LMFDB - Embedded newform 798.2.bc.a.31.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(31,798)]

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([0, 1, 5]))

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

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

chi := DirichletCharacter("798.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bc (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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.6
Character	$\chi$	$=$	798.31
Dual form			798.2.bc.a.103.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.57310 + 0.908227i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.235464 - 2.63525i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.57310 + 0.908227i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.235464 - 2.63525i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-0.908227 - 1.57310i) q^{10} +(-0.129396 + 0.224121i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.29238 - 2.23847i) q^{13} +(-1.52154 + 2.16446i) q^{14} +(-1.57310 - 0.908227i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.82842i q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.07092 + 4.22530i) q^{19} +1.81645i q^{20} +(-0.235464 + 2.63525i) q^{21} +(0.224121 - 0.129396i) q^{22} -4.55594 q^{23} +1.00000i q^{24} +(-0.850246 - 1.47267i) q^{25} +(-2.23847 + 1.29238i) q^{26} -1.00000 q^{27} +(2.39993 - 1.11371i) q^{28} +(8.32743 + 4.80785i) q^{29} +(0.908227 + 1.57310i) q^{30} +(2.97991 - 5.16135i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.129396 - 0.224121i) q^{33} +(-1.91421 + 3.31551i) q^{34} +(2.76382 - 3.93165i) q^{35} +(0.500000 + 0.866025i) q^{36} +(7.15136 - 4.12884i) q^{37} +(3.04010 - 3.12375i) q^{38} +(-1.29238 + 2.23847i) q^{39} +(0.908227 - 1.57310i) q^{40} +(-0.785169 - 1.35995i) q^{41} +(1.52154 - 2.16446i) q^{42} +(-6.02263 - 10.4315i) q^{43} -0.258793 q^{44} +(1.57310 + 0.908227i) q^{45} +(3.94556 + 2.27797i) q^{46} +6.75183i q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.88911 - 1.24101i) q^{49} +1.70049i q^{50} +3.82842i q^{51} +2.58476 q^{52} +(0.403342 - 0.232869i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.407106 + 0.235043i) q^{55} +(-2.63525 - 0.235464i) q^{56} +(1.07092 - 4.22530i) q^{57} +(-4.80785 - 8.32743i) q^{58} +11.0803 q^{59} -1.81645i q^{60} -7.86246i q^{61} +(-5.16135 + 2.97991i) q^{62} +(0.235464 - 2.63525i) q^{63} -1.00000 q^{64} +(4.06608 - 2.34755i) q^{65} +(-0.224121 + 0.129396i) q^{66} +(8.06288 - 4.65511i) q^{67} +(3.31551 - 1.91421i) q^{68} +4.55594 q^{69} +(-4.35936 + 2.02300i) q^{70} +(-3.54400 + 2.04613i) q^{71} -1.00000i q^{72} -12.0707i q^{73} -8.25768 q^{74} +(0.850246 + 1.47267i) q^{75} +(-4.19468 + 1.18520i) q^{76} +(0.560148 + 0.393765i) q^{77} +(2.23847 - 1.29238i) q^{78} +(-11.4590 - 6.61587i) q^{79} +(-1.57310 + 0.908227i) q^{80} +1.00000 q^{81} +1.57034i q^{82} -10.1119i q^{83} +(-2.39993 + 1.11371i) q^{84} +(3.47707 - 6.02247i) q^{85} +12.0453i q^{86} +(-8.32743 - 4.80785i) q^{87} +(0.224121 + 0.129396i) q^{88} +11.0409 q^{89} +(-0.908227 - 1.57310i) q^{90} +(-5.59463 - 3.93283i) q^{91} +(-2.27797 - 3.94556i) q^{92} +(-2.97991 + 5.16135i) q^{93} +(3.37592 - 5.84726i) q^{94} +(-5.52220 + 5.67415i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(2.70017 + 4.67684i) q^{97} +(5.34564 + 4.51930i) q^{98} +(-0.129396 + 0.224121i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 28 q^{3} + 14 q^{4} + 6 q^{5} + 4 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - 28 * q^3 + 14 * q^4 + 6 * q^5 + 4 * q^7 + 28 * q^9	$ 28 q - 28 q^{3} + 14 q^{4} + 6 q^{5} + 4 q^{7} + 28 q^{9} - 2 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} - 6 q^{15} - 14 q^{16} + 12 q^{19} - 4 q^{21} - 12 q^{22} + 14 q^{25} - 28 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} - 4 q^{31} - 8 q^{34} - 10 q^{35} + 14 q^{36} - 12 q^{37} + 6 q^{38} + 2 q^{39} + 2 q^{40} + 8 q^{41} + 4 q^{42} + 10 q^{43} + 6 q^{45} + 24 q^{46} + 14 q^{48} - 4 q^{52} - 12 q^{53} - 30 q^{55} + 4 q^{56} - 12 q^{57} - 2 q^{58} + 4 q^{59} + 12 q^{62} + 4 q^{63} - 28 q^{64} + 96 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{70} - 42 q^{71} + 12 q^{74} - 14 q^{75} + 12 q^{76} + 16 q^{77} + 12 q^{79} - 6 q^{80} + 28 q^{81} - 2 q^{84} - 8 q^{85} - 18 q^{87} - 12 q^{88} - 16 q^{89} - 2 q^{90} + 8 q^{91} + 4 q^{93} - 18 q^{94} - 82 q^{95} - 8 q^{97} + 20 q^{98}+O(q^{100}) $ 28 * q - 28 * q^3 + 14 * q^4 + 6 * q^5 + 4 * q^7 + 28 * q^9 - 2 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 - 6 * q^15 - 14 * q^16 + 12 * q^19 - 4 * q^21 - 12 * q^22 + 14 * q^25 - 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 - 8 * q^34 - 10 * q^35 + 14 * q^36 - 12 * q^37 + 6 * q^38 + 2 * q^39 + 2 * q^40 + 8 * q^41 + 4 * q^42 + 10 * q^43 + 6 * q^45 + 24 * q^46 + 14 * q^48 - 4 * q^52 - 12 * q^53 - 30 * q^55 + 4 * q^56 - 12 * q^57 - 2 * q^58 + 4 * q^59 + 12 * q^62 + 4 * q^63 - 28 * q^64 + 96 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^70 - 42 * q^71 + 12 * q^74 - 14 * q^75 + 12 * q^76 + 16 * q^77 + 12 * q^79 - 6 * q^80 + 28 * q^81 - 2 * q^84 - 8 * q^85 - 18 * q^87 - 12 * q^88 - 16 * q^89 - 2 * q^90 + 8 * q^91 + 4 * q^93 - 18 * q^94 - 82 * q^95 - 8 * q^97 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.57310	+	0.908227i	0.703510	+	0.406172i	0.808653	−	0.588285i	$-0.200197\pi$
$5$	1.57310	+	0.908227i	0.703510	+	0.406172i	−0.105143	+	0.994457i	$0.533530\pi$
$6$	0.866025	+	0.500000i	0.353553	+	0.204124i
$7$	0.235464	−	2.63525i	0.0889968	−	0.996032i
$7$	0.235464	−	2.63525i	0.0889968	−	0.996032i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−0.908227	−	1.57310i	−0.287207	−	0.497457i
$11$	−0.129396	+	0.224121i	−0.0390145	+	0.0675751i	−0.884873	−	0.465832i	$-0.845755\pi$
$11$	−0.129396	+	0.224121i	−0.0390145	+	0.0675751i	0.845859	+	0.533407i	$0.179089\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	1.29238	−	2.23847i	0.358442	−	0.620840i	−0.629258	−	0.777196i	$-0.716641\pi$
$13$	1.29238	−	2.23847i	0.358442	−	0.620840i	0.987701	+	0.156356i	$0.0499746\pi$
$14$	−1.52154	+	2.16446i	−0.406650	+	0.578477i
$15$	−1.57310	−	0.908227i	−0.406172	−	0.234503i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		−	3.82842i		−	0.928527i	−0.885697	−	0.464264i	$-0.846319\pi$
$17$		−	3.82842i		−	0.928527i	0.885697	−	0.464264i	$-0.153681\pi$
$18$	−0.866025	−	0.500000i	−0.204124	−	0.117851i
$19$	−1.07092	+	4.22530i	−0.245687	+	0.969349i
$19$	−1.07092	+	4.22530i	−0.245687	+	0.969349i
$20$			1.81645i			0.406172i
$21$	−0.235464	+	2.63525i	−0.0513823	+	0.575059i
$22$	0.224121	−	0.129396i	0.0477828	−	0.0275874i
$23$	−4.55594			−0.949979			−0.474989	−	0.879992i	$-0.657548\pi$
$23$	−4.55594			−0.949979			−0.474989	+	0.879992i	$0.657548\pi$
$24$			1.00000i			0.204124i
$25$	−0.850246	−	1.47267i	−0.170049	−	0.294534i
$26$	−2.23847	+	1.29238i	−0.439000	+	0.253457i
$27$	−1.00000			−0.192450
$28$	2.39993	−	1.11371i	0.453544	−	0.210471i
$29$	8.32743	+	4.80785i	1.54637	+	0.892795i	0.998415	+	0.0562842i	$0.0179253\pi$
$29$	8.32743	+	4.80785i	1.54637	+	0.892795i	0.547951	+	0.836510i	$0.315408\pi$
$30$	0.908227	+	1.57310i	0.165819	+	0.287207i
$31$	2.97991	−	5.16135i	0.535207	−	0.927006i	−0.463946	−	0.885863i	$-0.653567\pi$
$31$	2.97991	−	5.16135i	0.535207	−	0.927006i	0.999153	−	0.0411427i	$-0.0130998\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	0.129396	−	0.224121i	0.0225250	−	0.0390145i
$34$	−1.91421	+	3.31551i	−0.328284	+	0.568605i
$35$	2.76382	−	3.93165i	0.467170	−	0.664570i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.15136	−	4.12884i	1.17568	−	0.678777i	0.220666	−	0.975349i	$-0.429177\pi$
$37$	7.15136	−	4.12884i	1.17568	−	0.678777i	0.955010	+	0.296572i	$0.0958436\pi$
$38$	3.04010	−	3.12375i	0.493169	−	0.506739i
$39$	−1.29238	+	2.23847i	−0.206947	+	0.358442i
$40$	0.908227	−	1.57310i	0.143603	−	0.248728i
$41$	−0.785169	−	1.35995i	−0.122623	−	0.212389i	0.798178	−	0.602421i	$-0.205797\pi$
$41$	−0.785169	−	1.35995i	−0.122623	−	0.212389i	−0.920801	+	0.390032i	$0.872464\pi$
$42$	1.52154	−	2.16446i	0.234779	−	0.333984i
$43$	−6.02263	−	10.4315i	−0.918443	−	1.59079i	−0.801781	−	0.597618i	$-0.796114\pi$
$43$	−6.02263	−	10.4315i	−0.918443	−	1.59079i	−0.116662	−	0.993172i	$-0.537219\pi$
$44$	−0.258793			−0.0390145
$45$	1.57310	+	0.908227i	0.234503	+	0.135391i
$46$	3.94556	+	2.27797i	0.581741	+	0.335868i
$47$			6.75183i			0.984856i	0.870353	+	0.492428i	$0.163891\pi$
$47$			6.75183i			0.984856i	−0.870353	+	0.492428i	$0.836109\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−6.88911	−	1.24101i	−0.984159	−	0.177287i
$50$			1.70049i			0.240486i
$51$			3.82842i			0.536085i
$52$	2.58476			0.358442
$53$	0.403342	−	0.232869i	0.0554032	−	0.0319871i	−0.472043	−	0.881576i	$-0.656483\pi$
$53$	0.403342	−	0.232869i	0.0554032	−	0.0319871i	0.527446	+	0.849589i	$0.323150\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$	−0.407106	+	0.235043i	−0.0548942	+	0.0316932i
$56$	−2.63525	−	0.235464i	−0.352150	−	0.0314651i
$57$	1.07092	−	4.22530i	0.141847	−	0.559654i
