LMFDB - Embedded newform 273.2.cc.a.50.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(50,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 7]))

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

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

chi := DirichletCharacter("273.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cc (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			50.11
Character	$\chi$	$=$	273.50
Dual form			273.2.cc.a.71.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.751420 - 0.201342i) q^{2} +(-1.18266 - 1.26543i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(2.48091 - 2.48091i) q^{5} +(0.633888 + 1.18899i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.86742 + 1.86742i) q^{8} +(-0.202642 + 2.99315i) q^{9} +O(q^{10})$	\(q+(-0.751420 - 0.201342i) q^{2} +(-1.18266 - 1.26543i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(2.48091 - 2.48091i) q^{5} +(0.633888 + 1.18899i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.86742 + 1.86742i) q^{8} +(-0.202642 + 2.99315i) q^{9} +(-2.36372 + 1.36469i) q^{10} +(1.16287 - 4.33987i) q^{11} +(0.546068 + 2.35339i) q^{12} +(-2.59448 - 2.50374i) q^{13} +0.777928i q^{14} +(-6.07349 - 0.205359i) q^{15} +(0.367602 + 0.636705i) q^{16} +(-2.53006 + 4.38220i) q^{17} +(0.754917 - 2.20831i) q^{18} +(-4.15985 + 1.11463i) q^{19} +(-4.72705 + 1.26661i) q^{20} +(-0.916220 + 1.46988i) q^{21} +(-1.74760 + 3.02693i) q^{22} +(1.39149 + 2.41014i) q^{23} +(0.154577 - 4.57161i) q^{24} -7.30982i q^{25} +(1.44543 + 2.40374i) q^{26} +(4.02729 - 3.28344i) q^{27} +(-0.361008 + 1.34730i) q^{28} +(-0.156921 + 0.0905985i) q^{29} +(4.52240 + 1.37716i) q^{30} +(-6.69080 - 6.69080i) q^{31} +(-1.51507 - 5.65433i) q^{32} +(-6.86709 + 3.66105i) q^{33} +(2.78347 - 2.78347i) q^{34} +(-3.03848 - 1.75427i) q^{35} +(2.33225 - 3.47427i) q^{36} +(7.89628 + 2.11580i) q^{37} +3.35022 q^{38} +(-0.0999316 + 6.24420i) q^{39} +9.26580 q^{40} +(5.61219 + 1.50378i) q^{41} +(0.984415 - 0.920022i) q^{42} +(0.515494 + 0.297621i) q^{43} +(-4.43138 + 4.43138i) q^{44} +(6.92299 + 7.92846i) q^{45} +(-0.560334 - 2.09119i) q^{46} +(-0.599020 - 0.599020i) q^{47} +(0.370961 - 1.21818i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-1.47178 + 5.49275i) q^{50} +(8.53758 - 1.98102i) q^{51} +(1.38788 + 4.83383i) q^{52} +5.43018i q^{53} +(-3.68728 + 1.65638i) q^{54} +(-7.88187 - 13.6518i) q^{55} +(1.32047 - 2.28711i) q^{56} +(6.33016 + 3.94578i) q^{57} +(0.136155 - 0.0364827i) q^{58} +(7.75661 - 2.07838i) q^{59} +(7.19330 + 4.48380i) q^{60} +(1.75531 - 3.04029i) q^{61} +(3.68046 + 6.37475i) q^{62} +(2.94361 - 0.578947i) q^{63} +3.08342i q^{64} +(-12.6482 + 0.225122i) q^{65} +(5.89720 - 1.36835i) q^{66} +(-0.450145 + 1.67996i) q^{67} +(6.11242 - 3.52901i) q^{68} +(1.40421 - 4.61121i) q^{69} +(1.92997 + 1.92997i) q^{70} +(-3.53048 - 13.1759i) q^{71} +(-5.96788 + 5.21105i) q^{72} +(0.693304 - 0.693304i) q^{73} +(-5.50742 - 3.17971i) q^{74} +(-9.25009 + 8.64501i) q^{75} +(5.80227 + 1.55471i) q^{76} -4.49297 q^{77} +(1.33231 - 4.67190i) q^{78} +0.480977 q^{79} +(2.49160 + 0.667621i) q^{80} +(-8.91787 - 1.21308i) q^{81} +(-3.91434 - 2.25995i) q^{82} +(8.15333 - 8.15333i) q^{83} +(2.13187 - 1.13656i) q^{84} +(4.59498 + 17.1487i) q^{85} +(-0.327429 - 0.327429i) q^{86} +(0.300230 + 0.0914263i) q^{87} +(10.2759 - 5.93281i) q^{88} +(0.837175 - 3.12438i) q^{89} +(-3.60574 - 7.35150i) q^{90} +(-1.74692 + 3.15409i) q^{91} -3.88179i q^{92} +(-0.553835 + 16.3797i) q^{93} +(0.329508 + 0.570724i) q^{94} +(-7.55491 + 13.0855i) q^{95} +(-5.36337 + 8.60437i) q^{96} +(-2.19811 + 0.588981i) q^{97} +(0.751420 - 0.201342i) q^{98} +(12.7542 + 4.36007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 12 q^{6}+O(q^{10}) $ 112 * q - 12 * q^6	$ 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) $ 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.751420	−	0.201342i	−0.531334	−	0.142371i	−0.0168300	−	0.999858i	$-0.505357\pi$
$2$	−0.751420	−	0.201342i	−0.531334	−	0.142371i	−0.514504	+	0.857488i	$0.672024\pi$
$3$	−1.18266	−	1.26543i	−0.682808	−	0.730598i
$3$	−1.18266	−	1.26543i	−0.682808	−	0.730598i
$4$	−1.20796	−	0.697414i	−0.603979	−	0.348707i
$5$	2.48091	−	2.48091i	1.10950	−	1.10950i	0.116280	−	0.993217i	$-0.462903\pi$
$5$	2.48091	−	2.48091i	1.10950	−	1.10950i	0.993217	−	0.116280i	$-0.0370969\pi$
$6$	0.633888	+	1.18899i	0.258784	+	0.485404i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	1.86742	+	1.86742i	0.660233	+	0.660233i
$9$	−0.202642	+	2.99315i	−0.0675473	+	0.997716i
$10$	−2.36372	+	1.36469i	−0.747473	+	0.431554i
$11$	1.16287	−	4.33987i	0.350617	−	1.30852i	−0.535294	−	0.844666i	$-0.679799\pi$
$11$	1.16287	−	4.33987i	0.350617	−	1.30852i	0.885911	−	0.463855i	$-0.153534\pi$
$12$	0.546068	+	2.35339i	0.157636	+	0.679366i
$13$	−2.59448	−	2.50374i	−0.719578	−	0.694411i
$13$	−2.59448	−	2.50374i	−0.719578	−	0.694411i
$14$			0.777928i			0.207910i
$15$	−6.07349	−	0.205359i	−1.56817	−	0.0530233i
$16$	0.367602	+	0.636705i	0.0919005	+	0.159176i
$17$	−2.53006	+	4.38220i	−0.613631	+	1.06284i	0.376992	+	0.926216i	$0.376958\pi$
$17$	−2.53006	+	4.38220i	−0.613631	+	1.06284i	−0.990623	+	0.136623i	$0.956375\pi$
$18$	0.754917	−	2.20831i	0.177936	−	0.520504i
$19$	−4.15985	+	1.11463i	−0.954334	+	0.255713i	−0.702200	−	0.711979i	$-0.747799\pi$
$19$	−4.15985	+	1.11463i	−0.954334	+	0.255713i	−0.252134	+	0.967692i	$0.581132\pi$
$20$	−4.72705	+	1.26661i	−1.05700	+	0.283223i
$21$	−0.916220	+	1.46988i	−0.199936	+	0.320754i
$22$	−1.74760	+	3.02693i	−0.372590	+	0.645345i
$23$	1.39149	+	2.41014i	0.290147	+	0.502548i	0.973844	−	0.227217i	$-0.0729626\pi$
$23$	1.39149	+	2.41014i	0.290147	+	0.502548i	−0.683698	+	0.729765i	$0.739629\pi$
$24$	0.154577	−	4.57161i	0.0315528	−	0.933177i
$25$		−	7.30982i		−	1.46196i
$26$	1.44543	+	2.40374i	0.283473	+	0.471411i
$27$	4.02729	−	3.28344i	0.775051	−	0.631898i
$28$	−0.361008	+	1.34730i	−0.0682241	+	0.254616i
$29$	−0.156921	+	0.0905985i	−0.0291395	+	0.0168237i	−0.514499	−	0.857491i	$-0.672022\pi$
$29$	−0.156921	+	0.0905985i	−0.0291395	+	0.0168237i	0.485359	+	0.874315i	$0.338689\pi$
$30$	4.52240	+	1.37716i	0.825673	+	0.251434i
$31$	−6.69080	−	6.69080i	−1.20170	−	1.20170i	−0.973648	−	0.228055i	$-0.926763\pi$
$31$	−6.69080	−	6.69080i	−1.20170	−	1.20170i	−0.228055	−	0.973648i	$-0.573237\pi$
$32$	−1.51507	−	5.65433i	−0.267830	−	0.999555i
$33$	−6.86709	+	3.66105i	−1.19541	+	0.637308i
$34$	2.78347	−	2.78347i	0.477360	−	0.477360i
$35$	−3.03848	−	1.75427i	−0.513597	−	0.296525i
$36$	2.33225	−	3.47427i	0.388708	−	0.579045i
$37$	7.89628	+	2.11580i	1.29814	+	0.347836i	0.840747	−	0.541429i	$-0.182116\pi$
$37$	7.89628	+	2.11580i	1.29814	+	0.347836i	0.457394	+	0.889264i	$0.348783\pi$
$38$	3.35022			0.543477
$39$	−0.0999316	+	6.24420i	−0.0160019	+	0.999872i
$40$	9.26580			1.46505
$41$	5.61219	+	1.50378i	0.876477	+	0.234851i	0.668887	−	0.743364i	$-0.266771\pi$
$41$	5.61219	+	1.50378i	0.876477	+	0.234851i	0.207591	+	0.978216i	$0.433438\pi$
$42$	0.984415	−	0.920022i	0.151899	−	0.141962i
$43$	0.515494	+	0.297621i	0.0786122	+	0.0453867i	0.538791	−	0.842440i	$-0.318881\pi$
$43$	0.515494	+	0.297621i	0.0786122	+	0.0453867i	−0.460179	+	0.887826i	$0.652215\pi$
$44$	−4.43138	+	4.43138i	−0.668056	+	0.668056i
$45$	6.92299	+	7.92846i	1.03202	+	1.18191i
$46$	−0.560334	−	2.09119i	−0.0826167	−	0.308330i
$47$	−0.599020	−	0.599020i	−0.0873760	−	0.0873760i	0.662068	−	0.749444i	$-0.269679\pi$
$47$	−0.599020	−	0.599020i	−0.0873760	−	0.0873760i	−0.749444	+	0.662068i	$0.769679\pi$
$48$	0.370961	−	1.21818i	0.0535436	−	0.175829i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	−1.47178	+	5.49275i	−0.208141	+	0.776792i
$51$	8.53758	−	1.98102i	1.19550	−	0.277398i
$52$	1.38788	+	4.83383i	0.192464	+	0.670332i
$53$			5.43018i			0.745893i	0.927853	+	0.372947i	$0.121653\pi$
$53$			5.43018i			0.745893i	−0.927853	+	0.372947i	$0.878347\pi$
$54$	−3.68728	+	1.65638i	−0.501775	+	0.225405i
$55$	−7.88187	−	13.6518i	−1.06279	−	1.84081i
$56$	1.32047	−	2.28711i	0.176455	−	0.305628i
$57$	6.33016	+	3.94578i	0.838450	+	0.522632i
$58$	0.136155	−	0.0364827i	0.0178780	−	0.00479041i
$59$	7.75661	−	2.07838i	1.00982	−	0.270582i	0.284269	−	0.958745i	$-0.408249\pi$
$59$	7.75661	−	2.07838i	1.00982	−	0.270582i	0.725556	+	0.688163i	$0.241583\pi$
$60$	7.19330	+	4.48380i	0.928650	+	0.578857i
$61$	1.75531	−	3.04029i	0.224744	−	0.389269i	−0.731498	−	0.681843i	$-0.761179\pi$
$61$	1.75531	−	3.04029i	0.224744	−	0.389269i	0.956243	+	0.292574i	$0.0945119\pi$
$62$	3.68046	+	6.37475i	0.467419	+	0.809594i
$63$	2.94361	−	0.578947i	0.370860	−	0.0729404i
$64$			3.08342i			0.385428i
$65$	−12.6482	+	0.225122i	−1.56882	+	0.0279229i
$66$	5.89720	−	1.36835i	0.725895	−	0.168433i
$67$	−0.450145	+	1.67996i	−0.0549939	+	0.205240i	−0.987956	−	0.154734i	$-0.950548\pi$
$67$	−0.450145	+	1.67996i	−0.0549939	+	0.205240i	0.932962	+	0.359974i	$0.117215\pi$
$68$	6.11242	−	3.52901i	0.741240	−	0.427955i
$69$	1.40421	−	4.61121i	0.169047	−	0.555124i
$70$	1.92997	+	1.92997i	0.230675	+	0.230675i
$71$	−3.53048	−	13.1759i	−0.418991	−	1.56370i	−0.776705	−	0.629864i	$-0.783111\pi$
$71$	−3.53048	−	13.1759i	−0.418991	−	1.56370i	0.357714	−	0.933831i	$-0.383556\pi$
$72$	−5.96788	+	5.21105i	−0.703322	+	0.614128i
$73$	0.693304	−	0.693304i	0.0811451	−	0.0811451i	−0.665369	−	0.746514i	$-0.731726\pi$
