LMFDB - Embedded newform 546.2.bu.a.71.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.a.323.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-1.38152 - 1.04470i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28362 + 1.28362i) q^{5} +(-1.60483 - 0.651543i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.817188 + 2.88656i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-1.38152 - 1.04470i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28362 + 1.28362i) q^{5} +(-1.60483 - 0.651543i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.817188 + 2.88656i) q^{9} +(1.57211 + 0.907660i) q^{10} +(1.42232 + 5.30817i) q^{11} +(-1.71878 - 0.213981i) q^{12} +(3.42359 + 1.13095i) q^{13} +1.00000i q^{14} +(-0.432344 - 3.11436i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.95532 - 6.85082i) q^{17} +(1.53644 + 2.57669i) q^{18} +(6.30492 + 1.68940i) q^{19} +(1.75346 + 0.469839i) q^{20} +(1.36667 - 1.06406i) q^{21} +(2.74771 + 4.75917i) q^{22} +(-2.33954 + 4.05220i) q^{23} +(-1.71560 + 0.238164i) q^{24} -1.70462i q^{25} +(3.59964 + 0.206327i) q^{26} +(1.88663 - 4.84155i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-0.994028 - 0.573902i) q^{29} +(-1.22367 - 2.89634i) q^{30} +(2.34297 - 2.34297i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.58050 - 8.81924i) q^{33} +(-5.59367 - 5.59367i) q^{34} +(-1.57211 + 0.907660i) q^{35} +(2.15098 + 2.09124i) q^{36} +(1.82773 - 0.489737i) q^{37} +6.52733 q^{38} +(-3.54824 - 5.13907i) q^{39} +1.81532 q^{40} +(8.51546 - 2.28171i) q^{41} +(1.04470 - 1.38152i) q^{42} +(-5.49929 + 3.17501i) q^{43} +(3.88585 + 3.88585i) q^{44} +(-2.65629 + 4.75422i) q^{45} +(-1.21104 + 4.51964i) q^{46} +(-7.34551 + 7.34551i) q^{47} +(-1.59550 + 0.674078i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.441187 - 1.64653i) q^{50} +(-1.69272 + 13.5967i) q^{51} +(3.53039 - 0.732359i) q^{52} -2.74622i q^{53} +(0.569264 - 5.16488i) q^{54} +(-4.98797 + 8.63942i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-6.94544 - 8.92071i) q^{57} +(-1.10869 - 0.297074i) q^{58} +(5.23839 + 1.40362i) q^{59} +(-1.93160 - 2.48094i) q^{60} +(-3.94096 - 6.82594i) q^{61} +(1.65673 - 2.86954i) q^{62} +(-2.99970 + 0.0422477i) q^{63} -1.00000i q^{64} +(2.94288 + 5.84632i) q^{65} +(1.17591 - 9.44543i) q^{66} +(2.85542 + 10.6566i) q^{67} +(-6.85082 - 3.95532i) q^{68} +(7.46547 - 3.15407i) q^{69} +(-1.28362 + 1.28362i) q^{70} +(1.69102 - 6.31098i) q^{71} +(2.61894 + 1.46326i) q^{72} +(-2.12247 - 2.12247i) q^{73} +(1.63869 - 0.946100i) q^{74} +(-1.78082 + 2.35496i) q^{75} +(6.30492 - 1.68940i) q^{76} -5.49542 q^{77} +(-4.75742 - 4.04561i) q^{78} +0.559199 q^{79} +(1.75346 - 0.469839i) q^{80} +(-7.66441 + 4.71772i) q^{81} +(7.63476 - 4.40793i) q^{82} +(-11.4710 - 11.4710i) q^{83} +(0.651543 - 1.60483i) q^{84} +(3.71673 - 13.8710i) q^{85} +(-4.49015 + 4.49015i) q^{86} +(0.773710 + 1.83132i) q^{87} +(4.75917 + 2.74771i) q^{88} +(3.08845 + 11.5262i) q^{89} +(-1.33530 + 5.27972i) q^{90} +(-1.97851 + 3.01422i) q^{91} +4.67908i q^{92} +(-5.68456 + 0.789147i) q^{93} +(-5.19406 + 8.99638i) q^{94} +(5.92460 + 10.2617i) q^{95} +(-1.36667 + 1.06406i) q^{96} +(-14.0135 - 3.75490i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(-14.1600 + 8.44338i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−1.38152	−	1.04470i	−0.797620	−	0.603160i
$3$	−1.38152	−	1.04470i	−0.797620	−	0.603160i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	1.28362	+	1.28362i	0.574054	+	0.574054i	0.933259	−	0.359204i	$-0.116952\pi$
$5$	1.28362	+	1.28362i	0.574054	+	0.574054i	−0.359204	+	0.933259i	$0.616952\pi$
$6$	−1.60483	−	0.651543i	−0.655171	−	0.265991i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.817188	+	2.88656i	0.272396	+	0.962185i
$10$	1.57211	+	0.907660i	0.497146	+	0.287027i
$11$	1.42232	+	5.30817i	0.428846	+	1.60047i	0.755379	+	0.655288i	$0.227453\pi$
$11$	1.42232	+	5.30817i	0.428846	+	1.60047i	−0.326534	+	0.945186i	$0.605881\pi$
$12$	−1.71878	−	0.213981i	−0.496170	−	0.0617709i
$13$	3.42359	+	1.13095i	0.949532	+	0.313670i
$13$	3.42359	+	1.13095i	0.949532	+	0.313670i
$14$			1.00000i			0.267261i
$15$	−0.432344	−	3.11436i	−0.111631	−	0.804124i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.95532	−	6.85082i	−0.959306	−	1.66157i	−0.724190	−	0.689600i	$-0.757786\pi$
$17$	−3.95532	−	6.85082i	−0.959306	−	1.66157i	−0.235116	−	0.971967i	$-0.575547\pi$
$18$	1.53644	+	2.57669i	0.362142	+	0.607333i
$19$	6.30492	+	1.68940i	1.44645	+	0.387574i	0.894787	−	0.446494i	$-0.147328\pi$
$19$	6.30492	+	1.68940i	1.44645	+	0.387574i	0.551661	+	0.834068i	$0.313994\pi$
$20$	1.75346	+	0.469839i	0.392086	+	0.105059i
$21$	1.36667	−	1.06406i	0.298232	−	0.232196i
$22$	2.74771	+	4.75917i	0.585814	+	1.01466i
$23$	−2.33954	+	4.05220i	−0.487828	+	0.844943i	−0.999902	−	0.0139986i	$-0.995544\pi$
$23$	−2.33954	+	4.05220i	−0.487828	+	0.844943i	0.512074	+	0.858941i	$0.328877\pi$
$24$	−1.71560	+	0.238164i	−0.350195	+	0.0486151i
$25$		−	1.70462i		−	0.340923i
$26$	3.59964	+	0.206327i	0.705948	+	0.0404641i
$27$	1.88663	−	4.84155i	0.363083	−	0.931757i
$28$	0.258819	+	0.965926i	0.0489122	+	0.182543i
$29$	−0.994028	−	0.573902i	−0.184586	−	0.106571i	0.404859	−	0.914379i	$-0.367320\pi$
$29$	−0.994028	−	0.573902i	−0.184586	−	0.106571i	−0.589446	+	0.807808i	$0.700654\pi$
$30$	−1.22367	−	2.89634i	−0.223410	−	0.528797i
$31$	2.34297	−	2.34297i	0.420809	−	0.420809i	−0.464673	−	0.885482i	$-0.653828\pi$
$31$	2.34297	−	2.34297i	0.420809	−	0.420809i	0.885482	+	0.464673i	$0.153828\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	3.58050	−	8.81924i	0.623286	−	1.53523i
$34$	−5.59367	−	5.59367i	−0.959306	−	0.959306i
$35$	−1.57211	+	0.907660i	−0.265736	+	0.153423i
$36$	2.15098	+	2.09124i	0.358497	+	0.348539i
$37$	1.82773	−	0.489737i	0.300476	−	0.0805123i	−0.105431	−	0.994427i	$-0.533622\pi$
$37$	1.82773	−	0.489737i	0.300476	−	0.0805123i	0.405907	+	0.913914i	$0.366956\pi$
$38$	6.52733			1.05887
$39$	−3.54824	−	5.13907i	−0.568173	−	0.822909i
$40$	1.81532			0.287027
$41$	8.51546	−	2.28171i	1.32989	−	0.356344i	0.477217	−	0.878785i	$-0.341645\pi$
$41$	8.51546	−	2.28171i	1.32989	−	0.356344i	0.852675	+	0.522442i	$0.174979\pi$
$42$	1.04470	−	1.38152i	0.161201	−	0.213173i
$43$	−5.49929	+	3.17501i	−0.838633	+	0.484185i	−0.856799	−	0.515650i	$-0.827551\pi$
$43$	−5.49929	+	3.17501i	−0.838633	+	0.484185i	0.0181660	+	0.999835i	$0.494217\pi$
$44$	3.88585	+	3.88585i	0.585814	+	0.585814i
$45$	−2.65629	+	4.75422i	−0.395977	+	0.708717i
$46$	−1.21104	+	4.51964i	−0.178557	+	0.666385i
$47$	−7.34551	+	7.34551i	−1.07145	+	1.07145i	−0.0742109	+	0.997243i	$0.523644\pi$
$47$	−7.34551	+	7.34551i	−1.07145	+	1.07145i	−0.997243	+	0.0742109i	$0.976356\pi$
$48$	−1.59550	+	0.674078i	−0.230290	+	0.0972948i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−0.441187	−	1.64653i	−0.0623932	−	0.232855i
$51$	−1.69272	+	13.5967i	−0.237029	+	1.90392i
$52$	3.53039	−	0.732359i	0.489577	−	0.101560i
$53$		−	2.74622i		−	0.377223i	−0.982052	−	0.188611i	$-0.939601\pi$
$53$		−	2.74622i		−	0.377223i	0.982052	−	0.188611i	$-0.0603987\pi$
$54$	0.569264	−	5.16488i	0.0774670	−	0.702851i
$55$	−4.98797	+	8.63942i	−0.672578	+	1.16494i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−6.94544	−	8.92071i	−0.919947	−	1.18158i
$58$	−1.10869	−	0.297074i	−0.145579	−	0.0390077i
$59$	5.23839	+	1.40362i	0.681980	+	0.182736i	0.583145	−	0.812368i	$-0.301822\pi$
$59$	5.23839	+	1.40362i	0.681980	+	0.182736i	0.0988349	+	0.995104i	$0.468488\pi$
$60$	−1.93160	−	2.48094i	−0.249369	−	0.320288i
$61$	−3.94096	−	6.82594i	−0.504588	−	0.873972i	−0.999986	−	0.00530588i	$-0.998311\pi$
$61$	−3.94096	−	6.82594i	−0.504588	−	0.873972i	0.495398	−	0.868666i	$-0.335022\pi$
$62$	1.65673	−	2.86954i	0.210405	−	0.364432i
$63$	−2.99970	+	0.0422477i	−0.377927	+	0.00532271i
$64$		−	1.00000i		−	0.125000i
$65$	2.94288	+	5.84632i	0.365020	+	0.725147i
$66$	1.17591	−	9.44543i	0.144745	−	1.16265i
$67$	2.85542	+	10.6566i	0.348845	+	1.30191i	0.888056	+	0.459735i	$0.152056\pi$
$67$	2.85542	+	10.6566i	0.348845	+	1.30191i	−0.539211	+	0.842170i	$0.681278\pi$
$68$	−6.85082	−	3.95532i	−0.830784	−	0.479653i
$69$	7.46547	−	3.15407i	0.898737	−	0.379705i
$70$	−1.28362	+	1.28362i	−0.153423	+	0.153423i
$71$	1.69102	−	6.31098i	0.200687	−	0.748976i	−0.790034	−	0.613064i	$-0.789937\pi$
$71$	1.69102	−	6.31098i	0.200687	−	0.748976i	0.990721	−	0.135912i	$-0.0433964\pi$
$72$	2.61894	+	1.46326i	0.308645	+	0.172447i
$73$	−2.12247	−	2.12247i	−0.248417	−	0.248417i	0.571904	−	0.820321i	$-0.306205\pi$
$73$	−2.12247	−	2.12247i	−0.248417	−	0.248417i	−0.820321	+	0.571904i	$0.806205\pi$
$74$	1.63869	−	0.946100i	0.190494	−	0.109982i
$75$	−1.78082	+	2.35496i	−0.205631	+	0.271927i
$76$	6.30492	−	1.68940i	0.723224	−	0.193787i
$77$	−5.49542			−0.626261
$78$	−4.75742	−	4.04561i	−0.538672	−	0.458075i
$79$	0.559199			0.0629148			0.0314574	−	0.999505i	$-0.489985\pi$
$79$	0.559199			0.0629148			0.0314574	+	0.999505i	$0.489985\pi$
$80$	1.75346	−	0.469839i	0.196043	−	0.0525296i
$81$	−7.66441	+	4.71772i	−0.851601	+	0.524191i