$58$	−4.80785	−	8.32743i	−0.631301	−	1.09345i
$59$	11.0803			1.44253			0.721267	−	0.692657i	$-0.243560\pi$
$59$	11.0803			1.44253			0.721267	+	0.692657i	$0.243560\pi$
$60$		−	1.81645i		−	0.234503i
$61$		−	7.86246i		−	1.00668i	−0.864087	−	0.503342i	$-0.832104\pi$
$61$		−	7.86246i		−	1.00668i	0.864087	−	0.503342i	$-0.167896\pi$
$62$	−5.16135	+	2.97991i	−0.655492	+	0.378449i
$63$	0.235464	−	2.63525i	0.0296656	−	0.332011i
$64$	−1.00000			−0.125000
$65$	4.06608	−	2.34755i	0.504335	−	0.291178i
$66$	−0.224121	+	0.129396i	−0.0275874	+	0.0159276i
$67$	8.06288	−	4.65511i	0.985038	−	0.568712i	0.0812505	−	0.996694i	$-0.474109\pi$
$67$	8.06288	−	4.65511i	0.985038	−	0.568712i	0.903787	+	0.427982i	$0.140775\pi$
$68$	3.31551	−	1.91421i	0.402064	−	0.232132i
$69$	4.55594			0.548470
$70$	−4.35936	+	2.02300i	−0.521043	+	0.241795i
$71$	−3.54400	+	2.04613i	−0.420596	+	0.242831i	−0.695332	−	0.718688i	$-0.744743\pi$
$71$	−3.54400	+	2.04613i	−0.420596	+	0.242831i	0.274736	+	0.961520i	$0.411409\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	12.0707i		−	1.41277i	−0.707829	−	0.706383i	$-0.750325\pi$
$73$		−	12.0707i		−	1.41277i	0.707829	−	0.706383i	$-0.249675\pi$
$74$	−8.25768			−0.959936
$75$	0.850246	+	1.47267i	0.0981779	+	0.170049i
$76$	−4.19468	+	1.18520i	−0.481162	+	0.135952i
$77$	0.560148	+	0.393765i	0.0638348	+	0.0448736i
$78$	2.23847	−	1.29238i	0.253457	−	0.146333i
$79$	−11.4590	−	6.61587i	−1.28924	−	0.744344i	−0.310722	−	0.950501i	$-0.600571\pi$
$79$	−11.4590	−	6.61587i	−1.28924	−	0.744344i	−0.978519	+	0.206157i	$0.933904\pi$
$80$	−1.57310	+	0.908227i	−0.175877	+	0.101543i
$81$	1.00000			0.111111
$82$			1.57034i			0.173415i
$83$		−	10.1119i		−	1.10993i	−0.831874	−	0.554965i	$-0.812732\pi$
$83$		−	10.1119i		−	1.10993i	0.831874	−	0.554965i	$-0.187268\pi$
$84$	−2.39993	+	1.11371i	−0.261854	+	0.121516i
$85$	3.47707	−	6.02247i	0.377141	−	0.653228i
$86$			12.0453i			1.29887i
$87$	−8.32743	−	4.80785i	−0.892795	−	0.515455i
$88$	0.224121	+	0.129396i	0.0238914	+	0.0137937i
$89$	11.0409			1.17034			0.585169	−	0.810912i	$-0.301028\pi$
$89$	11.0409			1.17034			0.585169	+	0.810912i	$0.301028\pi$
$90$	−0.908227	−	1.57310i	−0.0957356	−	0.165819i
$91$	−5.59463	−	3.93283i	−0.586477	−	0.412273i
$92$	−2.27797	−	3.94556i	−0.237495	−	0.411353i
$93$	−2.97991	+	5.16135i	−0.309002	+	0.535207i
$94$	3.37592	−	5.84726i	0.348199	−	0.603099i
$95$	−5.52220	+	5.67415i	−0.566565	+	0.582156i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	2.70017	+	4.67684i	0.274161	+	0.474861i	0.969923	−	0.243412i	$-0.0782665\pi$
$97$	2.70017	+	4.67684i	0.274161	+	0.474861i	−0.695762	+	0.718272i	$0.744933\pi$
$98$	5.34564	+	4.51930i	0.539991	+	0.456519i
$99$	−0.129396	+	0.224121i	−0.0130048	+	0.0225250i
$100$	0.850246	−	1.47267i	0.0850246	−	0.147267i
$101$	−0.900889	+	0.520129i	−0.0896418	+	0.0517547i	−0.544151	−	0.838987i	$-0.683148\pi$
$101$	−0.900889	+	0.520129i	−0.0896418	+	0.0517547i	0.454509	+	0.890742i	$0.349815\pi$
$102$	1.91421	−	3.31551i	0.189535	−	0.328284i
$103$	9.66141	+	16.7341i	0.951967	+	1.64886i	0.741160	+	0.671328i	$0.234276\pi$
$103$	9.66141	+	16.7341i	0.951967	+	1.64886i	0.210807	+	0.977528i	$0.432391\pi$
$104$	−2.23847	−	1.29238i	−0.219500	−	0.126729i
$105$	−2.76382	+	3.93165i	−0.269721	+	0.383690i
$106$	−0.465739			−0.0452366
$107$	−13.6641	+	7.88898i	−1.32096	+	0.762657i	−0.983882	−	0.178820i	$-0.942772\pi$
$107$	−13.6641	+	7.88898i	−1.32096	+	0.762657i	−0.337078	+	0.941477i	$0.609439\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$		−	16.4872i		−	1.57919i	−0.613628	−	0.789595i	$-0.710290\pi$
$109$		−	16.4872i		−	1.57919i	0.613628	−	0.789595i	$-0.289710\pi$
$110$	0.470086			0.0448209
$111$	−7.15136	+	4.12884i	−0.678777	+	0.391892i
$112$	2.16446	+	1.52154i	0.204523	+	0.143772i
$113$		−	7.46716i		−	0.702451i	−0.936291	−	0.351226i	$-0.885765\pi$
$113$		−	7.46716i		−	0.702451i	0.936291	−	0.351226i	$-0.114235\pi$
$114$	−3.04010	+	3.12375i	−0.284731	+	0.292566i
$115$	−7.16693	−	4.13783i	−0.668319	−	0.385854i
$116$			9.61569i			0.892795i
$117$	1.29238	−	2.23847i	0.119481	−	0.206947i
$118$	−9.59583	−	5.54016i	−0.883368	−	0.510013i
$119$	−10.0888	−	0.901452i	−0.924843	−	0.0826360i
$120$	−0.908227	+	1.57310i	−0.0829094	+	0.143603i
$121$	5.46651	+	9.46828i	0.496956	+	0.860753i
$122$	−3.93123	+	6.80909i	−0.355917	+	0.616466i
$123$	0.785169	+	1.35995i	0.0707963	+	0.122623i
$124$	5.95982			0.535207
$125$		−	12.1711i		−	1.08862i
$126$	−1.52154	+	2.16446i	−0.135550	+	0.192826i
$127$	2.40109	+	1.38627i	0.213062	+	0.123012i	0.602734	−	0.797942i	$-0.294078\pi$
$127$	2.40109	+	1.38627i	0.213062	+	0.123012i	−0.389672	+	0.920954i	$0.627411\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	6.02263	+	10.4315i	0.530263	+	0.918443i
$130$	−4.69511			−0.411788
$131$	6.78469	+	3.91714i	0.592781	+	0.342242i	0.766196	−	0.642606i	$-0.222147\pi$
$131$	6.78469	+	3.91714i	0.592781	+	0.342242i	−0.173415	+	0.984849i	$0.555480\pi$
$132$	0.258793			0.0225250
$133$	10.8826	+	3.81706i	0.943637	+	0.330981i
$134$	−9.31021			−0.804280
$135$	−1.57310	−	0.908227i	−0.135391	−	0.0781678i
$136$	−3.82842			−0.328284
$137$	1.78919	+	3.09897i	0.152861	+	0.264763i	0.932278	−	0.361743i	$-0.117818\pi$
$137$	1.78919	+	3.09897i	0.152861	+	0.264763i	−0.779417	+	0.626505i	$0.784485\pi$
$138$	−3.94556	−	2.27797i	−0.335868	−	0.193914i
$139$	8.60772	+	4.96967i	0.730097	+	0.421522i	0.818458	−	0.574567i	$-0.194829\pi$
$139$	8.60772	+	4.96967i	0.730097	+	0.421522i	−0.0883604	+	0.996089i	$0.528163\pi$
$140$	4.78682	+	0.427709i	0.404560	+	0.0361480i
$141$		−	6.75183i		−	0.568607i
$142$	4.09226			0.343415
$143$	0.334459	+	0.579300i	0.0279689	+	0.0484435i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	8.73324	+	15.1264i	0.725256	+	1.25618i
$146$	−6.03534	+	10.4535i	−0.499489	+	0.865139i
$147$	6.88911	+	1.24101i	0.568205	+	0.102357i
$148$	7.15136	+	4.12884i	0.587838	+	0.339389i
$149$	−10.3164	+	17.8684i	−0.845149	+	1.46384i	0.0403434	+	0.999186i	$0.487155\pi$
$149$	−10.3164	+	17.8684i	−0.845149	+	1.46384i	−0.885492	+	0.464654i	$0.846179\pi$
$150$		−	1.70049i		−	0.138845i
$151$	−0.217648	−	0.125659i	−0.0177119	−	0.0102260i	0.491118	−	0.871093i	$-0.336588\pi$
$151$	−0.217648	−	0.125659i	−0.0177119	−	0.0102260i	−0.508830	+	0.860867i	$0.669922\pi$
$152$	4.22530	+	1.07092i	0.342717	+	0.0868634i
$153$		−	3.82842i		−	0.309509i
$154$	−0.288220	−	0.621084i	−0.0232254	−	0.0500484i
$155$	9.37536	−	5.41287i	0.753047	−	0.434772i
$156$	−2.58476			−0.206947
$157$			20.8882i			1.66706i	0.552474	+	0.833530i	$0.313684\pi$
$157$			20.8882i			1.66706i	−0.552474	+	0.833530i	$0.686316\pi$
$158$	6.61587	+	11.4590i	0.526331	+	0.911631i
$159$	−0.403342	+	0.232869i	−0.0319871	+	0.0184677i
$160$	1.81645			0.143603
$161$	−1.07276	+	12.0060i	−0.0845451	+	0.946209i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−5.74741	−	9.95481i	−0.450172	−	0.779721i	0.548224	−	0.836331i	$-0.315304\pi$
$163$	−5.74741	−	9.95481i	−0.450172	−	0.779721i	−0.998396	+	0.0566104i	$0.981971\pi$
$164$	0.785169	−	1.35995i	0.0613114	−	0.106194i
$165$	0.407106	−	0.235043i	0.0316932	−	0.0182981i
$166$	−5.05597	+	8.75720i	−0.392420	+	0.679691i
$167$	7.39501	−	12.8085i	0.572243	−	0.991155i	−0.424092	−	0.905619i	$-0.639407\pi$
$167$	7.39501	−	12.8085i	0.572243	−	0.991155i	0.996335	−	0.0855354i	$-0.0272601\pi$
$168$	2.63525	+	0.235464i	0.203314	+	0.0181664i
$169$	3.15950	+	5.47241i	0.243038	+	0.420954i
$170$	−6.02247	+	3.47707i	−0.461902	+	0.266679i
$171$	−1.07092	+	4.22530i	−0.0818956	+	0.323116i
$172$	6.02263	−	10.4315i	0.459221	−	0.795395i
$173$	−9.09894	+	15.7598i	−0.691779	+	1.19820i	0.279475	+	0.960153i	$0.409840\pi$
$173$	−9.09894	+	15.7598i	−0.691779	+	1.19820i	−0.971254	+	0.238044i	$0.923494\pi$
$174$	4.80785	+	8.32743i	0.364482	+	0.631301i
$175$	−4.08106	+	1.89385i	−0.308499	+	0.143162i
$176$	−0.129396	−	0.224121i	−0.00975362	−	0.0168938i
$177$	−11.0803			−0.832847
$178$	−9.56174	−	5.52047i	−0.716682	−	0.413777i
$179$	0.00614716	+	0.00354907i	0.000459461	+	0.000265270i	0.500230	−	0.865893i	$-0.333249\pi$
$179$	0.00614716	+	0.00354907i	0.000459461	+	0.000265270i	−0.499770	+	0.866158i	$0.666582\pi$
$180$			1.81645i			0.135391i
$181$	1.77687	−	3.07762i	0.132073	−	0.228758i	−0.792402	−	0.609999i	$-0.791170\pi$
$181$	1.77687	−	3.07762i	0.132073	−	0.228758i	0.924476	+	0.381241i	$0.124503\pi$
$182$	2.87868	+	6.20325i	0.213382	+	0.459815i
$183$			7.86246i			0.581209i
$184$			4.55594i			0.335868i
$185$	14.9997			1.10280
$186$	5.16135	−	2.97991i	0.378449	−	0.218497i
$187$	0.858029	+	0.495383i	0.0627453	+	0.0362260i
$188$	−5.84726	+	3.37592i	−0.426455	+	0.246214i
$189$	−0.235464	+	2.63525i	−0.0171274	+	0.191686i
$190$	7.61944	−	2.15286i	0.552772	−	0.156185i
$191$	2.72860	+	4.72607i	0.197434	+	0.341966i	0.947696	−	0.319175i	$-0.103406\pi$
$191$	2.72860	+	4.72607i	0.197434	+	0.341966i	−0.750262	+	0.661141i	$0.770072\pi$
$192$	1.00000			0.0721688
$193$			18.0133i			1.29662i	0.761375	+	0.648312i	$0.224525\pi$
$193$			18.0133i			1.29662i	−0.761375	+	0.648312i	$0.775475\pi$
$194$		−	5.40035i		−	0.387722i
