LMFDB - Embedded newform 546.2.bu.b.71.7

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			71.7
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.b.323.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.59550 + 0.674078i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.28362 - 1.28362i) q^{5} +(-1.71560 - 0.238164i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.09124 + 2.15098i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.59550 + 0.674078i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.28362 - 1.28362i) q^{5} +(-1.71560 - 0.238164i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.09124 + 2.15098i) 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} +(-1.18276 - 2.91329i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.95532 + 6.85082i) q^{17} +(-2.57669 - 1.53644i) q^{18} +(6.30492 + 1.68940i) q^{19} +(-1.75346 - 0.469839i) q^{20} +(-1.06406 + 1.36667i) q^{21} +(2.74771 + 4.75917i) q^{22} +(2.33954 - 4.05220i) q^{23} +(-1.60483 + 0.651543i) 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} +(1.89647 + 2.50790i) q^{30} +(2.34297 - 2.34297i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.30881 - 9.42794i) q^{33} +(-5.59367 - 5.59367i) q^{34} +(1.57211 - 0.907660i) q^{35} +(2.88656 + 0.817188i) q^{36} +(1.82773 - 0.489737i) q^{37} -6.52733 q^{38} +(4.69998 + 4.11220i) q^{39} +1.81532 q^{40} +(-8.51546 + 2.28171i) q^{41} +(0.674078 - 1.59550i) q^{42} +(-5.49929 + 3.17501i) q^{43} +(-3.88585 - 3.88585i) q^{44} +(0.0766930 - 5.44542i) q^{45} +(-1.21104 + 4.51964i) q^{46} +(7.34551 - 7.34551i) q^{47} +(1.38152 - 1.04470i) 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} +(-3.07543 - 4.18828i) q^{54} +(-4.98797 + 8.63942i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(8.92071 + 6.94544i) q^{57} +(-1.10869 - 0.297074i) q^{58} +(-5.23839 - 1.40362i) q^{59} +(-2.48094 - 1.93160i) q^{60} +(-3.94096 - 6.82594i) q^{61} +(-1.65673 + 2.86954i) q^{62} +(-2.61894 + 1.46326i) 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} +(6.46424 - 4.88825i) q^{69} +(-1.28362 + 1.28362i) q^{70} +(-1.69102 + 6.31098i) q^{71} +(-2.99970 - 0.0422477i) q^{72} +(-2.12247 - 2.12247i) q^{73} +(-1.63869 + 0.946100i) q^{74} +(1.14904 - 2.71971i) q^{75} +(6.30492 - 1.68940i) q^{76} +5.49542 q^{77} +(-5.60415 - 2.75564i) q^{78} +0.559199 q^{79} +(-1.75346 + 0.469839i) q^{80} +(-0.253461 + 8.99643i) q^{81} +(7.63476 - 4.40793i) q^{82} +(11.4710 + 11.4710i) q^{83} +(-0.238164 + 1.71560i) q^{84} +(3.71673 - 13.8710i) q^{85} +(4.49015 - 4.49015i) q^{86} +(1.19912 + 1.58571i) 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} +(5.31755 - 2.15886i) q^{93} +(-5.19406 + 8.99638i) q^{94} +(-5.92460 - 10.2617i) q^{95} +(-1.06406 + 1.36667i) q^{96} +(-14.0135 - 3.75490i) q^{97} +(0.965926 + 0.258819i) q^{98} +(8.44338 - 14.1600i) 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^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 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} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * 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
$3$	1.59550	+	0.674078i	0.921162	+	0.389179i
$3$	1.59550	+	0.674078i	0.921162	+	0.389179i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.28362	−	1.28362i	−0.574054	−	0.574054i	0.359204	−	0.933259i	$-0.383048\pi$
$5$	−1.28362	−	1.28362i	−0.574054	−	0.574054i	−0.933259	+	0.359204i	$0.883048\pi$
$6$	−1.71560	−	0.238164i	−0.700390	−	0.0972301i
$7$	−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
$9$	2.09124	+	2.15098i	0.697079	+	0.716995i
$10$	1.57211	+	0.907660i	0.497146	+	0.287027i
$11$	−1.42232	−	5.30817i	−0.428846	−	1.60047i	−0.755379	−	0.655288i	$-0.772547\pi$
$11$	−1.42232	−	5.30817i	−0.428846	−	1.60047i	0.326534	−	0.945186i	$-0.394119\pi$
$12$	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
$15$	−1.18276	−	2.91329i	−0.305387	−	0.752207i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.95532	+	6.85082i	0.959306	+	1.66157i	0.724190	+	0.689600i	$0.242214\pi$
$17$	3.95532	+	6.85082i	0.959306	+	1.66157i	0.235116	+	0.971967i	$0.424453\pi$
$18$	−2.57669	−	1.53644i	−0.607333	−	0.362142i
$19$	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
$21$	−1.06406	+	1.36667i	−0.232196	+	0.298232i
$22$	2.74771	+	4.75917i	0.585814	+	1.01466i
$23$	2.33954	−	4.05220i	0.487828	−	0.844943i	−0.512074	−	0.858941i	$-0.671123\pi$
$23$	2.33954	−	4.05220i	0.487828	−	0.844943i	0.999902	+	0.0139986i	$0.00445604\pi$
$24$	−1.60483	+	0.651543i	−0.327585	+	0.132996i
$25$		−	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	0.589446	−	0.807808i	$-0.299346\pi$
$29$	0.994028	+	0.573902i	0.184586	+	0.106571i	−0.404859	+	0.914379i	$0.632680\pi$
$30$	1.89647	+	2.50790i	0.346247	+	0.457877i
$31$	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
$33$	1.30881	−	9.42794i	0.227835	−	1.64119i
$34$	−5.59367	−	5.59367i	−0.959306	−	0.959306i
$35$	1.57211	−	0.907660i	0.265736	−	0.153423i
$36$	2.88656	+	0.817188i	0.481093	+	0.136198i
$37$	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
$39$	4.69998	+	4.11220i	0.752599	+	0.658479i
$40$	1.81532			0.287027
$41$	−8.51546	+	2.28171i	−1.32989	+	0.356344i	−0.852675	−	0.522442i	$-0.825021\pi$
$41$	−8.51546	+	2.28171i	−1.32989	+	0.356344i	−0.477217	+	0.878785i	$0.658355\pi$
$42$	0.674078	−	1.59550i	0.104013	−	0.246191i
$43$	−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
$45$	0.0766930	−	5.44542i	0.0114327	−	0.811755i
$46$	−1.21104	+	4.51964i	−0.178557	+	0.666385i
$47$	7.34551	−	7.34551i	1.07145	−	1.07145i	0.0742109	−	0.997243i	$-0.476356\pi$
$47$	7.34551	−	7.34551i	1.07145	−	1.07145i	0.997243	−	0.0742109i	$-0.0236438\pi$
$48$	1.38152	−	1.04470i	0.199405	−	0.150790i
$49$	−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	$0.0603987\pi$
$53$			2.74622i			0.377223i	−0.982052	+	0.188611i	$0.939601\pi$
$54$	−3.07543	−	4.18828i	−0.418514	−	0.569953i
$55$	−4.98797	+	8.63942i	−0.672578	+	1.16494i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	8.92071	+	6.94544i	1.18158	+	0.919947i
$58$	−1.10869	−	0.297074i	−0.145579	−	0.0390077i
$59$	−5.23839	−	1.40362i	−0.681980	−	0.182736i	−0.0988349	−	0.995104i	$-0.531512\pi$
$59$	−5.23839	−	1.40362i	−0.681980	−	0.182736i	−0.583145	+	0.812368i	$0.698178\pi$
$60$	−2.48094	−	1.93160i	−0.320288	−	0.249369i
$61$	−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
$63$	−2.61894	+	1.46326i	−0.329956	+	0.184354i
$64$		−	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
$69$	6.46424	−	4.88825i	0.778203	−	0.588476i
$70$	−1.28362	+	1.28362i	−0.153423	+	0.153423i
$71$	−1.69102	+	6.31098i	−0.200687	+	0.748976i	0.790034	+	0.613064i	$0.210063\pi$
