LMFDB - Embedded newform 819.2.o.d.568.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(568,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("819.568");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.o (of order $3$, 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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.771147.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 6x^{3} + 15x^{2} + 4x + 1 $ x^6 - x^5 + 5x^4 + 6x^3 + 15x^2 + 4x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			568.2
Root			$1.32555 - 2.29591i$ of defining polynomial
Character	$\chi$	$=$	819.568
Dual form			819.2.o.d.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.636945 + 1.10322i) q^{2} +(0.188601 + 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 + 0.866025i) q^{7} -3.02830 q^{8} +O(q^{10})$	\(q+(-0.636945 + 1.10322i) q^{2} +(0.188601 + 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 + 0.866025i) q^{7} -3.02830 q^{8} +(0.702750 - 1.21720i) q^{10} +(-0.174453 + 0.302162i) q^{11} +(-3.47664 + 0.955496i) q^{13} -1.27389 q^{14} +(1.55166 - 2.68755i) q^{16} +(0.363055 + 0.628829i) q^{17} +(-1.15109 - 1.99375i) q^{19} +(-0.208086 - 0.360416i) q^{20} +(-0.222234 - 0.384921i) q^{22} +(0.0375080 - 0.0649658i) q^{23} -3.78270 q^{25} +(1.16031 - 4.44410i) q^{26} +(-0.188601 + 0.326667i) q^{28} +(0.240258 - 0.416138i) q^{29} -6.85772 q^{31} +(-1.05166 - 1.82152i) q^{32} -0.924984 q^{34} +(-0.551656 - 0.955496i) q^{35} +(0.551656 - 0.955496i) q^{37} +2.93273 q^{38} +3.34116 q^{40} +(1.54778 - 2.68084i) q^{41} +(2.31140 + 4.00346i) q^{43} -0.131609 q^{44} +(0.0477811 + 0.0827593i) q^{46} -4.70769 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.40937 - 4.17316i) q^{50} +(-0.967829 - 0.955496i) q^{52} -5.54778 q^{53} +(0.192476 - 0.333379i) q^{55} +(-1.51415 - 2.62258i) q^{56} +(0.306062 + 0.530115i) q^{58} +(-1.96249 - 3.39914i) q^{59} +(-2.77389 - 4.80452i) q^{61} +(4.36799 - 7.56558i) q^{62} +8.88601 q^{64} +(3.83582 - 1.05421i) q^{65} +(-4.06193 + 7.03547i) q^{67} +(-0.136945 + 0.237196i) q^{68} +1.40550 q^{70} +(-4.76468 - 8.25267i) q^{71} -10.4338 q^{73} +(0.702750 + 1.21720i) q^{74} +(0.434196 - 0.752049i) q^{76} -0.348907 q^{77} +17.1054 q^{79} +(-1.71196 + 2.96520i) q^{80} +(1.97170 + 3.41509i) q^{82} +11.9143 q^{83} +(-0.400563 - 0.693795i) q^{85} -5.88894 q^{86} +(0.528296 - 0.915036i) q^{88} +(-5.98052 + 10.3586i) q^{89} +(-2.56580 - 2.53311i) q^{91} +0.0282963 q^{92} +(2.99854 - 5.19362i) q^{94} +(1.27002 + 2.19973i) q^{95} +(-5.05166 - 8.74973i) q^{97} +(-0.636945 - 1.10322i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	$ 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.636945	+	1.10322i	−0.450388	+	0.780095i	−0.998410	−	0.0563687i	$-0.982048\pi$
$2$	−0.636945	+	1.10322i	−0.450388	+	0.780095i	0.548022	+	0.836464i	$0.315381\pi$
$3$		0			0
$3$		0			0
$4$	0.188601	+	0.326667i	0.0943007	+	0.163334i
$5$	−1.10331			−0.493416			−0.246708	−	0.969090i	$-0.579349\pi$
$5$	−1.10331			−0.493416			−0.246708	+	0.969090i	$0.579349\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	−3.02830			−1.07066
$9$		0			0
$10$	0.702750	−	1.21720i	0.222229	−	0.384912i
$11$	−0.174453	+	0.302162i	−0.0525996	+	0.0911053i	−0.891126	−	0.453755i	$-0.850084\pi$
$11$	−0.174453	+	0.302162i	−0.0525996	+	0.0911053i	0.838527	+	0.544860i	$0.183417\pi$
$12$		0			0
$13$	−3.47664	+	0.955496i	−0.964246	+	0.265007i
$13$	−3.47664	+	0.955496i	−0.964246	+	0.265007i
$14$	−1.27389			−0.340462
$15$		0			0
$16$	1.55166	−	2.68755i	0.387914	−	0.671887i
$17$	0.363055	+	0.628829i	0.0880537	+	0.152513i	0.906688	−	0.421801i	$-0.138602\pi$
$17$	0.363055	+	0.628829i	0.0880537	+	0.152513i	−0.818635	+	0.574315i	$0.805269\pi$
$18$		0			0
$19$	−1.15109	−	1.99375i	−0.264079	−	0.457398i	0.703243	−	0.710950i	$-0.251735\pi$
$19$	−1.15109	−	1.99375i	−0.264079	−	0.457398i	−0.967322	+	0.253551i	$0.918401\pi$
$20$	−0.208086	−	0.360416i	−0.0465295	−	0.0805915i
$21$		0			0
$22$	−0.222234	−	0.384921i	−0.0473805	−	0.0820655i
$23$	0.0375080	−	0.0649658i	0.00782096	−	0.0135463i	−0.862088	−	0.506758i	$-0.830844\pi$
$23$	0.0375080	−	0.0649658i	0.00782096	−	0.0135463i	0.869909	+	0.493212i	$0.164177\pi$
$24$		0			0
$25$	−3.78270			−0.756540
$26$	1.16031	−	4.44410i	0.227555	−	0.871560i
$27$		0			0
$28$	−0.188601	+	0.326667i	−0.0356423	+	0.0617343i
$29$	0.240258	−	0.416138i	0.0446147	−	0.0772749i	−0.842856	−	0.538140i	$-0.819127\pi$
$29$	0.240258	−	0.416138i	0.0446147	−	0.0772749i	0.887470	+	0.460865i	$0.152461\pi$
$30$		0			0
$31$	−6.85772			−1.23168			−0.615841	−	0.787870i	$-0.711184\pi$
$31$	−6.85772			−1.23168			−0.615841	+	0.787870i	$0.711184\pi$
$32$	−1.05166	−	1.82152i	−0.185908	−	0.322003i
$33$		0			0
$34$	−0.924984			−0.158633
$35$	−0.551656	−	0.955496i	−0.0932469	−	0.161508i
$36$		0			0
$37$	0.551656	−	0.955496i	0.0906917	−	0.157083i	−0.817111	−	0.576481i	$-0.804426\pi$
$37$	0.551656	−	0.955496i	0.0906917	−	0.157083i	0.907802	+	0.419398i	$0.137759\pi$
$38$	2.93273			0.475752
$39$		0			0
$40$	3.34116			0.528283
$41$	1.54778	−	2.68084i	0.241723	−	0.418676i	−0.719482	−	0.694511i	$-0.755621\pi$
$41$	1.54778	−	2.68084i	0.241723	−	0.418676i	0.961205	+	0.275835i	$0.0889542\pi$
$42$		0			0
$43$	2.31140	+	4.00346i	0.352485	+	0.610522i	0.986684	−	0.162648i	$-0.0520034\pi$
$43$	2.31140	+	4.00346i	0.352485	+	0.610522i	−0.634199	+	0.773170i	$0.718670\pi$
$44$	−0.131609			−0.0198407
$45$		0			0
$46$	0.0477811	+	0.0827593i	0.00704494	+	0.0122022i
$47$	−4.70769			−0.686687			−0.343343	−	0.939210i	$-0.611559\pi$
$47$	−4.70769			−0.686687			−0.343343	+	0.939210i	$0.611559\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	2.40937	−	4.17316i	0.340737	−	0.590174i
$51$		0			0
$52$	−0.967829	−	0.955496i	−0.134214	−	0.132504i
$53$	−5.54778			−0.762046			−0.381023	−	0.924565i	$-0.624428\pi$
$53$	−5.54778			−0.762046			−0.381023	+	0.924565i	$0.624428\pi$
$54$		0			0
$55$	0.192476	−	0.333379i	0.0259535	−	0.0449528i
$56$	−1.51415	−	2.62258i	−0.202337	−	0.350457i
$57$		0			0
$58$	0.306062	+	0.530115i	0.0401879	+	0.0696075i
$59$	−1.96249	−	3.39914i	−0.255495	−	0.442530i	0.709535	−	0.704670i	$-0.248905\pi$
$59$	−1.96249	−	3.39914i	−0.255495	−	0.442530i	−0.965030	+	0.262140i	$0.915572\pi$
$60$		0			0
$61$	−2.77389	−	4.80452i	−0.355160	−	0.615156i	0.631985	−	0.774981i	$-0.282240\pi$
$61$	−2.77389	−	4.80452i	−0.355160	−	0.615156i	−0.987145	+	0.159825i	$0.948907\pi$
$62$	4.36799	−	7.56558i	0.554735	−	0.960830i
$63$		0			0
$64$	8.88601			1.11075
$65$	3.83582	−	1.05421i	0.475775	−	0.130759i
$66$		0			0
$67$	−4.06193	+	7.03547i	−0.496244	+	0.859519i	−0.999991	−	0.00433206i	$-0.998621\pi$
$67$	−4.06193	+	7.03547i	−0.496244	+	0.859519i	0.503747	+	0.863851i	$0.331954\pi$
$68$	−0.136945	+	0.237196i	−0.0166071	+	0.0287643i
$69$		0			0
$70$	1.40550			0.167989
$71$	−4.76468	−	8.25267i	−0.565463	−	0.979411i	−0.997006	−	0.0773189i	$-0.975364\pi$
$71$	−4.76468	−	8.25267i	−0.565463	−	0.979411i	0.431543	−	0.902092i	$-0.357969\pi$
$72$		0			0
$73$	−10.4338			−1.22118			−0.610592	−	0.791946i	$-0.709068\pi$
$73$	−10.4338			−1.22118			−0.610592	+	0.791946i	$0.709068\pi$
$74$	0.702750	+	1.21720i	0.0816930	+	0.141496i
$75$		0			0
$76$	0.434196	−	0.752049i	0.0498057	−	0.0862659i
