LMFDB - Embedded newform 930.2.v.a.401.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, degree $4$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.1
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-1.73130 - 0.0510207i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.05891 - 1.37066i) q^{6} +(-0.425822 - 1.31054i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.99479 + 0.176664i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.73130 - 0.0510207i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.05891 - 1.37066i) q^{6} +(-0.425822 - 1.31054i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.99479 + 0.176664i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.950001 + 2.92380i) q^{11} +(0.486477 + 1.66233i) q^{12} +(-1.04822 - 1.44275i) q^{13} +(1.31054 + 0.425822i) q^{14} +(-0.0510207 + 1.73130i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.246018 + 0.757167i) q^{17} +(-1.90322 + 2.31900i) q^{18} +(1.60849 + 1.16864i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(0.670360 + 2.29067i) q^{21} +(-2.92380 - 0.950001i) q^{22} +(1.04450 - 3.21465i) q^{23} +(-1.63080 - 0.583524i) q^{24} -1.00000 q^{25} +1.78333 q^{26} +(-5.17587 - 0.458655i) q^{27} +(-1.11482 + 0.809961i) q^{28} +(1.35083 + 0.981432i) q^{29} +(-1.37066 - 1.05891i) q^{30} +(-5.23325 - 1.90082i) q^{31} -1.00000i q^{32} +(-1.49556 - 5.11044i) q^{33} +(-0.467955 - 0.644084i) q^{34} +(-1.31054 + 0.425822i) q^{35} +(-0.757424 - 2.90281i) q^{36} -10.5109i q^{37} +(-1.89089 + 0.614388i) q^{38} +(1.74117 + 2.55131i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.01264 + 4.14654i) q^{41} +(-2.24722 - 0.804090i) q^{42} +(-0.341884 + 0.470564i) q^{43} +(2.48713 - 1.80701i) q^{44} +(0.176664 - 2.99479i) q^{45} +(1.98676 + 2.73454i) q^{46} +(-1.43737 - 1.97837i) q^{47} +(1.43064 - 0.976355i) q^{48} +(4.12692 - 2.99838i) q^{49} +(0.587785 - 0.809017i) q^{50} +(0.464563 - 1.29833i) q^{51} +(-1.04822 + 1.44275i) q^{52} +(2.91595 - 8.97438i) q^{53} +(3.41336 - 3.91778i) q^{54} +(2.92380 - 0.950001i) q^{55} -1.37799i q^{56} +(-2.72515 - 2.10532i) q^{57} +(-1.58799 + 0.515970i) q^{58} +(-3.50962 - 4.83057i) q^{59} +(1.66233 - 0.486477i) q^{60} -9.86353i q^{61} +(4.61382 - 3.11651i) q^{62} +(-1.04372 - 4.00004i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.44275 + 1.04822i) q^{65} +(5.01350 + 1.79391i) q^{66} -8.47961 q^{67} +0.796132 q^{68} +(-1.97236 + 5.51223i) q^{69} +(0.425822 - 1.31054i) q^{70} +(-2.43862 - 0.792357i) q^{71} +(2.79363 + 1.09346i) q^{72} +(8.26641 - 2.68592i) q^{73} +(8.50350 + 6.17816i) q^{74} +(1.73130 + 0.0510207i) q^{75} +(0.614388 - 1.89089i) q^{76} +(3.42724 - 2.49004i) q^{77} +(-3.08749 - 0.0909871i) q^{78} +(7.35404 + 2.38947i) q^{79} +(0.587785 + 0.809017i) q^{80} +(8.93758 + 1.05815i) q^{81} +(-1.58384 - 4.87455i) q^{82} +(3.00001 + 2.17963i) q^{83} +(1.97140 - 1.34541i) q^{84} +(0.757167 + 0.246018i) q^{85} +(-0.179739 - 0.553181i) q^{86} +(-2.28861 - 1.76807i) q^{87} +3.07427i q^{88} +(-1.54528 - 4.75588i) q^{89} +(2.31900 + 1.90322i) q^{90} +(-1.44443 + 1.98809i) q^{91} -3.38008 q^{92} +(8.96334 + 3.55789i) q^{93} +2.44540 q^{94} +(1.16864 - 1.60849i) q^{95} +(-0.0510207 + 1.73130i) q^{96} +(-3.15890 - 9.72211i) q^{97} +5.10115i q^{98} +(2.32852 + 8.92401i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−1.73130	−	0.0510207i	−0.999566	−	0.0294568i
$3$	−1.73130	−	0.0510207i	−0.999566	−	0.0294568i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.05891	−	1.37066i	0.432298	−	0.559570i
$7$	−0.425822	−	1.31054i	−0.160946	−	0.495339i	0.837769	−	0.546025i	$-0.183859\pi$
$7$	−0.425822	−	1.31054i	−0.160946	−	0.495339i	−0.998715	+	0.0506852i	$0.983859\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	2.99479	+	0.176664i	0.998265	+	0.0588881i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	0.950001	+	2.92380i	0.286436	+	0.881559i	0.985965	+	0.166955i	$0.0533933\pi$
$11$	0.950001	+	2.92380i	0.286436	+	0.881559i	−0.699529	+	0.714605i	$0.746607\pi$
$12$	0.486477	+	1.66233i	0.140434	+	0.479873i
$13$	−1.04822	−	1.44275i	−0.290723	−	0.400146i	0.638526	−	0.769601i	$-0.279545\pi$
$13$	−1.04822	−	1.44275i	−0.290723	−	0.400146i	−0.929249	+	0.369454i	$0.879545\pi$
$14$	1.31054	+	0.425822i	0.350258	+	0.113806i
$15$	−0.0510207	+	1.73130i	−0.0131735	+	0.447020i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.246018	+	0.757167i	−0.0596682	+	0.183640i	−0.976448	−	0.215754i	$-0.930779\pi$
$17$	−0.246018	+	0.757167i	−0.0596682	+	0.183640i	0.916780	+	0.399393i	$0.130779\pi$
$18$	−1.90322	+	2.31900i	−0.448593	+	0.546593i
$19$	1.60849	+	1.16864i	0.369013	+	0.268103i	0.756801	−	0.653645i	$-0.226761\pi$
$19$	1.60849	+	1.16864i	0.369013	+	0.268103i	−0.387789	+	0.921748i	$0.626761\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	0.670360	+	2.29067i	0.146285	+	0.499865i
$22$	−2.92380	−	0.950001i	−0.623356	−	0.202541i
$23$	1.04450	−	3.21465i	0.217794	−	0.670301i	−0.781150	−	0.624344i	$-0.785366\pi$
$23$	1.04450	−	3.21465i	0.217794	−	0.670301i	0.998943	−	0.0459567i	$-0.0146336\pi$
$24$	−1.63080	−	0.583524i	−0.332885	−	0.119111i
$25$	−1.00000			−0.200000
$26$	1.78333			0.349741
$27$	−5.17587	−	0.458655i	−0.996097	−	0.0882683i
$28$	−1.11482	+	0.809961i	−0.210680	+	0.153068i
$29$	1.35083	+	0.981432i	0.250842	+	0.182247i	0.706100	−	0.708112i	$-0.250453\pi$
$29$	1.35083	+	0.981432i	0.250842	+	0.182247i	−0.455258	+	0.890360i	$0.650453\pi$
$30$	−1.37066	−	1.05891i	−0.250247	−	0.193329i
$31$	−5.23325	−	1.90082i	−0.939919	−	0.341397i
$31$	−5.23325	−	1.90082i	−0.939919	−	0.341397i
$32$		−	1.00000i		−	0.176777i
$33$	−1.49556	−	5.11044i	−0.260344	−	0.889614i
$34$	−0.467955	−	0.644084i	−0.0802536	−	0.110460i
$35$	−1.31054	+	0.425822i	−0.221523	+	0.0719770i
$36$	−0.757424	−	2.90281i	−0.126237	−	0.483802i
$37$		−	10.5109i		−	1.72798i	−0.503506	−	0.863991i	$-0.667957\pi$
$37$		−	10.5109i		−	1.72798i	0.503506	−	0.863991i	$-0.332043\pi$
$38$	−1.89089	+	0.614388i	−0.306743	+	0.0996669i
$39$	1.74117	+	2.55131i	0.278810	+	0.408537i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	−3.01264	+	4.14654i	−0.470495	+	0.647580i	−0.976644	−	0.214866i	$-0.931069\pi$
$41$	−3.01264	+	4.14654i	−0.470495	+	0.647580i	0.506149	+	0.862446i	$0.331069\pi$
$42$	−2.24722	−	0.804090i	−0.346753	−	0.124074i
$43$	−0.341884	+	0.470564i	−0.0521369	+	0.0717603i	−0.834289	−	0.551327i	$-0.814122\pi$
$43$	−0.341884	+	0.470564i	−0.0521369	+	0.0717603i	0.782153	+	0.623087i	$0.214122\pi$
$44$	2.48713	−	1.80701i	0.374950	−	0.272417i
$45$	0.176664	−	2.99479i	0.0263356	−	0.446437i
$46$	1.98676	+	2.73454i	0.292932	+	0.403187i
$47$	−1.43737	−	1.97837i	−0.209662	−	0.288575i	0.691215	−	0.722649i	$-0.257076\pi$
$47$	−1.43737	−	1.97837i	−0.209662	−	0.288575i	−0.900877	+	0.434074i	$0.857076\pi$
$48$	1.43064	−	0.976355i	0.206495	−	0.140925i
$49$	4.12692	−	2.99838i	0.589559	−	0.428340i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	0.464563	−	1.29833i	0.0650518	−	0.181803i
$52$	−1.04822	+	1.44275i	−0.145362	+	0.200073i
$53$	2.91595	−	8.97438i	0.400537	−	1.23273i	−0.524028	−	0.851701i	$-0.675571\pi$
$53$	2.91595	−	8.97438i	0.400537	−	1.23273i	0.924565	−	0.381025i	$-0.124429\pi$
$54$	3.41336	−	3.91778i	0.464500	−	0.533142i
$55$	2.92380	−	0.950001i	0.394245	−	0.128098i
$56$		−	1.37799i		−	0.184141i
$57$	−2.72515	−	2.10532i	−0.360955	−	0.278857i
$58$	−1.58799	+	0.515970i	−0.208513	+	0.0677501i
$59$	−3.50962	−	4.83057i	−0.456913	−	0.628887i	0.516952	−	0.856014i	$-0.327067\pi$
$59$	−3.50962	−	4.83057i	−0.456913	−	0.628887i	−0.973865	+	0.227128i	$0.927067\pi$
$60$	1.66233	−	0.486477i	0.214606	−	0.0628039i
$61$		−	9.86353i		−	1.26290i	−0.775418	−	0.631448i	$-0.782461\pi$
$61$		−	9.86353i		−	1.26290i	0.775418	−	0.631448i	$-0.217539\pi$
$62$	4.61382	−	3.11651i	0.585956	−	0.395798i
$63$	−1.04372	−	4.00004i	−0.131497	−	0.503958i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−1.44275	+	1.04822i	−0.178951	+	0.130015i
$66$	5.01350	+	1.79391i	0.617120	+	0.220815i
$67$	−8.47961			−1.03595			−0.517975	−	0.855396i	$-0.673314\pi$
$67$	−8.47961			−1.03595			−0.517975	+	0.855396i	$0.673314\pi$
$68$	0.796132			0.0965452
$69$	−1.97236	+	5.51223i	−0.237444	+	0.663594i
$70$	0.425822	−	1.31054i	0.0508954	−	0.156640i
$71$	−2.43862	−	0.792357i	−0.289412	−	0.0940355i	0.160713	−	0.987001i	$-0.448621\pi$
$71$	−2.43862	−	0.792357i	−0.289412	−	0.0940355i	−0.450125	+	0.892966i	$0.648621\pi$
$72$	2.79363	+	1.09346i	0.329232	+	0.128865i
$73$	8.26641	−	2.68592i	0.967510	−	0.314363i	0.217699	−	0.976016i	$-0.430145\pi$
$73$	8.26641	−	2.68592i	0.967510	−	0.314363i	0.749810	+	0.661653i	$0.230145\pi$
$74$	8.50350	+	6.17816i	0.988512	+	0.718196i
$75$	1.73130	+	0.0510207i	0.199913	+	0.00589137i
$76$	0.614388	−	1.89089i	0.0704752	−	0.216900i
$77$	3.42724	−	2.49004i	0.390570	−	0.283766i
$78$	−3.08749	−	0.0909871i	−0.349589	−	0.0103023i
$79$	7.35404	+	2.38947i	0.827394	+	0.268837i	0.691947	−	0.721948i	$-0.256753\pi$
