0.775920i
$802$	−17.7984			−0.628482
$803$		0			0
$804$	4.23607			0.149395
$805$	−2.47214	+	7.60845i	−0.0871313	+	0.268163i
$806$	−2.00000	+	1.45309i	−0.0704470	+	0.0511827i
$807$	−1.90983	−	1.38757i	−0.0672292	−	0.0488449i
$808$	−1.29180	−	3.97574i	−0.0454452	−	0.139866i
$809$	5.22542	+	16.0822i	0.183716	+	0.565420i	0.999924	−	0.0123384i	$-0.00392753\pi$
$809$	5.22542	+	16.0822i	0.183716	+	0.565420i	−0.816208	+	0.577759i	$0.803928\pi$
$810$	−20.1803	−	14.6619i	−0.709065	−	0.515166i
$811$	−6.78115	+	4.92680i	−0.238118	+	0.173003i	−0.700445	−	0.713707i	$-0.747015\pi$
$811$	−6.78115	+	4.92680i	−0.238118	+	0.173003i	0.462326	+	0.886710i	$0.347015\pi$
$812$	−2.76393	+	8.50651i	−0.0969950	+	0.298520i
$813$	0.763932			0.0267923
$814$		0			0
$815$	2.94427			0.103133
$816$	−0.0729490	+	0.224514i	−0.00255373	+	0.00785956i
$817$	−40.5517	+	29.4625i	−1.41872	+	1.03076i
$818$	10.8541	+	7.88597i	0.379505	+	0.275726i
$819$	2.18034	+	6.71040i	0.0761872	+	0.234480i
$820$	5.61803	+	17.2905i	0.196190	+	0.603812i
$821$	−24.7082	−	17.9516i	−0.862322	−	0.626514i	0.0661935	−	0.997807i	$-0.478915\pi$
$821$	−24.7082	−	17.9516i	−0.862322	−	0.626514i	−0.928516	+	0.371293i	$0.878915\pi$
$822$	−4.97214	+	3.61247i	−0.173423	+	0.125999i
$823$	7.29180	−	22.4418i	0.254176	−	0.782273i	−0.739815	−	0.672811i	$-0.765087\pi$
$823$	7.29180	−	22.4418i	0.254176	−	0.782273i	0.993991	−	0.109463i	$-0.0349131\pi$
$824$	15.7082			0.547221
$825$		0			0
$826$	17.2361			0.599720
$827$	12.1697	−	37.4545i	0.423182	−	1.30242i	−0.481543	−	0.876423i	$-0.659923\pi$
$827$	12.1697	−	37.4545i	0.423182	−	1.30242i	0.904725	−	0.425997i	$-0.140077\pi$
$828$	2.85410	−	2.07363i	0.0991869	−	0.0720635i
$829$	−25.1246	−	18.2541i	−0.872614	−	0.633991i	0.0586732	−	0.998277i	$-0.481313\pi$
$829$	−25.1246	−	18.2541i	−0.872614	−	0.633991i	−0.931287	+	0.364286i	$0.881313\pi$
$830$	9.32624	+	28.7032i	0.323718	+	0.996303i
$831$	−2.79837	−	8.61251i	−0.0970745	−	0.298765i
$832$	−1.00000	−	0.726543i	−0.0346688	−	0.0251883i
$833$	−1.50000	+	1.08981i	−0.0519719	+	0.0377598i
$834$		0			0
$835$	−47.7771			−1.65339
$836$		0			0
$837$	−4.47214			−0.154580
$838$	−3.35410	+	10.3229i	−0.115866	+	0.356597i
$839$	−9.79837	+	7.11894i	−0.338277	+	0.245773i	−0.743935	−	0.668252i	$-0.767043\pi$
$839$	−9.79837	+	7.11894i	−0.338277	+	0.245773i	0.405657	+	0.914025i	$0.367043\pi$
$840$	2.00000	+	1.45309i	0.0690066	+	0.0501362i
$841$	−2.78115	−	8.55951i	−0.0959018	−	0.295155i
$842$	−9.70820	−	29.8788i	−0.334567	−	1.02969i
$843$	4.97214	+	3.61247i	0.171249	+	0.124420i
