LMFDB - Embedded newform 270.2.r.a.77.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(23,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 27]))

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

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

chi := DirichletCharacter("270.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.r (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			77.7
Character	$\chi$	$=$	270.77
Dual form			270.2.r.a.263.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.906308 + 0.422618i) q^{2} +(1.33891 + 1.09878i) q^{3} +(0.642788 - 0.766044i) q^{4} +(-2.00011 + 0.999773i) q^{5} +(-1.67783 - 0.429980i) q^{6} +(-3.41173 - 0.298488i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.585380 + 2.94233i) q^{9} +O(q^{10})$	\(q+(-0.906308 + 0.422618i) q^{2} +(1.33891 + 1.09878i) q^{3} +(0.642788 - 0.766044i) q^{4} +(-2.00011 + 0.999773i) q^{5} +(-1.67783 - 0.429980i) q^{6} +(-3.41173 - 0.298488i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.585380 + 2.94233i) q^{9} +(1.39020 - 1.75139i) q^{10} +(-4.70038 + 0.828804i) q^{11} +(1.70235 - 0.319387i) q^{12} +(-0.816512 + 1.75102i) q^{13} +(3.21823 - 1.17134i) q^{14} +(-3.77651 - 0.859067i) q^{15} +(-0.173648 - 0.984808i) q^{16} +(1.39278 + 5.19794i) q^{17} +(-1.77402 - 2.41927i) q^{18} +(5.37612 - 3.10390i) q^{19} +(-0.519777 + 2.17482i) q^{20} +(-4.24004 - 4.14838i) q^{21} +(3.90972 - 2.73762i) q^{22} +(0.0973994 + 1.11328i) q^{23} +(-1.40787 + 1.00891i) q^{24} +(3.00091 - 3.99932i) q^{25} -1.93203i q^{26} +(-2.44919 + 4.58273i) q^{27} +(-2.42167 + 2.42167i) q^{28} +(-0.0131911 - 0.00480116i) q^{29} +(3.78574 - 0.817441i) q^{30} +(1.74674 + 1.46569i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-7.20407 - 4.05497i) q^{33} +(-3.45904 - 4.12232i) q^{34} +(7.12227 - 2.81395i) q^{35} +(2.63023 + 1.44287i) q^{36} +(-9.61180 + 2.57547i) q^{37} +(-3.56065 + 5.08514i) q^{38} +(-3.01722 + 1.44730i) q^{39} +(-0.448040 - 2.19072i) q^{40} +(-0.132710 - 0.364617i) q^{41} +(5.59597 + 1.96779i) q^{42} +(3.98494 + 2.79028i) q^{43} +(-2.38644 + 4.13344i) q^{44} +(-4.11249 - 5.29975i) q^{45} +(-0.558767 - 0.967812i) q^{46} +(-0.0692108 + 0.791084i) q^{47} +(0.849584 - 1.50937i) q^{48} +(4.65717 + 0.821184i) q^{49} +(-1.02956 + 4.89285i) q^{50} +(-3.84656 + 8.48995i) q^{51} +(0.816512 + 1.75102i) q^{52} +(5.53811 + 5.53811i) q^{53} +(0.282978 - 5.18844i) q^{54} +(8.57267 - 6.35701i) q^{55} +(1.17134 - 3.21823i) q^{56} +(10.6087 + 1.75129i) q^{57} +(0.0139842 - 0.00122346i) q^{58} +(2.02310 - 11.4736i) q^{59} +(-3.08558 + 2.34077i) q^{60} +(1.20616 - 1.01209i) q^{61} +(-2.20251 - 0.590162i) q^{62} +(-1.11891 - 10.2132i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.117503 - 4.31856i) q^{65} +(8.24281 + 0.630478i) q^{66} +(10.2083 + 4.76023i) q^{67} +(4.87712 + 2.27424i) q^{68} +(-1.09284 + 1.59761i) q^{69} +(-5.26574 + 5.56031i) q^{70} +(-2.10165 - 1.21339i) q^{71} +(-2.99358 - 0.196099i) q^{72} +(8.26239 + 2.21390i) q^{73} +(7.62281 - 6.39630i) q^{74} +(8.41231 - 2.05742i) q^{75} +(1.07797 - 6.11349i) q^{76} +(16.2838 - 1.42465i) q^{77} +(2.12287 - 2.58683i) q^{78} +(-3.80042 + 10.4416i) q^{79} +(1.33190 + 1.79612i) q^{80} +(-8.31466 + 3.44477i) q^{81} +(0.274370 + 0.274370i) q^{82} +(-5.81691 - 12.4744i) q^{83} +(-5.90329 + 0.581534i) q^{84} +(-7.98249 - 9.00400i) q^{85} +(-4.79081 - 0.844748i) q^{86} +(-0.0123863 - 0.0209224i) q^{87} +(0.415985 - 4.75473i) q^{88} +(7.52167 + 13.0279i) q^{89} +(5.96696 + 3.06519i) q^{90} +(3.30838 - 5.73028i) q^{91} +(0.915429 + 0.640991i) q^{92} +(0.728270 + 3.88171i) q^{93} +(-0.271600 - 0.746215i) q^{94} +(-7.64964 + 11.5831i) q^{95} +(-0.132096 + 1.72701i) q^{96} +(-10.2282 + 14.6074i) q^{97} +(-4.56787 + 1.22396i) q^{98} +(-5.19012 - 13.3449i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6}+O(q^{10}) $ 216 * q + 12 * q^6	$ 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50} - 192 q^{51} - 12 q^{56} - 36 q^{57} + 36 q^{61} + 84 q^{63} + 24 q^{65} - 72 q^{67} + 36 q^{68} - 48 q^{72} - 36 q^{75} - 240 q^{77} + 24 q^{78} - 24 q^{81} - 60 q^{83} + 72 q^{86} - 252 q^{87} - 48 q^{92} - 96 q^{93} - 60 q^{95} - 72 q^{97}+O(q^{100}) $ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$2$	−0.906308	+	0.422618i	−0.640856	+	0.298836i
$3$	1.33891	+	1.09878i	0.773022	+	0.634379i
$3$	1.33891	+	1.09878i	0.773022	+	0.634379i
$4$	0.642788	−	0.766044i	0.321394	−	0.383022i
$5$	−2.00011	+	0.999773i	−0.894478	+	0.447112i
$5$	−2.00011	+	0.999773i	−0.894478	+	0.447112i
$6$	−1.67783	−	0.429980i	−0.684972	−	0.175539i
$7$	−3.41173	−	0.298488i	−1.28951	−	0.112818i	−0.578318	−	0.815812i	$-0.696291\pi$
$7$	−3.41173	−	0.298488i	−1.28951	−	0.112818i	−0.711196	+	0.702994i	$0.751846\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$	0.585380	+	2.94233i	0.195127	+	0.980778i
$10$	1.39020	−	1.75139i	0.439618	−	0.553837i
$11$	−4.70038	+	0.828804i	−1.41722	+	0.249894i	−0.829199	−	0.558954i	$-0.811203\pi$
$11$	−4.70038	+	0.828804i	−1.41722	+	0.249894i	−0.588019	+	0.808847i	$0.700092\pi$
$12$	1.70235	−	0.319387i	0.491426	−	0.0921992i
$13$	−0.816512	+	1.75102i	−0.226460	+	0.485645i	−0.986403	−	0.164345i	$-0.947449\pi$
$13$	−0.816512	+	1.75102i	−0.226460	+	0.485645i	0.759943	+	0.649990i	$0.225227\pi$
$14$	3.21823	−	1.17134i	0.860107	−	0.313053i
$15$	−3.77651	−	0.859067i	−0.975090	−	0.221810i
$16$	−0.173648	−	0.984808i	−0.0434120	−	0.246202i
$17$	1.39278	+	5.19794i	0.337800	+	1.26069i	0.900802	+	0.434230i	$0.142980\pi$
$17$	1.39278	+	5.19794i	0.337800	+	1.26069i	−0.563002	+	0.826455i	$0.690354\pi$
$18$	−1.77402	−	2.41927i	−0.418140	−	0.570227i
$19$	5.37612	−	3.10390i	1.23337	−	0.712084i	0.265636	−	0.964073i	$-0.414418\pi$
$19$	5.37612	−	3.10390i	1.23337	−	0.712084i	0.967730	+	0.251989i	$0.0810848\pi$
$20$	−0.519777	+	2.17482i	−0.116226	+	0.486304i
$21$	−4.24004	−	4.14838i	−0.925253	−	0.905251i
$22$	3.90972	−	2.73762i	0.833556	−	0.583662i
$23$	0.0973994	+	1.11328i	0.0203092	+	0.232135i	0.999565	+	0.0295054i	$0.00939321\pi$
$23$	0.0973994	+	1.11328i	0.0203092	+	0.232135i	−0.979255	+	0.202630i	$0.935051\pi$
$24$	−1.40787	+	1.00891i	−0.287381	+	0.205942i
$25$	3.00091	−	3.99932i	0.600181	−	0.799864i
$26$		−	1.93203i		−	0.378903i
$27$	−2.44919	+	4.58273i	−0.471348	+	0.881947i
$28$	−2.42167	+	2.42167i	−0.457653	+	0.457653i
$29$	−0.0131911	−	0.00480116i	−0.00244952	−	0.000891553i	0.340795	−	0.940138i	$-0.389304\pi$
$29$	−0.0131911	−	0.00480116i	−0.00244952	−	0.000891553i	−0.343245	+	0.939246i	$0.611526\pi$
$30$	3.78574	−	0.817441i	0.691177	−	0.149244i
$31$	1.74674	+	1.46569i	0.313724	+	0.263246i	0.786029	−	0.618189i	$-0.212133\pi$
$31$	1.74674	+	1.46569i	0.313724	+	0.263246i	−0.472305	+	0.881435i	$0.656578\pi$
$32$	0.573576	+	0.819152i	0.101395	+	0.144807i
$33$	−7.20407	−	4.05497i	−1.25407	−	0.705880i
$34$	−3.45904	−	4.12232i	−0.593220	−	0.706972i
$35$	7.12227	−	2.81395i	1.20388	−	0.475644i
$36$	2.63023	+	1.44287i	0.438372	+	0.240478i
$37$	−9.61180	+	2.57547i	−1.58017	+	0.423405i	−0.938979	−	0.343975i	$-0.888226\pi$
$37$	−9.61180	+	2.57547i	−1.58017	+	0.423405i	−0.641192	+	0.767381i	$0.721560\pi$
$38$	−3.56065	+	5.08514i	−0.577614	+	0.824918i
$39$	−3.01722	+	1.44730i	−0.483141	+	0.231753i
$40$	−0.448040	−	2.19072i	−0.0708413	−	0.346383i
$41$	−0.132710	−	0.364617i	−0.0207258	−	0.0569436i	0.928898	−	0.370335i	$-0.120757\pi$
$41$	−0.132710	−	0.364617i	−0.0207258	−	0.0569436i	−0.949624	+	0.313391i	$0.898535\pi$
$42$	5.59597	+	1.96779i	0.863476	+	0.303637i
$43$	3.98494	+	2.79028i	0.607697	+	0.425514i	0.836506	−	0.547957i	$-0.184594\pi$
$43$	3.98494	+	2.79028i	0.607697	+	0.425514i	−0.228809	+	0.973471i	$0.573483\pi$
$44$	−2.38644	+	4.13344i	−0.359770	+	0.623140i
$45$	−4.11249	−	5.29975i	−0.613054	−	0.790041i
$46$	−0.558767	−	0.967812i	−0.0823856	−	0.142696i
$47$	−0.0692108	+	0.791084i	−0.0100954	+	0.115391i	−0.999570	−	0.0293137i	$-0.990668\pi$
$47$	−0.0692108	+	0.791084i	−0.0100954	+	0.115391i	0.989475	+	0.144705i	$0.0462234\pi$
$48$	0.849584	−	1.50937i	0.122627	−	0.217859i
$49$	4.65717	+	0.821184i	0.665310	+	0.117312i
$50$	−1.02956	+	4.89285i	−0.145602	+	0.691954i
$51$	−3.84656	+	8.48995i	−0.538626	+	1.18883i
$52$	0.816512	+	1.75102i	0.113230	+	0.242822i
$53$	5.53811	+	5.53811i	0.760717	+	0.760717i	0.976452	−	0.215735i	$-0.0692146\pi$
$53$	5.53811	+	5.53811i	0.760717	+	0.760717i	−0.215735	+	0.976452i	$0.569215\pi$
$54$	0.282978	−	5.18844i	0.0385084	−	0.706057i
$55$	8.57267	−	6.35701i	1.15594	−	0.857180i
$56$	1.17134	−	3.21823i	0.156527	−	0.430054i
$57$	10.6087	+	1.75129i	1.40515	+	0.231965i
$58$	0.0139842	−	0.00122346i	0.00183622	−	0.000160648i
$59$	2.02310	−	11.4736i	0.263385	−	1.49373i	−0.510210	−	0.860050i	$-0.670432\pi$
$59$	2.02310	−	11.4736i	0.263385	−	1.49373i	0.773595	−	0.633681i	$-0.218457\pi$
$60$	−3.08558	+	2.34077i	−0.398346	+	0.302193i
$61$	1.20616	−	1.01209i	0.154433	−	0.129584i	−0.562298	−	0.826935i	$-0.690082\pi$
$61$	1.20616	−	1.01209i	0.154433	−	0.129584i	0.716730	+	0.697351i	$0.245638\pi$
$62$	−2.20251	−	0.590162i	−0.279720	−	0.0749506i
$63$	−1.11891	−	10.2132i	−0.140969	−	1.28674i
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	−0.117503	−	4.31856i	−0.0145744	−	0.535651i
$66$	8.24281	+	0.630478i	1.01462	+	0.0776065i
$67$	10.2083	+	4.76023i	1.24715	+	0.581555i	0.930257	−	0.366907i	$-0.119583\pi$
$67$	10.2083	+	4.76023i	1.24715	+	0.581555i	0.316891	+	0.948462i	$0.397361\pi$
$68$	4.87712	+	2.27424i	0.591437	+	0.275792i
$69$	−1.09284	+	1.59761i	−0.131562	+	0.192329i
$70$	−5.26574	+	5.56031i	−0.629377	+	0.664584i