$195$	−4.06608	+	2.34755i	−0.291178	+	0.168112i
$196$	−2.36981	−	6.58665i	−0.169272	−	0.470475i
$197$	9.02943			0.643320			0.321660	−	0.946855i	$-0.395759\pi$
$197$	9.02943			0.643320			0.321660	+	0.946855i	$0.395759\pi$
$198$	0.224121	−	0.129396i	0.0159276	−	0.00919580i
$199$	−7.02447	+	4.05558i	−0.497951	+	0.287492i	−0.727867	−	0.685718i	$-0.759488\pi$
$199$	−7.02447	+	4.05558i	−0.497951	+	0.287492i	0.229916	+	0.973211i	$0.426155\pi$
$200$	−1.47267	+	0.850246i	−0.104133	+	0.0601215i
$201$	−8.06288	+	4.65511i	−0.568712	+	0.328346i
$202$	1.04026			0.0731922
$203$	14.6307	−	20.8128i	1.02687	−	1.46077i
$204$	−3.31551	+	1.91421i	−0.232132	+	0.134021i
$205$		−	2.85245i		−	0.199224i
$206$		−	19.3228i		−	1.34629i
$207$	−4.55594			−0.316660
$208$	1.29238	+	2.23847i	0.0896106	+	0.155210i
$209$	−0.808404	−	0.786755i	−0.0559185	−	0.0544210i
$210$	4.35936	−	2.02300i	0.300824	−	0.139600i
$211$	−20.4933	+	11.8318i	−1.41082	+	0.814535i	−0.995465	−	0.0951262i	$-0.969675\pi$
$211$	−20.4933	+	11.8318i	−1.41082	+	0.814535i	−0.415351	+	0.909661i	$0.636341\pi$
$212$	0.403342	+	0.232869i	0.0277016	+	0.0159935i
$213$	3.54400	−	2.04613i	0.242831	−	0.140199i
$214$	15.7780			1.07856
$215$		−	21.8797i		−	1.49218i
$216$			1.00000i			0.0680414i
$217$	−12.8998	−	9.06812i	−0.875696	−	0.615584i
$218$	−8.24362	+	14.2784i	−0.558328	+	0.967053i
$219$			12.0707i			0.815661i
$220$	−0.407106	−	0.235043i	−0.0274471	−	0.0158466i
$221$	−8.56980	−	4.94778i	−0.576467	−	0.332824i
$222$	8.25768			0.554219
$223$	−4.96103	−	8.59275i	−0.332215	−	0.575413i	0.650731	−	0.759308i	$-0.274463\pi$
$223$	−4.96103	−	8.59275i	−0.332215	−	0.575413i	−0.982946	+	0.183895i	$0.941129\pi$
$224$	−1.11371	−	2.39993i	−0.0744128	−	0.160352i
$225$	−0.850246	−	1.47267i	−0.0566831	−	0.0981779i
$226$	−3.73358	+	6.46675i	−0.248354	+	0.430162i
$227$	−0.104603	+	0.181178i	−0.00694277	+	0.0120252i	−0.869476	−	0.493975i	$-0.835543\pi$
$227$	−0.104603	+	0.181178i	−0.00694277	+	0.0120252i	0.862533	+	0.506001i	$0.168877\pi$
$228$	4.19468	−	1.18520i	0.277799	−	0.0784918i
$229$	6.73515	−	3.88854i	0.445071	−	0.256962i	−0.260675	−	0.965427i	$-0.583945\pi$
$229$	6.73515	−	3.88854i	0.445071	−	0.256962i	0.705746	+	0.708465i	$0.250612\pi$
$230$	4.13783	+	7.16693i	0.272840	+	0.472573i
$231$	−0.560148	−	0.393765i	−0.0368550	−	0.0259078i
$232$	4.80785	−	8.32743i	0.315651	−	0.546723i
$233$	−8.53254	+	14.7788i	−0.558985	+	0.968191i	0.438596	+	0.898684i	$0.355476\pi$
$233$	−8.53254	+	14.7788i	−0.558985	+	0.968191i	−0.997581	+	0.0695069i	$0.977857\pi$
$234$	−2.23847	+	1.29238i	−0.146333	+	0.0844857i
$235$	−6.13220	+	10.6213i	−0.400021	+	0.692856i
$236$	5.54016	+	9.59583i	0.360634	+	0.624636i
$237$	11.4590	+	6.61587i	0.744344	+	0.429747i
$238$	8.28647	+	5.82510i	0.537132	+	0.377585i
$239$	−13.2143			−0.854764			−0.427382	−	0.904071i	$-0.640564\pi$
$239$	−13.2143			−0.854764			−0.427382	+	0.904071i	$0.640564\pi$
$240$	1.57310	−	0.908227i	0.101543	−	0.0586258i
$241$	4.11900	+	7.13432i	0.265328	+	0.459562i	0.967650	−	0.252298i	$-0.0811863\pi$
$241$	4.11900	+	7.13432i	0.265328	+	0.459562i	−0.702321	+	0.711860i	$0.747853\pi$
$242$		−	10.9330i		−	0.702802i
$243$	−1.00000			−0.0641500
$244$	6.80909	−	3.93123i	0.435907	−	0.251671i
$245$	−9.71012	−	8.20911i	−0.620357	−	0.524461i
$246$		−	1.57034i		−	0.100121i
$247$	8.07416	+	7.85793i	0.513747	+	0.499988i
$248$	−5.16135	−	2.97991i	−0.327746	−	0.189224i
$249$			10.1119i			0.640819i
$250$	−6.08557	+	10.5405i	−0.384885	+	0.666641i
$251$	−10.5332	−	6.08135i	−0.664850	−	0.383851i	0.129273	−	0.991609i	$-0.458736\pi$
$251$	−10.5332	−	6.08135i	−0.664850	−	0.383851i	−0.794122	+	0.607758i	$0.792069\pi$
$252$	2.39993	−	1.11371i	0.151181	−	0.0701571i
$253$	0.589522	−	1.02108i	0.0370629	−	0.0641949i
$254$	−1.38627	−	2.40109i	−0.0869823	−	0.150658i
$255$	−3.47707	+	6.02247i	−0.217743	+	0.377141i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	25.7830			1.60830			0.804149	−	0.594427i	$-0.202621\pi$
$257$	25.7830			1.60830			0.804149	+	0.594427i	$0.202621\pi$
$258$		−	12.0453i		−	0.749906i
$259$	−9.19665	−	19.8178i	−0.571452	−	1.23142i
$260$	4.06608	+	2.34755i	0.252168	+	0.145589i
$261$	8.32743	+	4.80785i	0.515455	+	0.297598i
$262$	−3.91714	−	6.78469i	−0.242002	−	0.419160i
$263$	−4.61871			−0.284802			−0.142401	−	0.989809i	$-0.545482\pi$
$263$	−4.61871			−0.284802			−0.142401	+	0.989809i	$0.545482\pi$
$264$	−0.224121	−	0.129396i	−0.0137937	−	0.00796380i
$265$	0.845994			0.0519690
$266$	−7.51604	−	8.74695i	−0.460838	−	0.536310i
$267$	−11.0409			−0.675695
$268$	8.06288	+	4.65511i	0.492519	+	0.284356i
$269$	−9.55342			−0.582482			−0.291241	−	0.956650i	$-0.594068\pi$
$269$	−9.55342			−0.582482			−0.291241	+	0.956650i	$0.594068\pi$
$270$	0.908227	+	1.57310i	0.0552730	+	0.0957356i
$271$	8.01046	+	4.62484i	0.486601	+	0.280939i	0.723163	−	0.690677i	$-0.242687\pi$
$271$	8.01046	+	4.62484i	0.486601	+	0.280939i	−0.236562	+	0.971616i	$0.576021\pi$
$272$	3.31551	+	1.91421i	0.201032	+	0.116066i
$273$	5.59463	+	3.93283i	0.338602	+	0.238026i
$274$		−	3.57838i		−	0.216178i
$275$	0.440075			0.0265375
$276$	2.27797	+	3.94556i	0.137118	+	0.237495i
$277$	−6.51868	+	11.2907i	−0.391669	+	0.678391i	−0.992670	−	0.120857i	$-0.961436\pi$
$277$	−6.51868	+	11.2907i	−0.391669	+	0.678391i	0.601001	+	0.799249i	$0.294769\pi$
$278$	−4.96967	−	8.60772i	−0.298061	−	0.516257i
$279$	2.97991	−	5.16135i	0.178402	−	0.309002i
$280$	−3.93165	−	2.76382i	−0.234961	−	0.165170i
$281$	−28.5544	−	16.4859i	−1.70341	−	0.983466i	−0.942254	−	0.334900i	$-0.891297\pi$
$281$	−28.5544	−	16.4859i	−1.70341	−	0.983466i	−0.761159	−	0.648566i	$-0.775369\pi$
$282$	−3.37592	+	5.84726i	−0.201033	+	0.348199i
$283$		−	18.7159i		−	1.11254i	−0.831000	−	0.556272i	$-0.812231\pi$
$283$		−	18.7159i		−	1.11254i	0.831000	−	0.556272i	$-0.187769\pi$
$284$	−3.54400	−	2.04613i	−0.210298	−	0.121416i
$285$	5.52220	−	5.67415i	0.327107	−	0.336108i
$286$		−	0.668919i		−	0.0395540i
$287$	−3.76870	+	1.74890i	−0.222459	+	0.103234i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	2.34323			0.137837
$290$		−	17.4665i		−	1.02567i
$291$	−2.70017	−	4.67684i	−0.158287	−	0.274161i
$292$	10.4535	−	6.03534i	0.611746	−	0.353192i
$293$	−1.03107			−0.0602356			−0.0301178	−	0.999546i	$-0.509588\pi$
$293$	−1.03107			−0.0602356			−0.0301178	+	0.999546i	$0.509588\pi$
$294$	−5.34564	−	4.51930i	−0.311764	−	0.263571i
$295$	17.4304	+	10.0634i	1.01484	+	0.585916i
$296$	−4.12884	−	7.15136i	−0.239984	−	0.415664i
$297$	0.129396	−	0.224121i	0.00750834	−	0.0130048i
$298$	17.8684	−	10.3164i	1.03509	−	0.597610i
$299$	−5.88801	+	10.1983i	−0.340513	+	0.589785i
$300$	−0.850246	+	1.47267i	−0.0490890	+	0.0850246i
$301$	−28.9078	+	13.4149i	−1.66622	+	0.773223i
$302$	0.125659	+	0.217648i	0.00723086	+	0.0125242i
$303$	0.900889	−	0.520129i	0.0517547	−	0.0298806i
$304$	−3.12375	−	3.04010i	−0.179159	−	0.174361i
$305$	7.14090	−	12.3684i	0.408887	−	0.708212i
$306$	−1.91421	+	3.31551i	−0.109428	+	0.189535i
$307$	−0.325950	−	0.564562i	−0.0186030	−	0.0322213i	0.856574	−	0.516024i	$-0.172589\pi$
$307$	−0.325950	−	0.564562i	−0.0186030	−	0.0322213i	−0.875177	+	0.483803i	$0.839255\pi$
$308$	−0.0609363	+	0.681985i	−0.00347217	+	0.0388597i
$309$	−9.66141	−	16.7341i	−0.549619	−	0.951967i
$310$	−10.8257			−0.614860
$311$	9.97341	+	5.75815i	0.565540	+	0.326515i	0.755366	−	0.655303i	$-0.227459\pi$
$311$	9.97341	+	5.75815i	0.565540	+	0.326515i	−0.189826	+	0.981818i	$0.560792\pi$
$312$	2.23847	+	1.29238i	0.126729	+	0.0731667i
$313$		−	2.02061i		−	0.114211i	−0.998368	−	0.0571057i	$-0.981813\pi$
$313$		−	2.02061i		−	0.114211i	0.998368	−	0.0571057i	$-0.0181872\pi$
$314$	10.4441	−	18.0897i	0.589395	−	1.02086i
$315$	2.76382	−	3.93165i	0.155723	−	0.221523i
$316$		−	13.2317i		−	0.744344i
$317$			21.2881i			1.19566i	0.801623	+	0.597830i	$0.203970\pi$
$317$			21.2881i			1.19566i	−0.801623	+	0.597830i	$0.796030\pi$
$318$	0.465739			0.0261173
$319$	−2.15508	+	1.24424i	−0.120661	+	0.0696639i
$320$	−1.57310	−	0.908227i	−0.0879387	−	0.0507715i
$321$	13.6641	−	7.88898i	0.762657	−	0.440320i
$322$	6.93206	−	9.86116i	0.386308	−	0.549541i
$323$	16.1762	+	4.09994i	0.900067	+	0.228127i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	−4.39537			−0.243811
$326$			11.4948i			0.636640i
$327$			16.4872i			0.911746i
$328$	−1.35995	+	0.785169i	−0.0750908	+	0.0433537i
$329$	17.7928	+	1.58981i	0.980948	+	0.0876491i
$330$	−0.470086			−0.0258774
$331$	−15.7802	+	9.11071i	−0.867359	+	0.500770i	−0.866470	−	0.499230i	$-0.833616\pi$
$331$	−15.7802	+	9.11071i	−0.867359	+	0.500770i	−0.000889270		1.00000i	$0.500283\pi$
$332$	8.75720	−	5.05597i	0.480614	−	0.277483i
$333$	7.15136	−	4.12884i	0.391892	−	0.226259i
$334$	−12.8085	+	7.39501i	−0.700852	+	0.404637i
$335$	16.9116			0.923979
$336$	−2.16446	−	1.52154i	−0.118081	−	0.0830070i
$337$	4.76439	−	2.75072i	0.259533	−	0.149841i	−0.364589	−	0.931169i	$-0.618790\pi$
$337$	4.76439	−	2.75072i	0.259533	−	0.149841i	0.624121	+	0.781327i	$0.285457\pi$
$338$		−	6.31899i		−	0.343708i
$339$			7.46716i			0.405560i
$340$	6.95415			0.377141