$71$	−1.69102	+	6.31098i	−0.200687	+	0.748976i	−0.990721	+	0.135912i	$0.956604\pi$
$72$	−2.99970	−	0.0422477i	−0.353518	−	0.00497894i
$73$	−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
$75$	1.14904	−	2.71971i	0.132680	−	0.314045i
$76$	6.30492	−	1.68940i	0.723224	−	0.193787i
$77$	5.49542			0.626261
$78$	−5.60415	−	2.75564i	−0.634545	−	0.312014i
$79$	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
$81$	−0.253461	+	8.99643i	−0.0281623	+	0.999603i
$82$	7.63476	−	4.40793i	0.843118	−	0.486774i
$83$	11.4710	+	11.4710i	1.25910	+	1.25910i	0.951522	+	0.307581i	$0.0995194\pi$
$83$	11.4710	+	11.4710i	1.25910	+	1.25910i	0.307581	+	0.951522i	$0.400481\pi$
$84$	−0.238164	+	1.71560i	−0.0259858	+	0.187187i
$85$	3.71673	−	13.8710i	0.403136	−	1.50452i
$86$	4.49015	−	4.49015i	0.484185	−	0.484185i
$87$	1.19912	+	1.58571i	0.128559	+	0.170006i
$88$	4.75917	+	2.74771i	0.507330	+	0.292907i
$89$	−3.08845	−	11.5262i	−0.327375	−	1.22178i	−0.911903	−	0.410406i	$-0.865387\pi$
$89$	−3.08845	−	11.5262i	−0.327375	−	1.22178i	0.584528	−	0.811373i	$-0.301280\pi$
$90$	1.33530	+	5.27972i	0.140753	+	0.556531i
$91$	−1.97851	+	3.01422i	−0.207404	+	0.315976i
$92$		−	4.67908i		−	0.487828i
$93$	5.31755	−	2.15886i	0.551404	−	0.223863i
$94$	−5.19406	+	8.99638i	−0.535727	+	0.927906i
$95$	−5.92460	−	10.2617i	−0.607851	−	1.05283i
$96$	−1.06406	+	1.36667i	−0.108600	+	0.139485i
$97$	−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
$99$	8.44338	−	14.1600i	0.848591	−	1.42314i
$100$	−0.852308	−	1.47624i	−0.0852308	−	0.147624i
$101$	1.37630	−	2.38382i	0.136947	−	0.237199i	−0.789393	−	0.613889i	$-0.789604\pi$
$101$	1.37630	−	2.38382i	0.136947	−	0.237199i	0.926339	+	0.376690i	$0.122938\pi$
$102$	−5.15412	−	12.6953i	−0.510334	−	1.25702i
$103$		−	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	0.469859	−	0.882742i	$-0.344305\pi$
$107$	−0.617420	−	0.356467i	−0.0596882	−	0.0344610i	−0.529547	+	0.848281i	$0.677638\pi$
$108$	4.05465	+	3.24959i	0.390159	+	0.312692i
$109$	−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
$111$	3.24626	+	0.450654i	0.308121	+	0.0427742i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	1.29822	−	0.749527i	0.122126	−	0.0705096i	−0.437692	−	0.899125i	$-0.644204\pi$
$113$	1.29822	−	0.749527i	0.122126	−	0.0705096i	0.559819	+	0.828615i	$0.310871\pi$
$114$	−10.4144	−	4.39993i	−0.975394	−	0.412092i
$115$	−8.20460	+	2.19842i	−0.765083	+	0.205003i
$116$	1.14780			0.106571
$117$	4.72687	+	9.72917i	0.436999	+	0.899462i
$118$	5.42318			0.499244
$119$	−7.64110	+	2.04743i	−0.700458	+	0.187687i
$120$	2.89634	+	1.22367i	0.264399	+	0.111705i
$121$	−16.6274	+	9.59983i	−1.51158	+	0.872712i
$122$	5.57336	+	5.57336i	0.504588	+	0.504588i
$123$	−15.1245	−	2.09962i	−1.36373	−	0.189317i
$124$	0.857586	−	3.20055i	0.0770135	−	0.287418i
$125$	−8.60621	+	8.60621i	−0.769763	+	0.769763i
$126$	2.15098	−	2.09124i	0.191625	−	0.186302i
$127$	−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	$0.197878\pi$
$131$			13.3313i			1.16476i	−0.812918	+	0.582379i	$0.802122\pi$
$132$	−3.58050	−	8.81924i	−0.311643	−	0.767616i
$133$	−3.26367	+	5.65284i	−0.282996	+	0.490163i
$134$	−5.51624	−	9.55441i	−0.476531	−	0.825375i
$135$	3.79300	−	8.63646i	0.326450	−	0.743309i
$136$	−7.64110	−	2.04743i	−0.655219	−	0.175565i
$137$	−11.0797	−	2.96881i	−0.946606	−	0.253642i	−0.247684	−	0.968841i	$-0.579670\pi$
$137$	−11.0797	−	2.96881i	−0.946606	−	0.253642i	−0.698921	+	0.715199i	$0.746336\pi$
$138$	−4.97880	+	6.39476i	−0.423824	+	0.544358i
$139$	−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
$141$	16.6712	−	6.76831i	1.40397	−	0.569995i
$142$		−	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
$147$	−1.04470	−	1.38152i	−0.0861657	−	0.113946i
$148$	1.33799	−	1.33799i	0.109982	−	0.109982i
$149$	0.123454	−	0.460735i	0.0101137	−	0.0377449i	−0.960685	−	0.277642i	$-0.910447\pi$
$149$	0.123454	−	0.460735i	0.0101137	−	0.0377449i	0.970798	+	0.239897i	$0.0771137\pi$
$150$	−0.405978	+	2.92443i	−0.0331480	+	0.238779i
$151$	−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
$153$	−6.46449	+	22.8345i	−0.522623	+	1.84606i
$154$	−5.30817	+	1.42232i	−0.427744	+	0.114614i
$155$	−6.01498			−0.483135
$156$	6.12640	+	1.21128i	0.490505	+	0.0969801i
$157$	−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
$159$	−1.85117	+	4.38160i	−0.146807	+	0.347483i
$160$	1.57211	−	0.907660i	0.124286	−	0.0717568i
$161$	3.30861	+	3.30861i	0.260755	+	0.260755i
$162$	−2.08362	−	8.75548i	−0.163705	−	0.687896i
$163$	−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
$165$	−13.7820	+	10.4219i	−1.07292	+	0.811344i
$166$	−14.0490	−	8.11120i	−1.09041	−	0.629551i
$167$	−3.46756	−	12.9411i	−0.268328	−	1.00141i	−0.960182	−	0.279376i	$-0.909872\pi$
$167$	−3.46756	−	12.9411i	−0.268328	−	1.00141i	0.691854	−	0.722038i	$-0.256794\pi$
$168$	−0.213981	−	1.71878i	−0.0165090	−	0.132607i
$169$	10.4419	+	7.74383i	0.803222	+	0.595679i
$170$			14.3603i			1.10139i
$171$	9.55121	+	17.0947i	0.730399	+	1.30727i
$172$	−3.17501	+	5.49929i	−0.242093	+	0.419317i
$173$	5.40274	+	9.35783i	0.410763	+	0.711463i	0.994973	−	0.100140i	$-0.0319290\pi$
$173$	5.40274	+	9.35783i	0.410763	+	0.711463i	−0.584210	+	0.811602i	$0.698596\pi$
$174$	−1.56867	−	1.22133i	−0.118921	−	0.0925886i
$175$	1.64653	+	0.441187i	0.124466	+	0.0333506i
$176$	−5.30817	−	1.42232i	−0.400118	−	0.107211i
$177$	−7.41170	−	5.77057i	−0.557097	−	0.433742i
$178$	5.96642	+	10.3341i	0.447202	+	0.774577i
$179$	−3.47073	+	6.01149i	−0.259415	+	0.449320i	−0.966085	−	0.258223i	$-0.916863\pi$
$179$	−3.47073	+	6.01149i	−0.259415	+	0.449320i	0.706670	+	0.707543i	$0.250196\pi$
$180$	−2.65629	−	4.75422i	−0.197988	−	0.354358i
$181$		−	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
$186$	−4.57760	+	3.46158i	−0.335646	+	0.253815i
$187$	30.7396	−	30.7396i	2.24790	−	2.24790i
$188$	2.68865	−	10.0342i	0.196090	−	0.731816i
$189$	−5.16488	+	0.569264i	−0.375689	+	0.0414078i
$190$	8.37865	+	8.37865i	0.607851	+	0.607851i
$191$	2.01605	−	1.16397i	0.145876	−	0.0842218i	−0.425285	−	0.905059i	$-0.639826\pi$
$191$	2.01605	−	1.16397i	0.145876	−	0.0842218i	0.571162	+	0.820838i	$0.306493\pi$
$192$	0.674078	−	1.59550i	0.0486474	−	0.115145i
$193$	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
$195$	−0.754487	−	11.3115i	−0.0540299	−	0.810036i
$196$	−1.00000			−0.0714286
$197$	−25.5999	+	6.85947i	−1.82392	+	0.488717i	−0.997259	−	0.0739889i	$-0.976427\pi$
$197$	−25.5999	+	6.85947i	−1.82392	+	0.488717i	−0.826657	+	0.562706i	$0.809760\pi$
$198$	−4.49079	+	15.8628i	−0.319147	+	1.12732i
$199$	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
$201$	−2.62754	+	18.9273i	−0.185333	+	1.33503i
