LMFDB - Embedded newform 520.2.ca.b.101.10

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			101.10
Character	$\chi$	$=$	520.101
Dual form			520.2.ca.b.381.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.615362 - 1.27331i) q^{2} +(-0.127180 + 0.0734274i) q^{3} +(-1.24266 + 1.56710i) q^{4} +1.00000 q^{5} +(0.171758 + 0.116756i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +(-0.615362 - 1.27331i) 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} +(-0.911597 - 3.89474i) q^{16} +(-0.605480 + 1.04872i) q^{17} +(4.20079 + 0.308977i) q^{18} +(-1.73602 + 3.00687i) q^{19} +(-1.24266 + 1.56710i) q^{20} +0.498102 q^{21} +(4.33397 - 6.37565i) q^{22} +(3.76612 + 6.52310i) q^{23} +(-0.396404 + 0.124074i) q^{24} +1.00000 q^{25} +(-5.05746 - 0.649697i) q^{26} -0.877962i q^{27} +(6.30781 - 2.49575i) q^{28} +(6.10639 - 3.52552i) q^{29} +(0.171758 + 0.116756i) q^{30} +7.60991i q^{31} +(-4.39826 + 3.55742i) q^{32} +(-0.693289 - 0.400271i) q^{33} +(1.70794 + 0.125623i) q^{34} +(-2.93738 - 1.69590i) q^{35} +(-2.19158 - 5.53906i) 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} +(-0.306513 - 0.634240i) q^{42} +(-1.45778 - 0.841651i) q^{43} +(-10.7852 - 1.59517i) q^{44} +(-1.48922 + 2.57940i) q^{45} +(5.98844 - 8.80952i) q^{46} -0.231346i q^{47} +(0.401917 + 0.428397i) q^{48} +(2.25215 + 3.90083i) q^{49} +(-0.615362 - 1.27331i) q^{50} -0.177835i q^{51} +(2.28490 + 6.83953i) q^{52} -5.16695i q^{53} +(-1.11792 + 0.540264i) q^{54} +(2.72562 + 4.72092i) q^{55} +(-7.05945 - 6.49603i) q^{56} -0.509884i q^{57} +(-8.24674 - 5.60587i) q^{58} +(-1.57758 + 2.73245i) q^{59} +(0.0429734 - 0.290549i) q^{60} +(7.73090 + 4.46344i) q^{61} +(9.68980 - 4.68285i) 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} +(-0.891046 - 2.25205i) q^{68} +(-0.957949 - 0.553072i) q^{69} +(-0.351858 + 4.78380i) q^{70} +(-13.9514 - 8.05487i) q^{71} +(-5.70435 + 6.19911i) q^{72} +10.1566i q^{73} +(6.08268 - 8.94816i) q^{74} +(-0.127180 + 0.0734274i) q^{75} +(-2.55478 - 6.45702i) q^{76} -18.4895i q^{77} +(0.690913 - 0.288728i) q^{78} +6.72360 q^{79} +(-0.911597 - 3.89474i) q^{80} +(-4.40318 - 7.62654i) q^{81} +(-4.68882 - 3.18731i) q^{82} +5.31813 q^{83} +(-0.618971 + 0.780575i) q^{84} +(-0.605480 + 1.04872i) q^{85} +(-0.174622 + 2.37414i) q^{86} +(-0.517740 + 0.896752i) q^{87} +(4.60563 + 14.7145i) 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} +(-0.294576 + 0.142361i) q^{94} +(-1.73602 + 3.00687i) q^{95} +(0.298159 - 0.775386i) q^{96} +(7.23275 + 4.17583i) q^{97} +(3.58110 - 5.26811i) q^{98} -16.2362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) $ 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

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 $

$2$	−0.615362	−	1.27331i	−0.435127	−	0.900369i
$2$	−0.615362	−	1.27331i	−0.435127	−	0.900369i
$3$	−0.127180	+	0.0734274i	−0.0734274	+	0.0423933i	−0.536264	−	0.844050i	$-0.680165\pi$
$3$	−0.127180	+	0.0734274i	−0.0734274	+	0.0423933i	0.462837	+	0.886444i	$0.346832\pi$
$4$	−1.24266	+	1.56710i	−0.621330	+	0.783549i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	0.171758	+	0.116756i	0.0701199	+	0.0476653i
$7$	−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
$10$	−0.615362	−	1.27331i	−0.194595	−	0.402657i
$11$	2.72562	+	4.72092i	0.821806	+	1.42341i	0.904336	+	0.426821i	$0.140367\pi$
$11$	2.72562	+	4.72092i	0.821806	+	1.42341i	−0.0825299	+	0.996589i	$0.526300\pi$
$12$	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
$16$	−0.911597	−	3.89474i	−0.227899	−	0.973685i
$17$	−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	−0.993513	−	0.113723i	$-0.963722\pi$
$19$	−1.73602	+	3.00687i	−0.398269	+	0.689823i	0.595243	+	0.803546i	$0.297056\pi$
$20$	−1.24266	+	1.56710i	−0.277867	+	0.350414i
$21$	0.498102			0.108695
$22$	4.33397	−	6.37565i	0.924005	−	1.35929i
$23$	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	$0.545847\pi$
$24$	−0.396404	+	0.124074i	−0.0809157	+	0.0253265i
$25$	1.00000			0.200000
$26$	−5.05746	−	0.649697i	−0.991849	−	0.127416i
$27$		−	0.877962i		−	0.168964i
$28$	6.30781	−	2.49575i	1.19206	−	0.471652i
$29$	6.10639	−	3.52552i	1.13393	−	0.654673i	0.189008	−	0.981976i	$-0.439473\pi$
$29$	6.10639	−	3.52552i	1.13393	−	0.654673i	0.944920	+	0.327302i	$0.106140\pi$
$30$	0.171758	+	0.116756i	0.0313586	+	0.0213166i
$31$			7.60991i			1.36678i	0.730054	+	0.683390i	$0.239495\pi$
$31$			7.60991i			1.36678i	−0.730054	+	0.683390i	$0.760505\pi$
$32$	−4.39826	+	3.55742i	−0.777511	+	0.628870i
$33$	−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
$36$	−2.19158	−	5.53906i	−0.365264	−	0.923177i
$37$	3.82539	+	6.62576i	0.628890	+	1.08927i	0.987775	+	0.155887i	$0.0498236\pi$
$37$	3.82539	+	6.62576i	0.628890	+	1.08927i	−0.358885	+	0.933382i	$0.616843\pi$
$38$	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	$0.231983\pi$
$42$	−0.306513	−	0.634240i	−0.0472960	−	0.0978654i
$43$	−1.45778	−	0.841651i	−0.222310	−	0.128351i	0.384710	−	0.923038i	$-0.374302\pi$
$43$	−1.45778	−	0.841651i	−0.222310	−	0.128351i	−0.607019	+	0.794687i	$0.707635\pi$
$44$	−10.7852	−	1.59517i	−1.62592	−	0.240481i
$45$	−1.48922	+	2.57940i	−0.221999	+	0.384514i
$46$	5.98844	−	8.80952i	0.882947	−	1.29889i
$47$		−	0.231346i		−	0.0337452i	−0.999858	−	0.0168726i	$-0.994629\pi$
$47$		−	0.231346i		−	0.0337452i	0.999858	−	0.0168726i	$-0.00537097\pi$
$48$	0.401917	+	0.428397i	0.0580118	+	0.0618337i
$49$	2.25215	+	3.90083i	0.321735	+	0.557261i
$50$	−0.615362	−	1.27331i	−0.0870253	−	0.180074i
$51$		−	0.177835i		−	0.0249019i
$52$	2.28490	+	6.83953i	0.316859	+	0.948473i
$53$		−	5.16695i		−	0.709735i	−0.934917	−	0.354867i	$-0.884526\pi$
$53$		−	5.16695i		−	0.709735i	0.934917	−	0.354867i	$-0.115474\pi$
$54$	−1.11792	+	0.540264i	−0.152130	+	0.0735207i
$55$	2.72562	+	4.72092i	0.367523	+	0.636568i
$56$	−7.05945	−	6.49603i	−0.943359	−	0.868069i
$57$		−	0.509884i		−	0.0675358i
$58$	−8.24674	−	5.60587i	−1.08285	−	0.736087i
$59$	−1.57758	+	2.73245i	−0.205383	+	0.355734i	−0.950255	−	0.311474i	$-0.899177\pi$
$59$	−1.57758	+	2.73245i	−0.205383	+	0.355734i	0.744872	+	0.667208i	$0.232511\pi$
$60$	0.0429734	−	0.290549i	0.00554784	−	0.0375097i
$61$	7.73090	+	4.46344i	0.989841	+	0.571485i	0.905227	−	0.424929i	$-0.139701\pi$
$61$	7.73090	+	4.46344i	0.989841	+	0.571485i	0.0846140	+	0.996414i	$0.473034\pi$
$62$	9.68980	−	4.68285i	1.23061	−	0.594722i
$63$	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	$-0.990061\pi$
$67$	−4.31199	−	7.46859i	−0.526794	−	0.912434i	0.472719	−	0.881213i	$-0.343273\pi$
$68$	−0.891046	−	2.25205i	−0.108055	−	0.273101i
$69$	−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	$-0.738489\pi$
$72$	−5.70435	+	6.19911i	−0.672264	+	0.730572i
$73$			10.1566i			1.18874i	0.804193	+	0.594368i	$0.202598\pi$
$73$			10.1566i			1.18874i	−0.804193	+	0.594368i	$0.797402\pi$
$74$	6.08268	−	8.94816i	0.707097	−	1.04020i
$75$	−0.127180	+	0.0734274i	−0.0146855	+	0.00847866i
$76$	−2.55478	−	6.45702i	−0.293054	−	0.740671i
$77$		−	18.4895i		−	2.10708i
$78$	0.690913	−	0.288728i	0.0782305	−	0.0326920i
$79$	6.72360			0.756464			0.378232	−	0.925711i	$-0.376532\pi$
$79$	6.72360			0.756464			0.378232	+	0.925711i	$0.376532\pi$
