LMFDB - Embedded newform 418.2.u.b.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 - 0.788011i) q^{2} +(-2.01318 + 1.94411i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(3.22722 - 2.01659i) q^{5} +(2.77142 + 0.389497i) q^{6} +(-3.27079 - 1.45625i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.168650 - 4.82951i) q^{9} +O(q^{10})$	\(q+(-0.615661 - 0.788011i) q^{2} +(-2.01318 + 1.94411i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(3.22722 - 2.01659i) q^{5} +(2.77142 + 0.389497i) q^{6} +(-3.27079 - 1.45625i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.168650 - 4.82951i) q^{9} +(-3.57597 - 1.30155i) q^{10} +(1.92925 + 2.69777i) q^{11} +(-1.39933 - 2.42370i) q^{12} +(-2.77299 + 1.47443i) q^{13} +(0.866159 + 3.47398i) q^{14} +(-2.57651 + 10.3338i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.201491 - 5.76995i) q^{17} +(-3.90954 + 2.84044i) q^{18} +(-3.65112 - 2.38104i) q^{19} +(1.17595 + 3.61921i) q^{20} +(9.41580 - 3.42707i) q^{21} +(0.938106 - 3.18119i) q^{22} +(6.86901 - 5.76378i) q^{23} +(-1.04839 + 2.59486i) q^{24} +(4.15645 - 8.52198i) q^{25} +(2.86909 + 1.27740i) q^{26} +(3.43157 + 3.81114i) q^{27} +(2.20427 - 2.82134i) q^{28} +(3.23360 - 0.927220i) q^{29} +(9.72942 - 4.33182i) q^{30} +(4.14805 - 4.60688i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-9.12870 - 1.68043i) q^{33} +(-4.42274 + 3.71112i) q^{34} +(-13.4922 + 1.89621i) q^{35} +(4.64525 + 1.33200i) q^{36} +(1.94310 - 1.41175i) q^{37} +(0.371571 + 4.34303i) q^{38} +(2.71609 - 8.35928i) q^{39} +(2.12799 - 3.15487i) q^{40} +(0.987917 - 0.954021i) q^{41} +(-8.49752 - 5.30984i) q^{42} +(2.73965 + 2.29884i) q^{43} +(-3.08437 + 1.21930i) q^{44} +(-9.19487 - 15.9260i) q^{45} +(-8.77091 - 1.86431i) q^{46} +(-0.0277000 - 0.0410670i) q^{47} +(2.69024 - 0.771413i) q^{48} +(3.89350 + 4.32417i) q^{49} +(-9.27438 + 1.97133i) q^{50} +(11.6230 + 11.2242i) q^{51} +(-0.759781 - 3.04732i) q^{52} +(-7.63591 - 4.77145i) q^{53} +(0.890536 - 5.05048i) q^{54} +(11.6664 + 4.81579i) q^{55} -3.58033 q^{56} +(11.9794 - 2.30471i) q^{57} +(-2.72146 - 1.97726i) q^{58} +(-1.88885 + 2.80033i) q^{59} +(-9.40355 - 4.99995i) q^{60} +(1.15184 + 2.85090i) q^{61} +(-6.18406 - 0.432432i) q^{62} +(-7.58459 + 15.5507i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-5.97574 + 10.3503i) q^{65} +(4.29599 + 8.22809i) q^{66} +(-7.81227 - 2.84344i) q^{67} +(5.64731 + 1.20037i) q^{68} +(-2.62315 + 24.9576i) q^{69} +(9.80087 + 9.46459i) q^{70} +(9.11934 - 5.69840i) q^{71} +(-1.81027 - 4.48057i) q^{72} +(-2.18357 - 4.47697i) q^{73} +(-2.30876 - 0.662027i) q^{74} +(8.19996 + 25.2369i) q^{75} +(3.19359 - 2.96664i) q^{76} +(-2.38156 - 11.6333i) q^{77} +(-8.25939 + 3.00617i) q^{78} +(-3.54486 + 0.498197i) q^{79} +(-3.79620 + 0.265456i) q^{80} +(0.144413 + 0.0100984i) q^{81} +(-1.36000 - 0.191136i) q^{82} +(-15.6420 + 3.32481i) q^{83} +(1.04738 + 9.96520i) q^{84} +(-12.2859 - 18.2146i) q^{85} +(0.124813 - 3.57418i) q^{86} +(-4.70721 + 8.15312i) q^{87} +(2.85974 + 1.67984i) q^{88} +(0.159616 + 0.905226i) q^{89} +(-6.88891 + 17.0507i) q^{90} +(11.2170 - 0.784369i) q^{91} +(3.93081 + 8.05936i) q^{92} +(0.605482 + 17.3387i) q^{93} +(-0.0153074 + 0.0471113i) q^{94} +(-16.5845 - 0.321316i) q^{95} +(-2.26416 - 1.64501i) q^{96} +(6.96182 + 8.91072i) q^{97} +(1.01041 - 5.73034i) q^{98} +(13.3543 - 8.86237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$3$	−2.01318	+	1.94411i	−1.16231	+	1.12243i	−0.171781	+	0.985135i	$0.554952\pi$
$3$	−2.01318	+	1.94411i	−1.16231	+	1.12243i	−0.990530	+	0.137295i	$0.956159\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	3.22722	−	2.01659i	1.44326	−	0.901846i	0.443271	−	0.896388i	$-0.353818\pi$
$5$	3.22722	−	2.01659i	1.44326	−	0.901846i	0.999985	−	0.00545855i	$-0.00173752\pi$
$6$	2.77142	+	0.389497i	1.13143	+	0.159012i
$7$	−3.27079	−	1.45625i	−1.23624	−	0.550411i	−0.318627	−	0.947880i	$-0.603222\pi$
$7$	−3.27079	−	1.45625i	−1.23624	−	0.550411i	−0.917615	+	0.397469i	$0.869889\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	0.168650	−	4.82951i	0.0562167	−	1.60984i
$10$	−3.57597	−	1.30155i	−1.13082	−	0.411585i
$11$	1.92925	+	2.69777i	0.581692	+	0.813409i
$11$	1.92925	+	2.69777i	0.581692	+	0.813409i
$12$	−1.39933	−	2.42370i	−0.403951	−	0.699663i
$13$	−2.77299	+	1.47443i	−0.769089	+	0.408932i	−0.807152	−	0.590343i	$-0.798992\pi$
$13$	−2.77299	+	1.47443i	−0.769089	+	0.408932i	0.0380630	+	0.999275i	$0.487881\pi$
$14$	0.866159	+	3.47398i	0.231491	+	0.928459i
$15$	−2.57651	+	10.3338i	−0.665252	+	2.66818i
$16$	−0.882948	−	0.469472i	−0.220737	−	0.117368i
$17$	−0.201491	−	5.76995i	−0.0488688	−	1.39942i	−0.738009	−	0.674791i	$-0.764234\pi$
$17$	−0.201491	−	5.76995i	−0.0488688	−	1.39942i	0.689140	−	0.724628i	$-0.257989\pi$
$18$	−3.90954	+	2.84044i	−0.921486	+	0.669499i
$19$	−3.65112	−	2.38104i	−0.837624	−	0.546247i
$19$	−3.65112	−	2.38104i	−0.837624	−	0.546247i
$20$	1.17595	+	3.61921i	0.262951	+	0.809281i
$21$	9.41580	−	3.42707i	2.05470	−	0.747848i
$22$	0.938106	−	3.18119i	0.200005	−	0.678232i
$23$	6.86901	−	5.76378i	1.43229	−	1.20183i	0.487943	−	0.872876i	$-0.337748\pi$
$23$	6.86901	−	5.76378i	1.43229	−	1.20183i	0.944345	−	0.328956i	$-0.106697\pi$
$24$	−1.04839	+	2.59486i	−0.214002	+	0.529675i
$25$	4.15645	−	8.52198i	0.831289	−	1.70440i
$26$	2.86909	+	1.27740i	0.562674	+	0.250519i
$27$	3.43157	+	3.81114i	0.660405	+	0.733454i
$28$	2.20427	−	2.82134i	0.416568	−	0.533182i
$29$	3.23360	−	0.927220i	0.600464	−	0.172180i	0.0383840	−	0.999263i	$-0.487779\pi$
$29$	3.23360	−	0.927220i	0.600464	−	0.172180i	0.562080	+	0.827083i	$0.310001\pi$
$30$	9.72942	−	4.33182i	1.77634	−	0.790878i
$31$	4.14805	−	4.60688i	0.745012	−	0.827419i	−0.244834	−	0.969565i	$-0.578733\pi$
$31$	4.14805	−	4.60688i	0.745012	−	0.827419i	0.989846	+	0.142146i	$0.0454001\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−9.12870	−	1.68043i	−1.58910	−	0.292525i
$34$	−4.42274	+	3.71112i	−0.758493	+	0.636451i
$35$	−13.4922	+	1.89621i	−2.28060	+	0.320518i
$36$	4.64525	+	1.33200i	0.774208	+	0.222001i
$37$	1.94310	−	1.41175i	0.319444	−	0.232090i	−0.416494	−	0.909138i	$-0.636741\pi$
$37$	1.94310	−	1.41175i	0.319444	−	0.232090i	0.735938	+	0.677049i	$0.236741\pi$
$38$	0.371571	+	4.34303i	0.0602767	+	0.704533i
$39$	2.71609	−	8.35928i	0.434923	−	1.33856i
$40$	2.12799	−	3.15487i	0.336465	−	0.498829i
$41$	0.987917	−	0.954021i	0.154287	−	0.148993i	−0.613509	−	0.789688i	$-0.710243\pi$
$41$	0.987917	−	0.954021i	0.154287	−	0.148993i	0.767796	+	0.640695i	$0.221354\pi$
$42$	−8.49752	−	5.30984i	−1.31120	−	0.819326i
$43$	2.73965	+	2.29884i	0.417793	+	0.350570i	0.827323	−	0.561727i	$-0.189863\pi$
$43$	2.73965	+	2.29884i	0.417793	+	0.350570i	−0.409530	+	0.912297i	$0.634307\pi$
$44$	−3.08437	+	1.21930i	−0.464986	+	0.183816i
$45$	−9.19487	−	15.9260i	−1.37069	−	2.37410i
$46$	−8.77091	−	1.86431i	−1.29320	−	0.274878i
$47$	−0.0277000	−	0.0410670i	−0.00404046	−	0.00599023i	0.827012	−	0.562184i	$-0.190039\pi$
$47$	−0.0277000	−	0.0410670i	−0.00404046	−	0.00599023i	−0.831052	+	0.556194i	$0.812261\pi$
$48$	2.69024	−	0.771413i	0.388302	−	0.111344i
$49$	3.89350	+	4.32417i	0.556214	+	0.617738i
$50$	−9.27438	+	1.97133i	−1.31159	+	0.278788i
$51$	11.6230	+	11.2242i	1.62755	+	1.57171i
$52$	−0.759781	−	3.04732i	−0.105363	−	0.422587i
$53$	−7.63591	−	4.77145i	−1.04887	−	0.655409i	−0.107994	−	0.994152i	$-0.534443\pi$
$53$	−7.63591	−	4.77145i	−1.04887	−	0.655409i	−0.940879	+	0.338743i	$0.889998\pi$
$54$	0.890536	−	5.05048i	0.121187	−	0.687284i
$55$	11.6664	+	4.81579i	1.57310	+	0.649360i
$56$	−3.58033			−0.478441
$57$	11.9794	−	2.30471i	1.58670	−	0.305266i
$58$	−2.72146	−	1.97726i	−0.357345	−	0.259627i
$59$	−1.88885	+	2.80033i	−0.245907	+	0.364572i	−0.931703	−	0.363222i	$-0.881677\pi$
$59$	−1.88885	+	2.80033i	−0.245907	+	0.364572i	0.685796	+	0.727794i	$0.259454\pi$
$60$	−9.40355	−	4.99995i	−1.21399	−	0.645491i
$61$	1.15184	+	2.85090i	0.147478	+	0.365020i	0.982782	−	0.184767i	$-0.0591531\pi$
$61$	1.15184	+	2.85090i	0.147478	+	0.365020i	−0.835305	+	0.549787i	$0.814709\pi$
$62$	−6.18406	−	0.432432i	−0.785377	−	0.0549189i
$63$	−7.58459	+	15.5507i	−0.955569	+	1.95921i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	−5.97574	+	10.3503i	−0.741199	+	1.28379i
$66$	4.29599	+	8.22809i	0.528800	+	1.01281i
$67$	−7.81227	−	2.84344i	−0.954421	−	0.347381i	−0.182576	−	0.983192i	$-0.558444\pi$
$67$	−7.81227	−	2.84344i	−0.954421	−	0.347381i	−0.771845	+	0.635811i	$0.780666\pi$
$68$	5.64731	+	1.20037i	0.684837	+	0.145566i
$69$	−2.62315	+	24.9576i	−0.315791	+	3.00455i
$70$	9.80087	+	9.46459i	1.17143	+	1.13123i
$71$	9.11934	−	5.69840i	1.08227	−	0.676276i	0.133117	−	0.991100i	$-0.457501\pi$
$71$	9.11934	−	5.69840i	1.08227	−	0.676276i	0.949150	+	0.314825i	$0.101946\pi$
$72$	−1.81027	−	4.48057i	−0.213342	−	0.528040i
$73$	−2.18357	−	4.47697i	−0.255567	−	0.523990i	0.731978	−	0.681329i	$-0.238598\pi$
$73$	−2.18357	−	4.47697i	−0.255567	−	0.523990i	−0.987545	+	0.157338i	$0.949709\pi$
$74$	−2.30876	−	0.662027i	−0.268388	−	0.0769591i
$75$	8.19996	+	25.2369i	0.946849	+	2.91410i
$76$	3.19359	−	2.96664i	0.366330	−	0.340297i
$77$	−2.38156	−	11.6333i	−0.271404	−	1.32574i
$78$	−8.25939	+	3.00617i	−0.935192	+	0.340382i
$79$	−3.54486	+	0.498197i	−0.398828	+	0.0560516i	−0.335736	−	0.941956i	$-0.608985\pi$
$79$	−3.54486	+	0.498197i	−0.398828	+	0.0560516i	−0.0630917	+	0.998008i	$0.520096\pi$