$202$	−0.712424	+	2.65880i	−0.0501260	+	0.187073i
$203$	−0.811620	+	0.811620i	−0.0569646	+	0.0569646i
$204$	8.26428	+	10.9287i	0.578615	+	0.765162i
$205$	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
$210$	−2.91329	+	1.18276i	−0.201036	+	0.0816181i
$211$	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
$213$	−6.95212	+	8.92928i	−0.476352	+	0.611824i
$214$	0.688642	+	0.184521i	0.0470746	+	0.0126136i
$215$	11.1345	+	2.98349i	0.759370	+	0.203473i
$216$	−4.75755	−	2.08944i	−0.323710	−	0.142168i
$217$	1.65673	+	2.86954i	0.112466	+	0.194797i
$218$	2.89844	−	5.02024i	0.196307	−	0.340013i
$219$	−1.95569	−	4.81712i	−0.132153	−	0.325511i
$220$			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
$225$	3.66660	−	3.56475i	0.244440	−	0.237650i
$226$	−1.05999	+	1.05999i	−0.0705096	+	0.0705096i
$227$	2.19126	−	8.17790i	0.145439	−	0.542786i	−0.854296	−	0.519786i	$-0.826012\pi$
$227$	2.19126	−	8.17790i	0.145439	−	0.542786i	0.999735	−	0.0229998i	$-0.00732172\pi$
$228$	11.1983	+	1.55458i	0.741624	+	0.102954i
$229$	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
$231$	8.76794	+	3.70435i	0.576888	+	0.243728i
$232$	−1.10869	+	0.297074i	−0.0727893	+	0.0195038i
$233$	−6.34880			−0.415924			−0.207962	−	0.978137i	$-0.566683\pi$
$233$	−6.34880			−0.415924			−0.207962	+	0.978137i	$0.566683\pi$
$234$	−7.08390	−	8.17425i	−0.463089	−	0.534368i
$235$	−18.8578			−1.23015
$236$	−5.23839	+	1.40362i	−0.340990	+	0.0913681i
$237$	0.892201	+	0.376944i	0.0579547	+	0.0244851i
$238$	6.85082	−	3.95532i	0.444073	−	0.256385i
$239$	8.03317	+	8.03317i	0.519623	+	0.519623i	0.917457	−	0.397834i	$-0.130238\pi$
$239$	8.03317	+	8.03317i	0.519623	+	0.519623i	−0.397834	+	0.917457i	$0.630238\pi$
$240$	−3.11436	−	0.432344i	−0.201031	−	0.0279077i
$241$	−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
$243$	−6.46870	+	14.1829i	−0.414967	+	0.909836i
$244$	−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
$249$	10.5696	+	26.0343i	0.669821	+	1.64985i
$250$	6.08551	−	10.5404i	0.384881	−	0.666634i
$251$	10.5065	+	18.1978i	0.663166	+	1.14864i	0.979779	+	0.200083i	$0.0641210\pi$
$251$	10.5065	+	18.1978i	0.663166	+	1.14864i	−0.316613	+	0.948555i	$0.602546\pi$
$252$	−1.53644	+	2.57669i	−0.0967865	+	0.162317i
$253$	−24.8374	−	6.65515i	−1.56151	−	0.418406i
$254$	12.6801	+	3.39763i	0.795623	+	0.213186i
$255$	15.2802	−	19.6258i	0.956884	−	1.22902i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.08238	−	8.80295i	0.317030	−	0.549113i	−0.662837	−	0.748764i	$-0.730648\pi$
$257$	5.08238	−	8.80295i	0.317030	−	0.549113i	0.979867	+	0.199651i	$0.0639810\pi$
$258$	10.1907	−	4.13732i	0.634448	−	0.257578i
$259$			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	0.898478	−	0.439018i	$-0.144673\pi$
$263$	15.6905	+	9.05891i	0.967517	+	0.558596i	0.0690387	+	0.997614i	$0.478007\pi$
$264$	5.74109	+	7.59203i	0.353339	+	0.467257i
$265$	3.52512	−	3.52512i	0.216547	−	0.216547i
$266$	1.68940	−	6.30492i	0.103584	−	0.386579i
$267$	2.84198	−	20.4720i	0.173926	−	1.25286i
$268$	7.80114	+	7.80114i	0.476531	+	0.476531i
$269$	4.00185	−	2.31047i	0.243997	−	0.140872i	−0.373015	−	0.927825i	$-0.621676\pi$
$269$	4.00185	−	2.31047i	0.243997	−	0.140872i	0.617012	+	0.786953i	$0.288343\pi$
$270$	−1.42848	+	9.32389i	−0.0869344	+	0.567434i
$271$	−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
$273$	−5.18853	+	3.47552i	−0.314024	+	0.210348i
$274$	11.4706			0.692963
$275$	−9.04839	+	2.42451i	−0.545638	+	0.146203i
$276$	3.15407	−	7.46547i	0.189853	−	0.449368i
$277$	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
$279$	9.93939	+	0.139986i	0.595055	+	0.00838073i
$280$	−0.469839	+	1.75346i	−0.0280783	+	0.104790i
$281$	−7.06261	+	7.06261i	−0.421320	+	0.421320i	−0.885658	−	0.464338i	$-0.846292\pi$
$281$	−7.06261	+	7.06261i	−0.421320	+	0.421320i	0.464338	+	0.885658i	$0.346292\pi$
$282$	−14.3514	+	10.8525i	−0.854613	+	0.646258i
$283$	−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
$288$	−2.61894	+	1.46326i	−0.154323	+	0.0862236i
$289$	−22.7891	+	39.4720i	−1.34054	+	2.32188i
$290$	1.04182	+	1.80448i	0.0611775	+	0.105963i
$291$	−19.8274	−	15.4371i	−1.16230	−	0.904940i
$292$	−2.89935	−	0.776879i	−0.169672	−	0.0454634i
$293$	10.4220	+	2.79256i	0.608857	+	0.163143i	0.550057	−	0.835127i	$-0.314606\pi$
$293$	10.4220	+	2.79256i	0.608857	+	0.163143i	0.0588001	+	0.998270i	$0.481273\pi$
$294$	1.36667	+	1.06406i	0.0797058	+	0.0620570i
$295$	4.92240	+	8.52585i	0.286593	+	0.496394i
$296$	−0.946100	+	1.63869i	−0.0549910	+	0.0952471i
$297$	23.0164	−	16.9008i	1.33555	−	0.980684i
$298$			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
$303$	3.80276	−	2.87565i	0.218463	−	0.165202i
$304$	4.61552	−	4.61552i	0.264718	−	0.264718i
$305$	−3.70323	+	13.8207i	−0.212047	+	0.791369i
$306$	0.334206	−	23.7296i	0.0191053	−	1.35653i
$307$	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
$309$	6.85812	−	16.2327i	0.390145	−	0.923447i
$310$	5.81003	−	1.55679i	0.329987	−	0.0884199i
$311$	−21.3065			−1.20818			−0.604091	−	0.796916i	$-0.706464\pi$
$311$	−21.3065			−1.20818			−0.604091	+	0.796916i	$0.706464\pi$
$312$	−6.23115	+	0.415622i	−0.352770	+	0.0235300i
$313$	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
$315$	5.24002	+	1.48346i	0.295242	+	0.0835834i
$316$	0.484280	−	0.279599i	0.0272429	−	0.0157287i
$317$	1.45164	+	1.45164i	0.0815321	+	0.0815321i	0.746697	−	0.665165i	$-0.231639\pi$
$317$	1.45164	+	1.45164i	0.0815321	+	0.0815321i	−0.665165	+	0.746697i	$0.731639\pi$
$318$	0.654052	−	4.71142i	0.0366774	−	0.264203i
$319$	1.63255	−	6.09274i	0.0914050	−	0.341128i
$320$	−1.28362	+	1.28362i	−0.0717568	+	0.0717568i
$321$	−0.744806	−	0.984933i	−0.0415710	−	0.0549736i
$322$	−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
$327$	−9.30302	+	3.77691i	−0.514458	+	0.208864i
$328$	4.40793	−	7.63476i	0.243387	−	0.421559i
$329$	5.19406	+	8.99638i	0.286358	+	0.495987i
$330$	10.6150	−	13.6338i	0.584334	−	0.750517i
$331$	−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
$333$	4.87562	+	2.90725i	0.267182	+	0.159316i
$334$	6.69882	+	11.6027i	0.366543	+	0.634871i
$335$	10.0137	−	17.3443i	0.547109	−	0.947621i
$336$	0.651543	+	1.60483i	0.0355446	+	0.0875509i
$337$			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
$342$	−13.6502	−	14.0402i	−0.738118	−	0.759206i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	1.64351	−	6.13366i	0.0886120	−	0.330705i
$345$	−14.5723	−	2.02297i	−0.784548	−	0.108913i
$346$	−7.64063	−	7.64063i	−0.410763	−	0.410763i
$347$	−7.32984	+	4.23188i	−0.393486	+	0.227179i	−0.683670	−	0.729792i	$-0.739617\pi$
$347$	−7.32984	+	4.23188i	−0.393486	+	0.227179i	0.290183	+	0.956971i	$0.406284\pi$
$348$	1.83132	+	0.773710i	0.0981691	+	0.0414752i