$82$	7.63476	−	4.40793i	0.843118	−	0.486774i
$83$	−11.4710	−	11.4710i	−1.25910	−	1.25910i	−0.951522	−	0.307581i	$-0.900481\pi$
$83$	−11.4710	−	11.4710i	−1.25910	−	1.25910i	−0.307581	−	0.951522i	$-0.599519\pi$
$84$	0.651543	−	1.60483i	0.0710892	−	0.175102i
$85$	3.71673	−	13.8710i	0.403136	−	1.50452i
$86$	−4.49015	+	4.49015i	−0.484185	+	0.484185i
$87$	0.773710	+	1.83132i	0.0829505	+	0.196338i
$88$	4.75917	+	2.74771i	0.507330	+	0.292907i
$89$	3.08845	+	11.5262i	0.327375	+	1.22178i	0.911903	+	0.410406i	$0.134613\pi$
$89$	3.08845	+	11.5262i	0.327375	+	1.22178i	−0.584528	+	0.811373i	$0.698720\pi$
$90$	−1.33530	+	5.27972i	−0.140753	+	0.556531i
$91$	−1.97851	+	3.01422i	−0.207404	+	0.315976i
$92$			4.67908i			0.487828i
$93$	−5.68456	+	0.789147i	−0.589462	+	0.0818307i
$94$	−5.19406	+	8.99638i	−0.535727	+	0.927906i
$95$	5.92460	+	10.2617i	0.607851	+	1.05283i
$96$	−1.36667	+	1.06406i	−0.139485	+	0.108600i
$97$	−14.0135	−	3.75490i	−1.42285	−	0.381252i	−0.536357	−	0.843991i	$-0.680200\pi$
$97$	−14.0135	−	3.75490i	−1.42285	−	0.381252i	−0.886495	+	0.462739i	$0.846867\pi$
$98$	−0.965926	−	0.258819i	−0.0975732	−	0.0261447i
$99$	−14.1600	+	8.44338i	−1.42314	+	0.848591i
$100$	−0.852308	−	1.47624i	−0.0852308	−	0.147624i
$101$	−1.37630	+	2.38382i	−0.136947	+	0.237199i	−0.926339	−	0.376690i	$-0.877062\pi$
$101$	−1.37630	+	2.38382i	−0.136947	+	0.237199i	0.789393	+	0.613889i	$0.210396\pi$
$102$	1.88403	+	13.5715i	0.186547	+	1.34378i
$103$		−	10.1741i		−	1.00248i	−0.865308	−	0.501240i	$-0.832877\pi$
$103$		−	10.1741i		−	1.00248i	0.865308	−	0.501240i	$-0.167123\pi$
$104$	3.22055	−	1.62114i	0.315801	−	0.158966i
$105$	3.12014	+	0.388443i	0.304494	+	0.0379082i
$106$	−0.710775	−	2.65265i	−0.0690366	−	0.257648i
$107$	0.617420	+	0.356467i	0.0596882	+	0.0344610i	0.529547	−	0.848281i	$-0.322362\pi$
$107$	0.617420	+	0.356467i	0.0596882	+	0.0344610i	−0.469859	+	0.882742i	$0.655695\pi$
$108$	−0.786902	−	5.13622i	−0.0757197	−	0.494233i
$109$	−4.09901	+	4.09901i	−0.392614	+	0.392614i	−0.875618	−	0.483004i	$-0.839546\pi$
$109$	−4.09901	+	4.09901i	−0.392614	+	0.392614i	0.483004	+	0.875618i	$0.339546\pi$
$110$	−2.58196	+	9.63602i	−0.246181	+	0.918759i
$111$	−3.03667	−	1.23285i	−0.288228	−	0.117017i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−1.29822	+	0.749527i	−0.122126	+	0.0705096i	−0.559819	−	0.828615i	$-0.689129\pi$
$113$	−1.29822	+	0.749527i	−0.122126	+	0.0705096i	0.437692	+	0.899125i	$0.355796\pi$
$114$	−9.01763	−	6.81913i	−0.844579	−	0.638670i
$115$	−8.20460	+	2.19842i	−0.765083	+	0.205003i
$116$	−1.14780			−0.106571
$117$	−0.466844	+	10.8066i	−0.0431597	+	0.999068i
$118$	5.42318			0.499244
$119$	7.64110	−	2.04743i	0.700458	−	0.187687i
$120$	−2.50790	−	1.89647i	−0.228939	−	0.173123i
$121$	−16.6274	+	9.59983i	−1.51158	+	0.872712i
$122$	−5.57336	−	5.57336i	−0.504588	−	0.504588i
$123$	−14.1480	−	5.74391i	−1.27568	−	0.517911i
$124$	0.857586	−	3.20055i	0.0770135	−	0.287418i
$125$	8.60621	−	8.60621i	0.769763	−	0.769763i
$126$	−2.88656	+	0.817188i	−0.257155	+	0.0728009i
$127$	−11.3687	−	6.56372i	−1.00881	−	0.582436i	−0.0979665	−	0.995190i	$-0.531234\pi$
$127$	−11.3687	−	6.56372i	−1.00881	−	0.582436i	−0.910843	+	0.412753i	$0.864567\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	10.9143	+	1.35878i	0.960952	+	0.119634i
$130$	4.35574	+	4.88544i	0.382024	+	0.428481i
$131$		−	13.3313i		−	1.16476i	−0.812918	−	0.582379i	$-0.802122\pi$
$131$		−	13.3313i		−	1.16476i	0.812918	−	0.582379i	$-0.197878\pi$
$132$	−1.30881	−	9.42794i	−0.113918	−	0.820597i
$133$	−3.26367	+	5.65284i	−0.282996	+	0.490163i
$134$	5.51624	+	9.55441i	0.476531	+	0.825375i
$135$	8.63646	−	3.79300i	0.743309	−	0.326450i
$136$	−7.64110	−	2.04743i	−0.655219	−	0.175565i
$137$	11.0797	+	2.96881i	0.946606	+	0.253642i	0.698921	−	0.715199i	$-0.253664\pi$
$137$	11.0797	+	2.96881i	0.946606	+	0.253642i	0.247684	+	0.968841i	$0.420330\pi$
$138$	6.39476	−	4.97880i	0.544358	−	0.423824i
$139$	−0.539791	−	0.934945i	−0.0457845	−	0.0793010i	0.842225	−	0.539126i	$-0.181245\pi$
$139$	−0.539791	−	0.934945i	−0.0457845	−	0.0793010i	−0.888009	+	0.459825i	$0.847912\pi$
$140$	−0.907660	+	1.57211i	−0.0767113	+	0.132868i
$141$	17.8219	−	2.47408i	1.50087	−	0.208355i
$142$		−	6.53361i		−	0.548288i
$143$	−1.13386	+	19.7816i	−0.0948177	+	1.65422i
$144$	2.90842	+	0.735572i	0.242369	+	0.0612977i
$145$	−0.539284	−	2.01263i	−0.0447851	−	0.167140i
$146$	−2.59949	−	1.50082i	−0.215135	−	0.124208i
$147$	0.674078	+	1.59550i	0.0555971	+	0.131595i
$148$	1.33799	−	1.33799i	0.109982	−	0.109982i
$149$	−0.123454	+	0.460735i	−0.0101137	+	0.0377449i	−0.970798	−	0.239897i	$-0.922886\pi$
$149$	−0.123454	+	0.460735i	−0.0101137	+	0.0377449i	0.960685	+	0.277642i	$0.0895529\pi$
$150$	−1.11063	+	2.73562i	−0.0906825	+	0.223363i
$151$	−5.38963	−	5.38963i	−0.438602	−	0.438602i	0.452940	−	0.891541i	$-0.350375\pi$
$151$	−5.38963	−	5.38963i	−0.438602	−	0.438602i	−0.891541	+	0.452940i	$0.850375\pi$
$152$	5.65284	−	3.26367i	0.458506	−	0.264718i
$153$	16.5430	−	17.0157i	1.33742	−	1.37564i
$154$	−5.30817	+	1.42232i	−0.427744	+	0.114614i
$155$	6.01498			0.483135
$156$	−5.64240	−	2.67644i	−0.451753	−	0.214287i
$157$	−20.7030			−1.65228			−0.826141	−	0.563463i	$-0.809469\pi$
$157$	−20.7030			−1.65228			−0.826141	+	0.563463i	$0.809469\pi$
$158$	0.540145	−	0.144731i	0.0429716	−	0.0115142i
$159$	−2.86899	+	3.79396i	−0.227526	+	0.300881i
$160$	1.57211	−	0.907660i	0.124286	−	0.0717568i
$161$	−3.30861	−	3.30861i	−0.260755	−	0.260755i
$162$	−6.18221	+	6.54066i	−0.485721	+	0.513883i
$163$	−0.126397	+	0.471720i	−0.00990018	+	0.0369480i	−0.970699	−	0.240298i	$-0.922755\pi$
$163$	−0.126397	+	0.471720i	−0.00990018	+	0.0369480i	0.960799	+	0.277246i	$0.0894216\pi$
$164$	6.23375	−	6.23375i	0.486774	−	0.486774i
$165$	15.9166	−	6.72457i	1.23911	−	0.523507i
$166$	−14.0490	−	8.11120i	−1.09041	−	0.629551i
$167$	3.46756	+	12.9411i	0.268328	+	1.00141i	0.960182	+	0.279376i	$0.0901277\pi$
$167$	3.46756	+	12.9411i	0.268328	+	1.00141i	−0.691854	+	0.722038i	$0.743206\pi$
$168$	0.213981	−	1.71878i	0.0165090	−	0.132607i
$169$	10.4419	+	7.74383i	0.803222	+	0.595679i
$170$		−	14.3603i		−	1.10139i
$171$	0.275765	+	19.5801i	0.0210882	+	1.49732i
$172$	−3.17501	+	5.49929i	−0.242093	+	0.419317i
$173$	−5.40274	−	9.35783i	−0.410763	−	0.711463i	0.584210	−	0.811602i	$-0.301404\pi$
$173$	−5.40274	−	9.35783i	−0.410763	−	0.711463i	−0.994973	+	0.100140i	$0.968071\pi$
$174$	1.22133	+	1.56867i	0.0925886	+	0.118921i
$175$	1.64653	+	0.441187i	0.124466	+	0.0333506i
$176$	5.30817	+	1.42232i	0.400118	+	0.107211i
$177$	−5.77057	−	7.41170i	−0.433742	−	0.557097i
$178$	5.96642	+	10.3341i	0.447202	+	0.774577i
$179$	3.47073	−	6.01149i	0.259415	−	0.449320i	−0.706670	−	0.707543i	$-0.749804\pi$
$179$	3.47073	−	6.01149i	0.259415	−	0.449320i	0.966085	+	0.258223i	$0.0831370\pi$
$180$	0.0766930	+	5.44542i	0.00571636	+	0.405878i
$181$		−	17.0010i		−	1.26368i	−0.775100	−	0.631839i	$-0.782301\pi$
$181$		−	17.0010i		−	1.26368i	0.775100	−	0.631839i	$-0.217699\pi$
$182$	−1.13095	+	3.42359i	−0.0838318	+	0.253773i
$183$	−1.68658	+	13.5473i	−0.124675	+	1.00145i
$184$	1.21104	+	4.51964i	0.0892787	+	0.333193i
$185$	2.97475	+	1.71747i	0.218708	+	0.126271i
$186$	−5.28662	+	2.23353i	−0.387634	+	0.163770i
$187$	30.7396	−	30.7396i	2.24790	−	2.24790i
$188$	−2.68865	+	10.0342i	−0.196090	+	0.731816i
$189$	4.18828	+	3.07543i	0.304653	+	0.223705i
$190$	8.37865	+	8.37865i	0.607851	+	0.607851i
$191$	−2.01605	+	1.16397i	−0.145876	+	0.0842218i	−0.571162	−	0.820838i	$-0.693507\pi$
$191$	−2.01605	+	1.16397i	−0.145876	+	0.0842218i	0.425285	+	0.905059i	$0.360174\pi$
$192$	−1.04470	+	1.38152i	−0.0753950	+	0.0997025i
$193$	7.80356	−	2.09096i	0.561713	−	0.150510i	0.0332195	−	0.999448i	$-0.489424\pi$
$193$	7.80356	−	2.09096i	0.561713	−	0.150510i	0.528493	+	0.848938i	$0.322757\pi$
$194$	−14.5078			−1.04160
$195$	2.04203	−	11.1512i	0.146233	−	0.798557i
$196$	−1.00000			−0.0714286
$197$	25.5999	−	6.85947i	1.82392	−	0.488717i	0.826657	−	0.562706i	$-0.190240\pi$
$197$	25.5999	−	6.85947i	1.82392	−	0.488717i	0.997259	+	0.0739889i	$0.0235729\pi$
$198$	−11.4922	+	11.8206i	−0.816717	+	0.840051i
$199$	17.8064	−	10.2805i	1.26226	−	0.728766i	0.288748	−	0.957405i	$-0.406761\pi$
$199$	17.8064	−	10.2805i	1.26226	−	0.728766i	0.973511	+	0.228639i	$0.0734276\pi$
$200$	−1.20534	−	1.20534i	−0.0852308	−	0.0852308i
$201$	7.18813	−	17.7053i	0.507012	−	1.24884i
$202$	−0.712424	+	2.65880i	−0.0501260	+	0.187073i
$203$	0.811620	−	0.811620i	0.0569646	−	0.0569646i
$204$	5.33239	+	12.6214i	0.373342	+	0.883677i
$205$	13.8595	+	8.00180i	0.967991	+	0.558870i
$206$	−2.63324	−	9.82739i	−0.183467	−	0.684707i
$207$	−13.6088	−	3.44180i	−0.945874	−	0.239222i
$208$	2.69123	−	2.39944i	0.186603	−	0.166371i
$209$			35.8704i			2.48121i
$210$	3.11436	−	0.432344i	0.214911	−	0.0298346i
$211$	7.94596	−	13.7628i	0.547022	−	0.947470i	−0.451454	−	0.892294i	$-0.649095\pi$
$211$	7.94596	−	13.7628i	0.547022	−	0.947470i	0.998477	−	0.0551761i	$-0.0175720\pi$
$212$	−1.37311	−	2.37830i	−0.0943057	−	0.163342i
