LMFDB - Embedded newform 550.2.h.j.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [550,2,Mod(201,550)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(550, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("550.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.h (of order $5$, 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.20164000000.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 6x^{6} + 76x^{4} + 781x^{2} + 5041 $ x^8 + 6x^6 + 76x^4 + 781*x^2 + 5041
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 110)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.2
Root			$-0.839592 + 2.58400i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.j.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{6} +(1.54947 + 4.76878i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{6} +(1.54947 + 4.76878i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +(-0.969425 - 3.17178i) q^{11} -1.61803 q^{12} +(1.88906 + 1.37249i) q^{13} +(1.54947 - 4.76878i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.0494717 - 0.0359433i) q^{17} +(-0.118034 - 0.363271i) q^{18} +(-0.636930 + 1.96027i) q^{19} -8.11314 q^{21} +(-1.08005 + 3.13584i) q^{22} -3.91525 q^{23} +(1.30902 + 0.951057i) q^{24} +(-0.721558 - 2.22073i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-4.05657 + 2.94727i) q^{28} +(-1.27844 - 3.93464i) q^{29} +(7.18170 + 5.21781i) q^{31} +1.00000 q^{32} +(5.36559 + 0.0941007i) q^{33} -0.0611504 q^{34} +(-0.118034 + 0.363271i) q^{36} +(-1.40815 - 4.33385i) q^{37} +(1.66751 - 1.21151i) q^{38} +(-3.05657 + 2.22073i) q^{39} +(-1.41525 + 4.35570i) q^{41} +(6.56367 + 4.76878i) q^{42} -3.61803 q^{43} +(2.71698 - 1.90211i) q^{44} +(3.16751 + 2.30133i) q^{46} +(-2.74317 + 8.44260i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-14.6773 + 10.6637i) q^{49} +(0.0305752 + 0.0941007i) q^{51} +(-0.721558 + 2.22073i) q^{52} +(1.79753 + 1.30598i) q^{53} +5.47214 q^{54} +5.01420 q^{56} +(-2.69808 - 1.96027i) q^{57} +(-1.27844 + 3.93464i) q^{58} +(0.599137 + 1.84396i) q^{59} +(7.84211 - 5.69763i) q^{61} +(-2.74317 - 8.44260i) q^{62} +(-0.591846 + 1.82151i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.28554 - 3.22994i) q^{66} -2.49573 q^{67} +(0.0494717 + 0.0359433i) q^{68} +(1.95763 - 6.02495i) q^{69} +(-7.13254 + 5.18210i) q^{71} +(0.309017 - 0.224514i) q^{72} +(-1.66751 - 5.13205i) q^{73} +(-1.40815 + 4.33385i) q^{74} -2.06115 q^{76} +(13.6235 - 9.53757i) q^{77} +3.77813 q^{78} +(5.38417 + 3.91183i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(3.70518 - 2.69197i) q^{82} +(8.94125 - 6.49620i) q^{83} +(-2.50710 - 7.71605i) q^{84} +(2.92705 + 2.12663i) q^{86} +6.69401 q^{87} +(-3.31611 - 0.0581575i) q^{88} +6.09017 q^{89} +(-3.61803 + 11.1352i) q^{91} +(-1.20988 - 3.72363i) q^{92} +(-11.6202 + 8.44260i) q^{93} +(7.18170 - 5.21781i) q^{94} +(-0.500000 + 1.53884i) q^{96} +(-5.90765 - 4.29216i) q^{97} +18.1422 q^{98} +(0.412541 - 1.19778i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	$ 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{11} - 4 q^{12} + 2 q^{13} + 6 q^{14} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} - 22 q^{27} - 4 q^{28} - 8 q^{29} - 2 q^{31} + 8 q^{32} + 10 q^{33} + 4 q^{34} + 8 q^{36} - 2 q^{37} - 2 q^{38} + 4 q^{39} + 20 q^{41} + 2 q^{42} - 20 q^{43} + 10 q^{46} + 18 q^{47} - 4 q^{48} - 42 q^{49} - 2 q^{51} - 8 q^{52} + 16 q^{53} + 8 q^{54} - 4 q^{56} - 4 q^{57} - 8 q^{58} + 10 q^{61} + 18 q^{62} - 14 q^{63} - 2 q^{64} - 10 q^{66} - 20 q^{67} - 6 q^{68} - 28 q^{71} - 2 q^{72} + 2 q^{73} - 2 q^{74} - 12 q^{76} + 24 q^{77} + 4 q^{78} - 18 q^{79} - 28 q^{81} - 10 q^{82} + 14 q^{83} + 2 q^{84} + 10 q^{86} + 44 q^{87} + 4 q^{89} - 20 q^{91} - 10 q^{92} - 14 q^{93} - 2 q^{94} - 4 q^{96} - 6 q^{97} + 48 q^{98} + 10 q^{99}+O(q^{100}) $ 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^11 - 4 * q^12 + 2 * q^13 + 6 * q^14 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 8 * q^19 - 8 * q^21 + 6 * q^24 - 8 * q^26 - 22 * q^27 - 4 * q^28 - 8 * q^29 - 2 * q^31 + 8 * q^32 + 10 * q^33 + 4 * q^34 + 8 * q^36 - 2 * q^37 - 2 * q^38 + 4 * q^39 + 20 * q^41 + 2 * q^42 - 20 * q^43 + 10 * q^46 + 18 * q^47 - 4 * q^48 - 42 * q^49 - 2 * q^51 - 8 * q^52 + 16 * q^53 + 8 * q^54 - 4 * q^56 - 4 * q^57 - 8 * q^58 + 10 * q^61 + 18 * q^62 - 14 * q^63 - 2 * q^64 - 10 * q^66 - 20 * q^67 - 6 * q^68 - 28 * q^71 - 2 * q^72 + 2 * q^73 - 2 * q^74 - 12 * q^76 + 24 * q^77 + 4 * q^78 - 18 * q^79 - 28 * q^81 - 10 * q^82 + 14 * q^83 + 2 * q^84 + 10 * q^86 + 44 * q^87 + 4 * q^89 - 20 * q^91 - 10 * q^92 - 14 * q^93 - 2 * q^94 - 4 * q^96 - 6 * q^97 + 48 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	0.696598	+	0.717462i	$0.254696\pi$
$3$	−0.500000	+	1.53884i	−0.288675	+	0.888451i	−0.985273	+	0.170989i	$0.945304\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$		0			0
$5$		0			0
$6$	1.30902	−	0.951057i	0.534404	−	0.388267i
$7$	1.54947	+	4.76878i	0.585645	+	1.80243i	0.596664	+	0.802491i	$0.296493\pi$
$7$	1.54947	+	4.76878i	0.585645	+	1.80243i	−0.0110184	+	0.999939i	$0.503507\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.309017	+	0.224514i	0.103006	+	0.0748380i
$10$		0			0
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$11$	−0.969425	−	3.17178i	−0.292293	−	0.956329i
$12$	−1.61803			−0.467086
$13$	1.88906	+	1.37249i	0.523932	+	0.380659i	0.818083	−	0.575100i	$-0.195037\pi$
$13$	1.88906	+	1.37249i	0.523932	+	0.380659i	−0.294151	+	0.955759i	$0.595037\pi$
$14$	1.54947	−	4.76878i	0.414114	−	1.27451i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.0494717	−	0.0359433i	0.0119986	−	0.00871753i	−0.581770	−	0.813354i	$-0.697640\pi$
$17$	0.0494717	−	0.0359433i	0.0119986	−	0.00871753i	0.593768	+	0.804636i	$0.297640\pi$
$18$	−0.118034	−	0.363271i	−0.0278209	−	0.0856239i
$19$	−0.636930	+	1.96027i	−0.146122	+	0.449717i	−0.997154	−	0.0753974i	$-0.975977\pi$
$19$	−0.636930	+	1.96027i	−0.146122	+	0.449717i	0.851032	+	0.525114i	$0.175977\pi$
$20$		0			0
$21$	−8.11314			−1.77043
$22$	−1.08005	+	3.13584i	−0.230267	+	0.668564i
$23$	−3.91525			−0.816387			−0.408193	−	0.912896i	$-0.633841\pi$
$23$	−3.91525			−0.816387			−0.408193	+	0.912896i	$0.633841\pi$
$24$	1.30902	+	0.951057i	0.267202	+	0.194134i
$25$		0			0
$26$	−0.721558	−	2.22073i	−0.141509	−	0.435521i
$27$	−4.42705	+	3.21644i	−0.851986	+	0.619004i
$28$	−4.05657	+	2.94727i	−0.766620	+	0.556982i
$29$	−1.27844	−	3.93464i	−0.237401	−	0.730644i	−0.996794	−	0.0800122i	$-0.974504\pi$
$29$	−1.27844	−	3.93464i	−0.237401	−	0.730644i	0.759393	−	0.650632i	$-0.225496\pi$
$30$		0			0
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.999803	−	0.0198592i	$-0.00632179\pi$
$31$	7.18170	+	5.21781i	1.28987	+	0.937147i	0.290069	+	0.957006i	$0.406322\pi$
$32$	1.00000			0.176777
$33$	5.36559	+	0.0941007i	0.934029	+	0.0163808i
$34$	−0.0611504			−0.0104872
$35$		0			0
$36$	−0.118034	+	0.363271i	−0.0196723	+	0.0605452i
$37$	−1.40815	−	4.33385i	−0.231499	−	0.712481i	−0.997567	−	0.0697209i	$-0.977789\pi$
$37$	−1.40815	−	4.33385i	−0.231499	−	0.712481i	0.766067	−	0.642760i	$-0.222211\pi$
$38$	1.66751	−	1.21151i	0.270505	−	0.196533i
$39$	−3.05657	+	2.22073i	−0.489443	+	0.355601i
$40$		0			0
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	0.777646	+	0.628703i	$0.216414\pi$
$41$	−1.41525	+	4.35570i	−0.221025	+	0.680246i	−0.998671	+	0.0515429i	$0.983586\pi$
$42$	6.56367	+	4.76878i	1.01280	+	0.735839i
$43$	−3.61803			−0.551745			−0.275873	−	0.961194i	$-0.588967\pi$
$43$	−3.61803			−0.551745			−0.275873	+	0.961194i	$0.588967\pi$
$44$	2.71698	−	1.90211i	0.409600	−	0.286754i
$45$		0			0
$46$	3.16751	+	2.30133i	0.467023	+	0.339312i
$47$	−2.74317	+	8.44260i	−0.400132	+	1.23148i	0.524760	+	0.851250i	$0.324155\pi$
$47$	−2.74317	+	8.44260i	−0.400132	+	1.23148i	−0.924892	+	0.380229i	$0.875845\pi$
$48$	−0.500000	−	1.53884i	−0.0721688	−	0.222113i
$49$	−14.6773	+	10.6637i	−2.09676	+	1.52338i
$50$		0			0
$51$	0.0305752	+	0.0941007i	0.00428138	+	0.0131767i
$52$	−0.721558	+	2.22073i	−0.100062	+	0.307960i
$53$	1.79753	+	1.30598i	0.246910	+	0.179391i	0.704356	−	0.709847i	$-0.251236\pi$
$53$	1.79753	+	1.30598i	0.246910	+	0.179391i	−0.457446	+	0.889237i	$0.651236\pi$
$54$	5.47214			0.744663
$55$		0			0
$56$	5.01420			0.670050
$57$	−2.69808	−	1.96027i	−0.357370	−	0.259644i
$58$	−1.27844	+	3.93464i	−0.167868	+	0.516643i
$59$	0.599137	+	1.84396i	0.0780011	+	0.240063i	0.982452	−	0.186515i	$-0.0597192\pi$
$59$	0.599137	+	1.84396i	0.0780011	+	0.240063i	−0.904451	+	0.426577i	$0.859719\pi$
$60$		0			0
