LMFDB - Embedded newform 324.2.b.b.323.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,2,Mod(323,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, 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:	$2.58715302549$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.3
Root			$0.774115 + 1.18353i$ of defining polynomial
Character	$\chi$	$=$	324.323
Dual form			324.2.b.b.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.637910 - 1.26217i) q^{2} +(-1.18614 + 1.61030i) q^{4} -0.792287i q^{5} +2.71519i q^{7} +(2.78912 + 0.469882i) q^{8} +O(q^{10})$	\(q+(-0.637910 - 1.26217i) q^{2} +(-1.18614 + 1.61030i) q^{4} -0.792287i q^{5} +2.71519i q^{7} +(2.78912 + 0.469882i) q^{8} +(-1.00000 + 0.505408i) q^{10} +3.42703 q^{11} +3.37228 q^{13} +(3.42703 - 1.73205i) q^{14} +(-1.18614 - 3.82009i) q^{16} -2.52434i q^{17} +2.20979i q^{19} +(1.27582 + 0.939764i) q^{20} +(-2.18614 - 4.32550i) q^{22} +2.15121 q^{23} +4.37228 q^{25} +(-2.15121 - 4.25639i) q^{26} +(-4.37228 - 3.22060i) q^{28} -0.792287i q^{29} +1.70438i q^{31} +(-4.06494 + 3.93398i) q^{32} +(-3.18614 + 1.61030i) q^{34} +2.15121 q^{35} +4.74456 q^{37} +(2.78912 - 1.40965i) q^{38} +(0.372281 - 2.20979i) q^{40} -0.147477i q^{41} -6.94661i q^{43} +(-4.06494 + 5.51856i) q^{44} +(-1.37228 - 2.71519i) q^{46} -11.5569 q^{47} -0.372281 q^{49} +(-2.78912 - 5.51856i) q^{50} +(-4.00000 + 5.43039i) q^{52} +8.51278i q^{53} -2.71519i q^{55} +(-1.27582 + 7.57301i) q^{56} +(-1.00000 + 0.505408i) q^{58} -5.17782 q^{59} +3.37228 q^{61} +(2.15121 - 1.08724i) q^{62} +(7.55842 + 2.62112i) q^{64} -2.67181i q^{65} +6.94661i q^{67} +(4.06494 + 2.99422i) q^{68} +(-1.37228 - 2.71519i) q^{70} -1.75079 q^{71} -2.37228 q^{73} +(-3.02661 - 5.98844i) q^{74} +(-3.55842 - 2.62112i) q^{76} +9.30506i q^{77} +10.1672i q^{79} +(-3.02661 + 0.939764i) q^{80} +(-0.186141 + 0.0940770i) q^{82} +7.25450 q^{83} -2.00000 q^{85} +(-8.76780 + 4.43132i) q^{86} +(9.55842 + 1.61030i) q^{88} -5.34363i q^{89} +9.15640i q^{91} +(-2.55164 + 3.46410i) q^{92} +(7.37228 + 14.5868i) q^{94} +1.75079 q^{95} -12.4891 q^{97} +(0.237482 + 0.469882i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4}+O(q^{10}) $ 8 * q + 2 * q^4	$ 8 q + 2 q^{4} - 8 q^{10} + 4 q^{13} + 2 q^{16} - 6 q^{22} + 12 q^{25} - 12 q^{28} - 14 q^{34} - 8 q^{37} - 20 q^{40} + 12 q^{46} + 20 q^{49} - 32 q^{52} - 8 q^{58} + 4 q^{61} + 26 q^{64} + 12 q^{70} + 4 q^{73} + 6 q^{76} + 10 q^{82} - 16 q^{85} + 42 q^{88} + 36 q^{94} - 8 q^{97}+O(q^{100}) $ 8 * q + 2 * q^4 - 8 * q^10 + 4 * q^13 + 2 * q^16 - 6 * q^22 + 12 * q^25 - 12 * q^28 - 14 * q^34 - 8 * q^37 - 20 * q^40 + 12 * q^46 + 20 * q^49 - 32 * q^52 - 8 * q^58 + 4 * q^61 + 26 * q^64 + 12 * q^70 + 4 * q^73 + 6 * q^76 + 10 * q^82 - 16 * q^85 + 42 * q^88 + 36 * q^94 - 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.637910	−	1.26217i	−0.451071	−	0.892488i
$2$	−0.637910	−	1.26217i	−0.451071	−	0.892488i
$3$		0			0
$3$		0			0
$4$	−1.18614	+	1.61030i	−0.593070	+	0.805151i
$5$		−	0.792287i		−	0.354322i	−0.984182	−	0.177161i	$-0.943309\pi$
$5$		−	0.792287i		−	0.354322i	0.984182	−	0.177161i	$-0.0566913\pi$
$6$		0			0
$7$			2.71519i			1.02625i	0.858315	+	0.513124i	$0.171512\pi$
$7$			2.71519i			1.02625i	−0.858315	+	0.513124i	$0.828488\pi$
$8$	2.78912	+	0.469882i	0.986104	+	0.166128i
$9$		0			0
$10$	−1.00000	+	0.505408i	−0.316228	+	0.159824i
$11$	3.42703			1.03329			0.516645	−	0.856200i	$-0.327181\pi$
$11$	3.42703			1.03329			0.516645	+	0.856200i	$0.327181\pi$
$12$		0			0
$13$	3.37228			0.935303			0.467651	−	0.883913i	$-0.345100\pi$
$13$	3.37228			0.935303			0.467651	+	0.883913i	$0.345100\pi$
$14$	3.42703	−	1.73205i	0.915913	−	0.462910i
$15$		0			0
$16$	−1.18614	−	3.82009i	−0.296535	−	0.955022i
$17$		−	2.52434i		−	0.612242i	−0.951993	−	0.306121i	$-0.900969\pi$
$17$		−	2.52434i		−	0.612242i	0.951993	−	0.306121i	$-0.0990312\pi$
$18$		0			0
$19$			2.20979i			0.506960i	0.967341	+	0.253480i	$0.0815752\pi$
$19$			2.20979i			0.506960i	−0.967341	+	0.253480i	$0.918425\pi$
$20$	1.27582	+	0.939764i	0.285282	+	0.210138i
$21$		0			0
$22$	−2.18614	−	4.32550i	−0.466087	−	0.922199i
$23$	2.15121			0.448559			0.224279	−	0.974525i	$-0.427997\pi$
$23$	2.15121			0.448559			0.224279	+	0.974525i	$0.427997\pi$
$24$		0			0
$25$	4.37228			0.874456
$26$	−2.15121	−	4.25639i	−0.421888	−	0.834746i
$27$		0			0
$28$	−4.37228	−	3.22060i	−0.826284	−	0.608637i
$29$		−	0.792287i		−	0.147124i	−0.997291	−	0.0735620i	$-0.976563\pi$
$29$		−	0.792287i		−	0.147124i	0.997291	−	0.0735620i	$-0.0234367\pi$
$30$		0			0
$31$			1.70438i			0.306115i	0.988217	+	0.153058i	$0.0489120\pi$
$31$			1.70438i			0.306115i	−0.988217	+	0.153058i	$0.951088\pi$
$32$	−4.06494	+	3.93398i	−0.718587	+	0.695437i
$33$		0			0
$34$	−3.18614	+	1.61030i	−0.546419	+	0.276164i
$35$	2.15121			0.363621
$36$		0			0
$37$	4.74456			0.780001			0.390001	−	0.920815i	$-0.372475\pi$
$37$	4.74456			0.780001			0.390001	+	0.920815i	$0.372475\pi$
$38$	2.78912	−	1.40965i	0.452456	−	0.228675i
$39$		0			0
$40$	0.372281	−	2.20979i	0.0588628	−	0.349398i
$41$		−	0.147477i		−	0.0230320i	−0.999934	−	0.0115160i	$-0.996334\pi$
$41$		−	0.147477i		−	0.0230320i	0.999934	−	0.0115160i	$-0.00366574\pi$
$42$		0			0
$43$		−	6.94661i		−	1.05935i	−0.848201	−	0.529674i	$-0.822314\pi$