$71$	−2.10165	−	1.21339i	−0.249420	−	0.144003i	0.370078	−	0.929001i	$-0.379331\pi$
$71$	−2.10165	−	1.21339i	−0.249420	−	0.144003i	−0.619499	+	0.784998i	$0.712664\pi$
$72$	−2.99358	−	0.196099i	−0.352797	−	0.0231104i
$73$	8.26239	+	2.21390i	0.967039	+	0.259117i	0.707577	−	0.706636i	$-0.249788\pi$
$73$	8.26239	+	2.21390i	0.967039	+	0.259117i	0.259462	+	0.965753i	$0.416455\pi$
$74$	7.62281	−	6.39630i	0.886133	−	0.743554i
$75$	8.41231	−	2.05742i	0.971370	−	0.237570i
$76$	1.07797	−	6.11349i	0.123652	−	0.701266i
$77$	16.2838	−	1.42465i	1.85571	−	0.162354i
$78$	2.12287	−	2.58683i	0.240368	−	0.292900i
$79$	−3.80042	+	10.4416i	−0.427580	+	1.17477i	0.519696	+	0.854351i	$0.326045\pi$
$79$	−3.80042	+	10.4416i	−0.427580	+	1.17477i	−0.947277	+	0.320417i	$0.896177\pi$
$80$	1.33190	+	1.79612i	0.148911	+	0.200812i
$81$	−8.31466	+	3.44477i	−0.923851	+	0.382752i
$82$	0.274370	+	0.274370i	0.0302990	+	0.0302990i
$83$	−5.81691	−	12.4744i	−0.638489	−	1.36924i	−0.913119	−	0.407693i	$-0.866333\pi$
$83$	−5.81691	−	12.4744i	−0.638489	−	1.36924i	0.274630	−	0.961550i	$-0.411445\pi$
$84$	−5.90329	+	0.581534i	−0.644102	+	0.0634505i
$85$	−7.98249	−	9.00400i	−0.865822	−	0.976621i
$86$	−4.79081	−	0.844748i	−0.516606	−	0.0910915i
$87$	−0.0123863	−	0.0209224i	−0.00132795	−	0.00224311i
$88$	0.415985	−	4.75473i	0.0443441	−	0.506856i
$89$	7.52167	+	13.0279i	0.797296	+	1.38096i	0.921371	+	0.388684i	$0.127070\pi$
$89$	7.52167	+	13.0279i	0.797296	+	1.38096i	−0.124075	+	0.992273i	$0.539596\pi$
$90$	5.96696	+	3.06519i	0.628973	+	0.323100i
$91$	3.30838	−	5.73028i	0.346812	−	0.600697i
$92$	0.915429	+	0.640991i	0.0954401	+	0.0668279i
$93$	0.728270	+	3.88171i	0.0755181	+	0.402515i
$94$	−0.271600	−	0.746215i	−0.0280134	−	0.0769662i
$95$	−7.64964	+	11.5831i	−0.784837	+	1.18840i
$96$	−0.132096	+	1.72701i	−0.0134820	+	0.176262i
$97$	−10.2282	+	14.6074i	−1.03852	+	1.48315i	−0.171301	+	0.985219i	$0.554797\pi$
$97$	−10.2282	+	14.6074i	−1.03852	+	1.48315i	−0.867215	+	0.497935i	$0.834092\pi$
$98$	−4.56787	+	1.22396i	−0.461425	+	0.123638i
$99$	−5.19012	−	13.3449i	−0.521627	−	1.34121i
$100$	−1.13471	−	4.86954i	−0.113471	−	0.486954i
$101$	−1.36748	−	1.62970i	−0.136069	−	0.162161i	0.693707	−	0.720257i	$-0.255976\pi$
$101$	−1.36748	−	1.62970i	−0.136069	−	0.162161i	−0.829776	+	0.558097i	$0.811532\pi$
$102$	−0.101843	−	9.32013i	−0.0100840	−	0.922831i
$103$	1.45888	+	2.08350i	0.143748	+	0.205293i	0.884569	−	0.466409i	$-0.154452\pi$
$103$	1.45888	+	2.08350i	0.143748	+	0.205293i	−0.740821	+	0.671702i	$0.765564\pi$
$104$	−1.48002	−	1.24189i	−0.145128	−	0.121777i
$105$	12.6280	+	4.05815i	1.23237	+	0.396035i
$106$	−7.35973	−	2.67872i	−0.714840	−	0.260181i
$107$	4.24792	−	4.24792i	0.410662	−	0.410662i	−0.471307	−	0.881969i	$-0.656218\pi$
$107$	4.24792	−	4.24792i	0.410662	−	0.410662i	0.881969	+	0.471307i	$0.156218\pi$
$108$	1.93627	+	4.82192i	0.186317	+	0.463989i
$109$		−	2.45742i		−	0.235378i	−0.993051	−	0.117689i	$-0.962451\pi$
$109$		−	2.45742i		−	0.235378i	0.993051	−	0.117689i	$-0.0375486\pi$
$110$	−5.08289	+	9.38438i	−0.484635	+	0.894766i
$111$	−15.6992	−	7.11288i	−1.49011	−	0.675125i
$112$	0.298488	+	3.41173i	0.0282045	+	0.322378i
$113$	−11.9224	+	8.34818i	−1.12157	+	0.785331i	−0.978880	−	0.204437i	$-0.934464\pi$
$113$	−11.9224	+	8.34818i	−1.12157	+	0.785331i	−0.142689	+	0.989768i	$0.545575\pi$
$114$	−10.3548	+	2.89620i	−0.969819	+	0.271254i
$115$	−1.30784	−	2.12931i	−0.121957	−	0.198559i
$116$	−0.0121570	+	0.00701882i	−0.00112875	+	0.000651681i
$117$	−5.63005	−	1.37744i	−0.520498	−	0.127345i
$118$	3.01539	+	11.2536i	0.277589	+	1.03598i
$119$	−3.20028	−	18.1497i	−0.293369	−	1.66378i
$120$	1.80723	−	3.42548i	0.164977	−	0.312702i
$121$	11.0700	−	4.02916i	1.00637	−	0.366287i
$122$	−0.665423	+	1.42701i	−0.0602446	+	0.129195i
$123$	0.222946	−	0.634009i	0.0201023	−	0.0571666i
$124$	2.24557	−	0.395954i	0.201658	−	0.0355577i
$125$	−2.00374	+	10.9993i	−0.179220	+	0.983809i
$126$	5.33035	+	8.78342i	0.474866	+	0.782489i
$127$	4.89147	−	18.2552i	0.434048	−	1.61989i	−0.309288	−	0.950969i	$-0.600091\pi$
$127$	4.89147	−	18.2552i	0.434048	−	1.61989i	0.743335	−	0.668919i	$-0.233243\pi$
$128$	0.996195	+	0.0871557i	0.0880520	+	0.00770355i
$129$	2.26959	+	8.11451i	0.199826	+	0.714442i
$130$	1.93160	+	3.86428i	0.169412	+	0.338920i
$131$	1.19590	−	1.42522i	0.104486	−	0.124522i	−0.711267	−	0.702922i	$-0.751878\pi$
$131$	1.19590	−	1.42522i	0.104486	−	0.124522i	0.815753	+	0.578400i	$0.196323\pi$
$132$	−7.73697	+	2.91215i	−0.673417	+	0.253471i
$133$	−19.2683	+	8.98498i	−1.67078	+	0.779096i
$134$	−11.2637			−0.973032
$135$	0.316972	−	11.6146i	0.0272806	−	0.999628i
$136$	−5.38130			−0.461443
$137$	−7.40450	+	3.45278i	−0.632609	+	0.294991i	−0.712349	−	0.701825i	$-0.752369\pi$
$137$	−7.40450	+	3.45278i	−0.632609	+	0.294991i	0.0797400	+	0.996816i	$0.474591\pi$
$138$	0.315269	−	1.90978i	0.0268375	−	0.162571i
$139$	−10.7748	+	12.8409i	−0.913904	+	1.08915i	0.0818088	+	0.996648i	$0.473930\pi$
$139$	−10.7748	+	12.8409i	−0.913904	+	1.08915i	−0.995713	+	0.0925002i	$0.970514\pi$
$140$	2.42250	−	7.26475i	0.204738	−	0.613983i
$141$	−0.961892	+	0.983145i	−0.0810059	+	0.0827958i
$142$	2.41755	+	0.211508i	0.202876	+	0.0177494i
$143$	2.38667	−	8.90717i	0.199583	−	0.744855i
$144$	2.79598	−	1.08742i	0.232999	−	0.0906181i
$145$	0.0311837	−	0.00358523i	0.00258967	−	0.000297737i
$146$	−8.42390	+	1.48536i	−0.697167	+	0.122929i
$147$	5.33325	+	6.21668i	0.439879	+	0.512743i
$148$	−4.20542	+	9.01855i	−0.345683	+	0.741320i
$149$	15.3073	−	5.57142i	1.25403	−	0.456428i	0.372266	−	0.928126i	$-0.378581\pi$
$149$	15.3073	−	5.57142i	1.25403	−	0.456428i	0.881760	+	0.471698i	$0.156359\pi$
$150$	−6.75464	+	5.41985i	−0.551514	+	0.442529i
$151$	2.09008	+	11.8534i	0.170088	+	0.964618i	0.943662	+	0.330911i	$0.107356\pi$
$151$	2.09008	+	11.8534i	0.170088	+	0.964618i	−0.773574	+	0.633706i	$0.781533\pi$
$152$	1.60670	+	5.99628i	0.130320	+	0.486362i
$153$	−14.4788	+	7.14081i	−1.17054	+	0.577300i
$154$	−14.1561	+	8.17301i	−1.14073	+	0.658600i
$155$	−4.95904	−	1.18520i	−0.398320	−	0.0951976i
$156$	−0.830736	+	3.24162i	−0.0665121	+	0.259538i
$157$	−9.03750	+	6.32813i	−0.721271	+	0.505039i	−0.875634	−	0.482975i	$-0.839556\pi$
$157$	−9.03750	+	6.32813i	−0.721271	+	0.505039i	0.154363	+	0.988014i	$0.450667\pi$
$158$	−0.968447	−	11.0694i	−0.0770455	−	0.880634i
$159$	1.32990	+	13.5002i	0.105468	+	1.07063i
$160$	−1.96618	−	1.06495i	−0.155441	−	0.0841917i
$161$		−	3.82729i		−	0.301633i
$162$	6.07982	−	6.63595i	0.477676	−	0.521369i
$163$	−7.80113	+	7.80113i	−0.611032	+	0.611032i	−0.943215	−	0.332183i	$-0.892215\pi$
$163$	−7.80113	+	7.80113i	−0.611032	+	0.611032i	0.332183	+	0.943215i	$0.392215\pi$
$164$	−0.364617	−	0.132710i	−0.0284718	−	0.0103629i
$165$	18.4630	+	0.907959i	1.43734	+	0.0706845i
$166$	10.5438	+	8.84731i	0.818359	+	0.686685i
$167$	−11.3321	−	16.1839i	−0.876903	−	1.25235i	−0.966577	−	0.256377i	$-0.917471\pi$
$167$	−11.3321	−	16.1839i	−0.876903	−	1.25235i	0.0896736	−	0.995971i	$-0.471418\pi$
$168$	5.10443	−	3.02189i	0.393816	−	0.233144i
$169$	5.95687	+	7.09912i	0.458221	+	0.546087i
$170$	11.0398	+	4.78685i	0.846718	+	0.367135i
$171$	12.2798	+	14.0014i	0.939059	+	1.07071i
$172$	4.69895	−	1.25908i	0.358292	−	0.0960039i
$173$	13.8009	−	19.7098i	1.04927	−	1.49851i	0.193529	−	0.981095i	$-0.438007\pi$
$173$	13.8009	−	19.7098i	1.04927	−	1.49851i	0.855736	−	0.517412i	$-0.173105\pi$
$174$	0.0200680	+	0.0137274i	0.00152135	+	0.00104067i
$175$	−11.4320	+	12.7489i	−0.864181	+	0.963724i
$176$	1.63242	+	4.48505i	0.123049	+	0.338073i
$177$	15.3156	−	13.1392i	1.15119	−	0.987601i
$178$	−12.3228	−	8.62851i	−0.923632	−	0.646734i
$179$	3.91228	−	6.77627i	0.292418	−	0.506482i	−0.681963	−	0.731386i	$-0.738874\pi$
$179$	3.91228	−	6.77627i	0.292418	−	0.506482i	0.974381	+	0.224904i	$0.0722070\pi$
$180$	−6.70331	−	0.256263i	−0.499635	−	0.0191007i
$181$	−0.435002	−	0.753445i	−0.0323334	−	0.0560032i	0.849406	−	0.527740i	$-0.176961\pi$
$181$	−0.435002	−	0.753445i	−0.0323334	−	0.0560032i	−0.881739	+	0.471737i	$0.843627\pi$
$182$	−0.576688	+	6.59158i	−0.0427470	+	0.488600i
$183$	2.72700	−	0.0297986i	0.201585	−	0.00220277i
$184$	−1.10056	−	0.194058i	−0.0811340	−	0.0143061i
$185$	16.6498	−	14.7609i	1.22412	−	1.08524i
$186$	−2.30052	−	3.21025i	−0.168682	−	0.235387i
$187$	−10.8547	−	23.2779i	−0.793773	−	1.70225i
$188$	0.561517	+	0.561517i	0.0409529	+	0.0409529i
$189$	9.72389	−	14.9040i	0.707309	−	1.08411i
$190$	2.03772	−	13.7307i	0.147832	−	0.996129i
$191$	−3.36360	+	9.24141i	−0.243381	+	0.668685i	0.756511	+	0.653981i	$0.226903\pi$
$191$	−3.36360	+	9.24141i	−0.243381	+	0.668685i	−0.999892	+	0.0147032i	$0.995320\pi$
$192$	−0.610145	−	1.62103i	−0.0440334	−	0.116987i
$193$	8.13419	−	0.711650i	0.585512	−	0.0512257i	0.209449	−	0.977820i	$-0.432833\pi$
$193$	8.13419	−	0.711650i	0.585512	−	0.0512257i	0.376063	+	0.926594i	$0.377278\pi$
$194$	3.09655	−	17.5614i	0.222319	−	1.26083i
$195$	4.58781	−	5.91129i	0.328540	−	0.423316i
$196$	3.62263	−	3.03975i	0.258759	−	0.217125i
$197$	−21.1806	−	5.67532i	−1.50905	−	0.404350i	−0.592933	−	0.805252i	$-0.702030\pi$
$197$	−21.1806	−	5.67532i	−1.50905	−	0.404350i	−0.916121	+	0.400902i	$0.868697\pi$
$198$	10.3437	+	9.90116i	0.735092	+	0.703645i
$199$	−4.58949	−	2.64974i	−0.325340	−	0.187835i	0.328430	−	0.944528i	$-0.393480\pi$
$199$	−4.58949	−	2.64974i	−0.325340	−	0.187835i	−0.653770	+	0.756693i	$0.726814\pi$
$200$	3.08636	+	3.93375i	0.218238	+	0.278158i
$201$	8.43767	+	17.5902i	0.595147	+	1.24072i
$202$	1.92809	+	0.899085i	0.135660	+	0.0632594i
