LMFDB - Embedded newform 550.2.h.n.301.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(201,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,2,4,-2,0,6,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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			301.1
Root			$0.839592 - 2.58400i$ of defining polynomial
Character	$\chi$	$=$	550.301
Dual form			550.2.h.n.201.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 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} - 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}+ \cdots + 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

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	$-0.745304\pi$
$3$	0.500000	−	1.53884i	0.288675	−	0.888451i	0.985273	−	0.170989i	$-0.0546962\pi$
$4$	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	$-0.703507\pi$
$7$	−1.54947	−	4.76878i	−0.585645	−	1.80243i	0.0110184	−	0.999939i	$-0.496493\pi$
$8$	−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	0.294151	−	0.955759i	$-0.404963\pi$
$13$	−1.88906	−	1.37249i	−0.523932	−	0.380659i	−0.818083	+	0.575100i	$0.804963\pi$
$14$	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	−0.593768	−	0.804636i	$-0.702360\pi$
$17$	−0.0494717	+	0.0359433i	−0.0119986	+	0.00871753i	0.581770	+	0.813354i	$0.302360\pi$
$18$	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	$-0.366159\pi$
$23$	3.91525			0.816387			0.408193	+	0.912896i	$0.366159\pi$
$24$	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	$0.0222109\pi$
$37$	1.40815	+	4.33385i	0.231499	+	0.712481i	−0.766067	+	0.642760i	$0.777789\pi$
$38$	−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	$-0.411033\pi$
$43$	3.61803			0.551745			0.275873	+	0.961194i	$0.411033\pi$
$44$	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	$-0.675845\pi$
$47$	2.74317	−	8.44260i	0.400132	−	1.23148i	0.924892	−	0.380229i	$-0.124155\pi$
$48$	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	0.457446	−	0.889237i	$-0.348764\pi$
$53$	−1.79753	−	1.30598i	−0.246910	−	0.179391i	−0.704356	+	0.709847i	$0.748764\pi$
$54$	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	$-0.451283\pi$
$67$	2.49573			0.304902			0.152451	+	0.988311i	$0.451283\pi$
$68$	−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	$0.00226833\pi$
$73$	1.66751	+	5.13205i	0.195167	+	0.600662i	−0.804808	+	0.593535i	$0.797732\pi$
$74$	−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	−0.958028	−	0.286676i	$-0.907450\pi$
$83$	−8.94125	+	6.49620i	−0.981429	+	0.713050i	−0.0234017	+	0.999726i	$0.507450\pi$
$84$	−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	0.845819	−	0.533470i	$-0.179112\pi$
$97$	5.90765	+	4.29216i	0.599831	+	0.435802i	−0.245988	+	0.969273i	$0.579112\pi$
$98$	−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	0.959304	−	0.282375i	$-0.0911221\pi$
$103$	0.174918	+	0.538341i	0.0172351	+	0.0530443i	−0.942069	+	0.335419i	$0.891122\pi$
$104$	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	−0.978825	−	0.204700i	$-0.934378\pi$
$107$	−0.689113	+	2.12087i	−0.0666191	+	0.205033i	0.912206	+	0.409733i	$0.134378\pi$
$108$	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	$0.301208\pi$
$113$	−3.88177	+	11.9469i	−0.365166	+	1.12387i	−0.949877	+	0.312624i	$0.898792\pi$
$114$	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	−0.969949	−	0.243310i	$-0.921767\pi$
$127$	−11.7008	+	8.50112i	−1.03828	+	0.754353i	−0.0683289	+	0.997663i	$0.521767\pi$
$128$	−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	−0.548964	−	0.835846i	$-0.684978\pi$
$137$	0.893451	−	0.649130i	0.0763326	−	0.0554589i	0.625297	+	0.780387i	$0.284978\pi$
$138$	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	−0.900078	−	0.435728i	$-0.856491\pi$
$157$	1.05521	−	3.24760i	0.0842148	−	0.259186i	0.984293	+	0.176542i	$0.0564910\pi$
$158$	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	−0.121657	−	0.992572i	$-0.538821\pi$
$163$	−14.0853	−	10.2336i	−1.10324	−	0.801554i	−0.981586	+	0.191019i	$0.938821\pi$
$164$	−4.57985			−0.357626
$165$		0			0
$166$	−11.0520			−0.857801
$167$	−2.67460	−	1.94321i	−0.206967	−	0.150370i	0.479473	−	0.877556i	$-0.340828\pi$
$167$	−2.67460	−	1.94321i	−0.206967	−	0.150370i	−0.686440	+	0.727186i	$0.740828\pi$