$213$	−8.92928	+	6.95212i	−0.611824	+	0.476352i
$214$	0.688642	+	0.184521i	0.0470746	+	0.0126136i
$215$	−11.1345	−	2.98349i	−0.759370	−	0.203473i
$216$	−2.08944	−	4.75755i	−0.142168	−	0.323710i
$217$	1.65673	+	2.86954i	0.112466	+	0.194797i
$218$	−2.89844	+	5.02024i	−0.196307	+	0.340013i
$219$	0.714881	+	5.14959i	0.0483072	+	0.347977i
$220$			9.97595i			0.672578i
$221$	−5.79343	−	27.9277i	−0.389709	−	1.87862i
$222$	−3.25228	−	0.404894i	−0.218279	−	0.0271747i
$223$	1.56411	+	5.83734i	0.104741	+	0.390897i	0.998316	−	0.0580168i	$-0.0184777\pi$
$223$	1.56411	+	5.83734i	0.104741	+	0.390897i	−0.893575	+	0.448914i	$0.851811\pi$
$224$	0.866025	+	0.500000i	0.0578638	+	0.0334077i
$225$	4.92047	−	1.39299i	0.328031	−	0.0928661i
$226$	−1.05999	+	1.05999i	−0.0705096	+	0.0705096i
$227$	−2.19126	+	8.17790i	−0.145439	+	0.542786i	0.854296	+	0.519786i	$0.173988\pi$
$227$	−2.19126	+	8.17790i	−0.145439	+	0.542786i	−0.999735	+	0.0229998i	$0.992678\pi$
$228$	−10.4753	−	4.25284i	−0.693743	−	0.281651i
$229$	0.488308	+	0.488308i	0.0322683	+	0.0322683i	0.723057	−	0.690789i	$-0.242736\pi$
$229$	0.488308	+	0.488308i	0.0322683	+	0.0322683i	−0.690789	+	0.723057i	$0.742736\pi$
$230$	−7.35604	+	4.24701i	−0.485043	+	0.280040i
$231$	7.59203	+	5.74109i	0.499519	+	0.377736i
$232$	−1.10869	+	0.297074i	−0.0727893	+	0.0195038i
$233$	6.34880			0.415924			0.207962	−	0.978137i	$-0.433317\pi$
$233$	6.34880			0.415924			0.207962	+	0.978137i	$0.433317\pi$
$234$	2.34601	+	10.5592i	0.153364	+	0.690275i
$235$	−18.8578			−1.23015
$236$	5.23839	−	1.40362i	0.340990	−	0.0913681i
$237$	−0.772544	−	0.584197i	−0.0501821	−	0.0379477i
$238$	6.85082	−	3.95532i	0.444073	−	0.256385i
$239$	−8.03317	−	8.03317i	−0.519623	−	0.519623i	0.397834	−	0.917457i	$-0.369762\pi$
$239$	−8.03317	−	8.03317i	−0.519623	−	0.519623i	−0.917457	+	0.397834i	$0.869762\pi$
$240$	−2.91329	−	1.18276i	−0.188052	−	0.0763467i
$241$	−2.44488	+	9.12442i	−0.157489	+	0.587755i	0.841391	+	0.540427i	$0.181737\pi$
$241$	−2.44488	+	9.12442i	−0.157489	+	0.587755i	−0.998879	+	0.0473283i	$0.984929\pi$
$242$	−13.5762	+	13.5762i	−0.872712	+	0.872712i
$243$	15.5171	+	1.48942i	0.995425	+	0.0955462i
$244$	−6.82594	−	3.94096i	−0.436986	−	0.252294i
$245$	−0.469839	−	1.75346i	−0.0300169	−	0.112025i
$246$	−15.1525	−	1.88642i	−0.966091	−	0.120274i
$247$	19.6748	+	12.9144i	1.25188	+	0.821722i
$248$		−	3.31346i		−	0.210405i
$249$	3.86360	+	27.8311i	0.244845	+	1.76373i
$250$	6.08551	−	10.5404i	0.384881	−	0.666634i
$251$	−10.5065	−	18.1978i	−0.663166	−	1.14864i	−0.979779	−	0.200083i	$-0.935879\pi$
$251$	−10.5065	−	18.1978i	−0.663166	−	1.14864i	0.316613	−	0.948555i	$-0.397454\pi$
$252$	−2.57669	+	1.53644i	−0.162317	+	0.0967865i
$253$	−24.8374	−	6.65515i	−1.56151	−	0.418406i
$254$	−12.6801	−	3.39763i	−0.795623	−	0.213186i
$255$	−19.6258	+	15.2802i	−1.22902	+	0.956884i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.08238	+	8.80295i	−0.317030	+	0.549113i	−0.979867	−	0.199651i	$-0.936019\pi$
$257$	−5.08238	+	8.80295i	−0.317030	+	0.549113i	0.662837	+	0.748764i	$0.269352\pi$
$258$	10.8941	−	1.51235i	0.678237	−	0.0941548i
$259$			1.89220i			0.117576i
$260$	5.47177	+	3.59162i	0.339345	+	0.222743i
$261$	0.844293	−	3.33830i	0.0522604	−	0.206636i
$262$	−3.45038	−	12.8770i	−0.213165	−	0.795544i
$263$	−15.6905	−	9.05891i	−0.967517	−	0.558596i	−0.0690387	−	0.997614i	$-0.521993\pi$
$263$	−15.6905	−	9.05891i	−0.967517	−	0.558596i	−0.898478	+	0.439018i	$0.855327\pi$
$264$	−3.70435	−	8.76794i	−0.227987	−	0.539629i
$265$	3.52512	−	3.52512i	0.216547	−	0.216547i
$266$	−1.68940	+	6.30492i	−0.103584	+	0.386579i
$267$	7.77476	−	19.1502i	0.475808	−	1.17198i
$268$	7.80114	+	7.80114i	0.476531	+	0.476531i
$269$	−4.00185	+	2.31047i	−0.243997	+	0.140872i	−0.617012	−	0.786953i	$-0.711657\pi$
$269$	−4.00185	+	2.31047i	−0.243997	+	0.140872i	0.373015	+	0.927825i	$0.378324\pi$
$270$	7.36048	−	5.89904i	0.447945	−	0.359004i
$271$	−27.2449	+	7.30024i	−1.65501	+	0.443458i	−0.961009	−	0.276517i	$-0.910820\pi$
$271$	−27.2449	+	7.30024i	−1.65501	+	0.443458i	−0.694000	+	0.719975i	$0.744153\pi$
$272$	−7.91064			−0.479653
$273$	5.88231	−	2.09725i	0.356014	−	0.126931i
$274$	11.4706			0.692963
$275$	9.04839	−	2.42451i	0.545638	−	0.146203i
$276$	4.88825	−	6.46424i	0.294238	−	0.389101i
$277$	17.1296	−	9.88980i	1.02922	−	0.594220i	0.112459	−	0.993656i	$-0.464127\pi$
$277$	17.1296	−	9.88980i	1.02922	−	0.594220i	0.916761	+	0.399436i	$0.130794\pi$
$278$	−0.763379	−	0.763379i	−0.0457845	−	0.0457845i
$279$	8.67775	+	4.84846i	0.519524	+	0.290270i
$280$	−0.469839	+	1.75346i	−0.0280783	+	0.104790i
$281$	7.06261	−	7.06261i	0.421320	−	0.421320i	−0.464338	−	0.885658i	$-0.653708\pi$
$281$	7.06261	−	7.06261i	0.421320	−	0.421320i	0.885658	+	0.464338i	$0.153708\pi$
$282$	16.5742	−	7.00241i	0.986982	−	0.416988i
$283$	−2.74658	−	1.58574i	−0.163267	−	0.0942624i	0.416140	−	0.909301i	$-0.363383\pi$
$283$	−2.74658	−	1.58574i	−0.163267	−	0.0942624i	−0.579407	+	0.815038i	$0.696716\pi$
$284$	−1.69102	−	6.31098i	−0.100344	−	0.374488i
$285$	2.53550	−	20.3662i	0.150190	−	1.20639i
$286$	4.02462	+	19.4010i	0.237981	+	1.14720i
$287$			8.81586i			0.520384i
$288$	2.99970	−	0.0422477i	0.176759	−	0.00248947i
$289$	−22.7891	+	39.4720i	−1.34054	+	2.32188i
$290$	−1.04182	−	1.80448i	−0.0611775	−	0.105963i
$291$	15.4371	+	19.8274i	0.904940	+	1.16230i
$292$	−2.89935	−	0.776879i	−0.169672	−	0.0454634i
$293$	−10.4220	−	2.79256i	−0.608857	−	0.163143i	−0.0588001	−	0.998270i	$-0.518727\pi$
$293$	−10.4220	−	2.79256i	−0.608857	−	0.163143i	−0.550057	+	0.835127i	$0.685394\pi$
$294$	1.06406	+	1.36667i	0.0620570	+	0.0797058i
$295$	4.92240	+	8.52585i	0.286593	+	0.496394i
$296$	0.946100	−	1.63869i	0.0549910	−	0.0952471i
$297$	28.3832	+	3.12834i	1.64696	+	0.181525i
$298$			0.476988i			0.0276312i
$299$	−12.5925	+	11.2272i	−0.728241	+	0.649283i
$300$	−0.364755	+	2.92986i	−0.0210591	+	0.169156i
$301$	−1.64351	−	6.13366i	−0.0947303	−	0.353538i
$302$	−6.60092	−	3.81104i	−0.379840	−	0.219301i
$303$	4.39177	−	1.85547i	0.252300	−	0.106594i
$304$	4.61552	−	4.61552i	0.264718	−	0.264718i
$305$	3.70323	−	13.8207i	0.212047	−	0.791369i
$306$	11.5754	−	20.7175i	0.661719	−	1.18434i
$307$	16.8884	+	16.8884i	0.963874	+	0.963874i	0.999370	−	0.0354960i	$-0.0113011\pi$
$307$	16.8884	+	16.8884i	0.963874	+	0.963874i	−0.0354960	+	0.999370i	$0.511301\pi$
$308$	−4.75917	+	2.74771i	−0.271179	+	0.156565i
$309$	−10.6289	+	14.0557i	−0.604656	+	0.799599i
$310$	5.81003	−	1.55679i	0.329987	−	0.0884199i
$311$	21.3065			1.20818			0.604091	−	0.796916i	$-0.293536\pi$
$311$	21.3065			1.20818			0.604091	+	0.796916i	$0.293536\pi$
$312$	−6.14285	−	1.12489i	−0.347771	−	0.0636841i
$313$	22.5085			1.27225			0.636127	−	0.771585i	$-0.280536\pi$
$313$	22.5085			1.27225			0.636127	+	0.771585i	$0.280536\pi$
$314$	−19.9976	+	5.35834i	−1.12853	+	0.302389i
$315$	−3.90472	−	3.79626i	−0.220006	−	0.213895i
$316$	0.484280	−	0.279599i	0.0272429	−	0.0157287i
$317$	−1.45164	−	1.45164i	−0.0815321	−	0.0815321i	0.665165	−	0.746697i	$-0.268361\pi$
$317$	−1.45164	−	1.45164i	−0.0815321	−	0.0815321i	−0.746697	+	0.665165i	$0.768361\pi$
$318$	−1.78928	+	4.40723i	−0.100338	+	0.247145i
$319$	1.63255	−	6.09274i	0.0914050	−	0.341128i
$320$	1.28362	−	1.28362i	0.0717568	−	0.0717568i
$321$	−0.480574	−	1.13749i	−0.0268230	−	0.0634883i
$322$	−4.05220	−	2.33954i	−0.225820	−	0.130377i
$323$	−13.3642	−	49.8760i	−0.743605	−	2.77517i
$324$	−4.27871	+	7.91787i	−0.237706	+	0.439882i
$325$	1.92784	−	5.83590i	0.106937	−	0.323717i
$326$			0.488361i			0.0270478i
$327$	9.94510	−	1.38061i	0.549965	−	0.0763478i
$328$	4.40793	−	7.63476i	0.243387	−	0.421559i
$329$	−5.19406	−	8.99638i	−0.286358	−	0.495987i
$330$	13.6338	−	10.6150i	0.750517	−	0.584334i
$331$	−25.6244	−	6.86603i	−1.40844	−	0.377391i	−0.527074	−	0.849819i	$-0.676711\pi$
$331$	−25.6244	−	6.86603i	−1.40844	−	0.377391i	−0.881369	+	0.472428i	$0.843378\pi$
$332$	−15.6696	−	4.19867i	−0.859983	−	0.230432i
$333$	2.90725	+	4.87562i	0.159316	+	0.267182i
$334$	6.69882	+	11.6027i	0.366543	+	0.634871i
$335$	−10.0137	+	17.3443i	−0.547109	+	0.947621i
$336$	−0.238164	−	1.71560i	−0.0129929	−	0.0935936i
$337$			4.31242i			0.234913i	0.993078	+	0.117456i	$0.0374740\pi$
$337$			4.31242i			0.234913i	−0.993078	+	0.117456i	$0.962526\pi$
$338$	12.0903	+	4.77741i	0.657628	+	0.259857i
$339$	2.57655	+	0.320768i	0.139939	+	0.0174218i
$340$	−3.71673	−	13.8710i	−0.201568	−	0.752262i
$341$	15.7693	+	9.10442i	0.853957	+	0.493032i
$342$	5.33406	+	18.8415i	0.288433	+	1.01883i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−1.64351	+	6.13366i	−0.0886120	+	0.330705i
$345$	13.6315	+	5.53422i	0.733895	+	0.297953i
$346$	−7.64063	−	7.64063i	−0.410763	−	0.410763i
$347$	7.32984	−	4.23188i	0.393486	−	0.227179i	−0.290183	−	0.956971i	$-0.593716\pi$
$347$	7.32984	−	4.23188i	0.393486	−	0.227179i	0.683670	+	0.729792i	$0.260383\pi$
$348$	1.58571	+	1.19912i	0.0850032	+	0.0642794i
$349$	−29.8009	+	7.98514i	−1.59521	+	0.427435i	−0.943591	−	0.331113i	$-0.892576\pi$
$349$	−29.8009	+	7.98514i	−1.59521	+	0.427435i	−0.651617	+	0.758548i	$0.725909\pi$