$349$	−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
$351$	0.983491	+	18.7092i	0.0524949	+	0.998621i
$352$	5.49542			0.292907
$353$	−11.6530	+	3.12242i	−0.620228	+	0.166190i	−0.555231	−	0.831696i	$-0.687370\pi$
$353$	−11.6530	+	3.12242i	−0.620228	+	0.166190i	−0.0649966	+	0.997885i	$0.520704\pi$
$354$	8.65268	+	3.65565i	0.459885	+	0.194296i
$355$	10.2716	−	5.93029i	0.545158	−	0.314747i
$356$	−8.43780	−	8.43780i	−0.447202	−	0.447202i
$357$	−13.5715	−	1.88403i	−0.718279	−	0.0997136i
$358$	1.79658	−	6.70494i	0.0949524	−	0.354367i
$359$	15.3078	−	15.3078i	0.807913	−	0.807913i	−0.176405	−	0.984318i	$-0.556447\pi$
$359$	15.3078	−	15.3078i	0.807913	−	0.807913i	0.984318	+	0.176405i	$0.0564467\pi$
$360$	3.79626	+	3.90472i	0.200081	+	0.205797i
$361$	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
$366$	5.13541	+	12.6492i	0.268432	+	0.661183i
$367$	−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
$369$	−22.7158	−	13.5450i	−1.18254	−	0.705126i
$370$	3.31791	+	0.889030i	0.172490	+	0.0462185i
$371$	−2.65265	−	0.710775i	−0.137719	−	0.0369016i
$372$	3.52570	−	4.52840i	0.182799	−	0.234787i
$373$	−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
$375$	−19.5325	+	7.92994i	−1.00865	+	0.409500i
$376$			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
$381$	−13.7143	−	18.1358i	−0.702605	−	0.929126i
$382$	−1.64610	+	1.64610i	−0.0842218	+	0.0842218i
$383$	−1.98302	+	7.40072i	−0.101327	+	0.378159i	−0.997903	−	0.0647325i	$-0.979381\pi$
$383$	−1.98302	+	7.40072i	−0.101327	+	0.378159i	0.896575	+	0.442891i	$0.146047\pi$
$384$	−0.238164	+	1.71560i	−0.0121538	+	0.0875488i
$385$	−7.05406	−	7.05406i	−0.359508	−	0.359508i
$386$	−6.99648	+	4.03942i	−0.356111	+	0.205601i
$387$	−18.3297	−	5.18917i	−0.931752	−	0.263780i
$388$	−14.0135	+	3.75490i	−0.711426	+	0.190626i
$389$	−15.2721			−0.774324			−0.387162	−	0.922012i	$-0.626545\pi$
$389$	−15.2721			−0.774324			−0.387162	+	0.922012i	$0.626545\pi$
$390$	3.65642	+	10.7308i	0.185150	+	0.543376i
$391$	37.0145			1.87191
$392$	0.965926	−	0.258819i	0.0487866	−	0.0130723i
$393$	−8.98631	+	21.2700i	−0.453299	+	1.07293i
$394$	22.9522	−	13.2515i	1.15632	−	0.667600i
$395$	−0.717801	−	0.717801i	−0.0361165	−	0.0361165i
$396$	0.232169	−	16.4846i	0.0116669	−	0.828384i
$397$	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
$399$	−9.01763	+	6.81913i	−0.451446	+	0.341383i
$400$	−1.47624	−	0.852308i	−0.0738120	−	0.0426154i
$401$	7.63320	+	28.4875i	0.381184	+	1.42260i	0.844095	+	0.536193i	$0.180138\pi$
$401$	7.63320	+	28.4875i	0.381184	+	1.42260i	−0.462912	+	0.886404i	$0.653195\pi$
$402$	−2.36074	−	18.9624i	−0.117743	−	0.945760i
$403$	10.6711	−	5.37157i	0.531567	−	0.267577i
$404$		−	2.75260i		−	0.136947i
$405$	11.8734	−	11.2227i	0.589993	−	0.557660i
$406$	0.573902	−	0.994028i	0.0284823	−	0.0493328i
$407$	−5.19922	−	9.00531i	−0.257716	−	0.446377i
$408$	−10.8112	−	8.41736i	−0.535236	−	0.416722i
$409$	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
$411$	−15.6765	−	12.2053i	−0.773265	−	0.602045i
$412$	−5.08703	−	8.81100i	−0.250620	−	0.434087i
$413$	2.71159	−	4.69661i	0.133429	−	0.231105i
$414$	−12.2542	+	6.84673i	−0.602263	+	0.336498i
$415$		−	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	0.553553	−	0.832814i	$-0.313271\pi$
$419$	2.23306	+	1.28926i	0.109092	+	0.0629845i	−0.444461	+	0.895798i	$0.646605\pi$
$420$	2.50790	−	1.89647i	0.122373	−	0.0925383i
$421$	−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
$423$	31.1613	+	0.438874i	1.51511	+	0.0213388i
$424$	−1.94187	−	1.94187i	−0.0943057	−	0.0943057i
$425$	11.6780	−	6.74230i	0.566467	−	0.327050i
$426$	4.40416	−	10.4244i	0.213382	−	0.505062i
$427$	7.61335	−	2.03999i	0.368436	−	0.0987220i
$428$	−0.712935			−0.0344610
$429$	15.1434	−	30.7972i	0.731130	−	1.48690i
$430$	−11.5273			−0.555897
$431$	26.0777	−	6.98751i	1.25612	−	0.336576i	0.431422	−	0.902150i	$-0.358012\pi$
$431$	26.0777	−	6.98751i	1.25612	−	0.336576i	0.824698	+	0.565574i	$0.191345\pi$
$432$	5.13622	+	0.786902i	0.247117	+	0.0378598i
$433$	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
$435$	0.496247	−	3.57468i	0.0237932	−	0.171393i
$436$	−1.50034	+	5.59935i	−0.0718533	+	0.268160i
$437$	21.5964	−	21.5964i	1.03310	−	1.03310i
$438$	3.13582	+	4.14681i	0.149835	+	0.198142i
$439$	−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	$-0.675492\pi$
$443$		−	35.8580i		−	1.70366i	0.523815	−	0.851832i	$-0.324508\pi$
$444$	3.03667	−	1.23285i	0.144114	−	0.0585085i
$445$	−10.8310	+	18.7598i	−0.513437	+	0.889299i
$446$	−3.02163	−	5.23361i	−0.143078	−	0.247819i
$447$	0.507542	−	0.651885i	0.0240059	−	0.0308331i
$448$	0.965926	+	0.258819i	0.0456357	+	0.0122281i
$449$	−16.1036	−	4.31494i	−0.759974	−	0.203634i	−0.142036	−	0.989861i	$-0.545365\pi$
$449$	−16.1036	−	4.31494i	−0.759974	−	0.203634i	−0.617938	+	0.786227i	$0.712032\pi$
$450$	−2.61904	+	4.39227i	−0.123463	+	0.207054i
$451$	24.2234	+	41.9562i	1.14064	+	1.97564i
$452$	0.749527	−	1.29822i	0.0352548	−	0.0610631i
$453$	−4.96611	−	12.2322i	−0.233328	−	0.574718i
$454$			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
$459$	−25.7063	+	32.0749i	−1.19987	+	1.49713i
$460$	−6.00618	+	6.00618i	−0.280040	+	0.280040i
$461$	4.01311	−	14.9771i	0.186909	−	0.697554i	−0.807305	−	0.590135i	$-0.799075\pi$
$461$	4.01311	−	14.9771i	0.186909	−	0.697554i	0.994214	−	0.107420i	$-0.0342588\pi$
$462$	−9.42794	−	1.30881i	−0.438627	−	0.0608915i
$463$	−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
$465$	−9.59690	−	4.05457i	−0.445046	−	0.188026i
$466$	6.13247	−	1.64319i	0.284081	−	0.0761193i
$467$	3.99462			0.184849			0.0924245	−	0.995720i	$-0.470538\pi$
$467$	3.99462			0.184849			0.0924245	+	0.995720i	$0.470538\pi$
$468$	8.95817	+	6.06227i	0.414092	+	0.280229i
$469$	−11.0325			−0.509433
$470$	18.2152	−	4.88075i	0.840205	−	0.225132i
$471$	−33.0317	−	13.9555i	−1.52202	−	0.643034i
$472$	4.69661	−	2.71159i	0.216179	−	0.124811i
$473$	24.6753	+	24.6753i	1.13457	+	1.13457i
$474$	−0.959361	−	0.133181i	−0.0440649	−	0.00611721i
$475$	2.87977	−	10.7475i	0.132133	−	0.493127i
$476$	−5.59367	+	5.59367i	−0.256385	+	0.256385i
$477$	−5.90708	+	5.74301i	−0.270467	+	0.262954i
$478$	−9.83859	−	5.68031i	−0.450007	−	0.259811i
$479$	−6.22647	−	23.2375i	−0.284495	−	1.06175i	−0.949208	−	0.314650i	$-0.898113\pi$
$479$	−6.22647	−	23.2375i	−0.284495	−	1.06175i	0.664713	−	0.747099i	$-0.268554\pi$
$480$	3.12014	−	0.388443i	0.142414	−	0.0177299i
$481$	6.81125	+	0.390413i	0.310566	+	0.0178013i
$482$		−	9.44629i		−	0.430267i
$483$	3.04862	+	7.50915i	0.138717	+	0.341678i
$484$	−9.59983	+	16.6274i	−0.436356	+	0.755790i
$485$	13.1682	+	22.8079i	0.597935	+	1.03565i
