LMFDB - Embedded newform 930.2.bk.a.47.51

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.51
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.51

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.156434 - 0.987688i) q^{2} +(0.424210 + 1.67930i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.08414 + 0.810158i) q^{5} +(1.72499 - 0.156287i) q^{6} +(2.37194 - 1.20856i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.64009 + 1.42475i) q^{9} +O(q^{10})$	\(q+(0.156434 - 0.987688i) q^{2} +(0.424210 + 1.67930i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.08414 + 0.810158i) q^{5} +(1.72499 - 0.156287i) q^{6} +(2.37194 - 1.20856i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.64009 + 1.42475i) q^{9} +(1.12621 - 1.93175i) q^{10} +(2.63793 + 0.857115i) q^{11} +(0.115485 - 1.72820i) q^{12} +(0.917596 - 0.145333i) q^{13} +(-0.822631 - 2.53180i) q^{14} +(-0.476384 + 3.84357i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.36156 + 0.693749i) q^{17} +(0.994208 + 2.83047i) q^{18} +(-1.62715 - 2.23958i) q^{19} +(-1.73178 - 1.41454i) q^{20} +(3.03574 + 3.47051i) q^{21} +(1.25923 - 2.47137i) q^{22} +(0.646536 - 1.26890i) q^{23} +(-1.68885 - 0.384412i) q^{24} +(3.68729 + 3.37697i) q^{25} -0.929034i q^{26} +(-3.51253 - 3.82911i) q^{27} +(-2.62932 + 0.416443i) q^{28} +(1.38108 - 1.00341i) q^{29} +(3.72173 + 1.07179i) q^{30} +(-4.79140 + 2.83593i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.320318 + 4.79347i) q^{33} +(0.898202 - 1.23627i) q^{34} +(5.92258 - 0.597172i) q^{35} +(2.95115 - 0.539185i) q^{36} +(-1.76024 - 1.76024i) q^{37} +(-2.46655 + 1.25677i) q^{38} +(0.633311 + 1.47927i) q^{39} +(-1.66804 + 1.48918i) q^{40} +(-0.267066 - 0.367584i) q^{41} +(3.90268 - 2.45546i) q^{42} +(-1.36663 + 8.62854i) q^{43} +(-2.24396 - 1.63033i) q^{44} +(-6.65660 + 0.830489i) q^{45} +(-1.15214 - 0.837075i) q^{46} +(8.72599 - 1.38206i) q^{47} +(-0.643874 + 1.60793i) q^{48} +(0.0509748 - 0.0701608i) q^{49} +(3.91221 - 3.11362i) q^{50} +(-0.587425 + 2.58076i) q^{51} +(-0.917596 - 0.145333i) q^{52} +(-0.749270 + 1.47053i) q^{53} +(-4.33145 + 2.87028i) q^{54} +(4.80342 + 3.92349i) q^{55} +2.66209i q^{56} +(3.07067 - 3.68253i) q^{57} +(-0.775010 - 1.52104i) q^{58} +(8.16490 + 5.93215i) q^{59} +(1.64080 - 3.50824i) q^{60} -1.40880 q^{61} +(2.05148 + 5.17604i) q^{62} +(-4.54024 + 6.57014i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(2.03014 + 0.440503i) q^{65} +(4.68435 + 1.06624i) q^{66} +(-8.54103 - 8.54103i) q^{67} +(-1.08054 - 1.08054i) q^{68} +(2.40513 + 0.547448i) q^{69} +(0.336677 - 5.94309i) q^{70} +(1.44860 - 0.470678i) q^{71} +(-0.0708850 - 2.99916i) q^{72} +(-1.04184 - 2.04472i) q^{73} +(-2.01393 + 1.46320i) q^{74} +(-4.10675 + 7.62460i) q^{75} +(0.855444 + 2.63279i) q^{76} +(7.29289 - 1.15508i) q^{77} +(1.56013 - 0.394105i) q^{78} +(9.08294 - 2.95123i) q^{79} +(1.20991 + 1.88046i) q^{80} +(4.94017 - 7.52294i) q^{81} +(-0.404837 + 0.206275i) q^{82} +(6.23348 + 0.987287i) q^{83} +(-1.81471 - 4.23875i) q^{84} +(2.27563 + 2.54895i) q^{85} +(8.30852 + 2.69960i) q^{86} +(2.27090 + 1.89359i) q^{87} +(-1.96129 + 1.96129i) q^{88} +(2.60352 - 8.01281i) q^{89} +(-0.221057 + 6.70456i) q^{90} +(2.00084 - 1.45369i) q^{91} +(-1.00700 + 1.00700i) q^{92} +(-6.79494 - 6.84316i) q^{93} -8.83476i q^{94} +(-1.57680 - 5.98585i) q^{95} +(1.48741 + 0.887482i) q^{96} +(-9.79448 + 4.99054i) q^{97} +(-0.0613228 - 0.0613228i) q^{98} +(-8.18555 + 1.49553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$2$	0.156434	−	0.987688i	0.110616	−	0.698401i
$3$	0.424210	+	1.67930i	0.244918	+	0.969544i
$3$	0.424210	+	1.67930i	0.244918	+	0.969544i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	2.08414	+	0.810158i	0.932056	+	0.362314i
$5$	2.08414	+	0.810158i	0.932056	+	0.362314i
$6$	1.72499	−	0.156287i	0.704222	−	0.0638038i
$7$	2.37194	−	1.20856i	0.896509	−	0.456794i	0.0558998	−	0.998436i	$-0.482197\pi$
$7$	2.37194	−	1.20856i	0.896509	−	0.456794i	0.840609	+	0.541642i	$0.182197\pi$
$8$	−0.453990	+	0.891007i	−0.160510	+	0.315018i
$9$	−2.64009	+	1.42475i	−0.880031	+	0.474917i
$10$	1.12621	−	1.93175i	0.356140	−	0.610872i
$11$	2.63793	+	0.857115i	0.795366	+	0.258430i	0.678387	−	0.734704i	$-0.262679\pi$
$11$	2.63793	+	0.857115i	0.795366	+	0.258430i	0.116978	+	0.993134i	$0.462679\pi$
$12$	0.115485	−	1.72820i	0.0333375	−	0.498887i
$13$	0.917596	−	0.145333i	0.254495	−	0.0403081i	−0.0278831	−	0.999611i	$-0.508877\pi$
$13$	0.917596	−	0.145333i	0.254495	−	0.0403081i	0.282378	+	0.959303i	$0.408877\pi$
$14$	−0.822631	−	2.53180i	−0.219857	−	0.676652i
$15$	−0.476384	+	3.84357i	−0.123002	+	0.992406i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	1.36156	+	0.693749i	0.330226	+	0.168259i	0.611241	−	0.791445i	$-0.290671\pi$
$17$	1.36156	+	0.693749i	0.330226	+	0.168259i	−0.281014	+	0.959704i	$0.590671\pi$
$18$	0.994208	+	2.83047i	0.234337	+	0.667148i
$19$	−1.62715	−	2.23958i	−0.373294	−	0.513795i	0.580498	−	0.814261i	$-0.302858\pi$
$19$	−1.62715	−	2.23958i	−0.373294	−	0.513795i	−0.953792	+	0.300466i	$0.902858\pi$
$20$	−1.73178	−	1.41454i	−0.387239	−	0.316301i
$21$	3.03574	+	3.47051i	0.662453	+	0.757328i
$22$	1.25923	−	2.47137i	0.268468	−	0.526898i
$23$	0.646536	−	1.26890i	0.134812	−	0.264584i	−0.813725	−	0.581250i	$-0.802564\pi$
$23$	0.646536	−	1.26890i	0.134812	−	0.264584i	0.948537	+	0.316667i	$0.102564\pi$
$24$	−1.68885	−	0.384412i	−0.344736	−	0.0784678i
$25$	3.68729	+	3.37697i	0.737458	+	0.675393i
$26$		−	0.929034i		−	0.182199i
$27$	−3.51253	−	3.82911i	−0.675988	−	0.736913i
$28$	−2.62932	+	0.416443i	−0.496894	+	0.0787003i
$29$	1.38108	−	1.00341i	0.256460	−	0.186329i	−0.452125	−	0.891955i	$-0.649334\pi$
$29$	1.38108	−	1.00341i	0.256460	−	0.186329i	0.708585	+	0.705626i	$0.249334\pi$
$30$	3.72173	+	1.07179i	0.679492	+	0.195681i
$31$	−4.79140	+	2.83593i	−0.860560	+	0.509349i
$31$	−4.79140	+	2.83593i	−0.860560	+	0.509349i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.320318	+	4.79347i	−0.0557602	+	0.834436i
$34$	0.898202	−	1.23627i	0.154040	−	0.212018i
$35$	5.92258	−	0.597172i	1.00110	−	0.100940i
$36$	2.95115	−	0.539185i	0.491858	−	0.0898641i
$37$	−1.76024	−	1.76024i	−0.289381	−	0.289381i	0.547454	−	0.836835i	$-0.315597\pi$
$37$	−1.76024	−	1.76024i	−0.289381	−	0.289381i	−0.836835	+	0.547454i	$0.815597\pi$
$38$	−2.46655	+	1.25677i	−0.400127	+	0.203875i
$39$	0.633311	+	1.47927i	0.101411	+	0.236872i
$40$	−1.66804	+	1.48918i	−0.263740	+	0.235460i
$41$	−0.267066	−	0.367584i	−0.0417087	−	0.0574070i	0.787653	−	0.616119i	$-0.211296\pi$
$41$	−0.267066	−	0.367584i	−0.0417087	−	0.0574070i	−0.829362	+	0.558712i	$0.811296\pi$
$42$	3.90268	−	2.45546i	0.602196	−	0.378885i
$43$	−1.36663	+	8.62854i	−0.208409	+	1.31584i	0.632457	+	0.774596i	$0.282047\pi$
$43$	−1.36663	+	8.62854i	−0.208409	+	1.31584i	−0.840865	+	0.541244i	$0.817953\pi$
$44$	−2.24396	−	1.63033i	−0.338289	−	0.245782i
$45$	−6.65660	+	0.830489i	−0.992307	+	0.123802i
$46$	−1.15214	−	0.837075i	−0.169873	−	0.123420i
$47$	8.72599	−	1.38206i	1.27282	−	0.201594i	0.516777	−	0.856120i	$-0.327132\pi$
$47$	8.72599	−	1.38206i	1.27282	−	0.201594i	0.756040	+	0.654526i	$0.227132\pi$
$48$	−0.643874	+	1.60793i	−0.0929353	+	0.232084i
$49$	0.0509748	−	0.0701608i	0.00728211	−	0.0100230i
$50$	3.91221	−	3.11362i	0.553270	−	0.440332i
$51$	−0.587425	+	2.58076i	−0.0822560	+	0.361379i
$52$	−0.917596	−	0.145333i	−0.127248	−	0.0201540i
$53$	−0.749270	+	1.47053i	−0.102920	+	0.201992i	−0.936724	−	0.350068i	$-0.886158\pi$
$53$	−0.749270	+	1.47053i	−0.102920	+	0.201992i	0.833804	+	0.552061i	$0.186158\pi$
$54$	−4.33145	+	2.87028i	−0.589436	+	0.390596i
$55$	4.80342	+	3.92349i	0.647693	+	0.529043i
$56$			2.66209i			0.355737i
$57$	3.07067	−	3.68253i	0.406721	−	0.487762i
$58$	−0.775010	−	1.52104i	−0.101764	−	0.199723i
$59$	8.16490	+	5.93215i	1.06298	+	0.772300i	0.974637	−	0.223791i	$-0.0718432\pi$
$59$	8.16490	+	5.93215i	1.06298	+	0.772300i	0.0883419	+	0.996090i	$0.471843\pi$
$60$	1.64080	−	3.50824i	0.211826	−	0.452912i
$61$	−1.40880			−0.180378			−0.0901892	−	0.995925i	$-0.528747\pi$
$61$	−1.40880			−0.180378			−0.0901892	+	0.995925i	$0.528747\pi$
$62$	2.05148	+	5.17604i	0.260538	+	0.657358i
$63$	−4.54024	+	6.57014i	−0.572016	+	0.827760i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	2.03014	+	0.440503i	0.251808	+	0.0546377i
$66$	4.68435	+	1.06624i	0.576603	+	0.131245i
$67$	−8.54103	−	8.54103i	−1.04345	−	1.04345i	−0.999012	−	0.0444405i	$-0.985849\pi$
$67$	−8.54103	−	8.54103i	−1.04345	−	1.04345i	−0.0444405	−	0.999012i	$-0.514151\pi$
$68$	−1.08054	−	1.08054i	−0.131035	−	0.131035i
$69$	2.40513	+	0.547448i	0.289543	+	0.0659050i
$70$	0.336677	−	5.94309i	0.0402406	−	0.710335i
$71$	1.44860	−	0.470678i	0.171917	−	0.0558592i	−0.221794	−	0.975094i	$-0.571191\pi$
$71$	1.44860	−	0.470678i	0.171917	−	0.0558592i	0.393711	+	0.919234i	$0.371191\pi$
$72$	−0.0708850	−	2.99916i	−0.00835387	−	0.353455i
$73$	−1.04184	−	2.04472i	−0.121938	−	0.239316i	0.821966	−	0.569536i	$-0.192877\pi$
$73$	−1.04184	−	2.04472i	−0.121938	−	0.239316i	−0.943904	+	0.330220i	$0.892877\pi$
$74$	−2.01393	+	1.46320i	−0.234114	+	0.170094i
$75$	−4.10675	+	7.62460i	−0.474207	+	0.880413i
$76$	0.855444	+	2.63279i	0.0981261	+	0.302001i
$77$	7.29289	−	1.15508i	0.831102	−	0.131634i
$78$	1.56013	−	0.394105i	0.176649	−	0.0446236i
$79$	9.08294	−	2.95123i	1.02191	−	0.332039i	0.250323	−	0.968162i	$-0.419463\pi$