$73$	0.693304	−	0.693304i	0.0811451	−	0.0811451i	0.746514	+	0.665369i	$0.231726\pi$
$74$	−5.50742	−	3.17971i	−0.640225	−	0.369634i
$75$	−9.25009	+	8.64501i	−1.06811	+	0.998240i
$76$	5.80227	+	1.55471i	0.665566	+	0.178338i
$77$	−4.49297			−0.512021
$78$	1.33231	−	4.67190i	0.150855	−	0.528988i
$79$	0.480977			0.0541142			0.0270571	−	0.999634i	$-0.491386\pi$
$79$	0.480977			0.0541142			0.0270571	+	0.999634i	$0.491386\pi$
$80$	2.49160	+	0.667621i	0.278569	+	0.0746423i
$81$	−8.91787	−	1.21308i	−0.990875	−	0.134786i
$82$	−3.91434	−	2.25995i	−0.432267	−	0.249569i
$83$	8.15333	−	8.15333i	0.894944	−	0.894944i	−0.100039	−	0.994984i	$-0.531897\pi$
$83$	8.15333	−	8.15333i	0.894944	−	0.894944i	0.994984	+	0.100039i	$0.0318968\pi$
$84$	2.13187	−	1.13656i	0.232606	−	0.124009i
$85$	4.59498	+	17.1487i	0.498396	+	1.86004i
$86$	−0.327429	−	0.327429i	−0.0353076	−	0.0353076i
$87$	0.300230	+	0.0914263i	0.0321881	+	0.00980193i
$88$	10.2759	−	5.93281i	1.09542	−	0.632439i
$89$	0.837175	−	3.12438i	0.0887403	−	0.331183i	−0.907256	−	0.420579i	$-0.861827\pi$
$89$	0.837175	−	3.12438i	0.0887403	−	0.331183i	0.995996	+	0.0893957i	$0.0284936\pi$
$90$	−3.60574	−	7.35150i	−0.380078	−	0.774916i
$91$	−1.74692	+	3.15409i	−0.183127	+	0.330638i
$92$		−	3.88179i		−	0.404705i
$93$	−0.553835	+	16.3797i	−0.0574300	+	1.69849i
$94$	0.329508	+	0.570724i	0.0339861	+	0.0588657i
$95$	−7.55491	+	13.0855i	−0.775118	+	1.34254i
$96$	−5.36337	+	8.60437i	−0.547396	+	0.878179i
$97$	−2.19811	+	0.588981i	−0.223184	+	0.0598020i	−0.368678	−	0.929557i	$-0.620190\pi$
$97$	−2.19811	+	0.588981i	−0.223184	+	0.0598020i	0.145494	+	0.989359i	$0.453523\pi$
$98$	0.751420	−	0.201342i	0.0759049	−	0.0203387i
$99$	12.7542	+	4.36007i	1.28185	+	0.438203i
$100$	−5.09797	+	8.82995i	−0.509797	+	0.882995i
$101$	−8.31306	−	14.3986i	−0.827181	−	1.43272i	−0.900241	−	0.435391i	$-0.856610\pi$
$101$	−8.31306	−	14.3986i	−0.827181	−	1.43272i	0.0730608	−	0.997327i	$-0.476723\pi$
$102$	−6.81418	−	0.230403i	−0.674704	−	0.0228133i
$103$		−	11.7781i		−	1.16053i	−0.814427	−	0.580266i	$-0.802949\pi$
$103$		−	11.7781i		−	1.16053i	0.814427	−	0.580266i	$-0.197051\pi$
$104$	−0.169453	−	9.52050i	−0.0166162	−	0.933562i
$105$	1.37357	+	5.91969i	0.134047	+	0.577703i
$106$	1.09333	−	4.08035i	0.106193	−	0.396319i
$107$	6.54031	−	3.77605i	0.632275	−	0.365044i	−0.149357	−	0.988783i	$-0.547721\pi$
$107$	6.54031	−	3.77605i	0.632275	−	0.365044i	0.781633	+	0.623739i	$0.214387\pi$
$108$	−7.15470	+	1.15757i	−0.688462	+	0.111387i
$109$	−3.51815	−	3.51815i	−0.336978	−	0.336978i	0.518251	−	0.855229i	$-0.326583\pi$
$109$	−3.51815	−	3.51815i	−0.336978	−	0.336978i	−0.855229	+	0.518251i	$0.826583\pi$
$110$	3.17391	+	11.8452i	0.302620	+	1.12939i
$111$	−6.66119	−	12.4945i	−0.632252	−	1.18592i
$112$	0.519868	−	0.519868i	0.0491229	−	0.0491229i
$113$	13.6298	+	7.86916i	1.28218	+	0.740268i	0.977247	−	0.212105i	$-0.0680320\pi$
$113$	13.6298	+	7.86916i	1.28218	+	0.740268i	0.304935	+	0.952373i	$0.401365\pi$
$114$	−3.96216	−	4.23947i	−0.371090	−	0.397063i
$115$	9.43150	+	2.52716i	0.879492	+	0.235659i
$116$	0.252739			0.0234662
$117$	8.01980	−	7.25829i	0.741431	−	0.671029i
$118$	−6.24694			−0.575078
$119$	4.88771	+	1.30966i	0.448056	+	0.120056i
$120$	−10.9583	−	11.7252i	−1.00035	−	1.07036i
$121$	−7.95596	−	4.59337i	−0.723269	−	0.417579i
$122$	−1.93111	+	1.93111i	−0.174835	+	0.174835i
$123$	−4.73437	−	8.88031i	−0.426883	−	0.800711i
$124$	3.41594	+	12.7485i	0.306760	+	1.14485i
$125$	−5.73045	−	5.73045i	−0.512547	−	0.512547i
$126$	−2.32845	−	0.157641i	−0.207435	−	0.0140438i
$127$	−18.0100	+	10.3981i	−1.59813	+	0.922681i	−0.606282	+	0.795250i	$0.707340\pi$
$127$	−18.0100	+	10.3981i	−1.59813	+	0.922681i	−0.991847	+	0.127431i	$0.959327\pi$
$128$	−2.40932	+	8.99172i	−0.212956	+	0.794763i
$129$	−0.233034	−	1.00431i	−0.0205175	−	0.0884243i
$130$	9.54944	+	2.37746i	0.837541	+	0.208517i
$131$			2.32681i			0.203294i	0.994821	+	0.101647i	$0.0324112\pi$
$131$			2.32681i			0.203294i	−0.994821	+	0.101647i	$0.967589\pi$
$132$	10.8484	+	0.366810i	0.944234	+	0.0319267i
$133$	2.15330	+	3.72962i	0.186714	+	0.323399i
$134$	0.676496	−	1.17172i	0.0584403	−	0.101222i
$135$	1.84541	−	18.1372i	0.158828	−	1.56101i
$136$	−12.9081	+	3.45872i	−1.10686	+	0.296582i
$137$	11.0253	−	2.95421i	0.941951	−	0.252395i	0.245008	−	0.969521i	$-0.421210\pi$
$137$	11.0253	−	2.95421i	0.941951	−	0.252395i	0.696943	+	0.717126i	$0.254543\pi$
$138$	−1.98358	+	3.18223i	−0.168854	+	0.270889i
$139$	2.62925	−	4.55400i	0.223010	−	0.386265i	−0.732710	−	0.680540i	$-0.761745\pi$
$139$	2.62925	−	4.55400i	0.223010	−	0.386265i	0.955721	+	0.294276i	$0.0950784\pi$
$140$	2.44690	+	4.23816i	0.206801	+	0.358190i
$141$	−0.0495842	+	1.46646i	−0.00417574	+	0.123498i
$142$			10.6115i			0.890497i
$143$	−13.8829	+	8.34819i	−1.16095	+	0.698111i
$144$	−1.98025	+	0.971264i	−0.165020	+	0.0809387i
$145$	−0.164541	+	0.614074i	−0.0136644	+	0.0509961i
$146$	−0.660555	+	0.381371i	−0.0546679	+	0.0315625i
$147$	1.65693	+	0.504568i	0.136661	+	0.0416161i
$148$	−8.06277	−	8.06277i	−0.662756	−	0.662756i
$149$	1.83391	+	6.84424i	0.150240	+	0.560702i	0.999466	+	0.0326734i	$0.0104021\pi$
$149$	1.83391	+	6.84424i	0.150240	+	0.560702i	−0.849226	+	0.528029i	$0.822931\pi$
$150$	8.69131	−	4.63360i	0.709643	−	0.378332i
$151$	12.7297	−	12.7297i	1.03593	−	1.03593i	0.0365972	−	0.999330i	$-0.488348\pi$
$151$	12.7297	−	12.7297i	1.03593	−	1.03593i	0.999330	−	0.0365972i	$-0.0116518\pi$
$152$	−9.84966	−	5.68670i	−0.798913	−	0.461253i
$153$	−12.6039	−	8.46088i	−1.01896	−	0.684021i
$154$	3.37611	+	0.904625i	0.272054	+	0.0728968i
$155$	−33.1985			−2.66657
$156$	4.47551	−	7.47303i	0.358327	−	0.598321i
$157$	7.20282			0.574848			0.287424	−	0.957803i	$-0.407201\pi$
$157$	7.20282			0.574848			0.287424	+	0.957803i	$0.407201\pi$
$158$	−0.361416	−	0.0968412i	−0.0287527	−	0.00770427i
$159$	6.87154	−	6.42205i	0.544948	−	0.509302i
$160$	−17.7866	−	10.2691i	−1.40616	−	0.811846i
$161$	1.96787	−	1.96787i	0.155090	−	0.155090i
$162$	6.45683	+	2.70708i	0.507296	+	0.212688i
$163$	−1.93783	−	7.23206i	−0.151782	−	0.566459i	−0.999359	−	0.0357869i	$-0.988606\pi$
$163$	−1.93783	−	7.23206i	−0.151782	−	0.566459i	0.847577	−	0.530672i	$-0.178060\pi$
$164$	−5.73053	−	5.73053i	−0.447479	−	0.447479i
$165$	−7.95388	+	26.1194i	−0.619209	+	2.03339i
$166$	−7.76819	+	4.48497i	−0.602929	+	0.348101i
$167$	−4.84548	+	18.0836i	−0.374955	+	1.39935i	0.478456	+	0.878112i	$0.341197\pi$
$167$	−4.84548	+	18.0836i	−0.374955	+	1.39935i	−0.853411	+	0.521239i	$0.825470\pi$
$168$	−4.45585	+	1.03391i	−0.343776	+	0.0797680i
$169$	0.462621	+	12.9918i	0.0355862	+	0.999367i
$170$		−	13.8110i		−	1.05926i
$171$	−2.49329	−	12.6769i	−0.190666	−	0.969427i
$172$	−0.415130	−	0.719026i	−0.0316534	−	0.0548252i
$173$	−0.999000	+	1.73032i	−0.0759526	+	0.131554i	−0.901500	−	0.432779i	$-0.857533\pi$
$173$	−0.999000	+	1.73032i	−0.0759526	+	0.131554i	0.825548	+	0.564333i	$0.190866\pi$
$174$	−0.207191	−	0.129149i	−0.0157071	−	0.00979074i
$175$	−7.06074	+	1.89192i	−0.533742	+	0.143016i
$176$	3.19069	−	0.854943i	0.240507	−	0.0644438i
$177$	−11.8035	−	7.35747i	−0.887203	−	0.553021i
$178$	−1.25814	+	2.17916i	−0.0943016	+	0.163335i
$179$	1.95622	+	3.38828i	0.146215	+	0.253252i	0.929826	−	0.368001i	$-0.119958\pi$
$179$	1.95622	+	3.38828i	0.146215	+	0.253252i	−0.783611	+	0.621252i	$0.786624\pi$
$180$	−2.83325	−	14.4054i	−0.211178	−	1.07372i
$181$			0.828935i			0.0616142i	0.999525	+	0.0308071i	$0.00980776\pi$
$181$			0.828935i			0.0616142i	−0.999525	+	0.0308071i	$0.990192\pi$
$182$	1.94772	−	2.01832i	0.144375	−	0.149607i
$183$	−5.92321	+	1.37439i	−0.437856	+	0.101598i
$184$	−1.90224	+	7.09924i	−0.140235	+	0.523363i
$185$	24.8391	−	14.3408i	1.82620	−	1.05436i
$186$	3.71409	−	12.1965i	0.272330	−	0.894292i
$187$	16.0761	+	16.0761i	1.17560	+	1.17560i
$188$	0.305825	+	1.14136i	0.0223046	+	0.0832419i
$189$	−4.21390	−	3.04024i	−0.306516	−	0.221145i
$190$	8.31158	−	8.31158i	0.602985	−	0.602985i
$191$	8.02535	+	4.63344i	0.580694	+	0.335264i	0.761409	−	0.648272i	$-0.224508\pi$
$191$	8.02535	+	4.63344i	0.580694	+	0.335264i	−0.180715	+	0.983535i	$0.557841\pi$
$192$	3.90187	−	3.64663i	0.281593	−	0.263173i
$193$	7.97663	+	2.13733i	0.574170	+	0.153848i	0.534209	−	0.845353i	$-0.320610\pi$
$193$	7.97663	+	2.13733i	0.574170	+	0.153848i	0.0399618	+	0.999201i	$0.487276\pi$
$194$	1.77029			0.127099
$195$	15.2434	+	15.7392i	1.09160	+	1.12711i
$196$	1.39483			0.0996306
$197$	9.34250	+	2.50331i	0.665625	+	0.178354i	0.575783	−	0.817602i	$-0.304697\pi$
$197$	9.34250	+	2.50331i	0.665625	+	0.178354i	0.0898420	+	0.995956i	$0.471364\pi$
$198$	−8.70593	−	5.84421i	−0.618703	−	0.415330i
$199$	−2.08418	−	1.20330i	−0.147744	−	0.0852998i	0.424306	−	0.905519i	$-0.360518\pi$
$199$	−2.08418	−	1.20330i	−0.147744	−	0.0852998i	−0.572049	+	0.820219i	$0.693851\pi$
$200$	13.6505	−	13.6505i	0.965236	−	0.965236i
$201$	2.65825	−	1.41719i	0.187498	−	0.0999611i
$202$	3.34754	+	12.4932i	0.235532	+	0.879019i
$203$	0.128126	+	0.128126i	0.00899266	+	0.00899266i
$204$	−11.6946	−	3.56125i	−0.818787	−	0.249337i
$205$	17.6541	−	10.1926i	1.23301	−	0.711882i
$206$	−2.37144	+	8.85032i	−0.165226	+	0.616631i
$207$	−7.49587	+	3.67655i	−0.520999	+	0.255538i
$208$	0.640407	−	2.57230i	0.0444042	−	0.178357i
$209$			19.3494i			1.33842i
$210$	0.159754	−	4.72474i	0.0110241	−	0.326038i