$486$	2.57746	−	15.3739i	0.116916	−	0.697374i
$487$	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
$489$	−0.519643	+	0.667427i	−0.0234991	+	0.0301821i
$490$	−0.907660	−	1.57211i	−0.0410039	−	0.0710208i
$491$	−14.1855	+	24.5700i	−0.640182	+	1.10883i	0.345210	+	0.938526i	$0.387808\pi$
$491$	−14.1855	+	24.5700i	−0.640182	+	1.10883i	−0.985392	+	0.170303i	$0.945526\pi$
$492$	−14.1480	+	5.74391i	−0.637841	+	0.258955i
$493$			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
$498$	−16.9476	−	22.4116i	−0.759440	−	1.00429i
$499$	−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
$501$	3.19084	−	22.9850i	0.142556	−	1.02689i
$502$	−14.8585	−	14.8585i	−0.663166	−	0.663166i
$503$	12.8930	−	7.44375i	0.574868	−	0.331900i	−0.184223	−	0.982884i	$-0.558977\pi$
$503$	12.8930	−	7.44375i	0.574868	−	0.331900i	0.759091	+	0.650984i	$0.225644\pi$
$504$	0.817188	−	2.88656i	0.0364005	−	0.128577i
$505$	−4.82658	+	1.29328i	−0.214780	+	0.0575501i
$506$	25.7135			1.14311
$507$	11.4401	+	19.3939i	0.508072	+	0.861315i
$508$	−13.1274			−0.582436
$509$	15.6508	−	4.19361i	0.693709	−	0.185879i	0.105298	−	0.994441i	$-0.466420\pi$
$509$	15.6508	−	4.19361i	0.693709	−	0.185879i	0.588411	+	0.808562i	$0.299754\pi$
$510$	−9.68000	+	22.9119i	−0.428638	+	1.01456i
$511$	2.59949	−	1.50082i	0.114995	−	0.0663922i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	3.71577	+	33.7129i	0.164055	+	1.48846i
$514$	−2.63083	+	9.81841i	−0.116041	+	0.433071i
$515$	−13.0597	+	13.0597i	−0.575478	+	0.575478i
$516$	−8.77269	+	6.63390i	−0.386196	+	0.292041i
$517$	−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	$0.140223\pi$
$521$			19.4661i			0.852827i	−0.904528	+	0.426413i	$0.859777\pi$
$522$	−1.67954	−	3.00603i	−0.0735115	−	0.131571i
$523$	−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
$525$	2.32965	+	1.81380i	0.101674	+	0.0791609i
$526$	−17.5005	−	4.68924i	−0.763057	−	0.204460i
$527$	25.3184	+	6.78406i	1.10289	+	0.295518i
$528$	−7.51043	−	5.84743i	−0.326849	−	0.254477i
$529$	0.553102	+	0.958002i	0.0240479	+	0.0416522i
$530$	−2.49264	+	4.31738i	−0.108273	+	0.187535i
$531$	−7.93554	−	14.2030i	−0.344373	−	0.616358i
$532$			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
$537$	−9.58977	+	7.25178i	−0.413829	+	0.312937i
$538$	−3.26750	+	3.26750i	−0.140872	+	0.140872i
$539$	−1.42232	+	5.30817i	−0.0612636	+	0.228639i
$540$	−1.03340	−	9.37590i	−0.0444702	−	0.403474i
$541$	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
$543$	11.4600	−	27.1251i	0.491797	−	1.16405i
$544$	−7.64110	+	2.04743i	−0.327609	+	0.0877826i
$545$	10.5232			0.450763
$546$	4.11220	−	4.69998i	0.175986	−	0.201141i
$547$	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
$549$	6.44101	−	22.7516i	0.274896	−	0.971014i
$550$	8.11256	−	4.68379i	0.345921	−	0.199717i
$551$	5.29772	+	5.29772i	0.225690	+	0.225690i
$552$	−1.11439	+	8.02742i	−0.0474316	+	0.341670i
$553$	−0.144731	+	0.540145i	−0.00615460	+	0.0229693i
$554$	−13.9863	+	13.9863i	−0.594220	+	0.594220i
$555$	−3.58850	−	4.74545i	−0.152323	−	0.201433i
$556$	−0.934945	−	0.539791i	−0.0396505	−	0.0228922i
$557$	−1.48980	−	5.56000i	−0.0631248	−	0.235585i	0.927154	−	0.374680i	$-0.122247\pi$
$557$	−1.48980	−	5.56000i	−0.0631248	−	0.235585i	−0.990279	+	0.139095i	$0.955581\pi$
$558$	−9.63694	+	2.43729i	−0.407964	+	0.103179i
$559$	−22.4181	+	4.65050i	−0.948184	+	0.196695i
$560$		−	1.81532i		−	0.0767113i
$561$	69.7659	−	28.3241i	2.94552	−	1.19584i
$562$	4.99402	−	8.64990i	0.210660	−	0.364874i
$563$	−1.81159	−	3.13777i	−0.0763495	−	0.132241i	0.825323	−	0.564661i	$-0.190993\pi$
$563$	−1.81159	−	3.13777i	−0.0763495	−	0.132241i	−0.901672	+	0.432420i	$0.857660\pi$
$564$	11.0535	−	14.1971i	0.465438	−	0.597807i
$565$	−2.62854	−	0.704314i	−0.110583	−	0.0296307i
$566$	3.06341	+	0.820839i	0.128765	+	0.0345024i
$567$	−8.62428	−	2.57327i	−0.362186	−	0.108067i
$568$	−3.26680	−	5.65827i	−0.137072	−	0.237416i
$569$	4.40720	−	7.63350i	0.184759	−	0.320013i	−0.758736	−	0.651398i	$-0.774183\pi$
$569$	4.40720	−	7.63350i	0.184759	−	0.320013i	0.943495	+	0.331386i	$0.107516\pi$
$570$	7.72026	+	19.0160i	0.323366	+	0.796492i
$571$		−	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
$576$	2.15098	−	2.09124i	0.0896243	−	0.0871348i
$577$	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
$579$	13.8600	+	1.92409i	0.576004	+	0.0799625i
$580$	−1.47335	−	1.47335i	−0.0611775	−	0.0611775i
$581$	−14.0490	+	8.11120i	−0.582851	+	0.336509i
$582$	23.1472	+	9.77940i	0.959482	+	0.405369i
$583$	14.5774	−	3.90601i	0.603735	−	0.161770i
$584$	3.00163			0.124208
$585$	6.42108	−	18.5561i	0.265479	−	0.767201i
$586$	−10.7896			−0.445714
$587$	16.8416	−	4.51270i	0.695129	−	0.186259i	0.106081	−	0.994357i	$-0.466170\pi$
$587$	16.8416	−	4.51270i	0.695129	−	0.186259i	0.589048	+	0.808098i	$0.299503\pi$
$588$	−1.59550	−	0.674078i	−0.0657973	−	0.0277985i
$589$	18.7304	−	10.8140i	0.771774	−	0.445584i
$590$	−6.96133	−	6.96133i	−0.286593	−	0.286593i
$591$	−45.4684	−	6.31205i	−1.87032	−	0.259643i
$592$	0.489737	−	1.82773i	0.0201281	−	0.0751190i
$593$	−4.18904	+	4.18904i	−0.172023	+	0.172023i	−0.787868	−	0.615844i	$-0.788815\pi$
$593$	−4.18904	+	4.18904i	−0.172023	+	0.172023i	0.615844	+	0.787868i	$0.288815\pi$
$594$	−17.8579	+	22.2820i	−0.732717	+	0.914242i
$595$	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	$-0.758761\pi$
$599$		−	33.6465i		−	1.37476i	0.726299	−	0.687379i	$-0.241239\pi$
$600$	1.11063	+	2.73562i	0.0453413	+	0.111681i
$601$	−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
$603$	−16.9507	+	28.4273i	−0.690287	+	1.15765i
$604$	−7.36237	−	1.97274i	−0.299570	−	0.0802697i
$605$	33.6659	+	9.02075i	1.36871	+	0.366746i
$606$	−2.92892	+	3.76189i	−0.118979	+	0.152816i
$607$	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
$609$	−1.84204	+	0.747844i	−0.0746431	+	0.0303042i
$610$		−	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
$615$	16.7190	+	22.1093i	0.674176	+	0.891532i
$616$	−3.88585	+	3.88585i	−0.156565	+	0.156565i
$617$	1.56573	−	5.84339i	0.0630340	−	0.235246i	−0.927220	−	0.374516i	$-0.877809\pi$
$617$	1.56573	−	5.84339i	0.0630340	−	0.235246i	0.990254	+	0.139270i	$0.0444756\pi$
$618$	−2.42310	+	17.4546i	−0.0974713	+	0.702127i
$619$	−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
$621$	24.0328	+	3.68198i	0.964403	+	0.147753i
$622$	20.5805	−	5.51453i	0.825203	−	0.221113i
$623$	11.9328			0.478079
$624$	5.91126	−	2.01420i	0.236640	−	0.0806326i
$625$	13.5712			0.542849
$626$	−21.7415	+	5.82562i	−0.868965	+	0.232838i
$627$	24.1795	−	57.2313i	0.965636	−	2.28560i
$628$	−17.9294	+	10.3515i	−0.715459	+	0.413071i
$629$	10.5843	+	10.5843i	0.422025	+	0.422025i
$630$	−5.44542	−	0.0766930i	−0.216951	−	0.00305552i