$80$	−0.911597	−	3.89474i	−0.101920	−	0.435445i
$81$	−4.40318	−	7.62654i	−0.489243	−	0.847393i
$82$	−4.68882	−	3.18731i	−0.517793	−	0.351980i
$83$	5.31813			0.583741			0.291870	−	0.956458i	$-0.405722\pi$
$83$	5.31813			0.583741			0.291870	+	0.956458i	$0.405722\pi$
$84$	−0.618971	+	0.780575i	−0.0675352	+	0.0851677i
$85$	−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
$88$	4.60563	+	14.7145i	0.490961	+	1.56857i
$89$	−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
$94$	−0.294576	+	0.142361i	−0.0303832	+	0.0146834i
$95$	−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	$0.527295\pi$
$98$	3.58110	−	5.26811i	0.361746	−	0.532160i
$99$	−16.2362			−1.63180
$100$	−1.24266	+	1.56710i	−0.124266	+	0.156710i
$101$	−2.63177	+	1.51945i	−0.261871	+	0.151191i	−0.625188	−	0.780475i	$-0.714978\pi$
$101$	−2.63177	+	1.51945i	−0.261871	+	0.151191i	0.363317	+	0.931666i	$0.381644\pi$
$102$	−0.226440	+	0.109433i	−0.0224209	+	0.0108355i
$103$	−8.79232			−0.866333			−0.433166	−	0.901314i	$-0.642604\pi$
$103$	−8.79232			−0.866333			−0.433166	+	0.901314i	$0.642604\pi$
$104$	7.30284	−	7.11819i	0.716102	−	0.697996i
$105$	0.498102			0.0486097
$106$	−6.57915	+	3.17954i	−0.639023	+	0.308825i
$107$	−2.50912	+	1.44864i	−0.242566	+	0.140045i	−0.616355	−	0.787468i	$-0.711391\pi$
$107$	−2.50912	+	1.44864i	−0.242566	+	0.140045i	0.373790	+	0.927513i	$0.378058\pi$
$108$	1.37585	+	1.09101i	0.132391	+	0.104982i
$109$	−10.1110			−0.968455			−0.484228	−	0.874942i	$-0.660899\pi$
$109$	−10.1110			−0.968455			−0.484228	+	0.874942i	$0.660899\pi$
$110$	4.33397	−	6.37565i	0.413227	−	0.607894i
$111$	−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	$0.204134\pi$
$114$	−0.649243	+	0.313764i	−0.0608072	+	0.0293866i
$115$	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
$120$	−0.396404	+	0.124074i	−0.0361866	+	0.0113264i
$121$	−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
$124$	−11.9255	−	9.45652i	−1.07094	−	0.849220i
$125$	1.00000			0.0894427
$126$	−11.8153	−	8.03170i	−1.05259	−	0.715521i
$127$	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	$0.820346\pi$
$128$	−0.109292	−	11.3132i	−0.00966018	−	0.999953i
$129$	0.247201			0.0217648
$130$	−5.05746	−	0.649697i	−0.443569	−	0.0569822i
$131$			17.0025i			1.48552i	0.669559	+	0.742759i	$0.266483\pi$
$131$			17.0025i			1.48552i	−0.669559	+	0.742759i	$0.733517\pi$
$132$	1.48879	−	0.589053i	0.129582	−	0.0512705i
$133$	10.1987	−	5.88821i	0.884338	−	0.510573i
$134$	−6.85643	+	10.0864i	−0.592305	+	0.871333i
$135$		−	0.877962i		−	0.0755629i
$136$	−2.31925	+	2.52041i	−0.198874	+	0.216123i
$137$	−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	0.389147	−	0.921176i	$-0.372770\pi$
$139$	−2.52352	−	1.45695i	−0.214042	−	0.123577i	−0.603188	+	0.797599i	$0.706103\pi$
$140$	6.30781	−	2.49575i	0.533107	−	0.210929i
$141$	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
$146$	12.9325	−	6.24996i	1.07030	−	0.517251i
$147$	−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	−0.597563	−	0.801822i	$-0.703864\pi$
$149$	4.82912	−	8.36428i	0.395617	−	0.685229i	0.993180	+	0.116593i	$0.0371975\pi$
$150$	0.171758	+	0.116756i	0.0140240	+	0.00953306i
$151$			8.82114i			0.717854i	0.933366	+	0.358927i	$0.116857\pi$
$151$			8.82114i			0.717854i	−0.933366	+	0.358927i	$0.883143\pi$
$152$	−6.64970	+	7.22645i	−0.539362	+	0.586142i
$153$	−1.80338	−	3.12355i	−0.145795	−	0.252524i
$154$	−23.5430	+	11.3777i	−1.89715	+	0.916845i
$155$			7.60991i			0.611242i
$156$	−0.792803	−	0.702078i	−0.0634750	−	0.0562112i
$157$		−	20.0331i		−	1.59882i	−0.600787	−	0.799409i	$-0.705146\pi$
$157$		−	20.0331i		−	1.59882i	0.600787	−	0.799409i	$-0.294854\pi$
$158$	−4.13745	−	8.56126i	−0.329158	−	0.681097i
$159$	0.379395	+	0.657132i	0.0300880	+	0.0521140i
$160$	−4.39826	+	3.55742i	−0.347713	+	0.281239i
$161$		−	25.5478i		−	2.01345i
$162$	−7.00143	+	10.2997i	−0.550084	+	0.809222i
$163$	0.778008	−	1.34755i	0.0609383	−	0.105548i	−0.833947	−	0.551845i	$-0.813924\pi$
$163$	0.778008	−	1.34755i	0.0609383	−	0.105548i	0.894885	+	0.446297i	$0.147257\pi$
$164$	−1.17313	+	7.93169i	−0.0916061	+	0.619361i
$165$	−0.693289	−	0.400271i	−0.0539725	−	0.0311610i
$166$	−3.27258	−	6.77165i	−0.254001	−	0.525582i
$167$	−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
$172$	3.13048	−	1.23860i	0.238697	−	0.0944426i
$173$	9.59373	+	5.53894i	0.729398	+	0.421118i	0.818202	−	0.574931i	$-0.194971\pi$
$173$	9.59373	+	5.53894i	0.729398	+	0.421118i	−0.0888039	+	0.996049i	$0.528304\pi$
$174$	1.46044	+	0.107419i	0.110716	+	0.00814338i
$175$	−2.93738	−	1.69590i	−0.222045	−	0.128198i
$176$	15.9021	−	14.9192i	1.19866	−	1.12457i
$177$		−	0.463350i		−	0.0348275i
$178$	11.8302	+	8.04182i	0.886713	+	0.602760i
$179$	15.5388	−	8.97132i	1.16142	−	0.670548i	0.209779	−	0.977749i	$-0.432726\pi$
$179$	15.5388	−	8.97132i	1.16142	−	0.670548i	0.951645	+	0.307201i	$0.0993924\pi$
$180$	−2.19158	−	5.53906i	−0.163351	−	0.412857i
$181$			5.36242i			0.398585i	0.979940	+	0.199293i	$0.0638644\pi$
$181$			5.36242i			0.398585i	−0.979940	+	0.199293i	$0.936136\pi$
$182$	13.7539	+	10.4853i	1.01950	+	0.777226i
$183$	−1.31095			−0.0969086
$184$	6.36380	+	20.3317i	0.469146	+	1.49887i
$185$	3.82539	+	6.62576i	0.281248	+	0.487136i
$186$	−0.888499	+	1.30706i	−0.0651479	+	0.0958384i
$187$	−6.60124			−0.482730
$188$	0.362541	+	0.287484i	0.0264410	+	0.0209669i
$189$	−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	$-0.0595397\pi$
$192$	−1.17079	+	0.0974934i	−0.0844942	+	0.00703598i
$193$	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	$-0.853678\pi$
$197$	−11.6822	−	20.2341i	−0.832321	−	1.44162i	0.0638720	−	0.997958i	$-0.479655\pi$
$198$	9.99112	+	20.6737i	0.710038	+	1.46922i
$199$	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
$202$	3.55423	+	2.41605i	0.250075	+	0.169993i
$203$	−23.9157			−1.67855
$204$	0.278685	+	0.220989i	0.0195119	+	0.0154723i
$205$	3.47189	−	2.00449i	0.242487	−	0.140000i
$206$	5.41046	+	11.1954i	0.376964	+	0.780019i
$207$	−22.4343			−1.55929
$208$	−13.5576	−	4.91855i	−0.940049	−	0.341040i
$209$	−18.9269			−1.30920
$210$	−0.306513	−	0.634240i	−0.0211514	−	0.0437667i
$211$	−2.12986	+	1.22968i	−0.146626	+	0.0846544i	−0.571518	−	0.820590i	$-0.693645\pi$
$211$	−2.12986	+	1.22968i	−0.146626	+	0.0846544i	0.424892	+	0.905244i	$0.360312\pi$
$212$	8.09712	+	6.42075i	0.556112	+	0.440979i
$213$	2.36579			0.162101
$214$	3.38859	+	2.30346i	0.231639	+	0.157461i
$215$	−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
$218$	6.22191	+	12.8744i	0.421401	+	0.871968i
$219$	−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	$0.309330\pi$
$224$	18.9524	−	2.99051i	1.26631	−	0.199812i
$225$	−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	−0.877806	−	0.479016i	$-0.840994\pi$
$227$	−0.362545	+	0.627947i	−0.0240630	+	0.0416783i	0.853743	+	0.520694i	$0.174327\pi$
$228$	0.799039	+	0.633612i	0.0529177	+	0.0419620i
$229$	1.05863			0.0699562			0.0349781	−	0.999388i	$-0.488864\pi$
$229$	1.05863			0.0699562			0.0349781	+	0.999388i	$0.488864\pi$
$230$	5.98844	−	8.80952i	0.394866	−	0.580883i
$231$	1.35764	+	2.35150i	0.0893260	+	0.154717i
$232$	19.0328	−	5.95726i	1.24957	−	0.391113i