$80$	−3.79620	+	0.265456i	−0.424428	+	0.0296789i
$81$	0.144413	+	0.0100984i	0.0160459	+	0.00112204i
$82$	−1.36000	−	0.191136i	−0.150187	−	0.0211074i
$83$	−15.6420	+	3.32481i	−1.71693	+	0.364945i	−0.958120	−	0.286366i	$-0.907553\pi$
$83$	−15.6420	+	3.32481i	−1.71693	+	0.364945i	−0.758811	+	0.651311i	$0.774219\pi$
$84$	1.04738	+	9.96520i	0.114279	+	1.08729i
$85$	−12.2859	−	18.2146i	−1.33259	−	1.97565i
$86$	0.124813	−	3.57418i	0.0134590	−	0.385414i
$87$	−4.70721	+	8.15312i	−0.504666	+	0.874107i
$88$	2.85974	+	1.67984i	0.304850	+	0.179071i
$89$	0.159616	+	0.905226i	0.0169192	+	0.0959538i	0.992098	−	0.125465i	$-0.0400423\pi$
$89$	0.159616	+	0.905226i	0.0169192	+	0.0959538i	−0.975179	+	0.221419i	$0.928931\pi$
$90$	−6.88891	+	17.0507i	−0.726155	+	1.79730i
$91$	11.2170	−	0.784369i	1.17586	−	0.0822243i
$92$	3.93081	+	8.05936i	0.409815	+	0.840246i
$93$	0.605482	+	17.3387i	0.0627855	+	1.79794i
$94$	−0.0153074	+	0.0471113i	−0.00157884	+	0.00485916i
$95$	−16.5845	−	0.321316i	−1.70154	−	0.0329663i
$96$	−2.26416	−	1.64501i	−0.231085	−	0.167893i
$97$	6.96182	+	8.91072i	0.706865	+	0.904747i	0.998661	−	0.0517342i	$-0.0164749\pi$
$97$	6.96182	+	8.91072i	0.706865	+	0.904747i	−0.291795	+	0.956481i	$0.594253\pi$
$98$	1.01041	−	5.73034i	0.102067	−	0.578852i
$99$	13.3543	−	8.86237i	1.34216	−	0.890702i
$100$	7.26330	+	6.09464i	0.726330	+	0.609464i
$101$	−0.254994	+	0.135583i	−0.0253729	+	0.0134910i	−0.482110	−	0.876111i	$-0.660129\pi$
$101$	−0.254994	+	0.135583i	−0.0253729	+	0.0134910i	0.456737	+	0.889602i	$0.349018\pi$
$102$	1.68896	−	16.0694i	0.167232	−	1.59111i
$103$	−1.15090	−	10.9501i	−0.113402	−	1.07894i	−0.892191	−	0.451659i	$-0.850832\pi$
$103$	−1.15090	−	10.9501i	−0.113402	−	1.07894i	0.778789	−	0.627286i	$-0.215834\pi$
$104$	−1.93355	+	2.47483i	−0.189600	+	0.242677i
$105$	23.4759	−	30.0477i	2.29101	−	2.93236i
$106$	0.941185	+	8.95477i	0.0914159	+	0.869765i
$107$	−0.629327	+	5.98764i	−0.0608393	+	0.578847i	0.921057	+	0.389428i	$0.127327\pi$
$107$	−0.629327	+	5.98764i	−0.0608393	+	0.578847i	−0.981896	+	0.189419i	$0.939339\pi$
$108$	−4.52810	+	2.40764i	−0.435717	+	0.231675i
$109$	11.4893	+	9.64066i	1.10047	+	0.923408i	0.997457	−	0.0712715i	$-0.0227057\pi$
$109$	11.4893	+	9.64066i	1.10047	+	0.923408i	0.103018	+	0.994680i	$0.467150\pi$
$110$	−3.38768	−	12.1582i	−0.323002	−	1.15924i
$111$	−1.16723	+	6.61970i	−0.110789	+	0.628314i
$112$	2.20427	+	2.82134i	0.208284	+	0.266591i
$113$	−1.32523	−	0.962838i	−0.124667	−	0.0905762i	0.523704	−	0.851900i	$-0.324550\pi$
$113$	−1.32523	−	0.962838i	−0.124667	−	0.0905762i	−0.648372	+	0.761324i	$0.724550\pi$
$114$	−9.19136	−	8.02094i	−0.860850	−	0.751230i
$115$	10.5446	−	32.4530i	0.983290	−	3.02625i
$116$	0.117399	+	3.36186i	0.0109002	+	0.312141i
$117$	6.65308	+	13.6408i	0.615078	+	1.26110i
$118$	3.36958	−	0.235624i	0.310195	−	0.0216910i
$119$	−7.74346	+	19.1657i	−0.709842	+	1.75692i
$120$	1.84938	+	10.4884i	0.168825	+	0.957453i
$121$	−3.55595	+	10.4094i	−0.323268	+	0.946307i
$122$	1.53740	−	2.66285i	0.139189	−	0.241083i
$123$	−0.134139	+	3.84123i	−0.0120949	+	0.346352i
$124$	3.46653	+	5.13934i	0.311303	+	0.461526i
$125$	−1.78268	−	16.9610i	−0.159447	−	1.51704i
$126$	16.9237	−	3.59724i	1.50768	−	0.320467i
$127$	−3.26116	−	0.458326i	−0.289381	−	0.0406699i	−0.00701116	−	0.999975i	$-0.502232\pi$
$127$	−3.26116	−	0.458326i	−0.289381	−	0.0406699i	−0.282370	+	0.959306i	$0.591121\pi$
$128$	−0.997564	−	0.0697565i	−0.0881730	−	0.00616566i
$129$	−9.98461	+	0.698192i	−0.879096	+	0.0614723i
$130$	11.8352	−	1.66332i	1.03801	−	0.145883i
$131$	3.85192	−	1.40198i	0.336544	−	0.122492i	−0.168220	−	0.985749i	$-0.553802\pi$
$131$	3.85192	−	1.40198i	0.336544	−	0.122492i	0.504764	+	0.863258i	$0.331580\pi$
$132$	3.83894	−	8.45100i	0.334137	−	0.735566i
$133$	8.47466	+	13.1048i	0.734846	+	1.13633i
$134$	2.56906	+	7.90675i	0.221933	+	0.683039i
$135$	18.7599	+	5.37932i	1.61460	+	0.462978i
$136$	−2.53092	−	5.18916i	−0.217025	−	0.444967i
$137$	−2.00488	−	4.96224i	−0.171288	−	0.423953i	0.816983	−	0.576661i	$-0.195645\pi$
$137$	−2.00488	−	4.96224i	−0.171288	−	0.423953i	−0.988271	+	0.152709i	$0.951200\pi$
$138$	21.2819	−	13.2984i	1.81163	−	1.13203i
$139$	−11.5488	−	11.1525i	−0.979554	−	0.945944i	0.0189937	−	0.999820i	$-0.493954\pi$
$139$	−11.5488	−	11.1525i	−0.979554	−	0.945944i	−0.998548	+	0.0538753i	$0.982843\pi$
$140$	1.42418	−	13.5502i	0.120365	−	1.14520i
$141$	0.135604	+	0.0288235i	0.0114199	+	0.00242737i
$142$	−10.1048	−	3.67786i	−0.847978	−	0.308639i
$143$	−9.32747	−	4.63636i	−0.780002	−	0.387712i
$144$	−2.41623	+	4.18503i	−0.201352	+	0.348752i
$145$	8.56571	−	9.51318i	0.711343	−	0.790027i
$146$	−2.18357	+	4.47697i	−0.180713	+	0.370517i
$147$	−16.2450	−	1.13596i	−1.33986	−	0.0936922i
$148$	0.899732	+	2.22692i	0.0739575	+	0.183051i
$149$	3.52815	+	1.87595i	0.289037	+	0.153684i	0.607659	−	0.794198i	$-0.292109\pi$
$149$	3.52815	+	1.87595i	0.289037	+	0.153684i	−0.318622	+	0.947882i	$0.603220\pi$
$150$	14.8385	−	21.9990i	1.21156	−	1.79621i
$151$	−2.26170	−	1.64322i	−0.184054	−	0.133723i	0.491943	−	0.870627i	$-0.336287\pi$
$151$	−2.26170	−	1.64322i	−0.184054	−	0.133723i	−0.675997	+	0.736904i	$0.736287\pi$
$152$	−4.30392	−	0.690141i	−0.349094	−	0.0559779i
$153$	−27.9000			−2.25558
$154$	−7.70095	+	9.03888i	−0.620561	+	0.728374i
$155$	4.09648	−	23.2323i	0.329037	−	1.86606i
$156$	7.45389	+	4.65771i	0.596789	+	0.372915i
$157$	3.20293	+	12.8463i	0.255622	+	1.02524i	0.951639	+	0.307218i	$0.0993982\pi$
$157$	3.20293	+	12.8463i	0.255622	+	1.02524i	−0.696017	+	0.718025i	$0.745046\pi$
$158$	2.57502	+	2.48666i	0.204857	+	0.197828i
$159$	24.6487	−	5.23924i	1.95477	−	0.415499i
$160$	2.54635	+	2.82801i	0.201307	+	0.223574i
$161$	−30.8606	+	8.84914i	−2.43216	+	0.697410i
$162$	−0.0809520	−	0.120016i	−0.00636019	−	0.00942937i
$163$	8.42677	+	1.79117i	0.660036	+	0.140295i	0.525739	−	0.850646i	$-0.323789\pi$
$163$	8.42677	+	1.79117i	0.660036	+	0.140295i	0.134297	+	0.990941i	$0.457122\pi$
$164$	0.686683	+	1.18937i	0.0536210	+	0.0928742i
$165$	−32.8490	+	12.9857i	−2.55729	+	1.01094i
$166$	12.2502	+	10.2791i	0.950796	+	0.797813i
$167$	−0.916032	−	0.572400i	−0.0708846	−	0.0442936i	0.494014	−	0.869454i	$-0.335529\pi$
$167$	−0.916032	−	0.572400i	−0.0708846	−	0.0442936i	−0.564899	+	0.825160i	$0.691085\pi$
$168$	7.20785	−	6.96054i	0.556098	−	0.537017i
$169$	−1.75396	+	2.60035i	−0.134920	+	0.200027i
$170$	−6.78933	+	20.8954i	−0.520718	+	1.60261i
$171$	−12.1150	+	17.2315i	−0.926457	+	1.31773i
$172$	−2.89334	+	2.10213i	−0.220615	+	0.160286i
$173$	12.5742	+	3.60560i	0.956001	+	0.274129i	0.717143	−	0.696926i	$-0.245449\pi$
$173$	12.5742	+	3.60560i	0.956001	+	0.274129i	0.238857	+	0.971055i	$0.423227\pi$
$174$	9.32280	−	1.31023i	0.706759	−	0.0993285i
$175$	−26.0050	+	21.8208i	−1.96579	+	1.64950i
$176$	−0.436903	−	3.28772i	−0.0329328	−	0.247821i
$177$	−1.64155	−	9.30970i	−0.123387	−	0.699760i
$178$	0.615059	−	0.683092i	0.0461006	−	0.0511999i
$179$	−12.7124	+	5.65993i	−0.950170	+	0.423043i	−0.822495	−	0.568773i	$-0.807418\pi$
$179$	−12.7124	+	5.65993i	−0.950170	+	0.423043i	−0.127676	+	0.991816i	$0.540752\pi$
$180$	17.6773	−	5.06890i	1.31759	−	0.377813i
$181$	−11.5641	+	14.8014i	−0.859553	+	1.10018i	0.134460	+	0.990919i	$0.457070\pi$
$181$	−11.5641	+	14.8014i	−0.859553	+	1.10018i	−0.994013	+	0.109259i	$0.965152\pi$
$182$	−7.52397	−	8.35622i	−0.557714	−	0.619404i
$183$	−7.86131	−	3.50008i	−0.581125	−	0.258733i
$184$	3.93081	−	8.05936i	0.289783	−	0.594144i
$185$	3.42390	−	8.47445i	0.251730	−	0.623054i
$186$	13.2903	−	11.1519i	0.974495	−	0.817698i
$187$	15.1773	−	11.6753i	1.10987	−	0.853782i
$188$	0.0465484	−	0.0169422i	0.00339489	−	0.00123564i
$189$	−5.67396	−	17.4627i	−0.412720	−	1.27022i
$190$	9.95726	+	13.2666i	0.722375	+	0.962461i
$191$	−10.7507	+	7.81087i	−0.777897	+	0.565175i	−0.904347	−	0.426798i	$-0.859642\pi$
$191$	−10.7507	+	7.81087i	−0.777897	+	0.565175i	0.126450	+	0.991973i	$0.459642\pi$
$192$	0.0976715	+	2.79695i	0.00704884	+	0.201852i
$193$	9.58887	+	5.09849i	0.690222	+	0.366997i	0.777236	−	0.629210i	$-0.216621\pi$
$193$	9.58887	+	5.09849i	0.690222	+	0.366997i	−0.0870138	+	0.996207i	$0.527732\pi$
$194$	2.73562	−	10.9720i	0.196406	−	0.787742i
$195$	−8.09180	−	32.4545i	−0.579466	−	2.32411i
$196$	−5.13764	+	2.73173i	−0.366974	+	0.195124i
$197$	3.31386	+	5.73977i	0.236103	+	0.408942i	0.959593	−	0.281393i	$-0.0907965\pi$
$197$	3.31386	+	5.73977i	0.236103	+	0.408942i	−0.723490	+	0.690335i	$0.757463\pi$
$198$	−15.2054	−	5.06710i	−1.08060	−	0.360103i
$199$	−3.75025	−	1.36498i	−0.265848	−	0.0967607i	0.205657	−	0.978624i	$-0.434067\pi$
$199$	−3.75025	−	1.36498i	−0.265848	−	0.0967607i	−0.471505	+	0.881863i	$0.656289\pi$
$200$	0.330902	−	9.47580i	0.0233983	−	0.670040i
$201$	21.2555	−	9.46354i	1.49925	−	0.667507i
$202$	0.263831	+	0.117465i	0.0185631	+	0.00826482i
$203$	−11.9267	−	1.67619i	−0.837090	−	0.117645i
$204$	−13.7027	+	8.56240i	−0.959381	+	0.599488i
$205$	1.26436	−	5.07106i	0.0883065	−	0.354178i
$206$	−7.92023	+	7.64847i	−0.551828	+	0.532894i
$207$	−26.6778	−	34.1460i	−1.85423	−	2.37331i
$208$	3.14061			0.217762
$209$	−0.620443	−	14.4435i	−0.0429169	−	0.999079i
$210$	−38.1311			−2.63130
$211$	3.48343	+	4.45859i	0.239809	+	0.306942i	0.892826	−	0.450401i	$-0.148719\pi$
$211$	3.48343	+	4.45859i	0.239809	+	0.306942i	−0.653017	+	0.757343i	$0.726497\pi$