$631$	−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
$633$	21.9550	−	16.6023i	0.872632	−	0.659884i
$634$	−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
$639$	−17.1111	+	9.56039i	−0.676906	+	0.378203i
$640$	0.907660	−	1.57211i	0.0358784	−	0.0621432i
$641$	−3.24392	−	5.61864i	−0.128127	−	0.221923i	0.794824	−	0.606840i	$-0.207563\pi$
$641$	−3.24392	−	5.61864i	−0.128127	−	0.221923i	−0.922951	+	0.384917i	$0.874230\pi$
$642$	0.974346	+	0.758602i	0.0384544	+	0.0299396i
$643$	−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
$645$	15.7541	+	12.2657i	0.620315	+	0.482962i
$646$	−25.8177	−	44.7176i	−1.01578	−	1.75939i
$647$	−11.8424	+	20.5117i	−0.465574	+	0.806397i	−0.999227	−	0.0393061i	$-0.987485\pi$
$647$	−11.8424	+	20.5117i	−0.465574	+	0.806397i	0.533654	+	0.845703i	$0.320819\pi$
$648$	−6.18221	−	6.54066i	−0.242860	−	0.256941i
$649$			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	−0.296736	−	0.954959i	$-0.595898\pi$
$653$	−32.5077	−	18.7683i	−1.27212	−	0.734461i	−0.975387	+	0.220499i	$0.929232\pi$
$654$	8.00849	−	6.05601i	0.313157	−	0.236809i
$655$	17.1123	−	17.1123i	0.668634	−	0.668634i
$656$	−2.28171	+	8.51546i	−0.0890859	+	0.332473i
$657$	0.126812	−	9.00400i	0.00494740	−	0.351280i
$658$	−7.34551	−	7.34551i	−0.286358	−	0.286358i
$659$	−23.1197	+	13.3482i	−0.900618	+	0.519972i	−0.877400	−	0.479759i	$-0.840724\pi$
$659$	−23.1197	+	13.3482i	−0.900618	+	0.519972i	−0.0232170	+	0.999730i	$0.507391\pi$
$660$	−6.72457	+	15.9166i	−0.261754	+	0.619553i
$661$	−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
$663$	−9.58201	+	48.4638i	−0.372134	+	1.88218i
$664$	−16.2224			−0.629551
$665$	11.4454	−	3.06680i	0.443835	−	0.118925i
$666$	−5.46194	−	1.54628i	−0.211646	−	0.0599173i
$667$	4.65114	−	2.68534i	0.180093	−	0.103977i
$668$	−9.47356	−	9.47356i	−0.366543	−	0.366543i
$669$	−1.43929	+	10.3678i	−0.0556460	+	0.400842i
$670$	−5.18349	+	19.3451i	−0.200256	+	0.747365i
$671$	−30.6279	+	30.6279i	−1.18238	+	1.18238i
$672$	−1.04470	−	1.38152i	−0.0403003	−	0.0532932i
$673$	−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	$-0.785987\pi$
$677$		−	32.4106i		−	1.24564i	0.782366	−	0.622819i	$-0.214013\pi$
$678$	−2.40573	+	0.976698i	−0.0923916	+	0.0375099i
$679$	7.25390	−	12.5641i	0.278379	−	0.482167i
$680$	7.18017	+	12.4364i	0.275347	+	0.476915i
$681$	9.00870	−	11.5707i	0.345214	−	0.443392i
$682$	17.5884	+	4.71280i	0.673494	+	0.180462i
$683$	−29.0808	−	7.79217i	−1.11274	−	0.298159i	−0.344801	−	0.938676i	$-0.612053\pi$
$683$	−29.0808	−	7.79217i	−1.11274	−	0.298159i	−0.767944	+	0.640517i	$0.778720\pi$
$684$	16.8189	+	10.0288i	0.643088	+	0.383463i
$685$	10.4114	+	18.0331i	0.397799	+	0.689008i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	0.449937	+	1.10825i	0.0171662	+	0.0422825i
$688$			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
$693$	11.4922	+	11.8206i	0.436554	+	0.449026i
$694$	5.98479	−	5.98479i	0.227179	−	0.227179i
$695$	−0.507230	+	1.89301i	−0.0192403	+	0.0718059i
$696$	−1.96917	−	0.273366i	−0.0746413	−	0.0103619i
$697$	−49.3130	−	49.3130i	−1.86786	−	1.86786i
$698$	26.7188	−	15.4261i	1.01132	−	0.583887i
$699$	−10.1295	−	4.27959i	−0.383133	−	0.161869i
$700$	1.64653	−	0.441187i	0.0622330	−	0.0166753i
$701$	−20.1374			−0.760581			−0.380290	−	0.924867i	$-0.624176\pi$
$701$	−20.1374			−0.760581			−0.380290	+	0.924867i	$0.624176\pi$
$702$	−5.79227	−	17.8171i	−0.218615	−	0.672464i
$703$	12.3510			0.465828
$704$	−5.30817	+	1.42232i	−0.200059	+	0.0536057i
$705$	−30.0876	−	12.7116i	−1.13316	−	0.478747i
$706$	10.4478	−	6.03205i	0.393209	−	0.227019i
$707$	1.94638	+	1.94638i	0.0732011	+	0.0732011i
$708$	−9.30400	−	1.29161i	−0.349666	−	0.0485416i
$709$	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
$711$	1.16942	+	1.20283i	0.0438566	+	0.0451096i
$712$	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
$717$	7.40193	+	18.2319i	0.276430	+	0.680883i
$718$	−10.8242	+	18.7481i	−0.403957	+	0.699673i
$719$	−12.6851	−	21.9713i	−0.473075	−	0.819390i	0.526450	−	0.850206i	$-0.323523\pi$
$719$	−12.6851	−	21.9713i	−0.473075	−	0.819390i	−0.999525	+	0.0308161i	$0.990189\pi$
$720$	−4.67752	−	2.78913i	−0.174321	−	0.103945i
$721$	9.82739	+	2.63324i	0.365991	+	0.0980671i
$722$	−22.8017	−	6.10970i	−0.848592	−	0.227380i
$723$	−10.0514	+	12.9100i	−0.373815	+	0.480127i
$724$	−8.50052	−	14.7233i	−0.315919	−	0.547188i
$725$	0.978282	−	1.69443i	0.0363325	−	0.0629297i
$726$	30.8123	−	12.5094i	1.14355	−	0.464267i
$727$			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
$732$	−8.23427	−	10.8890i	−0.304347	−	0.402470i
$733$	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
$735$	−0.432344	+	3.11436i	−0.0159473	+	0.114875i
$736$	3.30861	+	3.30861i	0.121957	+	0.121957i
$737$	52.5055	−	30.3141i	1.93407	−	1.11663i
$738$	25.4475	+	7.20422i	0.936734	+	0.265191i
$739$	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
$741$	22.6858	+	33.8672i	0.833385	+	1.24414i
$742$	2.74622			0.100817
$743$	0.759466	−	0.203498i	0.0278621	−	0.00746563i	−0.244861	−	0.969558i	$-0.578742\pi$
$743$	0.759466	−	0.203498i	0.0278621	−	0.00746563i	0.272723	+	0.962093i	$0.412076\pi$
$744$	−2.23353	+	5.28662i	−0.0818852	+	0.193817i
$745$	−0.749879	+	0.432943i	−0.0274734	+	0.0158618i
$746$	9.78177	+	9.78177i	0.358136	+	0.358136i
$747$	−0.685359	+	48.6624i	−0.0250760	+	1.78046i
$748$	11.2515	−	41.9910i	0.411394	−	1.53534i
$749$	0.504121	−	0.504121i	0.0184202	−	0.0184202i
$750$	16.8145	−	12.7151i	0.613978	−	0.464290i
$751$	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
$756$	−4.18828	+	3.07543i	−0.152326	+	0.111852i
$757$	−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
$759$	−35.1419	−	27.3606i	−1.27557	−	0.993127i
$760$	11.4454	+	3.06680i	0.415170	+	0.111244i
$761$	−14.8093	−	3.96814i	−0.536837	−	0.143845i	−0.0197932	−	0.999804i	$-0.506301\pi$
$761$	−14.8093	−	3.96814i	−0.536837	−	0.143845i	−0.517043	+	0.855959i	$0.672967\pi$
$762$	17.9409	+	13.9683i	0.649930	+	0.506019i
$763$	−2.89844	−	5.02024i	−0.104930	−	0.181745i
$764$	1.16397	−	2.01605i	0.0421109	−	0.0729382i
$765$	37.6089	−	21.0130i	1.35975	−	0.759726i
$766$		−	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
$771$	14.0428	−	10.6192i	0.505740	−	0.382440i
$772$	5.71260	−	5.71260i	0.205601	−	0.205601i
$773$	−9.33990	+	34.8570i	−0.335933	+	1.25372i	0.566922	+	0.823772i	$0.308134\pi$
$773$	−9.33990	+	34.8570i	−0.335933	+	1.25372i	−0.902854	+	0.429946i	$0.858532\pi$
$774$	19.0482	+	0.268274i	0.684673	+	0.00964291i
$775$	−3.99386	−	3.99386i	−0.143464	−	0.143464i
$776$	12.5641	−	7.25390i	0.451026	−	0.260400i
$777$	−1.27549	+	3.01900i	−0.0457580	+	0.108306i
