LMFDB - Embedded newform 1089.2.e.o.727.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.18
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.o.364.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.16450 - 2.01697i) q^{2} +(-1.02841 + 1.39369i) q^{3} +(-1.71213 - 2.96549i) q^{4} +(0.158510 + 0.274547i) q^{5} +(1.61346 + 3.69723i) q^{6} +(-0.709246 + 1.22845i) q^{7} -3.31708 q^{8} +(-0.884754 - 2.86657i) q^{9} +0.738340 q^{10} +(5.89374 + 0.663556i) q^{12} +(2.09852 + 3.63474i) q^{13} +(1.65184 + 2.86106i) q^{14} +(-0.545647 - 0.0614326i) q^{15} +(-0.438496 + 0.759497i) q^{16} +6.24422 q^{17} +(-6.81209 - 1.55359i) q^{18} -3.09786 q^{19} +(0.542778 - 0.940119i) q^{20} +(-0.982687 - 2.25182i) q^{21} +(2.26025 + 3.91487i) q^{23} +(3.41131 - 4.62299i) q^{24} +(2.44975 - 4.24309i) q^{25} +9.77491 q^{26} +(4.90500 + 1.71493i) q^{27} +4.85727 q^{28} +(1.46422 - 2.53611i) q^{29} +(-0.759315 + 1.02902i) q^{30} +(4.77088 + 8.26341i) q^{31} +(-2.29583 - 3.97649i) q^{32} +(7.27140 - 12.5944i) q^{34} -0.449690 q^{35} +(-6.98596 + 7.53165i) q^{36} +0.847494 q^{37} +(-3.60746 + 6.24830i) q^{38} +(-7.22384 - 0.813308i) q^{39} +(-0.525791 - 0.910696i) q^{40} +(-1.93480 - 3.35118i) q^{41} +(-5.68620 - 0.640191i) q^{42} +(1.77651 - 3.07700i) q^{43} +(0.646766 - 0.697286i) q^{45} +10.5282 q^{46} +(3.72550 - 6.45275i) q^{47} +(-0.607552 - 1.39220i) q^{48} +(2.49394 + 4.31963i) q^{49} +(-5.70547 - 9.88217i) q^{50} +(-6.42160 + 8.70251i) q^{51} +(7.18585 - 12.4463i) q^{52} +6.68304 q^{53} +(9.17084 - 7.89623i) q^{54} +(2.35263 - 4.07487i) q^{56} +(3.18586 - 4.31746i) q^{57} +(-3.41018 - 5.90660i) q^{58} +(6.03739 + 10.4571i) q^{59} +(0.752039 + 1.72329i) q^{60} +(2.31016 - 4.00131i) q^{61} +22.2228 q^{62} +(4.14895 + 0.946226i) q^{63} -12.4479 q^{64} +(-0.665272 + 1.15229i) q^{65} +(-4.98385 - 8.63229i) q^{67} +(-10.6909 - 18.5172i) q^{68} +(-7.78058 - 0.875989i) q^{69} +(-0.523665 + 0.907014i) q^{70} +2.93068 q^{71} +(2.93480 + 9.50864i) q^{72} -4.24167 q^{73} +(0.986908 - 1.70938i) q^{74} +(3.39422 + 7.77782i) q^{75} +(5.30392 + 9.18665i) q^{76} +(-10.0526 + 13.6232i) q^{78} +(-1.69099 + 2.92889i) q^{79} -0.278024 q^{80} +(-7.43442 + 5.07241i) q^{81} -9.01233 q^{82} +(-6.74374 + 11.6805i) q^{83} +(-4.99526 + 6.76954i) q^{84} +(0.989771 + 1.71433i) q^{85} +(-4.13749 - 7.16635i) q^{86} +(2.02873 + 4.64883i) q^{87} +2.69745 q^{89} +(-0.653249 - 2.11650i) q^{90} -5.95347 q^{91} +(7.73966 - 13.4055i) q^{92} +(-16.4231 - 1.84902i) q^{93} +(-8.67670 - 15.0285i) q^{94} +(-0.491041 - 0.850508i) q^{95} +(7.90304 + 0.889777i) q^{96} +(2.62872 - 4.55308i) q^{97} +11.6168 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.16450	−	2.01697i	0.823427	−	1.42622i	−0.0796893	−	0.996820i	$-0.525393\pi$
$2$	1.16450	−	2.01697i	0.823427	−	1.42622i	0.903116	−	0.429397i	$-0.141274\pi$
$3$	−1.02841	+	1.39369i	−0.593752	+	0.804648i
$3$	−1.02841	+	1.39369i	−0.593752	+	0.804648i
$4$	−1.71213	−	2.96549i	−0.856063	−	1.48274i
$5$	0.158510	+	0.274547i	0.0708878	+	0.122781i	0.899291	−	0.437352i	$-0.144083\pi$
$5$	0.158510	+	0.274547i	0.0708878	+	0.122781i	−0.828403	+	0.560133i	$0.810750\pi$
$6$	1.61346	+	3.69723i	0.658692	+	1.50939i
$7$	−0.709246	+	1.22845i	−0.268070	+	0.464311i	−0.968363	−	0.249544i	$-0.919719\pi$
$7$	−0.709246	+	1.22845i	−0.268070	+	0.464311i	0.700293	+	0.713855i	$0.253052\pi$
$8$	−3.31708			−1.17277
$9$	−0.884754	−	2.86657i	−0.294918	−	0.955523i
$10$	0.738340			0.233484
$11$		0			0
$11$		0			0
$12$	5.89374	+	0.663556i	1.70138	+	0.191552i
$13$	2.09852	+	3.63474i	0.582024	+	1.00810i	0.995239	+	0.0974621i	$0.0310725\pi$
$13$	2.09852	+	3.63474i	0.582024	+	1.00810i	−0.413215	+	0.910634i	$0.635594\pi$
$14$	1.65184	+	2.86106i	0.441472	+	0.764652i
$15$	−0.545647	−	0.0614326i	−0.140886	−	0.0158618i
$16$	−0.438496	+	0.759497i	−0.109624	+	0.189874i
$17$	6.24422			1.51445			0.757223	−	0.653157i	$-0.226556\pi$
$17$	6.24422			1.51445			0.757223	+	0.653157i	$0.226556\pi$
$18$	−6.81209	−	1.55359i	−1.60563	−	0.366186i
$19$	−3.09786			−0.710697			−0.355348	−	0.934734i	$-0.615638\pi$
$19$	−3.09786			−0.710697			−0.355348	+	0.934734i	$0.615638\pi$
$20$	0.542778	−	0.940119i	0.121369	−	0.210217i
$21$	−0.982687	−	2.25182i	−0.214440	−	0.491387i
$22$		0			0
$23$	2.26025	+	3.91487i	0.471295	+	0.816306i	0.999461	−	0.0328349i	$-0.0104536\pi$
$23$	2.26025	+	3.91487i	0.471295	+	0.816306i	−0.528166	+	0.849141i	$0.677120\pi$
$24$	3.41131	−	4.62299i	0.696332	−	0.943664i
$25$	2.44975	−	4.24309i	0.489950	−	0.848618i
$26$	9.77491			1.91702
$27$	4.90500	+	1.71493i	0.943968	+	0.330038i
$28$	4.85727			0.917939
$29$	1.46422	−	2.53611i	0.271899	−	0.470943i	−0.697449	−	0.716635i	$-0.745682\pi$
$29$	1.46422	−	2.53611i	0.271899	−	0.470943i	0.969348	+	0.245691i	$0.0790149\pi$
$30$	−0.759315	+	1.02902i	−0.138631	+	0.187872i
$31$	4.77088	+	8.26341i	0.856876	+	1.48415i	0.874894	+	0.484314i	$0.160931\pi$
$31$	4.77088	+	8.26341i	0.856876	+	1.48415i	−0.0180185	+	0.999838i	$0.505736\pi$
$32$	−2.29583	−	3.97649i	−0.405848	−	0.702950i
$33$		0			0
$34$	7.27140	−	12.5944i	1.24703	−	2.15993i
$35$	−0.449690			−0.0760116
$36$	−6.98596	+	7.53165i	−1.16433	+	1.25528i
$37$	0.847494			0.139327			0.0696636	−	0.997571i	$-0.477807\pi$
$37$	0.847494			0.139327			0.0696636	+	0.997571i	$0.477807\pi$
$38$	−3.60746	+	6.24830i	−0.585207	+	1.01361i
$39$	−7.22384	−	0.813308i	−1.15674	−	0.130234i
$40$	−0.525791	−	0.910696i	−0.0831348	−	0.143994i
$41$	−1.93480	−	3.35118i	−0.302166	−	0.523366i	0.674461	−	0.738311i	$-0.264376\pi$
$41$	−1.93480	−	3.35118i	−0.302166	−	0.523366i	−0.976626	+	0.214945i	$0.931043\pi$
$42$	−5.68620	−	0.640191i	−0.877400	−	0.0987835i
$43$	1.77651	−	3.07700i	0.270915	−	0.469239i	−0.698181	−	0.715921i	$-0.746007\pi$
$43$	1.77651	−	3.07700i	0.270915	−	0.469239i	0.969096	+	0.246682i	$0.0793404\pi$
$44$		0			0
$45$	0.646766	−	0.697286i	0.0964142	−	0.103945i
$46$	10.5282			1.55231
$47$	3.72550	−	6.45275i	0.543420	−	0.941231i	−0.455285	−	0.890346i	$-0.650462\pi$
$47$	3.72550	−	6.45275i	0.543420	−	0.941231i	0.998705	−	0.0508850i	$-0.0162042\pi$
$48$	−0.607552	−	1.39220i	−0.0876926	−	0.200947i
$49$	2.49394	+	4.31963i	0.356277	+	0.617090i
$50$	−5.70547	−	9.88217i	−0.806875	−	1.39755i
$51$	−6.42160	+	8.70251i	−0.899204	+	1.21860i
$52$	7.18585	−	12.4463i	0.996498	−	1.72599i
$53$	6.68304			0.917986			0.458993	−	0.888440i	$-0.348210\pi$
$53$	6.68304			0.917986			0.458993	+	0.888440i	$0.348210\pi$
$54$	9.17084	−	7.89623i	1.24799	−	1.07454i
$55$		0			0
$56$	2.35263	−	4.07487i	0.314383	−	0.544528i
$57$	3.18586	−	4.31746i	0.421977	−	0.571861i
$58$	−3.41018	−	5.90660i	−0.447778	−	0.775575i
$59$	6.03739	+	10.4571i	0.786001	+	1.36139i	0.928399	+	0.371584i	$0.121185\pi$
$59$	6.03739	+	10.4571i	0.786001	+	1.36139i	−0.142399	+	0.989809i	$0.545482\pi$
$60$	0.752039	+	1.72329i	0.0970878	+	0.222476i
$61$	2.31016	−	4.00131i	0.295786	−	0.512316i	−0.679382	−	0.733785i	$-0.737752\pi$
$61$	2.31016	−	4.00131i	0.295786	−	0.512316i	0.975167	+	0.221469i	$0.0710853\pi$
$62$	22.2228			2.82230
$63$	4.14895	+	0.946226i	0.522718	+	0.119213i
$64$	−12.4479			−1.55599
$65$	−0.665272	+	1.15229i	−0.0825169	+	0.142923i
$66$		0			0
$67$	−4.98385	−	8.63229i	−0.608875	−	1.05460i	−0.991426	−	0.130668i	$-0.958288\pi$
$67$	−4.98385	−	8.63229i	−0.608875	−	1.05460i	0.382552	−	0.923934i	$-0.375045\pi$
$68$	−10.6909	−	18.5172i	−1.29646	−	2.24553i
$69$	−7.78058	−	0.875989i	−0.936671	−	0.105457i
$70$	−0.523665	+	0.907014i	−0.0625899	+	0.108409i
$71$	2.93068			0.347808			0.173904	−	0.984763i	$-0.444362\pi$
$71$	2.93068			0.347808			0.173904	+	0.984763i	$0.444362\pi$
$72$	2.93480	+	9.50864i	0.345870	+	1.12060i
$73$	−4.24167			−0.496450			−0.248225	−	0.968702i	$-0.579847\pi$
$73$	−4.24167			−0.496450			−0.248225	+	0.968702i	$0.579847\pi$
$74$	0.986908	−	1.70938i	0.114726	−	0.198711i
$75$	3.39422	+	7.77782i	0.391931	+	0.898106i
$76$	5.30392	+	9.18665i	0.608401	+	1.05378i
$77$		0			0
$78$	−10.0526	+	13.6232i	−1.13823	+	1.54252i
$79$	−1.69099	+	2.92889i	−0.190252	+	0.329526i	−0.945334	−	0.326105i	$-0.894264\pi$
$79$	−1.69099	+	2.92889i	−0.190252	+	0.329526i	0.755082	+	0.655630i	$0.227597\pi$
$80$	−0.278024			−0.0310840
$81$	−7.43442	+	5.07241i	−0.826047	+	0.563602i
$82$	−9.01233			−0.995245
$83$	−6.74374	+	11.6805i	−0.740221	+	1.28210i	0.212173	+	0.977232i	$0.431946\pi$
$83$	−6.74374	+	11.6805i	−0.740221	+	1.28210i	−0.952394	+	0.304869i	$0.901387\pi$
$84$	−4.99526	+	6.76954i	−0.545027	+	0.738618i