$844$	4.92705	−	3.57971i	0.169596	−	0.123219i
$845$	−11.4721	+	35.3076i	−0.394653	+	1.21462i
$846$	18.4721			0.635085
$847$		0			0
$848$	−1.52786			−0.0524671
$849$	2.83282	−	8.71851i	0.0972220	−	0.299219i
$850$	2.73607	−	1.98787i	0.0938464	−	0.0681834i
$851$	3.70820	+	2.69417i	0.127116	+	0.0923549i
$852$	−0.618034	−	1.90211i	−0.0211735	−	0.0651653i
$853$	−9.41641	−	28.9807i	−0.322412	−	0.992281i	−0.972595	−	0.232504i	$-0.925308\pi$
$853$	−9.41641	−	28.9807i	−0.322412	−	0.992281i	0.650184	−	0.759777i	$-0.274692\pi$
$854$	−4.00000	−	2.90617i	−0.136877	−	0.0994471i
$855$	−43.7426	+	31.7809i	−1.49597	+	1.08688i
$856$	−0.354102	+	1.08981i	−0.0121030	+	0.0372491i
$857$	−10.7426			−0.366962			−0.183481	−	0.983023i	$-0.558737\pi$
$857$	−10.7426			−0.366962			−0.183481	+	0.983023i	$0.558737\pi$
$858$		0			0
$859$	46.5066			1.58678			0.793392	−	0.608711i	$-0.208313\pi$
$859$	46.5066			1.58678			0.793392	+	0.608711i	$0.208313\pi$
$860$	−8.56231	+	26.3521i	−0.291972	+	0.898598i
$861$	3.47214	−	2.52265i	0.118330	−	0.0859718i
$862$	13.7082	+	9.95959i	0.466903	+	0.339225i
$863$	−10.2705	−	31.6094i	−0.349612	−	1.07600i	−0.959068	−	0.283176i	$-0.908612\pi$
$863$	−10.2705	−	31.6094i	−0.349612	−	1.07600i	0.609456	−	0.792820i	$-0.291388\pi$
$864$	−0.690983	−	2.12663i	−0.0235077	−	0.0723493i
$865$	−57.3050	−	41.6345i	−1.94843	−	1.41561i
$866$	−22.4443	+	16.3067i	−0.762687	+	0.554125i
$867$	−1.96149	+	6.03685i	−0.0666158	+	0.205022i
$868$	−4.00000			−0.135769
$869$		0			0
$870$	5.52786			0.187412
$871$	4.23607	−	13.0373i	0.143534	−	0.441751i
$872$	−15.3262	+	11.1352i	−0.519012	+	0.377084i
$873$	16.5000	+	11.9880i	0.558440	+	0.405731i
$874$	−2.23607	−	6.88191i	−0.0756361	−	0.232784i
$875$	−0.944272	−	2.90617i	−0.0319222	−	0.0982465i
$876$	−3.20820	−	2.33090i	−0.108395	−	0.0787537i
$877$	22.7984	−	16.5640i	0.769846	−	0.559326i	−0.132068	−	0.991241i	$-0.542162\pi$
$877$	22.7984	−	16.5640i	0.769846	−	0.559326i	0.901915	+	0.431914i	$0.142162\pi$
$878$	−2.03444	+	6.26137i	−0.0686591	+	0.211311i
$879$	−10.8328			−0.365382
$880$		0			0
$881$	−46.3394			−1.56121			−0.780607	−	0.625022i	$-0.785090\pi$
$881$	−46.3394			−1.56121			−0.780607	+	0.625022i	$0.785090\pi$
$882$	2.64590	−	8.14324i	0.0890920	−	0.274197i
$883$	2.78115	−	2.02063i	0.0935932	−	0.0679995i	−0.540004	−	0.841662i	$-0.681577\pi$
$883$	2.78115	−	2.02063i	0.0935932	−	0.0679995i	0.633598	+	0.773663i	$0.281577\pi$
$884$	0.618034	+	0.449028i	0.0207867	+	0.0151024i
$885$	−3.29180	−	10.1311i	−0.110653	−	0.340553i