$341$	0.771179	+	1.33572i	0.0417617	+	0.0723333i
$342$	3.04010	−	3.12375i	0.164390	−	0.168913i
$343$	−4.89251	+	17.8623i	−0.264171	+	0.964476i
$344$	−10.4315	+	6.02263i	−0.562429	+	0.324719i
$345$	7.16693	+	4.13783i	0.385854	+	0.222773i
$346$	15.7598	−	9.09894i	0.847253	−	0.489162i
$347$	−9.31992			−0.500319			−0.250160	−	0.968205i	$-0.580483\pi$
$347$	−9.31992			−0.500319			−0.250160	+	0.968205i	$0.580483\pi$
$348$		−	9.61569i		−	0.515455i
$349$			25.0862i			1.34283i	0.741079	+	0.671417i	$0.234314\pi$
$349$			25.0862i			1.34283i	−0.741079	+	0.671417i	$0.765686\pi$
$350$	4.48123	+	0.400404i	0.239532	+	0.0214025i
$351$	−1.29238	+	2.23847i	−0.0689823	+	0.119481i
$352$			0.258793i			0.0137937i
$353$	−5.34607	−	3.08655i	−0.284543	−	0.164281i	0.350936	−	0.936400i	$-0.385864\pi$
$353$	−5.34607	−	3.08655i	−0.284543	−	0.164281i	−0.635478	+	0.772119i	$0.719197\pi$
$354$	9.59583	+	5.54016i	0.510013	+	0.294456i
$355$	−7.43341			−0.394525
$356$	5.52047	+	9.56174i	0.292584	+	0.506771i
$357$	10.0888	+	0.901452i	0.533958	+	0.0477099i
$358$	−0.00354907	−	0.00614716i	−0.000187574	−	0.000324888i
$359$	6.76009	−	11.7088i	0.356784	−	0.617968i	−0.630638	−	0.776077i	$-0.717207\pi$
$359$	6.76009	−	11.7088i	0.356784	−	0.617968i	0.987422	+	0.158110i	$0.0505400\pi$
$360$	0.908227	−	1.57310i	0.0478678	−	0.0829094i
$361$	−16.7062	−	9.04994i	−0.879276	−	0.476313i
$362$	−3.07762	+	1.77687i	−0.161756	+	0.0933900i
$363$	−5.46651	−	9.46828i	−0.286918	−	0.496956i
$364$	0.608618	−	6.81151i	0.0319002	−	0.357020i
$365$	10.9629	−	18.9883i	0.573826	−	0.993896i
$366$	3.93123	−	6.80909i	0.205489	−	0.355917i
$367$	3.77123	−	2.17732i	0.196857	−	0.113655i	−0.398332	−	0.917241i	$-0.630411\pi$
$367$	3.77123	−	2.17732i	0.196857	−	0.113655i	0.595188	+	0.803586i	$0.297077\pi$
$368$	2.27797	−	3.94556i	0.118747	−	0.205676i
$369$	−0.785169	−	1.35995i	−0.0408743	−	0.0707963i
$370$	−12.9901	−	7.49985i	−0.675324	−	0.389899i
$371$	−0.518698	−	1.11774i	−0.0269294	−	0.0580301i
$372$	−5.95982			−0.309002
$373$	3.15661	−	1.82247i	0.163443	−	0.0943640i	−0.416047	−	0.909343i	$-0.636585\pi$
$373$	3.15661	−	1.82247i	0.163443	−	0.0943640i	0.579491	+	0.814979i	$0.303252\pi$
$374$	−0.495383	−	0.858029i	−0.0256157	−	0.0443676i
$375$			12.1711i			0.628515i
$376$	6.75183			0.348199
$377$	21.5245	−	12.4272i	1.10857	−	0.640031i
$378$	1.52154	−	2.16446i	0.0782598	−	0.111328i
$379$		−	5.61048i		−	0.288191i	−0.989564	−	0.144095i	$-0.953973\pi$
$379$		−	5.61048i		−	0.288191i	0.989564	−	0.144095i	$-0.0460272\pi$
$380$	−7.67506	−	1.94528i	−0.393722	−	0.0997910i
$381$	−2.40109	−	1.38627i	−0.123012	−	0.0710207i
$382$		−	5.45719i		−	0.279214i
$383$	−1.79932	+	3.11651i	−0.0919408	+	0.159246i	−0.908328	−	0.418259i	$-0.862640\pi$
$383$	−1.79932	+	3.11651i	−0.0919408	+	0.159246i	0.816387	+	0.577505i	$0.195974\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	0.523538	+	1.12817i	0.0266820	+	0.0574969i
$386$	9.00664	−	15.6000i	0.458426	−	0.794017i
$387$	−6.02263	−	10.4315i	−0.306148	−	0.530263i
$388$	−2.70017	+	4.67684i	−0.137080	+	0.237430i
$389$	−7.35919	−	12.7465i	−0.373126	−	0.646272i	0.616919	−	0.787027i	$-0.288381\pi$
$389$	−7.35919	−	12.7465i	−0.373126	−	0.646272i	−0.990045	+	0.140754i	$0.955047\pi$
$390$	4.69511			0.237746
$391$			17.4420i			0.882081i
$392$	−1.24101	+	6.88911i	−0.0626806	+	0.347953i
$393$	−6.78469	−	3.91714i	−0.342242	−	0.197594i
$394$	−7.81971	−	4.51471i	−0.393951	−	0.227448i
$395$	−12.0174	−	20.8148i	−0.604663	−	1.04731i
$396$	−0.258793			−0.0130048
$397$	−1.85225	−	1.06940i	−0.0929620	−	0.0536716i	0.452798	−	0.891613i	$-0.350426\pi$
$397$	−1.85225	−	1.06940i	−0.0929620	−	0.0536716i	−0.545760	+	0.837941i	$0.683759\pi$
$398$	8.11116			0.406575
$399$	−10.8826	−	3.81706i	−0.544809	−	0.191092i
$400$	1.70049			0.0850246
$401$	−18.3409	−	10.5891i	−0.915901	−	0.528796i	−0.0335759	−	0.999436i	$-0.510690\pi$
$401$	−18.3409	−	10.5891i	−0.915901	−	0.528796i	−0.882325	+	0.470641i	$0.844023\pi$
$402$	9.31021			0.464351
$403$	−7.70236	−	13.3409i	−0.383682	−	0.664557i
$404$	−0.900889	−	0.520129i	−0.0448209	−	0.0258774i
$405$	1.57310	+	0.908227i	0.0781678	+	0.0451302i
$406$	−23.0770	+	10.7091i	−1.14529	+	0.531483i
$407$			2.13703i			0.105929i
$408$	3.82842			0.189535
$409$	8.27132	+	14.3263i	0.408990	+	0.708392i	0.994777	−	0.102073i	$-0.0325476\pi$
$409$	8.27132	+	14.3263i	0.408990	+	0.708392i	−0.585786	+	0.810465i	$0.699214\pi$
$410$	−1.42622	+	2.47029i	−0.0704362	+	0.121999i
$411$	−1.78919	−	3.09897i	−0.0882542	−	0.152861i
$412$	−9.66141	+	16.7341i	−0.475984	+	0.824428i
$413$	2.60901	−	29.1994i	0.128381	−	1.43681i
$414$	3.94556	+	2.27797i	0.193914	+	0.111956i
$415$	9.18395	−	15.9071i	0.450822	−	0.780847i
$416$		−	2.58476i		−	0.126729i
$417$	−8.60772	−	4.96967i	−0.421522	−	0.243366i
$418$	0.306721	+	1.08555i	0.0150022	+	0.0530961i
$419$			23.0313i			1.12515i	0.826746	+	0.562576i	$0.190189\pi$
$419$			23.0313i			1.12515i	−0.826746	+	0.562576i	$0.809811\pi$
$420$	−4.78682	−	0.427709i	−0.233573	−	0.0208701i
$421$	8.09796	−	4.67536i	0.394670	−	0.227863i	−0.289511	−	0.957175i	$-0.593493\pi$
$421$	8.09796	−	4.67536i	0.394670	−	0.227863i	0.684182	+	0.729311i	$0.260159\pi$
$422$	23.6636			1.15193
$423$			6.75183i			0.328285i
$424$	−0.232869	−	0.403342i	−0.0113091	−	0.0195880i
$425$	−5.63799	+	3.25510i	−0.273483	+	0.157895i
$426$	−4.09226			−0.198271
$427$	−20.7196	−	1.85132i	−1.00269	−	0.0895917i
$428$	−13.6641	−	7.88898i	−0.660480	−	0.381328i
$429$	−0.334459	−	0.579300i	−0.0161478	−	0.0279689i
$430$	−10.9398	+	18.9484i	−0.527566	+	0.913771i
$431$	−23.0043	+	13.2816i	−1.10808	+	0.639750i	−0.938331	−	0.345737i	$-0.887629\pi$
$431$	−23.0043	+	13.2816i	−1.10808	+	0.639750i	−0.169748	+	0.985487i	$0.554296\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−7.02797	+	12.1728i	−0.337743	+	0.584988i	−0.984008	−	0.178125i	$-0.942997\pi$
$433$	−7.02797	+	12.1728i	−0.337743	+	0.584988i	0.646265	+	0.763113i	$0.276330\pi$
$434$	6.63750	+	14.3031i	0.318610	+	0.686572i
$435$	−8.73324	−	15.1264i	−0.418727	−	0.725256i
$436$	14.2784	−	8.24362i	0.683810	−	0.394798i
$437$	4.87906	−	19.2502i	0.233397	−	0.920861i
$438$	6.03534	−	10.4535i	0.288380	−	0.499489i
$439$	8.41220	−	14.5704i	0.401492	−	0.695405i	−0.592414	−	0.805634i	$-0.701825\pi$
$439$	8.41220	−	14.5704i	0.401492	−	0.695405i	0.993906	+	0.110229i	$0.0351583\pi$
$440$	0.235043	+	0.407106i	0.0112052	+	0.0194080i
$441$	−6.88911	−	1.24101i	−0.328053	−	0.0590958i
$442$	4.94778	+	8.56980i	0.235342	+	0.407624i
$443$	23.7915			1.13037			0.565183	−	0.824965i	$-0.308805\pi$
$443$	23.7915			1.13037			0.565183	+	0.824965i	$0.308805\pi$
$444$	−7.15136	−	4.12884i	−0.339389	−	0.195946i
$445$	17.3685	+	10.0277i	0.823344	+	0.475358i
$446$			9.92205i			0.469823i
$447$	10.3164	−	17.8684i	0.487947	−	0.845149i
$448$	−0.235464	+	2.63525i	−0.0111246	+	0.124504i
$449$			19.9208i			0.940119i	0.882635	+	0.470060i	$0.155768\pi$
$449$			19.9208i			0.940119i	−0.882635	+	0.470060i	$0.844232\pi$
$450$			1.70049i			0.0801620i
$451$	0.406392			0.0191363
$452$	6.46675	−	3.73358i	0.304170	−	0.175613i
$453$	0.217648	+	0.125659i	0.0102260	+	0.00590397i
$454$	0.181178	−	0.104603i	0.00850312	−	0.00490928i
$455$	−5.22898	−	11.2679i	−0.245139	−	0.528248i
$456$	−4.22530	−	1.07092i	−0.197868	−	0.0501506i
$457$	−7.87468	−	13.6393i	−0.368362	−	0.638022i	0.620948	−	0.783852i	$-0.286748\pi$
$457$	−7.87468	−	13.6393i	−0.368362	−	0.638022i	−0.989310	+	0.145830i	$0.953415\pi$
$458$	−7.77708			−0.363399
$459$			3.82842i			0.178695i
$460$		−	8.27565i		−	0.385854i
$461$	4.10504	−	2.37005i	0.191191	−	0.110384i	−0.401349	−	0.915925i	$-0.631459\pi$
$461$	4.10504	−	2.37005i	0.191191	−	0.110384i	0.592540	+	0.805541i	$0.298125\pi$
$462$	0.288220	+	0.621084i	0.0134092	+	0.0288954i
$463$	−10.7795			−0.500967			−0.250484	−	0.968121i	$-0.580590\pi$
$463$	−10.7795			−0.500967			−0.250484	+	0.968121i	$0.580590\pi$
$464$	−8.32743	+	4.80785i	−0.386591	+	0.223199i
$465$	−9.37536	+	5.41287i	−0.434772	+	0.251016i
$466$	14.7788	−	8.53254i	0.684615	−	0.395262i
$467$	−1.01015	+	0.583209i	−0.0467440	+	0.0269877i	−0.523190	−	0.852216i	$-0.675258\pi$
$467$	−1.01015	+	0.583209i	−0.0467440	+	0.0269877i	0.476446	+	0.879204i	$0.341925\pi$
$468$	2.58476			0.119481
$469$	−10.3689	−	22.3438i	−0.478790	−	1.03174i
$470$	10.6213	−	6.13220i	0.489923	−	0.282857i
$471$		−	20.8882i		−	0.962477i
$472$		−	11.0803i		−	0.510013i
$473$	3.11723			0.143330
$474$	−6.61587	−	11.4590i	−0.303877	−	0.526331i
$475$	7.13301	−	2.01542i	0.327285	−	0.0924740i
$476$	−4.26374	−	9.18792i	−0.195428	−	0.421128i
$477$	0.403342	−	0.232869i	0.0184677	−	0.0106624i
$478$	11.4439	+	6.60716i	0.523434	+	0.302205i
$479$	19.2436	−	11.1103i	0.879263	−	0.507643i	0.00884794	−	0.999961i	$-0.497184\pi$
$479$	19.2436	−	11.1103i	0.879263	−	0.507643i	0.870415	+	0.492318i	$0.163850\pi$
$480$	−1.81645			−0.0829094
$481$		−	21.3442i		−	0.973210i
$482$		−	8.23801i		−	0.375231i
$483$	1.07276	−	12.0060i	0.0488121	−	0.546294i
$484$	−5.46651	+	9.46828i	−0.248478	+	0.430376i