$233$	15.6477			1.02511			0.512557	−	0.858653i	$-0.328698\pi$
$233$	15.6477			1.02511			0.512557	+	0.858653i	$0.328698\pi$
$234$	9.20748	−	12.0777i	0.601912	−	0.789542i
$235$		−	0.231346i		−	0.0150913i
$236$	−2.32162	−	5.86772i	−0.151125	−	0.381956i
$237$	−0.855108	+	0.493697i	−0.0555452	+	0.0320690i
$238$	−4.80384	−	3.26550i	−0.311387	−	0.211671i
$239$		−	27.2609i		−	1.76336i	−0.471846	−	0.881681i	$-0.656412\pi$
$239$		−	27.2609i		−	1.76336i	0.471846	−	0.881681i	$-0.343588\pi$
$240$	0.401917	+	0.428397i	0.0259437	+	0.0276529i
$241$	−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
$244$	−16.6015	+	6.56856i	−1.06280	+	0.420509i
$245$	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
$250$	−0.615362	−	1.27331i	−0.0389189	−	0.0805315i
$251$	21.0067	+	12.1283i	1.32593	+	0.765528i	0.984668	−	0.174438i	$-0.0558110\pi$
$251$	21.0067	+	12.1283i	1.32593	+	0.765528i	0.341266	+	0.939967i	$0.389144\pi$
$252$	−2.95617	+	19.9871i	−0.186221	+	1.25907i
$253$	−20.5300	+	35.5590i	−1.29071	+	2.23558i
$254$	0.730944	−	1.07528i	0.0458635	−	0.0674692i
$255$		−	0.177835i		−	0.0111365i
$256$	−14.3380	+	7.10087i	−0.896124	+	0.443804i
$257$	−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	$-0.418344\pi$
$258$	−0.152118	−	0.314764i	−0.00947046	−	0.0195964i
$259$		−	25.9499i		−	1.61245i
$260$	2.28490	+	6.83953i	0.141703	+	0.424170i
$261$			21.0011i			1.29993i
$262$	21.6496	−	10.4627i	1.33751	−	0.646388i
$263$	−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	$-0.373313\pi$
$264$	−1.66619	−	1.53321i	−0.102547	−	0.0943627i
$265$		−	5.16695i		−	0.317403i
$266$	−13.7734	−	9.36275i	−0.844503	−	0.574067i
$267$	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	0.934947	−	0.354788i	$-0.115447\pi$
$269$	17.9620	+	10.3704i	1.09517	+	0.632294i	0.160218	+	0.987082i	$0.448780\pi$
$270$	−1.11792	+	0.540264i	−0.0680345	+	0.0328794i
$271$	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
$276$	2.05712	−	0.813921i	0.123824	−	0.0489923i
$277$	1.31522	+	0.759340i	0.0790237	+	0.0456243i	0.538991	−	0.842311i	$-0.318806\pi$
$277$	1.31522	+	0.759340i	0.0790237	+	0.0456243i	−0.459967	+	0.887936i	$0.652139\pi$
$278$	−0.302283	+	4.10978i	−0.0181297	+	0.246488i
$279$	−19.6290	−	11.3328i	−1.17516	−	0.678477i
$280$	−7.05945	−	6.49603i	−0.421883	−	0.388212i
$281$			20.1172i			1.20009i	0.799967	+	0.600045i	$0.204851\pi$
$281$			20.1172i			1.20009i	−0.799967	+	0.600045i	$0.795149\pi$
$282$	0.0270109	−	0.0397354i	0.00160848	−	0.00236621i
$283$	7.96718	−	4.59985i	0.473599	−	0.273433i	−0.244146	−	0.969739i	$-0.578508\pi$
$283$	7.96718	−	4.59985i	0.473599	−	0.273433i	0.717745	+	0.696306i	$0.245174\pi$
$284$	29.9596	−	11.8538i	1.77778	−	0.703395i
$285$		−	0.509884i		−	0.0302029i
$286$	−10.7176	−	25.6467i	−0.633742	−	1.51652i
$287$	−13.5977			−0.802646
$288$	−2.62605	−	16.6427i	−0.154741	−	0.980678i
$289$	7.76679	+	13.4525i	0.456870	+	0.791322i
$290$	−8.24674	−	5.60587i	−0.484265	−	0.329188i
$291$	−1.22648			−0.0718976
$292$	−15.9163	−	12.6211i	−0.931433	−	0.738596i
$293$	8.01484	−	13.8821i	0.468232	−	0.811001i	−0.531109	−	0.847303i	$-0.678225\pi$
$293$	8.01484	−	13.8821i	0.468232	−	0.811001i	0.999341	+	0.0363022i	$0.0115579\pi$
$294$	−0.0686203	+	0.932949i	−0.00400201	+	0.0544107i
$295$	−1.57758	+	2.73245i	−0.0918501	+	0.159089i
$296$	6.46396	+	20.6517i	0.375710	+	1.20035i
$297$	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
$302$	11.2321	−	5.42820i	0.646334	−	0.312358i
$303$	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
$306$	−2.86753	+	4.21839i	−0.163926	+	0.241149i
$307$	29.2653			1.67026			0.835130	−	0.550053i	$-0.185392\pi$
$307$	29.2653			1.67026			0.835130	+	0.550053i	$0.185392\pi$
$308$	28.9749	+	22.9762i	1.65100	+	1.30919i
$309$	1.11821	−	0.645597i	0.0636125	−	0.0367267i
$310$	9.68980	−	4.68285i	0.550344	−	0.265968i
$311$	15.3665			0.871354			0.435677	−	0.900103i	$-0.356509\pi$
$311$	15.3665			0.871354			0.435677	+	0.900103i	$0.356509\pi$
$312$	−0.406105	+	1.44152i	−0.0229912	+	0.0816099i
$313$	−8.88208			−0.502045			−0.251022	−	0.967981i	$-0.580767\pi$
$313$	−8.88208			−0.502045			−0.251022	+	0.967981i	$0.580767\pi$
$314$	−25.5085	+	12.3276i	−1.43953	+	0.695689i
$315$	8.74880	−	5.05112i	0.492939	−	0.284598i
$316$	−8.35515	+	10.5365i	−0.470014	+	0.592727i
$317$	3.82033			0.214571			0.107285	−	0.994228i	$-0.465784\pi$
$317$	3.82033			0.214571			0.107285	+	0.994228i	$0.465784\pi$
$318$	0.603270	−	0.887464i	0.0338297	−	0.0497665i
$319$	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
$322$	−32.5304	+	15.7212i	−1.81285	+	0.876105i
$323$	−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
$328$	10.8214	−	3.38710i	0.597514	−	0.187021i
$329$	−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	−0.942146	−	0.335202i	$-0.891195\pi$
$331$	−3.28900	+	5.69671i	−0.180780	+	0.313120i	0.761367	+	0.648322i	$0.224529\pi$
$332$	−6.60862	+	8.33404i	−0.362695	+	0.457390i
$333$	−22.7873			−1.24874
$334$	18.7275	+	12.7304i	1.02472	+	0.696574i
$335$	−4.31199	−	7.46859i	−0.235589	−	0.408053i
$336$	−0.454068	−	1.93998i	−0.0247714	−	0.105834i
$337$	34.4718			1.87780			0.938898	−	0.344196i	$-0.111848\pi$
$337$	34.4718			1.87780			0.938898	+	0.344196i	$0.111848\pi$
$338$	−11.9238	+	13.9936i	−0.648571	+	0.761154i
$339$		−	0.366655i		−	0.0199140i
$340$	−0.891046	−	2.25205i	−0.0483238	−	0.122135i
$341$	−35.9257	+	20.7417i	−1.94549	+	1.12323i
$342$	−8.22170	+	12.0948i	−0.444578	+	0.654014i
$343$			8.46494i			0.457064i
$344$	−3.50351	−	3.22389i	−0.188896	−	0.173821i
$345$	−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	0.440110	−	0.897944i	$-0.354940\pi$
$347$	−2.18837	−	1.26345i	−0.117478	−	0.0678258i	−0.557587	+	0.830118i	$0.688273\pi$
$348$	−0.761925	−	1.92571i	−0.0408434	−	0.103229i
$349$	−1.81444	−	3.14271i	−0.0971249	−	0.168225i	0.813369	−	0.581749i	$-0.197631\pi$
$349$	−1.81444	−	3.14271i	−0.0971249	−	0.168225i	−0.910493	+	0.413523i	$0.864298\pi$
$350$	−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	$0.992056\pi$
$354$	−0.589990	+	0.285128i	−0.0313576	+	0.0151544i
$355$	−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
$358$	−20.9853	−	14.2651i	−1.10911	−	0.753936i
$359$			3.95113i			0.208533i	0.994549	+	0.104266i	$0.0332494\pi$
$359$			3.95113i			0.208533i	−0.994549	+	0.104266i	$0.966751\pi$
$360$	−5.70435	+	6.19911i	−0.300646	+	0.326722i
$361$	3.47250	+	6.01454i	0.182763	+	0.316555i
$362$	6.82804	−	3.29983i	0.358874	−	0.173435i
$363$		−	2.74854i		−	0.144261i
$364$	4.88753	−	23.9653i	0.256176	−	1.25612i
$365$			10.1566i			0.531619i
$366$	0.806712	+	1.66926i	0.0421675	+	0.0872535i
$367$	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	$0.818416\pi$
$368$	21.9726	−	20.6145i	1.14540	−	1.07460i
$369$			11.9405i			0.621598i
$370$	6.08268	−	8.94816i	0.316224	−	0.465193i
$371$	−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	−0.363491	−	0.931598i	$-0.618415\pi$
$373$	−26.1119	−	15.0757i	−1.35202	−	0.780591i	−0.988533	+	0.151006i	$0.951749\pi$
$374$	4.06215	+	8.40545i	0.210049	+	0.434636i
$375$	−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	0.801473	−	0.598031i	$-0.204050\pi$