$77$	−0.348907			−0.0397616
$78$		0			0
$79$	17.1054			1.92451			0.962256	−	0.272146i	$-0.0877335\pi$
$79$	17.1054			1.92451			0.962256	+	0.272146i	$0.0877335\pi$
$80$	−1.71196	+	2.96520i	−0.191403	+	0.331520i
$81$		0			0
$82$	1.97170	+	3.41509i	0.217738	+	0.377134i
$83$	11.9143			1.30777			0.653883	−	0.756596i	$-0.273139\pi$
$83$	11.9143			1.30777			0.653883	+	0.756596i	$0.273139\pi$
$84$		0			0
$85$	−0.400563	−	0.693795i	−0.0434471	−	0.0752526i
$86$	−5.88894			−0.635020
$87$		0			0
$88$	0.528296	−	0.915036i	0.0563166	−	0.0975432i
$89$	−5.98052	+	10.3586i	−0.633933	+	1.09800i	0.352807	+	0.935696i	$0.385227\pi$
$89$	−5.98052	+	10.3586i	−0.633933	+	1.09800i	−0.986740	+	0.162309i	$0.948106\pi$
$90$		0			0
$91$	−2.56580	−	2.53311i	−0.268969	−	0.265542i
$92$	0.0282963			0.00295009
$93$		0			0
$94$	2.99854	−	5.19362i	0.309276	−	0.535681i
$95$	1.27002	+	2.19973i	0.130301	+	0.225688i
$96$		0			0
$97$	−5.05166	−	8.74973i	−0.512918	−	0.888400i	−0.999888	−	0.0149812i	$-0.995231\pi$
$97$	−5.05166	−	8.74973i	−0.512918	−	0.888400i	0.486970	−	0.873419i	$-0.338102\pi$
$98$	−0.636945	−	1.10322i	−0.0643412	−	0.111442i
$99$		0			0
$100$	−0.713423	−	1.23568i	−0.0713423	−	0.123568i
$101$	2.03751	−	3.52907i	0.202740	−	0.351155i	−0.746671	−	0.665194i	$-0.768349\pi$
$101$	2.03751	−	3.52907i	0.202740	−	0.351155i	0.949410	+	0.314039i	$0.101682\pi$
$102$		0			0
$103$	−4.11106			−0.405075			−0.202538	−	0.979275i	$-0.564919\pi$
$103$	−4.11106			−0.405075			−0.202538	+	0.979275i	$0.564919\pi$
$104$	10.5283	−	2.89353i	1.03238	−	0.283734i
$105$		0			0
$106$	3.53363	−	6.12043i	0.343217	−	0.594469i
$107$	−3.08529	+	5.34388i	−0.298266	+	0.516612i	−0.975739	−	0.218935i	$-0.929742\pi$
$107$	−3.08529	+	5.34388i	−0.298266	+	0.516612i	0.677473	+	0.735547i	$0.263075\pi$
$108$		0			0
$109$	−8.82167			−0.844963			−0.422481	−	0.906372i	$-0.638841\pi$
$109$	−8.82167			−0.844963			−0.422481	+	0.906372i	$0.638841\pi$
$110$	0.245194	+	0.424688i	0.0233783	+	0.0404924i
$111$		0			0
$112$	3.10331			0.293235
$113$	6.00494	+	10.4009i	0.564897	+	0.978430i	0.997059	+	0.0766343i	$0.0244174\pi$
$113$	6.00494	+	10.4009i	0.564897	+	0.978430i	−0.432162	+	0.901796i	$0.642249\pi$
$114$		0			0
$115$	−0.0413831	+	0.0716776i	−0.00385899	+	0.00668397i
$116$	0.181252			0.0168288
$117$		0			0
$118$	5.00000			0.460287
$119$	−0.363055	+	0.628829i	−0.0332812	+	0.0576447i
$120$		0			0
$121$	5.43913	+	9.42085i	0.494467	+	0.856441i
$122$	7.06727			0.639840
$123$		0			0
$124$	−1.29338	−	2.24019i	−0.116149	−	0.201175i
$125$	9.69006			0.866706
$126$		0			0
$127$	2.92886	−	5.07293i	0.259894	−	0.450150i	−0.706319	−	0.707894i	$-0.749646\pi$
$127$	2.92886	−	5.07293i	0.259894	−	0.450150i	0.966213	+	0.257744i	$0.0829790\pi$
$128$	−3.55659	+	6.16020i	−0.314361	+	0.544490i
$129$		0			0
$130$	−1.28018	+	4.90323i	−0.112279	+	0.430042i
$131$	−22.4055			−1.95758			−0.978789	−	0.204872i	$-0.934322\pi$
$131$	−22.4055			−1.95758			−0.978789	+	0.204872i	$0.934322\pi$
$132$		0			0
$133$	1.15109	−	1.99375i	0.0998125	−	0.172880i
$134$	−5.17445	−	8.96242i	−0.447005	−	0.774235i
$135$		0			0
$136$	−1.09944	−	1.90428i	−0.0942760	−	0.163291i
$137$	10.1044	+	17.5013i	0.863275	+	1.49524i	0.868750	+	0.495251i	$0.164924\pi$
$137$	10.1044	+	17.5013i	0.863275	+	1.49524i	−0.00547505	+	0.999985i	$0.501743\pi$
$138$		0			0
$139$	−2.13695	−	3.70130i	−0.181253	−	0.313940i	0.761054	−	0.648688i	$-0.224682\pi$
$139$	−2.13695	−	3.70130i	−0.181253	−	0.313940i	−0.942308	+	0.334748i	$0.891349\pi$
$140$	0.208086	−	0.360416i	0.0175865	−	0.0304607i
$141$		0			0
$142$	12.1394			1.01871
$143$	0.317797	−	1.21720i	0.0265755	−	0.101787i
$144$		0			0
$145$	−0.265079	+	0.459131i	−0.0220136	+	0.0381287i
$146$	6.64576	−	11.5108i	0.550007	−	0.952640i
$147$		0			0
$148$	0.416173			0.0342092
$149$	−2.44834	−	4.24066i	−0.200576	−	0.347408i	0.748138	−	0.663543i	$-0.230948\pi$
$149$	−2.44834	−	4.24066i	−0.200576	−	0.347408i	−0.948714	+	0.316135i	$0.897615\pi$
$150$		0			0
$151$	−8.94553			−0.727977			−0.363988	−	0.931403i	$-0.618585\pi$
$151$	−8.94553			−0.727977			−0.363988	+	0.931403i	$0.618585\pi$
$152$	3.48585	+	6.03767i	0.282740	+	0.489720i
$153$		0			0
$154$	0.222234	−	0.384921i	0.0179082	−	0.0310178i
$155$	7.56620			0.607732
$156$		0			0
$157$	6.59450			0.526298			0.263149	−	0.964755i	$-0.415239\pi$
$157$	6.59450			0.526298			0.263149	+	0.964755i	$0.415239\pi$
$158$	−10.8952	+	18.8711i	−0.866778	+	1.50130i
$159$		0			0
$160$	1.16031	+	2.00971i	0.0917302	+	0.158881i
$161$	0.0750160			0.00591209
$162$		0			0
$163$	4.95222	+	8.57749i	0.387888	+	0.671841i	0.992165	−	0.124933i	$-0.0398715\pi$
$163$	4.95222	+	8.57749i	0.387888	+	0.671841i	−0.604277	+	0.796774i	$0.706538\pi$
$164$	1.16765			0.0911785
$165$		0			0
$166$	−7.58876	+	13.1441i	−0.589002	+	1.02018i
$167$	−8.37826	+	14.5116i	−0.648330	+	1.12294i	0.335192	+	0.942150i	$0.391199\pi$
$167$	−8.37826	+	14.5116i	−0.648330	+	1.12294i	−0.983522	+	0.180790i	$0.942135\pi$
$168$		0			0
$169$	11.1741	−	6.64383i	0.859543	−	0.511064i
$170$	1.02055			0.0782723
$171$		0			0
$172$	−0.871866	+	1.51012i	−0.0664792	+	0.115145i
$173$	6.85918	+	11.8804i	0.521494	+	0.903254i	0.999687	+	0.0249993i	$0.00795836\pi$
$173$	6.85918	+	11.8804i	0.521494	+	0.903254i	−0.478194	+	0.878254i	$0.658708\pi$
$174$		0			0
$175$	−1.89135	−	3.27592i	−0.142973	−	0.247636i
$176$	0.541383	+	0.937703i	0.0408083	+	0.0706820i
$177$		0			0
$178$	−7.61852	−	13.1957i	−0.571032	−	0.989057i
$179$	−11.0152	+	19.0789i	−0.823315	+	1.42602i	0.0798846	+	0.996804i	$0.474545\pi$
$179$	−11.0152	+	19.0789i	−0.823315	+	1.42602i	−0.903200	+	0.429220i	$0.858789\pi$
$180$		0			0
$181$	9.43380			0.701208			0.350604	−	0.936524i	$-0.385976\pi$
$181$	9.43380			0.701208			0.350604	+	0.936524i	$0.385976\pi$
$182$	4.42886	−	1.21720i	0.328289	−	0.0902247i
$183$		0			0
$184$	−0.113585	+	0.196736i	−0.00837363	+	0.0145035i
$185$	−0.608649	+	1.05421i	−0.0447488	+	0.0775071i
$186$		0			0
$187$	−0.253344			−0.0185264
$188$	−0.887876	−	1.53785i	−0.0647550	−	0.112159i
$189$		0			0
$190$	−3.23572			−0.234744
$191$	−1.68860	−	2.92474i	−0.122183	−	0.211627i	0.798445	−	0.602067i	$-0.205656\pi$
$191$	−1.68860	−	2.92474i	−0.122183	−	0.211627i	−0.920628	+	0.390440i	$0.872323\pi$
$192$		0			0
$193$	−11.1614	+	19.3321i	−0.803413	+	1.39155i	0.113945	+	0.993487i	$0.463651\pi$
$193$	−11.1614	+	19.3321i	−0.803413	+	1.39155i	−0.917357	+	0.398065i	$0.869682\pi$
$194$	12.8705			0.924049
$195$		0			0
$196$	−0.377203			−0.0269431
$197$	−12.7257	+	22.0416i	−0.906669	+	1.57040i	−0.0880085	+	0.996120i	$0.528050\pi$
$197$	−12.7257	+	22.0416i	−0.906669	+	1.57040i	−0.818661	+	0.574277i	$0.805283\pi$
$198$		0			0
$199$	11.1702	+	19.3473i	0.791833	+	1.37149i	0.924831	+	0.380379i	$0.124206\pi$
$199$	11.1702	+	19.3473i	0.791833	+	1.37149i	−0.132998	+	0.991116i	$0.542460\pi$
$200$	11.4551			0.810001
$201$		0			0
$202$	2.59556	+	4.49565i	0.182623	+	0.316313i
$203$	0.480515			0.0337256
$204$		0			0
$205$	−1.70769	+	2.95780i	−0.119270	+	0.206582i
$206$	2.61852	−	4.53541i	0.182441	−	0.315997i
$207$		0			0
$208$	−2.82661	+	10.8262i	−0.195990	+	0.750664i
$209$	0.803248			0.0555618
$210$		0			0
$211$	−5.01908	+	8.69331i	−0.345528	+	0.598472i	−0.985450	−	0.169968i	$-0.945634\pi$