$485$			9.80948i			0.445426i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	26.2526	+	15.1569i	1.18962	+	0.686826i	0.958220	−	0.286033i	$-0.0923367\pi$
$487$	26.2526	+	15.1569i	1.18962	+	0.686826i	0.231398	+	0.972859i	$0.425670\pi$
$488$	−7.86246			−0.355917
$489$	5.74741	+	9.95481i	0.259907	+	0.450172i
$490$	4.30465	+	11.9644i	0.194464	+	0.540495i
$491$	−0.269598	−	0.466957i	−0.0121668	−	0.0210735i	0.859878	−	0.510500i	$-0.170540\pi$
$491$	−0.269598	−	0.466957i	−0.0121668	−	0.0210735i	−0.872045	+	0.489426i	$0.837206\pi$
$492$	−0.785169	+	1.35995i	−0.0353981	+	0.0613114i
$493$	18.4064	−	31.8809i	0.828984	−	1.43584i
$494$	−3.06346	−	10.8422i	−0.137832	−	0.487816i
$495$	−0.407106	+	0.235043i	−0.0182981	+	0.0105644i
$496$	2.97991	+	5.16135i	0.133802	+	0.231752i
$497$	4.55759	+	9.82114i	0.204436	+	0.440538i
$498$	5.05597	−	8.75720i	0.226564	−	0.392420i
$499$	−4.08298	+	7.07193i	−0.182779	+	0.316583i	−0.942826	−	0.333286i	$-0.891843\pi$
$499$	−4.08298	+	7.07193i	−0.182779	+	0.316583i	0.760047	+	0.649868i	$0.225176\pi$
$500$	10.5405	−	6.08557i	0.471386	−	0.272155i
$501$	−7.39501	+	12.8085i	−0.330385	+	0.572243i
$502$	6.08135	+	10.5332i	0.271424	+	0.470120i
$503$	18.1386	+	10.4723i	0.808760	+	0.466938i	0.846525	−	0.532349i	$-0.178690\pi$
$503$	18.1386	+	10.4723i	0.808760	+	0.466938i	−0.0377649	+	0.999287i	$0.512024\pi$
$504$	−2.63525	−	0.235464i	−0.117383	−	0.0104884i
$505$	−1.88958			−0.0840852
$506$	−1.02108	+	0.589522i	−0.0453926	+	0.0262074i
$507$	−3.15950	−	5.47241i	−0.140318	−	0.243038i
$508$			2.77254i			0.123012i
$509$	12.9165			0.572513			0.286257	−	0.958153i	$-0.407589\pi$
$509$	12.9165			0.572513			0.286257	+	0.958153i	$0.407589\pi$
$510$	6.02247	−	3.47707i	0.266679	−	0.153967i
$511$	−31.8093	−	2.84221i	−1.40716	−	0.125732i
$512$			1.00000i			0.0441942i
$513$	1.07092	−	4.22530i	0.0472824	−	0.186551i
$514$	−22.3287	−	12.8915i	−0.984878	−	0.568620i
$515$			35.0990i			1.54665i
$516$	−6.02263	+	10.4315i	−0.265132	+	0.459221i
$517$	−1.51323	−	0.873663i	−0.0665517	−	0.0384237i
$518$	−1.94438	+	21.7611i	−0.0854312	+	0.956127i
$519$	9.09894	−	15.7598i	0.399399	−	0.691779i
$520$	−2.34755	−	4.06608i	−0.102947	−	0.178310i
$521$	−9.84547	+	17.0529i	−0.431338	+	0.747099i	−0.996989	−	0.0775455i	$-0.975292\pi$
$521$	−9.84547	+	17.0529i	−0.431338	+	0.747099i	0.565651	+	0.824645i	$0.308625\pi$
$522$	−4.80785	−	8.32743i	−0.210434	−	0.364482i
$523$	38.2740			1.67360			0.836802	−	0.547506i	$-0.184423\pi$
$523$	38.2740			1.67360			0.836802	+	0.547506i	$0.184423\pi$
$524$			7.83429i			0.342242i
$525$	4.08106	−	1.89385i	0.178112	−	0.0826545i
$526$	3.99992	+	2.30936i	0.174405	+	0.100693i
$527$	−19.7598	−	11.4083i	−0.860751	−	0.496955i
$528$	0.129396	+	0.224121i	0.00563126	+	0.00975362i
$529$	−2.24344			−0.0975408
$530$	−0.732652	−	0.422997i	−0.0318244	−	0.0183738i
$531$	11.0803			0.480845
$532$	2.13561	+	11.3331i	0.0925904	+	0.491352i
$533$	−4.05895			−0.175813
$534$	9.56174	+	5.52047i	0.413777	+	0.238894i
$535$	−28.6600			−1.23908
$536$	−4.65511	−	8.06288i	−0.201070	−	0.348263i
$537$	−0.00614716	−	0.00354907i	−0.000265270	−	0.000153154i
$538$	8.27350	+	4.77671i	0.356696	+	0.205939i
$539$	1.16956	−	1.38341i	0.0503767	−	0.0595879i
$540$		−	1.81645i		−	0.0781678i
$541$	26.3116			1.13122			0.565611	−	0.824672i	$-0.308640\pi$
$541$	26.3116			1.13122			0.565611	+	0.824672i	$0.308640\pi$
$542$	−4.62484	−	8.01046i	−0.198654	−	0.344079i
$543$	−1.77687	+	3.07762i	−0.0762526	+	0.132073i
$544$	−1.91421	−	3.31551i	−0.0820710	−	0.142151i
$545$	14.9742	−	25.9360i	0.641423	−	1.11098i
$546$	−2.87868	−	6.20325i	−0.123196	−	0.265474i
$547$	38.9542	+	22.4902i	1.66556	+	0.961612i	0.969987	+	0.243157i	$0.0781831\pi$
$547$	38.9542	+	22.4902i	1.66556	+	0.961612i	0.695574	+	0.718455i	$0.255150\pi$
$548$	−1.78919	+	3.09897i	−0.0764304	+	0.132381i
$549$		−	7.86246i		−	0.335561i
$550$	−0.381116	−	0.220038i	−0.0162509	−	0.00938243i
$551$	−29.2326	+	30.0370i	−1.24535	+	1.27962i
$552$		−	4.55594i		−	0.193914i
$553$	−20.1327	+	28.6396i	−0.856129	+	1.21788i
$554$	11.2907	−	6.51868i	0.479695	−	0.276952i
$555$	−14.9997			−0.636702
$556$			9.93934i			0.421522i
$557$	−15.5502	−	26.9337i	−0.658881	−	1.14122i	−0.980906	−	0.194484i	$-0.937697\pi$
$557$	−15.5502	−	26.9337i	−0.658881	−	1.14122i	0.322024	−	0.946731i	$-0.395637\pi$
$558$	−5.16135	+	2.97991i	−0.218497	+	0.126150i
$559$	−31.1342			−1.31684
$560$	2.02300	+	4.35936i	0.0854874	+	0.184217i
$561$	−0.858029	−	0.495383i	−0.0362260	−	0.0209151i
$562$	16.4859	+	28.5544i	0.695415	+	1.20449i
$563$	−9.91023	+	17.1650i	−0.417666	+	0.723419i	−0.995704	−	0.0925905i	$-0.970485\pi$
$563$	−9.91023	+	17.1650i	−0.417666	+	0.723419i	0.578038	+	0.816010i	$0.303819\pi$
$564$	5.84726	−	3.37592i	0.246214	−	0.142152i
$565$	6.78188	−	11.7466i	0.285316	−	0.494181i
$566$	−9.35795	+	16.2084i	−0.393344	+	0.681292i
$567$	0.235464	−	2.63525i	0.00988854	−	0.110670i
$568$	2.04613	+	3.54400i	0.0858538	+	0.148703i
$569$	−10.6072	+	6.12407i	−0.444677	+	0.256734i	−0.705580	−	0.708631i	$-0.749313\pi$
$569$	−10.6072	+	6.12407i	−0.444677	+	0.256734i	0.260902	+	0.965365i	$0.415980\pi$
$570$	−7.61944	+	2.15286i	−0.319143	+	0.0901735i
$571$	−0.635560	+	1.10082i	−0.0265973	+	0.0460679i	−0.879018	−	0.476789i	$-0.841801\pi$
$571$	−0.635560	+	1.10082i	−0.0265973	+	0.0460679i	0.852420	+	0.522857i	$0.175134\pi$
$572$	−0.334459	+	0.579300i	−0.0139844	+	0.0242218i
$573$	−2.72860	−	4.72607i	−0.113989	−	0.197434i
$574$	4.13824	+	0.369757i	0.172727	+	0.0154334i
$575$	3.87367	+	6.70939i	0.161543	+	0.279801i
$576$	−1.00000			−0.0416667
$577$	21.3369	+	12.3188i	0.888265	+	0.512840i	0.873375	−	0.487049i	$-0.161927\pi$
$577$	21.3369	+	12.3188i	0.888265	+	0.512840i	0.0148907	+	0.999889i	$0.495260\pi$
$578$	−2.02930	−	1.17161i	−0.0844076	−	0.0487328i
$579$		−	18.0133i		−	0.748606i
$580$	−8.73324	+	15.1264i	−0.362628	+	0.628090i
$581$	−26.6475	−	2.38099i	−1.10553	−	0.0987803i
$582$			5.40035i			0.223852i
$583$			0.120530i			0.00499184i
$584$	−12.0707			−0.499489
$585$	4.06608	−	2.34755i	0.168112	−	0.0970594i
$586$	0.892930	+	0.515534i	0.0368866	+	0.0212965i
$587$	31.2730	−	18.0555i	1.29077	−	0.745229i	0.311983	−	0.950088i	$-0.399007\pi$
$587$	31.2730	−	18.0555i	1.29077	−	0.745229i	0.978791	+	0.204859i	$0.0656736\pi$
$588$	2.36981	+	6.58665i	0.0977293	+	0.271629i
$589$	18.6170	+	18.1184i	0.767099	+	0.746556i
$590$	−10.0634	−	17.4304i	−0.414305	−	0.717598i
$591$	−9.02943			−0.371421
$592$			8.25768i			0.339389i
$593$		−	29.0873i		−	1.19447i	−0.802066	−	0.597235i	$-0.796266\pi$
$593$		−	29.0873i		−	1.19447i	0.802066	−	0.597235i	$-0.203734\pi$
$594$	−0.224121	+	0.129396i	−0.00919580	+	0.00530920i
$595$	−15.0520	−	10.5810i	−0.617072	−	0.433780i
$596$	−20.6327			−0.845149
$597$	7.02447	−	4.05558i	0.287492	−	0.165984i
$598$	10.1983	−	5.88801i	0.417041	−	0.240779i
$599$	30.4259	−	17.5664i	1.24317	−	0.717745i	0.273432	−	0.961891i	$-0.411841\pi$
$599$	30.4259	−	17.5664i	1.24317	−	0.717745i	0.969738	+	0.244147i	$0.0785078\pi$
$600$	1.47267	−	0.850246i	0.0601215	−	0.0347111i
$601$	25.2214			1.02880			0.514401	−	0.857549i	$-0.328014\pi$
$601$	25.2214			1.02880			0.514401	+	0.857549i	$0.328014\pi$
$602$	31.7423	+	2.83622i	1.29372	+	0.115596i
$603$	8.06288	−	4.65511i	0.328346	−	0.189571i
$604$		−	0.251318i		−	0.0102260i
$605$			19.8593i			0.807397i
$606$	−1.04026			−0.0422576
$607$	−3.91573	−	6.78225i	−0.158935	−	0.275283i	0.775550	−	0.631286i	$-0.217473\pi$
$607$	−3.91573	−	6.78225i	−0.158935	−	0.275283i	−0.934485	+	0.356003i	$0.884139\pi$
$608$	1.18520	+	4.19468i	0.0480662	+	0.170117i
$609$	−14.6307	+	20.8128i	−0.592866	+	0.843378i
$610$	−12.3684	+	7.14090i	−0.500782	+	0.289127i
$611$	15.1138	+	8.72595i	0.611438	+	0.353014i
$612$	3.31551	−	1.91421i	0.134021	−	0.0773773i
$613$	−1.11246			−0.0449318			−0.0224659	−	0.999748i	$-0.507152\pi$
$613$	−1.11246			−0.0449318			−0.0224659	+	0.999748i	$0.507152\pi$
$614$			0.651900i			0.0263086i
$615$			2.85245i			0.115022i
$616$	0.393765	−	0.560148i	0.0158652	−	0.0225690i
$617$	−15.7564	+	27.2909i	−0.634328	+	1.09869i	0.352329	+	0.935876i	$0.385390\pi$
$617$	−15.7564	+	27.2909i	−0.634328	+	1.09869i	−0.986657	+	0.162813i	$0.947943\pi$
$618$			19.3228i			0.777278i
$619$	27.0634	+	15.6251i	1.08777	+	0.628025i	0.932982	−	0.359923i	$-0.117197\pi$
$619$	27.0634	+	15.6251i	1.08777	+	0.628025i	0.154788	+	0.987948i	$0.450530\pi$
$620$	9.37536	+	5.41287i	0.376524	+	0.217386i
$621$	4.55594			0.182823
$622$	−5.75815	−	9.97341i	−0.230881	−	0.399897i
$623$	2.59974	−	29.0957i	0.104156	−	1.16569i
$624$	−1.29238	−	2.23847i	−0.0517367	−	0.0896106i
$625$	6.80293	−	11.7830i	0.272117	−	0.471321i
$626$	−1.01030	+	1.74990i	−0.0403798	+	0.0699399i
$627$	0.808404	+	0.786755i	0.0322846	+	0.0314200i
$628$	−18.0897	+	10.4441i	−0.721858	+	0.416765i
$629$	−15.8069	−	27.3784i	−0.630263	−	1.09165i
$630$	−4.35936	+	2.02300i	−0.173681	+	0.0805983i
$631$	−4.57992	+	7.93265i	−0.182324	+	0.315794i	−0.942671	−	0.333722i	$-0.891695\pi$
$631$	−4.57992	+	7.93265i	−0.182324	+	0.315794i	0.760348	+	0.649516i	$0.225029\pi$