$886$	−2.64590	−	8.14324i	−0.0888907	−	0.273577i
$887$	30.5623	+	22.2048i	1.02618	+	0.745565i	0.967541	−	0.252714i	$-0.0813233\pi$
$887$	30.5623	+	22.2048i	1.02618	+	0.745565i	0.0586409	+	0.998279i	$0.481323\pi$
$888$	1.14590	−	0.832544i	0.0384538	−	0.0279383i
$889$	6.76393	−	20.8172i	0.226855	−	0.698188i
$890$	−26.1803			−0.877567
$891$		0			0
$892$	25.7082			0.860774
$893$	11.7082	−	36.0341i	0.391800	−	1.20584i
$894$	1.90983	−	1.38757i	0.0638743	−	0.0464074i
$895$	22.5623	+	16.3925i	0.754175	+	0.547940i
$896$	−0.618034	−	1.90211i	−0.0206471	−	0.0635451i
$897$	0.180340	+	0.555029i	0.00602137	+	0.0185319i
$898$	−7.50000	−	5.44907i	−0.250278	−	0.181838i
$899$	−7.23607	+	5.25731i	−0.241336	+	0.175341i
$900$	−4.82624	+	14.8536i	−0.160875	+	0.495121i
$901$	0.944272			0.0314583
$902$		0			0
$903$	6.54102			0.217672
$904$	−0.572949	+	1.76336i	−0.0190560	+	0.0586483i
$905$	10.9443	−	7.95148i	0.363800	−	0.264316i
$906$	2.47214	+	1.79611i	0.0821312	+	0.0596718i
$907$	3.22542	+	9.92684i	0.107098	+	0.329615i	0.990217	−	0.139534i	$-0.0445605\pi$
$907$	3.22542	+	9.92684i	0.107098	+	0.329615i	−0.883119	+	0.469149i	$0.844561\pi$
$908$	4.48278	+	13.7966i	0.148766	+	0.457855i
$909$	−9.65248	−	7.01293i	−0.320152	−	0.232604i
$910$	6.47214	−	4.70228i	0.214549	−	0.155879i
$911$	5.61803	−	17.2905i	0.186134	−	0.572861i	−0.813832	−	0.581100i	$-0.802623\pi$
$911$	5.61803	−	17.2905i	0.186134	−	0.572861i	0.999966	+	0.00823898i	$0.00262258\pi$
$912$	−2.23607			−0.0740436
$913$		0			0
$914$	−9.43769			−0.312171
$915$	−0.944272	+	2.90617i	−0.0312167	+	0.0960750i
$916$	−1.38197	+	1.00406i	−0.0456614	+	0.0331750i
$917$	11.0000	+	7.99197i	0.363252	+	0.263918i
$918$	0.427051	+	1.31433i	0.0140948	+	0.0433793i
$919$	13.4164	+	41.2915i	0.442566	+	1.36208i	0.885131	+	0.465343i	$0.154069\pi$
$919$	13.4164	+	41.2915i	0.442566	+	1.36208i	−0.442564	+	0.896737i	$0.645931\pi$
$920$	−3.23607	−	2.35114i	−0.106690	−	0.0775148i
$921$	−8.59017	+	6.24112i	−0.283056	+	0.205652i
$922$	0.416408	−	1.28157i	0.0137137	−	0.0422063i
$923$	−6.47214			−0.213033
$924$		0			0
$925$	−20.2918			−0.667190
$926$	−6.00000	+	18.4661i	−0.197172	+	0.606834i
$927$	36.2705	−	26.3521i	1.19128	−	0.865515i
$928$	−3.61803	−	2.62866i	−0.118768	−	0.0862898i
$929$	−5.02380	−	15.4617i	−0.164825	−	0.507281i	0.834198	−	0.551465i	$-0.185931\pi$
$929$	−5.02380	−	15.4617i	−0.164825	−	0.507281i	−0.999023	+	0.0441845i	$0.985931\pi$
$930$	0.763932	+	2.35114i	0.0250503	+	0.0770970i
$931$	−14.2082	−	10.3229i	−0.465655	−	0.338318i