$379$	−2.28113	−	3.95103i	−0.117174	−	0.202951i	−0.918647	+	0.395080i	$0.870717\pi$
$380$	−2.55478	−	6.45702i	−0.131058	−	0.331238i
$381$	−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	$0.759072\pi$
$384$	0.844597	+	1.43078i	0.0431007	+	0.0730144i
$385$		−	18.4895i		−	0.942313i
$386$	−14.8426	−	10.0895i	−0.755467	−	0.513543i
$387$	4.34191	−	2.50680i	0.220712	−	0.127428i
$388$	−15.5318	+	6.14530i	−0.788507	+	0.311980i
$389$		−	34.4332i		−	1.74583i	−0.487872	−	0.872915i	$-0.662227\pi$
$389$		−	34.4332i		−	1.74583i	0.487872	−	0.872915i	$-0.337773\pi$
$390$	0.690913	−	0.288728i	0.0349857	−	0.0146203i
$391$	−9.12123			−0.461280
$392$	3.80557	+	12.1584i	0.192210	+	0.614092i
$393$	−1.24845	−	2.16238i	−0.0629760	−	0.109078i
$394$	−18.5756	+	27.3264i	−0.935827	+	1.37668i
$395$	6.72360			0.338301
$396$	20.1760	−	25.4437i	1.01388	−	1.27859i
$397$	−11.9556	+	20.7078i	−0.600037	+	1.03929i	0.392778	+	0.919633i	$0.371514\pi$
$397$	−11.9556	+	20.7078i	−0.600037	+	1.03929i	−0.992815	+	0.119661i	$0.961819\pi$
$398$	−13.9819	−	1.02840i	−0.700849	−	0.0515488i
$399$	−0.864712	+	1.49773i	−0.0432898	+	0.0749801i
$400$	−0.911597	−	3.89474i	−0.0455799	−	0.194737i
$401$	−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
$406$	14.7168	+	30.4522i	0.730384	+	1.51132i
$407$	−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	$0.942073\pi$
$410$	−4.68882	−	3.18731i	−0.231564	−	0.157410i
$411$	0.714125			0.0352252
$412$	10.9259	−	13.7784i	0.538278	−	0.678814i
$413$	9.26790	−	5.35083i	0.456044	−	0.263297i
$414$	13.8052	+	28.5659i	0.678488	+	1.40394i
$415$	5.31813			0.261057
$416$	2.07996	+	20.2897i	0.101979	+	0.994787i
$417$	0.427921			0.0209554
$418$	11.6469	+	24.0999i	0.569668	+	1.17876i
$419$	−4.72278	+	2.72670i	−0.230723	+	0.133208i	−0.610905	−	0.791704i	$-0.709194\pi$
$419$	−4.72278	+	2.72670i	−0.230723	+	0.133208i	0.380183	+	0.924911i	$0.375861\pi$
$420$	−0.618971	+	0.780575i	−0.0302027	+	0.0380881i
$421$	27.2961			1.33033			0.665166	−	0.746696i	$-0.268361\pi$
$421$	27.2961			1.33033			0.665166	+	0.746696i	$0.268361\pi$
$422$	2.87640	+	1.95529i	0.140021	+	0.0951819i
$423$	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
$426$	−1.45582	−	3.01240i	−0.0705346	−	0.145951i
$427$	−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	$0.418406\pi$
$432$	−3.41943	+	0.800347i	−0.164517	+	0.0385067i
$433$	−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
$436$	12.5645	−	15.8449i	0.601730	−	0.758833i
$437$	−26.1521			−1.25103
$438$	−1.18584	+	1.74447i	−0.0566614	+	0.0833540i
$439$	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	$0.597419\pi$
$440$	4.60563	+	14.7145i	0.219565	+	0.701487i
$441$	−13.4157			−0.638844
$442$	3.74354	−	4.91049i	0.178062	−	0.233568i
$443$		−	28.1253i		−	1.33627i	−0.744039	−	0.668137i	$-0.767092\pi$
$443$		−	28.1253i		−	1.33627i	0.744039	−	0.668137i	$-0.232908\pi$
$444$	2.08950	−	0.826730i	0.0991632	−	0.0392349i
$445$	−8.75982	+	5.05748i	−0.415255	+	0.239748i
$446$	−2.63158	−	1.78886i	−0.124609	−	0.0847052i
$447$			1.41836i			0.0670861i
$448$	−15.4705	−	22.2921i	−0.730910	−	1.05320i
$449$	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
$452$	−1.83713	−	4.64320i	−0.0864113	−	0.218398i
$453$	−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	$0.0593328\pi$
$458$	−0.651440	−	1.34797i	−0.0304398	−	0.0629864i
$459$	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	−0.592191	−	0.805798i	$-0.701737\pi$
$461$	8.62585	−	14.9404i	0.401746	−	0.695844i	0.993937	+	0.109954i	$0.0350702\pi$
$462$	2.15876	−	3.17572i	0.100434	−	0.147748i
$463$		−	7.21332i		−	0.335232i	−0.985852	−	0.167616i	$-0.946393\pi$
$463$		−	7.21332i		−	0.335232i	0.985852	−	0.167616i	$-0.0536068\pi$
$464$	−19.2976	−	20.5689i	−0.895867	−	0.954888i
$465$	−0.558775	−	0.967828i	−0.0259126	−	0.0448819i
$466$	−9.62899	−	19.9244i	−0.446055	−	0.922981i
$467$		−	14.9377i		−	0.691234i	−0.938376	−	0.345617i	$-0.887670\pi$
$467$		−	14.9377i		−	0.691234i	0.938376	−	0.345617i	$-0.112330\pi$
$468$	−21.0446	−	4.29188i	−0.972787	−	0.198392i
$469$			29.2508i			1.35068i
$470$	−0.294576	+	0.142361i	−0.0135878	+	0.00656664i
$471$	1.47098	+	2.54781i	0.0677792	+	0.117397i
$472$	−6.04281	+	6.56692i	−0.278143	+	0.302267i
$473$		−	9.17609i		−	0.421917i
$474$	1.15483	+	0.785019i	0.0530432	+	0.0360571i
$475$	−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
$478$	−34.7117	+	16.7753i	−1.58768	+	0.767286i
$479$	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
$484$	−13.7716	−	34.8067i	−0.625983	−	1.58212i
$485$	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	$0.692832\pi$
$488$	18.5798	+	17.0969i	0.841067	+	0.773941i
$489$			0.228508i			0.0103335i
$490$	3.58110	−	5.26811i	0.161778	−	0.237989i
$491$	23.9285	−	13.8151i	1.07988	−	0.623468i	0.149014	−	0.988835i	$-0.452390\pi$
$491$	23.9285	−	13.8151i	1.07988	−	0.623468i	0.930863	+	0.365368i	$0.119057\pi$
$492$	−0.433205	−	1.09489i	−0.0195304	−	0.0493616i
$493$			8.53853i			0.384556i
$494$	10.7334	−	14.0792i	0.482918	−	0.633454i
$495$	−16.2362			−0.729762
$496$	29.6386	−	6.93717i	1.33081	−	0.311488i
$497$	27.3205	+	47.3204i	1.22549	+	2.12261i
$498$	0.913431	+	0.620922i	0.0409318	+	0.0278242i
$499$	−12.0413			−0.539043			−0.269521	−	0.962994i	$-0.586866\pi$
$499$	−12.0413			−0.539043			−0.269521	+	0.962994i	$0.586866\pi$
$500$	−1.24266	+	1.56710i	−0.0555734	+	0.0700828i
$501$	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	$0.219164\pi$
$504$	27.2689	−	8.53515i	1.21465	−	0.380186i
$505$	−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	0.821476	−	0.570243i	$-0.193151\pi$
$509$	−1.87496	−	3.24753i	−0.0831063	−	0.143944i	−0.904583	+	0.426298i	$0.859817\pi$
$510$	−0.226440	+	0.109433i	−0.0100269	+	0.00484578i
$511$	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
$514$	−18.1196	+	26.6555i	−0.799220	+	1.17572i
$515$	−8.79232			−0.387436
$516$	−0.307186	+	0.387388i	−0.0135231	+	0.0170538i
$517$	1.09216	−	0.630561i	0.0480333	−	0.0277320i
$518$	−33.0423	+	15.9686i	−1.45180	+	0.701619i
$519$	−1.62684			−0.0714104
$520$	7.30284	−	7.11819i	0.320251	−	0.312153i
$521$	45.4889			1.99290			0.996452	−	0.0841592i	$-0.0268204\pi$
$521$	45.4889			1.99290			0.996452	+	0.0841592i	$0.0268204\pi$
$522$	26.7410	−	12.9233i	1.17042	−	0.565636i
$523$	−29.8587	+	17.2390i	−1.30563	+	0.753807i	−0.981364	−	0.192158i	$-0.938451\pi$
$523$	−29.8587	+	17.2390i	−1.30563	+	0.753807i	−0.324268	+	0.945965i	$0.605118\pi$
$524$	−26.6446	−	21.1283i	−1.16398	−	0.922996i
$525$	0.498102			0.0217389
$526$	−15.5894	+	22.9334i	−0.679730	+	0.999943i
$527$	−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
$530$	−6.57915	+	3.17954i	−0.285780	+	0.138111i
$531$	−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
$536$	−7.28620	−	23.2787i	−0.314716	−	1.00549i
$537$	−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
$540$	1.37585	+	1.09101i	0.0592073	+	0.0469495i
$541$	−24.6819			−1.06116			−0.530579	−	0.847635i	$-0.678026\pi$
$541$	−24.6819			−1.06116			−0.530579	+	0.847635i	$0.678026\pi$
$542$	−30.1752	−	20.5122i	−1.29614	−	0.881074i
$543$	−0.393748	−	0.681992i	−0.0168974	−	0.0292671i
$544$	−1.06769	−	6.76651i	−0.0457768	−	0.290112i
$545$	−10.1110			−0.433106