$211$	−0.518546	−	0.898148i	−0.0356982	−	0.0618311i	0.847624	−	0.530597i	$-0.178032\pi$
$211$	−0.518546	−	0.898148i	−0.0356982	−	0.0618311i	−0.883323	+	0.468766i	$0.844699\pi$
$212$	3.78709	−	6.55943i	0.260098	−	0.450503i
$213$	−12.4979	+	20.0502i	−0.856343	+	1.37382i
$214$	−5.67480	+	1.52056i	−0.387921	+	0.103943i
$215$	2.01726	−	0.540524i	0.137576	−	0.0368635i
$216$	13.6522	+	1.38907i	0.928914	+	0.0945144i
$217$	−4.73111	+	8.19453i	−0.321169	+	0.556281i
$218$	1.93526	+	3.35196i	0.131072	+	0.227023i
$219$	−1.69727	−	0.0573886i	−0.114691	−	0.00387796i
$220$			21.9877i			1.48241i
$221$	17.5361	−	5.03491i	1.17960	−	0.338684i
$222$	2.48968	+	10.7298i	0.167097	+	0.720136i
$223$	−6.10194	+	22.7727i	−0.408616	+	1.52498i	0.388672	+	0.921376i	$0.372934\pi$
$223$	−6.10194	+	22.7727i	−0.408616	+	1.52498i	−0.797288	+	0.603599i	$0.793733\pi$
$224$	−5.06954	+	2.92690i	−0.338723	+	0.195562i
$225$	21.8794	+	1.48128i	1.45862	+	0.0987518i
$226$	−8.65730	−	8.65730i	−0.575875	−	0.575875i
$227$	6.46981	+	24.1457i	0.429416	+	1.60260i	0.754086	+	0.656776i	$0.228080\pi$
$227$	6.46981	+	24.1457i	0.429416	+	1.60260i	−0.324670	+	0.945828i	$0.605253\pi$
$228$	−4.89472	−	9.18108i	−0.324160	−	0.608032i
$229$	16.6026	−	16.6026i	1.09713	−	1.09713i	0.102384	−	0.994745i	$-0.467353\pi$
$229$	16.6026	−	16.6026i	1.09713	−	1.09713i	0.994745	−	0.102384i	$-0.0326471\pi$
$230$	−6.57820	−	3.79792i	−0.433753	−	0.250428i
$231$	5.31364	+	5.68555i	0.349612	+	0.374082i
$232$	−0.462223	−	0.123852i	−0.0303465	−	0.00813131i
$233$	2.65471			0.173916			0.0869579	−	0.996212i	$-0.472285\pi$
$233$	2.65471			0.173916			0.0869579	+	0.996212i	$0.472285\pi$
$234$	−7.48764	+	3.83930i	−0.489483	+	0.250983i
$235$	−2.97223			−0.193887
$236$	−10.8191	−	2.89898i	−0.704266	−	0.188708i
$237$	−0.568832	−	0.608645i	−0.0369496	−	0.0395357i
$238$	−3.40904	−	1.96821i	−0.220975	−	0.127580i
$239$	−9.53436	+	9.53436i	−0.616726	+	0.616726i	−0.944690	−	0.327964i	$-0.893638\pi$
$239$	−9.53436	+	9.53436i	−0.616726	+	0.616726i	0.327964	+	0.944690i	$0.393638\pi$
$240$	−2.10187	−	3.94251i	−0.135675	−	0.254488i
$241$	−3.48866	−	13.0198i	−0.224724	−	0.838682i	−0.982515	−	0.186184i	$-0.940388\pi$
$241$	−3.48866	−	13.0198i	−0.224724	−	0.838682i	0.757791	−	0.652498i	$-0.226279\pi$
$242$	5.05343	+	5.05343i	0.324847	+	0.324847i
$243$	9.01172	+	12.7196i	0.578102	+	0.815964i
$244$	−4.24068	+	2.44836i	−0.271482	+	0.156740i
$245$	−0.908076	+	3.38898i	−0.0580148	+	0.216514i
$246$	1.76951	+	7.62608i	0.112820	+	0.486221i
$247$	13.5834	+	7.52328i	0.864288	+	0.478695i
$248$		−	24.9891i		−	1.58681i
$249$	−19.9601	−	0.674896i	−1.26492	−	0.0427698i
$250$	3.15219	+	5.45976i	0.199362	+	0.345306i
$251$	10.2809	−	17.8070i	0.648922	−	1.12397i	−0.334459	−	0.942410i	$-0.608553\pi$
$251$	10.2809	−	17.8070i	0.648922	−	1.12397i	0.983381	−	0.181555i	$-0.0581132\pi$
$252$	−3.95952	−	1.35357i	−0.249426	−	0.0852669i
$253$	12.0778	−	3.23624i	0.759325	−	0.203461i
$254$	15.6267	−	4.18715i	0.980504	−	0.262725i
$255$	16.2662	−	26.0957i	1.01863	−	1.63418i
$256$	6.70425	−	11.6121i	0.419016	−	0.725757i
$257$	−14.3294	−	24.8193i	−0.893844	−	1.54818i	−0.835229	−	0.549902i	$-0.814665\pi$
$257$	−14.3294	−	24.8193i	−0.893844	−	1.54818i	−0.0586143	−	0.998281i	$-0.518668\pi$
$258$	−0.0271031	+	0.801576i	−0.00168737	+	0.0499040i
$259$		−	8.17483i		−	0.507959i
$260$	15.4355	+	8.54910i	0.957268	+	0.530193i
$261$	−0.239376	−	0.488048i	−0.0148170	−	0.0302094i
$262$	0.468485	−	1.74841i	0.0289431	−	0.108017i
$263$	−7.02527	+	4.05604i	−0.433197	+	0.250106i	−0.700708	−	0.713448i	$-0.747132\pi$
$263$	−7.02527	+	4.05604i	−0.433197	+	0.250106i	0.267511	+	0.963555i	$0.413799\pi$
$264$	−19.6605	−	5.98701i	−1.21002	−	0.368475i
$265$	13.4718	+	13.4718i	0.827566	+	0.827566i
$266$	−0.867100	−	3.23606i	−0.0531653	−	0.198416i
$267$	−4.94378	+	2.63568i	−0.302555	+	0.161301i
$268$	1.71539	−	1.71539i	0.104784	−	0.104784i
$269$	−11.7464	−	6.78177i	−0.716189	−	0.413492i	0.0971595	−	0.995269i	$-0.469024\pi$
$269$	−11.7464	−	6.78177i	−0.716189	−	0.413492i	−0.813348	+	0.581777i	$0.802358\pi$
$270$	−5.03848	+	13.2571i	−0.306632	+	0.806803i
$271$	7.09262	+	1.90046i	0.430846	+	0.115445i	0.467723	−	0.883875i	$-0.345074\pi$
$271$	7.09262	+	1.90046i	0.430846	+	0.115445i	−0.0368772	+	0.999320i	$0.511741\pi$
$272$	−3.72023			−0.225572
$273$	6.05730	−	1.51959i	0.366604	−	0.0919698i
$274$	−8.87941			−0.536425
$275$	−31.7237	−	8.50033i	−1.91301	−	0.512589i
$276$	−4.91215	+	4.59083i	−0.295676	+	0.276335i
$277$	9.42219	+	5.43990i	0.566124	+	0.326852i	0.755600	−	0.655033i	$-0.227345\pi$
$277$	9.42219	+	5.43990i	0.566124	+	0.326852i	−0.189475	+	0.981885i	$0.560679\pi$
$278$	−2.89259	+	2.89259i	−0.173486	+	0.173486i
$279$	21.3824	−	18.6707i	1.28013	−	1.11779i
$280$	−2.39817	−	8.95007i	−0.143318	−	0.534869i
$281$	10.2652	+	10.2652i	0.612373	+	0.612373i	0.943564	−	0.331191i	$-0.107450\pi$
$281$	10.2652	+	10.2652i	0.612373	+	0.612373i	−0.331191	+	0.943564i	$0.607450\pi$
$282$	0.332518	−	1.09194i	0.0198012	−	0.0650241i
$283$	−3.03747	+	1.75369i	−0.180559	+	0.104246i	−0.587555	−	0.809184i	$-0.699910\pi$
$283$	−3.03747	+	1.75369i	−0.180559	+	0.104246i	0.406996	+	0.913430i	$0.366576\pi$
$284$	−4.92441	+	18.3782i	−0.292210	+	1.09054i
$285$	25.4937	−	5.91542i	1.51012	−	0.350399i
$286$	12.1128	−	3.47778i	0.716242	−	0.205645i
$287$		−	5.81017i		−	0.342963i
$288$	17.2313	−	3.38904i	1.01536	−	0.199701i
$289$	−4.30246	−	7.45207i	−0.253086	−	0.438357i
$290$	0.247278	−	0.428299i	0.0145207	−	0.0251506i
$291$	3.34492	+	2.08499i	0.196083	+	0.122225i
$292$	−1.32100	+	0.353961i	−0.0773058	+	0.0207140i
$293$	−16.8739	+	4.52134i	−0.985782	+	0.264139i	−0.715478	−	0.698635i	$-0.753791\pi$
$293$	−16.8739	+	4.52134i	−0.985782	+	0.264139i	−0.270304	+	0.962775i	$0.587124\pi$
$294$	−1.14346	−	0.712753i	−0.0666879	−	0.0415686i
$295$	14.0872	−	24.3997i	0.820188	−	1.42061i
$296$	10.7946	+	18.6968i	0.627422	+	1.08673i
$297$	−9.56652	−	21.2961i	−0.555106	−	1.23573i
$298$		−	5.51215i		−	0.319310i
$299$	2.42415	−	9.73698i	0.140192	−	0.563104i
$300$	17.2029	−	3.99166i	0.993208	−	0.230459i
$301$	0.154060	−	0.574959i	0.00887986	−	0.0331401i
$302$	−12.1284	+	7.00232i	−0.697909	+	0.402938i
$303$	−8.38902	+	27.5483i	−0.481936	+	1.58261i
$304$	−2.23886	−	2.23886i	−0.128407	−	0.128407i
$305$	−3.18791	−	11.8974i	−0.182539	−	0.681245i
$306$	7.76728	+	8.89537i	0.444026	+	0.508515i
$307$	−21.2970	+	21.2970i	−1.21548	+	1.21548i	−0.246283	+	0.969198i	$0.579209\pi$
$307$	−21.2970	+	21.2970i	−1.21548	+	1.21548i	−0.969198	+	0.246283i	$0.920791\pi$
$308$	5.42731	+	3.13346i	0.309250	+	0.178545i
$309$	−14.9044	+	13.9295i	−0.847883	+	0.792420i
$310$	24.9461	+	6.68428i	1.41684	+	0.379641i
$311$	31.6210			1.79306			0.896532	−	0.442978i	$-0.146078\pi$
$311$	31.6210			1.79306			0.896532	+	0.442978i	$0.146078\pi$
$312$	−11.8472	+	11.4739i	−0.670713	+	0.649583i
$313$	−0.406180			−0.0229586			−0.0114793	−	0.999934i	$-0.503654\pi$
$313$	−0.406180			−0.0229586			−0.0114793	+	0.999934i	$0.503654\pi$
$314$	−5.41235	−	1.45023i	−0.305436	−	0.0818414i
$315$	5.86651	−	8.73913i	0.330540	−	0.492394i
$316$	−0.581000	−	0.335441i	−0.0326838	−	0.0188700i
$317$	−19.4304	+	19.4304i	−1.09132	+	1.09132i	−0.0959323	+	0.995388i	$0.530583\pi$
$317$	−19.4304	+	19.4304i	−1.09132	+	1.09132i	−0.995388	+	0.0959323i	$0.969417\pi$
$318$	−6.45644	+	3.44213i	−0.362059	+	0.193025i
$319$	0.210708	+	0.786372i	0.0117974	+	0.0440284i
$320$	7.64969	+	7.64969i	0.427631	+	0.427631i
$321$	−12.5133	−	3.81055i	−0.698423	−	0.212684i
$322$	−1.87491	+	1.08248i	−0.104485	+	0.0603243i
$323$	5.64016	−	21.0494i	0.313827	−	1.17122i
$324$	9.92639	+	7.68479i	0.551466	+	0.426933i
$325$	−18.3019	+	18.9652i	−1.01520	+	1.05200i
$326$			5.82449i			0.322588i
$327$	−0.291217	+	8.61275i	−0.0161043	+	0.476286i
$328$	7.67213	+	13.2885i	0.423622	+	0.733736i
$329$	−0.423571	+	0.733647i	−0.0233522	+	0.0404472i
$330$	11.2356	−	18.0252i	0.618502	−	0.992253i
$331$	5.34167	−	1.43130i	0.293605	−	0.0786712i	−0.109010	−	0.994041i	$-0.534768\pi$
$331$	5.34167	−	1.43130i	0.293605	−	0.0786712i	0.402615	+	0.915369i	$0.368101\pi$
$332$	−15.5351	+	4.16262i	−0.852601	+	0.228454i
$333$	−7.93302	+	23.2060i	−0.434727	+	1.27168i
$334$	7.28199	−	12.6128i	0.398453	−	0.690141i
$335$	3.05107	+	5.28460i	0.166698	+	0.288729i
$336$	−1.27268	−	0.0430323i	−0.0694306	−	0.00234761i
$337$			1.45460i			0.0792370i	0.999215	+	0.0396185i	$0.0126143\pi$
$337$			1.45460i			0.0792370i	−0.999215	+	0.0396185i	$0.987386\pi$
$338$	2.26817	−	9.85542i	0.123372	−	0.536064i
$339$	−6.16147	−	26.5541i	−0.334645	−	1.44222i
$340$	6.40921	−	23.9195i	0.347588	−	1.29722i
$341$	−36.8177	+	21.2567i	−1.99379	+	1.15112i
$342$	−0.678894	+	10.0277i	−0.0367104	+	0.542235i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	0.406861	+	1.51843i	0.0219365	+	0.0818681i
$345$	−7.95628	−	14.9237i	−0.428352	−	0.803465i
$346$	1.09906	−	1.09906i	0.0590856	−	0.0590856i
$347$	−3.72070	−	2.14814i	−0.199737	−	0.115318i	0.396796	−	0.917907i	$-0.370122\pi$
$347$	−3.72070	−	2.14814i	−0.199737	−	0.115318i	−0.596533	+	0.802589i	$0.703456\pi$
$348$	−0.298903	−	0.319824i	−0.0160229	−	0.0171444i
$349$	16.3054	+	4.36902i	0.872809	+	0.233868i	0.667302	−	0.744787i	$-0.267449\pi$
$349$	16.3054	+	4.36902i	0.872809	+	0.233868i	0.205507	+	0.978656i	$0.434116\pi$
$350$	5.68651			0.303957
