LMFDB - Embedded newform 520.2.ca.a.101.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(101,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 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("520.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.ca (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.20
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.a.381.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.795042 + 1.16958i) q^{2} +(0.127180 - 0.0734274i) q^{3} +(-0.735818 + 1.85972i) q^{4} -1.00000 q^{5} +(0.186992 + 0.0903689i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(-2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +O(q^{10})$	\(q+(0.795042 + 1.16958i) q^{2} +(0.127180 - 0.0734274i) q^{3} +(-0.735818 + 1.85972i) q^{4} -1.00000 q^{5} +(0.186992 + 0.0903689i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(-2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +(-0.795042 - 1.16958i) q^{10} +(-2.72562 - 4.72092i) q^{11} +(0.0429734 + 0.290549i) q^{12} +(-1.96972 + 3.01997i) q^{13} +(-0.351858 - 4.78380i) q^{14} +(-0.127180 + 0.0734274i) q^{15} +(-2.91714 - 2.73684i) q^{16} +(-0.605480 + 1.04872i) q^{17} +(-4.20079 + 0.308977i) q^{18} +(1.73602 - 3.00687i) q^{19} +(0.735818 - 1.85972i) q^{20} -0.498102 q^{21} +(3.35449 - 6.94115i) q^{22} +(3.76612 + 6.52310i) q^{23} +(-0.305653 + 0.281259i) q^{24} +1.00000 q^{25} +(-5.09809 + 0.0972636i) q^{26} +0.877962i q^{27} +(5.31528 - 4.21485i) q^{28} +(-6.10639 + 3.52552i) q^{29} +(-0.186992 - 0.0903689i) q^{30} +7.60991i q^{31} +(0.881688 - 5.58772i) q^{32} +(-0.693289 - 0.400271i) q^{33} +(-1.70794 + 0.125623i) q^{34} +(2.93738 + 1.69590i) q^{35} +(-3.70118 - 4.66750i) q^{36} +(-3.82539 - 6.62576i) q^{37} +(4.89697 - 0.360182i) q^{38} +(-0.0287604 + 0.528711i) q^{39} +(2.76009 - 0.617962i) q^{40} +(3.47189 - 2.00449i) q^{41} +(-0.396012 - 0.582568i) q^{42} +(1.45778 + 0.841651i) q^{43} +(10.7852 - 1.59517i) q^{44} +(1.48922 - 2.57940i) q^{45} +(-4.63505 + 9.59090i) q^{46} -0.231346i q^{47} +(-0.571961 - 0.133872i) q^{48} +(2.25215 + 3.90083i) q^{49} +(0.795042 + 1.16958i) q^{50} +0.177835i q^{51} +(-4.16695 - 5.88528i) q^{52} +5.16695i q^{53} +(-1.02684 + 0.698016i) q^{54} +(2.72562 + 4.72092i) q^{55} +(9.15546 + 2.86565i) q^{56} -0.509884i q^{57} +(-8.97820 - 4.33895i) q^{58} +(1.57758 - 2.73245i) q^{59} +(-0.0429734 - 0.290549i) q^{60} +(-7.73090 - 4.46344i) q^{61} +(-8.90037 + 6.05019i) q^{62} +(8.74880 - 5.05112i) q^{63} +(7.23624 - 3.41127i) q^{64} +(1.96972 - 3.01997i) q^{65} +(-0.0830466 - 1.12909i) q^{66} +(4.31199 + 7.46859i) q^{67} +(-1.50481 - 1.89769i) q^{68} +(0.957949 + 0.553072i) q^{69} +(0.351858 + 4.78380i) q^{70} +(-13.9514 - 8.05487i) q^{71} +(2.51641 - 8.03967i) q^{72} +10.1566i q^{73} +(4.70800 - 9.74184i) q^{74} +(0.127180 - 0.0734274i) q^{75} +(4.31455 + 5.44102i) q^{76} +18.4895i q^{77} +(-0.641233 + 0.386710i) q^{78} +6.72360 q^{79} +(2.91714 + 2.73684i) q^{80} +(-4.40318 - 7.62654i) q^{81} +(5.10470 + 2.46698i) q^{82} -5.31813 q^{83} +(0.366512 - 0.926332i) q^{84} +(0.605480 - 1.04872i) q^{85} +(0.174622 + 2.37414i) q^{86} +(-0.517740 + 0.896752i) q^{87} +(10.4403 + 11.3458i) q^{88} +(-8.75982 + 5.05748i) q^{89} +(4.20079 - 0.308977i) q^{90} +(10.9074 - 5.53036i) q^{91} +(-14.9023 + 2.20412i) q^{92} +(0.558775 + 0.967828i) q^{93} +(0.270576 - 0.183929i) q^{94} +(-1.73602 + 3.00687i) q^{95} +(-0.298159 - 0.775386i) q^{96} +(7.23275 + 4.17583i) q^{97} +(-2.77177 + 5.73538i) q^{98} +16.2362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	$ 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) $ 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$	$1$

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 $

$2$	0.795042	+	1.16958i	0.562179	+	0.827015i
$2$	0.795042	+	1.16958i	0.562179	+	0.827015i
$3$	0.127180	−	0.0734274i	0.0734274	−	0.0423933i	−0.462837	−	0.886444i	$-0.653168\pi$
$3$	0.127180	−	0.0734274i	0.0734274	−	0.0423933i	0.536264	+	0.844050i	$0.319835\pi$
$4$	−0.735818	+	1.85972i	−0.367909	+	0.929862i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	0.186992	+	0.0903689i	0.0763393	+	0.0368929i
$7$	−2.93738	−	1.69590i	−1.11023	−	0.640989i	−0.171338	−	0.985212i	$-0.554809\pi$
$7$	−2.93738	−	1.69590i	−1.11023	−	0.640989i	−0.938888	+	0.344223i	$0.888142\pi$
$8$	−2.76009	+	0.617962i	−0.975841	+	0.218483i
$9$	−1.48922	+	2.57940i	−0.496406	+	0.859800i
$10$	−0.795042	−	1.16958i	−0.251414	−	0.369853i
$11$	−2.72562	−	4.72092i	−0.821806	−	1.42341i	−0.904336	−	0.426821i	$-0.859633\pi$
$11$	−2.72562	−	4.72092i	−0.821806	−	1.42341i	0.0825299	−	0.996589i	$-0.473700\pi$
$12$	0.0429734	+	0.290549i	0.0124053	+	0.0838742i
$13$	−1.96972	+	3.01997i	−0.546302	+	0.837588i
$13$	−1.96972	+	3.01997i	−0.546302	+	0.837588i
$14$	−0.351858	−	4.78380i	−0.0940381	−	1.27853i
$15$	−0.127180	+	0.0734274i	−0.0328377	+	0.0189589i
$16$	−2.91714	−	2.73684i	−0.729286	−	0.684209i
$17$	−0.605480	+	1.04872i	−0.146850	+	0.254352i	−0.930062	−	0.367403i	$-0.880247\pi$
$17$	−0.605480	+	1.04872i	−0.146850	+	0.254352i	0.783211	+	0.621756i	$0.213580\pi$
$18$	−4.20079	+	0.308977i	−0.990137	+	0.0728265i
$19$	1.73602	−	3.00687i	0.398269	−	0.689823i	−0.595243	−	0.803546i	$-0.702944\pi$
$19$	1.73602	−	3.00687i	0.398269	−	0.689823i	0.993513	+	0.113723i	$0.0362776\pi$
$20$	0.735818	−	1.85972i	0.164534	−	0.415847i
$21$	−0.498102			−0.108695
$22$	3.35449	−	6.94115i	0.715180	−	1.47986i
$23$	3.76612	+	6.52310i	0.785289	+	1.36016i	0.928826	+	0.370516i	$0.120819\pi$
$23$	3.76612	+	6.52310i	0.785289	+	1.36016i	−0.143537	+	0.989645i	$0.545847\pi$
$24$	−0.305653	+	0.281259i	−0.0623912	+	0.0574118i
$25$	1.00000			0.200000
$26$	−5.09809	+	0.0972636i	−0.999818	+	0.0190750i
$27$			0.877962i			0.168964i
$28$	5.31528	−	4.21485i	1.00449	−	0.796531i
$29$	−6.10639	+	3.52552i	−1.13393	+	0.654673i	−0.944920	−	0.327302i	$-0.893860\pi$
$29$	−6.10639	+	3.52552i	−1.13393	+	0.654673i	−0.189008	+	0.981976i	$0.560527\pi$
$30$	−0.186992	−	0.0903689i	−0.0341400	−	0.0164990i
$31$			7.60991i			1.36678i	0.730054	+	0.683390i	$0.239495\pi$
$31$			7.60991i			1.36678i	−0.730054	+	0.683390i	$0.760505\pi$
$32$	0.881688	−	5.58772i	0.155862	−	0.987779i
$33$	−0.693289	−	0.400271i	−0.120686	−	0.0696782i
$34$	−1.70794	+	0.125623i	−0.292910	+	0.0215441i
$35$	2.93738	+	1.69590i	0.496508	+	0.286659i
$36$	−3.70118	−	4.66750i	−0.616863	−	0.777917i
$37$	−3.82539	−	6.62576i	−0.628890	−	1.08927i	−0.987775	−	0.155887i	$-0.950176\pi$
$37$	−3.82539	−	6.62576i	−0.628890	−	1.08927i	0.358885	−	0.933382i	$-0.383157\pi$
$38$	4.89697	−	0.360182i	0.794393	−	0.0584292i
$39$	−0.0287604	+	0.528711i	−0.00460535	+	0.0846615i
$40$	2.76009	−	0.617962i	0.436409	−	0.0977084i
$41$	3.47189	−	2.00449i	0.542218	−	0.313049i	−0.203760	−	0.979021i	$-0.565316\pi$
$41$	3.47189	−	2.00449i	0.542218	−	0.313049i	0.745977	+	0.665971i	$0.231983\pi$
$42$	−0.396012	−	0.582568i	−0.0611059	−	0.0898922i
$43$	1.45778	+	0.841651i	0.222310	+	0.128351i	0.607019	−	0.794687i	$-0.292365\pi$
$43$	1.45778	+	0.841651i	0.222310	+	0.128351i	−0.384710	+	0.923038i	$0.625698\pi$
$44$	10.7852	−	1.59517i	1.62592	−	0.240481i
$45$	1.48922	−	2.57940i	0.221999	−	0.384514i
$46$	−4.63505	+	9.59090i	−0.683401	+	1.41410i
$47$		−	0.231346i		−	0.0337452i	−0.999858	−	0.0168726i	$-0.994629\pi$
$47$		−	0.231346i		−	0.0337452i	0.999858	−	0.0168726i	$-0.00537097\pi$