$350$	1.70462			0.0911155
$351$	11.9346	−	14.4418i	0.637023	−	0.770845i
$352$	5.49542			0.292907
$353$	11.6530	−	3.12242i	0.620228	−	0.166190i	0.0649966	−	0.997885i	$-0.479296\pi$
$353$	11.6530	−	3.12242i	0.620228	−	0.166190i	0.555231	+	0.831696i	$0.312630\pi$
$354$	−7.49223	−	5.66562i	−0.398207	−	0.301124i
$355$	10.2716	−	5.93029i	0.545158	−	0.314747i
$356$	8.43780	+	8.43780i	0.447202	+	0.447202i
$357$	−12.6953	−	5.15412i	−0.671905	−	0.272785i
$358$	1.79658	−	6.70494i	0.0949524	−	0.354367i
$359$	−15.3078	+	15.3078i	−0.807913	+	0.807913i	−0.984318	−	0.176405i	$-0.943553\pi$
$359$	−15.3078	+	15.3078i	−0.807913	+	0.807913i	0.176405	+	0.984318i	$0.443553\pi$
$360$	1.48346	+	5.24002i	0.0781851	+	0.276173i
$361$	20.4435	+	11.8030i	1.07597	+	0.621212i
$362$	−4.40019	−	16.4217i	−0.231269	−	0.863108i
$363$	33.0000	+	4.10835i	1.73205	+	0.215633i
$364$	−0.206327	+	3.59964i	−0.0108145	+	0.188673i
$365$		−	5.44892i		−	0.285209i
$366$	1.87719	+	13.5222i	0.0981223	+	0.706817i
$367$	−3.09102	+	5.35380i	−0.161350	+	0.279466i	−0.935353	−	0.353716i	$-0.884918\pi$
$367$	−3.09102	+	5.35380i	−0.161350	+	0.279466i	0.774003	+	0.633182i	$0.218251\pi$
$368$	2.33954	+	4.05220i	0.121957	+	0.211236i
$369$	13.5450	+	22.7158i	0.705126	+	1.18254i
$370$	3.31791	+	0.889030i	0.172490	+	0.0462185i
$371$	2.65265	+	0.710775i	0.137719	+	0.0369016i
$372$	−4.52840	+	3.52570i	−0.234787	+	0.182799i
$373$	−6.91676	−	11.9802i	−0.358136	−	0.620310i	0.629513	−	0.776990i	$-0.283254\pi$
$373$	−6.91676	−	11.9802i	−0.358136	−	0.620310i	−0.987649	+	0.156680i	$0.949921\pi$
$374$	21.7362	−	37.6481i	1.12395	−	1.94674i
$375$	−20.8806	+	2.89870i	−1.07827	+	0.149688i
$376$			10.3881i			0.535727i
$377$	−2.75408	−	3.08900i	−0.141843	−	0.159092i
$378$	4.84155	+	1.88663i	0.249022	+	0.0970380i
$379$	4.41950	+	16.4938i	0.227015	+	0.847230i	0.981587	+	0.191014i	$0.0611775\pi$
$379$	4.41950	+	16.4938i	0.227015	+	0.847230i	−0.754573	+	0.656216i	$0.772156\pi$
$380$	10.2617	+	5.92460i	0.526414	+	0.303925i
$381$	8.84893	+	20.9448i	0.453344	+	1.07304i
$382$	−1.64610	+	1.64610i	−0.0842218	+	0.0842218i
$383$	1.98302	−	7.40072i	0.101327	−	0.378159i	−0.896575	−	0.442891i	$-0.853953\pi$
$383$	1.98302	−	7.40072i	0.101327	−	0.378159i	0.997903	+	0.0647325i	$0.0206194\pi$
$384$	−0.651543	+	1.60483i	−0.0332489	+	0.0818963i
$385$	−7.05406	−	7.05406i	−0.359508	−	0.359508i
$386$	6.99648	−	4.03942i	0.356111	−	0.205601i
$387$	−13.6588	−	13.2794i	−0.694316	−	0.675031i
$388$	−14.0135	+	3.75490i	−0.711426	+	0.190626i
$389$	15.2721			0.774324			0.387162	−	0.922012i	$-0.373455\pi$
$389$	15.2721			0.774324			0.387162	+	0.922012i	$0.373455\pi$
$390$	−0.913707	−	11.2998i	−0.0462674	−	0.572187i
$391$	37.0145			1.87191
$392$	−0.965926	+	0.258819i	−0.0487866	+	0.0130723i
$393$	−13.9272	+	18.4174i	−0.702535	+	0.929034i
$394$	22.9522	−	13.2515i	1.15632	−	0.667600i
$395$	0.717801	+	0.717801i	0.0361165	+	0.0361165i
$396$	−8.04125	+	14.3922i	−0.404088	+	0.723235i
$397$	0.0947550	−	0.353630i	0.00475561	−	0.0177482i	−0.963507	−	0.267682i	$-0.913742\pi$
$397$	0.0947550	−	0.353630i	0.00475561	−	0.0177482i	0.968263	+	0.249934i	$0.0804089\pi$
$398$	14.5388	−	14.5388i	0.728766	−	0.728766i
$399$	10.4144	−	4.39993i	0.521370	−	0.220272i
$400$	−1.47624	−	0.852308i	−0.0738120	−	0.0426154i
$401$	−7.63320	−	28.4875i	−0.381184	−	1.42260i	−0.844095	−	0.536193i	$-0.819862\pi$
$401$	−7.63320	−	28.4875i	−0.381184	−	1.42260i	0.462912	−	0.886404i	$-0.346805\pi$
$402$	2.36074	−	18.9624i	0.117743	−	0.945760i
$403$	10.6711	−	5.37157i	0.531567	−	0.267577i
$404$			2.75260i			0.136947i
$405$	−15.8940	−	3.78244i	−0.789779	−	0.187951i
$406$	0.573902	−	0.994028i	0.0284823	−	0.0493328i
$407$	5.19922	+	9.00531i	0.257716	+	0.446377i
$408$	8.41736	+	10.8112i	0.416722	+	0.535236i
$409$	6.36813	+	1.70634i	0.314884	+	0.0843728i	0.412800	−	0.910822i	$-0.364551\pi$
$409$	6.36813	+	1.70634i	0.314884	+	0.0843728i	−0.0979159	+	0.995195i	$0.531218\pi$
$410$	15.4583	+	4.14204i	0.763430	+	0.204561i
$411$	−12.2053	−	15.6765i	−0.602045	−	0.773265i
$412$	−5.08703	−	8.81100i	−0.250620	−	0.434087i
$413$	−2.71159	+	4.69661i	−0.133429	+	0.231105i
$414$	−14.0358	+	0.197680i	−0.689824	+	0.00971545i
$415$		−	29.4488i		−	1.44559i
$416$	1.97851	−	3.01422i	0.0970042	−	0.147784i
$417$	−0.231009	+	1.85557i	−0.0113126	+	0.0908674i
$418$	9.28395	+	34.6482i	0.454093	+	1.69470i
$419$	−2.23306	−	1.28926i	−0.109092	−	0.0629845i	0.444461	−	0.895798i	$-0.353395\pi$
$419$	−2.23306	−	1.28926i	−0.109092	−	0.0629845i	−0.553553	+	0.832814i	$0.686729\pi$
$420$	2.89634	−	1.22367i	0.141327	−	0.0597089i
$421$	−6.49697	+	6.49697i	−0.316643	+	0.316643i	−0.847476	−	0.530833i	$-0.821879\pi$
$421$	−6.49697	+	6.49697i	−0.316643	+	0.316643i	0.530833	+	0.847476i	$0.321879\pi$
$422$	4.11313	−	15.3504i	0.200224	−	0.747246i
$423$	−27.2059	−	15.2006i	−1.32280	−	0.739077i
$424$	−1.94187	−	1.94187i	−0.0943057	−	0.0943057i
$425$	−11.6780	+	6.74230i	−0.566467	+	0.327050i
$426$	−6.82568	+	9.02630i	−0.330706	+	0.437326i
$427$	7.61335	−	2.03999i	0.368436	−	0.0987220i
$428$	0.712935			0.0344610
$429$	22.2323	−	26.1440i	1.07339	−	1.26225i
$430$	−11.5273			−0.555897
$431$	−26.0777	+	6.98751i	−1.25612	+	0.336576i	−0.824698	−	0.565574i	$-0.808655\pi$
$431$	−26.0777	+	6.98751i	−1.25612	+	0.336576i	−0.431422	+	0.902150i	$0.641988\pi$
$432$	−3.24959	−	4.05465i	−0.156346	−	0.195079i
$433$	2.31772	−	1.33814i	0.111383	−	0.0643067i	−0.443274	−	0.896386i	$-0.646183\pi$
$433$	2.31772	−	1.33814i	0.111383	−	0.0643067i	0.554656	+	0.832080i	$0.312850\pi$
$434$	2.34297	+	2.34297i	0.112466	+	0.112466i
$435$	−1.35758	+	3.34388i	−0.0650908	+	0.160327i
$436$	−1.50034	+	5.59935i	−0.0718533	+	0.268160i
$437$	−21.5964	+	21.5964i	−1.03310	+	1.03310i
$438$	2.02333	+	4.78910i	0.0966787	+	0.228832i
$439$	−4.46812	−	2.57967i	−0.213252	−	0.123121i	0.389570	−	0.920997i	$-0.372624\pi$
$439$	−4.46812	−	2.57967i	−0.213252	−	0.123121i	−0.602822	+	0.797876i	$0.705957\pi$
$440$	2.58196	+	9.63602i	0.123090	+	0.459379i
$441$	0.735572	−	2.90842i	0.0350272	−	0.138496i
$442$	−12.8242	−	25.4766i	−0.609987	−	1.21180i
$443$			35.8580i			1.70366i	0.523815	+	0.851832i	$0.324508\pi$
$443$			35.8580i			1.70366i	−0.523815	+	0.851832i	$0.675492\pi$
$444$	−3.24626	+	0.450654i	−0.154060	+	0.0213871i
$445$	−10.8310	+	18.7598i	−0.513437	+	0.889299i
$446$	3.02163	+	5.23361i	0.143078	+	0.247819i
$447$	0.651885	−	0.507542i	0.0308331	−	0.0240059i
$448$	0.965926	+	0.258819i	0.0456357	+	0.0122281i
$449$	16.1036	+	4.31494i	0.759974	+	0.203634i	0.617938	−	0.786227i	$-0.287968\pi$
$449$	16.1036	+	4.31494i	0.759974	+	0.203634i	0.142036	+	0.989861i	$0.454635\pi$
$450$	4.39227	−	2.61904i	0.207054	−	0.123463i
$451$	24.2234	+	41.9562i	1.14064	+	1.97564i
$452$	−0.749527	+	1.29822i	−0.0352548	+	0.0610631i
$453$	1.81531	+	13.0764i	0.0852906	+	0.614384i
$454$			8.46638i			0.397347i
$455$	−6.40878	+	1.32947i	−0.300448	+	0.0623263i
$456$	−11.2191	−	1.39672i	−0.525381	−	0.0654075i
$457$	−9.26890	−	34.5920i	−0.433581	−	1.61815i	−0.744439	−	0.667690i	$-0.767283\pi$
$457$	−9.26890	−	34.5920i	−0.433581	−	1.61815i	0.310858	−	0.950456i	$-0.399384\pi$
$458$	0.598053	+	0.345286i	0.0279452	+	0.0161341i
$459$	−40.6308	+	6.22490i	−1.89648	+	0.290553i
$460$	−6.00618	+	6.00618i	−0.280040	+	0.280040i
$461$	−4.01311	+	14.9771i	−0.186909	+	0.697554i	0.807305	+	0.590135i	$0.200925\pi$
$461$	−4.01311	+	14.9771i	−0.186909	+	0.697554i	−0.994214	+	0.107420i	$0.965741\pi$
$462$	8.81924	+	3.58050i	0.410308	+	0.166580i
$463$	−12.4123	−	12.4123i	−0.576847	−	0.576847i	0.357186	−	0.934033i	$-0.383736\pi$
$463$	−12.4123	−	12.4123i	−0.576847	−	0.576847i	−0.934033	+	0.357186i	$0.883736\pi$
$464$	−0.994028	+	0.573902i	−0.0461466	+	0.0266427i
$465$	−8.30981	−	6.28388i	−0.385358	−	0.291408i
$466$	6.13247	−	1.64319i	0.284081	−	0.0761193i
$467$	−3.99462			−0.184849			−0.0924245	−	0.995720i	$-0.529462\pi$
$467$	−3.99462			−0.184849			−0.0924245	+	0.995720i	$0.529462\pi$
$468$	4.99899	+	9.59219i	0.231078	+	0.443399i
$469$	−11.0325			−0.509433
$470$	−18.2152	+	4.88075i	−0.840205	+	0.225132i
$471$	28.6016	+	21.6285i	1.31789	+	0.996591i
$472$	4.69661	−	2.71159i	0.216179	−	0.124811i
$473$	−24.6753	−	24.6753i	−1.13457	−	1.13457i
$474$	−0.897421	−	0.364342i	−0.0412199	−	0.0167348i
$475$	2.87977	−	10.7475i	0.132133	−	0.493127i
$476$	5.59367	−	5.59367i	0.256385	−	0.256385i
$477$	7.92713	−	2.24418i	0.362958	−	0.102754i
$478$	−9.83859	−	5.68031i	−0.450007	−	0.259811i
$479$	6.22647	+	23.2375i	0.284495	+	1.06175i	0.949208	+	0.314650i	$0.101887\pi$
$479$	6.22647	+	23.2375i	0.284495	+	1.06175i	−0.664713	+	0.747099i	$0.731446\pi$
$480$	−3.12014	−	0.388443i	−0.142414	−	0.0177299i
$481$	6.81125	+	0.390413i	0.310566	+	0.0178013i
$482$			9.44629i			0.430267i
$483$	1.11439	+	8.02742i	0.0507065	+	0.365260i
$484$	−9.59983	+	16.6274i	−0.436356	+	0.755790i
$485$	−13.1682	−	22.8079i	−0.597935	−	1.03565i
$486$	15.3739	−	2.57746i	0.697374	−	0.116916i
$487$	6.68781	+	1.79199i	0.303054	+	0.0812030i	0.407141	−	0.913365i	$-0.366526\pi$
$487$	6.68781	+	1.79199i	0.303054	+	0.0812030i	−0.104088	+	0.994568i	$0.533192\pi$