$43$		−	6.94661i		−	1.05935i	0.848201	−	0.529674i	$-0.177686\pi$
$44$	−4.06494	+	5.51856i	−0.612813	+	0.831954i
$45$		0			0
$46$	−1.37228	−	2.71519i	−0.202332	−	0.400334i
$47$	−11.5569			−1.68575			−0.842875	−	0.538109i	$-0.819139\pi$
$47$	−11.5569			−1.68575			−0.842875	+	0.538109i	$0.819139\pi$
$48$		0			0
$49$	−0.372281			−0.0531830
$50$	−2.78912	−	5.51856i	−0.394442	−	0.780442i
$51$		0			0
$52$	−4.00000	+	5.43039i	−0.554700	+	0.753059i
$53$			8.51278i			1.16932i	0.811278	+	0.584660i	$0.198772\pi$
$53$			8.51278i			1.16932i	−0.811278	+	0.584660i	$0.801228\pi$
$54$		0			0
$55$		−	2.71519i		−	0.366117i
$56$	−1.27582	+	7.57301i	−0.170489	+	1.01199i
$57$		0			0
$58$	−1.00000	+	0.505408i	−0.131306	+	0.0663633i
$59$	−5.17782			−0.674095			−0.337047	−	0.941488i	$-0.609428\pi$
$59$	−5.17782			−0.674095			−0.337047	+	0.941488i	$0.609428\pi$
$60$		0			0
$61$	3.37228			0.431776			0.215888	−	0.976418i	$-0.430735\pi$
$61$	3.37228			0.431776			0.215888	+	0.976418i	$0.430735\pi$
$62$	2.15121	−	1.08724i	0.273204	−	0.138080i
$63$		0			0
$64$	7.55842	+	2.62112i	0.944803	+	0.327640i
$65$		−	2.67181i		−	0.331398i
$66$		0			0
$67$			6.94661i			0.848664i	0.905507	+	0.424332i	$0.139491\pi$
$67$			6.94661i			0.848664i	−0.905507	+	0.424332i	$0.860509\pi$
$68$	4.06494	+	2.99422i	0.492947	+	0.363102i
$69$		0			0
$70$	−1.37228	−	2.71519i	−0.164019	−	0.324528i
$71$	−1.75079			−0.207780			−0.103890	−	0.994589i	$-0.533129\pi$
$71$	−1.75079			−0.207780			−0.103890	+	0.994589i	$0.533129\pi$
$72$		0			0
$73$	−2.37228			−0.277655			−0.138827	−	0.990317i	$-0.544333\pi$
$73$	−2.37228			−0.277655			−0.138827	+	0.990317i	$0.544333\pi$
$74$	−3.02661	−	5.98844i	−0.351836	−	0.696142i
$75$		0			0
$76$	−3.55842	−	2.62112i	−0.408179	−	0.300663i
$77$			9.30506i			1.06041i
$78$		0			0
$79$			10.1672i			1.14390i	0.820288	+	0.571951i	$0.193813\pi$
$79$			10.1672i			1.14390i	−0.820288	+	0.571951i	$0.806187\pi$
$80$	−3.02661	+	0.939764i	−0.338385	+	0.105069i
$81$		0			0
$82$	−0.186141	+	0.0940770i	−0.0205558	+	0.0103891i
$83$	7.25450			0.796284			0.398142	−	0.917324i	$-0.369655\pi$
$83$	7.25450			0.796284			0.398142	+	0.917324i	$0.369655\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	−8.76780	+	4.43132i	−0.945456	+	0.477841i
$87$		0			0
$88$	9.55842	+	1.61030i	1.01893	+	0.171659i
$89$		−	5.34363i		−	0.566424i	−0.959057	−	0.283212i	$-0.908600\pi$
$89$		−	5.34363i		−	0.566424i	0.959057	−	0.283212i	$-0.0913999\pi$
$90$		0			0
$91$			9.15640i			0.959852i
$92$	−2.55164	+	3.46410i	−0.266027	+	0.361158i
$93$		0			0
$94$	7.37228	+	14.5868i	0.760393	+	1.50451i
$95$	1.75079			0.179627
$96$		0			0
$97$	−12.4891			−1.26808			−0.634039	−	0.773301i	$-0.718604\pi$
$97$	−12.4891			−1.26808			−0.634039	+	0.773301i	$0.718604\pi$
$98$	0.237482	+	0.469882i	0.0239893	+	0.0474652i
$99$		0			0
$100$	−5.18614	+	7.04069i	−0.518614	+	0.704069i
$101$			17.8178i			1.77294i	0.462785	+	0.886471i	$0.346850\pi$
$101$			17.8178i			1.77294i	−0.462785	+	0.886471i	$0.653150\pi$
$102$		0			0
$103$		−	14.5868i		−	1.43728i	−0.695383	−	0.718640i	$-0.744765\pi$
$103$		−	14.5868i		−	1.43728i	0.695383	−	0.718640i	$-0.255235\pi$
$104$	9.40571	+	1.58457i	0.922306	+	0.155380i
$105$		0			0
$106$	10.7446	−	5.43039i	1.04360	−	0.527446i
$107$	−13.2332			−1.27930			−0.639650	−	0.768667i	$-0.720920\pi$
$107$	−13.2332			−1.27930			−0.639650	+	0.768667i	$0.720920\pi$
$108$		0			0
$109$	−9.48913			−0.908893			−0.454447	−	0.890774i	$-0.650163\pi$
$109$	−9.48913			−0.908893			−0.454447	+	0.890774i	$0.650163\pi$
$110$	−3.42703	+	1.73205i	−0.326755	+	0.165145i
$111$		0			0
$112$	10.3723	−	3.22060i	0.980088	−	0.304318i
$113$		−	15.9383i		−	1.49935i	−0.661806	−	0.749675i	$-0.730210\pi$
$113$		−	15.9383i		−	1.49935i	0.661806	−	0.749675i	$-0.269790\pi$
$114$		0			0
$115$		−	1.70438i		−	0.158934i
$116$	1.27582	+	0.939764i	0.118457	+	0.0872549i
$117$		0			0
$118$	3.30298	+	6.53528i	0.304064	+	0.601621i
$119$	6.85407			0.628311
$120$		0			0
$121$	0.744563			0.0676875
$122$	−2.15121	−	4.25639i	−0.194762	−	0.385355i
$123$		0			0
$124$	−2.74456	−	2.02163i	−0.246469	−	0.181548i
$125$		−	7.42554i		−	0.664160i
$126$		0			0
$127$		−	16.2912i		−	1.44561i	−0.691053	−	0.722804i	$-0.742853\pi$
$127$		−	16.2912i		−	1.44561i	0.691053	−	0.722804i	$-0.257147\pi$
$128$	−1.51330	−	11.2120i	−0.133758	−	0.991014i
$129$		0			0
$130$	−3.37228	+	1.70438i	−0.295769	+	0.149484i
$131$	−7.25450			−0.633828			−0.316914	−	0.948454i	$-0.602647\pi$
$131$	−7.25450			−0.633828			−0.316914	+	0.948454i	$0.602647\pi$
$132$		0			0
$133$	−6.00000			−0.520266
$134$	8.76780	−	4.43132i	0.757423	−	0.382807i
$135$		0			0
$136$	1.18614	−	7.04069i	0.101711	−	0.603734i
$137$		−	18.7576i		−	1.60257i	−0.598283	−	0.801285i	$-0.704150\pi$
$137$		−	18.7576i		−	1.60257i	0.598283	−	0.801285i	$-0.295850\pi$
$138$		0			0
$139$		−	9.34455i		−	0.792595i	−0.918122	−	0.396297i	$-0.870295\pi$
$139$		−	9.34455i		−	0.792595i	0.918122	−	0.396297i	$-0.129705\pi$
$140$	−2.55164	+	3.46410i	−0.215653	+	0.292770i
$141$		0			0
$142$	1.11684	+	2.20979i	0.0937235	+	0.185441i
$143$	11.5569			0.966438
$144$		0			0
$145$	−0.627719			−0.0521292
$146$	1.51330	+	2.99422i	0.125242	+	0.247803i
$147$		0			0