$212$	6.47701	−	6.25477i	0.444843	−	0.429580i
$213$	−7.28060	+	29.2009i	−0.498858	+	2.00081i
$214$	5.10578	−	3.19045i	0.349024	−	0.218094i
$215$	13.4773	+	1.89411i	0.919142	+	0.129177i
$216$	4.68502	+	2.08591i	0.318775	+	0.141928i
$217$	−20.2762	+	9.02753i	−1.37644	+	0.612829i
$218$	0.523430	−	14.9891i	0.0354511	−	1.01519i
$219$	13.0996	+	4.76788i	0.885191	+	0.322183i
$220$	−7.49510	+	10.1548i	−0.505320	+	0.684639i
$221$	9.06610	+	15.7029i	0.609852	+	1.05629i
$222$	5.93501	−	3.15570i	0.398332	−	0.211797i
$223$	2.25350	+	9.03829i	0.150905	+	0.605249i	0.997349	+	0.0727699i	$0.0231839\pi$
$223$	2.25350	+	9.03829i	0.150905	+	0.605249i	−0.846443	+	0.532479i	$0.821261\pi$
$224$	0.866159	−	3.47398i	0.0578727	−	0.232115i
$225$	−40.4560	−	21.5108i	−2.69707	−	1.43406i
$226$	0.0571681	+	1.63708i	0.00380277	+	0.108897i
$227$	17.5777	−	12.7709i	1.16667	−	0.847636i	0.176065	−	0.984379i	$-0.443663\pi$
$227$	17.5777	−	12.7709i	1.16667	−	0.847636i	0.990607	+	0.136742i	$0.0436632\pi$
$228$	−0.661822	+	12.1811i	−0.0438302	+	0.806711i
$229$	−3.23265	−	9.94907i	−0.213619	−	0.657453i	−0.999249	−	0.0387555i	$-0.987661\pi$
$229$	−3.23265	−	9.94907i	−0.213619	−	0.657453i	0.785629	−	0.618698i	$-0.212339\pi$
$230$	−32.0652	+	11.6708i	−2.11432	+	0.769548i
$231$	27.4109	+	18.7900i	1.80351	+	1.23629i
$232$	2.57691	−	2.16228i	0.169182	−	0.141961i
$233$	3.84697	−	9.52160i	0.252024	−	0.623780i	−0.747140	−	0.664667i	$-0.768574\pi$
$233$	3.84697	−	9.52160i	0.252024	−	0.623780i	0.999164	+	0.0408861i	$0.0130181\pi$
$234$	6.65308	−	13.6408i	0.434926	−	0.891730i
$235$	−0.172209	−	0.0766725i	−0.0112337	−	0.00500156i
$236$	−2.26020	−	2.51020i	−0.147126	−	0.163400i
$237$	6.16789	−	7.89454i	0.400648	−	0.512806i
$238$	19.8702	−	5.69768i	1.28799	−	0.369325i
$239$	21.5541	−	9.59648i	1.39422	−	0.620745i	0.434232	−	0.900801i	$-0.357020\pi$
$239$	21.5541	−	9.59648i	1.39422	−	0.620745i	0.959984	+	0.280056i	$0.0903530\pi$
$240$	7.12636	−	7.91462i	0.460004	−	0.510887i
$241$	−4.86513	−	27.5915i	−0.313390	−	1.77733i	−0.581106	−	0.813828i	$-0.697380\pi$
$241$	−4.86513	−	27.5915i	−0.313390	−	1.77733i	0.267716	−	0.963498i	$-0.413731\pi$
$242$	10.3920	−	3.60653i	0.668021	−	0.231836i
$243$	−12.0961	+	10.1498i	−0.775965	+	0.651112i
$244$	−3.04487	+	0.427929i	−0.194928	+	0.0273953i
$245$	21.2852	+	6.10344i	1.35986	+	0.389935i
$246$	3.10952	−	2.25920i	0.198256	−	0.144041i
$247$	13.6352	+	1.21929i	0.867586	+	0.0775816i
$248$	1.91565	−	5.89575i	0.121644	−	0.374381i
$249$	25.0264	−	37.1031i	1.58598	−	2.35132i
$250$	−12.2680	+	11.8470i	−0.775894	+	0.749272i
$251$	24.9749	+	15.6060i	1.57640	+	0.985045i	0.983741	+	0.179592i	$0.0574778\pi$
$251$	24.9749	+	15.6060i	1.57640	+	0.985045i	0.592660	+	0.805453i	$0.298078\pi$
$252$	−13.2539	−	11.1214i	−0.834918	−	0.700579i
$253$	28.8014	+	7.41122i	1.81073	+	0.465939i
$254$	1.64661	+	2.85200i	0.103317	+	0.178951i
$255$	60.1448	+	12.7842i	3.76641	+	0.800576i
$256$	0.559193	+	0.829038i	0.0349496	+	0.0518148i
$257$	−16.5426	+	4.74352i	−1.03190	+	0.295892i	−0.748518	−	0.663115i	$-0.769234\pi$
$257$	−16.5426	+	4.74352i	−1.03190	+	0.295892i	−0.283382	+	0.959007i	$0.591456\pi$
$258$	6.69732	+	7.43813i	0.416957	+	0.463078i
$259$	−8.41133	+	1.78788i	−0.522655	+	0.111094i
$260$	−8.59717	−	8.30219i	−0.533174	−	0.514880i
$261$	−3.93267	−	15.7731i	−0.243426	−	0.976328i
$262$	−3.47625	−	2.17221i	−0.214764	−	0.134199i
$263$	−3.09326	+	17.5428i	−0.190739	+	1.08173i	0.727619	+	0.685982i	$0.240627\pi$
$263$	−3.09326	+	17.5428i	−0.190739	+	1.08173i	−0.918358	+	0.395751i	$0.870484\pi$
$264$	−9.02297	+	2.17783i	−0.555326	+	0.134036i
$265$	−34.2648			−2.10487
$266$	5.10921	−	14.7463i	0.313266	−	0.904151i
$267$	−2.08119	−	1.51208i	−0.127367	−	0.0925375i
$268$	4.64893	−	6.89233i	0.283979	−	0.421016i
$269$	2.91462	+	1.54973i	0.177708	+	0.0944888i	0.555942	−	0.831221i	$-0.312358\pi$
$269$	2.91462	+	1.54973i	0.177708	+	0.0944888i	−0.378235	+	0.925710i	$0.623469\pi$
$270$	−7.31080	−	18.0949i	−0.444921	−	1.10122i
$271$	15.7545	+	1.10166i	0.957018	+	0.0669212i	0.539716	−	0.841847i	$-0.318532\pi$
$271$	15.7545	+	1.10166i	0.957018	+	0.0669212i	0.417301	+	0.908768i	$0.362976\pi$
$272$	−2.53092	+	5.18916i	−0.153460	+	0.314639i
$273$	−21.0570	+	23.3861i	−1.27443	+	1.41539i
$274$	−2.67597	+	4.63492i	−0.161662	+	0.280006i
$275$	31.0092	−	5.22792i	1.86993	−	0.315255i
$276$	−23.5817	−	8.58303i	−1.41945	−	0.516638i
$277$	8.55801	+	1.81906i	0.514201	+	0.109297i	0.457702	−	0.889106i	$-0.348673\pi$
$277$	8.55801	+	1.81906i	0.514201	+	0.109297i	0.0564992	+	0.998403i	$0.482006\pi$
$278$	−1.67817	+	15.9667i	−0.100650	+	0.957621i
$279$	−21.5494	−	20.8100i	−1.29013	−	1.24586i
$280$	−11.5545	+	7.22005i	−0.690513	+	0.431481i
$281$	−1.29056	−	3.19426i	−0.0769886	−	0.190554i	0.883781	−	0.467900i	$-0.154989\pi$
$281$	−1.29056	−	3.19426i	−0.0769886	−	0.190554i	−0.960770	+	0.277347i	$0.910545\pi$
$282$	−0.0607728	−	0.124603i	−0.00361897	−	0.00741999i
$283$	2.77436	+	0.795536i	0.164919	+	0.0472897i	0.357081	−	0.934074i	$-0.383772\pi$
$283$	2.77436	+	0.795536i	0.164919	+	0.0472897i	−0.192162	+	0.981363i	$0.561550\pi$
$284$	3.32296	+	10.2270i	0.197182	+	0.606862i
$285$	34.0123	−	31.5952i	2.01472	−	1.87154i
$286$	2.08907	+	10.2046i	0.123529	+	0.603409i
$287$	−4.62056	+	1.68175i	−0.272743	+	0.0992704i
$288$	4.78542	−	0.672547i	0.281984	−	0.0396302i
$289$	−16.2932	+	1.13933i	−0.958422	+	0.0670194i
$290$	−12.7701	−	0.892970i	−0.749884	−	0.0524370i
$291$	−31.3388	−	4.40438i	−1.83711	−	0.258189i
$292$	4.87224	−	1.03563i	0.285126	−	0.0606055i
$293$	−0.760985	−	7.24028i	−0.0444572	−	0.422982i	−0.994003	−	0.109353i	$-0.965122\pi$
$293$	−0.760985	−	7.24028i	−0.0444572	−	0.422982i	0.949546	−	0.313629i	$-0.101545\pi$
$294$	9.10625	+	13.5006i	0.531087	+	0.787369i
$295$	−0.448603	+	12.8463i	−0.0261187	+	0.747941i
$296$	1.20090	−	2.08002i	0.0698011	−	0.120899i
$297$	−3.66122	+	16.6102i	−0.212446	+	0.963824i
$298$	−0.693876	−	3.93517i	−0.0401952	−	0.227958i
$299$	−10.5494	+	26.1108i	−0.610089	+	1.51002i
$300$	−26.4710	+	1.85103i	−1.52830	+	0.106869i
$301$	−5.61314	−	11.5086i	−0.323536	−	0.663347i
$302$	0.0975655	+	2.79391i	0.00561426	+	0.160771i
$303$	0.249762	−	0.768690i	0.0143485	−	0.0441601i
$304$	2.10592	+	3.81643i	0.120783	+	0.218887i
$305$	9.46633	+	6.87769i	0.542040	+	0.393815i
$306$	17.1770	+	21.9855i	0.981942	+	1.25683i
$307$	3.96713	−	22.4987i	0.226416	−	1.28407i	−0.633543	−	0.773708i	$-0.718400\pi$
$307$	3.96713	−	22.4987i	0.226416	−	1.28407i	0.859959	−	0.510363i	$-0.170489\pi$
$308$	11.8639	+	0.503541i	0.676010	+	0.0286919i
$309$	23.6051	+	19.8071i	1.34285	+	1.12678i
$310$	−20.8294	+	11.0752i	−1.18303	+	0.629027i
$311$	1.44599	−	13.7577i	0.0819946	−	0.780127i	−0.873838	−	0.486216i	$-0.838377\pi$
$311$	1.44599	−	13.7577i	0.0819946	−	0.780127i	0.955833	−	0.293910i	$-0.0949567\pi$
$312$	−0.918749	−	8.74131i	−0.0520139	−	0.494879i
$313$	14.6720	−	18.7792i	0.829308	−	1.06147i	−0.167827	−	0.985817i	$-0.553675\pi$
$313$	14.6720	−	18.7792i	0.829308	−	1.06147i	0.997135	−	0.0756490i	$-0.0241029\pi$
$314$	8.15107	−	10.4329i	0.459992	−	0.588762i
$315$	6.88228	+	65.4806i	0.387773	+	3.68941i
$316$	0.374180	−	3.56008i	0.0210493	−	0.200270i
$317$	−11.7705	+	6.25849i	−0.661098	+	0.351512i	−0.765880	−	0.642983i	$-0.777696\pi$
$317$	−11.7705	+	6.25849i	−0.661098	+	0.351512i	0.104782	+	0.994495i	$0.466585\pi$
$318$	−19.3038	−	16.1978i	−1.08250	−	0.908329i
$319$	8.73986	+	6.93467i	0.489338	+	0.388267i
$320$	0.660812	−	3.74765i	0.0369405	−	0.209500i
$321$	−10.3737	−	13.2777i	−0.579002	−	0.741089i
$322$	25.9729	+	18.8704i	1.44741	+	1.05161i
$323$	−13.0028	+	21.5465i	−0.723495	+	1.19888i
$324$	−0.0447351	+	0.137680i	−0.00248528	+	0.00764892i
$325$	1.03923	+	29.7597i	0.0576463	+	1.65077i
$326$	−3.77658	−	7.74314i	−0.209166	−	0.428853i
$327$	−41.8725	+	2.92801i	−2.31556	+	0.161919i
$328$	0.514472	−	1.27336i	0.0284070	−	0.0703097i
$329$	0.0307972	+	0.174660i	0.00169791	+	0.00962930i
$330$	30.4568	+	17.8906i	1.67659	+	0.984844i
$331$	8.78141	−	15.2098i	0.482670	−	0.836008i	−0.517132	−	0.855905i	$-0.673000\pi$
$331$	8.78141	−	15.2098i	0.482670	−	0.836008i	0.999802	+	0.0198970i	$0.00633382\pi$
$332$	0.558093	−	15.9817i	0.0306293	−	0.877109i
$333$	−6.49033	−	9.62232i	−0.355668	−	0.527300i
$334$	0.112908	+	1.07425i	0.00617805	+	0.0587802i
$335$	−30.9460	+	6.57777i	−1.69076	+	0.359382i
$336$	−9.92257	−	1.39453i	−0.541321	−	0.0760777i
$337$	11.8134	+	0.826073i	0.643517	+	0.0449991i	0.387787	−	0.921749i	$-0.373240\pi$
$337$	11.8134	+	0.826073i	0.643517	+	0.0449991i	0.255730	+	0.966748i	$0.417684\pi$
$338$	3.12895	−	0.218798i	0.170193	−	0.0119010i
$339$	4.53980	−	0.638027i	0.246568	−	0.0346529i
$340$	20.6457	−	7.51444i	1.11967	−	0.407528i
$341$	20.4309	+	2.30266i	1.10640	+	0.124696i
$342$	21.0374	−	1.06205i	1.13757	−	0.0574291i
$343$	1.30693	+	4.02230i	0.0705673	+	0.217184i
$344$	3.43782	+	0.985778i	0.185355	+	0.0531496i
$345$	41.8638	+	85.8336i	2.25387	+	4.62112i
$346$	−4.90021	−	12.1285i	−0.263437	−	0.652030i
$347$	17.9722	−	11.2303i	0.964800	−	0.602874i	0.0465670	−	0.998915i	$-0.485172\pi$
$347$	17.9722	−	11.2303i	0.964800	−	0.602874i	0.918233	+	0.396041i	$0.129616\pi$
$348$	−6.77216	−	6.53980i	−0.363026	−	0.350570i
$349$	0.0604863	−	0.575488i	0.00323776	−	0.0308052i	−0.992784	−	0.119919i	$-0.961737\pi$
