LMFDB - Embedded newform 798.2.p.d.179.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(107,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 5]))

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

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

chi := DirichletCharacter("798.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.p (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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$50$
Relative dimension:	$25$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			179.14
Character	$\chi$	$=$	798.179
Dual form			798.2.p.d.107.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.309702 + 1.70414i) q^{3} +1.00000 q^{4} +0.0905266i q^{5} +(0.309702 + 1.70414i) q^{6} +(2.19691 + 1.47431i) q^{7} +1.00000 q^{8} +(-2.80817 + 1.05555i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.309702 + 1.70414i) q^{3} +1.00000 q^{4} +0.0905266i q^{5} +(0.309702 + 1.70414i) q^{6} +(2.19691 + 1.47431i) q^{7} +1.00000 q^{8} +(-2.80817 + 1.05555i) q^{9} +0.0905266i q^{10} +(1.62630 + 0.938943i) q^{11} +(0.309702 + 1.70414i) q^{12} +(-1.58384 + 0.914430i) q^{13} +(2.19691 + 1.47431i) q^{14} +(-0.154270 + 0.0280363i) q^{15} +1.00000 q^{16} +(2.76844 - 1.59836i) q^{17} +(-2.80817 + 1.05555i) q^{18} +(-4.22852 + 1.05811i) q^{19} +0.0905266i q^{20} +(-1.83204 + 4.20043i) q^{21} +(1.62630 + 0.938943i) q^{22} +(0.0885975 + 0.0511518i) q^{23} +(0.309702 + 1.70414i) q^{24} +4.99180 q^{25} +(-1.58384 + 0.914430i) q^{26} +(-2.66850 - 4.45860i) q^{27} +(2.19691 + 1.47431i) q^{28} +(2.95022 + 5.10993i) q^{29} +(-0.154270 + 0.0280363i) q^{30} +(-5.97874 - 3.45183i) q^{31} +1.00000 q^{32} +(-1.09642 + 3.06223i) q^{33} +(2.76844 - 1.59836i) q^{34} +(-0.133464 + 0.198879i) q^{35} +(-2.80817 + 1.05555i) q^{36} +(-3.44122 + 1.98679i) q^{37} +(-4.22852 + 1.05811i) q^{38} +(-2.04883 - 2.41588i) q^{39} +0.0905266i q^{40} +(5.54889 - 9.61096i) q^{41} +(-1.83204 + 4.20043i) q^{42} +(-2.92421 + 5.06488i) q^{43} +(1.62630 + 0.938943i) q^{44} +(-0.0955553 - 0.254214i) q^{45} +(0.0885975 + 0.0511518i) q^{46} +(3.30117 + 1.90593i) q^{47} +(0.309702 + 1.70414i) q^{48} +(2.65282 + 6.47785i) q^{49} +4.99180 q^{50} +(3.58122 + 4.22279i) q^{51} +(-1.58384 + 0.914430i) q^{52} +1.79033 q^{53} +(-2.66850 - 4.45860i) q^{54} +(-0.0849993 + 0.147223i) q^{55} +(2.19691 + 1.47431i) q^{56} +(-3.11275 - 6.87828i) q^{57} +(2.95022 + 5.10993i) q^{58} +(-6.80692 - 11.7899i) q^{59} +(-0.154270 + 0.0280363i) q^{60} +(-2.93339 + 5.08079i) q^{61} +(-5.97874 - 3.45183i) q^{62} +(-7.72550 - 1.82116i) q^{63} +1.00000 q^{64} +(-0.0827802 - 0.143380i) q^{65} +(-1.09642 + 3.06223i) q^{66} -10.7024i q^{67} +(2.76844 - 1.59836i) q^{68} +(-0.0597308 + 0.166824i) q^{69} +(-0.133464 + 0.198879i) q^{70} +(5.67452 - 9.82856i) q^{71} +(-2.80817 + 1.05555i) q^{72} +(6.12163 + 10.6030i) q^{73} +(-3.44122 + 1.98679i) q^{74} +(1.54597 + 8.50672i) q^{75} +(-4.22852 + 1.05811i) q^{76} +(2.18853 + 4.46044i) q^{77} +(-2.04883 - 2.41588i) q^{78} +4.09675i q^{79} +0.0905266i q^{80} +(6.77163 - 5.92833i) q^{81} +(5.54889 - 9.61096i) q^{82} +10.2906i q^{83} +(-1.83204 + 4.20043i) q^{84} +(0.144694 + 0.250618i) q^{85} +(-2.92421 + 5.06488i) q^{86} +(-7.79433 + 6.61014i) q^{87} +(1.62630 + 0.938943i) q^{88} +(3.81294 - 6.60421i) q^{89} +(-0.0955553 - 0.254214i) q^{90} +(-4.82770 - 0.326150i) q^{91} +(0.0885975 + 0.0511518i) q^{92} +(4.03076 - 11.2576i) q^{93} +(3.30117 + 1.90593i) q^{94} +(-0.0957873 - 0.382794i) q^{95} +(0.309702 + 1.70414i) q^{96} +(-14.1132 - 8.14828i) q^{97} +(2.65282 + 6.47785i) q^{98} +(-5.55802 - 0.920073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	$ 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) $ 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.309702	+	1.70414i	0.178807	+	0.983884i
$3$	0.309702	+	1.70414i	0.178807	+	0.983884i
$4$	1.00000			0.500000
$5$			0.0905266i			0.0404847i	0.999795	+	0.0202424i	$0.00644378\pi$
$5$			0.0905266i			0.0404847i	−0.999795	+	0.0202424i	$0.993556\pi$
$6$	0.309702	+	1.70414i	0.126435	+	0.695711i
$7$	2.19691	+	1.47431i	0.830354	+	0.557237i
$7$	2.19691	+	1.47431i	0.830354	+	0.557237i
$8$	1.00000			0.353553
$9$	−2.80817	+	1.05555i	−0.936056	+	0.351850i
$10$			0.0905266i			0.0286270i
$11$	1.62630	+	0.938943i	0.490347	+	0.283102i	0.724718	−	0.689045i	$-0.241970\pi$
$11$	1.62630	+	0.938943i	0.490347	+	0.283102i	−0.234371	+	0.972147i	$0.575303\pi$
$12$	0.309702	+	1.70414i	0.0894033	+	0.491942i
$13$	−1.58384	+	0.914430i	−0.439278	+	0.253617i	−0.703291	−	0.710902i	$-0.748287\pi$
$13$	−1.58384	+	0.914430i	−0.439278	+	0.253617i	0.264013	+	0.964519i	$0.414954\pi$
$14$	2.19691	+	1.47431i	0.587149	+	0.394026i
$15$	−0.154270	+	0.0280363i	−0.0398323	+	0.00723894i
$16$	1.00000			0.250000
$17$	2.76844	−	1.59836i	0.671446	−	0.387660i	−0.125178	−	0.992134i	$-0.539950\pi$
$17$	2.76844	−	1.59836i	0.671446	−	0.387660i	0.796624	+	0.604475i	$0.206617\pi$
$18$	−2.80817	+	1.05555i	−0.661892	+	0.248796i
$19$	−4.22852	+	1.05811i	−0.970089	+	0.242748i
$19$	−4.22852	+	1.05811i	−0.970089	+	0.242748i
$20$			0.0905266i			0.0202424i
$21$	−1.83204	+	4.20043i	−0.399784	+	0.916610i
$22$	1.62630	+	0.938943i	0.346728	+	0.200183i
$23$	0.0885975	+	0.0511518i	0.0184739	+	0.0106659i	0.509208	−	0.860643i	$-0.329938\pi$
$23$	0.0885975	+	0.0511518i	0.0184739	+	0.0106659i	−0.490735	+	0.871309i	$0.663272\pi$
$24$	0.309702	+	1.70414i	0.0632177	+	0.347856i
$25$	4.99180			0.998361
$26$	−1.58384	+	0.914430i	−0.310616	+	0.179334i
$27$	−2.66850	−	4.45860i	−0.513553	−	0.858058i
$28$	2.19691	+	1.47431i	0.415177	+	0.278618i
$29$	2.95022	+	5.10993i	0.547842	+	0.948890i	0.998422	+	0.0561541i	$0.0178838\pi$
$29$	2.95022	+	5.10993i	0.547842	+	0.948890i	−0.450580	+	0.892736i	$0.648783\pi$
$30$	−0.154270	+	0.0280363i	−0.0281657	+	0.00511870i
$31$	−5.97874	−	3.45183i	−1.07381	−	0.619966i	−0.144592	−	0.989491i	$-0.546187\pi$
$31$	−5.97874	−	3.45183i	−1.07381	−	0.619966i	−0.929221	+	0.369525i	$0.879520\pi$
$32$	1.00000			0.176777
$33$	−1.09642	+	3.06223i	−0.190862	+	0.533065i
$34$	2.76844	−	1.59836i	0.474784	−	0.274117i
$35$	−0.133464	+	0.198879i	−0.0225596	+	0.0336166i
$36$	−2.80817	+	1.05555i	−0.468028	+	0.175925i
$37$	−3.44122	+	1.98679i	−0.565733	+	0.326626i	−0.755443	−	0.655214i	$-0.772578\pi$
$37$	−3.44122	+	1.98679i	−0.565733	+	0.326626i	0.189710	+	0.981840i	$0.439245\pi$
$38$	−4.22852	+	1.05811i	−0.685957	+	0.171649i
$39$	−2.04883	−	2.41588i	−0.328076	−	0.386850i
$40$			0.0905266i			0.0143135i
$41$	5.54889	−	9.61096i	0.866592	−	1.50098i	0.00113331	−	0.999999i	$-0.499639\pi$
$41$	5.54889	−	9.61096i	0.866592	−	1.50098i	0.865458	−	0.500981i	$-0.167027\pi$
$42$	−1.83204	+	4.20043i	−0.282690	+	0.648141i
$43$	−2.92421	+	5.06488i	−0.445938	+	0.772387i	−0.998117	−	0.0613382i	$-0.980463\pi$
$43$	−2.92421	+	5.06488i	−0.445938	+	0.772387i	0.552179	+	0.833726i	$0.313797\pi$
$44$	1.62630	+	0.938943i	0.245174	+	0.141551i
$45$	−0.0955553	−	0.254214i	−0.0142445	−	0.0378960i
$46$	0.0885975	+	0.0511518i	0.0130630	+	0.00754192i
$47$	3.30117	+	1.90593i	0.481525	+	0.278009i	0.721052	−	0.692881i	$-0.243659\pi$
$47$	3.30117	+	1.90593i	0.481525	+	0.278009i	−0.239527	+	0.970890i	$0.576992\pi$
$48$	0.309702	+	1.70414i	0.0447017	+	0.245971i
$49$	2.65282	+	6.47785i	0.378975	+	0.925407i
$50$	4.99180			0.705948
$51$	3.58122	+	4.22279i	0.501471	+	0.591309i
$52$	−1.58384	+	0.914430i	−0.219639	+	0.126809i
$53$	1.79033			0.245921			0.122961	−	0.992412i	$-0.460761\pi$
$53$	1.79033			0.245921			0.122961	+	0.992412i	$0.460761\pi$
$54$	−2.66850	−	4.45860i	−0.363137	−	0.606739i
$55$	−0.0849993	+	0.147223i	−0.0114613	+	0.0198516i
$56$	2.19691	+	1.47431i	0.293574	+	0.197013i
$57$	−3.11275	−	6.87828i	−0.412294	−	0.911051i
$58$	2.95022	+	5.10993i	0.387383	+	0.670967i
$59$	−6.80692	−	11.7899i	−0.886185	−	1.53492i	−0.844349	−	0.535793i	$-0.820013\pi$
$59$	−6.80692	−	11.7899i	−0.886185	−	1.53492i	−0.0418361	−	0.999124i	$-0.513321\pi$
$60$	−0.154270	+	0.0280363i	−0.0199161	+	0.00361947i
$61$	−2.93339	+	5.08079i	−0.375582	+	0.650528i	−0.990414	−	0.138131i	$-0.955891\pi$
$61$	−2.93339	+	5.08079i	−0.375582	+	0.650528i	0.614832	+	0.788658i	$0.289224\pi$
$62$	−5.97874	−	3.45183i	−0.759300	−	0.438382i
$63$	−7.72550	−	1.82116i	−0.973322	−	0.229445i
$64$	1.00000			0.125000
$65$	−0.0827802	−	0.143380i	−0.0102676	−	0.0177840i
$66$	−1.09642	+	3.06223i	−0.134960	+	0.376934i
$67$		−	10.7024i		−	1.30751i	−0.756708	−	0.653754i	$-0.773193\pi$
$67$		−	10.7024i		−	1.30751i	0.756708	−	0.653754i	$-0.226807\pi$
$68$	2.76844	−	1.59836i	0.335723	−	0.193830i
$69$	−0.0597308	+	0.166824i	−0.00719075	+	0.0200833i
$70$	−0.133464	+	0.198879i	−0.0159520	+	0.0237705i
$71$	5.67452	−	9.82856i	0.673442	−	1.16644i	−0.303480	−	0.952838i	$-0.598149\pi$
$71$	5.67452	−	9.82856i	0.673442	−	1.16644i	0.976922	−	0.213597i	$-0.0685180\pi$
$72$	−2.80817	+	1.05555i	−0.330946	+	0.124398i
$73$	6.12163	+	10.6030i	0.716482	+	1.24098i	0.962385	+	0.271689i	$0.0875824\pi$
$73$	6.12163	+	10.6030i	0.716482	+	1.24098i	−0.245902	+	0.969295i	$0.579084\pi$
$74$	−3.44122	+	1.98679i	−0.400034	+	0.230960i
$75$	1.54597	+	8.50672i	0.178514	+	0.982272i
$76$	−4.22852	+	1.05811i	−0.485045	+	0.121374i