$48$	−0.571961	−	0.133872i	−0.0825555	−	0.0193228i
$49$	2.25215	+	3.90083i	0.321735	+	0.557261i
$50$	0.795042	+	1.16958i	0.112436	+	0.165403i
$51$			0.177835i			0.0249019i
$52$	−4.16695	−	5.88528i	−0.577852	−	0.816141i
$53$			5.16695i			0.709735i	0.934917	+	0.354867i	$0.115474\pi$
$53$			5.16695i			0.709735i	−0.934917	+	0.354867i	$0.884526\pi$
$54$	−1.02684	+	0.698016i	−0.139736	+	0.0949879i
$55$	2.72562	+	4.72092i	0.367523	+	0.636568i
$56$	9.15546	+	2.86565i	1.22345	+	0.382938i
$57$		−	0.509884i		−	0.0675358i
$58$	−8.97820	−	4.33895i	−1.17890	−	0.569732i
$59$	1.57758	−	2.73245i	0.205383	−	0.355734i	−0.744872	−	0.667208i	$-0.767489\pi$
$59$	1.57758	−	2.73245i	0.205383	−	0.355734i	0.950255	+	0.311474i	$0.100823\pi$
$60$	−0.0429734	−	0.290549i	−0.00554784	−	0.0375097i
$61$	−7.73090	−	4.46344i	−0.989841	−	0.571485i	−0.0846140	−	0.996414i	$-0.526966\pi$
$61$	−7.73090	−	4.46344i	−0.989841	−	0.571485i	−0.905227	+	0.424929i	$0.860299\pi$
$62$	−8.90037	+	6.05019i	−1.13035	+	0.768375i
$63$	8.74880	−	5.05112i	1.10225	−	0.636382i
$64$	7.23624	−	3.41127i	0.904531	−	0.426409i
$65$	1.96972	−	3.01997i	0.244314	−	0.374581i
$66$	−0.0830466	−	1.12909i	−0.0102223	−	0.138981i
$67$	4.31199	+	7.46859i	0.526794	+	0.912434i	0.999513	+	0.0312204i	$0.00993937\pi$
$67$	4.31199	+	7.46859i	0.526794	+	0.912434i	−0.472719	+	0.881213i	$0.656727\pi$
$68$	−1.50481	−	1.89769i	−0.182485	−	0.230129i
$69$	0.957949	+	0.553072i	0.115324	+	0.0665821i
$70$	0.351858	+	4.78380i	0.0420551	+	0.571774i
$71$	−13.9514	−	8.05487i	−1.65573	−	0.955937i	−0.974652	−	0.223727i	$-0.928178\pi$
$71$	−13.9514	−	8.05487i	−1.65573	−	0.955937i	−0.681079	−	0.732210i	$-0.738489\pi$
$72$	2.51641	−	8.03967i	0.296561	−	0.947484i
$73$			10.1566i			1.18874i	0.804193	+	0.594368i	$0.202598\pi$
$73$			10.1566i			1.18874i	−0.804193	+	0.594368i	$0.797402\pi$
$74$	4.70800	−	9.74184i	0.547293	−	1.13247i
$75$	0.127180	−	0.0734274i	0.0146855	−	0.00847866i
$76$	4.31455	+	5.44102i	0.494913	+	0.624127i
$77$			18.4895i			2.10708i
$78$	−0.641233	+	0.386710i	−0.0726054	+	0.0437862i
$79$	6.72360			0.756464			0.378232	−	0.925711i	$-0.376532\pi$
$79$	6.72360			0.756464			0.378232	+	0.925711i	$0.376532\pi$
$80$	2.91714	+	2.73684i	0.326147	+	0.305988i
$81$	−4.40318	−	7.62654i	−0.489243	−	0.847393i
$82$	5.10470	+	2.46698i	0.563720	+	0.272432i
$83$	−5.31813			−0.583741			−0.291870	−	0.956458i	$-0.594278\pi$
$83$	−5.31813			−0.583741			−0.291870	+	0.956458i	$0.594278\pi$
$84$	0.366512	−	0.926332i	0.0399898	−	0.101071i
$85$	0.605480	−	1.04872i	0.0656735	−	0.113750i
$86$	0.174622	+	2.37414i	0.0188300	+	0.256010i
$87$	−0.517740	+	0.896752i	−0.0555075	+	0.0961419i
$88$	10.4403	+	11.3458i	1.11294	+	1.20947i
$89$	−8.75982	+	5.05748i	−0.928539	+	0.536092i	−0.886349	−	0.463017i	$-0.846767\pi$
$89$	−8.75982	+	5.05748i	−0.928539	+	0.536092i	−0.0421898	+	0.999110i	$0.513433\pi$
$90$	4.20079	−	0.308977i	0.442803	−	0.0325690i
$91$	10.9074	−	5.53036i	1.14340	−	0.579739i
$92$	−14.9023	+	2.20412i	−1.55368	+	0.229795i
$93$	0.558775	+	0.967828i	0.0579423	+	0.100359i
$94$	0.270576	−	0.183929i	0.0279078	−	0.0189709i
$95$	−1.73602	+	3.00687i	−0.178111	+	0.308498i
$96$	−0.298159	−	0.775386i	−0.0304307	−	0.0791375i
$97$	7.23275	+	4.17583i	0.734375	+	0.423991i	0.820020	−	0.572334i	$-0.193962\pi$
$97$	7.23275	+	4.17583i	0.734375	+	0.423991i	−0.0856459	+	0.996326i	$0.527295\pi$
$98$	−2.77177	+	5.73538i	−0.279991	+	0.579361i
$99$	16.2362			1.63180
$100$	−0.735818	+	1.85972i	−0.0735818	+	0.185972i
$101$	2.63177	−	1.51945i	0.261871	−	0.151191i	−0.363317	−	0.931666i	$-0.618356\pi$
$101$	2.63177	−	1.51945i	0.261871	−	0.151191i	0.625188	+	0.780475i	$0.285022\pi$
$102$	−0.207992	+	0.141386i	−0.0205943	+	0.0139993i
$103$	−8.79232			−0.866333			−0.433166	−	0.901314i	$-0.642604\pi$
$103$	−8.79232			−0.866333			−0.433166	+	0.901314i	$0.642604\pi$
$104$	3.57038	−	9.55261i	0.350105	−	0.936710i
$105$	0.498102			0.0486097
$106$	−6.04314	+	4.10794i	−0.586962	+	0.398998i
$107$	2.50912	−	1.44864i	0.242566	−	0.140045i	−0.373790	−	0.927513i	$-0.621942\pi$
$107$	2.50912	−	1.44864i	0.242566	−	0.140045i	0.616355	+	0.787468i	$0.288609\pi$
$108$	−1.63277	−	0.646020i	−0.157113	−	0.0621633i
$109$	10.1110			0.968455			0.484228	−	0.874942i	$-0.339101\pi$
$109$	10.1110			0.968455			0.484228	+	0.874942i	$0.339101\pi$
$110$	−3.35449	+	6.94115i	−0.319838	+	0.661813i
$111$	−0.973025	−	0.561776i	−0.0923555	−	0.0533214i
$112$	3.92737	+	12.9863i	0.371102	+	1.22709i
$113$	−1.24836	+	2.16222i	−0.117436	+	0.203405i	−0.918751	−	0.394838i	$-0.870801\pi$
$113$	−1.24836	+	2.16222i	−0.117436	+	0.203405i	0.801315	+	0.598243i	$0.204134\pi$
$114$	0.596349	−	0.405379i	0.0558532	−	0.0379673i
$115$	−3.76612	−	6.52310i	−0.351192	−	0.608283i
$116$	−2.06331	−	13.9503i	−0.191574	−	1.29526i
$117$	−4.85637	−	9.57808i	−0.448971	−	0.885494i
$118$	4.45004	−	0.327310i	0.409660	−	0.0301313i
$119$	3.55705	−	2.05367i	0.326075	−	0.188259i
$120$	0.305653	−	0.281259i	0.0279022	−	0.0256753i
$121$	−9.35803	+	16.2086i	−0.850730	+	1.47351i
$122$	−0.926056	−	12.5905i	−0.0838412	−	1.13989i
$123$	0.294370	−	0.509863i	0.0265424	−	0.0459728i
$124$	−14.1523	−	5.59950i	−1.27092	−	0.502850i
$125$	−1.00000			−0.0894427
$126$	12.8633	+	6.21654i	1.14596	+	0.553813i
$127$	0.459689	+	0.796205i	0.0407908	+	0.0706517i	0.885700	−	0.464258i	$-0.153679\pi$
$127$	0.459689	+	0.796205i	0.0407908	+	0.0706517i	−0.844909	+	0.534910i	$0.820346\pi$
$128$	9.74286	+	5.75124i	0.861155	+	0.508343i
$129$	0.247201			0.0217648
$130$	5.09809	−	0.0972636i	0.447132	−	0.00853058i
$131$		−	17.0025i		−	1.48552i	−0.669559	−	0.742759i	$-0.733517\pi$
$131$		−	17.0025i		−	1.48552i	0.669559	−	0.742759i	$-0.266483\pi$
$132$	1.25453	−	0.994800i	0.109193	−	0.0865862i
$133$	−10.1987	+	5.88821i	−0.884338	+	0.510573i
$134$	−5.30688	+	10.9810i	−0.458444	+	0.948618i
$135$		−	0.877962i		−	0.0755629i
$136$	1.02311	−	3.26874i	0.0877311	−	0.280292i
$137$	−4.21131	−	2.43140i	−0.359796	−	0.207728i	0.309195	−	0.950999i	$-0.399940\pi$
$137$	−4.21131	−	2.43140i	−0.359796	−	0.207728i	−0.668991	+	0.743270i	$0.733274\pi$
$138$	0.114749	+	1.56011i	0.00976810	+	0.132805i
$139$	2.52352	+	1.45695i	0.214042	+	0.123577i	0.603188	−	0.797599i	$-0.293897\pi$
$139$	2.52352	+	1.45695i	0.214042	+	0.123577i	−0.389147	+	0.921176i	$0.627230\pi$
$140$	−5.31528	+	4.21485i	−0.449223	+	0.356220i
$141$	−0.0169871	−	0.0294225i	−0.00143057	−	0.00247782i
$142$	−1.67119	−	22.7212i	−0.140243	−	1.90672i
$143$	19.6257	+	1.06758i	1.64119	+	0.0892759i
$144$	11.4037	−	3.44874i	0.950304	−	0.287395i
$145$	6.10639	−	3.52552i	0.507108	−	0.292779i
$146$	−11.8789	+	8.07489i	−0.983102	+	0.668282i
$147$	0.572856	+	0.330738i	0.0472483	+	0.0272788i
$148$	15.1369	−	2.23881i	1.24424	−	0.184029i
$149$	−4.82912	+	8.36428i	−0.395617	+	0.685229i	−0.993180	−	0.116593i	$-0.962803\pi$
$149$	−4.82912	+	8.36428i	−0.395617	+	0.685229i	0.597563	+	0.801822i	$0.296136\pi$
$150$	0.186992	+	0.0903689i	0.0152679	+	0.00737859i
$151$			8.82114i			0.717854i	0.933366	+	0.358927i	$0.116857\pi$
$151$			8.82114i			0.717854i	−0.933366	+	0.358927i	$0.883143\pi$
$152$	−2.93344	+	9.37203i	−0.237933	+	0.760172i
$153$	−1.80338	−	3.12355i	−0.145795	−	0.252524i
$154$	−21.6249	+	14.6999i	−1.74258	+	1.18455i
$155$		−	7.60991i		−	0.611242i
$156$	−0.962094	−	0.442521i	−0.0770291	−	0.0354301i
$157$			20.0331i			1.59882i	0.600787	+	0.799409i	$0.294854\pi$