$79$	9.08294	−	2.95123i	1.02191	−	0.332039i	0.771587	+	0.636124i	$0.219463\pi$
$80$	1.20991	+	1.88046i	0.135272	+	0.210242i
$81$	4.94017	−	7.52294i	0.548908	−	0.835883i
$82$	−0.404837	+	0.206275i	−0.0447068	+	0.0227792i
$83$	6.23348	+	0.987287i	0.684214	+	0.108369i	0.488858	−	0.872364i	$-0.337414\pi$
$83$	6.23348	+	0.987287i	0.684214	+	0.108369i	0.195356	+	0.980732i	$0.437414\pi$
$84$	−1.81471	−	4.23875i	−0.198001	−	0.462485i
$85$	2.27563	+	2.54895i	0.246827	+	0.276472i
$86$	8.30852	+	2.69960i	0.895931	+	0.291106i
$87$	2.27090	+	1.89359i	0.243466	+	0.203014i
$88$	−1.96129	+	1.96129i	−0.209074	+	0.209074i
$89$	2.60352	−	8.01281i	0.275972	−	0.849356i	−0.712988	−	0.701176i	$-0.752659\pi$
$89$	2.60352	−	8.01281i	0.275972	−	0.849356i	0.988960	−	0.148180i	$-0.0473413\pi$
$90$	−0.221057	+	6.70456i	−0.0233014	+	0.706723i
$91$	2.00084	−	1.45369i	0.209745	−	0.152389i
$92$	−1.00700	+	1.00700i	−0.104987	+	0.104987i
$93$	−6.79494	−	6.84316i	−0.704602	−	0.709602i
$94$		−	8.83476i		−	0.911236i
$95$	−1.57680	−	5.98585i	−0.161776	−	0.614136i
$96$	1.48741	+	0.887482i	0.151808	+	0.0905783i
$97$	−9.79448	+	4.99054i	−0.994479	+	0.506712i	−0.873960	−	0.485999i	$-0.838456\pi$
$97$	−9.79448	+	4.99054i	−0.994479	+	0.506712i	−0.120520	+	0.992711i	$0.538456\pi$
$98$	−0.0613228	−	0.0613228i	−0.00619454	−	0.00619454i
$99$	−8.18555	+	1.49553i	−0.822679	+	0.150306i
$100$	−2.46328	−	4.35112i	−0.246328	−	0.435112i
$101$	−8.71855	+	2.83283i	−0.867528	+	0.281877i	−0.708769	−	0.705441i	$-0.750749\pi$
$101$	−8.71855	+	2.83283i	−0.867528	+	0.281877i	−0.158759	+	0.987317i	$0.550749\pi$
$102$	2.45709	+	0.983913i	0.243288	+	0.0974219i
$103$	−1.19804	+	7.56415i	−0.118047	+	0.745318i	0.855664	+	0.517531i	$0.173149\pi$
$103$	−1.19804	+	7.56415i	−0.118047	+	0.745318i	−0.973711	+	0.227787i	$0.926851\pi$
$104$	−0.287087	+	0.883564i	−0.0281512	+	0.0866405i
$105$	3.51525	+	9.69247i	0.343053	+	0.945888i
$106$	1.33521	+	0.970087i	0.129687	+	0.0942231i
$107$	−4.33025	−	2.20637i	−0.418621	−	0.213298i	0.231976	−	0.972722i	$-0.425481\pi$
$107$	−4.33025	−	2.20637i	−0.418621	−	0.213298i	−0.650596	+	0.759424i	$0.725481\pi$
$108$	2.15736	+	4.72713i	0.207592	+	0.454869i
$109$	4.64345	−	6.39115i	0.444761	−	0.612162i	−0.526500	−	0.850175i	$-0.676496\pi$
$109$	4.64345	−	6.39115i	0.444761	−	0.612162i	0.971262	+	0.238013i	$0.0764962\pi$
$110$	4.62660	−	4.13051i	0.441129	−	0.393829i
$111$	2.20925	−	3.70267i	0.209693	−	0.351442i
$112$	2.62932	+	0.416443i	0.248447	+	0.0393501i
$113$	−4.42678	+	2.25556i	−0.416436	+	0.212185i	−0.649638	−	0.760243i	$-0.725080\pi$
$113$	−4.42678	+	2.25556i	−0.416436	+	0.212185i	0.233202	+	0.972428i	$0.425080\pi$
$114$	−3.15683	−	3.60894i	−0.295664	−	0.338008i
$115$	2.37548	−	2.12077i	0.221515	−	0.197763i
$116$	−1.62356	+	0.527525i	−0.150743	+	0.0489795i
$117$	−2.21547	+	1.69104i	−0.204821	+	0.156336i
$118$	7.13638	−	7.13638i	0.656957	−	0.656957i
$119$	4.06797			0.372910
$120$	−3.20838	−	2.16941i	−0.292883	−	0.198039i
$121$	−2.67516	−	1.94362i	−0.243196	−	0.176692i
$122$	−0.220385	+	1.39146i	−0.0199527	+	0.125976i
$123$	0.503992	−	0.604416i	0.0454435	−	0.0544984i
$124$	5.43324	−	1.21651i	0.487919	−	0.109246i
$125$	4.94895	+	10.0254i	0.442648	+	0.896695i
$126$	5.77900	+	5.51214i	0.514834	+	0.491060i
$127$	−1.46395	−	9.24300i	−0.129904	−	0.820184i	−0.963480	−	0.267779i	$-0.913710\pi$
$127$	−1.46395	−	9.24300i	−0.129904	−	0.820184i	0.833576	−	0.552405i	$-0.186290\pi$
$128$	−0.891007	+	0.453990i	−0.0787546	+	0.0401275i
$129$	−15.0696	+	1.36534i	−1.32681	+	0.120211i
$130$	0.752664	−	1.93624i	0.0660130	−	0.169819i
$131$	−6.50793	−	2.11455i	−0.568600	−	0.184749i	0.0105869	−	0.999944i	$-0.496630\pi$
$131$	−6.50793	−	2.11455i	−0.568600	−	0.184749i	−0.579187	+	0.815194i	$0.696630\pi$
$132$	1.78590	−	4.45988i	0.155443	−	0.388183i
$133$	−6.56618	−	3.34564i	−0.569360	−	0.290103i
$134$	−9.77198	+	7.09976i	−0.844171	+	0.613326i
$135$	−4.21843	−	10.8261i	−0.363065	−	0.931764i
$136$	−1.23627	+	0.898202i	−0.106009	+	0.0770202i
$137$	−16.3585	+	2.59093i	−1.39760	+	0.221358i	−0.809353	−	0.587322i	$-0.800182\pi$
$137$	−16.3585	+	2.59093i	−1.39760	+	0.221358i	−0.588248	+	0.808681i	$0.700182\pi$
$138$	0.916953	−	2.28988i	0.0780562	−	0.194927i
$139$	8.32973	−	11.4649i	0.706518	−	0.972439i	−0.293347	−	0.956006i	$-0.594769\pi$
$139$	8.32973	−	11.4649i	0.706518	−	0.972439i	0.999865	−	0.0164327i	$-0.00523093\pi$
$140$	−5.81725	−	1.26224i	−0.491647	−	0.106678i
$141$	6.02255	+	14.0673i	0.507190	+	1.18468i
$142$	−0.238273	−	1.50439i	−0.0199954	−	0.126246i
$143$	2.54512	+	0.403108i	0.212834	+	0.0337095i
$144$	−2.97333	−	0.399160i	−0.247777	−	0.0332633i
$145$	3.69129	−	0.972361i	0.306545	−	0.0807502i
$146$	−2.18253	+	0.709145i	−0.180627	+	0.0586893i
$147$	0.139445	+	0.0558390i	0.0115012	+	0.00460553i
$148$	1.13014	+	2.21803i	0.0928970	+	0.182321i
$149$	−12.9942			−1.06452			−0.532262	−	0.846580i	$-0.678658\pi$
$149$	−12.9942			−1.06452			−0.532262	+	0.846580i	$0.678658\pi$
$150$	6.88829	+	5.24894i	0.562427	+	0.428574i
$151$	6.78820	−	20.8919i	0.552416	−	1.70016i	−0.150257	−	0.988647i	$-0.548010\pi$
$151$	6.78820	−	20.8919i	0.552416	−	1.70016i	0.702673	−	0.711513i	$-0.251990\pi$
$152$	2.73419	−	0.433054i	0.221772	−	0.0351253i
$153$	−4.58306	+	0.108320i	−0.370518	+	0.00875717i
$154$		−	7.38380i		−	0.595003i
$155$	−12.2835	+	2.02870i	−0.986634	+	0.162949i
$156$	−0.145196	−	1.60257i	−0.0116250	−	0.128308i
$157$	−10.0484	−	1.59151i	−0.801950	−	0.127016i	−0.258012	−	0.966142i	$-0.583067\pi$
$157$	−10.0484	−	1.59151i	−0.801950	−	0.127016i	−0.543938	+	0.839125i	$0.683067\pi$
$158$	−1.49401	−	9.43278i	−0.118857	−	0.750432i
$159$	−2.78730	−	0.634438i	−0.221047	−	0.0503142i
$160$	2.04658	−	0.900842i	0.161796	−	0.0712178i
$161$		−	3.79113i		−	0.298783i
$162$	−6.65751	−	6.05620i	−0.523063	−	0.475820i
$163$	−22.6753	−	11.5536i	−1.77607	−	0.904951i	−0.925094	−	0.379739i	$-0.876014\pi$
$163$	−22.6753	−	11.5536i	−1.77607	−	0.904951i	−0.850972	−	0.525212i	$-0.823986\pi$
$164$	0.140405	+	0.432121i	0.0109638	+	0.0337430i
$165$	−4.55106	+	9.73076i	−0.354299	+	0.757539i
$166$	1.95026	−	6.00229i	0.151370	−	0.465868i
$167$	2.38862	−	15.0812i	0.184837	−	1.16702i	−0.704480	−	0.709724i	$-0.748820\pi$
$167$	2.38862	−	15.0812i	0.184837	−	1.16702i	0.889317	−	0.457291i	$-0.151180\pi$
$168$	−4.47045	+	1.12928i	−0.344902	+	0.0871262i
$169$	−11.5429	+	3.75051i	−0.887913	+	0.288501i
$170$	2.87355	−	1.84887i	0.220391	−	0.141802i
$171$	7.48667	+	3.59442i	0.572520	+	0.274872i
$172$	3.96610	−	7.78392i	0.302413	−	0.593518i
$173$	0.379437	+	2.39567i	0.0288480	+	0.182139i	0.997905	−	0.0646984i	$-0.0206085\pi$
$173$	0.379437	+	2.39567i	0.0288480	+	0.182139i	−0.969057	+	0.246838i	$0.920609\pi$
$174$	2.22552	−	1.94672i	0.168716	−	0.147580i
$175$	12.8273	+	3.55364i	0.969653	+	0.268630i
$176$	1.63033	+	2.24396i	0.122891	+	0.169145i
$177$	−6.49822	+	16.2278i	−0.488436	+	1.21975i
$178$	−7.50687	−	3.82494i	−0.562664	−	0.286692i
$179$	−0.534401	+	1.64472i	−0.0399430	+	0.122932i	−0.969040	−	0.246905i	$-0.920586\pi$
$179$	−0.534401	+	1.64472i	−0.0399430	+	0.122932i	0.929097	+	0.369837i	$0.120586\pi$
$180$	6.58744	+	1.26716i	0.490998	+	0.0944485i
$181$	−11.2825			−0.838622			−0.419311	−	0.907843i	$-0.637728\pi$
$181$	−11.2825			−0.838622			−0.419311	+	0.907843i	$0.637728\pi$
$182$	−1.12280	−	2.20361i	−0.0832272	−	0.163343i
$183$	−0.597627	−	2.36580i	−0.0441778	−	0.174885i
$184$	0.837075	+	1.15214i	0.0617100	+	0.0849365i
$185$	−2.24251	−	5.09465i	−0.164873	−	0.374566i
$186$	−7.82187	+	5.64078i	−0.573527	+	0.413602i
$187$	2.99707	+	2.99707i	0.219168	+	0.219168i
$188$	−8.72599	−	1.38206i	−0.636408	−	0.100797i
$189$	−12.9592	−	4.83730i	−0.942646	−	0.351862i
$190$	−6.15882	+	0.620992i	−0.446808	+	0.0450515i
$191$		−	4.46054i		−	0.322753i	−0.986893	−	0.161377i	$-0.948407\pi$
$191$		−	4.46054i		−	0.322753i	0.986893	−	0.161377i	$-0.0515934\pi$
$192$	1.10924	−	1.33026i	0.0800523	−	0.0960033i
$193$	5.06111	+	9.93299i	0.364307	+	0.714993i	0.998296	−	0.0583492i	$-0.0185837\pi$
$193$	5.06111	+	9.93299i	0.364307	+	0.714993i	−0.633989	+	0.773342i	$0.718584\pi$
$194$	3.39690	+	10.4546i	0.243883	+	0.750596i
$195$	0.121469	+	3.59608i	0.00869860	+	0.257521i
$196$	−0.0701608	+	0.0509748i	−0.00501148	+	0.00364106i
$197$	10.4983	+	20.6041i	0.747975	+	1.46798i	0.879110	+	0.476618i	$0.158138\pi$
$197$	10.4983	+	20.6041i	0.747975	+	1.46798i	−0.131136	+	0.991364i	$0.541862\pi$
$198$	0.196612	+	8.31873i	0.0139726	+	0.591186i
$199$	10.4454	−	14.3768i	0.740453	−	1.01915i	−0.258140	−	0.966108i	$-0.583109\pi$
$199$	10.4454	−	14.3768i	0.740453	−	1.01915i	0.998592	−	0.0530382i	$-0.0168905\pi$
$200$	−4.68289	+	1.75229i	−0.331131	+	0.123905i
$201$	10.7198	−	17.9661i	0.756113	−	1.26723i
$202$	1.43407	+	9.05436i	0.100901	+	0.637062i
$203$	2.06315	−	4.04916i	0.144805	−	0.284195i
$204$	1.35617	−	2.27292i	0.0949511	−	0.159136i
$205$	−0.258801	−	0.982463i	−0.0180755	−	0.0686182i
$206$	7.28361	+	2.36659i	0.507473	+	0.164888i
$207$	0.100949	+	4.27116i	0.00701641	+	0.296866i
$208$	0.827775	+	0.421773i	0.0573959	+	0.0292447i
$209$	−2.37273	−	7.30251i	−0.164125	−	0.505126i
$210$	10.1230	−	1.95573i	0.698556	−	0.134958i
$211$	17.5098			1.20542			0.602712	−	0.797959i	$-0.294087\pi$
$211$	17.5098			1.20542			0.602712	+	0.797959i	$0.294087\pi$