$79$	7.35404	+	2.38947i	0.827394	+	0.268837i	0.135447	+	0.990785i	$0.456753\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	8.93758	+	1.05815i	0.993064	+	0.117572i
$82$	−1.58384	−	4.87455i	−0.174905	−	0.538304i
$83$	3.00001	+	2.17963i	0.329294	+	0.239246i	0.740131	−	0.672463i	$-0.234764\pi$
$83$	3.00001	+	2.17963i	0.329294	+	0.239246i	−0.410837	+	0.911709i	$0.634764\pi$
$84$	1.97140	−	1.34541i	0.215098	−	0.146796i
$85$	0.757167	+	0.246018i	0.0821263	+	0.0266844i
$86$	−0.179739	−	0.553181i	−0.0193818	−	0.0596510i
$87$	−2.28861	−	1.76807i	−0.245365	−	0.189557i
$88$			3.07427i			0.327718i
$89$	−1.54528	−	4.75588i	−0.163799	−	0.504123i	0.835146	−	0.550028i	$-0.185383\pi$
$89$	−1.54528	−	4.75588i	−0.163799	−	0.504123i	−0.998946	+	0.0459050i	$0.985383\pi$
$90$	2.31900	+	1.90322i	0.244444	+	0.200617i
$91$	−1.44443	+	1.98809i	−0.151418	+	0.208409i
$92$	−3.38008			−0.352398
$93$	8.96334	+	3.55789i	0.929455	+	0.368936i
$94$	2.44540			0.252224
$95$	1.16864	−	1.60849i	0.119900	−	0.165028i
$96$	−0.0510207	+	1.73130i	−0.00520728	+	0.176700i
$97$	−3.15890	−	9.72211i	−0.320738	−	0.987130i	−0.973328	−	0.229419i	$-0.926317\pi$
$97$	−3.15890	−	9.72211i	−0.320738	−	0.987130i	0.652590	−	0.757711i	$-0.273683\pi$
$98$			5.10115i			0.515294i
$99$	2.32852	+	8.92401i	0.234025	+	0.896897i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−8.65892	−	2.81345i	−0.861595	−	0.279949i	−0.155300	−	0.987867i	$-0.549635\pi$
$101$	−8.65892	−	2.81345i	−0.861595	−	0.279949i	−0.706294	+	0.707918i	$0.749635\pi$
$102$	0.777308	+	1.13898i	0.0769650	+	0.112776i
$103$	−2.51498	−	1.82724i	−0.247808	−	0.180043i	0.456947	−	0.889494i	$-0.348943\pi$
$103$	−2.51498	−	1.82724i	−0.247808	−	0.180043i	−0.704755	+	0.709451i	$0.748943\pi$
$104$	−0.551081	−	1.69605i	−0.0540379	−	0.166312i
$105$	2.29067	−	0.670360i	0.223547	−	0.0654204i
$106$	5.54647	+	7.63407i	0.538721	+	0.741486i
$107$	−12.7508	−	4.14298i	−1.23267	−	0.400517i	−0.380986	−	0.924581i	$-0.624415\pi$
$107$	−12.7508	−	4.14298i	−1.23267	−	0.400517i	−0.851679	+	0.524064i	$0.824415\pi$
$108$	1.16322	+	5.06428i	0.111931	+	0.487310i
$109$	9.55536	−	6.94238i	0.915238	−	0.664959i	−0.0270963	−	0.999633i	$-0.508626\pi$
$109$	9.55536	−	6.94238i	0.915238	−	0.664959i	0.942334	+	0.334674i	$0.108626\pi$
$110$	−0.950001	+	2.92380i	−0.0905790	+	0.278773i
$111$	−0.536275	+	18.1975i	−0.0509009	+	1.72723i
$112$	1.11482	+	0.809961i	0.105340	+	0.0765341i
$113$	−3.73772	+	1.21446i	−0.351616	+	0.114247i	−0.479499	−	0.877542i	$-0.659182\pi$
$113$	−3.73772	+	1.21446i	−0.351616	+	0.114247i	0.127884	+	0.991789i	$0.459182\pi$
$114$	3.30505	−	0.967215i	0.309546	−	0.0905880i
$115$	−3.21465	−	1.04450i	−0.299768	−	0.0974004i
$116$	0.515970	−	1.58799i	0.0479066	−	0.147441i
$117$	−2.88431	−	4.50592i	−0.266655	−	0.416572i
$118$	5.97091			0.549667
$119$	1.09706			0.100567
$120$	−0.583524	+	1.63080i	−0.0532683	+	0.148871i
$121$	1.25308	−	0.910413i	0.113916	−	0.0827648i
$122$	7.97976	+	5.79764i	0.722454	+	0.524893i
$123$	5.42733	−	7.02519i	0.489366	−	0.633440i
$124$	−0.190623	+	5.56450i	−0.0171184	+	0.499707i
$125$			1.00000i			0.0894427i
$126$	3.84958	+	1.50678i	0.342948	+	0.134234i
$127$	−2.21763	−	3.05230i	−0.196782	−	0.270848i	0.699211	−	0.714916i	$-0.253535\pi$
$127$	−2.21763	−	3.05230i	−0.196782	−	0.270848i	−0.895993	+	0.444068i	$0.853535\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	0.615913	−	0.797243i	0.0542281	−	0.0701933i
$130$		−	1.78333i		−	0.156409i
$131$	−13.2582	+	4.30784i	−1.15837	+	0.376378i	−0.824291	−	0.566167i	$-0.808426\pi$
$131$	−13.2582	+	4.30784i	−1.15837	+	0.376378i	−0.334081	+	0.942544i	$0.608426\pi$
$132$	−4.39817	+	3.00158i	−0.382811	+	0.261254i
$133$	0.846620	−	2.60563i	0.0734113	−	0.225937i
$134$	4.98419	−	6.86015i	0.430568	−	0.592627i
$135$	−0.458655	+	5.17587i	−0.0394748	+	0.445468i
$136$	−0.467955	+	0.644084i	−0.0401268	+	0.0552298i
$137$	−9.29480	+	6.75307i	−0.794108	+	0.576953i	−0.909180	−	0.416404i	$-0.863290\pi$
$137$	−9.29480	+	6.75307i	−0.794108	+	0.576953i	0.115071	+	0.993357i	$0.463290\pi$
$138$	−3.30016	−	4.83568i	−0.280928	−	0.411640i
$139$	2.82088	+	3.88261i	0.239264	+	0.329319i	0.911715	−	0.410823i	$-0.134759\pi$
$139$	2.82088	+	3.88261i	0.239264	+	0.329319i	−0.672451	+	0.740141i	$0.734759\pi$
$140$	0.809961	+	1.11482i	0.0684542	+	0.0942191i
$141$	2.38758	+	3.49849i	0.201071	+	0.294626i
$142$	2.07442	−	1.50715i	0.174081	−	0.126477i
$143$	3.22250	−	4.43539i	0.269479	−	0.370906i
$144$	−2.52668	+	1.61737i	−0.210557	+	0.134781i
$145$	0.981432	−	1.35083i	0.0815035	−	0.112180i
$146$	−2.68592	+	8.26641i	−0.222288	+	0.684133i
$147$	−7.29790	+	4.98053i	−0.601921	+	0.410788i
$148$	−9.99647	+	3.24805i	−0.821705	+	0.266988i
$149$		−	8.27034i		−	0.677533i	−0.940871	−	0.338766i	$-0.889990\pi$
$149$		−	8.27034i		−	0.677533i	0.940871	−	0.338766i	$-0.110010\pi$
$150$	−1.05891	+	1.37066i	−0.0864595	+	0.111914i
$151$	4.54350	−	1.47627i	0.369745	−	0.120137i	−0.118250	−	0.992984i	$-0.537729\pi$
$151$	4.54350	−	1.47627i	0.369745	−	0.120137i	0.487995	+	0.872847i	$0.337729\pi$
$152$	1.16864	+	1.60849i	0.0947889	+	0.130466i
$153$	−0.870539	+	2.22410i	−0.0703789	+	0.179807i
$154$			4.23630i			0.341371i
$155$	−1.90082	+	5.23325i	−0.152677	+	0.420345i
$156$	1.88839	−	2.44435i	0.151192	−	0.195704i
$157$	−16.6266	−	12.0799i	−1.32695	−	0.964083i	−0.999818	−	0.0191033i	$-0.993919\pi$
$157$	−16.6266	−	12.0799i	−1.32695	−	0.964083i	−0.327129	−	0.944980i	$-0.606081\pi$
$158$	−6.25572	+	4.54505i	−0.497678	+	0.361584i
$159$	−5.50627	+	15.3886i	−0.436675	+	1.22039i
$160$	−1.00000			−0.0790569
$161$	−4.65771			−0.367079
$162$	−6.10944	+	6.60869i	−0.480003	+	0.519228i
$163$	−1.04094	+	3.20369i	−0.0815329	+	0.250932i	−0.983511	−	0.180850i	$-0.942115\pi$
$163$	−1.04094	+	3.20369i	−0.0815329	+	0.250932i	0.901978	+	0.431782i	$0.142115\pi$
$164$	4.87455	+	1.58384i	0.380638	+	0.123677i
$165$	−5.11044	+	1.49556i	−0.397848	+	0.116429i
$166$	−3.52672	+	1.14590i	−0.273727	+	0.0889391i
$167$	13.6135	+	9.89081i	1.05345	+	0.765374i	0.972865	−	0.231374i	$-0.0743222\pi$
$167$	13.6135	+	9.89081i	1.05345	+	0.765374i	0.0805817	+	0.996748i	$0.474322\pi$
$168$	−0.0703060	+	2.38571i	−0.00542423	+	0.184062i
$169$	3.03446	−	9.33911i	0.233420	−	0.718393i
$170$	−0.644084	+	0.467955i	−0.0493990	+	0.0358905i
$171$	4.61064	+	3.78399i	0.352584	+	0.289369i
$172$	0.553181	+	0.179739i	0.0421796	+	0.0137050i
$173$	−5.39900	−	7.43109i	−0.410478	−	0.564975i	0.552857	−	0.833276i	$-0.313538\pi$
$173$	−5.39900	−	7.43109i	−0.410478	−	0.564975i	−0.963335	+	0.268301i	$0.913538\pi$
$174$	2.77561	−	0.812277i	0.210419	−	0.0615786i
$175$	0.425822	+	1.31054i	0.0321891	+	0.0990679i
$176$	−2.48713	−	1.80701i	−0.187475	−	0.136208i
$177$	5.82974	+	8.54223i	0.438190	+	0.642073i
$178$	4.75588	+	1.54528i	0.356469	+	0.115824i
$179$	−2.01878	−	6.21316i	−0.150891	−	0.464393i	0.846831	−	0.531862i	$-0.178508\pi$
$179$	−2.01878	−	6.21316i	−0.150891	−	0.464393i	−0.997721	+	0.0674690i	$0.978508\pi$
$180$	−2.90281	+	0.757424i	−0.216363	+	0.0564551i
$181$		−	11.9506i		−	0.888284i	−0.895956	−	0.444142i	$-0.853509\pi$
$181$		−	11.9506i		−	0.888284i	0.895956	−	0.444142i	$-0.146491\pi$
$182$	−0.759383	−	2.33714i	−0.0562892	−	0.173240i
$183$	−0.503245	+	17.0767i	−0.0372009	+	1.26235i
$184$	1.98676	−	2.73454i	0.146466	−	0.201593i
$185$	−10.5109			−0.772777
$186$	−8.14691	+	5.16022i	−0.597360	+	0.378366i
$187$	−2.44752			−0.178981
$188$	−1.43737	+	1.97837i	−0.104831	+	0.144288i
$189$	1.60291	+	6.97852i	0.116595	+	0.507612i
$190$	0.614388	+	1.89089i	0.0445724	+	0.137180i
$191$			17.8266i			1.28988i	0.764231	+	0.644942i	$0.223119\pi$
$191$			17.8266i			1.28988i	−0.764231	+	0.644942i	$0.776881\pi$
$192$	−1.37066	−	1.05891i	−0.0989190	−	0.0764202i
$193$	4.19546	+	12.9123i	0.301996	+	0.929447i	0.980781	+	0.195111i	$0.0625066\pi$
$193$	4.19546	+	12.9123i	0.301996	+	0.929447i	−0.678785	+	0.734337i	$0.737493\pi$
$194$	9.72211	+	3.15890i	0.698006	+	0.226796i
$195$	2.55131	−	1.74117i	0.182703	−	0.124688i
$196$	−4.12692	−	2.99838i	−0.294780	−	0.214170i
$197$	5.72466	+	17.6187i	0.407865	+	1.25528i	0.918479	+	0.395470i	$0.129418\pi$
$197$	5.72466	+	17.6187i	0.407865	+	1.25528i	−0.510614	+	0.859810i	$0.670582\pi$
$198$	−8.58835	−	3.36159i	−0.610347	−	0.238898i
$199$	2.85956	+	3.93585i	0.202709	+	0.279005i	0.898253	−	0.439478i	$-0.144837\pi$
$199$	2.85956	+	3.93585i	0.202709	+	0.279005i	−0.695544	+	0.718483i	$0.744837\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	14.6807	+	0.432636i	1.03550	+	0.0305158i
$202$	7.36572	−	5.35151i	0.518250	−	0.376531i
$203$	0.711000	−	2.18823i	0.0499024	−	0.153584i
$204$	−1.37834	−	0.0406193i	−0.0965033	−	0.00284392i
$205$	4.14654	+	3.01264i	0.289607	+	0.210412i
$206$	2.95654	−	0.960637i	0.205992	−	0.0669307i
$207$	3.69598	−	9.44269i	0.256889	−	0.656312i
$208$	1.69605	+	0.551081i	0.117600	+	0.0382106i
$209$	−1.88879	+	5.81311i	−0.130651	+	0.402101i
$210$	−0.804090	+	2.24722i	−0.0554875	+	0.155073i
$211$	2.18111			0.150154			0.0750770	−	0.997178i	$-0.476080\pi$
$211$	2.18111			0.150154			0.0750770	+	0.997178i	$0.476080\pi$