$632$	−6.61587	+	11.4590i	−0.263165	+	0.455816i
$633$	20.4933	−	11.8318i	0.814535	−	0.470272i
$634$	10.6441	−	18.4360i	0.422730	−	0.732189i
$635$	2.51810	+	4.36147i	0.0999276	+	0.173080i
$636$	−0.403342	−	0.232869i	−0.0159935	−	0.00923387i
$637$	−11.6813	+	13.8172i	−0.462831	+	0.547458i
$638$	2.48847			0.0985196
$639$	−3.54400	+	2.04613i	−0.140199	+	0.0809437i
$640$	0.908227	+	1.57310i	0.0359008	+	0.0621821i
$641$			29.5040i			1.16534i	0.812710	+	0.582669i	$0.197992\pi$
$641$			29.5040i			1.16534i	−0.812710	+	0.582669i	$0.802008\pi$
$642$	−15.7780			−0.622707
$643$	−40.0230	+	23.1073i	−1.57835	+	0.911262i	−0.583262	+	0.812284i	$0.698224\pi$
$643$	−40.0230	+	23.1073i	−1.57835	+	0.911262i	−0.995090	+	0.0989776i	$0.968443\pi$
$644$	−10.9339	+	5.07399i	−0.430857	+	0.199943i
$645$			21.8797i			0.861512i
$646$	−11.9590	−	11.6387i	−0.470521	−	0.457920i
$647$	10.6338	+	6.13942i	0.418057	+	0.241365i	0.694246	−	0.719738i	$-0.255738\pi$
$647$	10.6338	+	6.13942i	0.418057	+	0.241365i	−0.276189	+	0.961103i	$0.589071\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−1.43375	+	2.48333i	−0.0562797	+	0.0974794i
$650$	3.80650	+	2.19769i	0.149303	+	0.0862003i
$651$	12.8998	+	9.06812i	0.505583	+	0.355408i
$652$	5.74741	−	9.95481i	0.225086	−	0.389861i
$653$	−1.45372	−	2.51791i	−0.0568883	−	0.0985334i	0.836179	−	0.548457i	$-0.184785\pi$
$653$	−1.45372	−	2.51791i	−0.0568883	−	0.0985334i	−0.893067	+	0.449924i	$0.851451\pi$
$654$	8.24362	−	14.2784i	0.322351	−	0.558328i
$655$	7.11531	+	12.3241i	0.278018	+	0.481542i
$656$	1.57034			0.0613114
$657$		−	12.0707i		−	0.470922i
$658$	−14.6141	−	10.2732i	−0.569717	−	0.400491i
$659$	36.0840	+	20.8331i	1.40563	+	0.811544i	0.994963	−	0.100240i	$-0.0319610\pi$
$659$	36.0840	+	20.8331i	1.40563	+	0.811544i	0.410671	+	0.911783i	$0.365294\pi$
$660$	0.407106	+	0.235043i	0.0158466	+	0.00914903i
$661$	9.46858	+	16.4001i	0.368285	+	0.637889i	0.989298	−	0.145912i	$-0.0466117\pi$
$661$	9.46858	+	16.4001i	0.368285	+	0.637889i	−0.621012	+	0.783801i	$0.713278\pi$
$662$	18.2214			0.708196
$663$	8.56980	+	4.94778i	0.332824	+	0.192156i
$664$	−10.1119			−0.392420
$665$	13.6526	+	15.8884i	0.529423	+	0.616127i
$666$	−8.25768			−0.319979
$667$	−37.9393	−	21.9042i	−1.46901	−	0.848136i
$668$	14.7900			0.572243
$669$	4.96103	+	8.59275i	0.191804	+	0.332215i
$670$	−14.6459	−	8.45579i	−0.565819	−	0.326676i
$671$	1.76214	+	1.01737i	0.0680268	+	0.0392753i
$672$	1.11371	+	2.39993i	0.0429623	+	0.0925792i
$673$			39.8132i			1.53469i	0.641236	+	0.767344i	$0.278422\pi$
$673$			39.8132i			1.53469i	−0.641236	+	0.767344i	$0.721578\pi$
$674$	−5.50144			−0.211908
$675$	0.850246	+	1.47267i	0.0327260	+	0.0566831i
$676$	−3.15950	+	5.47241i	−0.121519	+	0.210477i
$677$	−14.2450	−	24.6730i	−0.547479	−	0.948261i	−0.998446	−	0.0557208i	$-0.982254\pi$
$677$	−14.2450	−	24.6730i	−0.547479	−	0.948261i	0.450968	−	0.892540i	$-0.351079\pi$
$678$	3.73358	−	6.46675i	0.143387	−	0.248354i
$679$	12.9604	−	6.01441i	0.497376	−	0.230812i
$680$	−6.02247	−	3.47707i	−0.230951	−	0.133340i
$681$	0.104603	−	0.181178i	0.00400841	−	0.00694277i
$682$		−	1.54236i		−	0.0590599i
$683$	−24.3206	−	14.0415i	−0.930601	−	0.537283i	−0.0435993	−	0.999049i	$-0.513882\pi$
$683$	−24.3206	−	14.0415i	−0.930601	−	0.537283i	−0.887002	+	0.461766i	$0.847216\pi$
$684$	−4.19468	+	1.18520i	−0.160387	+	0.0453173i
$685$			6.49996i			0.248351i
$686$	13.1682	−	13.0230i	0.502765	−	0.497220i
$687$	−6.73515	+	3.88854i	−0.256962	+	0.148357i
$688$	12.0453			0.459221
$689$		−	1.20383i		−	0.0458621i
$690$	−4.13783	−	7.16693i	−0.157524	−	0.272840i
$691$	−38.5171	+	22.2378i	−1.46526	+	0.845967i	−0.999247	−	0.0388119i	$-0.987643\pi$
$691$	−38.5171	+	22.2378i	−1.46526	+	0.845967i	−0.466011	+	0.884779i	$0.654309\pi$
$692$	−18.1979			−0.691779
$693$	0.560148	+	0.393765i	0.0212783	+	0.0149579i
$694$	8.07129	+	4.65996i	0.306382	+	0.176890i
$695$	9.02718	+	15.6355i	0.342421	+	0.593090i
$696$	−4.80785	+	8.32743i	−0.182241	+	0.315651i
$697$	−5.20646	+	3.00595i	−0.197209	+	0.113859i
$698$	12.5431	−	21.7253i	0.474764	−	0.822315i
$699$	8.53254	−	14.7788i	0.322730	−	0.558985i
$700$	−3.68065	−	2.58737i	−0.139116	−	0.0977935i
$701$	−22.0211	−	38.1416i	−0.831724	−	1.44059i	−0.896670	−	0.442699i	$-0.854021\pi$
$701$	−22.0211	−	38.1416i	−0.831724	−	1.44059i	0.0649468	−	0.997889i	$-0.479312\pi$
$702$	2.23847	−	1.29238i	0.0844857	−	0.0487778i
$703$	9.78701	+	34.6383i	0.369124	+	1.30641i
$704$	0.129396	−	0.224121i	0.00487681	−	0.00844688i
$705$	6.13220	−	10.6213i	0.230952	−	0.400021i
$706$	3.08655	+	5.34607i	0.116164	+	0.201202i
$707$	1.15854	+	2.49654i	0.0435715	+	0.0938921i
$708$	−5.54016	−	9.59583i	−0.208212	−	0.360634i
$709$	18.4353			0.692351			0.346176	−	0.938170i	$-0.387480\pi$
$709$	18.4353			0.692351			0.346176	+	0.938170i	$0.387480\pi$
$710$	6.43752	+	3.71671i	0.241596	+	0.139486i
$711$	−11.4590	−	6.61587i	−0.429747	−	0.248115i
$712$		−	11.0409i		−	0.413777i
$713$	−13.5763	+	23.5148i	−0.508435	+	0.880636i
$714$	−8.28647	−	5.82510i	−0.310113	−	0.217999i
$715$			1.21506i			0.0454407i
$716$			0.00709813i			0.000265270i
$717$	13.2143			0.493498
$718$	−11.7088	+	6.76009i	−0.436969	+	0.252284i
$719$	45.4077	+	26.2161i	1.69342	+	0.977697i	0.951721	+	0.306965i	$0.0993135\pi$
$719$	45.4077	+	26.2161i	1.69342	+	0.977697i	0.741700	+	0.670732i	$0.234020\pi$
$720$	−1.57310	+	0.908227i	−0.0586258	+	0.0338476i
$721$	46.3734	−	21.5200i	1.72704	−	0.801447i
$722$	9.94306	+	16.1906i	0.370042	+	0.602552i
$723$	−4.11900	−	7.13432i	−0.153187	−	0.265328i
$724$	3.55373			0.132073
$725$		−	16.3514i		−	0.607276i
$726$			10.9330i			0.405763i
$727$	−37.1957	+	21.4750i	−1.37951	+	0.796463i	−0.992101	−	0.125444i	$-0.959965\pi$
$727$	−37.1957	+	21.4750i	−1.37951	+	0.796463i	−0.387413	+	0.921906i	$0.626631\pi$
$728$	−3.93283	+	5.59463i	−0.145760	+	0.207351i
$729$	1.00000			0.0370370
$730$	−18.9883	+	10.9629i	−0.702790	+	0.405756i
$731$	−39.9361	+	23.0571i	−1.47709	+	0.852799i
$732$	−6.80909	+	3.93123i	−0.251671	+	0.145302i
$733$	11.3847	−	6.57297i	0.420504	−	0.242778i	−0.274789	−	0.961505i	$-0.588608\pi$
$733$	11.3847	−	6.57297i	0.420504	−	0.242778i	0.695293	+	0.718726i	$0.255275\pi$
$734$	−4.35464			−0.160733
$735$	9.71012	+	8.20911i	0.358163	+	0.302798i
$736$	−3.94556	+	2.27797i	−0.145435	+	0.0839670i
$737$			2.40942i			0.0887520i
$738$			1.57034i			0.0578049i
$739$	4.78357			0.175967			0.0879833	−	0.996122i	$-0.471958\pi$
$739$	4.78357			0.175967			0.0879833	+	0.996122i	$0.471958\pi$
$740$	7.49985	+	12.9901i	0.275700	+	0.477526i
$741$	−8.07416	−	7.85793i	−0.296612	−	0.288668i
$742$	−0.109664	+	1.22734i	−0.00402591	+	0.0450571i
$743$	−12.8507	+	7.41938i	−0.471448	+	0.272191i	−0.716846	−	0.697232i	$-0.754415\pi$
$743$	−12.8507	+	7.41938i	−0.471448	+	0.272191i	0.245398	+	0.969423i	$0.421082\pi$
$744$	5.16135	+	2.97991i	0.189224	+	0.109249i
$745$	−32.4572	+	18.7392i	−1.18914	+	0.686551i
$746$	−3.64494			−0.133451
$747$		−	10.1119i		−	0.369977i
$748$			0.990767i			0.0362260i
$749$	17.5721	+	37.8660i	0.642069	+	1.38359i
$750$	6.08557	−	10.5405i	0.222214	−	0.384885i
$751$		−	4.38976i		−	0.160185i	−0.996787	−	0.0800923i	$-0.974479\pi$
$751$		−	4.38976i		−	0.160185i	0.996787	−	0.0800923i	$-0.0255215\pi$
$752$	−5.84726	−	3.37592i	−0.213228	−	0.123107i
$753$	10.5332	+	6.08135i	0.383851	+	0.221617i
$754$	−24.8543			−0.905140
$755$	−0.228254	−	0.395347i	−0.00830700	−	0.0143882i
$756$	−2.39993	+	1.11371i	−0.0872845	+	0.0405052i
$757$	−18.8072	−	32.5750i	−0.683559	−	1.18396i	−0.973887	−	0.227031i	$-0.927098\pi$
$757$	−18.8072	−	32.5750i	−0.683559	−	1.18396i	0.290329	−	0.956927i	$-0.406235\pi$
$758$	−2.80524	+	4.85881i	−0.101891	+	0.176480i
$759$	−0.589522	+	1.02108i	−0.0213983	+	0.0370629i
$760$	5.67415	+	5.52220i	0.205823	+	0.200311i
$761$	−30.3477	+	17.5212i	−1.10010	+	0.635145i	−0.936248	−	0.351340i	$-0.885726\pi$
$761$	−30.3477	+	17.5212i	−1.10010	+	0.635145i	−0.163855	+	0.986484i	$0.552393\pi$
$762$	1.38627	+	2.40109i	0.0502192	+	0.0869823i
$763$	−43.4480	−	3.88214i	−1.57292	−	0.140543i
$764$	−2.72860	+	4.72607i	−0.0987171	+	0.170983i
$765$	3.47707	−	6.02247i	0.125714	−	0.217743i
$766$	3.11651	−	1.79932i	0.112604	−	0.0650119i
$767$	14.3200	−	24.8030i	0.517065	−	0.895583i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	25.0843	+	14.4825i	0.904565	+	0.522251i	0.878678	−	0.477414i	$-0.158426\pi$
$769$	25.0843	+	14.4825i	0.904565	+	0.522251i	0.0258863	+	0.999665i	$0.491759\pi$
$770$	0.110688	−	1.23879i	0.00398892	−	0.0446430i
$771$	−25.7830			−0.928552
$772$	−15.6000	+	9.00664i	−0.561455	+	0.324156i
$773$	−4.25159	−	7.36398i	−0.152919	−	0.264864i	0.779380	−	0.626551i	$-0.215534\pi$
$773$	−4.25159	−	7.36398i	−0.152919	−	0.264864i	−0.932299	+	0.361687i	$0.882201\pi$
$774$			12.0453i			0.432958i
$775$	−10.1346			−0.364046
$776$	4.67684	−	2.70017i	0.167889	−	0.0969306i
$777$	9.19665	+	19.8178i	0.329928	+	0.710961i
$778$			14.7184i			0.527679i
$779$	6.58706	−	1.86116i	0.236006	−	0.0666831i
$780$	−4.06608	−	2.34755i	−0.145589	−	0.0840559i
$781$		−	1.05905i		−	0.0378957i
$782$	8.72101	−	15.1052i	0.311863	−	0.540162i