$778$	14.7517	−	3.95270i	0.528873	−	0.141711i
$779$	−57.5440			−2.06173
$780$	−6.30917	−	9.41883i	−0.225905	−	0.337248i
$781$	35.9049			1.28478
$782$	−35.7533	+	9.58007i	−1.27854	+	0.342583i
$783$	−0.903210	+	5.89538i	−0.0322781	+	0.210684i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	26.5749	+	26.5749i	0.948500	+	0.948500i
$786$	3.17503	−	22.8711i	0.113249	−	0.815784i
$787$	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
$789$	18.9278	+	25.0301i	0.673846	+	0.891095i
$790$	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
$795$	8.00054	−	3.24812i	0.283750	−	0.115199i
$796$	10.2805	−	17.8064i	0.364383	−	0.631130i
$797$	6.66860	+	11.5504i	0.236214	+	0.409135i	0.959625	−	0.281283i	$-0.0907600\pi$
$797$	6.66860	+	11.5504i	0.236214	+	0.409135i	−0.723411	+	0.690418i	$0.757427\pi$
$798$	6.94544	−	8.92071i	0.245866	−	0.315790i
$799$	79.3767	+	21.2689i	2.80814	+	0.752440i
$800$	1.64653	+	0.441187i	0.0582137	+	0.0155983i
$801$	18.3341	−	30.7473i	0.647803	−	1.08640i
$802$	−14.7462	−	25.5412i	−0.520707	−	0.901891i
$803$	−8.24761	+	14.2853i	−0.291052	+	0.504117i
$804$	7.18813	+	17.7053i	0.253506	+	0.624418i
$805$		−	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	0.421819	−	0.906680i	$-0.361392\pi$
$809$	−4.33697	−	2.50395i	−0.152480	−	0.0880342i	−0.574299	+	0.818646i	$0.694725\pi$
$810$	−8.56417	+	13.9133i	−0.300914	+	0.488865i
$811$	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
$813$	−48.3901	−	6.71765i	−1.69712	−	0.235598i
$814$	7.35281	+	7.35281i	0.257716	+	0.257716i
$815$	0.767758	−	0.443265i	0.0268934	−	0.0155269i
$816$	12.6214	+	5.33239i	0.441838	+	0.186671i
$817$	−40.0364	+	10.7277i	−1.40070	+	0.375316i
$818$	−6.59277			−0.230511
$819$	−10.6211	+	2.04771i	−0.371130	+	0.0715528i
$820$	16.0036			0.558870
$821$	2.31532	−	0.620389i	0.0808054	−	0.0216517i	−0.218190	−	0.975906i	$-0.570015\pi$
$821$	2.31532	−	0.620389i	0.0808054	−	0.0216517i	0.298995	+	0.954255i	$0.403349\pi$
$822$	18.3013	+	7.73208i	0.638332	+	0.269687i
$823$	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
$825$	−16.0710	−	2.23102i	−0.559520	−	0.0776742i
$826$	−1.40362	+	5.23839i	−0.0488383	+	0.182267i
$827$	20.8129	−	20.8129i	0.723735	−	0.723735i	−0.245629	−	0.969364i	$-0.578995\pi$
$827$	20.8129	−	20.8129i	0.723735	−	0.723735i	0.969364	+	0.245629i	$0.0789946\pi$
$828$	10.0646	−	9.78506i	0.349770	−	0.340054i
$829$	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
$834$	0.703394	+	1.73255i	0.0243565	+	0.0599933i
$835$	−12.1605	+	21.0626i	−0.420831	+	0.728901i
$836$	−17.9352	−	31.0647i	−0.620303	−	1.07440i
$837$	15.7639	+	6.92327i	0.544881	+	0.239303i
$838$	−2.49066	−	0.667370i	−0.0860384	−	0.0230539i
$839$	−8.14694	−	2.18297i	−0.281264	−	0.0753644i	0.115429	−	0.993316i	$-0.463176\pi$
$839$	−8.14694	−	2.18297i	−0.281264	−	0.0753644i	−0.396693	+	0.917951i	$0.629842\pi$
$840$	−1.93160	+	2.48094i	−0.0666466	+	0.0856006i
$841$	−13.8413	−	23.9738i	−0.477285	−	0.826682i
$842$	4.59405	−	7.95713i	0.158322	−	0.274221i
$843$	−16.0291	+	6.50764i	−0.552073	+	0.224135i
$844$		−	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
$849$	−3.31326	−	4.38146i	−0.113711	−	0.150371i
$850$	−9.53505	+	9.53505i	−0.327050	+	0.327050i
$851$	2.29152	−	8.55207i	0.0785523	−	0.293161i
$852$	−1.55607	+	11.2090i	−0.0533101	+	0.384016i
$853$	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
$855$	9.68302	−	34.2034i	0.331152	−	1.16973i
$856$	0.688642	−	0.184521i	0.0235373	−	0.00630680i
$857$	−42.2144			−1.44202			−0.721008	−	0.692927i	$-0.756321\pi$
$857$	−42.2144			−1.44202			−0.721008	+	0.692927i	$0.756321\pi$
$858$	−6.65650	+	33.6672i	−0.227249	+	1.14938i
$859$	−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
$861$	5.94258	−	14.0657i	0.202523	−	0.479358i
$862$	−23.3807	+	13.4988i	−0.796348	+	0.459772i
$863$	1.90689	+	1.90689i	0.0649112	+	0.0649112i	0.738817	−	0.673906i	$-0.235385\pi$
$863$	1.90689	+	1.90689i	0.0649112	+	0.0649112i	−0.673906	+	0.738817i	$0.735385\pi$
$864$	−5.16488	+	0.569264i	−0.175713	+	0.0193667i
$865$	5.07684	−	18.9470i	0.172618	−	0.644219i
$866$	−1.89241	+	1.89241i	−0.0643067	+	0.0643067i
$867$	−62.9673	+	47.6158i	−2.13848	+	1.61712i
$868$	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
$873$	−21.2288	−	37.9951i	−0.718484	−	1.28594i
$874$	−15.2710	+	26.4501i	−0.516548	+	0.894687i
$875$	−6.08551	−	10.5404i	−0.205728	−	0.356331i
$876$	−4.10224	−	3.19390i	−0.138602	−	0.107912i
$877$	−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
$879$	14.7458	+	11.4807i	0.497364	+	0.387236i
$880$	4.98797	+	8.63942i	0.168145	+	0.291235i
$881$	10.9926	−	19.0397i	0.370349	−	0.641463i	−0.619270	−	0.785178i	$-0.712572\pi$
$881$	10.9926	−	19.0397i	0.370349	−	0.641463i	0.989619	+	0.143715i	$0.0459049\pi$
$882$	1.46326	+	2.61894i	0.0492707	+	0.0881844i
$883$		−	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	0.949043	−	0.315148i	$-0.102054\pi$
$887$	34.2689	+	19.7852i	1.15064	+	0.664321i	0.201595	+	0.979469i	$0.435388\pi$
$888$	−2.61411	+	1.97679i	−0.0877238	+	0.0663367i
$889$	9.28251	−	9.28251i	0.311325	−	0.311325i
$890$	5.60652	−	20.9238i	0.187931	−	0.701368i
$891$	48.1151	−	11.4504i	1.61192	−	0.383602i
$892$	4.27323	+	4.27323i	0.143078	+	0.143078i
$893$	58.7224	−	33.9034i	1.96507	−	1.13453i
$894$	−0.321527	+	0.761034i	−0.0107535	+	0.0254528i
$895$	12.1716	−	3.26137i	0.406852	−	0.109016i
$896$	−1.00000			−0.0334077
$897$	27.6593	−	9.42461i	0.923516	−	0.314679i
$898$	16.6716			0.556340
$899$	3.67361	−	0.984341i	0.122522	−	0.0328296i
$900$	1.39299	−	4.92047i	0.0464330	−	0.164016i
$901$	−18.8139	+	10.8622i	−0.626781	+	0.361872i
$902$	−34.2571	−	34.2571i	−1.14064	−	1.14064i
$903$	1.51235	−	10.8941i	0.0503279	−	0.362533i
$904$	−0.387984	+	1.44797i	−0.0129041	+	0.0481589i
$905$	−21.8230	+	21.8230i	−0.725420	+	0.725420i
$906$	7.96282	+	10.5301i	0.264547	+	0.349838i
$907$	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	$-0.957355\pi$
$911$		−	8.06312i		−	0.267143i	0.991039	−	0.133571i	$-0.0426446\pi$
$912$	10.4753	−	4.25284i	0.346871	−	0.140826i
$913$	44.5745	−	77.2053i	1.47520	−	2.55512i
$914$	17.9061	+	31.0144i	0.592283	+	1.02586i
$915$	−15.2247	+	19.5546i	−0.503314	+	0.646454i
$916$	0.667041	+	0.178733i	0.0220397	+	0.00590551i
$917$	−12.8770	−	3.45038i	−0.425236	−	0.113942i
$918$	16.5288	−	37.6352i	0.545532	−	1.24215i
$919$	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
$921$	15.5614	+	38.3296i	0.512764	+	1.26300i
$922$			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
$927$	21.8842	−	21.2764i	0.718773	−	0.698808i
$928$	−0.811620	+	0.811620i	−0.0266427	+	0.0266427i
$929$	12.6931	−	47.3714i	0.416448	−	1.55421i	−0.365469	−	0.930824i	$-0.619091\pi$