$148$	−5.62772	+	7.64018i	−0.462596	+	0.628019i
$149$			9.60002i			0.786464i	0.919439	+	0.393232i	$0.128643\pi$
$149$			9.60002i			0.786464i	−0.919439	+	0.393232i	$0.871357\pi$
$150$		0			0
$151$		−	9.15640i		−	0.745137i	−0.928005	−	0.372569i	$-0.878477\pi$
$151$		−	9.15640i		−	0.745137i	0.928005	−	0.372569i	$-0.121523\pi$
$152$	−1.03834	+	6.16337i	−0.0842204	+	0.499915i
$153$		0			0
$154$	11.7446	−	5.93580i	0.946404	−	0.478320i
$155$	1.35036			0.108463
$156$		0			0
$157$	−16.8614			−1.34569			−0.672843	−	0.739785i	$-0.734927\pi$
$157$	−16.8614			−1.34569			−0.672843	+	0.739785i	$0.734927\pi$
$158$	12.8327	−	6.48577i	1.02092	−	0.515980i
$159$		0			0
$160$	3.11684	+	3.22060i	0.246408	+	0.254611i
$161$			5.84096i			0.460332i
$162$		0			0
$163$		−	11.8716i		−	0.929855i	−0.885349	−	0.464928i	$-0.846080\pi$
$163$		−	11.8716i		−	0.929855i	0.885349	−	0.464928i	$-0.153920\pi$
$164$	0.237482	+	0.174928i	0.0185442	+	0.0136596i
$165$		0			0
$166$	−4.62772	−	9.15640i	−0.359181	−	0.710674i
$167$	19.2118			1.48666			0.743329	−	0.668926i	$-0.233246\pi$
$167$	19.2118			1.48666			0.743329	+	0.668926i	$0.233246\pi$
$168$		0			0
$169$	−1.62772			−0.125209
$170$	1.27582	+	2.52434i	0.0978510	+	0.193608i
$171$		0			0
$172$	11.1861	+	8.23966i	0.852935	+	0.628268i
$173$		−	5.54601i		−	0.421655i	−0.977523	−	0.210828i	$-0.932384\pi$
$173$		−	5.54601i		−	0.421655i	0.977523	−	0.210828i	$-0.0676159\pi$
$174$		0			0
$175$			11.8716i			0.897408i
$176$	−4.06494	−	13.0916i	−0.306407	−	0.986814i
$177$		0			0
$178$	−6.74456	+	3.40876i	−0.505526	+	0.255497i
$179$	18.8114			1.40603			0.703016	−	0.711174i	$-0.251836\pi$
$179$	18.8114			1.40603			0.703016	+	0.711174i	$0.251836\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	11.5569	−	5.84096i	0.856656	−	0.432961i
$183$		0			0
$184$	6.00000	+	1.01082i	0.442326	+	0.0745184i
$185$		−	3.75906i		−	0.276371i
$186$		0			0
$187$		−	8.65099i		−	0.632623i
$188$	13.7081	−	18.6101i	0.999769	−	1.35728i
$189$		0			0
$190$	−1.11684	−	2.20979i	−0.0810244	−	0.160315i
$191$	−3.90200			−0.282339			−0.141169	−	0.989985i	$-0.545086\pi$
$191$	−3.90200			−0.282339			−0.141169	+	0.989985i	$0.545086\pi$
$192$		0			0
$193$	−3.74456			−0.269540			−0.134770	−	0.990877i	$-0.543029\pi$
$193$	−3.74456			−0.269540			−0.134770	+	0.990877i	$0.543029\pi$
$194$	7.96694	+	15.7634i	0.571993	+	1.13175i
$195$		0			0
$196$	0.441578	−	0.599485i	0.0315413	−	0.0428204i
$197$			10.6873i			0.761436i	0.924691	+	0.380718i	$0.124323\pi$
$197$			10.6873i			0.761436i	−0.924691	+	0.380718i	$0.875677\pi$
$198$		0			0
$199$			19.3236i			1.36981i	0.728630	+	0.684907i	$0.240157\pi$
$199$			19.3236i			1.36981i	−0.728630	+	0.684907i	$0.759843\pi$
$200$	12.1948	+	2.05446i	0.862305	+	0.145272i
$201$		0			0
$202$	22.4891	−	11.3662i	1.58233	−	0.799722i
$203$	2.15121			0.150986
$204$		0			0
$205$	−0.116844			−0.00816074
$206$	−18.4110	+	9.30506i	−1.28275	+	0.648315i
$207$		0			0
$208$	−4.00000	−	12.8824i	−0.277350	−	0.893234i
$209$			7.57301i			0.523836i
$210$		0			0
$211$			6.12395i			0.421590i	0.977530	+	0.210795i	$0.0676053\pi$
$211$			6.12395i			0.421590i	−0.977530	+	0.210795i	$0.932395\pi$
$212$	−13.7081	−	10.0974i	−0.941479	−	0.693489i
$213$		0			0
$214$	8.44158	+	16.7025i	0.577054	+	1.14176i
$215$	−5.50371			−0.375350
$216$		0			0
$217$	−4.62772			−0.314150
$218$	6.05321	+	11.9769i	0.409975	+	0.811177i
$219$		0			0
$220$	4.37228	+	3.22060i	0.294779	+	0.217133i
$221$		−	8.51278i		−	0.572631i
$222$		0			0
$223$		−	1.70438i		−	0.114134i	−0.998370	−	0.0570668i	$-0.981825\pi$
$223$		−	1.70438i		−	0.114134i	0.998370	−	0.0570668i	$-0.0181748\pi$
$224$	−10.6815	−	11.0371i	−0.713690	−	0.737448i
$225$		0			0
$226$	−20.1168	+	10.1672i	−1.33815	+	0.676313i
$227$	−18.8860			−1.25350			−0.626752	−	0.779218i	$-0.715616\pi$
$227$	−18.8860			−1.25350			−0.626752	+	0.779218i	$0.715616\pi$
$228$		0			0
$229$	9.37228			0.619338			0.309669	−	0.950844i	$-0.399782\pi$
$229$	9.37228			0.619338			0.309669	+	0.950844i	$0.399782\pi$
$230$	−2.15121	+	1.08724i	−0.141847	+	0.0716905i
$231$		0			0
$232$	0.372281	−	2.20979i	0.0244415	−	0.145080i
$233$		−	28.0627i		−	1.83845i	−0.393737	−	0.919223i	$-0.628818\pi$
$233$		−	28.0627i		−	1.83845i	0.393737	−	0.919223i	$-0.371182\pi$
$234$		0			0
$235$			9.15640i			0.597298i
$236$	6.14162	−	8.33785i	0.399786	−	0.542748i
$237$		0			0
$238$	−4.37228	−	8.65099i	−0.283413	−	0.560761i
$239$	−16.6602			−1.07766			−0.538830	−	0.842415i	$-0.681133\pi$
$239$	−16.6602			−1.07766			−0.538830	+	0.842415i	$0.681133\pi$
$240$		0			0
$241$	16.4891			1.06216			0.531079	−	0.847322i	$-0.321787\pi$
$241$	16.4891			1.06216			0.531079	+	0.847322i	$0.321787\pi$
$242$	−0.474964	−	0.939764i	−0.0305319	−	0.0604103i
$243$		0			0
$244$	−4.00000	+	5.43039i	−0.256074	+	0.347645i
$245$			0.294954i			0.0188439i
$246$		0			0
$247$			7.45202i			0.474161i
$248$	−0.800857	+	4.75372i	−0.0508544	+	0.301862i
$249$		0			0
$250$	−9.37228	+	4.73683i	−0.592755	+	0.299583i
$251$	−16.7347			−1.05629			−0.528144	−	0.849155i	$-0.677112\pi$
$251$	−16.7347			−1.05629			−0.528144	+	0.849155i	$0.677112\pi$
$252$		0			0
$253$	7.37228			0.463491
$254$	−20.5622	+	10.3923i	−1.29019	+	0.652071i
$255$		0			0
$256$	−13.1861	+	9.06232i	−0.824134	+	0.566395i