$932$	7.78115	−	5.65334i	0.254880	−	0.185181i
$933$	3.07701	−	9.47008i	0.100737	−	0.310036i
$934$	−33.3050			−1.08977
$935$		0			0
$936$	−3.52786			−0.115312
$937$	−11.6976	+	36.0014i	−0.382143	+	1.17611i	0.556389	+	0.830922i	$0.312186\pi$
$937$	−11.6976	+	36.0014i	−0.382143	+	1.17611i	−0.938532	+	0.345192i	$0.887814\pi$
$938$	17.9443	−	13.0373i	0.585901	−	0.425682i
$939$	−1.33688	−	0.971301i	−0.0436275	−	0.0316972i
$940$	−6.47214	−	19.9192i	−0.211098	−	0.649692i
$941$	14.8885	+	45.8222i	0.485353	+	1.49376i	0.831469	+	0.555570i	$0.187500\pi$
$941$	14.8885	+	45.8222i	0.485353	+	1.49376i	−0.346117	+	0.938191i	$0.612500\pi$
$942$	−3.00000	−	2.17963i	−0.0977453	−	0.0710161i
$943$	−5.61803	+	4.08174i	−0.182948	+	0.132920i
$944$	−2.66312	+	8.19624i	−0.0866771	+	0.266765i
$945$	14.4721			0.470779
$946$		0			0
$947$	−30.2148			−0.981848			−0.490924	−	0.871202i	$-0.663341\pi$
$947$	−30.2148			−0.981848			−0.490924	+	0.871202i	$0.663341\pi$
$948$	1.58359	−	4.87380i	0.0514327	−	0.158294i
$949$	−10.3820	+	7.54294i	−0.337013	+	0.244854i
$950$	25.9164	+	18.8294i	0.840839	+	0.610906i
$951$	−0.437694	−	1.34708i	−0.0141932	−	0.0436822i
$952$	0.381966	+	1.17557i	0.0123796	+	0.0381005i
$953$	9.16312	+	6.65740i	0.296823	+	0.215654i	0.726222	−	0.687461i	$-0.241275\pi$
$953$	9.16312	+	6.65740i	0.296823	+	0.215654i	−0.429399	+	0.903115i	$0.641275\pi$
$954$	−3.52786	+	2.56314i	−0.114219	+	0.0829848i
$955$	4.76393	−	14.6619i	0.154157	−	0.474447i
$956$	−21.7082			−0.702093
$957$		0			0
$958$	−34.4721			−1.11374
$959$	−9.94427	+	30.6053i	−0.321117	+	0.988297i
$960$	−1.00000	+	0.726543i	−0.0322749	+	0.0234491i
$961$	21.8435	+	15.8702i	0.704628	+	0.511942i
$962$	−1.41641	−	4.35926i	−0.0456668	−	0.140548i
$963$	1.01064	+	3.11044i	0.0325675	+	0.100233i
$964$	8.97214	+	6.51864i	0.288973	+	0.209951i
$965$	−45.5967	+	33.1280i	−1.46781	+	1.06643i
$966$	−0.291796	+	0.898056i	−0.00938838	+	0.0288945i
$967$	38.0000			1.22200			0.610999	−	0.791632i	$-0.290768\pi$
$967$	38.0000			1.22200			0.610999	+	0.791632i	$0.290768\pi$
$968$		0			0
$969$	1.38197			0.0443951
$970$	7.14590	−	21.9928i	0.229441	−	0.706147i
$971$	8.18034	−	5.94336i	0.262520	−	0.190732i	−0.448737	−	0.893664i	$-0.648126\pi$
$971$	8.18034	−	5.94336i	0.262520	−	0.190732i	0.711257	+	0.702932i	$0.248126\pi$
$972$	−7.80902	−	5.67358i	−0.250474	−	0.181980i
$973$		0			0
$974$	−0.416408	−	1.28157i	−0.0133426	−	0.0410642i
$975$	−2.09017	−	1.51860i	−0.0669390	−	0.0486340i
$976$	2.00000	−	1.45309i	0.0640184	−	0.0465121i