$77$	2.18853	+	4.46044i	0.249407	+	0.508314i
$78$	−2.04883	−	2.41588i	−0.231985	−	0.273544i
$79$			4.09675i			0.460921i	0.973082	+	0.230460i	$0.0740232\pi$
$79$			4.09675i			0.460921i	−0.973082	+	0.230460i	$0.925977\pi$
$80$			0.0905266i			0.0101212i
$81$	6.77163	−	5.92833i	0.752403	−	0.658703i
$82$	5.54889	−	9.61096i	0.612773	−	1.06135i
$83$			10.2906i			1.12954i	0.825248	+	0.564771i	$0.191035\pi$
$83$			10.2906i			1.12954i	−0.825248	+	0.564771i	$0.808965\pi$
$84$	−1.83204	+	4.20043i	−0.199892	+	0.458305i
$85$	0.144694	+	0.250618i	0.0156943	+	0.0271833i
$86$	−2.92421	+	5.06488i	−0.315326	+	0.546160i
$87$	−7.79433	+	6.61014i	−0.835640	+	0.708681i
$88$	1.62630	+	0.938943i	0.173364	+	0.100092i
$89$	3.81294	−	6.60421i	0.404171	−	0.700045i	−0.590054	−	0.807364i	$-0.700893\pi$
$89$	3.81294	−	6.60421i	0.404171	−	0.700045i	0.994225	+	0.107319i	$0.0342267\pi$
$90$	−0.0955553	−	0.254214i	−0.0100724	−	0.0267965i
$91$	−4.82770	−	0.326150i	−0.506081	−	0.0341898i
$92$	0.0885975	+	0.0511518i	0.00923693	+	0.00533294i
$93$	4.03076	−	11.2576i	0.417970	−	1.16736i
$94$	3.30117	+	1.90593i	0.340490	+	0.196582i
$95$	−0.0957873	−	0.382794i	−0.00982757	−	0.0392738i
$96$	0.309702	+	1.70414i	0.0316088	+	0.173928i
$97$	−14.1132	−	8.14828i	−1.43298	−	0.827333i	−0.435635	−	0.900123i	$-0.643476\pi$
$97$	−14.1132	−	8.14828i	−1.43298	−	0.827333i	−0.997347	+	0.0727902i	$0.976810\pi$
$98$	2.65282	+	6.47785i	0.267975	+	0.654362i
$99$	−5.55802	−	0.920073i	−0.558602	−	0.0924708i
$100$	4.99180			0.499180
$101$		−	19.0334i		−	1.89389i	−0.321393	−	0.946946i	$-0.604151\pi$
$101$		−	19.0334i		−	1.89389i	0.321393	−	0.946946i	$-0.395849\pi$
$102$	3.58122	+	4.22279i	0.354594	+	0.418119i
$103$	0.696199	−	0.401951i	0.0685985	−	0.0396054i	−0.465308	−	0.885149i	$-0.654057\pi$
$103$	0.696199	−	0.401951i	0.0685985	−	0.0396054i	0.533907	+	0.845543i	$0.320723\pi$
$104$	−1.58384	+	0.914430i	−0.155308	+	0.0896672i
$105$	−0.380251	−	0.165848i	−0.0371087	−	0.0161851i
$106$	1.79033			0.173893
$107$	2.82375	+	4.89088i	0.272982	+	0.472819i	0.969624	−	0.244600i	$-0.0786566\pi$
$107$	2.82375	+	4.89088i	0.272982	+	0.472819i	−0.696642	+	0.717419i	$0.745323\pi$
$108$	−2.66850	−	4.45860i	−0.256776	−	0.429029i
$109$	10.4998	−	6.06208i	1.00570	−	0.580642i	0.0957711	−	0.995403i	$-0.469468\pi$
$109$	10.4998	−	6.06208i	1.00570	−	0.580642i	0.909930	+	0.414761i	$0.136135\pi$
$110$	−0.0849993	+	0.147223i	−0.00810436	+	0.0140372i
$111$	−4.45152	−	5.24900i	−0.422519	−	0.498213i
$112$	2.19691	+	1.47431i	0.207588	+	0.139309i
$113$	−0.251685			−0.0236765			−0.0118383	−	0.999930i	$-0.503768\pi$
$113$	−0.251685			−0.0236765			−0.0118383	+	0.999930i	$0.503768\pi$
$114$	−3.11275	−	6.87828i	−0.291536	−	0.644210i
$115$	−0.00463060	+	0.00802043i	−0.000431805	+	0.000747909i
$116$	2.95022	+	5.10993i	0.273921	+	0.474445i
$117$	3.48246	−	4.23970i	0.321954	−	0.391960i
$118$	−6.80692	−	11.7899i	−0.626628	−	1.08535i
$119$	8.43850	+	0.570087i	0.773556	+	0.0522598i
$120$	−0.154270	+	0.0280363i	−0.0140828	+	0.00255935i
$121$	−3.73677	−	6.47228i	−0.339707	−	0.588389i
$122$	−2.93339	+	5.08079i	−0.265577	+	0.459993i
$123$	18.0969	+	6.47954i	1.63174	+	0.584240i
$124$	−5.97874	−	3.45183i	−0.536906	−	0.309983i
$125$			0.904524i			0.0809031i
$126$	−7.72550	−	1.82116i	−0.688242	−	0.162242i
$127$	13.4584	−	7.77018i	1.19424	−	0.689492i	0.234971	−	0.972002i	$-0.424500\pi$
$127$	13.4584	−	7.77018i	1.19424	−	0.689492i	0.959264	+	0.282510i	$0.0911670\pi$
$128$	1.00000			0.0883883
$129$	−9.53689	−	3.41465i	−0.839677	−	0.300643i
$130$	−0.0827802	−	0.143380i	−0.00726030	−	0.0125752i
$131$			8.33637i			0.728352i	0.931330	+	0.364176i	$0.118649\pi$
$131$			8.33637i			0.728352i	−0.931330	+	0.364176i	$0.881351\pi$
$132$	−1.09642	+	3.06223i	−0.0954311	+	0.266533i
$133$	−10.8497	−	3.90957i	−0.940785	−	0.339003i
$134$		−	10.7024i		−	0.924547i
$135$	0.403622	−	0.241570i	0.0347382	−	0.0207910i
$136$	2.76844	−	1.59836i	0.237392	−	0.137058i
$137$		−	10.9211i		−	0.933051i	−0.884508	−	0.466526i	$-0.845506\pi$
$137$		−	10.9211i		−	0.933051i	0.884508	−	0.466526i	$-0.154494\pi$
$138$	−0.0597308	+	0.166824i	−0.00508463	+	0.0142010i
$139$	−4.24309	−	7.34924i	−0.359894	−	0.623354i	0.628049	−	0.778174i	$-0.283854\pi$
$139$	−4.24309	−	7.34924i	−0.359894	−	0.623354i	−0.987943	+	0.154819i	$0.950520\pi$
$140$	−0.133464	+	0.198879i	−0.0112798	+	0.0168083i
$141$	−2.22559	+	6.21592i	−0.187429	+	0.523475i
$142$	5.67452	−	9.82856i	0.476195	−	0.824794i
$143$	−3.43439			−0.287198
$144$	−2.80817	+	1.05555i	−0.234014	+	0.0879625i
$145$	−0.462584	+	0.267073i	−0.0384155	+	0.0221792i
$146$	6.12163	+	10.6030i	0.506630	+	0.877508i
$147$	−10.2176	+	6.52698i	−0.842730	+	0.538336i
$148$	−3.44122	+	1.98679i	−0.282867	+	0.163313i
$149$		−	16.8735i		−	1.38233i	−0.722697	−	0.691165i	$-0.757098\pi$
$149$		−	16.8735i		−	1.38233i	0.722697	−	0.691165i	$-0.242902\pi$
$150$	1.54597	+	8.50672i	0.126228	+	0.694571i
$151$	19.3381	+	11.1648i	1.57371	+	0.908583i	0.995708	+	0.0925480i	$0.0295011\pi$
$151$	19.3381	+	11.1648i	1.57371	+	0.908583i	0.578003	+	0.816035i	$0.303832\pi$
$152$	−4.22852	+	1.05811i	−0.342978	+	0.0858243i
$153$	−6.08711	+	7.41070i	−0.492113	+	0.599120i
$154$	2.18853	+	4.46044i	0.176357	+	0.359432i
$155$	0.312482	−	0.541235i	0.0250992	−	0.0434730i
$156$	−2.04883	−	2.41588i	−0.164038	−	0.193425i
$157$	−6.14717	−	10.6472i	−0.490598	−	0.849740i	0.509344	−	0.860563i	$-0.329888\pi$
$157$	−6.14717	−	10.6472i	−0.490598	−	0.849740i	−0.999941	+	0.0108231i	$0.996555\pi$
$158$			4.09675i			0.325920i
$159$	0.554470	+	3.05098i	0.0439724	+	0.241958i
$160$			0.0905266i			0.00715675i
$161$	0.119227	+	0.242996i	0.00939641	+	0.0191508i
$162$	6.77163	−	5.92833i	0.532029	−	0.465773i
$163$	−2.62307	−	4.54329i	−0.205455	−	0.355858i	0.744823	−	0.667262i	$-0.232534\pi$
$163$	−2.62307	−	4.54329i	−0.205455	−	0.355858i	−0.950278	+	0.311404i	$0.899201\pi$
$164$	5.54889	−	9.61096i	0.433296	−	0.750490i
$165$	−0.277213	−	0.0992552i	−0.0215810	−	0.00772700i
$166$			10.2906i			0.798707i
$167$	4.81106	+	8.33300i	0.372291	+	0.644827i	0.989918	−	0.141645i	$-0.0452391\pi$
$167$	4.81106	+	8.33300i	0.372291	+	0.644827i	−0.617627	+	0.786471i	$0.711906\pi$
$168$	−1.83204	+	4.20043i	−0.141345	+	0.324070i
$169$	−4.82764	+	8.36171i	−0.371357	+	0.643209i
$170$	0.144694	+	0.250618i	0.0110975	+	0.0192215i
$171$	10.7575	−	7.43478i	0.822648	−	0.568552i
$172$	−2.92421	+	5.06488i	−0.222969	+	0.386194i
$173$	17.1075			1.30066			0.650328	−	0.759653i	$-0.274631\pi$
$173$	17.1075			1.30066			0.650328	+	0.759653i	$0.274631\pi$
$174$	−7.79433	+	6.61014i	−0.590887	+	0.501113i
$175$	10.9665	+	7.35947i	0.828993	+	0.556323i
$176$	1.62630	+	0.938943i	0.122587	+	0.0707755i
$177$	17.9835	−	15.2513i	1.35173	−	1.14636i
$178$	3.81294	−	6.60421i	0.285792	−	0.495006i
$179$	−1.70761	+	2.95767i	−0.127633	+	0.221067i	−0.922759	−	0.385377i	$-0.874071\pi$
$179$	−1.70761	+	2.95767i	−0.127633	+	0.221067i	0.795126	+	0.606444i	$0.207405\pi$
$180$	−0.0955553	−	0.254214i	−0.00712227	−	0.0189480i
$181$	1.93919	−	1.11959i	0.144139	−	0.0832184i	−0.426196	−	0.904631i	$-0.640147\pi$
$181$	1.93919	−	1.11959i	0.144139	−	0.0832184i	0.570335	+	0.821412i	$0.306813\pi$
$182$	−4.82770	−	0.326150i	−0.357853	−	0.0241758i
$183$	−9.56684	−	3.42537i	−0.707201	−	0.253211i
$184$	0.0885975	+	0.0511518i	0.00653149	+	0.00377096i
$185$	−0.179857	−	0.311522i	−0.0132234	−	0.0229035i
$186$	4.03076	−	11.2576i	0.295549	−	0.825449i
$187$	6.00308			0.438989
$188$	3.30117	+	1.90593i	0.240763	+	0.139004i
$189$	0.710907	−	13.7293i	0.0517109	−	0.998662i
$190$	−0.0957873	−	0.382794i	−0.00694914	−	0.0277708i
$191$	−14.0910	+	8.13546i	−1.01959	+	0.588661i	−0.913986	−	0.405747i	$-0.867012\pi$
$191$	−14.0910	+	8.13546i	−1.01959	+	0.588661i	−0.105606	+	0.994408i	$0.533678\pi$
$192$	0.309702	+	1.70414i	0.0223508	+	0.122986i
$193$	10.4521	−	6.03452i	0.752358	−	0.434374i	−0.0741873	−	0.997244i	$-0.523636\pi$
$193$	10.4521	−	6.03452i	0.752358	−	0.434374i	0.826545	+	0.562870i	$0.190303\pi$
$194$	−14.1132	−	8.14828i	−1.01327	−	0.585013i
$195$	0.218701	−	0.185474i	0.0156615	−	0.0132821i
$196$	2.65282	+	6.47785i	0.189487	+	0.462704i
$197$			5.03412i			0.358666i	0.983788	+	0.179333i	$0.0573939\pi$
$197$			5.03412i			0.358666i	−0.983788	+	0.179333i	$0.942606\pi$
$198$	−5.55802	−	0.920073i	−0.394991	−	0.0653867i
$199$	−15.6860			−1.11195			−0.555977	−	0.831198i	$-0.687656\pi$
$199$	−15.6860			−1.11195			−0.555977	+	0.831198i	$0.687656\pi$
$200$	4.99180			0.352974
$201$	18.2384	−	3.31456i	1.28644	−	0.233791i
$202$		−	19.0334i		−	1.33918i
$203$	−1.05225	+	15.5756i	−0.0738538	+	1.09319i
$204$	3.58122	+	4.22279i	0.250736	+	0.295655i
$205$	0.870048	+	0.502322i	0.0607668	+	0.0350837i
$206$	0.696199	−	0.401951i	0.0485065	−	0.0280052i
$207$	−0.302790	−	0.0501238i	−0.0210454	−	0.00348384i
$208$	−1.58384	+	0.914430i	−0.109819	+	0.0634043i
$209$	−7.87034	−	2.24954i	−0.544403	−	0.155604i
$210$	−0.380251	−	0.165848i	−0.0262398	−	0.0114446i
$211$	−13.7770	−	7.95416i	−0.948448	−	0.547587i	−0.0558495	−	0.998439i	$-0.517787\pi$
$211$	−13.7770	−	7.95416i	−0.948448	−	0.547587i	−0.892598	+	0.450853i	$0.851120\pi$
$212$	1.79033			0.122961
$213$	18.5066	+	6.62624i	1.26805	+	0.454022i
$214$	2.82375	+	4.89088i	0.193028	+	0.334334i