$85$	0.989771	+	1.71433i	0.107356	+	0.185946i
$86$	−4.13749	−	7.16635i	−0.446157	−	0.772767i
$87$	2.02873	+	4.64883i	0.217503	+	0.498407i
$88$		0			0
$89$	2.69745			0.285929			0.142965	−	0.989728i	$-0.454336\pi$
$89$	2.69745			0.285929			0.142965	+	0.989728i	$0.454336\pi$
$90$	−0.653249	−	2.11650i	−0.0688585	−	0.223099i
$91$	−5.95347			−0.624093
$92$	7.73966	−	13.4055i	0.806915	−	1.39762i
$93$	−16.4231	−	1.84902i	−1.70299	−	0.191734i
$94$	−8.67670	−	15.0285i	−0.894933	−	1.55007i
$95$	−0.491041	−	0.850508i	−0.0503797	−	0.0872603i
$96$	7.90304	+	0.889777i	0.806601	+	0.0908125i
$97$	2.62872	−	4.55308i	0.266906	−	0.462295i	−0.701155	−	0.713009i	$-0.747332\pi$
$97$	2.62872	−	4.55308i	0.266906	−	0.462295i	0.968061	+	0.250714i	$0.0806653\pi$
$98$	11.6168			1.17347
$99$		0			0
$100$	−16.7771			−1.67771
$101$	−4.76487	+	8.25300i	−0.474123	+	0.821204i	−0.999561	−	0.0296273i	$-0.990568\pi$
$101$	−4.76487	+	8.25300i	−0.474123	+	0.821204i	0.525438	+	0.850832i	$0.323901\pi$
$102$	10.0748	+	23.0863i	0.997553	+	2.28588i
$103$	−4.76782	−	8.25810i	−0.469787	−	0.813695i	0.529616	−	0.848237i	$-0.322336\pi$
$103$	−4.76782	−	8.25810i	−0.469787	−	0.813695i	−0.999403	+	0.0345427i	$0.989003\pi$
$104$	−6.96096	−	12.0567i	−0.682578	−	1.18226i
$105$	0.462465	−	0.626730i	0.0451320	−	0.0611626i
$106$	7.78241	−	13.4795i	0.755894	−	1.30925i
$107$	−5.17260			−0.500054			−0.250027	−	0.968239i	$-0.580440\pi$
$107$	−5.17260			−0.500054			−0.250027	+	0.968239i	$0.580440\pi$
$108$	−3.31238	−	17.4819i	−0.318734	−	1.68220i
$109$	−14.4767			−1.38661			−0.693307	−	0.720643i	$-0.743847\pi$
$109$	−14.4767			−1.38661			−0.693307	+	0.720643i	$0.743847\pi$
$110$		0			0
$111$	−0.871570	+	1.18115i	−0.0827258	+	0.112109i
$112$	−0.622003	−	1.07734i	−0.0587737	−	0.101799i
$113$	3.71580	+	6.43596i	0.349553	+	0.605444i	0.986170	−	0.165736i	$-0.0530000\pi$
$113$	3.71580	+	6.43596i	0.349553	+	0.605444i	−0.636617	+	0.771180i	$0.719667\pi$
$114$	−4.99826	−	11.4535i	−0.468130	−	1.07272i
$115$	−0.716544	+	1.24109i	−0.0668181	+	0.115732i
$116$	−10.0277			−0.931051
$117$	8.56256	−	9.23140i	0.791609	−	0.853443i
$118$	28.1222			2.58886
$119$	−4.42869	+	7.67071i	−0.405977	+	0.703173i
$120$	1.80996	+	0.203777i	0.165226	+	0.0186022i
$121$		0			0
$122$	−5.38037	−	9.31907i	−0.487116	−	0.843709i
$123$	6.66028	+	0.749859i	0.600537	+	0.0676125i
$124$	16.3367	−	28.2960i	1.46708	−	2.54105i
$125$	3.13834			0.280702
$126$	6.73996	−	7.26644i	0.600444	−	0.647346i
$127$	13.2044			1.17171			0.585853	−	0.810418i	$-0.300760\pi$
$127$	13.2044			1.17171			0.585853	+	0.810418i	$0.300760\pi$
$128$	−9.90400	+	17.1542i	−0.875398	+	1.51623i
$129$	2.46142	+	5.64032i	0.216716	+	0.496603i
$130$	1.54942	+	2.68367i	0.135893	+	0.235374i
$131$	−3.65021	−	6.32236i	−0.318921	−	0.552387i	0.661342	−	0.750084i	$-0.269987\pi$
$131$	−3.65021	−	6.32236i	−0.318921	−	0.552387i	−0.980263	+	0.197697i	$0.936654\pi$
$132$		0			0
$133$	2.19714	−	3.80556i	0.190516	−	0.329984i
$134$	−23.2148			−2.00545
$135$	0.306663	+	1.61849i	0.0263933	+	0.139297i
$136$	−20.7126			−1.77609
$137$	−4.90367	+	8.49340i	−0.418948	+	0.725640i	−0.995834	−	0.0911850i	$-0.970935\pi$
$137$	−4.90367	+	8.49340i	−0.418948	+	0.725640i	0.576886	+	0.816825i	$0.304268\pi$
$138$	−10.8273	+	14.6731i	−0.921684	+	1.24906i
$139$	−4.73845	−	8.20723i	−0.401910	−	0.696128i	0.592047	−	0.805904i	$-0.298320\pi$
$139$	−4.73845	−	8.20723i	−0.401910	−	0.696128i	−0.993956	+	0.109775i	$0.964987\pi$
$140$	0.769926	+	1.33355i	0.0650707	+	0.112706i
$141$	5.16182	+	11.8283i	0.434703	+	0.996119i
$142$	3.41278	−	5.91111i	0.286394	−	0.496049i
$143$		0			0
$144$	2.56511	+	0.585009i	0.213759	+	0.0487508i
$145$	0.928375			0.0770974
$146$	−4.93943	+	8.55534i	−0.408790	+	0.708045i
$147$	−8.58502	−	0.966559i	−0.708081	−	0.0797204i
$148$	−1.45102	−	2.51323i	−0.119273	−	0.206587i
$149$	−2.06372	−	3.57448i	−0.169067	−	0.292832i	0.769025	−	0.639218i	$-0.220742\pi$
$149$	−2.06372	−	3.57448i	−0.169067	−	0.292832i	−0.938092	+	0.346386i	$0.887409\pi$
$150$	19.6402	+	2.21123i	1.60362	+	0.180546i
$151$	−8.88763	+	15.3938i	−0.723265	+	1.25273i	0.236419	+	0.971651i	$0.424026\pi$
$151$	−8.88763	+	15.3938i	−0.723265	+	1.25273i	−0.959684	+	0.281081i	$0.909307\pi$
$152$	10.2758			0.833481
$153$	−5.52460	−	17.8995i	−0.446637	−	1.44709i
$154$		0			0
$155$	−1.51246	+	2.61967i	−0.121484	+	0.210417i
$156$	9.95627	+	22.8147i	0.797139	+	1.82664i
$157$	1.00863	+	1.74700i	0.0804974	+	0.139426i	0.903464	−	0.428665i	$-0.141016\pi$
$157$	1.00863	+	1.74700i	0.0804974	+	0.139426i	−0.822966	+	0.568090i	$0.807682\pi$
$158$	3.93833	+	6.82138i	0.313317	+	0.542680i
$159$	−6.87289	+	9.31410i	−0.545056	+	0.738656i
$160$	0.727822	−	1.26063i	0.0575394	−	0.0996612i
$161$	−6.41229			−0.505359
$162$	1.57354	+	20.9019i	0.123629	+	1.64221i
$163$	−1.58042			−0.123788			−0.0618940	−	0.998083i	$-0.519714\pi$
$163$	−1.58042			−0.123788			−0.0618940	+	0.998083i	$0.519714\pi$
$164$	−6.62526	+	11.4753i	−0.517346	+	0.896069i
$165$		0			0
$166$	15.7062	+	27.2039i	1.21904	+	2.11143i
$167$	7.66081	+	13.2689i	0.592812	+	1.02678i	0.993852	+	0.110719i	$0.0353155\pi$
$167$	7.66081	+	13.2689i	0.592812	+	1.02678i	−0.401040	+	0.916061i	$0.631351\pi$
$168$	3.25965	+	7.46947i	0.251488	+	0.576282i
$169$	−2.30756	+	3.99681i	−0.177505	+	0.307447i
$170$	4.61036			0.353598
$171$	2.74084	+	8.88021i	0.209597	+	0.679087i
$172$	−12.1664			−0.927681
$173$	−0.493020	+	0.853935i	−0.0374836	+	0.0649235i	−0.884159	−	0.467187i	$-0.845268\pi$
$173$	−0.493020	+	0.853935i	−0.0374836	+	0.0649235i	0.846675	+	0.532110i	$0.178601\pi$
$174$	11.7390	+	1.32166i	0.889934	+	0.100195i
$175$	3.47495	+	6.01879i	0.262682	+	0.454978i
$176$		0			0
$177$	−20.7828	−	2.33987i	−1.56213	−	0.175875i
$178$	3.14119	−	5.44070i	0.235442	−	0.407797i
$179$	−11.2258			−0.839056			−0.419528	−	0.907742i	$-0.637804\pi$
$179$	−11.2258			−0.839056			−0.419528	+	0.907742i	$0.637804\pi$
$180$	−3.17514	−	0.724135i	−0.236661	−	0.0539739i
$181$	17.9256			1.33240			0.666201	−	0.745773i	$-0.267919\pi$
$181$	17.9256			1.33240			0.666201	+	0.745773i	$0.267919\pi$
$182$	−6.93282	+	12.0080i	−0.513895	+	0.890091i
$183$	3.20081	+	7.33463i	0.236611	+	0.542192i
$184$	−7.49743	−	12.9859i	−0.552718	−	0.957336i
$185$	0.134336	+	0.232677i	0.00987660	+	0.0171068i
$186$	−22.8541	+	30.9717i	−1.67574	+	2.27096i
$187$		0			0
$188$	−25.5141			−1.86081
$189$	−5.58556	+	4.80925i	−0.406289	+	0.349821i
$190$	−2.28727			−0.165936
$191$	−6.44397	+	11.1613i	−0.466269	+	0.807602i	−0.999258	−	0.0385203i	$-0.987736\pi$
$191$	−6.44397	+	11.1613i	−0.466269	+	0.807602i	0.532988	+	0.846123i	$0.321069\pi$
$192$	12.8016	−	17.3486i	0.923874	−	1.25203i
$193$	−11.5755	−	20.0494i	−0.833224	−	1.44319i	−0.895469	−	0.445125i	$-0.853159\pi$
$193$	−11.5755	−	20.0494i	−0.833224	−	1.44319i	0.0622450	−	0.998061i	$-0.480174\pi$
$194$	−6.12230	−	10.6041i	−0.439555	−	0.761332i
$195$	−0.921759	−	2.11220i	−0.0660086	−	0.151258i
$196$	8.53987	−	14.7915i	0.609991	−	1.05654i
$197$	−1.07766			−0.0767801			−0.0383900	−	0.999263i	$-0.512223\pi$
$197$	−1.07766			−0.0767801			−0.0383900	+	0.999263i	$0.512223\pi$
$198$		0			0
$199$	16.4307			1.16474			0.582371	−	0.812923i	$-0.302125\pi$
$199$	16.4307			1.16474			0.582371	+	0.812923i	$0.302125\pi$
$200$	−8.12602	+	14.0747i	−0.574596	+	0.995230i
$201$	17.1562	+	1.93156i	1.21010	+	0.136242i
$202$	11.0974	+	19.2213i	0.780810	+	1.35240i
$203$	2.07699	+	3.59745i	0.145776	+	0.252491i
$204$	36.8018	+	4.14339i	2.57664	+	0.290095i
$205$	0.613372	−	1.06239i	0.0428397	−	0.0742006i
$206$	−22.2085			−1.54734
$207$	9.22246	−	9.94285i	0.641006	−	0.691076i
$208$	−3.68076			−0.255215
$209$		0			0
$210$	−0.725557	−	1.66261i	−0.0500682	−	0.114731i
$211$	−7.47489	−	12.9469i	−0.514593	−	0.891301i	−0.999857	−	0.0169331i	$-0.994610\pi$
$211$	−7.47489	−	12.9469i	−0.514593	−	0.891301i	0.485264	−	0.874368i	$-0.338724\pi$
$212$	−11.4422	−	19.8185i	−0.785854	−	1.36114i
$213$	−3.01394	+	4.08447i	−0.206511	+	0.279863i
$214$	−6.02350	+	10.4330i	−0.411758	+	0.713186i
$215$	1.12638			0.0768183
$216$	−16.2703	−	5.68855i	−1.10705	−	0.387057i
$217$	−13.5349			−0.918810
$218$	−16.8581	+	29.1991i	−1.14177	+	1.97761i
$219$	4.36217	−	5.91158i	0.294768	−	0.399468i
$220$		0			0
$221$	13.1036	+	22.6961i	0.881444	+	1.52671i
$222$	1.36740	+	3.13338i	0.0917737	+	0.210299i
$223$	−0.963139	+	1.66821i	−0.0644966	+	0.111711i	−0.896471	−	0.443103i	$-0.853877\pi$