$212$	1.16702	−	1.16702i	0.0801510	−	0.0801510i
$213$	1.40492	+	2.23296i	0.0962635	+	0.153000i
$214$	−2.85661	+	3.93178i	−0.195274	+	0.268771i
$215$	−9.83872	+	16.8759i	−0.670995	+	1.15093i
$216$	5.00642	−	1.39131i	0.340644	−	0.0946667i
$217$	−7.93750	+	12.5174i	−0.538832	+	0.849735i
$218$	−5.58607	−	5.58607i	−0.378337	−	0.378337i
$219$	2.99174	−	2.61695i	0.202163	−	0.176837i
$220$	−3.35590	−	5.21580i	−0.226255	−	0.351649i
$221$	1.35018	+	0.438702i	0.0908232	+	0.0295103i
$222$	−3.31148	−	2.76128i	−0.222252	−	0.185325i
$223$	−11.4000	+	11.4000i	−0.763401	+	0.763401i	−0.976936	−	0.213534i	$-0.931502\pi$
$223$	−11.4000	+	11.4000i	−0.763401	+	0.763401i	0.213534	+	0.976936i	$0.431502\pi$
$224$	0.822631	−	2.53180i	0.0549644	−	0.169163i
$225$	−14.5461	−	3.66204i	−0.969741	−	0.244136i
$226$	1.53529	+	4.72512i	0.102126	+	0.314311i
$227$	−3.10031	+	19.5746i	−0.205775	+	1.29921i	0.641115	+	0.767445i	$0.278472\pi$
$227$	−3.10031	+	19.5746i	−0.205775	+	1.29921i	−0.846890	+	0.531768i	$0.821528\pi$
$228$	−4.05835	+	2.55340i	−0.268771	+	0.169103i
$229$	1.36793	+	1.88280i	0.0903956	+	0.124419i	0.851819	−	0.523836i	$-0.175499\pi$
$229$	1.36793	+	1.88280i	0.0903956	+	0.124419i	−0.761424	+	0.648254i	$0.775499\pi$
$230$	−1.72305	−	2.67799i	−0.113615	−	0.176582i
$231$	5.03344	+	11.7569i	0.331176	+	0.773550i
$232$	0.267050	+	1.68609i	0.0175327	+	0.110697i
$233$	−1.54513	−	9.75557i	−0.101225	−	0.639109i	−0.985178	−	0.171534i	$-0.945128\pi$
$233$	−1.54513	−	9.75557i	−0.101225	−	0.639109i	0.883953	−	0.467575i	$-0.154872\pi$
$234$	1.32364	+	2.45273i	0.0865291	+	0.160340i
$235$	19.3059	+	4.18902i	1.25938	+	0.273262i
$236$	−5.93215	−	8.16490i	−0.386150	−	0.531490i
$237$	8.80906	+	14.0010i	0.572210	+	0.909465i
$238$	0.636371	−	4.01789i	0.0412498	−	0.260441i
$239$	−2.05059	−	6.31108i	−0.132642	−	0.408230i	0.862574	−	0.505931i	$-0.168851\pi$
$239$	−2.05059	−	6.31108i	−0.132642	−	0.408230i	−0.995216	+	0.0977015i	$0.968851\pi$
$240$	−2.64460	+	2.82950i	−0.170708	+	0.182644i
$241$	−0.603516	+	1.85743i	−0.0388759	+	0.119648i	−0.968611	−	0.248581i	$-0.920036\pi$
$241$	−0.603516	+	1.85743i	−0.0388759	+	0.119648i	0.929735	+	0.368229i	$0.120036\pi$
$242$	−2.33817	+	2.33817i	−0.150304	+	0.150304i
$243$	14.7289	+	5.10472i	0.944862	+	0.327468i
$244$	1.33985	+	0.435343i	0.0857750	+	0.0278700i
$245$	0.163080	−	0.104927i	0.0104188	−	0.00670356i
$246$	−0.518133	−	0.592339i	−0.0330350	−	0.0377661i
$247$	−1.81855	−	1.81855i	−0.115712	−	0.115712i
$248$	−0.351588	−	5.55665i	−0.0223258	−	0.352848i
$249$	0.986355	+	10.8867i	0.0625077	+	0.689917i
$250$	10.6761	−	3.31971i	0.675217	−	0.209957i
$251$	−2.45208	+	3.37501i	−0.154774	+	0.213028i	−0.879362	−	0.476154i	$-0.842030\pi$
$251$	−2.45208	+	3.37501i	−0.154774	+	0.213028i	0.724587	+	0.689183i	$0.242030\pi$
$252$	6.34831	−	4.84556i	0.399906	−	0.305242i
$253$	2.79311	−	2.79311i	0.175601	−	0.175601i
$254$	−9.35822			−0.587187
$255$	−3.31510	+	4.90276i	−0.207600	+	0.307023i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−17.7186	−	9.02806i	−1.10525	−	0.563155i	−0.196507	−	0.980502i	$-0.562960\pi$
$257$	−17.7186	−	9.02806i	−1.10525	−	0.563155i	−0.908747	+	0.417348i	$0.862960\pi$
$258$	−1.00888	+	15.0977i	−0.0628104	+	0.939941i
$259$	−6.30253	−	2.04782i	−0.391620	−	0.127245i
$260$	−1.79466	−	1.04629i	−0.111300	−	0.0648883i
$261$	−2.21656	+	4.61679i	−0.137202	+	0.285772i
$262$	−3.10658	+	6.09702i	−0.191925	+	0.376675i
$263$	3.88831	+	24.5498i	0.239763	+	1.51381i	0.754410	+	0.656403i	$0.227923\pi$
$263$	3.88831	+	24.5498i	0.239763	+	1.51381i	−0.514647	+	0.857402i	$0.672077\pi$
$264$	−4.12559	−	2.46160i	−0.253913	−	0.151501i
$265$	−2.75294	+	2.45776i	−0.169112	+	0.150979i
$266$	−4.33162	+	5.96197i	−0.265589	+	0.365552i
$267$	14.5603	+	0.972976i	0.891078	+	0.0595452i
$268$	5.48368	+	10.7623i	0.334969	+	0.657413i
$269$	20.6230	−	14.9835i	1.25741	−	0.913560i	0.258780	−	0.965936i	$-0.416680\pi$
$269$	20.6230	−	14.9835i	1.25741	−	0.913560i	0.998627	+	0.0523765i	$0.0166796\pi$
$270$	−11.3527	+	2.47292i	−0.690906	+	0.150497i
$271$	−7.74942	−	23.8502i	−0.470743	−	1.44880i	−0.851613	−	0.524171i	$-0.824375\pi$
$271$	−7.74942	−	23.8502i	−0.470743	−	1.44880i	0.380870	−	0.924629i	$-0.375625\pi$
$272$	0.693749	+	1.36156i	0.0420647	+	0.0825566i
$273$	3.28996	+	2.74333i	0.199118	+	0.166034i
$274$			16.5624i			1.00057i
$275$	6.83236	+	12.0686i	0.412007	+	0.727766i
$276$	−2.11824	−	1.26388i	−0.127503	−	0.0760766i
$277$	4.41612	+	0.699444i	0.265339	+	0.0420255i	0.287686	−	0.957725i	$-0.407114\pi$
$277$	4.41612	+	0.699444i	0.265339	+	0.0420255i	−0.0223474	+	0.999750i	$0.507114\pi$
$278$	−10.0207	−	10.0207i	−0.601000	−	0.601000i
$279$	8.60923	−	14.3137i	0.515421	−	0.856937i
$280$	−2.15671	+	5.54817i	−0.128888	+	0.331567i
$281$	−12.2443	−	16.8529i	−0.730437	−	1.00536i	−0.999112	−	0.0421289i	$-0.986586\pi$
$281$	−12.2443	−	16.8529i	−0.730437	−	1.00536i	0.268676	−	0.963231i	$-0.413414\pi$
$282$	14.8362	−	3.74779i	0.883483	−	0.223178i
$283$	8.19495	+	16.0835i	0.487139	+	0.956065i	0.995486	+	0.0949121i	$0.0302570\pi$
$283$	8.19495	+	16.0835i	0.487139	+	0.956065i	−0.508346	+	0.861153i	$0.669743\pi$
$284$	−1.52315			−0.0903821
$285$	9.38315	−	5.18717i	0.555810	−	0.307262i
$286$	0.796289	−	2.45073i	0.0470856	−	0.144914i
$287$	−1.07771	−	0.549122i	−0.0636154	−	0.0324137i
$288$	−0.859377	+	2.87428i	−0.0506392	+	0.169368i
$289$	−8.61980	−	11.8641i	−0.507047	−	0.697890i
$290$	−0.382946	−	3.79795i	−0.0224874	−	0.223023i
$291$	−12.5355	−	14.3308i	−0.734845	−	0.840088i
$292$	0.358992	+	2.26659i	0.0210084	+	0.132642i
$293$	4.40529	−	8.64587i	0.257360	−	0.505097i	−0.725786	−	0.687921i	$-0.758524\pi$
$293$	4.40529	−	8.64587i	0.257360	−	0.505097i	0.983146	+	0.182823i	$0.0585237\pi$
$294$	0.0769656	−	0.128993i	0.00448872	−	0.00752303i
$295$	12.2108	+	18.9783i	0.710942	+	1.10496i
$296$	2.36751	−	0.769251i	0.137609	−	0.0447118i
$297$	−5.98383	−	13.1116i	−0.347217	−	0.760811i
$298$	−2.03274	+	12.8342i	−0.117753	+	0.743464i
$299$	0.408846	−	1.25830i	0.0236442	−	0.0727693i
$300$	6.26189	−	5.98237i	0.361530	−	0.345392i
$301$	7.18658	+	22.1180i	0.414228	+	1.27486i
$302$	−19.5728	−	9.97284i	−1.12629	−	0.573872i
$303$	−8.45566	−	13.4393i	−0.485765	−	0.772070i
$304$		−	2.76827i		−	0.158771i
$305$	−2.93614	−	1.14135i	−0.168123	−	0.0653535i
$306$	−0.609962	+	4.54358i	−0.0348692	+	0.259739i
$307$	−4.23103	−	26.7137i	−0.241477	−	1.52463i	−0.748755	−	0.662846i	$-0.769348\pi$
$307$	−4.23103	−	26.7137i	−0.241477	−	1.52463i	0.507278	−	0.861782i	$-0.330652\pi$
$308$	−7.29289	−	1.15508i	−0.415551	−	0.0658168i
$309$	−13.2107	+	1.19691i	−0.751530	+	0.0680899i
$310$	0.0821609	+	12.4496i	0.00466643	+	0.707091i
$311$		−	5.99066i		−	0.339699i	−0.985470	−	0.169850i	$-0.945672\pi$
$311$		−	5.99066i		−	0.339699i	0.985470	−	0.169850i	$-0.0543282\pi$
$312$	−1.60555	−	0.107289i	−0.0908965	−	0.00607405i
$313$	−22.6965	+	3.59477i	−1.28288	+	0.203189i	−0.760397	−	0.649459i	$-0.774995\pi$
$313$	−22.6965	+	3.59477i	−1.28288	+	0.203189i	−0.522486	+	0.852648i	$0.674995\pi$
$314$	−3.14383	+	9.67572i	−0.177417	+	0.546033i
$315$	−14.7853	+	10.0148i	−0.833060	+	0.564270i
$316$	−9.55036			−0.537250
$317$	−1.34004	−	2.62997i	−0.0752639	−	0.147714i	0.850308	−	0.526285i	$-0.176415\pi$
$317$	−1.34004	−	2.62997i	−0.0752639	−	0.147714i	−0.925572	+	0.378571i	$0.876415\pi$
$318$	−1.06266	+	2.65374i	−0.0595908	+	0.148814i
$319$	4.50323	−	1.46319i	0.252132	−	0.0819228i
$320$	−0.569596	−	2.16230i	−0.0318414	−	0.120876i
$321$	1.86822	−	8.20775i	0.104274	−	0.458112i
$322$	−3.74445	−	0.593063i	−0.208670	−	0.0330501i
$323$	−0.661755	−	4.17815i	−0.0368210	−	0.232479i
$324$	−7.02310	+	5.62815i	−0.390172	+	0.312675i
$325$	3.87422	+	2.56281i	0.214903	+	0.142159i
$326$	−14.9586	+	20.5887i	−0.828479	+	1.14030i
$327$	12.7025	+	5.08655i	0.702447	+	0.281287i
$328$	0.448765	−	0.0710775i	0.0247789	−	0.00392460i
$329$	19.0272	−	13.8241i	1.04900	−	0.762146i
$330$	8.89902	+	6.01725i	0.489875	+	0.331239i
$331$	18.5915	−	13.5075i	1.02188	−	0.742441i	0.0552144	−	0.998475i	$-0.482416\pi$
$331$	18.5915	−	13.5075i	1.02188	−	0.742441i	0.966668	+	0.256034i	$0.0824158\pi$
$332$	−5.62331	−	2.86522i	−0.308619	−	0.157249i
$333$	7.15508	+	2.13929i	0.392096	+	0.117232i
$334$	−14.5218	−	4.71843i	−0.794599	−	0.258181i
$335$	−10.8811	−	24.7203i	−0.594499	−	1.35061i
$336$	0.416049	+	4.59207i	0.0226974	+	0.250518i
$337$	−5.59836	+	2.85251i	−0.304962	+	0.155386i	−0.599774	−	0.800169i	$-0.704743\pi$
$337$	−5.59836	+	2.85251i	−0.304962	+	0.155386i	0.294812	+	0.955555i	$0.404743\pi$
$338$	1.89863	+	11.9875i	0.103272	+	0.652032i
$339$	−5.66564	−	6.47706i	−0.307715	−	0.351785i
$340$	−1.37659	−	3.12740i	−0.0746560	−	0.169607i
$341$	−15.0701	+	3.37422i	−0.816091	+	0.182724i
$342$	4.72134	−	6.83221i	0.255301	−	0.369444i
$343$	−2.87898	+	18.1772i	−0.155450	+	0.981476i
$344$	−7.06765	−	5.13495i	−0.381062	−	0.276858i
$345$	4.56910	+	3.08949i	0.245992	+	0.166333i
$346$	2.42553			0.130397
$347$	−17.6941	+	17.6941i	−0.949872	+	0.949872i	−0.998802	−	0.0489307i	$-0.984419\pi$
$347$	−17.6941	+	17.6941i	−0.949872	+	0.949872i	0.0489307	+	0.998802i	$0.484419\pi$
$348$	−1.57460	−	2.50265i	−0.0844075	−	0.134156i
$349$	−18.3385	+	5.95854i	−0.981638	+	0.318954i	−0.755505	−	0.655143i	$-0.772608\pi$
$349$	−18.3385	+	5.95854i	−0.981638	+	0.318954i	−0.226133	+	0.974096i	$0.572608\pi$