$212$	−9.43622			−0.648083
$213$	4.18156	+	1.49623i	0.286516	+	0.102520i
$214$	10.8465	−	7.88042i	0.741449	−	0.538694i
$215$	0.470564	+	0.341884i	0.0320922	+	0.0233163i
$216$	−4.78081	−	2.03564i	−0.325293	−	0.138508i
$217$	−0.262676	+	7.66782i	−0.0178316	+	0.520525i
$218$			11.8111i			0.799947i
$219$	−14.4487	+	4.22837i	−0.976350	+	0.285727i
$220$	−1.80701	−	2.48713i	−0.121828	−	0.167683i
$221$	1.35028	−	0.438733i	0.0908298	−	0.0295124i
$222$	−14.4069	−	11.1301i	−0.966928	−	0.747003i
$223$		−	0.462227i		−	0.0309530i	−0.999880	−	0.0154765i	$-0.995073\pi$
$223$		−	0.462227i		−	0.0309530i	0.999880	−	0.0154765i	$-0.00492652\pi$
$224$	−1.31054	+	0.425822i	−0.0875645	+	0.0284514i
$225$	−2.99479	−	0.176664i	−0.199653	−	0.0117776i
$226$	1.21446	−	3.73772i	0.0807847	−	0.248630i
$227$	−7.64582	+	10.5236i	−0.507471	+	0.698474i	−0.983490	−	0.180961i	$-0.942079\pi$
$227$	−7.64582	+	10.5236i	−0.507471	+	0.698474i	0.476019	+	0.879435i	$0.342079\pi$
$228$	−1.16016	+	3.24235i	−0.0768338	+	0.214730i
$229$	−13.0548	+	17.9684i	−0.862688	+	1.18739i	0.118234	+	0.992986i	$0.462277\pi$
$229$	−13.0548	+	17.9684i	−0.862688	+	1.18739i	−0.980922	+	0.194403i	$0.937723\pi$
$230$	2.73454	−	1.98676i	0.180310	−	0.131003i
$231$	−6.06062	+	4.13614i	−0.398760	+	0.272138i
$232$	0.981432	+	1.35083i	0.0644342	+	0.0886861i
$233$	6.36656	+	8.76282i	0.417087	+	0.574072i	0.964929	−	0.262510i	$-0.0845504\pi$
$233$	6.36656	+	8.76282i	0.417087	+	0.574072i	−0.547842	+	0.836582i	$0.684550\pi$
$234$	5.34072	+	0.315052i	0.349134	+	0.0205956i
$235$	−1.97837	+	1.43737i	−0.129055	+	0.0937638i
$236$	−3.50962	+	4.83057i	−0.228457	+	0.314443i
$237$	−12.6101	−	4.51210i	−0.819116	−	0.293092i
$238$	−0.644836	+	0.887541i	−0.0417985	+	0.0575307i
$239$	7.89492	−	24.2981i	0.510680	−	1.57171i	−0.280327	−	0.959905i	$-0.590443\pi$
$239$	7.89492	−	24.2981i	0.510680	−	1.57171i	0.791007	−	0.611807i	$-0.209557\pi$
$240$	−0.976355	−	1.43064i	−0.0630235	−	0.0923474i
$241$	7.13604	−	2.31864i	0.459672	−	0.149357i	−0.0700215	−	0.997545i	$-0.522307\pi$
$241$	7.13604	−	2.31864i	0.459672	−	0.149357i	0.529694	+	0.848189i	$0.322307\pi$
$242$			1.54889i			0.0995662i
$243$	−15.4196	−	2.28797i	−0.989170	−	0.146773i
$244$	−9.38077	+	3.04800i	−0.600542	+	0.195128i
$245$	−2.99838	−	4.12692i	−0.191559	−	0.263659i
$246$	2.49339	+	8.52011i	0.158973	+	0.543222i
$247$		−	3.54563i		−	0.225603i
$248$	−4.38973	−	3.42495i	−0.278748	−	0.217484i
$249$	−5.08270	−	3.92666i	−0.322103	−	0.248842i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−9.66476	+	7.02186i	−0.610034	+	0.443216i	−0.849426	−	0.527707i	$-0.823052\pi$
$251$	−9.66476	+	7.02186i	−0.610034	+	0.443216i	0.239392	+	0.970923i	$0.423052\pi$
$252$	−3.48174	+	2.22872i	−0.219329	+	0.140396i
$253$	10.3913			0.653294
$254$	3.77285			0.236730
$255$	−1.29833	−	0.464563i	−0.0813046	−	0.0290920i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−10.4633	−	3.39973i	−0.652683	−	0.212070i	−0.0360861	−	0.999349i	$-0.511489\pi$
$257$	−10.4633	−	3.39973i	−0.652683	−	0.212070i	−0.616597	+	0.787279i	$0.711489\pi$
$258$	0.282959	+	0.966892i	0.0176162	+	0.0601960i
$259$	−13.7750	+	4.47577i	−0.855938	+	0.278111i
$260$	1.44275	+	1.04822i	0.0894755	+	0.0650077i
$261$	3.87206	+	3.17783i	0.239675	+	0.196703i
$262$	4.30784	−	13.2582i	0.266139	−	0.819092i
$263$	21.1673	−	15.3789i	1.30523	−	0.948305i	0.305238	−	0.952276i	$-0.401264\pi$
$263$	21.1673	−	15.3789i	1.30523	−	0.948305i	0.999992	+	0.00397107i	$0.00126404\pi$
$264$	0.156851	−	5.32247i	0.00965353	−	0.327576i
$265$	−8.97438	−	2.91595i	−0.551292	−	0.179126i
$266$	1.61037	+	2.21648i	0.0987379	+	0.135901i
$267$	2.43269	+	8.31270i	0.148878	+	0.508729i
$268$	2.62034	+	8.06459i	0.160063	+	0.492623i
$269$	8.09527	+	5.88156i	0.493577	+	0.358605i	0.806558	−	0.591154i	$-0.201328\pi$
$269$	8.09527	+	5.88156i	0.493577	+	0.358605i	−0.312981	+	0.949759i	$0.601328\pi$
$270$	−3.91778	−	3.41336i	−0.238428	−	0.207730i
$271$	8.11852	+	2.63787i	0.493165	+	0.160239i	0.545033	−	0.838415i	$-0.316517\pi$
$271$	8.11852	+	2.63787i	0.493165	+	0.160239i	−0.0518673	+	0.998654i	$0.516517\pi$
$272$	−0.246018	−	0.757167i	−0.0149171	−	0.0459100i
$273$	2.60218	−	3.36828i	0.157491	−	0.203858i
$274$		−	11.4890i		−	0.694076i
$275$	−0.950001	−	2.92380i	−0.0572872	−	0.176312i
$276$	5.85193	+	0.172454i	0.352245	+	0.0103805i
$277$	−4.16441	+	5.73182i	−0.250215	+	0.344392i	−0.915587	−	0.402121i	$-0.868273\pi$
$277$	−4.16441	+	5.73182i	−0.250215	+	0.344392i	0.665371	+	0.746512i	$0.268273\pi$
$278$	−4.79917			−0.287835
$279$	−15.3367	−	6.61709i	−0.918184	−	0.396155i
$280$	−1.37799			−0.0823506
$281$	15.3139	−	21.0778i	0.913554	−	1.25740i	−0.0523850	−	0.998627i	$-0.516682\pi$
$281$	15.3139	−	21.0778i	0.913554	−	1.25740i	0.965939	−	0.258772i	$-0.0833177\pi$
$282$	−4.23372	−	0.124766i	−0.252115	−	0.00742972i
$283$	−1.24886	−	3.84360i	−0.0742371	−	0.228478i	0.907052	−	0.421019i	$-0.138327\pi$
$283$	−1.24886	−	3.84360i	−0.0742371	−	0.228478i	−0.981289	+	0.192540i	$0.938327\pi$
$284$			2.56412i			0.152153i
$285$	−2.10532	+	2.72515i	−0.124709	+	0.161424i
$286$	1.69417	+	5.21412i	0.100178	+	0.308317i
$287$	6.71707	+	2.18251i	0.396496	+	0.128829i
$288$	0.176664	−	2.99479i	0.0104100	−	0.176470i
$289$	13.2405	+	9.61980i	0.778854	+	0.565870i
$290$	0.515970	+	1.58799i	0.0302988	+	0.0932500i
$291$	4.97298	+	16.9930i	0.291521	+	0.996150i
$292$	−5.10892	−	7.03182i	−0.298977	−	0.411506i
$293$	−2.91137	−	0.945962i	−0.170084	−	0.0552637i	0.222737	−	0.974879i	$-0.428501\pi$
$293$	−2.91137	−	0.945962i	−0.170084	−	0.0552637i	−0.392821	+	0.919615i	$0.628501\pi$
$294$	0.260264	−	8.83161i	0.0151789	−	0.515070i
$295$	−4.83057	+	3.50962i	−0.281247	+	0.204338i
$296$	3.24805	−	9.99647i	0.188789	−	0.581033i
$297$	−3.57606	−	15.5689i	−0.207504	−	0.903401i
$298$	6.69084	+	4.86118i	0.387590	+	0.281601i
$299$	−5.73280	+	1.86270i	−0.331536	+	0.107723i
$300$	−0.486477	−	1.66233i	−0.0280868	−	0.0959746i
$301$	0.762277	+	0.247679i	0.0439369	+	0.0142760i
$302$	−1.47627	+	4.54350i	−0.0849499	+	0.261449i
$303$	14.8476	+	5.31271i	0.852974	+	0.305207i
$304$	−1.98820			−0.114031
$305$	−9.86353			−0.564784
$306$	−1.28764	−	2.01157i	−0.0736095	−	0.114994i
$307$	−17.5424	+	12.7453i	−1.00120	+	0.727411i	−0.962344	−	0.271834i	$-0.912370\pi$
$307$	−17.5424	+	12.7453i	−1.00120	+	0.727411i	−0.0388514	+	0.999245i	$0.512370\pi$
$308$	−3.42724	−	2.49004i	−0.195285	−	0.141883i
$309$	4.26096	+	3.29182i	0.242397	+	0.187265i
$310$	−3.11651	−	4.61382i	−0.177006	−	0.262047i
$311$		−	27.3035i		−	1.54824i	−0.633039	−	0.774120i	$-0.718193\pi$
$311$		−	27.3035i		−	1.54824i	0.633039	−	0.774120i	$-0.281807\pi$
$312$	0.867552	+	2.96449i	0.0491155	+	0.167831i
$313$	18.4458	+	25.3885i	1.04262	+	1.43504i	0.895037	+	0.445992i	$0.147149\pi$
$313$	18.4458	+	25.3885i	1.04262	+	1.43504i	0.147582	+	0.989050i	$0.452851\pi$
$314$	19.5457	−	6.35079i	1.10303	−	0.358396i
$315$	−4.00004	+	1.04372i	−0.225377	+	0.0588071i
$316$		−	7.73249i		−	0.434987i
$317$	−5.29298	+	1.71979i	−0.297283	+	0.0965932i	−0.453861	−	0.891072i	$-0.649954\pi$
$317$	−5.29298	+	1.71979i	−0.297283	+	0.0965932i	0.156578	+	0.987666i	$0.449954\pi$
$318$	−9.21311	−	13.4998i	−0.516645	−	0.757033i
$319$	−1.58623	+	4.88191i	−0.0888117	+	0.273334i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	21.8641	+	7.82330i	1.22033	+	0.436654i
$322$	2.73774	−	3.76817i	0.152568	−	0.209992i
$323$	−1.28057	+	0.930389i	−0.0712528	+	0.0517682i
$324$	−1.75551	−	8.82713i	−0.0975281	−	0.490396i
$325$	1.04822	+	1.44275i	0.0581447	+	0.0800293i
$326$	−1.97999	−	2.72522i	−0.109661	−	0.150936i
$327$	−16.8974	+	11.5318i	−0.934428	+	0.637711i
$328$	−4.14654	+	3.01264i	−0.228954	+	0.166345i
$329$	−1.98068	+	2.72617i	−0.109198	+	0.150299i
$330$	1.79391	−	5.01350i	0.0987515	−	0.275984i
$331$	14.5433	−	20.0171i	0.799372	−	1.10024i	−0.193506	−	0.981099i	$-0.561986\pi$
$331$	14.5433	−	20.0171i	0.799372	−	1.10024i	0.992877	−	0.119141i	$-0.0380142\pi$
$332$	1.14590	−	3.52672i	0.0628895	−	0.193554i
$333$	1.85690	−	31.4780i	0.101758	−	1.72498i
$334$	−16.0037	+	5.19991i	−0.875682	+	0.284526i
$335$			8.47961i			0.463291i
$336$	−1.88876	−	1.45916i	−0.103040	−	0.0796039i
$337$	17.3501	−	5.63739i	0.945121	−	0.307088i	0.204389	−	0.978890i	$-0.434479\pi$
$337$	17.3501	−	5.63739i	0.945121	−	0.307088i	0.740731	+	0.671801i	$0.234479\pi$
$338$	5.77188	+	7.94432i	0.313949	+	0.432114i
$339$	6.53308	−	1.91189i	0.354828	−	0.103840i
$340$		−	0.796132i		−	0.0431763i
$341$	0.586025	−	17.1068i	0.0317350	−	0.926383i
$342$	−5.77137	+	1.50591i	−0.312080	+	0.0814304i
$343$	−13.4906	−	9.80146i	−0.728421	−	0.529229i
$344$	−0.470564	+	0.341884i	−0.0253711	+	0.0184332i
$345$	5.51223	+	1.97236i	0.296768	+	0.106188i
$346$	9.18533			0.493806
$347$	11.0027			0.590655			0.295327	−	0.955396i	$-0.404571\pi$
$347$	11.0027			0.590655			0.295327	+	0.955396i	$0.404571\pi$
$348$	−0.974318	+	2.72296i	−0.0522289	+	0.145966i
$349$	−5.28661	+	16.2705i	−0.282986	+	0.870941i	0.704009	+	0.710191i	$0.251391\pi$