$223$	−0.963139	+	1.66821i	−0.0644966	+	0.111711i	0.831974	+	0.554815i	$0.187211\pi$
$224$	6.51322			0.435183
$225$	−14.3305	−	3.26828i	−0.955369	−	0.217885i
$226$	17.3082			1.15133
$227$	−8.00554	+	13.8660i	−0.531347	+	0.920319i	0.467984	+	0.883737i	$0.344980\pi$
$227$	−8.00554	+	13.8660i	−0.531347	+	0.920319i	−0.999331	+	0.0365825i	$0.988353\pi$
$228$	−18.2580	−	2.05560i	−1.20916	−	0.136136i
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	0.874535	−	0.484962i	$-0.161167\pi$
$229$	0.261463	+	0.452867i	0.0172779	+	0.0299263i	−0.857257	+	0.514888i	$0.827833\pi$
$230$	1.66883	+	2.89050i	0.110040	+	0.190594i
$231$		0			0
$232$	−4.85695	+	8.41248i	−0.318874	+	0.552306i
$233$	10.2525			0.671665			0.335833	−	0.941922i	$-0.390982\pi$
$233$	10.2525			0.671665			0.335833	+	0.941922i	$0.390982\pi$
$234$	−8.64839	−	28.0204i	−0.565363	−	1.83175i
$235$	2.36212			0.154087
$236$	20.6735	−	35.8076i	1.34573	−	2.33088i
$237$	−2.34293	−	5.36882i	−0.152190	−	0.348742i
$238$	10.3144	+	17.8651i	0.668585	+	1.15802i
$239$	−4.82052	−	8.34939i	−0.311814	−	0.540077i	0.666941	−	0.745110i	$-0.267603\pi$
$239$	−4.82052	−	8.34939i	−0.311814	−	0.540077i	−0.978755	+	0.205033i	$0.934270\pi$
$240$	0.285922	−	0.387479i	0.0184562	−	0.0250117i
$241$	−0.139366	+	0.241388i	−0.00897733	+	0.0155492i	−0.870479	−	0.492205i	$-0.836191\pi$
$241$	−0.139366	+	0.241388i	−0.00897733	+	0.0155492i	0.861502	+	0.507754i	$0.169524\pi$
$242$		0			0
$243$	0.576234	−	15.5778i	0.0369654	−	0.999317i
$244$	−15.8211			−1.01284
$245$	−0.790628	+	1.36941i	−0.0505114	+	0.0874883i
$246$	9.26835	−	12.5604i	0.590928	−	0.800822i
$247$	−6.50091	−	11.2599i	−0.413643	−	0.716450i
$248$	−15.8254	−	27.4104i	−1.00491	−	1.74056i
$249$	−9.34370	−	21.4110i	−0.592133	−	1.35687i
$250$	3.65460	−	6.32995i	0.231137	−	0.400341i
$251$	4.42541			0.279329			0.139665	−	0.990199i	$-0.455398\pi$
$251$	4.42541			0.279329			0.139665	+	0.990199i	$0.455398\pi$
$252$	−4.29749	−	13.9237i	−0.270717	−	0.877111i
$253$		0			0
$254$	15.3766	−	26.6330i	0.964813	−	1.67111i
$255$	−3.40714	−	0.383598i	−0.213363	−	0.0240219i
$256$	10.6185	+	18.3917i	0.663655	+	1.14948i
$257$	−1.82726	−	3.16491i	−0.113981	−	0.197422i	0.803391	−	0.595452i	$-0.203027\pi$
$257$	−1.82726	−	3.16491i	−0.113981	−	0.197422i	−0.917372	+	0.398031i	$0.869694\pi$
$258$	14.2427	+	1.60354i	0.886712	+	0.0998320i
$259$	−0.601082	+	1.04111i	−0.0373494	+	0.0646911i
$260$	4.55612			0.282558
$261$	−8.56540	−	1.95346i	−0.530185	−	0.120916i
$262$	−17.0027			−1.05043
$263$	−7.22621	+	12.5162i	−0.445587	+	0.771780i	−0.998093	−	0.0617294i	$-0.980338\pi$
$263$	−7.22621	+	12.5162i	−0.445587	+	0.771780i	0.552506	+	0.833509i	$0.313672\pi$
$264$		0			0
$265$	1.05933	+	1.83481i	0.0650741	+	0.112712i
$266$	−5.11715	−	8.86316i	−0.313753	−	0.543435i
$267$	−2.77408	+	3.75942i	−0.169771	+	0.230073i
$268$	−17.0660	+	29.5591i	−1.04247	+	1.80561i
$269$	0.917748			0.0559561			0.0279780	−	0.999609i	$-0.491093\pi$
$269$	0.917748			0.0559561			0.0279780	+	0.999609i	$0.491093\pi$
$270$	3.62156	+	1.26620i	0.220401	+	0.0770584i
$271$	2.64421			0.160624			0.0803120	−	0.996770i	$-0.474408\pi$
$271$	2.64421			0.160624			0.0803120	+	0.996770i	$0.474408\pi$
$272$	−2.73806	+	4.74246i	−0.166019	+	0.287554i
$273$	6.12259	−	8.29730i	0.370556	−	0.502175i
$274$	11.4206	+	19.7811i	0.689947	+	1.19502i
$275$		0			0
$276$	10.7236	+	24.5730i	0.645484	+	1.47912i
$277$	14.4522	−	25.0320i	0.868351	−	1.50403i	0.00467084	−	0.999989i	$-0.498513\pi$
$277$	14.4522	−	25.0320i	0.868351	−	1.50403i	0.863681	−	0.504040i	$-0.168153\pi$
$278$	−22.0717			−1.32377
$279$	19.4666	−	20.9871i	1.16543	−	1.25647i
$280$	1.49166			0.0891437
$281$	4.37128	−	7.57129i	0.260769	−	0.451665i	−0.705678	−	0.708533i	$-0.749357\pi$
$281$	4.37128	−	7.57129i	0.260769	−	0.451665i	0.966446	+	0.256868i	$0.0826906\pi$
$282$	29.8683	+	3.36277i	1.77863	+	0.200250i
$283$	−11.6086	−	20.1067i	−0.690061	−	1.19522i	−0.971817	−	0.235735i	$-0.924250\pi$
$283$	−11.6086	−	20.1067i	−0.690061	−	1.19522i	0.281756	−	0.959486i	$-0.409083\pi$
$284$	−5.01769	−	8.69090i	−0.297745	−	0.515710i
$285$	1.69034	+	0.190309i	0.100127	+	0.0112730i
$286$		0			0
$287$	5.48901			0.324006
$288$	−9.36763	+	10.0994i	−0.551993	+	0.595110i
$289$	21.9902			1.29354
$290$	1.08109	−	1.87251i	0.0634840	−	0.109958i
$291$	3.64219	+	8.34605i	0.213509	+	0.489254i
$292$	7.26227	+	12.5786i	0.424992	+	0.736108i
$293$	−10.4877	−	18.1652i	−0.612698	−	1.06122i	−0.990784	−	0.135453i	$-0.956751\pi$
$293$	−10.4877	−	18.1652i	−0.612698	−	1.06122i	0.378086	−	0.925770i	$-0.376582\pi$
$294$	−11.9468	+	16.1902i	−0.696751	+	0.944232i
$295$	−1.91397	+	3.31510i	−0.111436	+	0.193012i
$296$	−2.81121			−0.163398
$297$		0			0
$298$	−9.61284			−0.556857
$299$	−9.48635	+	16.4308i	−0.548610	+	0.950220i
$300$	17.2537	−	23.3821i	0.996144	−	1.34997i
$301$	2.51996	+	4.36471i	0.145248	+	0.251577i
$302$	20.6993	+	35.8523i	1.19111	+	2.06307i
$303$	−6.60191	−	15.1282i	−0.379270	−	0.869093i
$304$	1.35840	−	2.35281i	0.0779094	−	0.134943i
$305$	1.46473			0.0838704
$306$	−42.5362	−	9.70098i	−2.43163	−	0.554568i
$307$	−23.1324			−1.32024			−0.660118	−	0.751162i	$-0.729494\pi$
$307$	−23.1324			−1.32024			−0.660118	+	0.751162i	$0.729494\pi$
$308$		0			0
$309$	16.4125	+	1.84783i	0.933675	+	0.105119i
$310$	3.52253	+	6.10121i	0.200066	+	0.346525i
$311$	−10.2074	−	17.6798i	−0.578809	−	1.00253i	−0.995616	−	0.0935319i	$-0.970184\pi$
$311$	−10.2074	−	17.6798i	−0.578809	−	1.00253i	0.416807	−	0.908995i	$-0.363149\pi$
$312$	23.9621	+	2.69781i	1.35659	+	0.152733i
$313$	17.0197	−	29.4789i	0.962008	−	1.66625i	0.244562	−	0.969634i	$-0.421356\pi$
$313$	17.0197	−	29.4789i	0.962008	−	1.66625i	0.717446	−	0.696614i	$-0.245311\pi$
$314$	4.69820			0.265135
$315$	0.397865	+	1.28907i	0.0224172	+	0.0726308i
$316$	11.5808			0.651469
$317$	13.7102	−	23.7468i	0.770042	−	1.33375i	−0.167498	−	0.985872i	$-0.553569\pi$
$317$	13.7102	−	23.7468i	0.770042	−	1.33375i	0.937539	−	0.347879i	$-0.113098\pi$
$318$	10.7828	+	24.7087i	0.604670	+	1.38560i
$319$		0			0
$320$	−1.97312	−	3.41755i	−0.110301	−	0.191047i
$321$	5.31954	−	7.20901i	0.296908	−	0.402368i
$322$	−7.46712	+	12.9334i	−0.416126	+	0.720752i
$323$	−19.3437			−1.07631
$324$	27.7708	+	13.3621i	1.54282	+	0.742338i
$325$	20.5634			1.14065
$326$	−1.84040	+	3.18767i	−0.101930	+	0.176549i
$327$	14.8879	−	20.1760i	0.823304	−	1.11574i
$328$	6.41791	+	11.1161i	0.354370	+	0.613786i
$329$	5.28459	+	9.15318i	0.291349	+	0.504631i
$330$		0			0
$331$	8.98622	−	15.5646i	0.493927	−	0.855507i	−0.506048	−	0.862505i	$-0.668894\pi$
$331$	8.98622	−	15.5646i	0.493927	−	0.855507i	0.999976	+	0.00699827i	$0.00222764\pi$
$332$	46.1845			2.53470
$333$	−0.749824	−	2.42940i	−0.0410901	−	0.133130i
$334$	35.6841			1.95255
$335$	1.57998	−	2.73661i	0.0863236	−	0.149517i
$336$	2.14115	+	0.241065i	0.116809	+	0.0131512i
$337$	5.48607	+	9.50216i	0.298845	+	0.517615i	0.975872	−	0.218343i	$-0.0700652\pi$
$337$	5.48607	+	9.50216i	0.298845	+	0.517615i	−0.677027	+	0.735958i	$0.736732\pi$
$338$	5.37431	+	9.30858i	0.292324	+	0.506320i
$339$	−12.7911	−	1.44011i	−0.694718	−	0.0782159i
$340$	3.38922	−	5.87031i	0.183806	−	0.318362i
$341$		0			0
$342$	21.1029	+	4.81281i	1.14111	+	0.260247i
$343$	−17.0047			−0.918168
$344$	−5.89283	+	10.2067i	−0.317720	+	0.550307i
$345$	−0.992798	−	2.27499i	−0.0534505	−	0.122481i
$346$	1.14824	+	1.98882i	0.0617300	+	0.106919i
$347$	11.0494	+	19.1381i	0.593163	+	1.02739i	0.993803	+	0.111153i	$0.0354545\pi$
$347$	11.0494	+	19.1381i	0.593163	+	1.02739i	−0.400640	+	0.916236i	$0.631212\pi$
$348$	10.3126	−	13.9756i	0.552813	−	0.749169i
$349$	−9.20186	+	15.9381i	−0.492564	+	0.853147i	−0.999963	−	0.00856475i	$-0.997274\pi$
$349$	−9.20186	+	15.9381i	−0.492564	+	0.853147i	0.507399	+	0.861711i	$0.330607\pi$
$350$	16.1863			0.865196
$351$	4.05992	+	21.4272i	0.216703	+	1.14370i
$352$		0			0
$353$	−16.5354	+	28.6401i	−0.880089	+	1.52436i	−0.0288486	+	0.999584i	$0.509184\pi$
$353$	−16.5354	+	28.6401i	−0.880089	+	1.52436i	−0.851241	+	0.524776i	$0.824149\pi$
$354$	−28.9211	+	39.1936i	−1.53714	+	2.08312i
$355$	0.464542	+	0.804611i	0.0246553	+	0.0427043i
$356$	−4.61838	−	7.99927i	−0.244774	−	0.423960i
$357$	−6.13611	−	14.0608i	−0.324757	−	0.744179i
$358$	−13.0725	+	22.6422i	−0.690901	+	1.19668i
$359$	−2.99864			−0.158262			−0.0791311	−	0.996864i	$-0.525215\pi$
$359$	−2.99864			−0.158262			−0.0791311	+	0.996864i	$0.525215\pi$
$360$	−2.14538	+	2.31296i	−0.113071	+	0.121904i