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.0411202	−	0.999154i	$-0.486907\pi$
$61$	7.84211	−	5.69763i	1.00408	−	0.729506i	0.962959	+	0.269648i	$0.0869073\pi$
$62$	−2.74317	−	8.44260i	−0.348382	−	1.07221i
$63$	−0.591846	+	1.82151i	−0.0745655	+	0.229489i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$		0			0
$66$	−4.28554	−	3.22994i	−0.527513	−	0.397578i
$67$	−2.49573			−0.304902			−0.152451	−	0.988311i	$-0.548717\pi$
$67$	−2.49573			−0.304902			−0.152451	+	0.988311i	$0.548717\pi$
$68$	0.0494717	+	0.0359433i	0.00599932	+	0.00435876i
$69$	1.95763	−	6.02495i	0.235670	−	0.725319i
$70$		0			0
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	−0.924172	−	0.381975i	$-0.875244\pi$
$71$	−7.13254	+	5.18210i	−0.846477	+	0.615002i	0.0776953	+	0.996977i	$0.475244\pi$
$72$	0.309017	−	0.224514i	0.0364180	−	0.0264592i
$73$	−1.66751	−	5.13205i	−0.195167	−	0.600662i	−0.999975	−	0.00712611i	$-0.997732\pi$
$73$	−1.66751	−	5.13205i	−0.195167	−	0.600662i	0.804808	−	0.593535i	$-0.202268\pi$
$74$	−1.40815	+	4.33385i	−0.163695	+	0.503800i
$75$		0			0
$76$	−2.06115			−0.236430
$77$	13.6235	−	9.53757i	1.55254	−	1.08691i
$78$	3.77813			0.427789
$79$	5.38417	+	3.91183i	0.605766	+	0.440115i	0.847921	−	0.530123i	$-0.177854\pi$
$79$	5.38417	+	3.91183i	0.605766	+	0.440115i	−0.242155	+	0.970238i	$0.577854\pi$
$80$		0			0
$81$	−2.38197	−	7.33094i	−0.264663	−	0.814549i
$82$	3.70518	−	2.69197i	0.409169	−	0.297278i
$83$	8.94125	−	6.49620i	0.981429	−	0.713050i	0.0234017	−	0.999726i	$-0.492550\pi$
$83$	8.94125	−	6.49620i	0.981429	−	0.713050i	0.958028	+	0.286676i	$0.0925503\pi$
$84$	−2.50710	−	7.71605i	−0.273547	−	0.841890i
$85$		0			0
$86$	2.92705	+	2.12663i	0.315632	+	0.229320i
$87$	6.69401			0.717673
$88$	−3.31611	−	0.0581575i	−0.353499	−	0.00619961i
$89$	6.09017			0.645557			0.322778	−	0.946475i	$-0.395383\pi$
$89$	6.09017			0.645557			0.322778	+	0.946475i	$0.395383\pi$
$90$		0			0
$91$	−3.61803	+	11.1352i	−0.379273	+	1.16728i
$92$	−1.20988	−	3.72363i	−0.126139	−	0.388215i
$93$	−11.6202	+	8.44260i	−1.20496	+	0.875456i
$94$	7.18170	−	5.21781i	0.740736	−	0.538176i
$95$		0			0
$96$	−0.500000	+	1.53884i	−0.0510310	+	0.157057i
$97$	−5.90765	−	4.29216i	−0.599831	−	0.435802i	0.245988	−	0.969273i	$-0.420888\pi$
$97$	−5.90765	−	4.29216i	−0.599831	−	0.435802i	−0.845819	+	0.533470i	$0.820888\pi$
$98$	18.1422			1.83263
$99$	0.412541	−	1.19778i	0.0414620	−	0.120382i
$100$		0			0
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	0.596680	−	0.802479i	$-0.296486\pi$
$101$	0.179498	+	0.130413i	0.0178608	+	0.0129766i	−0.578819	+	0.815456i	$0.696486\pi$
$102$	0.0305752	−	0.0941007i	0.00302739	−	0.00931736i
$103$	−0.174918	−	0.538341i	−0.0172351	−	0.0530443i	0.942069	−	0.335419i	$-0.108878\pi$
$103$	−0.174918	−	0.538341i	−0.0172351	−	0.0530443i	−0.959304	+	0.282375i	$0.908878\pi$
$104$	1.88906	−	1.37249i	0.185238	−	0.134583i
$105$		0			0
$106$	−0.686596	−	2.11313i	−0.0666881	−	0.205245i
$107$	0.689113	−	2.12087i	0.0666191	−	0.205033i	−0.912206	−	0.409733i	$-0.865622\pi$
$107$	0.689113	−	2.12087i	0.0666191	−	0.205033i	0.978825	+	0.204700i	$0.0656220\pi$
$108$	−4.42705	−	3.21644i	−0.425993	−	0.309502i
$109$	7.86288			0.753127			0.376563	−	0.926391i	$-0.377106\pi$
$109$	7.86288			0.753127			0.376563	+	0.926391i	$0.377106\pi$
$110$		0			0
$111$	7.37319			0.699832
$112$	−4.05657	−	2.94727i	−0.383310	−	0.278491i
$113$	3.88177	−	11.9469i	0.365166	−	1.12387i	−0.584710	−	0.811242i	$-0.698792\pi$
$113$	3.88177	−	11.9469i	0.365166	−	1.12387i	0.949877	−	0.312624i	$-0.101208\pi$
$114$	1.03058	+	3.17178i	0.0965222	+	0.297065i
$115$		0			0
$116$	3.34700	−	2.43174i	0.310762	−	0.225781i
$117$	0.275611	+	0.848243i	0.0254802	+	0.0784200i
$118$	0.599137	−	1.84396i	0.0551551	−	0.169750i
$119$	0.248061	+	0.180227i	0.0227397	+	0.0165214i
$120$		0			0
$121$	−9.12043	+	6.14961i	−0.829130	+	0.559056i
$122$	−9.69338			−0.877597
$123$	−5.99511	−	4.35570i	−0.540560	−	0.392740i
$124$	−2.74317	+	8.44260i	−0.246344	+	0.758168i
$125$		0			0
$126$	1.54947	−	1.12576i	0.138038	−	0.100290i
$127$	11.7008	−	8.50112i	1.03828	−	0.754353i	0.0683289	−	0.997663i	$-0.478233\pi$
$127$	11.7008	−	8.50112i	1.03828	−	0.754353i	0.969949	+	0.243310i	$0.0782333\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	1.80902	−	5.56758i	0.159275	−	0.490198i
$130$		0			0
$131$	15.3256			1.33900			0.669502	−	0.742810i	$-0.266507\pi$
$131$	15.3256			1.33900			0.669502	+	0.742810i	$0.266507\pi$
$132$	1.56856	+	5.13205i	0.136526	+	0.446688i
$133$	−10.3350			−0.896159
$134$	2.01909	+	1.46696i	0.174423	+	0.126726i
$135$		0			0
$136$	−0.0188965	−	0.0581575i	−0.00162036	−	0.00498696i
$137$	−0.893451	+	0.649130i	−0.0763326	+	0.0554589i	−0.625297	−	0.780387i	$-0.715022\pi$
$137$	−0.893451	+	0.649130i	−0.0763326	+	0.0554589i	0.548964	+	0.835846i	$0.315022\pi$
$138$	−5.12513	+	3.72363i	−0.436280	+	0.316976i
$139$	−3.06115	−	9.42125i	−0.259643	−	0.799100i	−0.992879	−	0.119126i	$-0.961991\pi$
$139$	−3.06115	−	9.42125i	−0.259643	−	0.799100i	0.733236	−	0.679974i	$-0.238009\pi$
$140$		0			0
$141$	−11.6202	−	8.44260i	−0.978600	−	0.710995i
$142$	8.81631			0.739848
$143$	2.52192	−	7.32222i	0.210894	−	0.612315i
$144$	−0.381966			−0.0318305
$145$		0			0
$146$	−1.66751	+	5.13205i	−0.138004	+	0.424732i
$147$	−9.07108	−	27.9179i	−0.748170	−	2.30263i
$148$	3.68660	−	2.67847i	0.303036	−	0.220169i
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	−0.839708	−	0.543039i	$-0.817274\pi$
$149$	−7.11314	+	5.16800i	−0.582731	+	0.423379i	0.256977	+	0.966418i	$0.417274\pi$
$150$		0			0
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	−0.182894	−	0.983133i	$-0.558547\pi$
$151$	6.67177	−	20.5336i	0.542941	−	1.67100i	0.725835	−	0.687868i	$-0.241453\pi$
$152$	1.66751	+	1.21151i	0.135253	+	0.0982667i
$153$	0.0233574			0.00188833
$154$	−16.6276	−	0.291613i	−1.33989	−	0.0234988i
$155$		0			0
$156$	−3.05657	−	2.22073i	−0.244721	−	0.177801i
$157$	−1.05521	+	3.24760i	−0.0842148	+	0.259186i	−0.984293	−	0.176542i	$-0.943509\pi$
$157$	−1.05521	+	3.24760i	−0.0842148	+	0.259186i	0.900078	+	0.435728i	$0.143509\pi$
$158$	−2.05657	−	6.32947i	−0.163612	−	0.503546i
$159$	−2.90847	+	2.11313i	−0.230657	+	0.167582i
$160$		0			0
$161$	−6.06657	−	18.6710i	−0.478113	−	1.47148i
$162$	−2.38197	+	7.33094i	−0.187145	+	0.575973i
$163$	14.0853	+	10.2336i	1.10324	+	0.801554i	0.981586	−	0.191019i	$-0.0611791\pi$
$163$	14.0853	+	10.2336i	1.10324	+	0.801554i	0.121657	+	0.992572i	$0.461179\pi$
$164$	−4.57985			−0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$	2.67460	+	1.94321i	0.206967	+	0.150370i	0.686440	−	0.727186i	$-0.259172\pi$
$167$	2.67460	+	1.94321i	0.206967	+	0.150370i	−0.479473	+	0.877556i	$0.659172\pi$
$168$	−2.50710	+	7.71605i	−0.193427	+	0.595306i
$169$	−2.33237	−	7.17831i	−0.179413	−	0.552178i
$170$		0			0
$171$	−0.636930	+	0.462757i	−0.0487073	+	0.0353879i
$172$	−1.11803	−	3.44095i	−0.0852493	−	0.262370i
$173$	−1.58482	+	4.87758i	−0.120492	+	0.370836i	−0.993053	−	0.117670i	$-0.962458\pi$
$173$	−1.58482	+	4.87758i	−0.120492	+	0.370836i	0.872561	+	0.488505i	$0.162458\pi$
$174$	−5.41557	−	3.93464i	−0.410553	−	0.298284i
$175$		0			0
$176$	2.64861	+	1.99621i	0.199646	+	0.150470i
$177$	−3.13712			−0.235801
$178$	−4.92705	−	3.57971i	−0.369298	−	0.268311i
$179$	−4.46201	+	13.7327i	−0.333507	+	1.02643i	0.633947	+	0.773377i	$0.281434\pi$
$179$	−4.46201	+	13.7327i	−0.333507	+	1.02643i	−0.967453	+	0.253051i	$0.918566\pi$
$180$		0			0
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	−0.885090	−	0.465419i	$-0.845903\pi$
$181$	−9.63223	+	6.99822i	−0.715958	+	0.520174i	0.169132	+	0.985593i	$0.445903\pi$
$182$	9.47214	−	6.88191i	0.702121	−	0.510121i
$183$	4.84669	+	14.9166i	0.358278	+	1.10267i
$184$	−1.20988	+	3.72363i	−0.0891935	+	0.274509i
$185$		0			0
$186$	14.3634			1.05318
$187$	−0.161963	−	0.122069i	−0.0118439	−	0.00892658i
$188$	−8.87707			−0.647427
$189$	−22.1981	−	16.1279i	−1.61467	−	1.17313i
$190$		0			0
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	0.997097	+	0.0761369i	$0.0242586\pi$
$191$	3.25026	+	10.0033i	0.235181	+	0.723812i	−0.761917	+	0.647675i	$0.775741\pi$
$192$	1.30902	−	0.951057i	0.0944702	−	0.0686366i
$193$	3.93885	−	2.86174i	0.283525	−	0.205993i	−0.436929	−	0.899496i	$-0.643934\pi$
$193$	3.93885	−	2.86174i	0.283525	−	0.205993i	0.720453	+	0.693503i	$0.243934\pi$
$194$	2.25652	+	6.94485i	0.162009	+	0.498612i
$195$		0			0
$196$	−14.6773	−	10.6637i	−1.04838	−	0.761692i
$197$	15.9760			1.13824			0.569122	−	0.822253i	$-0.307283\pi$
$197$	15.9760			1.13824			0.569122	+	0.822253i	$0.307283\pi$