$257$			11.5344i			0.719499i	0.933049	+	0.359750i	$0.117138\pi$
$257$			11.5344i			0.719499i	−0.933049	+	0.359750i	$0.882862\pi$
$258$		0			0
$259$			12.8824i			0.800474i
$260$	4.30243	+	3.16915i	0.266825	+	0.196542i
$261$		0			0
$262$	4.62772	+	9.15640i	0.285901	+	0.565684i
$263$	12.5069			0.771206			0.385603	−	0.922665i	$-0.373994\pi$
$263$	12.5069			0.771206			0.385603	+	0.922665i	$0.373994\pi$
$264$		0			0
$265$	6.74456			0.414315
$266$	3.82746	+	7.57301i	0.234677	+	0.464331i
$267$		0			0
$268$	−11.1861	−	8.23966i	−0.683302	−	0.503317i
$269$			24.9484i			1.52113i	0.649260	+	0.760566i	$0.275079\pi$
$269$			24.9484i			1.52113i	−0.649260	+	0.760566i	$0.724921\pi$
$270$		0			0
$271$			1.38712i			0.0842618i	0.999112	+	0.0421309i	$0.0134147\pi$
$271$			1.38712i			0.0842618i	−0.999112	+	0.0421309i	$0.986585\pi$
$272$	−9.64319	+	2.99422i	−0.584704	+	0.181551i
$273$		0			0
$274$	−23.6753	+	11.9657i	−1.43028	+	0.722873i
$275$	14.9840			0.903567
$276$		0			0
$277$	0.627719			0.0377160			0.0188580	−	0.999822i	$-0.493997\pi$
$277$	0.627719			0.0377160			0.0188580	+	0.999822i	$0.493997\pi$
$278$	−11.7944	+	5.96099i	−0.707381	+	0.357516i
$279$		0			0
$280$	6.00000	+	1.01082i	0.358569	+	0.0604078i
$281$		−	6.43087i		−	0.383634i	−0.981431	−	0.191817i	$-0.938562\pi$
$281$		−	6.43087i		−	0.383634i	0.981431	−	0.191817i	$-0.0614379\pi$
$282$		0			0
$283$		−	10.1672i		−	0.604378i	−0.953248	−	0.302189i	$-0.902283\pi$
$283$		−	10.1672i		−	0.604378i	0.953248	−	0.302189i	$-0.0977174\pi$
$284$	2.07668	−	2.81929i	0.123228	−	0.167294i
$285$		0			0
$286$	−7.37228	−	14.5868i	−0.435932	−	0.862535i
$287$	0.400428			0.0236365
$288$		0			0
$289$	10.6277			0.625160
$290$	0.400428	+	0.792287i	0.0235140	+	0.0465247i
$291$		0			0
$292$	2.81386	−	3.82009i	0.164669	−	0.223554i
$293$			19.9923i			1.16796i	0.811767	+	0.583982i	$0.198506\pi$
$293$			19.9923i			1.16796i	−0.811767	+	0.583982i	$0.801494\pi$
$294$		0			0
$295$			4.10232i			0.238846i
$296$	13.2332	+	2.22938i	0.769163	+	0.129580i
$297$		0			0
$298$	12.1168	−	6.12395i	0.701910	−	0.354751i
$299$	7.25450			0.419538
$300$		0			0
$301$	18.8614			1.08715
$302$	−11.5569	+	5.84096i	−0.665026	+	0.336110i
$303$		0			0
$304$	8.44158	−	2.62112i	0.484158	−	0.150331i
$305$		−	2.67181i		−	0.152988i
$306$		0			0
$307$		−	25.9530i		−	1.48121i	−0.671938	−	0.740607i	$-0.734538\pi$
$307$		−	25.9530i		−	1.48121i	0.671938	−	0.740607i	$-0.265462\pi$
$308$	−14.9840	−	11.0371i	−0.853790	−	0.628898i
$309$		0			0
$310$	−0.861407	−	1.70438i	−0.0489246	−	0.0968022i
$311$	−31.3183			−1.77590			−0.887948	−	0.459944i	$-0.847870\pi$
$311$	−31.3183			−1.77590			−0.887948	+	0.459944i	$0.847870\pi$
$312$		0			0
$313$	4.48913			0.253740			0.126870	−	0.991919i	$-0.459507\pi$
$313$	4.48913			0.253740			0.126870	+	0.991919i	$0.459507\pi$
$314$	10.7561	+	21.2819i	0.607000	+	1.20101i
$315$		0			0
$316$	−16.3723	−	12.0597i	−0.921013	−	0.678414i
$317$			23.8612i			1.34018i	0.742281	+	0.670089i	$0.233744\pi$
$317$			23.8612i			1.34018i	−0.742281	+	0.670089i	$0.766256\pi$
$318$		0			0
$319$		−	2.71519i		−	0.152022i
$320$	2.07668	−	5.98844i	0.116090	−	0.334764i
$321$		0			0
$322$	7.37228	−	3.72601i	0.410841	−	0.207642i
$323$	5.57825			0.310382
$324$		0			0
$325$	14.7446			0.817881
$326$	−14.9840	+	7.57301i	−0.829885	+	0.419430i
$327$		0			0
$328$	0.0692967	−	0.411331i	0.00382627	−	0.0227120i
$329$		−	31.3793i		−	1.73000i
$330$		0			0
$331$			27.8455i			1.53053i	0.643717	+	0.765264i	$0.277391\pi$
$331$			27.8455i			1.53053i	−0.643717	+	0.765264i	$0.722609\pi$
$332$	−8.60485	+	11.6819i	−0.472253	+	0.641129i
$333$		0			0
$334$	−12.2554	−	24.2486i	−0.670588	−	1.32682i
$335$	5.50371			0.300700
$336$		0			0
$337$	−4.25544			−0.231808			−0.115904	−	0.993260i	$-0.536977\pi$
$337$	−4.25544			−0.231808			−0.115904	+	0.993260i	$0.536977\pi$
$338$	1.03834	+	2.05446i	0.0564782	+	0.111748i
$339$		0			0
$340$	2.37228	−	3.22060i	0.128655	−	0.174662i
$341$			5.84096i			0.316306i
$342$		0			0
$343$			17.9955i			0.971668i
$344$	3.26409	−	19.3750i	0.175988	−	1.04463i
$345$		0			0
$346$	−7.00000	+	3.53786i	−0.376322	+	0.190196i
$347$	7.72946			0.414939			0.207470	−	0.978241i	$-0.433477\pi$
$347$	7.72946			0.414939			0.207470	+	0.978241i	$0.433477\pi$
$348$		0			0
$349$	−11.3723			−0.608744			−0.304372	−	0.952553i	$-0.598447\pi$
$349$	−11.3723			−0.608744			−0.304372	+	0.952553i	$0.598447\pi$
$350$	14.9840	−	7.57301i	0.800926	−	0.404795i
$351$		0			0
$352$	−13.9307	+	13.4819i	−0.742509	+	0.718587i
$353$		−	4.90120i		−	0.260864i	−0.991457	−	0.130432i	$-0.958363\pi$
$353$		−	4.90120i		−	0.260864i	0.991457	−	0.130432i	$-0.0416365\pi$
$354$		0			0
$355$			1.38712i			0.0736209i
$356$	8.60485	+	6.33830i	0.456056	+	0.335929i
$357$		0			0
$358$	−12.0000	−	23.7432i	−0.634220	−	1.25487i
$359$	−29.9679			−1.58165			−0.790823	−	0.612045i	$-0.790347\pi$
$359$	−29.9679			−1.58165			−0.790823	+	0.612045i	$0.790347\pi$
$360$		0			0
$361$	14.1168			0.742992
$362$	2.55164	+	5.04868i	0.134111	+	0.265352i
$363$		0			0
$364$	−14.7446	−	10.8608i	−0.772825	−	0.569259i
$365$			1.87953i			0.0983790i
$366$		0			0
$367$		−	13.5760i		−	0.708660i	−0.935120	−	0.354330i	$-0.884709\pi$
$367$		−	13.5760i		−	0.708660i	0.935120	−	0.354330i	$-0.115291\pi$