$157$			20.0331i			1.59882i	−0.600787	+	0.799409i	$0.705146\pi$
$158$	5.34554	+	7.86377i	0.425269	+	0.625608i
$159$	0.379395	+	0.657132i	0.0300880	+	0.0521140i
$160$	−0.881688	+	5.58772i	−0.0697035	+	0.441748i
$161$		−	25.5478i		−	2.01345i
$162$	5.41911	−	11.2133i	0.425765	−	0.880998i
$163$	−0.778008	+	1.34755i	−0.0609383	+	0.105548i	−0.894885	−	0.446297i	$-0.852743\pi$
$163$	−0.778008	+	1.34755i	−0.0609383	+	0.105548i	0.833947	+	0.551845i	$0.186076\pi$
$164$	1.17313	+	7.93169i	0.0916061	+	0.619361i
$165$	0.693289	+	0.400271i	0.0539725	+	0.0311610i
$166$	−4.22814	−	6.21996i	−0.328167	−	0.482763i
$167$	−13.8670	+	8.00610i	−1.07306	+	0.619531i	−0.929015	−	0.370041i	$-0.879344\pi$
$167$	−13.8670	+	8.00610i	−1.07306	+	0.619531i	−0.144043	+	0.989571i	$0.546010\pi$
$168$	1.37481	−	0.307808i	0.106069	−	0.0237479i
$169$	−5.24042	−	11.8970i	−0.403109	−	0.915152i
$170$	1.70794	−	0.125623i	0.130993	−	0.00963481i
$171$	5.17061	+	8.95576i	0.395406	+	0.684864i
$172$	−2.63790	+	2.09177i	−0.201138	+	0.159496i
$173$	−9.59373	−	5.53894i	−0.729398	−	0.421118i	0.0888039	−	0.996049i	$-0.471696\pi$
$173$	−9.59373	−	5.53894i	−0.729398	−	0.421118i	−0.818202	+	0.574931i	$0.805029\pi$
$174$	−1.46044	+	0.107419i	−0.110716	+	0.00814338i
$175$	−2.93738	−	1.69590i	−0.222045	−	0.128198i
$176$	−4.96934	+	21.2312i	−0.374578	+	1.60036i
$177$		−	0.463350i		−	0.0348275i
$178$	−12.8795	−	6.22437i	−0.965362	−	0.466536i
$179$	−15.5388	+	8.97132i	−1.16142	+	0.670548i	−0.951645	−	0.307201i	$-0.900608\pi$
$179$	−15.5388	+	8.97132i	−1.16142	+	0.670548i	−0.209779	+	0.977749i	$0.567274\pi$
$180$	3.70118	+	4.66750i	0.275869	+	0.347895i
$181$		−	5.36242i		−	0.398585i	−0.979940	−	0.199293i	$-0.936136\pi$
$181$		−	5.36242i		−	0.398585i	0.979940	−	0.199293i	$-0.0638644\pi$
$182$	15.1400	+	8.36015i	1.12225	+	0.619695i
$183$	−1.31095			−0.0969086
$184$	−14.4259	−	15.6771i	−1.06349	−	1.15573i
$185$	3.82539	+	6.62576i	0.281248	+	0.487136i
$186$	−0.687698	+	1.42299i	−0.0504245	+	0.104339i
$187$	6.60124			0.482730
$188$	0.430239	+	0.170228i	0.0313784	+	0.0124152i
$189$	1.48893	−	2.57891i	0.108304	−	0.187588i
$190$	−4.89697	+	0.360182i	−0.355263	+	0.0261303i
$191$	9.01532	−	15.6150i	0.652325	−	1.12986i	−0.330232	−	0.943900i	$-0.607127\pi$
$191$	9.01532	−	15.6150i	0.652325	−	1.12986i	0.982557	−	0.185961i	$-0.0595397\pi$
$192$	0.669825	−	0.965184i	0.0483404	−	0.0696561i
$193$	10.9903	−	6.34528i	0.791102	−	0.456743i	−0.0492484	−	0.998787i	$-0.515683\pi$
$193$	10.9903	−	6.34528i	0.791102	−	0.456743i	0.840350	+	0.542044i	$0.182349\pi$
$194$	0.866384	+	11.7792i	0.0622028	+	0.845698i
$195$	0.0287604	−	0.528711i	0.00205957	−	0.0378618i
$196$	−8.91164	+	1.31807i	−0.636545	+	0.0941477i
$197$	11.6822	+	20.2341i	0.832321	+	1.44162i	0.896193	+	0.443664i	$0.146322\pi$
$197$	11.6822	+	20.2341i	0.832321	+	1.44162i	−0.0638720	+	0.997958i	$0.520345\pi$
$198$	12.9084	+	18.9894i	0.917362	+	1.34952i
$199$	4.95670	−	8.58525i	0.351371	−	0.608593i	−0.635119	−	0.772414i	$-0.719049\pi$
$199$	4.95670	−	8.58525i	0.351371	−	0.608593i	0.986490	+	0.163822i	$0.0523822\pi$
$200$	−2.76009	+	0.617962i	−0.195168	+	0.0436965i
$201$	1.09680	+	0.633237i	0.0773622	+	0.0446651i
$202$	3.86948	+	1.87002i	0.272255	+	0.131574i
$203$	23.9157			1.67855
$204$	−0.330724	−	0.130854i	−0.0231553	−	0.00916164i
$205$	−3.47189	+	2.00449i	−0.242487	+	0.140000i
$206$	−6.99026	−	10.2833i	−0.487034	−	0.716470i
$207$	−22.4343			−1.55929
$208$	14.0111	−	3.41889i	0.971496	−	0.237057i
$209$	−18.9269			−1.30920
$210$	0.396012	+	0.582568i	0.0273274	+	0.0402010i
$211$	2.12986	−	1.22968i	0.146626	−	0.0846544i	−0.424892	−	0.905244i	$-0.639688\pi$
$211$	2.12986	−	1.22968i	0.146626	−	0.0846544i	0.571518	+	0.820590i	$0.306355\pi$
$212$	−9.60909	−	3.80193i	−0.659955	−	0.261118i
$213$	−2.36579			−0.162101
$214$	3.68915	+	1.78288i	0.252185	+	0.121875i
$215$	−1.45778	−	0.841651i	−0.0994199	−	0.0574001i
$216$	−0.542547	−	2.42326i	−0.0369157	−	0.164882i
$217$	12.9056	−	22.3532i	0.876091	−	1.51743i
$218$	8.03864	+	11.8256i	0.544446	+	0.800928i
$219$	0.745770	+	1.29171i	0.0503944	+	0.0872857i
$220$	−10.7852	+	1.59517i	−0.727135	+	0.107546i
$221$	−1.97448	−	3.89422i	−0.132818	−	0.261953i
$222$	−0.116555	−	1.58466i	−0.00782267	−	0.106356i
$223$	1.94858	−	1.12501i	0.130487	−	0.0753365i	−0.433336	−	0.901233i	$-0.642664\pi$
$223$	1.94858	−	1.12501i	0.130487	−	0.0753365i	0.563822	+	0.825896i	$0.309330\pi$
$224$	−12.0661	+	14.9180i	−0.806198	+	0.996752i
$225$	−1.48922	+	2.57940i	−0.0992811	+	0.171960i
$226$	−3.52138	+	0.259004i	−0.234239	+	0.0172287i
$227$	0.362545	−	0.627947i	0.0240630	−	0.0416783i	−0.853743	−	0.520694i	$-0.825673\pi$
$227$	0.362545	−	0.627947i	0.0240630	−	0.0416783i	0.877806	+	0.479016i	$0.159006\pi$
$228$	0.948244	+	0.375182i	0.0627990	+	0.0248470i
$229$	−1.05863			−0.0699562			−0.0349781	−	0.999388i	$-0.511136\pi$
$229$	−1.05863			−0.0699562			−0.0349781	+	0.999388i	$0.511136\pi$
$230$	4.63505	−	9.59090i	0.305626	−	0.632405i
$231$	1.35764	+	2.35150i	0.0893260	+	0.154717i
$232$	14.6756	−	13.5043i	0.963498	−	0.886600i
$233$	15.6477			1.02511			0.512557	−	0.858653i	$-0.328698\pi$
$233$	15.6477			1.02511			0.512557	+	0.858653i	$0.328698\pi$
$234$	7.34128	−	13.2949i	0.479915	−	0.869112i
$235$			0.231346i			0.0150913i
$236$	3.92078	+	4.94444i	0.255221	+	0.321856i
$237$	0.855108	−	0.493697i	0.0555452	−	0.0320690i
$238$	5.22992	+	2.52750i	0.339006	+	0.163833i
$239$		−	27.2609i		−	1.76336i	−0.471846	−	0.881681i	$-0.656412\pi$
$239$		−	27.2609i		−	1.76336i	0.471846	−	0.881681i	$-0.343588\pi$
$240$	0.571961	+	0.133872i	0.0369199	+	0.00864143i
$241$	−0.202491	−	0.116908i	−0.0130436	−	0.00753071i	0.493464	−	0.869766i	$-0.335730\pi$
$241$	−0.202491	−	0.116908i	−0.0130436	−	0.00753071i	−0.506508	+	0.862235i	$0.669064\pi$
$242$	−26.3972	+	1.94157i	−1.69688	+	0.124809i
$243$	−3.40100	−	1.96357i	−0.218175	−	0.125963i
$244$	13.9893	−	11.0931i	0.895573	−	0.710161i
$245$	−2.25215	−	3.90083i	−0.143884	−	0.249215i
$246$	0.830360	−	0.0610746i	0.0529418	−	0.00389398i
$247$	5.66118	+	11.1654i	0.360212	+	0.710437i
$248$	−4.70264	−	21.0041i	−0.298618	−	1.33376i
$249$	−0.676360	+	0.390497i	−0.0428626	+	0.0247467i
$250$	−0.795042	−	1.16958i	−0.0502828	−	0.0739705i
$251$	−21.0067	−	12.1283i	−1.32593	−	0.765528i	−0.341266	−	0.939967i	$-0.610856\pi$
$251$	−21.0067	−	12.1283i	−1.32593	−	0.765528i	−0.984668	+	0.174438i	$0.944189\pi$
$252$	2.95617	+	19.9871i	0.186221	+	1.25907i
$253$	20.5300	−	35.5590i	1.29071	−	2.23558i
$254$	−0.565750	+	1.17066i	−0.0354983	+	0.0734536i
$255$		−	0.177835i		−	0.0111365i
$256$	1.01946	+	15.9675i	0.0637163	+	0.997968i
$257$	−11.3954	−	19.7373i	−0.710823	−	1.23118i	−0.964549	−	0.263905i	$-0.914990\pi$
$257$	−11.3954	−	19.7373i	−0.710823	−	1.23118i	0.253726	−	0.967276i	$-0.418344\pi$
$258$	0.196535	+	0.289120i	0.0122357	+	0.0179998i
$259$			25.9499i			1.61245i
$260$	4.16695	+	5.88528i	0.258423	+	0.364990i
$261$		−	21.0011i		−	1.29993i
$262$	19.8857	−	13.5177i	1.22855	−	0.835127i
$263$	−9.80414	−	16.9813i	−0.604549	−	1.04711i	−0.992123	−	0.125271i	$-0.960020\pi$
$263$	−9.80414	−	16.9813i	−0.604549	−	1.04711i	0.387573	−	0.921839i	$-0.373313\pi$
$264$	2.16090	+	0.676358i	0.132994	+	0.0416270i
$265$		−	5.16695i		−	0.317403i
$266$	−14.9951	−	7.24677i	−0.919408	−	0.444328i
$267$	−0.742716	+	1.28642i	−0.0454535	+	0.0787277i
$268$	−17.0624	+	2.52359i	−1.04225	+	0.154153i