$198$	−1.03779	+	0.726543i	−0.0737527	+	0.0516331i
$199$	16.7076			1.18437			0.592184	−	0.805803i	$-0.298266\pi$
$199$	16.7076			1.18437			0.592184	+	0.805803i	$0.298266\pi$
$200$		0			0
$201$	1.24787	−	3.84054i	0.0880177	−	0.270891i
$202$	−0.0685623	−	0.211013i	−0.00482403	−	0.0148468i
$203$	16.7825	−	12.1932i	1.17790	−	0.855797i
$204$	−0.0800469	+	0.0581575i	−0.00560440	+	0.00407184i
$205$		0			0
$206$	−0.174918	+	0.538341i	−0.0121871	+	0.0375080i
$207$	−1.20988	−	0.879029i	−0.0840924	−	0.0610967i
$208$	−2.33501			−0.161904
$209$	6.83501	+	0.119871i	0.472788	+	0.00829167i
$210$		0			0
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	0.932449	−	0.361301i	$-0.117667\pi$
$211$	12.7388	+	9.25526i	0.876974	+	0.637159i	−0.0554754	+	0.998460i	$0.517667\pi$
$212$	−0.686596	+	2.11313i	−0.0471556	+	0.145130i
$213$	−4.40815	−	13.5669i	−0.302042	−	0.929589i
$214$	−1.80412	+	1.31077i	−0.123327	+	0.0896025i
$215$		0			0
$216$	1.69098	+	5.20431i	0.115057	+	0.354108i
$217$	−13.7548	+	42.3328i	−0.933735	+	2.87374i
$218$	−6.36120	−	4.62168i	−0.430835	−	0.313020i
$219$	8.73117			0.589998
$220$		0			0
$221$	0.142787			0.00960488
$222$	−5.96504	−	4.33385i	−0.400347	−	0.290869i
$223$	−4.49794	+	13.8432i	−0.301204	+	0.927011i	0.679862	+	0.733340i	$0.262039\pi$
$223$	−4.49794	+	13.8432i	−0.301204	+	0.927011i	−0.981067	+	0.193671i	$0.937961\pi$
$224$	1.54947	+	4.76878i	0.103528	+	0.318628i
$225$		0			0
$226$	−10.1626	+	7.38357i	−0.676007	+	0.491148i
$227$	3.03966	+	9.35512i	0.201749	+	0.620921i	0.999831	+	0.0183719i	$0.00584828\pi$
$227$	3.03966	+	9.35512i	0.201749	+	0.620921i	−0.798082	+	0.602549i	$0.794152\pi$
$228$	1.03058	−	3.17178i	0.0682515	−	0.210057i
$229$	12.5785	+	9.13881i	0.831210	+	0.603909i	0.919901	−	0.392150i	$-0.128268\pi$
$229$	12.5785	+	9.13881i	0.831210	+	0.603909i	−0.0886913	+	0.996059i	$0.528268\pi$
$230$		0			0
$231$	7.86508	+	25.7331i	0.517484	+	1.69312i
$232$	−4.13712			−0.271616
$233$	20.9509	+	15.2217i	1.37254	+	0.997206i	0.997534	+	0.0701824i	$0.0223581\pi$
$233$	20.9509	+	15.2217i	1.37254	+	0.997206i	0.375002	+	0.927024i	$0.377642\pi$
$234$	0.275611	−	0.848243i	0.0180172	−	0.0554513i
$235$		0			0
$236$	−1.56856	+	1.13963i	−0.102105	+	0.0741834i
$237$	−8.71177	+	6.32947i	−0.565890	+	0.411143i
$238$	−0.0947508	−	0.291613i	−0.00614178	−	0.0189025i
$239$	6.17911	−	19.0173i	0.399693	−	1.23013i	−0.525552	−	0.850761i	$-0.676141\pi$
$239$	6.17911	−	19.0173i	0.399693	−	1.23013i	0.925246	−	0.379369i	$-0.123859\pi$
$240$		0			0
$241$	9.01381			0.580630			0.290315	−	0.956931i	$-0.406240\pi$
$241$	9.01381			0.580630			0.290315	+	0.956931i	$0.406240\pi$
$242$	10.9932	+	0.385714i	0.706672	+	0.0247946i
$243$	−3.94427			−0.253025
$244$	7.84211	+	5.69763i	0.502040	+	0.364753i
$245$		0			0
$246$	2.28993	+	7.04767i	0.146000	+	0.449343i
$247$	−3.89364	+	2.82890i	−0.247747	+	0.179998i
$248$	7.18170	−	5.21781i	0.456038	−	0.331331i
$249$	5.52599	+	17.0073i	0.350196	+	1.07779i
$250$		0			0
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	0.553792	−	0.832655i	$-0.313180\pi$
$251$	−1.06115	−	0.770971i	−0.0669792	−	0.0486632i	−0.620771	+	0.783992i	$0.713180\pi$
$252$	−1.91525			−0.120650
$253$	3.79554	+	12.4183i	0.238624	+	0.780734i
$254$	−14.4630			−0.907488
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.37945	−	4.24551i	−0.0860477	−	0.264827i	0.898770	−	0.438421i	$-0.144462\pi$
$257$	−1.37945	−	4.24551i	−0.0860477	−	0.264827i	−0.984817	+	0.173594i	$0.944462\pi$
$258$	−4.73607	+	3.44095i	−0.294855	+	0.214224i
$259$	18.4853	−	13.4304i	1.14862	−	0.834522i
$260$		0			0
$261$	0.488321	−	1.50290i	0.0302263	−	0.0930271i
$262$	−12.3987	−	9.00817i	−0.765993	−	0.556526i
$263$	−14.1791			−0.874320			−0.437160	−	0.899384i	$-0.644016\pi$
$263$	−14.1791			−0.874320			−0.437160	+	0.899384i	$0.644016\pi$
$264$	1.74755	−	5.07390i	0.107554	−	0.312277i
$265$		0			0
$266$	8.36120	+	6.07477i	0.512658	+	0.372468i
$267$	−3.04508	+	9.37181i	−0.186356	+	0.573545i
$268$	−0.771224	−	2.37358i	−0.0471100	−	0.144990i
$269$	25.8847	−	18.8063i	1.57822	−	1.14664i	0.659516	−	0.751691i	$-0.270761\pi$
$269$	25.8847	−	18.8063i	1.57822	−	1.14664i	0.918702	−	0.394952i	$-0.129239\pi$
$270$		0			0
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	0.960524	−	0.278197i	$-0.0897367\pi$
$271$	0.327988	+	1.00944i	0.0199238	+	0.0613192i	−0.940600	+	0.339516i	$0.889737\pi$
$272$	−0.0188965	+	0.0581575i	−0.00114577	+	0.00352631i
$273$	−15.3262	−	11.1352i	−0.927586	−	0.673931i
$274$	1.10437			0.0667172
$275$		0			0
$276$	6.33501			0.381323
$277$	−5.36641	−	3.89892i	−0.322436	−	0.234264i	0.414778	−	0.909923i	$-0.363859\pi$
$277$	−5.36641	−	3.89892i	−0.322436	−	0.234264i	−0.737214	+	0.675659i	$0.763859\pi$
$278$	−3.06115	+	9.42125i	−0.183596	+	0.565049i
$279$	1.04780	+	3.22478i	0.0627299	+	0.193063i
$280$		0			0
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	−0.897412	−	0.441194i	$-0.854555\pi$
$281$	−12.6582	+	9.19674i	−0.755126	+	0.548631i	0.142285	+	0.989826i	$0.454555\pi$
$282$	4.43854	+	13.6604i	0.264311	+	0.813465i
$283$	−6.95305	+	21.3993i	−0.413316	+	1.27205i	0.500433	+	0.865775i	$0.333174\pi$
$283$	−6.95305	+	21.3993i	−0.413316	+	1.27205i	−0.913749	+	0.406280i	$0.866826\pi$
$284$	−7.13254	−	5.18210i	−0.423239	−	0.307501i
$285$		0			0
$286$	−6.34417	+	4.44146i	−0.375139	+	0.262629i
$287$	−22.9643			−1.35554
$288$	0.309017	+	0.224514i	0.0182090	+	0.0132296i
$289$	−5.25213	+	16.1644i	−0.308949	+	0.950847i
$290$		0			0
$291$	9.55877	−	6.94485i	0.560345	−	0.407115i
$292$	4.36559	−	3.17178i	0.255477	−	0.185615i
$293$	−5.62063	−	17.2985i	−0.328360	−	1.01059i	−0.969901	−	0.243500i	$-0.921704\pi$
$293$	−5.62063	−	17.2985i	−0.328360	−	1.01059i	0.641540	−	0.767089i	$-0.278296\pi$
$294$	−9.07108	+	27.9179i	−0.529036	+	1.62821i
$295$		0			0
$296$	−4.55688			−0.264863
$297$	14.4935	+	10.9236i	0.841001	+	0.633849i
$298$	8.79232			0.509326
$299$	−7.39616	−	5.37363i	−0.427731	−	0.310765i
$300$		0			0
$301$	−5.60604	−	17.2536i	−0.323127	−	0.994482i
$302$	−17.4669	+	12.6905i	−1.00511	+	0.730254i
$303$	−0.290435	+	0.211013i	−0.0166850	+	0.0121224i
$304$	−0.636930	−	1.96027i	−0.0365305	−	0.112429i
$305$		0			0
$306$	−0.0188965	−	0.0137291i	−0.00108024	−	0.000784841i
$307$	12.3820			0.706676			0.353338	−	0.935496i	$-0.385047\pi$
$307$	12.3820			0.706676			0.353338	+	0.935496i	$0.385047\pi$
$308$	13.2806	+	10.0094i	0.756735	+	0.570339i
$309$	0.915880			0.0521026
$310$		0			0
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	−0.834140	−	0.551553i	$-0.814035\pi$
$311$	2.90784	−	8.94941i	0.164889	−	0.507475i	0.999028	+	0.0440788i	$0.0140353\pi$
$312$	1.16751	+	3.59321i	0.0660970	+	0.203426i
$313$	−12.3227	+	8.95297i	−0.696520	+	0.506052i	−0.878797	−	0.477196i	$-0.841653\pi$
$313$	−12.3227	+	8.95297i	−0.696520	+	0.506052i	0.182277	+	0.983247i	$0.441653\pi$
$314$	2.76257	−	2.00712i	0.155901	−	0.113269i
$315$		0			0
$316$	−2.05657	+	6.32947i	−0.115691	+	0.356061i
$317$	10.8867	+	7.90964i	0.611457	+	0.444250i	0.849927	−	0.526900i	$-0.176646\pi$
$317$	10.8867	+	7.90964i	0.611457	+	0.444250i	−0.238470	+	0.971150i	$0.576646\pi$
$318$	3.59506			0.201601
$319$	−11.2405	+	7.86928i	−0.629346	+	0.440595i
$320$		0			0
$321$	2.91913	+	2.12087i	0.162930	+	0.118376i
$322$	−6.06657	+	18.6710i	−0.338077	+	1.04049i
$323$	0.0389485	+	0.119871i	0.00216715	+	0.00666982i
$324$	6.23607	−	4.53077i	0.346448	−	0.251709i
$325$		0			0
$326$	−5.38010	−	16.5582i	−0.297976	−	0.917076i
$327$	−3.93144	+	12.0997i	−0.217409	+	0.669116i
$328$	3.70518	+	2.69197i	0.204584	+	0.148639i
$329$	−44.5114			−2.45399
$330$		0			0
$331$	−3.82236			−0.210096			−0.105048	−	0.994467i	$-0.533500\pi$
$331$	−3.82236			−0.210096			−0.105048	+	0.994467i	$0.533500\pi$
$332$	8.94125	+	6.49620i	0.490715	+	0.356525i
$333$	0.537867	−	1.65538i	0.0294749	−	0.0907145i
$334$	−1.02161	−	3.14419i	−0.0558999	−	0.172042i
$335$		0			0
$336$	6.56367	−	4.76878i	0.358077	−	0.260158i
$337$	−2.92538	−	9.00338i	−0.159355	−	0.490445i	0.839221	−	0.543791i	$-0.183012\pi$
$337$	−2.92538	−	9.00338i	−0.159355	−	0.490445i	−0.998576	+	0.0533455i	$0.983012\pi$
$338$	−2.33237	+	7.17831i	−0.126864	+	0.390449i
$339$	16.4434	+	11.9469i	0.893086	+	0.648865i
$340$		0			0
$341$	9.58765	−	27.8371i	0.519201	−	1.50746i
$342$	0.787289			0.0425717
$343$	−45.1989	−	32.8390i	−2.44051	−	1.77314i
$344$	−1.11803	+	3.44095i	−0.0602804	+	0.185524i
$345$		0			0
$346$	4.14912	−	3.01451i	0.223058	−	0.162061i
$347$	13.3831	−	9.72341i	0.718444	−	0.521980i	−0.167443	−	0.985882i	$-0.553551\pi$