$350$	5.51652	−	12.1135i	0.294870	−	0.647492i
$351$	−3.77958	−	3.00309i	−0.201739	−	0.160293i
$352$	2.47137	−	1.25923i	0.131724	−	0.0671170i
$353$	5.60708	+	0.888075i	0.298435	+	0.0472675i	0.303856	−	0.952718i	$-0.401726\pi$
$353$	5.60708	+	0.888075i	0.298435	+	0.0472675i	−0.00542143	+	0.999985i	$0.501726\pi$
$354$	15.0114	+	8.95680i	0.797849	+	0.476049i
$355$	3.40041	+	0.192634i	0.180475	+	0.0102239i
$356$	−4.95219	+	6.81610i	−0.262465	+	0.361253i
$357$	1.72567	+	6.83134i	0.0913323	+	0.361553i
$358$	1.54087	+	0.785113i	0.0814375	+	0.0414945i
$359$	25.5492	+	18.5626i	1.34843	+	0.979695i	0.999088	+	0.0427009i	$0.0135963\pi$
$359$	25.5492	+	18.5626i	1.34843	+	0.979695i	0.349346	+	0.936994i	$0.386404\pi$
$360$	2.28206	−	6.30811i	0.120275	−	0.332466i
$361$	3.50322	−	10.7818i	0.184380	−	0.567463i
$362$	−1.76497	+	11.1436i	−0.0927649	+	0.585695i
$363$	2.12909	−	5.31689i	0.111748	−	0.279065i
$364$	−2.35213	+	0.764252i	−0.123285	+	0.0400577i
$365$	−0.514789	−	5.10554i	−0.0269453	−	0.267236i
$366$	−2.43016	+	0.220177i	−0.127026	+	0.0115088i
$367$	−17.9825	−	17.9825i	−0.938681	−	0.938681i	0.0595447	−	0.998226i	$-0.481035\pi$
$367$	−17.9825	−	17.9825i	−0.938681	−	0.938681i	−0.998226	+	0.0595447i	$0.981035\pi$
$368$	1.26890	−	0.646536i	0.0661459	−	0.0337030i
$369$	1.22879	+	0.589955i	0.0639685	+	0.0307118i
$370$	−5.38273	+	1.41792i	−0.279835	+	0.0737143i
$371$			4.39354i			0.228101i
$372$	4.34772	+	8.60798i	0.225419	+	0.446303i
$373$	−16.6577	+	16.6577i	−0.862502	+	0.862502i	−0.991628	−	0.129127i	$-0.958783\pi$
$373$	−16.6577	+	16.6577i	−0.862502	+	0.862502i	0.129127	+	0.991628i	$0.458783\pi$
$374$	3.42902	−	2.49133i	0.177310	−	0.128824i
$375$	−14.7362	+	12.5636i	−0.760973	+	0.648783i
$376$	−2.73009	+	8.40236i	−0.140794	+	0.433319i
$377$	1.12144	−	1.12144i	0.0577573	−	0.0577573i
$378$	−6.80502	+	12.0430i	−0.350012	+	0.619424i
$379$	0.522705	+	0.169837i	0.0268496	+	0.00872395i	0.322411	−	0.946600i	$-0.395507\pi$
$379$	0.522705	+	0.169837i	0.0268496	+	0.00872395i	−0.295561	+	0.955324i	$0.595507\pi$
$380$	−0.350106	+	6.18014i	−0.0179601	+	0.317035i
$381$	14.9007	−	6.37938i	0.763388	−	0.326825i
$382$	−4.40562	−	0.697782i	−0.225411	−	0.0357016i
$383$	20.0815	−	10.2320i	1.02611	−	0.522831i	0.141884	−	0.989883i	$-0.454684\pi$
$383$	20.0815	−	10.2320i	1.02611	−	0.522831i	0.884230	+	0.467052i	$0.154684\pi$
$384$	−1.14036	−	1.30368i	−0.0581937	−	0.0665281i
$385$	16.1352	+	3.50104i	0.822326	+	0.178430i
$386$	10.6024	−	3.44494i	0.539650	−	0.175343i
$387$	−8.68549	−	24.7272i	−0.441508	−	1.25696i
$388$	10.8573	−	1.71962i	0.551194	−	0.0873006i
$389$	3.70906	+	11.4153i	0.188057	+	0.578779i	0.999988	−	0.00497425i	$-0.00158336\pi$
$389$	3.70906	+	11.4153i	0.188057	+	0.578779i	−0.811931	+	0.583754i	$0.801583\pi$
$390$	3.57081	+	0.442577i	0.180815	+	0.0224108i
$391$	1.76059	−	1.27915i	0.0890370	−	0.0646892i
$392$	0.0393716	+	0.0772712i	0.00198857	+	0.00390279i
$393$	0.790243	−	11.8258i	0.0398625	−	0.596531i
$394$	21.9927	−	7.14588i	1.10798	−	0.360004i
$395$	21.3211	+	1.20784i	1.07278	+	0.0607732i
$396$	8.24707	+	1.10714i	0.414431	+	0.0556361i
$397$	14.8881	+	14.8881i	0.747212	+	0.747212i	0.973955	−	0.226742i	$-0.0728075\pi$
$397$	14.8881	+	14.8881i	0.747212	+	0.747212i	−0.226742	+	0.973955i	$0.572808\pi$
$398$	−12.5658	−	12.5658i	−0.629867	−	0.629867i
$399$	2.83289	−	12.4458i	0.141822	−	0.623071i
$400$	0.998148	+	4.89936i	0.0499074	+	0.244968i
$401$	−7.86252	−	10.8218i	−0.392636	−	0.540417i	0.566241	−	0.824240i	$-0.308397\pi$
$401$	−7.86252	−	10.8218i	−0.392636	−	0.540417i	−0.958877	+	0.283823i	$0.908397\pi$
$402$	−16.0680	−	13.3983i	−0.801399	−	0.668246i
$403$	−3.98441	+	3.29859i	−0.198478	+	0.164314i
$404$	9.16722			0.456086
$405$	16.3908	−	11.6766i	0.814465	−	0.580213i
$406$	−3.67656	−	2.67117i	−0.182464	−	0.132568i
$407$	−3.13465	−	6.15210i	−0.155379	−	0.304949i
$408$	−2.03279	−	1.69504i	−0.100638	−	0.0839170i
$409$		−	16.9980i		−	0.840499i	−0.907409	−	0.420250i	$-0.861943\pi$
$409$		−	16.9980i		−	0.840499i	0.907409	−	0.420250i	$-0.138057\pi$
$410$	−1.01085	+	0.101924i	−0.0499225	+	0.00503366i
$411$	−11.2904	−	26.3717i	−0.556914	−	1.30082i
$412$	3.47686	−	6.82372i	0.171292	−	0.336180i
$413$	26.5360	+	4.20289i	1.30575	+	0.206811i
$414$	4.23437	+	0.568451i	0.208108	+	0.0279378i
$415$	12.1916	+	7.10775i	0.598462	+	0.348906i
$416$	0.546072	−	0.751604i	0.0267734	−	0.0368504i
$417$	22.7865	+	9.12459i	1.11586	+	0.446833i
$418$	−7.58379	+	1.20115i	−0.370935	+	0.0587503i
$419$	27.8897	+	20.2631i	1.36250	+	0.989916i	0.998281	+	0.0586039i	$0.0186649\pi$
$419$	27.8897	+	20.2631i	1.36250	+	0.989916i	0.364222	+	0.931312i	$0.381335\pi$
$420$	−0.348063	−	10.3044i	−0.0169837	−	0.502801i
$421$	1.40647	+	1.02186i	0.0685471	+	0.0498024i	0.621531	−	0.783390i	$-0.286511\pi$
$421$	1.40647	+	1.02186i	0.0685471	+	0.0498024i	−0.552984	+	0.833192i	$0.686511\pi$
$422$	2.73913	−	17.2942i	0.133339	−	0.841869i
$423$	−21.0683	+	16.0811i	−1.02438	+	0.781891i
$424$	−0.970087	−	1.33521i	−0.0471116	−	0.0648435i
$425$	2.67769	+	7.15599i	0.129887	+	0.347116i
$426$	2.42525	−	1.03831i	0.117504	−	0.0503063i
$427$	−3.34159	+	1.70262i	−0.161711	+	0.0823958i
$428$	3.43650	+	3.43650i	0.166110	+	0.166110i
$429$	0.402727	+	4.44502i	0.0194438	+	0.214608i
$430$	15.1290	+	12.3576i	0.729586	+	0.595935i
$431$	−18.0649	+	24.8643i	−0.870158	+	1.19767i	0.108893	+	0.994053i	$0.465269\pi$
$431$	−18.0649	+	24.8643i	−0.870158	+	1.19767i	−0.979051	+	0.203616i	$0.934731\pi$
$432$	−0.591005	−	5.16243i	−0.0284347	−	0.248378i
$433$	28.4839	−	28.4839i	1.36885	−	1.36885i	0.506769	−	0.862082i	$-0.330840\pi$
$433$	28.4839	−	28.4839i	1.36885	−	1.36885i	0.862082	−	0.506769i	$-0.169160\pi$
$434$	11.1216	+	9.79792i	0.533852	+	0.470315i
$435$	3.19877	+	5.78629i	0.153369	+	0.277431i
$436$	−6.39115	+	4.64345i	−0.306081	+	0.222381i
$437$	−3.89381	+	0.616719i	−0.186266	+	0.0295017i
$438$	−2.11672	−	3.36429i	−0.101141	−	0.160752i
$439$			9.78098i			0.466821i	0.972378	+	0.233410i	$0.0749885\pi$
$439$			9.78098i			0.466821i	−0.972378	+	0.233410i	$0.925011\pi$
$440$	−5.67656	+	2.49865i	−0.270619	+	0.119119i
$441$	−0.0346166	+	0.257857i	−0.00164841	+	0.0122789i
$442$	0.644516	−	1.26493i	0.0306565	−	0.0601668i
$443$	14.0102	−	27.4966i	0.665646	−	1.30640i	−0.273163	−	0.961968i	$-0.588070\pi$
$443$	14.0102	−	27.4966i	0.665646	−	1.30640i	0.938810	−	0.344436i	$-0.111930\pi$
$444$	−3.24531	+	2.83875i	−0.154016	+	0.134721i
$445$	11.9177	−	14.5906i	0.564955	−	0.691659i
$446$	9.47630	+	13.0430i	0.448716	+	0.617605i
$447$	−5.51225	−	21.8211i	−0.260721	−	1.03210i
$448$	−2.37194	−	1.20856i	−0.112064	−	0.0570993i
$449$	28.3119	+	20.5698i	1.33612	+	0.970749i	0.999577	+	0.0290812i	$0.00925813\pi$
$449$	28.3119	+	20.5698i	1.33612	+	0.970749i	0.336544	+	0.941668i	$0.390742\pi$
$450$	−5.89247	+	13.7942i	−0.277773	+	0.650263i
$451$	−0.389438	−	1.19857i	−0.0183379	−	0.0564384i
$452$	4.90712	−	0.777212i	0.230812	−	0.0365570i
$453$	37.9634	+	2.53686i	1.78368	+	0.119192i
$454$	18.8486	+	6.12429i	0.884609	+	0.287427i
$455$	5.34775	−	1.40871i	0.250706	−	0.0660413i
$456$	1.88710	+	4.40782i	0.0883714	+	0.206415i
$457$	−17.4768	+	34.3001i	−0.817530	+	1.60449i	−0.0210887	+	0.999778i	$0.506713\pi$
$457$	−17.4768	+	34.3001i	−0.817530	+	1.60449i	−0.796441	+	0.604716i	$0.793287\pi$
$458$	2.07361	−	1.05656i	0.0968934	−	0.0493697i
$459$	−2.12608	−	7.65038i	−0.0992369	−	0.357089i
$460$	−2.91457	+	1.28291i	−0.135892	+	0.0598158i
$461$	−2.87222	−	0.933242i	−0.133773	−	0.0434654i	0.241365	−	0.970434i	$-0.422405\pi$
$461$	−2.87222	−	0.933242i	−0.133773	−	0.0434654i	−0.375138	+	0.926969i	$0.622405\pi$
$462$	12.3996	−	3.13228i	0.576882	−	0.145727i
$463$	−1.86171	+	11.7544i	−0.0865209	+	0.546271i	0.905910	+	0.423469i	$0.139188\pi$
$463$	−1.86171	+	11.7544i	−0.0865209	+	0.546271i	−0.992431	+	0.122802i	$0.960812\pi$
$464$	1.70711			0.0792505
$465$	−8.61758	−	19.7671i	−0.399630	−	0.916676i
$466$	−9.87718			−0.457551
$467$	5.40369	−	34.1175i	0.250053	−	1.57877i	−0.468605	−	0.883408i	$-0.655243\pi$
$467$	5.40369	−	34.1175i	0.250053	−	1.57877i	0.718658	−	0.695364i	$-0.244757\pi$
$468$	2.62960	−	0.923653i	0.121553	−	0.0426959i
$469$	−30.5812	−	9.93643i	−1.41211	−	0.458822i
$470$	7.15755	−	18.4129i	0.330153	−	0.849323i
$471$	−1.59001	−	17.5494i	−0.0732637	−	0.808634i
$472$	−8.99237	+	4.58184i	−0.413907	+	0.210896i
$473$	−11.0007	+	21.5901i	−0.505814	+	0.992715i
$474$	15.2067	−	6.51036i	0.698467	−	0.299031i
$475$	1.56322	−	13.7528i	0.0717252	−	0.631023i
$476$	−3.86887	−	1.25707i	−0.177329	−	0.0576178i
$477$	−0.116989	−	4.94985i	−0.00535657	−	0.226638i
$478$	−6.55416	+	1.03808i	−0.299780	+	0.0474805i
$479$	−0.318077	−	0.978939i	−0.0145333	−	0.0447289i	0.943527	−	0.331296i	$-0.107486\pi$
$479$	−0.318077	−	0.978939i	−0.0145333	−	0.0447289i	−0.958060	+	0.286567i	$0.907486\pi$
$480$	2.38096	+	3.05467i	0.108676	+	0.139426i
$481$	−1.87101	−	1.35937i	−0.0853105	−	0.0619817i
$482$	1.74015	+	0.886652i	0.0792618	+	0.0403859i
$483$	6.36644	−	1.60823i	0.289683	−	0.0731772i
$484$	1.94362	+	2.67516i	0.0883462	+	0.121598i
$485$	−24.4562	+	2.46591i	−1.11050	+	0.111971i
$486$	7.34599	−	13.7491i	0.333221	−	0.623670i
$487$	−6.18226	+	12.1334i	−0.280145	+	0.549816i	−0.987609	−	0.156934i	$-0.949839\pi$
$487$	−6.18226	+	12.1334i	−0.280145	+	0.549816i	0.707464	+	0.706749i	$0.249839\pi$