$977$	−13.3820	+	41.1855i	−0.428127	+	1.31764i	0.471841	+	0.881684i	$0.343590\pi$
$977$	−13.3820	+	41.1855i	−0.428127	+	1.31764i	−0.899968	+	0.435956i	$0.856410\pi$
$978$	0.347524			0.0111126
$979$		0			0
$980$	−9.70820			−0.310117
$981$	−16.7082	+	51.4226i	−0.533452	+	1.64180i
$982$	−18.4894	+	13.4333i	−0.590019	+	0.428674i
$983$	4.85410	+	3.52671i	0.154822	+	0.112485i	0.662499	−	0.749063i	$-0.269496\pi$
$983$	4.85410	+	3.52671i	0.154822	+	0.112485i	−0.507677	+	0.861547i	$0.669496\pi$
$984$	0.663119	+	2.04087i	0.0211395	+	0.0650606i
$985$	−20.9443	−	64.4598i	−0.667340	−	2.05386i
$986$	2.23607	+	1.62460i	0.0712109	+	0.0517378i
$987$	−4.00000	+	2.90617i	−0.127321	+	0.0925044i
$988$	−2.23607	+	6.88191i	−0.0711388	+	0.218943i
$989$	−10.5836			−0.336539
$990$		0			0
$991$	30.5410			0.970167			0.485084	−	0.874468i	$-0.338789\pi$
$991$	30.5410			0.970167			0.485084	+	0.874468i	$0.338789\pi$
$992$	0.618034	−	1.90211i	0.0196226	−	0.0603921i
$993$	−1.93769	+	1.40782i	−0.0614909	+	0.0446757i
$994$	−8.47214	−	6.15537i	−0.268720	−	0.195236i
$995$	−18.9443	−	58.3045i	−0.600574	−	1.84838i
$996$	1.10081	+	3.38795i	0.0348806	+	0.107351i
$997$	−7.00000	−	5.08580i	−0.221692	−	0.161069i	0.471396	−	0.881922i	$-0.343750\pi$
$997$	−7.00000	−	5.08580i	−0.221692	−	0.161069i	−0.693088	+	0.720853i	$0.743750\pi$
$998$	24.9615	−	18.1356i	0.790142	−	0.574072i
$999$	2.56231	−	7.88597i	0.0810678	−	0.249501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	242.2.c.a.9.1		4
11.2	odd	10		242.2.c.c.3.1		4
11.3	even	5		22.2.c.a.15.1	yes	4
11.4	even	5		242.2.a.f.1.1		2
11.5	even	5	inner	242.2.c.a.27.1		4
11.6	odd	10		242.2.c.d.27.1		4
11.7	odd	10		242.2.a.d.1.1		2
11.8	odd	10		242.2.c.c.81.1		4
11.9	even	5		22.2.c.a.3.1	✓	4
11.10	odd	2		242.2.c.d.9.1		4
33.14	odd	10		198.2.f.e.37.1		4
33.20	odd	10		198.2.f.e.91.1		4
33.26	odd	10		2178.2.a.p.1.1		2
33.29	even	10		2178.2.a.x.1.1		2
44.3	odd	10		176.2.m.c.81.1		4
44.7	even	10		1936.2.a.n.1.2		2
44.15	odd	10		1936.2.a.o.1.2		2
44.31	odd	10		176.2.m.c.113.1		4
55.3	odd	20		550.2.ba.c.499.1		8
55.4	even	10		6050.2.a.bs.1.2		2
55.9	even	10		550.2.h.h.201.1		4
55.14	even	10		550.2.h.h.301.1		4
55.29	odd	10		6050.2.a.ci.1.2		2
55.42	odd	20		550.2.ba.c.399.1		8
55.47	odd	20		550.2.ba.c.499.2		8
55.53	odd	20		550.2.ba.c.399.2		8
88.3	odd	10		704.2.m.a.257.1		4
88.29	odd	10		7744.2.a.bn.1.2		2
88.37	even	10		7744.2.a.bm.1.2		2
88.51	even	10		7744.2.a.cy.1.1		2
88.53	even	10		704.2.m.h.641.1		4
88.59	odd	10		7744.2.a.cz.1.1		2
88.69	even	10		704.2.m.h.257.1		4