$546$	−2.51913	−	0.323615i	−0.107809	−	0.0138495i
$547$		−	28.3241i		−	1.21105i	−0.795827	−	0.605525i	$-0.792963\pi$
$547$		−	28.3241i		−	1.21105i	0.795827	−	0.605525i	$-0.207037\pi$
$548$	9.04346	−	3.57813i	0.386318	−	0.152850i
$549$	−23.0260	+	13.2941i	−0.982725	+	0.567377i
$550$	4.33397	−	6.37565i	0.184801	−	0.271859i
$551$			24.4815i			1.04295i
$552$	−2.30225	−	2.11851i	−0.0979904	−	0.0901697i
$553$	−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
$556$	5.41906	−	2.14410i	0.229819	−	0.0909302i
$557$	−3.35261	−	5.80689i	−0.142055	−	0.246046i	0.786216	−	0.617952i	$-0.212038\pi$
$557$	−3.35261	−	5.80689i	−0.142055	−	0.246046i	−0.928270	+	0.371906i	$0.878704\pi$
$558$	−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
$562$	25.6155	−	12.3793i	1.08052	−	0.522191i
$563$	11.1526	+	6.43893i	0.470024	+	0.271369i	0.716250	−	0.697844i	$-0.245857\pi$
$563$	11.1526	+	6.43893i	0.470024	+	0.271369i	−0.246226	+	0.969213i	$0.579190\pi$
$564$	−0.0672172	−	0.00994170i	−0.00283035	−	0.000418621i
$565$	−1.24836	+	2.16222i	−0.0525189	+	0.0909653i
$566$	−10.7598	−	7.31415i	−0.452266	−	0.307436i
$567$			29.8694i			1.25440i
$568$	−33.5297	−	30.8537i	−1.40687	−	1.29459i
$569$	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	$0.648638\pi$
$570$	−0.649243	+	0.313764i	−0.0271938	+	0.0131421i
$571$		−	30.8229i		−	1.28990i	−0.764225	−	0.644950i	$-0.776878\pi$
$571$		−	30.8229i		−	1.28990i	0.764225	−	0.644950i	$-0.223122\pi$
$572$	−26.0611	+	29.4288i	−1.08967	+	1.23048i
$573$			2.64788i			0.110617i
$574$	8.36750	+	17.3141i	0.349253	+	0.722677i
$575$	3.76612	+	6.52310i	0.157058	+	0.272032i
$576$	−19.5754	+	13.5850i	−0.815640	+	0.566044i
$577$			29.0460i			1.20920i	0.796529	+	0.604600i	$0.206667\pi$
$577$			29.0460i			1.20920i	−0.796529	+	0.604600i	$0.793333\pi$
$578$	12.3498	−	18.1677i	0.513686	−	0.755677i
$579$	−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
$582$	0.754730	+	1.56170i	0.0312846	+	0.0647344i
$583$	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	0.928671	−	0.370905i	$-0.120952\pi$
$587$	3.46758	+	6.00603i	0.143122	+	0.247895i	−0.785548	+	0.618800i	$0.787619\pi$
$588$	1.23016	−	0.486726i	0.0507311	−	0.0200723i
$589$	−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
$592$	22.3184	−	20.9389i	0.917281	−	0.860584i
$593$		−	39.4077i		−	1.61828i	−0.587616	−	0.809140i	$-0.699933\pi$
$593$		−	39.4077i		−	1.61828i	0.587616	−	0.809140i	$-0.300067\pi$
$594$	−5.59757	−	3.80506i	−0.229671	−	0.156123i
$595$	3.55705	−	2.05367i	0.145825	−	0.0841921i
$596$	7.10671	+	17.9617i	0.291102	+	0.735738i
$597$			1.45583i			0.0595832i
$598$	−14.8089	−	35.4372i	−0.605582	−	1.44913i
$599$	−23.2940			−0.951765			−0.475883	−	0.879509i	$-0.657871\pi$
$599$	−23.2940			−0.951765			−0.475883	+	0.879509i	$0.657871\pi$
$600$	−0.396404	+	0.124074i	−0.0161831	+	0.00506530i
$601$	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	$0.711902\pi$
$602$	4.53923	−	6.67760i	0.185005	−	0.272159i
$603$	25.6860			1.04601
$604$	−13.8236	−	10.9617i	−0.562474	−	0.446024i
$605$	−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	$0.204389\pi$
$608$	−3.06125	−	19.4007i	−0.124150	−	0.786804i
$609$	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	0.828143	−	0.560517i	$-0.189398\pi$
$613$	−1.76656	−	3.05977i	−0.0713506	−	0.123583i	−0.899493	+	0.436934i	$0.856064\pi$
$614$	−18.0088	−	37.2639i	−0.726775	−	1.50385i
$615$	−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	$0.629836\pi$
$618$	−1.51015	−	1.02655i	−0.0607471	−	0.0412940i
$619$	18.0996			0.727484			0.363742	−	0.931500i	$-0.381499\pi$
$619$	18.0996			0.727484			0.363742	+	0.931500i	$0.381499\pi$
$620$	−11.9255	−	9.45652i	−0.478939	−	0.379783i
$621$	5.72703	−	3.30650i	0.229818	−	0.132685i
$622$	−9.45596	−	19.5664i	−0.379150	−	0.784541i
$623$	34.3079			1.37452
$624$	2.08541	−	0.369957i	0.0834831	−	0.0148101i
$625$	1.00000			0.0400000
$626$	5.46569	+	11.3097i	0.218453	+	0.452026i
$627$	2.40712	−	1.38975i	0.0961312	−	0.0555014i
$628$	31.3939	+	24.8944i	1.25275	+	0.993393i
$629$	−9.26478			−0.369411
$630$	−11.8153	−	8.03170i	−0.470735	−	0.319991i
$631$	−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
$634$	−2.35088	−	4.86448i	−0.0933656	−	0.193193i
$635$	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
$640$	−0.109292	−	11.3132i	−0.00432016	−	0.447193i
$641$	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	$-0.649191\pi$
$643$	13.8647	−	24.0143i	0.546769	−	0.947032i	0.998493	−	0.0548745i	$-0.0174759\pi$
$644$	40.0359	+	31.7472i	1.57764	+	1.25102i
$645$	0.247201			0.00973353
$646$	−3.34275	+	4.91747i	−0.131519	+	0.193475i
$647$	−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	$0.833983\pi$
$648$	−7.44029	−	23.7710i	−0.292282	−	0.933812i
$649$	−17.1995			−0.675141
$650$	−5.05746	−	0.649697i	−0.198370	−	0.0254832i
$651$			3.79051i			0.148562i
$652$	1.14494	+	2.89376i	0.0448395	+	0.113328i
$653$	−7.14976	+	4.12792i	−0.279792	+	0.161538i	−0.633329	−	0.773882i	$-0.718312\pi$
$653$	−7.14976	+	4.12792i	−0.279792	+	0.161538i	0.353537	+	0.935420i	$0.384979\pi$
$654$	−1.73664	−	1.18051i	−0.0679080	−	0.0461617i
$655$			17.0025i			0.664344i
$656$	−10.9719	−	11.6948i	−0.428382	−	0.456605i
$657$	−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	0.155273	−	0.987872i	$-0.450374\pi$
$659$	−15.9831	−	9.22782i	−0.622612	−	0.359465i	−0.777885	+	0.628407i	$0.783707\pi$
$660$	1.48879	−	0.589053i	0.0579509	−	0.0229288i
$661$	15.8508	+	27.4545i	0.616526	+	1.06785i	0.990115	+	0.140260i	$0.0447939\pi$
$661$	15.8508	+	27.4545i	0.616526	+	1.06785i	−0.373589	+	0.927595i	$0.621873\pi$
$662$	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
$666$	14.0225	+	29.0154i	0.543359	+	1.12432i
$667$	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
$670$	−6.85643	+	10.0864i	−0.264887	+	0.389672i
$671$			48.6626i			1.87860i
$672$	−2.19078	+	1.77196i	−0.0845113	+	0.0683548i
$673$	−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	$0.919241\pi$
$674$	−21.2126	−	43.8934i	−0.817079	−	1.69071i
$675$		−	0.877962i		−	0.0337928i
$676$	25.1558	+	6.57164i	0.967530	+	0.252755i
$677$			17.0929i			0.656933i	0.944516	+	0.328467i	$0.106532\pi$
$677$			17.0929i			0.656933i	−0.944516	+	0.328467i	$0.893468\pi$
$678$	−0.466867	+	0.225626i	−0.0179299	+	0.00866510i
$679$	−14.1636	−	24.5320i	−0.543548	−	0.941453i
$680$	−2.31925	+	2.52041i	−0.0889393	+	0.0966532i
$681$		−	0.106483i		−	0.00408044i
$682$	48.5181	+	32.9811i	1.85785	+	1.26291i
$683$	4.19956	−	7.27386i	0.160692	−	0.278326i	−0.774425	−	0.632666i	$-0.781961\pi$
$683$	4.19956	−	7.27386i	0.160692	−	0.278326i	0.935117	+	0.354339i	$0.115294\pi$
$684$	20.4599	+	3.02610i	0.782302	+	0.115706i
$685$	−4.21131	−	2.43140i	−0.160906	−	0.0928990i
$686$	10.7785	−	5.20900i	0.411526	−	0.198881i
$687$	−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	$-0.801664\pi$
$691$	−23.9580	−	41.4965i	−0.911406	−	1.57860i	−0.0993267	−	0.995055i	$-0.531669\pi$
$692$	−20.6018	+	8.15131i	−0.783163	+	0.309866i
$693$	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
$696$	−1.98317	+	2.15518i	−0.0751719	+	0.0816917i
$697$			4.85473i			0.183886i
$698$	−2.88512	+	4.24426i	−0.109203	+	0.160648i