$349$	0.0604863	−	0.575488i	0.00323776	−	0.0308052i	0.996021	+	0.0891133i	$0.0284033\pi$
$350$	33.2053	+	7.05800i	1.77490	+	0.377266i
$351$	−15.1349	−	5.50867i	−0.807843	−	0.294031i
$352$	−2.32178	+	2.36841i	−0.123751	+	0.126237i
$353$	−10.2538	+	17.7602i	−0.545756	+	0.945278i	0.452803	+	0.891611i	$0.350424\pi$
$353$	−10.2538	+	17.7602i	−0.545756	+	0.945278i	−0.998559	+	0.0536669i	$0.982909\pi$
$354$	−6.32550	+	7.02518i	−0.336197	+	0.373384i
$355$	17.9388	−	36.7800i	0.952092	−	1.95208i
$356$	−0.916952	−	0.0641195i	−0.0485984	−	0.00339833i
$357$	−21.6712	−	53.6382i	−1.14696	−	2.83884i
$358$	12.2866	+	6.53291i	0.649368	+	0.345275i
$359$	5.57977	−	8.27236i	0.294489	−	0.436598i	−0.652536	−	0.757758i	$-0.726295\pi$
$359$	5.57977	−	8.27236i	0.294489	−	0.436598i	0.947025	+	0.321160i	$0.104073\pi$
$360$	−14.8776	−	10.8092i	−0.784119	−	0.569696i
$361$	7.66133	+	17.3869i	0.403228	+	0.915100i
$362$	18.7832			0.987224
$363$	−13.0782	−	27.8691i	−0.686426	−	1.46275i
$364$	−1.95257	+	11.0736i	−0.102342	+	0.580413i
$365$	−16.0751	−	10.0448i	−0.841407	−	0.525770i
$366$	2.08180	+	8.34966i	0.108818	+	0.436444i
$367$	−19.5527	−	18.8818i	−1.02064	−	0.985622i	−0.0207415	−	0.999785i	$-0.506603\pi$
$367$	−19.5527	−	18.8818i	−1.02064	−	0.985622i	−0.999900	+	0.0141631i	$0.995492\pi$
$368$	−8.77091	+	1.86431i	−0.457215	+	0.0971841i
$369$	−4.44084	−	4.93205i	−0.231181	−	0.256752i
$370$	−8.78592	+	2.51932i	−0.456758	+	0.130973i
$371$	18.0270	+	26.7262i	0.935918	+	1.38756i
$372$	−16.9702	−	3.60712i	−0.879863	−	0.187021i
$373$	−4.14263	−	7.17524i	−0.214497	−	0.371520i	0.738620	−	0.674122i	$-0.235478\pi$
$373$	−4.14263	−	7.17524i	−0.214497	−	0.371520i	−0.953117	+	0.302602i	$0.902145\pi$
$374$	−18.5443	−	4.77185i	−0.958904	−	0.246746i
$375$	36.5629	+	30.6799i	1.88810	+	1.58431i
$376$	−0.0420087	−	0.0262499i	−0.00216643	−	0.00135374i
$377$	−7.59962	+	7.33887i	−0.391401	+	0.377971i
$378$	−10.2675	+	15.2222i	−0.528104	+	0.782947i
$379$	6.30037	−	19.3906i	0.323628	−	0.996026i	−0.648427	−	0.761277i	$-0.724573\pi$
$379$	6.30037	−	19.3906i	0.323628	−	0.996026i	0.972056	−	0.234750i	$-0.0754270\pi$
$380$	4.32393	−	16.0142i	0.221813	−	0.821509i
$381$	7.45635	−	5.41735i	0.382000	−	0.277539i
$382$	12.7739	+	3.66285i	0.653568	+	0.187408i
$383$	−8.24414	+	1.15864i	−0.421256	+	0.0592036i	−0.346616	−	0.938007i	$-0.612669\pi$
$383$	−8.24414	+	1.15864i	−0.421256	+	0.0592036i	−0.0746394	+	0.997211i	$0.523781\pi$
$384$	2.14389	−	1.79894i	0.109405	−	0.0918017i
$385$	−31.1455	−	32.7407i	−1.58732	−	1.66862i
$386$	−1.88583	−	10.6951i	−0.0959862	−	0.544365i
$387$	11.5643	−	12.8435i	0.587847	−	0.652870i
$388$	−10.3302	+	4.59932i	−0.524439	+	0.233495i
$389$	−12.3463	+	3.54026i	−0.625984	+	0.179498i	−0.573609	−	0.819129i	$-0.694457\pi$
$389$	−12.3463	+	3.54026i	−0.625984	+	0.179498i	−0.0523754	+	0.998627i	$0.516679\pi$
$390$	−20.5926	+	26.3574i	−1.04275	+	1.33466i
$391$	−34.6408	−	38.4725i	−1.75186	−	1.94564i
$392$	5.31568	+	2.36669i	0.268483	+	0.119536i
$393$	−5.02900	+	10.3110i	−0.253680	+	0.520120i
$394$	2.48279	−	6.14511i	0.125081	−	0.309586i
$395$	−10.4354	+	8.75631i	−0.525060	+	0.440578i
$396$	5.36843	+	15.1016i	0.269774	+	0.758884i
$397$	−15.0263	+	5.46914i	−0.754151	+	0.274488i	−0.690351	−	0.723474i	$-0.742544\pi$
$397$	−15.0263	+	5.46914i	−0.754151	+	0.274488i	−0.0637994	+	0.997963i	$0.520322\pi$
$398$	1.23326	+	3.79560i	0.0618180	+	0.190256i
$399$	−42.5382	−	9.90672i	−2.12957	−	0.495956i
$400$	−7.67075	+	5.57313i	−0.383538	+	0.278656i
$401$	1.16606	+	33.3915i	0.0582301	+	1.66749i	0.580160	+	0.814503i	$0.302990\pi$
$401$	1.16606	+	33.3915i	0.0582301	+	1.66749i	−0.521930	+	0.852988i	$0.674788\pi$
$402$	−20.5435	−	10.9232i	−1.02462	−	0.544800i
$403$	−4.71001	+	18.8908i	−0.234622	+	0.941019i
$404$	−0.0698668	−	0.280221i	−0.00347600	−	0.0139415i
$405$	0.486417	−	0.258633i	0.0241703	−	0.0128516i
$406$	6.02195	+	10.4303i	0.298864	+	0.517648i
$407$	7.55731	+	2.51843i	0.374602	+	0.124834i
$408$	15.1835	+	5.52634i	0.751695	+	0.273595i
$409$	0.0495602	−	1.41922i	0.00245059	−	0.0701758i	−0.997549	−	0.0699659i	$-0.977711\pi$
$409$	0.0495602	−	1.41922i	0.00245059	−	0.0701758i	1.00000		0.000209935i	$-6.68243e-5\pi$
$410$	−4.77446	+	2.12573i	−0.235794	+	0.104982i
$411$	13.6833	+	6.09220i	0.674948	+	0.300506i
$412$	10.9033	+	1.53235i	0.537165	+	0.0754936i
$413$	10.2560	−	6.40867i	0.504665	−	0.315350i
$414$	−10.4829	+	42.0448i	−0.515208	+	2.06639i
$415$	−43.7753	+	42.2733i	−2.14885	+	2.07512i
$416$	−1.93355	−	2.47483i	−0.0948001	−	0.121339i
$417$	44.9315			2.20030
$418$	−10.9997	+	9.38123i	−0.538011	+	0.458851i
$419$	17.0507			0.832983			0.416492	−	0.909140i	$-0.363259\pi$
$419$	17.0507			0.832983			0.416492	+	0.909140i	$0.363259\pi$
$420$	23.4759	+	30.0477i	1.14550	+	1.46618i
$421$	4.54798	−	4.39194i	0.221655	−	0.214050i	−0.575537	−	0.817776i	$-0.695207\pi$
$421$	4.54798	−	4.39194i	0.221655	−	0.214050i	0.797192	+	0.603726i	$0.206318\pi$
$422$	1.36880	−	5.48997i	0.0666323	−	0.267247i
$423$	−0.203005	+	0.126852i	−0.00987044	+	0.00616773i
$424$	−8.91647	−	1.25313i	−0.433022	−	0.0608573i
$425$	−50.0089	−	22.2654i	−2.42579	−	1.08003i
$426$	27.4930	−	12.2407i	1.33204	−	0.593063i
$427$	0.384200	−	11.0021i	0.0185928	−	0.532427i
$428$	−5.65754	−	2.05918i	−0.273467	−	0.0995340i
$429$	27.7915	−	8.79977i	1.34178	−	0.424857i
$430$	−6.80486	−	11.7864i	−0.328159	−	0.568389i
$431$	−13.3965	+	7.12303i	−0.645286	+	0.343104i	−0.759648	−	0.650335i	$-0.774629\pi$
$431$	−13.3965	+	7.12303i	−0.645286	+	0.343104i	0.114362	+	0.993439i	$0.463518\pi$
$432$	−1.24067	−	4.97606i	−0.0596918	−	0.239411i
$433$	1.29909	−	5.21037i	0.0624303	−	0.250394i	−0.930970	−	0.365097i	$-0.881036\pi$
$433$	1.29909	−	5.21037i	0.0624303	−	0.250394i	0.993400	+	0.114702i	$0.0365915\pi$
$434$	19.5970	+	10.4199i	0.940688	+	0.500173i
$435$	1.25032	+	35.8044i	0.0599481	+	1.71669i
$436$	−12.1338	+	8.81573i	−0.581104	+	0.422197i
$437$	−38.8034	+	4.68889i	−1.85622	+	0.224300i
$438$	−4.30780	−	13.2580i	−0.205835	−	0.633494i
$439$	−17.2363	+	6.27351i	−0.822645	+	0.299418i	−0.718837	−	0.695179i	$-0.755325\pi$
$439$	−17.2363	+	6.27351i	−0.822645	+	0.299418i	−0.103808	+	0.994597i	$0.533103\pi$
$440$	12.6166	−	0.345724i	0.601471	−	0.0164818i
$441$	21.5402	−	18.0744i	1.02573	−	0.860686i
$442$	6.79244	−	16.8119i	0.323083	−	0.799660i
$443$	3.27531	−	6.71538i	0.155615	−	0.319057i	−0.806716	−	0.590940i	$-0.798757\pi$
$443$	3.27531	−	6.71538i	0.155615	−	0.319057i	0.962331	+	0.271882i	$0.0876461\pi$
$444$	−6.14069	−	2.73401i	−0.291424	−	0.129750i
$445$	2.34059	+	2.59948i	0.110954	+	0.123227i
$446$	5.73488	−	7.34031i	0.271554	−	0.347574i
$447$	−10.7498	+	3.08247i	−0.508450	+	0.145796i
$448$	−3.27079	+	1.45625i	−0.154530	+	0.0688013i
$449$	20.1290	−	22.3556i	0.949948	−	1.05502i	−0.0484720	−	0.998825i	$-0.515435\pi$
$449$	20.1290	−	22.3556i	0.949948	−	1.05502i	0.998420	−	0.0561991i	$-0.0178982\pi$
$450$	7.95643	+	45.1231i	0.375070	+	2.12713i
$451$	4.47967	+	0.824627i	0.210940	+	0.0388302i
$452$	1.25484	−	1.05294i	0.0590227	−	0.0495260i
$453$	7.74780	−	1.08888i	0.364024	−	0.0511602i
$454$	−20.8855	−	5.98883i	−0.980206	−	0.281070i
$455$	34.6180	−	25.1514i	1.62292	−	1.17912i
$456$	10.0063	−	6.97790i	0.468587	−	0.326770i
$457$	−7.88201	+	24.2583i	−0.368705	+	1.13476i	0.578924	+	0.815382i	$0.303473\pi$
$457$	−7.88201	+	24.2583i	−0.368705	+	1.13476i	−0.947628	+	0.319375i	$0.896527\pi$
$458$	−5.84976	+	8.67262i	−0.273341	+	0.405245i
$459$	21.2987	−	20.5679i	0.994137	−	0.960027i
$460$	28.9380	+	18.0825i	1.34924	+	0.843100i
$461$	1.02156	+	0.857195i	0.0475790	+	0.0399235i	0.666267	−	0.745713i	$-0.267891\pi$
$461$	1.02156	+	0.857195i	0.0475790	+	0.0399235i	−0.618688	+	0.785637i	$0.712336\pi$
$462$	−2.06914	−	33.1684i	−0.0962651	−	1.54313i
$463$	7.84720	+	13.5917i	0.364690	+	0.631662i	0.988726	−	0.149733i	$-0.0478416\pi$
$463$	7.84720	+	13.5917i	0.364690	+	0.631662i	−0.624036	+	0.781395i	$0.714508\pi$
$464$	−3.29040	−	0.699396i	−0.152753	−	0.0324687i
$465$	36.9191	+	54.7349i	1.71208	+	2.53827i
$466$	−9.87155	+	2.83062i	−0.457291	+	0.131126i
$467$	20.2838	+	22.5274i	0.938621	+	1.04244i	0.999020	+	0.0442697i	$0.0140961\pi$
$467$	20.2838	+	22.5274i	0.938621	+	1.04244i	−0.0603988	+	0.998174i	$0.519237\pi$
$468$	−14.8452	+	3.15544i	−0.686219	+	0.145860i
$469$	21.4116	+	20.6769i	0.988694	+	0.954771i
$470$	0.0456039	+	0.182907i	0.00210355	+	0.00843687i
$471$	−31.4226	−	19.6350i	−1.44788	−	0.904734i
$472$	−0.586551	+	3.32649i	−0.0269982	+	0.153114i
$473$	−0.916263	+	11.8260i	−0.0421298	+	0.543760i
$474$	−10.0183			−0.460157
$475$	−35.4668	+	21.2181i	−1.62733	+	0.973553i
$476$	−16.7231	−	12.1501i	−0.766503	−	0.556897i
$477$	−24.3315	+	36.0730i	−1.11406	+	1.65167i
$478$	−20.8321	−	11.0766i	−0.952840	−	0.506634i
$479$	8.42185	+	20.8448i	0.384804	+	0.952423i	0.987947	+	0.154790i	$0.0494703\pi$
$479$	8.42185	+	20.8448i	0.384804	+	0.952423i	−0.603143	+	0.797633i	$0.706085\pi$
$480$	−10.6242	−	0.742919i	−0.484928	−	0.0339094i
$481$	−3.30669	+	6.77972i	−0.150772	+	0.309128i
$482$	−18.7471	+	20.8208i	−0.853909	+	0.948362i
$483$	44.9243	−	77.8112i	2.04413	−	3.54053i
$484$	−9.23991	−	5.96858i	−0.419996	−	0.271299i
$485$	40.4366	+	14.7177i	1.83613	+	0.668297i
$486$	15.4453	+	3.28299i	0.700612	+	0.148920i
$487$	−3.70781	+	35.2775i	−0.168017	+	1.59857i	0.507780	+	0.861487i	$0.330466\pi$