$349$	−5.28661	+	16.2705i	−0.282986	+	0.870941i	−0.986995	+	0.160750i	$0.948609\pi$
$350$	−1.31054	−	0.425822i	−0.0700516	−	0.0227611i
$351$	4.76372	+	7.94825i	0.254268	+	0.424246i
$352$	2.92380	−	0.950001i	0.155839	−	0.0506352i
$353$	25.4131	+	18.4637i	1.35260	+	0.982724i	0.998877	+	0.0473743i	$0.0150854\pi$
$353$	25.4131	+	18.4637i	1.35260	+	0.982724i	0.353726	+	0.935349i	$0.384915\pi$
$354$	−10.3374	−	0.304641i	−0.549429	−	0.0161915i
$355$	−0.792357	+	2.43862i	−0.0420540	+	0.129429i
$356$	−4.04560	+	2.93930i	−0.214416	+	0.155782i
$357$	−1.89934	−	0.0559729i	−0.100524	−	0.00296240i
$358$	6.21316	+	2.01878i	0.328376	+	0.106696i
$359$	0.724724	+	0.997497i	0.0382495	+	0.0526459i	0.827713	−	0.561151i	$-0.189641\pi$
$359$	0.724724	+	0.997497i	0.0382495	+	0.0526459i	−0.789464	+	0.613797i	$0.789641\pi$
$360$	1.09346	−	2.79363i	0.0576304	−	0.147237i
$361$	−4.64979	−	14.3106i	−0.244726	−	0.753189i
$362$	9.66827	+	7.02441i	0.508153	+	0.369195i
$363$	−2.21590	+	1.51226i	−0.116305	+	0.0793733i
$364$	2.33714	+	0.759383i	0.122499	+	0.0398025i
$365$	−2.68592	−	8.26641i	−0.140587	−	0.432683i
$366$	−13.5196	−	10.4446i	−0.706679	−	0.545947i
$367$		−	1.24868i		−	0.0651808i	−0.999469	−	0.0325904i	$-0.989624\pi$
$367$		−	1.24868i		−	0.0651808i	0.999469	−	0.0325904i	$-0.0103757\pi$
$368$	1.04450	+	3.21465i	0.0544485	+	0.167575i
$369$	−9.75477	+	11.8858i	−0.507813	+	0.618750i
$370$	6.17816	−	8.50350i	0.321187	−	0.442076i
$371$	−13.0030			−0.675082
$372$	0.613930	−	9.62409i	0.0318308	−	0.498986i
$373$	18.5807			0.962070			0.481035	−	0.876701i	$-0.340261\pi$
$373$	18.5807			0.962070			0.481035	+	0.876701i	$0.340261\pi$
$374$	1.43862	−	1.98009i	0.0743891	−	0.102388i
$375$	0.0510207	−	1.73130i	0.00263470	−	0.0894039i
$376$	−0.755671	−	2.32572i	−0.0389707	−	0.119940i
$377$		−	2.97766i		−	0.153357i
$378$	−6.58790	−	2.80509i	−0.338845	−	0.144278i
$379$	11.8858	+	36.5806i	0.610531	+	1.87902i	0.453013	+	0.891504i	$0.350349\pi$
$379$	11.8858	+	36.5806i	0.610531	+	1.87902i	0.157517	+	0.987516i	$0.449651\pi$
$380$	−1.89089	−	0.614388i	−0.0970008	−	0.0315175i
$381$	3.68364	+	5.39759i	0.188719	+	0.276527i
$382$	−14.4220	−	10.4782i	−0.737893	−	0.536111i
$383$	2.06209	+	6.34647i	0.105368	+	0.324290i	0.989817	−	0.142348i	$-0.0454652\pi$
$383$	2.06209	+	6.34647i	0.105368	+	0.324290i	−0.884449	+	0.466638i	$0.845465\pi$
$384$	1.66233	−	0.486477i	0.0848304	−	0.0248254i
$385$	−2.49004	−	3.42724i	−0.126904	−	0.174668i
$386$	−12.9123	−	4.19546i	−0.657219	−	0.213543i
$387$	−1.10701	+	1.34884i	−0.0562722	+	0.0685655i
$388$	−8.27012	+	6.00859i	−0.419852	+	0.305040i
$389$	2.44522	−	7.52562i	0.123978	−	0.381564i	−0.869736	−	0.493518i	$-0.835711\pi$
$389$	2.44522	−	7.52562i	0.123978	−	0.381564i	0.993713	+	0.111954i	$0.0357108\pi$
$390$	−0.0909871	+	3.08749i	−0.00460731	+	0.156341i
$391$	2.17706	+	1.58173i	0.110099	+	0.0799913i
$392$	4.85148	−	1.57634i	0.245037	−	0.0796173i
$393$	23.1736	−	6.78172i	1.16896	−	0.342092i
$394$	−17.6187	−	5.72466i	−0.887617	−	0.288404i
$395$	2.38947	−	7.35404i	0.120227	−	0.370022i
$396$	7.76769	−	4.97223i	0.390341	−	0.249864i
$397$	15.0936			0.757528			0.378764	−	0.925493i	$-0.376349\pi$
$397$	15.0936			0.757528			0.378764	+	0.925493i	$0.376349\pi$
$398$	−4.86498			−0.243859
$399$	−1.59869	+	4.46793i	−0.0800348	+	0.223676i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−13.1814	−	9.57685i	−0.658248	−	0.478245i	0.207823	−	0.978166i	$-0.433362\pi$
$401$	−13.1814	−	9.57685i	−0.658248	−	0.478245i	−0.866071	+	0.499922i	$0.833362\pi$
$402$	−8.97913	+	11.6227i	−0.447838	+	0.579686i
$403$	2.74318	+	9.54273i	0.136648	+	0.475357i
$404$			9.10453i			0.452967i
$405$	1.05815	−	8.93758i	0.0525797	−	0.444112i
$406$	1.35240	+	1.86142i	0.0671186	+	0.0923808i
$407$	30.7318	−	9.98537i	1.52332	−	0.494956i
$408$	0.843031	−	1.09123i	0.0417363	−	0.0540238i
$409$		−	8.65301i		−	0.427864i	−0.976849	−	0.213932i	$-0.931373\pi$
$409$		−	8.65301i		−	0.427864i	0.976849	−	0.213932i	$-0.0686271\pi$
$410$	−4.87455	+	1.58384i	−0.240737	+	0.0782201i
$411$	16.4366	−	11.2174i	0.810759	−	0.553311i
$412$	−0.960637	+	2.95654i	−0.0473272	+	0.145658i
$413$	−4.83621	+	6.65647i	−0.237974	+	0.327544i
$414$	5.46685	+	8.54039i	0.268681	+	0.419737i
$415$	2.17963	−	3.00001i	0.106994	−	0.147265i
$416$	−1.44275	+	1.04822i	−0.0707366	+	0.0513931i
$417$	−4.68570	−	6.86588i	−0.229459	−	0.336224i
$418$	−3.59270	−	4.94492i	−0.175725	−	0.241864i
$419$	15.5127	+	21.3514i	0.757844	+	1.04308i	0.997390	+	0.0721974i	$0.0230012\pi$
$419$	15.5127	+	21.3514i	0.757844	+	1.04308i	−0.239547	+	0.970885i	$0.576999\pi$
$420$	−1.34541	−	1.97140i	−0.0656491	−	0.0961947i
$421$	−12.7423	+	9.25786i	−0.621024	+	0.451200i	−0.853279	−	0.521455i	$-0.825390\pi$
$421$	−12.7423	+	9.25786i	−0.621024	+	0.451200i	0.232255	+	0.972655i	$0.425390\pi$
$422$	−1.28203	+	1.76456i	−0.0624081	+	0.0858974i
$423$	−3.95512	−	6.17875i	−0.192305	−	0.300421i
$424$	5.54647	−	7.63407i	0.269361	−	0.370743i
$425$	0.246018	−	0.757167i	0.0119336	−	0.0367280i
$426$	−3.66833	+	2.50349i	−0.177731	+	0.121295i
$427$	−12.9266	+	4.20011i	−0.625562	+	0.203257i
$428$			13.4070i			0.648050i
$429$	−5.80541	+	7.51458i	−0.280288	+	0.362807i
$430$	−0.553181	+	0.179739i	−0.0266767	+	0.00866780i
$431$	5.99748	+	8.25482i	0.288888	+	0.397621i	0.928653	−	0.370950i	$-0.120968\pi$
$431$	5.99748	+	8.25482i	0.288888	+	0.397621i	−0.639764	+	0.768571i	$0.720968\pi$
$432$	4.45696	−	2.67124i	0.214435	−	0.128520i
$433$		−	14.6161i		−	0.702404i	−0.936300	−	0.351202i	$-0.885773\pi$
$433$		−	14.6161i		−	0.702404i	0.936300	−	0.351202i	$-0.114227\pi$
$434$	−6.04900	−	4.71954i	−0.290361	−	0.226545i
$435$	−1.76807	+	2.28861i	−0.0847726	+	0.109730i
$436$	−9.55536	−	6.94238i	−0.457619	−	0.332480i
$437$	5.43683	−	3.95009i	0.260079	−	0.188958i
$438$	5.07189	−	14.1746i	0.242344	−	0.677288i
$439$	−7.55340			−0.360504			−0.180252	−	0.983620i	$-0.557691\pi$
$439$	−7.55340			−0.360504			−0.180252	+	0.983620i	$0.557691\pi$
$440$	3.07427			0.146560
$441$	12.8890	−	8.25045i	0.613760	−	0.392879i
$442$	−0.438733	+	1.35028i	−0.0208684	+	0.0642264i
$443$	5.11645	+	1.66243i	0.243090	+	0.0789846i	0.428028	−	0.903766i	$-0.359208\pi$
$443$	5.11645	+	1.66243i	0.243090	+	0.0789846i	−0.184938	+	0.982750i	$0.559208\pi$
$444$	17.4726	−	5.11332i	0.829213	−	0.242667i
$445$	−4.75588	+	1.54528i	−0.225450	+	0.0732533i
$446$	0.373949	+	0.271690i	0.0177070	+	0.0128649i
$447$	−0.421959	+	14.3184i	−0.0199580	+	0.677239i
$448$	0.425822	−	1.31054i	0.0201182	−	0.0619174i
$449$	11.4823	−	8.34241i	0.541885	−	0.393703i	−0.282899	−	0.959150i	$-0.591296\pi$
$449$	11.4823	−	8.34241i	0.541885	−	0.393703i	0.824785	+	0.565447i	$0.191296\pi$
$450$	1.90322	−	2.31900i	0.0897187	−	0.109319i
$451$	−14.9857	−	4.86914i	−0.705647	−	0.229279i
$452$	2.31004	+	3.17950i	0.108655	+	0.149551i
$453$	−7.94147	+	2.32406i	−0.373123	+	0.109194i
$454$	−4.01965	−	12.3712i	−0.188651	−	0.580609i
$455$	1.98809	+	1.44443i	0.0932031	+	0.0677160i
$456$	−1.94119	−	2.84440i	−0.0909047	−	0.133201i
$457$	−1.07525	−	0.349369i	−0.0502980	−	0.0163428i	0.283760	−	0.958895i	$-0.408418\pi$
$457$	−1.07525	−	0.349369i	−0.0502980	−	0.0163428i	−0.334058	+	0.942553i	$0.608418\pi$
$458$	−6.86334	−	21.1232i	−0.320703	−	0.987021i
$459$	1.62064	−	3.80616i	0.0756449	−	0.177656i
$460$			3.38008i			0.157597i
$461$	1.18139	+	3.63594i	0.0550227	+	0.169342i	0.974791	−	0.223119i	$-0.0716238\pi$
$461$	1.18139	+	3.63594i	0.0550227	+	0.169342i	−0.919769	+	0.392461i	$0.871624\pi$
$462$	0.216139	−	7.33431i	0.0100557	−	0.341223i
$463$	−1.64334	+	2.26187i	−0.0763727	+	0.105118i	−0.845494	−	0.533985i	$-0.820694\pi$
$463$	−1.64334	+	2.26187i	−0.0763727	+	0.105118i	0.769122	+	0.639103i	$0.220694\pi$
$464$	−1.66971			−0.0775145
$465$	3.55789	−	8.96334i	0.164993	−	0.415665i
$466$	−10.8314			−0.501757
$467$	18.0364	−	24.8250i	0.834625	−	1.14876i	−0.152420	−	0.988316i	$-0.548707\pi$
$467$	18.0364	−	24.8250i	0.834625	−	1.14876i	0.987044	−	0.160447i	$-0.0512935\pi$
$468$	−3.39408	+	4.13555i	−0.156891	+	0.191166i
$469$	3.61080	+	11.1129i	0.166731	+	0.513146i
$470$		−	2.44540i		−	0.112798i
$471$	28.1693	+	21.7623i	1.29797	+	1.00275i
$472$	−1.84511	−	5.67868i	−0.0849283	−	0.261382i
$473$	−1.70062	−	0.552566i	−0.0781948	−	0.0254070i
$474$	11.0624	−	7.54966i	0.508113	−	0.346767i
$475$	−1.60849	−	1.16864i	−0.0738026	−	0.0536207i
$476$	−0.339010	−	1.04337i	−0.0155385	−	0.0478226i
$477$	10.3181	−	26.3613i	0.472435	−	1.20700i
$478$	15.0170	+	20.6692i	0.686863	+	0.945386i
$479$	−32.2693	−	10.4849i	−1.47442	−	0.479068i	−0.541979	−	0.840392i	$-0.682325\pi$
$479$	−32.2693	−	10.4849i	−1.47442	−	0.479068i	−0.932440	+	0.361324i	$0.882325\pi$
$480$	1.73130	+	0.0510207i	0.0790226	+	0.00232877i
$481$	−15.1646	+	11.0177i	−0.691446	+	0.502365i
$482$	−2.31864	+	7.13604i	−0.105611	+	0.325038i
$483$	8.06390	+	0.237640i	0.366920	+	0.0108130i
$484$	−1.25308	−	0.910413i	−0.0569580	−	0.0413824i
$485$	−9.72211	+	3.15890i	−0.441458	+	0.143438i
$486$	10.9144	−	11.1299i	0.495089	−	0.504863i