$488$	−7.61335	−	2.03999i	−0.344640	−	0.0923460i
$489$	0.667427	−	0.519643i	0.0301821	−	0.0234991i
$490$	−0.907660	−	1.57211i	−0.0410039	−	0.0710208i
$491$	14.1855	−	24.5700i	0.640182	−	1.10883i	−0.345210	−	0.938526i	$-0.612192\pi$
$491$	14.1855	−	24.5700i	0.640182	−	1.10883i	0.985392	−	0.170303i	$-0.0544745\pi$
$492$	−15.1245	+	2.09962i	−0.681864	+	0.0946583i
$493$			9.07987i			0.408937i
$494$	22.3469	+	7.38211i	1.00543	+	0.332137i
$495$	−29.0143	−	7.33803i	−1.30410	−	0.329820i
$496$	−0.857586	−	3.20055i	−0.0385067	−	0.143709i
$497$	5.65827	+	3.26680i	0.253808	+	0.146536i
$498$	10.9352	+	25.8828i	0.490017	+	1.15984i
$499$	−15.6565	+	15.6565i	−0.700883	+	0.700883i	−0.964600	−	0.263717i	$-0.915051\pi$
$499$	−15.6565	+	15.6565i	−0.700883	+	0.700883i	0.263717	+	0.964600i	$0.415051\pi$
$500$	3.15009	−	11.7563i	0.140876	−	0.525758i
$501$	8.72914	−	21.5010i	0.389989	−	0.960593i
$502$	−14.8585	−	14.8585i	−0.663166	−	0.663166i
$503$	−12.8930	+	7.44375i	−0.574868	+	0.331900i	−0.759091	−	0.650984i	$-0.774356\pi$
$503$	−12.8930	+	7.44375i	−0.574868	+	0.331900i	0.184223	+	0.982884i	$0.441023\pi$
$504$	−2.09124	+	2.15098i	−0.0931511	+	0.0958124i
$505$	−4.82658	+	1.29328i	−0.214780	+	0.0575501i
$506$	−25.7135			−1.14311
$507$	−6.33566	−	21.6069i	−0.281377	−	0.959597i
$508$	−13.1274			−0.582436
$509$	−15.6508	+	4.19361i	−0.693709	+	0.185879i	−0.588411	−	0.808562i	$-0.700246\pi$
$509$	−15.6508	+	4.19361i	−0.693709	+	0.185879i	−0.105298	+	0.994441i	$0.533580\pi$
$510$	−15.0023	+	19.8391i	−0.664313	+	0.878490i
$511$	2.59949	−	1.50082i	0.114995	−	0.0663922i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	20.0744	−	27.3383i	0.886306	−	1.20702i
$514$	−2.63083	+	9.81841i	−0.116041	+	0.433071i
$515$	13.0597	−	13.0597i	0.575478	−	0.575478i
$516$	10.1315	−	4.28042i	0.446013	−	0.188435i
$517$	−49.4389	−	28.5436i	−2.17432	−	1.25534i
$518$	0.489737	+	1.82773i	0.0215178	+	0.0803056i
$519$	−2.31216	+	18.5723i	−0.101493	+	0.815233i
$520$	6.21490	+	2.05304i	0.272542	+	0.0900318i
$521$		−	19.4661i		−	0.852827i	−0.904528	−	0.426413i	$-0.859777\pi$
$521$		−	19.4661i		−	0.852827i	0.904528	−	0.426413i	$-0.140223\pi$
$522$	−0.0484921	−	3.44307i	−0.00212244	−	0.150699i
$523$	−1.38914	+	2.40606i	−0.0607429	+	0.105210i	−0.894798	−	0.446472i	$-0.852680\pi$
$523$	−1.38914	+	2.40606i	−0.0607429	+	0.105210i	0.834055	+	0.551682i	$0.186014\pi$
$524$	−6.66563	−	11.5452i	−0.291189	−	0.504355i
$525$	−1.81380	−	2.32965i	−0.0791609	−	0.101674i
$526$	−17.5005	−	4.68924i	−0.763057	−	0.204460i
$527$	−25.3184	−	6.78406i	−1.10289	−	0.295518i
$528$	−5.84743	−	7.51043i	−0.254477	−	0.326849i
$529$	0.553102	+	0.958002i	0.0240479	+	0.0416522i
$530$	2.49264	−	4.31738i	0.108273	−	0.187535i
$531$	0.229117	+	16.2679i	0.00994282	+	0.705968i
$532$			6.52733i			0.282996i
$533$	31.7339	+	1.81895i	1.37455	+	0.0787875i
$534$	2.55340	−	20.5100i	0.110496	−	0.887553i
$535$	0.334965	+	1.25011i	0.0144818	+	0.0540468i
$536$	9.55441	+	5.51624i	0.412688	+	0.238265i
$537$	−11.0751	+	4.67909i	−0.477926	+	0.201918i
$538$	−3.26750	+	3.26750i	−0.140872	+	0.140872i
$539$	1.42232	−	5.30817i	0.0612636	−	0.228639i
$540$	5.58290	−	7.60307i	0.240250	−	0.327184i
$541$	25.6508	+	25.6508i	1.10281	+	1.10281i	0.994070	+	0.108745i	$0.0346832\pi$
$541$	25.6508	+	25.6508i	1.10281	+	1.10281i	0.108745	+	0.994070i	$0.465317\pi$
$542$	−24.4271	+	14.1030i	−1.04923	+	0.605775i
$543$	−17.7611	+	23.4873i	−0.762200	+	1.00793i
$544$	−7.64110	+	2.04743i	−0.327609	+	0.0877826i
$545$	−10.5232			−0.450763
$546$	5.13907	−	3.54824i	0.219932	−	0.151851i
$547$	21.9423			0.938185			0.469092	−	0.883149i	$-0.344581\pi$
$547$	21.9423			0.938185			0.469092	+	0.883149i	$0.344581\pi$
$548$	11.0797	−	2.96881i	0.473303	−	0.126821i
$549$	16.4830	−	16.9539i	0.703475	−	0.723574i
$550$	8.11256	−	4.68379i	0.345921	−	0.199717i
$551$	−5.29772	−	5.29772i	−0.225690	−	0.225690i
$552$	3.04862	−	7.50915i	0.129758	−	0.319611i
$553$	−0.144731	+	0.540145i	−0.00615460	+	0.0229693i
$554$	13.9863	−	13.9863i	0.594220	−	0.594220i
$555$	−2.31542	−	5.48046i	−0.0982843	−	0.232632i
$556$	−0.934945	−	0.539791i	−0.0396505	−	0.0228922i
$557$	1.48980	+	5.56000i	0.0631248	+	0.235585i	0.990279	−	0.139095i	$-0.0444193\pi$
$557$	1.48980	+	5.56000i	0.0631248	+	0.235585i	−0.927154	+	0.374680i	$0.877753\pi$
$558$	9.63694	+	2.43729i	0.407964	+	0.103179i
$559$	−22.4181	+	4.65050i	−0.948184	+	0.196695i
$560$			1.81532i			0.0767113i
$561$	−74.5810	+	10.3536i	−3.14881	+	0.437127i
$562$	4.99402	−	8.64990i	0.210660	−	0.364874i
$563$	1.81159	+	3.13777i	0.0763495	+	0.132241i	0.901672	−	0.432420i	$-0.142340\pi$
$563$	1.81159	+	3.13777i	0.0763495	+	0.132241i	−0.825323	+	0.564661i	$0.809007\pi$
$564$	14.1971	−	11.0535i	0.597807	−	0.465438i
$565$	−2.62854	−	0.704314i	−0.110583	−	0.0296307i
$566$	−3.06341	−	0.820839i	−0.128765	−	0.0345024i
$567$	−2.57327	−	8.62428i	−0.108067	−	0.362186i
$568$	−3.26680	−	5.65827i	−0.137072	−	0.237416i
$569$	−4.40720	+	7.63350i	−0.184759	+	0.320013i	−0.943495	−	0.331386i	$-0.892484\pi$
$569$	−4.40720	+	7.63350i	−0.184759	+	0.320013i	0.758736	+	0.651398i	$0.225817\pi$
$570$	−2.82205	−	20.3285i	−0.118203	−	0.851465i
$571$		−	25.3120i		−	1.05927i	−0.848225	−	0.529636i	$-0.822328\pi$
$571$		−	25.3120i		−	1.05927i	0.848225	−	0.529636i	$-0.177672\pi$
$572$	8.90883	+	17.6983i	0.372497	+	0.740001i
$573$	4.00122	+	0.498133i	0.167153	+	0.0208098i
$574$	2.28171	+	8.51546i	0.0952368	+	0.355429i
$575$	6.90745	+	3.98802i	0.288060	+	0.166312i
$576$	2.88656	−	0.817188i	0.120273	−	0.0340495i
$577$	16.4990	−	16.4990i	0.686861	−	0.686861i	−0.274676	−	0.961537i	$-0.588571\pi$
$577$	16.4990	−	16.4990i	0.686861	−	0.686861i	0.961537	+	0.274676i	$0.0885706\pi$
$578$	−11.7965	+	44.0252i	−0.490671	+	1.83121i
$579$	−12.9652	−	5.26371i	−0.538815	−	0.218752i
$580$	−1.47335	−	1.47335i	−0.0611775	−	0.0611775i
$581$	14.0490	−	8.11120i	0.582851	−	0.336509i
$582$	20.0428	+	15.1564i	0.830801	+	0.628251i
$583$	14.5774	−	3.90601i	0.603735	−	0.161770i
$584$	−3.00163			−0.124208
$585$	−14.4708	+	13.2723i	−0.598296	+	0.548743i
$586$	−10.7896			−0.445714
$587$	−16.8416	+	4.51270i	−0.695129	+	0.186259i	−0.589048	−	0.808098i	$-0.700497\pi$
$587$	−16.8416	+	4.51270i	−0.695129	+	0.186259i	−0.106081	+	0.994357i	$0.533830\pi$
$588$	1.38152	+	1.04470i	0.0569729	+	0.0430829i
$589$	18.7304	−	10.8140i	0.771774	−	0.445584i
$590$	6.96133	+	6.96133i	0.286593	+	0.286593i
$591$	−42.5328	−	17.2678i	−1.74957	−	0.710303i
$592$	0.489737	−	1.82773i	0.0201281	−	0.0751190i
$593$	4.18904	−	4.18904i	0.172023	−	0.172023i	−0.615844	−	0.787868i	$-0.711185\pi$
$593$	4.18904	−	4.18904i	0.172023	−	0.172023i	0.787868	+	0.615844i	$0.211185\pi$
$594$	28.2257	−	4.32436i	1.15811	−	0.177431i
$595$	12.4364	+	7.18017i	0.509844	+	0.294358i
$596$	0.123454	+	0.460735i	0.00505685	+	0.0188724i
$597$	−35.3399	−	4.39966i	−1.44637	−	0.180066i
$598$	−9.25759	+	14.1038i	−0.378571	+	0.576746i
$599$			33.6465i			1.37476i	0.726299	+	0.687379i	$0.241239\pi$
$599$			33.6465i			1.37476i	−0.726299	+	0.687379i	$0.758761\pi$
$600$	0.405978	+	2.92443i	0.0165740	+	0.119390i
$601$	−12.4651	+	21.5902i	−0.508462	+	0.880682i	0.491490	+	0.870883i	$0.336453\pi$
$601$	−12.4651	+	21.5902i	−0.508462	+	0.880682i	−0.999952	+	0.00979909i	$0.996881\pi$
$602$	−3.17501	−	5.49929i	−0.129404	−	0.224134i
$603$	−28.4273	+	16.9507i	−1.15765	+	0.690287i
$604$	−7.36237	−	1.97274i	−0.299570	−	0.0802697i
$605$	−33.6659	−	9.02075i	−1.36871	−	0.366746i
$606$	3.76189	−	2.92892i	0.152816	−	0.118979i
$607$	0.826429	+	1.43142i	0.0335437	+	0.0580994i	0.882310	−	0.470669i	$-0.155987\pi$
$607$	0.826429	+	1.43142i	0.0335437	+	0.0580994i	−0.848766	+	0.528768i	$0.822654\pi$
$608$	3.26367	−	5.65284i	0.132359	−	0.229253i
$609$	−1.96917	+	0.273366i	−0.0797949	+	0.0110773i
$610$		−	14.3082i		−	0.579322i
$611$	−33.4554	+	16.8406i	−1.35346	+	0.681297i
$612$	5.81885	−	23.0075i	0.235213	−	0.930024i
$613$	7.66738	+	28.6151i	0.309683	+	1.15575i	0.928839	+	0.370484i	$0.120808\pi$
$613$	7.66738	+	28.6151i	0.309683	+	1.15575i	−0.619156	+	0.785268i	$0.712525\pi$
$614$	20.6840	+	11.9419i	0.834739	+	0.481937i
$615$	−10.7877	−	25.5337i	−0.435001	−	1.02962i
$616$	−3.88585	+	3.88585i	−0.156565	+	0.156565i
$617$	−1.56573	+	5.84339i	−0.0630340	+	0.235246i	−0.990254	−	0.139270i	$-0.955524\pi$
$617$	−1.56573	+	5.84339i	−0.0630340	+	0.235246i	0.927220	+	0.374516i	$0.122191\pi$
$618$	−6.62884	+	16.3277i	−0.266651	+	0.656796i
$619$	−13.6908	−	13.6908i	−0.550280	−	0.550280i	0.376242	−	0.926521i	$-0.377216\pi$
$619$	−13.6908	−	13.6908i	−0.550280	−	0.550280i	−0.926521	+	0.376242i	$0.877216\pi$
$620$	5.20913	−	3.00749i	0.209204	−	0.120784i
$621$	15.2051	+	18.9720i	0.610159	+	0.761321i
$622$	20.5805	−	5.51453i	0.825203	−	0.221113i
$623$	−11.9328			−0.478079
$624$	−6.22468	+	0.503331i	−0.249187	+	0.0201494i
$625$	13.5712			0.542849
$626$	21.7415	−	5.82562i	0.868965	−	0.232838i
$627$	37.4740	−	49.5557i	1.49657	−	1.97906i
$628$	−17.9294	+	10.3515i	−0.715459	+	0.413071i
$629$	−10.5843	−	10.5843i	−0.422025	−	0.422025i