$215$	−0.458507	−	0.264719i	−0.0312699	−	0.0180537i
$216$	−2.66850	−	4.45860i	−0.181568	−	0.303369i
$217$	−8.04569	−	16.3979i	−0.546177	−	1.11316i
$218$	10.4998	−	6.06208i	0.711138	−	0.410576i
$219$	−16.1730	+	13.7159i	−1.09287	+	0.926832i
$220$	−0.0849993	+	0.147223i	−0.00573065	+	0.00992578i
$221$	−2.92318	+	5.06310i	−0.196634	+	0.340581i
$222$	−4.45152	−	5.24900i	−0.298766	−	0.352290i
$223$	−10.1739	−	5.87393i	−0.681297	−	0.393347i	0.119046	−	0.992889i	$-0.462016\pi$
$223$	−10.1739	−	5.87393i	−0.681297	−	0.393347i	−0.800344	+	0.599542i	$0.795350\pi$
$224$	2.19691	+	1.47431i	0.146787	+	0.0985065i
$225$	−14.0178	+	5.26910i	−0.934522	+	0.351273i
$226$	−0.251685			−0.0167418
$227$	1.44306	−	2.49946i	0.0957796	−	0.165895i	−0.814154	−	0.580649i	$-0.802799\pi$
$227$	1.44306	−	2.49946i	0.0957796	−	0.165895i	0.909934	+	0.414754i	$0.136132\pi$
$228$	−3.11275	−	6.87828i	−0.206147	−	0.455525i
$229$	2.28168	+	3.95198i	0.150778	+	0.261155i	0.931514	−	0.363707i	$-0.118489\pi$
$229$	2.28168	+	3.95198i	0.150778	+	0.261155i	−0.780736	+	0.624861i	$0.785156\pi$
$230$	−0.00463060	+	0.00802043i	−0.000305332	+	0.000528851i
$231$	−6.92341	+	5.11097i	−0.455527	+	0.336277i
$232$	2.95022	+	5.10993i	0.193691	+	0.335483i
$233$		−	14.2793i		−	0.935466i	−0.883870	−	0.467733i	$-0.845071\pi$
$233$		−	14.2793i		−	0.935466i	0.883870	−	0.467733i	$-0.154929\pi$
$234$	3.48246	−	4.23970i	0.227656	−	0.277158i
$235$	−0.172538	+	0.298844i	−0.0112551	+	0.0194944i
$236$	−6.80692	−	11.7899i	−0.443093	−	0.767459i
$237$	−6.98143	+	1.26877i	−0.453493	+	0.0824157i
$238$	8.43850	+	0.570087i	0.546987	+	0.0369533i
$239$			1.81920i			0.117675i	0.998268	+	0.0588373i	$0.0187393\pi$
$239$			1.81920i			0.117675i	−0.998268	+	0.0588373i	$0.981261\pi$
$240$	−0.154270	+	0.0280363i	−0.00995807	+	0.00180973i
$241$			11.5528i			0.744180i	0.928197	+	0.372090i	$0.121359\pi$
$241$			11.5528i			0.744180i	−0.928197	+	0.372090i	$0.878641\pi$
$242$	−3.73677	−	6.47228i	−0.240209	−	0.416054i
$243$	12.1999	+	9.70377i	0.782622	+	0.622497i
$244$	−2.93339	+	5.08079i	−0.187791	+	0.325264i
$245$	−0.586418	+	0.240151i	−0.0374648	+	0.0153427i
$246$	18.0969	+	6.47954i	1.15382	+	0.413120i
$247$	5.72973	−	5.54257i	0.364574	−	0.352665i
$248$	−5.97874	−	3.45183i	−0.379650	−	0.219191i
$249$	−17.5366	+	3.18703i	−1.11134	+	0.201970i
$250$			0.904524i			0.0572071i
$251$	−13.2066	+	7.62481i	−0.833590	+	0.481274i	−0.855080	−	0.518496i	$-0.826492\pi$
$251$	−13.2066	+	7.62481i	−0.833590	+	0.481274i	0.0214901	+	0.999769i	$0.493159\pi$
$252$	−7.72550	−	1.82116i	−0.486661	−	0.114722i
$253$	0.0960572	+	0.166376i	0.00603907	+	0.0104600i
$254$	13.4584	−	7.77018i	0.844452	−	0.487545i
$255$	−0.382275	+	0.324196i	−0.0239390	+	0.0203019i
$256$	1.00000			0.0625000
$257$	−11.4472	+	19.8271i	−0.714056	+	1.23678i	0.249266	+	0.968435i	$0.419811\pi$
$257$	−11.4472	+	19.8271i	−0.714056	+	1.23678i	−0.963322	+	0.268347i	$0.913523\pi$
$258$	−9.53689	−	3.41465i	−0.593741	−	0.212587i
$259$	−10.4892	−	0.708628i	−0.651767	−	0.0440320i
$260$	−0.0827802	−	0.143380i	−0.00513381	−	0.00889202i
$261$	−13.6785	−	11.2354i	−0.846678	−	0.695456i
$262$			8.33637i			0.515023i
$263$	−12.3675	+	7.14039i	−0.762613	+	0.440295i	−0.830233	−	0.557416i	$-0.811793\pi$
$263$	−12.3675	+	7.14039i	−0.762613	+	0.440295i	0.0676198	+	0.997711i	$0.478460\pi$
$264$	−1.09642	+	3.06223i	−0.0674800	+	0.188467i
$265$			0.162073i			0.00995606i
$266$	−10.8497	−	3.90957i	−0.665236	−	0.239711i
$267$	12.4354	+	4.45244i	0.761031	+	0.272485i
$268$		−	10.7024i		−	0.653754i
$269$	6.97690	+	12.0843i	0.425389	+	0.736796i	0.996457	−	0.0841074i	$-0.0268039\pi$
$269$	6.97690	+	12.0843i	0.425389	+	0.736796i	−0.571067	+	0.820903i	$0.693471\pi$
$270$	0.403622	−	0.241570i	0.0245636	−	0.0147015i
$271$	−16.7092			−1.01501			−0.507507	−	0.861648i	$-0.669433\pi$
$271$	−16.7092			−1.01501			−0.507507	+	0.861648i	$0.669433\pi$
$272$	2.76844	−	1.59836i	0.167862	−	0.0969149i
$273$	−0.939347	−	8.32808i	−0.0568518	−	0.504038i
$274$		−	10.9211i		−	0.659767i
$275$	8.11816	+	4.68702i	0.489543	+	0.282638i
$276$	−0.0597308	+	0.166824i	−0.00359537	+	0.0100416i
$277$	−4.08796	+	7.08056i	−0.245622	+	0.425430i	−0.962306	−	0.271968i	$-0.912326\pi$
$277$	−4.08796	+	7.08056i	−0.245622	+	0.425430i	0.716684	+	0.697398i	$0.245659\pi$
$278$	−4.24309	−	7.34924i	−0.254483	−	0.440778i
$279$	20.4329	+	3.38245i	1.22328	+	0.202502i
$280$	−0.133464	+	0.198879i	−0.00797601	+	0.0118853i
$281$	−3.11754	−	5.39973i	−0.185977	−	0.322121i	0.757929	−	0.652338i	$-0.226212\pi$
$281$	−3.11754	−	5.39973i	−0.185977	−	0.322121i	−0.943905	+	0.330217i	$0.892878\pi$
$282$	−2.22559	+	6.21592i	−0.132532	+	0.370153i
$283$	5.07861	+	8.79642i	0.301892	+	0.522893i	0.976565	−	0.215225i	$-0.0690484\pi$
$283$	5.07861	+	8.79642i	0.301892	+	0.522893i	−0.674672	+	0.738117i	$0.735715\pi$
$284$	5.67452	−	9.82856i	0.336721	−	0.583218i
$285$	0.622667	−	0.281787i	0.0368836	−	0.0166916i
$286$	−3.43439			−0.203080
$287$	26.3600	−	12.9336i	1.55598	−	0.763448i
$288$	−2.80817	+	1.05555i	−0.165473	+	0.0621989i
$289$	−3.39048	+	5.87248i	−0.199440	+	0.345440i
$290$	−0.462584	+	0.267073i	−0.0271639	+	0.0156831i
$291$	9.51490	−	26.5744i	0.557773	−	1.55782i
$292$	6.12163	+	10.6030i	0.358241	+	0.620492i
$293$	−19.3187			−1.12861			−0.564304	−	0.825567i	$-0.690856\pi$
$293$	−19.3187			−1.12861			−0.564304	+	0.825567i	$0.690856\pi$
$294$	−10.2176	+	6.52698i	−0.595900	+	0.380661i
$295$	1.06730	−	0.616207i	0.0621407	−	0.0358770i
$296$	−3.44122	+	1.98679i	−0.200017	+	0.115480i
$297$	−0.153400	−	9.75658i	−0.00890117	−	0.566134i
$298$		−	16.8735i		−	0.977455i
$299$	−0.187099			−0.0108202
$300$	1.54597	+	8.50672i	0.0892568	+	0.491136i
$301$	−13.8914	+	6.81590i	−0.800689	+	0.392862i
$302$	19.3381	+	11.1648i	1.11278	+	0.642465i
$303$	32.4355	−	5.89468i	1.86337	−	0.338640i
$304$	−4.22852	+	1.05811i	−0.242522	+	0.0606869i
$305$	−0.459946	−	0.265550i	−0.0263364	−	0.0152053i
$306$	−6.08711	+	7.41070i	−0.347977	+	0.423642i
$307$	−9.73811	−	5.62230i	−0.555783	−	0.320882i	0.195668	−	0.980670i	$-0.437313\pi$
$307$	−9.73811	−	5.62230i	−0.555783	−	0.320882i	−0.751451	+	0.659789i	$0.770646\pi$
$308$	2.18853	+	4.46044i	0.124703	+	0.254157i
$309$	0.900593	+	1.06193i	0.0512330	+	0.0604113i
$310$	0.312482	−	0.541235i	0.0177478	−	0.0307401i
$311$	1.35583	+	0.782790i	0.0768822	+	0.0443880i	0.537948	−	0.842978i	$-0.319200\pi$
$311$	1.35583	+	0.782790i	0.0768822	+	0.0443880i	−0.461066	+	0.887366i	$0.652533\pi$
$312$	−2.04883	−	2.41588i	−0.115992	−	0.136772i
$313$	−7.14229	+	12.3708i	−0.403706	+	0.699239i	−0.994170	−	0.107825i	$-0.965611\pi$
$313$	−7.14229	+	12.3708i	−0.403706	+	0.699239i	0.590464	+	0.807064i	$0.298945\pi$
$314$	−6.14717	−	10.6472i	−0.346905	−	0.600857i
$315$	0.164864	−	0.699363i	0.00928901	−	0.0394046i
$316$			4.09675i			0.230460i
$317$	7.57169	−	13.1145i	0.425268	−	0.736586i	−0.571177	−	0.820827i	$-0.693513\pi$
$317$	7.57169	−	13.1145i	0.425268	−	0.736586i	0.996445	+	0.0842405i	$0.0268464\pi$
$318$	0.554470	+	3.05098i	0.0310932	+	0.171090i
$319$			11.0804i			0.620381i
$320$			0.0905266i			0.00506059i
$321$	−7.46021	+	6.32678i	−0.416388	+	0.353126i
$322$	0.119227	+	0.242996i	0.00664427	+	0.0135416i
$323$	−10.0152	+	9.68803i	−0.557259	+	0.539057i
$324$	6.77163	−	5.92833i	0.376202	−	0.329351i
$325$	−7.90622	+	4.56466i	−0.438558	+	0.253202i
$326$	−2.62307	−	4.54329i	−0.145279	−	0.251630i
$327$	13.5824	+	16.0157i	0.751110	+	0.885671i
$328$	5.54889	−	9.61096i	0.306386	−	0.530677i
$329$	4.44244	+	9.05411i	0.244920	+	0.499169i
$330$	−0.277213	−	0.0992552i	−0.0152601	−	0.00546382i
$331$	−22.4496	+	12.9613i	−1.23394	+	0.712417i	−0.967850	−	0.251530i	$-0.919066\pi$
$331$	−22.4496	+	12.9613i	−1.23394	+	0.712417i	−0.266094	+	0.963947i	$0.585733\pi$
$332$			10.2906i			0.564771i
$333$	7.56637	−	9.21162i	0.414635	−	0.504794i
$334$	4.81106	+	8.33300i	0.263249	+	0.455961i
$335$	0.968852			0.0529341
$336$	−1.83204	+	4.20043i	−0.0999459	+	0.229152i
$337$	6.71787	+	3.87856i	0.365946	+	0.211279i	0.671686	−	0.740836i	$-0.265571\pi$
$337$	6.71787	+	3.87856i	0.365946	+	0.211279i	−0.305740	+	0.952115i	$0.598904\pi$
$338$	−4.82764	+	8.36171i	−0.262589	+	0.454817i
$339$	−0.0779473	−	0.428905i	−0.00423352	−	0.0232949i
$340$	0.144694	+	0.250618i	0.00784715	+	0.0135917i
$341$	−6.48214	−	11.2274i	−0.351027	−	0.607997i
$342$	10.7575	−	7.43478i	0.581700	−	0.402027i
$343$	−3.72235	+	18.1423i	−0.200988	+	0.979594i
$344$	−2.92421	+	5.06488i	−0.157663	+	0.273080i
$345$	−0.0151020	−	0.00540723i	−0.000813065	−	0.000291115i
$346$	17.1075			0.919703
$347$	−12.5471	+	7.24405i	−0.673562	+	0.388881i	−0.797425	−	0.603418i	$-0.793805\pi$
$347$	−12.5471	+	7.24405i	−0.673562	+	0.388881i	0.123863	+	0.992299i	$0.460472\pi$
$348$	−7.79433	+	6.61014i	−0.417820	+	0.354340i
$349$	6.56991			0.351679			0.175840	−	0.984419i	$-0.443736\pi$
$349$	6.56991			0.351679			0.175840	+	0.984419i	$0.443736\pi$
$350$	10.9665	+	7.35947i	0.586186	+	0.393380i
$351$	8.30355	+	4.62155i	0.443211	+	0.246680i
$352$	1.62630	+	0.938943i	0.0866819	+	0.0500458i
$353$	0.273677	+	0.158008i	0.0145664	+	0.00840990i	0.507266	−	0.861790i	$-0.330656\pi$
$353$	0.273677	+	0.158008i	0.0145664	+	0.00840990i	−0.492699	+	0.870200i	$0.663990\pi$