$203$	0.0435713	+	0.0203176i	0.00305811	+	0.00142602i
$204$	4.03116	+	8.40387i	0.282238	+	0.588389i
$205$	0.629969	+	0.596595i	0.0439989	+	0.0416680i
$206$	−2.20272	−	1.27174i	−0.153471	−	0.0886064i
$207$	−3.21863	+	0.938274i	−0.223710	+	0.0652145i
$208$	1.86620	+	0.500047i	0.129398	+	0.0346720i
$209$	−22.6973	+	19.0453i	−1.57000	+	1.31739i
$210$	−13.1599	+	1.65889i	−0.908120	+	0.114475i
$211$	2.85111	−	16.1695i	0.196279	−	1.11315i	−0.714308	−	0.699832i	$-0.753258\pi$
$211$	2.85111	−	16.1695i	0.196279	−	1.11315i	0.910586	−	0.413319i	$-0.135631\pi$
$212$	7.80226	−	0.682609i	0.535861	−	0.0468818i
$213$	−1.48069	−	3.93387i	−0.101455	−	0.269545i
$214$	−2.05467	+	5.64517i	−0.140455	+	0.385896i
$215$	−10.7600	−	1.59685i	−0.733824	−	0.108904i
$216$	−3.79268	−	3.55184i	−0.258059	−	0.241672i
$217$	−5.52193	−	5.52193i	−0.374853	−	0.374853i
$218$	1.03855	+	2.22718i	0.0703395	+	0.150843i
$219$	8.63004	+	12.0427i	0.583164	+	0.813773i
$220$	0.640653	−	10.6533i	0.0431928	−	0.718243i
$221$	−10.2389	−	1.80540i	−0.688743	−	0.121444i
$222$	17.2344	−	0.188324i	1.15670	−	0.0126395i
$223$	0.866913	−	9.90886i	0.0580528	−	0.663547i	−0.910298	−	0.413954i	$-0.864148\pi$
$223$	0.866913	−	9.90886i	0.0580528	−	0.663547i	0.968351	−	0.249593i	$-0.0802968\pi$
$224$	−1.71238	−	2.96593i	−0.114413	−	0.198170i
$225$	13.5240	+	6.48855i	0.901600	+	0.432570i
$226$	7.27730	−	12.6047i	0.484079	−	0.838450i
$227$	9.94373	+	6.96268i	0.659989	+	0.462129i	0.854970	−	0.518678i	$-0.173576\pi$
$227$	9.94373	+	6.96268i	0.659989	+	0.462129i	−0.194981	+	0.980807i	$0.562465\pi$
$228$	8.16068	−	7.00099i	0.540454	−	0.463652i
$229$	3.56444	+	9.79323i	0.235545	+	0.647155i	0.999997	+	0.00247388i	$0.000787462\pi$
$229$	3.56444	+	9.79323i	0.235545	+	0.647155i	−0.764452	+	0.644681i	$0.776990\pi$
$230$	2.08519	+	1.37709i	0.137493	+	0.0908029i
$231$	23.3680	+	15.9848i	1.53750	+	1.05172i
$232$	0.00805166	−	0.0114990i	0.000528618	−	0.000754944i
$233$	9.67519	−	2.59246i	0.633843	−	0.169838i	0.0724298	−	0.997374i	$-0.476925\pi$
$233$	9.67519	−	2.59246i	0.633843	−	0.169838i	0.561413	+	0.827536i	$0.310258\pi$
$234$	5.68469	−	1.13097i	0.371620	−	0.0739340i
$235$	−0.652475	−	1.65145i	−0.0425628	−	0.107729i
$236$	−7.48884	−	8.92485i	−0.487482	−	0.580958i
$237$	−16.5614	+	9.80454i	−1.07578	+	0.636873i
$238$	10.5708	+	15.0967i	0.685206	+	0.978575i
$239$	0.520564	+	0.436805i	0.0336725	+	0.0282546i	0.659469	−	0.751732i	$-0.270781\pi$
$239$	0.520564	+	0.436805i	0.0336725	+	0.0282546i	−0.625796	+	0.779987i	$0.715226\pi$
$240$	−0.190233	+	3.86831i	−0.0122795	+	0.249698i
$241$	18.3051	+	6.66251i	1.17913	+	0.429170i	0.855896	−	0.517148i	$-0.173006\pi$
$241$	18.3051	+	6.66251i	1.17913	+	0.429170i	0.323238	+	0.946318i	$0.395229\pi$
$242$	−8.33005	+	8.33005i	−0.535476	+	0.535476i
$243$	−14.9176	−	4.52371i	−0.956967	−	0.290196i
$244$		−	1.57453i		−	0.100799i
$245$	−10.1359	+	3.01365i	−0.647556	+	0.192535i
$246$	0.0658863	+	0.668828i	0.00420076	+	0.0426429i
$247$	1.04532	+	11.9480i	0.0665120	+	0.760236i
$248$	−1.86784	+	1.30787i	−0.118608	+	0.0830501i
$249$	5.91824	−	23.0936i	0.375053	−	1.46350i
$250$	−2.83251	−	10.8156i	−0.179144	−	0.684038i
$251$	−3.84250	+	2.21847i	−0.242537	+	0.140029i	−0.616342	−	0.787479i	$-0.711386\pi$
$251$	−3.84250	+	2.21847i	−0.242537	+	0.140029i	0.373805	+	0.927507i	$0.378053\pi$
$252$	−8.54297	−	5.70778i	−0.538157	−	0.359556i
$253$	−1.38051	−	5.15211i	−0.0867916	−	0.323911i
$254$	3.28181	+	18.6121i	0.205919	+	1.16782i
$255$	−0.794477	−	20.8266i	−0.0497521	−	1.30421i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	−5.48091	+	11.7539i	−0.341890	+	0.733185i	−0.999802	−	0.0199097i	$-0.993662\pi$
$257$	−5.48091	+	11.7539i	−0.341890	+	0.733185i	0.657912	+	0.753095i	$0.271440\pi$
$258$	−5.48629	−	6.39507i	−0.341561	−	0.398140i
$259$	33.5616	−	5.91782i	2.08542	−	0.367716i
$260$	−3.38374	−	2.68590i	−0.209850	−	0.166573i
$261$	0.00640482	−	0.0416230i	0.000396449	−	0.00257640i
$262$	−0.481530	+	1.79709i	−0.0297490	+	0.111025i
$263$	25.0764	+	2.19390i	1.54628	+	0.135282i	0.828100	−	0.560580i	$-0.189422\pi$
$263$	25.0764	+	2.19390i	1.54628	+	0.135282i	0.718175	+	0.695862i	$0.244978\pi$
$264$	5.78135	−	5.90910i	0.355818	−	0.363680i
$265$	−16.6137	−	5.53999i	−1.02057	−	0.340319i
$266$	13.6658	−	16.2863i	0.837906	−	0.998578i
$267$	−4.24390	+	25.7079i	−0.259723	+	1.57330i
$268$	10.2083	−	4.76023i	0.623574	−	0.290777i
$269$	−0.955430			−0.0582536			−0.0291268	−	0.999576i	$-0.509273\pi$
$269$	−0.955430			−0.0582536			−0.0291268	+	0.999576i	$0.509273\pi$
$270$	4.62128	+	10.6604i	0.281242	+	0.648770i
$271$	−7.26969			−0.441602			−0.220801	−	0.975319i	$-0.570867\pi$
$271$	−7.26969			−0.441602			−0.220801	+	0.975319i	$0.570867\pi$
$272$	4.87712	−	2.27424i	0.295719	−	0.137896i
$273$	10.7259	−	4.03718i	0.649163	−	0.244341i
$274$	5.25155	−	6.25856i	0.317258	−	0.378093i
$275$	−10.7907	+	21.2855i	−0.650706	+	1.28356i
$276$	0.521376	+	1.86408i	0.0313831	+	0.112205i
$277$	5.18616	+	0.453730i	0.311606	+	0.0272620i	0.241886	−	0.970305i	$-0.422234\pi$
$277$	5.18616	+	0.453730i	0.311606	+	0.0272620i	0.0697199	+	0.997567i	$0.477789\pi$
$278$	4.33847	−	16.1914i	0.260204	−	0.971095i
$279$	−3.29004	+	5.99749i	−0.196970	+	0.359060i
$280$	0.874687	+	7.60789i	0.0522726	+	0.454658i
$281$	8.66284	−	1.52749i	0.516782	−	0.0911226i	0.0908264	−	0.995867i	$-0.471049\pi$
$281$	8.66284	−	1.52749i	0.516782	−	0.0911226i	0.425955	+	0.904744i	$0.359938\pi$
$282$	0.456275	−	1.29755i	0.0271708	−	0.0772677i
$283$	4.92646	−	10.5648i	0.292848	−	0.628014i	−0.703749	−	0.710449i	$-0.748492\pi$
$283$	4.92646	−	10.5648i	0.292848	−	0.628014i	0.996596	+	0.0824351i	$0.0262697\pi$
$284$	−2.28043	+	0.830008i	−0.135319	+	0.0492519i
$285$	−22.9694	+	7.10346i	−1.36059	+	0.420773i
$286$	1.60128	+	9.08129i	0.0946854	+	0.536988i
$287$	0.343936	+	1.28359i	0.0203019	+	0.0757678i
$288$	−2.07446	+	2.16717i	−0.122239	+	0.127702i
$289$	−10.3563	+	5.97921i	−0.609194	+	0.351718i
$290$	−0.0267469	+	0.0164281i	−0.00157063	+	0.000964693i
$291$	−29.7449	+	8.31951i	−1.74368	+	0.487698i
$292$	7.00691	−	4.90629i	0.410048	−	0.287119i
$293$	1.06878	+	12.2162i	0.0624388	+	0.713679i	0.961311	+	0.275467i	$0.0888324\pi$
$293$	1.06878	+	12.2162i	0.0624388	+	0.713679i	−0.898872	+	0.438212i	$0.855612\pi$
$294$	−7.46085	−	3.38030i	−0.435125	−	0.197143i
$295$	7.42454	+	24.9711i	0.432273	+	1.45387i
$296$		−	9.95087i		−	0.578383i
$297$	7.71396	−	23.5705i	0.447609	−	1.36770i
$298$	−11.5186	+	11.5186i	−0.667254	+	0.667254i
$299$	−2.02890	−	0.738459i	−0.117334	−	0.0427062i
$300$	3.83126	−	7.76669i	0.221198	−	0.448410i
$301$	−12.7627	−	10.7092i	−0.735628	−	0.617266i
$302$	−6.90372	−	9.85954i	−0.397265	−	0.567353i
$303$	−0.0402623	−	3.68457i	−0.00231301	−	0.211673i
$304$	−3.99030	−	4.75545i	−0.228859	−	0.272744i
$305$	−1.40059	+	3.23017i	−0.0801978	+	0.184959i
$306$	10.1044	−	12.5908i	0.577629	−	0.719766i
$307$	−25.1777	+	6.74634i	−1.43697	+	0.385034i	−0.891470	−	0.453080i	$-0.850325\pi$
$307$	−25.1777	+	6.74634i	−1.43697	+	0.385034i	−0.545495	+	0.838114i	$0.683658\pi$
$308$	9.37569	−	13.3899i	0.534230	−	0.762959i
$309$	−0.335983	+	4.39261i	−0.0191134	+	0.249887i
$310$	4.99530	−	1.02162i	0.283714	−	0.0580244i
$311$	7.56811	+	20.7932i	0.429148	+	1.17908i	0.946331	+	0.323200i	$0.104759\pi$
$311$	7.56811	+	20.7932i	0.429148	+	1.17908i	−0.517182	+	0.855875i	$0.673019\pi$
$312$	−0.617067	−	3.28899i	−0.0349345	−	0.186203i
$313$	−17.9286	−	12.5537i	−1.01338	−	0.709578i	−0.0560084	−	0.998430i	$-0.517837\pi$
$313$	−17.9286	−	12.5537i	−1.01338	−	0.709578i	−0.957374	+	0.288853i	$0.906726\pi$
$314$	5.51638	−	9.55464i	0.311307	−	0.539200i
$315$	12.4488	+	19.3089i	0.701411	+	1.08793i
$316$	5.55584	+	9.62300i	0.312540	+	0.541336i
$317$	0.865153	−	9.88874i	0.0485918	−	0.555407i	−0.932409	−	0.361404i	$-0.882297\pi$
$317$	0.865153	−	9.88874i	0.0485918	−	0.555407i	0.981001	−	0.194003i	$-0.0621471\pi$
$318$	−6.91073	−	11.6733i	−0.387534	−	0.654605i
$319$	0.0659823	+	0.0116345i	0.00369430	+	0.000651404i
$320$	2.23204	+	0.134227i	0.124775	+	0.00750354i
$321$	10.3551	−	1.02008i	0.577966	−	0.0569355i
$322$	1.61748	+	3.46870i	0.0901387	+	0.193303i
$323$	23.6217	+	23.6217i	1.31434	+	1.31434i
$324$	−2.70572	+	8.58365i	−0.150318	+	0.476870i
$325$	4.55260	+	8.52013i	0.252533	+	0.472612i
$326$	3.77333	−	10.3671i	0.208985	−	0.574182i
$327$	2.70015	−	3.29027i	0.149319	−	0.181952i
$328$	0.386541	−	0.0338179i	0.0213431	−	0.00186728i
$329$	0.472258	−	2.67831i	0.0260364	−	0.147660i
$330$	−17.1169	+	6.97991i	−0.942254	+	0.384232i
$331$	22.7451	−	19.0854i	1.25018	−	1.04903i	0.253527	−	0.967328i	$-0.418409\pi$
$331$	22.7451	−	19.0854i	1.25018	−	1.04903i	0.996657	−	0.0817003i	$-0.0260350\pi$
$332$	−13.2950	−	3.56238i	−0.729657	−	0.195511i
$333$	−13.2045	−	26.7735i	−0.723600	−	1.46718i
$334$	17.1100	+	9.87845i	0.936216	+	0.540525i
$335$	−25.1770	+	0.685035i	−1.37557	+	0.0374274i
$336$	−3.34908	+	4.89599i	−0.182707	+	0.267098i
$337$	−14.7628	−	6.88399i	−0.804179	−	0.374995i	−0.0233403	−	0.999728i	$-0.507430\pi$
$337$	−14.7628	−	6.88399i	−0.804179	−	0.374995i	−0.780839	+	0.624733i	$0.785208\pi$
$338$	−8.39898	−	3.91651i	−0.456844	−	0.213030i
$339$	−25.1359	−	1.92260i	−1.36519	−	0.104421i
$340$	−12.0285	+	0.327281i	−0.652337	+	0.0177493i
$341$	−9.42512	−	5.44160i	−0.510399	−	0.294679i
$342$	−17.0465	−	7.49989i	−0.921769	−	0.405547i
$343$	7.51259	+	2.01299i	0.405642	+	0.108691i
$344$	−3.72658	+	3.12698i	−0.200924	+	0.168595i
$345$	0.588553	−	4.28798i	0.0316866	−	0.230857i
$346$	−4.17818	+	23.6957i	−0.224620	+	1.27389i