$351$	−18.6696	−	1.56445i	−0.996507	−	0.0835040i
$352$	−26.3009			−1.40184
$353$	19.3490	+	5.18454i	1.02984	+	0.275945i	0.733898	−	0.679260i	$-0.237699\pi$
$353$	19.3490	+	5.18454i	1.02984	+	0.275945i	0.295945	+	0.955205i	$0.404366\pi$
$354$	7.38799	+	7.90509i	0.392667	+	0.420151i
$355$	−41.4471	−	23.9295i	−2.19978	−	1.27005i
$356$	−3.19026	+	3.19026i	−0.169083	+	0.169083i
$357$	−4.12320	−	7.73395i	−0.218223	−	0.409324i
$358$	−0.787741	−	2.93989i	−0.0416334	−	0.155378i
$359$	7.53985	+	7.53985i	0.397938	+	0.397938i	0.877505	−	0.479567i	$-0.159206\pi$
$359$	7.53985	+	7.53985i	0.397938	+	0.397938i	−0.479567	+	0.877505i	$0.659206\pi$
$360$	−1.87764	+	27.7339i	−0.0989603	+	1.46171i
$361$	−0.392554	+	0.226641i	−0.0206607	+	0.0119285i
$362$	0.166900	−	0.622878i	0.00877206	−	0.0327378i
$363$	3.59656	+	15.5001i	0.188771	+	0.813545i
$364$	4.30991	−	2.59167i	0.225901	−	0.135841i
$365$		−	3.44005i		−	0.180060i
$366$	4.72754	+	0.159849i	0.247113	+	0.00835544i
$367$	−7.46522	−	12.9301i	−0.389681	−	0.674948i	0.602725	−	0.797949i	$-0.294082\pi$
$367$	−7.46522	−	12.9301i	−0.389681	−	0.674948i	−0.992407	+	0.123001i	$0.960748\pi$
$368$	−1.02303	+	1.77194i	−0.0533292	+	0.0923689i
$369$	−5.63831	+	16.4934i	−0.293519	+	0.858612i
$370$	−21.5520	+	5.77484i	−1.12043	+	0.300220i
$371$	5.24516	−	1.40544i	0.272315	−	0.0729666i
$372$	12.0924	−	19.3997i	0.626964	−	1.00583i
$373$	5.21339	−	9.02985i	0.269939	−	0.467548i	−0.698907	−	0.715213i	$-0.746330\pi$
$373$	5.21339	−	9.02985i	0.269939	−	0.467548i	0.968846	+	0.247665i	$0.0796631\pi$
$374$	−8.84309	−	15.3167i	−0.457265	−	0.792007i
$375$	−0.474341	+	14.0287i	−0.0244949	+	0.724437i
$376$		−	2.23724i		−	0.115377i
$377$	0.633963	+	0.157833i	0.0326508	+	0.00812884i
$378$	2.55428	+	3.13294i	0.131378	+	0.161141i
$379$	−4.53057	+	16.9083i	−0.232720	+	0.868522i	0.746444	+	0.665448i	$0.231760\pi$
$379$	−4.53057	+	16.9083i	−0.232720	+	0.868522i	−0.979164	+	0.203073i	$0.934907\pi$
$380$	18.2520	−	10.5378i	0.936309	−	0.540578i
$381$	34.4577	+	10.4931i	1.76532	+	0.537577i
$382$	−5.09750	−	5.09750i	−0.260811	−	0.260811i
$383$	−5.82855	−	21.7524i	−0.297825	−	1.11150i	−0.938948	−	0.344059i	$-0.888198\pi$
$383$	−5.82855	−	21.7524i	−0.297825	−	1.11150i	0.641123	−	0.767438i	$-0.278469\pi$
$384$	14.2278	−	7.58529i	0.726061	−	0.387085i
$385$	−11.1466	+	11.1466i	−0.568085	+	0.568085i
$386$	−5.56347	−	3.21207i	−0.283173	−	0.163490i
$387$	−0.995284	+	1.48264i	−0.0505931	+	0.0753669i
$388$	3.06598	+	0.821528i	0.155652	+	0.0417067i
$389$	3.03623			0.153943			0.0769716	−	0.997033i	$-0.475475\pi$
$389$	3.03623			0.153943			0.0769716	+	0.997033i	$0.475475\pi$
$390$	−8.28521	−	14.8959i	−0.419538	−	0.754283i
$391$	−14.0823			−0.712171
$392$	−2.55094	−	0.683523i	−0.128842	−	0.0345231i
$393$	2.94442	−	2.75182i	0.148526	−	0.138811i
$394$	−6.51612	−	3.76208i	−0.328277	−	0.189531i
$395$	1.19326	−	1.19326i	0.0600395	−	0.0600395i
$396$	−12.3658	−	14.1618i	−0.621405	−	0.711655i
$397$	−2.69287	−	10.0499i	−0.135151	−	0.504392i	−0.999997	−	0.00235427i	$-0.999251\pi$
$397$	−2.69287	−	10.0499i	−0.135151	−	0.504392i	0.864846	−	0.502037i	$-0.167416\pi$
$398$	1.32382	+	1.32382i	0.0663571	+	0.0663571i
$399$	2.17297	−	7.13571i	0.108785	−	0.357232i
$400$	4.65420	−	2.68710i	0.232710	−	0.134355i
$401$	6.76497	−	25.2472i	0.337827	−	1.26079i	−0.562946	−	0.826494i	$-0.690332\pi$
$401$	6.76497	−	25.2472i	0.337827	−	1.26079i	0.900772	−	0.434292i	$-0.143001\pi$
$402$	−2.28280	+	0.529689i	−0.113856	+	0.0264185i
$403$	0.607135	+	34.1111i	0.0302436	+	1.69920i
$404$			23.1906i			1.15378i
$405$	−25.1340	+	19.1149i	−1.24892	+	0.949827i
$406$	−0.0704791	−	0.122073i	−0.00349782	−	0.00605840i
$407$	18.3646	−	31.8084i	0.910300	−	1.57669i
$408$	19.6426	+	12.2439i	0.972456	+	0.606162i
$409$	−21.1087	+	5.65606i	−1.04376	+	0.279674i	−0.739670	−	0.672969i	$-0.765019\pi$
$409$	−21.1087	+	5.65606i	−1.04376	+	0.279674i	−0.304089	+	0.952644i	$0.598352\pi$
$410$	−15.3178	+	4.10440i	−0.756494	+	0.202702i
$411$	−16.7775	−	10.4579i	−0.827571	−	0.515850i
$412$	−8.21423	+	14.2275i	−0.404686	+	0.700937i
$413$	−4.01512	−	6.95439i	−0.197571	−	0.342203i
$414$	6.37280	−	1.25340i	0.313206	−	0.0616011i
$415$		−	40.4553i		−	1.98587i
$416$	−10.2261	+	18.4634i	−0.501377	+	0.905242i
$417$	−8.87228	+	2.05868i	−0.434477	+	0.100814i
$418$	3.89585	−	14.5395i	0.190552	−	0.711151i
$419$	3.28067	−	1.89410i	0.160271	−	0.0925327i	−0.417719	−	0.908576i	$-0.637170\pi$
$419$	3.28067	−	1.89410i	0.160271	−	0.0925327i	0.577990	+	0.816044i	$0.303837\pi$
$420$	2.46926	−	8.10868i	0.120488	−	0.395663i
$421$	−26.6573	−	26.6573i	−1.29920	−	1.29920i	−0.928921	−	0.370278i	$-0.879262\pi$
$421$	−26.6573	−	26.6573i	−1.29920	−	1.29920i	−0.370278	−	0.928921i	$-0.620738\pi$
$422$	0.208811	+	0.779292i	0.0101647	+	0.0379354i
$423$	1.91434	−	1.67157i	0.0930785	−	0.0812745i
$424$	−10.1404	+	10.1404i	−0.492463	+	0.492463i
$425$	32.0331	+	18.4943i	1.55383	+	0.897106i
$426$	13.4281	−	12.5498i	0.650596	−	0.608038i
$427$	−3.39100	−	0.908616i	−0.164102	−	0.0439710i
$428$	−10.5339			−0.509174
$429$	26.9828	+	7.69485i	1.30274	+	0.371511i
$430$	−1.62464			−0.0783473
$431$	1.34467	+	0.360304i	0.0647706	+	0.0173552i	0.291059	−	0.956705i	$-0.405992\pi$
$431$	1.34467	+	0.360304i	0.0647706	+	0.0173552i	−0.226288	+	0.974060i	$0.572659\pi$
$432$	3.57102	+	1.35720i	0.171811	+	0.0652981i
$433$	14.0773	+	8.12751i	0.676510	+	0.390583i	0.798539	−	0.601943i	$-0.205607\pi$
$433$	14.0773	+	8.12751i	0.676510	+	0.390583i	−0.122029	+	0.992527i	$0.538940\pi$
$434$	5.20496	−	5.20496i	0.249846	−	0.249846i
$435$	0.971665	−	0.518024i	0.0465878	−	0.0248374i
$436$	1.79617	+	6.70338i	0.0860207	+	0.321034i
$437$	−8.47481	−	8.47481i	−0.405405	−	0.405405i
$438$	1.26381	+	0.384856i	0.0603872	+	0.0183891i
$439$	−21.0565	+	12.1570i	−1.00497	+	0.580222i	−0.909716	−	0.415231i	$-0.863701\pi$
$439$	−21.0565	+	12.1570i	−1.00497	+	0.580222i	−0.0952576	+	0.995453i	$0.530367\pi$
$440$	10.7749	−	40.2124i	0.513672	−	1.91705i
$441$	−1.32108	−	2.69346i	−0.0629086	−	0.128260i
$442$	−14.1907	+	0.252577i	−0.674983	+	0.0120138i
$443$			19.7974i			0.940603i	0.882506	+	0.470302i	$0.155855\pi$
$443$			19.7974i			0.940603i	−0.882506	+	0.470302i	$0.844145\pi$
$444$	−0.667400	+	19.7384i	−0.0316734	+	0.936743i
$445$	−5.67434	−	9.82825i	−0.268990	−	0.465904i
$446$	9.17024	−	15.8833i	0.434223	−	0.752097i
$447$	6.49205	−	10.4151i	0.307063	−	0.492617i
$448$	2.97836	−	0.798048i	0.140714	−	0.0377042i
$449$	−22.2109	+	5.95139i	−1.04820	+	0.280863i	−0.741506	−	0.670946i	$-0.765888\pi$
$449$	−22.2109	+	5.95139i	−1.04820	+	0.280863i	−0.306690	+	0.951809i	$0.599221\pi$
$450$	−16.1424	−	5.51831i	−0.760958	−	0.260136i
$451$	13.0524	−	22.6075i	0.614616	−	1.06455i
$452$	−10.9761	−	19.0112i	−0.516273	−	0.894212i
$453$	−31.1634	−	1.05371i	−1.46419	−	0.0495075i
$454$		−	19.4462i		−	0.912655i
$455$	3.49105	+	12.1590i	0.163663	+	0.570021i
$456$	4.45263	+	19.1895i	0.208514	+	0.898631i
$457$	2.81689	−	10.5128i	0.131769	−	0.491767i	−0.868222	−	0.496177i	$-0.834737\pi$
$457$	2.81689	−	10.5128i	0.131769	−	0.491767i	0.999990	+	0.00440926i	$0.00140351\pi$
$458$	−15.8183	+	9.13271i	−0.739141	+	0.426744i
$459$	4.19940	+	25.9557i	0.196011	+	1.21151i
$460$	−9.63037	−	9.63037i	−0.449018	−	0.449018i
$461$	3.11425	+	11.6225i	0.145045	+	0.541316i	0.999753	+	0.0222070i	$0.00706929\pi$
$461$	3.11425	+	11.6225i	0.145045	+	0.541316i	−0.854708	+	0.519109i	$0.826264\pi$
$462$	−2.84804	−	5.34210i	−0.132503	−	0.248537i
$463$	28.0743	−	28.0743i	1.30472	−	1.30472i	0.379551	−	0.925171i	$-0.376079\pi$
$463$	28.0743	−	28.0743i	1.30472	−	1.30472i	0.925171	−	0.379551i	$-0.123921\pi$
$464$	−0.115369	−	0.0666084i	−0.00535588	−	0.00309222i
$465$	39.2625	+	42.0105i	1.82076	+	1.94819i
$466$	−1.99480	−	0.534506i	−0.0924075	−	0.0247605i
$467$	27.3292			1.26464			0.632321	−	0.774706i	$-0.282102\pi$
$467$	27.3292			1.26464			0.632321	+	0.774706i	$0.282102\pi$
$468$	−14.7496	+	3.17458i	−0.681801	+	0.146745i
$469$	1.73923			0.0803100
$470$	2.23339	+	0.598436i	0.103019	+	0.0276038i
$471$	−8.51847	−	9.11469i	−0.392510	−	0.419983i
$472$	18.3661	+	10.6037i	0.845366	+	0.488073i
$473$	1.89109	−	1.89109i	0.0869523	−	0.0869523i
$474$	0.304886	+	0.571878i	0.0140039	+	0.0262672i
$475$	8.14773	+	30.4077i	0.373843	+	1.39520i
$476$	−4.99077	−	4.99077i	−0.228752	−	0.228752i
$477$	−16.2533	−	1.10038i	−0.744190	−	0.0503831i
$478$	9.08398	−	5.24464i	0.415492	−	0.239884i
$479$	−3.92086	+	14.6328i	−0.179149	+	0.668591i	0.816659	+	0.577120i	$0.195824\pi$
$479$	−3.92086	+	14.6328i	−0.179149	+	0.668591i	−0.995808	+	0.0914712i	$0.970843\pi$
$480$	8.04062	+	34.6527i	0.367003	+	1.58167i
$481$	−15.1893	−	25.2596i	−0.692573	−	1.15174i
$482$			10.4858i			0.477615i
$483$	−4.81752	−	0.162891i	−0.219205	−	0.00741182i
$484$	6.40697	+	11.0972i	0.291226	+	0.504418i
$485$	−3.99210	+	6.91451i	−0.181272	+	0.313972i
$486$	−4.21059	−	11.3722i	−0.190996	−	0.515855i
$487$	3.68481	−	0.987342i	0.166975	−	0.0447407i	−0.174363	−	0.984681i	$-0.555787\pi$
$487$	3.68481	−	0.987342i	0.166975	−	0.0447407i	0.341338	+	0.939941i	$0.389120\pi$
$488$	8.95539	−	2.39959i	0.405392	−	0.108624i
$489$	−6.85991	+	11.0052i	−0.310216	+	0.497674i
$490$	1.36469	−	2.36372i	0.0616506	−	0.106782i
$491$	9.73797	+	16.8667i	0.439468	+	0.761182i	0.997648	−	0.0685383i	$-0.0218335\pi$