$361$	−9.40329			−0.494910
$362$	20.8744	−	36.1555i	1.09713	−	1.90029i
$363$		0			0
$364$	10.1931	+	17.6549i	0.534262	+	0.925370i
$365$	−0.672347	−	1.16454i	−0.0351922	−	0.0609548i
$366$	18.5211	+	2.08523i	0.968115	+	0.108997i
$367$	−0.831230	+	1.43973i	−0.0433899	+	0.0751534i	−0.886905	−	0.461952i	$-0.847149\pi$
$367$	−0.831230	+	1.43973i	−0.0433899	+	0.0751534i	0.843515	+	0.537106i	$0.180482\pi$
$368$	−3.96444			−0.206661
$369$	−7.89456	+	8.51122i	−0.410974	+	0.443076i
$370$	0.625739			0.0325306
$371$	−4.73992	+	8.20979i	−0.246085	+	0.426231i
$372$	22.6351	+	51.8681i	1.17357	+	2.68924i
$373$	−10.7543	−	18.6271i	−0.556839	−	0.964473i	−0.997758	−	0.0669259i	$-0.978681\pi$
$373$	−10.7543	−	18.6271i	−0.556839	−	0.964473i	0.440919	−	0.897547i	$-0.354652\pi$
$374$		0			0
$375$	−3.22749	+	4.37388i	−0.166667	+	0.225866i
$376$	−12.3578	+	21.4043i	−0.637304	+	1.10384i
$377$	12.2908			0.633008
$378$	3.19574	+	16.8663i	0.164371	+	0.867509i
$379$	12.4193			0.637938			0.318969	−	0.947765i	$-0.396663\pi$
$379$	12.4193			0.637938			0.318969	+	0.947765i	$0.396663\pi$
$380$	−1.68145	+	2.91235i	−0.0862564	+	0.149401i
$381$	−13.5796	+	18.4029i	−0.695702	+	0.942811i
$382$	15.0080	+	25.9947i	0.767877	+	1.33000i
$383$	−0.399838	−	0.692540i	−0.0204308	−	0.0353872i	0.855629	−	0.517589i	$-0.173170\pi$
$383$	−0.399838	−	0.692540i	−0.0204308	−	0.0353872i	−0.876060	+	0.482202i	$0.839837\pi$
$384$	−13.7224	−	31.4447i	−0.700266	−	1.60465i
$385$		0			0
$386$	−53.9188			−2.74439
$387$	−10.3922	−	2.37009i	−0.528266	−	0.120479i
$388$	−18.0028			−0.913954
$389$	0.868343	−	1.50401i	0.0440267	−	0.0762565i	−0.843172	−	0.537643i	$-0.819315\pi$
$389$	0.868343	−	1.50401i	0.0440267	−	0.0762565i	0.887199	+	0.461387i	$0.152648\pi$
$390$	−5.33365	−	0.600498i	−0.270080	−	0.0304074i
$391$	14.1135	+	24.4453i	0.713750	+	1.23625i
$392$	−8.27260	−	14.3286i	−0.417830	−	0.723702i
$393$	12.5653	+	1.41469i	0.633837	+	0.0713616i
$394$	−1.25494	+	2.17361i	−0.0632228	+	0.109505i
$395$	−1.07216			−0.0539461
$396$		0			0
$397$	−24.7599			−1.24267			−0.621333	−	0.783547i	$-0.713409\pi$
$397$	−24.7599			−1.24267			−0.621333	+	0.783547i	$0.713409\pi$
$398$	19.1336	−	33.1403i	0.959080	−	1.66117i
$399$	3.04422	+	6.97581i	0.152402	+	0.349227i
$400$	2.14841	+	3.72115i	0.107420	+	0.186058i
$401$	−10.9262	−	18.9247i	−0.545627	−	0.945053i	−0.998567	−	0.0535126i	$-0.982958\pi$
$401$	−10.9262	−	18.9247i	−0.545627	−	0.945053i	0.452940	−	0.891541i	$-0.350375\pi$
$402$	23.8743	−	32.3543i	1.19074	−	1.61369i
$403$	−20.0236	+	34.6818i	−0.997445	+	1.72762i
$404$	32.6322			1.62351
$405$	−2.57105	−	1.23707i	−0.127756	−	0.0614706i
$406$	9.67462			0.480143
$407$		0			0
$408$	21.3010	−	28.8670i	1.05456	−	1.42913i
$409$	4.01739	+	6.95832i	0.198647	+	0.344067i	0.948090	−	0.318002i	$-0.103012\pi$
$409$	4.01739	+	6.95832i	0.198647	+	0.344067i	−0.749443	+	0.662069i	$0.769679\pi$
$410$	−1.42854	−	2.47431i	−0.0705507	−	0.122197i
$411$	−6.79421	−	15.5689i	−0.335134	−	0.767956i
$412$	−16.3262	+	28.2778i	−0.804334	+	1.39315i
$413$	−17.1280			−0.842812
$414$	−9.31491	−	30.1799i	−0.457803	−	1.48326i
$415$	−4.27580			−0.209891
$416$	9.63566	−	16.6895i	0.472427	−	0.818268i
$417$	16.3114	+	1.83645i	0.798773	+	0.0899312i
$418$		0			0
$419$	2.79840	+	4.84698i	0.136711	+	0.236790i	0.926250	−	0.376910i	$-0.123014\pi$
$419$	2.79840	+	4.84698i	0.136711	+	0.236790i	−0.789539	+	0.613701i	$0.789680\pi$
$420$	−2.65036	−	0.298395i	−0.129324	−	0.0145602i
$421$	−18.9272	+	32.7829i	−0.922455	+	1.59774i	−0.126851	+	0.991922i	$0.540487\pi$
$421$	−18.9272	+	32.7829i	−0.922455	+	1.59774i	−0.795604	+	0.605817i	$0.792846\pi$
$422$	−34.8181			−1.69492
$423$	−21.7934	−	4.97030i	−1.05963	−	0.241664i
$424$	−22.1682			−1.07658
$425$	15.2968	−	26.4948i	0.742002	−	1.28519i
$426$	4.72854	+	10.8354i	0.229098	+	0.524977i
$427$	3.27694	+	5.67583i	0.158582	+	0.274673i
$428$	8.85614	+	15.3393i	0.428078	+	0.741452i
$429$		0			0
$430$	1.31167	−	2.27187i	0.0632542	−	0.109560i
$431$	29.7844			1.43466			0.717332	−	0.696731i	$-0.245363\pi$
$431$	29.7844			1.43466			0.717332	+	0.696731i	$0.245363\pi$
$432$	−3.45330	+	2.97334i	−0.166147	+	0.143055i
$433$	−0.279271			−0.0134209			−0.00671046	−	0.999977i	$-0.502136\pi$
$433$	−0.279271			−0.0134209			−0.00671046	+	0.999977i	$0.502136\pi$
$434$	−15.7614	+	27.2996i	−0.756573	+	1.31042i
$435$	−0.954749	+	1.29387i	−0.0457767	+	0.0620363i
$436$	24.7859	+	42.9304i	1.18703	+	2.05599i
$437$	−7.00193	−	12.1277i	−0.334948	−	0.580146i
$438$	−6.84376	−	15.6824i	−0.327008	−	0.749335i
$439$	7.49827	−	12.9874i	0.357873	−	0.619854i	−0.629732	−	0.776812i	$-0.716835\pi$
$439$	7.49827	−	12.9874i	0.357873	−	0.619854i	0.987605	+	0.156958i	$0.0501687\pi$
$440$		0			0
$441$	10.1760	−	10.9709i	0.484571	−	0.522422i
$442$	61.0366			2.90322
$443$	−7.24991	+	12.5572i	−0.344453	+	0.596611i	−0.985254	−	0.171096i	$-0.945269\pi$
$443$	−7.24991	+	12.5572i	−0.344453	+	0.596611i	0.640801	+	0.767707i	$0.278602\pi$
$444$	4.99491	+	0.562360i	0.237048	+	0.0266884i
$445$	0.427573	+	0.740579i	0.0202689	+	0.0351068i
$446$	2.24315	+	3.88525i	0.106216	+	0.183972i
$447$	7.10407	+	0.799823i	0.336011	+	0.0378303i
$448$	8.82866	−	15.2917i	0.417115	−	0.722464i
$449$	−21.2217			−1.00151			−0.500757	−	0.865588i	$-0.666945\pi$
$449$	−21.2217			−1.00151			−0.500757	+	0.865588i	$0.666945\pi$
$450$	−23.2800	+	25.0984i	−1.09743	+	1.18315i
$451$		0			0
$452$	12.7238	−	22.0383i	0.598479	−	1.03660i
$453$	−12.3141	−	28.2178i	−0.578569	−	1.32579i
$454$	18.6449	+	32.2940i	0.875050	+	1.51563i
$455$	−0.943684	−	1.63451i	−0.0442406	−	0.0766269i
$456$	−10.5678	+	14.3214i	−0.494881	+	0.670659i
$457$	−1.60475	+	2.77951i	−0.0750671	+	0.130020i	−0.901115	−	0.433579i	$-0.857250\pi$
$457$	−1.60475	+	2.77951i	−0.0750671	+	0.130020i	0.826048	+	0.563599i	$0.190584\pi$
$458$	1.21789			0.0569085
$459$	30.6279	+	10.7084i	1.42959	+	0.499824i
$460$	4.90725			0.228802
$461$	13.1628	−	22.7986i	0.613052	−	1.06184i	−0.377671	−	0.925940i	$-0.623275\pi$
$461$	13.1628	−	22.7986i	0.613052	−	1.06184i	0.990723	−	0.135897i	$-0.0433918\pi$
$462$		0			0
$463$	−1.81412	−	3.14215i	−0.0843093	−	0.146028i	0.820787	−	0.571234i	$-0.193535\pi$
$463$	−1.81412	−	3.14215i	−0.0843093	−	0.146028i	−0.905097	+	0.425206i	$0.860202\pi$
$464$	1.28411	+	2.22414i	0.0596133	+	0.103253i
$465$	−2.09558	−	4.80199i	−0.0971800	−	0.222687i
$466$	11.9391	−	20.6791i	0.553067	−	0.957940i
$467$	−18.4952			−0.855854			−0.427927	−	0.903813i	$-0.640756\pi$
$467$	−18.4952			−0.855854			−0.427927	+	0.903813i	$0.640756\pi$
$468$	−42.0358	−	9.58685i	−1.94310	−	0.443152i
$469$	14.1391			0.652884
$470$	2.75069	−	4.76433i	0.126880	−	0.219762i
$471$	−3.47206	−	0.390907i	−0.159984	−	0.0180121i
$472$	−20.0265	−	34.6869i	−0.921795	−	1.59660i
$473$		0			0
$474$	−13.5571	−	1.52635i	−0.622699	−	0.0701076i
$475$	−7.58897	+	13.1445i	−0.348206	+	0.603110i
$476$	30.3299			1.39017
$477$	−5.91285	−	19.1574i	−0.270731	−	0.877157i
$478$	−22.4540			−1.02702
$479$	−0.0784991	+	0.135964i	−0.00358672	+	0.00621238i	−0.867813	−	0.496891i	$-0.834475\pi$
$479$	−0.0784991	+	0.135964i	−0.00358672	+	0.00621238i	0.864226	+	0.503103i	$0.167808\pi$
$480$	1.00843	+	2.31080i	0.0460281	+	0.105473i
$481$	1.77848	+	3.08042i	0.0810918	+	0.140455i
$482$	0.324583	+	0.562194i	0.0147843	+	0.0256072i
$483$	6.59445	−	8.93676i	0.300058	−	0.406637i
$484$		0			0
$485$	1.66671			0.0756816
$486$	−30.7490	−	19.3026i	−1.39480	−	0.875585i
$487$	17.9265			0.812327			0.406164	−	0.913800i	$-0.366866\pi$
$487$	17.9265			0.812327			0.406164	+	0.913800i	$0.366866\pi$
$488$	−7.66299	+	13.2727i	−0.346887	+	0.600826i
$489$	1.62532	−	2.20262i	0.0734993	−	0.0996058i
$490$	1.84138	+	3.18936i	0.0831849	+	0.144080i
$491$	−3.32399	−	5.75731i	−0.150009	−	0.259824i	0.781221	−	0.624254i	$-0.214597\pi$
$491$	−3.32399	−	5.75731i	−0.150009	−	0.259824i	−0.931231	+	0.364430i	$0.881264\pi$
$492$	−9.17954	−	21.0348i	−0.413846	−	0.948324i
$493$	9.14292	−	15.8360i	0.411777	−	0.713218i
$494$	−30.2813			−1.36242
$495$		0			0
$496$	−8.36804			−0.375736
$497$	−2.07857	+	3.60020i	−0.0932368	+	0.161491i
$498$	−54.0662	−	6.08713i	−2.42276	−	0.272771i
$499$	−16.9737	−	29.3993i	−0.759846	−	1.31609i	−0.942929	−	0.332994i	$-0.891941\pi$
$499$	−16.9737	−	29.3993i	−0.759846	−	1.31609i	0.183083	−	0.983097i	$-0.441392\pi$
$500$	−5.37323	−	9.30670i	−0.240298	−	0.416208i
$501$	−26.3712	−	2.96905i	−1.17818	−	0.132647i
$502$	5.15339	−	8.92594i	0.230007	−	0.398384i