$354$	17.9835	−	15.2513i	0.955814	−	0.810597i
$355$	0.889746	+	0.513695i	0.0472228	+	0.0272641i
$356$	3.81294	−	6.60421i	0.202086	−	0.350022i
$357$	1.64191	+	14.5569i	0.0868993	+	0.770434i
$358$	−1.70761	+	2.95767i	−0.0902501	+	0.156318i
$359$			12.2434i			0.646181i	0.946368	+	0.323091i	$0.104722\pi$
$359$			12.2434i			0.646181i	−0.946368	+	0.323091i	$0.895278\pi$
$360$	−0.0955553	−	0.254214i	−0.00503621	−	0.0133982i
$361$	16.7608	−	8.94850i	0.882147	−	0.470974i
$362$	1.93919	−	1.11959i	0.101921	−	0.0588443i
$363$	9.87237	−	8.37245i	0.518165	−	0.439440i
$364$	−4.82770	−	0.326150i	−0.253040	−	0.0170949i
$365$	−0.959851	+	0.554170i	−0.0502409	+	0.0290066i
$366$	−9.56684	−	3.42537i	−0.500066	−	0.179047i
$367$	12.6912			0.662477			0.331239	−	0.943547i	$-0.392533\pi$
$367$	12.6912			0.662477			0.331239	+	0.943547i	$0.392533\pi$
$368$	0.0885975	+	0.0511518i	0.00461846	+	0.00266647i
$369$	−5.43737	+	32.8463i	−0.283058	+	1.70991i
$370$	−0.179857	−	0.311522i	−0.00935033	−	0.0161953i
$371$	3.93320	+	2.63951i	0.204202	+	0.137036i
$372$	4.03076	−	11.2576i	0.208985	−	0.583681i
$373$	−18.1523	+	10.4802i	−0.939890	+	0.542646i	−0.889926	−	0.456105i	$-0.849244\pi$
$373$	−18.1523	+	10.4802i	−0.939890	+	0.542646i	−0.0499642	+	0.998751i	$0.515911\pi$
$374$	6.00308			0.310412
$375$	−1.54143	+	0.280133i	−0.0795993	+	0.0144660i
$376$	3.30117	+	1.90593i	0.170245	+	0.0982910i
$377$	−9.34534	−	5.39554i	−0.481310	−	0.277884i
$378$	0.710907	−	13.7293i	0.0365651	−	0.706161i
$379$			4.49852i			0.231074i	0.993303	+	0.115537i	$0.0368588\pi$
$379$			4.49852i			0.231074i	−0.993303	+	0.115537i	$0.963141\pi$
$380$	−0.0957873	−	0.382794i	−0.00491378	−	0.0196369i
$381$	17.4095	+	20.5284i	0.891918	+	1.05170i
$382$	−14.0910	+	8.13546i	−0.720960	+	0.416246i
$383$	12.3514			0.631126			0.315563	−	0.948905i	$-0.397807\pi$
$383$	12.3514			0.631126			0.315563	+	0.948905i	$0.397807\pi$
$384$	0.309702	+	1.70414i	0.0158044	+	0.0869639i
$385$	−0.403788	+	0.198121i	−0.0205790	+	0.0100972i
$386$	10.4521	−	6.03452i	0.531997	−	0.307149i
$387$	2.86544	−	17.3097i	0.145659	−	0.879902i
$388$	−14.1132	−	8.14828i	−0.716491	−	0.413666i
$389$			31.7661i			1.61060i	0.592865	+	0.805302i	$0.297997\pi$
$389$			31.7661i			1.61060i	−0.592865	+	0.805302i	$0.702003\pi$
$390$	0.218701	−	0.185474i	0.0110744	−	0.00939183i
$391$	0.327036			0.0165389
$392$	2.65282	+	6.47785i	0.133988	+	0.327181i
$393$	−14.2063	+	2.58179i	−0.716614	+	0.130234i
$394$			5.03412i			0.253615i
$395$	−0.370865			−0.0186603
$396$	−5.55802	−	0.920073i	−0.279301	−	0.0462354i
$397$	17.4032			0.873443			0.436721	−	0.899597i	$-0.356140\pi$
$397$	17.4032			0.873443			0.436721	+	0.899597i	$0.356140\pi$
$398$	−15.6860			−0.786270
$399$	3.30229	−	19.7001i	0.165321	−	0.986240i
$400$	4.99180			0.249590
$401$	20.2675			1.01211			0.506055	−	0.862501i	$-0.331103\pi$
$401$	20.2675			1.01211			0.506055	+	0.862501i	$0.331103\pi$
$402$	18.2384	−	3.31456i	0.909647	−	0.165315i
$403$	12.6258			0.628936
$404$		−	19.0334i		−	0.946946i
$405$	0.536671	+	0.613012i	0.0266674	+	0.0304608i
$406$	−1.05225	+	15.5756i	−0.0522225	+	0.773004i
$407$	−7.46193			−0.369874
$408$	3.58122	+	4.22279i	0.177297	+	0.209059i
$409$		−	36.5351i		−	1.80655i	−0.429065	−	0.903273i	$-0.641157\pi$
$409$		−	36.5351i		−	1.80655i	0.429065	−	0.903273i	$-0.358843\pi$
$410$	0.870048	+	0.502322i	0.0429686	+	0.0248079i
$411$	18.6110	−	3.38228i	0.918015	−	0.166836i
$412$	0.696199	−	0.401951i	0.0342993	−	0.0198027i
$413$	2.42782	−	35.9369i	0.119465	−	1.76834i
$414$	−0.302790	−	0.0501238i	−0.0148813	−	0.00246345i
$415$	−0.931574			−0.0457292
$416$	−1.58384	+	0.914430i	−0.0776541	+	0.0448336i
$417$	11.2100	−	9.50688i	0.548957	−	0.465554i
$418$	−7.87034	−	2.24954i	−0.384951	−	0.110028i
$419$			13.1281i			0.641349i	0.947189	+	0.320674i	$0.103910\pi$
$419$			13.1281i			0.641349i	−0.947189	+	0.320674i	$0.896090\pi$
$420$	−0.380251	−	0.165848i	−0.0185543	−	0.00809256i
$421$	11.4043	+	6.58427i	0.555811	+	0.320898i	0.751463	−	0.659776i	$-0.229349\pi$
$421$	11.4043	+	6.58427i	0.555811	+	0.320898i	−0.195651	+	0.980674i	$0.562682\pi$
$422$	−13.7770	−	7.95416i	−0.670654	−	0.387202i
$423$	−11.2821	−	1.86763i	−0.548552	−	0.0908072i
$424$	1.79033			0.0869463
$425$	13.8195	−	7.97871i	0.670346	−	0.387024i
$426$	18.5066	+	6.62624i	0.896649	+	0.321042i
$427$	−13.9350	+	6.83730i	−0.674364	+	0.330880i
$428$	2.82375	+	4.89088i	0.136491	+	0.236410i
$429$	−1.06364	−	5.85267i	−0.0513529	−	0.282570i
$430$	−0.458507	−	0.264719i	−0.0221111	−	0.0127659i
$431$	−2.33455			−0.112451			−0.0562257	−	0.998418i	$-0.517907\pi$
$431$	−2.33455			−0.112451			−0.0562257	+	0.998418i	$0.517907\pi$
$432$	−2.66850	−	4.45860i	−0.128388	−	0.214514i
$433$	0.945018	−	0.545606i	0.0454147	−	0.0262202i	−0.477121	−	0.878838i	$-0.658320\pi$
$433$	0.945018	−	0.545606i	0.0454147	−	0.0262202i	0.522535	+	0.852618i	$0.324986\pi$
$434$	−8.04569	−	16.3979i	−0.386205	−	0.787122i
$435$	−0.598393	−	0.705594i	−0.0286907	−	0.0338307i
$436$	10.4998	−	6.06208i	0.502851	−	0.290321i
$437$	−0.428761	−	0.122550i	−0.0205104	−	0.00586238i
$438$	−16.1730	+	13.7159i	−0.772778	+	0.655369i
$439$			28.8102i			1.37503i	0.726168	+	0.687517i	$0.241299\pi$
$439$			28.8102i			1.37503i	−0.726168	+	0.687517i	$0.758701\pi$
$440$	−0.0849993	+	0.147223i	−0.00405218	+	0.00701859i
$441$	−14.2873	−	15.3907i	−0.680346	−	0.732891i
$442$	−2.92318	+	5.06310i	−0.139041	+	0.240827i
$443$	−1.06924	−	0.617325i	−0.0508010	−	0.0293300i	0.474384	−	0.880318i	$-0.342671\pi$
$443$	−1.06924	−	0.617325i	−0.0508010	−	0.0293300i	−0.525185	+	0.850988i	$0.676004\pi$
$444$	−4.45152	−	5.24900i	−0.211260	−	0.249107i
$445$	0.597856	+	0.345173i	0.0283411	+	0.0163627i
$446$	−10.1739	−	5.87393i	−0.481750	−	0.278138i
$447$	28.7548	−	5.22576i	1.36005	−	0.247170i
$448$	2.19691	+	1.47431i	0.103794	+	0.0696546i
$449$	−28.4175			−1.34111			−0.670553	−	0.741862i	$-0.733943\pi$
$449$	−28.4175			−1.34111			−0.670553	+	0.741862i	$0.733943\pi$
$450$	−14.0178	+	5.26910i	−0.660807	+	0.248388i
$451$	18.0483	−	10.4202i	0.849861	−	0.490668i
$452$	−0.251685			−0.0118383
$453$	−13.0374	+	36.4125i	−0.612550	+	1.71081i
$454$	1.44306	−	2.49946i	0.0677264	−	0.117306i
$455$	0.0295252	−	0.437035i	0.00138416	−	0.0204885i
$456$	−3.11275	−	6.87828i	−0.145768	−	0.322105i
$457$	2.08484	+	3.61105i	0.0975247	+	0.168918i	0.910660	−	0.413158i	$-0.135574\pi$
$457$	2.08484	+	3.61105i	0.0975247	+	0.168918i	−0.813135	+	0.582075i	$0.802241\pi$
$458$	2.28168	+	3.95198i	0.106616	+	0.184664i
$459$	−14.5140	−	8.07816i	−0.677458	−	0.377056i
$460$	−0.00463060	+	0.00802043i	−0.000215903	+	0.000373954i
$461$	2.42290	+	1.39886i	0.112846	+	0.0651514i	0.555360	−	0.831610i	$-0.312580\pi$
$461$	2.42290	+	1.39886i	0.112846	+	0.0651514i	−0.442515	+	0.896761i	$0.645914\pi$
$462$	−6.92341	+	5.11097i	−0.322106	+	0.237784i
$463$	−8.95643			−0.416241			−0.208120	−	0.978103i	$-0.566735\pi$
$463$	−8.95643			−0.416241			−0.208120	+	0.978103i	$0.566735\pi$
$464$	2.95022	+	5.10993i	0.136960	+	0.237223i
$465$	1.01911	+	0.364891i	0.0472603	+	0.0169214i
$466$		−	14.2793i		−	0.661474i
$467$	−1.30881	+	0.755639i	−0.0605643	+	0.0349668i	−0.529976	−	0.848012i	$-0.677799\pi$
$467$	−1.30881	+	0.755639i	−0.0605643	+	0.0349668i	0.469412	+	0.882979i	$0.344466\pi$
$468$	3.48246	−	4.23970i	0.160977	−	0.195980i
$469$	15.7787	−	23.5122i	0.728591	−	1.08569i
$470$	−0.172538	+	0.298844i	−0.00795856	+	0.0137846i
$471$	16.2405	−	13.7731i	0.748324	−	0.634630i
$472$	−6.80692	−	11.7899i	−0.313314	−	0.542675i
$473$	−9.51127	+	5.49134i	−0.437329	+	0.252492i
$474$	−6.98143	+	1.26877i	−0.320668	+	0.0582767i
$475$	−21.1080	+	5.28189i	−0.968499	+	0.242350i
$476$	8.43850	+	0.570087i	0.386778	+	0.0261299i
$477$	−5.02756	+	1.88979i	−0.230196	+	0.0865274i
$478$			1.81920i			0.0832085i
$479$		−	9.31146i		−	0.425451i	−0.977112	−	0.212726i	$-0.931766\pi$
$479$		−	9.31146i		−	0.425451i	0.977112	−	0.212726i	$-0.0682341\pi$
$480$	−0.154270	+	0.0280363i	−0.00704142	+	0.00127968i
$481$	3.63356	−	6.29351i	0.165676	−	0.286959i
$482$			11.5528i			0.526215i
$483$	−0.377174	+	0.278436i	−0.0171620	+	0.0126693i
$484$	−3.73677	−	6.47228i	−0.169853	−	0.294194i
$485$	0.737636	−	1.27762i	0.0334943	−	0.0580139i
$486$	12.1999	+	9.70377i	0.553397	+	0.440172i
$487$	9.73527	+	5.62066i	0.441147	+	0.254696i	0.704084	−	0.710117i	$-0.251358\pi$
$487$	9.73527	+	5.62066i	0.441147	+	0.254696i	−0.262937	+	0.964813i	$0.584691\pi$
$488$	−2.93339	+	5.08079i	−0.132788	+	0.229996i
$489$	6.93003	−	5.87714i	0.313387	−	0.265774i
$490$	−0.586418	+	0.240151i	−0.0264916	+	0.0108489i
$491$	23.5616	+	13.6033i	1.06332	+	0.613909i	0.926349	−	0.376666i	$-0.122930\pi$
$491$	23.5616	+	13.6033i	1.06332	+	0.613909i	0.136972	+	0.990575i	$0.456263\pi$
$492$	18.0969	+	6.47954i	0.815872	+	0.292120i
$493$	16.3350	+	9.43104i	0.735693	+	0.424752i
$494$	5.72973	−	5.54257i	0.257793	−	0.249372i
$495$	0.0832910	−	0.503148i	0.00374365	−	0.0226148i
$496$	−5.97874	−	3.45183i	−0.268453	−	0.154992i
$497$	26.9567	−	13.2264i	1.20918	−	0.593287i
$498$	−17.5366	+	3.18703i	−0.785835	+	0.142814i
$499$	1.22541			0.0548567			0.0274283	−	0.999624i	$-0.491268\pi$
$499$	1.22541			0.0548567			0.0274283	+	0.999624i	$0.491268\pi$
$500$			0.904524i			0.0404515i