$168$	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	−0.872561	−	0.488505i	$-0.837542\pi$
$173$	1.58482	−	4.87758i	0.120492	−	0.370836i	0.993053	+	0.117670i	$0.0375424\pi$
$174$	−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	−0.720453	−	0.693503i	$-0.756066\pi$
$193$	−3.93885	+	2.86174i	−0.283525	+	0.205993i	0.436929	+	0.899496i	$0.356066\pi$
$194$	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	$-0.692717\pi$
$197$	−15.9760			−1.13824			−0.569122	+	0.822253i	$0.692717\pi$
$198$	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	$-0.737961\pi$
$223$	4.49794	−	13.8432i	0.301204	−	0.927011i	0.981067	−	0.193671i	$-0.0620395\pi$
$224$	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	$-0.994152\pi$
$227$	−3.03966	−	9.35512i	−0.201749	−	0.620921i	0.798082	−	0.602549i	$-0.205848\pi$
$228$	−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	$-0.977642\pi$
$233$	−20.9509	−	15.2217i	−1.37254	−	0.997206i	−0.375002	−	0.927024i	$-0.622358\pi$
$234$	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	0.984817	−	0.173594i	$-0.0555379\pi$
$257$	1.37945	+	4.24551i	0.0860477	+	0.264827i	−0.898770	+	0.438421i	$0.855538\pi$
$258$	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	$-0.355984\pi$
$263$	14.1791			0.874320			0.437160	+	0.899384i	$0.355984\pi$
$264$	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	0.737214	−	0.675659i	$-0.236141\pi$
$277$	5.36641	+	3.89892i	0.322436	+	0.234264i	−0.414778	+	0.909923i	$0.636141\pi$
$278$	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	$-0.666826\pi$
$283$	6.95305	−	21.3993i	0.413316	−	1.27205i	0.913749	−	0.406280i	$-0.133174\pi$
$284$	−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	$0.0782957\pi$
$293$	5.62063	+	17.2985i	0.328360	+	1.01059i	−0.641540	+	0.767089i	$0.721704\pi$
$294$	−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	$-0.614953\pi$
$307$	−12.3820			−0.706676			−0.353338	+	0.935496i	$0.614953\pi$
$308$	−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	−0.182277	−	0.983247i	$-0.558347\pi$
$313$	12.3227	−	8.95297i	0.696520	−	0.506052i	0.878797	+	0.477196i	$0.158347\pi$
$314$	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	0.238470	−	0.971150i	$-0.423354\pi$
$317$	−10.8867	−	7.90964i	−0.611457	−	0.444250i	−0.849927	+	0.526900i	$0.823354\pi$
$318$	−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	0.998576	−	0.0533455i	$-0.0169885\pi$
$337$	2.92538	+	9.00338i	0.159355	+	0.490445i	−0.839221	+	0.543791i	$0.816988\pi$
$338$	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	−0.885887	−	0.463902i	$-0.846449\pi$
$347$	−13.3831	+	9.72341i	−0.718444	+	0.521980i	0.167443	+	0.985882i	$0.446449\pi$
$348$	−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	$-0.766606\pi$
$353$	−27.9200			−1.48603			−0.743017	+	0.669272i	$0.766606\pi$
$354$	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	$0.178925\pi$
$367$	9.09719	+	27.9983i	0.474870	+	1.46150i	−0.371264	+	0.928527i	$0.621075\pi$
$368$	−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	$-0.636620\pi$
$373$	−16.0743			−0.832297			−0.416149	+	0.909297i	$0.636620\pi$
$374$	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	0.280200	−	0.959942i	$-0.409599\pi$
$383$	−10.6888	−	7.76587i	−0.546172	−	0.396817i	−0.826372	+	0.563124i	$0.809599\pi$
$384$	−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	$-0.224722\pi$
$397$	30.3246			1.52195			0.760974	+	0.648783i	$0.224722\pi$
$398$	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	$0.189972\pi$
$433$	10.1611	+	31.2725i	0.488309	+	1.50286i	−0.338821	+	0.940851i	$0.610028\pi$
$434$	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	$0.229103\pi$
$443$	−5.13247	+	15.7961i	−0.243851	+	0.750496i	−0.995823	+	0.0913015i	$0.970897\pi$
$444$	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	−0.517330	−	0.855786i	$-0.673074\pi$
$457$	2.92247	−	2.12330i	0.136707	−	0.0993237i	0.654037	+	0.756462i	$0.273074\pi$
$458$	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	$-0.515678\pi$
$463$	−2.11880			−0.0984690			−0.0492345	+	0.998787i	$0.515678\pi$
$464$	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	−0.299754	−	0.954017i	$-0.596905\pi$