$487$	18.9689	+	6.16336i	0.859561	+	0.279288i	0.705445	−	0.708764i	$-0.250747\pi$
$487$	18.9689	+	6.16336i	0.859561	+	0.279288i	0.154116	+	0.988053i	$0.450747\pi$
$488$	3.04800	−	9.38077i	0.137976	−	0.424648i
$489$	1.96564	−	5.49344i	0.0888892	−	0.248422i
$490$	5.10115			0.230446
$491$	14.9764			0.675876			0.337938	−	0.941168i	$-0.390271\pi$
$491$	14.9764			0.675876			0.337938	+	0.941168i	$0.390271\pi$
$492$	−8.35849	−	2.99080i	−0.376830	−	0.134836i
$493$	−1.07544	+	0.781350i	−0.0484352	+	0.0351902i
$494$	2.86848	+	2.08407i	0.129059	+	0.0937667i
$495$	8.92401	−	2.32852i	0.401105	−	0.104659i
$496$	5.35106	−	1.53823i	0.240270	−	0.0690687i
$497$			3.53333i			0.158492i
$498$	6.16427	−	1.80396i	0.276228	−	0.0808374i
$499$	−19.8730	−	27.3528i	−0.889636	−	1.22448i	−0.973658	−	0.228014i	$-0.926777\pi$
$499$	−19.8730	−	27.3528i	−0.889636	−	1.22448i	0.0840221	−	0.996464i	$-0.473223\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−23.0645	−	17.8185i	−1.03044	−	0.796073i
$502$		−	11.9463i		−	0.533190i
$503$	7.37054	−	2.39483i	0.328636	−	0.106780i	−0.140052	−	0.990144i	$-0.544727\pi$
$503$	7.37054	−	2.39483i	0.328636	−	0.106780i	0.468688	+	0.883364i	$0.344727\pi$
$504$	0.243441	−	4.12679i	0.0108437	−	0.183822i
$505$	−2.81345	+	8.65892i	−0.125197	+	0.385317i
$506$	−6.10784	+	8.40672i	−0.271526	+	0.373724i
$507$	−5.73004	+	16.0140i	−0.254480	+	0.711205i
$508$	−2.21763	+	3.05230i	−0.0983912	+	0.135424i
$509$	2.21290	−	1.60777i	0.0980851	−	0.0712630i	−0.537662	−	0.843161i	$-0.680692\pi$
$509$	2.21290	−	1.60777i	0.0980851	−	0.0712630i	0.635747	+	0.771898i	$0.280692\pi$
$510$	1.13898	−	0.777308i	0.0504348	−	0.0344198i
$511$	−7.04003	−	9.68977i	−0.311433	−	0.428650i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−7.78933	−	6.78645i	−0.343907	−	0.299629i
$514$	8.90062	−	6.46668i	0.392589	−	0.285233i
$515$	−1.82724	+	2.51498i	−0.0805178	+	0.110823i
$516$	−0.948551	−	0.339406i	−0.0417576	−	0.0149415i
$517$	4.41886	−	6.08204i	0.194341	−	0.267488i
$518$	4.47577	−	13.7750i	0.196654	−	0.605240i
$519$	8.96815	+	13.1409i	0.393658	+	0.576821i
$520$	−1.69605	+	0.551081i	−0.0743768	+	0.0241665i
$521$		−	40.5197i		−	1.77520i	−0.460614	−	0.887601i	$-0.652371\pi$
$521$		−	40.5197i		−	1.77520i	0.460614	−	0.887601i	$-0.347629\pi$
$522$	−4.84686	+	1.26468i	−0.212141	+	0.0553536i
$523$	9.17992	−	2.98274i	0.401410	−	0.130426i	−0.101353	−	0.994851i	$-0.532317\pi$
$523$	9.17992	−	2.98274i	0.401410	−	0.130426i	0.502763	+	0.864425i	$0.332317\pi$
$524$	8.19400	+	11.2781i	0.357956	+	0.492685i
$525$	−0.670360	−	2.29067i	−0.0292569	−	0.0999731i
$526$			26.1642i			1.14081i
$527$	2.72671	−	3.49481i	0.118777	−	0.152236i
$528$	4.21378	+	3.25537i	0.183381	+	0.141672i
$529$	9.36441	+	6.80364i	0.407148	+	0.295810i
$530$	7.63407	−	5.54647i	0.331603	−	0.240923i
$531$	−9.65719	−	15.0866i	−0.419086	−	0.654702i
$532$	−2.73972			−0.118782
$533$	9.14031			0.395911
$534$	−8.15502	−	2.91799i	−0.352902	−	0.126274i
$535$	−4.14298	+	12.7508i	−0.179117	+	0.551265i
$536$	−8.06459	−	2.62034i	−0.348337	−	0.113182i
$537$	3.17811	+	10.8598i	0.137146	+	0.468637i
$538$	−9.51656	+	3.09212i	−0.410288	+	0.133311i
$539$	12.6872	+	9.21782i	0.546478	+	0.397040i
$540$	5.06428	−	1.16322i	0.217932	−	0.0500572i
$541$	−8.70690	+	26.7971i	−0.374339	+	1.15210i	0.569585	+	0.821933i	$0.307104\pi$
$541$	−8.70690	+	26.7971i	−0.374339	+	1.15210i	−0.943924	+	0.330164i	$0.892896\pi$
$542$	−6.90603	+	5.01752i	−0.296639	+	0.215521i
$543$	−0.609731	+	20.6901i	−0.0261661	+	0.887899i
$544$	0.757167	+	0.246018i	0.0324633	+	0.0105480i
$545$	−6.94238	−	9.55536i	−0.297379	−	0.409307i
$546$	1.19548	+	4.08503i	0.0511617	+	0.174823i
$547$	−5.74425	−	17.6790i	−0.245606	−	0.755899i	−0.995536	−	0.0943814i	$-0.969913\pi$
$547$	−5.74425	−	17.6790i	−0.245606	−	0.755899i	0.749930	−	0.661518i	$-0.230087\pi$
$548$	9.29480	+	6.75307i	0.397054	+	0.288477i
$549$	1.74253	−	29.5392i	0.0743695	−	1.26070i
$550$	2.92380	+	0.950001i	0.124671	+	0.0405082i
$551$	1.02585	+	3.15725i	0.0437028	+	0.134503i
$552$	−3.57920	+	4.63295i	−0.152341	+	0.197191i
$553$		−	10.6553i		−	0.453109i
$554$	−2.18936	−	6.73816i	−0.0930170	−	0.286277i
$555$	18.1975	+	0.536275i	0.772442	+	0.0227636i
$556$	2.82088	−	3.88261i	0.119632	−	0.164659i
$557$	−33.7523			−1.43013			−0.715065	−	0.699058i	$-0.753603\pi$
$557$	−33.7523			−1.43013			−0.715065	+	0.699058i	$0.753603\pi$
$558$	14.3680	−	8.51822i	0.608247	−	0.360605i
$559$	1.03727			0.0438720
$560$	0.809961	−	1.11482i	0.0342271	−	0.0471096i
$561$	4.23739	+	0.124874i	0.178903	+	0.00527220i
$562$	8.05102	+	24.7785i	0.339612	+	1.04522i
$563$		−	30.5756i		−	1.28861i	−0.764770	−	0.644304i	$-0.777147\pi$
$563$		−	30.5756i		−	1.28861i	0.764770	−	0.644304i	$-0.222853\pi$
$564$	2.58946	−	3.35182i	0.109036	−	0.141137i
$565$	1.21446	+	3.73772i	0.0510927	+	0.157247i
$566$	3.84360	+	1.24886i	0.161559	+	0.0524936i
$567$	−2.41907	−	12.1637i	−0.101591	−	0.510827i
$568$	−2.07442	−	1.50715i	−0.0870407	−	0.0632387i
$569$	10.2899	+	31.6692i	0.431377	+	1.32764i	0.896754	+	0.442529i	$0.145919\pi$
$569$	10.2899	+	31.6692i	0.431377	+	1.32764i	−0.465378	+	0.885112i	$0.654081\pi$
$570$	−0.967215	−	3.30505i	−0.0405122	−	0.138433i
$571$	−5.50932	−	7.58293i	−0.230558	−	0.317336i	0.678026	−	0.735038i	$-0.262836\pi$
$571$	−5.50932	−	7.58293i	−0.230558	−	0.317336i	−0.908584	+	0.417702i	$0.862836\pi$
$572$	−5.21412	−	1.69417i	−0.218013	−	0.0708368i
$573$	0.909525	−	30.8631i	0.0379959	−	1.28933i
$574$	−5.71388	+	4.15138i	−0.238493	+	0.173275i
$575$	−1.04450	+	3.21465i	−0.0435588	+	0.134060i
$576$	2.31900	+	1.90322i	0.0966249	+	0.0793008i
$577$	20.4088	+	14.8278i	0.849628	+	0.617291i	0.925044	−	0.379861i	$-0.124028\pi$
$577$	20.4088	+	14.8278i	0.849628	+	0.617291i	−0.0754152	+	0.997152i	$0.524028\pi$
$578$	−15.5652	+	5.05743i	−0.647425	+	0.210361i
$579$	−6.60480	−	22.5691i	−0.274486	−	0.937940i
$580$	−1.58799	−	0.515970i	−0.0659377	−	0.0214245i
$581$	1.57904	−	4.85978i	0.0655095	−	0.201618i
$582$	−16.6707	−	5.96504i	−0.691023	−	0.247259i
$583$	29.0095			1.20145
$584$	8.69181			0.359670
$585$	−4.50592	+	2.88431i	−0.186297	+	0.119252i
$586$	2.47656	−	1.79933i	0.102306	−	0.0743295i
$587$	27.1813	+	19.7484i	1.12189	+	0.815102i	0.984495	−	0.175414i	$-0.0561263\pi$
$587$	27.1813	+	19.7484i	1.12189	+	0.815102i	0.137397	+	0.990516i	$0.456126\pi$
$588$	6.99195	+	5.40165i	0.288343	+	0.222760i
$589$	−6.19626	−	9.17321i	−0.255312	−	0.377975i
$590$		−	5.97091i		−	0.245819i
$591$	−9.01218	−	30.7953i	−0.370711	−	1.26675i
$592$	6.17816	+	8.50350i	0.253921	+	0.349492i
$593$	−3.77070	+	1.22518i	−0.154844	+	0.0503120i	−0.385414	−	0.922744i	$-0.625941\pi$
$593$	−3.77070	+	1.22518i	−0.154844	+	0.0503120i	0.230569	+	0.973056i	$0.425941\pi$
$594$	14.6975	+	6.25810i	0.603045	+	0.256773i
$595$		−	1.09706i		−	0.0449751i
$596$	−7.86556	+	2.55568i	−0.322186	+	0.104685i
$597$	−4.74995	−	6.96003i	−0.194402	−	0.284855i
$598$	1.86270	−	5.73280i	0.0761714	−	0.234431i
$599$	−0.529129	+	0.728283i	−0.0216196	+	0.0297568i	−0.819690	−	0.572807i	$-0.805854\pi$
$599$	−0.529129	+	0.728283i	−0.0216196	+	0.0297568i	0.798070	+	0.602564i	$0.205854\pi$
$600$	1.63080	+	0.583524i	0.0665770	+	0.0238223i
$601$	−23.1776	+	31.9013i	−0.945436	+	1.30128i	0.00808915	+	0.999967i	$0.497425\pi$
$601$	−23.1776	+	31.9013i	−0.945436	+	1.30128i	−0.953525	+	0.301314i	$0.902575\pi$
$602$	−0.648431	+	0.471113i	−0.0264281	+	0.0192011i
$603$	−25.3947	−	1.49804i	−1.03415	−	0.0610051i
$604$	−2.80804	−	3.86493i	−0.114257	−	0.157262i
$605$	−0.910413	−	1.25308i	−0.0370135	−	0.0509448i
$606$	−13.0253	+	8.88925i	−0.529117	+	0.361101i
$607$	−38.6135	+	28.0543i	−1.56727	+	1.13869i	−0.637560	+	0.770400i	$0.720056\pi$
$607$	−38.6135	+	28.0543i	−1.56727	+	1.13869i	−0.929711	+	0.368289i	$0.879944\pi$
$608$	1.16864	−	1.60849i	0.0473944	−	0.0652329i
$609$	−1.34260	+	3.75221i	−0.0544049	+	0.152047i
$610$	5.79764	−	7.97976i	0.234739	−	0.323091i
$611$	−1.34761	+	4.14753i	−0.0545186	+	0.167791i
$612$	2.38425	+	0.140648i	0.0963777	+	0.00568537i
$613$	−39.4610	+	12.8216i	−1.59381	+	0.517861i	−0.965567	−	0.260154i	$-0.916227\pi$
$613$	−39.4610	+	12.8216i	−1.59381	+	0.517861i	−0.628246	+	0.778015i	$0.716227\pi$
$614$		−	21.6836i		−	0.875077i
$615$	−7.02519	−	5.42733i	−0.283283	−	0.218851i
$616$	4.02896	−	1.30909i	0.162332	−	0.0527447i
$617$	9.33979	+	12.8551i	0.376006	+	0.517527i	0.954521	−	0.298144i	$-0.0963677\pi$
$617$	9.33979	+	12.8551i	0.376006	+	0.517527i	−0.578515	+	0.815672i	$0.696368\pi$
$618$	−5.16766	+	1.51231i	−0.207874	+	0.0608338i
$619$		−	3.35933i		−	0.135023i	−0.997719	−	0.0675114i	$-0.978494\pi$
$619$		−	3.35933i		−	0.135023i	0.997719	−	0.0675114i	$-0.0215059\pi$
$620$	5.56450	+	0.190623i	0.223476	+	0.00765559i
$621$	−6.88063	+	16.1595i	−0.276110	+	0.648460i
$622$	22.0890	+	16.0486i	0.885688	+	0.643490i
$623$	−5.57478	+	4.05032i	−0.223349	+	0.162273i
$624$	−2.90826	−	1.04062i	−0.116423	−	0.0416581i
$625$	1.00000			0.0400000
$626$	−31.3819			−1.25427
$627$	3.56666	−	9.96786i	0.142438	−	0.398078i