$503$	−3.13729			−0.139885			−0.0699423	−	0.997551i	$-0.522282\pi$
$503$	−3.13729			−0.139885			−0.0699423	+	0.997551i	$0.522282\pi$
$504$	−13.7624	−	3.13871i	−0.613026	−	0.139809i
$505$	−3.02112			−0.134438
$506$		0			0
$507$	−3.19721	−	7.32638i	−0.141993	−	0.325376i
$508$	−22.6077	−	39.1576i	−1.00305	−	1.73734i
$509$	−11.4017	−	19.7484i	−0.505374	−	0.875333i	−0.999981	−	0.00621612i	$-0.998021\pi$
$509$	−11.4017	−	19.7484i	−0.505374	−	0.875333i	0.494607	−	0.869117i	$-0.335312\pi$
$510$	−4.74133	+	6.42542i	−0.209949	+	0.284522i
$511$	3.00839	−	5.21068i	0.133083	−	0.230507i
$512$	9.84494			0.435089
$513$	−15.1950	−	5.31260i	−0.670875	−	0.234557i
$514$	−8.51139			−0.375421
$515$	1.51149	−	2.61798i	0.0666043	−	0.115362i
$516$	12.5120	−	16.9562i	0.550812	−	0.746457i
$517$		0			0
$518$	1.39992	+	2.42474i	0.0615090	+	0.106537i
$519$	−0.683097	−	1.56531i	−0.0299846	−	0.0687095i
$520$	2.20676	−	3.82223i	0.0967729	−	0.167616i
$521$	5.26812			0.230801			0.115400	−	0.993319i	$-0.463185\pi$
$521$	5.26812			0.230801			0.115400	+	0.993319i	$0.463185\pi$
$522$	−13.9145	+	15.0014i	−0.609021	+	0.656593i
$523$	−11.8956			−0.520159			−0.260080	−	0.965587i	$-0.583749\pi$
$523$	−11.8956			−0.520159			−0.260080	+	0.965587i	$0.583749\pi$
$524$	−12.4992	+	21.6493i	−0.546032	+	0.945756i
$525$	−11.9620	−	1.34676i	−0.522065	−	0.0587775i
$526$	16.8299	+	29.1502i	0.733817	+	1.27101i
$527$	29.7904	+	51.5985i	1.29769	+	2.24767i
$528$		0			0
$529$	1.28255	−	2.22144i	0.0557629	−	0.0965843i
$530$	4.93436			0.214335
$531$	24.6343	−	26.5585i	1.06904	−	1.15254i
$532$	−15.0471			−0.652376
$533$	8.12045	−	14.0650i	0.351736	−	0.609224i
$534$	4.35223	+	9.97310i	0.188339	+	0.431578i
$535$	−0.819909	−	1.42012i	−0.0354477	−	0.0613973i
$536$	16.5319	+	28.6340i	0.714067	+	1.23680i
$537$	11.5447	−	15.6453i	0.498191	−	0.675145i
$538$	1.06872	−	1.85108i	0.0460757	−	0.0798055i
$539$		0			0
$540$	4.27456	−	3.68046i	0.183948	−	0.158382i
$541$	−40.5807			−1.74470			−0.872350	−	0.488882i	$-0.837405\pi$
$541$	−40.5807			−1.74470			−0.872350	+	0.488882i	$0.837405\pi$
$542$	3.07918	−	5.33330i	0.132262	−	0.229085i
$543$	−18.4349	+	24.9828i	−0.791115	+	1.07211i
$544$	−14.3356	−	24.8300i	−0.614635	−	1.06458i
$545$	−2.29470	−	3.97453i	−0.0982940	−	0.170250i
$546$	−9.60567	−	22.0113i	−0.411085	−	0.941998i
$547$	11.7672	−	20.3813i	0.503127	−	0.871442i	−0.496866	−	0.867827i	$-0.665516\pi$
$547$	11.7672	−	20.3813i	0.503127	−	0.871442i	0.999993	−	0.00361458i	$-0.00115056\pi$
$548$	33.5828			1.43458
$549$	−13.5140	−	3.08205i	−0.576762	−	0.131539i
$550$		0			0
$551$	−4.53595	+	7.85650i	−0.193238	+	0.334698i
$552$	25.8088	+	2.90573i	1.09850	+	0.123676i
$553$	−2.39866	−	4.15460i	−0.102001	−	0.176672i
$554$	−33.6593	−	58.2996i	−1.43005	−	2.47691i
$555$	−0.462433	−	0.0520638i	−0.0196292	−	0.00220998i
$556$	−16.2256	+	28.1036i	−0.688120	+	1.19186i
$557$	6.28652			0.266369			0.133184	−	0.991091i	$-0.457480\pi$
$557$	6.28652			0.266369			0.133184	+	0.991091i	$0.457480\pi$
$558$	−19.6617	−	63.7031i	−0.832346	−	2.69677i
$559$	14.9121			0.630716
$560$	0.197187	−	0.341538i	0.00833268	−	0.0144326i
$561$		0			0
$562$	−10.1807	−	17.6335i	−0.429448	−	0.743826i
$563$	−8.48320	−	14.6933i	−0.357524	−	0.619250i	0.630022	−	0.776577i	$-0.283046\pi$
$563$	−8.48320	−	14.6933i	−0.357524	−	0.619250i	−0.987547	+	0.157327i	$0.949712\pi$
$564$	26.2389	−	35.5588i	1.10486	−	1.49729i
$565$	−1.17798	+	2.04033i	−0.0495582	+	0.0858373i
$566$	−54.0731			−2.27286
$567$	−0.958376	−	12.7304i	−0.0402480	−	0.534627i
$568$	−9.72131			−0.407897
$569$	11.1253	−	19.2695i	0.466395	−	0.807819i	−0.532868	−	0.846198i	$-0.678886\pi$
$569$	11.1253	−	19.2695i	0.466395	−	0.807819i	0.999263	+	0.0383786i	$0.0122193\pi$
$570$	2.35225	−	3.18775i	0.0985248	−	0.133520i
$571$	17.6576	+	30.5838i	0.738947	+	1.27989i	0.952970	+	0.303065i	$0.0980100\pi$
$571$	17.6576	+	30.5838i	0.738947	+	1.27989i	−0.214023	+	0.976829i	$0.568657\pi$
$572$		0			0
$573$	−8.92836	−	20.4593i	−0.372988	−	0.854698i
$574$	6.39196	−	11.0712i	0.266795	−	0.462103i
$575$	22.1482			0.923643
$576$	11.0134	+	35.6829i	0.458890	+	1.48679i
$577$	−38.2361			−1.59179			−0.795894	−	0.605436i	$-0.792999\pi$
$577$	−38.2361			−1.59179			−0.795894	+	0.605436i	$0.792999\pi$
$578$	25.6077	−	44.3538i	1.06514	−	1.84487i
$579$	39.8470	+	4.48624i	1.65598	+	0.186442i
$580$	−1.58950	−	2.75309i	−0.0660002	−	0.114316i
$581$	−9.56594	−	16.5687i	−0.396862	−	0.687385i
$582$	21.0751	+	2.37278i	0.873592	+	0.0983547i
$583$		0			0
$584$	14.0700			0.582219
$585$	3.89171	+	0.887559i	0.160902	+	0.0366960i
$586$	−48.8517			−2.01805
$587$	6.19482	−	10.7297i	0.255688	−	0.442864i	−0.709394	−	0.704812i	$-0.751031\pi$
$587$	6.19482	−	10.7297i	0.255688	−	0.442864i	0.965082	+	0.261948i	$0.0843648\pi$
$588$	11.8323	+	27.1136i	0.487956	+	1.11815i
$589$	−14.7795	−	25.5988i	−0.608979	−	1.05478i
$590$	4.45764	+	7.72087i	0.183518	+	0.317863i
$591$	1.10827	−	1.50193i	0.0455883	−	0.0617810i
$592$	−0.371623	+	0.643669i	−0.0152736	+	0.0264546i
$593$	−4.18039			−0.171668			−0.0858340	−	0.996309i	$-0.527355\pi$
$593$	−4.18039			−0.171668			−0.0858340	+	0.996309i	$0.527355\pi$
$594$		0			0
$595$	−2.80796			−0.115115
$596$	−7.06671	+	12.2399i	−0.289464	+	0.501366i
$597$	−16.8975	+	22.8993i	−0.691568	+	0.937208i
$598$	22.0937	+	38.2675i	0.903480	+	1.56487i
$599$	22.0394	+	38.1733i	0.900505	+	1.55972i	0.826840	+	0.562437i	$0.190136\pi$
$599$	22.0394	+	38.1733i	0.900505	+	1.55972i	0.0736641	+	0.997283i	$0.476531\pi$
$600$	−11.2589	−	25.7997i	−0.459643	−	1.05327i
$601$	−0.875658	+	1.51668i	−0.0357188	+	0.0618668i	−0.883332	−	0.468748i	$-0.844705\pi$
$601$	−0.875658	+	1.51668i	−0.0357188	+	0.0618668i	0.847613	+	0.530614i	$0.178039\pi$
$602$	11.7380			0.478405
$603$	−20.3356	+	21.9240i	−0.828128	+	0.892815i
$604$	60.8670			2.47664
$605$		0			0
$606$	−38.2012	−	4.30094i	−1.55182	−	0.174714i
$607$	−5.43457	−	9.41296i	−0.220583	−	0.382060i	0.734402	−	0.678714i	$-0.237462\pi$
$607$	−5.43457	−	9.41296i	−0.220583	−	0.382060i	−0.954985	+	0.296654i	$0.904129\pi$
$608$	7.11214	+	12.3186i	0.288435	+	0.499584i
$609$	−7.14973	−	0.804964i	−0.289722	−	0.0326188i
$610$	1.70568	−	2.95433i	0.0690611	−	0.119617i
$611$	31.2721			1.26513
$612$	−43.6219	+	47.0293i	−1.76331	+	1.90105i
$613$	−17.7933			−0.718665			−0.359333	−	0.933210i	$-0.616996\pi$
$613$	−17.7933			−0.718665			−0.359333	+	0.933210i	$0.616996\pi$
$614$	−26.9377	+	46.6575i	−1.08712	+	1.88294i
$615$	0.849849	+	1.94742i	0.0342692	+	0.0785276i
$616$		0			0
$617$	−1.99805	−	3.46073i	−0.0804386	−	0.139324i	0.823000	−	0.568042i	$-0.192299\pi$
$617$	−1.99805	−	3.46073i	−0.0804386	−	0.139324i	−0.903438	+	0.428718i	$0.858965\pi$
$618$	22.8394	−	30.9518i	0.918735	−	1.24506i
$619$	5.48769	−	9.50496i	0.220569	−	0.382037i	−0.734412	−	0.678704i	$-0.762542\pi$
$619$	5.48769	−	9.50496i	0.220569	−	0.382037i	0.954981	+	0.296667i	$0.0958753\pi$
$620$	10.3581			0.415992
$621$	4.37281	+	23.0786i	0.175475	+	0.926112i
$622$	−47.5462			−1.90643
$623$	−1.91316	+	3.31369i	−0.0766491	+	0.132760i
$624$	3.78533	−	5.12985i	0.151534	−	0.205358i
$625$	−11.7513	−	20.3538i	−0.470052	−	0.814153i
$626$	−39.6388	−	68.6565i	−1.58429	−	2.74407i
$627$		0			0
$628$	3.45380	−	5.98216i	0.137822	−	0.238714i
$629$	5.29194			0.211003
$630$	3.06333	+	0.698636i	0.122046	+	0.0278343i
$631$	8.64921			0.344319			0.172160	−	0.985069i	$-0.444925\pi$
$631$	8.64921			0.344319			0.172160	+	0.985069i	$0.444925\pi$
$632$	5.60917	−	9.71536i	0.223121	−	0.386456i
$633$	25.7312	+	2.89699i	1.02272	+	0.115145i
$634$	−31.9311	−	55.3063i	−1.26815	−	2.19649i
$635$	2.09304	+	3.62525i	0.0830596	+	0.143863i
$636$	39.3881	+	4.43458i	1.56184	+	0.175842i
$637$	−10.4672	+	18.1296i	−0.414724	+	0.718323i
$638$		0			0
$639$	−2.59293	−	8.40100i	−0.102575	−	0.332338i
$640$	−6.27953			−0.248220
$641$	−18.5438	+	32.1188i	−0.732436	+	1.26862i	0.223403	+	0.974726i	$0.428283\pi$
$641$	−18.5438	+	32.1188i	−0.732436	+	1.26862i	−0.955839	+	0.293891i	$0.905050\pi$
$642$	−8.34578	−	19.1243i	−0.329382	−	0.754775i
$643$	20.3663	+	35.2755i	0.803168	+	1.39113i	0.917521	+	0.397688i	$0.130187\pi$
$643$	20.3663	+	35.2755i	0.803168	+	1.39113i	−0.114353	+	0.993440i	$0.536479\pi$
$644$	10.9786	+	19.0156i	0.432619	+	0.749319i
$645$	−1.15838	+	1.56982i	−0.0456110	+	0.0618117i
$646$	−22.5257	+	39.0157i	−0.886263	+	1.53505i
$647$	−0.568944			−0.0223675			−0.0111837	−	0.999937i	$-0.503560\pi$