$630$	−4.75422	−	2.65629i	−0.189413	−	0.105829i
$631$	−7.70811	+	28.7671i	−0.306855	+	1.14520i	0.624481	+	0.781040i	$0.285310\pi$
$631$	−7.70811	+	28.7671i	−0.306855	+	1.14520i	−0.931337	+	0.364159i	$0.881356\pi$
$632$	0.395413	−	0.395413i	0.0157287	−	0.0157287i
$633$	−25.3555	+	10.7124i	−1.00779	+	0.425780i
$634$	−1.77788	−	1.02646i	−0.0706088	−	0.0407660i
$635$	−6.16779	−	23.0185i	−0.244761	−	0.913462i
$636$	−0.587639	+	4.72016i	−0.0233014	+	0.187167i
$637$	−2.39944	−	2.69123i	−0.0950691	−	0.106630i
$638$		−	6.30767i		−	0.249723i
$639$	19.5989	−	0.276030i	0.775320	−	0.0109196i
$640$	0.907660	−	1.57211i	0.0358784	−	0.0621432i
$641$	3.24392	+	5.61864i	0.128127	+	0.221923i	0.922951	−	0.384917i	$-0.125770\pi$
$641$	3.24392	+	5.61864i	0.128127	+	0.221923i	−0.794824	+	0.606840i	$0.792437\pi$
$642$	−0.758602	−	0.974346i	−0.0299396	−	0.0384544i
$643$	−12.5107	−	3.35224i	−0.493375	−	0.132200i	0.00354841	−	0.999994i	$-0.498871\pi$
$643$	−12.5107	−	3.35224i	−0.493375	−	0.132200i	−0.496924	+	0.867794i	$0.665537\pi$
$644$	−4.51964	−	1.21104i	−0.178099	−	0.0477215i
$645$	12.2657	+	15.7541i	0.482962	+	0.620315i
$646$	−25.8177	−	44.7176i	−1.01578	−	1.75939i
$647$	11.8424	−	20.5117i	0.465574	−	0.806397i	−0.533654	−	0.845703i	$-0.679181\pi$
$647$	11.8424	−	20.5117i	0.465574	−	0.806397i	0.999227	+	0.0393061i	$0.0125147\pi$
$648$	−2.08362	+	8.75548i	−0.0818524	+	0.343948i
$649$			29.8027i			1.16986i
$650$	0.351709	−	6.13601i	0.0137951	−	0.240674i
$651$	0.709015	−	5.69511i	0.0277885	−	0.223209i
$652$	0.126397	+	0.471720i	0.00495009	+	0.0184740i
$653$	32.5077	+	18.7683i	1.27212	+	0.734461i	0.975387	−	0.220499i	$-0.0707685\pi$
$653$	32.5077	+	18.7683i	1.27212	+	0.734461i	0.296736	+	0.954959i	$0.404102\pi$
$654$	9.24891	−	3.90755i	0.361661	−	0.152797i
$655$	17.1123	−	17.1123i	0.668634	−	0.668634i
$656$	2.28171	−	8.51546i	0.0890859	−	0.332473i
$657$	4.39218	−	7.86110i	0.171355	−	0.306691i
$658$	−7.34551	−	7.34551i	−0.286358	−	0.286358i
$659$	23.1197	−	13.3482i	0.900618	−	0.519972i	0.0232170	−	0.999730i	$-0.492609\pi$
$659$	23.1197	−	13.3482i	0.900618	−	0.519972i	0.877400	+	0.479759i	$0.159276\pi$
$660$	10.4219	−	13.7820i	0.405672	−	0.536462i
$661$	−7.46788	+	2.00101i	−0.290467	+	0.0778304i	−0.401110	−	0.916030i	$-0.631376\pi$
$661$	−7.46788	+	2.00101i	−0.290467	+	0.0778304i	0.110643	+	0.993860i	$0.464709\pi$
$662$	−26.5283			−1.03105
$663$	−21.1724	+	44.6350i	−0.822267	+	1.73348i
$664$	−16.2224			−0.629551
$665$	−11.4454	+	3.06680i	−0.443835	+	0.118925i
$666$	4.07009	+	3.95704i	0.157713	+	0.153332i
$667$	4.65114	−	2.68534i	0.180093	−	0.103977i
$668$	9.47356	+	9.47356i	0.366543	+	0.366543i
$669$	3.93744	−	9.69842i	0.152230	−	0.374963i
$670$	−5.18349	+	19.3451i	−0.200256	+	0.747365i
$671$	30.6279	−	30.6279i	1.18238	−	1.18238i
$672$	−0.674078	−	1.59550i	−0.0260031	−	0.0615477i
$673$	−9.60536	−	5.54566i	−0.370260	−	0.213769i	0.303312	−	0.952891i	$-0.401907\pi$
$673$	−9.60536	−	5.54566i	−0.370260	−	0.213769i	−0.673572	+	0.739122i	$0.735241\pi$
$674$	1.11614	+	4.16548i	0.0429920	+	0.160448i
$675$	−8.25298	−	3.21599i	−0.317657	−	0.123783i
$676$	12.9149	+	1.48541i	0.496725	+	0.0571311i
$677$			32.4106i			1.24564i	0.782366	+	0.622819i	$0.214013\pi$
$677$			32.4106i			1.24564i	−0.782366	+	0.622819i	$0.785987\pi$
$678$	2.57177	−	0.357021i	0.0987684	−	0.0137113i
$679$	7.25390	−	12.5641i	0.278379	−	0.482167i
$680$	−7.18017	−	12.4364i	−0.275347	−	0.476915i
$681$	11.5707	−	9.00870i	0.443392	−	0.345214i
$682$	17.5884	+	4.71280i	0.673494	+	0.180462i
$683$	29.0808	+	7.79217i	1.11274	+	0.298159i	0.767944	−	0.640517i	$-0.221280\pi$
$683$	29.0808	+	7.79217i	1.11274	+	0.298159i	0.344801	+	0.938676i	$0.387947\pi$
$684$	10.0288	+	16.8189i	0.383463	+	0.643088i
$685$	10.4114	+	18.0331i	0.397799	+	0.689008i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−0.164469	−	1.18474i	−0.00627490	−	0.0452008i
$688$			6.35003i			0.242093i
$689$	3.10585	−	9.40194i	0.118324	−	0.358185i
$690$	14.5994	+	1.81756i	0.555789	+	0.0691932i
$691$	4.29147	+	16.0160i	0.163255	+	0.609276i	0.998256	+	0.0590282i	$0.0188002\pi$
$691$	4.29147	+	16.0160i	0.163255	+	0.609276i	−0.835001	+	0.550248i	$0.814533\pi$
$692$	−9.35783	−	5.40274i	−0.355731	−	0.205382i
$693$	−4.49079	−	15.8628i	−0.170591	−	0.602579i
$694$	5.98479	−	5.98479i	0.227179	−	0.227179i
$695$	0.507230	−	1.89301i	0.0192403	−	0.0718059i
$696$	1.84204	+	0.747844i	0.0698222	+	0.0283470i
$697$	−49.3130	−	49.3130i	−1.86786	−	1.86786i
$698$	−26.7188	+	15.4261i	−1.01132	+	0.583887i
$699$	−8.77098	−	6.63261i	−0.331749	−	0.250868i
$700$	1.64653	−	0.441187i	0.0622330	−	0.0166753i
$701$	20.1374			0.760581			0.380290	−	0.924867i	$-0.375824\pi$
$701$	20.1374			0.760581			0.380290	+	0.924867i	$0.375824\pi$
$702$	7.79015	−	17.0386i	0.294020	−	0.643080i
$703$	12.3510			0.465828
$704$	5.30817	−	1.42232i	0.200059	−	0.0536057i
$705$	26.0524	+	19.7008i	0.981189	+	0.741974i
$706$	10.4478	−	6.03205i	0.393209	−	0.227019i
$707$	−1.94638	−	1.94638i	−0.0732011	−	0.0732011i
$708$	−8.70331	−	3.53344i	−0.327090	−	0.132795i
$709$	0.390797	−	1.45848i	0.0146767	−	0.0547742i	−0.958199	−	0.286102i	$-0.907640\pi$
$709$	0.390797	−	1.45848i	0.0146767	−	0.0547742i	0.972876	+	0.231328i	$0.0743070\pi$
$710$	8.38670	−	8.38670i	0.314747	−	0.314747i
$711$	0.456971	+	1.61416i	0.0171377	+	0.0605357i
$712$	10.3341	+	5.96642i	0.387289	+	0.223601i
$713$	4.01271	+	14.9756i	0.150277	+	0.560842i
$714$	−13.5967	−	1.69272i	−0.508843	−	0.0633486i
$715$	−26.8475	+	23.9366i	−1.00404	+	0.895180i
$716$		−	6.94147i		−	0.259415i
$717$	2.70569	+	19.4903i	0.101046	+	0.727877i
$718$	−10.8242	+	18.7481i	−0.403957	+	0.699673i
$719$	12.6851	+	21.9713i	0.473075	+	0.819390i	0.999525	−	0.0308161i	$-0.00981062\pi$
$719$	12.6851	+	21.9713i	0.473075	+	0.819390i	−0.526450	+	0.850206i	$0.676477\pi$
$720$	2.78913	+	4.67752i	0.103945	+	0.174321i
$721$	9.82739	+	2.63324i	0.365991	+	0.0980671i
$722$	22.8017	+	6.10970i	0.848592	+	0.227380i
$723$	12.9100	−	10.0514i	0.480127	−	0.373815i
$724$	−8.50052	−	14.7233i	−0.315919	−	0.547188i
$725$	−0.978282	+	1.69443i	−0.0363325	+	0.0629297i
$726$	32.9389	−	4.57267i	1.22248	−	0.169708i
$727$			10.6469i			0.394871i	0.980316	+	0.197435i	$0.0632613\pi$
$727$			10.6469i			0.394871i	−0.980316	+	0.197435i	$0.936739\pi$
$728$	0.732359	+	3.53039i	0.0271430	+	0.130845i
$729$	−19.8812	−	18.2685i	−0.736342	−	0.676610i
$730$	−1.41028	−	5.26325i	−0.0521970	−	0.194802i
$731$	43.5029	+	25.1164i	1.60901	+	0.928964i
$732$	5.31303	+	12.5756i	0.196375	+	0.464807i
$733$	3.08031	−	3.08031i	0.113774	−	0.113774i	−0.647928	−	0.761702i	$-0.724364\pi$
$733$	3.08031	−	3.08031i	0.113774	−	0.113774i	0.761702	+	0.647928i	$0.224364\pi$
$734$	−1.60003	+	5.97139i	−0.0590581	+	0.220408i
$735$	−1.18276	+	2.91329i	−0.0436267	+	0.107458i
$736$	3.30861	+	3.30861i	0.121957	+	0.121957i
$737$	−52.5055	+	30.3141i	−1.93407	+	1.11663i
$738$	18.9628	+	18.4360i	0.698029	+	0.678640i
$739$	6.16372	−	1.65156i	0.226736	−	0.0607537i	−0.143662	−	0.989627i	$-0.545888\pi$
$739$	6.16372	−	1.65156i	0.226736	−	0.0607537i	0.370398	+	0.928873i	$0.379221\pi$
$740$	3.43495			0.126271
$741$	−13.6894	−	38.3958i	−0.502894	−	1.41050i
$742$	2.74622			0.100817
$743$	−0.759466	+	0.203498i	−0.0278621	+	0.00746563i	−0.272723	−	0.962093i	$-0.587924\pi$
$743$	−0.759466	+	0.203498i	−0.0278621	+	0.00746563i	0.244861	+	0.969558i	$0.421258\pi$
$744$	−3.46158	+	4.57760i	−0.126908	+	0.167823i
$745$	−0.749879	+	0.432943i	−0.0274734	+	0.0158618i
$746$	−9.78177	−	9.78177i	−0.358136	−	0.358136i
$747$	23.7377	−	42.4855i	0.868515	−	1.55446i
$748$	11.2515	−	41.9910i	0.411394	−	1.53534i
$749$	−0.504121	+	0.504121i	−0.0184202	+	0.0184202i
$750$	−19.4189	+	8.20422i	−0.709076	+	0.299576i
$751$	11.4267	+	6.59723i	0.416967	+	0.240736i	0.693779	−	0.720188i	$-0.255944\pi$
$751$	11.4267	+	6.59723i	0.416967	+	0.240736i	−0.276812	+	0.960924i	$0.589278\pi$
$752$	2.68865	+	10.0342i	0.0980448	+	0.365908i
$753$	−4.49639	+	36.1169i	−0.163857	+	1.31617i
$754$	−3.45973	−	2.27094i	−0.125996	−	0.0827027i
$755$		−	13.8365i		−	0.503562i
$756$	5.16488	+	0.569264i	0.187845	+	0.0207039i
$757$	−15.2305	+	26.3799i	−0.553560	+	0.958795i	0.444454	+	0.895802i	$0.353398\pi$
$757$	−15.2305	+	26.3799i	−0.553560	+	0.958795i	−0.998014	+	0.0629928i	$0.979935\pi$
$758$	8.53783	+	14.7879i	0.310108	+	0.537122i
$759$	27.3606	+	35.1419i	0.993127	+	1.27557i
$760$	11.4454	+	3.06680i	0.415170	+	0.111244i
$761$	14.8093	+	3.96814i	0.536837	+	0.143845i	0.517043	−	0.855959i	$-0.327033\pi$
$761$	14.8093	+	3.96814i	0.536837	+	0.143845i	0.0197932	+	0.999804i	$0.493699\pi$
$762$	13.9683	+	17.9409i	0.506019	+	0.649930i
$763$	−2.89844	−	5.02024i	−0.104930	−	0.181745i
$764$	−1.16397	+	2.01605i	−0.0421109	+	0.0729382i
$765$	43.0768	−	0.606691i	1.55744	−	0.0219350i
$766$		−	7.66178i		−	0.276832i
$767$	16.3467	+	10.7298i	0.590243	+	0.387431i
$768$	−0.213981	+	1.71878i	−0.00772136	+	0.0620212i
$769$	0.511064	+	1.90732i	0.0184294	+	0.0687795i	0.974528	−	0.224265i	$-0.0719982\pi$