$211$	−5.01908	+	8.69331i	−0.345528	+	0.598472i	0.639922	+	0.768440i	$0.278967\pi$
$212$	−1.04632	−	1.81228i	−0.0718615	−	0.124468i
$213$		0			0
$214$	−3.93032	−	6.80752i	−0.268671	−	0.465352i
$215$	−2.55019	−	4.41707i	−0.173922	−	0.301241i
$216$		0			0
$217$	−3.42886	−	5.93896i	−0.232766	−	0.403163i
$218$	5.61892	−	9.73226i	0.380561	−	0.659152i
$219$		0			0
$220$	0.145205			0.00978974
$221$	−1.86305	−	1.83932i	−0.125323	−	0.123726i
$222$		0			0
$223$	2.56727	−	4.44664i	0.171917	−	0.297769i	−0.767173	−	0.641440i	$-0.778337\pi$
$223$	2.56727	−	4.44664i	0.171917	−	0.297769i	0.939090	+	0.343671i	$0.111671\pi$
$224$	1.05166	−	1.82152i	0.0702667	−	0.121706i
$225$		0			0
$226$	−15.2993			−1.01769
$227$	−14.4855	−	25.0895i	−0.961433	−	1.66525i	−0.718907	−	0.695106i	$-0.755357\pi$
$227$	−14.4855	−	25.0895i	−0.961433	−	1.66525i	−0.242526	−	0.970145i	$-0.577976\pi$
$228$		0			0
$229$	0.679390			0.0448953			0.0224477	−	0.999748i	$-0.492854\pi$
$229$	0.679390			0.0448953			0.0224477	+	0.999748i	$0.492854\pi$
$230$	−0.0527175	−	0.0913094i	−0.00347609	−	0.00602076i
$231$		0			0
$232$	−0.727571	+	1.26019i	−0.0477674	+	0.0827355i
$233$	18.3022			1.19902			0.599508	−	0.800369i	$-0.295363\pi$
$233$	18.3022			1.19902			0.599508	+	0.800369i	$0.295363\pi$
$234$		0			0
$235$	5.19405			0.338822
$236$	0.740258	−	1.28216i	0.0481867	−	0.0834618i
$237$		0			0
$238$	−0.462492	−	0.801060i	−0.0299789	−	0.0519250i
$239$	5.45222			0.352675			0.176337	−	0.984330i	$-0.443575\pi$
$239$	5.45222			0.352675			0.176337	+	0.984330i	$0.443575\pi$
$240$		0			0
$241$	7.73105	+	13.3906i	0.498000	+	0.862562i	0.999997	−	0.00230736i	$-0.000734455\pi$
$241$	7.73105	+	13.3906i	0.498000	+	0.862562i	−0.501997	+	0.864869i	$0.667401\pi$
$242$	−13.8577			−0.890808
$243$		0			0
$244$	1.04632	−	1.81228i	0.0669837	−	0.116019i
$245$	0.551656	−	0.955496i	0.0352440	−	0.0610444i
$246$		0			0
$247$	5.90696	+	5.83169i	0.375851	+	0.371062i
$248$	20.7672			1.31872
$249$		0			0
$250$	−6.17204	+	10.6903i	−0.390354	+	0.676113i
$251$	−4.14722	−	7.18319i	−0.261770	−	0.453399i	0.704942	−	0.709265i	$-0.250973\pi$
$251$	−4.14722	−	7.18319i	−0.261770	−	0.453399i	−0.966712	+	0.255866i	$0.917640\pi$
$252$		0			0
$253$	0.0130868	+	0.0226670i	0.000822760	+	0.00142506i
$254$	3.73105	+	6.46236i	0.234107	+	0.405485i
$255$		0			0
$256$	4.35530	+	7.54361i	0.272207	+	0.471476i
$257$	−7.51908	+	13.0234i	−0.469028	+	0.812380i	−0.999373	−	0.0354019i	$-0.988729\pi$
$257$	−7.51908	+	13.0234i	−0.469028	+	0.812380i	0.530346	+	0.847782i	$0.322062\pi$
$258$		0			0
$259$	1.10331			0.0685565
$260$	1.06782	+	1.05421i	0.0662232	+	0.0653794i
$261$		0			0
$262$	14.2711	−	24.7182i	0.881670	−	1.52710i
$263$	−8.62240	+	14.9344i	−0.531680	+	0.920896i	0.467636	+	0.883921i	$0.345106\pi$
$263$	−8.62240	+	14.9344i	−0.531680	+	0.920896i	−0.999316	+	0.0369754i	$0.988228\pi$
$264$		0			0
$265$	6.12094			0.376006
$266$	1.46637	+	2.53982i	0.0899087	+	0.155726i
$267$		0			0
$268$	−3.06434			−0.187185
$269$	−12.1472	−	21.0396i	−0.740629	−	1.28281i	−0.952209	−	0.305446i	$-0.901194\pi$
$269$	−12.1472	−	21.0396i	−0.740629	−	1.28281i	0.211580	−	0.977361i	$-0.432139\pi$
$270$		0			0
$271$	−9.16630	+	15.8765i	−0.556813	+	0.964429i	0.440947	+	0.897533i	$0.354643\pi$
$271$	−9.16630	+	15.8765i	−0.556813	+	0.964429i	−0.997760	+	0.0668956i	$0.978691\pi$
$272$	2.25334			0.136629
$273$		0			0
$274$	−25.7437			−1.55524
$275$	0.659905	−	1.14299i	0.0397938	−	0.0689248i
$276$		0			0
$277$	−4.22717	−	7.32167i	−0.253986	−	0.439917i	0.710634	−	0.703562i	$-0.248408\pi$
$277$	−4.22717	−	7.32167i	−0.253986	−	0.439917i	−0.964620	+	0.263646i	$0.915075\pi$
$278$	5.44447			0.326538
$279$		0			0
$280$	1.67058	+	2.89353i	0.0998361	+	0.172921i
$281$	25.0120			1.49209			0.746045	−	0.665895i	$-0.231950\pi$
$281$	25.0120			1.49209			0.746045	+	0.665895i	$0.231950\pi$
$282$		0			0
$283$	−13.5707	+	23.5052i	−0.806697	+	1.39724i	0.108443	+	0.994103i	$0.465414\pi$
$283$	−13.5707	+	23.5052i	−0.806697	+	1.39724i	−0.915140	+	0.403137i	$0.867920\pi$
$284$	1.79725	−	3.11293i	0.106647	−	0.184718i
$285$		0			0
$286$	1.14042	+	1.12589i	0.0674344	+	0.0665752i
$287$	3.09556			0.182725
$288$		0			0
$289$	8.23638	−	14.2658i	0.484493	−	0.839167i
$290$	−0.337682	−	0.584882i	−0.0198294	−	0.0343455i
$291$		0			0
$292$	−1.96783	−	3.40838i	−0.115158	−	0.199460i
$293$	−5.27002	−	9.12793i	−0.307878	−	0.533260i	0.670020	−	0.742343i	$-0.266285\pi$
$293$	−5.27002	−	9.12793i	−0.307878	−	0.533260i	−0.977898	+	0.209083i	$0.932952\pi$
$294$		0			0
$295$	2.16524	+	3.75031i	0.126065	+	0.218351i
$296$	−1.67058	+	2.89353i	−0.0971004	+	0.168183i
$297$		0			0
$298$	6.23784			0.361349
$299$	−0.0683273	+	0.261701i	−0.00395147	+	0.0151346i
$300$		0			0
$301$	−2.31140	+	4.00346i	−0.133227	+	0.230756i
$302$	5.69781	−	9.86890i	0.327872	−	0.567891i
$303$		0			0
$304$	−7.14440			−0.409760
$305$	3.06047	+	5.30089i	0.175242	+	0.303528i
$306$		0			0
$307$	−4.40842			−0.251602			−0.125801	−	0.992055i	$-0.540150\pi$
$307$	−4.40842			−0.251602			−0.125801	+	0.992055i	$0.540150\pi$
$308$	−0.0658043	−	0.113976i	−0.00374955	−	0.00649441i
$309$		0			0
$310$	−4.81926	+	8.34720i	−0.273715	+	0.474089i
$311$	2.32836			0.132029			0.0660146	−	0.997819i	$-0.478972\pi$
$311$	2.32836			0.132029			0.0660146	+	0.997819i	$0.478972\pi$
$312$		0			0
$313$	12.6687			0.716078			0.358039	−	0.933707i	$-0.383445\pi$
$313$	12.6687			0.716078			0.358039	+	0.933707i	$0.383445\pi$
$314$	−4.20034	+	7.27520i	−0.237039	+	0.410563i
$315$		0			0
$316$	3.22611	+	5.58779i	0.181483	+	0.314337i
$317$	12.2915			0.690360			0.345180	−	0.938536i	$-0.387818\pi$
$317$	12.2915			0.690360			0.345180	+	0.938536i	$0.387818\pi$
$318$		0			0
$319$	0.0838275	+	0.145193i	0.00469344	+	0.00812927i
$320$	−9.80405			−0.548063
$321$		0			0
$322$	−0.0477811	+	0.0827593i	−0.00266274	+	0.00461200i
$323$	0.835820	−	1.44768i	0.0465063	−	0.0805512i
$324$		0			0
$325$	13.1511	−	3.61436i	0.729491	−	0.200489i
$326$	−12.6172			−0.698800
$327$		0			0
$328$	−4.68714	+	8.11836i	−0.258804	+	0.448262i
$329$	−2.35384	−	4.07698i	−0.129772	−	0.224771i
$330$		0			0
$331$	−6.64576	−	11.5108i	−0.365284	−	0.632690i	0.623538	−	0.781793i	$-0.285695\pi$
$331$	−6.64576	−	11.5108i	−0.365284	−	0.632690i	−0.988822	+	0.149103i	$0.952361\pi$
$332$	2.24706	+	3.89202i	0.123323	+	0.213602i
$333$		0			0
$334$	−10.6730	−	18.4862i	−0.584000	−	1.01152i
$335$	4.48158	−	7.76232i	0.244855	−	0.424101i
$336$		0			0
$337$	−3.40550			−0.185509			−0.0927547	−	0.995689i	$-0.529567\pi$
$337$	−3.40550			−0.185509			−0.0927547	+	0.995689i	$0.529567\pi$
$338$	0.212362	+	16.5592i	0.0115510	+	0.900703i
$339$		0			0
$340$	0.151093	−	0.261701i	0.00819419	−	0.0141928i
$341$	1.19635	−	2.07214i	0.0647861	−	0.112213i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−6.99960	−	12.1237i	−0.377393	−	0.653664i
$345$		0			0
$346$	−17.4757			−0.939499
$347$	−16.7491	−	29.0102i	−0.899137	−	1.55735i	−0.828599	−	0.559842i	$-0.810862\pi$
$347$	−16.7491	−	29.0102i	−0.899137	−	1.55735i	−0.0705378	−	0.997509i	$-0.522472\pi$
$348$		0			0
$349$	14.0902	−	24.4050i	0.754232	−	1.30637i	−0.191523	−	0.981488i	$-0.561342\pi$
$349$	14.0902	−	24.4050i	0.754232	−	1.30637i	0.945755	−	0.324881i	$-0.105324\pi$
$350$	4.81875			0.257573
$351$		0			0