$783$	−8.32743	−	4.80785i	−0.297598	−	0.171818i
$784$	4.51930	−	5.34564i	0.161404	−	0.190916i
$785$	−18.9712	+	32.8591i	−0.677112	+	1.17279i
$786$	3.91714	+	6.78469i	0.139720	+	0.242002i
$787$	11.9726	−	20.7372i	0.426779	−	0.739202i	−0.569806	−	0.821779i	$-0.692982\pi$
$787$	11.9726	−	20.7372i	0.426779	−	0.739202i	0.996585	+	0.0825769i	$0.0263150\pi$
$788$	4.51471	+	7.81971i	0.160830	+	0.278566i
$789$	4.61871			0.164430
$790$			24.0349i			0.855122i
$791$	−19.6778	−	1.75824i	−0.699664	−	0.0625159i
$792$	0.224121	+	0.129396i	0.00796380	+	0.00459790i
$793$	−17.5999	−	10.1613i	−0.624990	−	0.360838i
$794$	1.06940	+	1.85225i	0.0379516	+	0.0657341i
$795$	−0.845994			−0.0300043
$796$	−7.02447	−	4.05558i	−0.248976	−	0.143746i
$797$	−21.5848			−0.764575			−0.382287	−	0.924044i	$-0.624864\pi$
$797$	−21.5848			−0.764575			−0.382287	+	0.924044i	$0.624864\pi$
$798$	7.51604	+	8.74695i	0.266065	+	0.309639i
$799$	25.8488			0.914466
$800$	−1.47267	−	0.850246i	−0.0520667	−	0.0300607i
$801$	11.0409			0.390112
$802$	10.5891	+	18.3409i	0.373915	+	0.647640i
$803$	2.70530	+	1.56190i	0.0954678	+	0.0551184i
$804$	−8.06288	−	4.65511i	−0.284356	−	0.164173i
$805$	−12.5918	+	17.9124i	−0.443802	+	0.631328i
$806$			15.4047i			0.542608i
$807$	9.55342			0.336296
$808$	0.520129	+	0.900889i	0.0182981	+	0.0316932i
$809$	19.3918	−	33.5875i	0.681778	−	1.18087i	−0.292660	−	0.956217i	$-0.594540\pi$
$809$	19.3918	−	33.5875i	0.681778	−	1.18087i	0.974438	−	0.224658i	$-0.0721263\pi$
$810$	−0.908227	−	1.57310i	−0.0319119	−	0.0552730i
$811$	7.84242	−	13.5835i	0.275385	−	0.476980i	−0.694847	−	0.719157i	$-0.744528\pi$
$811$	7.84242	−	13.5835i	0.275385	−	0.476980i	0.970232	+	0.242177i	$0.0778614\pi$
$812$	25.3398	+	2.26414i	0.889252	+	0.0794559i
$813$	−8.01046	−	4.62484i	−0.280939	−	0.162200i
$814$	1.06851	−	1.85072i	0.0374514	−	0.0648677i
$815$		−	20.8798i		−	0.731389i
$816$	−3.31551	−	1.91421i	−0.116066	−	0.0670107i
$817$	50.5260	−	14.2761i	1.76768	−	0.499456i
$818$		−	16.5426i		−	0.578400i
$819$	−5.59463	−	3.93283i	−0.195492	−	0.137424i
$820$	2.47029	−	1.42622i	0.0862663	−	0.0498059i
$821$	15.7755			0.550569			0.275285	−	0.961363i	$-0.411228\pi$
$821$	15.7755			0.550569			0.275285	+	0.961363i	$0.411228\pi$
$822$			3.57838i			0.124810i
$823$	0.0366184	+	0.0634249i	0.00127644	+	0.00221085i	0.866663	−	0.498894i	$-0.166260\pi$
$823$	0.0366184	+	0.0634249i	0.00127644	+	0.00221085i	−0.865386	+	0.501105i	$0.832927\pi$
$824$	16.7341	−	9.66141i	0.582959	−	0.336571i
$825$	−0.440075			−0.0153214
$826$	−16.8592	+	23.9829i	−0.586606	+	0.834473i
$827$	37.9959	+	21.9369i	1.32125	+	0.762822i	0.983927	−	0.178569i	$-0.0571467\pi$
$827$	37.9959	+	21.9369i	1.32125	+	0.762822i	0.337319	+	0.941391i	$0.390480\pi$
$828$	−2.27797	−	3.94556i	−0.0791649	−	0.137118i
$829$	0.855806	−	1.48230i	0.0297234	−	0.0514824i	−0.850781	−	0.525520i	$-0.823871\pi$
$829$	0.855806	−	1.48230i	0.0297234	−	0.0514824i	0.880504	+	0.474038i	$0.157204\pi$
$830$	−15.9071	+	9.18395i	−0.552142	+	0.318780i
$831$	6.51868	−	11.2907i	0.226130	−	0.391669i
$832$	−1.29238	+	2.23847i	−0.0448053	+	0.0776050i
$833$	−4.75111	+	26.3744i	−0.164616	+	0.913819i
$834$	4.96967	+	8.60772i	0.172086	+	0.298061i
$835$	23.2661	−	13.4327i	0.805158	−	0.464858i
$836$	0.277147	−	1.09348i	0.00958534	−	0.0378187i
$837$	−2.97991	+	5.16135i	−0.103001	+	0.178402i
$838$	11.5156	−	19.9457i	0.397801	−	0.689012i
$839$	15.3899	+	26.6561i	0.531319	+	0.920272i	0.999332	+	0.0365499i	$0.0116368\pi$
$839$	15.3899	+	26.6561i	0.531319	+	0.920272i	−0.468013	+	0.883722i	$0.655030\pi$
$840$	3.93165	+	2.76382i	0.135655	+	0.0953607i
$841$	31.7308	+	54.9593i	1.09416	+	1.89515i
$842$	−9.35072			−0.322247
$843$	28.5544	+	16.4859i	0.983466	+	0.567804i
$844$	−20.4933	−	11.8318i	−0.705408	−	0.407268i
$845$			11.4782i			0.394861i
$846$	3.37592	−	5.84726i	0.116066	−	0.201033i
$847$	26.2385	−	12.1762i	0.901565	−	0.418380i
$848$			0.465739i			0.0159935i
$849$			18.7159i			0.642328i
$850$	6.51019			0.223298
$851$	−32.5811	+	18.8107i	−1.11687	+	0.644824i
$852$	3.54400	+	2.04613i	0.121416	+	0.0700993i
$853$	29.5390	−	17.0543i	1.01139	−	0.583929i	0.0997951	−	0.995008i	$-0.468181\pi$
$853$	29.5390	−	17.0543i	1.01139	−	0.583929i	0.911600	+	0.411079i	$0.134848\pi$
$854$	17.0180	+	11.9631i	0.582344	+	0.409368i
$855$	−5.52220	+	5.67415i	−0.188855	+	0.194052i
$856$	7.88898	+	13.6641i	0.269640	+	0.467030i
$857$	−44.1985			−1.50979			−0.754896	−	0.655845i	$-0.772313\pi$
$857$	−44.1985			−1.50979			−0.754896	+	0.655845i	$0.772313\pi$
$858$			0.668919i			0.0228365i
$859$		−	31.5900i		−	1.07784i	−0.842358	−	0.538919i	$-0.818833\pi$
$859$		−	31.5900i		−	1.07784i	0.842358	−	0.538919i	$-0.181167\pi$
$860$	18.9484	−	10.9398i	0.646134	−	0.373045i
$861$	3.76870	−	1.74890i	0.128437	−	0.0596023i
$862$	26.5631			0.904743
$863$	21.1750	−	12.2254i	0.720805	−	0.416157i	−0.0942442	−	0.995549i	$-0.530043\pi$
$863$	21.1750	−	12.2254i	0.720805	−	0.416157i	0.815049	+	0.579392i	$0.196710\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$	−28.6270	+	16.5278i	−0.973347	+	0.561962i
$866$	12.1728	−	7.02797i	0.413649	−	0.238820i
$867$	−2.34323			−0.0795803
$868$	1.40332	−	15.7056i	0.0476318	−	0.533084i
$869$	2.96551	−	1.71214i	0.100598	−	0.0580804i
$870$			17.4665i			0.592169i
$871$		−	24.0647i		−	0.815402i
$872$	−16.4872			−0.558328
$873$	2.70017	+	4.67684i	0.0913870	+	0.158287i
$874$	−13.8505	+	14.2316i	−0.468500	+	0.481392i
$875$	−32.0740	−	2.86586i	−1.08430	−	0.0968837i
$876$	−10.4535	+	6.03534i	−0.353192	+	0.203915i
$877$	−39.3605	−	22.7248i	−1.32911	−	0.767362i	−0.343948	−	0.938989i	$-0.611764\pi$
$877$	−39.3605	−	22.7248i	−1.32911	−	0.767362i	−0.985162	+	0.171627i	$0.945098\pi$
$878$	−14.5704	+	8.41220i	−0.491726	+	0.283898i
$879$	1.03107			0.0347770
$880$		−	0.470086i		−	0.0158466i
$881$		−	38.7954i		−	1.30705i	−0.756906	−	0.653524i	$-0.773290\pi$
$881$		−	38.7954i		−	1.30705i	0.756906	−	0.653524i	$-0.226710\pi$
$882$	5.34564	+	4.51930i	0.179997	+	0.152173i
$883$	−6.65295	+	11.5232i	−0.223889	+	0.387788i	−0.955986	−	0.293413i	$-0.905209\pi$
$883$	−6.65295	+	11.5232i	−0.223889	+	0.387788i	0.732096	+	0.681201i	$0.238542\pi$
$884$		−	9.89555i		−	0.332824i
$885$	−17.4304	−	10.0634i	−0.585916	−	0.338279i
$886$	−20.6040	−	11.8957i	−0.692206	−	0.399645i
$887$	−34.5152			−1.15891			−0.579453	−	0.815005i	$-0.696734\pi$
$887$	−34.5152			−1.15891			−0.579453	+	0.815005i	$0.696734\pi$
$888$	4.12884	+	7.15136i	0.138555	+	0.239984i
$889$	4.21854	−	6.00106i	0.141485	−	0.201269i
$890$	−10.0277	−	17.3685i	−0.336129	−	0.582192i
$891$	−0.129396	+	0.224121i	−0.00433494	+	0.00750834i
$892$	4.96103	−	8.59275i	0.166107	−	0.287707i
$893$	−28.5285	−	7.23070i	−0.954669	−	0.241966i
$894$	−17.8684	+	10.3164i	−0.597610	+	0.345030i
$895$	0.00644672	+	0.0111660i	0.000215490	+	0.000373240i
$896$	1.52154	−	2.16446i	0.0508312	−	0.0723097i
$897$	5.88801	−	10.1983i	0.196595	−	0.340513i
$898$	9.96039	−	17.2519i	0.332382	−	0.575703i
$899$	49.6300	−	28.6539i	1.65525	−	0.955660i
$900$	0.850246	−	1.47267i	0.0283415	−	0.0490890i
$901$	−0.891521	−	1.54416i	−0.0297009	−	0.0514434i
$902$	−0.351946	−	0.203196i	−0.0117185	−	0.00676569i
$903$	28.9078	−	13.4149i	0.961990	−	0.446421i
$904$	−7.46716			−0.248354
$905$	5.59036	−	3.22760i	0.185830	−	0.107289i
$906$	−0.125659	−	0.217648i	−0.00417474	−	0.00723086i
$907$		−	14.8413i		−	0.492796i	−0.969169	−	0.246398i	$-0.920753\pi$
$907$		−	14.8413i		−	0.492796i	0.969169	−	0.246398i	$-0.0792470\pi$
$908$	−0.209207			−0.00694277
$909$	−0.900889	+	0.520129i	−0.0298806	+	0.0172516i
$910$	−1.10553	+	12.3728i	−0.0366478	+	0.410154i
$911$		−	28.2209i		−	0.935001i	−0.883993	−	0.467500i	$-0.845155\pi$
$911$		−	28.2209i		−	0.935001i	0.883993	−	0.467500i	$-0.154845\pi$
$912$	3.12375	+	3.04010i	0.103438	+	0.100668i
$913$	2.26630	+	1.30845i	0.0750036	+	0.0433034i
$914$			15.7494i			0.520942i
$915$	−7.14090	+	12.3684i	−0.236071	+	0.408887i
$916$	6.73515	+	3.88854i	0.222536	+	0.128481i
$917$	11.9202	−	16.9570i	0.393640	−	0.559971i
$918$	1.91421	−	3.31551i	0.0631783	−	0.109428i
$919$	−23.7483	−	41.1332i	−0.783383	−	1.35686i	−0.929960	−	0.367660i	$-0.880159\pi$
$919$	−23.7483	−	41.1332i	−0.783383	−	1.35686i	0.146578	−	0.989199i	$-0.453174\pi$
$920$	−4.13783	+	7.16693i	−0.136420	+	0.236287i
$921$	0.325950	+	0.564562i	0.0107404	+	0.0186030i
$922$	−4.74009			−0.156107
$923$			10.5775i			0.348164i
$924$	0.0609363	−	0.681985i	0.00200466	−	0.0224356i
$925$	−12.1608	−	7.02106i	−0.399846	−	0.230851i
$926$	9.33535	+	5.38977i	0.306779	+	0.177119i
$927$	9.66141	+	16.7341i	0.317322	+	0.549619i
$928$	9.61569			0.315651
$929$	−28.0762	−	16.2098i	−0.921151	−	0.531827i	−0.0371486	−	0.999310i	$-0.511827\pi$
$929$	−28.0762	−	16.2098i	−0.921151	−	0.531827i	−0.884002	+	0.467483i	$0.845161\pi$
$930$	10.8257			0.354990
$931$	12.6214	−	27.7795i	0.413648	−	0.910437i
$932$	−17.0651			−0.558985
$933$	−9.97341	−	5.75815i	−0.326515	−	0.188513i
$934$	1.16642			0.0381663
$935$	0.899841	+	1.55857i	0.0294280	+	0.0509707i
$936$	−2.23847	−	1.29238i	−0.0731667	−	0.0422428i