$628$	−6.35079	+	19.5457i	−0.253424	+	0.779960i
$629$	7.95851	+	2.58588i	0.317327	+	0.103106i
$630$	1.50678	−	3.84958i	0.0600314	−	0.153371i
$631$	10.1237	−	3.28938i	0.403017	−	0.130948i	−0.100493	−	0.994938i	$-0.532042\pi$
$631$	10.1237	−	3.28938i	0.403017	−	0.130948i	0.503509	+	0.863990i	$0.332042\pi$
$632$	6.25572	+	4.54505i	0.248839	+	0.180792i
$633$	−3.77616	−	0.111282i	−0.150089	−	0.00442307i
$634$	1.71979	−	5.29298i	0.0683017	−	0.210211i
$635$	−3.05230	+	2.21763i	−0.121127	+	0.0880038i
$636$	16.3369	+	0.481443i	0.647801	+	0.0190905i
$637$	−8.65181	−	2.81114i	−0.342797	−	0.111382i
$638$	−3.01718	−	4.15280i	−0.119451	−	0.164411i
$639$	−7.16320	−	2.80376i	−0.283372	−	0.110915i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−22.8726	−	16.6179i	−0.903415	−	0.656369i	0.0359262	−	0.999354i	$-0.488562\pi$
$641$	−22.8726	−	16.6179i	−0.903415	−	0.656369i	−0.939341	+	0.342985i	$0.888562\pi$
$642$	−19.1805	+	13.0900i	−0.756996	+	0.516620i
$643$	−32.6612	−	10.6123i	−1.28803	−	0.418507i	−0.416631	−	0.909076i	$-0.636789\pi$
$643$	−32.6612	−	10.6123i	−1.28803	−	0.418507i	−0.871403	+	0.490568i	$0.836789\pi$
$644$	1.43931	+	4.42975i	0.0567169	+	0.174557i
$645$	−0.797243	−	0.615913i	−0.0313914	−	0.0242515i
$646$		−	1.58287i		−	0.0622773i
$647$	−9.26124	−	28.5032i	−0.364097	−	1.12058i	−0.950545	−	0.310588i	$-0.899474\pi$
$647$	−9.26124	−	28.5032i	−0.364097	−	1.12058i	0.586448	−	0.809987i	$-0.300526\pi$
$648$	8.17316	+	3.76822i	0.321072	+	0.148030i
$649$	10.7895	−	14.8505i	0.423525	−	0.582932i
$650$	−1.78333			−0.0699482
$651$	0.845988	−	13.2619i	0.0331569	−	0.519774i
$652$	3.36856			0.131923
$653$	−5.28772	+	7.27792i	−0.206924	+	0.284807i	−0.899848	−	0.436204i	$-0.856322\pi$
$653$	−5.28772	+	7.27792i	−0.206924	+	0.284807i	0.692923	+	0.721011i	$0.256322\pi$
$654$	0.602610	−	20.4485i	0.0235639	−	0.799600i
$655$	4.30784	+	13.2582i	0.168321	+	0.518039i
$656$		−	5.12540i		−	0.200113i
$657$	25.2307	−	6.58339i	0.984343	−	0.256843i
$658$	−1.04131	−	3.20481i	−0.0405943	−	0.124936i
$659$	−21.2396	−	6.90118i	−0.827379	−	0.268832i	−0.135438	−	0.990786i	$-0.543244\pi$
$659$	−21.2396	−	6.90118i	−0.827379	−	0.268832i	−0.691941	+	0.721954i	$0.743244\pi$
$660$	3.00158	+	4.39817i	0.116836	+	0.171198i
$661$	−23.3908	−	16.9944i	−0.909797	−	0.661007i	0.0311662	−	0.999514i	$-0.490078\pi$
$661$	−23.3908	−	16.9944i	−0.909797	−	0.661007i	−0.940964	+	0.338508i	$0.890078\pi$
$662$	7.64586	+	23.5315i	0.297165	+	0.914579i
$663$	−2.36013	+	0.690686i	−0.0916597	+	0.0268240i
$664$	2.17963	+	3.00001i	0.0845862	+	0.116423i
$665$	−2.60563	−	0.846620i	−0.101042	−	0.0328305i
$666$	24.3748	+	20.0046i	0.944504	+	0.775162i
$667$	4.56590	−	3.31732i	0.176792	−	0.128447i
$668$	5.19991	−	16.0037i	0.201190	−	0.619200i
$669$	−0.0235831	+	0.800252i	−0.000911777	+	0.0309395i
$670$	−6.86015	−	4.98419i	−0.265031	−	0.192556i
$671$	28.8390	−	9.37036i	1.11332	−	0.361739i
$672$	2.29067	−	0.670360i	0.0883645	−	0.0258597i
$673$	16.1258	+	5.23958i	0.621602	+	0.201971i	0.602852	−	0.797853i	$-0.294031\pi$
$673$	16.1258	+	5.23958i	0.621602	+	0.201971i	0.0187507	+	0.999824i	$0.494031\pi$
$674$	−5.63739	+	17.3501i	−0.217144	+	0.668301i
$675$	5.17587	+	0.458655i	0.199219	+	0.0176537i
$676$	−9.81972			−0.377681
$677$	42.7674			1.64368			0.821842	−	0.569715i	$-0.192946\pi$
$677$	42.7674			1.64368			0.821842	+	0.569715i	$0.192946\pi$
$678$	−2.29330	+	6.40916i	−0.0880735	+	0.246142i
$679$	−11.3961	+	8.27977i	−0.437343	+	0.317748i
$680$	0.644084	+	0.467955i	0.0246995	+	0.0179452i
$681$	13.7741	−	17.8294i	0.527826	−	0.683222i
$682$	13.4952	+	10.5292i	0.516758	+	0.403184i
$683$			29.8904i			1.14372i	0.820350	+	0.571862i	$0.193779\pi$
$683$			29.8904i			1.14372i	−0.820350	+	0.571862i	$0.806221\pi$
$684$	2.17402	−	5.55429i	0.0831257	−	0.212374i
$685$	6.75307	+	9.29480i	0.258021	+	0.355136i
$686$	15.8591	−	5.15293i	0.605503	−	0.196740i
$687$	23.5186	−	30.4427i	0.897291	−	1.16146i
$688$		−	0.581649i		−	0.0221751i
$689$	−16.0043	+	5.20012i	−0.609716	+	0.198109i
$690$	−4.83568	+	3.30016i	−0.184091	+	0.125635i
$691$	−0.790515	+	2.43295i	−0.0300726	+	0.0925539i	−0.964966	−	0.262374i	$-0.915495\pi$
$691$	−0.790515	+	2.43295i	−0.0300726	+	0.0925539i	0.934894	+	0.354928i	$0.115495\pi$
$692$	−5.39900	+	7.43109i	−0.205239	+	0.282488i
$693$	10.7038	−	6.85167i	0.406603	−	0.260274i
$694$	−6.46721	+	8.90135i	−0.245492	+	0.337891i
$695$	3.88261	−	2.82088i	0.147276	−	0.107002i
$696$	−1.63023	−	2.38876i	−0.0617938	−	0.0905456i
$697$	−2.39846	−	3.30119i	−0.0908480	−	0.125042i
$698$	−10.0557	−	13.8405i	−0.380615	−	0.523872i
$699$	−10.5753	−	15.4959i	−0.399996	−	0.586109i
$700$	1.11482	−	0.809961i	0.0421361	−	0.0306137i
$701$	−23.7547	+	32.6955i	−0.897202	+	1.23489i	0.0741501	+	0.997247i	$0.476376\pi$
$701$	−23.7547	+	32.6955i	−0.897202	+	1.23489i	−0.971352	+	0.237645i	$0.923624\pi$
$702$	−9.23031	−	0.817936i	−0.348376	−	0.0308710i
$703$	12.2834	−	16.9067i	0.463278	−	0.637648i
$704$	−0.950001	+	2.92380i	−0.0358045	+	0.110195i
$705$	3.49849	−	2.38758i	0.131761	−	0.0899215i
$706$	−29.8749	+	9.70694i	−1.12436	+	0.365326i
$707$			12.5459i			0.471838i
$708$	6.32265	−	8.18410i	0.237620	−	0.307577i
$709$	43.7910	−	14.2285i	1.64460	−	0.534364i	0.667043	−	0.745019i	$-0.267560\pi$
$709$	43.7910	−	14.2285i	1.64460	−	0.534364i	0.977561	+	0.210655i	$0.0675596\pi$
$710$	−1.50715	−	2.07442i	−0.0565624	−	0.0778515i
$711$	21.6017	+	8.45517i	0.810127	+	0.317094i
$712$		−	5.00063i		−	0.187407i
$713$	−11.5766	+	14.8376i	−0.433547	+	0.555674i
$714$	1.16169	−	1.50370i	0.0434751	−	0.0562745i
$715$	−4.43539	−	3.22250i	−0.165874	−	0.120515i
$716$	−5.28523	+	3.83994i	−0.197518	+	0.143505i
$717$	−14.9082	+	41.6644i	−0.556756	+	1.55599i
$718$	−1.23297			−0.0460142
$719$	−26.1457			−0.975069			−0.487534	−	0.873104i	$-0.662104\pi$
$719$	−26.1457			−0.975069			−0.487534	+	0.873104i	$0.662104\pi$
$720$	1.61737	+	2.52668i	0.0602759	+	0.0941638i
$721$	−1.32375	+	4.07407i	−0.0492989	+	0.151726i
$722$	14.3106	+	4.64979i	0.532585	+	0.173047i
$723$	−12.4729	+	3.65017i	−0.463873	+	0.135751i
$724$	−11.3657	+	3.69295i	−0.422404	+	0.137247i
$725$	−1.35083	−	0.981432i	−0.0501684	−	0.0364495i
$726$	0.0790254	−	2.68159i	0.00293291	−	0.0995230i
$727$	−14.8650	+	45.7497i	−0.551311	+	1.69676i	0.154180	+	0.988043i	$0.450726\pi$
$727$	−14.8650	+	45.7497i	−0.551311	+	1.69676i	−0.705492	+	0.708718i	$0.749274\pi$
$728$	−1.98809	+	1.44443i	−0.0736835	+	0.0535342i
$729$	26.5793	+	4.74788i	0.984417	+	0.175848i
$730$	8.26641	+	2.68592i	0.305953	+	0.0994103i
$731$	−0.272185	−	0.374631i	−0.0100671	−	0.0138562i
$732$	16.3964	−	4.79838i	0.606030	−	0.177353i
$733$	−7.25432	−	22.3265i	−0.267944	−	0.824648i	−0.991000	−	0.133859i	$-0.957263\pi$
$733$	−7.25432	−	22.3265i	−0.267944	−	0.824648i	0.723056	−	0.690789i	$-0.242737\pi$
$734$	1.01021	+	0.733959i	0.0372874	+	0.0270909i
$735$	4.98053	+	7.29790i	0.183710	+	0.269187i
$736$	−3.21465	−	1.04450i	−0.118494	−	0.0385009i
$737$	−8.05563	−	24.7927i	−0.296733	−	0.913251i
$738$	−3.88211	−	14.8781i	−0.142902	−	0.547669i
$739$		−	15.5874i		−	0.573390i	−0.958022	−	0.286695i	$-0.907443\pi$
$739$		−	15.5874i		−	0.573390i	0.958022	−	0.286695i	$-0.0925567\pi$
$740$	3.24805	+	9.99647i	0.119401	+	0.367478i
$741$	−0.180901	+	6.13855i	−0.00664555	+	0.225505i
$742$	7.64298	−	10.5197i	0.280582	−	0.386189i
$743$	−23.7509			−0.871336			−0.435668	−	0.900107i	$-0.643488\pi$
$743$	−23.7509			−0.871336			−0.435668	+	0.900107i	$0.643488\pi$
$744$	7.42519	+	6.15358i	0.272221	+	0.225601i
$745$	−8.27034			−0.303002
$746$	−10.9214	+	15.0321i	−0.399862	+	0.550363i
$747$	8.59934	+	7.05754i	0.314633	+	0.258222i
$748$	0.756326	+	2.32773i	0.0276540	+	0.0851103i
$749$			18.4747i			0.675049i
$750$	1.37066	+	1.05891i	0.0500495	+	0.0386659i
$751$	6.60119	+	20.3164i	0.240881	+	0.741355i	0.996287	+	0.0860976i	$0.0274397\pi$
$751$	6.60119	+	20.3164i	0.240881	+	0.741355i	−0.755406	+	0.655257i	$0.772560\pi$
$752$	2.32572	+	0.755671i	0.0848101	+	0.0275565i
$753$	17.0909	−	11.6638i	0.622825	−	0.425054i
$754$	2.40897	+	1.75022i	0.0877297	+	0.0637394i
$755$	−1.47627	−	4.54350i	−0.0537270	−	0.165355i
$756$	6.14164	−	3.68094i	0.223369	−	0.133874i
$757$	3.42630	+	4.71590i	0.124531	+	0.171402i	0.866730	−	0.498777i	$-0.166217\pi$
$757$	3.42630	+	4.71590i	0.124531	+	0.171402i	−0.742199	+	0.670179i	$0.766217\pi$
$758$	−36.5806	−	11.8858i	−1.32867	−	0.431710i
$759$	−17.9904	−	0.530171i	−0.653010	−	0.0192440i
$760$	1.60849	−	1.16864i	0.0583460	−	0.0423909i
$761$	2.94919	−	9.07668i	0.106908	−	0.329029i	−0.883265	−	0.468873i	$-0.844660\pi$
$761$	2.94919	−	9.07668i	0.106908	−	0.329029i	0.990174	+	0.139844i	$0.0446601\pi$
$762$	−6.53193	−	0.192494i	−0.236627	−	0.00697331i
$763$	−13.1672	−	9.56652i	−0.476684	−	0.346331i
$764$	16.9541	−	5.50871i	0.613377	−	0.199298i
$765$	2.22410	+	0.870539i	0.0804123	+	0.0314744i
$766$	−6.34647	−	2.06209i	−0.229307	−	0.0745065i
$767$	−3.29046	+	10.1270i	−0.118812	+	0.365664i
$768$	−0.583524	+	1.63080i	−0.0210561	+	0.0588463i