$929$	12.6931	−	47.3714i	0.416448	−	1.55421i	0.781917	−	0.623383i	$-0.214242\pi$
$930$	10.3193	+	1.43255i	0.338383	+	0.0469753i
$931$	−4.61552	−	4.61552i	−0.151268	−	0.151268i
$932$	−5.49822	+	3.17440i	−0.180100	+	0.103981i
$933$	−33.9945	−	14.3623i	−1.11293	−	0.470199i
$934$	−3.85851	+	1.03388i	−0.126254	+	0.0338297i
$935$	−78.9162			−2.58083
$936$	−10.2220	−	3.53716i	−0.334115	−	0.115616i
$937$	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
$939$	35.9122	+	15.1725i	1.17195	+	0.495135i
$940$	−16.3313	+	9.42888i	−0.532669	+	0.307536i
$941$	12.5887	+	12.5887i	0.410380	+	0.410380i	0.881871	−	0.471491i	$-0.156284\pi$
$941$	12.5887	+	12.5887i	0.410380	+	0.410380i	−0.471491	+	0.881871i	$0.656284\pi$
$942$	35.5181	+	4.93072i	1.15724	+	0.160652i
$943$	−10.6763	+	39.8445i	−0.347669	+	1.29752i
$944$	−3.83477	+	3.83477i	−0.124811	+	0.124811i
$945$	7.36048	+	5.89904i	0.239437	+	0.191896i
$946$	−30.2209	−	17.4480i	−0.982566	−	0.567285i
$947$	0.749425	+	2.79689i	0.0243530	+	0.0908868i	0.977033	−	0.213089i	$-0.0683525\pi$
$947$	0.749425	+	2.79689i	0.0243530	+	0.0908868i	−0.952680	+	0.303976i	$0.901686\pi$
$948$	0.961141	−	0.119658i	0.0312164	−	0.00388630i
$949$	−4.86605	−	9.66689i	−0.157959	−	0.313801i
$950$			11.1266i			0.360994i
$951$	1.33757	+	3.29460i	0.0433736	+	0.106835i
$952$	3.95532	−	6.85082i	0.128193	−	0.222036i
$953$	−13.8544	−	23.9965i	−0.448788	−	0.777323i	0.549520	−	0.835481i	$-0.314811\pi$
$953$	−13.8544	−	23.9965i	−0.448788	−	0.777323i	−0.998307	+	0.0581576i	$0.981477\pi$
$954$	4.21941	−	7.07618i	0.136608	−	0.229100i
$955$	−4.08196	−	1.09376i	−0.132089	−	0.0353931i
$956$	10.9735	+	2.94035i	0.354909	+	0.0950976i
$957$	6.71171	−	8.62050i	0.216959	−	0.278661i
$958$	12.0286	+	20.8342i	0.388627	+	0.673122i
$959$	5.73529	−	9.93382i	0.185202	−	0.320780i
$960$	−2.91329	+	1.18276i	−0.0940259	+	0.0381734i
$961$			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
$966$	−4.88825	−	6.46424i	−0.157277	−	0.207983i
$967$	−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
$969$	−12.2977	+	88.5856i	−0.395059	+	2.84578i
$970$	−18.6226	−	18.6226i	−0.597935	−	0.597935i
$971$	9.02730	−	5.21191i	0.289700	−	0.167258i	−0.348107	−	0.937455i	$-0.613175\pi$
$971$	9.02730	−	5.21191i	0.289700	−	0.167258i	0.637806	+	0.770197i	$0.279842\pi$
$972$	1.48942	+	15.5171i	0.0477731	+	0.497712i
$973$	1.04280	−	0.279416i	0.0334305	−	0.00895767i
$974$	−6.92373			−0.221851
$975$	7.00972	−	8.01166i	0.224491	−	0.256578i
$976$	−7.88192			−0.252294
$977$	−19.6124	+	5.25512i	−0.627456	+	0.168126i	−0.558515	−	0.829494i	$-0.688629\pi$
$977$	−19.6124	+	5.25512i	−0.627456	+	0.168126i	−0.0689410	+	0.997621i	$0.521962\pi$
$978$	0.329193	−	0.779179i	0.0105264	−	0.0249154i
$979$	−56.7905	+	32.7880i	−1.81503	+	1.04791i
$980$	1.28362	+	1.28362i	0.0410039	+	0.0410039i
$981$	−17.3889	−	0.244904i	−0.555185	−	0.00781919i
$982$	7.34295	−	27.4043i	0.234323	−	0.874505i
$983$	26.1651	−	26.1651i	0.834537	−	0.834537i	−0.153597	−	0.988134i	$-0.549086\pi$
$983$	26.1651	−	26.1651i	0.834537	−	0.834537i	0.988134	+	0.153597i	$0.0490857\pi$
$984$	12.1793	−	9.20996i	0.388261	−	0.293603i
$985$	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
$990$	26.1264	−	14.5974i	0.830352	−	0.463937i
$991$	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
$993$	−36.2554	−	28.2276i	−1.15053	−	0.895776i
$994$	6.31098	+	1.69102i	0.200172	+	0.0536360i
$995$	−36.0530	−	9.66037i	−1.14296	−	0.306254i
$996$	22.1707	+	17.2615i	0.702504	+	0.546953i
$997$	−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
$999$	5.81934	+	7.92507i	0.184116	+	0.250738i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.59550 + 0.674078i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.28362 - 1.28362i) q^{5} +(-1.71560 - 0.238164i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.09124 + 2.15098i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.59550 + 0.674078i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.28362 - 1.28362i) q^{5} +(-1.71560 - 0.238164i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.09124 + 2.15098i) 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} +(-1.18276 - 2.91329i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.95532 + 6.85082i) q^{17} +(-2.57669 - 1.53644i) q^{18} +(6.30492 + 1.68940i) q^{19} +(-1.75346 - 0.469839i) q^{20} +(-1.06406 + 1.36667i) q^{21} +(2.74771 + 4.75917i) q^{22} +(2.33954 - 4.05220i) q^{23} +(-1.60483 + 0.651543i) 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} +(1.89647 + 2.50790i) q^{30} +(2.34297 - 2.34297i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.30881 - 9.42794i) q^{33} +(-5.59367 - 5.59367i) q^{34} +(1.57211 - 0.907660i) q^{35} +(2.88656 + 0.817188i) q^{36} +(1.82773 - 0.489737i) q^{37} -6.52733 q^{38} +(4.69998 + 4.11220i) q^{39} +1.81532 q^{40} +(-8.51546 + 2.28171i) q^{41} +(0.674078 - 1.59550i) q^{42} +(-5.49929 + 3.17501i) q^{43} +(-3.88585 - 3.88585i) q^{44} +(0.0766930 - 5.44542i) q^{45} +(-1.21104 + 4.51964i) q^{46} +(7.34551 - 7.34551i) q^{47} +(1.38152 - 1.04470i) 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} +(-3.07543 - 4.18828i) q^{54} +(-4.98797 + 8.63942i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(8.92071 + 6.94544i) q^{57} +(-1.10869 - 0.297074i) q^{58} +(-5.23839 - 1.40362i) q^{59} +(-2.48094 - 1.93160i) q^{60} +(-3.94096 - 6.82594i) q^{61} +(-1.65673 + 2.86954i) q^{62} +(-2.61894 + 1.46326i) 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} +(6.46424 - 4.88825i) q^{69} +(-1.28362 + 1.28362i) q^{70} +(-1.69102 + 6.31098i) q^{71} +(-2.99970 - 0.0422477i) q^{72} +(-2.12247 - 2.12247i) q^{73} +(-1.63869 + 0.946100i) q^{74} +(1.14904 - 2.71971i) q^{75} +(6.30492 - 1.68940i) q^{76} +5.49542 q^{77} +(-5.60415 - 2.75564i) q^{78} +0.559199 q^{79} +(-1.75346 + 0.469839i) q^{80} +(-0.253461 + 8.99643i) q^{81} +(7.63476 - 4.40793i) q^{82} +(11.4710 + 11.4710i) q^{83} +(-0.238164 + 1.71560i) q^{84} +(3.71673 - 13.8710i) q^{85} +(4.49015 - 4.49015i) q^{86} +(1.19912 + 1.58571i) 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} +(5.31755 - 2.15886i) q^{93} +(-5.19406 + 8.99638i) q^{94} +(-5.92460 - 10.2617i) q^{95} +(-1.06406 + 1.36667i) q^{96} +(-14.0135 - 3.75490i) q^{97} +(0.965926 + 0.258819i) q^{98} +(8.44338 - 14.1600i) 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	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 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^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 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 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

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