$347$	−0.00836757		0.000732067i	−0.000449195		3.92994e-5i	−0.0873803	−	0.996175i	$-0.527850\pi$
$347$	−0.00836757		0.000732067i	−0.000449195		3.92994e-5i	0.0869311	+	0.996214i	$0.472294\pi$
$348$	−0.0239892	−	0.00396018i	−0.00128596	−	0.000212288i
$349$	4.18645	−	11.5022i	0.224096	−	0.615697i	−0.775787	−	0.630994i	$-0.782647\pi$
$349$	4.18645	−	11.5022i	0.224096	−	0.615697i	0.999883	+	0.0152969i	$0.00486935\pi$
$350$	4.97304	−	16.3858i	0.265820	−	0.875857i
$351$	−6.02464	−	8.03044i	−0.321572	−	0.428633i
$352$	−3.37494	−	3.37494i	−0.179885	−	0.179885i
$353$	8.17015	+	17.5209i	0.434853	+	0.932545i	0.994590	+	0.103875i	$0.0331243\pi$
$353$	8.17015	+	17.5209i	0.434853	+	0.932545i	−0.559737	+	0.828670i	$0.689098\pi$
$354$	−8.32782	+	18.3808i	−0.442619	+	0.976929i
$355$	5.41666	+	0.325741i	0.287487	+	0.0172885i
$356$	14.8148	+	2.61225i	0.785183	+	0.138449i
$357$	15.6576	−	27.8173i	0.828687	−	1.47225i
$358$	−0.681955	+	7.79479i	−0.0360425	+	0.411967i
$359$	4.88715	+	8.46479i	0.257934	+	0.446754i	0.965688	−	0.259704i	$-0.0836250\pi$
$359$	4.88715	+	8.46479i	0.257934	+	0.446754i	−0.707754	+	0.706459i	$0.750292\pi$
$360$	6.18356	−	2.60069i	0.325902	−	0.137068i
$361$	9.76842	−	16.9194i	0.514127	−	0.890495i
$362$	0.712665	+	0.499014i	0.0374569	+	0.0262276i
$363$	19.2490	+	6.76879i	1.01031	+	0.355269i
$364$	−2.26306	−	6.21772i	−0.118617	−	0.325897i
$365$	−18.7391	+	3.83247i	−0.980850	+	0.200600i
$366$	−2.45890	+	1.17949i	−0.128529	+	0.0616527i
$367$	12.8485	−	18.3496i	0.670688	−	0.957842i	−0.329220	−	0.944253i	$-0.606786\pi$
$367$	12.8485	−	18.3496i	0.670688	−	0.957842i	0.999908	−	0.0135884i	$-0.00432544\pi$
$368$	1.07945	−	0.289239i	0.0562704	−	0.0150776i
$369$	0.995139	−	0.603916i	0.0518049	−	0.0314386i
$370$	−8.85163	+	20.4144i	−0.460174	+	1.06129i
$371$	−17.2415	−	20.5476i	−0.895133	−	1.06678i
$372$	3.44169	+	1.93723i	0.178443	+	0.100441i
$373$	2.19410	+	3.13349i	0.113606	+	0.162246i	0.871928	−	0.489634i	$-0.162870\pi$
$373$	2.19410	+	3.13349i	0.113606	+	0.162246i	−0.758322	+	0.651880i	$0.773981\pi$
$374$	19.6754	+	16.5096i	1.01739	+	0.853691i
$375$	−14.7686	+	12.5255i	−0.762649	+	0.646813i
$376$	−0.746215	−	0.271600i	−0.0384831	−	0.0140067i
$377$	0.0191776	−	0.0191776i	0.000987696	−	0.000987696i
$378$	−2.51413	+	17.6171i	−0.129313	+	0.906126i
$379$		−	14.9557i		−	0.768225i	−0.923286	−	0.384112i	$-0.874507\pi$
$379$		−	14.9557i		−	0.768225i	0.923286	−	0.384112i	$-0.125493\pi$
$380$	3.95604	+	13.3054i	0.202941	+	0.682553i
$381$	26.6076	−	19.0675i	1.36315	−	0.976858i
$382$	−0.857133	−	9.79707i	−0.0438547	−	0.501262i
$383$	0.914955	−	0.640659i	0.0467520	−	0.0327361i	−0.549967	−	0.835187i	$-0.685360\pi$
$383$	0.914955	−	0.640659i	0.0467520	−	0.0327361i	0.596719	+	0.802450i	$0.296471\pi$
$384$	1.23805	+	1.21129i	0.0631792	+	0.0618134i
$385$	−31.1452	+	19.1296i	−1.58730	+	0.974934i
$386$	−7.07133	+	4.08263i	−0.359921	+	0.207800i
$387$	−5.87724	+	13.3584i	−0.298757	+	0.679045i
$388$	4.61534	+	17.2247i	0.234308	+	0.874451i
$389$	5.28039	+	29.9466i	0.267726	+	1.51835i	0.761158	+	0.648566i	$0.224631\pi$
$389$	5.28039	+	29.9466i	0.267726	+	1.51835i	−0.493432	+	0.869784i	$0.664258\pi$
$390$	−1.65975	+	7.29634i	−0.0840445	+	0.369464i
$391$	−5.65111	+	2.05684i	−0.285789	+	0.104019i
$392$	−1.99857	+	4.28594i	−0.100943	+	0.216473i
$393$	3.16720	−	0.594216i	0.159764	−	0.0299742i
$394$	21.5946	−	3.80772i	1.08792	−	0.191830i
$395$	−2.83793	−	24.6839i	−0.142792	−	1.24198i
$396$	−13.5589	−	4.60208i	−0.681363	−	0.231263i
$397$	2.92694	−	10.9235i	0.146899	−	0.548234i	−0.852765	−	0.522295i	$-0.825076\pi$
$397$	2.92694	−	10.9235i	0.146899	−	0.548234i	0.999664	−	0.0259385i	$-0.00825740\pi$
$398$	5.27932	+	0.461881i	0.264628	+	0.0231520i
$399$	−35.6711	−	9.14150i	−1.78579	−	0.457647i
$400$	−4.45966	−	2.26084i	−0.222983	−	0.113042i
$401$	8.78262	−	10.4667i	0.438583	−	0.522683i	−0.500795	−	0.865566i	$-0.666959\pi$
$401$	8.78262	−	10.4667i	0.438583	−	0.522683i	0.939378	+	0.342883i	$0.111403\pi$
$402$	−15.0811	−	12.3763i	−0.752176	−	0.617271i
$403$	−3.99269	+	1.86182i	−0.198890	+	0.0927438i
$404$	−2.12742			−0.105843
$405$	13.1863	−	15.2027i	0.655231	−	0.755428i
$406$	−0.0480756			−0.00238595
$407$	43.0445	−	20.0720i	2.13364	−	0.994932i
$408$	−7.20510	−	5.91285i	−0.356706	−	0.292730i
$409$	−13.3918	+	15.9597i	−0.662183	+	0.789159i	−0.987697	−	0.156378i	$-0.950018\pi$
$409$	−13.3918	+	15.9597i	−0.662183	+	0.789159i	0.325515	+	0.945537i	$0.394462\pi$
$410$	−0.823078	−	0.274463i	−0.0406489	−	0.0135548i
$411$	−13.7078	−	3.51292i	−0.676157	−	0.173280i
$412$	2.53380	+	0.221679i	0.124831	+	0.0109213i
$413$	−10.3270	+	38.5408i	−0.508158	+	1.89647i
$414$	2.52054	−	2.21062i	0.123878	−	0.108646i
$415$	24.1060	+	19.1346i	1.18332	+	0.939282i
$416$	−1.90268	+	0.335494i	−0.0932866	+	0.0164489i
$417$	−28.5357	+	5.35375i	−1.39740	+	0.262174i
$418$	12.5218	−	26.8531i	0.612463	−	1.31343i
$419$	−6.74264	+	2.45412i	−0.329399	+	0.119892i	−0.501426	−	0.865201i	$-0.667191\pi$
$419$	−6.74264	+	2.45412i	−0.329399	+	0.119892i	0.172026	+	0.985092i	$0.444969\pi$
$420$	11.2258	−	7.06509i	0.547765	−	0.344741i
$421$	3.74087	+	21.2156i	0.182319	+	1.03398i	0.929352	+	0.369195i	$0.120367\pi$
$421$	3.74087	+	21.2156i	0.182319	+	1.03398i	−0.747033	+	0.664787i	$0.768522\pi$
$422$	4.24952	+	15.8594i	0.206863	+	0.772025i
$423$	−2.36815	+	0.259443i	−0.115143	+	0.0126146i
$424$	−6.78277	+	3.91603i	−0.329400	+	0.190179i
$425$	24.9678	+	10.0283i	1.21112	+	0.486446i
$426$	3.00449	+	2.93953i	0.145568	+	0.142421i
$427$	−4.41718	+	3.09294i	−0.213762	+	0.149678i
$428$	−0.523585	−	5.98460i	−0.0253084	−	0.289277i
$429$	12.9825	−	9.30351i	0.626803	−	0.449178i
$430$	10.4267	−	3.10013i	0.502821	−	0.149501i
$431$			21.6869i			1.04462i	0.852756	+	0.522310i	$0.174930\pi$
$431$			21.6869i			1.04462i	−0.852756	+	0.522310i	$0.825070\pi$
$432$	4.93841	+	1.61620i	0.237599	+	0.0777596i
$433$	9.64432	−	9.64432i	0.463476	−	0.463476i	−0.436317	−	0.899793i	$-0.643717\pi$
$433$	9.64432	−	9.64432i	0.463476	−	0.463476i	0.899793	+	0.436317i	$0.143717\pi$
$434$	7.33823	+	2.67090i	0.352246	+	0.128207i
$435$	0.0456917	+	0.0294636i	0.00219075	+	0.00141267i
$436$	−1.88249	−	1.57960i	−0.0901550	−	0.0756490i
$437$	3.97914	+	5.68281i	0.190348	+	0.271846i
$438$	−12.9110	−	7.26722i	−0.616909	−	0.347241i
$439$	18.8665	+	22.4842i	0.900449	+	1.07311i	0.996970	+	0.0777820i	$0.0247838\pi$
$439$	18.8665	+	22.4842i	0.900449	+	1.07311i	−0.0965218	+	0.995331i	$0.530772\pi$
$440$	3.92163	+	9.92588i	0.186957	+	0.473198i
$441$	0.310014	+	14.1836i	0.0147626	+	0.675412i
$442$	10.0426	−	2.69090i	0.477677	−	0.127993i
$443$	−10.1169	+	14.4484i	−0.480669	+	0.686466i	−0.984109	−	0.177564i	$-0.943178\pi$
$443$	−10.1169	+	14.4484i	−0.480669	+	0.686466i	0.503440	+	0.864030i	$0.332067\pi$
$444$	−15.5401	+	7.45424i	−0.737499	+	0.353763i
$445$	−28.0692	−	18.5373i	−1.33061	−	0.878755i
$446$	3.40198	+	9.34685i	0.161088	+	0.442586i
$447$	26.6170	+	9.35971i	1.25894	+	0.442699i
$448$	2.80540	+	1.96436i	0.132543	+	0.0928075i
$449$	3.52178	−	6.09990i	0.166203	−	0.287872i	−0.770879	−	0.636982i	$-0.780183\pi$
$449$	3.52178	−	6.09990i	0.166203	−	0.287872i	0.937082	+	0.349110i	$0.113516\pi$
$450$	−14.9991	−	0.165128i	−0.707064	−	0.00778421i
$451$	0.925982	+	1.60385i	0.0436028	+	0.0755222i
$452$	−1.26852	+	14.4992i	−0.0596661	+	0.681986i
$453$	−10.2258	+	18.1672i	−0.480451	+	0.853571i
$454$	−11.9546	−	2.10792i	−0.561059	−	0.0989298i
$455$	−0.888150	+	14.7688i	−0.0416371	+	0.692374i
$456$	−4.43734	+	9.79390i	−0.207798	+	0.458641i
$457$	−2.14412	−	4.59808i	−0.100298	−	0.215089i	0.849756	−	0.527177i	$-0.176749\pi$
$457$	−2.14412	−	4.59808i	−0.100298	−	0.215089i	−0.950053	+	0.312088i	$0.898972\pi$
$458$	−7.36928	−	7.36928i	−0.344344	−	0.344344i
$459$	−27.2320	−	6.34801i	−1.27108	−	0.296300i
$460$	−2.47181	−	0.366832i	−0.115249	−	0.0171036i
$461$	−0.701773	+	1.92811i	−0.0326848	+	0.0898009i	−0.954962	−	0.296729i	$-0.904104\pi$
$461$	−0.701773	+	1.92811i	−0.0326848	+	0.0898009i	0.922277	+	0.386530i	$0.126326\pi$
$462$	−27.9341	−	4.61140i	−1.29961	−	0.214542i
$463$	13.8800	−	1.21434i	0.645058	−	0.0564353i	0.240068	−	0.970756i	$-0.422830\pi$
$463$	13.8800	−	1.21434i	0.645058	−	0.0564353i	0.404990	+	0.914321i	$0.367275\pi$
$464$	−0.00243761	+	0.0138244i	−0.000113163	+	0.000641781i
$465$	−5.33746	−	7.03576i	−0.247519	−	0.326276i
$466$	−7.67308	+	6.43848i	−0.355448	+	0.298257i
$467$	1.32327	+	0.354570i	0.0612338	+	0.0164076i	0.289306	−	0.957237i	$-0.406576\pi$
$467$	1.32327	+	0.354570i	0.0612338	+	0.0164076i	−0.228072	+	0.973644i	$0.573242\pi$
$468$	−4.67411	+	3.42746i	−0.216061	+	0.158434i
$469$	−33.4073	−	19.2877i	−1.54260	−	0.890623i
$470$	1.28928	+	1.22098i	0.0594699	+	0.0563194i
$471$	−19.0536	−	1.45738i	−0.877945	−	0.0671525i
$472$	10.5590	+	4.92374i	0.486017	+	0.226633i
$473$	−21.0433	−	9.81266i	−0.967573	−	0.451187i
$474$	10.8661	−	15.8851i	0.499098	−	0.729626i
$475$	3.71972	−	30.8153i	0.170673	−	1.41390i
$476$	−15.9606	−	9.21485i	−0.731552	−	0.422362i
$477$	−13.0531	+	19.5369i	−0.597659	+	0.894531i
$478$	−0.656393	−	0.175880i	−0.0300227	−	0.00804456i
$479$	5.32223	−	4.46588i	0.243179	−	0.204051i	−0.513050	−	0.858359i	$-0.671484\pi$
$479$	5.32223	−	4.46588i	0.243179	−	0.204051i	0.756228	+	0.654308i	$0.227040\pi$
$480$	−1.46241	−	3.58627i	−0.0667495	−	0.163690i
$481$	3.33846	−	18.9333i	0.152221	−	0.863285i
$482$	−19.4057	+	1.69778i	−0.883907	+	0.0773319i
$483$	4.20533	−	5.12441i	0.191349	−	0.233169i
$484$	4.02916	−	11.0700i	0.183144	−	0.503183i
$485$	5.85348	−	39.4423i	0.265793	−	1.79098i