$769$	0.511064	+	1.90732i	0.0184294	+	0.0687795i	−0.956099	+	0.293045i	$0.905332\pi$
$770$	−8.63942	−	4.98797i	−0.311343	−	0.179754i
$771$	16.2179	−	6.85185i	0.584073	−	0.246763i
$772$	5.71260	−	5.71260i	0.205601	−	0.205601i
$773$	9.33990	−	34.8570i	0.335933	−	1.25372i	−0.566922	−	0.823772i	$-0.691866\pi$
$773$	9.33990	−	34.8570i	0.335933	−	1.25372i	0.902854	−	0.429946i	$-0.141468\pi$
$774$	−16.6304	−	9.29177i	−0.597766	−	0.333986i
$775$	−3.99386	−	3.99386i	−0.143464	−	0.143464i
$776$	−12.5641	+	7.25390i	−0.451026	+	0.260400i
$777$	1.97679	−	2.61411i	0.0709169	−	0.0937807i
$778$	14.7517	−	3.95270i	0.528873	−	0.141711i
$779$	57.5440			2.06173
$780$	−3.80717	−	10.6783i	−0.136319	−	0.382343i
$781$	35.9049			1.28478
$782$	35.7533	−	9.58007i	1.27854	−	0.342583i
$783$	−4.65394	+	3.72989i	−0.166318	+	0.133295i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	−26.5749	−	26.5749i	−0.948500	−	0.948500i
$786$	−8.68588	+	21.3944i	−0.309815	+	0.763115i
$787$	11.1401	−	41.5753i	0.397100	−	1.48200i	−0.421073	−	0.907027i	$-0.638346\pi$
$787$	11.1401	−	41.5753i	0.397100	−	1.48200i	0.818173	−	0.574972i	$-0.194987\pi$
$788$	18.7404	−	18.7404i	0.667600	−	0.667600i
$789$	12.2128	+	28.9070i	0.434788	+	1.02912i
$790$	0.879124	+	0.507562i	0.0312778	+	0.0180583i
$791$	−0.387984	−	1.44797i	−0.0137951	−	0.0514841i
$792$	−4.04228	+	15.9830i	−0.143636	+	0.567932i
$793$	−5.77239	−	27.8262i	−0.204984	−	0.988139i
$794$		−	0.366105i		−	0.0129926i
$795$	−8.55273	+	1.18731i	−0.303334	+	0.0421097i
$796$	10.2805	−	17.8064i	0.364383	−	0.631130i
$797$	−6.66860	−	11.5504i	−0.236214	−	0.409135i	0.723411	−	0.690418i	$-0.242573\pi$
$797$	−6.66860	−	11.5504i	−0.236214	−	0.409135i	−0.959625	+	0.281283i	$0.909240\pi$
$798$	8.92071	−	6.94544i	0.315790	−	0.245866i
$799$	79.3767	+	21.2689i	2.80814	+	0.752440i
$800$	−1.64653	−	0.441187i	−0.0582137	−	0.0155983i
$801$	−30.7473	+	18.3341i	−1.08640	+	0.647803i
$802$	−14.7462	−	25.5412i	−0.520707	−	0.901891i
$803$	8.24761	−	14.2853i	0.291052	−	0.504117i
$804$	−2.62754	−	18.9273i	−0.0926663	−	0.667515i
$805$		−	8.49403i		−	0.299375i
$806$	8.91727	−	7.95043i	0.314097	−	0.280042i
$807$	7.94239	+	0.988791i	0.279585	+	0.0348071i
$808$	0.712424	+	2.65880i	0.0250630	+	0.0935364i
$809$	4.33697	+	2.50395i	0.152480	+	0.0880342i	0.574299	−	0.818646i	$-0.305275\pi$
$809$	4.33697	+	2.50395i	0.152480	+	0.0880342i	−0.421819	+	0.906680i	$0.638608\pi$
$810$	−16.3314	+	0.460112i	−0.573827	+	0.0161667i
$811$	23.4413	−	23.4413i	0.823135	−	0.823135i	−0.163421	−	0.986556i	$-0.552253\pi$
$811$	23.4413	−	23.4413i	0.823135	−	0.823135i	0.986556	+	0.163421i	$0.0522529\pi$
$812$	0.297074	−	1.10869i	0.0104252	−	0.0389075i
$813$	45.2659	+	18.3774i	1.58754	+	0.644524i
$814$	7.35281	+	7.35281i	0.257716	+	0.257716i
$815$	−0.767758	+	0.443265i	−0.0268934	+	0.0155269i
$816$	10.9287	+	8.26428i	0.382581	+	0.289308i
$817$	−40.0364	+	10.7277i	−1.40070	+	0.375316i
$818$	6.59277			0.230511
$819$	−10.3175	−	3.24788i	−0.360523	−	0.113490i
$820$	16.0036			0.558870
$821$	−2.31532	+	0.620389i	−0.0808054	+	0.0216517i	−0.298995	−	0.954255i	$-0.596651\pi$
$821$	−2.31532	+	0.620389i	−0.0808054	+	0.0216517i	0.218190	+	0.975906i	$0.429985\pi$
$822$	−15.8468	−	11.9834i	−0.552722	−	0.417968i
$823$	5.75083	−	3.32024i	0.200461	−	0.115736i	−0.396409	−	0.918074i	$-0.629744\pi$
$823$	5.75083	−	3.32024i	0.200461	−	0.115736i	0.596871	+	0.802337i	$0.296411\pi$
$824$	−7.19415	−	7.19415i	−0.250620	−	0.250620i
$825$	−15.0334	−	6.10338i	−0.523396	−	0.212492i
$826$	−1.40362	+	5.23839i	−0.0488383	+	0.182267i
$827$	−20.8129	+	20.8129i	−0.723735	+	0.723735i	−0.969364	−	0.245629i	$-0.921005\pi$
$827$	−20.8129	+	20.8129i	−0.723735	+	0.723735i	0.245629	+	0.969364i	$0.421005\pi$
$828$	−13.5064	+	3.82369i	−0.469381	+	0.132882i
$829$	14.7776	+	8.53185i	0.513247	+	0.296324i	0.734168	−	0.678968i	$-0.237573\pi$
$829$	14.7776	+	8.53185i	0.513247	+	0.296324i	−0.220920	+	0.975292i	$0.570906\pi$
$830$	−7.62192	−	28.4454i	−0.264561	−	0.987354i
$831$	−33.9968	−	4.23245i	−1.17934	−	0.146822i
$832$	1.13095	−	3.42359i	0.0392087	−	0.118692i
$833$			7.91064i			0.274088i
$834$	0.257118	+	1.85213i	0.00890326	+	0.0641340i
$835$	−12.1605	+	21.0626i	−0.420831	+	0.728901i
$836$	17.9352	+	31.0647i	0.620303	+	1.07440i
$837$	−6.92327	−	15.7639i	−0.239303	−	0.544881i
$838$	−2.49066	−	0.667370i	−0.0860384	−	0.0230539i
$839$	8.14694	+	2.18297i	0.281264	+	0.0753644i	0.396693	−	0.917951i	$-0.370158\pi$
$839$	8.14694	+	2.18297i	0.281264	+	0.0753644i	−0.115429	+	0.993316i	$0.536824\pi$
$840$	2.48094	−	1.93160i	0.0856006	−	0.0666466i
$841$	−13.8413	−	23.9738i	−0.477285	−	0.826682i
$842$	−4.59405	+	7.95713i	−0.158322	+	0.274221i
$843$	−17.1355	+	2.37879i	−0.590177	+	0.0819300i
$844$		−	15.8919i		−	0.547022i
$845$	3.46330	+	23.3436i	0.119141	+	0.803046i
$846$	−30.2131	−	7.64122i	−1.03875	−	0.262710i
$847$	−4.96924	−	18.5454i	−0.170745	−	0.637229i
$848$	−2.37830	−	1.37311i	−0.0816712	−	0.0471529i
$849$	2.13783	+	5.06009i	0.0733700	+	0.173662i
$850$	−9.53505	+	9.53505i	−0.327050	+	0.327050i
$851$	−2.29152	+	8.55207i	−0.0785523	+	0.293161i
$852$	−4.25693	+	10.4854i	−0.145840	+	0.359222i
$853$	22.8520	+	22.8520i	0.782438	+	0.782438i	0.980242	−	0.197804i	$-0.0633810\pi$
$853$	22.8520	+	22.8520i	0.782438	+	0.782438i	−0.197804	+	0.980242i	$0.563381\pi$
$854$	6.82594	−	3.94096i	0.233579	−	0.134857i
$855$	−24.7795	+	25.4874i	−0.847440	+	0.871651i
$856$	0.688642	−	0.184521i	0.0235373	−	0.00630680i
$857$	42.2144			1.44202			0.721008	−	0.692927i	$-0.243679\pi$
$857$	42.2144			1.44202			0.721008	+	0.692927i	$0.243679\pi$
$858$	14.7082	−	31.0074i	0.502129	−	1.05857i
$859$	−25.2390			−0.861145			−0.430573	−	0.902556i	$-0.641688\pi$
$859$	−25.2390			−0.861145			−0.430573	+	0.902556i	$0.641688\pi$
$860$	−11.1345	+	2.98349i	−0.379685	+	0.101736i
$861$	9.20996	−	12.1793i	0.313875	−	0.415069i
$862$	−23.3807	+	13.4988i	−0.796348	+	0.459772i
$863$	−1.90689	−	1.90689i	−0.0649112	−	0.0649112i	0.673906	−	0.738817i	$-0.264615\pi$
$863$	−1.90689	−	1.90689i	−0.0649112	−	0.0649112i	−0.738817	+	0.673906i	$0.764615\pi$
$864$	−4.18828	−	3.07543i	−0.142488	−	0.104628i
$865$	5.07684	−	18.9470i	0.172618	−	0.644219i
$866$	1.89241	−	1.89241i	0.0643067	−	0.0643067i
$867$	72.7201	−	30.7233i	2.46971	−	1.04342i
$868$	2.86954	+	1.65673i	0.0973985	+	0.0562330i
$869$	0.795359	+	2.96832i	0.0269807	+	0.100693i
$870$	−0.445857	+	3.58131i	−0.0151160	+	0.121418i
$871$	−2.27630	+	39.7130i	−0.0771295	+	1.34562i
$872$			5.79687i			0.196307i
$873$	−0.612921	−	43.5191i	−0.0207442	−	1.47290i
$874$	−15.2710	+	26.4501i	−0.516548	+	0.894687i
$875$	6.08551	+	10.5404i	0.205728	+	0.356331i
$876$	3.19390	+	4.10224i	0.107912	+	0.138602i
$877$	−3.72222	−	0.997365i	−0.125690	−	0.0336786i	0.195425	−	0.980719i	$-0.437391\pi$
$877$	−3.72222	−	0.997365i	−0.125690	−	0.0336786i	−0.321116	+	0.947040i	$0.604058\pi$
$878$	−4.98354	−	1.33534i	−0.168186	−	0.0450654i
$879$	11.4807	+	14.7458i	0.387236	+	0.497364i
$880$	4.98797	+	8.63942i	0.168145	+	0.291235i
$881$	−10.9926	+	19.0397i	−0.370349	+	0.641463i	−0.989619	−	0.143715i	$-0.954095\pi$
$881$	−10.9926	+	19.0397i	−0.370349	+	0.641463i	0.619270	+	0.785178i	$0.287428\pi$
$882$	−0.0422477	−	2.99970i	−0.00142255	−	0.101005i
$883$		−	6.52996i		−	0.219751i	−0.993945	−	0.109875i	$-0.964955\pi$
$883$		−	6.52996i		−	0.219751i	0.993945	−	0.109875i	$-0.0350452\pi$
$884$	−18.9811	−	21.2893i	−0.638403	−	0.716038i
$885$	2.10660	−	16.9211i	0.0708125	−	0.568796i
$886$	9.28073	+	34.6361i	0.311792	+	1.16362i
$887$	−34.2689	−	19.7852i	−1.15064	−	0.664321i	−0.201595	−	0.979469i	$-0.564612\pi$
$887$	−34.2689	−	19.7852i	−1.15064	−	0.664321i	−0.949043	+	0.315148i	$0.897946\pi$
$888$	−3.01900	+	1.27549i	−0.101311	+	0.0428027i
$889$	9.28251	−	9.28251i	0.311325	−	0.311325i
$890$	−5.60652	+	20.9238i	−0.187931	+	0.701368i
$891$	−35.9437	−	33.9739i	−1.20416	−	1.13817i
$892$	4.27323	+	4.27323i	0.143078	+	0.143078i
$893$	−58.7224	+	33.9034i	−1.96507	+	1.13453i
$894$	0.498311	−	0.658968i	0.0166660	−	0.0220392i
$895$	12.1716	−	3.26137i	0.406852	−	0.109016i
$896$	1.00000			0.0334077
$897$	29.1258	−	2.35513i	0.972482	−	0.0786354i
$898$	16.6716			0.556340
$899$	−3.67361	+	0.984341i	−0.122522	+	0.0328296i
$900$	3.56475	−	3.66660i	0.118825	−	0.122220i
$901$	−18.8139	+	10.8622i	−0.626781	+	0.361872i
$902$	34.2571	+	34.2571i	1.14064	+	1.14064i
$903$	−4.13732	+	10.1907i	−0.137681	+	0.339127i
$904$	−0.387984	+	1.44797i	−0.0129041	+	0.0481589i
$905$	21.8230	−	21.8230i	0.725420	−	0.725420i
$906$	5.13788	+	12.1610i	0.170695	+	0.404023i
$907$	22.3049	+	12.8777i	0.740621	+	0.427598i	0.822295	−	0.569061i	$-0.192693\pi$
$907$	22.3049	+	12.8777i	0.740621	+	0.427598i	−0.0816742	+	0.996659i	$0.526027\pi$
$908$	2.19126	+	8.17790i	0.0727195	+	0.271393i
$909$	−8.00572	−	2.02473i	−0.265533	−	0.0671562i
$910$	−5.84632	+	2.94288i	−0.193804	+	0.0975556i
$911$			8.06312i			0.267143i	0.991039	+	0.133571i	$0.0426446\pi$
$911$			8.06312i			0.267143i	−0.991039	+	0.133571i	$0.957355\pi$
$912$	−11.1983	+	1.55458i	−0.370812	+	0.0514772i
$913$	44.5745	−	77.2053i	1.47520	−	2.55512i