$269$	−17.9620	−	10.3704i	−1.09517	−	0.632294i	−0.160218	−	0.987082i	$-0.551220\pi$
$269$	−17.9620	−	10.3704i	−1.09517	−	0.632294i	−0.934947	+	0.354788i	$0.884553\pi$
$270$	1.02684	−	0.698016i	0.0624917	−	0.0424799i
$271$	22.3436	−	12.9001i	1.35728	−	0.783624i	0.368020	−	0.929818i	$-0.380036\pi$
$271$	22.3436	−	12.9001i	1.35728	−	0.783624i	0.989256	+	0.146194i	$0.0467024\pi$
$272$	4.63645	−	1.40217i	0.281126	−	0.0850193i
$273$	0.981120	−	1.50425i	0.0593801	−	0.0910414i
$274$	−0.504457	−	6.85851i	−0.0304754	−	0.414338i
$275$	−2.72562	−	4.72092i	−0.164361	−	0.284682i
$276$	−1.73344	+	1.37456i	−0.104341	+	0.0827388i
$277$	−1.31522	−	0.759340i	−0.0790237	−	0.0456243i	0.459967	−	0.887936i	$-0.347861\pi$
$277$	−1.31522	−	0.759340i	−0.0790237	−	0.0456243i	−0.538991	+	0.842311i	$0.681194\pi$
$278$	0.302283	+	4.10978i	0.0181297	+	0.246488i
$279$	−19.6290	−	11.3328i	−1.17516	−	0.678477i
$280$	−9.15546	−	2.86565i	−0.547143	−	0.171255i
$281$			20.1172i			1.20009i	0.799967	+	0.600045i	$0.204851\pi$
$281$			20.1172i			1.20009i	−0.799967	+	0.600045i	$0.795149\pi$
$282$	0.0209064	−	0.0432598i	0.00124496	−	0.00257609i
$283$	−7.96718	+	4.59985i	−0.473599	+	0.273433i	−0.717745	−	0.696306i	$-0.754826\pi$
$283$	−7.96718	+	4.59985i	−0.473599	+	0.273433i	0.244146	+	0.969739i	$0.421492\pi$
$284$	25.2455	−	20.0189i	1.49805	−	1.18790i
$285$			0.509884i			0.0302029i
$286$	14.3546	+	23.8026i	0.848808	+	1.40747i
$287$	−13.5977			−0.802646
$288$	13.0999	+	10.5956i	0.771921	+	0.624349i
$289$	7.76679	+	13.4525i	0.456870	+	0.791322i
$290$	8.97820	+	4.33895i	0.527218	+	0.254792i
$291$	1.22648			0.0718976
$292$	−18.8884	−	7.47338i	−1.10536	−	0.437346i
$293$	−8.01484	+	13.8821i	−0.468232	+	0.811001i	−0.999341	−	0.0363022i	$-0.988442\pi$
$293$	−8.01484	+	13.8821i	−0.468232	+	0.811001i	0.531109	+	0.847303i	$0.321775\pi$
$294$	0.0686203	+	0.932949i	0.00400201	+	0.0544107i
$295$	−1.57758	+	2.73245i	−0.0918501	+	0.159089i
$296$	14.6529	+	15.9238i	0.851683	+	0.925552i
$297$	4.14478	−	2.39299i	0.240505	−	0.138855i
$298$	−13.6220	+	1.00193i	−0.789102	+	0.0580400i
$299$	−27.1178	−	1.47513i	−1.56826	−	0.0853090i
$300$	0.0429734	+	0.290549i	0.00248107	+	0.0167748i
$301$	−2.85471	−	4.94450i	−0.164543	−	0.284996i
$302$	−10.3170	+	7.01317i	−0.593677	+	0.403563i
$303$	0.223139	−	0.386487i	0.0128190	−	0.0222031i
$304$	−13.2935	+	4.02028i	−0.762435	+	0.230579i
$305$	7.73090	+	4.46344i	0.442670	+	0.255576i
$306$	2.21947	−	4.59254i	0.126878	−	0.262538i
$307$	−29.2653			−1.67026			−0.835130	−	0.550053i	$-0.814608\pi$
$307$	−29.2653			−1.67026			−0.835130	+	0.550053i	$0.814608\pi$
$308$	−34.3854	−	13.6049i	−1.95929	−	0.775212i
$309$	−1.11821	+	0.645597i	−0.0636125	+	0.0367267i
$310$	8.90037	−	6.05019i	0.505507	−	0.343628i
$311$	15.3665			0.871354			0.435677	−	0.900103i	$-0.356509\pi$
$311$	15.3665			0.871354			0.435677	+	0.900103i	$0.356509\pi$
$312$	−0.247342	−	1.47706i	−0.0140030	−	0.0836223i
$313$	−8.88208			−0.502045			−0.251022	−	0.967981i	$-0.580767\pi$
$313$	−8.88208			−0.502045			−0.251022	+	0.967981i	$0.580767\pi$
$314$	−23.4303	+	15.9272i	−1.32225	+	0.898823i
$315$	−8.74880	+	5.05112i	−0.492939	+	0.284598i
$316$	−4.94735	+	12.5040i	−0.278310	+	0.703407i
$317$	−3.82033			−0.214571			−0.107285	−	0.994228i	$-0.534216\pi$
$317$	−3.82033			−0.214571			−0.107285	+	0.994228i	$0.534216\pi$
$318$	−0.466931	+	0.966179i	−0.0261842	+	0.0541807i
$319$	33.2874	+	19.2185i	1.86374	+	1.07603i
$320$	−7.23624	+	3.41127i	−0.404518	+	0.190696i
$321$	0.212740	−	0.368476i	0.0118740	−	0.0205663i
$322$	29.8801	−	20.3116i	1.66515	−	1.13192i
$323$	2.10225	+	3.64120i	0.116972	+	0.202602i
$324$	17.4232	−	2.57696i	0.967955	−	0.143165i
$325$	−1.96972	+	3.01997i	−0.109260	+	0.167518i
$326$	−2.19461	+	0.161418i	−0.121548	+	0.00894011i
$327$	1.28591	−	0.742422i	0.0711112	−	0.0410560i
$328$	−8.34403	+	7.67809i	−0.460722	+	0.423952i
$329$	−0.392339	+	0.679550i	−0.0216303	+	0.0374648i
$330$	0.0830466	+	1.12909i	0.00457156	+	0.0621542i
$331$	3.28900	−	5.69671i	0.180780	−	0.313120i	−0.761367	−	0.648322i	$-0.775471\pi$
$331$	3.28900	−	5.69671i	0.180780	−	0.313120i	0.942146	+	0.335202i	$0.108805\pi$
$332$	3.91318	−	9.89025i	0.214763	−	0.542798i
$333$	22.7873			1.24874
$334$	−20.3886	−	9.85330i	−1.11561	−	0.539149i
$335$	−4.31199	−	7.46859i	−0.235589	−	0.408053i
$336$	1.45303	+	1.36322i	0.0792695	+	0.0743699i
$337$	34.4718			1.87780			0.938898	−	0.344196i	$-0.111848\pi$
$337$	34.4718			1.87780			0.938898	+	0.344196i	$0.111848\pi$
$338$	9.74807	−	15.5877i	0.530225	−	0.847857i
$339$			0.366655i			0.0199140i
$340$	1.50481	+	1.89769i	0.0816098	+	0.102917i
$341$	35.9257	−	20.7417i	1.94549	−	1.12323i
$342$	−6.36359	+	13.1676i	−0.344104	+	0.712023i
$343$			8.46494i			0.457064i
$344$	−4.54373	−	1.42218i	−0.244981	−	0.0766789i
$345$	−0.957949	−	0.553072i	−0.0515742	−	0.0297764i
$346$	−1.14920	−	15.6243i	−0.0617813	−	0.839967i
$347$	2.18837	+	1.26345i	0.117478	+	0.0678258i	0.557587	−	0.830118i	$-0.311727\pi$
$347$	2.18837	+	1.26345i	0.117478	+	0.0678258i	−0.440110	+	0.897944i	$0.645060\pi$
$348$	−1.28675	−	1.62270i	−0.0689770	−	0.0869858i
$349$	1.81444	+	3.14271i	0.0971249	+	0.168225i	0.910493	−	0.413523i	$-0.135702\pi$
$349$	1.81444	+	3.14271i	0.0971249	+	0.168225i	−0.813369	+	0.581749i	$0.802369\pi$
$350$	−0.351858	−	4.78380i	−0.0188076	−	0.255705i
$351$	−2.65142	−	1.72934i	−0.141522	−	0.0923052i
$352$	−28.7823	+	11.0676i	−1.53410	+	0.589907i
$353$	−28.5797	+	16.5005i	−1.52114	+	0.878232i	−0.521454	+	0.853279i	$0.674610\pi$
$353$	−28.5797	+	16.5005i	−1.52114	+	0.878232i	−0.999689	+	0.0249532i	$0.992056\pi$
$354$	0.541923	−	0.368382i	0.0288029	−	0.0195793i
$355$	13.9514	+	8.05487i	0.740465	+	0.427508i
$356$	−2.95989	−	20.0122i	−0.156874	−	1.06065i
$357$	0.301591	−	0.522370i	0.0159619	−	0.0276468i
$358$	−22.8466	−	11.0412i	−1.20748	−	0.583547i
$359$			3.95113i			0.208533i	0.994549	+	0.104266i	$0.0332494\pi$
$359$			3.95113i			0.208533i	−0.994549	+	0.104266i	$0.966751\pi$
$360$	−2.51641	+	8.03967i	−0.132626	+	0.423728i
$361$	3.47250	+	6.01454i	0.182763	+	0.316555i
$362$	6.27176	−	4.26334i	0.329636	−	0.224076i
$363$			2.74854i			0.144261i
$364$	2.25910	+	24.3540i	0.118409	+	1.27650i
$365$		−	10.1566i		−	0.531619i
$366$	−1.04226	−	1.53326i	−0.0544800	−	0.0801449i
$367$	0.897482	+	1.55448i	0.0468482	+	0.0811434i	0.888499	−	0.458879i	$-0.151749\pi$
$367$	0.897482	+	1.55448i	0.0468482	+	0.0811434i	−0.841650	+	0.540023i	$0.818416\pi$
$368$	6.86636	−	29.3361i	0.357934	−	1.52925i
$369$			11.9405i			0.621598i
$370$	−4.70800	+	9.74184i	−0.244757	+	0.506454i
$371$	8.76262	−	15.1773i	0.454933	−	0.787966i
$372$	−2.21105	+	0.327023i	−0.114638	+	0.0169554i
$373$	26.1119	+	15.0757i	1.35202	+	0.780591i	0.988533	−	0.151006i	$-0.0482514\pi$
$373$	26.1119	+	15.0757i	1.35202	+	0.780591i	0.363491	+	0.931598i	$0.381585\pi$
$374$	5.24826	+	7.72065i	0.271381	+	0.399225i
$375$	−0.127180	+	0.0734274i	−0.00656755	+	0.00379177i
$376$	0.142963	+	0.638536i	0.00737275	+	0.0329300i
$377$	1.38089	−	25.3854i	0.0711197	−	1.30741i
$378$	4.20000	−	0.308918i	0.216024	−	0.0158890i
$379$	2.28113	+	3.95103i	0.117174	+	0.202951i	0.918647	−	0.395080i	$-0.129283\pi$
$379$	2.28113	+	3.95103i	0.117174	+	0.202951i	−0.801473	+	0.598031i	$0.795950\pi$
$380$	−4.31455	−	5.44102i	−0.221332	−	0.279118i
$381$	0.116926	+	0.0675075i	0.00599033	+	0.00345852i