$937$	−2.86298	−	1.65294i	−0.0935295	−	0.0539993i	0.452506	−	0.891761i	$-0.350530\pi$
$937$	−2.86298	−	1.65294i	−0.0935295	−	0.0539993i	−0.546035	+	0.837762i	$0.683864\pi$
$938$	−2.19222	+	24.5348i	−0.0715784	+	0.801089i
$939$			2.02061i			0.0659400i
$940$	−12.2644			−0.400021
$941$	6.37130	+	11.0354i	0.207698	+	0.359744i	0.950989	−	0.309224i	$-0.100069\pi$
$941$	6.37130	+	11.0354i	0.207698	+	0.359744i	−0.743291	+	0.668969i	$0.766736\pi$
$942$	−10.4441	+	18.0897i	−0.340287	+	0.589395i
$943$	3.57718	+	6.19586i	0.116489	+	0.201765i
$944$	−5.54016	+	9.59583i	−0.180317	+	0.312318i
$945$	−2.76382	+	3.93165i	−0.0899069	+	0.127897i
$946$	−2.69960	−	1.55861i	−0.0877715	−	0.0506749i
$947$	−24.8561	+	43.0519i	−0.807713	+	1.39900i	0.106731	+	0.994288i	$0.465962\pi$
$947$	−24.8561	+	43.0519i	−0.807713	+	1.39900i	−0.914444	+	0.404712i	$0.867372\pi$
$948$			13.2317i			0.429747i
$949$	−27.0199	−	15.5999i	−0.877103	−	0.506395i
$950$	−7.18508	−	1.82110i	−0.233115	−	0.0590842i
$951$		−	21.2881i		−	0.690314i
$952$	−0.901452	+	10.0888i	−0.0292162	+	0.326981i
$953$	18.4491	−	10.6516i	0.597625	−	0.345039i	−0.170482	−	0.985361i	$-0.554532\pi$
$953$	18.4491	−	10.6516i	0.597625	−	0.345039i	0.768107	+	0.640322i	$0.221199\pi$
$954$	−0.465739			−0.0150789
$955$			9.91274i			0.320769i
$956$	−6.60716	−	11.4439i	−0.213691	−	0.370124i
$957$	2.15508	−	1.24424i	0.0696639	−	0.0402204i
$958$	−22.2206			−0.717916
$959$	8.58785	−	3.98527i	0.277316	−	0.128691i
$960$	1.57310	+	0.908227i	0.0507715	+	0.0293129i
$961$	−2.25970	−	3.91392i	−0.0728936	−	0.126255i
$962$	−10.6721	+	18.4846i	−0.344082	+	0.595967i
$963$	−13.6641	+	7.88898i	−0.440320	+	0.254219i
$964$	−4.11900	+	7.13432i	−0.132664	+	0.229781i
$965$	−16.3602	+	28.3366i	−0.526652	+	0.912188i
$966$	−6.93206	+	9.86116i	−0.223035	+	0.317278i
$967$	10.1880	+	17.6462i	0.327625	+	0.567464i	0.982040	−	0.188672i	$-0.0604183\pi$
$967$	10.1880	+	17.6462i	0.327625	+	0.567464i	−0.654415	+	0.756136i	$0.727085\pi$
$968$	9.46828	−	5.46651i	0.304322	−	0.175700i
$969$	−16.1762	−	4.09994i	−0.519654	−	0.131709i
$970$	4.90474	−	8.49526i	0.157482	−	0.272766i
$971$	17.3252	−	30.0081i	0.555992	−	0.963007i	−0.441833	−	0.897097i	$-0.645672\pi$
$971$	17.3252	−	30.0081i	0.555992	−	0.963007i	0.997826	−	0.0659098i	$-0.0209949\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	15.1231	−	21.5133i	0.484826	−	0.689686i
$974$	−15.1569	−	26.2526i	−0.485659	−	0.841187i
$975$	4.39537			0.140765
$976$	6.80909	+	3.93123i	0.217954	+	0.125836i
$977$	41.3425	+	23.8691i	1.32266	+	0.763641i	0.984153	−	0.177322i	$-0.0567434\pi$
$977$	41.3425	+	23.8691i	1.32266	+	0.763641i	0.338511	+	0.940962i	$0.390077\pi$
$978$		−	11.4948i		−	0.367564i
$979$	−1.42866	+	2.47451i	−0.0456601	+	0.0790856i
$980$	2.25424	−	12.5138i	0.0720091	−	0.399738i
$981$		−	16.4872i		−	0.526397i
$982$			0.539196i			0.0172064i
$983$	53.0871			1.69322			0.846608	−	0.532218i	$-0.178641\pi$
$983$	53.0871			1.69322			0.846608	+	0.532218i	$0.178641\pi$
$984$	1.35995	−	0.785169i	0.0433537	−	0.0250303i
$985$	14.2042	+	8.20077i	0.452582	+	0.261298i
$986$	−31.8809	+	18.4064i	−1.01529	+	0.586180i
$987$	−17.7928	−	1.58981i	−0.566351	−	0.0506042i
$988$	−2.76809	+	10.9214i	−0.0880646	+	0.347456i
$989$	27.4387	+	47.5253i	0.872501	+	1.51122i
$990$	0.470086			0.0149403
$991$			9.84777i			0.312825i	0.987692	+	0.156412i	$0.0499929\pi$
$991$			9.84777i			0.312825i	−0.987692	+	0.156412i	$0.950007\pi$
$992$		−	5.95982i		−	0.189224i
$993$	15.7802	−	9.11071i	0.500770	−	0.289120i
$994$	0.963579	−	10.7841i	0.0305629	−	0.342052i
$995$	−14.7335			−0.467085
$996$	−8.75720	+	5.05597i	−0.277483	+	0.160205i
$997$	−24.0693	+	13.8964i	−0.762283	+	0.440104i	−0.830115	−	0.557592i	$-0.811725\pi$
$997$	−24.0693	+	13.8964i	−0.762283	+	0.440104i	0.0678316	+	0.997697i	$0.478392\pi$
$998$	7.07193	−	4.08298i	0.223858	−	0.129244i
$999$	−7.15136	+	4.12884i	−0.226259	+	0.130631i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bc.a.31.6	yes	28
7.5	odd	6		798.2.m.a.145.13	✓	28
19.8	odd	6		798.2.m.a.787.2	yes	28
133.103	even	6	inner	798.2.bc.a.103.6	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.a.145.13	✓	28	7.5	odd	6
798.2.m.a.787.2	yes	28	19.8	odd	6
798.2.bc.a.31.6	yes	28	1.1	even	1	trivial
798.2.bc.a.103.6	yes	28	133.103	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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.57310 + 0.908227i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.235464 - 2.63525i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 + 0.866025i) q^{4} +(1.57310 + 0.908227i) q^{5} +(0.866025 + 0.500000i) q^{6} +(0.235464 - 2.63525i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +(-0.908227 - 1.57310i) q^{10} +(-0.129396 + 0.224121i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(1.29238 - 2.23847i) q^{13} +(-1.52154 + 2.16446i) q^{14} +(-1.57310 - 0.908227i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.82842i q^{17} +(-0.866025 - 0.500000i) q^{18} +(-1.07092 + 4.22530i) q^{19} +1.81645i q^{20} +(-0.235464 + 2.63525i) q^{21} +(0.224121 - 0.129396i) q^{22} -4.55594 q^{23} +1.00000i q^{24} +(-0.850246 - 1.47267i) q^{25} +(-2.23847 + 1.29238i) q^{26} -1.00000 q^{27} +(2.39993 - 1.11371i) q^{28} +(8.32743 + 4.80785i) q^{29} +(0.908227 + 1.57310i) q^{30} +(2.97991 - 5.16135i) q^{31} +(0.866025 - 0.500000i) q^{32} +(0.129396 - 0.224121i) q^{33} +(-1.91421 + 3.31551i) q^{34} +(2.76382 - 3.93165i) q^{35} +(0.500000 + 0.866025i) q^{36} +(7.15136 - 4.12884i) q^{37} +(3.04010 - 3.12375i) q^{38} +(-1.29238 + 2.23847i) q^{39} +(0.908227 - 1.57310i) q^{40} +(-0.785169 - 1.35995i) q^{41} +(1.52154 - 2.16446i) q^{42} +(-6.02263 - 10.4315i) q^{43} -0.258793 q^{44} +(1.57310 + 0.908227i) q^{45} +(3.94556 + 2.27797i) q^{46} +6.75183i q^{47} +(0.500000 - 0.866025i) q^{48} +(-6.88911 - 1.24101i) q^{49} +1.70049i q^{50} +3.82842i q^{51} +2.58476 q^{52} +(0.403342 - 0.232869i) q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.407106 + 0.235043i) q^{55} +(-2.63525 - 0.235464i) q^{56} +(1.07092 - 4.22530i) q^{57} +(-4.80785 - 8.32743i) q^{58} +11.0803 q^{59} -1.81645i q^{60} -7.86246i q^{61} +(-5.16135 + 2.97991i) q^{62} +(0.235464 - 2.63525i) q^{63} -1.00000 q^{64} +(4.06608 - 2.34755i) q^{65} +(-0.224121 + 0.129396i) q^{66} +(8.06288 - 4.65511i) q^{67} +(3.31551 - 1.91421i) q^{68} +4.55594 q^{69} +(-4.35936 + 2.02300i) q^{70} +(-3.54400 + 2.04613i) q^{71} -1.00000i q^{72} -12.0707i q^{73} -8.25768 q^{74} +(0.850246 + 1.47267i) q^{75} +(-4.19468 + 1.18520i) q^{76} +(0.560148 + 0.393765i) q^{77} +(2.23847 - 1.29238i) q^{78} +(-11.4590 - 6.61587i) q^{79} +(-1.57310 + 0.908227i) q^{80} +1.00000 q^{81} +1.57034i q^{82} -10.1119i q^{83} +(-2.39993 + 1.11371i) q^{84} +(3.47707 - 6.02247i) q^{85} +12.0453i q^{86} +(-8.32743 - 4.80785i) q^{87} +(0.224121 + 0.129396i) q^{88} +11.0409 q^{89} +(-0.908227 - 1.57310i) q^{90} +(-5.59463 - 3.93283i) q^{91} +(-2.27797 - 3.94556i) q^{92} +(-2.97991 + 5.16135i) q^{93} +(3.37592 - 5.84726i) q^{94} +(-5.52220 + 5.67415i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(2.70017 + 4.67684i) q^{97} +(5.34564 + 4.51930i) q^{98} +(-0.129396 + 0.224121i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 28 q^{3} + 14 q^{4} + 6 q^{5} + 4 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - 28 * q^3 + 14 * q^4 + 6 * q^5 + 4 * q^7 + 28 * q^9	\( 28 q - 28 q^{3} + 14 q^{4} + 6 q^{5} + 4 q^{7} + 28 q^{9} - 2 q^{10} - 14 q^{12} - 2 q^{13} - 4 q^{14} - 6 q^{15} - 14 q^{16} + 12 q^{19} - 4 q^{21} - 12 q^{22} + 14 q^{25} - 28 q^{27} + 2 q^{28} + 18 q^{29} + 2 q^{30} - 4 q^{31} - 8 q^{34} - 10 q^{35} + 14 q^{36} - 12 q^{37} + 6 q^{38} + 2 q^{39} + 2 q^{40} + 8 q^{41} + 4 q^{42} + 10 q^{43} + 6 q^{45} + 24 q^{46} + 14 q^{48} - 4 q^{52} - 12 q^{53} - 30 q^{55} + 4 q^{56} - 12 q^{57} - 2 q^{58} + 4 q^{59} + 12 q^{62} + 4 q^{63} - 28 q^{64} + 96 q^{65} + 12 q^{66} - 6 q^{67} + 6 q^{68} - 6 q^{70} - 42 q^{71} + 12 q^{74} - 14 q^{75} + 12 q^{76} + 16 q^{77} + 12 q^{79} - 6 q^{80} + 28 q^{81} - 2 q^{84} - 8 q^{85} - 18 q^{87} - 12 q^{88} - 16 q^{89} - 2 q^{90} + 8 q^{91} + 4 q^{93} - 18 q^{94} - 82 q^{95} - 8 q^{97} + 20 q^{98}+O(q^{100}) \) 28 * q - 28 * q^3 + 14 * q^4 + 6 * q^5 + 4 * q^7 + 28 * q^9 - 2 * q^10 - 14 * q^12 - 2 * q^13 - 4 * q^14 - 6 * q^15 - 14 * q^16 + 12 * q^19 - 4 * q^21 - 12 * q^22 + 14 * q^25 - 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 - 4 * q^31 - 8 * q^34 - 10 * q^35 + 14 * q^36 - 12 * q^37 + 6 * q^38 + 2 * q^39 + 2 * q^40 + 8 * q^41 + 4 * q^42 + 10 * q^43 + 6 * q^45 + 24 * q^46 + 14 * q^48 - 4 * q^52 - 12 * q^53 - 30 * q^55 + 4 * q^56 - 12 * q^57 - 2 * q^58 + 4 * q^59 + 12 * q^62 + 4 * q^63 - 28 * q^64 + 96 * q^65 + 12 * q^66 - 6 * q^67 + 6 * q^68 - 6 * q^70 - 42 * q^71 + 12 * q^74 - 14 * q^75 + 12 * q^76 + 16 * q^77 + 12 * q^79 - 6 * q^80 + 28 * q^81 - 2 * q^84 - 8 * q^85 - 18 * q^87 - 12 * q^88 - 16 * q^89 - 2 * q^90 + 8 * q^91 + 4 * q^93 - 18 * q^94 - 82 * q^95 - 8 * q^97 + 20 * q^98

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