88.75	odd	10		704.2.m.a.641.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.2.c.a.3.1	✓	4	11.9	even	5
22.2.c.a.15.1	yes	4	11.3	even	5
176.2.m.c.81.1		4	44.3	odd	10
176.2.m.c.113.1		4	44.31	odd	10
198.2.f.e.37.1		4	33.14	odd	10
198.2.f.e.91.1		4	33.20	odd	10
242.2.a.d.1.1		2	11.7	odd	10
242.2.a.f.1.1		2	11.4	even	5
242.2.c.a.9.1		4	1.1	even	1	trivial
242.2.c.a.27.1		4	11.5	even	5	inner
242.2.c.c.3.1		4	11.2	odd	10
242.2.c.c.81.1		4	11.8	odd	10
242.2.c.d.9.1		4	11.10	odd	2
242.2.c.d.27.1		4	11.6	odd	10
550.2.h.h.201.1		4	55.9	even	10
550.2.h.h.301.1		4	55.14	even	10
550.2.ba.c.399.1		8	55.42	odd	20
550.2.ba.c.399.2		8	55.53	odd	20
550.2.ba.c.499.1		8	55.3	odd	20
550.2.ba.c.499.2		8	55.47	odd	20
704.2.m.a.257.1		4	88.3	odd	10
704.2.m.a.641.1		4	88.75	odd	10
704.2.m.h.257.1		4	88.69	even	10
704.2.m.h.641.1		4	88.53	even	10
1936.2.a.n.1.2		2	44.7	even	10
1936.2.a.o.1.2		2	44.15	odd	10
2178.2.a.p.1.1		2	33.26	odd	10
2178.2.a.x.1.1		2	33.29	even	10
6050.2.a.bs.1.2		2	55.4	even	10
6050.2.a.ci.1.2		2	55.29	odd	10
7744.2.a.bm.1.2		2	88.37	even	10
7744.2.a.bn.1.2		2	88.29	odd	10
7744.2.a.cy.1.1		2	88.51	even	10
7744.2.a.cz.1.1		2	88.59	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 242 = 2 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	242.c (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.224514i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(1.00000 + 3.07768i) q^{5} +(0.118034 + 0.363271i) q^{6} +(1.61803 + 1.17557i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.881966 + 2.71441i) q^{9} +3.23607 q^{10} +0.381966 q^{12} +(0.381966 - 1.17557i) q^{13} +(1.61803 - 1.17557i) q^{14} +(-1.00000 - 0.726543i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.190983 - 0.587785i) q^{17} +(2.30902 + 1.67760i) q^{18} +(4.73607 - 3.44095i) q^{19} +(1.00000 - 3.07768i) q^{20} -0.763932 q^{21} +1.23607 q^{23} +(0.118034 - 0.363271i) q^{24} +(-4.42705 + 3.21644i) q^{25} +(-1.00000 - 0.726543i) q^{26} +(-0.690983 - 2.12663i) q^{27} +(-0.618034 - 1.90211i) q^{28} +(-3.61803 - 2.62866i) q^{29} +(-1.00000 + 0.726543i) q^{30} +(0.618034 - 1.90211i) q^{31} +1.00000 q^{32} -0.618034 q^{34} +(-2.00000 + 6.15537i) q^{35} +(2.30902 - 1.67760i) q^{36} +(3.00000 + 2.17963i) q^{37} +(-1.80902 - 5.56758i) q^{38} +(0.145898 + 0.449028i) q^{39} +(-2.61803 - 1.90211i) q^{40} +(-4.54508 + 3.30220i) q^{41} +(-0.236068 + 0.726543i) q^{42} -8.56231 q^{43} -9.23607 q^{45} +(0.381966 - 1.17557i) q^{46} +(5.23607 - 3.80423i) q^{47} +(-0.309017 - 0.224514i) q^{48} +(-0.927051 - 2.85317i) q^{49} +(1.69098 + 5.20431i) q^{50} +(0.190983 + 0.138757i) q^{51} +(-1.00000 + 0.726543i) q^{52} +(-0.472136 + 1.45309i) q^{53} -2.23607 q^{54} -2.00000 q^{56} +(-0.690983 + 2.12663i) q^{57} +(-3.61803 + 2.62866i) q^{58} +(6.97214 + 5.06555i) q^{59} +(0.381966 + 1.17557i) q^{60} +(-0.763932 - 2.35114i) q^{61} +(-1.61803 - 1.17557i) q^{62} +(-4.61803 + 3.35520i) q^{63} +(0.309017 - 0.951057i) q^{64} +4.00000 q^{65} +11.0902 q^{67} +(-0.190983 + 0.587785i) q^{68} +(-0.381966 + 0.277515i) q^{69} +(5.23607 + 3.80423i) q^{70} +(-1.61803 - 4.97980i) q^{71} +(-0.881966 - 2.71441i) q^{72} +(-8.39919 - 6.10237i) q^{73} +(3.00000 - 2.17963i) q^{74} +(0.645898 - 1.98787i) q^{75} -5.85410 q^{76} +0.472136 q^{78} +(4.14590 - 12.7598i) q^{79} +(-2.61803 + 1.90211i) q^{80} +(-6.23607 - 4.53077i) q^{81} +(1.73607 + 5.34307i) q^{82} +(2.88197 + 8.86978i) q^{83} +(0.618034 + 0.449028i) q^{84} +(1.61803 - 1.17557i) q^{85} +(-2.64590 + 8.14324i) q^{86} +1.70820 q^{87} -8.09017 q^{89} +(-2.85410 + 8.78402i) q^{90} +(2.00000 - 1.45309i) q^{91} +(-1.00000 - 0.726543i) q^{92} +(0.236068 + 0.726543i) q^{93} +(-2.00000 - 6.15537i) q^{94} +(15.3262 + 11.1352i) q^{95} +(-0.309017 + 0.224514i) q^{96} +(2.20820 - 6.79615i) q^{97} -3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{3} - q^{4} + 4 q^{5} - 4 q^{6} + 2 q^{7} - q^{8} - 8 q^{9} + 4 q^{10} + 6 q^{12} + 6 q^{13} + 2 q^{14} - 4 q^{15} - q^{16} - 3 q^{17} + 7 q^{18} + 10 q^{19} + 4 q^{20} - 12 q^{21}+ \cdots - 12 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^3 - q^4 + 4 * q^5 - 4 * q^6 + 2 * q^7 - q^8 - 8 * q^9 + 4 * q^10 + 6 * q^12 + 6 * q^13 + 2 * q^14 - 4 * q^15 - q^16 - 3 * q^17 + 7 * q^18 + 10 * q^19 + 4 * q^20 - 12 * q^21 - 4 * q^23 - 4 * q^24 - 11 * q^25 - 4 * q^26 - 5 * q^27 + 2 * q^28 - 10 * q^29 - 4 * q^30 - 2 * q^31 + 4 * q^32 + 2 * q^34 - 8 * q^35 + 7 * q^36 + 12 * q^37 - 5 * q^38 + 14 * q^39 - 6 * q^40 - 7 * q^41 + 8 * q^42 + 6 * q^43 - 28 * q^45 + 6 * q^46 + 12 * q^47 + q^48 + 3 * q^49 + 9 * q^50 + 3 * q^51 - 4 * q^52 + 16 * q^53 - 8 * q^56 - 5 * q^57 - 10 * q^58 + 10 * q^59 + 6 * q^60 - 12 * q^61 - 2 * q^62 - 14 * q^63 - q^64 + 16 * q^65 + 22 * q^67 - 3 * q^68 - 6 * q^69 + 12 * q^70 - 2 * q^71 - 8 * q^72 - 9 * q^73 + 12 * q^74 + 16 * q^75 - 10 * q^76 - 16 * q^78 + 30 * q^79 - 6 * q^80 - 16 * q^81 - 2 * q^82 + 16 * q^83 - 2 * q^84 + 2 * q^85 - 24 * q^86 - 20 * q^87 - 10 * q^89 + 2 * q^90 + 8 * q^91 - 4 * q^92 - 8 * q^93 - 8 * q^94 + 30 * q^95 + q^96 - 18 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more