$347$	13.3831	−	9.72341i	0.718444	−	0.521980i	0.885887	+	0.463902i	$0.153551\pi$
$348$	2.06856	+	6.36638i	0.110887	+	0.341274i
$349$	9.03161	−	27.7964i	0.483451	−	1.48791i	−0.350761	−	0.936465i	$-0.614077\pi$
$349$	9.03161	−	27.7964i	0.483451	−	1.48791i	0.834212	−	0.551444i	$-0.185923\pi$
$350$		0			0
$351$	−12.7775			−0.682012
$352$	−0.969425	−	3.17178i	−0.0516705	−	0.169057i
$353$	27.9200			1.48603			0.743017	−	0.669272i	$-0.233394\pi$
$353$	27.9200			1.48603			0.743017	+	0.669272i	$0.233394\pi$
$354$	2.53799	+	1.84396i	0.134892	+	0.0980051i
$355$		0			0
$356$	1.88197	+	5.79210i	0.0997440	+	0.306980i
$357$	−0.401371	+	0.291613i	−0.0212428	+	0.0154338i
$358$	11.6817	−	8.48725i	0.617397	−	0.448565i
$359$	5.25768	+	16.1815i	0.277490	+	0.854025i	0.988550	+	0.150894i	$0.0482152\pi$
$359$	5.25768	+	16.1815i	0.277490	+	0.854025i	−0.711060	+	0.703131i	$0.751785\pi$
$360$		0			0
$361$	11.9343	+	8.67081i	0.628123	+	0.456358i
$362$	11.9061			0.625770
$363$	−4.90307	−	17.1097i	−0.257344	−	0.898027i
$364$	−11.7082			−0.613677
$365$		0			0
$366$	4.84669	−	14.9166i	0.253341	−	0.779702i
$367$	−9.09719	−	27.9983i	−0.474870	−	1.46150i	−0.846133	−	0.532971i	$-0.821075\pi$
$367$	−9.09719	−	27.9983i	−0.474870	−	1.46150i	0.371264	−	0.928527i	$-0.378925\pi$
$368$	3.16751	−	2.30133i	0.165118	−	0.119965i
$369$	−1.41525	+	1.02824i	−0.0736751	+	0.0535281i
$370$		0			0
$371$	−3.44273	+	10.5956i	−0.178738	+	0.550098i
$372$	−11.6202	−	8.44260i	−0.602481	−	0.437728i
$373$	16.0743			0.832297			0.416149	−	0.909297i	$-0.363380\pi$
$373$	16.0743			0.832297			0.416149	+	0.909297i	$0.363380\pi$
$374$	0.0592807	+	0.193956i	0.00306533	+	0.0100292i
$375$		0			0
$376$	7.18170	+	5.21781i	0.370368	+	0.269088i
$377$	2.98518	−	9.18743i	0.153744	−	0.473177i
$378$	8.47892	+	26.0954i	0.436109	+	1.34220i
$379$	−14.6618	+	10.6524i	−0.753125	+	0.547178i	−0.896794	−	0.442448i	$-0.854110\pi$
$379$	−14.6618	+	10.6524i	−0.753125	+	0.547178i	0.143669	+	0.989626i	$0.454110\pi$
$380$		0			0
$381$	7.23149	+	22.2562i	0.370480	+	1.14022i
$382$	3.25026	−	10.0033i	0.166298	−	0.511812i
$383$	10.6888	+	7.76587i	0.546172	+	0.396817i	0.826372	−	0.563124i	$-0.190401\pi$
$383$	10.6888	+	7.76587i	0.546172	+	0.396817i	−0.280200	+	0.959942i	$0.590401\pi$
$384$	−1.61803			−0.0825700
$385$		0			0
$386$	−4.86869			−0.247810
$387$	−1.11803	−	0.812299i	−0.0568329	−	0.0412915i
$388$	2.25652	−	6.94485i	0.114557	−	0.352572i
$389$	−8.19653	−	25.2263i	−0.415580	−	1.27902i	−0.911731	−	0.410788i	$-0.865254\pi$
$389$	−8.19653	−	25.2263i	−0.415580	−	1.27902i	0.496150	−	0.868237i	$-0.334746\pi$
$390$		0			0
$391$	−0.193694	+	0.140727i	−0.00979553	+	0.00711687i
$392$	5.60624	+	17.2542i	0.283158	+	0.871470i
$393$	−7.66280	+	23.5837i	−0.386537	+	1.18964i
$394$	−12.9249	−	9.39047i	−0.651145	−	0.473085i
$395$		0			0
$396$	1.26664	+	0.0222142i	0.0636512	+	0.00111630i
$397$	−30.3246			−1.52195			−0.760974	−	0.648783i	$-0.775278\pi$
$397$	−30.3246			−1.52195			−0.760974	+	0.648783i	$0.775278\pi$
$398$	−13.5167	−	9.82047i	−0.677532	−	0.492256i
$399$	5.16751	−	15.9039i	0.258699	−	0.796193i
$400$		0			0
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	−0.907025	−	0.421076i	$-0.861652\pi$
$401$	−15.7565	+	11.4478i	−0.786844	+	0.571676i	0.120181	+	0.992752i	$0.461652\pi$
$402$	−3.26696	+	2.37358i	−0.162941	+	0.118384i
$403$	6.40532	+	19.7136i	0.319072	+	0.982002i
$404$	−0.0685623	+	0.211013i	−0.00341110	+	0.0104983i
$405$		0			0
$406$	−20.7444			−1.02952
$407$	−12.3809	+	8.66771i	−0.613701	+	0.429642i
$408$	0.0989434			0.00489843
$409$	22.9197	+	16.6521i	1.13330	+	0.823394i	0.986172	−	0.165723i	$-0.0529958\pi$
$409$	22.9197	+	16.6521i	1.13330	+	0.823394i	0.147132	+	0.989117i	$0.452996\pi$
$410$		0			0
$411$	−0.552183	−	1.69944i	−0.0272372	−	0.0838274i
$412$	0.457940	−	0.332713i	0.0225611	−	0.0163916i
$413$	−7.86508	+	5.71431i	−0.387015	+	0.281183i
$414$	0.462133	+	1.42230i	0.0227126	+	0.0699022i
$415$		0			0
$416$	1.88906	+	1.37249i	0.0926190	+	0.0672916i
$417$	16.0284			0.784914
$418$	−5.45918	−	4.11450i	−0.267017	−	0.201247i
$419$	−15.4826			−0.756374			−0.378187	−	0.925729i	$-0.623452\pi$
$419$	−15.4826			−0.756374			−0.378187	+	0.925729i	$0.623452\pi$
$420$		0			0
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	−0.648474	−	0.761237i	$-0.724592\pi$
$421$	6.63964	−	20.4347i	0.323596	−	0.995927i	0.972070	−	0.234690i	$-0.0754076\pi$
$422$	−4.86578	−	14.9753i	−0.236862	−	0.728988i
$423$	−2.74317	+	1.99303i	−0.133377	+	0.0969043i
$424$	1.79753	−	1.30598i	0.0872959	−	0.0634242i
$425$		0			0
$426$	−4.40815	+	13.5669i	−0.213576	+	0.657319i
$427$	39.3219	+	28.5690i	1.90292	+	1.38255i
$428$	2.23002			0.107792
$429$	10.0068	+	7.54195i	0.483132	+	0.364129i
$430$		0			0
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.0619316	−	0.998080i	$-0.519726\pi$
$431$	−21.3896	−	15.5404i	−1.03030	−	0.748557i	−0.968369	+	0.249523i	$0.919726\pi$
$432$	1.69098	−	5.20431i	0.0813575	−	0.250393i
$433$	−10.1611	−	31.2725i	−0.488309	−	1.50286i	−0.827130	−	0.562010i	$-0.810028\pi$
$433$	−10.1611	−	31.2725i	−0.488309	−	1.50286i	0.338821	−	0.940851i	$-0.389972\pi$
$434$	36.0105	−	26.1631i	1.72856	−	1.25587i
$435$		0			0
$436$	2.42976	+	7.47804i	0.116365	+	0.358133i
$437$	2.49374	−	7.67495i	0.119292	−	0.367143i
$438$	−7.06367	−	5.13205i	−0.337515	−	0.245219i
$439$	−12.1796			−0.581299			−0.290649	−	0.956830i	$-0.593871\pi$
$439$	−12.1796			−0.581299			−0.290649	+	0.956830i	$0.593871\pi$
$440$		0			0
$441$	−6.92969			−0.329985
$442$	−0.115517	−	0.0839280i	−0.00549458	−	0.00399205i
$443$	5.13247	−	15.7961i	0.243851	−	0.750496i	−0.751972	−	0.659195i	$-0.770897\pi$
$443$	5.13247	−	15.7961i	0.243851	−	0.750496i	0.995823	−	0.0913015i	$-0.0291027\pi$
$444$	2.27844	+	7.01232i	0.108130	+	0.332790i
$445$		0			0
$446$	11.7757	−	8.55558i	0.557598	−	0.405119i
$447$	−4.39616	−	13.5300i	−0.207931	−	0.639947i
$448$	1.54947	−	4.76878i	0.0732057	−	0.225304i
$449$	4.33928	+	3.15267i	0.204783	+	0.148784i	0.685450	−	0.728119i	$-0.259605\pi$
$449$	4.33928	+	3.15267i	0.204783	+	0.148784i	−0.480667	+	0.876903i	$0.659605\pi$
$450$		0			0
$451$	15.1873	+	0.266353i	0.715143	+	0.0125421i
$452$	12.5617			0.590852
$453$	28.2621	+	20.5336i	1.32787	+	0.964753i
$454$	3.03966	−	9.35512i	0.142658	−	0.439058i
$455$		0			0
$456$	−2.69808	+	1.96027i	−0.126349	+	0.0917981i
$457$	−2.92247	+	2.12330i	−0.136707	+	0.0993237i	−0.654037	−	0.756462i	$-0.726926\pi$
$457$	−2.92247	+	2.12330i	−0.136707	+	0.0993237i	0.517330	+	0.855786i	$0.326926\pi$
$458$	−4.80456	−	14.7869i	−0.224502	−	0.690947i
$459$	−0.103404	+	0.318246i	−0.00482650	+	0.0148544i
$460$		0			0
$461$	−40.6625			−1.89384			−0.946922	−	0.321464i	$-0.895825\pi$
$461$	−40.6625			−1.89384			−0.946922	+	0.321464i	$0.895825\pi$
$462$	8.76257	−	25.4415i	0.407672	−	1.18365i
$463$	2.11880			0.0984690			0.0492345	−	0.998787i	$-0.484322\pi$
$463$	2.11880			0.0984690			0.0492345	+	0.998787i	$0.484322\pi$
$464$	3.34700	+	2.43174i	0.155381	+	0.112891i
$465$		0			0
$466$	−8.00252	−	24.6292i	−0.370709	−	1.14093i
$467$	−11.1280	+	8.08494i	−0.514941	+	0.374126i	−0.814695	−	0.579890i	$-0.803095\pi$
$467$	−11.1280	+	8.08494i	−0.514941	+	0.374126i	0.299754	+	0.954017i	$0.403095\pi$
$468$	−0.721558	+	0.524243i	−0.0333540	+	0.0242331i
$469$	−3.86707	−	11.9016i	−0.178565	−	0.549565i
$470$		0			0
$471$	−4.46993	−	3.24760i	−0.205964	−	0.149641i
$472$	1.93885			0.0892428
$473$	3.50741	+	11.4756i	0.161271	+	0.527650i
$474$	10.7683			0.494606
$475$		0			0
$476$	−0.0947508	+	0.291613i	−0.00434289	+	0.0133661i
$477$	0.262256	+	0.807142i	0.0120079	+	0.0369565i
$478$	−16.1771	+	11.7534i	−0.739924	+	0.537586i
$479$	−25.4118	+	18.4628i	−1.16110	+	0.843586i	−0.989916	−	0.141654i	$-0.954758\pi$
$479$	−25.4118	+	18.4628i	−1.16110	+	0.843586i	−0.171180	+	0.985240i	$0.554758\pi$
$480$		0			0
$481$	3.28806	−	10.1196i	0.149922	−	0.461414i
$482$	−7.29232	−	5.29818i	−0.332156	−	0.241326i
$483$	31.7650			1.44536
$484$	−8.66700	−	6.77371i	−0.393954	−	0.307896i
$485$		0			0
$486$	3.19098	+	2.31838i	0.144746	+	0.105164i
$487$	2.32082	−	7.14274i	0.105166	−	0.323668i	−0.884603	−	0.466344i	$-0.845571\pi$
$487$	2.32082	−	7.14274i	0.105166	−	0.323668i	0.989769	+	0.142676i	$0.0455707\pi$
$488$	−2.99542	−	9.21895i	−0.135596	−	0.417322i
$489$	−22.7905	+	16.5582i	−1.03062	+	0.748789i
$490$		0			0
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	0.998363	−	0.0571923i	$-0.0182148\pi$
$491$	3.48008	+	10.7106i	0.157054	+	0.483361i	−0.841310	+	0.540554i	$0.818215\pi$
$492$	2.28993	−	7.04767i	0.103238	−	0.317733i