$491$	9.73797	+	16.8667i	0.439468	+	0.761182i	−0.558180	+	0.829720i	$0.688500\pi$
$492$	−0.474348	+	14.0289i	−0.0213852	+	0.632470i
$493$		−	0.916881i		−	0.0412942i
$494$	−8.69206	−	8.38805i	−0.391074	−	0.377396i
$495$	42.4590	−	20.8252i	1.90839	−	0.936022i
$496$	1.80052	−	6.71962i	0.0808456	−	0.301720i
$497$	−11.8132	+	6.82036i	−0.529895	+	0.305935i
$498$	14.8625	+	4.52595i	0.666006	+	0.202812i
$499$	4.22889	+	4.22889i	0.189311	+	0.189311i	0.795398	−	0.606087i	$-0.207262\pi$
$499$	4.22889	+	4.22889i	0.189311	+	0.189311i	−0.606087	+	0.795398i	$0.707262\pi$
$500$	2.92564	+	10.9186i	0.130839	+	0.488296i
$501$	28.6141	−	15.2551i	1.27838	−	0.681546i
$502$	−11.3105	+	11.3105i	−0.504814	+	0.504814i
$503$	−2.60705	−	1.50518i	−0.116243	−	0.0671128i	0.440751	−	0.897629i	$-0.354712\pi$
$503$	−2.60705	−	1.50518i	−0.116243	−	0.0671128i	−0.556994	+	0.830516i	$0.688045\pi$
$504$	6.57809	+	4.41581i	0.293011	+	0.196696i
$505$	−56.3457	−	15.0978i	−2.50735	−	0.671842i
$506$	−9.72711			−0.432423
$507$	15.8931	−	15.9502i	0.705837	−	0.708374i
$508$	29.0071			1.28698
$509$	9.82903	+	2.63368i	0.435664	+	0.116736i	0.469984	−	0.882675i	$-0.344260\pi$
$509$	9.82903	+	2.63368i	0.435664	+	0.116736i	−0.0343197	+	0.999411i	$0.510926\pi$
$510$	−17.4770	+	16.3337i	−0.773893	+	0.723270i
$511$	−0.849121	−	0.490240i	−0.0375629	−	0.0216869i
$512$	5.78907	−	5.78907i	0.255843	−	0.255843i
$513$	−13.0931	+	18.1475i	−0.578073	+	0.801233i
$514$	5.77024	+	21.5348i	0.254514	+	0.949860i
$515$	−29.2204	−	29.2204i	−1.28761	−	1.28761i
$516$	−0.418923	+	1.37568i	−0.0184421	+	0.0605610i
$517$	−3.29625	+	1.90309i	−0.144969	+	0.0836978i
$518$	−1.64594	+	6.14273i	−0.0723185	+	0.269896i
$519$	3.37108	−	0.782207i	0.147974	−	0.0343351i
$520$	−24.0399	−	23.1991i	−1.05422	−	1.01735i
$521$			21.2194i			0.929637i	0.885406	+	0.464818i	$0.153880\pi$
$521$			21.2194i			0.929637i	−0.885406	+	0.464818i	$0.846120\pi$
$522$	0.0816073	+	0.414925i	0.00357185	+	0.0181608i
$523$	15.9463	+	27.6198i	0.697283	+	1.20773i	0.969405	+	0.245466i	$0.0789411\pi$
$523$	15.9463	+	27.6198i	0.697283	+	1.20773i	−0.272122	+	0.962263i	$0.587726\pi$
$524$	1.62275	−	2.81068i	0.0708901	−	0.122785i
$525$	10.7445	+	6.69740i	0.468930	+	0.292299i
$526$	6.09559	−	1.63331i	0.265780	−	0.0712156i
$527$	46.2486	−	12.3923i	2.01462	−	0.539816i
$528$	−4.85537	−	3.02650i	−0.211303	−	0.131712i
$529$	7.62749	−	13.2112i	0.331630	−	0.574400i
$530$	−7.41054	−	12.8354i	−0.321893	−	0.557535i
$531$	4.64908	+	23.6379i	0.201753	+	1.02580i
$532$		−	6.00695i		−	0.260435i
$533$	−10.7956	−	17.9530i	−0.467611	−	0.777630i
$534$	4.24553	−	0.985111i	0.183722	−	0.0426299i
$535$	6.85787	−	25.5939i	0.296492	−	1.10652i
$536$	−3.97781	+	2.29659i	−0.171815	+	0.0991975i
$537$	1.97410	−	6.48264i	0.0851885	−	0.279747i
$538$	7.46100	+	7.46100i	0.321667	+	0.321667i
$539$	1.16287	+	4.33987i	0.0500882	+	0.186932i
$540$	−14.8784	+	20.6220i	−0.640262	+	0.887429i
$541$	−24.9062	+	24.9062i	−1.07080	+	1.07080i	−0.0735064	+	0.997295i	$0.523419\pi$
$541$	−24.9062	+	24.9062i	−1.07080	+	1.07080i	−0.997295	+	0.0735064i	$0.976581\pi$
$542$	−4.94690	−	2.85609i	−0.212487	−	0.122680i
$543$	1.04896	−	0.980346i	0.0450152	−	0.0420707i
$544$	28.6117	+	7.66647i	1.22672	+	0.328697i
$545$	−17.4564			−0.747751
$546$	−4.85753	−	0.0777395i	−0.207883	−	0.00332695i
$547$	−39.4776			−1.68794			−0.843970	−	0.536390i	$-0.819788\pi$
$547$	−39.4776			−1.68794			−0.843970	+	0.536390i	$0.819788\pi$
$548$	−15.3783	−	4.12061i	−0.656930	−	0.176024i
$549$	8.74433	+	5.86999i	0.373199	+	0.250525i
$550$	22.1263	+	12.7746i	0.943470	+	0.544713i
$551$	0.551785	−	0.551785i	0.0235068	−	0.0235068i
$552$	11.2333	−	5.98882i	0.478122	−	0.254901i
$553$	−0.124486	−	0.464588i	−0.00529369	−	0.0197563i
$554$	−5.98474	−	5.98474i	−0.254267	−	0.254267i
$555$	−47.5235	−	14.4719i	−2.01726	−	0.614297i
$556$	−6.35204	+	3.66735i	−0.269387	+	0.155530i
$557$	2.15704	−	8.05019i	0.0913968	−	0.341097i	−0.905052	−	0.425301i	$-0.860168\pi$
$557$	2.15704	−	8.05019i	0.0913968	−	0.341097i	0.996449	+	0.0842040i	$0.0268348\pi$
$558$	−19.8264	+	9.72438i	−0.839318	+	0.411666i
$559$	−0.592275	−	2.06283i	−0.0250505	−	0.0872485i
$560$		−	2.57949i		−	0.109003i
$561$	1.33070	−	39.3557i	0.0561824	−	1.66160i
$562$	−5.64668	−	9.78034i	−0.238191	−	0.412559i
$563$	−4.81351	+	8.33724i	−0.202865	+	0.351373i	−0.949450	−	0.313917i	$-0.898359\pi$
$563$	−4.81351	+	8.33724i	−0.202865	+	0.351373i	0.746585	+	0.665290i	$0.231692\pi$
$564$	1.08262	−	1.73683i	0.0455866	−	0.0731339i
$565$	53.3369	−	14.2916i	2.24390	−	0.601251i
$566$	2.63551	−	0.706183i	0.110779	−	0.0296831i
$567$	1.13637	+	8.92797i	0.0477233	+	0.374940i
$568$	18.0121	−	31.1979i	0.755771	−	1.30903i
$569$	−15.3876	−	26.6521i	−0.645081	−	1.11731i	−0.984283	−	0.176599i	$-0.943490\pi$
$569$	−15.3876	−	26.6521i	−0.645081	−	1.11731i	0.339202	−	0.940714i	$-0.389843\pi$
$570$	−20.3475	−	0.687995i	−0.852263	−	0.0288170i
$571$			19.4625i			0.814482i	0.913321	+	0.407241i	$0.133509\pi$
$571$			19.4625i			0.814482i	−0.913321	+	0.407241i	$0.866491\pi$
$572$	22.5921	−	0.402111i	0.944624	−	0.0168131i
$573$	−3.62794	−	15.6353i	−0.151559	−	0.653175i
$574$	−1.16983	+	4.36588i	−0.0488279	+	0.182228i
$575$	17.6177	−	10.1716i	0.734708	−	0.424184i
$576$	−9.22914	−	0.624831i	−0.384548	−	0.0260346i
$577$	7.38296	+	7.38296i	0.307357	+	0.307357i	0.843883	−	0.536527i	$-0.180264\pi$
$577$	7.38296	+	7.38296i	0.307357	+	0.307357i	−0.536527	+	0.843883i	$0.680264\pi$
$578$	1.73253	+	6.46591i	0.0720640	+	0.268946i
$579$	−6.72897	−	12.6216i	−0.279646	−	0.524537i
$580$	0.627022	−	0.627022i	0.0260357	−	0.0260357i
$581$	−9.98575	−	5.76528i	−0.414279	−	0.239184i
$582$	−2.09365	−	2.24018i	−0.0867844	−	0.0928586i
$583$	23.5663	+	6.31457i	0.976017	+	0.261523i
$584$	2.58938			0.107149
$585$	1.88923	−	37.9036i	0.0781102	−	1.56712i
$586$	13.5897			0.561386
$587$	12.6654	+	3.39369i	0.522758	+	0.140072i	0.510542	−	0.859853i	$-0.329445\pi$
$587$	12.6654	+	3.39369i	0.522758	+	0.140072i	0.0122157	+	0.999925i	$0.496112\pi$
$588$	−1.64960	−	1.76506i	−0.0680285	−	0.0727899i
$589$	35.2905	+	20.3750i	1.45412	+	0.839536i
$590$	−15.4981	+	15.4981i	−0.638047	+	0.638047i
$591$	−7.88120	−	14.7829i	−0.324189	−	0.608086i
$592$	1.55555	+	5.80538i	0.0639325	+	0.238599i
$593$	9.76489	+	9.76489i	0.400996	+	0.400996i	0.878584	−	0.477588i	$-0.158489\pi$
$593$	9.76489	+	9.76489i	0.400996	+	0.400996i	−0.477588	+	0.878584i	$0.658489\pi$
$594$	2.90067	+	17.9285i	0.119016	+	0.735614i
$595$	15.3751	−	8.87682i	0.630318	−	0.363914i
$596$	2.55799	−	9.54655i	0.104779	−	0.391042i
$597$	0.942173	+	4.06048i	0.0385606	+	0.166185i
$598$	−3.78202	+	6.82848i	−0.154658	+	0.279237i
$599$			11.5553i			0.472135i	0.971737	+	0.236067i	$0.0758586\pi$
$599$			11.5553i			0.472135i	−0.971737	+	0.236067i	$0.924141\pi$
$600$	−33.4177	−	1.12993i	−1.36427	−	0.0461291i
$601$	12.4061	+	21.4880i	0.506055	+	0.876514i	0.999975	+	0.00700628i	$0.00223019\pi$
$601$	12.4061	+	21.4880i	0.506055	+	0.876514i	−0.493920	+	0.869507i	$0.664436\pi$
$602$	−0.231527	+	0.401017i	−0.00943635	+	0.0163442i
$603$	−4.93716	−	1.68778i	−0.201057	−	0.0687317i
$604$	−24.2548	+	6.49905i	−0.986913	+	0.264443i
$605$	−31.1337	+	8.34226i	−1.26577	+	0.339161i
$606$	11.8503	−	19.0113i	0.481386	−	0.772280i
$607$	−10.4788	+	18.1499i	−0.425323	+	0.736681i	−0.996451	−	0.0841805i	$-0.973173\pi$
$607$	−10.4788	+	18.1499i	−0.425323	+	0.736681i	0.571128	+	0.820861i	$0.306506\pi$
$608$	12.6050	+	21.8324i	0.511198	+	0.885422i
$609$	0.0106057	−	0.313663i	0.000429763	−	0.0127103i
$610$			9.58184i			0.387957i
$611$	0.0543561	+	3.05393i	0.00219901	+	0.123549i
$612$	9.32421	+	19.0105i	0.376909	+	0.768454i
$613$	1.35054	−	5.04028i	0.0545477	−	0.203575i	−0.933274	−	0.359165i	$-0.883061\pi$
$613$	1.35054	−	5.04028i	0.0545477	−	0.203575i	0.987822	+	0.155591i	$0.0497280\pi$
$614$	20.2909	−	11.7150i	0.818876	−	0.472778i
$615$	−33.7768	−	10.2857i	−1.36201	−	0.414760i
$616$	−8.39026	−	8.39026i	−0.338053	−	0.338053i
$617$	6.09399	+	22.7431i	0.245335	+	0.915602i	0.973215	+	0.229898i	$0.0738391\pi$
$617$	6.09399	+	22.7431i	0.245335	+	0.915602i	−0.727880	+	0.685705i	$0.759494\pi$
$618$	14.0041	−	7.46600i	0.563327	−	0.300327i
$619$	−16.2097	+	16.2097i	−0.651524	+	0.651524i	−0.953360	−	0.301836i	$-0.902401\pi$
$619$	−16.2097	+	16.2097i	−0.651524	+	0.651524i	0.301836	+	0.953360i	$0.402401\pi$
$620$	40.1024	+	23.1531i	1.61055	+	0.929852i
$621$	13.5175	+	5.13743i	0.542438	+	0.206158i
$622$	−23.7607	−	6.36666i	−0.952717	−	0.255280i
$623$	−3.23459			−0.129591
$624$	−4.01245	+	2.23175i	−0.160627	+	0.0893416i
$625$	8.11564			0.324626
$626$	0.305212	+	0.0817813i	0.0121987	+	0.00326864i
$627$	24.4853	−	22.8837i	0.977850	−	0.913886i
$628$	−8.70070	−	5.02335i	−0.347196	−	0.200454i
$629$	−29.2500	+	29.2500i	−1.16627	+	1.16627i
$630$	−6.16777	+	5.38559i	−0.245730	+	0.214567i
$631$	8.86996	+	33.1031i	0.353108	+	1.31782i	0.882849	+	0.469656i	$0.155622\pi$
$631$	8.86996	+	33.1031i	0.353108	+	1.31782i	−0.529742	+	0.848159i	$0.677711\pi$
$632$	0.898187	+	0.898187i	0.0357280	+	0.0357280i
$633$	−0.523284	+	1.71839i	−0.0207987	+	0.0682998i
$634$	18.5126	−	10.6882i	0.735228	−	0.424484i
$635$	−18.8845	+	70.4779i	−0.749408	+	2.79683i
$636$	−12.7793	+	2.96525i	−0.506734	+	0.117580i
$637$	3.49875	+	0.871060i	0.138626	+	0.0345126i
$638$		−	0.633320i		−	0.0250734i
$639$	40.1529	−	7.89725i	1.58843	−	0.312410i