$382$	25.4305	−	1.87046i	1.30114	−	0.0957011i
$383$	−9.70267	−	5.60184i	−0.495783	−	0.286241i	0.231187	−	0.972909i	$-0.425739\pi$
$383$	−9.70267	−	5.60184i	−0.495783	−	0.286241i	−0.726970	+	0.686669i	$0.759072\pi$
$384$	1.66139	+	0.0160501i	0.0847827	+	0.000819054i
$385$		−	18.4895i		−	0.942313i
$386$	16.1591	+	7.80928i	0.822475	+	0.397482i
$387$	−4.34191	+	2.50680i	−0.220712	+	0.127428i
$388$	−13.0879	+	10.3783i	−0.664436	+	0.526877i
$389$			34.4332i			1.74583i	0.487872	+	0.872915i	$0.337773\pi$
$389$			34.4332i			1.74583i	−0.487872	+	0.872915i	$0.662227\pi$
$390$	0.641233	−	0.386710i	0.0324701	−	0.0195818i
$391$	−9.12123			−0.461280
$392$	−8.62670	−	9.37492i	−0.435714	−	0.473505i
$393$	−1.24845	−	2.16238i	−0.0629760	−	0.109078i
$394$	−14.3775	+	29.7502i	−0.724330	+	1.49879i
$395$	−6.72360			−0.338301
$396$	−11.9469	+	30.1948i	−0.600353	+	1.51735i
$397$	11.9556	−	20.7078i	0.600037	−	1.03929i	−0.392778	−	0.919633i	$-0.628486\pi$
$397$	11.9556	−	20.7078i	0.600037	−	1.03929i	0.992815	−	0.119661i	$-0.0381807\pi$
$398$	13.9819	−	1.02840i	0.700849	−	0.0515488i
$399$	−0.864712	+	1.49773i	−0.0432898	+	0.0749801i
$400$	−2.91714	−	2.73684i	−0.145857	−	0.136842i
$401$	−33.1268	+	19.1258i	−1.65427	+	0.955096i	−0.678989	+	0.734148i	$0.737582\pi$
$401$	−33.1268	+	19.1258i	−1.65427	+	0.955096i	−0.975286	+	0.220948i	$0.929085\pi$
$402$	0.131381	+	1.78624i	0.00655271	+	0.0890895i
$403$	−22.9817	−	14.9894i	−1.14480	−	0.746674i
$404$	0.889258	+	6.01240i	0.0442422	+	0.299128i
$405$	4.40318	+	7.62654i	0.218796	+	0.378966i
$406$	19.0140	+	27.9713i	0.943649	+	1.38819i
$407$	−20.8531	+	36.1187i	−1.03365	+	1.79034i
$408$	−0.109896	−	0.490842i	−0.00544064	−	0.0243003i
$409$	−26.6649	−	15.3950i	−1.31850	−	0.761234i	−0.335009	−	0.942215i	$-0.608739\pi$
$409$	−26.6649	−	15.3950i	−1.31850	−	0.761234i	−0.983487	+	0.180981i	$0.942073\pi$
$410$	−5.10470	−	2.46698i	−0.252103	−	0.121835i
$411$	−0.714125			−0.0352252
$412$	6.46954	−	16.3513i	0.318732	−	0.805570i
$413$	−9.26790	+	5.35083i	−0.456044	+	0.263297i
$414$	−17.8362	−	26.2386i	−0.876600	−	1.28956i
$415$	5.31813			0.261057
$416$	15.1381	+	13.6689i	0.742205	+	0.670173i
$417$	0.427921			0.0209554
$418$	−15.0477	−	22.1364i	−0.736005	−	1.08273i
$419$	4.72278	−	2.72670i	0.230723	−	0.133208i	−0.380183	−	0.924911i	$-0.624139\pi$
$419$	4.72278	−	2.72670i	0.230723	−	0.133208i	0.610905	+	0.791704i	$0.290806\pi$
$420$	−0.366512	+	0.926332i	−0.0178840	+	0.0452003i
$421$	−27.2961			−1.33033			−0.665166	−	0.746696i	$-0.731639\pi$
$421$	−27.2961			−1.33033			−0.665166	+	0.746696i	$0.731639\pi$
$422$	3.13153	+	1.51339i	0.152440	+	0.0736707i
$423$	0.596732	+	0.344524i	0.0290141	+	0.0167513i
$424$	−3.19298	−	14.2613i	−0.155065	−	0.692588i
$425$	−0.605480	+	1.04872i	−0.0293701	+	0.0508705i
$426$	−1.88090	−	2.76697i	−0.0911300	−	0.134060i
$427$	15.1391	+	26.2217i	0.732632	+	1.26896i
$428$	0.847816	+	5.73220i	0.0409807	+	0.277076i
$429$	2.57439	−	1.30529i	0.124293	−	0.0630200i
$430$	−0.174622	−	2.37414i	−0.00842104	−	0.114491i
$431$	−9.49630	+	5.48269i	−0.457421	+	0.264092i	−0.710959	−	0.703233i	$-0.751739\pi$
$431$	−9.49630	+	5.48269i	−0.457421	+	0.264092i	0.253538	+	0.967325i	$0.418406\pi$
$432$	2.40284	−	2.56114i	0.115607	−	0.123223i
$433$	−18.5815	+	32.1841i	−0.892969	+	1.54667i	−0.0566711	+	0.998393i	$0.518049\pi$
$433$	−18.5815	+	32.1841i	−0.892969	+	1.54667i	−0.836298	+	0.548275i	$0.815285\pi$
$434$	36.4043	−	2.67761i	1.74746	−	0.128529i
$435$	0.517740	−	0.896752i	0.0248237	−	0.0429960i
$436$	−7.43983	+	18.8036i	−0.356303	+	0.900530i
$437$	26.1521			1.25103
$438$	−0.917837	+	1.89920i	−0.0438559	+	0.0907472i
$439$	14.1456	+	24.5009i	0.675134	+	1.16937i	0.976430	+	0.215835i	$0.0692474\pi$
$439$	14.1456	+	24.5009i	0.675134	+	1.16937i	−0.301296	+	0.953531i	$0.597419\pi$
$440$	−10.4403	−	11.3458i	−0.497723	−	0.540892i
$441$	−13.4157			−0.638844
$442$	2.98479	−	5.40537i	0.141972	−	0.257107i
$443$			28.1253i			1.33627i	0.744039	+	0.668137i	$0.232908\pi$
$443$			28.1253i			1.33627i	−0.744039	+	0.668137i	$0.767092\pi$
$444$	1.76072	−	1.39619i	0.0835600	−	0.0662604i
$445$	8.75982	−	5.05748i	0.415255	−	0.239748i
$446$	2.86499	+	1.38458i	0.135661	+	0.0655618i
$447$			1.41836i			0.0670861i
$448$	−27.0408	−	2.25173i	−1.27756	−	0.106384i
$449$	1.91654	+	1.10651i	0.0904470	+	0.0522196i	0.544541	−	0.838734i	$-0.316704\pi$
$449$	1.91654	+	1.10651i	0.0904470	+	0.0522196i	−0.454094	+	0.890954i	$0.650037\pi$
$450$	−4.20079	+	0.308977i	−0.198027	+	0.0145653i
$451$	−18.9261	−	10.9270i	−0.891195	−	0.514532i
$452$	−3.10257	−	3.91260i	−0.145933	−	0.184033i
$453$	0.647713	+	1.12187i	0.0304322	+	0.0527102i
$454$	1.02267	−	0.0752195i	0.0479963	−	0.00353022i
$455$	−10.9074	+	5.53036i	−0.511346	+	0.259267i
$456$	0.315089	+	1.40733i	0.0147554	+	0.0659042i
$457$	28.0799	−	16.2119i	1.31352	−	0.758363i	0.330845	−	0.943685i	$-0.392666\pi$
$457$	28.0799	−	16.2119i	1.31352	−	0.758363i	0.982678	+	0.185322i	$0.0593328\pi$
$458$	−0.841654	−	1.23815i	−0.0393279	−	0.0578549i
$459$	−0.920738	−	0.531588i	−0.0429764	−	0.0248124i
$460$	14.9023	−	2.20412i	0.694825	−	0.102768i
$461$	−8.62585	+	14.9404i	−0.401746	+	0.695844i	−0.993937	−	0.109954i	$-0.964930\pi$
$461$	−8.62585	+	14.9404i	−0.401746	+	0.695844i	0.592191	+	0.805798i	$0.298263\pi$
$462$	−1.67088	+	3.45740i	−0.0777362	+	0.160853i
$463$		−	7.21332i		−	0.335232i	−0.985852	−	0.167616i	$-0.946393\pi$
$463$		−	7.21332i		−	0.335232i	0.985852	−	0.167616i	$-0.0536068\pi$
$464$	27.4620	+	6.42771i	1.27489	+	0.298399i
$465$	−0.558775	−	0.967828i	−0.0259126	−	0.0448819i
$466$	12.4406	+	18.3012i	0.576298	+	0.847785i
$467$			14.9377i			0.691234i	0.938376	+	0.345617i	$0.112330\pi$
$467$			14.9377i			0.691234i	−0.938376	+	0.345617i	$0.887670\pi$
$468$	21.3860	−	1.98378i	0.988567	−	0.0917001i
$469$		−	29.2508i		−	1.35068i
$470$	−0.270576	+	0.183929i	−0.0124808	+	0.00848403i
$471$	1.47098	+	2.54781i	0.0677792	+	0.117397i
$472$	−2.66572	+	8.51669i	−0.122700	+	0.392013i
$473$		−	9.17609i		−	0.421917i
$474$	1.25726	+	0.607604i	0.0577480	+	0.0279082i
$475$	1.73602	−	3.00687i	0.0796539	−	0.137965i
$476$	1.20191	+	8.12626i	0.0550893	+	0.372466i
$477$	−13.3276	−	7.69471i	−0.610230	−	0.352316i
$478$	31.8837	−	21.6736i	1.45833	−	0.991326i
$479$	25.2108	−	14.5554i	1.15191	−	0.665055i	0.202558	−	0.979270i	$-0.435075\pi$
$479$	25.2108	−	14.5554i	1.15191	−	0.665055i	0.949352	+	0.314215i	$0.101741\pi$
$480$	0.298159	+	0.775386i	0.0136090	+	0.0353914i
$481$	27.5445	+	1.49835i	1.25592	+	0.0683187i
$482$	−0.0242556	−	0.329775i	−0.00110481	−	0.0150208i
$483$	−1.87591	−	3.24917i	−0.0853568	−	0.147842i
$484$	−23.2577	−	29.3299i	−1.05717	−	1.33318i
$485$	−7.23275	−	4.17583i	−0.328422	−	0.189615i
$486$	−0.407394	−	5.53886i	−0.0184798	−	0.251248i
$487$	−3.13837	−	1.81194i	−0.142213	−	0.0821069i	0.427205	−	0.904155i	$-0.359498\pi$
$487$	−3.13837	−	1.81194i	−0.142213	−	0.0821069i	−0.569418	+	0.822048i	$0.692832\pi$
$488$	24.0963	+	7.54211i	1.09079	+	0.341415i
$489$			0.228508i			0.0103335i
$490$	2.77177	−	5.73538i	0.125216	−	0.259098i
$491$	−23.9285	+	13.8151i	−1.07988	+	0.623468i	−0.930863	−	0.365368i	$-0.880943\pi$
$491$	−23.9285	+	13.8151i	−1.07988	+	0.623468i	−0.149014	+	0.988835i	$0.547610\pi$
$492$	0.731602	+	0.922613i	0.0329832	+	0.0415946i
$493$		−	8.53853i		−	0.384556i
$494$	−8.55791	+	15.4981i	−0.385039	+	0.697294i
$495$	−16.2362			−0.729762