$493$	−0.204671	−	0.148702i	−0.00921790	−	0.00669719i
$494$	4.81281			0.216539
$495$		0			0
$496$	−8.87707			−0.398592
$497$	−35.7640	−	25.9840i	−1.60423	−	1.16554i
$498$	5.52599	−	17.0073i	0.247626	−	0.762114i
$499$	−8.33753	−	25.6603i	−0.373239	−	1.14871i	−0.944659	−	0.328054i	$-0.893607\pi$
$499$	−8.33753	−	25.6603i	−0.373239	−	1.14871i	0.571420	−	0.820658i	$-0.306393\pi$
$500$		0			0
$501$	−4.32760	+	3.14419i	−0.193343	+	0.140472i
$502$	0.405323	+	1.24746i	0.0180905	+	0.0556767i
$503$	9.93662	−	30.5818i	0.443052	−	1.36357i	−0.441554	−	0.897235i	$-0.645573\pi$
$503$	9.93662	−	30.5818i	0.443052	−	1.36357i	0.884606	−	0.466339i	$-0.154427\pi$
$504$	1.54947	+	1.12576i	0.0690190	+	0.0501452i
$505$		0			0
$506$	4.22866	−	12.2776i	0.187987	−	0.545806i
$507$	12.2125			0.542375
$508$	11.7008	+	8.50112i	0.519139	+	0.377176i
$509$	3.64048	−	11.2043i	0.161362	−	0.496620i	−0.837388	−	0.546609i	$-0.815919\pi$
$509$	3.64048	−	11.2043i	0.161362	−	0.496620i	0.998750	+	0.0499888i	$0.0159186\pi$
$510$		0			0
$511$	21.8899	−	15.9039i	0.968352	−	0.703549i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−3.48537	−	10.7269i	−0.153883	−	0.473603i
$514$	−1.37945	+	4.24551i	−0.0608449	+	0.187261i
$515$		0			0
$516$	5.85410			0.257712
$517$	29.4374	+	0.516268i	1.29465	+	0.0227054i
$518$	−22.8491			−1.00393
$519$	−6.71341	−	4.87758i	−0.294686	−	0.214102i
$520$		0			0
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	0.965568	−	0.260152i	$-0.0837728\pi$
$521$	0.718847	+	2.21238i	0.0314933	+	0.0969263i	−0.934074	+	0.357079i	$0.883773\pi$
$522$	−1.27844	+	0.928842i	−0.0559559	+	0.0406543i
$523$	1.24096	−	0.901612i	0.0542635	−	0.0394248i	−0.560323	−	0.828274i	$-0.689323\pi$
$523$	1.24096	−	0.901612i	0.0542635	−	0.0394248i	0.614586	+	0.788850i	$0.289323\pi$
$524$	4.73587	+	14.5755i	0.206888	+	0.636735i
$525$		0			0
$526$	11.4711	+	8.33426i	0.500165	+	0.363391i
$527$	0.542836			0.0236463
$528$	−4.39616	+	3.07768i	−0.191318	+	0.133939i
$529$	−7.67080			−0.333513
$530$		0			0
$531$	−0.228850	+	0.704328i	−0.00993125	+	0.0305652i
$532$	−3.19369	−	9.82918i	−0.138464	−	0.426149i
$533$	−8.65163	+	6.28578i	−0.374744	+	0.272267i
$534$	7.97214	−	5.79210i	0.344988	−	0.250648i
$535$		0			0
$536$	−0.771224	+	2.37358i	−0.0333118	+	0.102523i
$537$	−18.9014	−	13.7327i	−0.815655	−	0.592608i
$538$	−31.9952			−1.37941
$539$	48.0515	+	36.2156i	2.06972	+	1.55992i
$540$		0			0
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	0.823008	−	0.568029i	$-0.192294\pi$
$541$	12.4927	+	9.07650i	0.537104	+	0.390229i	−0.285904	+	0.958258i	$0.592294\pi$
$542$	0.327988	−	1.00944i	0.0140883	−	0.0433593i
$543$	−5.95305	−	18.3216i	−0.255470	−	0.786255i
$544$	0.0494717	−	0.0359433i	0.00212108	−	0.00154106i
$545$		0			0
$546$	5.85410	+	18.0171i	0.250532	+	0.771060i
$547$	3.29017	−	10.1261i	0.140677	−	0.432960i	−0.855752	−	0.517385i	$-0.826905\pi$
$547$	3.29017	−	10.1261i	0.140677	−	0.432960i	0.996430	+	0.0844251i	$0.0269054\pi$
$548$	−0.893451	−	0.649130i	−0.0381663	−	0.0277295i
$549$	3.70254			0.158021
$550$		0			0
$551$	8.52724			0.363272
$552$	−5.12513	−	3.72363i	−0.218140	−	0.158488i
$553$	−10.3120	+	31.7372i	−0.438513	+	1.34960i
$554$	2.04979	+	6.30859i	0.0870871	+	0.268026i
$555$		0			0
$556$	8.01420	−	5.82265i	0.339878	−	0.246936i
$557$	−10.4818	−	32.2595i	−0.444126	−	1.36688i	−0.883439	−	0.468545i	$-0.844778\pi$
$557$	−10.4818	−	32.2595i	−0.444126	−	1.36688i	0.439313	−	0.898334i	$-0.355222\pi$
$558$	1.04780	−	3.22478i	0.0443567	−	0.136516i
$559$	−6.83470	−	4.96570i	−0.289077	−	0.210027i
$560$		0			0
$561$	0.268827	−	0.188201i	0.0113499	−	0.00794587i
$562$	15.6464			0.660005
$563$	1.08714	+	0.789857i	0.0458177	+	0.0332885i	0.610458	−	0.792048i	$-0.290985\pi$
$563$	1.08714	+	0.789857i	0.0458177	+	0.0332885i	−0.564641	+	0.825337i	$0.690985\pi$
$564$	4.43854	−	13.6604i	0.186896	−	0.575207i
$565$		0			0
$566$	18.2033	−	13.2255i	0.765142	−	0.555908i
$567$	31.2689	−	22.7182i	1.31317	−	0.954073i
$568$	2.72439	+	8.38481i	0.114313	+	0.351819i
$569$	−9.70595	+	29.8718i	−0.406894	+	1.25229i	0.512409	+	0.858742i	$0.328753\pi$
$569$	−9.70595	+	29.8718i	−0.406894	+	1.25229i	−0.919303	+	0.393550i	$0.871247\pi$
$570$		0			0
$571$	9.25361			0.387252			0.193626	−	0.981075i	$-0.437975\pi$
$571$	9.25361			0.387252			0.193626	+	0.981075i	$0.437975\pi$
$572$	7.74317	+	0.135798i	0.323758	+	0.00567801i
$573$	−17.0186			−0.710962
$574$	18.5785	+	13.4981i	0.775451	+	0.563398i
$575$		0			0
$576$	−0.118034	−	0.363271i	−0.00491808	−	0.0151363i
$577$	35.0975	−	25.4998i	1.46113	−	1.06157i	0.478060	−	0.878327i	$-0.341340\pi$
$577$	35.0975	−	25.4998i	1.46113	−	1.06157i	0.983068	−	0.183244i	$-0.0586598\pi$
$578$	13.7503	−	9.99015i	0.571936	−	0.415536i
$579$	2.43434	+	7.49214i	0.101168	+	0.311363i
$580$		0			0
$581$	44.8332	+	32.5732i	1.85999	+	1.35136i
$582$	−11.8153			−0.489760
$583$	2.39973	−	6.96744i	0.0993865	−	0.288562i
$584$	−5.39616			−0.223295
$585$		0			0
$586$	−5.62063	+	17.2985i	−0.232186	+	0.714595i
$587$	0.992708	+	3.05524i	0.0409734	+	0.126103i	0.969451	−	0.245285i	$-0.0788817\pi$
$587$	0.992708	+	3.05524i	0.0409734	+	0.126103i	−0.928477	+	0.371389i	$0.878882\pi$
$588$	23.7484	−	17.2542i	0.979367	−	0.711552i
$589$	−14.8026	+	10.7547i	−0.609929	+	0.443139i
$590$		0			0
$591$	−7.98801	+	24.5846i	−0.328583	+	1.01127i
$592$	3.68660	+	2.67847i	0.151518	+	0.110084i
$593$	−0.0315027			−0.00129366			−0.000646829	−	1.00000i	$-0.500206\pi$
$593$	−0.0315027			−0.00129366			−0.000646829		1.00000i	$0.500206\pi$
$594$	−5.30482	−	17.3564i	−0.217660	−	0.712143i
$595$		0			0
$596$	−7.11314	−	5.16800i	−0.291366	−	0.211689i
$597$	−8.35379	+	25.7103i	−0.341898	+	1.05225i
$598$	2.82508	+	8.69471i	0.115526	+	0.355553i
$599$	8.50993	−	6.18283i	0.347706	−	0.252623i	−0.400200	−	0.916428i	$-0.631059\pi$
$599$	8.50993	−	6.18283i	0.347706	−	0.252623i	0.747906	+	0.663804i	$0.231059\pi$
$600$		0			0
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	0.980043	+	0.198788i	$0.0637005\pi$
$601$	7.45305	+	22.9381i	0.304016	+	0.935665i	−0.676026	+	0.736877i	$0.736300\pi$
$602$	−5.60604	+	17.2536i	−0.228485	+	0.703205i
$603$	−0.771224	−	0.560327i	−0.0314067	−	0.0228183i
$604$	21.5903			0.878497
$605$		0			0
$606$	0.358997			0.0145833
$607$	2.01420	+	1.46340i	0.0817537	+	0.0593975i	0.627911	−	0.778285i	$-0.283910\pi$
$607$	2.01420	+	1.46340i	0.0817537	+	0.0593975i	−0.546158	+	0.837682i	$0.683910\pi$
$608$	−0.636930	+	1.96027i	−0.0258309	+	0.0794995i
$609$	10.3722	+	31.9223i	0.420302	+	1.29356i
$610$		0			0
$611$	−16.7694	+	12.1836i	−0.678415	+	0.492898i
$612$	0.00721782	+	0.0222142i	0.000291763	+	0.000897955i
$613$	11.6106	−	35.7338i	0.468949	−	1.44328i	−0.384999	−	0.922917i	$-0.625798\pi$
$613$	11.6106	−	35.7338i	0.468949	−	1.44328i	0.853948	−	0.520359i	$-0.174202\pi$
$614$	−10.0172	−	7.27794i	−0.404262	−	0.293714i
$615$		0			0
$616$	−4.86089	−	15.9039i	−0.195851	−	0.640788i
$617$	45.5803			1.83499			0.917496	−	0.397744i	$-0.130207\pi$
$617$	45.5803			1.83499			0.917496	+	0.397744i	$0.130207\pi$
$618$	−0.740963	−	0.538341i	−0.0298059	−	0.0216553i
$619$	1.77382	−	5.45924i	0.0712957	−	0.219425i	−0.909059	−	0.416667i	$-0.863198\pi$
$619$	1.77382	−	5.45924i	0.0712957	−	0.219425i	0.980355	+	0.197241i	$0.0631982\pi$
$620$		0			0
$621$	17.3330	−	12.5932i	0.695550	−	0.505347i
$622$	−7.61283	+	5.53104i	−0.305246	+	0.221775i
$623$	9.43655	+	29.0427i	0.378067	+	1.16357i
$624$	1.16751	−	3.59321i	0.0467376	−	0.143844i
$625$		0			0
$626$	15.2317			0.608781
$627$	−3.60197	+	10.4581i	−0.143849	+	0.417655i
$628$	−3.41472			−0.136262
$629$	−0.225437	−	0.163789i	−0.00898875	−	0.00653071i
$630$		0			0
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	0.997304	−	0.0733811i	$-0.0233790\pi$
$631$	3.70103	+	11.3906i	0.147336	+	0.453453i	−0.849968	+	0.526834i	$0.823379\pi$
$632$	5.38417	−	3.91183i	0.214171	−	0.155604i
$633$	−20.6118	+	14.9753i	−0.819245	+	0.595216i
$634$	−4.15834	−	12.7981i	−0.165149	−	0.508276i
$635$		0			0
$636$	−2.90847	−	2.11313i	−0.115328	−	0.0837909i
$637$	−42.3621			−1.67845
$638$	13.7192	+	0.240605i	0.543148	+	0.00952563i
$639$	−3.36753			−0.133217
$640$		0			0
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	0.470805	+	0.882237i	$0.343964\pi$
$641$	−10.8526	+	33.4007i	−0.428650	+	1.31925i	−0.899455	+	0.437013i	$0.856036\pi$
$642$	−1.11501	−	3.43164i	−0.0440059	−	0.135436i
$643$	28.8392	−	20.9529i	1.13731	−	0.826302i	0.150565	−	0.988600i	$-0.451891\pi$
$643$	28.8392	−	20.9529i	1.13731	−	0.826302i	0.986742	+	0.162298i	$0.0518907\pi$