$488$	0.639582	−	1.25525i	0.0289525	−	0.0568225i
$489$	9.78293	−	42.9798i	0.442400	−	1.94361i
$490$	−0.0781242	−	0.177486i	−0.00352929	−	0.00801802i
$491$			21.1558i			0.954750i	0.878700	+	0.477375i	$0.158412\pi$
$491$			21.1558i			0.954750i	−0.878700	+	0.477375i	$0.841588\pi$
$492$	−0.666100	+	0.419092i	−0.0300301	+	0.0188941i
$493$	2.57654	−	0.408083i	0.116041	−	0.0183791i
$494$	−2.08065	+	1.51168i	−0.0936127	+	0.0680136i
$495$	−18.2715	−	3.51470i	−0.821241	−	0.157974i
$496$	−5.54324	−	0.521993i	−0.248899	−	0.0234382i
$497$	2.86714	−	2.86714i	0.128609	−	0.128609i
$498$	10.9070	+	0.728845i	0.488753	+	0.0326603i
$499$	15.1177	−	20.8077i	0.676761	−	0.931482i	−0.323128	−	0.946355i	$-0.604735\pi$
$499$	15.1177	−	20.8077i	0.676761	−	0.931482i	0.999889	+	0.0148735i	$0.00473457\pi$
$500$	−1.60873	−	11.0640i	−0.0719445	−	0.494797i
$501$	26.3391	−	2.38637i	1.17674	−	0.106615i
$502$	2.94986	+	2.94986i	0.131659	+	0.131659i
$503$	29.0821	−	14.8181i	1.29671	−	0.660706i	0.336947	−	0.941524i	$-0.390606\pi$
$503$	29.0821	−	14.8181i	1.29671	−	0.660706i	0.959761	+	0.280818i	$0.0906058\pi$
$504$	−3.79281	−	7.02816i	−0.168945	−	0.313059i
$505$	−20.4657	−	1.15939i	−0.910712	−	0.0515920i
$506$	−2.32178	−	3.19566i	−0.103216	−	0.142064i
$507$	−11.1948	−	17.7929i	−0.497180	−	0.790212i
$508$	−1.46395	+	9.24300i	−0.0649522	+	0.410092i
$509$	21.7992	+	15.8380i	0.966231	+	0.702008i	0.954590	−	0.297924i	$-0.0962943\pi$
$509$	21.7992	+	15.8380i	0.966231	+	0.702008i	0.0116417	+	0.999932i	$0.496294\pi$
$510$	4.32380	+	4.04124i	0.191461	+	0.178949i
$511$	−4.94235	−	3.59083i	−0.218637	−	0.158849i
$512$	0.987688	−	0.156434i	0.0436501	−	0.00691349i
$513$	−2.86018	+	14.0972i	−0.126280	+	0.622404i
$514$	−11.6887	+	16.0881i	−0.515567	+	0.709617i
$515$	−8.62505	+	14.7941i	−0.380065	+	0.651908i
$516$	14.7540	+	3.35826i	0.649508	+	0.147839i
$517$	24.2031	+	3.83340i	1.06445	+	0.168593i
$518$	−3.00854	+	5.90459i	−0.132188	+	0.259433i
$519$	−3.86208	+	1.65345i	−0.169527	+	0.0725786i
$520$	−1.31416	+	1.60889i	−0.0576296	+	0.0705543i
$521$			16.5556i			0.725313i	0.931923	+	0.362657i	$0.118130\pi$
$521$			16.5556i			0.725313i	−0.931923	+	0.362657i	$0.881870\pi$
$522$	4.21321	+	2.91150i	0.184407	+	0.127433i
$523$	−19.2810	−	37.8410i	−0.843098	−	1.65467i	−0.752316	−	0.658803i	$-0.771063\pi$
$523$	−19.2810	−	37.8410i	−0.843098	−	1.65467i	−0.0907825	−	0.995871i	$-0.528937\pi$
$524$	5.53597	+	4.02212i	0.241840	+	0.175707i
$525$	−0.526154	+	23.0484i	−0.0229632	+	1.00591i
$526$	24.8558			1.08376
$527$	−8.49119	+	0.537265i	−0.369882	+	0.0234037i
$528$	−3.07667	+	3.68972i	−0.133895	+	0.160575i
$529$	12.3270	+	16.9666i	0.535955	+	0.737679i
$530$	1.99684	+	3.10353i	0.0867373	+	0.134809i
$531$	−30.0079	−	4.02847i	−1.30223	−	0.174821i
$532$	5.21095	+	5.21095i	0.225923	+	0.225923i
$533$	−0.298480	−	0.298480i	−0.0129286	−	0.0129286i
$534$	3.23874	−	14.2289i	0.140154	−	0.615743i
$535$	−7.23734	−	8.10657i	−0.312897	−	0.350478i
$536$	11.4877	−	3.73257i	0.496191	−	0.161222i
$537$	−2.98867	−	0.199714i	−0.128971	−	0.00861831i
$538$	−11.5729	−	22.7130i	−0.498942	−	0.979229i
$539$	0.194604	−	0.141388i	0.00838218	−	0.00609001i
$540$	0.666514	+	11.5998i	0.0286822	+	0.499177i
$541$	−3.69046	−	11.3581i	−0.158665	−	0.488321i	0.839849	−	0.542821i	$-0.182644\pi$
$541$	−3.69046	−	11.3581i	−0.158665	−	0.488321i	−0.998514	+	0.0544995i	$0.982644\pi$
$542$	−24.7689	+	3.92301i	−1.06391	+	0.168508i
$543$	−4.78615	−	18.9467i	−0.205393	−	0.813081i
$544$	1.45332	−	0.472213i	0.0623106	−	0.0202460i
$545$	14.8554	−	9.55814i	0.636337	−	0.409426i
$546$	3.22422	−	2.82030i	0.137984	−	0.120698i
$547$	24.8394	−	12.6563i	1.06206	−	0.541145i	0.166477	−	0.986045i	$-0.446761\pi$
$547$	24.8394	−	12.6563i	1.06206	−	0.541145i	0.895580	+	0.444900i	$0.146761\pi$
$548$	16.3585	+	2.59093i	0.698801	+	0.110679i
$549$	3.71936	−	2.00719i	0.158739	−	0.0856647i
$550$	12.9889	−	4.86029i	0.553847	−	0.207244i
$551$	−4.49445	−	1.46033i	−0.191470	−	0.0622123i
$552$	−1.57968	+	1.89445i	−0.0672358	+	0.0806330i
$553$	17.9774	−	17.9774i	0.764478	−	0.764478i
$554$	1.38167	−	4.25233i	0.0587014	−	0.180664i
$555$	7.60415	−	5.92705i	0.322778	−	0.251589i
$556$	−11.4649	+	8.32973i	−0.486219	+	0.353259i
$557$	−16.0179	+	16.0179i	−0.678701	+	0.678701i	−0.959706	−	0.281005i	$-0.909332\pi$
$557$	−16.0179	+	16.0179i	−0.678701	+	0.678701i	0.281005	+	0.959706i	$0.409332\pi$
$558$	−12.7907	−	10.7424i	−0.541472	−	0.454762i
$559$			8.11613i			0.343276i
$560$	5.14248	+	2.99809i	0.217309	+	0.126692i
$561$	−3.76159	+	6.30437i	−0.158815	+	0.266171i
$562$	−18.5608	+	9.45723i	−0.782942	+	0.398929i
$563$	7.42955	+	7.42955i	0.313118	+	0.313118i	0.846116	−	0.532998i	$-0.178935\pi$
$563$	7.42955	+	7.42955i	0.313118	+	0.313118i	−0.532998	+	0.846116i	$0.678935\pi$
$564$	−1.38076	−	15.2398i	−0.0581403	−	0.641713i
$565$	−11.0534	+	1.11451i	−0.465019	+	0.0468877i
$566$	17.1675	−	5.57805i	0.721602	−	0.234463i
$567$	2.62584	−	23.8145i	0.110275	−	1.00011i
$568$	−0.238273	+	1.50439i	−0.00999770	+	0.0631230i
$569$	1.83950	−	5.66139i	0.0771158	−	0.237338i	−0.905066	−	0.425271i	$-0.860179\pi$
$569$	1.83950	−	5.66139i	0.0771158	−	0.237338i	0.982182	+	0.187933i	$0.0601788\pi$
$570$	−3.65546	−	10.0791i	−0.153111	−	0.422166i
$571$	26.3542	+	19.1474i	1.10289	+	0.801295i	0.981529	−	0.191314i	$-0.0612749\pi$
$571$	26.3542	+	19.1474i	1.10289	+	0.801295i	0.121359	+	0.992609i	$0.461275\pi$
$572$	−2.29599	−	1.16986i	−0.0960000	−	0.0489145i
$573$	7.49058	−	1.89220i	0.312924	−	0.0790480i
$574$	−0.710953	+	0.978543i	−0.0296746	+	0.0408436i
$575$	6.66899	−	2.49546i	0.278116	−	0.104068i
$576$	2.70445	+	1.29843i	0.112686	+	0.0541013i
$577$	11.0494	+	1.75005i	0.459993	+	0.0728557i	0.382130	−	0.924108i	$-0.375191\pi$
$577$	11.0494	+	1.75005i	0.459993	+	0.0728557i	0.0778623	+	0.996964i	$0.475191\pi$
$578$	−13.0665	+	6.65771i	−0.543495	+	0.276924i
$579$	−14.5335	+	12.7128i	−0.603992	+	0.528326i
$580$	−3.81110	−	0.215899i	−0.158247	−	0.00896473i
$581$	15.9786	−	5.19178i	0.662906	−	0.215391i
$582$	−16.1154	+	10.1394i	−0.668004	+	0.420290i
$583$	−3.23693	+	3.23693i	−0.134060	+	0.134060i
$584$	2.29484			0.0949613
$585$	−5.98737	+	1.72948i	−0.247547	+	0.0715050i
$586$	−7.85029	−	5.70357i	−0.324292	−	0.235612i
$587$	−3.75421	+	23.7031i	−0.154953	+	0.978333i	0.780570	+	0.625068i	$0.214929\pi$
$587$	−3.75421	+	23.7031i	−0.154953	+	0.978333i	−0.935523	+	0.353265i	$0.885071\pi$
$588$	−0.115365	−	0.0961970i	−0.00475757	−	0.00396710i
$589$	14.1476	+	6.11623i	0.582943	+	0.252015i
$590$	20.6548	−	9.09163i	0.850346	−	0.374297i
$591$	−30.1470	+	26.3703i	−1.24008	+	1.08473i
$592$	−0.389420	−	2.45870i	−0.0160051	−	0.101052i
$593$	−35.4347	+	18.0549i	−1.45513	+	0.741425i	−0.989632	−	0.143624i	$-0.954124\pi$
$593$	−35.4347	+	18.0549i	−1.45513	+	0.741425i	−0.465497	+	0.885049i	$0.654124\pi$
$594$	−13.8862	+	3.85906i	−0.569759	+	0.158339i
$595$	8.47823	+	3.29570i	0.347574	+	0.135111i
$596$	12.3582	+	4.01542i	0.506211	+	0.164478i
$597$	28.5740	+	11.4421i	1.16946	+	0.468295i
$598$	−1.17885	−	0.600654i	−0.0482067	−	0.0245626i
$599$	27.4267	−	19.9266i	1.12062	−	0.814180i	0.136320	−	0.990665i	$-0.456473\pi$
$599$	27.4267	−	19.9266i	1.12062	−	0.814180i	0.984303	+	0.176484i	$0.0564725\pi$
$600$	−4.92914	−	7.12064i	−0.201231	−	0.290699i
$601$	23.7836	−	17.2798i	0.970152	−	0.704857i	0.0146661	−	0.999892i	$-0.495331\pi$
$601$	23.7836	−	17.2798i	0.970152	−	0.704857i	0.955486	+	0.295036i	$0.0953315\pi$
$602$	22.9699	−	3.63808i	0.936185	−	0.148277i
$603$	34.7179	+	10.3803i	1.41382	+	0.422717i
$604$	−12.9119	+	17.7717i	−0.525378	+	0.723121i
$605$	−4.00077	−	6.21807i	−0.162655	−	0.252801i
$606$	−14.5966	+	6.24918i	−0.592948	+	0.253856i
$607$	4.16422	+	26.2918i	0.169020	+	1.06715i	0.915669	+	0.401934i	$0.131662\pi$
$607$	4.16422	+	26.2918i	0.169020	+	1.06715i	−0.746648	+	0.665219i	$0.768338\pi$
$608$	−2.73419	−	0.433054i	−0.110886	−	0.0175626i
$609$	7.67495	+	1.74695i	0.311005	+	0.0707900i
$610$	−1.58661	+	2.72144i	−0.0642400	+	0.110188i
$611$	7.80607	−	2.53635i	0.315800	−	0.102610i
$612$	4.39222	+	1.31322i	0.177545	+	0.0530839i
$613$	0.198130	+	0.388852i	0.00800240	+	0.0157056i	0.894973	−	0.446120i	$-0.147195\pi$
$613$	0.198130	+	0.388852i	0.00800240	+	0.0157056i	−0.886971	+	0.461826i	$0.847195\pi$
$614$	−27.0466			−1.09151
$615$	1.54006	−	0.851375i	0.0621014	−	0.0343308i
$616$	−2.28172	+	7.02241i	−0.0919331	+	0.282941i
$617$	9.15979	−	1.45077i	0.368759	−	0.0584057i	0.0306951	−	0.999529i	$-0.490228\pi$
$617$	9.15979	−	1.45077i	0.368759	−	0.0584057i	0.338064	+	0.941123i	$0.390228\pi$
$618$	−0.884431	+	13.2353i	−0.0355770	+	0.532401i
$619$		−	22.9404i		−	0.922054i	−0.887386	−	0.461027i	$-0.847481\pi$
$619$		−	22.9404i		−	0.922054i	0.887386	−	0.461027i	$-0.152519\pi$
$620$	12.3092	+	1.86640i	0.494350	+	0.0749565i
$621$	−7.12973	+	1.98139i	−0.286106	+	0.0795105i
$622$	−5.91691	−	0.937146i	−0.237246	−	0.0375761i
$623$	−3.50860	−	22.1524i	−0.140569	−	0.887517i
$624$	−0.357132	+	1.56900i	−0.0142967	+	0.0628104i
$625$	2.19219	+	24.9037i	0.0876878	+	0.996148i
$626$			22.9794i			0.918443i
$627$	11.2566	−	7.08232i	0.449544	−	0.282841i
$628$	9.06480	+	4.61874i	0.361725	+	0.184308i
$629$	−1.17550	−	3.61783i	−0.0468704	−	0.144252i
$630$	7.57855	+	16.1700i	0.301937	+	0.644227i
$631$	−4.82652	+	14.8545i	−0.192141	+	0.591348i	0.807857	+	0.589378i	$0.200627\pi$