$467$	11.1280	−	8.08494i	0.514941	−	0.374126i	0.814695	+	0.579890i	$0.196905\pi$
$468$	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	−0.989769	−	0.142676i	$-0.954429\pi$
$487$	−2.32082	+	7.14274i	−0.105166	+	0.323668i	0.884603	+	0.466344i	$0.154429\pi$
$488$	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	$0.354427\pi$
$503$	−9.93662	+	30.5818i	−0.443052	+	1.36357i	−0.884606	+	0.466339i	$0.845573\pi$
$504$	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	−0.614586	−	0.788850i	$-0.710677\pi$
$523$	−1.24096	+	0.901612i	−0.0542635	+	0.0394248i	0.560323	+	0.828274i	$0.310677\pi$
$524$	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	−0.996430	−	0.0844251i	$-0.973095\pi$
$547$	−3.29017	+	10.1261i	−0.140677	+	0.432960i	0.855752	+	0.517385i	$0.173095\pi$
$548$	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	$0.155222\pi$
$557$	10.4818	+	32.2595i	0.444126	+	1.36688i	−0.439313	+	0.898334i	$0.644778\pi$
$558$	−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	0.564641	−	0.825337i	$-0.309015\pi$
$563$	−1.08714	−	0.789857i	−0.0458177	−	0.0332885i	−0.610458	+	0.792048i	$0.709015\pi$
$564$	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	$0.658660\pi$
$577$	−35.0975	+	25.4998i	−1.46113	+	1.06157i	−0.983068	+	0.183244i	$0.941340\pi$
$578$	−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	0.928477	−	0.371389i	$-0.121118\pi$
$587$	−0.992708	−	3.05524i	−0.0409734	−	0.126103i	−0.969451	+	0.245285i	$0.921118\pi$
$588$	−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	$-0.499794\pi$
$593$	0.0315027			0.00129366			0.000646829		1.00000i	$0.499794\pi$
$594$	−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	0.546158	−	0.837682i	$-0.316090\pi$
$607$	−2.01420	−	1.46340i	−0.0817537	−	0.0593975i	−0.627911	+	0.778285i	$0.716090\pi$
$608$	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	$0.374202\pi$
$613$	−11.6106	+	35.7338i	−0.468949	+	1.44328i	−0.853948	+	0.520359i	$0.825798\pi$
$614$	−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	$-0.869793\pi$
$617$	−45.5803			−1.83499			−0.917496	+	0.397744i	$0.869793\pi$
$618$	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	−0.986742	−	0.162298i	$-0.948109\pi$
$643$	−28.8392	+	20.9529i	−1.13731	+	0.826302i	−0.150565	+	0.988600i	$0.548109\pi$
$644$	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	0.860224	−	0.509917i	$-0.170324\pi$
$647$	16.3068	+	11.8476i	0.641088	+	0.465778i	−0.219136	+	0.975694i	$0.570324\pi$
$648$	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	$-0.941685\pi$
$653$	−7.53504	−	23.1905i	−0.294869	−	0.907513i	0.688397	−	0.725334i	$-0.258315\pi$
$654$	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	0.705062	−	0.709146i	$-0.250919\pi$
$673$	6.44665	+	4.68377i	0.248500	+	0.180546i	−0.456562	+	0.889692i	$0.650919\pi$
$674$	−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	−0.340313	−	0.940312i	$-0.610533\pi$
$677$	11.6778	−	8.48443i	0.448815	−	0.326083i	0.789128	+	0.614229i	$0.210533\pi$
$678$	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	$-0.307837\pi$
$683$	29.6723			1.13538			0.567690	+	0.823242i	$0.307837\pi$
$684$	−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	$-0.351318\pi$
$727$	24.2826			0.900593			0.450297	+	0.892879i	$0.351318\pi$
$728$	−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	$0.0293395\pi$
$733$	6.61345	+	20.3541i	0.244273	+	0.751796i	−0.751482	+	0.659754i	$0.770660\pi$
$734$	−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	0.0474407	−	0.998874i	$-0.484893\pi$
$743$	27.5875	−	20.0435i	1.01209	−	0.735324i	0.964646	+	0.263550i	$0.0848935\pi$
$744$	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	0.171544	−	0.985176i	$-0.445124\pi$
$757$	−19.6008	−	14.2408i	−0.712404	−	0.517592i	−0.883948	+	0.467584i	$0.845124\pi$
$758$	−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	−0.995436	−	0.0954286i	$-0.969578\pi$
$773$	−3.72614	+	11.4679i	−0.134020	+	0.412471i	0.861416	+	0.507899i	$0.169578\pi$
$774$	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	−0.294343	−	0.955700i	$-0.595101\pi$
$787$	14.6895	−	10.6725i	0.523624	−	0.380435i	0.817967	+	0.575265i	$0.195101\pi$