$368$	−2.55164	−	8.21782i	−0.133014	−	0.428384i
$369$		0			0
$370$	−4.74456	+	2.39794i	−0.246658	+	0.124663i
$371$	−23.1138			−1.20001
$372$		0			0
$373$	8.86141			0.458826			0.229413	−	0.973329i	$-0.426319\pi$
$373$	8.86141			0.458826			0.229413	+	0.973329i	$0.426319\pi$
$374$	−10.9190	+	5.51856i	−0.564609	+	0.285358i
$375$		0			0
$376$	−32.2337	−	5.43039i	−1.66233	−	0.280051i
$377$		−	2.67181i		−	0.137605i
$378$		0			0
$379$			9.66181i			0.496294i	0.968722	+	0.248147i	$0.0798216\pi$
$379$			9.66181i			0.496294i	−0.968722	+	0.248147i	$0.920178\pi$
$380$	−2.07668	+	2.81929i	−0.106531	+	0.144627i
$381$		0			0
$382$	2.48913	+	4.92498i	0.127355	+	0.251984i
$383$	0.400428			0.0204609			0.0102305	−	0.999948i	$-0.496743\pi$
$383$	0.400428			0.0204609			0.0102305	+	0.999948i	$0.496743\pi$
$384$		0			0
$385$	7.37228			0.375726
$386$	2.38870	+	4.72627i	0.121581	+	0.240561i
$387$		0			0
$388$	14.8139	−	20.1113i	0.752060	−	1.02099i
$389$			8.31040i			0.421354i	0.977556	+	0.210677i	$0.0675668\pi$
$389$			8.31040i			0.421354i	−0.977556	+	0.210677i	$0.932433\pi$
$390$		0			0
$391$		−	5.43039i		−	0.274627i
$392$	−1.03834	−	0.174928i	−0.0524440	−	0.00883521i
$393$		0			0
$394$	13.4891	−	6.81751i	0.679572	−	0.343461i
$395$	8.05535			0.405309
$396$		0			0
$397$	−7.25544			−0.364140			−0.182070	−	0.983286i	$-0.558280\pi$
$397$	−7.25544			−0.364140			−0.182070	+	0.983286i	$0.558280\pi$
$398$	24.3897	−	12.3267i	1.22254	−	0.617883i
$399$		0			0
$400$	−5.18614	−	16.7025i	−0.259307	−	0.835125i
$401$			21.9268i			1.09497i	0.836816	+	0.547485i	$0.184415\pi$
$401$			21.9268i			1.09497i	−0.836816	+	0.547485i	$0.815585\pi$
$402$		0			0
$403$			5.74764i			0.286310i
$404$	−28.6921	−	21.1345i	−1.42749	−	1.05148i
$405$		0			0
$406$	−1.37228	−	2.71519i	−0.0681052	−	0.134753i
$407$	16.2598			0.805967
$408$		0			0
$409$	2.25544			0.111524			0.0557621	−	0.998444i	$-0.482241\pi$
$409$	2.25544			0.111524			0.0557621	+	0.998444i	$0.482241\pi$
$410$	0.0745360	+	0.147477i	0.00368107	+	0.00728336i
$411$		0			0
$412$	23.4891	+	17.3020i	1.15723	+	0.852408i
$413$		−	14.0588i		−	0.691788i
$414$		0			0
$415$		−	5.74764i		−	0.282141i
$416$	−13.7081	+	13.2665i	−0.672097	+	0.650444i
$417$		0			0
$418$	9.55842	−	4.83090i	0.467518	−	0.236287i
$419$	5.65278			0.276157			0.138078	−	0.990421i	$-0.455907\pi$
$419$	5.65278			0.276157			0.138078	+	0.990421i	$0.455907\pi$
$420$		0			0
$421$	29.6060			1.44291			0.721453	−	0.692463i	$-0.243474\pi$
$421$	29.6060			1.44291			0.721453	+	0.692463i	$0.243474\pi$
$422$	7.72946	−	3.90653i	0.376264	−	0.190167i
$423$		0			0
$424$	−4.00000	+	23.7432i	−0.194257	+	1.15307i
$425$		−	11.0371i		−	0.535379i
$426$		0			0
$427$			9.15640i			0.443109i
$428$	15.6964	−	21.3094i	0.758714	−	1.03003i
$429$		0			0
$430$	3.51087	+	6.94661i	0.169309	+	0.334995i
$431$	14.6581			0.706054			0.353027	−	0.935613i	$-0.385152\pi$
$431$	14.6581			0.706054			0.353027	+	0.935613i	$0.385152\pi$
$432$		0			0
$433$	−14.3723			−0.690688			−0.345344	−	0.938476i	$-0.612238\pi$
$433$	−14.3723			−0.690688			−0.345344	+	0.938476i	$0.612238\pi$
$434$	2.95207	+	5.84096i	0.141704	+	0.280375i
$435$		0			0
$436$	11.2554	−	15.2804i	0.539038	−	0.731796i
$437$			4.75372i			0.227401i
$438$		0			0
$439$		−	32.8996i		−	1.57021i	−0.619362	−	0.785106i	$-0.712609\pi$
$439$		−	32.8996i		−	1.57021i	0.619362	−	0.785106i	$-0.287391\pi$
$440$	1.27582	−	7.57301i	0.0608224	−	0.361029i
$441$		0			0
$442$	−10.7446	+	5.43039i	−0.511067	+	0.258297i
$443$	5.17782			0.246006			0.123003	−	0.992406i	$-0.460748\pi$
$443$	5.17782			0.246006			0.123003	+	0.992406i	$0.460748\pi$
$444$		0			0
$445$	−4.23369			−0.200696
$446$	−2.15121	+	1.08724i	−0.101863	+	0.0514823i
$447$		0			0
$448$	−7.11684	+	20.5226i	−0.336239	+	0.969601i
$449$		−	3.81396i		−	0.179992i	−0.995942	−	0.0899959i	$-0.971315\pi$
$449$		−	3.81396i		−	0.179992i	0.995942	−	0.0899959i	$-0.0286854\pi$
$450$		0			0
$451$		−	0.505408i		−	0.0237987i
$452$	25.6655	+	18.9051i	1.20720	+	0.889220i
$453$		0			0
$454$	12.0475	+	23.8373i	0.565419	+	1.11874i
$455$	7.25450			0.340096
$456$		0			0
$457$	−5.97825			−0.279651			−0.139825	−	0.990176i	$-0.544654\pi$
$457$	−5.97825			−0.279651			−0.139825	+	0.990176i	$0.544654\pi$
$458$	−5.97868	−	11.8294i	−0.279365	−	0.552752i
$459$		0			0
$460$	2.74456	+	2.02163i	0.127966	+	0.0942591i
$461$		−	22.8665i		−	1.06500i	−0.846430	−	0.532500i	$-0.821253\pi$
$461$		−	22.8665i		−	1.06500i	0.846430	−	0.532500i	$-0.178747\pi$
$462$		0			0
$463$			21.0280i			0.977254i	0.872493	+	0.488627i	$0.162502\pi$
$463$			21.0280i			0.977254i	−0.872493	+	0.488627i	$0.837498\pi$
$464$	−3.02661	+	0.939764i	−0.140507	+	0.0436274i
$465$		0			0
$466$	−35.4198	+	17.9015i	−1.64079	+	0.829270i
$467$	24.3897			1.12862			0.564310	−	0.825563i	$-0.309142\pi$
$467$	24.3897			1.12862			0.564310	+	0.825563i	$0.309142\pi$
$468$		0			0
$469$	−18.8614			−0.870939
$470$	11.5569	−	5.84096i	0.533081	−	0.269424i
$471$		0			0
$472$	−14.4416	−	2.43296i	−0.664728	−	0.111986i
$473$		−	23.8063i		−	1.09461i
$474$		0			0
$475$			9.66181i			0.443314i
$476$	−8.12989	+	11.0371i	−0.372633	+	0.505885i
$477$		0			0
$478$	10.6277	+	21.0280i	0.486101	+	0.961798i