$352$	0.733860			0.0391148
$353$	−1.49612	+	2.59136i	−0.0796307	+	0.137924i	−0.903091	−	0.429450i	$-0.858707\pi$
$353$	−1.49612	+	2.59136i	−0.0796307	+	0.137924i	0.823460	+	0.567374i	$0.192041\pi$
$354$		0			0
$355$	5.25693	+	9.10527i	0.279009	+	0.483257i
$356$	−4.51173			−0.239121
$357$		0			0
$358$	−14.0322	−	24.3044i	−0.741623	−	1.28453i
$359$	−3.80888			−0.201025			−0.100512	−	0.994936i	$-0.532048\pi$
$359$	−3.80888			−0.201025			−0.100512	+	0.994936i	$0.532048\pi$
$360$		0			0
$361$	6.84997	−	11.8645i	0.360525	−	0.624447i
$362$	−6.00881	+	10.4076i	−0.315816	+	0.547010i
$363$		0			0
$364$	0.343570	−	1.31591i	0.0180080	−	0.0689726i
$365$	11.5117			0.602552
$366$		0			0
$367$	13.2257	−	22.9076i	0.690376	−	1.19577i	−0.281338	−	0.959609i	$-0.590778\pi$
$367$	13.2257	−	22.9076i	0.690376	−	1.19577i	0.971715	−	0.236158i	$-0.0758884\pi$
$368$	−0.116399	−	0.201609i	−0.00606772	−	0.0105096i
$369$		0			0
$370$	−0.775352	−	1.34295i	−0.0403086	−	0.0698166i
$371$	−2.77389	−	4.80452i	−0.144013	−	0.249438i
$372$		0			0
$373$	−1.06580	−	1.84603i	−0.0551853	−	0.0955837i	0.837113	−	0.547030i	$-0.184242\pi$
$373$	−1.06580	−	1.84603i	−0.0551853	−	0.0955837i	−0.892298	+	0.451446i	$0.850908\pi$
$374$	0.161367	−	0.279495i	0.00834406	−	0.0144523i
$375$		0			0
$376$	14.2563			0.735211
$377$	−0.437670	+	1.67633i	−0.0225412	+	0.0863353i
$378$		0			0
$379$	6.97170	−	12.0753i	0.358112	−	0.620269i	−0.629533	−	0.776974i	$-0.716754\pi$
$379$	6.97170	−	12.0753i	0.358112	−	0.620269i	0.987645	+	0.156705i	$0.0500871\pi$
$380$	−0.479053	+	0.829745i	−0.0245749	+	0.0425650i
$381$		0			0
$382$	4.30219			0.220119
$383$	−9.30219	−	16.1119i	−0.475320	−	0.823278i	0.524281	−	0.851545i	$-0.324334\pi$
$383$	−9.30219	−	16.1119i	−0.475320	−	0.823278i	−0.999600	+	0.0282678i	$0.991001\pi$
$384$		0			0
$385$	0.384953			0.0196190
$386$	−14.2184	−	24.6269i	−0.723695	−	1.25348i
$387$		0			0
$388$	1.90550	−	3.30042i	0.0967371	−	0.167554i
$389$	1.23009			0.0623682			0.0311841	−	0.999514i	$-0.490072\pi$
$389$	1.23009			0.0623682			0.0311841	+	0.999514i	$0.490072\pi$
$390$		0			0
$391$	0.0544699			0.00275466
$392$	1.51415	−	2.62258i	0.0764760	−	0.132460i
$393$		0			0
$394$	−16.2112	−	28.0786i	−0.816706	−	1.41458i
$395$	−18.8726			−0.949585
$396$		0			0
$397$	−14.8071	−	25.6467i	−0.743148	−	1.28717i	−0.951055	−	0.309022i	$-0.899998\pi$
$397$	−14.8071	−	25.6467i	−0.743148	−	1.28717i	0.207907	−	0.978149i	$-0.433335\pi$
$398$	−28.4592			−1.42653
$399$		0			0
$400$	−5.86945	+	10.1662i	−0.293473	+	0.508310i
$401$	4.09023	−	7.08448i	0.204256	−	0.353782i	−0.745639	−	0.666350i	$-0.767856\pi$
$401$	4.09023	−	7.08448i	0.204256	−	0.353782i	0.949895	+	0.312568i	$0.101189\pi$
$402$		0			0
$403$	23.8418	−	6.55253i	1.18765	−	0.326405i
$404$	1.53711			0.0764740
$405$		0			0
$406$	−0.306062	+	0.530115i	−0.0151896	+	0.0263092i
$407$	0.192476	+	0.333379i	0.00954070	+	0.0165250i
$408$		0			0
$409$	−5.03363	−	8.71851i	−0.248897	−	0.431102i	0.714323	−	0.699816i	$-0.246735\pi$
$409$	−5.03363	−	8.71851i	−0.248897	−	0.431102i	−0.963220	+	0.268714i	$0.913401\pi$
$410$	−2.17540	−	3.76791i	−0.107436	−	0.186084i
$411$		0			0
$412$	−0.775352	−	1.34295i	−0.0381989	−	0.0661624i
$413$	1.96249	−	3.39914i	0.0965679	−	0.167261i
$414$		0			0
$415$	−13.1452			−0.645273
$416$	5.39669	+	5.32792i	0.264594	+	0.261223i
$417$		0			0
$418$	−0.511625	+	0.886161i	−0.0250244	+	0.0433435i
$419$	4.72998	−	8.19257i	0.231075	−	0.400233i	−0.727050	−	0.686585i	$-0.759109\pi$
$419$	4.72998	−	8.19257i	0.231075	−	0.400233i	0.958125	+	0.286351i	$0.0924424\pi$
$420$		0			0
$421$	31.0643			1.51398			0.756992	−	0.653424i	$-0.226668\pi$
$421$	31.0643			1.51398			0.756992	+	0.653424i	$0.226668\pi$
$422$	−6.39376	−	11.0743i	−0.311244	−	0.539090i
$423$		0			0
$424$	16.8003			0.815896
$425$	−1.37333	−	2.37867i	−0.0666162	−	0.115383i
$426$		0			0
$427$	2.77389	−	4.80452i	0.134238	−	0.232507i
$428$	−2.32756			−0.112507
$429$		0			0
$430$	6.49734			0.313329
$431$	−12.6093	+	21.8400i	−0.607369	+	1.05199i	0.384303	+	0.923207i	$0.374442\pi$
$431$	−12.6093	+	21.8400i	−0.607369	+	1.05199i	−0.991672	+	0.128787i	$0.958892\pi$
$432$		0			0
$433$	−1.88495	−	3.26483i	−0.0905851	−	0.156898i	0.817172	−	0.576393i	$-0.195540\pi$
$433$	−1.88495	−	3.26483i	−0.0905851	−	0.156898i	−0.907757	+	0.419495i	$0.862207\pi$
$434$	8.73598			0.419341
$435$		0			0
$436$	−1.66378	−	2.88175i	−0.0796806	−	0.138011i
$437$	−0.172701			−0.00826141
$438$		0			0
$439$	11.3174	−	19.6023i	0.540150	−	0.935567i	−0.458745	−	0.888568i	$-0.651701\pi$
$439$	11.3174	−	19.6023i	0.540150	−	0.935567i	0.998895	−	0.0469991i	$-0.0149658\pi$
$440$	−0.582876	+	1.00957i	−0.0277875	+	0.0481294i
$441$		0			0
$442$	3.21584	−	0.883819i	0.152962	−	0.0420390i
$443$	−4.64334			−0.220612			−0.110306	−	0.993898i	$-0.535183\pi$
$443$	−4.64334			−0.220612			−0.110306	+	0.993898i	$0.535183\pi$
$444$		0			0
$445$	6.59838	−	11.4287i	0.312793	−	0.541773i
$446$	3.27042	+	5.66453i	0.154859	+	0.268223i
$447$		0			0
$448$	4.44301	+	7.69551i	0.209912	+	0.363579i
$449$	4.71156	+	8.16066i	0.222352	+	0.385125i	0.955522	−	0.294920i	$-0.0952931\pi$
$449$	4.71156	+	8.16066i	0.222352	+	0.385125i	−0.733170	+	0.680046i	$0.761960\pi$
$450$		0			0
$451$	0.540031	+	0.935361i	0.0254291	+	0.0440444i
$452$	−2.26508	+	3.92323i	−0.106540	+	0.184533i
$453$		0			0
$454$	36.9058			1.73207
$455$	2.83088	+	2.79481i	0.132714	+	0.131023i
$456$		0			0
$457$	−6.35812	+	11.0126i	−0.297420	+	0.515147i	−0.975545	−	0.219800i	$-0.929460\pi$
$457$	−6.35812	+	11.0126i	−0.297420	+	0.515147i	0.678125	+	0.734947i	$0.262793\pi$
$458$	−0.432734	+	0.749517i	−0.0202203	+	0.0350226i
$459$		0			0
$460$	−0.0312196			−0.00145562
$461$	−14.8627	−	25.7429i	−0.692223	−	1.19897i	−0.971108	−	0.238641i	$-0.923298\pi$
$461$	−14.8627	−	25.7429i	−0.692223	−	1.19897i	0.278885	−	0.960324i	$-0.410035\pi$
$462$		0			0
$463$	−15.2838			−0.710297			−0.355148	−	0.934810i	$-0.615570\pi$
$463$	−15.2838			−0.710297			−0.355148	+	0.934810i	$0.615570\pi$
$464$	−0.745594	−	1.29141i	−0.0346133	−	0.0599521i
$465$		0			0
$466$	−11.6575	+	20.1914i	−0.540023	+	0.935347i
$467$	26.6503			1.23323			0.616614	−	0.787265i	$-0.288504\pi$
$467$	26.6503			1.23323			0.616614	+	0.787265i	$0.288504\pi$
$468$		0			0
$469$	−8.12386			−0.375125
$470$	−3.30832	+	5.73019i	−0.152602	+	0.264314i
$471$		0			0
$472$	5.94301	+	10.2936i	0.273549	+	0.473801i
$473$	−1.61292			−0.0741623
$474$		0			0
$475$	4.35424	+	7.54177i	0.199786	+	0.346040i
$476$	−0.273891			−0.0125538
$477$		0			0
$478$	−3.47277	+	6.01501i	−0.158841	+	0.275120i
$479$	−11.1058	+	19.2359i	−0.507439	+	0.878909i	0.492524	+	0.870299i	$0.336074\pi$
$479$	−11.1058	+	19.2359i	−0.507439	+	0.878909i	−0.999963	+	0.00861072i	$0.997259\pi$
$480$		0			0
$481$	−1.00494	+	3.84902i	−0.0458212	+	0.175500i
$482$	−19.6970			−0.897174
$483$		0			0
$484$	−2.05166	+	3.55357i	−0.0932571	+	0.161526i
$485$	5.57355	+	9.65368i	0.253082	+	0.438351i
$486$		0			0
$487$	0.485852	+	0.841520i	0.0220160	+	0.0381329i	0.876824	−	0.480812i	$-0.159658\pi$
$487$	0.485852	+	0.841520i	0.0220160	+	0.0381329i	−0.854807	+	0.518945i	$0.826325\pi$
$488$	8.40016	+	14.5495i	0.380257	+	0.658625i
$489$		0			0
$490$	0.702750	+	1.21720i	0.0317470	+	0.0549874i