$487$	−3.70781	+	35.2775i	−0.168017	+	1.59857i	−0.675797	+	0.737088i	$0.736200\pi$
$488$	2.21182	+	2.13593i	0.100124	+	0.0966891i
$489$	−20.4468	+	12.7766i	−0.924638	+	0.577778i
$490$	−8.29492	−	20.5306i	−0.374726	−	0.927480i
$491$	−2.81621	−	5.77409i	−0.127094	−	0.260581i	0.825753	−	0.564031i	$-0.190750\pi$
$491$	−2.81621	−	5.77409i	−0.127094	−	0.260581i	−0.952847	+	0.303450i	$0.901861\pi$
$492$	−3.69468	−	1.05943i	−0.166569	−	0.0477629i
$493$	−6.00156	−	18.4709i	−0.270296	−	0.831887i
$494$	−7.43384	−	11.4953i	−0.334464	−	0.517200i
$495$	25.2254	−	55.5309i	1.13380	−	2.49593i
$496$	−5.82531	+	2.12024i	−0.261564	+	0.0952015i
$497$	−38.1258	+	5.35823i	−1.71017	+	0.240349i
$498$	−44.6454	+	3.12191i	−2.00061	+	0.139896i
$499$	26.4394	+	1.84882i	1.18359	+	0.0827648i	0.647951	−	0.761682i	$-0.275626\pi$
$499$	26.4394	+	1.84882i	1.18359	+	0.0827648i	0.535640	+	0.844447i	$0.320070\pi$
$500$	16.8885	+	2.37352i	0.755276	+	0.106147i
$501$	2.95694	−	0.628518i	0.132107	−	0.0280801i
$502$	−3.07835	−	29.2885i	−0.137393	−	1.30721i
$503$	14.7209	+	21.8247i	0.656374	+	0.973115i	0.999429	+	0.0337993i	$0.0107607\pi$
$503$	14.7209	+	21.8247i	0.656374	+	0.973115i	−0.343054	+	0.939316i	$0.611462\pi$
$504$	−0.603823	+	17.2912i	−0.0268964	+	0.770212i
$505$	−0.549508	+	0.951775i	−0.0244528	+	0.0423534i
$506$	−11.8918	−	27.2587i	−0.528656	−	1.21179i
$507$	−1.52432	−	8.64487i	−0.0676976	−	0.383932i
$508$	1.23366	−	3.05341i	0.0547347	−	0.135473i
$509$	−23.7667	+	1.66193i	−1.05344	+	0.0736637i	−0.585960	−	0.810340i	$-0.699282\pi$
$509$	−23.7667	+	1.66193i	−1.05344	+	0.0736637i	−0.467480	+	0.884004i	$0.654838\pi$
$510$	−26.9548	−	55.2655i	−1.19358	−	2.44720i
$511$	0.622395	+	17.8231i	0.0275331	+	0.788446i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−3.45459	−	22.0856i	−0.152524	−	0.975103i
$514$	13.9226	+	10.1154i	0.614099	+	0.446169i
$515$	−25.7961	−	33.0175i	−1.13671	−	1.45492i
$516$	1.73804	−	9.85693i	0.0765130	−	0.433927i
$517$	0.0573490	−	0.153957i	0.00252220	−	0.00677102i
$518$	6.58741	+	5.52749i	0.289434	+	0.242864i
$519$	−32.3239	+	17.1869i	−1.41886	+	0.754422i
$520$	−1.24927	+	11.8860i	−0.0547841	+	0.521236i
$521$	1.09642	+	10.4318i	0.0480352	+	0.457025i	0.991931	+	0.126781i	$0.0404644\pi$
$521$	1.09642	+	10.4318i	0.0480352	+	0.457025i	−0.943896	+	0.330244i	$0.892869\pi$
$522$	−10.0082	+	12.8099i	−0.438045	+	0.560672i
$523$	14.8139	−	18.9609i	0.647767	−	0.829104i	−0.346272	−	0.938134i	$-0.612552\pi$
$523$	14.8139	−	18.9609i	0.647767	−	0.829104i	0.994038	+	0.109031i	$0.0347747\pi$
$524$	0.428475	+	4.07667i	0.0187180	+	0.178090i
$525$	9.93085	−	94.4857i	0.433418	−	4.12369i
$526$	15.7283	−	8.36288i	0.685786	−	0.364639i
$527$	−27.4173	−	23.0058i	−1.19431	−	1.00215i
$528$	7.27125	+	5.76939i	0.316440	+	0.251081i
$529$	9.96819	−	56.5324i	0.433400	−	2.45793i
$530$	21.0955	+	27.0010i	0.916331	+	1.17285i
$531$	13.2057	+	9.59448i	0.573077	+	0.416365i
$532$	−14.7658	+	5.05259i	−0.640177	+	0.219057i
$533$	−1.33285	+	4.10210i	−0.0577323	+	0.177682i
$534$	0.0897788	+	2.57093i	0.00388511	+	0.111255i
$535$	10.0436	+	20.5925i	0.434225	+	0.890293i
$536$	−8.29340	+	0.579931i	−0.358220	+	0.0250492i
$537$	14.5889	−	36.1087i	0.629557	−	1.55821i
$538$	−0.573215	−	3.25086i	−0.0247131	−	0.140155i
$539$	−4.15407	+	18.8462i	−0.178928	+	0.811763i
$540$	−9.75796	+	16.9013i	−0.419916	+	0.727316i
$541$	0.799595	−	22.8974i	0.0343773	−	0.984436i	−0.852583	−	0.522591i	$-0.824965\pi$
$541$	0.799595	−	22.8974i	0.0343773	−	0.984436i	0.886961	−	0.461845i	$-0.152812\pi$
$542$	−8.83132	−	13.0930i	−0.379338	−	0.562391i
$543$	−5.49482	−	52.2797i	−0.235805	−	2.24354i
$544$	5.64731	−	1.20037i	0.242126	−	0.0514655i
$545$	56.5197	+	7.94333i	2.42104	+	0.340255i
$546$	31.3925	+	2.19518i	1.34347	+	0.0939449i
$547$	29.2010	−	2.04193i	1.24854	−	0.0873067i	0.569863	−	0.821740i	$-0.306996\pi$
$547$	29.2010	−	2.04193i	1.24854	−	0.0873067i	0.678681	+	0.734433i	$0.262552\pi$
$548$	5.29986	−	0.744847i	0.226399	−	0.0318183i
$549$	13.9627	−	5.08201i	0.595913	−	0.216895i
$550$	−23.2108	−	21.2170i	−0.989713	−	0.904694i
$551$	−14.0140	−	4.31393i	−0.597016	−	0.183780i
$552$	7.75482	+	23.8669i	0.330067	+	1.01584i
$553$	12.3200	+	3.53270i	0.523899	+	0.150226i
$554$	−3.83540	−	7.86373i	−0.162950	−	0.334098i
$555$	9.58230	+	23.7170i	0.406746	+	1.00673i
$556$	13.6151	−	8.50768i	0.577411	−	0.360806i
$557$	22.8868	+	22.1015i	0.969746	+	0.936473i	0.998005	−	0.0631279i	$-0.0201076\pi$
$557$	22.8868	+	22.1015i	0.969746	+	0.936473i	−0.0282596	+	0.999601i	$0.508997\pi$
$558$	−3.13138	+	29.7930i	−0.132562	+	1.26124i
$559$	−10.9865	−	2.33525i	−0.464679	−	0.0987706i
$560$	12.8031	+	4.65996i	0.541031	+	0.196919i
$561$	−7.85664	+	53.0108i	−0.331708	+	2.23812i
$562$	−1.72256	+	2.98356i	−0.0726618	+	0.125854i
$563$	20.8105	−	23.1124i	0.877057	−	0.974070i	−0.122775	−	0.992435i	$-0.539179\pi$
$563$	20.8105	−	23.1124i	0.877057	−	0.974070i	0.999831	+	0.0183644i	$0.00584591\pi$
$564$	−0.0607728	+	0.124603i	−0.00255900	+	0.00524672i
$565$	−6.21847	−	0.434838i	−0.261613	−	0.0182938i
$566$	−1.08118	−	2.67601i	−0.0454453	−	0.112481i
$567$	−0.457640	−	0.243331i	−0.0192191	−	0.0102190i
$568$	6.01319	−	8.91492i	0.252308	−	0.374062i
$569$	−19.4616	−	14.1397i	−0.815875	−	0.592768i	0.0996531	−	0.995022i	$-0.468227\pi$
$569$	−19.4616	−	14.1397i	−0.815875	−	0.592768i	−0.915528	+	0.402255i	$0.868227\pi$
$570$	−45.8375	−	7.35012i	−1.91992	−	0.307863i
$571$	−33.7215			−1.41120			−0.705601	−	0.708609i	$-0.749323\pi$
$571$	−33.7215			−1.41120			−0.705601	+	0.708609i	$0.749323\pi$
$572$	6.75516	−	7.92877i	0.282447	−	0.331518i
$573$	6.45803	−	36.6253i	0.269788	−	1.53004i
$574$	4.16994	+	2.60567i	0.174050	+	0.108758i
$575$	−20.5682	−	82.4944i	−0.857752	−	3.44026i
$576$	−3.47617	−	3.35690i	−0.144841	−	0.139871i
$577$	−25.4118	+	5.40145i	−1.05791	+	0.224865i	−0.703843	−	0.710356i	$-0.748534\pi$
$577$	−25.4118	+	5.40145i	−1.05791	+	0.224865i	−0.354065	+	0.935221i	$0.615201\pi$
$578$	10.9289	+	12.1378i	0.454582	+	0.504864i
$579$	−29.2161	+	8.37759i	−1.21418	+	0.348161i
$580$	7.15837	+	10.6127i	0.297235	+	0.440669i
$581$	56.0034	+	11.9039i	2.32341	+	0.493857i
$582$	15.8234	+	27.4069i	0.655901	+	1.13605i
$583$	−1.85934	−	29.8053i	−0.0770060	−	1.23441i
$584$	−3.81574	−	3.20178i	−0.157896	−	0.132491i
$585$	48.9789	+	30.6054i	2.02503	+	1.26538i
$586$	−5.23691	+	5.05723i	−0.216335	+	0.208912i
$587$	−25.4923	+	37.7940i	−1.05218	+	1.55992i	−0.245087	+	0.969501i	$0.578817\pi$
$587$	−25.4923	+	37.7940i	−1.05218	+	1.55992i	−0.807094	+	0.590422i	$0.798961\pi$
$588$	5.03223	−	15.4876i	0.207525	−	0.638698i
$589$	−26.1142	+	6.94359i	−1.07602	+	0.286106i
$590$	10.3992	−	7.55547i	0.428129	−	0.311054i
$591$	−17.8301	−	5.11271i	−0.733434	−	0.210309i
$592$	−2.37843	+	0.334267i	−0.0977529	+	0.0137383i
$593$	16.0700	−	13.4844i	0.659917	−	0.553736i	−0.250145	−	0.968208i	$-0.580478\pi$
$593$	16.0700	−	13.4844i	0.659917	−	0.553736i	0.910062	+	0.414472i	$0.136034\pi$
$594$	15.3431	−	7.34120i	0.629536	−	0.301213i
$595$	13.6596	+	77.4674i	0.559989	+	3.17585i
$596$	−2.67376	+	2.96951i	−0.109522	+	0.121636i
$597$	10.2036	−	4.54293i	0.417605	−	0.185930i
$598$	27.0704	−	7.76232i	1.10699	−	0.317425i
$599$	17.6933	−	22.6464i	0.722929	−	0.925307i	−0.276432	−	0.961033i	$-0.589152\pi$
$599$	17.6933	−	22.6464i	0.722929	−	0.925307i	0.999362	+	0.0357260i	$0.0113744\pi$
$600$	17.7558	+	19.7198i	0.724877	+	0.805058i
$601$	8.93786	+	3.97939i	0.364583	+	0.162323i	0.580848	−	0.814012i	$-0.302721\pi$
$601$	8.93786	+	3.97939i	0.364583	+	0.162323i	−0.216265	+	0.976335i	$0.569388\pi$
$602$	−5.61314	+	11.5086i	−0.228775	+	0.469057i
$603$	−15.0499	+	37.2499i	−0.612881	+	1.51693i
$604$	2.14156	−	1.79698i	0.0871390	−	0.0731183i
$605$	9.51561	+	40.7642i	0.386865	+	1.65730i
$606$	−0.759505	+	0.276437i	−0.0308528	+	0.0112295i
$607$	9.46168	+	29.1201i	0.384038	+	1.18195i	0.937176	+	0.348857i	$0.113430\pi$
$607$	9.46168	+	29.1201i	0.384038	+	1.18195i	−0.553138	+	0.833089i	$0.686570\pi$
$608$	1.71085	−	4.00911i	0.0693843	−	0.162591i
$609$	27.2693	−	19.8123i	1.10501	−	0.802835i
$610$	−0.408360	−	11.6939i	−0.0165340	−	0.473472i
$611$	0.137362	+	0.0730367i	0.00555708	+	0.00295475i
$612$	6.74963	−	27.0713i	0.272837	−	1.09429i
$613$	0.675436	+	2.70903i	0.0272806	+	0.109417i	0.982392	−	0.186829i	$-0.0598210\pi$
$613$	0.675436	+	2.70903i	0.0272806	+	0.109417i	−0.955112	+	0.296245i	$0.904265\pi$
$614$	−20.1717	+	10.7255i	−0.814062	+	0.432844i
$615$	7.31330	+	12.6670i	0.294901	+	0.510783i
$616$	−6.90736	−	9.65891i	−0.278306	−	0.389168i
$617$	−1.12087	−	0.407963i	−0.0451245	−	0.0164240i	0.319359	−	0.947634i	$-0.396532\pi$
$617$	−1.12087	−	0.407963i	−0.0451245	−	0.0164240i	−0.364484	+	0.931210i	$0.618755\pi$
$618$	1.07540	−	30.7955i	0.0432591	−	1.23878i
$619$	−24.3243	+	10.8299i	−0.977677	+	0.435290i	−0.832445	−	0.554108i	$-0.813059\pi$
$619$	−24.3243	+	10.8299i	−0.977677	+	0.435290i	−0.145232	+	0.989398i	$0.546393\pi$
$620$	21.5512	+	9.59520i	0.865516	+	0.385353i
$621$	45.5380	+	6.39995i	1.82738	+	0.256821i
$622$	−11.7314	+	7.33062i	−0.470388	+	0.293931i
$623$	0.796166	−	3.19325i	0.0318977	−	0.127935i
$624$	−6.32261	+	6.10567i	−0.253107	+	0.244423i
$625$	−10.7694	−	13.7841i	−0.430774	−	0.551366i
$626$	−23.8312			−0.952486
$627$	29.3288	+	27.8712i	1.17128	+	1.11307i
$628$	−13.2395			−0.528315
$629$	−8.53723	−	10.9272i	−0.340402	−	0.435694i