$647$	−0.568944			−0.0223675			−0.0111837	+	0.999937i	$0.503560\pi$
$648$	24.6606	−	16.8256i	0.968759	−	0.660973i
$649$		0			0
$650$	23.9461	−	41.4758i	0.939242	−	1.62682i
$651$	13.9194	−	18.8635i	0.545545	−	0.739319i
$652$	2.70588	+	4.68672i	0.105970	+	0.183546i
$653$	18.2638	+	31.6338i	0.714718	+	1.23793i	0.963068	+	0.269257i	$0.0867781\pi$
$653$	18.2638	+	31.6338i	0.714718	+	1.23793i	−0.248351	+	0.968670i	$0.579889\pi$
$654$	−23.3575	−	53.5235i	−0.913351	−	2.09294i
$655$	1.15719	−	2.00431i	0.0452152	−	0.0783150i
$656$	3.39361			0.132498
$657$	3.75283	+	12.1590i	0.146412	+	0.474369i
$658$	24.6157			0.959618
$659$	−12.0035	+	20.7907i	−0.467590	+	0.809889i	−0.999314	−	0.0370284i	$-0.988211\pi$
$659$	−12.0035	+	20.7907i	−0.467590	+	0.809889i	0.531725	+	0.846917i	$0.321544\pi$
$660$		0			0
$661$	−6.49165	−	11.2439i	−0.252496	−	0.437336i	0.711717	−	0.702467i	$-0.247918\pi$
$661$	−6.49165	−	11.2439i	−0.252496	−	0.437336i	−0.964212	+	0.265131i	$0.914585\pi$
$662$	−20.9289	−	36.2499i	−0.813425	−	1.40889i
$663$	−45.1072	−	5.07847i	−1.75182	−	0.197232i
$664$	22.3695	−	38.7452i	0.868106	−	1.50360i
$665$	1.39308			0.0540212
$666$	−5.77321	−	1.31666i	−0.223707	−	0.0510196i
$667$	13.2380			0.512579
$668$	26.2325	−	45.4361i	1.01497	−	1.75798i
$669$	−1.33446	−	3.05792i	−0.0515934	−	0.118226i
$670$	−3.67978	−	6.37356i	−0.142162	−	0.246232i
$671$		0			0
$672$	−6.69825	+	9.07743i	−0.258391	+	0.350169i
$673$	8.51283	−	14.7447i	0.328145	−	0.568365i	−0.653998	−	0.756496i	$-0.726910\pi$
$673$	8.51283	−	14.7447i	0.328145	−	0.568365i	0.982144	+	0.188131i	$0.0602431\pi$
$674$	25.5541			0.984309
$675$	19.2926	−	16.6112i	0.742573	−	0.639366i
$676$	15.8033			0.607820
$677$	−17.7158	+	30.6847i	−0.680874	+	1.17931i	0.293840	+	0.955855i	$0.405067\pi$
$677$	−17.7158	+	30.6847i	−0.680874	+	1.17931i	−0.974714	+	0.223454i	$0.928267\pi$
$678$	−17.7999	+	24.1223i	−0.683602	+	0.926413i
$679$	3.72882	+	6.45851i	0.143099	+	0.247855i
$680$	−3.28315	−	5.68658i	−0.125903	−	0.218071i
$681$	−11.0920	−	25.4172i	−0.425046	−	0.973988i
$682$		0			0
$683$	23.8967			0.914381			0.457191	−	0.889369i	$-0.348856\pi$
$683$	23.8967			0.914381			0.457191	+	0.889369i	$0.348856\pi$
$684$	21.6415	−	23.3320i	0.827484	−	0.892120i
$685$	−3.10912			−0.118793
$686$	−19.8020	+	34.2981i	−0.756044	+	1.30951i
$687$	−0.900047	−	0.101333i	−0.0343389	−	0.00386610i
$688$	1.55798	+	2.69850i	0.0593975	+	0.102880i
$689$	14.0245	+	24.2911i	0.534290	+	0.925418i
$690$	−5.74471	−	0.646778i	−0.218697	−	0.0246224i
$691$	0.296307	−	0.513219i	0.0112721	−	0.0195238i	−0.860334	−	0.509730i	$-0.829745\pi$
$691$	0.296307	−	0.513219i	0.0112721	−	0.0195238i	0.871606	+	0.490206i	$0.163079\pi$
$692$	3.37645			0.128353
$693$		0			0
$694$	51.4682			1.95371
$695$	1.50218	−	2.60186i	0.0569810	−	0.0986940i
$696$	−6.72948	−	15.4205i	−0.255080	−	0.584514i
$697$	−12.0813	−	20.9255i	−0.457613	−	0.792610i
$698$	21.4312	+	37.1198i	0.811181	+	1.40501i
$699$	−10.5438	+	14.2889i	−0.398802	+	0.540454i
$700$	11.8991	−	20.6099i	0.449744	−	0.778979i
$701$	25.4261			0.960329			0.480164	−	0.877179i	$-0.340577\pi$
$701$	25.4261			0.960329			0.480164	+	0.877179i	$0.340577\pi$
$702$	47.9459	+	16.7632i	1.80960	+	0.632688i
$703$	−2.62542			−0.0990194
$704$		0			0
$705$	−2.42922	+	3.29206i	−0.0914896	+	0.123986i
$706$	38.5109	+	66.7029i	1.44938	+	2.51040i
$707$	−6.75894	−	11.7068i	−0.254196	−	0.440280i
$708$	28.6439	+	65.6373i	1.07650	+	2.46680i
$709$	−7.55233	+	13.0810i	−0.283634	+	0.491268i	−0.972277	−	0.233832i	$-0.924873\pi$
$709$	−7.55233	+	13.0810i	−0.283634	+	0.491268i	0.688643	+	0.725100i	$0.258207\pi$
$710$	2.16384			0.0812074
$711$	9.89197	+	2.25600i	0.370978	+	0.0846067i
$712$	−8.94768			−0.335328
$713$	−21.5668	+	37.3547i	−0.807681	+	1.39895i
$714$	−35.5059	−	3.99749i	−1.32877	−	0.149602i
$715$		0			0
$716$	19.2200	+	33.2900i	0.718284	+	1.24410i
$717$	16.5939	+	1.86826i	0.619712	+	0.0697713i
$718$	−3.49192	+	6.04818i	−0.130317	+	0.225716i
$719$	12.0428			0.449120			0.224560	−	0.974460i	$-0.427906\pi$
$719$	12.0428			0.449120			0.224560	+	0.974460i	$0.427906\pi$
$720$	0.245983	+	0.796974i	0.00916723	+	0.0297015i
$721$	13.5262			0.503743
$722$	−10.9501	+	18.9662i	−0.407522	+	0.705849i
$723$	−0.193096	−	0.442478i	−0.00718132	−	0.0164559i
$724$	−30.6909	−	53.1582i	−1.14062	−	1.97561i
$725$	−7.17396	−	12.4257i	−0.266434	−	0.461477i
$726$		0			0
$727$	−24.7966	+	42.9489i	−0.919654	+	1.59289i	−0.119714	+	0.992808i	$0.538198\pi$
$727$	−24.7966	+	42.9489i	−0.919654	+	1.59289i	−0.799940	+	0.600079i	$0.795136\pi$
$728$	19.7481			0.731915
$729$	21.1181	+	16.8234i	0.782150	+	0.623090i
$730$	−3.13179			−0.115913
$731$	11.0929	−	19.2135i	0.410286	−	0.710636i
$732$	16.2706	−	22.0498i	0.601378	−	0.814983i
$733$	−16.1327	−	27.9426i	−0.595875	−	1.03209i	−0.993423	−	0.114504i	$-0.963472\pi$
$733$	−16.1327	−	27.9426i	−0.595875	−	1.03209i	0.397548	−	0.917581i	$-0.369861\pi$
$734$	1.93594	+	3.35314i	0.0714567	+	0.123767i
$735$	−1.09545	−	2.51020i	−0.0404061	−	0.0925902i
$736$	10.3783	−	17.9757i	0.382548	−	0.662593i
$737$		0			0
$738$	7.97369	+	25.8344i	0.293516	+	0.950979i
$739$	3.13253			0.115232			0.0576160	−	0.998339i	$-0.481650\pi$
$739$	3.13253			0.115232			0.0576160	+	0.998339i	$0.481650\pi$
$740$	0.460001	−	0.796745i	0.0169100	−	0.0292889i
$741$	22.3784	+	2.51951i	0.822092	+	0.0925566i
$742$	11.0393	+	19.1206i	0.405265	+	0.701940i
$743$	3.89438	+	6.74527i	0.142871	+	0.247460i	0.928577	−	0.371141i	$-0.121033\pi$
$743$	3.89438	+	6.74527i	0.142871	+	0.247460i	−0.785706	+	0.618601i	$0.787700\pi$
$744$	54.4766	+	6.13334i	1.99721	+	0.224859i
$745$	0.654242	−	1.13318i	0.0239696	−	0.0415165i
$746$	−50.0938			−1.83406
$747$	39.4495	+	8.99701i	1.44338	+	0.329183i
$748$		0			0
$749$	3.66865	−	6.35428i	0.134049	−	0.232180i
$750$	5.06358	+	11.6032i	0.184896	+	0.423687i
$751$	−24.8445	−	43.0320i	−0.906589	−	1.57026i	−0.818770	−	0.574122i	$-0.805344\pi$
$751$	−24.8445	−	43.0320i	−0.906589	−	1.57026i	−0.0878193	−	0.996136i	$-0.527990\pi$
$752$	3.26723	+	5.65901i	0.119144	+	0.206363i
$753$	−4.55113	+	6.16766i	−0.165852	+	0.224762i
$754$	14.3126	−	24.7902i	0.521236	−	0.902807i
$755$	−5.63511			−0.205083
$756$	23.8249	+	8.32987i	0.866504	+	0.302954i
$757$	−27.0307			−0.982449			−0.491225	−	0.871033i	$-0.663451\pi$
$757$	−27.0307			−0.982449			−0.491225	+	0.871033i	$0.663451\pi$
$758$	14.4623	−	25.0495i	0.525295	−	0.909838i
$759$		0			0
$760$	1.62882	+	2.82121i	0.0590836	+	0.102336i
$761$	22.2553	+	38.5473i	0.806753	+	1.39734i	0.915101	+	0.403224i	$0.132111\pi$
$761$	22.2553	+	38.5473i	0.806753	+	1.39734i	−0.108348	+	0.994113i	$0.534556\pi$
$762$	21.3048	+	48.8199i	0.771793	+	1.76856i
$763$	10.2675	−	17.7839i	0.371709	−	0.643819i
$764$	44.1315			1.59662
$765$	4.03855	−	4.35401i	0.146014	−	0.157419i
$766$	−1.86245			−0.0672930
$767$	−25.3391	+	43.8887i	−0.914943	+	1.58473i
$768$	−36.5526	−	4.11533i	−1.31898	−	0.148499i
$769$	−1.65952	−	2.87438i	−0.0598440	−	0.103653i	0.834551	−	0.550930i	$-0.185727\pi$
$769$	−1.65952	−	2.87438i	−0.0598440	−	0.103653i	−0.894395	+	0.447277i	$0.852394\pi$
$770$		0			0
$771$	6.29008	+	0.708179i	0.226532	+	0.0255044i
$772$	−39.6375	+	68.6541i	−1.42658	+	2.47091i
$773$	28.4878			1.02463			0.512317	−	0.858797i	$-0.328787\pi$
$773$	28.4878			1.02463			0.512317	+	0.858797i	$0.328787\pi$
$774$	−16.8822	+	18.2009i	−0.606817	+	0.654216i
$775$	46.7498			1.67930
$776$	−8.71969	+	15.1029i	−0.313019	+	0.542164i
$777$	−0.832822	−	1.90840i	−0.0298773	−	0.0684636i
$778$	−2.02237	−	3.50285i	−0.0725055	−	0.125583i
$779$	5.99375	+	10.3815i	0.214748	+	0.371955i
$780$	−4.68555	+	6.34982i	−0.167769	+	0.227360i
$781$		0			0
$782$	65.7407			2.35088
$783$	11.5313	−	9.92858i	0.412093	−	0.354818i
$784$	−4.37433			−0.156226
$785$	−0.319756	+	0.553833i	−0.0114126	+	0.0197671i
$786$	17.4857	−	23.6965i	0.623695	−	0.845228i
$787$	6.52435	+	11.3005i	0.232568	+	0.402820i	0.958563	−	0.284880i	$-0.0919538\pi$
$787$	6.52435	+	11.3005i	0.232568	+	0.402820i	−0.725995	+	0.687700i	$0.758621\pi$
$788$	1.84509	+	3.19579i	0.0657286	+	0.113845i
$789$	−10.0122	−	22.9428i	−0.356443	−	0.816786i
$790$	−1.24853	+	2.16251i	−0.0444207	+	0.0769388i
$791$	−10.5417			−0.374819
$792$		0			0
$793$	19.3917			0.688618
$794$	−28.8330	+	49.9402i	−1.02324	+	1.77231i
$795$	−3.64658	−	0.410557i	−0.129331	−	0.0145609i
$796$	−28.1314	−	48.7251i	−0.997092	−	1.72701i
$797$	−25.0867	−	43.4514i	−0.888616	−	1.53913i	−0.841513	−	0.540237i	$-0.818334\pi$