$640$	16.3303	+	28.2850i	0.645513	+	1.11806i
$641$	−18.2550	+	31.6186i	−0.721029	+	1.24886i	0.239559	+	0.970882i	$0.422997\pi$
$641$	−18.2550	+	31.6186i	−0.721029	+	1.24886i	−0.960588	+	0.277977i	$0.910336\pi$
$642$	8.63551	+	5.38278i	0.340816	+	0.212441i
$643$	−11.5608	+	3.09770i	−0.455912	+	0.122161i	−0.479464	−	0.877561i	$-0.659169\pi$
$643$	−11.5608	+	3.09770i	−0.455912	+	0.122161i	0.0235522	+	0.999723i	$0.492502\pi$
$644$	−3.74952	+	1.00468i	−0.147752	+	0.0395900i
$645$	−3.06973	−	1.91346i	−0.120871	−	0.0753423i
$646$	−8.47626	+	14.6813i	−0.333494	+	0.577629i
$647$	0.357320	+	0.618896i	0.0140477	+	0.0243313i	0.872964	−	0.487785i	$-0.162195\pi$
$647$	0.357320	+	0.618896i	0.0140477	+	0.0243313i	−0.858916	+	0.512116i	$0.828862\pi$
$648$	−14.3881	−	18.9187i	−0.565218	−	0.743198i
$649$		−	36.0796i		−	1.41625i
$650$	17.5709	−	10.5659i	0.689186	−	0.414427i
$651$	15.9649	−	3.70441i	0.625714	−	0.145187i
$652$	−2.70293	+	10.0875i	−0.105855	+	0.395057i
$653$	30.5471	−	17.6364i	1.19540	−	0.690165i	0.235875	−	0.971783i	$-0.424204\pi$
$653$	30.5471	−	17.6364i	1.19540	−	0.690165i	0.959527	+	0.281618i	$0.0908711\pi$
$654$	1.95294	−	6.41316i	0.0763659	−	0.250774i
$655$	5.77260	+	5.77260i	0.225554	+	0.225554i
$656$	1.10559	+	4.12611i	0.0431659	+	0.161097i
$657$	1.93467	+	2.21565i	0.0754787	+	0.0864409i
$658$	0.465994	−	0.465994i	0.0181663	−	0.0181663i
$659$	2.45622	+	1.41810i	0.0956806	+	0.0552412i	0.547077	−	0.837082i	$-0.315741\pi$
$659$	2.45622	+	1.41810i	0.0956806	+	0.0552412i	−0.451396	+	0.892324i	$0.649074\pi$
$660$	27.8240	−	26.0039i	1.08305	−	1.01220i
$661$	−6.27813	−	1.68222i	−0.244191	−	0.0654308i	0.134648	−	0.990894i	$-0.457010\pi$
$661$	−6.27813	−	1.68222i	−0.244191	−	0.0654308i	−0.378839	+	0.925463i	$0.623676\pi$
$662$	−4.30202			−0.167203
$663$	−27.1105	−	16.2361i	−1.05288	−	0.630560i
$664$	30.4514			1.18174
$665$	14.5950	+	3.91071i	0.565969	+	0.151651i
$666$	10.6334	−	15.8402i	0.412035	−	0.613795i
$667$	−0.436710	−	0.252135i	−0.0169095	−	0.00976269i
$668$	18.4649	−	18.4649i	0.714428	−	0.714428i
$669$	36.0339	−	19.2108i	1.39315	−	0.742731i
$670$	−1.22862	−	4.58527i	−0.0474657	−	0.177144i
$671$	−11.1533	−	11.1533i	−0.430567	−	0.430567i
$672$	9.69932	+	2.95364i	0.374159	+	0.113939i
$673$	34.1938	−	19.7418i	1.31807	−	0.760989i	0.334654	−	0.942341i	$-0.391381\pi$
$673$	34.1938	−	19.7418i	1.31807	−	0.760989i	0.983418	+	0.181352i	$0.0580472\pi$
$674$	0.292873	−	1.09302i	0.0112810	−	0.0421014i
$675$	−24.0013	−	29.4387i	−0.923812	−	1.13310i
$676$	8.50182	−	16.0161i	0.326993	−	0.616005i
$677$		−	22.2942i		−	0.856836i	−0.903581	−	0.428418i	$-0.859071\pi$
$677$		−	22.2942i		−	0.856836i	0.903581	−	0.428418i	$-0.140929\pi$
$678$	−0.716612	+	21.1938i	−0.0275213	+	0.813945i
$679$	1.13782	+	1.97077i	0.0436657	+	0.0756312i
$680$	−23.4431	+	40.6046i	−0.899001	+	1.55712i
$681$	22.9031	−	36.7432i	0.877650	−	1.40800i
$682$	31.9455	−	8.55976i	1.22326	−	0.327770i
$683$	8.79388	−	2.35631i	0.336488	−	0.0901618i	−0.0866185	−	0.996242i	$-0.527606\pi$
$683$	8.79388	−	2.35631i	0.336488	−	0.0901618i	0.423107	+	0.906080i	$0.360939\pi$
$684$	−5.82927	+	17.0520i	−0.222888	+	0.652000i
$685$	20.0235	−	34.6818i	0.765060	−	1.32512i
$686$	−0.388964	−	0.673705i	−0.0148507	−	0.0257222i
$687$	−40.6446	−	1.37429i	−1.55069	−	0.0524323i
$688$			0.437624i			0.0166843i
$689$	13.5957	−	14.0885i	0.517957	−	0.536729i
$690$	2.97374	+	12.8159i	0.113208	+	0.487893i
$691$	−4.37461	+	16.3263i	−0.166418	+	0.621081i	0.831437	+	0.555619i	$0.187519\pi$
$691$	−4.37461	+	16.3263i	−0.166418	+	0.621081i	−0.997855	+	0.0654616i	$0.979148\pi$
$692$	2.41350	−	1.39343i	0.0917475	−	0.0529704i
$693$	0.910464	−	13.4481i	0.0345857	−	0.510852i
$694$	2.36329	+	2.36329i	0.0897094	+	0.0897094i
$695$	−4.77512	−	17.8210i	−0.181131	−	0.675988i
$696$	0.389925	+	0.731388i	0.0147801	+	0.0277232i
$697$	−20.7891	+	20.7891i	−0.787443	+	0.787443i
$698$	−11.3726	−	6.56595i	−0.430457	−	0.248525i
$699$	−3.13961	−	3.35936i	−0.118751	−	0.127063i
$700$	9.84853	+	2.63890i	0.372239	+	0.0997412i
$701$	38.7119			1.46213			0.731063	−	0.682310i	$-0.239024\pi$
$701$	38.7119			1.46213			0.731063	+	0.682310i	$0.239024\pi$
$702$	13.7137	+	4.93453i	0.517590	+	0.186242i
$703$	−35.2056			−1.32781
$704$	13.3817	+	3.58560i	0.504340	+	0.135138i
$705$	3.51513	+	3.76116i	0.132387	+	0.141653i
$706$	−13.4954	−	7.79155i	−0.507904	−	0.293239i
$707$	−11.7564	+	11.7564i	−0.442147	+	0.442147i
$708$	9.12688	+	17.1194i	0.343009	+	0.643387i
$709$	−5.05872	−	18.8794i	−0.189984	−	0.709031i	−0.993508	−	0.113759i	$-0.963711\pi$
$709$	−5.05872	−	18.8794i	−0.189984	−	0.709031i	0.803524	−	0.595272i	$-0.202956\pi$
$710$	26.3262	+	26.3262i	0.988003	+	0.988003i
$711$	−0.0974662	+	1.43964i	−0.00365527	+	0.0539906i
$712$	7.39788	−	4.27117i	0.277247	−	0.160069i
$713$	6.81555	−	25.4360i	0.255244	−	0.952584i
$714$	1.54109	+	6.64162i	0.0576737	+	0.248556i
$715$	−13.7312	+	55.1534i	−0.513516	+	2.06262i
$716$		−	5.45719i		−	0.203945i
$717$	23.3410	+	0.789211i	0.871684	+	0.0294736i
$718$	−4.14750	−	7.18369i	−0.154783	−	0.268093i
$719$	0.214709	−	0.371886i	0.00800729	−	0.0138690i	−0.861994	−	0.506918i	$-0.830785\pi$
$719$	0.214709	−	0.371886i	0.00800729	−	0.0138690i	0.870001	+	0.493049i	$0.164118\pi$
$720$	−2.50319	+	7.32243i	−0.0932884	+	0.272891i
$721$	−11.3768	+	3.04840i	−0.423694	+	0.113528i
$722$	0.340606	−	0.0912650i	0.0126760	−	0.00339653i
$723$	−12.3499	+	19.8127i	−0.459296	+	0.736842i
$724$	0.578111	−	1.00132i	0.0214853	−	0.0372137i
$725$	0.662259	+	1.14707i	0.0245957	+	0.0426010i
$726$	0.418300	−	12.3712i	0.0155246	−	0.459140i
$727$		−	43.8176i		−	1.62511i	−0.582888	−	0.812553i	$-0.698077\pi$
$727$		−	43.8176i		−	1.62511i	0.582888	−	0.812553i	$-0.301923\pi$
$728$	−9.15224	+	2.62777i	−0.339205	+	0.0973915i
$729$	5.43805	−	26.4467i	0.201409	−	0.979507i
$730$	−0.692628	+	2.58492i	−0.0256353	+	0.0956723i
$731$	−2.60847	+	1.50600i	−0.0964777	+	0.0557014i
$732$	8.11350	+	2.47073i	0.299884	+	0.0913207i
$733$	34.6540	+	34.6540i	1.27998	+	1.27998i	0.940679	+	0.339297i	$0.110189\pi$
$733$	34.6540	+	34.6540i	1.27998	+	1.27998i	0.339297	+	0.940679i	$0.389811\pi$
$734$	3.00613	+	11.2190i	0.110958	+	0.414102i
$735$	5.36248	−	2.85890i	0.197798	−	0.105452i
$736$	11.5195	−	11.5195i	0.424615	−	0.424615i
$737$	6.76737	+	3.90714i	0.249279	+	0.143921i
$738$	7.55756	−	11.2582i	0.278198	−	0.414422i
$739$	−2.52567	−	0.676752i	−0.0929083	−	0.0248947i	0.212065	−	0.977255i	$-0.431981\pi$
$739$	−2.52567	−	0.676752i	−0.0929083	−	0.0248947i	−0.304974	+	0.952361i	$0.598648\pi$
$740$	−40.0060			−1.47065
$741$	−6.54426	−	26.0863i	−0.240409	−	0.958304i
$742$	−4.22429			−0.155079
$743$	12.4271	+	3.32983i	0.455906	+	0.122160i	0.479462	−	0.877563i	$-0.340832\pi$
$743$	12.4271	+	3.32983i	0.455906	+	0.122160i	−0.0235556	+	0.999723i	$0.507499\pi$
$744$	−31.6220	+	29.5535i	−1.15932	+	1.08348i
$745$	21.5297	+	12.4302i	0.788788	+	0.455407i
$746$	−5.73554	+	5.73554i	−0.209993	+	0.209993i
$747$	22.7519	+	26.0563i	0.832449	+	0.953351i
$748$	−8.20752	−	30.6309i	−0.300097	−	1.11998i
$749$	−5.34014	−	5.34014i	−0.195124	−	0.195124i
$750$	3.18100	−	10.4459i	0.116154	−	0.381431i
$751$	−2.01789	+	1.16503i	−0.0736339	+	0.0425126i	−0.536365	−	0.843986i	$-0.680203\pi$
$751$	−2.01789	+	1.16503i	−0.0736339	+	0.0425126i	0.462731	+	0.886499i	$0.346870\pi$
$752$	0.161198	−	0.601600i	0.00587830	−	0.0219381i
$753$	−34.6923	+	8.04981i	−1.26426	+	0.293351i
$754$	−0.444594	−	0.246243i	−0.0161912	−	0.00896764i
$755$		−	63.1624i		−	2.29871i
$756$	2.96990	+	6.61131i	0.108014	+	0.240451i
$757$	7.22715	+	12.5178i	0.262675	+	0.454967i	0.966952	−	0.254959i	$-0.0820619\pi$
$757$	7.22715	+	12.5178i	0.262675	+	0.454967i	−0.704277	+	0.709926i	$0.748729\pi$
$758$	6.80872	−	11.7931i	0.247304	−	0.428343i
$759$	−18.3792	−	11.4563i	−0.667121	−	0.415837i
$760$	−38.5443	+	10.3279i	−1.39815	+	0.374633i
$761$	−37.8495	+	10.1417i	−1.37204	+	0.367638i	−0.868225	−	0.496171i	$-0.834739\pi$
$761$	−37.8495	+	10.1417i	−1.37204	+	0.367638i	−0.503819	+	0.863809i	$0.668072\pi$
$762$	−23.7796	−	14.8225i	−0.861442	−	0.536964i
$763$	−2.48771	+	4.30883i	−0.0900610	+	0.155990i
$764$	−6.46285	−	11.1940i	−0.233818	−	0.404984i
$765$	−52.2597	+	10.2784i	−1.88946	+	0.371617i
$766$			17.5188i			0.632978i
$767$	−25.3281	−	14.0282i	−0.914543	−	0.506529i
$768$	−22.6232	+	5.24936i	−0.816344	+	0.189420i
$769$	4.61632	−	17.2283i	0.166469	−	0.621270i	−0.831380	−	0.555705i	$-0.812448\pi$
$769$	4.61632	−	17.2283i	0.166469	−	0.621270i	0.997848	−	0.0655648i	$-0.0208849\pi$
$770$	10.6201	−	6.13152i	0.382722	−	0.220965i
$771$	−14.4603	+	47.4856i	−0.520776	+	1.71015i
$772$	−8.14482	−	8.14482i	−0.293138	−	0.293138i
$773$	−10.0848	−	37.6369i	−0.362724	−	1.35371i	−0.870480	−	0.492205i	$-0.836191\pi$
$773$	−10.0848	−	37.6369i	−0.362724	−	1.35371i	0.507755	−	0.861501i	$-0.330475\pi$
$774$	1.04640	−	0.913693i	0.0376119	−	0.0328420i
$775$	−48.9086	+	48.9086i	−1.75685	+	1.75685i
$776$	−5.20466	−	3.00491i	−0.186837	−	0.107870i
$777$	−10.3447	+	9.66802i	−0.371114	+	0.346838i
$778$	−2.28149	−	0.611323i	−0.0817953	−	0.0219170i
$779$	−25.0220			−0.896507
$780$	−7.43658	−	29.6432i	−0.266272	−	1.06140i
$781$	−61.2873			−2.19303
$782$	10.5817	+	2.83536i	0.378401	+	0.101392i
$783$	−0.334492	+	0.880107i	−0.0119538	+	0.0314525i
$784$	−0.636705	−	0.367602i	−0.0227395	−	0.0131286i