$630$	47.3622	−	45.7372i	1.88696	−	1.82221i
$631$	5.99158	−	24.0309i	0.238521	−	0.956656i	−0.724941	−	0.688811i	$-0.758133\pi$
$631$	5.99158	−	24.0309i	0.238521	−	0.956656i	0.963462	−	0.267845i	$-0.0863115\pi$
$632$	−3.03575	+	1.89695i	−0.120756	+	0.0754566i
$633$	−15.6808	−	2.20379i	−0.623254	−	0.0875927i
$634$	12.1784	+	5.42218i	0.483666	+	0.215342i
$635$	−11.4487	+	5.09731i	−0.454329	+	0.202280i
$636$	−0.879444	+	25.1840i	−0.0348722	+	0.998610i
$637$	−17.1723	−	6.25020i	−0.680391	−	0.247642i
$638$	0.0837985	−	11.1565i	0.00331762	−	0.441691i
$639$	−25.9825	−	45.0030i	−1.02785	−	1.78029i
$640$	−3.36003	+	1.78656i	−0.132817	+	0.0706199i
$641$	−0.210173	−	0.842959i	−0.00830134	−	0.0332949i	0.966002	−	0.258534i	$-0.0832393\pi$
$641$	−0.210173	−	0.842959i	−0.00830134	−	0.0332949i	−0.974304	+	0.225239i	$0.927684\pi$
$642$	−4.07630	+	16.3491i	−0.160879	+	0.645249i
$643$	28.0088	+	14.8925i	1.10456	+	0.587305i	0.918575	−	0.395248i	$-0.129341\pi$
$643$	28.0088	+	14.8925i	1.10456	+	0.587305i	0.185985	+	0.982553i	$0.440452\pi$
$644$	−1.12042	−	32.0847i	−0.0441509	−	1.26432i
$645$	−30.8145	+	22.3881i	−1.21332	+	0.881529i
$646$	24.9842	−	3.01903i	0.982991	−	0.118782i
$647$	15.0553	+	46.3355i	0.591886	+	1.82164i	0.569653	+	0.821885i	$0.307078\pi$
$647$	15.0553	+	46.3355i	0.591886	+	1.82164i	0.0222331	+	0.999753i	$0.492922\pi$
$648$	0.136035	−	0.0495128i	0.00534398	−	0.00194505i
$649$	−11.1987	+	0.306872i	−0.439588	+	0.0120458i
$650$	22.8112	−	19.1409i	0.894728	−	0.750766i
$651$	23.2691	−	57.5931i	0.911989	−	2.25725i
$652$	−3.77658	+	7.74314i	−0.147902	+	0.303245i
$653$	4.29579	+	1.91261i	0.168107	+	0.0748462i	0.489065	−	0.872247i	$-0.337338\pi$
$653$	4.29579	+	1.91261i	0.168107	+	0.0748462i	−0.320958	+	0.947094i	$0.604005\pi$
$654$	28.0866	+	31.1933i	1.09827	+	1.21976i
$655$	9.60375	−	12.2922i	0.375250	−	0.480298i
$656$	−1.32016	+	0.378551i	−0.0515438	+	0.0147799i
$657$	−21.9898	+	9.79051i	−0.857905	+	0.381964i
$658$	0.118673	−	0.131800i	0.00462636	−	0.00513809i
$659$	0.481375	+	2.73002i	0.0187517	+	0.106346i	0.992747	−	0.120222i	$-0.0383605\pi$
$659$	0.481375	+	2.73002i	0.0187517	+	0.106346i	−0.973995	+	0.226568i	$0.927249\pi$
$660$	−4.65310	−	35.0148i	−0.181122	−	1.36295i
$661$	−2.31066	+	1.93888i	−0.0898744	+	0.0754136i	−0.686618	−	0.727018i	$-0.740905\pi$
$661$	−2.31066	+	1.93888i	−0.0898744	+	0.0754136i	0.596743	+	0.802432i	$0.296461\pi$
$662$	−17.3919	+	2.44427i	−0.675955	+	0.0949993i
$663$	−48.7799	−	13.9874i	−1.89445	−	0.543226i
$664$	−12.9373	+	9.39953i	−0.502066	+	0.364773i
$665$	53.7766	+	25.2022i	2.08537	+	0.977299i
$666$	−3.58664	+	11.0385i	−0.138979	+	0.427735i
$667$	16.8673	−	25.0068i	0.653106	−	0.968269i
$668$	0.777005	−	0.750345i	0.0300632	−	0.0290317i
$669$	−22.1081	−	13.8147i	−0.854749	−	0.534106i
$670$	24.2356	+	20.3361i	0.936302	+	0.785651i
$671$	−5.46889	+	8.60751i	−0.211124	+	0.332289i
$672$	5.01004	+	8.67765i	0.193267	+	0.334748i
$673$	20.4409	+	4.34485i	0.787938	+	0.167481i	0.584271	−	0.811559i	$-0.301381\pi$
$673$	20.4409	+	4.34485i	0.787938	+	0.167481i	0.203667	+	0.979040i	$0.434714\pi$
$674$	−6.62210	−	9.81766i	−0.255074	−	0.378162i
$675$	46.7416	−	13.4029i	1.79908	−	0.515879i
$676$	−2.09879	−	2.33094i	−0.0807227	−	0.0896516i
$677$	−11.5230	+	2.44929i	−0.442865	+	0.0941338i	−0.423946	−	0.905687i	$-0.639356\pi$
$677$	−11.5230	+	2.44929i	−0.442865	+	0.0941338i	−0.0189181	+	0.999821i	$0.506022\pi$
$678$	−3.29775	−	3.18460i	−0.126649	−	0.122304i
$679$	−9.79441	−	39.2833i	−0.375875	−	1.50755i
$680$	−18.6322	−	11.6427i	−0.714514	−	0.446478i
$681$	−10.5590	+	59.8831i	−0.404622	+	2.29472i
$682$	−10.7640	−	17.5175i	−0.412176	−	0.670778i
$683$	−45.7990			−1.75245			−0.876224	−	0.481903i	$-0.839946\pi$
$683$	−45.7990			−1.75245			−0.876224	+	0.481903i	$0.839946\pi$
$684$	−13.7888	−	15.9238i	−0.527228	−	0.608862i
$685$	−16.4770	−	11.9712i	−0.629553	−	0.457397i
$686$	2.36499	−	3.50625i	0.0902959	−	0.133869i
$687$	25.8500	+	13.7447i	0.986238	+	0.524392i
$688$	−1.33973	−	3.31594i	−0.0510767	−	0.126419i
$689$	28.2094	+	1.97260i	1.07469	+	0.0751500i
$690$	41.8638	−	85.8336i	1.59373	−	3.26763i
$691$	17.5240	−	19.4623i	0.666643	−	0.740382i	−0.311057	−	0.950391i	$-0.600683\pi$
$691$	17.5240	−	19.4623i	0.666643	−	0.740382i	0.977699	+	0.210010i	$0.0673496\pi$
$692$	−6.54048	+	11.3284i	−0.248632	+	0.430643i
$693$	−56.5849	+	9.53979i	−2.14948	+	0.362387i
$694$	−19.9144	−	7.24825i	−0.755940	−	0.275140i
$695$	−59.7605	−	12.7025i	−2.26684	−	0.481832i
$696$	−0.984074	+	9.36284i	−0.0373012	+	0.354898i
$697$	−5.70371	−	5.50801i	−0.216043	−	0.208631i
$698$	−0.490730	+	0.306642i	−0.0185744	+	0.0116066i
$699$	10.7663	+	26.6476i	0.407220	+	1.00791i
$700$	−14.8814	−	30.5115i	−0.562466	−	1.15323i
$701$	16.8221	+	4.82366i	0.635362	+	0.182187i	0.577831	−	0.816157i	$-0.303899\pi$
$701$	16.8221	+	4.82366i	0.635362	+	0.182187i	0.0575312	+	0.998344i	$0.481677\pi$
$702$	4.97711	+	15.3180i	0.187849	+	0.578140i
$703$	−10.4559	+	0.527856i	−0.394352	+	0.0199085i
$704$	3.29576	+	0.371446i	0.124214	+	0.0139994i
$705$	0.495748	−	0.180438i	0.0186710	−	0.00679567i
$706$	20.3081	−	2.85411i	0.764305	−	0.107416i
$707$	1.03148	−	0.0721279i	0.0387927	−	0.00271265i
$708$	9.43029	+	0.659430i	0.354412	+	0.0247829i
$709$	−11.9117	−	1.67409i	−0.447355	−	0.0628716i	−0.0881010	−	0.996112i	$-0.528080\pi$
$709$	−11.9117	−	1.67409i	−0.447355	−	0.0628716i	−0.359254	+	0.933240i	$0.616969\pi$
$710$	−40.0272	+	8.50805i	−1.50219	+	0.319301i
$711$	1.80821	+	17.2039i	0.0678131	+	0.645198i
$712$	0.514005	+	0.762044i	0.0192632	+	0.0285588i
$713$	1.93996	−	55.5531i	0.0726520	−	2.08048i
$714$	−28.9253	+	50.1002i	−1.08250	+	1.87495i
$715$	−39.4514	+	3.84715i	−1.47540	+	0.143875i
$716$	−2.41640	−	13.7041i	−0.0903049	−	0.512145i
$717$	−24.7356	+	61.2229i	−0.923769	+	2.28641i
$718$	−9.95396	+	0.696049i	−0.371478	+	0.0259763i
$719$	−11.1155	−	22.7902i	−0.414539	−	0.849931i	−0.999251	−	0.0386904i	$-0.987681\pi$
$719$	−11.1155	−	22.7902i	−0.414539	−	0.849931i	0.584712	−	0.811241i	$-0.301207\pi$
$720$	0.641792	+	18.3785i	0.0239182	+	0.684927i
$721$	−12.1817	+	37.4915i	−0.453671	+	1.39626i
$722$	8.98427	−	16.7417i	0.334360	−	0.623060i
$723$	63.4352	+	46.0884i	2.35918	+	1.71405i
$724$	−11.5641	−	14.8014i	−0.429777	−	0.550089i
$725$	5.53854	−	31.4106i	0.205696	−	1.16656i
$726$	−13.9094	+	27.4637i	−0.516228	+	1.01927i
$727$	9.86848	+	8.28063i	0.366002	+	0.307112i	0.807177	−	0.590309i	$-0.200994\pi$
$727$	9.86848	+	8.28063i	0.366002	+	0.307112i	−0.441176	+	0.897421i	$0.645439\pi$
$728$	9.92821	−	5.27892i	0.367964	−	0.195650i
$729$	4.57389	−	43.5176i	0.169403	−	1.61176i
$730$	1.98138	+	18.8515i	0.0733340	+	0.697726i
$731$	12.7122	−	16.2709i	0.470177	−	0.601799i
$732$	5.29794	−	6.78105i	0.195817	−	0.250635i
$733$	−3.73491	−	35.5353i	−0.137952	−	1.31252i	−0.816233	−	0.577722i	$-0.803942\pi$
$733$	−3.73491	−	35.5353i	−0.137952	−	1.31252i	0.678281	−	0.734802i	$-0.262725\pi$
$734$	−2.84123	+	27.0325i	−0.104872	+	0.997788i
$735$	−54.7168	+	29.0934i	−2.01826	+	1.07313i
$736$	6.86901	+	5.76378i	0.253195	+	0.212456i
$737$	−7.40093	−	26.5615i	−0.272617	−	0.978404i
$738$	−1.15246	+	6.53590i	−0.0424225	+	0.240590i
$739$	−3.60757	−	4.61748i	−0.132707	−	0.169857i	0.717067	−	0.697004i	$-0.245484\pi$
$739$	−3.60757	−	4.61748i	−0.132707	−	0.169857i	−0.849774	+	0.527147i	$0.823262\pi$
$740$	7.39441	+	5.37235i	0.271824	+	0.197492i
$741$	−29.8205	+	24.0536i	−1.09548	+	0.883631i
$742$	9.96197	−	30.6598i	0.365716	−	1.12556i
$743$	−1.45161	−	41.5688i	−0.0532546	−	1.52501i	−0.672667	−	0.739945i	$-0.734851\pi$
$743$	−1.45161	−	41.5688i	−0.0532546	−	1.52501i	0.619412	−	0.785066i	$-0.287371\pi$
$744$	7.60543	+	15.5934i	0.278829	+	0.571684i
$745$	15.1691	−	1.06073i	0.555754	−	0.0388621i
$746$	−3.10371	+	7.68195i	−0.113635	+	0.281256i
$747$	13.4192	+	76.1038i	0.490981	+	2.78449i
$748$	7.65676	+	17.5510i	0.279959	+	0.641727i
$749$	10.7779	−	18.6679i	0.393816	−	0.682109i
$750$	1.66574	−	47.7004i	0.0608241	−	1.74177i
$751$	28.4582	+	42.1910i	1.03845	+	1.53957i	0.827014	+	0.562182i	$0.190038\pi$
$751$	28.4582	+	42.1910i	1.03845	+	1.53957i	0.211441	+	0.977391i	$0.432184\pi$
$752$	0.00517789	+	0.0492644i	0.000188818	+	0.00179649i
$753$	−80.6188	+	17.1361i	−2.93791	+	0.624473i
$754$	10.4619	+	1.47033i	0.381000	+	0.0535461i
$755$	−10.6127	−	0.742112i	−0.386235	−	0.0270082i
$756$	18.3166	−	1.28082i	0.666168	−	0.0465830i
$757$	36.0244	−	5.06290i	1.30933	−	0.184014i	0.550244	−	0.835004i	$-0.314535\pi$
$757$	36.0244	−	5.06290i	1.30933	−	0.184014i	0.759087	+	0.650990i	$0.225646\pi$
$758$	−19.1589	+	6.97326i	−0.695881	+	0.253280i
$759$	−72.3908	+	41.0730i	−2.62762	+	1.49085i
$760$	−15.2814	+	6.45200i	−0.554315	+	0.234039i
$761$	−11.6312	−	35.7971i	−0.421630	−	1.29764i	−0.906184	−	0.422883i	$-0.861018\pi$
$761$	−11.6312	−	35.7971i	−0.421630	−	1.29764i	0.484554	−	0.874761i	$-0.338982\pi$
$762$	−8.85952	−	2.54043i	−0.320946	−	0.0920299i
$763$	−23.5399	−	48.2639i	−0.852200	−	1.74727i
$764$	−4.97802	−	12.3210i	−0.180098	−	0.445759i
$765$	−90.0394	+	56.2629i	−3.25538	+	2.03419i
$766$	5.98862	+	5.78314i	0.216378	+	0.208953i
$767$	1.10888	−	10.5503i	0.0400392	−	0.380948i
$768$	−2.73749	−	0.581872i	−0.0987808	−	0.0209965i
$769$	11.7883	+	4.29059i	0.425097	+	0.154722i	0.545704	−	0.837978i	$-0.316262\pi$
$769$	11.7883	+	4.29059i	0.425097	+	0.154722i	−0.120608	+	0.992700i	$0.538484\pi$