$914$	−17.9061	−	31.0144i	−0.592283	−	1.02586i
$915$	−19.5546	+	15.2247i	−0.646454	+	0.503314i
$916$	0.667041	+	0.178733i	0.0220397	+	0.00590551i
$917$	12.8770	+	3.45038i	0.425236	+	0.113942i
$918$	−37.6352	+	16.5288i	−1.24215	+	0.545532i
$919$	8.61477	+	14.9212i	0.284175	+	0.492206i	0.972409	−	0.233283i	$-0.0749470\pi$
$919$	8.61477	+	14.9212i	0.284175	+	0.492206i	−0.688234	+	0.725489i	$0.741614\pi$
$920$	−4.24701	+	7.35604i	−0.140020	+	0.242522i
$921$	−5.68828	−	40.9751i	−0.187435	−	1.35018i
$922$			15.5055i			0.510645i
$923$	12.9268	−	19.6937i	0.425490	−	0.648227i
$924$	9.44543	+	1.17591i	0.310732	+	0.0386847i
$925$	−0.834814	−	3.11557i	−0.0274485	−	0.102439i
$926$	−15.2019	−	8.77679i	−0.499564	−	0.288423i
$927$	29.3680	−	8.31413i	0.964572	−	0.273072i
$928$	−0.811620	+	0.811620i	−0.0266427	+	0.0266427i
$929$	−12.6931	+	47.3714i	−0.416448	+	1.55421i	0.365469	+	0.930824i	$0.380909\pi$
$929$	−12.6931	+	47.3714i	−0.416448	+	1.55421i	−0.781917	+	0.623383i	$0.785758\pi$
$930$	−9.65305	−	3.91902i	−0.316536	−	0.128510i
$931$	−4.61552	−	4.61552i	−0.151268	−	0.151268i
$932$	5.49822	−	3.17440i	0.180100	−	0.103981i
$933$	−29.4353	−	22.2590i	−0.963670	−	0.728727i
$934$	−3.85851	+	1.03388i	−0.126254	+	0.0338297i
$935$	78.9162			2.58083
$936$	7.31129	+	7.97151i	0.238977	+	0.260557i
$937$	43.3921			1.41756			0.708779	−	0.705430i	$-0.249246\pi$
$937$	43.3921			1.41756			0.708779	+	0.705430i	$0.249246\pi$
$938$	−10.6566	+	2.85542i	−0.347949	+	0.0932326i
$939$	−31.0959	−	23.5147i	−1.01477	−	0.767372i
$940$	−16.3313	+	9.42888i	−0.532669	+	0.307536i
$941$	−12.5887	−	12.5887i	−0.410380	−	0.410380i	0.471491	−	0.881871i	$-0.343716\pi$
$941$	−12.5887	−	12.5887i	−0.410380	−	0.410380i	−0.881871	+	0.471491i	$0.843716\pi$
$942$	33.2249	+	13.4889i	1.08253	+	0.439493i
$943$	−10.6763	+	39.8445i	−0.347669	+	1.29752i
$944$	3.83477	−	3.83477i	0.124811	−	0.124811i
$945$	1.42848	+	9.32389i	0.0464684	+	0.303306i
$946$	−30.2209	−	17.4480i	−0.982566	−	0.567285i
$947$	−0.749425	−	2.79689i	−0.0243530	−	0.0908868i	0.952680	−	0.303976i	$-0.0983142\pi$
$947$	−0.749425	−	2.79689i	−0.0243530	−	0.0908868i	−0.977033	+	0.213089i	$0.931648\pi$
$948$	−0.961141	−	0.119658i	−0.0312164	−	0.00388630i
$949$	−4.86605	−	9.66689i	−0.157959	−	0.313801i
$950$		−	11.1266i		−	0.360994i
$951$	0.488933	+	3.52199i	0.0158547	+	0.114208i
$952$	3.95532	−	6.85082i	0.128193	−	0.222036i
$953$	13.8544	+	23.9965i	0.448788	+	0.777323i	0.998307	−	0.0581576i	$-0.0185226\pi$
$953$	13.8544	+	23.9965i	0.448788	+	0.777323i	−0.549520	+	0.835481i	$0.685189\pi$
$954$	7.07618	−	4.21941i	0.229100	−	0.136608i
$955$	−4.08196	−	1.09376i	−0.132089	−	0.0353931i
$956$	−10.9735	−	2.94035i	−0.354909	−	0.0950976i
$957$	−8.62050	+	6.71171i	−0.278661	+	0.216959i
$958$	12.0286	+	20.8342i	0.388627	+	0.673122i
$959$	−5.73529	+	9.93382i	−0.185202	+	0.320780i
$960$	−3.11436	+	0.432344i	−0.100516	+	0.0139538i
$961$			20.0210i			0.645839i
$962$	6.68020	−	1.38577i	0.215378	−	0.0446790i
$963$	−0.524415	+	2.07352i	−0.0168990	+	0.0668182i
$964$	2.44488	+	9.12442i	0.0787443	+	0.293878i
$965$	12.7008	+	7.33284i	0.408855	+	0.236052i
$966$	3.15407	+	7.46547i	0.101480	+	0.240198i
$967$	−19.9179	+	19.9179i	−0.640516	+	0.640516i	−0.950682	−	0.310166i	$-0.899615\pi$
$967$	−19.9179	+	19.9179i	−0.640516	+	0.640516i	0.310166	+	0.950682i	$0.399615\pi$
$968$	−4.96924	+	18.5454i	−0.159717	+	0.596073i
$969$	−33.6427	+	82.8662i	−1.08076	+	2.66205i
$970$	−18.6226	−	18.6226i	−0.597935	−	0.597935i
$971$	−9.02730	+	5.21191i	−0.289700	+	0.167258i	−0.637806	−	0.770197i	$-0.720158\pi$
$971$	−9.02730	+	5.21191i	−0.289700	+	0.167258i	0.348107	+	0.937455i	$0.386825\pi$
$972$	14.1829	−	6.46870i	0.454918	−	0.207484i
$973$	1.04280	−	0.279416i	0.0334305	−	0.00895767i
$974$	6.92373			0.221851
$975$	−8.76013	+	6.04838i	−0.280549	+	0.193703i
$976$	−7.88192			−0.252294
$977$	19.6124	−	5.25512i	0.627456	−	0.168126i	0.0689410	−	0.997621i	$-0.478038\pi$
$977$	19.6124	−	5.25512i	0.627456	−	0.168126i	0.558515	+	0.829494i	$0.311371\pi$
$978$	0.510192	−	0.674679i	0.0163141	−	0.0215739i
$979$	−56.7905	+	32.7880i	−1.81503	+	1.04791i
$980$	−1.28362	−	1.28362i	−0.0410039	−	0.0410039i
$981$	−15.1817	−	8.48235i	−0.484714	−	0.270821i
$982$	7.34295	−	27.4043i	0.234323	−	0.874505i
$983$	−26.1651	+	26.1651i	−0.834537	+	0.834537i	−0.988134	−	0.153597i	$-0.950914\pi$
$983$	−26.1651	+	26.1651i	−0.834537	+	0.834537i	0.153597	+	0.988134i	$0.450914\pi$
$984$	−14.0657	+	5.94258i	−0.448398	+	0.189443i
$985$	41.6656	+	24.0557i	1.32758	+	0.766477i
$986$	2.35004	+	8.77048i	0.0748407	+	0.279309i
$987$	−2.22286	+	17.8549i	−0.0707543	+	0.568329i
$988$	23.4961	+	1.34677i	0.747509	+	0.0428464i
$989$		−	29.7123i		−	0.944796i
$990$	−29.9249	+	0.421460i	−0.951075	+	0.0133949i
$991$	16.2637	−	28.1695i	0.516633	−	0.894835i	−0.483180	−	0.875521i	$-0.660518\pi$
$991$	16.2637	−	28.1695i	0.516633	−	0.894835i	0.999813	−	0.0193141i	$-0.00614825\pi$
$992$	−1.65673	−	2.86954i	−0.0526012	−	0.0911079i
$993$	28.2276	+	36.2554i	0.895776	+	1.15053i
$994$	6.31098	+	1.69102i	0.200172	+	0.0536360i
$995$	36.0530	+	9.66037i	1.14296	+	0.306254i
$996$	17.2615	+	22.1707i	0.546953	+	0.702504i
$997$	−19.0654	−	33.0223i	−0.603808	−	1.04583i	−0.992239	−	0.124348i	$-0.960316\pi$
$997$	−19.0654	−	33.0223i	−0.603808	−	1.04583i	0.388431	−	0.921478i	$-0.373017\pi$
$998$	−11.0708	+	19.1753i	−0.350441	+	0.606982i
$999$	1.07716	−	9.77298i	0.0340799	−	0.309203i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.71.10	✓	56
3.2	odd	2		546.2.bu.b.71.7	yes	56
13.11	odd	12		546.2.bu.b.323.7	yes	56
39.11	even	12	inner	546.2.bu.a.323.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.10	✓	56	1.1	even	1	trivial
546.2.bu.a.323.10	yes	56	39.11	even	12	inner
546.2.bu.b.71.7	yes	56	3.2	odd	2
546.2.bu.b.323.7	yes	56	13.11	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.38152 - 1.04470i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28362 + 1.28362i) q^{5} +(-1.60483 - 0.651543i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.817188 + 2.88656i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-1.38152 - 1.04470i) q^{3} +(0.866025 - 0.500000i) q^{4} +(1.28362 + 1.28362i) q^{5} +(-1.60483 - 0.651543i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.817188 + 2.88656i) q^{9} +(1.57211 + 0.907660i) q^{10} +(1.42232 + 5.30817i) q^{11} +(-1.71878 - 0.213981i) q^{12} +(3.42359 + 1.13095i) q^{13} +1.00000i q^{14} +(-0.432344 - 3.11436i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.95532 - 6.85082i) q^{17} +(1.53644 + 2.57669i) q^{18} +(6.30492 + 1.68940i) q^{19} +(1.75346 + 0.469839i) q^{20} +(1.36667 - 1.06406i) q^{21} +(2.74771 + 4.75917i) q^{22} +(-2.33954 + 4.05220i) q^{23} +(-1.71560 + 0.238164i) q^{24} -1.70462i q^{25} +(3.59964 + 0.206327i) q^{26} +(1.88663 - 4.84155i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-0.994028 - 0.573902i) q^{29} +(-1.22367 - 2.89634i) q^{30} +(2.34297 - 2.34297i) q^{31} +(0.258819 - 0.965926i) q^{32} +(3.58050 - 8.81924i) q^{33} +(-5.59367 - 5.59367i) q^{34} +(-1.57211 + 0.907660i) q^{35} +(2.15098 + 2.09124i) q^{36} +(1.82773 - 0.489737i) q^{37} +6.52733 q^{38} +(-3.54824 - 5.13907i) q^{39} +1.81532 q^{40} +(8.51546 - 2.28171i) q^{41} +(1.04470 - 1.38152i) q^{42} +(-5.49929 + 3.17501i) q^{43} +(3.88585 + 3.88585i) q^{44} +(-2.65629 + 4.75422i) q^{45} +(-1.21104 + 4.51964i) q^{46} +(-7.34551 + 7.34551i) q^{47} +(-1.59550 + 0.674078i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.441187 - 1.64653i) q^{50} +(-1.69272 + 13.5967i) q^{51} +(3.53039 - 0.732359i) q^{52} -2.74622i q^{53} +(0.569264 - 5.16488i) q^{54} +(-4.98797 + 8.63942i) q^{55} +(0.500000 + 0.866025i) q^{56} +(-6.94544 - 8.92071i) q^{57} +(-1.10869 - 0.297074i) q^{58} +(5.23839 + 1.40362i) q^{59} +(-1.93160 - 2.48094i) q^{60} +(-3.94096 - 6.82594i) q^{61} +(1.65673 - 2.86954i) q^{62} +(-2.99970 + 0.0422477i) q^{63} -1.00000i q^{64} +(2.94288 + 5.84632i) q^{65} +(1.17591 - 9.44543i) q^{66} +(2.85542 + 10.6566i) q^{67} +(-6.85082 - 3.95532i) q^{68} +(7.46547 - 3.15407i) q^{69} +(-1.28362 + 1.28362i) q^{70} +(1.69102 - 6.31098i) q^{71} +(2.61894 + 1.46326i) q^{72} +(-2.12247 - 2.12247i) q^{73} +(1.63869 - 0.946100i) q^{74} +(-1.78082 + 2.35496i) q^{75} +(6.30492 - 1.68940i) q^{76} -5.49542 q^{77} +(-4.75742 - 4.04561i) q^{78} +0.559199 q^{79} +(1.75346 - 0.469839i) q^{80} +(-7.66441 + 4.71772i) q^{81} +(7.63476 - 4.40793i) q^{82} +(-11.4710 - 11.4710i) q^{83} +(0.651543 - 1.60483i) q^{84} +(3.71673 - 13.8710i) q^{85} +(-4.49015 + 4.49015i) q^{86} +(0.773710 + 1.83132i) q^{87} +(4.75917 + 2.74771i) q^{88} +(3.08845 + 11.5262i) q^{89} +(-1.33530 + 5.27972i) q^{90} +(-1.97851 + 3.01422i) q^{91} +4.67908i q^{92} +(-5.68456 + 0.789147i) q^{93} +(-5.19406 + 8.99638i) q^{94} +(5.92460 + 10.2617i) q^{95} +(-1.36667 + 1.06406i) q^{96} +(-14.0135 - 3.75490i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(-14.1600 + 8.44338i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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