$769$	43.4262			1.56599			0.782995	−	0.622028i	$-0.213691\pi$
$769$	43.4262			1.56599			0.782995	+	0.622028i	$0.213691\pi$
$770$	4.23630			0.152666
$771$	17.9416	+	6.41980i	0.646153	+	0.231203i
$772$	10.9839	−	7.98024i	0.395318	−	0.287215i
$773$	−33.6253	−	24.4302i	−1.20942	−	0.878694i	−0.214241	−	0.976781i	$-0.568728\pi$
$773$	−33.6253	−	24.4302i	−1.20942	−	0.878694i	−0.995178	+	0.0980864i	$0.968728\pi$
$774$	−0.440555	−	1.68842i	−0.0158354	−	0.0606888i
$775$	5.23325	+	1.90082i	0.187984	+	0.0682794i
$776$		−	10.2224i		−	0.366964i
$777$	24.0770	−	7.04609i	0.863759	−	0.252777i
$778$	4.65109	+	6.40168i	0.166750	+	0.229511i
$779$	−9.69159	+	3.14899i	−0.347237	+	0.112824i
$780$	−2.44435	−	1.88839i	−0.0875217	−	0.0676152i
$781$		−	7.88279i		−	0.282069i
$782$	−2.55929	+	0.831562i	−0.0915199	+	0.0297366i
$783$	−6.54156	−	5.69933i	−0.233776	−	0.203677i
$784$	−1.57634	+	4.85148i	−0.0562979	+	0.173267i
$785$	−12.0799	+	16.6266i	−0.431151	+	0.593428i
$786$	−8.13460	+	22.7341i	−0.290152	+	0.810897i
$787$	16.8632	−	23.2102i	0.601107	−	0.827353i	−0.394702	−	0.918809i	$-0.629152\pi$
$787$	16.8632	−	23.2102i	0.601107	−	0.827353i	0.995809	+	0.0914561i	$0.0291521\pi$
$788$	14.9874	−	10.8889i	0.533902	−	0.387903i
$789$	−37.4315	+	25.5455i	−1.33260	+	0.909446i
$790$	4.54505	+	6.25572i	0.161705	+	0.222568i
$791$	3.18321	+	4.38131i	0.113182	+	0.155782i
$792$	−0.543113	+	9.20679i	−0.0192987	+	0.327149i
$793$	−14.2306	+	10.3391i	−0.505343	+	0.367153i
$794$	−8.87181	+	12.2110i	−0.314849	+	0.433352i
$795$	15.3886	+	5.50627i	0.545776	+	0.195287i
$796$	2.85956	−	3.93585i	0.101354	−	0.139502i
$797$	−7.94949	+	24.4660i	−0.281585	+	0.866630i	0.705816	+	0.708395i	$0.250580\pi$
$797$	−7.94949	+	24.4660i	−0.281585	+	0.866630i	−0.987401	+	0.158235i	$0.949420\pi$
$798$	−2.67494	−	3.91955i	−0.0946919	−	0.138751i
$799$	1.85158	−	0.601614i	0.0655041	−	0.0212836i
$800$			1.00000i			0.0353553i
$801$	−3.78760	−	14.5159i	−0.133828	−	0.512894i
$802$	15.4957	−	5.03485i	0.547171	−	0.177787i
$803$	15.7062	+	21.6177i	0.554259	+	0.762872i
$804$	−4.12514	−	14.0959i	−0.145482	−	0.497124i
$805$			4.65771i			0.164163i
$806$	−9.33264	−	3.38980i	−0.328728	−	0.119400i
$807$	−13.7153	−	10.5958i	−0.482800	−	0.372989i
$808$	−7.36572	−	5.35151i	−0.259125	−	0.188265i
$809$	−31.0113	+	22.5310i	−1.09030	+	0.792149i	−0.979450	−	0.201688i	$-0.935357\pi$
$809$	−31.0113	+	22.5310i	−1.09030	+	0.792149i	−0.110850	+	0.993837i	$0.535357\pi$
$810$	6.60869	+	6.10944i	0.232206	+	0.214664i
$811$	23.0512			0.809436			0.404718	−	0.914441i	$-0.367370\pi$
$811$	23.0512			0.809436			0.404718	+	0.914441i	$0.367370\pi$
$812$	−2.30084			−0.0807438
$813$	−13.9210	−	4.98115i	−0.488231	−	0.174697i
$814$	−9.98537	+	30.7318i	−0.349987	+	1.07715i
$815$	3.20369	+	1.04094i	0.112220	+	0.0364626i
$816$	0.387300	+	1.32343i	0.0135582	+	0.0463295i
$817$	−1.09984	+	0.357358i	−0.0384784	+	0.0125024i
$818$	7.00043	+	5.08611i	0.244764	+	0.177832i
$819$	−4.67700	+	5.69874i	−0.163428	+	0.199130i
$820$	1.58384	−	4.87455i	0.0553100	−	0.170227i
$821$	8.67769	−	6.30471i	0.302853	−	0.220036i	−0.425971	−	0.904737i	$-0.640067\pi$
$821$	8.67769	−	6.30471i	0.302853	−	0.220036i	0.728824	+	0.684701i	$0.240067\pi$
$822$	−0.586178	+	19.8909i	−0.0204453	+	0.693775i
$823$	−2.72175	−	0.884351i	−0.0948743	−	0.0308265i	0.261195	−	0.965286i	$-0.415883\pi$
$823$	−2.72175	−	0.884351i	−0.0948743	−	0.0308265i	−0.356070	+	0.934459i	$0.615883\pi$
$824$	−1.82724	−	2.51498i	−0.0636549	−	0.0876135i
$825$	1.49556	+	5.11044i	0.0520687	+	0.177923i
$826$	−2.54255	−	7.82515i	−0.0884665	−	0.272272i
$827$	16.8696	+	12.2565i	0.586612	+	0.426199i	0.841102	−	0.540877i	$-0.181907\pi$
$827$	16.8696	+	12.2565i	0.586612	+	0.426199i	−0.254489	+	0.967076i	$0.581907\pi$
$828$	−10.1226	−	0.597140i	−0.351786	−	0.0207521i
$829$	20.6849	+	6.72092i	0.718415	+	0.233427i	0.645336	−	0.763899i	$-0.276717\pi$
$829$	20.6849	+	6.72092i	0.718415	+	0.233427i	0.0730792	+	0.997326i	$0.476717\pi$
$830$	1.14590	+	3.52672i	0.0397748	+	0.122414i
$831$	7.50228	−	9.71102i	0.260251	−	0.336872i
$832$		−	1.78333i		−	0.0618260i
$833$	1.25498	+	3.86242i	0.0434823	+	0.133825i
$834$	8.30880	+	0.244857i	0.287710	+	0.00847871i
$835$	9.89081	−	13.6135i	0.342286	−	0.471116i
$836$	6.11226			0.211397
$837$	26.2148	+	12.2386i	0.906116	+	0.423030i
$838$	−26.3917			−0.911687
$839$	−13.2000	+	18.1683i	−0.455716	+	0.627239i	−0.973613	−	0.228204i	$-0.926715\pi$
$839$	−13.2000	+	18.1683i	−0.455716	+	0.627239i	0.517898	+	0.855443i	$0.326715\pi$
$840$	2.38571	+	0.0703060i	0.0823148	+	0.00242579i
$841$	−8.09997	−	24.9292i	−0.279309	−	0.859626i
$842$		−	15.7504i		−	0.542795i
$843$	−27.5884	+	35.7107i	−0.950196	+	1.22994i
$844$	−0.674001	−	2.07436i	−0.0232001	−	0.0714025i
$845$	−9.33911	−	3.03446i	−0.321275	−	0.104389i
$846$	7.32347	+	0.432015i	0.251786	+	0.0148530i
$847$	−1.72672	−	1.25454i	−0.0593309	−	0.0431064i
$848$	2.91595	+	8.97438i	0.100134	+	0.308182i
$849$	1.96605	+	6.71814i	0.0674747	+	0.230566i
$850$	0.467955	+	0.644084i	0.0160507	+	0.0220919i
$851$	−33.7889	−	10.9787i	−1.15827	−	0.376344i
$852$	0.130823	−	4.43926i	0.00448194	−	0.152087i
$853$	−23.3990	+	17.0004i	−0.801167	+	0.582082i	−0.911256	−	0.411840i	$-0.864886\pi$
$853$	−23.3990	+	17.0004i	−0.801167	+	0.582082i	0.110089	+	0.993922i	$0.464886\pi$
$854$	4.20011	−	12.9266i	0.143725	−	0.442339i
$855$	3.78399	−	4.61064i	0.129410	−	0.157680i
$856$	−10.8465	−	7.88042i	−0.370725	−	0.269347i
$857$	12.2065	−	3.96614i	0.416967	−	0.135481i	−0.0930174	−	0.995664i	$-0.529651\pi$
$857$	12.2065	−	3.96614i	0.416967	−	0.135481i	0.509984	+	0.860184i	$0.329651\pi$
$858$	−2.66709	−	9.11363i	−0.0910528	−	0.311134i
$859$	−40.4062	−	13.1288i	−1.37864	−	0.447948i	−0.476420	−	0.879218i	$-0.658066\pi$
$859$	−40.4062	−	13.1288i	−1.37864	−	0.447948i	−0.902223	+	0.431270i	$0.858066\pi$
$860$	0.179739	−	0.553181i	0.00612906	−	0.0188633i
$861$	−11.5179	−	4.12128i	−0.392529	−	0.140453i
$862$	−10.2035			−0.347533
$863$	6.96289			0.237020			0.118510	−	0.992953i	$-0.462188\pi$
$863$	6.96289			0.237020			0.118510	+	0.992953i	$0.462188\pi$
$864$	−0.458655	+	5.17587i	−0.0156038	+	0.176087i
$865$	−7.43109	+	5.39900i	−0.252665	+	0.183572i
$866$	11.8247	+	8.59112i	0.401818	+	0.291938i
$867$	−22.4325	−	17.3303i	−0.761847	−	0.588567i
$868$	7.37370	−	2.11967i	0.250280	−	0.0719462i
$869$			23.7717i			0.806401i
$870$	−0.812277	−	2.77561i	−0.0275388	−	0.0941021i
$871$	8.88848	+	12.2339i	0.301175	+	0.414531i
$872$	11.2330	−	3.64982i	0.380397	−	0.123599i
$873$	−7.74272	−	29.6738i	−0.262051	−	1.00430i
$874$			6.72029i			0.227317i
$875$	1.31054	−	0.425822i	0.0443045	−	0.0143954i
$876$	8.48630	+	12.4349i	0.286725	+	0.420135i
$877$	−6.41386	+	19.7398i	−0.216581	+	0.666567i	0.782457	+	0.622705i	$0.213966\pi$
$877$	−6.41386	+	19.7398i	−0.216581	+	0.666567i	−0.999038	+	0.0438621i	$0.986034\pi$
$878$	4.43978	−	6.11083i	0.149835	−	0.206230i
$879$	4.99219	+	1.78628i	0.168382	+	0.0602499i
$880$	−1.80701	+	2.48713i	−0.0609142	+	0.0838413i
$881$	−46.1009	+	33.4943i	−1.55318	+	1.12845i	−0.611844	+	0.790978i	$0.709572\pi$
$881$	−46.1009	+	33.4943i	−1.55318	+	1.12845i	−0.941335	+	0.337473i	$0.890428\pi$
$882$	−0.901191	+	15.2769i	−0.0303447	+	0.514400i
$883$	−3.01648	−	4.15182i	−0.101512	−	0.139720i	0.755239	−	0.655450i	$-0.227521\pi$
$883$	−3.01648	−	4.15182i	−0.101512	−	0.139720i	−0.856751	+	0.515730i	$0.827521\pi$
$884$	−0.834520	−	1.14862i	−0.0280679	−	0.0386322i
$885$	8.54223	−	5.82974i	0.287144	−	0.195964i
$886$	−4.35231	+	3.16214i	−0.146219	+	0.106234i
$887$	27.6522	−	38.0600i	0.928470	−	1.27793i	−0.0319827	−	0.999488i	$-0.510182\pi$
$887$	27.6522	−	38.0600i	0.928470	−	1.27793i	0.960453	−	0.278442i	$-0.0898179\pi$
$888$	−6.13337	+	17.1412i	−0.205823	+	0.575220i
$889$	−3.05586	+	4.20603i	−0.102490	+	0.141066i
$890$	1.54528	−	4.75588i	0.0517979	−	0.159418i
$891$	5.39689	+	27.1369i	0.180803	+	0.909122i
$892$	−0.439604	+	0.142836i	−0.0147190	+	0.00478250i
$893$		−	4.86195i		−	0.162699i
$894$	−11.3358	−	8.75753i	−0.379127	−	0.292896i
$895$	−6.21316	+	2.01878i	−0.207683	+	0.0674803i
$896$	0.809961	+	1.11482i	0.0270589	+	0.0372434i
$897$	10.0202	−	2.93240i	0.334565	−	0.0979099i
$898$			14.1930i			0.473625i
$899$	−5.20368	−	7.70375i	−0.173553	−	0.256935i
$900$	0.757424	+	2.90281i	0.0252475	+	0.0967603i
$901$	6.07773	+	4.41573i	0.202478	+	0.147109i
$902$	12.7476	−	9.26165i	0.424447	−	0.308379i
$903$	−1.30709	−	0.467698i	−0.0434973	−	0.0155640i
$904$	−3.93008			−0.130712
$905$	−11.9506			−0.397253
$906$	2.78768	−	7.79083i	0.0926145	−	0.258833i
$907$	−14.4252	+	44.3962i	−0.478981	+	1.47415i	0.361531	+	0.932360i	$0.382254\pi$
$907$	−14.4252	+	44.3962i	−0.478981	+	1.47415i	−0.840512	+	0.541792i	$0.817746\pi$
$908$	12.3712	+	4.01965i	0.410553	+	0.133397i
$909$	−25.4346	−	9.95544i	−0.843614	−	0.330201i
$910$	−2.33714	+	0.759383i	−0.0774755	+	0.0251733i
$911$	2.17792	+	1.58235i	0.0721578	+	0.0524257i	0.623279	−	0.781999i	$-0.285800\pi$
$911$	2.17792	+	1.58235i	0.0721578	+	0.0524257i	−0.551122	+	0.834425i	$0.685800\pi$