$631$	−4.82652	+	14.8545i	−0.192141	+	0.591348i	−0.999998	+	0.00197030i	$0.999373\pi$
$632$	−1.49401	+	9.43278i	−0.0594284	+	0.375216i
$633$	7.42782	+	29.4042i	0.295229	+	1.16871i
$634$	−2.80722	+	0.912120i	−0.111489	+	0.0362249i
$635$	4.43722	−	20.4497i	0.176086	−	0.811523i
$636$	2.45483	+	1.46471i	0.0973403	+	0.0580795i
$637$	0.0365776	−	0.0717876i	0.00144926	−	0.00284433i
$638$	−0.740713	−	4.67668i	−0.0293251	−	0.185152i
$639$	−3.15384	+	3.30653i	−0.124764	+	0.130804i
$640$	−2.22479	+	0.224324i	−0.0879424	+	0.00886720i
$641$	−13.3327	−	18.3509i	−0.526609	−	0.724816i	0.460000	−	0.887919i	$-0.347850\pi$
$641$	−13.3327	−	18.3509i	−0.526609	−	0.724816i	−0.986609	+	0.163103i	$0.947850\pi$
$642$	−7.81444	−	3.12920i	−0.308411	−	0.123500i
$643$	−9.86235	−	5.02512i	−0.388933	−	0.198171i	0.248579	−	0.968612i	$-0.420036\pi$
$643$	−9.86235	−	5.02512i	−0.388933	−	0.198171i	−0.637512	+	0.770440i	$0.720036\pi$
$644$	−1.17152	+	3.60558i	−0.0461645	+	0.142080i
$645$	−32.5134	−	9.36323i	−1.28021	−	0.368677i
$646$	−4.23024			−0.166436
$647$	−4.31802	−	8.47459i	−0.169759	−	0.333170i	0.790416	−	0.612570i	$-0.209864\pi$
$647$	−4.31802	−	8.47459i	−0.169759	−	0.333170i	−0.960175	+	0.279400i	$0.909864\pi$
$648$	4.46020	+	7.81707i	0.175213	+	0.307084i
$649$	16.4539	+	22.6468i	0.645872	+	0.888966i
$650$	3.13732	−	3.42562i	0.123056	−	0.134364i
$651$	−24.3876	−	8.01944i	−0.955824	−	0.314307i
$652$	17.9952	+	17.9952i	0.704747	+	0.704747i
$653$	10.3185	+	1.63429i	0.403795	+	0.0639549i	0.355029	−	0.934855i	$-0.384471\pi$
$653$	10.3185	+	1.63429i	0.403795	+	0.0639549i	0.0487663	+	0.998810i	$0.484471\pi$
$654$	7.01102	−	11.7504i	0.274153	−	0.459475i
$655$	−11.8503	−	9.67948i	−0.463030	−	0.378209i
$656$		−	0.454359i		−	0.0177397i
$657$	5.66376	+	3.91389i	0.220964	+	0.152695i
$658$	−10.6774	−	20.9555i	−0.416247	−	0.816931i
$659$	13.7492	+	42.3155i	0.535591	+	1.64838i	0.742369	+	0.669992i	$0.233702\pi$
$659$	13.7492	+	42.3155i	0.535591	+	1.64838i	−0.206778	+	0.978388i	$0.566298\pi$
$660$	7.33528	−	7.84815i	0.285525	−	0.305489i
$661$	−31.6237	+	22.9760i	−1.23002	+	0.893662i	−0.996892	−	0.0787842i	$-0.974896\pi$
$661$	−31.6237	+	22.9760i	−1.23002	+	0.893662i	−0.233128	+	0.972446i	$0.574896\pi$
$662$	−10.4329	−	20.4757i	−0.405485	−	0.795809i
$663$	−0.163950	+	2.45347i	−0.00636728	+	0.0952847i
$664$	−3.70962	+	5.10586i	−0.143961	+	0.198146i
$665$	−10.9744	−	12.2924i	−0.425567	−	0.476680i
$666$	3.23225	−	6.73233i	0.125247	−	0.260873i
$667$	−0.380311	−	2.40119i	−0.0147257	−	0.0929745i
$668$	−6.93205	+	13.6049i	−0.268209	+	0.526390i
$669$	−23.9800	−	14.3080i	−0.927121	−	0.553181i
$670$	−26.1181	+	6.88006i	−1.00903	+	0.265800i
$671$	−3.71632	−	1.20750i	−0.143467	−	0.0466152i
$672$	4.60061	+	0.307430i	0.177473	+	0.0118594i
$673$	13.3479	+	6.80107i	0.514522	+	0.262162i	0.691916	−	0.721978i	$-0.256767\pi$
$673$	13.3479	+	6.80107i	0.514522	+	0.262162i	−0.177394	+	0.984140i	$0.556767\pi$
$674$	1.94161	+	5.97566i	0.0747881	+	0.230174i
$675$	−0.0209468	−	25.9808i	−0.000806245	−	1.00000i
$676$	12.1369			0.466804
$677$	−8.78786	+	8.78786i	−0.337745	+	0.337745i	−0.855518	−	0.517773i	$-0.826761\pi$
$677$	−8.78786	+	8.78786i	−0.337745	+	0.337745i	0.517773	+	0.855518i	$0.326761\pi$
$678$	−7.28361	+	4.58265i	−0.279725	+	0.175996i
$679$	−17.2005	+	23.6745i	−0.660096	+	0.908544i
$680$	−3.30424	+	0.870407i	−0.126712	+	0.0333786i
$681$	−34.1868	+	3.09739i	−1.31004	+	0.118692i
$682$	0.975193	+	15.4124i	0.0373421	+	0.590171i
$683$	1.61894	+	1.61894i	0.0619470	+	0.0619470i	0.737402	−	0.675455i	$-0.236053\pi$
$683$	1.61894	+	1.61894i	0.0619470	+	0.0619470i	−0.675455	+	0.737402i	$0.736053\pi$
$684$	−6.00951	−	5.73200i	−0.229779	−	0.219169i
$685$	−36.1925	−	7.85310i	−1.38284	−	0.300052i
$686$	17.5030	+	5.68708i	0.668268	+	0.217134i
$687$	−2.58149	+	3.09587i	−0.0984900	+	0.118115i
$688$	−6.17735	+	6.17735i	−0.235509	+	0.235509i
$689$	−0.473812	+	1.45824i	−0.0180508	+	0.0555546i
$690$	3.76622	−	4.02955i	0.143378	−	0.153402i
$691$	11.8070	+	36.3381i	0.449158	+	1.38237i	0.877858	+	0.478920i	$0.158972\pi$
$691$	11.8070	+	36.3381i	0.449158	+	1.38237i	−0.428700	+	0.903447i	$0.641028\pi$
$692$	0.379437	−	2.39567i	0.0144240	−	0.0910697i
$693$	−17.6082	+	13.4401i	−0.668880	+	0.510546i
$694$	14.7083	+	20.2443i	0.558320	+	0.768462i
$695$	26.6487	−	17.1460i	1.01084	−	0.650387i
$696$	−2.71816	+	1.16371i	−0.103032	+	0.0441104i
$697$	−0.108614	−	0.685764i	−0.00411406	−	0.0259752i
$698$	3.01641	+	19.0449i	0.114173	+	0.720858i
$699$	15.7271	−	6.73315i	0.594852	−	0.254671i
$700$	−11.1014	−	7.34357i	−0.419592	−	0.277561i
$701$	10.3003	+	14.1772i	0.389039	+	0.535466i	0.957951	−	0.286932i	$-0.0926355\pi$
$701$	10.3003	+	14.1772i	0.389039	+	0.535466i	−0.568912	+	0.822398i	$0.692636\pi$
$702$	−3.55737	+	3.26326i	−0.134264	+	0.123164i
$703$	−1.07802	+	6.80636i	−0.0406584	+	0.256707i
$704$	−0.857115	−	2.63793i	−0.0323038	−	0.0994207i
$705$	1.15513	+	34.1974i	0.0435046	+	1.28795i
$706$	1.75428	−	5.39913i	0.0660233	−	0.203199i
$707$	−17.2562	+	17.2562i	−0.648987	+	0.648987i
$708$	11.1948	−	13.4255i	0.420728	−	0.504560i
$709$	−32.1496	−	10.4460i	−1.20740	−	0.392309i	−0.364924	−	0.931037i	$-0.618905\pi$
$709$	−32.1496	−	10.4460i	−1.20740	−	0.392309i	−0.842480	+	0.538728i	$0.818905\pi$
$710$	0.722203	−	3.32841i	0.0271038	−	0.124913i
$711$	−19.7750	+	20.7324i	−0.741622	+	0.777527i
$712$	5.95749	+	5.95749i	0.223266	+	0.223266i
$713$	0.500702	+	7.91333i	0.0187514	+	0.296356i
$714$	7.01719	−	0.635770i	0.262612	−	0.0237931i
$715$	4.97781	+	2.90208i	0.186160	+	0.108532i
$716$	1.01649	−	1.39908i	0.0379881	−	0.0522861i
$717$	9.72830	−	6.12078i	0.363310	−	0.228585i
$718$	22.3308	−	22.3308i	0.833378	−	0.833378i
$719$	−27.6282			−1.03036			−0.515179	−	0.857083i	$-0.672274\pi$
$719$	−27.6282			−1.03036			−0.515179	+	0.857083i	$0.672274\pi$
$720$	−5.87345	−	3.24077i	−0.218891	−	0.120776i
$721$	6.30007	+	19.3896i	0.234627	+	0.722107i
$722$	−10.1010	−	5.14673i	−0.375922	−	0.191542i
$723$	−3.37520	−	0.225544i	−0.125525	−	0.00838806i
$724$	10.7303	+	3.48649i	0.398788	+	0.129574i
$725$	8.48093	+	0.963985i	0.314974	+	0.0358015i
$726$	−4.91837	−	2.93462i	−0.182538	−	0.108914i
$727$	3.25490	−	6.38810i	0.120717	−	0.236921i	−0.822738	−	0.568421i	$-0.807555\pi$
$727$	3.25490	−	6.38810i	0.120717	−	0.236921i	0.943455	+	0.331500i	$0.107555\pi$
$728$	0.386889	+	2.44272i	0.0143391	+	0.0905333i
$729$	−2.32420	+	26.8998i	−0.0860814	+	0.996288i
$730$	−5.12321	−	0.290231i	−0.189619	−	0.0107419i
$731$	−7.84678	+	10.8002i	−0.290224	+	0.399458i
$732$	−0.162695	+	2.43468i	−0.00601337	+	0.0899885i
$733$	14.8262	+	29.0981i	0.547618	+	1.07476i	0.984523	+	0.175254i	$0.0560746\pi$
$733$	14.8262	+	29.0981i	0.547618	+	1.07476i	−0.436905	+	0.899508i	$0.643925\pi$
$734$	−20.5742	+	14.9481i	−0.759409	+	0.551743i
$735$	0.245385	+	0.229349i	0.00905115	+	0.00845966i
$736$	−0.440077	−	1.35442i	−0.0162214	−	0.0499245i
$737$	−15.2100	−	29.8513i	−0.560267	−	1.09959i
$738$	0.774917	−	1.12138i	0.0285251	−	0.0412784i
$739$			42.3113i			1.55645i	0.627987	+	0.778224i	$0.283879\pi$
$739$			42.3113i			1.55645i	−0.627987	+	0.778224i	$0.716121\pi$
$740$	0.558422	+	5.53827i	0.0205280	+	0.203591i
$741$	2.28245	−	3.82534i	0.0838477	−	0.140527i
$742$	4.33945	+	0.687301i	0.159306	+	0.0252316i
$743$	−37.6854	−	37.6854i	−1.38254	−	1.38254i	−0.840079	−	0.542464i	$-0.817491\pi$
$743$	−37.6854	−	37.6854i	−1.38254	−	1.38254i	−0.542464	−	0.840079i	$-0.682509\pi$
$744$	9.18214	−	2.94761i	0.336633	−	0.108065i
$745$	−27.0817	−	10.5273i	−0.992196	−	0.385691i
$746$	13.8468	+	19.0584i	0.506966	+	0.697778i
$747$	−17.8636	+	6.27463i	−0.653595	+	0.229577i
$748$	−1.92424	−	3.77653i	−0.0703572	−	0.138084i
$749$	−12.9376			−0.472731
$750$	10.1037	+	16.5201i	0.368935	+	0.603230i
$751$	−5.51920	+	16.9863i	−0.201398	+	0.619841i	0.798444	+	0.602070i	$0.205657\pi$
$751$	−5.51920	+	16.9863i	−0.201398	+	0.619841i	−0.999842	+	0.0177711i	$0.994343\pi$
$752$	7.87183	+	4.01090i	0.287056	+	0.146262i
$753$	−6.70784	−	2.68607i	−0.244447	−	0.0978860i
$754$	−0.932204	−	1.28307i	−0.0339489	−	0.0467266i
$755$	31.0733	−	38.0422i	1.13087	−	1.38450i
$756$	10.8302	+	8.60517i	0.393889	+	0.312967i
$757$	3.25826	+	20.5718i	0.118423	+	0.747696i	0.973414	+	0.229053i	$0.0735628\pi$
$757$	3.25826	+	20.5718i	0.118423	+	0.747696i	−0.854991	+	0.518644i	$0.826437\pi$
$758$	0.249515	−	0.489701i	0.00906280	−	0.0177868i
$759$	5.87533	+	3.50560i	0.213261	+	0.127245i
$760$	6.04929	+	1.31258i	0.219431	+	0.0476124i
$761$	−9.06370	+	2.94497i	−0.328559	+	0.106755i	−0.468651	−	0.883383i	$-0.655260\pi$
$761$	−9.06370	+	2.94497i	−0.328559	+	0.106755i	0.140093	+	0.990138i	$0.455260\pi$
$762$	−3.96985	−	15.7152i	−0.143812	−	0.569303i
$763$	3.28986	−	20.7713i	0.119101	−	0.751973i
$764$	−1.37838	+	4.24223i	−0.0498681	+	0.153478i
$765$	−9.63950	−	3.48725i	−0.348517	−	0.126082i
$766$	−6.96461	−	21.4349i	−0.251641	−	0.774473i
$767$	8.35421	+	4.25668i	0.301653	+	0.153700i
$768$	−1.46602	+	0.922379i	−0.0529005	+	0.0332835i
$769$			40.1193i			1.44674i	0.690461	+	0.723370i	$0.257408\pi$
$769$			40.1193i			1.44674i	−0.690461	+	0.723370i	$0.742592\pi$
$770$	5.98204	−	15.3889i	0.215578	−	0.554576i
$771$	7.64443	−	33.5846i	0.275307	−	1.20952i
$772$	−1.74394	−	11.0108i	−0.0627658	−	0.396288i
$773$	−46.7369	−	7.40239i	−1.68101	−	0.266246i	−0.758345	−	0.651853i	$-0.773992\pi$