$491$	13.4674	−	23.3263i	0.607777	−	1.05270i	−0.383830	−	0.923404i	$-0.625395\pi$
$491$	13.4674	−	23.3263i	0.607777	−	1.05270i	0.991606	−	0.129296i	$-0.0412717\pi$
$492$		0			0
$493$	0.348907			0.0157140
$494$	−10.1961	+	2.80222i	−0.458742	+	0.126078i
$495$		0			0
$496$	−10.6408	+	18.4304i	−0.477787	+	0.827551i
$497$	4.76468	−	8.25267i	0.213725	−	0.370183i
$498$		0			0
$499$	−21.1239			−0.945634			−0.472817	−	0.881161i	$-0.656763\pi$
$499$	−21.1239			−0.945634			−0.472817	+	0.881161i	$0.656763\pi$
$500$	1.82756	+	3.16543i	0.0817310	+	0.141562i
$501$		0			0
$502$	10.5662			0.471593
$503$	6.28270	+	10.8820i	0.280132	+	0.485203i	0.971417	−	0.237379i	$-0.0762885\pi$
$503$	6.28270	+	10.8820i	0.280132	+	0.485203i	−0.691285	+	0.722582i	$0.742955\pi$
$504$		0			0
$505$	−2.24801	+	3.89366i	−0.100035	+	0.173266i
$506$	−0.0333423			−0.00148225
$507$		0			0
$508$	2.20955			0.0980328
$509$	13.8032	−	23.9079i	0.611818	−	1.05970i	−0.379116	−	0.925349i	$-0.623772\pi$
$509$	13.8032	−	23.9079i	0.611818	−	1.05970i	0.990934	−	0.134351i	$-0.0428949\pi$
$510$		0			0
$511$	−5.21690	−	9.03593i	−0.230782	−	0.399726i
$512$	−25.3227			−1.11912
$513$		0			0
$514$	−9.57849	−	16.5904i	−0.422489	−	0.731773i
$515$	4.53579			0.199871
$516$		0			0
$517$	0.821271	−	1.42248i	0.0361195	−	0.0625608i
$518$	−0.702750	+	1.21720i	−0.0308770	+	0.0534806i
$519$		0			0
$520$	−11.6160	+	3.19246i	−0.509395	+	0.139999i
$521$	36.8783			1.61567			0.807833	−	0.589411i	$-0.200640\pi$
$521$	36.8783			1.61567			0.807833	+	0.589411i	$0.200640\pi$
$522$		0			0
$523$	−15.4027	+	26.6782i	−0.673512	+	1.16656i	0.303389	+	0.952867i	$0.401882\pi$
$523$	−15.4027	+	26.6782i	−0.673512	+	1.16656i	−0.976901	+	0.213691i	$0.931451\pi$
$524$	−4.22571	−	7.31914i	−0.184601	−	0.319738i
$525$		0			0
$526$	−10.9840	−	19.0248i	−0.478925	−	0.829522i
$527$	−2.48973	−	4.31233i	−0.108454	−	0.187848i
$528$		0			0
$529$	11.4972	+	19.9137i	0.499878	+	0.865814i
$530$	−3.89870	+	6.75275i	−0.169349	+	0.293321i
$531$		0			0
$532$	0.868391			0.0376495
$533$	−2.81955	+	10.7992i	−0.122128	+	0.467765i
$534$		0			0
$535$	3.40404	−	5.89597i	0.147169	−	0.254905i
$536$	12.3007	−	21.3055i	0.531310	−	0.920257i
$537$		0			0
$538$	30.9485			1.33428
$539$	−0.174453	−	0.302162i	−0.00751424	−	0.0130150i
$540$		0			0
$541$	−41.4981			−1.78414			−0.892072	−	0.451893i	$-0.850749\pi$
$541$	−41.4981			−1.78414			−0.892072	+	0.451893i	$0.850749\pi$
$542$	−11.6769	−	20.2249i	−0.501564	−	0.868735i
$543$		0			0
$544$	0.763617	−	1.32262i	0.0327398	−	0.0567070i
$545$	9.73306			0.416918
$546$		0			0
$547$	−41.3716			−1.76892			−0.884460	−	0.466615i	$-0.845473\pi$
$547$	−41.3716			−1.76892			−0.884460	+	0.466615i	$0.845473\pi$
$548$	−3.81140	+	6.60154i	−0.162815	+	0.282004i
$549$		0			0
$550$	0.840647	+	1.45604i	0.0358453	+	0.0620859i
$551$	−1.10624			−0.0471272
$552$		0			0
$553$	8.55272	+	14.8137i	0.363699	+	0.629944i
$554$	10.7699			0.457569
$555$		0			0
$556$	0.806062	−	1.39614i	0.0341846	−	0.0592095i
$557$	15.0075	−	25.9937i	0.635886	−	1.10139i	−0.350440	−	0.936585i	$-0.613968\pi$
$557$	15.0075	−	25.9937i	0.635886	−	1.10139i	0.986327	−	0.164803i	$-0.0526987\pi$
$558$		0			0
$559$	−11.8612	−	11.7101i	−0.501675	−	0.495283i
$560$	−3.42392			−0.144687
$561$		0			0
$562$	−15.9313	+	27.5938i	−0.672020	+	1.16397i
$563$	12.9674	+	22.4602i	0.546512	+	0.946586i	0.998510	+	0.0545676i	$0.0173780\pi$
$563$	12.9674	+	22.4602i	0.546512	+	0.946586i	−0.451998	+	0.892019i	$0.649289\pi$
$564$		0			0
$565$	−6.62532	−	11.4754i	−0.278729	−	0.482773i
$566$	−17.2876	−	29.9431i	−0.726654	−	1.25860i
$567$		0			0
$568$	14.4289	+	24.9915i	0.605421	+	1.04862i
$569$	−3.28310	+	5.68650i	−0.137635	+	0.238390i	−0.926601	−	0.376046i	$-0.877283\pi$
$569$	−3.28310	+	5.68650i	−0.137635	+	0.238390i	0.788966	+	0.614437i	$0.210617\pi$
$570$		0			0
$571$	−30.0539			−1.25772			−0.628858	−	0.777520i	$-0.716477\pi$
$571$	−30.0539			−1.25772			−0.628858	+	0.777520i	$0.716477\pi$
$572$	0.457556	−	0.125752i	0.0191314	−	0.00525794i
$573$		0			0
$574$	−1.97170	+	3.41509i	−0.0822973	+	0.142543i
$575$	−0.141882	+	0.245746i	−0.00591687	+	0.0102483i
$576$		0			0
$577$	21.1706			0.881343			0.440671	−	0.897669i	$-0.354740\pi$
$577$	21.1706			0.881343			0.440671	+	0.897669i	$0.354740\pi$
$578$	10.4922	+	18.1731i	0.436420	+	0.755902i
$579$		0			0
$580$	−0.199977			−0.00830360
$581$	5.95716	+	10.3181i	0.247144	+	0.428067i
$582$		0			0
$583$	0.967829	−	1.67633i	0.0400834	−	0.0694264i
$584$	31.5966			1.30748
$585$		0			0
$586$	13.4268			0.554658
$587$	0.0156098	−	0.0270370i	0.000644286	−	0.00111594i	−0.865703	−	0.500558i	$-0.833128\pi$
$587$	0.0156098	−	0.0270370i	0.000644286	−	0.00111594i	0.866347	+	0.499442i	$0.166462\pi$
$588$		0			0
$589$	7.89387	+	13.6726i	0.325261	+	0.563369i
$590$	−5.51656			−0.227113
$591$		0			0
$592$	−1.71196	−	2.96520i	−0.0703612	−	0.121869i
$593$	10.3150			0.423586			0.211793	−	0.977315i	$-0.432070\pi$
$593$	10.3150			0.423586			0.211793	+	0.977315i	$0.432070\pi$
$594$		0			0
$595$	0.400563	−	0.693795i	0.0164215	−	0.0284428i
$596$	0.923522	−	1.59959i	0.0378289	−	0.0655217i
$597$		0			0
$598$	−0.245194	−	0.242070i	−0.0100267	−	0.00989896i
$599$	−44.0176			−1.79851			−0.899256	−	0.437423i	$-0.855891\pi$
$599$	−44.0176			−1.79851			−0.899256	+	0.437423i	$0.855891\pi$
$600$		0			0
$601$	−2.52336	+	4.37059i	−0.102930	+	0.178280i	−0.912891	−	0.408204i	$-0.866155\pi$
$601$	−2.52336	+	4.37059i	−0.102930	+	0.178280i	0.809961	+	0.586484i	$0.199488\pi$
$602$	−2.94447	−	5.09997i	−0.120008	−	0.207859i
$603$		0			0
$604$	−1.68714	−	2.92221i	−0.0686487	−	0.118903i
$605$	−6.00106	−	10.3941i	−0.243978	−	0.422582i
$606$		0			0
$607$	−8.32409	−	14.4177i	−0.337864	−	0.585198i	0.646167	−	0.763196i	$-0.276371\pi$
$607$	−8.32409	−	14.4177i	−0.337864	−	0.585198i	−0.984031	+	0.177998i	$0.943038\pi$
$608$	−2.42111	+	4.19348i	−0.0981889	+	0.170068i
$609$		0			0
$610$	−7.79740			−0.315708
$611$	16.3669	−	4.49818i	0.662135	−	0.181977i
$612$		0			0
$613$	−19.0060	+	32.9194i	−0.767645	+	1.32960i	0.171192	+	0.985238i	$0.445238\pi$
$613$	−19.0060	+	32.9194i	−0.767645	+	1.32960i	−0.938837	+	0.344362i	$0.888095\pi$
$614$	2.80792	−	4.86347i	0.113319	−	0.196274i
$615$		0			0
$616$	1.05659			0.0425713
$617$	7.83330	+	13.5677i	0.315357	+	0.546214i	0.979513	−	0.201380i	$-0.0645425\pi$
$617$	7.83330	+	13.5677i	0.315357	+	0.546214i	−0.664157	+	0.747593i	$0.731209\pi$
$618$		0			0
$619$	3.26109			0.131074			0.0655372	−	0.997850i	$-0.479124\pi$
$619$	3.26109			0.131074			0.0655372	+	0.997850i	$0.479124\pi$
$620$	1.42700	+	2.47163i	0.0573096	+	0.0992631i
$621$		0			0
$622$	−1.48304	+	2.56870i	−0.0594644	+	0.102995i
$623$	−11.9610			−0.479209
$624$		0			0
$625$	8.22234			0.328894
$626$	−8.06928	+	13.9764i	−0.322513	+	0.558609i
$627$		0			0
$628$	1.24373	+	2.15421i	0.0496303	+	0.0859622i
$629$	0.801125			0.0319430
$630$		0			0
$631$	−0.799773	−	1.38525i	−0.0318385	−	0.0551459i	0.849667	−	0.527319i	$-0.176803\pi$
$631$	−0.799773	−	1.38525i	−0.0318385	−	0.0551459i	−0.881506	+	0.472174i	$0.843470\pi$
$632$	−51.8003			−2.06051
$633$		0			0
$634$	−7.82902	+	13.5603i	−0.310930	+	0.538547i
$635$	−3.23145	+	5.59703i	−0.128236	+	0.222111i
$636$		0			0
$637$	0.910836	−	3.48861i	0.0360886	−	0.138224i
$638$	−0.213574			−0.00845548