$644$	15.8825	−	11.5393i	0.625858	−	0.454712i
$645$		0			0
$646$	0.0389485	−	0.119871i	0.00153241	−	0.00471627i
$647$	−16.3068	−	11.8476i	−0.641088	−	0.465778i	0.219136	−	0.975694i	$-0.429676\pi$
$647$	−16.3068	−	11.8476i	−0.641088	−	0.465778i	−0.860224	+	0.509917i	$0.829676\pi$
$648$	−7.70820			−0.302807
$649$	5.26781	−	3.68791i	0.206780	−	0.144763i
$650$		0			0
$651$	−58.2661	−	42.3328i	−2.28363	−	1.65915i
$652$	−5.38010	+	16.5582i	−0.210701	+	0.648470i
$653$	7.53504	+	23.1905i	0.294869	+	0.907513i	0.983266	+	0.182178i	$0.0583148\pi$
$653$	7.53504	+	23.1905i	0.294869	+	0.907513i	−0.688397	+	0.725334i	$0.741685\pi$
$654$	10.2926	−	7.47804i	0.402474	−	0.292414i
$655$		0			0
$656$	−1.41525	−	4.35570i	−0.0552563	−	0.170061i
$657$	0.636930	−	1.96027i	0.0248490	−	0.0764774i
$658$	36.0105	+	26.1631i	1.40383	+	1.01994i
$659$	−6.98788			−0.272209			−0.136104	−	0.990694i	$-0.543458\pi$
$659$	−6.98788			−0.272209			−0.136104	+	0.990694i	$0.543458\pi$
$660$		0			0
$661$	−3.61827			−0.140735			−0.0703673	−	0.997521i	$-0.522417\pi$
$661$	−3.61827			−0.140735			−0.0703673	+	0.997521i	$0.522417\pi$
$662$	3.09235	+	2.24673i	0.120188	+	0.0873215i
$663$	−0.0713934	+	0.219726i	−0.00277269	+	0.00853346i
$664$	−3.41525	−	10.5111i	−0.132537	−	0.407908i
$665$		0			0
$666$	−1.40815	+	1.02308i	−0.0545649	+	0.0396437i
$667$	5.00542	+	15.4051i	0.193811	+	0.596488i
$668$	−1.02161	+	3.14419i	−0.0395272	+	0.121652i
$669$	−19.0536	−	13.8432i	−0.736653	−	0.535210i
$670$		0			0
$671$	−25.6740	−	19.3501i	−0.991133	−	0.747001i
$672$	−8.11314			−0.312971
$673$	−6.44665	−	4.68377i	−0.248500	−	0.180546i	0.456562	−	0.889692i	$-0.349081\pi$
$673$	−6.44665	−	4.68377i	−0.248500	−	0.180546i	−0.705062	+	0.709146i	$0.749081\pi$
$674$	−2.92538	+	9.00338i	−0.112681	+	0.346797i
$675$		0			0
$676$	6.10624	−	4.43644i	0.234855	−	0.170632i
$677$	−11.6778	+	8.48443i	−0.448815	+	0.326083i	−0.789128	−	0.614229i	$-0.789467\pi$
$677$	−11.6778	+	8.48443i	−0.448815	+	0.326083i	0.340313	+	0.940312i	$0.389467\pi$
$678$	−6.28084	−	19.3304i	−0.241214	−	0.742381i
$679$	11.3146	−	34.8229i	0.434216	−	1.33638i
$680$		0			0
$681$	−15.9159			−0.609898
$682$	−24.1188	+	16.8852i	−0.923557	+	0.646567i
$683$	−29.6723			−1.13538			−0.567690	−	0.823242i	$-0.692163\pi$
$683$	−29.6723			−1.13538			−0.567690	+	0.823242i	$0.692163\pi$
$684$	−0.636930	−	0.462757i	−0.0243536	−	0.0176940i
$685$		0			0
$686$	17.2645	+	53.1345i	0.659160	+	2.02869i
$687$	−20.3524	+	14.7869i	−0.776493	+	0.564156i
$688$	2.92705	−	2.12663i	0.111593	−	0.0810769i
$689$	1.60321	+	4.93417i	0.0610774	+	0.187977i
$690$		0			0
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.0347577	−	0.999396i	$-0.511066\pi$
$691$	−26.1812	−	19.0218i	−0.995980	−	0.723622i	−0.961223	+	0.275774i	$0.911066\pi$
$692$	−5.12859			−0.194960
$693$	6.35120	+	0.111386i	0.241262	+	0.00423121i
$694$	−16.5424			−0.627943
$695$		0			0
$696$	2.06856	−	6.36638i	0.0784087	−	0.241317i
$697$	0.0865432	+	0.266353i	0.00327806	+	0.0100888i
$698$	−23.6451	+	17.1791i	−0.894979	+	0.650240i
$699$	−33.8992	+	24.6292i	−1.28219	+	0.931562i
$700$		0			0
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	−0.777278	−	0.629157i	$-0.783400\pi$
$701$	5.86089	−	18.0380i	0.221363	−	0.681284i	0.998640	−	0.0521266i	$-0.0165999\pi$
$702$	10.3372	+	7.51043i	0.390153	+	0.283463i
$703$	9.39242			0.354242
$704$	−1.08005	+	3.13584i	−0.0407058	+	0.118186i
$705$		0			0
$706$	−22.5878	−	16.4110i	−0.850103	−	0.617636i
$707$	−0.343785	+	1.05806i	−0.0129294	+	0.0397925i
$708$	−0.969425	−	2.98358i	−0.0364332	−	0.112130i
$709$	−6.78617	+	4.93044i	−0.254860	+	0.185167i	−0.707878	−	0.706335i	$-0.750347\pi$
$709$	−6.78617	+	4.93044i	−0.254860	+	0.185167i	0.453018	+	0.891501i	$0.350347\pi$
$710$		0			0
$711$	0.785540	+	2.41764i	0.0294600	+	0.0906687i
$712$	1.88197	−	5.79210i	0.0705297	−	0.217068i
$713$	−28.1182	−	20.4290i	−1.05303	−	0.765074i
$714$	0.496121			0.0185669
$715$		0			0
$716$	−14.4394			−0.539625
$717$	26.1751	+	19.0173i	0.977528	+	0.710216i
$718$	5.25768	−	16.1815i	0.196215	−	0.603887i
$719$	2.33218	+	7.17771i	0.0869756	+	0.267684i	0.985079	−	0.172100i	$-0.0550552\pi$
$719$	2.33218	+	7.17771i	0.0869756	+	0.267684i	−0.898104	+	0.439783i	$0.855055\pi$
$720$		0			0
$721$	2.29620	−	1.66829i	0.0855150	−	0.0621303i
$722$	−4.55851	−	14.0297i	−0.169650	−	0.522130i
$723$	−4.50690	+	13.8708i	−0.167614	+	0.515861i
$724$	−9.63223	−	6.99822i	−0.357979	−	0.260087i
$725$		0			0
$726$	−6.09017	+	16.7240i	−0.226027	+	0.620686i
$727$	−24.2826			−0.900593			−0.450297	−	0.892879i	$-0.648682\pi$
$727$	−24.2826			−0.900593			−0.450297	+	0.892879i	$0.648682\pi$
$728$	9.47214	+	6.88191i	0.351061	+	0.255061i
$729$	9.11803	−	28.0624i	0.337705	−	1.03935i
$730$		0			0
$731$	−0.178990	+	0.130044i	−0.00662019	+	0.00480985i
$732$	−12.6888	+	9.21895i	−0.468992	+	0.340742i
$733$	−6.61345	−	20.3541i	−0.244273	−	0.751796i	−0.995755	−	0.0920424i	$-0.970660\pi$
$733$	−6.61345	−	20.3541i	−0.244273	−	0.751796i	0.751482	−	0.659754i	$-0.229340\pi$
$734$	−9.09719	+	27.9983i	−0.335784	+	1.03344i
$735$		0			0
$736$	−3.91525			−0.144318
$737$	2.41943	+	7.91593i	0.0891207	+	0.291587i
$738$	1.74935			0.0643944
$739$	−28.4419	−	20.6642i	−1.04625	−	0.760147i	−0.0747558	−	0.997202i	$-0.523818\pi$
$739$	−28.4419	−	20.6642i	−1.04625	−	0.760147i	−0.971496	+	0.237055i	$0.923818\pi$
$740$		0			0
$741$	−2.40640	−	7.40615i	−0.0884015	−	0.272072i
$742$	9.01318	−	6.54846i	0.330884	−	0.240401i
$743$	−27.5875	+	20.0435i	−1.01209	+	0.735324i	−0.964646	−	0.263550i	$-0.915107\pi$
$743$	−27.5875	+	20.0435i	−1.01209	+	0.735324i	−0.0474407	+	0.998874i	$0.515107\pi$
$744$	4.43854	+	13.6604i	0.162725	+	0.500815i
$745$		0			0
$746$	−13.0044	−	9.44825i	−0.476125	−	0.345925i
$747$	4.22148			0.154456
$748$	0.0660453	−	0.191758i	0.00241485	−	0.00701136i
$749$	11.1817			0.408572
$750$		0			0
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	0.517884	+	0.855451i	$0.326720\pi$
$751$	−11.0690	+	34.0669i	−0.403914	+	1.24312i	−0.921799	+	0.387669i	$0.873280\pi$
$752$	−2.74317	−	8.44260i	−0.100033	−	0.307870i
$753$	1.71698	−	1.24746i	0.0625701	−	0.0454599i
$754$	−7.81529	+	5.67814i	−0.284616	+	0.206786i
$755$		0			0
$756$	8.47892	−	26.0954i	0.308375	−	0.949082i
$757$	19.6008	+	14.2408i	0.712404	+	0.517592i	0.883948	−	0.467584i	$-0.154876\pi$
$757$	19.6008	+	14.2408i	0.712404	+	0.517592i	−0.171544	+	0.985176i	$0.554876\pi$
$758$	18.1230			0.658256
$759$	−21.0076	−	0.368428i	−0.762528	−	0.0133731i
$760$		0			0
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	0.420443	−	0.907319i	$-0.361875\pi$
$761$	−8.62191	−	6.26419i	−0.312544	−	0.227077i	−0.732987	+	0.680242i	$0.761875\pi$
$762$	7.23149	−	22.2562i	0.261969	−	0.806258i
$763$	12.1833	+	37.4964i	0.441065	+	1.35746i
$764$	−8.50930	+	6.18237i	−0.307856	+	0.223670i
$765$		0			0
$766$	−4.08276	−	12.5654i	−0.147516	−	0.454008i
$767$	−1.39899	+	4.30566i	−0.0505147	+	0.155468i
$768$	1.30902	+	0.951057i	0.0472351	+	0.0343183i
$769$	25.8297			0.931444			0.465722	−	0.884931i	$-0.345795\pi$
$769$	25.8297			0.931444			0.465722	+	0.884931i	$0.345795\pi$
$770$		0			0
$771$	7.22289			0.260126
$772$	3.93885	+	2.86174i	0.141762	+	0.102996i
$773$	3.72614	−	11.4679i	0.134020	−	0.412471i	−0.861416	−	0.507899i	$-0.830422\pi$
$773$	3.72614	−	11.4679i	0.134020	−	0.412471i	0.995436	+	0.0954286i	$0.0304222\pi$
$774$	0.427051	+	1.31433i	0.0153500	+	0.0472425i
$775$		0			0
$776$	−5.90765	+	4.29216i	−0.212072	+	0.154079i
$777$	11.4246	+	35.1612i	0.409854	+	1.26140i
$778$	−8.19653	+	25.2263i	−0.293860	+	0.904407i
$779$	−7.63693	−	5.54855i	−0.273621	−	0.198798i
$780$		0			0
$781$	23.3510	+	17.5992i	0.835563	+	0.629750i
$782$	0.239419			0.00856161
$783$	18.3153	+	13.3068i	0.654534	+	0.475547i
$784$	5.60624	−	17.2542i	0.200223	−	0.616222i
$785$		0			0
$786$	20.0615	−	14.5755i	0.715569	−	0.519892i
$787$	−14.6895	+	10.6725i	−0.523624	+	0.380435i	−0.817967	−	0.575265i	$-0.804899\pi$
$787$	−14.6895	+	10.6725i	−0.523624	+	0.380435i	0.294343	+	0.955700i	$0.404899\pi$
$788$	4.93686	+	15.1941i	0.175868	+	0.541267i
$789$	7.08954	−	21.8194i	0.252394	−	0.776790i
$790$		0			0
$791$	62.9867			2.23955
$792$	−1.01168	−	0.762486i	−0.0359484	−	0.0270938i
$793$	22.6342			0.803762
$794$	24.5331	+	17.8243i	0.870648	+	0.632562i
$795$		0			0
$796$	5.16292	+	15.8898i	0.182995	+	0.563201i
$797$	1.30306	−	0.946725i	0.0461566	−	0.0335347i	−0.564468	−	0.825455i	$-0.690919\pi$
$797$	1.30306	−	0.946725i	0.0461566	−	0.0335347i	0.610624	+	0.791920i	$0.290919\pi$
$798$	−13.5287	+	9.82918i	−0.478911	+	0.347949i