$496$	20.8271	−	22.1992i	0.935163	−	0.996773i
$497$	27.3205	+	47.3204i	1.22549	+	2.12261i
$498$	−0.994450	−	0.480594i	−0.0445624	−	0.0215359i
$499$	12.0413			0.539043			0.269521	−	0.962994i	$-0.413134\pi$
$499$	12.0413			0.539043			0.269521	+	0.962994i	$0.413134\pi$
$500$	0.735818	−	1.85972i	0.0329068	−	0.0831694i
$501$	−1.17573	+	2.03643i	−0.0525279	+	0.0909810i
$502$	−2.51632	−	34.2115i	−0.112309	−	1.52693i
$503$	−3.68212	+	6.37762i	−0.164178	+	0.284364i	−0.936363	−	0.351033i	$-0.885830\pi$
$503$	−3.68212	+	6.37762i	−0.164178	+	0.284364i	0.772185	+	0.635397i	$0.219164\pi$
$504$	−21.0261	+	19.3480i	−0.936578	+	0.861829i
$505$	−2.63177	+	1.51945i	−0.117112	+	0.0676147i
$506$	57.9112	−	4.25949i	2.57447	−	0.189357i
$507$	−1.54004	−	1.12827i	−0.0683956	−	0.0501081i
$508$	−1.81897	+	0.269033i	−0.0807037	+	0.0119364i
$509$	1.87496	+	3.24753i	0.0831063	+	0.143944i	0.904583	−	0.426298i	$-0.140183\pi$
$509$	1.87496	+	3.24753i	0.0831063	+	0.143944i	−0.821476	+	0.570243i	$0.806849\pi$
$510$	0.207992	−	0.141386i	0.00921004	−	0.00626070i
$511$	17.2245	−	29.8337i	0.761967	−	1.31977i
$512$	−17.8647	+	13.8872i	−0.789515	+	0.613731i
$513$	2.63991	+	1.52416i	0.116555	+	0.0672931i
$514$	14.0245	−	29.0197i	0.618596	−	1.28001i
$515$	8.79232			0.387436
$516$	−0.181895	+	0.459725i	−0.00800747	+	0.0202383i
$517$	−1.09216	+	0.630561i	−0.0480333	+	0.0277320i
$518$	−30.3504	+	20.6312i	−1.33352	+	0.906484i
$519$	−1.62684			−0.0714104
$520$	−3.57038	+	9.55261i	−0.156572	+	0.418910i
$521$	45.4889			1.99290			0.996452	−	0.0841592i	$-0.0268204\pi$
$521$	45.4889			1.99290			0.996452	+	0.0841592i	$0.0268204\pi$
$522$	24.5624	−	16.6967i	1.07507	−	0.730796i
$523$	29.8587	−	17.2390i	1.30563	−	0.753807i	0.324268	−	0.945965i	$-0.394882\pi$
$523$	29.8587	−	17.2390i	1.30563	−	0.753807i	0.981364	+	0.192158i	$0.0615487\pi$
$524$	31.6200	+	12.5108i	1.38133	+	0.546535i
$525$	−0.498102			−0.0217389
$526$	12.0662	−	24.9675i	0.526111	−	1.08864i
$527$	−7.98068	−	4.60765i	−0.347644	−	0.200712i
$528$	0.926949	+	3.06507i	0.0403403	+	0.133390i
$529$	−16.8673	+	29.2149i	−0.733359	+	1.27021i
$530$	6.04314	−	4.10794i	0.262497	−	0.178437i
$531$	4.69871	+	8.13841i	0.203907	+	0.353177i
$532$	−3.44608	−	23.2994i	−0.149406	−	1.01016i
$533$	−0.785130	+	14.4333i	−0.0340078	+	0.625175i
$534$	−2.09506	+	0.154096i	−0.0906620	+	0.00666837i
$535$	−2.50912	+	1.44864i	−0.108479	+	0.0626302i
$536$	−16.5168	−	17.9494i	−0.713418	−	0.775295i
$537$	−1.31748	+	2.28194i	−0.0568535	+	0.0984732i
$538$	−2.15161	−	29.2529i	−0.0927624	−	1.26118i
$539$	12.2770	−	21.2644i	0.528808	−	0.915922i
$540$	1.63277	+	0.646020i	0.0702631	+	0.0278003i
$541$	24.6819			1.06116			0.530579	−	0.847635i	$-0.321974\pi$
$541$	24.6819			1.06116			0.530579	+	0.847635i	$0.321974\pi$
$542$	32.8517	+	15.8764i	1.41110	+	0.681951i
$543$	−0.393748	−	0.681992i	−0.0168974	−	0.0292671i
$544$	5.32612	+	4.30790i	0.228356	+	0.184700i
$545$	−10.1110			−0.433106
$546$	2.53937	−	0.0484472i	0.108675	−	0.00207335i
$547$			28.3241i			1.21105i	0.795827	+	0.605525i	$0.207037\pi$
$547$			28.3241i			1.21105i	−0.795827	+	0.605525i	$0.792963\pi$
$548$	7.62049	−	6.04280i	0.325531	−	0.258136i
$549$	23.0260	−	13.2941i	0.982725	−	0.567377i
$550$	3.35449	−	6.94115i	0.143036	−	0.295972i
$551$			24.4815i			1.04295i
$552$	−2.98581	−	0.934555i	−0.127084	−	0.0397773i
$553$	−19.7498	−	11.4025i	−0.839847	−	0.484886i
$554$	−0.157545	−	2.14195i	−0.00669344	−	0.0910029i
$555$	0.973025	+	0.561776i	0.0413026	+	0.0238461i
$556$	−4.56638	+	3.62099i	−0.193658	+	0.153564i
$557$	3.35261	+	5.80689i	0.142055	+	0.246046i	0.928270	−	0.371906i	$-0.121296\pi$
$557$	3.35261	+	5.80689i	0.142055	+	0.246046i	−0.786216	+	0.617952i	$0.787962\pi$
$558$	−2.35128	−	31.9676i	−0.0995378	−	1.35330i
$559$	−5.41318	+	2.74464i	−0.228953	+	0.116086i
$560$	−3.92737	−	12.9863i	−0.165962	−	0.548772i
$561$	0.839545	−	0.484712i	0.0354456	−	0.0204645i
$562$	−23.5286	+	15.9940i	−0.992492	+	0.674665i
$563$	−11.1526	−	6.43893i	−0.470024	−	0.271369i	0.246226	−	0.969213i	$-0.420810\pi$
$563$	−11.1526	−	6.43893i	−0.470024	−	0.271369i	−0.716250	+	0.697844i	$0.754143\pi$
$564$	0.0672172	−	0.00994170i	0.00283035	−	0.000418621i
$565$	1.24836	−	2.16222i	0.0525189	−	0.0909653i
$566$	−11.7141	−	5.66115i	−0.492381	−	0.237956i
$567$			29.8694i			1.25440i
$568$	43.4849	+	13.6107i	1.82459	+	0.571093i
$569$	13.0771	+	22.6502i	0.548221	+	0.949547i	0.998397	+	0.0566071i	$0.0180282\pi$
$569$	13.0771	+	22.6502i	0.548221	+	0.949547i	−0.450175	+	0.892940i	$0.648638\pi$
$570$	−0.596349	+	0.405379i	−0.0249783	+	0.0169795i
$571$			30.8229i			1.28990i	0.764225	+	0.644950i	$0.223122\pi$
$571$			30.8229i			1.28990i	−0.764225	+	0.644950i	$0.776878\pi$
$572$	−16.4264	+	35.7129i	−0.686821	+	1.49323i
$573$		−	2.64788i		−	0.110617i
$574$	−10.8107	−	15.9035i	−0.451231	−	0.663800i
$575$	3.76612	+	6.52310i	0.157058	+	0.272032i
$576$	−1.97731	+	23.7453i	−0.0823880	+	0.989387i
$577$			29.0460i			1.20920i	0.796529	+	0.604600i	$0.206667\pi$
$577$			29.0460i			1.20920i	−0.796529	+	0.604600i	$0.793333\pi$
$578$	−9.55877	+	19.7791i	−0.397593	+	0.822703i
$579$	0.931834	−	1.61398i	0.0387257	−	0.0670749i
$580$	2.06331	+	13.9503i	0.0856743	+	0.579256i
$581$	15.6214	+	9.01901i	0.648084	+	0.374172i
$582$	0.975104	+	1.43446i	0.0404193	+	0.0594604i
$583$	24.3927	−	14.0831i	1.01024	−	0.583264i
$584$	−6.27637	−	28.0331i	−0.259718	−	1.16002i
$585$	4.85637	+	9.57808i	0.200786	+	0.396005i
$586$	−22.6083	+	1.66289i	−0.933941	+	0.0686932i
$587$	−3.46758	−	6.00603i	−0.143122	−	0.247895i	0.785548	−	0.618800i	$-0.212381\pi$
$587$	−3.46758	−	6.00603i	−0.143122	−	0.247895i	−0.928671	+	0.370905i	$0.879048\pi$
$588$	−1.03660	+	0.821990i	−0.0427486	+	0.0338983i
$589$	22.8820	+	13.2109i	0.942835	+	0.544346i
$590$	−4.45004	+	0.327310i	−0.183205	+	0.0134751i
$591$	2.97148	+	1.71558i	0.122230	+	0.0705697i
$592$	−6.97442	+	29.7978i	−0.286647	+	1.22468i
$593$		−	39.4077i		−	1.61828i	−0.587616	−	0.809140i	$-0.699933\pi$
$593$		−	39.4077i		−	1.61828i	0.587616	−	0.809140i	$-0.300067\pi$
$594$	6.09406	+	2.94511i	0.250042	+	0.120839i
$595$	−3.55705	+	2.05367i	−0.145825	+	0.0841921i
$596$	−12.0019	−	15.1354i	−0.491617	−	0.619971i
$597$		−	1.45583i		−	0.0595832i
$598$	−19.8345	−	32.8891i	−0.811092	−	1.34493i
$599$	−23.2940			−0.951765			−0.475883	−	0.879509i	$-0.657871\pi$
$599$	−23.2940			−0.951765			−0.475883	+	0.879509i	$0.657871\pi$
$600$	−0.305653	+	0.281259i	−0.0124782	+	0.0114824i
$601$	9.12710	+	15.8086i	0.372302	+	0.644846i	0.989919	−	0.141633i	$-0.0452351\pi$
$601$	9.12710	+	15.8086i	0.372302	+	0.644846i	−0.617617	+	0.786479i	$0.711902\pi$
$602$	3.51336	−	7.26989i	0.143194	−	0.296298i
$603$	−25.6860			−1.04601
$604$	−16.4049	−	6.49075i	−0.667505	−	0.264105i
$605$	9.35803	−	16.2086i	0.380458	−	0.658973i
$606$	0.629431	−	0.0462959i	0.0255689	−	0.00188064i
$607$	−2.91289	+	5.04527i	−0.118230	+	0.204781i	−0.919067	−	0.394102i	$-0.871056\pi$
$607$	−2.91289	+	5.04527i	−0.118230	+	0.204781i	0.800836	+	0.598884i	$0.204389\pi$
$608$	−15.2709	−	12.3515i	−0.619317	−	0.500919i
$609$	3.04160	−	1.75607i	0.123252	−	0.0711595i
$610$	0.926056	+	12.5905i	0.0374949	+	0.509775i
$611$	0.698656	+	0.455686i	0.0282646	+	0.0184351i
$612$	7.13590	−	1.05543i	0.288452	−	0.0426632i
$613$	1.76656	+	3.05977i	0.0713506	+	0.123583i	0.899493	−	0.436934i	$-0.143936\pi$