$639$		0			0
$640$	3.92403	−	6.79662i	0.155111	−	0.268660i
$641$	15.6779	+	27.1550i	0.619241	+	1.07256i	0.989625	+	0.143678i	$0.0458929\pi$
$641$	15.6779	+	27.1550i	0.619241	+	1.07256i	−0.370384	+	0.928879i	$0.620774\pi$
$642$		0			0
$643$	9.33154	+	16.1627i	0.368000	+	0.637395i	0.989253	−	0.146215i	$-0.0467092\pi$
$643$	9.33154	+	16.1627i	0.368000	+	0.637395i	−0.621253	+	0.783610i	$0.713376\pi$
$644$	0.0141481	+	0.0245053i	0.000557514	+	0.000965643i
$645$		0			0
$646$	1.06474	+	1.84419i	0.0418918	+	0.0725586i
$647$	3.26855	−	5.66130i	0.128500	−	0.222569i	−0.794596	−	0.607139i	$-0.792317\pi$
$647$	3.26855	−	5.66130i	0.128500	−	0.222569i	0.923096	+	0.384570i	$0.125650\pi$
$648$		0			0
$649$	1.36945			0.0537557
$650$	−4.38909	+	16.8107i	−0.172154	+	0.659371i
$651$		0			0
$652$	−1.86799	+	3.23546i	−0.0731562	+	0.126710i
$653$	7.92605	−	13.7283i	0.310170	−	0.537230i	−0.668229	−	0.743956i	$-0.732947\pi$
$653$	7.92605	−	13.7283i	0.310170	−	0.537230i	0.978399	+	0.206725i	$0.0662806\pi$
$654$		0			0
$655$	24.7203			0.965901
$656$	−4.80325	−	8.31947i	−0.187535	−	0.324821i
$657$		0			0
$658$	5.99708			0.233790
$659$	−24.8987	−	43.1258i	−0.969916	−	1.67994i	−0.695784	−	0.718251i	$-0.744943\pi$
$659$	−24.8987	−	43.1258i	−0.969916	−	1.67994i	−0.274132	−	0.961692i	$-0.588390\pi$
$660$		0			0
$661$	−1.78552	+	3.09260i	−0.0694485	+	0.120288i	−0.898659	−	0.438649i	$-0.855457\pi$
$661$	−1.78552	+	3.09260i	−0.0694485	+	0.120288i	0.829210	+	0.558937i	$0.188791\pi$
$662$	16.9319			0.658078
$663$		0			0
$664$	−36.0801			−1.40018
$665$	−1.27002	+	2.19973i	−0.0492491	+	0.0853019i
$666$		0			0
$667$	−0.0180232	−	0.0312170i	−0.000697860	−	0.00120873i
$668$	−6.32061			−0.244552
$669$		0			0
$670$	5.70904	+	9.88834i	0.220559	+	0.382020i
$671$	1.93566			0.0747252
$672$		0			0
$673$	−5.86693	+	10.1618i	−0.226154	+	0.391709i	−0.956665	−	0.291191i	$-0.905948\pi$
$673$	−5.86693	+	10.1618i	−0.226154	+	0.391709i	0.730511	+	0.682901i	$0.239282\pi$
$674$	2.16912	−	3.75702i	0.0835512	−	0.144715i
$675$		0			0
$676$	4.27777	+	2.39716i	0.164529	+	0.0921985i
$677$	−17.3326			−0.666146			−0.333073	−	0.942901i	$-0.608086\pi$
$677$	−17.3326			−0.666146			−0.333073	+	0.942901i	$0.608086\pi$
$678$		0			0
$679$	5.05166	−	8.74973i	0.193865	−	0.335784i
$680$	1.21302	+	2.10102i	0.0465173	+	0.0805703i
$681$		0			0
$682$	1.52402	+	2.63968i	0.0583578	+	0.101079i
$683$	8.48198	+	14.6912i	0.324554	+	0.562144i	0.981422	−	0.191862i	$-0.0614525\pi$
$683$	8.48198	+	14.6912i	0.324554	+	0.562144i	−0.656868	+	0.754005i	$0.728119\pi$
$684$		0			0
$685$	−11.1483	−	19.3094i	−0.425954	−	0.737774i
$686$	0.636945	−	1.10322i	0.0243187	−	0.0421212i
$687$		0			0
$688$	14.3460			0.546935
$689$	19.2876	−	5.30089i	0.734801	−	0.201948i
$690$		0			0
$691$	−18.3213	+	31.7334i	−0.696974	+	1.20719i	0.272537	+	0.962145i	$0.412137\pi$
$691$	−18.3213	+	31.7334i	−0.696974	+	1.20719i	−0.969511	+	0.245049i	$0.921196\pi$
$692$	−2.58730	+	4.48134i	−0.0983545	+	0.170355i
$693$		0			0
$694$	42.6730			1.61984
$695$	2.35772	+	4.08369i	0.0894333	+	0.154903i
$696$		0			0
$697$	2.24772			0.0851384
$698$	17.9494	+	31.0893i	0.679395	+	1.17675i
$699$		0			0
$700$	0.713423	−	1.23568i	0.0269649	−	0.0467045i
$701$	14.6092			0.551782			0.275891	−	0.961189i	$-0.411027\pi$
$701$	14.6092			0.551782			0.275891	+	0.961189i	$0.411027\pi$
$702$		0			0
$703$	−2.54003			−0.0957991
$704$	−1.55019	+	2.68502i	−0.0584252	+	0.101195i
$705$		0			0
$706$	−1.90590	−	3.30111i	−0.0717295	−	0.124239i
$707$	4.07502			0.153257
$708$		0			0
$709$	11.7930	+	20.4260i	0.442894	+	0.767116i	0.997903	−	0.0647290i	$-0.0206183\pi$
$709$	11.7930	+	20.4260i	0.442894	+	0.767116i	−0.555008	+	0.831845i	$0.687285\pi$
$710$	−13.3935			−0.502649
$711$		0			0
$712$	18.1108	−	31.3688i	0.678730	−	1.17559i
$713$	−0.257219	+	0.445517i	−0.00963294	+	0.0166847i
$714$		0			0
$715$	−0.350629	+	1.34295i	−0.0131128	+	0.0502235i
$716$	−8.30994			−0.310557
$717$		0			0
$718$	2.42605	−	4.20203i	0.0905392	−	0.156819i
$719$	17.0669	+	29.5607i	0.636487	+	1.10243i	0.986198	+	0.165570i	$0.0529463\pi$
$719$	17.0669	+	29.5607i	0.636487	+	1.10243i	−0.349711	+	0.936857i	$0.613720\pi$
$720$		0			0
$721$	−2.05553	−	3.56028i	−0.0765520	−	0.132592i
$722$	8.72611	+	15.1141i	0.324752	+	0.562487i
$723$		0			0
$724$	1.77923	+	3.08171i	0.0661245	+	0.114531i
$725$	−0.908823	+	1.57413i	−0.0337528	+	0.0584616i
$726$		0			0
$727$	−15.3481			−0.569230			−0.284615	−	0.958642i	$-0.591866\pi$
$727$	−15.3481			−0.569230			−0.284615	+	0.958642i	$0.591866\pi$
$728$	7.77002	+	7.67101i	0.287976	+	0.284307i
$729$		0			0
$730$	−7.33235	+	12.7000i	−0.271382	+	0.470048i
$731$	−1.67833	+	2.90695i	−0.0620752	+	0.107517i
$732$		0			0
$733$	23.2894			0.860213			0.430107	−	0.902778i	$-0.358476\pi$
$733$	23.2894			0.860213			0.430107	+	0.902778i	$0.358476\pi$
$734$	16.8481	+	29.1818i	0.621875	+	1.07712i
$735$		0			0
$736$	−0.157782			−0.00581593
$737$	−1.41723	−	2.45472i	−0.0522045	−	0.0904208i
$738$		0			0
$739$	5.13307	−	8.89074i	0.188823	−	0.327051i	−0.756035	−	0.654531i	$-0.772866\pi$
$739$	5.13307	−	8.89074i	0.188823	−	0.327051i	0.944858	+	0.327480i	$0.106199\pi$
$740$	−0.459168			−0.0168794
$741$		0			0
$742$	7.06727			0.259447
$743$	−22.6741	+	39.2726i	−0.831830	+	1.44077i	0.0647549	+	0.997901i	$0.479373\pi$
$743$	−22.6741	+	39.2726i	−0.831830	+	1.44077i	−0.896585	+	0.442871i	$0.853960\pi$
$744$		0			0
$745$	2.70129	+	4.67877i	0.0989675	+	0.171417i
$746$	2.71544			0.0994192
$747$		0			0
$748$	−0.0477811	−	0.0827593i	−0.00174705	−	0.00302598i
$749$	−6.17058			−0.225468
$750$		0			0
$751$	14.8057	−	25.6442i	0.540266	−	0.935769i	−0.458622	−	0.888631i	$-0.651657\pi$
$751$	14.8057	−	25.6442i	0.540266	−	0.935769i	0.998888	−	0.0471372i	$-0.0150098\pi$
$752$	−7.30471	+	12.6521i	−0.266375	+	0.461376i
$753$		0			0
$754$	−1.57059	−	1.55058i	−0.0571975	−	0.0564687i
$755$	9.86971			0.359196
$756$		0			0
$757$	12.9908	−	22.5007i	0.472158	−	0.817802i	−0.527334	−	0.849658i	$-0.676808\pi$
$757$	12.9908	−	22.5007i	0.472158	−	0.817802i	0.999492	+	0.0318559i	$0.0101418\pi$
$758$	8.88119	+	15.3827i	0.322579	+	0.558724i
$759$		0			0
$760$	−3.84598	−	6.66144i	−0.139508	−	0.241636i
$761$	−27.0332	−	46.8229i	−0.979954	−	1.69733i	−0.662510	−	0.749053i	$-0.730509\pi$
$761$	−27.0332	−	46.8229i	−0.979954	−	1.69733i	−0.317444	−	0.948277i	$-0.602824\pi$
$762$		0			0
$763$	−4.41084	−	7.63979i	−0.159683	−	0.276579i
$764$	0.636945	−	1.10322i	0.0230439	−	0.0399132i
$765$		0			0
$766$	23.6999			0.856313
$767$	10.0707	+	9.94242i	0.363633	+	0.359000i
$768$		0			0
$769$	−12.8967	+	22.3377i	−0.465066	+	0.805519i	−0.999205	−	0.0398785i	$-0.987303\pi$
$769$	−12.8967	+	22.3377i	−0.465066	+	0.805519i	0.534138	+	0.845397i	$0.320636\pi$
$770$	−0.245194	+	0.424688i	−0.00883618	+	0.0153047i
$771$		0			0
$772$	−8.42020			−0.303050
$773$	−0.0608679	−	0.105426i	−0.00218927	−	0.00379192i	0.864929	−	0.501895i	$-0.167364\pi$
$773$	−0.0608679	−	0.105426i	−0.00218927	−	0.00379192i	−0.867118	+	0.498103i	$0.834030\pi$
$774$		0			0
$775$	25.9407			0.931818
$776$	15.2979	+	26.4968i	0.549163	+	0.951178i
$777$		0			0
$778$	−0.783503	+	1.35707i	−0.0280899	+	0.0486532i
$779$	−7.12656			−0.255336
$780$		0			0
$781$	3.32486			0.118973