$699$	−1.99007	+	1.14897i	−0.0752715	+	0.0434580i
$700$	6.30781	−	2.49575i	0.238413	−	0.0943303i
$701$		−	13.8974i		−	0.524898i	−0.964946	−	0.262449i	$-0.915470\pi$
$701$		−	13.8974i		−	0.524898i	0.964946	−	0.262449i	$-0.0845301\pi$
$702$	−0.570409	+	4.44025i	−0.0215287	+	0.167587i
$703$	−26.5637			−1.00187
$704$	3.61895	+	43.4595i	0.136394	+	1.63794i
$705$	0.0169871	+	0.0294225i	0.000639771	+	0.00110812i
$706$	38.5972	+	26.2371i	1.45262	+	0.987448i
$707$	10.3073			0.387647
$708$	0.726115	+	0.575786i	0.0272891	+	0.0216394i
$709$	−14.0154	+	24.2754i	−0.526360	+	0.911682i	0.473169	+	0.880972i	$0.343110\pi$
$709$	−14.0154	+	24.2754i	−0.526360	+	0.911682i	−0.999528	+	0.0307098i	$0.990223\pi$
$710$	−1.67119	+	22.7212i	−0.0627187	+	0.852712i
$711$	−10.0129	+	17.3429i	−0.375513	+	0.650408i
$712$	−27.3033	+	8.54590i	−1.02323	+	0.320271i
$713$	−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
$718$	5.03103	−	2.43137i	0.187756	−	0.0907381i
$719$	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
$722$	5.52156	−	8.12271i	0.205491	−	0.302296i
$723$	0.0343370			0.00127701
$724$	−8.40344	−	6.66366i	−0.312311	−	0.247653i
$725$	6.10639	−	3.52552i	0.226785	−	0.130935i
$726$	−3.49976	+	1.69135i	−0.129888	+	0.0627719i
$727$	−37.8645			−1.40432			−0.702158	−	0.712022i	$-0.747780\pi$
$727$	−37.8645			−1.40432			−0.702158	+	0.712022i	$0.747780\pi$
$728$	−33.5230	+	8.52396i	−1.24244	+	0.315919i
$729$	25.8424			0.957125
$730$	12.9325	−	6.24996i	0.478653	−	0.231321i
$731$	1.76532	−	1.01921i	0.0652926	−	0.0376967i
$732$	1.62907	−	2.05440i	0.0602121	−	0.0759326i
$733$	21.9460			0.810593			0.405297	−	0.914185i	$-0.367168\pi$
$733$	21.9460			0.810593			0.405297	+	0.914185i	$0.367168\pi$
$734$	1.42707	−	2.09935i	0.0526741	−	0.0774883i
$735$	−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
$738$	15.2040	−	7.34774i	0.559668	−	0.270474i
$739$	18.5348	+	32.1031i	0.681812	+	1.18093i	0.974427	+	0.224703i	$0.0721412\pi$
$739$	18.5348	+	32.1031i	0.681812	+	1.18093i	−0.292615	+	0.956230i	$0.594525\pi$
$740$	−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	$0.622384\pi$
$744$	−0.944192	−	3.01660i	−0.0346158	−	0.110594i
$745$	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
$748$	8.20309	−	10.3448i	0.299935	−	0.378243i
$749$	9.82699			0.359070
$750$	0.171758	+	0.116756i	0.00627171	+	0.00426331i
$751$	−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	$0.851132\pi$
$752$	−0.901030	+	0.210894i	−0.0328572	+	0.00769051i
$753$	−3.56218			−0.129813
$754$	−33.1733	+	13.8629i	−1.20810	+	0.504857i
$755$			8.82114i			0.321034i
$756$	−2.19117	−	5.53801i	−0.0796920	−	0.201416i
$757$	−0.238409	+	0.137646i	−0.00866512	+	0.00500281i	−0.504326	−	0.863513i	$-0.668259\pi$
$757$	−0.238409	+	0.137646i	−0.00866512	+	0.00500281i	0.495661	+	0.868516i	$0.334926\pi$
$758$	−3.62718	+	5.33591i	−0.131745	+	0.193809i
$759$		−	6.02986i		−	0.218870i
$760$	−6.64970	+	7.22645i	−0.241210	+	0.262131i
$761$	−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
$764$	13.2673	+	33.5320i	0.479993	+	1.21314i
$765$	−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
$769$	−30.3182	+	17.5042i	−1.09330	+	0.631219i	−0.934454	−	0.356084i	$-0.884112\pi$
$769$	−30.3182	+	17.5042i	−1.09330	+	0.631219i	−0.158849	+	0.987303i	$0.550778\pi$
$770$	−23.5430	+	11.3777i	−0.848430	+	0.410026i
$771$	2.89852	+	1.67346i	0.104388	+	0.0602683i
$772$	−3.71357	+	25.1080i	−0.133654	+	0.903655i
$773$	−15.1194	+	26.1876i	−0.543808	+	0.941902i	0.454873	+	0.890556i	$0.349685\pi$
$773$	−15.1194	+	26.1876i	−0.543808	+	0.941902i	−0.998681	+	0.0513463i	$0.983649\pi$
$774$	−5.86379	−	3.98602i	−0.210770	−	0.143275i
$775$			7.60991i			0.273356i
$776$	17.3826	+	15.9953i	0.623998	+	0.574196i
$777$	1.90543	+	3.30030i	0.0683570	+	0.118398i
$778$	−43.8442	+	21.1889i	−1.57189	+	0.759657i
$779$			13.9193i			0.498712i
$780$	−0.792803	−	0.702078i	−0.0283869	−	0.0251384i
$781$		−	87.8181i		−	3.14238i
$782$	5.61286	+	11.6142i	0.200715	+	0.415323i
$783$	−3.09527	−	5.36117i	−0.110616	−	0.191593i
$784$	13.1397	−	12.3275i	0.469274	−	0.440268i
$785$		−	20.0331i		−	0.715013i
$786$	−1.98514	+	2.92032i	−0.0708076	+	0.104164i
$787$	−26.7704	+	46.3677i	−0.954263	+	1.65283i	−0.218217	+	0.975900i	$0.570024\pi$
$787$	−26.7704	+	46.3677i	−0.954263	+	1.65283i	−0.736046	+	0.676931i	$0.763309\pi$
$788$	46.2259	+	6.83699i	1.64673	+	0.243558i
$789$	2.49378	+	1.43979i	0.0887810	+	0.0512577i
$790$	−4.13745	−	8.56126i	−0.147204	−	0.304596i
$791$	7.33382	−	4.23418i	0.260760	−	0.150550i
$792$	−44.8134	−	10.0333i	−1.59237	−	0.356519i
$793$	28.7071	−	14.5554i	1.01942	−	0.516876i
$794$	33.7246	+	2.48051i	1.19684	+	0.0880300i
$795$	0.379395	+	0.657132i	0.0134558	+	0.0233061i
$796$	7.29446	+	18.4362i	0.258545	+	0.653453i
$797$	−4.88240	−	2.81886i	−0.172944	−	0.0998490i	0.411029	−	0.911622i	$-0.365169\pi$
$797$	−4.88240	−	2.81886i	−0.172944	−	0.0998490i	−0.583973	+	0.811773i	$0.698503\pi$
$798$	2.43919	+	0.179407i	0.0863463	+	0.00635094i
$799$	0.242617	+	0.140075i	0.00858318	+	0.00495550i
$800$	−4.39826	+	3.55742i	−0.155502	+	0.125774i
$801$		−	30.1268i		−	1.06448i
$802$	44.7381	+	30.4116i	1.57976	+	1.07387i
$803$	−47.9483	+	27.6829i	−1.69206	+	0.976910i
$804$	−2.35529	+	0.931894i	−0.0830647	+	0.0328654i
$805$		−	25.5478i		−	0.900442i
$806$	4.94413	−	38.4868i	0.174150	−	1.35564i
$807$	−3.04588			−0.107220
$808$	−8.20289	+	2.56750i	−0.288577	+	0.0903242i
$809$	17.1082	+	29.6322i	0.601491	+	1.04181i	0.992596	+	0.121466i	$0.0387597\pi$
$809$	17.1082	+	29.6322i	0.601491	+	1.04181i	−0.391105	+	0.920346i	$0.627907\pi$
$810$	−7.00143	+	10.2997i	−0.246005	+	0.361895i
$811$	13.1897			0.463154			0.231577	−	0.972817i	$-0.425611\pi$
$811$	13.1897			0.463154			0.231577	+	0.972817i	$0.425611\pi$
$812$	29.7191	−	37.4783i	1.04294	−	1.31523i
$813$	−1.89444	+	3.28126i	−0.0664408	+	0.115079i
$814$	58.8226	+	4.32652i	2.06173	+	0.151644i
$815$	0.778008	−	1.34755i	0.0272524	−	0.0472026i
$816$	−0.692622	+	0.162114i	−0.0242466	+	0.00567513i
$817$	5.06147	−	2.92224i	0.177078	−	0.102236i
$818$	−3.19409	+	43.4263i	−0.111679	+	1.51837i
$819$	1.97845	−	36.3704i	0.0691326	−	1.27088i
$820$	−1.17313	+	7.93169i	−0.0409675	+	0.276987i
$821$	4.22185	+	7.31246i	0.147344	+	0.255207i	0.930245	−	0.366939i	$-0.119594\pi$
$821$	4.22185	+	7.31246i	0.147344	+	0.255207i	−0.782901	+	0.622146i	$0.786261\pi$
$822$	−0.439446	−	0.909306i	−0.0153274	−	0.0317157i
$823$	2.89141	−	5.00807i	0.100788	−	0.174570i	−0.811221	−	0.584739i	$-0.801197\pi$
$823$	2.89141	−	5.00807i	0.100788	−	0.174570i	0.912010	+	0.410169i	$0.134530\pi$
$824$	−24.2676	−	5.43332i	−0.845403	−	0.189279i
$825$	−0.693289	−	0.400271i	−0.0241372	−	0.0139356i
$826$	−12.5164	−	8.50826i	−0.435501	−	0.296040i
$827$	−42.1491			−1.46567			−0.732834	−	0.680408i	$-0.761803\pi$
$827$	−42.1491			−1.46567			−0.732834	+	0.680408i	$0.761803\pi$
$828$	27.8781	−	35.1567i	0.968832	−	1.22178i
$829$	14.6749	−	8.47258i	0.509682	−	0.294265i	−0.223021	−	0.974814i	$-0.571592\pi$
$829$	14.6749	−	8.47258i	0.509682	−	0.294265i	0.732703	+	0.680549i	$0.238259\pi$
$830$	−3.27258	−	6.77165i	−0.113593	−	0.235048i
$831$	−0.223026			−0.00773667