$501$	−12.7106	+	10.7795i	−0.567867	+	0.481590i
$502$	−13.2066	+	7.62481i	−0.589437	+	0.340312i
$503$	−10.5418	+	6.08633i	−0.470037	+	0.271376i	−0.716255	−	0.697838i	$-0.754145\pi$
$503$	−10.5418	+	6.08633i	−0.470037	+	0.271376i	0.246218	+	0.969214i	$0.420812\pi$
$504$	−7.72550	−	1.82116i	−0.344121	−	0.0811210i
$505$	1.72303			0.0766737
$506$	0.0960572	+	0.166376i	0.00427027	+	0.00739632i
$507$	−15.7446	−	5.63732i	−0.699244	−	0.250362i
$508$	13.4584	−	7.77018i	0.597118	−	0.344746i
$509$	−15.2510	+	26.4155i	−0.675989	+	1.17085i	0.300189	+	0.953880i	$0.402950\pi$
$509$	−15.2510	+	26.4155i	−0.675989	+	1.17085i	−0.976179	+	0.216968i	$0.930383\pi$
$510$	−0.382275	+	0.324196i	−0.0169274	+	0.0143556i
$511$	−2.18340	+	32.3189i	−0.0965879	+	1.42971i
$512$	1.00000			0.0441942
$513$	16.0015	+	16.0297i	0.706484	+	0.707729i
$514$	−11.4472	+	19.8271i	−0.504914	+	0.874537i
$515$	0.0363872	+	0.0630245i	0.00160341	+	0.00277719i
$516$	−9.53689	−	3.41465i	−0.419838	−	0.150322i
$517$	3.57912	+	6.19923i	0.157410	+	0.272642i
$518$	−10.4892	−	0.708628i	−0.460869	−	0.0311353i
$519$	5.29822	+	29.1535i	0.232566	+	1.27970i
$520$	−0.0827802	−	0.143380i	−0.00363015	−	0.00628761i
$521$	−0.127223	+	0.220356i	−0.00557373	+	0.00965398i	−0.868799	−	0.495165i	$-0.835108\pi$
$521$	−0.127223	+	0.220356i	−0.00557373	+	0.00965398i	0.863225	+	0.504819i	$0.168441\pi$
$522$	−13.6785	−	11.2354i	−0.598692	−	0.491762i
$523$	5.85779	+	3.38200i	0.256143	+	0.147884i	0.622574	−	0.782561i	$-0.286087\pi$
$523$	5.85779	+	3.38200i	0.256143	+	0.147884i	−0.366431	+	0.930445i	$0.619420\pi$
$524$			8.33637i			0.364176i
$525$	−9.14518	+	20.9677i	−0.399128	+	0.915107i
$526$	−12.3675	+	7.14039i	−0.539249	+	0.311336i
$527$	−22.0691			−0.961344
$528$	−1.09642	+	3.06223i	−0.0477156	+	0.133266i
$529$	−11.4948	−	19.9095i	−0.499772	−	0.865631i
$530$			0.162073i			0.00703999i
$531$	31.5598	+	25.9231i	1.36958	+	1.12497i
$532$	−10.8497	−	3.90957i	−0.470393	−	0.169502i
$533$			20.2963i			0.879130i
$534$	12.4354	+	4.45244i	0.538131	+	0.192676i
$535$	−0.442755	+	0.255625i	−0.0191420	+	0.0110516i
$536$		−	10.7024i		−	0.462274i
$537$	−5.56913	−	1.99401i	−0.240326	−	0.0860478i
$538$	6.97690	+	12.0843i	0.300796	+	0.520993i
$539$	−1.76806	+	13.0258i	−0.0761555	+	0.561059i
$540$	0.403622	−	0.241570i	0.0173691	−	0.0103955i
$541$	−6.01454	+	10.4175i	−0.258585	+	0.447883i	−0.965863	−	0.259053i	$-0.916590\pi$
$541$	−6.01454	+	10.4175i	−0.258585	+	0.447883i	0.707278	+	0.706936i	$0.249923\pi$
$542$	−16.7092			−0.717723
$543$	2.50850	+	2.95790i	0.107650	+	0.126936i
$544$	2.76844	−	1.59836i	0.118696	−	0.0685292i
$545$	0.548779	+	0.950514i	0.0235071	+	0.0407155i
$546$	−0.939347	−	8.32808i	−0.0402003	−	0.356409i
$547$	−11.5503	+	6.66855i	−0.493854	+	0.285127i	−0.726172	−	0.687513i	$-0.758702\pi$
$547$	−11.5503	+	6.66855i	−0.493854	+	0.285127i	0.232318	+	0.972640i	$0.425369\pi$
$548$		−	10.9211i		−	0.466526i
$549$	2.87444	−	17.3640i	0.122678	−	0.741080i
$550$	8.11816	+	4.68702i	0.346159	+	0.199855i
$551$	−17.8819	−	18.4858i	−0.761797	−	0.787521i
$552$	−0.0597308	+	0.166824i	−0.00254231	+	0.00710051i
$553$	−6.03989	+	9.00020i	−0.256842	+	0.382727i
$554$	−4.08796	+	7.08056i	−0.173681	+	0.300824i
$555$	0.475174	−	0.402981i	0.0201700	−	0.0171056i
$556$	−4.24309	−	7.34924i	−0.179947	−	0.311677i
$557$			26.9567i			1.14219i	0.820883	+	0.571097i	$0.193482\pi$
$557$			26.9567i			1.14219i	−0.820883	+	0.571097i	$0.806518\pi$
$558$	20.4329	+	3.38245i	0.864993	+	0.143191i
$559$		−	10.6959i		−	0.452390i
$560$	−0.133464	+	0.198879i	−0.00563989	+	0.00840416i
$561$	1.85917	+	10.2301i	0.0784941	+	0.431914i
$562$	−3.11754	−	5.39973i	−0.131505	−	0.227774i
$563$	3.65745	−	6.33489i	0.154143	−	0.266984i	−0.778603	−	0.627516i	$-0.784072\pi$
$563$	3.65745	−	6.33489i	0.154143	−	0.266984i	0.932747	+	0.360532i	$0.117405\pi$
$564$	−2.22559	+	6.21592i	−0.0937143	+	0.261738i
$565$		−	0.0227842i		−	0.000958537i
$566$	5.07861	+	8.79642i	0.213470	+	0.369741i
$567$	23.6168	−	3.04052i	0.991814	−	0.127690i
$568$	5.67452	−	9.82856i	0.238098	−	0.412397i
$569$	−16.7940	−	29.0881i	−0.704041	−	1.21943i	−0.967037	−	0.254638i	$-0.918044\pi$
$569$	−16.7940	−	29.0881i	−0.704041	−	1.21943i	0.262996	−	0.964797i	$-0.415289\pi$
$570$	0.622667	−	0.281787i	0.0260807	−	0.0118027i
$571$	−19.6018	+	33.9512i	−0.820308	+	1.42081i	0.0851453	+	0.996369i	$0.472865\pi$
$571$	−19.6018	+	33.9512i	−0.820308	+	1.42081i	−0.905453	+	0.424446i	$0.860469\pi$
$572$	−3.43439			−0.143599
$573$	−18.2280	−	21.4935i	−0.761484	−	0.897903i
$574$	26.3600	−	12.9336i	1.10024	−	0.539839i
$575$	0.442261	+	0.255340i	0.0184436	+	0.0106484i
$576$	−2.80817	+	1.05555i	−0.117007	+	0.0439813i
$577$	11.4238	−	19.7866i	0.475578	−	0.823725i	−0.524031	−	0.851699i	$-0.675572\pi$
$577$	11.4238	−	19.7866i	0.475578	−	0.823725i	0.999609	+	0.0279744i	$0.00890568\pi$
$578$	−3.39048	+	5.87248i	−0.141025	+	0.244263i
$579$	13.5207	+	15.9429i	0.561900	+	0.662564i
$580$	−0.462584	+	0.267073i	−0.0192078	+	0.0110896i
$581$	−15.1716	+	22.6075i	−0.629422	+	0.937919i
$582$	9.51490	−	26.5744i	0.394405	−	1.10155i
$583$	2.91162	+	1.68102i	0.120587	+	0.0696208i
$584$	6.12163	+	10.6030i	0.253315	+	0.438754i
$585$	0.383805	+	0.315255i	0.0158684	+	0.0130342i
$586$	−19.3187			−0.798047
$587$	−33.2304	−	19.1856i	−1.37157	−	0.791874i	−0.380440	−	0.924806i	$-0.624227\pi$
$587$	−33.2304	−	19.1856i	−1.37157	−	0.791874i	−0.991125	+	0.132932i	$0.957561\pi$
$588$	−10.2176	+	6.52698i	−0.421365	+	0.269168i
$589$	28.9336	+	8.26994i	1.19219	+	0.340757i
$590$	1.06730	−	0.616207i	0.0439401	−	0.0253688i
$591$	−8.57883	+	1.55908i	−0.352886	+	0.0641319i
$592$	−3.44122	+	1.98679i	−0.141433	+	0.0816566i
$593$	−4.71824	−	2.72407i	−0.193755	−	0.111864i	0.399984	−	0.916522i	$-0.369016\pi$
$593$	−4.71824	−	2.72407i	−0.193755	−	0.111864i	−0.593739	+	0.804658i	$0.702349\pi$
$594$	−0.153400	−	9.75658i	−0.00629408	−	0.400317i
$595$	−0.0516081	+	0.763909i	−0.00211572	+	0.0313172i
$596$		−	16.8735i		−	0.691165i
$597$	−4.85800	−	26.7312i	−0.198825	−	1.09403i
$598$	−0.187099			−0.00765104
$599$	−28.0105			−1.14448			−0.572238	−	0.820088i	$-0.693925\pi$
$599$	−28.0105			−1.14448			−0.572238	+	0.820088i	$0.693925\pi$
$600$	1.54597	+	8.50672i	0.0631141	+	0.347285i
$601$			18.7615i			0.765299i	0.923894	+	0.382649i	$0.124988\pi$
$601$			18.7615i			0.765299i	−0.923894	+	0.382649i	$0.875012\pi$
$602$	−13.8914	+	6.81590i	−0.566173	+	0.277795i
$603$	11.2969	+	30.0542i	0.460046	+	1.22390i
$604$	19.3381	+	11.1648i	0.786856	+	0.454291i
$605$	0.585913	−	0.338277i	0.0238208	−	0.0137529i
$606$	32.4355	−	5.89468i	1.31760	−	0.239455i
$607$	42.3555	−	24.4540i	1.71916	−	0.992555i	0.798681	−	0.601755i	$-0.205531\pi$
$607$	42.3555	−	24.4540i	1.71916	−	0.992555i	0.920475	−	0.390801i	$-0.127802\pi$
$608$	−4.22852	+	1.05811i	−0.171489	+	0.0429121i
$609$	−26.8688	+	3.03061i	−1.08878	+	0.122806i
$610$	−0.459946	−	0.265550i	−0.0186227	−	0.0107518i
$611$	−6.97137			−0.282031
$612$	−6.08711	+	7.41070i	−0.246057	+	0.299560i
$613$	−11.0185	−	19.0846i	−0.445033	−	0.770820i	0.553021	−	0.833167i	$-0.313475\pi$
$613$	−11.0185	−	19.0846i	−0.445033	−	0.770820i	−0.998055	+	0.0623468i	$0.980142\pi$
$614$	−9.73811	−	5.62230i	−0.392998	−	0.226898i
$615$	−0.586571	+	1.63825i	−0.0236528	+	0.0660607i
$616$	2.18853	+	4.46044i	0.0881786	+	0.179716i
$617$	29.4701	−	17.0146i	1.18642	−	0.684982i	0.228932	−	0.973443i	$-0.426477\pi$
$617$	29.4701	−	17.0146i	1.18642	−	0.684982i	0.957492	+	0.288461i	$0.0931434\pi$
$618$	0.900593	+	1.06193i	0.0362272	+	0.0427172i
$619$	−12.2543	+	21.2250i	−0.492540	+	0.853104i	−0.999963	−	0.00859277i	$-0.997265\pi$
$619$	−12.2543	+	21.2250i	−0.492540	+	0.853104i	0.507423	+	0.861697i	$0.330598\pi$
$620$	0.312482	−	0.541235i	0.0125496	−	0.0217365i
$621$	−0.00835694	−	0.531519i	−0.000335352	−	0.0213291i
$622$	1.35583	+	0.782790i	0.0543639	+	0.0313870i
$623$	18.1133	−	8.88739i	0.725696	−	0.356066i
$624$	−2.04883	−	2.41588i	−0.0820189	−	0.0967125i
$625$	24.8771			0.995086
$626$	−7.14229	+	12.3708i	−0.285463	+	0.494437i
$627$	1.39606	−	14.1088i	0.0557532	−	0.563452i
$628$	−6.14717	−	10.6472i	−0.245299	−	0.424870i
$629$	−6.35122	+	11.0006i	−0.253240	+	0.438624i
$630$	0.164864	−	0.699363i	0.00656832	−	0.0278633i
$631$	3.64819	+	6.31885i	0.145232	+	0.251550i	0.929460	−	0.368924i	$-0.120274\pi$
$631$	3.64819	+	6.31885i	0.145232	+	0.251550i	−0.784227	+	0.620474i	$0.786940\pi$
$632$			4.09675i			0.162960i
$633$	9.28821	−	25.9413i	0.369173	−	1.03108i
$634$	7.57169	−	13.1145i	0.300710	−	0.520845i
$635$	0.703408	+	1.21834i	0.0279139	+	0.0483483i
$636$	0.554470	+	3.05098i	0.0219862	+	0.120979i
$637$	−10.1252	−	7.83405i	−0.401174	−	0.310396i
$638$			11.0804i			0.438675i
$639$	−5.56048	+	33.5900i	−0.219969	+	1.32880i
$640$			0.0905266i			0.00357838i
$641$	−1.27754	−	2.21277i	−0.0504600	−	0.0873993i	0.839692	−	0.543063i	$-0.182735\pi$
$641$	−1.27754	−	2.21277i	−0.0504600	−	0.0873993i	−0.890152	+	0.455663i	$0.849402\pi$
$642$	−7.46021	+	6.32678i	−0.294431	+	0.249698i
$643$	19.0961	−	33.0754i	0.753076	−	1.30437i	−0.193249	−	0.981150i	$-0.561903\pi$
$643$	19.0961	−	33.0754i	0.753076	−	1.30437i	0.946325	−	0.323216i	$-0.104764\pi$
$644$	0.119227	+	0.242996i	0.00469821	+	0.00957538i