$782$	−0.0346943	+	0.0600923i	−0.00124067	+	0.00214890i
$783$		0			0
$784$	1.55166	+	2.68755i	0.0554163	+	0.0959838i
$785$	−7.27579			−0.259684
$786$		0			0
$787$	10.1108	+	17.5124i	0.360410	+	0.624249i	0.988028	−	0.154273i	$-0.0493034\pi$
$787$	10.1108	+	17.5124i	0.360410	+	0.624249i	−0.627618	+	0.778521i	$0.715970\pi$
$788$	−9.60035			−0.341998
$789$		0			0
$790$	12.0208	−	20.8207i	0.427682	−	0.740767i
$791$	−6.00494	+	10.4009i	−0.213511	+	0.369812i
$792$		0			0
$793$	14.2345	+	14.0531i	0.505483	+	0.499042i
$794$	37.7253			1.33882
$795$		0			0
$796$	−4.21342	+	7.29786i	−0.149341	+	0.258666i
$797$	16.2062	+	28.0700i	0.574054	+	0.994291i	0.996144	+	0.0877365i	$0.0279634\pi$
$797$	16.2062	+	28.0700i	0.574054	+	0.994291i	−0.422090	+	0.906554i	$0.638703\pi$
$798$		0			0
$799$	−1.70915	−	2.96033i	−0.0604653	−	0.104729i
$800$	3.97810	+	6.89027i	0.140647	+	0.243608i
$801$		0			0
$802$	5.21050	+	9.02485i	0.183989	+	0.318679i
$803$	1.82021	−	3.15270i	0.0642338	−	0.111256i
$804$		0			0
$805$	−0.0827661			−0.00291712
$806$	−7.95705	+	30.4764i	−0.280275	+	1.07349i
$807$		0			0
$808$	−6.17018	+	10.6871i	−0.217066	+	0.375970i
$809$	12.2314	−	21.1855i	0.430035	−	0.744842i	−0.566841	−	0.823827i	$-0.691835\pi$
$809$	12.2314	−	21.1855i	0.430035	−	0.744842i	0.996876	+	0.0789852i	$0.0251680\pi$
$810$		0			0
$811$	−45.2448			−1.58876			−0.794380	−	0.607421i	$-0.792204\pi$
$811$	−45.2448			−1.58876			−0.794380	+	0.607421i	$0.792204\pi$
$812$	0.0906258	+	0.156969i	0.00318034	+	0.00550852i
$813$		0			0
$814$	−0.490388			−0.0171881
$815$	−5.46384	−	9.46366i	−0.191390	−	0.331497i
$816$		0			0
$817$	5.32127	−	9.21671i	0.186168	−	0.322452i
$818$	12.8246			0.448401
$819$		0			0
$820$	−1.28829			−0.0449890
$821$	18.3665	−	31.8118i	0.640996	−	1.11024i	−0.344214	−	0.938891i	$-0.611855\pi$
$821$	18.3665	−	31.8118i	0.640996	−	1.11024i	0.985211	−	0.171347i	$-0.0548120\pi$
$822$		0			0
$823$	−21.3238	−	36.9339i	−0.743301	−	1.28743i	−0.950984	−	0.309239i	$-0.899926\pi$
$823$	−21.3238	−	36.9339i	−0.743301	−	1.28743i	0.207684	−	0.978196i	$-0.433408\pi$
$824$	12.4495			0.433699
$825$		0			0
$826$	2.50000	+	4.33013i	0.0869861	+	0.150664i
$827$	50.0635			1.74088			0.870440	−	0.492275i	$-0.163834\pi$
$827$	50.0635			1.74088			0.870440	+	0.492275i	$0.163834\pi$
$828$		0			0
$829$	−12.9455	+	22.4223i	−0.449617	+	0.778759i	−0.998361	−	0.0572312i	$-0.981773\pi$
$829$	−12.9455	+	22.4223i	−0.449617	+	0.778759i	0.548744	+	0.835990i	$0.315106\pi$
$830$	8.37278	−	14.5021i	0.290623	−	0.503374i
$831$		0			0
$832$	−30.8935	+	8.49056i	−1.07104	+	0.294357i
$833$	−0.726109			−0.0251582
$834$		0			0
$835$	9.24384	−	16.0108i	0.319896	−	0.554077i
$836$	0.151494	+	0.262395i	0.00523952	+	0.00907512i
$837$		0			0
$838$	6.02548	+	10.4364i	0.208147	+	0.360521i
$839$	−14.4674	−	25.0583i	−0.499471	−	0.865109i	0.500529	−	0.865720i	$-0.333139\pi$
$839$	−14.4674	−	25.0583i	−0.499471	−	0.865109i	−1.00000		0.000610619i	$0.999806\pi$
$840$		0			0
$841$	14.3846	+	24.9148i	0.496019	+	0.859130i
$842$	−19.7863	+	34.2709i	−0.681880	+	1.18105i
$843$		0			0
$844$	−3.78643			−0.130334
$845$	−12.3285	+	7.33022i	−0.424112	+	0.252167i
$846$		0			0
$847$	−5.43913	+	9.42085i	−0.186891	+	0.323704i
$848$	−8.60825	+	14.9099i	−0.295608	+	0.512009i
$849$		0			0
$850$	3.49894			0.120013
$851$	−0.0413831	−	0.0716776i	−0.00141859	−	0.00245708i
$852$		0			0
$853$	40.3094			1.38017			0.690083	−	0.723730i	$-0.257574\pi$
$853$	40.3094			1.38017			0.690083	+	0.723730i	$0.257574\pi$
$854$	3.53363	+	6.12043i	0.120918	+	0.209437i
$855$		0			0
$856$	9.34317	−	16.1828i	0.319343	−	0.553118i
$857$	−40.0459			−1.36794			−0.683971	−	0.729509i	$-0.739749\pi$
$857$	−40.0459			−1.36794			−0.683971	+	0.729509i	$0.739749\pi$
$858$		0			0
$859$	6.66659			0.227461			0.113731	−	0.993512i	$-0.463720\pi$
$859$	6.66659			0.227461			0.113731	+	0.993512i	$0.463720\pi$
$860$	0.961941	−	1.66613i	0.0328019	−	0.0568146i
$861$		0			0
$862$	−16.0629	−	27.8217i	−0.547104	−	0.947612i
$863$	5.85289			0.199235			0.0996174	−	0.995026i	$-0.468238\pi$
$863$	5.85289			0.199235			0.0996174	+	0.995026i	$0.468238\pi$
$864$		0			0
$865$	−7.56782	−	13.1078i	−0.257314	−	0.445680i
$866$	4.80245			0.163194
$867$		0			0
$868$	1.29338	−	2.24019i	0.0439000	−	0.0760371i
$869$	−2.98410	+	5.16861i	−0.101229	+	0.175333i
$870$		0			0
$871$	7.39950	−	28.3409i	0.250723	−	0.960296i
$872$	26.7146			0.904672
$873$		0			0
$874$	0.110001	−	0.190527i	0.00372084	−	0.00644469i
$875$	4.84503	+	8.39184i	0.163792	+	0.283696i
$876$		0			0
$877$	−2.18367	−	3.78222i	−0.0737371	−	0.127716i	0.826799	−	0.562497i	$-0.190159\pi$
$877$	−2.18367	−	3.78222i	−0.0737371	−	0.127716i	−0.900536	+	0.434781i	$0.856826\pi$
$878$	14.4171	+	24.9712i	0.486554	+	0.842737i
$879$		0			0
$880$	−0.597315	−	1.03458i	−0.0201355	−	0.0348757i
$881$	1.57366	−	2.72567i	0.0530181	−	0.0918300i	−0.838298	−	0.545212i	$-0.816449\pi$
$881$	1.57366	−	2.72567i	0.0530181	−	0.0918300i	0.891316	+	0.453382i	$0.149783\pi$
$882$		0			0
$883$	14.9554			0.503289			0.251645	−	0.967820i	$-0.419029\pi$
$883$	14.9554			0.503289			0.251645	+	0.967820i	$0.419029\pi$
$884$	0.249469	−	0.955496i	0.00839056	−	0.0321368i
$885$		0			0
$886$	2.95756	−	5.12264i	0.0993610	−	0.172098i
$887$	11.2632	−	19.5085i	0.378182	−	0.655030i	−0.612616	−	0.790381i	$-0.709883\pi$
$887$	11.2632	−	19.5085i	0.378182	−	0.655030i	0.990798	+	0.135351i	$0.0432161\pi$
$888$		0			0
$889$	5.85772			0.196462
$890$	8.40561	+	14.5589i	0.281757	+	0.488017i
$891$		0			0
$892$	1.93676			0.0648475
$893$	5.41899	+	9.38596i	0.181339	+	0.314089i
$894$		0			0
$895$	12.1532	−	21.0500i	0.406237	−	0.703623i
$896$	−7.11319			−0.237635
$897$		0			0
$898$	−12.0040			−0.400580
$899$	−1.64762	+	2.85376i	−0.0549512	+	0.0951782i
$900$		0			0
$901$	−2.01415	−	3.48861i	−0.0671010	−	0.116222i
$902$	−1.37588			−0.0458118
$903$		0			0
$904$	−18.1847	−	31.4969i	−0.604815	−	1.04757i
$905$	−10.4084			−0.345988
$906$		0			0
$907$	9.32661	−	16.1542i	0.309685	−	0.536390i	−0.668608	−	0.743615i	$-0.733110\pi$
$907$	9.32661	−	16.1542i	0.309685	−	0.536390i	0.978293	+	0.207225i	$0.0664431\pi$
$908$	5.46395	−	9.46385i	0.181328	−	0.314069i
$909$		0			0
$910$	−4.88641	+	1.34295i	−0.161983	+	0.0445183i
$911$	−18.3278			−0.607226			−0.303613	−	0.952795i	$-0.598193\pi$
$911$	−18.3278			−0.607226			−0.303613	+	0.952795i	$0.598193\pi$
$912$		0			0
$913$	−2.07849	+	3.60005i	−0.0687880	+	0.119144i
$914$	−8.09955	−	14.0288i	−0.267909	−	0.464032i
$915$		0			0
$916$	0.128134	+	0.221934i	0.00423366	+	0.00733292i
$917$	−11.2027	−	19.4037i	−0.369947	−	0.640768i
$918$		0			0
$919$	−7.55272	−	13.0817i	−0.249141	−	0.431525i	0.714147	−	0.699996i	$-0.246815\pi$
$919$	−7.55272	−	13.0817i	−0.249141	−	0.431525i	−0.963288	+	0.268471i	$0.913482\pi$
$920$	0.125320	−	0.217061i	0.00413168	−	0.00715629i
$921$		0			0
$922$	37.8668			1.24708
$923$	24.4505	+	24.1389i	0.804797	+	0.794542i
$924$		0			0
$925$	−2.08675	+	3.61436i	−0.0686119	+	0.118839i
$926$	9.73492	−	16.8614i	0.319909	−	0.554099i
$927$		0			0
$928$	−1.01067			−0.0331770
$929$	−3.12909	−	5.41974i	−0.102662	−	0.177816i	0.810119	−	0.586266i	$-0.199403\pi$
$929$	−3.12909	−	5.41974i	−0.102662	−	0.177816i	−0.912781	+	0.408450i	$0.866069\pi$
$930$		0			0
$931$	2.30219			0.0754511