$912$	3.44217	+	0.101440i	0.113982	+	0.00335900i
$913$	−3.52280	+	10.8421i	−0.116588	+	0.358820i
$914$	0.914661	−	0.664540i	0.0302543	−	0.0219810i
$915$	17.0767	+	0.503245i	0.564539	+	0.0166368i
$916$	21.1232	+	6.86334i	0.697929	+	0.226771i
$917$	11.2912	+	15.5411i	0.372869	+	0.513211i
$918$	2.12666	+	3.54833i	0.0701903	+	0.117112i
$919$	0.511688	+	1.57481i	0.0168790	+	0.0519483i	0.959141	−	0.282928i	$-0.0913056\pi$
$919$	0.511688	+	1.57481i	0.0168790	+	0.0519483i	−0.942262	+	0.334876i	$0.891306\pi$
$920$	−2.73454	−	1.98676i	−0.0901552	−	0.0655016i
$921$	31.0214	−	21.1709i	1.02219	−	0.697603i
$922$	−3.63594	−	1.18139i	−0.119743	−	0.0389069i
$923$	1.41304	+	4.34888i	0.0465107	+	0.143145i
$924$	5.80654	+	4.48586i	0.191021	+	0.147574i
$925$			10.5109i			0.345597i
$926$	−0.863958	−	2.65899i	−0.0283914	−	0.0873798i
$927$	−7.20904	−	5.91651i	−0.236776	−	0.194324i
$928$	0.981432	−	1.35083i	0.0322171	−	0.0443430i
$929$	−15.9104			−0.522004			−0.261002	−	0.965338i	$-0.584053\pi$
$929$	−15.9104			−0.522004			−0.261002	+	0.965338i	$0.584053\pi$
$930$	5.16022	+	8.14691i	0.169210	+	0.267148i
$931$	10.1421			0.332394
$932$	6.36656	−	8.76282i	0.208544	−	0.287036i
$933$	−1.39304	+	47.2705i	−0.0456062	+	1.54757i
$934$	9.48229	+	29.1835i	0.310270	+	0.954913i
$935$			2.44752i			0.0800425i
$936$	−1.35074	−	5.17668i	−0.0441504	−	0.169205i
$937$	13.4804	+	41.4885i	0.440387	+	1.35537i	0.887465	+	0.460876i	$0.152465\pi$
$937$	13.4804	+	41.4885i	0.440387	+	1.35537i	−0.447078	+	0.894495i	$0.647535\pi$
$938$	−11.1129	−	3.61080i	−0.362849	−	0.117897i
$939$	−30.6399	−	44.8962i	−0.999895	−	1.46513i
$940$	1.97837	+	1.43737i	0.0645274	+	0.0468819i
$941$	4.66871	+	14.3688i	0.152196	+	0.468410i	0.997866	−	0.0652958i	$-0.0207991\pi$
$941$	4.66871	+	14.3688i	0.152196	+	0.468410i	−0.845670	+	0.533706i	$0.820799\pi$
$942$	−34.1635	+	9.99788i	−1.11311	+	0.325749i
$943$	10.1830	+	14.0156i	0.331603	+	0.456412i
$944$	5.67868	+	1.84511i	0.184825	+	0.0600534i
$945$	6.97852	−	1.60291i	0.227011	−	0.0521427i
$946$	1.44664	−	1.05104i	0.0470343	−	0.0341724i
$947$	−9.04194	+	27.8282i	−0.293824	+	0.904296i	0.689790	+	0.724009i	$0.257703\pi$
$947$	−9.04194	+	27.8282i	−0.293824	+	0.904296i	−0.983614	+	0.180287i	$0.942297\pi$
$948$	−0.394518	+	13.3873i	−0.0128133	+	0.434798i
$949$	−12.5401	−	9.11092i	−0.407069	−	0.295753i
$950$	1.89089	−	0.614388i	0.0613487	−	0.0199334i
$951$	9.25147	−	2.70742i	0.300000	−	0.0877942i
$952$	1.04337	+	0.339010i	0.0338157	+	0.0109874i
$953$	−16.3298	+	50.2580i	−0.528974	+	1.62802i	0.227346	+	0.973814i	$0.426995\pi$
$953$	−16.3298	+	50.2580i	−0.528974	+	1.62802i	−0.756320	+	0.654202i	$0.773005\pi$
$954$	15.2619	+	23.8423i	0.494121	+	0.771923i
$955$	17.8266			0.576854
$956$	−25.5485			−0.826298
$957$	2.99531	−	8.37111i	0.0968247	−	0.270600i
$958$	27.4499	−	19.9435i	0.886865	−	0.644345i
$959$	12.8081	+	9.30565i	0.413596	+	0.300495i
$960$	−1.05891	+	1.37066i	−0.0341761	+	0.0442379i
$961$	23.7738	+	19.8949i	0.766896	+	0.641771i
$962$		−	18.7445i		−	0.604346i
$963$	−37.4541	−	14.6600i	−1.20694	−	0.472411i
$964$	−4.41031	−	6.07027i	−0.142047	−	0.195510i
$965$	12.9123	−	4.19546i	0.415661	−	0.135057i
$966$	−4.93209	+	6.38415i	−0.158688	+	0.205407i
$967$		−	24.4953i		−	0.787716i	−0.919171	−	0.393858i	$-0.871140\pi$
$967$		−	24.4953i		−	0.787716i	0.919171	−	0.393858i	$-0.128860\pi$
$968$	1.47308	−	0.478632i	0.0473465	−	0.0153838i
$969$	2.26452	−	1.54545i	0.0727468	−	0.0496469i
$970$	3.15890	−	9.72211i	0.101426	−	0.312158i
$971$	−9.04396	+	12.4479i	−0.290234	+	0.399473i	−0.929090	−	0.369853i	$-0.879408\pi$
$971$	−9.04396	+	12.4479i	−0.290234	+	0.399473i	0.638856	+	0.769326i	$0.279408\pi$
$972$	2.58894	+	15.3720i	0.0830403	+	0.493056i
$973$	3.88714	−	5.35019i	0.124616	−	0.171519i
$974$	−16.1359	+	11.7234i	−0.517027	+	0.375642i
$975$	−1.74117	−	2.55131i	−0.0557620	−	0.0817073i
$976$	5.79764	+	7.97976i	0.185578	+	0.255426i
$977$	5.04768	+	6.94754i	0.161490	+	0.222271i	0.882092	−	0.471077i	$-0.156135\pi$
$977$	5.04768	+	6.94754i	0.161490	+	0.222271i	−0.720602	+	0.693349i	$0.756135\pi$
$978$	3.28891	+	4.81919i	0.105168	+	0.154101i
$979$	12.4372	−	9.03618i	0.397496	−	0.288798i
$980$	−2.99838	+	4.12692i	−0.0957797	+	0.131829i
$981$	29.8428	−	19.1029i	0.952808	−	0.609909i
$982$	−8.80291	+	12.1162i	−0.280912	+	0.386642i
$983$	17.4361	−	53.6629i	0.556126	−	1.71158i	−0.136824	−	0.990595i	$-0.543689\pi$
$983$	17.4361	−	53.6629i	0.556126	−	1.71158i	0.692950	−	0.720986i	$-0.256311\pi$
$984$	7.33260	−	5.00422i	0.233755	−	0.159529i
$985$	17.6187	−	5.72466i	0.561378	−	0.182403i
$986$		−	1.32931i		−	0.0423339i
$987$	3.56824	−	4.61877i	0.113578	−	0.147017i
$988$	−3.37210	+	1.09566i	−0.107281	+	0.0348576i
$989$	1.15560	+	1.59054i	0.0367459	+	0.0505763i
$990$	−3.36159	+	8.58835i	−0.106838	+	0.272956i
$991$			40.1345i			1.27491i	0.770486	+	0.637457i	$0.220014\pi$
$991$			40.1345i			1.27491i	−0.770486	+	0.637457i	$0.779986\pi$
$992$	−1.90082	+	5.23325i	−0.0603510	+	0.166156i
$993$	−26.2001	+	33.9136i	−0.831434	+	1.07622i
$994$	−2.85852	−	2.07684i	−0.0906669	−	0.0658733i
$995$	3.93585	−	2.85956i	0.124775	−	0.0906542i
$996$	−2.16383	+	6.04734i	−0.0685637	+	0.191617i
$997$	−24.4026			−0.772837			−0.386419	−	0.922323i	$-0.626288\pi$
$997$	−24.4026			−0.772837			−0.386419	+	0.922323i	$0.626288\pi$
$998$	33.8099			1.07023
$999$	−4.82089	+	54.4031i	−0.152526	+	1.72124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.401.1	✓	80
3.2	odd	2	inner	930.2.v.a.401.17	yes	80
31.15	odd	10	inner	930.2.v.a.821.17	yes	80
93.77	even	10	inner	930.2.v.a.821.1	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.1	✓	80	1.1	even	1	trivial
930.2.v.a.401.17	yes	80	3.2	odd	2	inner
930.2.v.a.821.1	yes	80	93.77	even	10	inner
930.2.v.a.821.17	yes	80	31.15	odd	10	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.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.73130 - 0.0510207i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.05891 - 1.37066i) q^{6} +(-0.425822 - 1.31054i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.99479 + 0.176664i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-1.73130 - 0.0510207i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.05891 - 1.37066i) q^{6} +(-0.425822 - 1.31054i) q^{7} +(0.951057 + 0.309017i) q^{8} +(2.99479 + 0.176664i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.950001 + 2.92380i) q^{11} +(0.486477 + 1.66233i) q^{12} +(-1.04822 - 1.44275i) q^{13} +(1.31054 + 0.425822i) q^{14} +(-0.0510207 + 1.73130i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.246018 + 0.757167i) q^{17} +(-1.90322 + 2.31900i) q^{18} +(1.60849 + 1.16864i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(0.670360 + 2.29067i) q^{21} +(-2.92380 - 0.950001i) q^{22} +(1.04450 - 3.21465i) q^{23} +(-1.63080 - 0.583524i) q^{24} -1.00000 q^{25} +1.78333 q^{26} +(-5.17587 - 0.458655i) q^{27} +(-1.11482 + 0.809961i) q^{28} +(1.35083 + 0.981432i) q^{29} +(-1.37066 - 1.05891i) q^{30} +(-5.23325 - 1.90082i) q^{31} -1.00000i q^{32} +(-1.49556 - 5.11044i) q^{33} +(-0.467955 - 0.644084i) q^{34} +(-1.31054 + 0.425822i) q^{35} +(-0.757424 - 2.90281i) q^{36} -10.5109i q^{37} +(-1.89089 + 0.614388i) q^{38} +(1.74117 + 2.55131i) q^{39} +(0.309017 - 0.951057i) q^{40} +(-3.01264 + 4.14654i) q^{41} +(-2.24722 - 0.804090i) q^{42} +(-0.341884 + 0.470564i) q^{43} +(2.48713 - 1.80701i) q^{44} +(0.176664 - 2.99479i) q^{45} +(1.98676 + 2.73454i) q^{46} +(-1.43737 - 1.97837i) q^{47} +(1.43064 - 0.976355i) q^{48} +(4.12692 - 2.99838i) q^{49} +(0.587785 - 0.809017i) q^{50} +(0.464563 - 1.29833i) q^{51} +(-1.04822 + 1.44275i) q^{52} +(2.91595 - 8.97438i) q^{53} +(3.41336 - 3.91778i) q^{54} +(2.92380 - 0.950001i) q^{55} -1.37799i q^{56} +(-2.72515 - 2.10532i) q^{57} +(-1.58799 + 0.515970i) q^{58} +(-3.50962 - 4.83057i) q^{59} +(1.66233 - 0.486477i) q^{60} -9.86353i q^{61} +(4.61382 - 3.11651i) q^{62} +(-1.04372 - 4.00004i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-1.44275 + 1.04822i) q^{65} +(5.01350 + 1.79391i) q^{66} -8.47961 q^{67} +0.796132 q^{68} +(-1.97236 + 5.51223i) q^{69} +(0.425822 - 1.31054i) q^{70} +(-2.43862 - 0.792357i) q^{71} +(2.79363 + 1.09346i) q^{72} +(8.26641 - 2.68592i) q^{73} +(8.50350 + 6.17816i) q^{74} +(1.73130 + 0.0510207i) q^{75} +(0.614388 - 1.89089i) q^{76} +(3.42724 - 2.49004i) q^{77} +(-3.08749 - 0.0909871i) q^{78} +(7.35404 + 2.38947i) q^{79} +(0.587785 + 0.809017i) q^{80} +(8.93758 + 1.05815i) q^{81} +(-1.58384 - 4.87455i) q^{82} +(3.00001 + 2.17963i) q^{83} +(1.97140 - 1.34541i) q^{84} +(0.757167 + 0.246018i) q^{85} +(-0.179739 - 0.553181i) q^{86} +(-2.28861 - 1.76807i) q^{87} +3.07427i q^{88} +(-1.54528 - 4.75588i) q^{89} +(2.31900 + 1.90322i) q^{90} +(-1.44443 + 1.98809i) q^{91} -3.38008 q^{92} +(8.96334 + 3.55789i) q^{93} +2.44540 q^{94} +(1.16864 - 1.60849i) q^{95} +(-0.0510207 + 1.73130i) q^{96} +(-3.15890 - 9.72211i) q^{97} +5.10115i q^{98} +(2.32852 + 8.92401i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more