$479$	−9.80614			−0.448054			−0.224027	−	0.974583i	$-0.571920\pi$
$479$	−9.80614			−0.448054			−0.224027	+	0.974583i	$0.571920\pi$
$480$		0			0
$481$	16.0000			0.729537
$482$	−10.5186	−	20.8121i	−0.479108	−	0.947963i
$483$		0			0
$484$	−0.883156	+	1.19897i	−0.0401435	+	0.0544986i
$485$			9.89497i			0.449308i
$486$		0			0
$487$			17.9365i			0.812780i	0.913700	+	0.406390i	$0.133213\pi$
$487$			17.9365i			0.812780i	−0.913700	+	0.406390i	$0.866787\pi$
$488$	9.40571	+	1.58457i	0.425776	+	0.0717303i
$489$		0			0
$490$	0.372281	−	0.188154i	0.0168180	−	0.00849993i
$491$	24.7901			1.11876			0.559381	−	0.828911i	$-0.311039\pi$
$491$	24.7901			1.11876			0.559381	+	0.828911i	$0.311039\pi$
$492$		0			0
$493$	−2.00000			−0.0900755
$494$	9.40571	−	4.75372i	0.423183	−	0.213880i
$495$		0			0
$496$	6.51087	−	2.02163i	0.292347	−	0.0907740i
$497$		−	4.75372i		−	0.213234i
$498$		0			0
$499$		−	0.505408i		−	0.0226252i	−0.999936	−	0.0113126i	$-0.996399\pi$
$499$		−	0.505408i		−	0.0226252i	0.999936	−	0.0113126i	$-0.00360099\pi$
$500$	11.9574	+	8.80773i	0.534749	+	0.393894i
$501$		0			0
$502$	10.6753	+	21.1221i	0.476460	+	0.942724i
$503$	12.9073			0.575507			0.287754	−	0.957704i	$-0.407092\pi$
$503$	12.9073			0.575507			0.287754	+	0.957704i	$0.407092\pi$
$504$		0			0
$505$	14.1168			0.628191
$506$	−4.70285	−	9.30506i	−0.209067	−	0.413661i
$507$		0			0
$508$	26.2337	+	19.3236i	1.16393	+	0.857347i
$509$		−	18.1128i		−	0.802836i	−0.915895	−	0.401418i	$-0.868518\pi$
$509$		−	18.1128i		−	0.802836i	0.915895	−	0.401418i	$-0.131482\pi$
$510$		0			0
$511$		−	6.44121i		−	0.284942i
$512$	19.8498	+	10.8622i	0.877244	+	0.480045i
$513$		0			0
$514$	14.5584	−	7.35794i	0.642144	−	0.324545i
$515$	−11.5569			−0.509259
$516$		0			0
$517$	−39.6060			−1.74187
$518$	16.2598	−	8.21782i	0.714414	−	0.361070i
$519$		0			0
$520$	1.25544	−	7.45202i	0.0550546	−	0.326793i
$521$			10.4472i			0.457700i	0.973462	+	0.228850i	$0.0734966\pi$
$521$			10.4472i			0.457700i	−0.973462	+	0.228850i	$0.926503\pi$
$522$		0			0
$523$		−	4.41957i		−	0.193254i	−0.995321	−	0.0966272i	$-0.969195\pi$
$523$		−	4.41957i		−	0.193254i	0.995321	−	0.0966272i	$-0.0308055\pi$
$524$	8.60485	−	11.6819i	0.375905	−	0.510327i
$525$		0			0
$526$	−7.97825	−	15.7858i	−0.347868	−	0.688292i
$527$	4.30243			0.187417
$528$		0			0
$529$	−18.3723			−0.798795
$530$	−4.30243	−	8.51278i	−0.186885	−	0.369771i
$531$		0			0
$532$	7.11684	−	9.66181i	0.308554	−	0.418892i
$533$		−	0.497333i		−	0.0215419i
$534$		0			0
$535$			10.4845i			0.453283i
$536$	−3.26409	+	19.3750i	−0.140987	+	0.836871i
$537$		0			0
$538$	31.4891	−	15.9149i	1.35759	−	0.686138i
$539$	−1.27582			−0.0549535
$540$		0			0
$541$	36.9783			1.58982			0.794910	−	0.606728i	$-0.207518\pi$
$541$	36.9783			1.58982			0.794910	+	0.606728i	$0.207518\pi$
$542$	1.75079	−	0.884861i	0.0752027	−	0.0380080i
$543$		0			0
$544$	9.93070	+	10.2613i	0.425775	+	0.439949i
$545$			7.51811i			0.322040i
$546$		0			0
$547$		−	8.33374i		−	0.356325i	−0.984001	−	0.178162i	$-0.942985\pi$
$547$		−	8.33374i		−	0.356325i	0.984001	−	0.178162i	$-0.0570153\pi$
$548$	30.2054	+	22.2492i	1.29031	+	0.950437i
$549$		0			0
$550$	−9.55842	−	18.9123i	−0.407572	−	0.806423i
$551$	1.75079			0.0745860
$552$		0			0
$553$	−27.6060			−1.17393
$554$	−0.400428	−	0.792287i	−0.0170126	−	0.0336610i
$555$		0			0
$556$	15.0475	+	11.0840i	0.638158	+	0.470064i
$557$		−	20.4897i		−	0.868175i	−0.900871	−	0.434087i	$-0.857071\pi$
$557$		−	20.4897i		−	0.868175i	0.900871	−	0.434087i	$-0.142929\pi$
$558$		0			0
$559$		−	23.4259i		−	0.990811i
$560$	−2.55164	−	8.21782i	−0.107827	−	0.347266i
$561$		0			0
$562$	−8.11684	+	4.10232i	−0.342388	+	0.173046i
$563$	−11.0820			−0.467049			−0.233524	−	0.972351i	$-0.575026\pi$
$563$	−11.0820			−0.467049			−0.233524	+	0.972351i	$0.575026\pi$
$564$		0			0
$565$	−12.6277			−0.531252
$566$	−12.8327	+	6.48577i	−0.539400	+	0.272617i
$567$		0			0
$568$	−4.88316	−	0.822662i	−0.204893	−	0.0345181i
$569$			1.14214i			0.0478811i	0.999713	+	0.0239406i	$0.00762125\pi$
$569$			1.14214i			0.0478811i	−0.999713	+	0.0239406i	$0.992379\pi$
$570$		0			0
$571$		−	16.7966i		−	0.702915i	−0.936204	−	0.351457i	$-0.885686\pi$
$571$		−	16.7966i		−	0.702915i	0.936204	−	0.351457i	$-0.114314\pi$
$572$	−13.7081	+	18.6101i	−0.573166	+	0.778129i
$573$		0			0
$574$	−0.255437	−	0.505408i	−0.0106617	−	0.0210953i
$575$	9.40571			0.392245
$576$		0			0
$577$	−42.8397			−1.78344			−0.891719	−	0.452589i	$-0.850500\pi$
$577$	−42.8397			−1.78344			−0.891719	+	0.452589i	$0.850500\pi$
$578$	−6.77953	−	13.4140i	−0.281991	−	0.557948i
$579$		0			0
$580$	0.744563	−	1.01082i	0.0309163	−	0.0419719i
$581$			19.6974i			0.817185i
$582$		0			0
$583$			29.1736i			1.20825i
$584$	−6.61659	−	1.11469i	−0.273796	−	0.0461263i
$585$		0			0
$586$	25.2337	−	12.7533i	1.04239	−	0.526834i
$587$	12.8327			0.529664			0.264832	−	0.964295i	$-0.414683\pi$
$587$	12.8327			0.529664			0.264832	+	0.964295i	$0.414683\pi$
$588$		0			0
$589$	−3.76631			−0.155188
$590$	5.17782	−	2.61691i	0.213167	−	0.107737i
$591$		0			0
$592$	−5.62772	−	18.1246i	−0.231298	−	0.744918i
$593$			15.4410i			0.634085i	0.948411	+	0.317043i	$0.102690\pi$
$593$			15.4410i			0.634085i	−0.948411	+	0.317043i	$0.897310\pi$
$594$		0			0
$595$		−	5.43039i		−	0.222624i