$773$	−46.7369	−	7.40239i	−1.68101	−	0.266246i	−0.922663	+	0.385608i	$0.873992\pi$
$774$	−25.7815	+	4.71037i	−0.926697	+	0.169311i
$775$	−27.2441	−	5.72348i	−0.978638	−	0.205593i
$776$		−	10.9926i		−	0.394612i
$777$	0.765302	−	11.4525i	0.0274550	−	0.410858i
$778$	11.8550	−	1.87765i	0.425022	−	0.0673169i
$779$	−0.388679	+	1.19623i	−0.0139259	+	0.0428594i
$780$	0.995726	−	3.45761i	0.0356527	−	0.123802i
$781$	4.22473			0.151173
$782$	−0.987980	−	1.93902i	−0.0353301	−	0.0693392i
$783$	−8.69327	−	1.76378i	−0.310672	−	0.0630325i
$784$	0.0824790	−	0.0267990i	0.00294568	−	0.000957108i
$785$	−19.6529	−	11.4577i	−0.701443	−	0.408944i
$786$	−11.5566	−	2.63047i	−0.412209	−	0.0938258i
$787$	0.139135	+	0.0220369i	0.00495964	+	0.000785531i	0.158914	−	0.987292i	$-0.449201\pi$
$787$	0.139135	+	0.0220369i	0.00495964	+	0.000785531i	−0.153954	+	0.988078i	$0.549201\pi$
$788$	−3.61748	−	22.8398i	−0.128867	−	0.813636i
$789$	−39.5770	+	16.9439i	−1.40898	+	0.603219i
$790$	4.52832	−	20.8696i	0.161111	−	0.742508i
$791$	−7.77407	+	10.7001i	−0.276414	+	0.380451i
$792$	2.38364	−	7.97234i	0.0846989	−	0.283285i
$793$	−1.29271	+	0.204745i	−0.0459055	+	0.00727071i
$794$	17.0338	−	12.3758i	0.604508	−	0.439200i
$795$	−5.29513	−	3.58041i	−0.187799	−	0.126984i
$796$	−14.3768	+	10.4454i	−0.509573	+	0.370226i
$797$	14.0831	+	7.17567i	0.498847	+	0.254175i	0.685263	−	0.728296i	$-0.259687\pi$
$797$	14.0831	+	7.17567i	0.498847	+	0.254175i	−0.186416	+	0.982471i	$0.559687\pi$
$798$	−11.8494	−	4.74497i	−0.419466	−	0.167970i
$799$	12.8397	+	4.17189i	0.454238	+	0.147591i
$800$	4.99518	−	0.219431i	0.176606	−	0.00775805i
$801$	4.54272	+	24.8639i	0.160509	+	0.878523i
$802$	−11.9186	+	6.07282i	−0.420859	+	0.214439i
$803$	−0.995732	−	6.28680i	−0.0351386	−	0.221856i
$804$	−15.7469	+	13.7742i	−0.555351	+	0.485779i
$805$	3.07141	−	7.90125i	0.108253	−	0.278482i
$806$	2.63468	+	4.45137i	0.0928026	+	0.156793i
$807$	33.9103	+	28.2761i	1.19370	+	0.995365i
$808$	1.43407	−	9.05436i	0.0504504	−	0.318531i
$809$	−29.4055	−	21.3643i	−1.03384	−	0.751130i	−0.0647674	−	0.997900i	$-0.520631\pi$
$809$	−29.4055	−	21.3643i	−1.03384	−	0.751130i	−0.969074	+	0.246771i	$0.920631\pi$
$810$	−8.96871	−	18.0156i	−0.315128	−	0.633004i
$811$	−9.15689			−0.321542			−0.160771	−	0.986992i	$-0.551398\pi$
$811$	−9.15689			−0.321542			−0.160771	+	0.986992i	$0.551398\pi$
$812$	−3.21343	+	3.21343i	−0.112769	+	0.112769i
$813$	36.7643	−	23.1311i	1.28938	−	0.811243i
$814$	−6.56673	+	2.13366i	−0.230164	+	0.0747847i
$815$	−37.8982	−	42.4500i	−1.32752	−	1.48696i
$816$	−1.99217	+	1.74260i	−0.0697399	+	0.0610031i
$817$	21.5480	−	10.9793i	0.753870	−	0.384116i
$818$	−16.7888	−	2.65908i	−0.587006	−	0.0929725i
$819$	−3.21125	+	6.68858i	−0.112210	+	0.233718i
$820$	−0.0574632	+	1.01435i	−0.00200670	+	0.0354227i
$821$	19.9579	−	27.4697i	0.696534	−	0.958697i	−0.303448	−	0.952848i	$-0.598138\pi$
$821$	19.9579	−	27.4697i	0.696534	−	0.958697i	0.999983	−	0.00584957i	$-0.00186199\pi$
$822$	−27.8132	+	7.02594i	−0.970098	+	0.245058i
$823$	10.7780	+	5.49165i	0.375697	+	0.191427i	0.631635	−	0.775266i	$-0.282384\pi$
$823$	10.7780	+	5.49165i	0.375697	+	0.191427i	−0.255938	+	0.966693i	$0.582384\pi$
$824$	−6.19581	−	4.50152i	−0.215841	−	0.156818i
$825$	−17.3685	+	16.5932i	−0.604693	+	0.577701i
$826$	8.30230	−	25.5518i	0.288874	−	0.889062i
$827$	3.25601	−	20.5577i	0.113223	−	0.714860i	−0.864134	−	0.503262i	$-0.832133\pi$
$827$	3.25601	−	20.5577i	0.113223	−	0.714860i	0.977357	−	0.211598i	$-0.0678668\pi$
$828$	1.22385	−	4.09331i	0.0425318	−	0.142252i
$829$	10.8358	−	3.52078i	0.376344	−	0.122282i	−0.114736	−	0.993396i	$-0.536602\pi$
$829$	10.8358	−	3.52078i	0.376344	−	0.122282i	0.491080	+	0.871114i	$0.336602\pi$
$830$	8.92743	−	10.9296i	0.309876	−	0.379372i
$831$	0.698784	+	7.71269i	0.0242405	+	0.267550i
$832$	−0.656926	−	0.656926i	−0.0227748	−	0.0227748i
$833$	0.118079	−	0.0601643i	0.00409120	−	0.00208457i
$834$	12.5768	−	21.0786i	0.435501	−	0.729892i
$835$	17.1963	−	29.4961i	0.595104	−	1.02075i
$836$			7.67832i			0.265560i
$837$	27.6891	+	8.38547i	0.957074	+	0.289844i
$838$	24.3765	−	24.3765i	0.842073	−	0.842073i
$839$	−14.8704	+	10.8040i	−0.513384	+	0.372995i	−0.814106	−	0.580717i	$-0.802772\pi$
$839$	−14.8704	+	10.8040i	−0.513384	+	0.372995i	0.300722	+	0.953712i	$0.402772\pi$
$840$	−10.2319	−	1.26818i	−0.353035	−	0.0437563i
$841$	−8.06095	+	24.8091i	−0.277964	+	0.855485i
$842$	1.22930	−	1.22930i	0.0423644	−	0.0423644i
$843$	23.1069	−	27.7111i	0.795844	−	0.954421i
$844$	−16.6528	−	5.41082i	−0.573213	−	0.186248i
$845$	−27.0955	−	1.53496i	−0.932113	−	0.0528043i
$846$	12.5873	+	23.3246i	0.432761	+	0.801916i
$847$	−8.69430	−	1.37704i	−0.298740	−	0.0473157i
$848$	−1.47053	+	0.749270i	−0.0504981	+	0.0257301i
$849$	−23.5326	+	20.5846i	−0.807638	+	0.706460i
$850$	7.48677	−	1.52528i	0.256794	−	0.0523168i
$851$	−3.37162	+	1.09550i	−0.115578	+	0.0375534i
$852$	−0.646134	−	2.55782i	−0.0221362	−	0.0876295i
$853$	−38.9434	+	6.16803i	−1.33340	+	0.211189i	−0.782117	−	0.623131i	$-0.785860\pi$
$853$	−38.9434	+	6.16803i	−1.33340	+	0.211189i	−0.551279	+	0.834321i	$0.685860\pi$
$854$	1.15892	+	3.56680i	0.0396575	+	0.122053i
$855$	12.6912	+	13.5567i	0.434031	+	0.463628i
$856$	3.93178	−	2.85661i	0.134386	−	0.0976368i
$857$	−0.286096	−	0.561495i	−0.00977286	−	0.0191803i	0.886068	−	0.463554i	$-0.153426\pi$
$857$	−0.286096	−	0.561495i	−0.00977286	−	0.0191803i	−0.895841	+	0.444374i	$0.853426\pi$
$858$	4.45330	+	0.297586i	0.152033	+	0.0101594i
$859$	21.7280	−	7.05986i	0.741351	−	0.240879i	0.0860954	−	0.996287i	$-0.472561\pi$
$859$	21.7280	−	7.05986i	0.741351	−	0.240879i	0.655255	+	0.755407i	$0.272561\pi$
$860$	14.5721	−	13.0096i	0.496905	−	0.443624i
$861$	0.464964	−	2.04275i	0.0158459	−	0.0696166i
$862$	21.7322	+	21.7322i	0.740200	+	0.740200i
$863$	−21.7186	−	21.7186i	−0.739310	−	0.739310i	0.233135	−	0.972444i	$-0.425102\pi$
$863$	−21.7186	−	21.7186i	−0.739310	−	0.739310i	−0.972444	+	0.233135i	$0.925102\pi$
$864$	−5.19133	−	0.223854i	−0.176613	−	0.00761566i
$865$	−1.15007	+	5.30032i	−0.0391036	+	0.180216i
$866$	−23.6774	−	32.5891i	−0.804590	−	1.10742i
$867$	16.2668	−	19.5081i	0.552450	−	0.662530i
$868$	11.4171	−	9.45191i	0.387521	−	0.320819i
$869$	26.4897			0.898601
$870$	6.21545	−	2.25421i	0.210723	−	0.0764248i
$871$	−9.07850	−	6.59592i	−0.307613	−	0.223494i
$872$	3.58648	+	7.03886i	0.121454	+	0.238366i
$873$	18.7481	−	27.1302i	0.634526	−	0.918217i
$874$			3.94235i			0.133352i
$875$	23.8549	+	17.7984i	0.806443	+	0.601697i
$876$	−3.65399	+	1.56437i	−0.123457	+	0.0528550i
$877$	3.65569	−	7.17470i	0.123444	−	0.242272i	−0.821012	−	0.570911i	$-0.806590\pi$
$877$	3.65569	−	7.17470i	0.123444	−	0.242272i	0.944456	+	0.328639i	$0.106590\pi$
$878$	9.66056	+	1.53008i	0.326028	+	0.0516378i
$879$	16.3878	+	3.73014i	0.552746	+	0.125815i
$880$	1.57988	+	5.99755i	0.0532577	+	0.202177i
$881$	5.75875	−	7.92624i	0.194017	−	0.267042i	−0.700914	−	0.713246i	$-0.747224\pi$
$881$	5.75875	−	7.92624i	0.194017	−	0.267042i	0.894931	+	0.446204i	$0.147224\pi$
$882$	0.249267	+	0.0745281i	0.00839327	+	0.00250949i
$883$	23.6742	−	3.74962i	0.796699	−	0.126185i	0.255203	−	0.966888i	$-0.417858\pi$
$883$	23.6742	−	3.74962i	0.796699	−	0.126185i	0.541497	+	0.840703i	$0.317858\pi$
$884$	−1.14854	−	0.834460i	−0.0386294	−	0.0280659i
$885$	−26.6903	+	28.5564i	−0.897184	+	0.959913i
$886$	−24.9664	−	18.1392i	−0.838763	−	0.609397i
$887$	−8.29388	+	52.3655i	−0.278481	+	1.75826i	0.310934	+	0.950432i	$0.399358\pi$
$887$	−8.29388	+	52.3655i	−0.278481	+	1.75826i	−0.589415	+	0.807830i	$0.700642\pi$
$888$	2.29612	+	3.64944i	0.0770529	+	0.122467i
$889$	−14.6431	−	20.1546i	−0.491115	−	0.675962i
$890$	−12.5466	−	14.0535i	−0.420562	−	0.471074i
$891$	19.4799	−	15.6107i	0.652600	−	0.522978i
$892$	14.3649	−	7.31926i	0.480971	−	0.245067i
$893$	−17.2937	−	17.2937i	−0.578713	−	0.578713i
$894$	−22.4147	+	2.03082i	−0.749661	+	0.0679206i
$895$	−2.44625	+	2.99488i	−0.0817691	+	0.100108i
$896$	−1.56474	+	2.15368i	−0.0522742	+	0.0719493i
$897$	2.28650	+	0.152792i	0.0763439	+	0.00510159i
$898$	24.7455	−	24.7455i	0.825768	−	0.825768i
$899$	−3.77168	+	8.72440i	−0.125793	+	0.290975i
$900$	12.7025	+	7.97780i	0.423418	+	0.265927i
$901$	−2.04035	+	1.48240i	−0.0679739	+	0.0493860i
$902$	−1.24473	+	0.197146i	−0.0414451	+	0.00656426i
$903$	−34.0942	+	21.4511i	−1.13458	+	0.713848i
$904$		−	4.96829i		−	0.165243i
$905$	−23.5143	−	9.14061i	−0.781643	−	0.303844i
$906$	8.44441	−	37.0992i	0.280547	−	1.23254i
$907$	−14.8360	+	29.1172i	−0.492620	+	0.966822i	0.502159	+	0.864775i	$0.332539\pi$
$907$	−14.8360	+	29.1172i	−0.492620	+	0.966822i	−0.994780	+	0.102047i	$0.967461\pi$
$908$	8.99746	−	17.6585i	0.298591	−	0.586018i
$909$	18.9817	−	19.9007i	0.629583	−	0.660064i
$910$	−0.554793	−	5.50228i	−0.0183912	−	0.182399i
$911$	34.0188	+	46.8229i	1.12709	+	1.55131i	0.793474	+	0.608604i	$0.208270\pi$
$911$	34.0188	+	46.8229i	1.12709	+	1.55131i	0.333619	+	0.942708i	$0.391730\pi$
$912$	4.64876	−	1.17433i	0.153936	−	0.0388859i
$913$	15.5973	+	7.94721i	0.516195	+	0.263014i
$914$	31.1439	+	22.6274i	1.03015	+	0.748446i
$915$	0.671131	−	5.41483i	0.0221869	−	0.179009i
$916$	−0.719165	−	2.21336i	−0.0237619	−	0.0731315i
$917$	−17.9920	+	2.84965i	−0.594148	+	0.0941038i
$918$	−7.88878	+	0.903122i	−0.260368	+	0.0298075i