$645$	0.309117	−	0.863342i	0.0121715	−	0.0339941i
$646$	−10.0152	+	9.68803i	−0.394042	+	0.381171i
$647$	28.0506	+	16.1950i	1.10278	+	0.636693i	0.936951	−	0.349461i	$-0.113635\pi$
$647$	28.0506	+	16.1950i	1.10278	+	0.636693i	0.165833	+	0.986154i	$0.446969\pi$
$648$	6.77163	−	5.92833i	0.266015	−	0.232887i
$649$		−	25.5652i		−	1.00352i
$650$	−7.90622	+	4.56466i	−0.310107	+	0.179041i
$651$	25.4524	−	18.7894i	0.997560	−	0.736415i
$652$	−2.62307	−	4.54329i	−0.102727	−	0.177929i
$653$	−36.8294	+	21.2634i	−1.44124	+	0.832103i	−0.997933	−	0.0642644i	$-0.979530\pi$
$653$	−36.8294	+	21.2634i	−1.44124	+	0.832103i	−0.443312	+	0.896367i	$0.646197\pi$
$654$	13.5824	+	16.0157i	0.531115	+	0.626264i
$655$	−0.754663			−0.0294871
$656$	5.54889	−	9.61096i	0.216648	−	0.375245i
$657$	−28.3825	−	23.3133i	−1.10731	−	0.909537i
$658$	4.44244	+	9.05411i	0.173184	+	0.352966i
$659$	−22.0563	−	38.2026i	−0.859191	−	1.48816i	−0.872702	−	0.488253i	$-0.837634\pi$
$659$	−22.0563	−	38.2026i	−0.859191	−	1.48816i	0.0135111	−	0.999909i	$-0.495699\pi$
$660$	−0.277213	−	0.0992552i	−0.0107905	−	0.00386350i
$661$			48.1339i			1.87219i	0.351746	+	0.936095i	$0.385588\pi$
$661$			48.1339i			1.87219i	−0.351746	+	0.936095i	$0.614412\pi$
$662$	−22.4496	+	12.9613i	−0.872530	+	0.503755i
$663$	−9.53353	−	3.41345i	−0.370251	−	0.132567i
$664$			10.2906i			0.399353i
$665$	0.353920	−	0.982183i	0.0137244	−	0.0380874i
$666$	7.56637	−	9.21162i	0.293191	−	0.356943i
$667$			0.603636i			0.0233729i
$668$	4.81106	+	8.33300i	0.186145	+	0.322413i
$669$	6.85909	−	19.1570i	0.265188	−	0.740651i
$670$	0.968852			0.0374300
$671$	−9.54114	+	5.50858i	−0.368331	+	0.212656i
$672$	−1.83204	+	4.20043i	−0.0706724	+	0.162035i
$673$		−	28.1003i		−	1.08319i	−0.840641	−	0.541593i	$-0.817821\pi$
$673$		−	28.1003i		−	1.08319i	0.840641	−	0.541593i	$-0.182179\pi$
$674$	6.71787	+	3.87856i	0.258763	+	0.149397i
$675$	−13.3206	−	22.2565i	−0.512711	−	0.856652i
$676$	−4.82764	+	8.36171i	−0.185678	+	0.321604i
$677$	−17.0816	−	29.5862i	−0.656499	−	1.13709i	−0.981516	−	0.191381i	$-0.938703\pi$
$677$	−17.0816	−	29.5862i	−0.656499	−	1.13709i	0.325017	−	0.945708i	$-0.394630\pi$
$678$	−0.0779473	−	0.428905i	−0.00299355	−	0.0164720i
$679$	−18.9924	−	38.7083i	−0.728862	−	1.48549i
$680$	0.144694	+	0.250618i	0.00554877	+	0.00961075i
$681$	4.70635	+	1.68509i	0.180348	+	0.0645729i
$682$	−6.48214	−	11.2274i	−0.248214	−	0.429919i
$683$	−2.46574	+	4.27078i	−0.0943487	+	0.163417i	−0.909337	−	0.416061i	$-0.863410\pi$
$683$	−2.46574	+	4.27078i	−0.0943487	+	0.163417i	0.814988	+	0.579478i	$0.196744\pi$
$684$	10.7575	−	7.43478i	0.411324	−	0.284276i
$685$	0.988649			0.0377743
$686$	−3.72235	+	18.1423i	−0.142120	+	0.692677i
$687$	−6.02808	+	5.11223i	−0.229986	+	0.195044i
$688$	−2.92421	+	5.06488i	−0.111485	+	0.193097i
$689$	−2.83560	+	1.63714i	−0.108028	+	0.0623699i
$690$	−0.0151020	−	0.00540723i	−0.000574924	−	0.000205850i
$691$	−11.4119	−	19.7661i	−0.434131	−	0.751937i	0.563093	−	0.826393i	$-0.309611\pi$
$691$	−11.4119	−	19.7661i	−0.434131	−	0.751937i	−0.997224	+	0.0744564i	$0.976278\pi$
$692$	17.1075			0.650328
$693$	−10.8540	−	10.2156i	−0.412309	−	0.388057i
$694$	−12.5471	+	7.24405i	−0.476280	+	0.274980i
$695$	0.665301	−	0.384112i	0.0252363	−	0.0145702i
$696$	−7.79433	+	6.61014i	−0.295443	+	0.250557i
$697$		−	35.4766i		−	1.34377i
$698$	6.56991			0.248675
$699$	24.3338	−	4.42232i	0.920390	−	0.167267i
$700$	10.9665	+	7.35947i	0.414496	+	0.278162i
$701$	−3.38667	−	1.95530i	−0.127913	−	0.0738505i	0.434678	−	0.900586i	$-0.356862\pi$
$701$	−3.38667	−	1.95530i	−0.127913	−	0.0738505i	−0.562591	+	0.826735i	$0.690195\pi$
$702$	8.30355	+	4.62155i	0.313397	+	0.174429i
$703$	12.4490	−	12.0424i	0.469524	−	0.454187i
$704$	1.62630	+	0.938943i	0.0612934	+	0.0353877i
$705$	−0.562706	−	0.201475i	−0.0211927	−	0.00758799i
$706$	0.273677	+	0.158008i	0.0103000	+	0.00594669i
$707$	28.0611	−	41.8146i	1.05535	−	1.57260i
$708$	17.9835	−	15.2513i	0.675863	−	0.573179i
$709$	22.2152	−	38.4778i	0.834308	−	1.44506i	−0.0602840	−	0.998181i	$-0.519201\pi$
$709$	22.2152	−	38.4778i	0.834308	−	1.44506i	0.894592	−	0.446883i	$-0.147466\pi$
$710$	0.889746	+	0.513695i	0.0333916	+	0.0192786i
$711$	−4.32433	−	11.5044i	−0.162175	−	0.431448i
$712$	3.81294	−	6.60421i	0.142896	−	0.247503i
$713$	−0.353134	−	0.611646i	−0.0132250	−	0.0229063i
$714$	1.64191	+	14.5569i	0.0614471	+	0.544779i
$715$		−	0.310904i		−	0.0116271i
$716$	−1.70761	+	2.95767i	−0.0638164	+	0.110533i
$717$	−3.10017	+	0.563412i	−0.115778	+	0.0210410i
$718$			12.2434i			0.456919i
$719$		−	32.5625i		−	1.21438i	−0.794558	−	0.607188i	$-0.792297\pi$
$719$		−	32.5625i		−	1.21438i	0.794558	−	0.607188i	$-0.207703\pi$
$720$	−0.0955553	−	0.254214i	−0.00356114	−	0.00947399i
$721$	2.12209	+	0.143364i	0.0790306	+	0.00533914i
$722$	16.7608	−	8.94850i	0.623772	−	0.333029i
$723$	−19.6875	+	3.57792i	−0.732187	+	0.133064i
$724$	1.93919	−	1.11959i	0.0720693	−	0.0416092i
$725$	14.7269	+	25.5078i	0.546944	+	0.947335i
$726$	9.87237	−	8.37245i	0.366398	−	0.310731i
$727$	4.48180	−	7.76271i	0.166221	−	0.287903i	−0.770867	−	0.636996i	$-0.780177\pi$
$727$	4.48180	−	7.76271i	0.166221	−	0.287903i	0.937088	+	0.349093i	$0.113510\pi$
$728$	−4.82770	−	0.326150i	−0.178927	−	0.0120879i
$729$	−12.7582	+	23.7955i	−0.472527	+	0.881316i
$730$	−0.959851	+	0.554170i	−0.0355257	+	0.0205108i
$731$			18.6958i			0.691489i
$732$	−9.56684	−	3.42537i	−0.353600	−	0.126605i
$733$	7.08326	+	12.2686i	0.261626	+	0.453150i	0.966674	−	0.256010i	$-0.0824080\pi$
$733$	7.08326	+	12.2686i	0.261626	+	0.453150i	−0.705048	+	0.709159i	$0.749075\pi$
$734$	12.6912			0.468442
$735$	−0.590865	−	0.924961i	−0.0217944	−	0.0341177i
$736$	0.0885975	+	0.0511518i	0.00326575	+	0.00188548i
$737$	10.0490	−	17.4053i	0.370158	−	0.641132i
$738$	−5.43737	+	32.8463i	−0.200153	+	1.20909i
$739$	18.2304	+	31.5760i	0.670617	+	1.16154i	0.977729	+	0.209869i	$0.0673039\pi$
$739$	18.2304	+	31.5760i	0.670617	+	1.16154i	−0.307113	+	0.951673i	$0.599363\pi$
$740$	−0.179857	−	0.311522i	−0.00661168	−	0.0114518i
$741$	11.2198	+	8.04770i	0.412170	+	0.295640i
$742$	3.93320	+	2.63951i	0.144392	+	0.0968994i
$743$	−15.5528	+	26.9382i	−0.570576	+	0.988266i	0.425931	+	0.904756i	$0.359947\pi$
$743$	−15.5528	+	26.9382i	−0.570576	+	0.988266i	−0.996507	+	0.0835106i	$0.973387\pi$
$744$	4.03076	−	11.2576i	0.147775	−	0.412725i
$745$	1.52750			0.0559633
$746$	−18.1523	+	10.4802i	−0.664603	+	0.383709i
$747$	−10.8623	−	28.8978i	−0.397429	−	1.05731i
$748$	6.00308			0.219494
$749$	−1.00715	+	14.9079i	−0.0368003	+	0.544723i
$750$	−1.54143	+	0.280133i	−0.0562852	+	0.0102290i
$751$	−19.8267	−	11.4470i	−0.723487	−	0.417705i	0.0925479	−	0.995708i	$-0.470499\pi$
$751$	−19.8267	−	11.4470i	−0.723487	−	0.417705i	−0.816035	+	0.578003i	$0.803832\pi$
$752$	3.30117	+	1.90593i	0.120381	+	0.0695022i
$753$	−17.0838	−	20.1444i	−0.622569	−	0.734101i
$754$	−9.34534	−	5.39554i	−0.340337	−	0.196494i
$755$	−1.01072	+	1.75061i	−0.0367837	+	0.0637112i
$756$	0.710907	−	13.7293i	0.0258554	−	0.499331i
$757$	19.2331	−	33.3127i	0.699039	−	1.21077i	−0.269761	−	0.962927i	$-0.586945\pi$
$757$	19.2331	−	33.3127i	0.699039	−	1.21077i	0.968800	−	0.247843i	$-0.0797218\pi$
$758$			4.49852i			0.163394i
$759$	−0.253778	+	0.215222i	−0.00921157	+	0.00781205i
$760$	−0.0957873	−	0.382794i	−0.00347457	−	0.0138854i
$761$	−22.1856	+	12.8089i	−0.804227	+	0.464321i	−0.844947	−	0.534850i	$-0.820368\pi$
$761$	−22.1856	+	12.8089i	−0.804227	+	0.464321i	0.0407199	+	0.999171i	$0.487035\pi$
$762$	17.4095	+	20.5284i	0.630681	+	0.743667i
$763$	32.0046	+	2.16216i	1.15864	+	0.0782755i
$764$	−14.0910	+	8.13546i	−0.509796	+	0.294331i
$765$	−0.670865	−	0.551045i	−0.0242552	−	0.0199231i
$766$	12.3514			0.446273
$767$	21.5621	+	12.4489i	0.778563	+	0.449504i
$768$	0.309702	+	1.70414i	0.0111754	+	0.0614928i
$769$	−21.4789	−	37.2025i	−0.774548	−	1.34156i	−0.935048	−	0.354521i	$-0.884644\pi$
$769$	−21.4789	−	37.2025i	−0.774548	−	1.34156i	0.160500	−	0.987036i	$-0.448689\pi$
$770$	−0.403788	+	0.198121i	−0.0145515	+	0.00713977i
$771$	−37.3334	−	13.3671i	−1.34453	−	0.481404i
$772$	10.4521	−	6.03452i	0.376179	−	0.217187i
$773$	45.6321			1.64127			0.820637	−	0.571450i	$-0.193619\pi$
$773$	45.6321			1.64127			0.820637	+	0.571450i	$0.193619\pi$
$774$	2.86544	−	17.3097i	0.102996	−	0.622184i
$775$	−29.8447	−	17.2308i	−1.07205	−	0.618950i
$776$	−14.1132	−	8.14828i	−0.506636	−	0.292506i
$777$	−2.04093	−	18.0945i	−0.0732178	−	0.649136i
$778$			31.7661i			1.13887i
$779$	−13.2941	+	46.5115i	−0.476312	+	1.66645i
$780$	0.218701	−	0.185474i	0.00783076	−	0.00664103i
$781$	18.4569	−	10.6561i	0.660440	−	0.381305i
$782$	0.327036			0.0116948
$783$	14.9105	−	26.7897i	0.532857	−	0.957385i
$784$	2.65282	+	6.47785i	0.0947436	+	0.231352i
$785$	0.963856	−	0.556482i	0.0344015	−	0.0198617i
$786$	−14.2063	+	2.58179i	−0.506723	+	0.0920895i
$787$	−20.0481	−	11.5748i	−0.714638	−	0.412596i	0.0981381	−	0.995173i	$-0.468711\pi$
$787$	−20.0481	−	11.5748i	−0.714638	−	0.412596i	−0.812776	+	0.582576i	$0.802045\pi$
$788$			5.03412i			0.179333i
$789$	−15.9984	−	18.8645i	−0.569560	−	0.671596i
$790$	−0.370865			−0.0131948
$791$	−0.552928	−	0.371061i	−0.0196599	−	0.0131934i
$792$	−5.55802	−	0.920073i	−0.197496	−	0.0326934i