$596$	−15.4589	−	11.3870i	−0.633222	−	0.466429i
$597$		0			0
$598$	−4.62772	−	9.15640i	−0.189241	−	0.374433i
$599$	−18.4110			−0.752253			−0.376126	−	0.926568i	$-0.622744\pi$
$599$	−18.4110			−0.752253			−0.376126	+	0.926568i	$0.622744\pi$
$600$		0			0
$601$	−29.9783			−1.22284			−0.611419	−	0.791307i	$-0.709401\pi$
$601$	−29.9783			−1.22284			−0.611419	+	0.791307i	$0.709401\pi$
$602$	−12.0319	−	23.8063i	−0.490383	−	0.970272i
$603$		0			0
$604$	14.7446	+	10.8608i	0.599948	+	0.441919i
$605$		−	0.589907i		−	0.0239831i
$606$		0			0
$607$		−	38.3300i		−	1.55577i	−0.628409	−	0.777883i	$-0.716294\pi$
$607$		−	38.3300i		−	1.55577i	0.628409	−	0.777883i	$-0.283706\pi$
$608$	−8.69326	−	8.98266i	−0.352558	−	0.364295i
$609$		0			0
$610$	−3.37228	+	1.70438i	−0.136540	+	0.0690083i
$611$	−38.9732			−1.57669
$612$		0			0
$613$	−30.2337			−1.22113			−0.610564	−	0.791967i	$-0.709057\pi$
$613$	−30.2337			−1.22113			−0.610564	+	0.791967i	$0.709057\pi$
$614$	−32.7570	+	16.5557i	−1.32197	+	0.668133i
$615$		0			0
$616$	−4.37228	+	25.9530i	−0.176164	+	1.04568i
$617$		−	8.36530i		−	0.336774i	−0.985721	−	0.168387i	$-0.946144\pi$
$617$		−	8.36530i		−	0.336774i	0.985721	−	0.168387i	$-0.0538559\pi$
$618$		0			0
$619$		−	27.6574i		−	1.11164i	−0.831302	−	0.555821i	$-0.812404\pi$
$619$		−	27.6574i		−	1.11164i	0.831302	−	0.555821i	$-0.187596\pi$
$620$	−1.60171	+	2.17448i	−0.0643263	+	0.0873293i
$621$		0			0
$622$	19.9783	+	39.5289i	0.801055	+	1.58497i
$623$	14.5090			0.581291
$624$		0			0
$625$	15.9783			0.639130
$626$	−2.86366	−	5.66603i	−0.114455	−	0.226460i
$627$		0			0
$628$	20.0000	−	27.1519i	0.798087	−	1.08348i
$629$		−	11.9769i		−	0.477549i
$630$		0			0
$631$		−	17.9365i		−	0.714040i	−0.934097	−	0.357020i	$-0.883793\pi$
$631$		−	17.9365i		−	0.714040i	0.934097	−	0.357020i	$-0.116207\pi$
$632$	−4.77739	+	28.3576i	−0.190034	+	1.12801i
$633$		0			0
$634$	30.1168	−	15.2213i	1.19609	−	0.604515i
$635$	−12.9073			−0.512210
$636$		0			0
$637$	−1.25544			−0.0497422
$638$	−3.42703	+	1.73205i	−0.135678	+	0.0685725i
$639$		0			0
$640$	−8.88316	+	1.19897i	−0.351138	+	0.0473935i
$641$			27.5653i			1.08877i	0.838837	+	0.544383i	$0.183236\pi$
$641$			27.5653i			1.08877i	−0.838837	+	0.544383i	$0.816764\pi$
$642$		0			0
$643$		−	6.31211i		−	0.248925i	−0.992224	−	0.124463i	$-0.960279\pi$
$643$		−	6.31211i		−	0.248925i	0.992224	−	0.124463i	$-0.0397207\pi$
$644$	−9.40571	−	6.92820i	−0.370637	−	0.273009i
$645$		0			0
$646$	−3.55842	−	7.04069i	−0.140004	−	0.277012i
$647$	−36.9711			−1.45348			−0.726741	−	0.686912i	$-0.758966\pi$
$647$	−36.9711			−1.45348			−0.726741	+	0.686912i	$0.758966\pi$
$648$		0			0
$649$	−17.7446			−0.696535
$650$	−9.40571	−	18.6101i	−0.368922	−	0.729949i
$651$		0			0
$652$	19.1168	+	14.0814i	0.748673	+	0.551469i
$653$		−	7.72049i		−	0.302126i	−0.988524	−	0.151063i	$-0.951730\pi$
$653$		−	7.72049i		−	0.302126i	0.988524	−	0.151063i	$-0.0482697\pi$
$654$		0			0
$655$			5.74764i			0.224579i
$656$	−0.563374	+	0.174928i	−0.0219961	+	0.00682980i
$657$		0			0
$658$	−39.6060	+	20.0172i	−1.54400	+	0.780351i
$659$	16.6602			0.648989			0.324495	−	0.945887i	$-0.394806\pi$
$659$	16.6602			0.648989			0.324495	+	0.945887i	$0.394806\pi$
$660$		0			0
$661$	21.3723			0.831285			0.415643	−	0.909528i	$-0.363557\pi$
$661$	21.3723			0.831285			0.415643	+	0.909528i	$0.363557\pi$
$662$	35.1457	−	17.7629i	1.36598	−	0.690376i
$663$		0			0
$664$	20.2337	+	3.40876i	0.785219	+	0.132285i
$665$			4.75372i			0.184341i
$666$		0			0
$667$		−	1.70438i		−	0.0659938i
$668$	−22.7880	+	30.9369i	−0.881692	+	1.19698i
$669$		0			0
$670$	−3.51087	−	6.94661i	−0.135637	−	0.268371i
$671$	11.5569			0.446150
$672$		0			0
$673$	1.13859			0.0438895			0.0219448	−	0.999759i	$-0.493014\pi$
$673$	1.13859			0.0438895			0.0219448	+	0.999759i	$0.493014\pi$
$674$	2.71459	+	5.37108i	0.104562	+	0.206886i
$675$		0			0
$676$	1.93070	−	2.62112i	0.0742578	−	0.100812i
$677$			32.9639i			1.26690i	0.773782	+	0.633452i	$0.218363\pi$
$677$			32.9639i			1.26690i	−0.773782	+	0.633452i	$0.781637\pi$
$678$		0			0
$679$		−	33.9104i		−	1.30136i
$680$	−5.57825	−	0.939764i	−0.213916	−	0.0360383i
$681$		0			0
$682$	7.37228	−	3.72601i	0.282299	−	0.142676i
$683$	−2.07668			−0.0794618			−0.0397309	−	0.999210i	$-0.512650\pi$
$683$	−2.07668			−0.0794618			−0.0397309	+	0.999210i	$0.512650\pi$
$684$		0			0
$685$	−14.8614			−0.567825
$686$	22.7134	−	11.4795i	0.867202	−	0.438291i
$687$		0			0
$688$	−26.5367	+	8.23966i	−1.01170	+	0.314134i
$689$			28.7075i			1.09367i
$690$		0			0
$691$			11.5543i			0.439548i	0.975551	+	0.219774i	$0.0705320\pi$
$691$			11.5543i			0.439548i	−0.975551	+	0.219774i	$0.929468\pi$
$692$	8.93075	+	6.57835i	0.339496	+	0.250071i
$693$		0			0
$694$	−4.93070	−	9.75588i	−0.187167	−	0.370328i
$695$	−7.40357			−0.280833
$696$		0			0
$697$	−0.372281			−0.0141012
$698$	7.25450	+	14.3537i	0.274587	+	0.543297i
$699$		0			0
$700$	−19.1168	−	14.0814i	−0.722549	−	0.532226i
$701$		−	26.1282i		−	0.986850i	−0.869788	−	0.493425i	$-0.835745\pi$
$701$		−	26.1282i		−	0.986850i	0.869788	−	0.493425i	$-0.164255\pi$
$702$		0			0
$703$			10.4845i			0.395429i
$704$	25.9030	+	8.98266i	0.976255	+	0.338547i
$705$		0			0
$706$	−6.18614	+	3.12653i	−0.232818	+	0.117668i