$832$	24.5553	−	15.1340i	0.851302	−	0.524677i
$833$	−5.45452			−0.188988
$834$	−0.263326	−	0.544878i	−0.00911824	−	0.0188676i
$835$	−13.8670	+	8.00610i	−0.479886	+	0.277062i
$836$	23.5197	−	29.6603i	0.813445	−	1.02582i
$837$	6.68120			0.230936
$838$	6.37816	+	4.33567i	0.220330	+	0.149773i
$839$	25.9767	+	14.9977i	0.896817	+	0.517777i	0.876166	−	0.482009i	$-0.160093\pi$
$839$	25.9767	+	14.9977i	0.896817	+	0.517777i	0.0206506	+	0.999787i	$0.493426\pi$
$840$	1.37481	+	0.307808i	0.0474354	+	0.0106204i
$841$	10.3586	−	17.9417i	0.357194	−	0.618678i
$842$	−16.7970	−	34.7565i	−0.578863	−	1.19779i
$843$	−1.47715	−	2.55850i	−0.0508758	−	0.0881194i
$844$	0.719667	−	4.86577i	0.0247720	−	0.167487i
$845$	−5.24042	−	11.8970i	−0.180276	−	0.409268i
$846$	0.0714804	−	0.971835i	0.00245755	−	0.0334124i
$847$	54.9763	−	31.7406i	1.88901	−	1.09062i
$848$	−20.1239	+	4.71018i	−0.691058	+	0.161748i
$849$	−0.675510	+	1.17002i	−0.0231834	+	0.0401549i
$850$	1.70794	+	0.125623i	0.0585819	+	0.00430882i
$851$	−28.8137	+	49.9068i	−0.987721	+	1.71078i
$852$	−2.93987	+	3.70743i	−0.100718	+	0.127014i
$853$	28.6856			0.982177			0.491089	−	0.871110i	$-0.336599\pi$
$853$	28.6856			0.982177			0.491089	+	0.871110i	$0.336599\pi$
$854$	−24.0724	+	35.4126i	−0.823741	+	1.21180i
$855$	−5.17061	−	8.95576i	−0.176831	−	0.306280i
$856$	−7.82061	+	2.44784i	−0.267303	+	0.0836656i
$857$	−15.3997			−0.526043			−0.263021	−	0.964790i	$-0.584719\pi$
$857$	−15.3997			−0.526043			−0.263021	+	0.964790i	$0.584719\pi$
$858$	3.24623	+	2.47478i	0.110824	+	0.0844876i
$859$		−	34.6943i		−	1.18375i	−0.806028	−	0.591877i	$-0.798387\pi$
$859$		−	34.6943i		−	1.18375i	0.806028	−	0.591877i	$-0.201613\pi$
$860$	3.13048	−	1.23860i	0.106748	−	0.0422360i
$861$	1.72935	−	0.998442i	0.0589362	−	0.0340268i
$862$	12.8249	+	8.71793i	0.436816	+	0.296934i
$863$		−	48.7133i		−	1.65822i	−0.559085	−	0.829110i	$-0.688848\pi$
$863$		−	48.7133i		−	1.65822i	0.559085	−	0.829110i	$-0.311152\pi$
$864$	3.12328	+	3.86151i	0.106256	+	0.131371i
$865$	9.59373	+	5.53894i	0.326197	+	0.188330i
$866$	52.4148	+	3.85521i	1.78113	+	0.131005i
$867$	−1.97556	−	1.14059i	−0.0670935	−	0.0387365i
$868$	18.9924	+	48.0018i	0.644644	+	1.62929i
$869$	18.3260	+	31.7416i	0.621667	+	1.07676i
$870$	1.46044	+	0.107419i	0.0495137	+	0.00364183i
$871$	−31.0483	−	1.68894i	−1.05203	−	0.0572276i
$872$	−27.9072	−	6.24820i	−0.945058	−	0.211591i
$873$	−21.5423	+	12.4374i	−0.729095	+	0.420943i
$874$	16.0930	+	33.2999i	0.544355	+	1.12639i
$875$	−2.93738	−	1.69590i	−0.0993017	−	0.0573318i
$876$	2.95098	+	0.436462i	0.0997042	+	0.0147467i
$877$	0.916510	−	1.58744i	0.0309483	−	0.0536041i	−0.850136	−	0.526563i	$-0.823481\pi$
$877$	0.916510	−	1.58744i	0.0309483	−	0.0536041i	0.881085	+	0.472958i	$0.156814\pi$
$878$	22.4927	−	33.0888i	0.759092	−	1.11669i
$879$			2.35403i			0.0793996i
$880$	15.9021	−	14.9192i	0.536059	−	0.502925i
$881$	6.09651	+	10.5595i	0.205397	+	0.355758i	0.950259	−	0.311461i	$-0.100818\pi$
$881$	6.09651	+	10.5595i	0.205397	+	0.355758i	−0.744862	+	0.667218i	$0.767485\pi$
$882$	8.25553	+	17.0824i	0.277978	+	0.575196i
$883$		−	30.6421i		−	1.03119i	−0.856832	−	0.515595i	$-0.827571\pi$
$883$		−	30.6421i		−	1.03119i	0.856832	−	0.515595i	$-0.172429\pi$
$884$	−8.55623	−	1.74498i	−0.287777	−	0.0586899i
$885$		−	0.463350i		−	0.0155753i
$886$	−35.8123	+	17.3072i	−1.20314	+	0.581448i
$887$	−23.2503	−	40.2706i	−0.780668	−	1.35216i	−0.931553	−	0.363605i	$-0.881546\pi$
$887$	−23.2503	−	40.2706i	−0.780668	−	1.35216i	0.150886	−	0.988551i	$-0.451787\pi$
$888$	−2.33848	−	2.15185i	−0.0784744	−	0.0722113i
$889$		−	3.11834i		−	0.104586i
$890$	11.8302	+	8.04182i	0.396550	+	0.269562i
$891$	24.0028	−	41.5741i	0.804125	−	1.39279i
$892$	−0.658414	+	4.45163i	−0.0220453	+	0.149051i
$893$	0.695625	+	0.401619i	0.0232782	+	0.0134397i
$894$	1.80602	−	0.872804i	0.0604022	−	0.0291909i
$895$	15.5388	−	8.97132i	0.519404	−	0.299878i
$896$	−18.8650	+	33.4165i	−0.630235	+	1.11637i
$897$	−3.55715	+	1.80358i	−0.118770	+	0.0602197i
$898$	0.229575	−	3.12126i	0.00766102	−	0.104158i
$899$	26.8289	+	46.4690i	0.894794	+	1.54983i
$900$	−2.19158	−	5.53906i	−0.0730528	−	0.184635i
$901$	5.41869	+	3.12848i	0.180523	+	0.104225i
$902$	2.26709	−	30.8229i	0.0754858	−	1.02629i
$903$	−0.726124	−	0.419228i	−0.0241639	−	0.0139510i
$904$	−4.78176	+	5.19650i	−0.159039	+	0.172833i
$905$			5.36242i			0.178253i
$906$	−1.02992	+	1.51510i	−0.0342167	+	0.0503359i
$907$	−21.5429	+	12.4378i	−0.715322	+	0.412991i	−0.813028	−	0.582224i	$-0.802183\pi$
$907$	−21.5429	+	12.4378i	−0.715322	+	0.412991i	0.0977067	+	0.995215i	$0.468849\pi$
$908$	−0.533535	−	1.34847i	−0.0177060	−	0.0447505i
$909$		−	9.05117i		−	0.300208i
$910$	13.7539	+	10.4853i	0.455936	+	0.347586i
$911$	35.9651			1.19158			0.595788	−	0.803142i	$-0.296840\pi$
$911$	35.9651			1.19158			0.595788	+	0.803142i	$0.296840\pi$
$912$	−1.98587	+	0.464809i	−0.0657586	+	0.0153914i
$913$	14.4952	+	25.1065i	0.479722	+	0.830902i
$914$	−37.9222	−	25.7783i	−1.25436	−	0.852672i
$915$	−1.31095			−0.0433388
$916$	−1.31552	+	1.65898i	−0.0434659	+	0.0548141i
$917$	28.8346	−	49.9429i	0.952201	−	1.64926i
$918$	0.110292	−	1.49951i	0.00364017	−	0.0494911i
$919$	−16.7986	+	29.0961i	−0.554136	+	0.959792i	0.443834	+	0.896109i	$0.353618\pi$
$919$	−16.7986	+	29.0961i	−0.554136	+	0.959792i	−0.997970	+	0.0636831i	$0.979715\pi$
$920$	6.36380	+	20.3317i	0.209808	+	0.670316i
$921$	−3.72196	+	2.14888i	−0.122643	+	0.0708079i
$922$	−24.3318	−	1.78966i	−0.801327	−	0.0589392i
$923$	−51.8058	+	26.2671i	−1.70521	+	0.864591i
$924$	−5.37211	−	0.794557i	−0.176729	−	0.0261390i
$925$	3.82539	+	6.62576i	0.125778	+	0.217854i
$926$	−9.18483	+	4.43881i	−0.301832	+	0.145868i
$927$	13.0937	−	22.6789i	0.430052	−	0.744873i
$928$	−14.3157	+	37.2292i	−0.469936	+	1.22211i
$929$	−13.3724	−	7.72054i	−0.438733	−	0.253303i	0.264327	−	0.964433i	$-0.414850\pi$
$929$	−13.3724	−	7.72054i	−0.438733	−	0.253303i	−0.703060	+	0.711130i	$0.748184\pi$
$930$	−0.888499	+	1.30706i	−0.0291350	+	0.0428602i
$931$	−15.6390			−0.512549
$932$	−19.4447	+	24.5215i	−0.636934	+	0.803228i
$933$	−1.95431	+	1.12832i	−0.0639813	+	0.0369396i
$934$	−19.0204	+	9.19209i	−0.622366	+	0.300774i
$935$	−6.60124			−0.215884
$936$	7.48514	+	29.4375i	0.244659	+	0.962193i
$937$	23.9331			0.781861			0.390930	−	0.920420i	$-0.372153\pi$
$937$	23.9331			0.781861			0.390930	+	0.920420i	$0.372153\pi$
$938$	37.2455	−	17.9998i	1.21611	−	0.587716i
$939$	1.12962	−	0.652188i	0.0368638	−	0.0212833i
$940$	0.362541	+	0.287484i	0.0118248	+	0.00937668i
$941$	43.1355			1.40618			0.703088	−	0.711102i	$-0.251804\pi$
$941$	43.1355			1.40618			0.703088	+	0.711102i	$0.251804\pi$
$942$	2.33898	−	3.44085i	0.0762082	−	0.112109i
$943$	26.1511	+	15.0983i	0.851595	+	0.491669i
$944$	12.0803	+	3.65337i	0.393180	+	0.118907i
$945$	−1.48893	+	2.57891i	−0.0484350	+	0.0838919i
$946$	−11.6840	+	5.64662i	−0.379881	+	0.183587i
$947$	24.3409	+	42.1597i	0.790974	+	1.37001i	0.925365	+	0.379078i	$0.123759\pi$
$947$	24.3409	+	42.1597i	0.790974	+	1.37001i	−0.134391	+	0.990928i	$0.542908\pi$
$948$	0.288936	−	1.95353i	0.00938420	−	0.0634479i
$949$	30.6725	+	20.0056i	0.995671	+	0.649408i