$793$		−	10.7295i		−	0.381017i
$794$	17.4032			0.617617
$795$	−0.276194	+	0.0501943i	−0.00979561	+	0.00178021i
$796$	−15.6860			−0.555977
$797$	−7.02011			−0.248665			−0.124332	−	0.992241i	$-0.539679\pi$
$797$	−7.02011			−0.248665			−0.124332	+	0.992241i	$0.539679\pi$
$798$	3.30229	−	19.7001i	0.116900	−	0.697377i
$799$	12.1855			0.431091
$800$	4.99180			0.176487
$801$	−3.73631	+	22.5705i	−0.132016	+	0.797489i
$802$	20.2675			0.715669
$803$			22.9914i			0.811350i
$804$	18.2384	−	3.31456i	0.643218	−	0.116895i
$805$	−0.0219976	+	0.0107932i	−0.000775313	+	0.000380411i
$806$	12.6258			0.444725
$807$	−18.4326	+	15.6321i	−0.648859	+	0.550278i
$808$		−	19.0334i		−	0.669592i
$809$	10.2653	+	5.92668i	0.360909	+	0.208371i	0.669479	−	0.742831i	$-0.266517\pi$
$809$	10.2653	+	5.92668i	0.360909	+	0.208371i	−0.308570	+	0.951201i	$0.599851\pi$
$810$	0.536671	+	0.613012i	0.0188567	+	0.0215391i
$811$	−21.7623	+	12.5645i	−0.764179	+	0.441199i	−0.830794	−	0.556580i	$-0.812113\pi$
$811$	−21.7623	+	12.5645i	−0.764179	+	0.441199i	0.0666154	+	0.997779i	$0.478780\pi$
$812$	−1.05225	+	15.5756i	−0.0369269	+	0.546596i
$813$	−5.17489	−	28.4748i	−0.181491	−	0.998656i
$814$	−7.46193			−0.261541
$815$	0.411289	−	0.237458i	0.0144068	−	0.00831778i
$816$	3.58122	+	4.22279i	0.125368	+	0.147827i
$817$	7.00588	−	24.5111i	0.245105	−	0.857535i
$818$		−	36.5351i		−	1.27742i
$819$	13.9013	−	4.18000i	0.485750	−	0.146061i
$820$	0.870048	+	0.502322i	0.0303834	+	0.0175419i
$821$	−16.7200	−	9.65328i	−0.583531	−	0.336902i	0.179004	−	0.983848i	$-0.442712\pi$
$821$	−16.7200	−	9.65328i	−0.583531	−	0.336902i	−0.762535	+	0.646947i	$0.776046\pi$
$822$	18.6110	−	3.38228i	0.649134	−	0.117971i
$823$	12.5484			0.437408			0.218704	−	0.975791i	$-0.429817\pi$
$823$	12.5484			0.437408			0.218704	+	0.975791i	$0.429817\pi$
$824$	0.696199	−	0.401951i	0.0242532	−	0.0140026i
$825$	−5.47312	+	15.2860i	−0.190549	+	0.532191i
$826$	2.42782	−	35.9369i	0.0844747	−	1.25040i
$827$	−12.2676	−	21.2481i	−0.426587	−	0.738870i	0.569980	−	0.821658i	$-0.306951\pi$
$827$	−12.2676	−	21.2481i	−0.426587	−	0.738870i	−0.996567	+	0.0827883i	$0.973617\pi$
$828$	−0.302790	−	0.0501238i	−0.0105227	−	0.00174192i
$829$	−2.24870	−	1.29829i	−0.0781005	−	0.0450914i	0.460441	−	0.887690i	$-0.347691\pi$
$829$	−2.24870	−	1.29829i	−0.0781005	−	0.0450914i	−0.538542	+	0.842599i	$0.681025\pi$
$830$	−0.931574			−0.0323354
$831$	−13.3323	−	4.77359i	−0.462492	−	0.165594i
$832$	−1.58384	+	0.914430i	−0.0549097	+	0.0317022i
$833$	17.6981	+	13.6934i	0.613204	+	0.474448i
$834$	11.2100	−	9.50688i	0.388171	−	0.329196i
$835$	−0.754358	+	0.435529i	−0.0261056	+	0.0150721i
$836$	−7.87034	−	2.24954i	−0.272201	−	0.0778018i
$837$	0.563943	+	35.8680i	0.0194927	+	1.23978i
$838$			13.1281i			0.453502i
$839$	16.2601	−	28.1634i	0.561362	−	0.972307i	−0.436016	−	0.899939i	$-0.643611\pi$
$839$	16.2601	−	28.1634i	0.561362	−	0.972307i	0.997378	−	0.0723682i	$-0.0230557\pi$
$840$	−0.380251	−	0.165848i	−0.0131199	−	0.00572231i
$841$	−2.90759	+	5.03609i	−0.100262	+	0.173658i
$842$	11.4043	+	6.58427i	0.393018	+	0.226909i
$843$	8.23638	−	6.98502i	0.283676	−	0.240577i
$844$	−13.7770	−	7.95416i	−0.474224	−	0.273793i
$845$	−0.756957	−	0.437029i	−0.0260401	−	0.0150343i
$846$	−11.2821	−	1.86763i	−0.387885	−	0.0642104i
$847$	1.33279	−	19.7282i	0.0457953	−	0.677868i
$848$	1.79033			0.0614803
$849$	−13.4174	+	11.3789i	−0.460485	+	0.390524i
$850$	13.8195	−	7.97871i	0.474006	−	0.273668i
$851$	−0.406511			−0.0139350
$852$	18.5066	+	6.62624i	0.634026	+	0.227011i
$853$	−17.7442	+	30.7338i	−0.607549	+	1.05231i	0.384094	+	0.923294i	$0.374514\pi$
$853$	−17.7442	+	30.7338i	−0.607549	+	1.05231i	−0.991643	+	0.129011i	$0.958820\pi$
$854$	−13.9350	+	6.83730i	−0.476848	+	0.233967i
$855$	0.673045	+	0.973841i	0.0230176	+	0.0333047i
$856$	2.82375	+	4.89088i	0.0965138	+	0.167167i
$857$	−25.1679	−	43.5921i	−0.859719	−	1.48908i	−0.872197	−	0.489156i	$-0.837305\pi$
$857$	−25.1679	−	43.5921i	−0.859719	−	1.48908i	0.0124772	−	0.999922i	$-0.496028\pi$
$858$	−1.06364	−	5.85267i	−0.0363120	−	0.199807i
$859$	12.8786	−	22.3063i	0.439411	−	0.761082i	−0.558233	−	0.829684i	$-0.688520\pi$
$859$	12.8786	−	22.3063i	0.439411	−	0.761082i	0.997644	+	0.0686018i	$0.0218538\pi$
$860$	−0.458507	−	0.264719i	−0.0156349	−	0.00902684i
$861$	30.2044	+	40.9154i	1.02936	+	1.39439i
$862$	−2.33455			−0.0795152
$863$	−12.6771	−	21.9573i	−0.431533	−	0.747436i	0.565473	−	0.824767i	$-0.308694\pi$
$863$	−12.6771	−	21.9573i	−0.431533	−	0.747436i	−0.997006	+	0.0773304i	$0.975360\pi$
$864$	−2.66850	−	4.45860i	−0.0907842	−	0.151685i
$865$			1.54868i			0.0526567i
$866$	0.945018	−	0.545606i	0.0321130	−	0.0185405i
$867$	−11.0576	−	3.95912i	−0.375534	−	0.134459i
$868$	−8.04569	−	16.3979i	−0.273088	−	0.556580i
$869$	−3.84662	+	6.66254i	−0.130488	+	0.226011i
$870$	−0.598393	−	0.705594i	−0.0202874	−	0.0239219i
$871$	9.78660	+	16.9509i	0.331606	+	0.574359i
$872$	10.4998	−	6.06208i	0.355569	−	0.205288i
$873$	48.2333	+	7.98453i	1.63245	+	0.270235i
$874$	−0.428761	−	0.122550i	−0.0145031	−	0.00414533i
$875$	−1.33355	+	1.98716i	−0.0450822	+	0.0671782i
$876$	−16.1730	+	13.7159i	−0.546436	+	0.463416i
$877$			44.7165i			1.50997i	0.655744	+	0.754984i	$0.272355\pi$
$877$			44.7165i			1.50997i	−0.655744	+	0.754984i	$0.727645\pi$
$878$			28.8102i			0.972296i
$879$	−5.98303	−	32.9217i	−0.201803	−	1.11042i
$880$	−0.0849993	+	0.147223i	−0.00286533	+	0.00496289i
$881$		−	55.5858i		−	1.87273i	−0.351024	−	0.936367i	$-0.614166\pi$
$881$		−	55.5858i		−	1.87273i	0.351024	−	0.936367i	$-0.385834\pi$
$882$	−14.2873	−	15.3907i	−0.481077	−	0.518232i
$883$	−11.2507	−	19.4868i	−0.378616	−	0.655783i	0.612245	−	0.790668i	$-0.290267\pi$
$883$	−11.2507	−	19.4868i	−0.378616	−	0.655783i	−0.990861	+	0.134885i	$0.956933\pi$
$884$	−2.92318	+	5.06310i	−0.0983172	+	0.170290i
$885$	1.38065	+	1.62799i	0.0464099	+	0.0547242i
$886$	−1.06924	−	0.617325i	−0.0359218	−	0.0207394i
$887$	7.66306	−	13.2728i	0.257300	−	0.445657i	−0.708218	−	0.705994i	$-0.750500\pi$
$887$	7.66306	−	13.2728i	0.257300	−	0.445657i	0.965518	+	0.260337i	$0.0838337\pi$
$888$	−4.45152	−	5.24900i	−0.149383	−	0.176145i
$889$	41.0224	+	2.77139i	1.37585	+	0.0929494i
$890$	0.597856	+	0.345173i	0.0200402	+	0.0115702i
$891$	16.5790	−	3.28305i	0.555419	−	0.109986i
$892$	−10.1739	−	5.87393i	−0.340649	−	0.196674i
$893$	−15.9758	−	4.56627i	−0.534609	−	0.152804i
$894$	28.7548	−	5.22576i	0.961703	−	0.174776i
$895$	−0.267748	−	0.154584i	−0.00894982	−	0.00516718i
$896$	2.19691	+	1.47431i	0.0733936	+	0.0492532i
$897$	−0.0579449	−	0.318842i	−0.00193473	−	0.0106458i
$898$	−28.4175			−0.948305
$899$		−	40.7346i		−	1.35857i
$900$	−14.0178	+	5.26910i	−0.467261	+	0.175637i
$901$	4.95644	−	2.86160i	0.165123	−	0.0953338i
$902$	18.0483	−	10.4202i	0.600943	−	0.346954i
$903$	−15.9174	−	21.5620i	−0.529699	−	0.717539i
$904$	−0.251685			−0.00837091
$905$	0.101353	+	0.175548i	0.00336907	+	0.00583541i
$906$	−13.0374	+	36.4125i	−0.433138	+	1.20973i
$907$	−34.5016	+	19.9195i	−1.14561	+	0.661417i	−0.947813	−	0.318826i	$-0.896711\pi$
$907$	−34.5016	+	19.9195i	−1.14561	+	0.661417i	−0.197795	+	0.980243i	$0.563378\pi$
$908$	1.44306	−	2.49946i	0.0478898	−	0.0829475i
$909$	20.0907	+	53.4489i	0.666366	+	1.77279i
$910$	0.0295252	−	0.437035i	0.000978751	−	0.0144876i
$911$	44.7880			1.48389			0.741946	−	0.670460i	$-0.233903\pi$
$911$	44.7880			1.48389			0.741946	+	0.670460i	$0.233903\pi$
$912$	−3.11275	−	6.87828i	−0.103074	−	0.227763i
$913$	−9.66230	+	16.7356i	−0.319775	+	0.553867i
$914$	2.08484	+	3.61105i	0.0689604	+	0.119443i
$915$	0.310087	−	0.866053i	0.0102512	−	0.0286308i
$916$	2.28168	+	3.95198i	0.0753888	+	0.130577i
$917$	−12.2904	+	18.3143i	−0.405865	+	0.604790i
$918$	−14.5140	−	8.07816i	−0.479035	−	0.266619i
$919$	11.1541	+	19.3194i	0.367939	+	0.637289i	0.989243	−	0.146280i	$-0.0467301\pi$
$919$	11.1541	+	19.3194i	0.367939	+	0.637289i	−0.621304	+	0.783570i	$0.713397\pi$
$920$	−0.00463060	+	0.00802043i	−0.000152666	+	0.000264426i
$921$	6.56526	−	18.3363i	0.216333	−	0.604202i
$922$	2.42290	+	1.39886i	0.0797938	+	0.0460690i
$923$			20.7558i			0.683186i
$924$	−6.92341	+	5.11097i	−0.227763	+	0.168139i
$925$	−17.1779	+	9.91767i	−0.564806	+	0.326091i
$926$	−8.95643			−0.294327
$927$	−1.53077	+	1.86362i	−0.0502769	+	0.0612093i
$928$	2.95022	+	5.10993i	0.0968457	+	0.167742i
$929$			6.69555i			0.219674i	0.993950	+	0.109837i	$0.0350328\pi$
$929$			6.69555i			0.219674i	−0.993950	+	0.109837i	$0.964967\pi$
$930$	1.01911	+	0.364891i	0.0334181	+	0.0119652i
$931$	−18.0718	−	24.5847i	−0.592280	−	0.805732i
$932$		−	14.2793i		−	0.467733i
$933$	−0.914078	+	2.55296i	−0.0299256	+	0.0835800i
$934$	−1.30881	+	0.755639i	−0.0428254	+	0.0247253i
$935$			0.543438i			0.0177723i
$936$	3.48246	−	4.23970i	0.113828	−	0.138579i
$937$	17.7173	+	30.6873i	0.578800	+	1.00251i	0.995617	+	0.0935205i	$0.0298121\pi$
$937$	17.7173	+	30.6873i	0.578800	+	1.00251i	−0.416818	+	0.908990i	$0.636855\pi$
$938$	15.7787	−	23.5122i	0.515192	−	0.767701i
$939$	−23.2935	−	8.34018i	−0.760156	−	0.272171i
$940$	−0.172538	+	0.298844i	−0.00562755	+	0.00974721i
$941$	13.6672			0.445538			0.222769	−	0.974871i	$-0.428490\pi$
$941$	13.6672			0.445538			0.222769	+	0.974871i	$0.428490\pi$