$770$	−6.62494	+	44.7001i	−0.238746	+	1.61088i
$771$	24.0814	−	41.7102i	0.867269	−	1.50215i
$772$	−7.26680	+	8.07060i	−0.261538	+	0.290467i
$773$	−8.29665	+	17.0107i	−0.298410	+	0.611831i	−0.994336	−	0.106283i	$-0.966105\pi$
$773$	−8.29665	+	17.0107i	−0.298410	+	0.611831i	0.695926	+	0.718113i	$0.254994\pi$
$774$	−17.2405	−	1.20557i	−0.619697	−	0.0433334i
$775$	−22.0186	−	54.4978i	−0.790930	−	1.95762i
$776$	9.98425	+	5.30872i	0.358414	+	0.190572i
$777$	13.4577	−	19.9519i	0.482793	−	0.715769i
$778$	10.3909	+	7.54945i	0.372533	+	0.270661i
$779$	−5.87856	+	1.13098i	−0.210621	+	0.0405214i
$780$	33.4480			1.19763
$781$	32.9665	+	13.6083i	1.17963	+	0.486942i
$782$	−8.98975	+	50.9834i	−0.321473	+	1.82316i
$783$	14.6301	+	9.14188i	0.522836	+	0.326704i
$784$	−1.40768	−	5.64590i	−0.0502743	−	0.201639i
$785$	36.2422	+	34.9987i	1.29354	+	1.24916i
$786$	11.2213	−	2.38517i	0.400252	−	0.0850761i
$787$	−1.22483	−	1.36031i	−0.0436605	−	0.0484899i	0.720919	−	0.693019i	$-0.243720\pi$
$787$	−1.22483	−	1.36031i	−0.0436605	−	0.0484899i	−0.764579	+	0.644529i	$0.777053\pi$
$788$	−6.37097	+	1.82685i	−0.226956	+	0.0650787i
$789$	−27.8777	−	41.3304i	−0.992473	−	1.47140i
$790$	13.3247	+	2.83226i	0.474072	+	0.100767i
$791$	2.93243	+	5.07911i	0.104265	+	0.180592i
$792$	8.59509	−	13.5279i	0.305413	−	0.480691i
$793$	−7.39747	−	6.20722i	−0.262692	−	0.220425i
$794$	13.5609	+	8.47378i	0.481258	+	0.300723i
$795$	68.9813	−	66.6144i	2.44651	−	2.36257i
$796$	2.23170	−	3.30863i	0.0791005	−	0.117271i
$797$	8.23628	−	25.3487i	0.291744	−	0.897896i	−0.692552	−	0.721368i	$-0.743513\pi$
$797$	8.23628	−	25.3487i	0.291744	−	0.897896i	0.984296	−	0.176528i	$-0.0564865\pi$
$798$	18.3825	+	39.6197i	0.650734	+	1.40252i
$799$	−0.231373	+	0.168103i	−0.00818540	+	0.00594704i
$800$	9.11427	+	2.61348i	0.322238	+	0.0924003i
$801$	4.39872	−	0.618199i	0.155421	−	0.0218430i
$802$	25.5950	−	21.4767i	0.903789	−	0.758369i
$803$	7.86520	−	14.5280i	0.277557	−	0.512682i
$804$	4.04027	+	22.9135i	0.142489	+	0.808098i
$805$	−81.7488	+	90.7913i	−2.88127	+	3.19997i
$806$	17.7859	−	7.91881i	0.626483	−	0.278928i
$807$	−8.88051	+	2.54645i	−0.312609	+	0.0896391i
$808$	−0.177802	+	0.227577i	−0.00625507	+	0.00800612i
$809$	1.50097	+	1.66699i	0.0527712	+	0.0586083i	0.768952	−	0.639306i	$-0.220778\pi$
$809$	1.50097	+	1.66699i	0.0527712	+	0.0586083i	−0.716181	+	0.697914i	$0.754112\pi$
$810$	−0.503274	−	0.224072i	−0.0176832	−	0.00787308i
$811$	1.42786	−	2.92755i	0.0501391	−	0.102800i	−0.872254	−	0.489054i	$-0.837342\pi$
$811$	1.42786	−	2.92755i	0.0501391	−	0.102800i	0.922393	+	0.386254i	$0.126231\pi$
$812$	4.51172	−	11.1669i	0.158331	−	0.391882i
$813$	−33.8584	+	28.4106i	−1.18747	+	0.996403i
$814$	−2.66819	−	7.50574i	−0.0935202	−	0.263076i
$815$	30.8071	−	11.2129i	1.07913	−	0.392769i
$816$	−4.99308	−	15.3671i	−0.174793	−	0.537956i
$817$	−4.52917	−	14.9165i	−0.158456	−	0.521864i
$818$	−1.14887	+	0.834704i	−0.0401694	+	0.0291847i
$819$	−1.89637	−	54.3049i	−0.0662645	−	1.89757i
$820$	4.61455	+	2.45360i	0.161147	+	0.0856834i
$821$	−0.512943	+	2.05730i	−0.0179018	+	0.0718003i	−0.978582	−	0.205856i	$-0.934002\pi$
$821$	−0.512943	+	2.05730i	−0.0179018	+	0.0718003i	0.960680	+	0.277656i	$0.0895577\pi$
$822$	−3.62356	−	14.5333i	−0.126386	−	0.506908i
$823$	48.6546	−	25.8701i	1.69599	−	0.901776i	0.717216	−	0.696851i	$-0.245416\pi$
$823$	48.6546	−	25.8701i	1.69599	−	0.901776i	0.978778	−	0.204924i	$-0.0656949\pi$
$824$	−5.50521	−	9.53530i	−0.191783	−	0.332178i
$825$	−52.2635	+	70.8100i	−1.81958	+	2.46529i
$826$	−11.3643	−	4.13628i	−0.395415	−	0.143919i
$827$	−0.544325	+	15.5874i	−0.0189280	+	0.542028i	0.952479	+	0.304606i	$0.0985246\pi$
$827$	−0.544325	+	15.5874i	−0.0189280	+	0.542028i	−0.971407	+	0.237422i	$0.923698\pi$
$828$	39.5857	−	17.6247i	1.37570	−	0.612500i
$829$	17.3269	+	7.71442i	0.601787	+	0.267933i	0.684935	−	0.728604i	$-0.259831\pi$
$829$	17.3269	+	7.71442i	0.601787	+	0.267933i	−0.0831479	+	0.996537i	$0.526497\pi$
$830$	60.2626	+	8.46936i	2.09175	+	0.293976i
$831$	−20.7653	+	12.9756i	−0.720339	+	0.450118i
$832$	−0.759781	+	3.04732i	−0.0263407	+	0.105647i
$833$	24.1657	−	23.3366i	0.837293	−	0.808564i
$834$	−27.6626	−	35.4065i	−0.957876	−	1.22603i
$835$	−4.11053			−0.142251
$836$	14.1646	+	2.89219i	0.489892	+	0.100028i
$837$	31.7918			1.09888
$838$	−10.4975	−	13.4362i	−0.362630	−	0.464145i
$839$	5.25035	−	5.07020i	0.181262	−	0.175043i	−0.598492	−	0.801129i	$-0.704233\pi$
$839$	5.25035	−	5.07020i	0.181262	−	0.175043i	0.779754	+	0.626086i	$0.215344\pi$
$840$	9.22475	−	36.9984i	0.318284	−	1.27657i
$841$	−14.9970	+	9.37115i	−0.517137	+	0.323143i
$842$	−6.26091	−	0.879913i	−0.215765	−	0.0303238i
$843$	8.80812	+	3.92163i	0.303368	+	0.135068i
$844$	−5.16887	+	2.30133i	−0.177920	+	0.0792150i
$845$	−0.416567	+	11.9289i	−0.0143303	+	0.410367i
$846$	0.224943	+	0.0818724i	0.00773369	+	0.00281483i
$847$	26.7894	−	28.8686i	0.920496	−	0.991935i
$848$	4.50205	+	7.79778i	0.154601	+	0.267777i
$849$	−7.13190	+	3.79210i	−0.244766	+	0.130145i
$850$	13.2432	+	53.1155i	0.454238	+	1.82185i
$851$	5.21019	−	20.8969i	0.178603	−	0.716337i
$852$	−26.5722	−	14.1287i	−0.910347	−	0.484040i
$853$	0.832042	+	23.8266i	0.0284886	+	0.815806i	0.926602	+	0.376043i	$0.122715\pi$
$853$	0.832042	+	23.8266i	0.0284886	+	0.815806i	−0.898114	+	0.439763i	$0.855062\pi$
$854$	−8.90628	+	6.47079i	−0.304767	+	0.221426i
$855$	−4.34878	+	80.0409i	−0.148725	+	2.73734i
$856$	1.86048	+	5.72596i	0.0635897	+	0.195709i
$857$	37.8666	−	13.7823i	1.29350	−	0.470795i	0.398624	−	0.917114i	$-0.369488\pi$
$857$	37.8666	−	13.7823i	1.29350	−	0.470795i	0.894874	+	0.446320i	$0.147266\pi$
$858$	−24.0444	−	16.4823i	−0.820864	−	0.562696i
$859$	−17.4222	+	14.6190i	−0.594439	+	0.498794i	−0.889653	−	0.456637i	$-0.849054\pi$
$859$	−17.4222	+	14.6190i	−0.594439	+	0.498794i	0.295214	+	0.955431i	$0.404609\pi$
$860$	−5.09829	+	12.6187i	−0.173850	+	0.430294i
$861$	6.03254	−	12.3685i	0.205588	−	0.421519i
$862$	13.8607	+	6.17119i	0.472098	+	0.210192i
$863$	15.3699	+	17.0699i	0.523196	+	0.581068i	0.945597	−	0.325341i	$-0.105479\pi$
$863$	15.3699	+	17.0699i	0.523196	+	0.581068i	−0.422401	+	0.906409i	$0.638813\pi$
$864$	−3.15735	+	4.04123i	−0.107415	+	0.137485i
$865$	47.8508	−	13.7210i	1.62698	−	0.466528i
$866$	−4.90562	+	2.18412i	−0.166700	+	0.0742196i
$867$	30.5861	−	33.9694i	1.03876	−	1.15366i
$868$	−3.85413	−	21.8578i	−0.130818	−	0.741903i
$869$	−8.18296	−	8.60207i	−0.277588	−	0.291805i
$870$	27.4445	−	23.0287i	0.930455	−	0.780745i
$871$	25.8558	−	3.63380i	0.876090	−	0.123126i
$872$	14.4172	+	4.13407i	0.488228	+	0.139997i
$873$	44.2085	−	32.1194i	1.49623	−	1.08708i
$874$	27.5846	+	27.6907i	0.933064	+	0.936651i
$875$	−18.8688	+	58.0720i	−0.637880	+	1.96319i
$876$	−7.79534	+	11.5571i	−0.263380	+	0.390477i
$877$	−14.7718	+	14.2650i	−0.498810	+	0.481695i	−0.900974	−	0.433872i	$-0.857147\pi$
$877$	−14.7718	+	14.2650i	−0.498810	+	0.481695i	0.402164	+	0.915567i	$0.368258\pi$
$878$	15.5553	+	9.72005i	0.524967	+	0.328036i
$879$	15.6079	+	13.0966i	0.526441	+	0.441736i
$880$	−8.03997	−	9.72914i	−0.271027	−	0.327969i
$881$	12.9424	+	22.4169i	0.436040	+	0.755244i	0.997380	−	0.0723419i	$-0.0230473\pi$
$881$	12.9424	+	22.4169i	0.436040	+	0.755244i	−0.561340	+	0.827585i	$0.689714\pi$
$882$	−27.5043	−	5.84622i	−0.926118	−	0.196853i
$883$	−1.20982	−	1.79363i	−0.0407136	−	0.0603604i	0.808131	−	0.589002i	$-0.200479\pi$
$883$	−1.20982	−	1.79363i	−0.0407136	−	0.0603604i	−0.848845	+	0.528642i	$0.822701\pi$
$884$	−17.4298	+	4.99791i	−0.586227	+	0.168098i
$885$	−24.0715	−	26.7341i	−0.809154	−	0.898657i
$886$	−7.30828	+	1.55342i	−0.245526	+	0.0521882i
$887$	−42.1169	−	40.6718i	−1.41415	−	1.36563i	−0.834811	−	0.550536i	$-0.814423\pi$
$887$	−42.1169	−	40.6718i	−1.41415	−	1.36563i	−0.579335	−	0.815089i	$-0.696688\pi$
$888$	1.62615	+	6.52215i	0.0545702	+	0.218869i
$889$	9.99914	+	6.24816i	0.335360	+	0.209556i
$890$	0.607413	−	3.44481i	0.0203605	−	0.115470i
$891$	0.251367	+	0.409076i	0.00842110	+	0.0137046i
$892$	−9.31499			−0.311889
$893$	0.00335411	+	0.215895i	0.000112241	+	0.00722466i
$894$	9.04729	+	6.57324i	0.302587	+	0.219842i
$895$	−29.6120	+	43.9015i	−0.989819	+	1.46747i
$896$	3.16124	+	1.68086i	0.105610	+	0.0561536i
$897$	−29.5242	−	73.0749i	−0.985784	−	2.43990i
$898$	−30.0091	−	2.09844i	−1.00142	−	0.0700258i
$899$	9.14154	−	18.7429i	0.304888	−	0.625112i
$900$	30.6591	−	34.0503i	1.02197	−	1.13501i
$901$	−25.9925	+	45.0203i	−0.865934	+	1.49984i
$902$	−2.10815	−	4.03772i	−0.0701937	−	0.134441i
$903$	33.6743	+	12.2564i	1.12061	+	0.407869i
$904$	−1.60228	−	0.340576i	−0.0532911	−	0.0113274i
$905$	−7.47158	+	71.0873i	−0.248364	+	2.36302i
$906$	−5.62808	−	5.43497i	−0.186980	−	0.180565i
$907$	7.11139	−	4.44369i	0.236130	−	0.147550i	−0.406694	−	0.913565i	$-0.633318\pi$
$907$	7.11139	−	4.44369i	0.236130	−	0.147550i	0.642824	+	0.766014i	$0.277763\pi$
$908$	8.13915	+	20.1451i	0.270107	+	0.668539i
$909$	0.611794	+	1.25436i	0.0202919	+	0.0416046i
$910$	−41.1325	−	11.7946i	−1.36353	−	0.390986i
$911$	−6.57499	−	20.2357i	−0.217839	−	0.670440i	−0.998940	−	0.0460349i	$-0.985341\pi$
$911$	−6.57499	−	20.2357i	−0.217839	−	0.670440i	0.781101	−	0.624405i	$-0.214659\pi$
$912$	−11.6591	−	3.58903i	−0.386073	−	0.118845i
$913$	−39.1469	−	35.7841i	−1.29557	−	1.18428i
$914$	23.9685	−	8.72381i	0.792806	−	0.288558i