$797$	−25.0867	−	43.4514i	−0.888616	−	1.53913i	−0.0471028	−	0.998890i	$-0.514999\pi$
$798$	17.6150	+	1.98322i	0.623566	+	0.0702052i
$799$	23.2628	−	40.2924i	0.822980	−	1.42544i
$800$	−22.4968			−0.795382
$801$	−2.38658	−	7.73243i	−0.0843258	−	0.273212i
$802$	−50.8941			−1.79713
$803$		0			0
$804$	−23.6455	−	54.1835i	−0.833914	−	1.91091i
$805$	−1.01641	−	1.76048i	−0.0358238	−	0.0620487i
$806$	46.6349	+	80.7741i	1.64264	+	2.84514i
$807$	−0.943820	+	1.27906i	−0.0332240	+	0.0450250i
$808$	15.8055	−	27.3759i	0.556035	−	0.963080i
$809$	35.1505			1.23583			0.617914	−	0.786246i	$-0.287978\pi$
$809$	35.1505			1.23583			0.617914	+	0.786246i	$0.287978\pi$
$810$	−5.48913	+	3.74517i	−0.192868	+	0.131592i
$811$	−22.1055			−0.776228			−0.388114	−	0.921611i	$-0.626873\pi$
$811$	−22.1055			−0.776228			−0.388114	+	0.921611i	$0.626873\pi$
$812$	7.11213	−	12.3186i	0.249587	−	0.432297i
$813$	−2.71932	+	3.68521i	−0.0953708	+	0.129246i
$814$		0			0
$815$	−0.250512	−	0.433900i	−0.00877506	−	0.0151989i
$816$	−3.79369	−	8.69320i	−0.132806	−	0.304323i
$817$	−5.50337	+	9.53211i	−0.192538	+	0.333486i
$818$	18.7130			0.654285
$819$	5.26735	+	17.0660i	0.184056	+	0.596335i
$820$	−4.20068			−0.146694
$821$	1.26860	−	2.19728i	0.0442744	−	0.0766855i	−0.843039	−	0.537852i	$-0.819236\pi$
$821$	1.26860	−	2.19728i	0.0442744	−	0.0766855i	0.887313	+	0.461167i	$0.152569\pi$
$822$	−39.3139	−	4.42622i	−1.37123	−	0.154382i
$823$	5.18635	+	8.98302i	0.180785	+	0.313128i	0.942148	−	0.335197i	$-0.108803\pi$
$823$	5.18635	+	8.98302i	0.180785	+	0.313128i	−0.761363	+	0.648326i	$0.775470\pi$
$824$	15.8152	+	27.3928i	0.550950	+	0.954273i
$825$		0			0
$826$	−19.9455	+	34.5467i	−0.693994	+	1.20203i
$827$	−52.7236			−1.83338			−0.916690	−	0.399599i	$-0.869149\pi$
$827$	−52.7236			−1.83338			−0.916690	+	0.399599i	$0.869149\pi$
$828$	−45.2754	−	10.3257i	−1.57343	−	0.358843i
$829$	37.8438			1.31437			0.657184	−	0.753730i	$-0.271747\pi$
$829$	37.8438			1.31437			0.657184	+	0.753730i	$0.271747\pi$
$830$	−4.97917	+	8.62418i	−0.172830	+	0.299350i
$831$	20.0241	+	45.8851i	0.694629	+	1.59174i
$832$	−26.1222	−	45.2451i	−0.905626	−	1.56859i
$833$	15.5727	+	26.9727i	0.539562	+	0.934549i
$834$	22.6987	−	30.7612i	0.785992	−	1.06517i
$835$	−2.42863	+	4.20651i	−0.0840462	+	0.145572i
$836$		0			0
$837$	9.23003	+	48.7137i	0.319037	+	1.68379i
$838$	13.0350			0.450286
$839$	10.0578	−	17.4206i	0.347233	−	0.601425i	−0.638524	−	0.769602i	$-0.720455\pi$
$839$	10.0578	−	17.4206i	0.347233	−	0.601425i	0.985757	+	0.168177i	$0.0537879\pi$
$840$	−1.53404	+	2.07891i	−0.0529292	+	0.0717294i
$841$	10.2121	+	17.6879i	0.352142	+	0.609927i
$842$	44.0815	+	76.3513i	1.51915	+	2.63124i
$843$	6.05658	+	13.8786i	0.208600	+	0.478004i
$844$	−25.5959	+	44.3334i	−0.881047	+	1.52602i
$845$	−1.46308			−0.0503316
$846$	−35.4034	+	38.1688i	−1.21719	+	1.31227i
$847$		0			0
$848$	−2.93048	+	5.07575i	−0.100633	+	0.174302i
$849$	39.9610	+	4.49908i	1.37146	+	0.154408i
$850$	−35.6262	−	61.7064i	−1.22197	−	2.11651i
$851$	1.91555	+	3.31783i	0.0656642	+	0.113734i
$852$	17.2727	+	1.94467i	0.591752	+	0.0666234i
$853$	4.56010	−	7.89832i	0.156135	−	0.270433i	−0.777337	−	0.629085i	$-0.783430\pi$
$853$	4.56010	−	7.89832i	0.156135	−	0.270433i	0.933472	+	0.358651i	$0.116763\pi$
$854$	15.2640			0.522324
$855$	−2.00359	+	2.16009i	−0.0685213	+	0.0738736i
$856$	17.1579			0.586446
$857$	−0.922678	+	1.59813i	−0.0315181	+	0.0545909i	−0.881354	−	0.472456i	$-0.843368\pi$
$857$	−0.922678	+	1.59813i	−0.0315181	+	0.0545909i	0.849836	+	0.527047i	$0.176701\pi$
$858$		0			0
$859$	−14.2555	−	24.6913i	−0.486392	−	0.842456i	0.513485	−	0.858098i	$-0.328354\pi$
$859$	−14.2555	−	24.6913i	−0.486392	−	0.842456i	−0.999878	+	0.0156422i	$0.995021\pi$
$860$	−1.92850	−	3.34026i	−0.0657613	−	0.113902i
$861$	−5.64494	+	7.64999i	−0.192379	+	0.260711i
$862$	34.6840	−	60.0744i	1.18134	−	2.04614i
$863$	−10.6994			−0.364210			−0.182105	−	0.983279i	$-0.558291\pi$
$863$	−10.6994			−0.364210			−0.182105	+	0.983279i	$0.558291\pi$
$864$	−4.44164	−	23.4418i	−0.151108	−	0.797508i
$865$	−0.312594			−0.0106285
$866$	−0.325212	+	0.563283i	−0.0110511	+	0.0191411i
$867$	−22.6149	+	30.6476i	−0.768044	+	1.04085i
$868$	23.1735	+	40.1376i	0.786559	+	1.36236i
$869$		0			0
$870$	1.49790	+	3.43242i	0.0507834	+	0.116370i
$871$	20.9174	−	36.2300i	0.708760	−	1.22761i
$872$	48.0203			1.62617
$873$	−15.3775	−	3.50705i	−0.520449	−	0.118696i
$874$	−32.6150			−1.10322
$875$	−2.22585	+	3.85529i	−0.0752476	+	0.130333i
$876$	−24.9993	−	2.81459i	−0.844648	−	0.0950961i
$877$	20.4161	+	35.3618i	0.689404	+	1.19408i	0.972031	+	0.234852i	$0.0754606\pi$
$877$	20.4161	+	35.3618i	0.689404	+	1.19408i	−0.282628	+	0.959230i	$0.591206\pi$
$878$	−17.4635	−	30.2477i	−0.589364	−	1.02081i
$879$	36.1024	+	4.06464i	1.21770	+	0.137097i
$880$		0			0
$881$	21.0458			0.709050			0.354525	−	0.935047i	$-0.384643\pi$
$881$	21.0458			0.709050			0.354525	+	0.935047i	$0.384643\pi$
$882$	−10.2780	−	33.3003i	−0.346078	−	1.12128i
$883$	12.7282			0.428338			0.214169	−	0.976797i	$-0.431296\pi$
$883$	12.7282			0.428338			0.214169	+	0.976797i	$0.431296\pi$
$884$	44.8700	−	77.7172i	1.50914	−	2.61391i
$885$	−2.65188	−	6.07676i	−0.0891419	−	0.204268i
$886$	16.8850	+	29.2458i	0.567264	+	0.982530i
$887$	5.36249	+	9.28811i	0.180055	+	0.311864i	0.941899	−	0.335896i	$-0.109039\pi$
$887$	5.36249	+	9.28811i	0.180055	+	0.311864i	−0.761844	+	0.647760i	$0.775706\pi$
$888$	2.89107	−	3.91796i	0.0970180	−	0.131478i
$889$	−9.36520	+	16.2210i	−0.314099	+	0.544035i
$890$	1.99164			0.0667599
$891$		0			0
$892$	6.59606			0.220852
$893$	−11.5411	+	19.9897i	−0.386207	+	0.668930i
$894$	9.88592	−	13.3973i	0.330635	−	0.448074i
$895$	−1.77940	−	3.08201i	−0.0594788	−	0.103020i
$896$	−14.0487	−	24.3331i	−0.469336	−	0.812913i
$897$	−13.1437	−	30.1187i	−0.438855	−	1.00563i
$898$	−24.7127	+	42.8036i	−0.824673	+	1.42838i
$899$	27.9425			0.931935
$900$	14.8436	+	48.0927i	0.494787	+	1.60309i
$901$	41.7304			1.39024
$902$		0			0
$903$	−8.67461	−	0.976645i	−0.288673	−	0.0325007i
$904$	−12.3256	−	21.3486i	−0.409944	−	0.710044i
$905$	2.84139	+	4.92143i	0.0944510	+	0.163594i
$906$	−71.2543	−	8.02229i	−2.36727	−	0.266523i
$907$	6.62279	−	11.4710i	0.219906	−	0.380889i	−0.734873	−	0.678205i	$-0.762758\pi$
$907$	6.62279	−	11.4710i	0.219906	−	0.380889i	0.954779	+	0.297316i	$0.0960916\pi$
$908$	54.8260			1.81946
$909$	27.8735	+	6.35695i	0.924507	+	0.210847i
$910$	−4.39568			−0.145715
$911$	28.5622	−	49.4712i	0.946309	−	1.63906i	0.193200	−	0.981159i	$-0.438113\pi$
$911$	28.5622	−	49.4712i	0.946309	−	1.63906i	0.753109	−	0.657896i	$-0.228553\pi$
$912$	1.88211	+	4.31283i	0.0623228	+	0.142812i
$913$		0			0
$914$	3.73747	+	6.47348i	0.123624	+	0.214124i
$915$	−1.50634	+	2.04139i	−0.0497982	+	0.0674862i
$916$	0.895314	−	1.55073i	0.0295820	−	0.0512375i
$917$	10.3556			0.341972
$918$	57.2647	−	49.3058i	1.89002	−	1.62733i
$919$	−16.5780			−0.546856			−0.273428	−	0.961892i	$-0.588158\pi$
$919$	−16.5780			−0.546856			−0.273428	+	0.961892i	$0.588158\pi$
$920$	2.37684	−	4.11680i	0.0783620	−	0.135727i
$921$	23.7895	−	32.2394i	0.783892	−	1.06233i
$922$	−30.6562	−	53.0980i	−1.00961	−	1.74869i
$923$	6.15009	+	10.6523i	0.202433	+	0.350624i
$924$		0			0
$925$	2.07615	−	3.59600i	0.0682634	−	0.118236i
$926$	−8.45018			−0.277690
$927$	−19.4541	+	20.9736i	−0.638955	+	0.688865i
$928$	−13.4464			−0.441400
$929$	3.68190	−	6.37723i	0.120799	−	0.209230i	−0.799284	−	0.600954i	$-0.794788\pi$
$929$	3.68190	−	6.37723i	0.120799	−	0.209230i	0.920083	+	0.391723i	$0.128121\pi$
$930$	−12.1258	−	1.36520i	−0.397621	−	0.0447668i
$931$	−7.72586	−	13.3816i	−0.253205	−	0.438564i
$932$	−17.5536	−	30.4037i	−0.574987	−	0.995908i
$933$	35.1375	+	3.95601i	1.15035	+	0.129514i
$934$	−21.5376	+	37.3043i	−0.704733	+	1.22063i
$935$		0			0
$936$	−28.4027	+	30.6213i	−0.928372	+	1.00089i
$937$	−47.2573			−1.54383			−0.771914	−	0.635727i	$-0.780701\pi$
$937$	−47.2573			−1.54383			−0.771914	+	0.635727i	$0.780701\pi$
$938$	16.4650	−	28.5183i	0.537602	−	0.931154i
$939$	23.5814	+	54.0365i	0.769549	+	1.76342i
$940$	−4.04424	−	7.00482i	−0.131908	−	0.228472i
$941$	−28.0644	−	48.6089i	−0.914872	−	1.58460i	−0.807089	−	0.590430i	$-0.798958\pi$
$941$	−28.0644	−	48.6089i	−0.914872	−	1.58460i	−0.107783	−	0.994174i	$-0.534375\pi$
$942$	−4.83166	+	6.54784i	−0.157424	+	0.213340i
$943$	8.74628	−	15.1490i	0.284818	−	0.493319i
$944$	−10.5895			−0.344658