$942$	16.2405	−	13.7731i	0.529145	−	0.448752i
$943$	0.983236	−	0.567672i	0.0320186	−	0.0184859i
$944$	−6.80692	−	11.7899i	−0.221546	−	0.383729i
$945$	1.24287	+	0.0643560i	0.0404305	+	0.00209350i
$946$	−9.51127	+	5.49134i	−0.309238	+	0.178539i
$947$		−	48.6555i		−	1.58109i	−0.612404	−	0.790545i	$-0.709797\pi$
$947$		−	48.6555i		−	1.58109i	0.612404	−	0.790545i	$-0.290203\pi$
$948$	−6.98143	+	1.26877i	−0.226746	+	0.0412079i
$949$	−19.3913	−	11.1956i	−0.629470	−	0.363425i
$950$	−21.1080	+	5.28189i	−0.684833	+	0.171367i
$951$	24.6940	+	8.84159i	0.800757	+	0.286708i
$952$	8.43850	+	0.570087i	0.273493	+	0.0184766i
$953$	30.7445	−	53.2510i	0.995911	−	1.72497i	0.419722	−	0.907653i	$-0.362127\pi$
$953$	30.7445	−	53.2510i	0.995911	−	1.72497i	0.576189	−	0.817317i	$-0.304539\pi$
$954$	−5.02756	+	1.88979i	−0.162773	+	0.0611841i
$955$	−0.736475	−	1.27561i	−0.0238318	−	0.0412779i
$956$			1.81920i			0.0588373i
$957$	−18.8824	+	3.43161i	−0.610383	+	0.110928i
$958$		−	9.31146i		−	0.300840i
$959$	16.1011	−	23.9926i	0.519930	−	0.774763i
$960$	−0.154270	+	0.0280363i	−0.00497903	+	0.000904867i
$961$	8.33020	+	14.4283i	0.268716	+	0.465430i
$962$	3.63356	−	6.29351i	0.117151	−	0.202911i
$963$	−13.0921	−	10.7538i	−0.421888	−	0.346537i
$964$			11.5528i			0.372090i
$965$	0.546284	+	0.946192i	0.0175855	+	0.0304590i
$966$	−0.377174	+	0.278436i	−0.0121354	+	0.00895852i
$967$	17.9679	−	31.1214i	0.577810	−	1.00080i	−0.417920	−	0.908484i	$-0.637241\pi$
$967$	17.9679	−	31.1214i	0.577810	−	1.00080i	0.995730	−	0.0923125i	$-0.0294259\pi$
$968$	−3.73677	−	6.47228i	−0.120104	−	0.208027i
$969$	−19.6115	−	14.0668i	−0.630011	−	0.451892i
$970$	0.737636	−	1.27762i	0.0236841	−	0.0410220i
$971$	0.119198			0.00382526			0.00191263	−	0.999998i	$-0.499391\pi$
$971$	0.119198			0.00382526			0.00191263	+	0.999998i	$0.499391\pi$
$972$	12.1999	+	9.70377i	0.391311	+	0.311249i
$973$	1.51338	−	22.4012i	0.0485168	−	0.718151i
$974$	9.73527	+	5.62066i	0.311938	+	0.180098i
$975$	−10.2274	−	12.0596i	−0.327538	−	0.386216i
$976$	−2.93339	+	5.08079i	−0.0938956	+	0.162632i
$977$	−14.3945	+	24.9320i	−0.460520	+	0.797644i	−0.998987	−	0.0450027i	$-0.985670\pi$
$977$	−14.3945	+	24.9320i	−0.460520	+	0.797644i	0.538467	+	0.842647i	$0.319004\pi$
$978$	6.93003	−	5.87714i	0.221598	−	0.187930i
$979$	12.4020	−	7.16027i	0.396368	−	0.228843i
$980$	−0.586418	+	0.240151i	−0.0187324	+	0.00767134i
$981$	−23.0865	+	28.1064i	−0.737094	+	0.897370i
$982$	23.5616	+	13.6033i	0.751881	+	0.434099i
$983$	25.3453	+	43.8993i	0.808389	+	1.40017i	0.913979	+	0.405760i	$0.132993\pi$
$983$	25.3453	+	43.8993i	0.808389	+	1.40017i	−0.105591	+	0.994410i	$0.533673\pi$
$984$	18.0969	+	6.47954i	0.576908	+	0.206560i
$985$	−0.455721			−0.0145205
$986$	16.3350	+	9.43104i	0.520213	+	0.300345i
$987$	−14.0536	+	10.3746i	−0.447332	+	0.330227i
$988$	5.72973	−	5.54257i	0.182287	−	0.176333i
$989$	−0.518156	+	0.299157i	−0.0164764	+	0.00951265i
$990$	0.0832910	−	0.503148i	0.00264716	−	0.0159911i
$991$	−29.6188	+	17.1004i	−0.940871	+	0.543212i	−0.890233	−	0.455505i	$-0.849459\pi$
$991$	−29.6188	+	17.1004i	−0.940871	+	0.543212i	−0.0506380	+	0.998717i	$0.516125\pi$
$992$	−5.97874	−	3.45183i	−0.189825	−	0.109596i
$993$	−29.0405	−	34.2431i	−0.921574	−	1.08667i
$994$	26.9567	−	13.2264i	0.855016	−	0.419517i
$995$		−	1.42000i		−	0.0450171i
$996$	−17.5366	+	3.18703i	−0.555669	+	0.100985i
$997$	−31.2063			−0.988314			−0.494157	−	0.869373i	$-0.664523\pi$
$997$	−31.2063			−0.988314			−0.494157	+	0.869373i	$0.664523\pi$
$998$	1.22541			0.0387895
$999$	18.0412	+	10.0413i	0.570798	+	0.317692i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.p.d.179.14	yes	50
3.2	odd	2		798.2.p.c.179.7	yes	50
7.2	even	3		798.2.bh.c.65.3	yes	50
19.12	odd	6		798.2.bh.d.221.23	yes	50
21.2	odd	6		798.2.bh.d.65.23	yes	50
57.50	even	6		798.2.bh.c.221.3	yes	50
133.107	odd	6		798.2.p.c.107.7	✓	50
399.107	even	6	inner	798.2.p.d.107.14	yes	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.p.c.107.7	✓	50	133.107	odd	6
798.2.p.c.179.7	yes	50	3.2	odd	2
798.2.p.d.107.14	yes	50	399.107	even	6	inner
798.2.p.d.179.14	yes	50	1.1	even	1	trivial
798.2.bh.c.65.3	yes	50	7.2	even	3
798.2.bh.c.221.3	yes	50	57.50	even	6
798.2.bh.d.65.23	yes	50	21.2	odd	6
798.2.bh.d.221.23	yes	50	19.12	odd	6

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.309702 + 1.70414i) q^{3} +1.00000 q^{4} +0.0905266i q^{5} +(0.309702 + 1.70414i) q^{6} +(2.19691 + 1.47431i) q^{7} +1.00000 q^{8} +(-2.80817 + 1.05555i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.309702 + 1.70414i) q^{3} +1.00000 q^{4} +0.0905266i q^{5} +(0.309702 + 1.70414i) q^{6} +(2.19691 + 1.47431i) q^{7} +1.00000 q^{8} +(-2.80817 + 1.05555i) q^{9} +0.0905266i q^{10} +(1.62630 + 0.938943i) q^{11} +(0.309702 + 1.70414i) q^{12} +(-1.58384 + 0.914430i) q^{13} +(2.19691 + 1.47431i) q^{14} +(-0.154270 + 0.0280363i) q^{15} +1.00000 q^{16} +(2.76844 - 1.59836i) q^{17} +(-2.80817 + 1.05555i) q^{18} +(-4.22852 + 1.05811i) q^{19} +0.0905266i q^{20} +(-1.83204 + 4.20043i) q^{21} +(1.62630 + 0.938943i) q^{22} +(0.0885975 + 0.0511518i) q^{23} +(0.309702 + 1.70414i) q^{24} +4.99180 q^{25} +(-1.58384 + 0.914430i) q^{26} +(-2.66850 - 4.45860i) q^{27} +(2.19691 + 1.47431i) q^{28} +(2.95022 + 5.10993i) q^{29} +(-0.154270 + 0.0280363i) q^{30} +(-5.97874 - 3.45183i) q^{31} +1.00000 q^{32} +(-1.09642 + 3.06223i) q^{33} +(2.76844 - 1.59836i) q^{34} +(-0.133464 + 0.198879i) q^{35} +(-2.80817 + 1.05555i) q^{36} +(-3.44122 + 1.98679i) q^{37} +(-4.22852 + 1.05811i) q^{38} +(-2.04883 - 2.41588i) q^{39} +0.0905266i q^{40} +(5.54889 - 9.61096i) q^{41} +(-1.83204 + 4.20043i) q^{42} +(-2.92421 + 5.06488i) q^{43} +(1.62630 + 0.938943i) q^{44} +(-0.0955553 - 0.254214i) q^{45} +(0.0885975 + 0.0511518i) q^{46} +(3.30117 + 1.90593i) q^{47} +(0.309702 + 1.70414i) q^{48} +(2.65282 + 6.47785i) q^{49} +4.99180 q^{50} +(3.58122 + 4.22279i) q^{51} +(-1.58384 + 0.914430i) q^{52} +1.79033 q^{53} +(-2.66850 - 4.45860i) q^{54} +(-0.0849993 + 0.147223i) q^{55} +(2.19691 + 1.47431i) q^{56} +(-3.11275 - 6.87828i) q^{57} +(2.95022 + 5.10993i) q^{58} +(-6.80692 - 11.7899i) q^{59} +(-0.154270 + 0.0280363i) q^{60} +(-2.93339 + 5.08079i) q^{61} +(-5.97874 - 3.45183i) q^{62} +(-7.72550 - 1.82116i) q^{63} +1.00000 q^{64} +(-0.0827802 - 0.143380i) q^{65} +(-1.09642 + 3.06223i) q^{66} -10.7024i q^{67} +(2.76844 - 1.59836i) q^{68} +(-0.0597308 + 0.166824i) q^{69} +(-0.133464 + 0.198879i) q^{70} +(5.67452 - 9.82856i) q^{71} +(-2.80817 + 1.05555i) q^{72} +(6.12163 + 10.6030i) q^{73} +(-3.44122 + 1.98679i) q^{74} +(1.54597 + 8.50672i) q^{75} +(-4.22852 + 1.05811i) q^{76} +(2.18853 + 4.46044i) q^{77} +(-2.04883 - 2.41588i) q^{78} +4.09675i q^{79} +0.0905266i q^{80} +(6.77163 - 5.92833i) q^{81} +(5.54889 - 9.61096i) q^{82} +10.2906i q^{83} +(-1.83204 + 4.20043i) q^{84} +(0.144694 + 0.250618i) q^{85} +(-2.92421 + 5.06488i) q^{86} +(-7.79433 + 6.61014i) q^{87} +(1.62630 + 0.938943i) q^{88} +(3.81294 - 6.60421i) q^{89} +(-0.0955553 - 0.254214i) q^{90} +(-4.82770 - 0.326150i) q^{91} +(0.0885975 + 0.0511518i) q^{92} +(4.03076 - 11.2576i) q^{93} +(3.30117 + 1.90593i) q^{94} +(-0.0957873 - 0.382794i) q^{95} +(0.309702 + 1.70414i) q^{96} +(-14.1132 - 8.14828i) q^{97} +(2.65282 + 6.47785i) q^{98} +(-5.55802 - 0.920073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9	\( 50 q + 50 q^{2} + 50 q^{4} + 50 q^{8} + 6 q^{9} - 3 q^{11} - 3 q^{13} - 13 q^{15} + 50 q^{16} + 3 q^{17} + 6 q^{18} + 10 q^{19} - 7 q^{21} - 3 q^{22} + 9 q^{23} - 58 q^{25} - 3 q^{26} + 6 q^{27} - 5 q^{29} - 13 q^{30} + 15 q^{31} + 50 q^{32} - q^{33} + 3 q^{34} + 6 q^{36} - 9 q^{37} + 10 q^{38} - 2 q^{39} - 17 q^{41} - 7 q^{42} + 15 q^{43} - 3 q^{44} - 22 q^{45} + 9 q^{46} + 21 q^{47} + 8 q^{49} - 58 q^{50} - 4 q^{51} - 3 q^{52} - 12 q^{53} + 6 q^{54} - 16 q^{55} - 19 q^{57} - 5 q^{58} - q^{59} - 13 q^{60} + 23 q^{61} + 15 q^{62} + 41 q^{63} + 50 q^{64} - 14 q^{65} - q^{66} + 3 q^{68} - 31 q^{69} + 3 q^{71} + 6 q^{72} + 15 q^{73} - 9 q^{74} + 7 q^{75} + 10 q^{76} - 57 q^{77} - 2 q^{78} - 70 q^{81} - 17 q^{82} - 7 q^{84} - 10 q^{85} + 15 q^{86} + 52 q^{87} - 3 q^{88} + 33 q^{89} - 22 q^{90} - 15 q^{91} + 9 q^{92} + 53 q^{93} + 21 q^{94} + 30 q^{95} - 21 q^{97} + 8 q^{98} - 2 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 50 * q^4 + 50 * q^8 + 6 * q^9 - 3 * q^11 - 3 * q^13 - 13 * q^15 + 50 * q^16 + 3 * q^17 + 6 * q^18 + 10 * q^19 - 7 * q^21 - 3 * q^22 + 9 * q^23 - 58 * q^25 - 3 * q^26 + 6 * q^27 - 5 * q^29 - 13 * q^30 + 15 * q^31 + 50 * q^32 - q^33 + 3 * q^34 + 6 * q^36 - 9 * q^37 + 10 * q^38 - 2 * q^39 - 17 * q^41 - 7 * q^42 + 15 * q^43 - 3 * q^44 - 22 * q^45 + 9 * q^46 + 21 * q^47 + 8 * q^49 - 58 * q^50 - 4 * q^51 - 3 * q^52 - 12 * q^53 + 6 * q^54 - 16 * q^55 - 19 * q^57 - 5 * q^58 - q^59 - 13 * q^60 + 23 * q^61 + 15 * q^62 + 41 * q^63 + 50 * q^64 - 14 * q^65 - q^66 + 3 * q^68 - 31 * q^69 + 3 * q^71 + 6 * q^72 + 15 * q^73 - 9 * q^74 + 7 * q^75 + 10 * q^76 - 57 * q^77 - 2 * q^78 - 70 * q^81 - 17 * q^82 - 7 * q^84 - 10 * q^85 + 15 * q^86 + 52 * q^87 - 3 * q^88 + 33 * q^89 - 22 * q^90 - 15 * q^91 + 9 * q^92 + 53 * q^93 + 21 * q^94 + 30 * q^95 - 21 * q^97 + 8 * q^98 - 2 * q^99

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