$950$	4.89697	+	0.360182i	0.158879	+	0.0116858i
$951$	−0.485869	+	0.280517i	−0.0157554	+	0.00909638i
$952$	11.0869	−	3.47019i	0.359328	−	0.112469i
$953$	10.3667	−	17.9557i	0.335812	−	0.581643i	−0.647829	−	0.761786i	$-0.724323\pi$
$953$	10.3667	−	17.9557i	0.335812	−	0.581643i	0.983640	+	0.180143i	$0.0576561\pi$
$954$	1.59647	−	21.7053i	0.0516875	−	0.702734i
$955$	9.01532	−	15.6150i	0.291729	−	0.505289i
$956$	42.7205	+	33.8760i	1.38168	+	1.09563i
$957$	−5.64465			−0.182466
$958$	−34.0474	−	23.1444i	−1.10002	−	0.747761i
$959$	8.24682	+	14.2839i	0.266304	+	0.461251i
$960$	−1.17079	+	0.0974934i	−0.0377870	+	0.00314659i
$961$	−26.9107			−0.868086
$962$	−15.0420	−	35.9949i	−0.484973	−	1.16052i
$963$		−	8.62936i		−	0.278077i
$964$	0.434833	−	0.172046i	0.0140050	−	0.00554123i
$965$	10.9903	−	6.34528i	0.353792	−	0.204262i
$966$	2.98285	−	4.38804i	0.0959716	−	0.141183i
$967$		−	24.9508i		−	0.802365i	−0.915998	−	0.401182i	$-0.868599\pi$
$967$		−	24.9508i		−	0.802365i	0.915998	−	0.401182i	$-0.131401\pi$
$968$	−35.8454	+	38.9543i	−1.15211	+	1.25204i
$969$	0.534727	+	0.308725i	0.0171779	+	0.00991767i
$970$	0.866384	−	11.7792i	0.0278179	−	0.378208i
$971$	−13.8848	−	8.01642i	−0.445586	−	0.257259i	0.260378	−	0.965507i	$-0.416153\pi$
$971$	−13.8848	−	8.01642i	−0.445586	−	0.257259i	−0.705964	+	0.708248i	$0.749486\pi$
$972$	−7.30340	+	2.88966i	−0.234257	+	0.0926859i
$973$	4.94169	+	8.55925i	0.158423	+	0.274397i
$974$	−0.375934	+	5.11114i	−0.0120457	+	0.163771i
$975$	−0.0287604	+	0.528711i	−0.000921070	+	0.0169323i
$976$	10.3365	−	34.1787i	0.330862	−	1.09403i
$977$	−7.66769	+	4.42694i	−0.245311	+	0.141630i	−0.617615	−	0.786480i	$-0.711901\pi$
$977$	−7.66769	+	4.42694i	−0.245311	+	0.141630i	0.372304	+	0.928111i	$0.378568\pi$
$978$	0.290963	−	0.140615i	0.00930397	−	0.00449638i
$979$	−47.7519	−	27.5696i	−1.52616	−	0.881128i
$980$	−8.91164	−	1.31807i	−0.284672	−	0.0421041i
$981$	15.0574	−	26.0802i	0.480747	−	0.832678i
$982$	−32.3157	−	21.9672i	−1.03123	−	0.701001i
$983$			7.64019i			0.243684i	0.992549	+	0.121842i	$0.0388802\pi$
$983$			7.64019i			0.243684i	−0.992549	+	0.121842i	$0.961120\pi$
$984$	−1.12756	+	1.22536i	−0.0359454	+	0.0390631i
$985$	−11.6822	−	20.2341i	−0.372225	−	0.644713i
$986$	10.8722	−	5.25429i	0.346243	−	0.167331i
$987$		−	0.115234i		−	0.00366793i
$988$	−24.5322	−	5.00315i	−0.780473	−	0.159171i
$989$		−	12.6790i		−	0.403169i
$990$	9.99112	+	20.6737i	0.317539	+	0.657055i
$991$	−23.3505	−	40.4442i	−0.741752	−	1.28475i	−0.951697	−	0.307039i	$-0.900662\pi$
$991$	−23.3505	−	40.4442i	−0.741752	−	1.28475i	0.209945	−	0.977713i	$-0.432672\pi$
$992$	−27.0717	−	33.4704i	−0.859526	−	1.06269i
$993$		−	0.966010i		−	0.0306554i
$994$	43.4418	−	63.9068i	1.37789	−	2.02700i
$995$	4.95670	−	8.58525i	0.157138	−	0.272171i
$996$	0.228538	−	1.54518i	0.00724150	−	0.0489608i
$997$	−16.0793	−	9.28340i	−0.509237	−	0.294008i	0.223283	−	0.974754i	$-0.428323\pi$
$997$	−16.0793	−	9.28340i	−0.509237	−	0.294008i	−0.732520	+	0.680746i	$0.761656\pi$
$998$	7.40976	+	15.3324i	0.234552	+	0.485338i
$999$	5.81717	−	3.35854i	0.184047	−	0.106260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.ca.b.101.10	yes	56
8.5	even	2		520.2.ca.a.101.20	✓	56
13.4	even	6		520.2.ca.a.381.20	yes	56
104.69	even	6	inner	520.2.ca.b.381.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.ca.a.101.20	✓	56	8.5	even	2
520.2.ca.a.381.20	yes	56	13.4	even	6
520.2.ca.b.101.10	yes	56	1.1	even	1	trivial
520.2.ca.b.381.10	yes	56	104.69	even	6	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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.ca (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615362 - 1.27331i) q^{2} +(-0.127180 + 0.0734274i) q^{3} +(-1.24266 + 1.56710i) q^{4} +1.00000 q^{5} +(0.171758 + 0.116756i) q^{6} +(-2.93738 - 1.69590i) q^{7} +(2.76009 + 0.617962i) q^{8} +(-1.48922 + 2.57940i) q^{9} +(-0.615362 - 1.27331i) 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} +(-0.911597 - 3.89474i) q^{16} +(-0.605480 + 1.04872i) q^{17} +(4.20079 + 0.308977i) q^{18} +(-1.73602 + 3.00687i) q^{19} +(-1.24266 + 1.56710i) q^{20} +0.498102 q^{21} +(4.33397 - 6.37565i) q^{22} +(3.76612 + 6.52310i) q^{23} +(-0.396404 + 0.124074i) q^{24} +1.00000 q^{25} +(-5.05746 - 0.649697i) q^{26} -0.877962i q^{27} +(6.30781 - 2.49575i) q^{28} +(6.10639 - 3.52552i) q^{29} +(0.171758 + 0.116756i) q^{30} +7.60991i q^{31} +(-4.39826 + 3.55742i) q^{32} +(-0.693289 - 0.400271i) q^{33} +(1.70794 + 0.125623i) q^{34} +(-2.93738 - 1.69590i) q^{35} +(-2.19158 - 5.53906i) 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} +(-0.306513 - 0.634240i) q^{42} +(-1.45778 - 0.841651i) q^{43} +(-10.7852 - 1.59517i) q^{44} +(-1.48922 + 2.57940i) q^{45} +(5.98844 - 8.80952i) q^{46} -0.231346i q^{47} +(0.401917 + 0.428397i) q^{48} +(2.25215 + 3.90083i) q^{49} +(-0.615362 - 1.27331i) q^{50} -0.177835i q^{51} +(2.28490 + 6.83953i) q^{52} -5.16695i q^{53} +(-1.11792 + 0.540264i) q^{54} +(2.72562 + 4.72092i) q^{55} +(-7.05945 - 6.49603i) q^{56} -0.509884i q^{57} +(-8.24674 - 5.60587i) q^{58} +(-1.57758 + 2.73245i) q^{59} +(0.0429734 - 0.290549i) q^{60} +(7.73090 + 4.46344i) q^{61} +(9.68980 - 4.68285i) 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} +(-0.891046 - 2.25205i) q^{68} +(-0.957949 - 0.553072i) q^{69} +(-0.351858 + 4.78380i) q^{70} +(-13.9514 - 8.05487i) q^{71} +(-5.70435 + 6.19911i) q^{72} +10.1566i q^{73} +(6.08268 - 8.94816i) q^{74} +(-0.127180 + 0.0734274i) q^{75} +(-2.55478 - 6.45702i) q^{76} -18.4895i q^{77} +(0.690913 - 0.288728i) q^{78} +6.72360 q^{79} +(-0.911597 - 3.89474i) q^{80} +(-4.40318 - 7.62654i) q^{81} +(-4.68882 - 3.18731i) q^{82} +5.31813 q^{83} +(-0.618971 + 0.780575i) q^{84} +(-0.605480 + 1.04872i) q^{85} +(-0.174622 + 2.37414i) q^{86} +(-0.517740 + 0.896752i) q^{87} +(4.60563 + 14.7145i) 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} +(-0.294576 + 0.142361i) q^{94} +(-1.73602 + 3.00687i) q^{95} +(0.298159 - 0.775386i) q^{96} +(7.23275 + 4.17583i) q^{97} +(3.58110 - 5.26811i) q^{98} -16.2362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 6 q^{4} + 56 q^{5} - 13 q^{6} + 28 q^{9} - 8 q^{11} + 6 q^{12} - 4 q^{14} + 14 q^{16} + 18 q^{18} - 16 q^{19} + 6 q^{20} - 6 q^{22} + 12 q^{23} + 22 q^{24} + 56 q^{25} - 37 q^{26} - 12 q^{28} - 13 q^{30}+ \cdots - 48 q^{99}+O(q^{100}) \) 56 * q + 6 * q^4 + 56 * q^5 - 13 * q^6 + 28 * q^9 - 8 * q^11 + 6 * q^12 - 4 * q^14 + 14 * q^16 + 18 * q^18 - 16 * q^19 + 6 * q^20 - 6 * q^22 + 12 * q^23 + 22 * q^24 + 56 * q^25 - 37 * q^26 - 12 * q^28 - 13 * q^30 - 30 * q^32 - 16 * q^34 + 15 * q^36 + 4 * q^37 - 24 * q^39 - 61 * q^42 + 24 * q^44 + 28 * q^45 - 19 * q^46 - 51 * q^48 + 20 * q^49 - 64 * q^52 - 5 * q^54 - 8 * q^55 - 23 * q^56 - q^58 - 16 * q^59 + 6 * q^60 + 10 * q^62 - 30 * q^64 + 14 * q^66 - 36 * q^67 - 51 * q^68 - 4 * q^70 - 81 * q^72 + 70 * q^74 - 60 * q^76 + 143 * q^78 + 14 * q^80 - 28 * q^81 + 21 * q^82 + 40 * q^83 + 31 * q^84 - 28 * q^86 - 36 * q^87 - 19 * q^88 + 18 * q^90 + 16 * q^91 - 18 * q^92 + 43 * q^94 - 16 * q^95 - 48 * q^96 + 24 * q^97 + 56 * q^98 - 48 * q^99

Introduction

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