$932$	3.45182	+	5.97873i	0.113068	+	0.195840i
$933$		0			0
$934$	−16.9748	+	29.4012i	−0.555432	+	0.962036i
$935$	0.279518			0.00914121
$936$		0			0
$937$	−22.6610			−0.740301			−0.370151	−	0.928972i	$-0.620694\pi$
$937$	−22.6610			−0.740301			−0.370151	+	0.928972i	$0.620694\pi$
$938$	5.17445	−	8.96242i	0.168952	−	0.292633i
$939$		0			0
$940$	0.979605	+	1.69673i	0.0319512	+	0.0553411i
$941$	−17.2944			−0.563783			−0.281891	−	0.959446i	$-0.590962\pi$
$941$	−17.2944			−0.563783			−0.281891	+	0.959446i	$0.590962\pi$
$942$		0			0
$943$	−0.116108	−	0.201106i	−0.00378101	−	0.00654890i
$944$	−12.1805			−0.396440
$945$		0			0
$946$	1.02734	−	1.77941i	0.0334019	−	0.0578537i
$947$	−13.8061	+	23.9128i	−0.448637	+	0.777062i	−0.998298	−	0.0583263i	$-0.981424\pi$
$947$	−13.8061	+	23.9128i	−0.448637	+	0.777062i	0.549661	+	0.835388i	$0.314757\pi$
$948$		0			0
$949$	36.2746	−	9.96945i	1.17752	−	0.323622i
$950$	−11.0937			−0.359926
$951$		0			0
$952$	1.09944	−	1.90428i	0.0356330	−	0.0617181i
$953$	2.19540	+	3.80254i	0.0711160	+	0.123176i	0.899391	−	0.437146i	$-0.144011\pi$
$953$	2.19540	+	3.80254i	0.0711160	+	0.123176i	−0.828275	+	0.560322i	$0.810677\pi$
$954$		0			0
$955$	1.86305	+	3.22691i	0.0602870	+	0.104420i
$956$	1.02830	+	1.78106i	0.0332575	+	0.0576036i
$957$		0			0
$958$	−14.1476	−	24.5044i	−0.457089	−	0.791701i
$959$	−10.1044	+	17.5013i	−0.326287	+	0.565146i
$960$		0			0
$961$	16.0283			0.517042
$962$	−3.60624	−	3.56028i	−0.116270	−	0.114788i
$963$		0			0
$964$	−2.91617	+	5.05096i	−0.0939236	+	0.162680i
$965$	12.3145	−	21.3293i	0.396417	−	0.686614i
$966$		0			0
$967$	−18.4875			−0.594517			−0.297258	−	0.954797i	$-0.596072\pi$
$967$	−18.4875			−0.594517			−0.297258	+	0.954797i	$0.596072\pi$
$968$	−16.4713	−	28.5291i	−0.529408	−	0.916961i
$969$		0			0
$970$	−14.2002			−0.455941
$971$	−26.1687	−	45.3255i	−0.839794	−	1.45457i	−0.890067	−	0.455830i	$-0.849342\pi$
$971$	−26.1687	−	45.3255i	−0.839794	−	1.45457i	0.0502726	−	0.998736i	$-0.483991\pi$
$972$		0			0
$973$	2.13695	−	3.70130i	0.0685073	−	0.118658i
$974$	−1.23784			−0.0396631
$975$		0			0
$976$	−17.2165			−0.551087
$977$	25.8223	−	44.7256i	0.826130	−	1.43090i	−0.0749233	−	0.997189i	$-0.523871\pi$
$977$	25.8223	−	44.7256i	0.826130	−	1.43090i	0.901053	−	0.433709i	$-0.142795\pi$
$978$		0			0
$979$	−2.08664	−	3.61417i	−0.0666893	−	0.115509i
$980$	0.416173			0.0132941
$981$		0			0
$982$	17.1560	+	29.7151i	0.547471	+	0.948247i
$983$	−37.5419			−1.19740			−0.598701	−	0.800973i	$-0.704316\pi$
$983$	−37.5419			−1.19740			−0.598701	+	0.800973i	$0.704316\pi$
$984$		0			0
$985$	14.0404	−	24.3187i	0.447365	−	0.774860i
$986$	−0.222234	+	0.384921i	−0.00707739	+	0.0122584i
$987$		0			0
$988$	−0.790962	+	3.02948i	−0.0251639	+	0.0963805i
$989$	0.346784			0.0110271
$990$		0			0
$991$	25.2862	−	43.7969i	0.803242	−	1.39126i	−0.114230	−	0.993454i	$-0.536440\pi$
$991$	25.2862	−	43.7969i	0.803242	−	1.39126i	0.917472	−	0.397801i	$-0.130227\pi$
$992$	7.21196	+	12.4915i	0.228980	+	0.396605i
$993$		0			0
$994$	6.06968	+	10.5130i	0.192519	+	0.333452i
$995$	−12.3242	−	21.3461i	−0.390703	−	0.676718i
$996$		0			0
$997$	12.9610	+	22.4492i	0.410480	+	0.710972i	0.994942	−	0.100449i	$-0.0320278\pi$
$997$	12.9610	+	22.4492i	0.410480	+	0.710972i	−0.584462	+	0.811421i	$0.698695\pi$
$998$	13.4547	−	23.3043i	0.425902	−	0.737685i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.o.d.568.2		6
3.2	odd	2		273.2.k.d.22.2	✓	6
13.3	even	3	inner	819.2.o.d.757.2		6
39.17	odd	6		3549.2.a.s.1.2		3
39.29	odd	6		273.2.k.d.211.2	yes	6
39.35	odd	6		3549.2.a.h.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.2	✓	6	3.2	odd	2
273.2.k.d.211.2	yes	6	39.29	odd	6
819.2.o.d.568.2		6	1.1	even	1	trivial
819.2.o.d.757.2		6	13.3	even	3	inner
3549.2.a.h.1.2		3	39.35	odd	6
3549.2.a.s.1.2		3	39.17	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.o (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636945 + 1.10322i) q^{2} +(0.188601 + 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 + 0.866025i) q^{7} -3.02830 q^{8} +O(q^{10})\)	\(q+(-0.636945 + 1.10322i) q^{2} +(0.188601 + 0.326667i) q^{4} -1.10331 q^{5} +(0.500000 + 0.866025i) q^{7} -3.02830 q^{8} +(0.702750 - 1.21720i) q^{10} +(-0.174453 + 0.302162i) q^{11} +(-3.47664 + 0.955496i) q^{13} -1.27389 q^{14} +(1.55166 - 2.68755i) q^{16} +(0.363055 + 0.628829i) q^{17} +(-1.15109 - 1.99375i) q^{19} +(-0.208086 - 0.360416i) q^{20} +(-0.222234 - 0.384921i) q^{22} +(0.0375080 - 0.0649658i) q^{23} -3.78270 q^{25} +(1.16031 - 4.44410i) q^{26} +(-0.188601 + 0.326667i) q^{28} +(0.240258 - 0.416138i) q^{29} -6.85772 q^{31} +(-1.05166 - 1.82152i) q^{32} -0.924984 q^{34} +(-0.551656 - 0.955496i) q^{35} +(0.551656 - 0.955496i) q^{37} +2.93273 q^{38} +3.34116 q^{40} +(1.54778 - 2.68084i) q^{41} +(2.31140 + 4.00346i) q^{43} -0.131609 q^{44} +(0.0477811 + 0.0827593i) q^{46} -4.70769 q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.40937 - 4.17316i) q^{50} +(-0.967829 - 0.955496i) q^{52} -5.54778 q^{53} +(0.192476 - 0.333379i) q^{55} +(-1.51415 - 2.62258i) q^{56} +(0.306062 + 0.530115i) q^{58} +(-1.96249 - 3.39914i) q^{59} +(-2.77389 - 4.80452i) q^{61} +(4.36799 - 7.56558i) q^{62} +8.88601 q^{64} +(3.83582 - 1.05421i) q^{65} +(-4.06193 + 7.03547i) q^{67} +(-0.136945 + 0.237196i) q^{68} +1.40550 q^{70} +(-4.76468 - 8.25267i) q^{71} -10.4338 q^{73} +(0.702750 + 1.21720i) q^{74} +(0.434196 - 0.752049i) q^{76} -0.348907 q^{77} +17.1054 q^{79} +(-1.71196 + 2.96520i) q^{80} +(1.97170 + 3.41509i) q^{82} +11.9143 q^{83} +(-0.400563 - 0.693795i) q^{85} -5.88894 q^{86} +(0.528296 - 0.915036i) q^{88} +(-5.98052 + 10.3586i) q^{89} +(-2.56580 - 2.53311i) q^{91} +0.0282963 q^{92} +(2.99854 - 5.19362i) q^{94} +(1.27002 + 2.19973i) q^{95} +(-5.05166 - 8.74973i) q^{97} +(-0.636945 - 1.10322i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8	\( 6 q - 2 q^{2} - 4 q^{4} + 3 q^{7} + 6 q^{8} - 13 q^{10} - 8 q^{11} - 4 q^{14} + 6 q^{16} + 4 q^{17} + 7 q^{19} - 13 q^{20} - q^{22} + 9 q^{23} + 22 q^{25} + 26 q^{26} + 4 q^{28} - 7 q^{29} - 14 q^{31} - 3 q^{32} + 12 q^{34} + 8 q^{38} + 26 q^{40} + 2 q^{41} + 19 q^{43} + 30 q^{44} - 7 q^{46} + 34 q^{47} - 3 q^{49} - 16 q^{50} - 26 q^{52} - 26 q^{53} + 3 q^{56} - 22 q^{58} - 3 q^{59} - 13 q^{61} - 17 q^{62} + 2 q^{64} - 5 q^{67} + q^{68} - 26 q^{70} + 8 q^{71} - 4 q^{73} - 13 q^{74} + 18 q^{76} - 16 q^{77} - 2 q^{79} - 26 q^{80} + 36 q^{82} - 4 q^{83} - 13 q^{85} - 34 q^{86} - 21 q^{88} - 19 q^{89} - 24 q^{92} - 7 q^{94} - 27 q^{97} - 2 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 + 3 * q^7 + 6 * q^8 - 13 * q^10 - 8 * q^11 - 4 * q^14 + 6 * q^16 + 4 * q^17 + 7 * q^19 - 13 * q^20 - q^22 + 9 * q^23 + 22 * q^25 + 26 * q^26 + 4 * q^28 - 7 * q^29 - 14 * q^31 - 3 * q^32 + 12 * q^34 + 8 * q^38 + 26 * q^40 + 2 * q^41 + 19 * q^43 + 30 * q^44 - 7 * q^46 + 34 * q^47 - 3 * q^49 - 16 * q^50 - 26 * q^52 - 26 * q^53 + 3 * q^56 - 22 * q^58 - 3 * q^59 - 13 * q^61 - 17 * q^62 + 2 * q^64 - 5 * q^67 + q^68 - 26 * q^70 + 8 * q^71 - 4 * q^73 - 13 * q^74 + 18 * q^76 - 16 * q^77 - 2 * q^79 - 26 * q^80 + 36 * q^82 - 4 * q^83 - 13 * q^85 - 34 * q^86 - 21 * q^88 - 19 * q^89 - 24 * q^92 - 7 * q^94 - 27 * q^97 - 2 * q^98

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