$486$	15.4318	−	2.20459i	0.700000	−	0.100002i
$487$	14.1069	+	14.1069i	0.639243	+	0.639243i	0.950369	−	0.311126i	$-0.100706\pi$
$487$	14.1069	+	14.1069i	0.639243	+	0.639243i	−0.311126	+	0.950369i	$0.600706\pi$
$488$	0.665423	+	1.42701i	0.0301223	+	0.0645975i
$489$	−19.0167	+	1.87334i	−0.859967	+	0.0847154i
$490$	7.91258	−	7.01489i	0.357454	−	0.316901i
$491$	−41.1519	−	7.25619i	−1.85716	−	0.327467i	−0.870743	−	0.491738i	$-0.836362\pi$
$491$	−41.1519	−	7.25619i	−1.85716	−	0.327467i	−0.986415	+	0.164271i	$0.947473\pi$
$492$	−0.342372	−	0.578319i	−0.0154353	−	0.0260726i
$493$	0.00658382	−	0.0752534i	0.000296520	−	0.00338924i
$494$	−5.99684	−	10.3868i	−0.269811	−	0.467326i
$495$	23.7227	+	21.5024i	1.06626	+	0.966461i
$496$	1.14010	−	1.97472i	0.0511922	−	0.0886675i
$497$	6.80810	+	4.76708i	0.305385	+	0.213833i
$498$	4.39604	+	23.4311i	0.196991	+	1.04997i
$499$	−1.84540	−	5.07021i	−0.0826116	−	0.226974i	0.891509	−	0.453004i	$-0.149648\pi$
$499$	−1.84540	−	5.07021i	−0.0826116	−	0.226974i	−0.974120	+	0.226030i	$0.927425\pi$
$500$	7.13799	+	8.60518i	0.319221	+	0.384835i
$501$	2.60980	−	34.1203i	0.116597	−	1.52438i
$502$	2.54492	−	3.63453i	0.113585	−	0.162217i
$503$	17.3675	−	4.65361i	0.774379	−	0.207494i	0.150074	−	0.988675i	$-0.452049\pi$
$503$	17.3675	−	4.65361i	0.774379	−	0.207494i	0.624305	+	0.781181i	$0.285382\pi$
$504$	10.1548	+	1.56258i	0.452330	+	0.0696030i
$505$	4.36443	+	1.89241i	0.194215	+	0.0842111i
$506$	3.42854	+	4.08598i	0.152417	+	0.181644i
$507$	0.175387	+	16.0504i	0.00778920	+	0.712823i
$508$	−10.8401	−	15.4813i	−0.480953	−	0.686872i
$509$	−7.61493	−	6.38969i	−0.337526	−	0.283218i	0.458232	−	0.888833i	$-0.348483\pi$
$509$	−7.61493	−	6.38969i	−0.337526	−	0.283218i	−0.795758	+	0.605615i	$0.792927\pi$
$510$	9.52172	+	18.5395i	0.421629	+	0.820943i
$511$	−27.5282	−	10.0195i	−1.21778	−	0.443235i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	1.05720	+	32.2394i	0.0466765	+	1.42340i
$514$		−	12.9689i		−	0.572036i
$515$	−5.00095	−	2.70868i	−0.220368	−	0.119359i
$516$	7.67494	+	3.47730i	0.337870	+	0.153079i
$517$	−0.330336	−	3.77575i	−0.0145281	−	0.166058i
$518$	−27.9162	+	19.5471i	−1.22657	+	0.858852i
$519$	40.1349	−	11.2255i	1.76173	−	0.492747i
$520$	4.20182	+	1.00423i	0.184262	+	0.0440382i
$521$	28.8597	−	16.6622i	1.26437	−	0.729983i	0.290451	−	0.956890i	$-0.406195\pi$
$521$	28.8597	−	16.6622i	1.26437	−	0.729983i	0.973917	+	0.226907i	$0.0728612\pi$
$522$	0.0117859	+	0.0404301i	0.000515856	+	0.00176958i
$523$	0.128833	+	0.480813i	0.00563349	+	0.0210245i	0.968685	−	0.248291i	$-0.0798691\pi$
$523$	0.128833	+	0.480813i	0.00563349	+	0.0210245i	−0.963052	+	0.269316i	$0.913202\pi$
$524$	−0.323070	−	1.83222i	−0.0141134	−	0.0800410i
$525$	−29.3147	+	4.50839i	−1.27940	+	0.196762i
$526$	−23.6541	+	8.60939i	−1.03137	+	0.375387i
$527$	−5.18574	+	11.1209i	−0.225894	+	0.484432i
$528$	−2.74239	+	7.79876i	−0.119347	+	0.339398i
$529$	21.4207	−	3.77704i	0.931334	−	0.164219i
$530$	17.3984	−	2.00031i	0.755739	−	0.0868881i
$531$	34.9433	−	0.763761i	1.51641	−	0.0331444i
$532$	−5.50256	+	20.5358i	−0.238566	+	0.890342i
$533$	0.746809	+	0.0653373i	0.0323479	+	0.00283007i
$534$	−7.01835	−	25.0928i	−0.303714	−	1.08587i
$535$	−4.24936	+	12.7433i	−0.183716	+	0.550940i
$536$	−7.24014	+	8.62847i	−0.312727	+	0.372693i
$537$	12.6838	−	4.77412i	0.547347	−	0.206018i
$538$	0.865913	−	0.403782i	0.0373322	−	0.0174083i
$539$	−22.5710			−0.972204
$540$	−8.69357	−	7.70855i	−0.374112	−	0.331723i
$541$	39.4681			1.69687			0.848433	−	0.529303i	$-0.177546\pi$
$541$	39.4681			1.69687			0.848433	+	0.529303i	$0.177546\pi$
$542$	6.58857	−	3.07230i	0.283004	−	0.131967i
$543$	0.245438	−	1.48677i	0.0105328	−	0.0638033i
$544$	−3.45904	+	4.12232i	−0.148305	+	0.176743i
$545$	2.45686	+	4.91511i	0.105240	+	0.210540i
$546$	−8.01481	+	8.19190i	−0.343002	+	0.350581i
$547$	19.7841	+	1.73088i	0.845906	+	0.0740072i	0.501863	−	0.864947i	$-0.332648\pi$
$547$	19.7841	+	1.73088i	0.845906	+	0.0740072i	0.344043	+	0.938954i	$0.388204\pi$
$548$	−2.11454	+	7.89158i	−0.0903288	+	0.337112i
$549$	3.68395	+	2.95646i	0.157227	+	0.126179i
$550$	0.784102	−	23.8516i	0.0334342	−	1.01703i
$551$	−0.0858191	+	0.0151322i	−0.00365602	+	0.000644654i
$552$	−1.26032	−	1.46909i	−0.0536429	−	0.0625287i
$553$	16.0827	−	34.4894i	0.683906	−	1.46664i
$554$	−4.89201	+	1.78055i	−0.207842	+	0.0756482i
$555$	38.5115	−	1.46911i	1.63472	−	0.0623604i
$556$	2.91079	+	16.5079i	0.123445	+	0.700091i
$557$	1.00253	+	3.74149i	0.0424786	+	0.158532i	0.983907	−	0.178680i	$-0.0571827\pi$
$557$	1.00253	+	3.74149i	0.0424786	+	0.158532i	−0.941429	+	0.337212i	$0.890516\pi$
$558$	0.447146	−	6.82600i	0.0189292	−	0.288968i
$559$	−8.13958	+	4.69939i	−0.344268	+	0.198763i
$560$	−4.00797	−	6.52543i	−0.169368	−	0.275750i
$561$	11.0438	−	43.0940i	0.466269	−	1.81943i
$562$	−7.20565	+	5.04545i	−0.303952	+	0.212830i
$563$	−2.77303	−	31.6959i	−0.116869	−	1.33582i	−0.797554	−	0.603247i	$-0.793873\pi$
$563$	−2.77303	−	31.6959i	−0.116869	−	1.33582i	0.680685	−	0.732576i	$-0.261682\pi$
$564$	0.134841	+	1.36881i	0.00567784	+	0.0576371i
$565$	15.4999	−	28.6170i	0.652087	−	1.20393i
$566$			11.6570i			0.489980i
$567$	29.3956	−	9.27080i	1.23450	−	0.389337i
$568$	1.71599	−	1.71599i	0.0720015	−	0.0720015i
$569$	−0.625558	−	0.227685i	−0.0262248	−	0.00954503i	0.328874	−	0.944374i	$-0.393331\pi$
$569$	−0.625558	−	0.227685i	−0.0262248	−	0.00954503i	−0.355099	+	0.934829i	$0.615553\pi$
$570$	17.8153	−	16.1452i	0.746201	−	0.676249i
$571$	15.8737	+	13.3196i	0.664295	+	0.557410i	0.911371	−	0.411586i	$-0.135025\pi$
$571$	15.8737	+	13.3196i	0.664295	+	0.557410i	−0.247076	+	0.968996i	$0.579470\pi$
$572$	−5.28917	−	7.55371i	−0.221151	−	0.315837i
$573$	−14.6578	+	8.67760i	−0.612339	+	0.362512i
$574$	−0.854179	−	1.01797i	−0.0356528	−	0.0424893i
$575$	4.74465	+	2.95132i	0.197866	+	0.123078i
$576$	0.964213	−	2.84083i	0.0401756	−	0.118368i
$577$	5.39239	−	1.44489i	0.224488	−	0.0601514i	−0.144822	−	0.989458i	$-0.546261\pi$
$577$	5.39239	−	1.44489i	0.224488	−	0.0601514i	0.369310	+	0.929306i	$0.379594\pi$
$578$	6.85907	−	9.79577i	0.285300	−	0.407450i
$579$	11.6729	+	7.98482i	0.485110	+	0.331838i
$580$	0.0172981	−	0.0261926i	0.000718263	−	0.00108759i
$581$	16.1223	+	44.2956i	0.668865	+	1.83769i
$582$	23.4421	−	20.1108i	0.971704	−	0.833618i
$583$	−30.6212	−	21.4412i	−1.26820	−	0.888003i
$584$	−4.27693	+	7.40785i	−0.176980	+	0.306539i
$585$	12.6379	−	2.87373i	0.522511	−	0.118814i
$586$	−6.13144	−	10.6200i	−0.253287	−	0.438707i
$587$	0.721578	−	8.24768i	0.0297827	−	0.340418i	−0.966655	−	0.256083i	$-0.917568\pi$
$587$	0.721578	−	8.24768i	0.0297827	−	0.340418i	0.996437	−	0.0843348i	$-0.0268765\pi$
$588$	8.19040	−	0.0894986i	0.337766	−	0.00369086i
$589$	13.9401	+	2.45801i	0.574390	+	0.101280i
$590$	−17.2821	−	19.4937i	−0.711495	−	0.802544i
$591$	−22.1231	−	30.8715i	−0.910021	−	1.26988i
$592$	4.20542	+	9.01855i	0.172842	+	0.370660i
$593$	11.2101	+	11.2101i	0.460343	+	0.460343i	0.898768	−	0.438425i	$-0.144464\pi$
$593$	11.2101	+	11.2101i	0.460343	+	0.460343i	−0.438425	+	0.898768i	$0.644464\pi$
$594$	2.97010	+	24.6222i	0.121865	+	1.01026i
$595$	24.5465	+	33.1019i	1.00631	+	1.35705i
$596$	5.57142	−	15.3073i	0.228214	−	0.627013i
$597$	−3.23345	−	8.59060i	−0.132336	−	0.351590i
$598$	2.15089	−	0.188179i	0.0879566	−	0.00769521i
$599$	1.64551	−	9.33216i	0.0672338	−	0.381302i	−0.932560	−	0.361014i	$-0.882431\pi$
$599$	1.64551	−	9.33216i	0.0672338	−	0.381302i	0.999794	−	0.0202877i	$-0.00645821\pi$
$600$	−0.189952	+	8.65817i	−0.00775478	+	0.353468i
$601$	−20.5855	+	17.2733i	−0.839699	+	0.704591i	−0.957496	−	0.288447i	$-0.906861\pi$
$601$	−20.5855	+	17.2733i	−0.839699	+	0.704591i	0.117797	+	0.993038i	$0.462417\pi$
$602$	16.0928	+	4.31205i	0.655893	+	0.175746i
$603$	−8.03043	+	32.8229i	−0.327024	+	1.33665i
$604$	10.4237	+	6.01814i	0.424135	+	0.244875i
$605$	−18.1131	+	19.1263i	−0.736401	+	0.777594i
$606$	1.59366	+	3.32234i	0.0647379	+	0.134961i
$607$	4.57123	+	2.13160i	0.185541	+	0.0865190i	0.513169	−	0.858288i	$-0.328472\pi$
$607$	4.57123	+	2.13160i	0.185541	+	0.0865190i	−0.327628	+	0.944807i	$0.606249\pi$
$608$	5.62618	+	2.62353i	0.228172	+	0.106398i
$609$	0.0360137	+	0.0750787i	0.00145935	+	0.00304234i
$610$	−0.0957597	−	3.51944i	−0.00387720	−	0.142498i
$611$	−1.32869	−	0.767119i	−0.0537530	−	0.0310343i
$612$	−3.83660	+	15.6814i	−0.155085	+	0.633883i
$613$	5.24282	+	1.40481i	0.211756	+	0.0567397i	0.363137	−	0.931736i	$-0.381706\pi$
$613$	5.24282	+	1.40481i	0.211756	+	0.0567397i	−0.151382	+	0.988475i	$0.548372\pi$
$614$	19.9676	−	16.7548i	0.805826	−	0.676169i
$615$	0.187949	+	1.49098i	0.00757882	+	0.0601223i
$616$	−2.83846	+	16.0977i	−0.114365	+	0.648594i
$617$	27.0727	−	2.36856i	1.08991	−	0.0953545i	0.471995	−	0.881601i	$-0.343534\pi$
$617$	27.0727	−	2.36856i	1.08991	−	0.0953545i	0.617913	+	0.786247i	$0.287979\pi$
$618$	−1.55189	−	4.12305i	−0.0624263	−	0.165853i
$619$	−3.84505	+	10.5642i	−0.154546	+	0.424611i	−0.992668	−	0.120871i	$-0.961431\pi$
$619$	−3.84505	+	10.5642i	−0.154546	+	0.424611i	0.838122	+	0.545482i	$0.183653\pi$
$620$	−4.09553	+	3.03701i	−0.164480	+	0.121969i
$621$	−5.34042	−	2.28029i	−0.214304	−	0.0915047i
$622$	−15.6466	−	15.6466i	−0.627373	−	0.627373i
$623$	−21.7733	−	46.6929i	−0.872327	−	1.87071i
$624$	1.94924	+	2.72006i	0.0780321	+	0.108889i
$625$	−6.98913	−	24.0032i	−0.279565	−	0.960127i
$626$	21.5542	+	3.80059i	0.861480	+	0.151902i
$627$	−51.3162	+	0.560745i	−2.04937	+	0.0223940i
$628$	−0.961568	+	10.9908i	−0.0383707	+	0.438579i
$629$	−26.7743	−	46.3745i	−1.06756	−	1.84907i