$915$	−32.4284	+	4.55751i	−1.07205	+	0.150667i
$916$	10.4356	−	0.729727i	0.344802	−	0.0241109i
$917$	−14.6405	−	1.02376i	−0.483470	−	0.0338075i
$918$	−29.3205	−	4.12073i	−0.967720	−	0.136004i
$919$	42.0720	−	8.94267i	1.38783	−	0.294992i	0.547379	−	0.836885i	$-0.315626\pi$
$919$	42.0720	−	8.94267i	1.38783	−	0.294992i	0.840447	+	0.541893i	$0.182292\pi$
$920$	−3.56683	−	33.9361i	−0.117595	−	1.11884i
$921$	35.7534	+	53.0066i	1.17811	+	1.74663i
$922$	0.0465405	−	1.33275i	0.00153273	−	0.0438916i
$923$	−16.8860	+	29.2474i	−0.555809	+	0.962690i
$924$	−24.8632	+	22.0510i	−0.817938	+	0.725425i
$925$	−3.95447	−	22.4269i	−0.130022	−	0.737393i
$926$	5.87922	−	14.5516i	0.193203	−	0.478195i
$927$	−53.0777	+	3.71155i	−1.74330	+	0.121903i
$928$	1.47464	+	3.02346i	0.0484075	+	0.0992501i
$929$	−0.0706214	−	2.02233i	−0.00231701	−	0.0663506i	0.997682	−	0.0680556i	$-0.0216795\pi$
$929$	−0.0706214	−	2.02233i	−0.00231701	−	0.0663506i	−0.999999	+	0.00170497i	$0.999457\pi$
$930$	20.4020	−	62.7908i	0.669007	−	2.05899i
$931$	−3.91962	−	25.0586i	−0.128460	−	0.821262i
$932$	8.30810	+	6.03618i	0.272141	+	0.197722i
$933$	23.8354	+	30.5079i	0.780335	+	0.998783i
$934$	5.26390	−	29.8531i	0.172240	−	0.976823i
$935$	25.4362	−	68.2851i	0.831852	−	2.23316i
$936$	11.6261	+	9.75548i	0.380012	+	0.318868i
$937$	−23.3517	+	12.4163i	−0.762868	+	0.405624i	−0.804838	−	0.593495i	$-0.797748\pi$
$937$	−23.3517	+	12.4163i	−0.762868	+	0.405624i	0.0419699	+	0.999119i	$0.486637\pi$
$938$	3.11135	−	29.6025i	0.101589	−	0.966557i
$939$	6.97155	+	66.3299i	0.227508	+	2.16459i
$940$	0.116056	−	0.148545i	0.00378534	−	0.00484501i
$941$	−34.6308	+	44.3253i	−1.12893	+	1.44496i	−0.249854	+	0.968283i	$0.580383\pi$
$941$	−34.6308	+	44.3253i	−1.12893	+	1.44496i	−0.879076	+	0.476682i	$0.841839\pi$
$942$	3.87308	+	36.8499i	0.126192	+	1.20063i
$943$	1.28725	−	12.2473i	0.0419185	−	0.398828i
$944$	2.98243	−	1.58579i	0.0970698	−	0.0516129i
$945$	−53.5261	−	44.9138i	−1.74121	−	1.46104i
$946$	9.88313	−	6.55879i	0.321328	−	0.213245i
$947$	−7.13427	+	40.4605i	−0.231833	+	1.31479i	0.617350	+	0.786689i	$0.288206\pi$
$947$	−7.13427	+	40.4605i	−0.231833	+	1.31479i	−0.849182	+	0.528100i	$0.822905\pi$
$948$	6.16789	+	7.89454i	0.200324	+	0.256403i
$949$	12.6560	+	9.19510i	0.410830	+	0.298486i
$950$	38.5557	+	14.8851i	1.25091	+	0.482935i
$951$	11.5290	−	35.4826i	0.373853	−	1.15060i
$952$	0.721404	+	20.6583i	0.0233809	+	0.669540i
$953$	23.1077	+	47.3778i	0.748532	+	1.53472i	0.842231	+	0.539117i	$0.181242\pi$
$953$	23.1077	+	47.3778i	0.748532	+	1.53472i	−0.0936997	+	0.995601i	$0.529869\pi$
$954$	43.4059	−	3.03524i	1.40532	−	0.0982694i
$955$	−18.9437	+	46.8872i	−0.613003	+	1.51724i
$956$	4.09703	+	23.2354i	0.132507	+	0.751487i
$957$	−31.0767	+	3.03048i	−1.00457	+	0.0979614i
$958$	11.2409	−	19.4698i	0.363178	−	0.629042i
$959$	−0.668735	+	19.1501i	−0.0215946	+	0.618387i
$960$	5.95550	+	8.82939i	0.192213	+	0.284967i
$961$	−0.776608	−	7.38893i	−0.0250519	−	0.238353i
$962$	7.37829	−	1.56830i	0.237886	−	0.0505642i
$963$	28.8112	+	4.04916i	0.928429	+	0.130482i
$964$	27.9489	+	1.95438i	0.900174	+	0.0629463i
$965$	41.2269	−	2.88287i	1.32714	−	0.0928028i
$966$	−88.9743	+	12.5045i	−2.86270	+	0.402326i
$967$	−40.6980	+	14.8129i	−1.30876	+	0.476350i	−0.899840	−	0.436220i	$-0.856317\pi$
$967$	−40.6980	+	14.8129i	−1.30876	+	0.476350i	−0.408921	+	0.912570i	$0.634095\pi$
$968$	0.985352	+	10.9558i	0.0316704	+	0.352132i
$969$	−15.7118	−	68.6559i	−0.504735	−	2.20555i
$970$	−13.2975	−	40.9256i	−0.426958	−	1.31404i
$971$	−37.9940	−	10.8946i	−1.21928	−	0.349624i	−0.396530	−	0.918022i	$-0.629786\pi$
$971$	−37.9940	−	10.8946i	−1.21928	−	0.349624i	−0.822754	+	0.568397i	$0.807564\pi$
$972$	−6.92203	−	14.1923i	−0.222024	−	0.455217i
$973$	21.5328	+	53.2955i	0.690309	+	1.70857i
$974$	30.0818	−	18.7972i	0.963882	−	0.602300i
$975$	−59.9483	−	57.8914i	−1.91988	−	1.85401i
$976$	0.321403	−	3.05795i	0.0102879	−	0.0978826i
$977$	11.3928	+	2.42161i	0.364487	+	0.0774742i	0.386515	−	0.922283i	$-0.373679\pi$
$977$	11.3928	+	2.42161i	0.364487	+	0.0774742i	−0.0220275	+	0.999757i	$0.507012\pi$
$978$	22.6564	+	8.24627i	0.724473	+	0.263687i
$979$	−2.13416	+	2.17702i	−0.0682079	+	0.0695779i
$980$	−11.0715	+	19.1764i	−0.353666	+	0.612568i
$981$	48.4973	−	53.8617i	1.54840	−	1.71967i
$982$	−2.81621	+	5.77409i	−0.0898689	+	0.184259i
$983$	28.4047	+	1.98625i	0.905968	+	0.0633515i	0.515134	−	0.857110i	$-0.327742\pi$
$983$	28.4047	+	1.98625i	0.905968	+	0.0633515i	0.390834	+	0.920461i	$0.372187\pi$
$984$	1.43983	+	3.56370i	0.0459001	+	0.113607i
$985$	22.2693	+	11.8408i	0.709559	+	0.377279i
$986$	−10.8603	+	16.1011i	−0.345863	+	0.512764i
$987$	−0.401557	−	0.291749i	−0.0127817	−	0.00928646i
$988$	−4.48172	+	12.9352i	−0.142583	+	0.411523i
$989$	32.0687			1.01973
$990$	−59.2893	+	14.3103i	−1.88434	+	0.454813i
$991$	−6.30324	+	35.7475i	−0.200229	+	1.13556i	0.704543	+	0.709661i	$0.251152\pi$
$991$	−6.30324	+	35.7475i	−0.200229	+	1.13556i	−0.904773	+	0.425895i	$0.859959\pi$
$992$	5.25719	+	3.28506i	0.166916	+	0.104301i
$993$	11.8910	+	47.6922i	0.377349	+	1.51347i
$994$	27.6949	+	26.7447i	0.878429	+	0.848289i
$995$	−14.8555	+	3.15763i	−0.470950	+	0.100103i
$996$	29.9466	+	33.2590i	0.948894	+	1.05385i
$997$	−5.91431	+	1.69590i	−0.187308	+	0.0537098i	−0.367980	−	0.929834i	$-0.619951\pi$
$997$	−5.91431	+	1.69590i	−0.187308	+	0.0537098i	0.180672	+	0.983543i	$0.442173\pi$
$998$	−14.8208	−	21.9728i	−0.469146	−	0.695537i
$999$	12.0482	+	2.56093i	0.381189	+	0.0810243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.5.2	✓	264
11.9	even	5	inner	418.2.u.b.119.10	yes	264
19.4	even	9	inner	418.2.u.b.137.10	yes	264
209.42	even	45	inner	418.2.u.b.251.2	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.2	✓	264	1.1	even	1	trivial
418.2.u.b.119.10	yes	264	11.9	even	5	inner
418.2.u.b.137.10	yes	264	19.4	even	9	inner
418.2.u.b.251.2	yes	264	209.42	even	45	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 - 0.788011i) q^{2} +(-2.01318 + 1.94411i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(3.22722 - 2.01659i) q^{5} +(2.77142 + 0.389497i) q^{6} +(-3.27079 - 1.45625i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.168650 - 4.82951i) q^{9} +O(q^{10})\)	\(q+(-0.615661 - 0.788011i) q^{2} +(-2.01318 + 1.94411i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(3.22722 - 2.01659i) q^{5} +(2.77142 + 0.389497i) q^{6} +(-3.27079 - 1.45625i) q^{7} +(0.913545 - 0.406737i) q^{8} +(0.168650 - 4.82951i) q^{9} +(-3.57597 - 1.30155i) q^{10} +(1.92925 + 2.69777i) q^{11} +(-1.39933 - 2.42370i) q^{12} +(-2.77299 + 1.47443i) q^{13} +(0.866159 + 3.47398i) q^{14} +(-2.57651 + 10.3338i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(-0.201491 - 5.76995i) q^{17} +(-3.90954 + 2.84044i) q^{18} +(-3.65112 - 2.38104i) q^{19} +(1.17595 + 3.61921i) q^{20} +(9.41580 - 3.42707i) q^{21} +(0.938106 - 3.18119i) q^{22} +(6.86901 - 5.76378i) q^{23} +(-1.04839 + 2.59486i) q^{24} +(4.15645 - 8.52198i) q^{25} +(2.86909 + 1.27740i) q^{26} +(3.43157 + 3.81114i) q^{27} +(2.20427 - 2.82134i) q^{28} +(3.23360 - 0.927220i) q^{29} +(9.72942 - 4.33182i) q^{30} +(4.14805 - 4.60688i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-9.12870 - 1.68043i) q^{33} +(-4.42274 + 3.71112i) q^{34} +(-13.4922 + 1.89621i) q^{35} +(4.64525 + 1.33200i) q^{36} +(1.94310 - 1.41175i) q^{37} +(0.371571 + 4.34303i) q^{38} +(2.71609 - 8.35928i) q^{39} +(2.12799 - 3.15487i) q^{40} +(0.987917 - 0.954021i) q^{41} +(-8.49752 - 5.30984i) q^{42} +(2.73965 + 2.29884i) q^{43} +(-3.08437 + 1.21930i) q^{44} +(-9.19487 - 15.9260i) q^{45} +(-8.77091 - 1.86431i) q^{46} +(-0.0277000 - 0.0410670i) q^{47} +(2.69024 - 0.771413i) q^{48} +(3.89350 + 4.32417i) q^{49} +(-9.27438 + 1.97133i) q^{50} +(11.6230 + 11.2242i) q^{51} +(-0.759781 - 3.04732i) q^{52} +(-7.63591 - 4.77145i) q^{53} +(0.890536 - 5.05048i) q^{54} +(11.6664 + 4.81579i) q^{55} -3.58033 q^{56} +(11.9794 - 2.30471i) q^{57} +(-2.72146 - 1.97726i) q^{58} +(-1.88885 + 2.80033i) q^{59} +(-9.40355 - 4.99995i) q^{60} +(1.15184 + 2.85090i) q^{61} +(-6.18406 - 0.432432i) q^{62} +(-7.58459 + 15.5507i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-5.97574 + 10.3503i) q^{65} +(4.29599 + 8.22809i) q^{66} +(-7.81227 - 2.84344i) q^{67} +(5.64731 + 1.20037i) q^{68} +(-2.62315 + 24.9576i) q^{69} +(9.80087 + 9.46459i) q^{70} +(9.11934 - 5.69840i) q^{71} +(-1.81027 - 4.48057i) q^{72} +(-2.18357 - 4.47697i) q^{73} +(-2.30876 - 0.662027i) q^{74} +(8.19996 + 25.2369i) q^{75} +(3.19359 - 2.96664i) q^{76} +(-2.38156 - 11.6333i) q^{77} +(-8.25939 + 3.00617i) q^{78} +(-3.54486 + 0.498197i) q^{79} +(-3.79620 + 0.265456i) q^{80} +(0.144413 + 0.0100984i) q^{81} +(-1.36000 - 0.191136i) q^{82} +(-15.6420 + 3.32481i) q^{83} +(1.04738 + 9.96520i) q^{84} +(-12.2859 - 18.2146i) q^{85} +(0.124813 - 3.57418i) q^{86} +(-4.70721 + 8.15312i) q^{87} +(2.85974 + 1.67984i) q^{88} +(0.159616 + 0.905226i) q^{89} +(-6.88891 + 17.0507i) q^{90} +(11.2170 - 0.784369i) q^{91} +(3.93081 + 8.05936i) q^{92} +(0.605482 + 17.3387i) q^{93} +(-0.0153074 + 0.0471113i) q^{94} +(-16.5845 - 0.321316i) q^{95} +(-2.26416 - 1.64501i) q^{96} +(6.96182 + 8.91072i) q^{97} +(1.01041 - 5.73034i) q^{98} +(13.3543 - 8.86237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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