$613$	1.76656	+	3.05977i	0.0713506	+	0.123583i	−0.828143	+	0.560517i	$0.810602\pi$
$614$	−23.2671	−	34.2280i	−0.938985	−	1.38133i
$615$	−0.294370	+	0.509863i	−0.0118701	+	0.0205597i
$616$	−11.4258	−	51.0328i	−0.460360	−	2.05617i
$617$	4.96703	+	2.86771i	0.199965	+	0.115450i	0.596639	−	0.802510i	$-0.296502\pi$
$617$	4.96703	+	2.86771i	0.199965	+	0.115450i	−0.396674	+	0.917959i	$0.629836\pi$
$618$	−1.64410	−	0.794552i	−0.0661352	−	0.0319616i
$619$	−18.0996			−0.727484			−0.363742	−	0.931500i	$-0.618501\pi$
$619$	−18.0996			−0.727484			−0.363742	+	0.931500i	$0.618501\pi$
$620$	14.1523	+	5.59950i	0.568371	+	0.224881i
$621$	−5.72703	+	3.30650i	−0.229818	+	0.132685i
$622$	12.2170	+	17.9723i	0.489857	+	0.720623i
$623$	34.3079			1.37452
$624$	1.53089	−	1.46361i	0.0612848	−	0.0585914i
$625$	1.00000			0.0400000
$626$	−7.06162	−	10.3883i	−0.282239	−	0.415199i
$627$	−2.40712	+	1.38975i	−0.0961312	+	0.0555014i
$628$	−37.2561	−	14.7407i	−1.48668	−	0.588220i
$629$	9.26478			0.369411
$630$	−12.8633	−	6.21654i	−0.512487	−	0.247673i
$631$	−5.34248	−	3.08448i	−0.212681	−	0.122791i	0.389876	−	0.920867i	$-0.372518\pi$
$631$	−5.34248	−	3.08448i	−0.212681	−	0.122791i	−0.602557	+	0.798076i	$0.705851\pi$
$632$	−18.5578	+	4.15493i	−0.738189	+	0.165274i
$633$	0.180584	−	0.312780i	0.00717756	−	0.0124319i
$634$	−3.03732	−	4.46817i	−0.120627	−	0.177454i
$635$	−0.459689	−	0.796205i	−0.0182422	−	0.0315964i
$636$	−1.50125	+	0.222041i	−0.0595285	+	0.00880450i
$637$	−16.2165	−	0.882131i	−0.642520	−	0.0349513i
$638$	3.98737	+	54.2117i	0.157862	+	2.14626i
$639$	41.5534	−	23.9909i	1.64383	−	0.949065i
$640$	−9.74286	−	5.75124i	−0.385120	−	0.227338i
$641$	6.27291	−	10.8650i	0.247765	−	0.429142i	−0.715140	−	0.698981i	$-0.753637\pi$
$641$	6.27291	−	10.8650i	0.247765	−	0.429142i	0.962905	+	0.269839i	$0.0869705\pi$
$642$	0.600098	−	0.0441384i	0.0236840	−	0.00174200i
$643$	−13.8647	+	24.0143i	−0.546769	+	0.947032i	0.451724	+	0.892158i	$0.350809\pi$
$643$	−13.8647	+	24.0143i	−0.546769	+	0.947032i	−0.998493	+	0.0548745i	$0.982524\pi$
$644$	47.5119	+	18.7985i	1.87223	+	0.740766i
$645$	−0.247201			−0.00973353
$646$	−2.58728	+	5.35364i	−0.101795	+	0.210636i
$647$	−0.0519060	−	0.0899038i	−0.00204063	−	0.00353448i	0.865003	−	0.501766i	$-0.167316\pi$
$647$	−0.0519060	−	0.0899038i	−0.00204063	−	0.00353448i	−0.867044	+	0.498232i	$0.833983\pi$
$648$	16.8661	+	18.3290i	0.662564	+	0.720030i
$649$	−17.1995			−0.675141
$650$	−5.09809	+	0.0972636i	−0.199964	+	0.00381499i
$651$		−	3.79051i		−	0.148562i
$652$	−1.93360	−	2.43843i	−0.0757255	−	0.0954963i
$653$	7.14976	−	4.12792i	0.279792	−	0.161538i	−0.353537	−	0.935420i	$-0.615021\pi$
$653$	7.14976	−	4.12792i	0.279792	−	0.161538i	0.633329	+	0.773882i	$0.281688\pi$
$654$	1.89067	+	0.913717i	0.0739312	+	0.0357292i
$655$			17.0025i			0.664344i
$656$	−15.6140	−	3.65458i	−0.609623	−	0.142688i
$657$	−26.1978	−	15.1253i	−1.02207	−	0.590095i
$658$	−1.10671	+	0.0814008i	−0.0431441	+	0.00317333i
$659$	15.9831	+	9.22782i	0.622612	+	0.359465i	0.777885	−	0.628407i	$-0.216293\pi$
$659$	15.9831	+	9.22782i	0.622612	+	0.359465i	−0.155273	+	0.987872i	$0.549626\pi$
$660$	−1.25453	+	0.994800i	−0.0488324	+	0.0387225i
$661$	−15.8508	−	27.4545i	−0.616526	−	1.06785i	−0.990115	−	0.140260i	$-0.955206\pi$
$661$	−15.8508	−	27.4545i	−0.616526	−	1.06785i	0.373589	−	0.927595i	$-0.378127\pi$
$662$	9.27763	−	0.682388i	0.360585	−	0.0265218i
$663$	−0.537057	−	0.350285i	−0.0208576	−	0.0136040i
$664$	14.6785	−	3.28641i	0.569638	−	0.127537i
$665$	10.1987	−	5.88821i	0.395488	−	0.228335i
$666$	18.1169	+	26.6515i	0.702014	+	1.03273i
$667$	−45.9947	−	26.5551i	−1.78092	−	1.02822i
$668$	−4.68557	−	31.6798i	−0.181290	−	1.22573i
$669$	0.165214	−	0.286158i	0.00638753	−	0.0110635i
$670$	5.30688	−	10.9810i	0.205022	−	0.424235i
$671$			48.6626i			1.87860i
$672$	−0.439170	+	2.78325i	−0.0169414	+	0.107366i
$673$	−6.91681	−	11.9803i	−0.266624	−	0.461805i	0.701364	−	0.712803i	$-0.252575\pi$
$673$	−6.91681	−	11.9803i	−0.266624	−	0.461805i	−0.967988	+	0.250998i	$0.919241\pi$
$674$	27.4065	+	40.3173i	1.05566	+	1.55297i
$675$			0.877962i			0.0337928i
$676$	25.9811	−	0.991718i	0.999272	−	0.0381430i
$677$		−	17.0929i		−	0.656933i	−0.944516	−	0.328467i	$-0.893468\pi$
$677$		−	17.0929i		−	0.656933i	0.944516	−	0.328467i	$-0.106532\pi$
$678$	−0.428831	+	0.291506i	−0.0164692	+	0.0111952i
$679$	−14.1636	−	24.5320i	−0.543548	−	0.941453i
$680$	−1.02311	+	3.26874i	−0.0392345	+	0.125350i
$681$		−	0.106483i		−	0.00408044i
$682$	52.8215	+	25.5273i	2.02264	+	0.977493i
$683$	−4.19956	+	7.27386i	−0.160692	+	0.278326i	−0.935117	−	0.354339i	$-0.884706\pi$
$683$	−4.19956	+	7.27386i	−0.160692	+	0.278326i	0.774425	+	0.632666i	$0.218039\pi$
$684$	−20.4599	+	3.02610i	−0.782302	+	0.115706i
$685$	4.21131	+	2.43140i	0.160906	+	0.0928990i
$686$	−9.90039	+	6.72998i	−0.377999	+	0.256952i
$687$	−0.134636	+	0.0777324i	−0.00513670	+	0.00296568i
$688$	−1.94910	−	6.44493i	−0.0743088	−	0.245711i
$689$	−15.6040	−	10.1774i	−0.594466	−	0.387729i
$690$	−0.114749	−	1.56011i	−0.00436843	−	0.0593924i
$691$	23.9580	+	41.4965i	0.911406	+	1.57860i	0.812079	+	0.583547i	$0.198336\pi$
$691$	23.9580	+	41.4965i	0.911406	+	1.57860i	0.0993267	+	0.995055i	$0.468331\pi$
$692$	17.3601	−	13.7660i	0.659934	−	0.523306i
$693$	−47.6919	−	27.5349i	−1.81166	−	1.04596i
$694$	0.262136	+	3.56396i	0.00995056	+	0.135286i
$695$	−2.52352	−	1.45695i	−0.0957224	−	0.0552654i
$696$	0.874852	−	2.79506i	0.0331612	−	0.105947i
$697$			4.85473i			0.183886i
$698$	−2.23308	+	4.62071i	−0.0845233	+	0.174897i
$699$	1.99007	−	1.14897i	0.0752715	−	0.0434580i
$700$	5.31528	−	4.21485i	0.200899	−	0.159306i
$701$			13.8974i			0.524898i	0.964946	+	0.262449i	$0.0845301\pi$
$701$			13.8974i			0.524898i	−0.964946	+	0.262449i	$0.915470\pi$
$702$	−0.0853937	−	4.47593i	−0.00322298	−	0.168933i
$703$	−26.5637			−1.00187
$704$	−35.8276	−	24.8639i	−1.35030	−	0.937093i
$705$	0.0169871	+	0.0294225i	0.000639771	+	0.00110812i
$706$	−42.0206	−	20.3075i	−1.58147	−	0.764285i
$707$	−10.3073			−0.387647
$708$	0.861703	+	0.340941i	0.0323848	+	0.0128133i
$709$	14.0154	−	24.2754i	0.526360	−	0.911682i	−0.473169	−	0.880972i	$-0.656890\pi$
$709$	14.0154	−	24.2754i	0.526360	−	0.911682i	0.999528	−	0.0307098i	$-0.00977678\pi$
$710$	1.67119	+	22.7212i	0.0627187	+	0.852712i
$711$	−10.0129	+	17.3429i	−0.375513	+	0.650408i
$712$	21.0526	−	19.3724i	0.788979	−	0.726010i
$713$	−49.6402	+	28.6598i	−1.85904	+	1.07332i
$714$	0.850729	−	0.0625728i	0.0318377	−	0.00234173i
$715$	−19.6257	−	1.06758i	−0.733961	−	0.0399254i
$716$	−5.25046	−	35.4991i	−0.196219	−	1.32666i
$717$	−2.00170	−	3.46704i	−0.0747548	−	0.129479i
$718$	−4.62115	+	3.14131i	−0.172460	+	0.117233i
$719$	15.6544	−	27.1142i	0.583810	−	1.01119i	−0.411213	−	0.911539i	$-0.634895\pi$
$719$	15.6544	−	27.1142i	0.583810	−	1.01119i	0.995023	−	0.0996491i	$-0.0317720\pi$
$720$	−11.4037	+	3.44874i	−0.424989	+	0.128527i
$721$	25.8264	+	14.9109i	0.961825	+	0.555310i
$722$	−4.27369	+	8.84317i	−0.159050	+	0.329109i
$723$	−0.0343370			−0.00127701
$724$	9.97261	+	3.94576i	0.370629	+	0.146643i
$725$	−6.10639	+	3.52552i	−0.226785	+	0.130935i
$726$	−3.21463	+	2.18521i	−0.119306	+	0.0811006i
$727$	−37.8645			−1.40432			−0.702158	−	0.712022i	$-0.747780\pi$
$727$	−37.8645			−1.40432			−0.702158	+	0.712022i	$0.747780\pi$
$728$	−26.6878	+	22.0047i	−0.989117	+	0.815547i
$729$	25.8424			0.957125
$730$	11.8789	−	8.07489i	0.439657	−	0.298865i