$785$	17.8695	−	17.8695i	0.637791	−	0.637791i
$786$	−2.76655	+	1.47493i	−0.0986797	+	0.0526092i
$787$	3.17668	+	11.8555i	0.113237	+	0.422605i	0.999149	−	0.0412480i	$-0.0131334\pi$
$787$	3.17668	+	11.8555i	0.113237	+	0.422605i	−0.885912	+	0.463853i	$0.846467\pi$
$788$	−9.53949	−	9.53949i	−0.339830	−	0.339830i
$789$	13.4411	+	4.09310i	0.478518	+	0.145718i
$790$	−1.13689	+	0.656387i	−0.0404489	+	0.0233532i
$791$	4.07337	−	15.2020i	0.144833	−	0.540522i
$792$	15.6754	+	31.9596i	0.557002	+	1.13563i
$793$	−12.1662	+	3.49312i	−0.432034	+	0.124044i
$794$			8.09392i			0.287242i
$795$	1.11513	−	32.9802i	0.0395498	−	1.16969i
$796$	1.67840	+	2.90707i	0.0594893	+	0.103038i
$797$	15.7312	−	27.2472i	0.557226	−	0.965144i	−0.440501	−	0.897752i	$-0.645199\pi$
$797$	15.7312	−	27.2472i	0.557226	−	0.965144i	0.997727	−	0.0673915i	$-0.0214677\pi$
$798$	−3.06954	+	4.92441i	−0.108660	+	0.174322i
$799$	4.14059	−	1.10947i	0.146483	−	0.0392501i
$800$	−41.3322	+	11.0749i	−1.46131	+	0.391557i
$801$	9.18208	+	3.13892i	0.324433	+	0.110908i
$802$	−10.1667	+	17.6092i	−0.358998	+	0.621802i
$803$	−2.20263	−	3.81507i	−0.0777292	−	0.134631i
$804$	−4.19942	−	0.141992i	−0.148102	−	0.00500767i
$805$		−	9.76421i		−	0.344143i
$806$	6.41181	−	25.7540i	0.225846	−	0.907147i
$807$	5.31006	+	22.8848i	0.186923	+	0.805582i
$808$	11.3643	−	42.4123i	0.399796	−	1.49206i
$809$	−13.8418	+	7.99158i	−0.486653	+	0.280969i	−0.723185	−	0.690655i	$-0.757323\pi$
$809$	−13.8418	+	7.99158i	−0.486653	+	0.280969i	0.236532	+	0.971624i	$0.423989\pi$
$810$	22.7348	−	9.30279i	0.798820	−	0.326867i
$811$	8.86374	+	8.86374i	0.311248	+	0.311248i	0.845393	−	0.534145i	$-0.179366\pi$
$811$	8.86374	+	8.86374i	0.311248	+	0.311248i	−0.534145	+	0.845393i	$0.679366\pi$
$812$	−0.0654136	−	0.244127i	−0.00229557	−	0.00856718i
$813$	−5.98324	−	11.2228i	−0.209841	−	0.393602i
$814$	−20.2039	+	20.2039i	−0.708148	+	0.708148i
$815$	−22.7497	−	13.1345i	−0.796886	−	0.460082i
$816$	4.39976	+	4.70770i	0.154022	+	0.164802i
$817$	−2.47611	−	0.663473i	−0.0866283	−	0.0232120i
$818$	17.0003			0.594403
$819$	−9.08665	−	5.86795i	−0.317513	−	0.205043i
$820$	−28.4338			−0.992953
$821$	4.45268	+	1.19309i	0.155400	+	0.0416392i	0.335680	−	0.941976i	$-0.391034\pi$
$821$	4.45268	+	1.19309i	0.155400	+	0.0416392i	−0.180280	+	0.983615i	$0.557701\pi$
$822$	10.5013	+	11.2363i	0.366275	+	0.391911i
$823$	−33.5844	−	19.3899i	−1.17068	−	0.675891i	−0.216838	−	0.976208i	$-0.569574\pi$
$823$	−33.5844	−	19.3899i	−1.17068	−	0.675891i	−0.953840	+	0.300316i	$0.902908\pi$
$824$	21.9947	−	21.9947i	0.766221	−	0.766221i
$825$	26.7616	+	50.1972i	0.931721	+	1.74764i
$826$	1.61683	+	6.03408i	0.0562566	+	0.209953i
$827$	−2.94012	−	2.94012i	−0.102238	−	0.102238i	0.654138	−	0.756376i	$-0.273032\pi$
$827$	−2.94012	−	2.94012i	−0.102238	−	0.102238i	−0.756376	+	0.654138i	$0.773032\pi$
$828$	11.6188	+	0.786614i	0.403780	+	0.0273367i
$829$	−9.37700	+	5.41381i	−0.325677	+	0.188030i	−0.653920	−	0.756564i	$-0.726877\pi$
$829$	−9.37700	+	5.41381i	−0.325677	+	0.188030i	0.328243	+	0.944593i	$0.393543\pi$
$830$	−8.14538	+	30.3990i	−0.282730	+	1.05516i
$831$	−4.25939	−	18.3567i	−0.147757	−	0.636787i
$832$	7.72007	−	7.99987i	0.267645	−	0.277346i
$833$		−	5.06013i		−	0.175323i
$834$	7.08131	+	0.239435i	0.245206	+	0.00829097i
$835$	32.8425	+	56.8850i	1.13656	+	1.96859i
$836$	13.4945	−	23.3732i	0.466718	−	0.808379i
$837$	−48.9146	−	4.97692i	−1.69074	−	0.172028i
$838$	−2.84653	+	0.762724i	−0.0983316	+	0.0263479i
$839$	13.3696	−	3.58236i	0.461569	−	0.123677i	−0.0205388	−	0.999789i	$-0.506538\pi$
$839$	13.3696	−	3.58236i	0.461569	−	0.123677i	0.482107	+	0.876112i	$0.339871\pi$
$840$	−8.48951	+	13.6196i	−0.292916	+	0.469921i
$841$	−14.4836	+	25.0863i	−0.499434	+	0.865045i
$842$	14.6636	+	25.3981i	0.505341	+	0.875277i
$843$	0.849711	−	25.1302i	0.0292656	−	0.865532i
$844$			1.44657i			0.0497929i
$845$	33.3791	+	31.0837i	1.14828	+	1.06931i
$846$	−1.77503	+	0.870613i	−0.0610269	+	0.0299323i
$847$	−2.37770	+	8.87372i	−0.0816989	+	0.304904i
$848$	−3.45743	+	1.99615i	−0.118729	+	0.0685480i
$849$	5.81147	+	1.76971i	0.199449	+	0.0607363i
$850$	−20.3466	−	20.3466i	−0.697884	−	0.697884i
$851$	5.88825	+	21.9752i	0.201847	+	0.753302i
$852$	29.0802	−	15.5036i	0.996272	−	0.531143i
$853$	−30.6895	+	30.6895i	−1.05079	+	1.05079i	−0.0521481	+	0.998639i	$0.516607\pi$
$853$	−30.6895	+	30.6895i	−1.05079	+	1.05079i	−0.998639	+	0.0521481i	$0.983393\pi$
$854$	2.36512	+	1.36550i	0.0809328	+	0.0467266i
$855$	−37.6359	−	25.2646i	−1.28712	−	0.864032i
$856$	19.2650	+	5.16203i	0.658463	+	0.176435i
$857$	−49.2792			−1.68334			−0.841672	−	0.539989i	$-0.818428\pi$
$857$	−49.2792			−1.68334			−0.841672	+	0.539989i	$0.818428\pi$
$858$	−18.7261	−	11.2149i	−0.639300	−	0.382869i
$859$	−20.7729			−0.708762			−0.354381	−	0.935101i	$-0.615308\pi$
$859$	−20.7729			−0.708762			−0.354381	+	0.935101i	$0.615308\pi$
$860$	−2.81374	−	0.753939i	−0.0959477	−	0.0257091i
$861$	−7.35238	+	6.87144i	−0.250568	+	0.234178i
$862$	−0.937870	−	0.541479i	−0.0319440	−	0.0184429i
$863$	2.07454	−	2.07454i	0.0706180	−	0.0706180i	−0.670916	−	0.741534i	$-0.734099\pi$
$863$	2.07454	−	2.07454i	0.0706180	−	0.0706180i	0.741534	+	0.670916i	$0.234099\pi$
$864$	−24.6673	−	17.7970i	−0.839199	−	0.605465i
$865$	1.81434	+	6.77119i	0.0616893	+	0.230227i
$866$	−8.94153	−	8.94153i	−0.303846	−	0.303846i
$867$	−4.34177	+	14.2577i	−0.147454	+	0.484218i
$868$	11.4300	−	6.59909i	0.387958	−	0.223988i
$869$	0.559312	−	2.08738i	0.0189734	−	0.0708095i
$870$	−0.834429	+	0.193616i	−0.0282898	+	0.00656421i
$871$	5.37407	−	3.23158i	0.182093	−	0.109498i
$872$		−	13.1397i		−	0.444967i
$873$	−1.31748	−	6.69861i	−0.0445899	−	0.226714i
$874$	4.66180	+	8.07448i	0.157688	+	0.273123i
$875$	−4.05204	+	7.01834i	−0.136984	+	0.237263i
$876$	2.01021	+	1.25302i	0.0679186	+	0.0423358i
$877$	52.0706	−	13.9523i	1.75830	−	0.471135i	0.771934	−	0.635702i	$-0.219289\pi$
$877$	52.0706	−	13.9523i	1.75830	−	0.471135i	0.986366	+	0.164567i	$0.0526227\pi$
$878$	18.2700	−	4.89544i	0.616584	−	0.165213i
$879$	25.6775	+	16.0056i	0.866079	+	0.539854i
$880$	5.79478	−	10.0369i	0.195342	−	0.338342i
$881$	16.7291	+	28.9756i	0.563616	+	0.976212i	0.997177	+	0.0750874i	$0.0239236\pi$
$881$	16.7291	+	28.9756i	0.563616	+	0.976212i	−0.433561	+	0.901124i	$0.642743\pi$
$882$	0.450379	+	2.28991i	0.0151650	+	0.0771054i
$883$			32.6502i			1.09877i	0.835571	+	0.549383i	$0.185137\pi$
$883$			32.6502i			1.09877i	−0.835571	+	0.549383i	$0.814863\pi$
$884$	−24.6942	−	6.14795i	−0.830557	−	0.206778i
$885$	−47.5365	+	11.0301i	−1.59792	+	0.370774i
$886$	3.98606	−	14.8762i	0.133914	−	0.499775i
$887$	−31.7441	+	18.3274i	−1.06586	+	0.615375i	−0.927048	−	0.374943i	$-0.877662\pi$
$887$	−31.7441	+	18.3274i	−1.06586	+	0.615375i	−0.138814	+	0.990319i	$0.544329\pi$
$888$	10.8932	−	35.7717i	0.365552	−	1.20042i
$889$	14.7051	+	14.7051i	0.493194	+	0.493194i
$890$	2.28497	+	8.52764i	0.0765925	+	0.285847i
$891$	−15.6349	+	37.2918i	−0.523788	+	1.24932i
$892$	23.2529	−	23.2529i	0.778565	−	0.778565i
$893$	3.15952	+	1.82415i	0.105729	+	0.0610428i
$894$	−6.97526	+	6.51898i	−0.233287	+	0.218027i
$895$	13.2592	+	3.55280i	0.443207	+	0.118757i
$896$	9.30892			0.310989
$897$	−15.1884	+	8.44791i	−0.507127	+	0.282068i
$898$	17.8880			0.596929
$899$	1.65611	+	0.443752i	0.0552342	+	0.0148000i
$900$	−25.3963	−	17.0483i	−0.846543	−	0.568277i
$901$	−23.7962	−	13.7387i	−0.792765	−	0.457703i
$902$	−14.3597	+	14.3597i	−0.478127	+	0.478127i
$903$	−0.909773	+	0.485027i	−0.0302753	+	0.0161407i
$904$	10.7575	+	40.1475i	0.357789	+	1.33529i
$905$	2.05651	+	2.05651i	0.0683608	+	0.0683608i
$906$	23.2047	+	7.06630i	0.770924	+	0.234762i
$907$	13.4532	−	7.76719i	0.446705	−	0.257905i	−0.259733	−	0.965681i	$-0.583634\pi$
$907$	13.4532	−	7.76719i	0.446705	−	0.257905i	0.706438	+	0.707775i	$0.250301\pi$
$908$	9.02427	−	33.6790i	0.299481	−	1.11768i
$909$	44.7819	−	21.9645i	1.48532	−	0.728515i
$910$	−0.175129	−	9.83938i	−0.00580546	−	0.326172i
$911$			15.1851i			0.503104i	0.967844	+	0.251552i	$0.0809410\pi$
$911$			15.1851i			0.503104i	−0.967844	+	0.251552i	$0.919059\pi$
$912$	−0.185323	+	5.48093i	−0.00613664	+	0.181492i
$913$	−25.9032	−	44.8656i	−0.857270	−	1.48484i
$914$	−4.23334	+	7.33236i	−0.140026	+	0.242533i
$915$	−11.2852	+	18.1047i	−0.373078	+	0.598522i
$916$	−31.6341	+	8.47632i	−1.04522	+	0.280066i
$917$	2.24752	−	0.602222i	0.0742198	−	0.0198871i
$918$	2.07047	−	20.3492i	0.0683356	−	0.671622i
$919$	26.0736	−	45.1609i	0.860090	−	1.48972i	−0.0117519	−	0.999931i	$-0.503741\pi$
$919$	26.0736	−	45.1609i	0.860090	−	1.48972i	0.871842	−	0.489788i	$-0.162926\pi$
$920$	12.8933	+	22.3319i	0.425080	+	0.736259i
$921$	52.1369	+	1.76287i	1.71797	+	0.0580884i
$922$		−	9.36044i		−	0.308270i
$923$	−23.8293	+	43.0240i	−0.784351	+	1.41615i
$924$	−2.45347	−	10.5737i	−0.0807131	−	0.347849i
$925$	15.4661	−	57.7204i	0.508523	−	1.89783i
$926$	−26.7481	+	15.4430i	−0.878998	+	0.507489i
$927$	35.2537	+	2.38674i	1.15788	+	0.0783909i
$928$	0.750022	+	0.750022i	0.0246207	+	0.0246207i
$929$	−8.38590	−	31.2966i	−0.275132	−	1.02681i	−0.955753	−	0.294172i	$-0.904956\pi$
$929$	−8.38590	−	31.2966i	−0.275132	−	1.02681i	0.680620	−	0.732636i	$-0.261710\pi$
$930$	−21.0441	−	39.4728i	−0.690065	−	1.29436i
$931$	3.04522	−	3.04522i	0.0998030	−	0.0998030i