$630$	−19.4427	−	12.2387i	−0.774617	−	0.487601i
$631$	−13.4777	+	23.3441i	−0.536539	+	0.929313i	0.462548	+	0.886594i	$0.346935\pi$
$631$	−13.4777	+	23.3441i	−0.536539	+	0.929313i	−0.999087	+	0.0427187i	$0.986398\pi$
$632$	−9.10216	−	6.37340i	−0.362064	−	0.253520i
$633$	21.5840	−	18.5168i	0.857887	−	0.735975i
$634$	3.39507	+	9.32788i	0.134835	+	0.370457i
$635$	8.46758	+	41.4028i	0.336026	+	1.64302i
$636$	11.1966	+	7.65899i	0.443974	+	0.303699i
$637$	−5.24054	+	7.48427i	−0.207638	+	0.296538i
$638$	−0.0647172	+	0.0173409i	−0.00256218	+	0.000686533i
$639$	2.33993	−	6.89406i	0.0925664	−	0.272725i
$640$	−2.07964	+	0.821648i	−0.0822049	+	0.0324785i
$641$	27.2802	+	32.5112i	1.07750	+	1.28412i	0.956585	+	0.291454i	$0.0941389\pi$
$641$	27.2802	+	32.5112i	1.07750	+	1.28412i	0.120917	+	0.992663i	$0.461417\pi$
$642$	−8.95381	+	5.30077i	−0.353379	+	0.209205i
$643$	−1.60171	−	2.28747i	−0.0631651	−	0.0902091i	0.786327	−	0.617811i	$-0.211980\pi$
$643$	−1.60171	−	2.28747i	−0.0631651	−	0.0902091i	−0.849492	+	0.527602i	$0.823091\pi$
$644$	−2.93187	−	2.46013i	−0.115532	−	0.0969428i
$645$	−12.6521	−	13.9609i	−0.498176	−	0.549708i
$646$	−31.3914	−	11.4256i	−1.23508	−	0.449532i
$647$	−3.37176	+	3.37176i	−0.132558	+	0.132558i	−0.770273	−	0.637715i	$-0.779880\pi$
$647$	−3.37176	+	3.37176i	−0.132558	+	0.132558i	0.637715	+	0.770273i	$0.279880\pi$
$648$	−1.17540	−	8.92292i	−0.0461739	−	0.350525i
$649$			55.6068i			2.18276i
$650$	−7.72682	−	5.79785i	−0.303071	−	0.227410i
$651$	−1.32602	−	13.4607i	−0.0519708	−	0.527568i
$652$	0.961543	+	10.9905i	0.0376569	+	0.430421i
$653$	9.31500	−	6.52243i	0.364524	−	0.255242i	−0.376936	−	0.926239i	$-0.623022\pi$
$653$	9.31500	−	6.52243i	0.364524	−	0.255242i	0.741460	+	0.670997i	$0.234134\pi$
$654$	−1.05664	+	4.12313i	−0.0413180	+	0.161227i
$655$	−0.967039	+	4.04622i	−0.0377853	+	0.158099i
$656$	−0.336033	+	0.194009i	−0.0131199	+	0.00757476i
$657$	−1.67740	+	25.6067i	−0.0654415	+	0.999012i
$658$	0.703890	+	2.62696i	0.0274405	+	0.102409i
$659$	0.995226	+	5.64421i	0.0387685	+	0.219867i	0.998037	−	0.0626293i	$-0.0199486\pi$
$659$	0.995226	+	5.64421i	0.0387685	+	0.219867i	−0.959268	+	0.282496i	$0.908837\pi$
$660$	12.5633	−	13.5599i	0.489027	−	0.527817i
$661$	−38.9403	+	14.1731i	−1.51460	+	0.551269i	−0.959793	−	0.280709i	$-0.909430\pi$
$661$	−38.9403	+	14.1731i	−1.51460	+	0.551269i	−0.554807	+	0.831979i	$0.687208\pi$
$662$	−12.5482	+	26.9097i	−0.487700	+	1.04588i
$663$	−11.7253	−	13.6675i	−0.455372	−	0.530803i
$664$	13.5549	−	2.39009i	0.526031	−	0.0927535i
$665$	29.5559	−	37.2350i	1.14613	−	1.44391i
$666$	23.2823	+	18.6846i	0.902170	+	0.724013i
$667$	0.00406023	−	0.0151530i	0.000157213	−	0.000586726i
$668$	−19.6817	−	1.72193i	−0.761508	−	0.0666233i
$669$	12.0483	−	12.3146i	0.465816	−	0.476109i
$670$	22.5286	−	11.2611i	0.870356	−	0.435055i
$671$	−4.83057	+	5.75685i	−0.186482	+	0.222241i
$672$	0.966166	−	5.85265i	0.0372707	−	0.225771i
$673$	32.8201	−	15.3043i	1.26512	−	0.589936i	0.329907	−	0.944014i	$-0.392983\pi$
$673$	32.8201	−	15.3043i	1.26512	−	0.589936i	0.935216	+	0.354077i	$0.115205\pi$
$674$	16.2889			0.627425
$675$	10.9780	+	23.5475i	0.422544	+	0.906342i
$676$	9.26725			0.356433
$677$	9.63788	−	4.49422i	0.370414	−	0.172727i	−0.228493	−	0.973546i	$-0.573380\pi$
$677$	9.63788	−	4.49422i	0.370414	−	0.172727i	0.598907	+	0.800819i	$0.295602\pi$
$678$	23.5934	−	8.88042i	0.906099	−	0.341051i
$679$	39.2560	−	46.7834i	1.50651	−	1.79538i
$680$	10.7632	−	5.38008i	0.412751	−	0.206317i
$681$	5.66337	+	20.2484i	0.217021	+	0.775919i
$682$	10.8418	+	0.948533i	0.415153	+	0.0363212i
$683$	3.39467	−	12.6691i	0.129893	−	0.484768i	−0.870074	−	0.492922i	$-0.835929\pi$
$683$	3.39467	−	12.6691i	0.129893	−	0.484768i	0.999967	+	0.00815378i	$0.00259546\pi$
$684$	18.6190	−	0.406957i	0.711914	−	0.0155604i
$685$	11.3578	−	14.3088i	0.433961	−	0.546710i
$686$	−7.65944	+	1.35057i	−0.292439	+	0.0515649i
$687$	−5.98809	+	17.0288i	−0.228460	+	0.649690i
$688$	2.05592	−	4.40893i	0.0783811	−	0.168089i
$689$	−14.2192	+	5.17538i	−0.541710	+	0.197166i
$690$	1.27877	+	4.13497i	0.0486819	+	0.157415i
$691$	3.47031	+	19.6811i	0.132017	+	0.748704i	0.976891	+	0.213739i	$0.0685642\pi$
$691$	3.47031	+	19.6811i	0.132017	+	0.748704i	−0.844874	+	0.534965i	$0.820325\pi$
$692$	−6.22750	−	23.2413i	−0.236734	−	0.883503i
$693$	13.7240	+	47.0785i	0.521332	+	1.78836i
$694$	0.00727421	−	0.00419977i	0.000276125	−	0.000159421i
$695$	8.71280	−	36.4555i	0.330495	−	1.38284i
$696$	0.0234153	−	0.00654915i	0.000887554	−	0.000248245i
$697$	1.71042	−	1.19765i	0.0647868	−	0.0453642i
$698$	1.06682	+	12.1938i	0.0403796	+	0.461541i
$699$	15.8028	+	7.15979i	0.597716	+	0.270808i
$700$	2.41783	+	16.9523i	0.0913855	+	0.640735i
$701$		−	20.1319i		−	0.760373i	−0.924910	−	0.380186i	$-0.875860\pi$
$701$		−	20.1319i		−	0.760373i	0.924910	−	0.380186i	$-0.124140\pi$
$702$	8.85399	+	4.73192i	0.334172	+	0.178595i
$703$	−43.6801	+	43.6801i	−1.64743	+	1.64743i
$704$	4.48505	+	1.63242i	0.169037	+	0.0615243i
$705$	0.940969	−	2.92808i	0.0354390	−	0.110278i
$706$	−14.8093	−	12.4265i	−0.557357	−	0.467678i
$707$	4.17902	+	5.96826i	0.157168	+	0.224459i
$708$	−0.220492	−	20.1782i	−0.00828659	−	0.758342i
$709$	−24.8113	−	29.5689i	−0.931808	−	1.11049i	−0.993663	−	0.112400i	$-0.964146\pi$
$709$	−24.8113	−	29.5689i	−0.931808	−	1.11049i	0.0618554	−	0.998085i	$-0.480298\pi$
$710$	−5.04683	+	1.99396i	−0.189404	+	0.0748320i
$711$	−32.9473	−	5.06982i	−1.23562	−	0.190133i
$712$	−14.5308	+	3.89350i	−0.544563	+	0.145915i
$713$	−1.46159	+	2.08737i	−0.0547371	+	0.0781727i
$714$	−2.43448	+	31.8282i	−0.0911083	+	1.19114i
$715$	4.13154	+	20.2015i	0.154511	+	0.755492i
$716$	−2.67616	−	7.35268i	−0.100013	−	0.274783i
$717$	0.217039	+	1.15683i	0.00810547	+	0.0432025i
$718$	−8.00664	−	5.60631i	−0.298805	−	0.209225i
$719$	−19.2505	+	33.3428i	−0.717922	+	1.24348i	0.243899	+	0.969801i	$0.421573\pi$
$719$	−19.2505	+	33.3428i	−0.717922	+	1.24348i	−0.961822	+	0.273677i	$0.911760\pi$
$720$	−4.50511	+	4.97031i	−0.167896	+	0.185232i
$721$	−4.35541	−	7.54379i	−0.162204	−	0.280946i
$722$	−1.70275	+	19.4625i	−0.0633697	+	0.724319i
$723$	17.1883	+	29.0337i	0.639241	+	1.07978i
$724$	−0.856787	−	0.151075i	−0.0318422	−	0.00561464i
$725$	−0.0587865	+	0.0383475i	−0.00218328	+	0.00142419i
$726$	−20.3061	+	2.00035i	−0.753630	+	0.0742401i
$727$	−9.08040	−	19.4730i	−0.336773	−	0.722213i	0.662875	−	0.748730i	$-0.269336\pi$
$727$	−9.08040	−	19.4730i	−0.336773	−	0.722213i	−0.999648	+	0.0265174i	$0.991558\pi$
$728$	4.67875	+	4.67875i	0.173406	+	0.173406i
$729$	−15.0029	−	22.4480i	−0.555663	−	0.831408i
$730$	15.3637	−	11.3929i	0.568637	−	0.421670i
$731$	−8.95357	+	24.5997i	−0.331160	+	0.909854i
$732$	1.73005	−	2.10815i	0.0639446	−	0.0779196i
$733$	−27.7657	+	2.42919i	−1.02555	+	0.0897240i	−0.587498	−	0.809225i	$-0.699887\pi$
$733$	−27.7657	+	2.42919i	−1.02555	+	0.0897240i	−0.438052	+	0.898950i	$0.644332\pi$
$734$	−3.88985	+	22.0604i	−0.143577	+	0.814265i
$735$	−16.8824	−	7.10203i	−0.622716	−	0.261962i
$736$	−0.856080	+	0.718336i	−0.0315555	+	0.0264782i
$737$	−51.9284	−	13.9142i	−1.91281	−	0.512535i
$738$	−0.646677	+	0.967897i	−0.0238045	+	0.0356288i
$739$	−38.2159	−	22.0640i	−1.40579	−	0.811636i	−0.410815	−	0.911719i	$-0.634756\pi$
$739$	−38.2159	−	22.0640i	−1.40579	−	0.811636i	−0.994979	+	0.100083i	$0.968089\pi$
$740$	−0.605193	−	22.2426i	−0.0222473	−	0.817654i
$741$	−11.7286	+	17.1460i	−0.430862	+	0.629873i
$742$	24.3099	+	11.3359i	0.892443	+	0.416153i
$743$	−21.7329	−	10.1342i	−0.797305	−	0.371789i	−0.0191139	−	0.999817i	$-0.506085\pi$
$743$	−21.7329	−	10.1342i	−0.797305	−	0.371789i	−0.778191	+	0.628028i	$0.783862\pi$
$744$	−3.93794	−	0.301206i	−0.144372	−	0.0110427i
$745$	−25.0463	+	26.4473i	−0.917624	+	0.968956i
$746$	−3.31280	−	1.91264i	−0.121290	−	0.0700269i
$747$	33.2987	−	24.4175i	1.21834	−	0.893391i
$748$	−24.8092	−	6.64760i	−0.907114	−	0.243060i
$749$	−15.7607	+	13.2248i	−0.575884	+	0.483224i
$750$	8.09143	−	17.5934i	0.295457	−	0.642421i
$751$	4.45381	−	25.2588i	0.162522	−	0.921707i	−0.789061	−	0.614315i	$-0.789433\pi$
$751$	4.45381	−	25.2588i	0.162522	−	0.921707i	0.951583	−	0.307392i	$-0.0994564\pi$
$752$	0.791084	−	0.0692108i	0.0288479	−	0.00252386i
$753$	−7.58238	−	1.25171i	−0.276317	−	0.0456149i
$754$	−0.00927600	+	0.0254856i	−0.000337812	+	0.000928130i
$755$	−16.0311	−	21.6186i	−0.583432	−	0.786781i
$756$	−5.16674	−	17.0290i	−0.187912	−	0.619340i
$757$	21.7829	+	21.7829i	0.791712	+	0.791712i	0.981772	−	0.190060i	$-0.0608684\pi$
$757$	21.7829	+	21.7829i	0.791712	+	0.791712i	−0.190060	+	0.981772i	$0.560868\pi$
$758$	6.32057	+	13.5545i	0.229573	+	0.492322i
$759$	3.81265	−	8.41510i	0.138390	−	0.305449i
$760$	−9.20850	−	10.3869i	−0.334027	−	0.376773i
$761$	17.2273	+	3.03764i	0.624490	+	0.110114i	0.476934	−	0.878939i	$-0.341748\pi$
$761$	17.2273	+	3.03764i	0.624490	+	0.110114i	0.147556	+	0.989054i	$0.452859\pi$
$762$	−16.0564	+	28.5259i	−0.581663	+	1.03338i
$763$	−0.733509	+	8.38405i	−0.0265548	+	0.303523i
$764$	4.91725	+	8.51692i	0.177900	+	0.308132i
$765$	21.8200	−	28.7579i	0.788903	−	1.03974i
$766$	−0.558477	+	0.967311i	−0.0201786	+	0.0349504i
$767$	18.4385	+	12.9108i	0.665776	+	0.466181i
$768$	−1.63397	−	0.574577i	−0.0589609	−	0.0207333i
$769$	−4.82741	−	13.2632i	−0.174081	−	0.478283i	0.821713	−	0.569901i	$-0.193018\pi$
$769$	−4.82741	−	13.2632i	−0.174081	−	0.478283i	−0.995794	+	0.0916178i	$0.970796\pi$
$770$	20.1426	−	30.4998i	0.725888	−	1.09914i
$771$	−20.2533	+	9.71510i	−0.729406	+	0.349881i
$772$	4.68340	−	6.68859i	0.168559	−	0.240728i