$799$	0.167746	+	0.516268i	0.00593441	+	0.0182642i
$800$		0			0
$801$	1.88197	+	1.36733i	0.0664960	+	0.0483122i
$802$	19.4762			0.687727
$803$	−14.6612	+	10.2641i	−0.517384	+	0.362213i
$804$	4.03818			0.142416
$805$		0			0
$806$	6.40532	−	19.7136i	0.225618	−	0.694380i
$807$	15.9976	+	49.2356i	0.563143	+	1.73318i
$808$	0.179498	−	0.130413i	0.00631473	−	0.00458792i
$809$	−20.7273	+	15.0593i	−0.728733	+	0.529455i	−0.889162	−	0.457592i	$-0.848712\pi$
$809$	−20.7273	+	15.0593i	−0.728733	+	0.529455i	0.160429	+	0.987047i	$0.448712\pi$
$810$		0			0
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	−0.369012	−	0.929424i	$-0.620304\pi$
$811$	13.5506	−	41.7045i	0.475827	−	1.46444i	0.844839	−	0.535020i	$-0.179696\pi$
$812$	16.7825	+	12.1932i	0.588951	+	0.427898i
$813$	−1.71737			−0.0602306
$814$	15.1111	+	0.265017i	0.529646	+	0.00928883i
$815$		0			0
$816$	−0.0800469	−	0.0581575i	−0.00280220	−	0.00203592i
$817$	2.30444	−	7.09233i	0.0806220	−	0.248129i
$818$	−8.75453	−	26.9437i	−0.306095	−	0.942063i
$819$	−3.61803	+	2.62866i	−0.126424	+	0.0918527i
$820$		0			0
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	0.810163	−	0.586205i	$-0.199379\pi$
$821$	−5.43938	−	16.7407i	−0.189836	−	0.584254i	−0.999998	+	0.00195152i	$0.999379\pi$
$822$	−0.552183	+	1.69944i	−0.0192596	+	0.0592749i
$823$	−10.2383	−	7.43854i	−0.356884	−	0.259291i	0.394867	−	0.918738i	$-0.370791\pi$
$823$	−10.2383	−	7.43854i	−0.356884	−	0.259291i	−0.751751	+	0.659447i	$0.770791\pi$
$824$	−0.566045			−0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$	7.15520	+	5.19856i	0.248811	+	0.180772i	0.705200	−	0.709009i	$-0.250857\pi$
$827$	7.15520	+	5.19856i	0.248811	+	0.180772i	−0.456389	+	0.889780i	$0.650857\pi$
$828$	0.462133	−	1.42230i	0.0160602	−	0.0494283i
$829$	11.6571	+	35.8767i	0.404866	+	1.24605i	0.921007	+	0.389546i	$0.127368\pi$
$829$	11.6571	+	35.8767i	0.404866	+	1.24605i	−0.516141	+	0.856504i	$0.672632\pi$
$830$		0			0
$831$	8.68303	−	6.30859i	0.301211	−	0.218843i
$832$	−0.721558	−	2.22073i	−0.0250155	−	0.0769899i
$833$	−0.342823	+	1.05510i	−0.0118781	+	0.0365571i
$834$	−12.9672	−	9.42125i	−0.449019	−	0.326231i
$835$		0			0
$836$	1.99813	+	6.53752i	0.0691068	+	0.226105i
$837$	−48.5765			−1.67905
$838$	12.5257	+	9.10044i	0.432692	+	0.314369i
$839$	−11.8934	+	36.6041i	−0.410606	+	1.26372i	0.505517	+	0.862817i	$0.331302\pi$
$839$	−11.8934	+	36.6041i	−0.410606	+	1.26372i	−0.916123	+	0.400898i	$0.868698\pi$
$840$		0			0
$841$	9.61452	−	6.98536i	0.331535	−	0.240874i
$842$	−17.3828	+	12.6293i	−0.599051	+	0.435236i
$843$	−7.82321	−	24.0774i	−0.269446	−	0.829269i
$844$	−4.86578	+	14.9753i	−0.167487	+	0.515472i
$845$		0			0
$846$	3.39074			0.116576
$847$	−43.4580	−	33.9647i	−1.49324	−	1.16704i
$848$	−2.22187			−0.0762994
$849$	−29.4536	−	21.3993i	−1.01084	−	0.734421i
$850$		0			0
$851$	5.51328	+	16.9681i	0.188993	+	0.581660i
$852$	11.5407	−	8.38481i	0.395378	−	0.287259i
$853$	41.1706	−	29.9122i	1.40965	−	1.02417i	0.416280	−	0.909237i	$-0.363334\pi$
$853$	41.1706	−	29.9122i	1.40965	−	1.02417i	0.993373	−	0.114936i	$-0.0366664\pi$
$854$	−15.0196	−	46.2256i	−0.513961	−	1.58181i
$855$		0			0
$856$	−1.80412	−	1.31077i	−0.0616636	−	0.0448012i
$857$	−11.5197			−0.393506			−0.196753	−	0.980453i	$-0.563040\pi$
$857$	−11.5197			−0.393506			−0.196753	+	0.980453i	$0.563040\pi$
$858$	−3.66261	−	11.9834i	−0.125039	−	0.409107i
$859$	23.9497			0.817153			0.408577	−	0.912724i	$-0.366025\pi$
$859$	23.9497			0.817153			0.408577	+	0.912724i	$0.366025\pi$
$860$		0			0
$861$	11.4821	−	35.3384i	0.391310	−	1.20433i
$862$	8.17010	+	25.1450i	0.278275	+	0.856441i
$863$	−32.3684	+	23.5170i	−1.10183	+	0.800530i	−0.981358	−	0.192187i	$-0.938442\pi$
$863$	−32.3684	+	23.5170i	−1.10183	+	0.800530i	−0.120476	+	0.992716i	$0.538442\pi$
$864$	−4.42705	+	3.21644i	−0.150611	+	0.109426i
$865$		0			0
$866$	−10.1611	+	31.2725i	−0.345287	+	1.06268i
$867$	−22.2484	−	16.1644i	−0.755595	−	0.548972i
$868$	−44.5114			−1.51081
$869$	7.18793	−	20.8696i	0.243834	−	0.707954i
$870$		0			0
$871$	−4.71460	−	3.42536i	−0.159748	−	0.116064i
$872$	2.42976	−	7.47804i	0.0822821	−	0.253238i
$873$	−0.861914	−	2.65270i	−0.0291714	−	0.0897802i
$874$	−6.52871	+	4.74338i	−0.220837	+	0.160447i
$875$		0			0
$876$	2.69808	+	8.30384i	0.0911597	+	0.280561i
$877$	8.02891	−	24.7104i	0.271117	−	0.834413i	−0.719104	−	0.694903i	$-0.755447\pi$
$877$	8.02891	−	24.7104i	0.271117	−	0.834413i	0.990221	−	0.139510i	$-0.0445526\pi$
$878$	9.85347	+	7.15897i	0.332539	+	0.241603i
$879$	29.4300			0.992648
$880$		0			0
$881$	25.1372			0.846893			0.423446	−	0.905921i	$-0.360820\pi$
$881$	25.1372			0.846893			0.423446	+	0.905921i	$0.360820\pi$
$882$	5.60624	+	4.07317i	0.188772	+	0.137151i
$883$	−13.4332	+	41.3431i	−0.452063	+	1.39131i	0.422486	+	0.906369i	$0.361157\pi$
$883$	−13.4332	+	41.3431i	−0.452063	+	1.39131i	−0.874549	+	0.484937i	$0.838843\pi$
$884$	0.0441236	+	0.135798i	0.00148404	+	0.00456739i
$885$		0			0
$886$	−13.4370	+	9.76254i	−0.451424	+	0.327979i
$887$	8.84036	+	27.2078i	0.296830	+	0.913549i	0.982601	+	0.185731i	$0.0594655\pi$
$887$	8.84036	+	27.2078i	0.296830	+	0.913549i	−0.685770	+	0.727818i	$0.740535\pi$
$888$	2.27844	−	7.01232i	0.0764595	−	0.235318i
$889$	58.6701	+	42.6263i	1.96773	+	1.42964i
$890$		0			0
$891$	−20.9430	+	14.6619i	−0.701617	+	0.491191i
$892$	−14.5556			−0.487358
$893$	−14.8026	−	10.7547i	−0.495349	−	0.359892i
$894$	−4.39616	+	13.5300i	−0.147030	+	0.452511i
$895$		0			0
$896$	−4.05657	+	2.94727i	−0.135520	+	0.0984614i
$897$	11.9672	−	8.69471i	0.399575	−	0.290308i
$898$	−1.65746	−	5.10113i	−0.0553100	−	0.170227i
$899$	11.3488	−	34.9281i	0.378504	−	1.16492i
$900$		0			0
$901$	0.135868			0.00452643
$902$	−12.1302	−	9.14237i	−0.403893	−	0.304407i
$903$	29.3536			0.976827
$904$	−10.1626	−	7.38357i	−0.338003	−	0.245574i
$905$		0			0
$906$	−10.7952	−	33.2241i	−0.358645	−	1.10380i
$907$	−38.5990	+	28.0438i	−1.28166	+	0.931179i	−0.999602	−	0.0282187i	$-0.991017\pi$
$907$	−38.5990	+	28.0438i	−1.28166	+	0.931179i	−0.282056	+	0.959398i	$0.591017\pi$
$908$	−7.95794	+	5.78178i	−0.264094	+	0.191875i
$909$	0.0261885	+	0.0805998i	0.000868617	+	0.00267333i
$910$		0			0
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.999606	−	0.0280809i	$-0.991060\pi$
$911$	−40.3003	−	29.2799i	−1.33521	−	0.970085i	−0.335602	−	0.942004i	$-0.608940\pi$
$912$	3.33501			0.110433
$913$	−29.2724	−	22.0621i	−0.968775	−	0.730150i
$914$	3.61237			0.119487
$915$		0			0
$916$	−4.80456	+	14.7869i	−0.158747	+	0.488573i
$917$	23.7466	+	73.0845i	0.784182	+	2.41346i
$918$	0.270716	−	0.196687i	0.00893495	−	0.00649162i
$919$	34.7058	−	25.2153i	1.14484	−	0.831775i	0.157053	−	0.987590i	$-0.449801\pi$
$919$	34.7058	−	25.2153i	1.14484	−	0.831775i	0.987786	+	0.155815i	$0.0498005\pi$
$920$		0			0
$921$	−6.19098	+	19.0539i	−0.204000	+	0.627847i
$922$	32.8967	+	23.9008i	1.08339	+	0.787132i
$923$	−20.5862			−0.677602
$924$	−22.0432	+	15.4321i	−0.725169	+	0.507679i
$925$		0			0
$926$	−1.71415	−	1.24540i	−0.0563303	−	0.0409264i
$927$	0.0668126	−	0.205628i	0.00219441	−	0.00675371i
$928$	−1.27844	−	3.93464i	−0.0419669	−	0.129161i
$929$	3.20719	−	2.33016i	0.105224	−	0.0764500i	−0.533929	−	0.845529i	$-0.679285\pi$
$929$	3.20719	−	2.33016i	0.105224	−	0.0764500i	0.639153	+	0.769079i	$0.279285\pi$
$930$		0			0
$931$	−11.5553	−	35.5635i	−0.378709	−	1.16555i
$932$	−8.00252	+	24.6292i	−0.262131	+	0.806757i
$933$	12.3178	+	8.94941i	0.403267	+	0.292991i
$934$	13.7549			0.450075
$935$		0			0
$936$	0.891895			0.0291525
$937$	1.71446	+	1.24563i	0.0560090	+	0.0406929i	0.615437	−	0.788186i	$-0.288979\pi$
$937$	1.71446	+	1.24563i	0.0560090	+	0.0406929i	−0.559429	+	0.828879i	$0.688979\pi$
$938$	−3.86707	+	11.9016i	−0.126264	+	0.388601i
$939$	−7.61585	−	23.4392i	−0.248534	−	0.764909i
$940$		0			0
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	−0.652316	−	0.757947i	$-0.726203\pi$
$941$	−4.08118	+	2.96515i	−0.133043	+	0.0966612i	0.519274	+	0.854608i	$0.326203\pi$
$942$	1.70736	+	5.25472i	0.0556289	+	0.171208i
$943$	5.54107	−	17.0537i	0.180442	−	0.555344i
$944$	−1.56856	−	1.13963i	−0.0510524	−	0.0370917i
$945$		0			0
$946$	3.90765	−	11.3456i	0.127049	−	0.368877i
$947$	−0.986192			−0.0320470			−0.0160235	−	0.999872i	$-0.505101\pi$
$947$	−0.986192			−0.0320470			−0.0160235	+	0.999872i	$0.505101\pi$
$948$	−8.71177	−	6.32947i	−0.282945	−	0.205572i
$949$	3.89364	−	11.9834i	0.126393	−	0.388998i
$950$		0			0
$951$	−17.6150	+	12.7981i	−0.571206	+	0.415006i
$952$	0.248061	−	0.180227i	0.00803969	−	0.00584118i