$788$	−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	−0.610624	−	0.791920i	$-0.709081\pi$
$797$	−1.30306	+	0.946725i	−0.0461566	+	0.0335347i	0.564468	+	0.825455i	$0.309081\pi$
$798$	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	0.751751	−	0.659447i	$-0.229209\pi$
$823$	10.2383	+	7.43854i	0.356884	+	0.259291i	−0.394867	+	0.918738i	$0.629209\pi$
$824$	−0.566045			−0.0197191
$825$		0			0
$826$	9.72177			0.338264
$827$	−7.15520	−	5.19856i	−0.248811	−	0.180772i	0.456389	−	0.889780i	$-0.349143\pi$
$827$	−7.15520	−	5.19856i	−0.248811	−	0.180772i	−0.705200	+	0.709009i	$0.749143\pi$
$828$	−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	$0.636666\pi$
$853$	−41.1706	+	29.9122i	−1.40965	+	1.02417i	−0.993373	+	0.114936i	$0.963334\pi$
$854$	−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	$-0.436960\pi$
$857$	11.5197			0.393506			0.196753	+	0.980453i	$0.436960\pi$
$858$	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	0.120476	−	0.992716i	$-0.461558\pi$
$863$	32.3684	−	23.5170i	1.10183	−	0.800530i	0.981358	+	0.192187i	$0.0615579\pi$
$864$	−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	$0.244553\pi$
$877$	−8.02891	+	24.7104i	−0.271117	+	0.834413i	−0.990221	+	0.139510i	$0.955447\pi$
$878$	−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	$-0.638843\pi$
$883$	13.4332	−	41.3431i	0.452063	−	1.39131i	0.874549	−	0.484937i	$-0.161157\pi$
$884$	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	$-0.940535\pi$
$887$	−8.84036	−	27.2078i	−0.296830	−	0.913549i	0.685770	−	0.727818i	$-0.259465\pi$
$888$	−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	0.282056	−	0.959398i	$-0.408983\pi$
$907$	38.5990	−	28.0438i	1.28166	−	0.931179i	0.999602	+	0.0282187i	$0.00898348\pi$
$908$	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	0.559429	−	0.828879i	$-0.311021\pi$
$937$	−1.71446	−	1.24563i	−0.0560090	−	0.0406929i	−0.615437	+	0.788186i	$0.711021\pi$
$938$	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	$-0.494899\pi$
$947$	0.986192			0.0320470			0.0160235	+	0.999872i	$0.494899\pi$
$948$	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	$-0.978702\pi$
$953$	−7.09580	−	21.8386i	−0.229855	−	0.707422i	0.767907	−	0.640562i	$-0.221298\pi$
$954$	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	$-0.604898\pi$
$967$	−20.1267			−0.647231			−0.323616	+	0.946189i	$0.604898\pi$
$968$	−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	$0.0936604\pi$
$977$	47.7788	+	34.7133i	1.52858	+	1.11058i	0.571557	+	0.820562i	$0.306340\pi$
$978$	−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	$-0.819796\pi$
$983$	−14.9382	−	45.9751i	−0.476455	−	1.46638i	0.367530	−	0.930012i	$-0.380204\pi$
$984$	−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	$0.0184978\pi$
$997$	7.09810	+	21.8457i	0.224799	+	0.691861i	−0.773513	+	0.633781i	$0.781502\pi$
$998$	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.n.301.1		8
5.2	odd	4		110.2.j.b.59.2	✓	16
5.3	odd	4		110.2.j.b.59.4	yes	16
5.4	even	2		550.2.h.j.301.2		8
11.3	even	5	inner	550.2.h.n.201.1		8
11.5	even	5		6050.2.a.dd.1.3		4
11.6	odd	10		6050.2.a.dl.1.4		4
15.2	even	4		990.2.ba.h.829.3		16
15.8	even	4		990.2.ba.h.829.1		16
20.3	even	4		880.2.cd.b.609.2		16
20.7	even	4		880.2.cd.b.609.4		16
55.3	odd	20		110.2.j.b.69.2	yes	16
55.14	even	10		550.2.h.j.201.2		8
55.17	even	20		1210.2.b.l.969.5		8
55.27	odd	20		1210.2.b.k.969.1		8
55.28	even	20		1210.2.b.l.969.3		8
55.38	odd	20		1210.2.b.k.969.7		8
55.39	odd	10		6050.2.a.da.1.1		4
55.47	odd	20		110.2.j.b.69.4	yes	16
55.49	even	10		6050.2.a.di.1.2		4
165.47	even	20		990.2.ba.h.289.1		16
165.113	even	20		990.2.ba.h.289.3		16
220.3	even	20		880.2.cd.b.289.4		16
220.47	even	20		880.2.cd.b.289.2		16

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

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 4 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} + 2 q^{8} - 2 q^{9} - 10 q^{11} + 4 q^{12} - 2 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} - 8 q^{18} + 8 q^{19} - 8 q^{21} + 6 q^{24} - 8 q^{26} + 22 q^{27}+ \cdots + 10 q^{99}+O(q^{100}) \) 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

Introduction

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