$932$	−3.20678	−	1.85143i	−0.105041	−	0.0606457i
$933$	−37.3969	−	40.0143i	−1.22432	−	1.31001i
$934$	−20.5357	−	5.50252i	−0.671948	−	0.180048i
$935$	79.7665			2.60864
$936$	28.5306	+	1.42206i	0.932552	+	0.0464814i
$937$	26.0509			0.851046			0.425523	−	0.904948i	$-0.360090\pi$
$937$	26.0509			0.851046			0.425523	+	0.904948i	$0.360090\pi$
$938$	−1.30689	−	0.350180i	−0.0426715	−	0.0114338i
$939$	0.480372	+	0.513993i	0.0156763	+	0.0167735i
$940$	3.59032	+	2.07287i	0.117103	+	0.0676097i
$941$	33.4066	−	33.4066i	1.08902	−	1.08902i	0.0933958	−	0.995629i	$-0.470228\pi$
$941$	33.4066	−	33.4066i	1.08902	−	1.08902i	0.995629	−	0.0933958i	$-0.0297722\pi$
$942$	4.56578	+	8.56409i	0.148761	+	0.279033i
$943$	4.18501	+	15.6187i	0.136283	+	0.508614i
$944$	4.17466	+	4.17466i	0.135874	+	0.135874i
$945$	−17.9969	+	2.91173i	−0.585438	+	0.0947186i
$946$	−1.80176	+	1.04024i	−0.0585802	+	0.0338213i
$947$	2.95823	−	11.0403i	0.0961296	−	0.358761i	−0.901059	−	0.433697i	$-0.857209\pi$
$947$	2.95823	−	11.0403i	0.0961296	−	0.358761i	0.997188	+	0.0749365i	$0.0238754\pi$
$948$	0.262647	+	1.13193i	0.00853036	+	0.0367633i
$949$	−3.53461	+	0.0629116i	−0.114738	+	0.00204220i
$950$		−	24.4895i		−	0.794543i
$951$	47.5674	+	1.60836i	1.54248	+	0.0521547i
$952$	6.68173	+	11.5731i	0.216556	+	0.375086i
$953$	−15.4255	+	26.7177i	−0.499680	+	0.865471i	−1.00000		0.000369668i	$-0.999882\pi$
$953$	−15.4255	+	26.7177i	−0.499680	+	0.865471i	0.500320	+	0.865841i	$0.333216\pi$
$954$	11.9915	+	4.09934i	0.388241	+	0.132721i
$955$	31.4053	−	8.41503i	1.01625	−	0.272304i
$956$	18.1665	−	4.86770i	0.587546	−	0.157433i
$957$	0.745906	−	1.19665i	0.0241117	−	0.0386821i
$958$	5.89242	−	10.2060i	0.190376	−	0.329740i
$959$	−5.70709	−	9.88497i	−0.184292	−	0.319202i
$960$	0.633207	−	18.7271i	0.0204367	−	0.604416i
$961$			58.5337i			1.88818i
$962$	6.32773	+	22.0388i	0.204014	+	0.710560i
$963$	9.97693	+	20.3413i	0.321502	+	0.655489i
$964$	−4.86608	+	18.1605i	−0.156726	+	0.584909i
$965$	25.0918	−	14.4868i	0.807734	−	0.466345i
$966$	3.58719	+	1.09237i	0.115416	+	0.0351465i
$967$	1.58014	+	1.58014i	0.0508139	+	0.0508139i	0.732057	−	0.681243i	$-0.238560\pi$
$967$	1.58014	+	1.58014i	0.0508139	+	0.0508139i	−0.681243	+	0.732057i	$0.738560\pi$
$968$	−6.27935	−	23.4349i	−0.201826	−	0.753225i
$969$	−33.3069	+	17.7569i	−1.06997	+	0.570435i
$970$	4.39193	−	4.39193i	0.141016	−	0.141016i
$971$	−27.1454	−	15.6724i	−0.871136	−	0.502951i	−0.00341055	−	0.999994i	$-0.501086\pi$
$971$	−27.1454	−	15.6724i	−0.871136	−	0.502951i	−0.867726	+	0.497043i	$0.834419\pi$
$972$	−2.01493	−	21.6497i	−0.0646288	−	0.694413i
$973$	−5.07932	−	1.36100i	−0.162836	−	0.0436317i
$974$	−2.96763			−0.0950892
$975$	45.6440	+	0.730482i	1.46178	+	0.0233941i
$976$	2.58102			0.0826165
$977$	−39.0767	−	10.4706i	−1.25018	−	0.334984i	−0.427771	−	0.903887i	$-0.640701\pi$
$977$	−39.0767	−	10.4706i	−1.25018	−	0.334984i	−0.822404	+	0.568903i	$0.807368\pi$
$978$	7.37050	−	6.88837i	0.235683	−	0.220266i
$979$	−12.5859	−	7.26646i	−0.402247	−	0.232237i
$980$	3.46044	−	3.46044i	0.110540	−	0.110540i
$981$	11.2433	−	9.81742i	0.358970	−	0.313446i
$982$	−3.92133	−	14.6346i	−0.125135	−	0.467009i
$983$	5.93903	+	5.93903i	0.189426	+	0.189426i	0.795448	−	0.606022i	$-0.207236\pi$
$983$	5.93903	+	5.93903i	0.189426	+	0.189426i	−0.606022	+	0.795448i	$0.707236\pi$
$984$	7.74223	−	25.4243i	0.246813	−	0.810498i
$985$	29.3884	−	16.9674i	0.936392	−	0.540626i
$986$	−0.184607	+	0.688963i	−0.00587909	+	0.0219410i
$987$	1.42932	−	0.331652i	0.0454958	−	0.0105566i
$988$	−11.1613	−	18.5610i	−0.355087	−	0.590505i
$989$			1.65655i			0.0526752i
$990$	−36.0976	+	7.09965i	−1.14726	+	0.225642i
$991$	26.1869	+	45.3571i	0.831855	+	1.44082i	0.896565	+	0.442912i	$0.146055\pi$
$991$	26.1869	+	45.3571i	0.831855	+	1.44082i	−0.0647097	+	0.997904i	$0.520612\pi$
$992$	−27.6950	+	47.9691i	−0.879316	+	1.52302i
$993$	−8.12858	−	5.06679i	−0.257953	−	0.160790i
$994$	10.2499	−	2.74646i	0.325108	−	0.0871124i
$995$	−8.15594	+	2.18538i	−0.258561	+	0.0692811i
$996$	23.6403	+	14.7357i	0.749070	+	0.466919i
$997$	10.9459	−	18.9589i	0.346661	−	0.600435i	−0.638993	−	0.769213i	$-0.720649\pi$
$997$	10.9459	−	18.9589i	0.346661	−	0.600435i	0.985654	+	0.168778i	$0.0539820\pi$
$998$	−2.32622	−	4.02913i	−0.0736352	−	0.127540i
$999$	38.7477	−	17.4060i	1.22592	−	0.550702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cc.a.50.11	✓	112
3.2	odd	2	inner	273.2.cc.a.50.18	yes	112
13.6	odd	12	inner	273.2.cc.a.71.18	yes	112
39.32	even	12	inner	273.2.cc.a.71.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.cc.a.50.11	✓	112	1.1	even	1	trivial
273.2.cc.a.50.18	yes	112	3.2	odd	2	inner
273.2.cc.a.71.11	yes	112	39.32	even	12	inner
273.2.cc.a.71.18	yes	112	13.6	odd	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.751420 - 0.201342i) q^{2} +(-1.18266 - 1.26543i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(2.48091 - 2.48091i) q^{5} +(0.633888 + 1.18899i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.86742 + 1.86742i) q^{8} +(-0.202642 + 2.99315i) q^{9} +O(q^{10})\)	\(q+(-0.751420 - 0.201342i) q^{2} +(-1.18266 - 1.26543i) q^{3} +(-1.20796 - 0.697414i) q^{4} +(2.48091 - 2.48091i) q^{5} +(0.633888 + 1.18899i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(1.86742 + 1.86742i) q^{8} +(-0.202642 + 2.99315i) q^{9} +(-2.36372 + 1.36469i) q^{10} +(1.16287 - 4.33987i) q^{11} +(0.546068 + 2.35339i) q^{12} +(-2.59448 - 2.50374i) q^{13} +0.777928i q^{14} +(-6.07349 - 0.205359i) q^{15} +(0.367602 + 0.636705i) q^{16} +(-2.53006 + 4.38220i) q^{17} +(0.754917 - 2.20831i) q^{18} +(-4.15985 + 1.11463i) q^{19} +(-4.72705 + 1.26661i) q^{20} +(-0.916220 + 1.46988i) q^{21} +(-1.74760 + 3.02693i) q^{22} +(1.39149 + 2.41014i) q^{23} +(0.154577 - 4.57161i) q^{24} -7.30982i q^{25} +(1.44543 + 2.40374i) q^{26} +(4.02729 - 3.28344i) q^{27} +(-0.361008 + 1.34730i) q^{28} +(-0.156921 + 0.0905985i) q^{29} +(4.52240 + 1.37716i) q^{30} +(-6.69080 - 6.69080i) q^{31} +(-1.51507 - 5.65433i) q^{32} +(-6.86709 + 3.66105i) q^{33} +(2.78347 - 2.78347i) q^{34} +(-3.03848 - 1.75427i) q^{35} +(2.33225 - 3.47427i) q^{36} +(7.89628 + 2.11580i) q^{37} +3.35022 q^{38} +(-0.0999316 + 6.24420i) q^{39} +9.26580 q^{40} +(5.61219 + 1.50378i) q^{41} +(0.984415 - 0.920022i) q^{42} +(0.515494 + 0.297621i) q^{43} +(-4.43138 + 4.43138i) q^{44} +(6.92299 + 7.92846i) q^{45} +(-0.560334 - 2.09119i) q^{46} +(-0.599020 - 0.599020i) q^{47} +(0.370961 - 1.21818i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(-1.47178 + 5.49275i) q^{50} +(8.53758 - 1.98102i) q^{51} +(1.38788 + 4.83383i) q^{52} +5.43018i q^{53} +(-3.68728 + 1.65638i) q^{54} +(-7.88187 - 13.6518i) q^{55} +(1.32047 - 2.28711i) q^{56} +(6.33016 + 3.94578i) q^{57} +(0.136155 - 0.0364827i) q^{58} +(7.75661 - 2.07838i) q^{59} +(7.19330 + 4.48380i) q^{60} +(1.75531 - 3.04029i) q^{61} +(3.68046 + 6.37475i) q^{62} +(2.94361 - 0.578947i) q^{63} +3.08342i q^{64} +(-12.6482 + 0.225122i) q^{65} +(5.89720 - 1.36835i) q^{66} +(-0.450145 + 1.67996i) q^{67} +(6.11242 - 3.52901i) q^{68} +(1.40421 - 4.61121i) q^{69} +(1.92997 + 1.92997i) q^{70} +(-3.53048 - 13.1759i) q^{71} +(-5.96788 + 5.21105i) q^{72} +(0.693304 - 0.693304i) q^{73} +(-5.50742 - 3.17971i) q^{74} +(-9.25009 + 8.64501i) q^{75} +(5.80227 + 1.55471i) q^{76} -4.49297 q^{77} +(1.33231 - 4.67190i) q^{78} +0.480977 q^{79} +(2.49160 + 0.667621i) q^{80} +(-8.91787 - 1.21308i) q^{81} +(-3.91434 - 2.25995i) q^{82} +(8.15333 - 8.15333i) q^{83} +(2.13187 - 1.13656i) q^{84} +(4.59498 + 17.1487i) q^{85} +(-0.327429 - 0.327429i) q^{86} +(0.300230 + 0.0914263i) q^{87} +(10.2759 - 5.93281i) q^{88} +(0.837175 - 3.12438i) q^{89} +(-3.60574 - 7.35150i) q^{90} +(-1.74692 + 3.15409i) q^{91} -3.88179i q^{92} +(-0.553835 + 16.3797i) q^{93} +(0.329508 + 0.570724i) q^{94} +(-7.55491 + 13.0855i) q^{95} +(-5.36337 + 8.60437i) q^{96} +(-2.19811 + 0.588981i) q^{97} +(0.751420 - 0.201342i) q^{98} +(12.7542 + 4.36007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 12 q^{6}+O(q^{10}) \) 112 * q - 12 * q^6	\( 112 q - 12 q^{6} - 48 q^{10} - 32 q^{13} + 4 q^{15} + 40 q^{16} - 16 q^{18} - 8 q^{19} - 4 q^{21} - 16 q^{22} - 88 q^{24} + 24 q^{27} - 72 q^{30} + 16 q^{31} + 48 q^{34} + 12 q^{36} + 48 q^{37} + 56 q^{39} + 32 q^{40} - 28 q^{45} + 72 q^{46} + 24 q^{48} - 144 q^{52} - 108 q^{54} - 28 q^{57} - 120 q^{58} - 116 q^{60} - 48 q^{61} + 16 q^{63} + 40 q^{66} - 16 q^{67} + 72 q^{69} + 48 q^{70} + 52 q^{72} - 16 q^{73} + 60 q^{75} + 16 q^{76} - 4 q^{78} + 16 q^{79} - 20 q^{81} + 120 q^{82} + 72 q^{84} - 40 q^{85} - 24 q^{87} + 72 q^{88} + 16 q^{91} + 92 q^{93} - 96 q^{94} + 28 q^{96} + 96 q^{97} - 144 q^{99}+O(q^{100}) \) 112 * q - 12 * q^6 - 48 * q^10 - 32 * q^13 + 4 * q^15 + 40 * q^16 - 16 * q^18 - 8 * q^19 - 4 * q^21 - 16 * q^22 - 88 * q^24 + 24 * q^27 - 72 * q^30 + 16 * q^31 + 48 * q^34 + 12 * q^36 + 48 * q^37 + 56 * q^39 + 32 * q^40 - 28 * q^45 + 72 * q^46 + 24 * q^48 - 144 * q^52 - 108 * q^54 - 28 * q^57 - 120 * q^58 - 116 * q^60 - 48 * q^61 + 16 * q^63 + 40 * q^66 - 16 * q^67 + 72 * q^69 + 48 * q^70 + 52 * q^72 - 16 * q^73 + 60 * q^75 + 16 * q^76 - 4 * q^78 + 16 * q^79 - 20 * q^81 + 120 * q^82 + 72 * q^84 - 40 * q^85 - 24 * q^87 + 72 * q^88 + 16 * q^91 + 92 * q^93 - 96 * q^94 + 28 * q^96 + 96 * q^97 - 144 * q^99

Introduction

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