$919$	−9.79121	−	3.18136i	−0.322982	−	0.104943i	0.143038	−	0.989717i	$-0.454313\pi$
$919$	−9.79121	−	3.18136i	−0.322982	−	0.104943i	−0.466021	+	0.884774i	$0.654313\pi$
$920$	0.811172	+	3.07938i	0.0267435	+	0.101524i
$921$	43.0654	−	18.4374i	1.41905	−	0.607531i
$922$	−1.37107	+	2.69087i	−0.0451537	+	0.0886191i
$923$	1.26082	−	0.642421i	0.0415005	−	0.0211456i
$924$	−1.15399	−	12.7369i	−0.0379635	−	0.419015i
$925$	−0.546240	−	12.4348i	−0.0179603	−	0.408852i
$926$	11.3184	+	3.67757i	0.371946	+	0.120853i
$927$	−7.61408	−	21.6770i	−0.250079	−	0.711965i
$928$	0.267050	−	1.68609i	0.00876636	−	0.0553486i
$929$	−53.1341			−1.74327			−0.871636	−	0.490153i	$-0.836941\pi$
$929$	−53.1341			−1.74327			−0.871636	+	0.490153i	$0.836941\pi$
$930$	−20.8718	+	5.41923i	−0.684413	+	0.177703i
$931$	−0.240074			−0.00786812
$932$	−1.54513	+	9.75557i	−0.0506124	+	0.319554i
$933$	10.0601	−	2.54130i	0.329353	−	0.0831984i
$934$	−32.8522	−	10.6743i	−1.07496	−	0.349274i
$935$	3.81822	+	8.67442i	0.124869	+	0.283684i
$936$	−0.500921	−	2.74172i	−0.0163731	−	0.0896158i
$937$	19.4996	−	9.93552i	0.637023	−	0.324579i	−0.105481	−	0.994421i	$-0.533638\pi$
$937$	19.4996	−	9.93552i	0.637023	−	0.324579i	0.742504	+	0.669842i	$0.233638\pi$
$938$	−14.5980	+	28.6503i	−0.476643	+	0.935464i
$939$	−15.6648	−	36.5893i	−0.511201	−	1.19405i
$940$	−17.0665	−	9.94984i	−0.556648	−	0.324528i
$941$	19.0423	+	6.18723i	0.620762	+	0.201698i	0.602479	−	0.798135i	$-0.294180\pi$
$941$	19.0423	+	6.18723i	0.620762	+	0.201698i	0.0182836	+	0.999833i	$0.494180\pi$
$942$	−17.5821	−	1.17490i	−0.572855	−	0.0382803i
$943$	−0.639095	+	0.101223i	−0.0208118	+	0.00329626i
$944$	3.11871	+	9.59841i	0.101505	+	0.312402i
$945$	−23.0899	−	20.5807i	−0.751115	−	0.669489i
$946$	19.6034	+	14.2427i	0.637362	+	0.463071i
$947$	43.0616	+	21.9410i	1.39931	+	0.712986i	0.980762	−	0.195207i	$-0.0625380\pi$
$947$	43.0616	+	21.9410i	1.39931	+	0.712986i	0.418551	+	0.908193i	$0.362538\pi$
$948$	−4.05136	−	16.0379i	−0.131582	−	0.520887i
$949$	−1.25315	−	1.72481i	−0.0406790	−	0.0559898i
$950$	−13.3390	−	3.69538i	−0.432773	−	0.119894i
$951$	3.84805	−	3.36598i	0.124781	−	0.109149i
$952$	−1.84682	+	3.62459i	−0.0598558	+	0.117474i
$953$	6.60332	−	12.9597i	0.213902	−	0.419807i	−0.758978	−	0.651116i	$-0.774301\pi$
$953$	6.60332	−	12.9597i	0.213902	−	0.419807i	0.972880	+	0.231309i	$0.0743010\pi$
$954$	−4.90721	−	0.658778i	−0.158877	−	0.0213287i
$955$	3.61374	−	9.29640i	0.116938	−	0.300824i
$956$			6.63586i			0.214619i
$957$	4.36744	+	6.94157i	0.141179	+	0.224389i
$958$	−1.01665	+	0.161021i	−0.0328463	+	0.00520234i
$959$	−35.6701	+	25.9158i	−1.15185	+	0.836866i
$960$	3.38953	−	1.87379i	0.109397	−	0.0604764i
$961$	14.9150	−	27.1762i	0.481128	−	0.876651i
$962$	−1.63532	+	1.63532i	−0.0527248	+	0.0527248i
$963$	14.5758	−	0.344497i	0.469698	−	0.0111013i
$964$	1.14796	−	1.58003i	0.0369732	−	0.0508892i
$965$	2.50078	+	24.8021i	0.0805030	+	0.798407i
$966$	−0.592503	−	6.53964i	−0.0190635	−	0.210410i
$967$	−0.465191	−	0.465191i	−0.0149595	−	0.0149595i	0.699587	−	0.714547i	$-0.253367\pi$
$967$	−0.465191	−	0.465191i	−0.0149595	−	0.0149595i	−0.714547	+	0.699587i	$0.753367\pi$
$968$	2.94627	−	1.50120i	0.0946968	−	0.0482504i
$969$	6.73565	−	2.88370i	0.216380	−	0.0926377i
$970$	−1.39024	+	24.5409i	−0.0446380	+	0.787960i
$971$	−2.74642	−	3.78013i	−0.0881369	−	0.121310i	0.762672	−	0.646786i	$-0.223887\pi$
$971$	−2.74642	−	3.78013i	−0.0881369	−	0.121310i	−0.850808	+	0.525476i	$0.823887\pi$
$972$	−12.4306	−	9.40638i	−0.398712	−	0.301710i
$973$	5.90157	−	37.2610i	0.189195	−	1.19453i
$974$	11.0169	+	8.00423i	0.353003	+	0.256472i
$975$	−2.66023	+	7.59315i	−0.0851957	+	0.243175i
$976$	−1.13974	−	0.828072i	−0.0364823	−	0.0265059i
$977$	11.3182	−	1.79263i	0.362101	−	0.0573512i	0.0272667	−	0.999628i	$-0.491320\pi$
$977$	11.3182	−	1.79263i	0.362101	−	0.0573512i	0.334834	+	0.942277i	$0.391320\pi$
$978$	−40.9202	−	16.3860i	−1.30848	−	0.523967i
$979$	13.7358	−	18.9057i	0.438998	−	0.604229i
$980$	−0.187523	+	0.0493974i	−0.00599019	+	0.00157794i
$981$	−3.15333	+	23.4890i	−0.100678	+	0.749946i
$982$	20.8954	+	3.30950i	0.666798	+	0.105610i
$983$	17.3200	−	33.9924i	0.552422	−	1.08419i	−0.430915	−	0.902393i	$-0.641809\pi$
$983$	17.3200	−	33.9924i	0.552422	−	1.08419i	0.983336	−	0.181796i	$-0.0581910\pi$
$984$	0.309731	+	0.723460i	0.00987386	+	0.0230630i
$985$	5.18740	+	51.4472i	0.165284	+	1.63924i
$986$		−	2.60865i		−	0.0830764i
$987$	31.2863	+	26.0881i	0.995854	+	0.830393i
$988$	1.16758	+	2.29151i	0.0371457	+	0.0729026i
$989$	10.0652	+	7.31277i	0.320054	+	0.232533i
$990$	−6.32971	+	17.4967i	−0.201172	+	0.556081i
$991$	−40.0672			−1.27278			−0.636388	−	0.771369i	$-0.719572\pi$
$991$	−40.0672			−1.27278			−0.636388	+	0.771369i	$0.719572\pi$
$992$	−1.38272	+	5.39334i	−0.0439014	+	0.171239i
$993$	30.5699	+	25.4907i	0.970106	+	0.808923i
$994$	−2.38332	−	3.28037i	−0.0755945	−	0.104047i
$995$	33.4171	−	21.5009i	1.05939	−	0.681625i
$996$	2.42610	−	10.6587i	0.0768738	−	0.337733i
$997$	−11.5462	−	11.5462i	−0.365673	−	0.365673i	0.500223	−	0.865897i	$-0.333251\pi$
$997$	−11.5462	−	11.5462i	−0.365673	−	0.365673i	−0.865897	+	0.500223i	$0.833251\pi$
$998$	−18.1866	−	18.1866i	−0.575687	−	0.575687i
$999$	−0.557251	+	12.9230i	−0.0176306	+	0.408867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.51	yes	512
3.2	odd	2	inner	930.2.bk.a.47.16	✓	512
5.3	odd	4	inner	930.2.bk.a.233.3	yes	512
15.8	even	4	inner	930.2.bk.a.233.64	yes	512
31.2	even	5	inner	930.2.bk.a.467.64	yes	512
93.2	odd	10	inner	930.2.bk.a.467.3	yes	512
155.33	odd	20	inner	930.2.bk.a.653.16	yes	512
465.188	even	20	inner	930.2.bk.a.653.51	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.16	✓	512	3.2	odd	2	inner
930.2.bk.a.47.51	yes	512	1.1	even	1	trivial
930.2.bk.a.233.3	yes	512	5.3	odd	4	inner
930.2.bk.a.233.64	yes	512	15.8	even	4	inner
930.2.bk.a.467.3	yes	512	93.2	odd	10	inner
930.2.bk.a.467.64	yes	512	31.2	even	5	inner
930.2.bk.a.653.16	yes	512	155.33	odd	20	inner
930.2.bk.a.653.51	yes	512	465.188	even	20	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.156434 - 0.987688i) q^{2} +(0.424210 + 1.67930i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.08414 + 0.810158i) q^{5} +(1.72499 - 0.156287i) q^{6} +(2.37194 - 1.20856i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.64009 + 1.42475i) q^{9} +O(q^{10})\)	\(q+(0.156434 - 0.987688i) q^{2} +(0.424210 + 1.67930i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(2.08414 + 0.810158i) q^{5} +(1.72499 - 0.156287i) q^{6} +(2.37194 - 1.20856i) q^{7} +(-0.453990 + 0.891007i) q^{8} +(-2.64009 + 1.42475i) q^{9} +(1.12621 - 1.93175i) q^{10} +(2.63793 + 0.857115i) q^{11} +(0.115485 - 1.72820i) q^{12} +(0.917596 - 0.145333i) q^{13} +(-0.822631 - 2.53180i) q^{14} +(-0.476384 + 3.84357i) q^{15} +(0.809017 + 0.587785i) q^{16} +(1.36156 + 0.693749i) q^{17} +(0.994208 + 2.83047i) q^{18} +(-1.62715 - 2.23958i) q^{19} +(-1.73178 - 1.41454i) q^{20} +(3.03574 + 3.47051i) q^{21} +(1.25923 - 2.47137i) q^{22} +(0.646536 - 1.26890i) q^{23} +(-1.68885 - 0.384412i) q^{24} +(3.68729 + 3.37697i) q^{25} -0.929034i q^{26} +(-3.51253 - 3.82911i) q^{27} +(-2.62932 + 0.416443i) q^{28} +(1.38108 - 1.00341i) q^{29} +(3.72173 + 1.07179i) q^{30} +(-4.79140 + 2.83593i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.320318 + 4.79347i) q^{33} +(0.898202 - 1.23627i) q^{34} +(5.92258 - 0.597172i) q^{35} +(2.95115 - 0.539185i) q^{36} +(-1.76024 - 1.76024i) q^{37} +(-2.46655 + 1.25677i) q^{38} +(0.633311 + 1.47927i) q^{39} +(-1.66804 + 1.48918i) q^{40} +(-0.267066 - 0.367584i) q^{41} +(3.90268 - 2.45546i) q^{42} +(-1.36663 + 8.62854i) q^{43} +(-2.24396 - 1.63033i) q^{44} +(-6.65660 + 0.830489i) q^{45} +(-1.15214 - 0.837075i) q^{46} +(8.72599 - 1.38206i) q^{47} +(-0.643874 + 1.60793i) q^{48} +(0.0509748 - 0.0701608i) q^{49} +(3.91221 - 3.11362i) q^{50} +(-0.587425 + 2.58076i) q^{51} +(-0.917596 - 0.145333i) q^{52} +(-0.749270 + 1.47053i) q^{53} +(-4.33145 + 2.87028i) q^{54} +(4.80342 + 3.92349i) q^{55} +2.66209i q^{56} +(3.07067 - 3.68253i) q^{57} +(-0.775010 - 1.52104i) q^{58} +(8.16490 + 5.93215i) q^{59} +(1.64080 - 3.50824i) q^{60} -1.40880 q^{61} +(2.05148 + 5.17604i) q^{62} +(-4.54024 + 6.57014i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(2.03014 + 0.440503i) q^{65} +(4.68435 + 1.06624i) q^{66} +(-8.54103 - 8.54103i) q^{67} +(-1.08054 - 1.08054i) q^{68} +(2.40513 + 0.547448i) q^{69} +(0.336677 - 5.94309i) q^{70} +(1.44860 - 0.470678i) q^{71} +(-0.0708850 - 2.99916i) q^{72} +(-1.04184 - 2.04472i) q^{73} +(-2.01393 + 1.46320i) q^{74} +(-4.10675 + 7.62460i) q^{75} +(0.855444 + 2.63279i) q^{76} +(7.29289 - 1.15508i) q^{77} +(1.56013 - 0.394105i) q^{78} +(9.08294 - 2.95123i) q^{79} +(1.20991 + 1.88046i) q^{80} +(4.94017 - 7.52294i) q^{81} +(-0.404837 + 0.206275i) q^{82} +(6.23348 + 0.987287i) q^{83} +(-1.81471 - 4.23875i) q^{84} +(2.27563 + 2.54895i) q^{85} +(8.30852 + 2.69960i) q^{86} +(2.27090 + 1.89359i) q^{87} +(-1.96129 + 1.96129i) q^{88} +(2.60352 - 8.01281i) q^{89} +(-0.221057 + 6.70456i) q^{90} +(2.00084 - 1.45369i) q^{91} +(-1.00700 + 1.00700i) q^{92} +(-6.79494 - 6.84316i) q^{93} -8.83476i q^{94} +(-1.57680 - 5.98585i) q^{95} +(1.48741 + 0.887482i) q^{96} +(-9.79448 + 4.99054i) q^{97} +(-0.0613228 - 0.0613228i) q^{98} +(-8.18555 + 1.49553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more