$945$	−2.20573	−	0.771186i	−0.0717525	−	0.0250867i
$946$		0			0
$947$	6.39323	−	11.0734i	0.207752	−	0.359837i	−0.743254	−	0.669009i	$-0.766719\pi$
$947$	6.39323	−	11.0734i	0.207752	−	0.359837i	0.951006	+	0.309172i	$0.100052\pi$
$948$	−11.9098	+	16.1400i	−0.386811	+	0.524204i
$949$	−8.90122	−	15.4174i	−0.288946	−	0.500469i
$950$	17.6747	+	30.6135i	0.573444	+	0.993234i
$951$	18.9960	+	43.5292i	0.615987	+	1.41153i
$952$	14.6903	−	25.4444i	0.476116	−	0.824657i
$953$	23.2974			0.754677			0.377338	−	0.926075i	$-0.376839\pi$
$953$	23.2974			0.754677			0.377338	+	0.926075i	$0.376839\pi$
$954$	−45.5255	−	10.3827i	−1.47394	−	0.336153i
$955$	−4.08573			−0.132211
$956$	−16.5067	+	28.5904i	−0.533864	+	0.924680i
$957$		0			0
$958$	0.182825	+	0.316662i	0.00590680	+	0.0102309i
$959$	−6.95581	−	12.0478i	−0.224615	−	0.389044i
$960$	6.79219	+	0.764710i	0.219217	+	0.0246809i
$961$	−30.0226	+	52.0007i	−0.968471	+	1.67744i
$962$	8.28418			0.267093
$963$	4.57648	+	14.8276i	0.147475	+	0.477813i
$964$	0.954445			0.0307406
$965$	3.66967	−	6.35605i	0.118131	−	0.204609i
$966$	−10.3460	−	23.7077i	−0.332876	−	0.762783i
$967$	−27.7586	−	48.0794i	−0.892657	−	1.54613i	−0.836677	−	0.547696i	$-0.815505\pi$
$967$	−27.7586	−	48.0794i	−0.892657	−	1.54613i	−0.0559798	−	0.998432i	$-0.517828\pi$
$968$		0			0
$969$	19.8932	−	26.9591i	0.639062	−	0.866052i
$970$	1.94089	−	3.36172i	0.0623182	−	0.107938i
$971$	−4.52027			−0.145063			−0.0725313	−	0.997366i	$-0.523108\pi$
$971$	−4.52027			−0.145063			−0.0725313	+	0.997366i	$0.523108\pi$
$972$	−47.1824	+	24.9623i	−1.51338	+	0.800667i
$973$	13.4429			0.430960
$974$	20.8754	−	36.1573i	0.668892	−	1.15855i
$975$	−21.1475	+	28.6590i	−0.677263	+	0.917823i
$976$	2.02599	+	3.50912i	0.0648503	+	0.112324i
$977$	13.5196	+	23.4167i	0.432532	+	0.749167i	0.997091	−	0.0762261i	$-0.0242871\pi$
$977$	13.5196	+	23.4167i	0.432532	+	0.749167i	−0.564559	+	0.825393i	$0.690954\pi$
$978$	−2.54994	−	5.84317i	−0.0815382	−	0.186844i
$979$		0			0
$980$	5.41462			0.172964
$981$	12.8083	+	41.4983i	0.408937	+	1.32494i
$982$	−15.4831			−0.494087
$983$	−5.31880	+	9.21243i	−0.169643	+	0.293831i	−0.938294	−	0.345837i	$-0.887595\pi$
$983$	−5.31880	+	9.21243i	−0.169643	+	0.293831i	0.768651	+	0.639668i	$0.220928\pi$
$984$	−22.0927	−	2.48734i	−0.704290	−	0.0792936i
$985$	−0.170820	−	0.295869i	−0.00544277	−	0.00942716i
$986$	−21.2939	−	36.8821i	−0.678136	−	1.17457i
$987$	−18.1914	−	2.04811i	−0.579040	−	0.0651921i
$988$	−22.2607	+	38.5567i	−0.708208	+	1.22665i
$989$	16.0614			0.510723
$990$		0			0
$991$	−18.7938			−0.597005			−0.298502	−	0.954409i	$-0.596487\pi$
$991$	−18.7938			−0.597005			−0.298502	+	0.954409i	$0.596487\pi$
$992$	21.9062	−	37.9427i	0.695523	−	1.20468i
$993$	12.4507	+	28.5308i	0.395112	+	0.905396i
$994$	4.84101	+	8.38487i	0.153547	+	0.265952i
$995$	2.60443	+	4.51101i	0.0825660	+	0.143009i
$996$	−47.4965	+	64.3669i	−1.50498	+	2.03954i
$997$	−13.0637	+	22.6270i	−0.413732	+	0.716605i	−0.995294	−	0.0968969i	$-0.969108\pi$
$997$	−13.0637	+	22.6270i	−0.413732	+	0.716605i	0.581562	+	0.813502i	$0.302442\pi$
$998$	−79.0634			−2.50271
$999$	4.15696	+	1.45339i	0.131520	+	0.0459832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.o.727.18		36
9.2	odd	6		9801.2.a.cn.1.18		18
9.4	even	3	inner	1089.2.e.o.364.18		36
9.7	even	3		9801.2.a.co.1.1		18
11.7	odd	10		99.2.m.b.16.1	✓	72
11.8	odd	10		99.2.m.b.97.9	yes	72
11.10	odd	2		1089.2.e.p.727.1		36
33.8	even	10		297.2.n.b.262.1		72
33.29	even	10		297.2.n.b.181.9		72
99.7	odd	30		891.2.f.f.82.9		36
99.29	even	30		891.2.f.e.82.1		36
99.40	odd	30		99.2.m.b.49.9	yes	72
99.41	even	30		297.2.n.b.64.9		72
99.43	odd	6		9801.2.a.cm.1.18		18
99.52	odd	30		891.2.f.f.163.9		36
99.65	even	6		9801.2.a.cp.1.1		18
99.74	even	30		891.2.f.e.163.1		36
99.76	odd	6		1089.2.e.p.364.1		36
99.85	odd	30		99.2.m.b.31.1	yes	72
99.95	even	30		297.2.n.b.280.1		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.1	✓	72	11.7	odd	10
99.2.m.b.31.1	yes	72	99.85	odd	30
99.2.m.b.49.9	yes	72	99.40	odd	30
99.2.m.b.97.9	yes	72	11.8	odd	10
297.2.n.b.64.9		72	99.41	even	30
297.2.n.b.181.9		72	33.29	even	10
297.2.n.b.262.1		72	33.8	even	10
297.2.n.b.280.1		72	99.95	even	30
891.2.f.e.82.1		36	99.29	even	30
891.2.f.e.163.1		36	99.74	even	30
891.2.f.f.82.9		36	99.7	odd	30
891.2.f.f.163.9		36	99.52	odd	30
1089.2.e.o.364.18		36	9.4	even	3	inner
1089.2.e.o.727.18		36	1.1	even	1	trivial
1089.2.e.p.364.1		36	99.76	odd	6
1089.2.e.p.727.1		36	11.10	odd	2
9801.2.a.cm.1.18		18	99.43	odd	6
9801.2.a.cn.1.18		18	9.2	odd	6
9801.2.a.co.1.1		18	9.7	even	3
9801.2.a.cp.1.1		18	99.65	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.16450 - 2.01697i) q^{2} +(-1.02841 + 1.39369i) q^{3} +(-1.71213 - 2.96549i) q^{4} +(0.158510 + 0.274547i) q^{5} +(1.61346 + 3.69723i) q^{6} +(-0.709246 + 1.22845i) q^{7} -3.31708 q^{8} +(-0.884754 - 2.86657i) q^{9} +0.738340 q^{10} +(5.89374 + 0.663556i) q^{12} +(2.09852 + 3.63474i) q^{13} +(1.65184 + 2.86106i) q^{14} +(-0.545647 - 0.0614326i) q^{15} +(-0.438496 + 0.759497i) q^{16} +6.24422 q^{17} +(-6.81209 - 1.55359i) q^{18} -3.09786 q^{19} +(0.542778 - 0.940119i) q^{20} +(-0.982687 - 2.25182i) q^{21} +(2.26025 + 3.91487i) q^{23} +(3.41131 - 4.62299i) q^{24} +(2.44975 - 4.24309i) q^{25} +9.77491 q^{26} +(4.90500 + 1.71493i) q^{27} +4.85727 q^{28} +(1.46422 - 2.53611i) q^{29} +(-0.759315 + 1.02902i) q^{30} +(4.77088 + 8.26341i) q^{31} +(-2.29583 - 3.97649i) q^{32} +(7.27140 - 12.5944i) q^{34} -0.449690 q^{35} +(-6.98596 + 7.53165i) q^{36} +0.847494 q^{37} +(-3.60746 + 6.24830i) q^{38} +(-7.22384 - 0.813308i) q^{39} +(-0.525791 - 0.910696i) q^{40} +(-1.93480 - 3.35118i) q^{41} +(-5.68620 - 0.640191i) q^{42} +(1.77651 - 3.07700i) q^{43} +(0.646766 - 0.697286i) q^{45} +10.5282 q^{46} +(3.72550 - 6.45275i) q^{47} +(-0.607552 - 1.39220i) q^{48} +(2.49394 + 4.31963i) q^{49} +(-5.70547 - 9.88217i) q^{50} +(-6.42160 + 8.70251i) q^{51} +(7.18585 - 12.4463i) q^{52} +6.68304 q^{53} +(9.17084 - 7.89623i) q^{54} +(2.35263 - 4.07487i) q^{56} +(3.18586 - 4.31746i) q^{57} +(-3.41018 - 5.90660i) q^{58} +(6.03739 + 10.4571i) q^{59} +(0.752039 + 1.72329i) q^{60} +(2.31016 - 4.00131i) q^{61} +22.2228 q^{62} +(4.14895 + 0.946226i) q^{63} -12.4479 q^{64} +(-0.665272 + 1.15229i) q^{65} +(-4.98385 - 8.63229i) q^{67} +(-10.6909 - 18.5172i) q^{68} +(-7.78058 - 0.875989i) q^{69} +(-0.523665 + 0.907014i) q^{70} +2.93068 q^{71} +(2.93480 + 9.50864i) q^{72} -4.24167 q^{73} +(0.986908 - 1.70938i) q^{74} +(3.39422 + 7.77782i) q^{75} +(5.30392 + 9.18665i) q^{76} +(-10.0526 + 13.6232i) q^{78} +(-1.69099 + 2.92889i) q^{79} -0.278024 q^{80} +(-7.43442 + 5.07241i) q^{81} -9.01233 q^{82} +(-6.74374 + 11.6805i) q^{83} +(-4.99526 + 6.76954i) q^{84} +(0.989771 + 1.71433i) q^{85} +(-4.13749 - 7.16635i) q^{86} +(2.02873 + 4.64883i) q^{87} +2.69745 q^{89} +(-0.653249 - 2.11650i) q^{90} -5.95347 q^{91} +(7.73966 - 13.4055i) q^{92} +(-16.4231 - 1.84902i) q^{93} +(-8.67670 - 15.0285i) q^{94} +(-0.491041 - 0.850508i) q^{95} +(7.90304 + 0.889777i) q^{96} +(2.62872 - 4.55308i) q^{97} +11.6168 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 2 q^{2} + 9 q^{3} - 12 q^{4} + q^{5} + q^{6} + q^{7} + 12 q^{8} - q^{9} + 4 q^{10} - 8 q^{12} + 3 q^{13} - 5 q^{15} + 8 q^{16} + 40 q^{17} - 17 q^{18} + 6 q^{19} + 5 q^{20} + 8 q^{21} + 10 q^{23}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - 2 * q^2 + 9 * q^3 - 12 * q^4 + q^5 + q^6 + q^7 + 12 * q^8 - q^9 + 4 * q^10 - 8 * q^12 + 3 * q^13 - 5 * q^15 + 8 * q^16 + 40 * q^17 - 17 * q^18 + 6 * q^19 + 5 * q^20 + 8 * q^21 + 10 * q^23 + 57 * q^24 - 7 * q^25 + 4 * q^26 - 9 * q^27 - 38 * q^28 - 21 * q^29 - 12 * q^30 - 6 * q^31 - 9 * q^32 + 4 * q^34 + 76 * q^35 - 65 * q^36 + 14 * q^37 - 13 * q^38 - 42 * q^39 - 20 * q^41 + 18 * q^42 + 4 * q^43 + 20 * q^45 - 16 * q^46 - 7 * q^47 + 10 * q^48 - 7 * q^49 - 25 * q^50 + 4 * q^51 - 19 * q^52 + 62 * q^53 - 17 * q^54 + 57 * q^56 + 18 * q^57 - 12 * q^58 + 12 * q^59 + 11 * q^60 - 16 * q^61 + 38 * q^62 - 5 * q^63 - 32 * q^64 - 42 * q^65 + 5 * q^67 - 51 * q^68 + 31 * q^69 - 8 * q^70 + 26 * q^71 - 51 * q^72 - 9 * q^74 - 16 * q^75 - 8 * q^76 - 32 * q^78 - 2 * q^79 + 92 * q^80 + 47 * q^81 - 68 * q^82 - 36 * q^83 - 60 * q^84 + 25 * q^85 - 26 * q^86 + 60 * q^87 - 28 * q^89 - 163 * q^90 - 30 * q^91 + 15 * q^92 - 39 * q^93 + 4 * q^94 - 64 * q^95 + 21 * q^96 + 16 * q^97 + 164 * q^98

Introduction

L-functions

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