$731$	−1.76532	+	1.01921i	−0.0652926	+	0.0376967i
$732$	0.964624	−	2.43801i	0.0356535	−	0.0901116i
$733$	−21.9460			−0.810593			−0.405297	−	0.914185i	$-0.632832\pi$
$733$	−21.9460			−0.810593			−0.405297	+	0.914185i	$0.632832\pi$
$734$	−1.10455	+	2.28555i	−0.0407698	+	0.0843613i
$735$	−0.572856	−	0.330738i	−0.0211301	−	0.0121995i
$736$	39.7698	−	15.2927i	1.46594	−	0.563695i
$737$	23.5057	−	40.7131i	0.865845	−	1.49969i
$738$	−13.9653	+	9.49320i	−0.514071	+	0.349450i
$739$	−18.5348	−	32.1031i	−0.681812	−	1.18093i	−0.974427	−	0.224703i	$-0.927859\pi$
$739$	−18.5348	−	32.1031i	−0.681812	−	1.18093i	0.292615	−	0.956230i	$-0.405475\pi$
$740$	−15.1369	+	2.23881i	−0.556443	+	0.0823002i
$741$	1.53983	+	1.00433i	0.0565672	+	0.0368949i
$742$	24.7177	−	1.81803i	0.907414	−	0.0667421i
$743$	−37.2186	+	21.4881i	−1.36542	+	0.788324i	−0.990339	−	0.138670i	$-0.955717\pi$
$743$	−37.2186	+	21.4881i	−1.36542	+	0.788324i	−0.375078	+	0.926993i	$0.622384\pi$
$744$	−2.14035	−	2.32599i	−0.0784692	−	0.0852751i
$745$	4.82912	−	8.36428i	0.176925	−	0.306444i
$746$	3.12785	+	42.5257i	0.114519	+	1.55698i
$747$	7.91985	−	13.7176i	0.289772	−	0.501900i
$748$	−4.85731	+	12.2765i	−0.177601	+	0.448873i
$749$	−9.82699			−0.359070
$750$	−0.186992	−	0.0903689i	−0.00682799	−	0.00329980i
$751$	−1.53153	−	2.65268i	−0.0558862	−	0.0967978i	0.836729	−	0.547617i	$-0.184465\pi$
$751$	−1.53153	−	2.65268i	−0.0558862	−	0.0967978i	−0.892615	+	0.450820i	$0.851132\pi$
$752$	−0.633155	+	0.674868i	−0.0230888	+	0.0246099i
$753$	−3.56218			−0.129813
$754$	30.7880	−	18.5674i	1.12123	−	0.676184i
$755$		−	8.82114i		−	0.321034i
$756$	3.70047	+	4.66661i	0.134585	+	0.169723i
$757$	0.238409	−	0.137646i	0.00866512	−	0.00500281i	−0.495661	−	0.868516i	$-0.665074\pi$
$757$	0.238409	−	0.137646i	0.00866512	−	0.00500281i	0.504326	+	0.863513i	$0.331741\pi$
$758$	−2.80744	+	5.80919i	−0.101971	+	0.210999i
$759$		−	6.02986i		−	0.218870i
$760$	2.93344	−	9.37203i	0.106407	−	0.339959i
$761$	−28.4579	−	16.4302i	−1.03160	−	0.595594i	−0.114157	−	0.993463i	$-0.536417\pi$
$761$	−28.4579	−	16.4302i	−1.03160	−	0.595594i	−0.917443	+	0.397868i	$0.869750\pi$
$762$	0.0140062	+	0.190426i	0.000507391	+	0.00689840i
$763$	−29.6998	−	17.1472i	−1.07520	−	0.620770i
$764$	22.4059	+	28.2558i	0.810618	+	1.02226i
$765$	1.80338	+	3.12355i	0.0652014	+	0.112932i
$766$	−1.16225	−	15.8017i	−0.0419937	−	0.570939i
$767$	5.14451	+	10.1464i	0.185758	+	0.366365i
$768$	1.30211	+	1.95589i	0.0469857	+	0.0705770i

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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.795042 + 1.16958i) q^{2} +(0.127180 - 0.0734274i) q^{3} +(-0.735818 + 1.85972i) q^{4} -1.00000 q^{5} +(0.186992 + 0.0903689i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(-2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +O(q^{10})\)	\(q+(0.795042 + 1.16958i) q^{2} +(0.127180 - 0.0734274i) q^{3} +(-0.735818 + 1.85972i) q^{4} -1.00000 q^{5} +(0.186992 + 0.0903689i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(-2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +(-0.795042 - 1.16958i) q^{10} +(-2.72562 - 4.72092i) q^{11} +(0.0429734 + 0.290549i) q^{12} +(-1.96972 + 3.01997i) q^{13} +(-0.351858 - 4.78380i) q^{14} +(-0.127180 + 0.0734274i) q^{15} +(-2.91714 - 2.73684i) q^{16} +(-0.605480 + 1.04872i) q^{17} +(-4.20079 + 0.308977i) q^{18} +(1.73602 - 3.00687i) q^{19} +(0.735818 - 1.85972i) q^{20} -0.498102 q^{21} +(3.35449 - 6.94115i) q^{22} +(3.76612 + 6.52310i) q^{23} +(-0.305653 + 0.281259i) q^{24} +1.00000 q^{25} +(-5.09809 + 0.0972636i) q^{26} +0.877962i q^{27} +(5.31528 - 4.21485i) q^{28} +(-6.10639 + 3.52552i) q^{29} +(-0.186992 - 0.0903689i) q^{30} +7.60991i q^{31} +(0.881688 - 5.58772i) q^{32} +(-0.693289 - 0.400271i) q^{33} +(-1.70794 + 0.125623i) q^{34} +(2.93738 + 1.69590i) q^{35} +(-3.70118 - 4.66750i) q^{36} +(-3.82539 - 6.62576i) q^{37} +(4.89697 - 0.360182i) q^{38} +(-0.0287604 + 0.528711i) q^{39} +(2.76009 - 0.617962i) q^{40} +(3.47189 - 2.00449i) q^{41} +(-0.396012 - 0.582568i) q^{42} +(1.45778 + 0.841651i) q^{43} +(10.7852 - 1.59517i) q^{44} +(1.48922 - 2.57940i) q^{45} +(-4.63505 + 9.59090i) q^{46} -0.231346i q^{47} +(-0.571961 - 0.133872i) q^{48} +(2.25215 + 3.90083i) q^{49} +(0.795042 + 1.16958i) q^{50} +0.177835i q^{51} +(-4.16695 - 5.88528i) q^{52} +5.16695i q^{53} +(-1.02684 + 0.698016i) q^{54} +(2.72562 + 4.72092i) q^{55} +(9.15546 + 2.86565i) q^{56} -0.509884i q^{57} +(-8.97820 - 4.33895i) q^{58} +(1.57758 - 2.73245i) q^{59} +(-0.0429734 - 0.290549i) q^{60} +(-7.73090 - 4.46344i) q^{61} +(-8.90037 + 6.05019i) q^{62} +(8.74880 - 5.05112i) q^{63} +(7.23624 - 3.41127i) q^{64} +(1.96972 - 3.01997i) q^{65} +(-0.0830466 - 1.12909i) q^{66} +(4.31199 + 7.46859i) q^{67} +(-1.50481 - 1.89769i) q^{68} +(0.957949 + 0.553072i) q^{69} +(0.351858 + 4.78380i) q^{70} +(-13.9514 - 8.05487i) q^{71} +(2.51641 - 8.03967i) q^{72} +10.1566i q^{73} +(4.70800 - 9.74184i) q^{74} +(0.127180 - 0.0734274i) q^{75} +(4.31455 + 5.44102i) q^{76} +18.4895i q^{77} +(-0.641233 + 0.386710i) q^{78} +6.72360 q^{79} +(2.91714 + 2.73684i) q^{80} +(-4.40318 - 7.62654i) q^{81} +(5.10470 + 2.46698i) q^{82} -5.31813 q^{83} +(0.366512 - 0.926332i) q^{84} +(0.605480 - 1.04872i) q^{85} +(0.174622 + 2.37414i) q^{86} +(-0.517740 + 0.896752i) q^{87} +(10.4403 + 11.3458i) q^{88} +(-8.75982 + 5.05748i) q^{89} +(4.20079 - 0.308977i) q^{90} +(10.9074 - 5.53036i) q^{91} +(-14.9023 + 2.20412i) q^{92} +(0.558775 + 0.967828i) q^{93} +(0.270576 - 0.183929i) q^{94} +(-1.73602 + 3.00687i) q^{95} +(-0.298159 - 0.775386i) q^{96} +(7.23275 + 4.17583i) q^{97} +(-2.77177 + 5.73538i) q^{98} +16.2362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9}+O(q^{10}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9	\( 56 q - 6 q^{4} - 56 q^{5} - 5 q^{6} + 28 q^{9} + 8 q^{11} + 6 q^{12} - 4 q^{14} - 10 q^{16} - 18 q^{18} + 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 2 q^{24} + 56 q^{25} + 11 q^{26} + 6 q^{28} + 5 q^{30} + 16 q^{34} - 21 q^{36} - 4 q^{37} - 24 q^{39} + 29 q^{42} - 24 q^{44} - 28 q^{45} - 11 q^{46} + 3 q^{48} + 20 q^{49} + 18 q^{52} - 49 q^{54} - 8 q^{55} + 61 q^{56} - 47 q^{58} + 16 q^{59} - 6 q^{60} - 2 q^{62} - 30 q^{64} + 14 q^{66} + 36 q^{67} + 33 q^{68} + 4 q^{70} - 51 q^{72} - 2 q^{74} - 48 q^{76} - 35 q^{78} + 10 q^{80} - 28 q^{81} - 21 q^{82} - 40 q^{83} - 61 q^{84} + 28 q^{86} - 36 q^{87} + 41 q^{88} + 18 q^{90} - 16 q^{91} - 18 q^{92} - 41 q^{94} - 16 q^{95} + 48 q^{96} + 24 q^{97} + 28 q^{98} + 48 q^{99}+O(q^{100}) \) 56 * q - 6 * q^4 - 56 * q^5 - 5 * q^6 + 28 * q^9 + 8 * q^11 + 6 * q^12 - 4 * q^14 - 10 * q^16 - 18 * q^18 + 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 2 * q^24 + 56 * q^25 + 11 * q^26 + 6 * q^28 + 5 * q^30 + 16 * q^34 - 21 * q^36 - 4 * q^37 - 24 * q^39 + 29 * q^42 - 24 * q^44 - 28 * q^45 - 11 * q^46 + 3 * q^48 + 20 * q^49 + 18 * q^52 - 49 * q^54 - 8 * q^55 + 61 * q^56 - 47 * q^58 + 16 * q^59 - 6 * q^60 - 2 * q^62 - 30 * q^64 + 14 * q^66 + 36 * q^67 + 33 * q^68 + 4 * q^70 - 51 * q^72 - 2 * q^74 - 48 * q^76 - 35 * q^78 + 10 * q^80 - 28 * q^81 - 21 * q^82 - 40 * q^83 - 61 * q^84 + 28 * q^86 - 36 * q^87 + 41 * q^88 + 18 * q^90 - 16 * q^91 - 18 * q^92 - 41 * q^94 - 16 * q^95 + 48 * q^96 + 24 * q^97 + 28 * q^98 + 48 * q^99

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