$773$	−31.5871	+	8.46375i	−1.13611	+	0.304420i	−0.777386	−	0.629024i	$-0.783455\pi$
$773$	−31.5871	+	8.46375i	−1.13611	+	0.304420i	−0.358724	+	0.933444i	$0.616788\pi$
$774$	−0.318910	−	14.5906i	−0.0114630	−	0.524450i
$775$	11.1036	−	2.58738i	0.398852	−	0.0929415i
$776$	−11.4624	−	13.6603i	−0.411476	−	0.490377i
$777$	51.4385	+	28.9533i	1.84535	+	1.03869i
$778$	−17.4416	−	24.9092i	−0.625312	−	0.893039i
$779$	−1.84520	−	1.54830i	−0.0661111	−	0.0554738i
$780$	−1.57932	−	7.31416i	−0.0565489	−	0.261889i
$781$	10.8842	+	3.96154i	0.389469	+	0.141755i
$782$	4.25239	−	4.25239i	0.152065	−	0.152065i
$783$	0.0543099	−	0.0486922i	0.00194088	−	0.00174012i
$784$		−	4.72901i		−	0.168893i
$785$	11.7493	−	21.6924i	0.419352	−	0.774236i
$786$	−2.61933	+	1.87706i	−0.0934284	+	0.0669525i
$787$	3.14542	+	35.9523i	0.112122	+	1.28156i	0.818821	+	0.574048i	$0.194628\pi$
$787$	3.14542	+	35.9523i	0.112122	+	1.28156i	−0.706699	+	0.707514i	$0.749817\pi$
$788$	−17.9622	+	12.5772i	−0.639876	+	0.448046i
$789$	31.1645	+	30.4908i	1.10949	+	1.08550i
$790$	13.0039	+	21.1718i	0.462658	+	0.753260i
$791$	43.1680	−	24.9231i	1.53488	−	0.886162i
$792$	14.2335	−	1.55936i	0.505766	−	0.0554093i
$793$	0.787337	+	2.93838i	0.0279592	+	0.104345i
$794$	1.96376	+	11.1370i	0.0696911	+	0.395238i
$795$	−16.1571	−	25.6723i	−0.573033	−	0.910503i
$796$	−4.97989	+	1.81253i	−0.176507	+	0.0642434i
$797$	12.9450	−	27.7606i	0.458534	−	0.983330i	−0.532087	−	0.846690i	$-0.678592\pi$
$797$	12.9450	−	27.7606i	0.458534	−	0.983330i	0.990621	−	0.136640i	$-0.0436303\pi$
$798$	36.1924	−	6.79026i	1.28120	−	0.240373i
$799$	−4.20840	+	0.742055i	−0.148883	+	0.0262520i
$800$	4.99730	+	0.164282i	0.176681	+	0.00580826i
$801$	−33.9295	+	29.7576i	−1.19884	+	1.05143i
$802$	−3.53633	+	13.1978i	−0.124872	+	0.466029i
$803$	−40.6712	−	3.55827i	−1.43526	−	0.125569i
$804$	18.8985	+	4.84316i	0.666500	+	0.170805i
$805$	3.82642	+	7.65501i	0.134864	+	0.269804i
$806$	2.83176	−	3.37476i	0.0997446	−	0.118871i
$807$	−1.27924	−	1.04980i	−0.0450313	−	0.0369548i
$808$	1.92809	−	0.899085i	0.0678301	−	0.0316297i
$809$	−19.4742			−0.684678			−0.342339	−	0.939577i	$-0.611219\pi$
$809$	−19.4742			−0.684678			−0.342339	+	0.939577i	$0.611219\pi$
$810$	−5.52589	+	19.3511i	−0.194160	+	0.679928i
$811$	−43.6309			−1.53209			−0.766044	−	0.642788i	$-0.777777\pi$
$811$	−43.6309			−1.53209			−0.766044	+	0.642788i	$0.777777\pi$
$812$	0.0435713	−	0.0203176i	0.00152905	−	0.000713009i
$813$	−9.73348	−	7.98776i	−0.341368	−	0.280143i
$814$	−30.5288	+	36.3828i	−1.07003	+	1.27522i
$815$	7.80378	−	23.4025i	0.273355	−	0.819754i
$816$	9.02892	+	2.31386i	0.316075	+	0.0810011i
$817$	30.0843	+	2.63203i	1.05252	+	0.0920831i
$818$	5.39223	−	20.1241i	0.188535	−	0.703621i
$819$	18.7971	+	6.37996i	0.656822	+	0.222934i
$820$	0.861955	−	0.0990999i	0.0301008	−	0.00346072i
$821$	2.91570	−	0.514117i	0.101759	−	0.0179428i	−0.122537	−	0.992464i	$-0.539103\pi$
$821$	2.91570	−	0.514117i	0.101759	−	0.0179428i	0.224296	+	0.974521i	$0.427992\pi$
$822$	13.9081	−	2.60938i	0.485102	−	0.0910127i
$823$	−15.2677	+	32.7417i	−0.532200	+	1.14131i	0.437995	+	0.898977i	$0.355689\pi$
$823$	−15.2677	+	32.7417i	−0.532200	+	1.14131i	−0.970194	+	0.242328i	$0.922089\pi$
$824$	−2.39009	+	0.869922i	−0.0832627	+	0.0303052i
$825$	−37.8359	+	16.6428i	−1.31728	+	0.579428i
$826$	−6.92864	−	39.2942i	−0.241078	−	1.36722i
$827$	2.70802	+	10.1065i	0.0941670	+	0.351436i	0.996892	−	0.0787823i	$-0.0251032\pi$
$827$	2.70802	+	10.1065i	0.0941670	+	0.351436i	−0.902725	+	0.430218i	$0.858437\pi$
$828$	−1.35013	+	3.06872i	−0.0469204	+	0.106645i
$829$	21.9321	−	12.6625i	0.761735	−	0.439788i	−0.0681835	−	0.997673i	$-0.521720\pi$
$829$	21.9321	−	12.6625i	0.761735	−	0.439788i	0.829918	+	0.557885i	$0.188387\pi$
$830$	−29.9341	−	7.15420i	−1.03903	−	0.248326i
$831$	6.44528	+	6.30594i	0.223584	+	0.218751i
$832$	1.58263	−	1.10817i	0.0548678	−	0.0384188i
$833$	2.21796	+	25.3514i	0.0768478	+	0.878374i
$834$	23.5996	−	16.9119i	0.817186	−	0.585610i
$835$	38.8457	+	21.0401i	1.34431	+	0.728123i
$836$			29.6292i			1.02475i
$837$	−10.9950	+	4.41509i	−0.380042	+	0.152608i
$838$	5.07375	−	5.07375i	0.175270	−	0.175270i
$839$	36.5830	+	13.3151i	1.26299	+	0.459689i	0.884770	−	0.466028i	$-0.154315\pi$
$839$	36.5830	+	13.3151i	1.26299	+	0.459689i	0.378216	+	0.925717i	$0.376538\pi$
$840$	−7.18824	+	11.1474i	−0.248018	+	0.384622i
$841$	−22.2151	−	18.6407i	−0.766039	−	0.642783i
$842$	−12.3565	−	17.6469i	−0.425832	−	0.608151i
$843$	13.2772	+	7.47335i	0.457290	+	0.257396i
$844$	−10.5539	−	12.5776i	−0.363279	−	0.432939i
$845$	−19.0119	−	8.24353i	−0.654031	−	0.283586i
$846$	2.03662	−	1.23596i	0.0700206	−	0.0424931i
$847$	−38.9706	+	10.4421i	−1.33905	+	0.358796i
$848$	4.49229	−	6.41565i	0.154266	−	0.220314i
$849$	18.2045	−	8.73231i	0.624776	−	0.299692i
$850$	−26.8667	+	1.46310i	−0.921521	+	0.0501840i
$851$	−3.80341	−	10.4498i	−0.130379	−	0.358214i
$852$	−3.96529	−	1.39437i	−0.135849	−	0.0477704i
$853$	−10.0582	−	7.04282i	−0.344386	−	0.241142i	0.388568	−	0.921420i	$-0.372970\pi$
$853$	−10.0582	−	7.04282i	−0.344386	−	0.241142i	−0.732954	+	0.680279i	$0.761859\pi$
$854$	2.69619	−	4.66994i	0.0922617	−	0.159802i
$855$	−38.5592	−	15.7273i	−1.31870	−	0.537863i
$856$	3.00373	+	5.20262i	0.102665	+	0.177822i
$857$	3.95395	−	45.1939i	0.135065	−	1.54379i	−0.562212	−	0.826993i	$-0.690050\pi$
$857$	3.95395	−	45.1939i	0.135065	−	1.54379i	0.697277	−	0.716802i	$-0.254395\pi$
$858$	−7.83433	+	13.9185i	−0.267460	+	0.475170i
$859$	−26.3810	−	4.65169i	−0.900110	−	0.158714i	−0.295600	−	0.955312i	$-0.595520\pi$
$859$	−26.3810	−	4.65169i	−0.900110	−	0.158714i	−0.604509	+	0.796598i	$0.706631\pi$
$860$	−8.13964	+	7.21619i	−0.277559	+	0.246070i
$861$	−0.949875	+	2.09652i	−0.0323716	+	0.0714493i
$862$	−9.16527	−	19.6550i	−0.312170	−	0.669451i
$863$	13.4724	+	13.4724i	0.458608	+	0.458608i	0.898198	−	0.439591i	$-0.144876\pi$
$863$	13.4724	+	13.4724i	0.458608	+	0.458608i	−0.439591	+	0.898198i	$0.644876\pi$
$864$	−5.15876	+	0.622285i	−0.175504	+	0.0211706i
$865$	−7.89812	+	53.2196i	−0.268544	+	1.80952i
$866$	−4.66485	+	12.8166i	−0.158518	+	0.435525i
$867$	−20.4360	−	3.37361i	−0.694044	−	0.114574i
$868$	−7.77947	+	0.680615i	−0.264052	+	0.0231016i
$869$	9.20940	−	52.2291i	0.312408	−	1.77175i
$870$	−0.0538626	−	0.00739298i	−0.00182611	−	0.000250646i
$871$	−16.6705	+	13.9882i	−0.564858	+	0.473972i
$872$	2.37368	+	0.636027i	0.0803831	+	0.0215386i
$873$	−48.9671	−	21.5439i	−1.65729	−	0.729150i
$874$	−6.00799	−	3.46871i	−0.203223	−	0.117331i
$875$	10.1194	−	36.9286i	0.342097	−	1.24842i
$876$	14.7726	+	1.12993i	0.499118	+	0.0381767i
$877$	35.5284	+	16.5672i	1.19971	+	0.559434i	0.916658	−	0.399671i	$-0.130876\pi$
$877$	35.5284	+	16.5672i	1.19971	+	0.559434i	0.283051	+	0.959105i	$0.408654\pi$
$878$	−26.6011	−	12.4043i	−0.897743	−	0.418625i
$879$	−11.9919	+	17.5308i	−0.404476	+	0.591299i
$880$	−7.74907	−	7.33855i	−0.261221	−	0.247383i
$881$	−22.1803	−	12.8058i	−0.747272	−	0.431438i	0.0774355	−	0.996997i	$-0.475327\pi$
$881$	−22.1803	−	12.8058i	−0.747272	−	0.431438i	−0.824707	+	0.565560i	$0.808660\pi$
$882$	−6.27524	−	12.7237i	−0.211298	−	0.428430i
$883$	2.67694	+	0.717285i	0.0900863	+	0.0241386i	0.303581	−	0.952806i	$-0.401818\pi$
$883$	2.67694	+	0.717285i	0.0900863	+	0.0241386i	−0.213494	+	0.976944i	$0.568484\pi$
$884$	−7.96445	+	6.68297i	−0.267874	+	0.224773i
$885$	−17.4968	+	41.5920i	−0.588149	+	1.39810i
$886$	3.06286	−	17.3703i	0.102899	−	0.583568i
$887$	−47.4566	+	4.15191i	−1.59344	+	0.139408i	−0.849039	−	0.528330i	$-0.822819\pi$
$887$	−47.4566	+	4.15191i	−1.59344	+	0.139408i	−0.744397	+	0.667737i	$0.767263\pi$
$888$	10.9338	−	13.3234i	0.366914	−	0.447103i
$889$	−22.1373	+	60.8218i	−0.742462	+	2.03990i
$890$	33.2735	+	4.93800i	1.11533	+	0.165522i
$891$	36.2270	−	23.0829i	1.21365	−	0.773307i
$892$	−7.03339	−	7.03339i	−0.235495	−	0.235495i
$893$	2.08336	+	4.46778i	0.0697170	+	0.149509i
$894$	−28.0787	+	2.76604i	−0.939094	+	0.0925102i
$895$	−1.05027	+	17.4647i	−0.0351067	+	0.583780i
$896$	−3.37273	−	0.594704i	−0.112675	−	0.0198677i
$897$	−1.90512	−	3.21804i	−0.0636101	−	0.107447i
$898$	−0.613887	+	7.01676i	−0.0204857	+	0.234152i
$899$	−0.0160044	−	0.0277204i	−0.000533776	−	0.000924528i
$900$	13.6636	−	6.18923i	0.455453	−	0.206308i
$901$	−21.0734	+	36.5001i	−0.702055	+	1.21600i
$902$	−1.51704	−	1.06224i	−0.0505119	−	0.0353688i
$903$	−5.32115	−	28.3620i	−0.177077	−	0.943827i
$904$	−4.97797	−	13.6769i	−0.165565	−	0.454886i
$905$	1.62333	+	1.07207i	0.0539612	+	0.0356369i
$906$	1.58994	−	20.7867i	0.0528223	−	0.690593i
$907$	16.4036	−	23.4268i	0.544673	−	0.777874i	−0.448592	−	0.893737i	$-0.648074\pi$
$907$	16.4036	−	23.4268i	0.544673	−	0.777874i	0.993265	+	0.115863i	$0.0369632\pi$
$908$	11.7254	−	3.14182i	0.389122	−	0.104265i
$909$	3.99462	−	4.97756i	0.132493	−	0.165095i
$910$	−5.43664	−	13.7605i	−0.180223	−	0.456155i
$911$	22.1960	+	26.4522i	0.735387	+	0.876400i	0.996028	−	0.0890359i	$-0.0283786\pi$
$911$	22.1960	+	26.4522i	0.735387	+	0.876400i	−0.260642	+	0.965436i	$0.583934\pi$
$912$	−0.117485	−	10.7516i	−0.00389033	−	0.356021i
$913$	37.6805	+	53.8133i	1.24704	+	1.78096i
$914$	3.88646	+	3.26113i	0.128553	+	0.107869i
$915$	−5.42451	+	2.78598i	−0.179329	+	0.0921016i
$916$	9.79323	+	3.56444i	0.323577	+	0.117773i
$917$	−4.50549	+	4.50549i	−0.148785	+	0.148785i
$918$	27.3633	−	5.75548i	0.903125	−	0.189959i
$919$		−	44.2093i		−	1.45833i	−0.684338	−	0.729165i	$-0.739909\pi$
$919$		−	44.2093i		−	1.45833i	0.684338	−	0.729165i	$-0.260091\pi$
$920$	2.39525	−	0.712169i	0.0789690	−	0.0234795i
$921$	−41.1234	−	18.6319i	−1.35506	−	0.613941i