$953$	7.09580	+	21.8386i	0.229855	+	0.707422i	0.997762	+	0.0668608i	$0.0212983\pi$
$953$	7.09580	+	21.8386i	0.229855	+	0.707422i	−0.767907	+	0.640562i	$0.778702\pi$
$954$	0.262256	−	0.807142i	0.00849087	−	0.0261322i
$955$		0			0
$956$	19.9960			0.646718
$957$	−6.48934	−	21.2320i	−0.209770	−	0.686331i
$958$	31.4107			1.01484
$959$	−4.47994	−	3.25486i	−0.144665	−	0.105105i
$960$		0			0
$961$	14.7718	+	45.4628i	0.476508	+	1.46654i
$962$	−8.60824	+	6.25426i	−0.277541	+	0.201645i
$963$	0.689113	−	0.500670i	0.0222064	−	0.0161339i
$964$	2.78542	+	8.57264i	0.0897123	+	0.276106i
$965$		0			0
$966$	−25.6984	−	18.6710i	−0.826833	−	0.600729i
$967$	20.1267			0.647231			0.323616	−	0.946189i	$-0.395102\pi$
$967$	20.1267			0.647231			0.323616	+	0.946189i	$0.395102\pi$
$968$	3.03026	+	10.5744i	0.0973963	+	0.339873i
$969$	−0.203937			−0.00655141
$970$		0			0
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	0.781431	+	0.623991i	$0.214490\pi$
$971$	−6.77852	+	20.8621i	−0.217533	+	0.669498i	−0.998964	+	0.0455060i	$0.985510\pi$
$972$	−1.21885	−	3.75123i	−0.0390945	−	0.120321i
$973$	40.1847	−	29.1959i	1.28826	−	0.935978i
$974$	−6.07597	+	4.41445i	−0.194687	+	0.141448i
$975$		0			0
$976$	−2.99542	+	9.21895i	−0.0958810	+	0.295091i
$977$	−47.7788	−	34.7133i	−1.52858	−	1.11058i	−0.957022	−	0.290015i	$-0.906340\pi$
$977$	−47.7788	−	34.7133i	−1.52858	−	1.11058i	−0.571557	−	0.820562i	$-0.693660\pi$
$978$	28.1706			0.900795
$979$	−5.90396	−	19.3167i	−0.188691	−	0.617365i
$980$		0			0
$981$	2.42976	+	1.76533i	0.0775763	+	0.0563625i
$982$	3.48008	−	10.7106i	0.111054	−	0.341788i
$983$	14.9382	+	45.9751i	0.476455	+	1.46638i	0.843985	+	0.536367i	$0.180204\pi$
$983$	14.9382	+	45.9751i	0.476455	+	1.46638i	−0.367530	+	0.930012i	$0.619796\pi$
$984$	−5.99511	+	4.35570i	−0.191117	+	0.138855i
$985$		0			0
$986$	0.0781772	+	0.240605i	0.00248967	+	0.00766241i
$987$	22.2557	−	68.4960i	0.708406	−	2.18025i
$988$	−3.89364	−	2.82890i	−0.123873	−	0.0899992i
$989$	14.1655			0.450437
$990$		0			0
$991$	−55.0154			−1.74762			−0.873811	−	0.486266i	$-0.838359\pi$
$991$	−55.0154			−1.74762			−0.873811	+	0.486266i	$0.838359\pi$
$992$	7.18170	+	5.21781i	0.228019	+	0.165666i
$993$	1.91118	−	5.88201i	0.0606495	−	0.186660i
$994$	13.6606	+	42.0431i	0.433289	+	1.33353i
$995$		0			0
$996$	−14.4672	+	10.5111i	−0.458412	+	0.333056i
$997$	−7.09810	−	21.8457i	−0.224799	−	0.691861i	−0.998312	−	0.0580799i	$-0.981502\pi$
$997$	−7.09810	−	21.8457i	−0.224799	−	0.691861i	0.773513	−	0.633781i	$-0.218498\pi$
$998$	−8.33753	+	25.6603i	−0.263920	+	0.812262i
$999$	20.1736	+	14.6569i	0.638263	+	0.463725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.h.j.301.2		8
5.2	odd	4		110.2.j.b.59.4	yes	16
5.3	odd	4		110.2.j.b.59.2	✓	16
5.4	even	2		550.2.h.n.301.1		8
11.3	even	5	inner	550.2.h.j.201.2		8
11.5	even	5		6050.2.a.di.1.2		4
11.6	odd	10		6050.2.a.da.1.1		4
15.2	even	4		990.2.ba.h.829.1		16
15.8	even	4		990.2.ba.h.829.3		16
20.3	even	4		880.2.cd.b.609.4		16
20.7	even	4		880.2.cd.b.609.2		16
55.3	odd	20		110.2.j.b.69.4	yes	16
55.14	even	10		550.2.h.n.201.1		8
55.17	even	20		1210.2.b.l.969.3		8
55.27	odd	20		1210.2.b.k.969.7		8
55.28	even	20		1210.2.b.l.969.5		8
55.38	odd	20		1210.2.b.k.969.1		8
55.39	odd	10		6050.2.a.dl.1.4		4
55.47	odd	20		110.2.j.b.69.2	yes	16
55.49	even	10		6050.2.a.dd.1.3		4
165.47	even	20		990.2.ba.h.289.3		16
165.113	even	20		990.2.ba.h.289.1		16
220.3	even	20		880.2.cd.b.289.2		16
220.47	even	20		880.2.cd.b.289.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.2.j.b.59.2	✓	16	5.3	odd	4
110.2.j.b.59.4	yes	16	5.2	odd	4
110.2.j.b.69.2	yes	16	55.47	odd	20
110.2.j.b.69.4	yes	16	55.3	odd	20
550.2.h.j.201.2		8	11.3	even	5	inner
550.2.h.j.301.2		8	1.1	even	1	trivial
550.2.h.n.201.1		8	55.14	even	10
550.2.h.n.301.1		8	5.4	even	2
880.2.cd.b.289.2		16	220.3	even	20
880.2.cd.b.289.4		16	220.47	even	20
880.2.cd.b.609.2		16	20.7	even	4
880.2.cd.b.609.4		16	20.3	even	4
990.2.ba.h.289.1		16	165.113	even	20
990.2.ba.h.289.3		16	165.47	even	20
990.2.ba.h.829.1		16	15.2	even	4
990.2.ba.h.829.3		16	15.8	even	4
1210.2.b.k.969.1		8	55.38	odd	20
1210.2.b.k.969.7		8	55.27	odd	20
1210.2.b.l.969.3		8	55.17	even	20
1210.2.b.l.969.5		8	55.28	even	20
6050.2.a.da.1.1		4	11.6	odd	10
6050.2.a.dd.1.3		4	55.49	even	10
6050.2.a.di.1.2		4	11.5	even	5
6050.2.a.dl.1.4		4	55.39	odd	10

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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{6} +(1.54947 + 4.76878i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.500000 + 1.53884i) q^{3} +(0.309017 + 0.951057i) q^{4} +(1.30902 - 0.951057i) q^{6} +(1.54947 + 4.76878i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.309017 + 0.224514i) q^{9} +(-0.969425 - 3.17178i) q^{11} -1.61803 q^{12} +(1.88906 + 1.37249i) q^{13} +(1.54947 - 4.76878i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(0.0494717 - 0.0359433i) q^{17} +(-0.118034 - 0.363271i) q^{18} +(-0.636930 + 1.96027i) q^{19} -8.11314 q^{21} +(-1.08005 + 3.13584i) q^{22} -3.91525 q^{23} +(1.30902 + 0.951057i) q^{24} +(-0.721558 - 2.22073i) q^{26} +(-4.42705 + 3.21644i) q^{27} +(-4.05657 + 2.94727i) q^{28} +(-1.27844 - 3.93464i) q^{29} +(7.18170 + 5.21781i) q^{31} +1.00000 q^{32} +(5.36559 + 0.0941007i) q^{33} -0.0611504 q^{34} +(-0.118034 + 0.363271i) q^{36} +(-1.40815 - 4.33385i) q^{37} +(1.66751 - 1.21151i) q^{38} +(-3.05657 + 2.22073i) q^{39} +(-1.41525 + 4.35570i) q^{41} +(6.56367 + 4.76878i) q^{42} -3.61803 q^{43} +(2.71698 - 1.90211i) q^{44} +(3.16751 + 2.30133i) q^{46} +(-2.74317 + 8.44260i) q^{47} +(-0.500000 - 1.53884i) q^{48} +(-14.6773 + 10.6637i) q^{49} +(0.0305752 + 0.0941007i) q^{51} +(-0.721558 + 2.22073i) q^{52} +(1.79753 + 1.30598i) q^{53} +5.47214 q^{54} +5.01420 q^{56} +(-2.69808 - 1.96027i) q^{57} +(-1.27844 + 3.93464i) q^{58} +(0.599137 + 1.84396i) q^{59} +(7.84211 - 5.69763i) q^{61} +(-2.74317 - 8.44260i) q^{62} +(-0.591846 + 1.82151i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.28554 - 3.22994i) q^{66} -2.49573 q^{67} +(0.0494717 + 0.0359433i) q^{68} +(1.95763 - 6.02495i) q^{69} +(-7.13254 + 5.18210i) q^{71} +(0.309017 - 0.224514i) q^{72} +(-1.66751 - 5.13205i) q^{73} +(-1.40815 + 4.33385i) q^{74} -2.06115 q^{76} +(13.6235 - 9.53757i) q^{77} +3.77813 q^{78} +(5.38417 + 3.91183i) q^{79} +(-2.38197 - 7.33094i) q^{81} +(3.70518 - 2.69197i) q^{82} +(8.94125 - 6.49620i) q^{83} +(-2.50710 - 7.71605i) q^{84} +(2.92705 + 2.12663i) q^{86} +6.69401 q^{87} +(-3.31611 - 0.0581575i) q^{88} +6.09017 q^{89} +(-3.61803 + 11.1352i) q^{91} +(-1.20988 - 3.72363i) q^{92} +(-11.6202 + 8.44260i) q^{93} +(7.18170 - 5.21781i) q^{94} +(-0.500000 + 1.53884i) q^{96} +(-5.90765 - 4.29216i) q^{97} +18.1422 q^{98} +(0.412541 - 1.19778i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 2 q^{4} + 6 q^{6} + 6 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{11} - 4 q^{12} + 2 q^{13} + 6 q^{14} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} - 22 q^{27} - 4 q^{28} - 8 q^{29} - 2 q^{31} + 8 q^{32} + 10 q^{33} + 4 q^{34} + 8 q^{36} - 2 q^{37} - 2 q^{38} + 4 q^{39} + 20 q^{41} + 2 q^{42} - 20 q^{43} + 10 q^{46} + 18 q^{47} - 4 q^{48} - 42 q^{49} - 2 q^{51} - 8 q^{52} + 16 q^{53} + 8 q^{54} - 4 q^{56} - 4 q^{57} - 8 q^{58} + 10 q^{61} + 18 q^{62} - 14 q^{63} - 2 q^{64} - 10 q^{66} - 20 q^{67} - 6 q^{68} - 28 q^{71} - 2 q^{72} + 2 q^{73} - 2 q^{74} - 12 q^{76} + 24 q^{77} + 4 q^{78} - 18 q^{79} - 28 q^{81} - 10 q^{82} + 14 q^{83} + 2 q^{84} + 10 q^{86} + 44 q^{87} + 4 q^{89} - 20 q^{91} - 10 q^{92} - 14 q^{93} - 2 q^{94} - 4 q^{96} - 6 q^{97} + 48 q^{98} + 10 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 2 * q^4 + 6 * q^6 + 6 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^11 - 4 * q^12 + 2 * q^13 + 6 * q^14 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 8 * q^19 - 8 * q^21 + 6 * q^24 - 8 * q^26 - 22 * q^27 - 4 * q^28 - 8 * q^29 - 2 * q^31 + 8 * q^32 + 10 * q^33 + 4 * q^34 + 8 * q^36 - 2 * q^37 - 2 * q^38 + 4 * q^39 + 20 * q^41 + 2 * q^42 - 20 * q^43 + 10 * q^46 + 18 * q^47 - 4 * q^48 - 42 * q^49 - 2 * q^51 - 8 * q^52 + 16 * q^53 + 8 * q^54 - 4 * q^56 - 4 * q^57 - 8 * q^58 + 10 * q^61 + 18 * q^62 - 14 * q^63 - 2 * q^64 - 10 * q^66 - 20 * q^67 - 6 * q^68 - 28 * q^71 - 2 * q^72 + 2 * q^73 - 2 * q^74 - 12 * q^76 + 24 * q^77 + 4 * q^78 - 18 * q^79 - 28 * q^81 - 10 * q^82 + 14 * q^83 + 2 * q^84 + 10 * q^86 + 44 * q^87 + 4 * q^89 - 20 * q^91 - 10 * q^92 - 14 * q^93 - 2 * q^94 - 4 * q^96 - 6 * q^97 + 48 * q^98 + 10 * q^99

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