$922$	−0.178830	−	2.04404i	−0.00588946	−	0.0673169i
$923$	3.84069	−	2.68928i	0.126418	−	0.0885188i
$924$	27.2657	−	7.62610i	0.896977	−	0.250880i
$925$	−18.5440	+	46.1694i	−0.609722	+	1.51804i
$926$	−12.0663	+	6.96651i	−0.396525	+	0.228934i
$927$	−5.27635	+	5.51215i	−0.173298	+	0.181043i
$928$	−0.00363321	−	0.0135593i	−0.000119266	−	0.000445107i
$929$	2.26170	+	12.8267i	0.0742039	+	0.420831i	0.999168	+	0.0407775i	$0.0129835\pi$
$929$	2.26170	+	12.8267i	0.0742039	+	0.420831i	−0.924964	+	0.380054i	$0.875905\pi$
$930$	7.81082	+	4.12086i	0.256127	+	0.135128i
$931$	27.5863	−	10.0406i	0.904106	−	0.329068i
$932$	4.23315	−	9.07802i	0.138662	−	0.297361i
$933$	−12.7141	+	36.1560i	−0.416239	+	1.18369i
$934$	−1.34914	+	0.237890i	−0.0441453	+	0.00778400i
$935$	44.9833	+	35.7063i	1.47111	+	1.16772i
$936$	2.78767	−	5.08170i	0.0911179	−	0.166100i
$937$	−10.1669	+	37.9433i	−0.332137	+	1.23955i	0.574803	+	0.818292i	$0.305079\pi$
$937$	−10.1669	+	37.9433i	−0.332137	+	1.23955i	−0.906940	+	0.421260i	$0.861588\pi$
$938$	38.4286	+	3.36207i	1.25474	+	0.109775i
$939$	−10.2111	−	36.5078i	−0.333226	−	1.19139i
$940$	−1.68449	−	0.561708i	−0.0549420	−	0.0183209i
$941$	33.7793	−	40.2566i	1.10117	−	1.31233i	0.155273	−	0.987872i	$-0.450374\pi$
$941$	33.7793	−	40.2566i	1.10117	−	1.31233i	0.945901	−	0.324456i	$-0.105181\pi$
$942$	17.8844	−	6.73158i	0.582704	−	0.219327i
$943$	0.392995	−	0.183257i	0.0127977	−	0.00596766i
$944$	−11.6506			−0.379193
$945$	−4.54825	+	39.5314i	−0.147955	+	1.28596i
$946$	23.2187			0.754906
$947$	−36.8009	+	17.1605i	−1.19587	+	0.557643i	−0.915527	−	0.402258i	$-0.868226\pi$
$947$	−36.8009	+	17.1605i	−1.19587	+	0.557643i	−0.280342	+	0.959900i	$0.590448\pi$
$948$	−3.13473	+	18.9890i	−0.101811	+	0.616734i
$949$	−10.6229	+	12.6599i	−0.344834	+	0.410958i
$950$	9.65191	+	29.5002i	0.313149	+	0.957113i
$951$	12.0239	−	12.2896i	0.389901	−	0.398516i
$952$	18.3596	+	1.60625i	0.595037	+	0.0520590i
$953$	−7.83630	+	29.2455i	−0.253843	+	0.947354i	0.714888	+	0.699239i	$0.246478\pi$
$953$	−7.83630	+	29.2455i	−0.253843	+	0.947354i	−0.968731	+	0.248115i	$0.920189\pi$
$954$	3.57346	−	23.2229i	0.115695	−	0.751868i
$955$	−2.51174	−	21.8467i	−0.0812779	−	0.706942i
$956$	0.669224	−	0.118002i	0.0216443	−	0.00381647i
$957$	0.0755609	+	0.0880773i	0.00244254	+	0.00284713i
$958$	−2.93621	+	6.29673i	−0.0948648	+	0.203438i
$959$	26.2928	−	9.56979i	0.849038	−	0.309025i
$960$	2.84102	+	2.63223i	0.0916934	+	0.0849548i
$961$	−4.48023	−	25.4087i	−0.144524	−	0.819635i
$962$	4.97590	+	18.5703i	0.160429	+	0.598731i
$963$	14.9854	+	10.0121i	0.482899	+	0.322637i
$964$	16.8701	−	9.73993i	0.543348	−	0.313702i
$965$	−15.5578	+	9.55573i	−0.500824	+	0.307610i
$966$	−1.64566	+	6.42154i	−0.0529482	+	0.206610i
$967$	−32.9473	+	23.0699i	−1.05951	+	0.741879i	−0.967242	−	0.253855i	$-0.918301\pi$
$967$	−32.9473	+	23.0699i	−1.05951	+	0.741879i	−0.0922710	+	0.995734i	$0.529413\pi$
$968$	1.02674	+	11.7356i	0.0330005	+	0.377198i
$969$	5.67244	+	57.5823i	0.182225	+	1.84981i
$970$	11.3640	+	38.2206i	0.364875	+	1.22719i
$971$		−	27.9762i		−	0.897800i	−0.893582	−	0.448900i	$-0.851816\pi$
$971$		−	27.9762i		−	0.897800i	0.893582	−	0.448900i	$-0.148184\pi$
$972$	−13.0542	+	8.51979i	−0.418715	+	0.273272i
$973$	40.5935	−	40.5935i	1.30137	−	1.30137i
$974$	−18.7470	−	6.82334i	−0.600692	−	0.218634i
$975$	−3.26618	+	16.4100i	−0.104602	+	0.525541i
$976$	−1.20616	−	1.01209i	−0.0386081	−	0.0323961i
$977$	5.53031	+	7.89810i	0.176930	+	0.252682i	0.897815	−	0.440372i	$-0.145153\pi$
$977$	5.53031	+	7.89810i	0.176930	+	0.252682i	−0.720885	+	0.693054i	$0.756265\pi$
$978$	16.4433	−	9.73465i	0.525799	−	0.311280i
$979$	−46.1523	−	55.0022i	−1.47503	−	1.75788i
$980$	−4.20661	+	9.70166i	−0.134375	+	0.309908i
$981$	7.23054	−	1.43852i	0.230854	−	0.0459285i
$982$	40.3629	−	10.8152i	1.28803	−	0.345127i
$983$	22.3485	−	31.9169i	0.712806	−	1.01799i	−0.285417	−	0.958403i	$-0.592132\pi$
$983$	22.3485	−	31.9169i	0.712806	−	1.01799i	0.998223	−	0.0595888i	$-0.0189789\pi$
$984$	0.554703	+	0.379443i	0.0176833	+	0.0120962i
$985$	48.0376	−	9.82450i	1.53061	−	0.313035i
$986$	0.0258365	+	0.0709852i	0.000822801	+	0.00226063i
$987$	3.57517	−	3.06712i	0.113799	−	0.0976274i
$988$	9.82465	+	6.87929i	0.312564	+	0.218859i
$989$	−2.71824	+	4.70813i	−0.0864349	+	0.149710i
$990$	−30.5874	−	9.46213i	−0.972132	−	0.300726i
$991$	−12.5007	−	21.6518i	−0.397097	−	0.687793i	0.596269	−	0.802785i	$-0.296649\pi$
$991$	−12.5007	−	21.6518i	−0.397097	−	0.687793i	−0.993366	+	0.114992i	$0.963316\pi$
$992$	−0.198733	+	2.27153i	−0.00630979	+	0.0721212i
$993$	51.4243	−	0.561927i	1.63190	−	0.0178322i
$994$	−8.18489	−	1.44322i	−0.259609	−	0.0457761i
$995$	11.8286	+	0.711336i	0.374993	+	0.0225509i
$996$	−13.8866	−	19.3779i	−0.440013	−	0.614013i
$997$	−9.78742	−	20.9892i	−0.309971	−	0.664735i	0.688179	−	0.725541i	$-0.258410\pi$
$997$	−9.78742	−	20.9892i	−0.309971	−	0.664735i	−0.998150	+	0.0608066i	$0.980633\pi$
$998$	3.81527	+	3.81527i	0.120770	+	0.120770i
$999$	11.7385	−	50.3562i	0.371388	−	1.59320i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.77.7	yes	216
3.2	odd	2		810.2.s.a.17.17		216
5.3	odd	4	inner	270.2.r.a.23.11	✓	216
15.8	even	4		810.2.s.a.503.7		216
27.7	even	9		810.2.s.a.467.7		216
27.20	odd	18	inner	270.2.r.a.47.11	yes	216
135.88	odd	36		810.2.s.a.143.17		216
135.128	even	36	inner	270.2.r.a.263.7	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.23.11	✓	216	5.3	odd	4	inner
270.2.r.a.47.11	yes	216	27.20	odd	18	inner
270.2.r.a.77.7	yes	216	1.1	even	1	trivial
270.2.r.a.263.7	yes	216	135.128	even	36	inner
810.2.s.a.17.17		216	3.2	odd	2
810.2.s.a.143.17		216	135.88	odd	36
810.2.s.a.467.7		216	27.7	even	9
810.2.s.a.503.7		216	15.8	even	4

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.906308 + 0.422618i) q^{2} +(1.33891 + 1.09878i) q^{3} +(0.642788 - 0.766044i) q^{4} +(-2.00011 + 0.999773i) q^{5} +(-1.67783 - 0.429980i) q^{6} +(-3.41173 - 0.298488i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.585380 + 2.94233i) q^{9} +O(q^{10})\)	\(q+(-0.906308 + 0.422618i) q^{2} +(1.33891 + 1.09878i) q^{3} +(0.642788 - 0.766044i) q^{4} +(-2.00011 + 0.999773i) q^{5} +(-1.67783 - 0.429980i) q^{6} +(-3.41173 - 0.298488i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.585380 + 2.94233i) q^{9} +(1.39020 - 1.75139i) q^{10} +(-4.70038 + 0.828804i) q^{11} +(1.70235 - 0.319387i) q^{12} +(-0.816512 + 1.75102i) q^{13} +(3.21823 - 1.17134i) q^{14} +(-3.77651 - 0.859067i) q^{15} +(-0.173648 - 0.984808i) q^{16} +(1.39278 + 5.19794i) q^{17} +(-1.77402 - 2.41927i) q^{18} +(5.37612 - 3.10390i) q^{19} +(-0.519777 + 2.17482i) q^{20} +(-4.24004 - 4.14838i) q^{21} +(3.90972 - 2.73762i) q^{22} +(0.0973994 + 1.11328i) q^{23} +(-1.40787 + 1.00891i) q^{24} +(3.00091 - 3.99932i) q^{25} -1.93203i q^{26} +(-2.44919 + 4.58273i) q^{27} +(-2.42167 + 2.42167i) q^{28} +(-0.0131911 - 0.00480116i) q^{29} +(3.78574 - 0.817441i) q^{30} +(1.74674 + 1.46569i) q^{31} +(0.573576 + 0.819152i) q^{32} +(-7.20407 - 4.05497i) q^{33} +(-3.45904 - 4.12232i) q^{34} +(7.12227 - 2.81395i) q^{35} +(2.63023 + 1.44287i) q^{36} +(-9.61180 + 2.57547i) q^{37} +(-3.56065 + 5.08514i) q^{38} +(-3.01722 + 1.44730i) q^{39} +(-0.448040 - 2.19072i) q^{40} +(-0.132710 - 0.364617i) q^{41} +(5.59597 + 1.96779i) q^{42} +(3.98494 + 2.79028i) q^{43} +(-2.38644 + 4.13344i) q^{44} +(-4.11249 - 5.29975i) q^{45} +(-0.558767 - 0.967812i) q^{46} +(-0.0692108 + 0.791084i) q^{47} +(0.849584 - 1.50937i) q^{48} +(4.65717 + 0.821184i) q^{49} +(-1.02956 + 4.89285i) q^{50} +(-3.84656 + 8.48995i) q^{51} +(0.816512 + 1.75102i) q^{52} +(5.53811 + 5.53811i) q^{53} +(0.282978 - 5.18844i) q^{54} +(8.57267 - 6.35701i) q^{55} +(1.17134 - 3.21823i) q^{56} +(10.6087 + 1.75129i) q^{57} +(0.0139842 - 0.00122346i) q^{58} +(2.02310 - 11.4736i) q^{59} +(-3.08558 + 2.34077i) q^{60} +(1.20616 - 1.01209i) q^{61} +(-2.20251 - 0.590162i) q^{62} +(-1.11891 - 10.2132i) q^{63} +(-0.866025 - 0.500000i) q^{64} +(-0.117503 - 4.31856i) q^{65} +(8.24281 + 0.630478i) q^{66} +(10.2083 + 4.76023i) q^{67} +(4.87712 + 2.27424i) q^{68} +(-1.09284 + 1.59761i) q^{69} +(-5.26574 + 5.56031i) q^{70} +(-2.10165 - 1.21339i) q^{71} +(-2.99358 - 0.196099i) q^{72} +(8.26239 + 2.21390i) q^{73} +(7.62281 - 6.39630i) q^{74} +(8.41231 - 2.05742i) q^{75} +(1.07797 - 6.11349i) q^{76} +(16.2838 - 1.42465i) q^{77} +(2.12287 - 2.58683i) q^{78} +(-3.80042 + 10.4416i) q^{79} +(1.33190 + 1.79612i) q^{80} +(-8.31466 + 3.44477i) q^{81} +(0.274370 + 0.274370i) q^{82} +(-5.81691 - 12.4744i) q^{83} +(-5.90329 + 0.581534i) q^{84} +(-7.98249 - 9.00400i) q^{85} +(-4.79081 - 0.844748i) q^{86} +(-0.0123863 - 0.0209224i) q^{87} +(0.415985 - 4.75473i) q^{88} +(7.52167 + 13.0279i) q^{89} +(5.96696 + 3.06519i) q^{90} +(3.30838 - 5.73028i) q^{91} +(0.915429 + 0.640991i) q^{92} +(0.728270 + 3.88171i) q^{93} +(-0.271600 - 0.746215i) q^{94} +(-7.64964 + 11.5831i) q^{95} +(-0.132096 + 1.72701i) q^{96} +(-10.2282 + 14.6074i) q^{97} +(-4.56787 + 1.22396i) q^{98} +(-5.19012 - 13.3449i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6}+O(q^{10}) \) 216 * q + 12 * q^6	\( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50} - 192 q^{51} - 12 q^{56} - 36 q^{57} + 36 q^{61} + 84 q^{63} + 24 q^{65} - 72 q^{67} + 36 q^{68} - 48 q^{72} - 36 q^{75} - 240 q^{77} + 24 q^{78} - 24 q^{81} - 60 q^{83} + 72 q^{86} - 252 q^{87} - 48 q^{92} - 96 q^{93} - 60 q^{95} - 72 q^{97}+O(q^{100}) \) 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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