$707$	−48.3789			−1.81948
$708$		0			0
$709$	−4.86141			−0.182574			−0.0912870	−	0.995825i	$-0.529098\pi$
$709$	−4.86141			−0.182574			−0.0912870	+	0.995825i	$0.529098\pi$
$710$	1.75079	−	0.884861i	0.0657058	−	0.0332082i
$711$		0			0
$712$	2.51087	−	14.9040i	0.0940990	−	0.558553i
$713$			3.66648i			0.137311i
$714$		0			0
$715$		−	9.15640i		−	0.342430i
$716$	−22.3130	+	30.2921i	−0.833876	+	1.13207i
$717$		0			0
$718$	19.1168	+	37.8246i	0.713434	+	1.41160i
$719$	7.65492			0.285481			0.142740	−	0.989760i	$-0.454409\pi$
$719$	7.65492			0.285481			0.142740	+	0.989760i	$0.454409\pi$
$720$		0			0
$721$	39.6060			1.47500
$722$	−9.00528	−	17.8178i	−0.335142	−	0.663111i
$723$		0			0
$724$	4.74456	−	6.44121i	0.176330	−	0.239386i
$725$		−	3.46410i		−	0.128654i
$726$		0			0
$727$		−	3.09150i		−	0.114657i	−0.998355	−	0.0573287i	$-0.981742\pi$
$727$		−	3.09150i		−	0.114657i	0.998355	−	0.0573287i	$-0.0182583\pi$
$728$	−4.30243	+	25.5383i	−0.159459	+	0.946514i
$729$		0			0
$730$	2.37228	−	1.19897i	0.0878021	−	0.0443759i
$731$	−17.5356			−0.648578
$732$		0			0
$733$	−5.37228			−0.198430			−0.0992149	−	0.995066i	$-0.531633\pi$
$733$	−5.37228			−0.198430			−0.0992149	+	0.995066i	$0.531633\pi$
$734$	−17.1352	+	8.66025i	−0.632471	+	0.319656i
$735$		0			0
$736$	−8.74456	+	8.46284i	−0.322329	+	0.311944i
$737$			23.8063i			0.876916i
$738$		0			0
$739$		−	9.66181i		−	0.355415i	−0.984083	−	0.177708i	$-0.943132\pi$
$739$		−	9.66181i		−	0.355415i	0.984083	−	0.177708i	$-0.0568681\pi$
$740$	6.05321	+	4.45877i	0.222520	+	0.163908i
$741$		0			0
$742$	14.7446	+	29.1736i	0.541290	+	1.07100i
$743$	45.0264			1.65186			0.825929	−	0.563774i	$-0.190651\pi$
$743$	45.0264			1.65186			0.825929	+	0.563774i	$0.190651\pi$
$744$		0			0
$745$	7.60597			0.278661
$746$	−5.65278	−	11.1846i	−0.206963	−	0.409497i
$747$		0			0
$748$	13.9307	+	10.2613i	0.509357	+	0.375190i
$749$		−	35.9306i		−	1.31288i
$750$		0			0
$751$			46.1583i			1.68434i	0.539212	+	0.842170i	$0.318722\pi$
$751$			46.1583i			1.68434i	−0.539212	+	0.842170i	$0.681278\pi$
$752$	13.7081	+	44.1485i	0.499884	+	1.60993i
$753$		0			0
$754$	−3.37228	+	1.70438i	−0.122811	+	0.0620698i
$755$	−7.25450			−0.264018
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	12.1948	−	6.16337i	0.442936	−	0.223864i
$759$		0			0
$760$	4.88316	+	0.822662i	0.177131	+	0.0298411i
$761$			19.1075i			0.692645i	0.938116	+	0.346322i	$0.112570\pi$
$761$			19.1075i			0.692645i	−0.938116	+	0.346322i	$0.887430\pi$
$762$		0			0
$763$		−	25.7648i		−	0.932749i
$764$	4.62832	−	6.28339i	0.167447	−	0.227325i
$765$		0			0
$766$	−0.255437	−	0.505408i	−0.00922933	−	0.0182611i
$767$	−17.4611			−0.630482
$768$		0			0
$769$	−55.0951			−1.98678			−0.993390	−	0.114788i	$-0.963381\pi$
$769$	−55.0951			−1.98678			−0.993390	+	0.114788i	$0.963381\pi$
$770$	−4.70285	−	9.30506i	−0.169479	−	0.335331i
$771$		0			0
$772$	4.44158	−	6.02987i	0.159856	−	0.217020i
$773$			45.7330i			1.64490i	0.568835	+	0.822451i	$0.307394\pi$
$773$			45.7330i			1.64490i	−0.568835	+	0.822451i	$0.692606\pi$
$774$		0			0
$775$			7.45202i			0.267685i
$776$	−34.8337	−	5.86841i	−1.25046	−	0.210664i
$777$		0			0
$778$	10.4891	−	5.30129i	0.376053	−	0.190060i
$779$	0.325892			0.0116763
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−6.85407	+	3.46410i	−0.245101	+	0.123876i
$783$		0			0
$784$	0.441578	+	1.42215i	0.0157706	+	0.0507910i
$785$			13.3591i			0.476806i
$786$		0			0
$787$			19.6409i			0.700121i	0.936727	+	0.350061i	$0.113839\pi$
$787$			19.6409i			0.700121i	−0.936727	+	0.350061i	$0.886161\pi$
$788$	−17.2097	−	12.6766i	−0.613070	−	0.451585i
$789$		0			0
$790$	−5.13859	−	10.1672i	−0.182823	−	0.361733i
$791$	43.2756			1.53870
$792$		0			0
$793$	11.3723			0.403842
$794$	4.62832	+	9.15759i	0.164253	+	0.324991i
$795$		0			0
$796$	−31.1168	−	22.9205i	−1.10291	−	0.812397i
$797$		−	47.1152i		−	1.66891i	−0.551078	−	0.834454i	$-0.685783\pi$
$797$		−	47.1152i		−	1.66891i	0.551078	−	0.834454i	$-0.314217\pi$
$798$		0			0
$799$			29.1736i			1.03209i
$800$	−17.7731	+	17.2005i	−0.628373	+	0.608129i
$801$		0			0
$802$	27.6753	−	13.9873i	0.977248	−	0.493909i
$803$	−8.12989			−0.286898
$804$		0			0
$805$	4.62772			0.163106
$806$	7.25450	−	3.66648i	0.255529	−	0.129146i
$807$		0			0
$808$	−8.37228	+	49.6962i	−0.294536	+	1.74830i
$809$		−	27.1778i		−	0.955521i	−0.878490	−	0.477760i	$-0.841449\pi$
$809$		−	27.1778i		−	0.955521i	0.878490	−	0.477760i	$-0.158551\pi$
$810$		0			0
$811$			25.9530i			0.911332i	0.890151	+	0.455666i	$0.150599\pi$
$811$			25.9530i			0.911332i	−0.890151	+	0.455666i	$0.849401\pi$
$812$	−2.55164	+	3.46410i	−0.0895451	+	0.121566i
$813$		0			0
$814$	−10.3723	−	20.5226i	−0.363548	−	0.719316i
$815$	−9.40571			−0.329468
$816$		0			0
$817$	15.3505			0.537047
$818$	−1.43877	−	2.84674i	−0.0503053	−	0.0995340i
$819$		0			0
$820$	0.138593	−	0.188154i	0.00483989	−	0.00657062i
$821$		−	21.5769i		−	0.753039i	−0.926409	−	0.376519i	$-0.877121\pi$
$821$		−	21.5769i		−	0.753039i	0.926409	−	0.376519i	$-0.122879\pi$
$822$		0			0
$823$			29.8671i			1.04110i	0.853830	+	0.520552i	$0.174274\pi$
$823$			29.8671i			1.04110i	−0.853830	+	0.520552i	$0.825726\pi$
$824$	6.85407	−	40.6844i	0.238773	−	1.41731i
$825$		0			0
$826$	−17.7446	+	8.96825i	−0.617412	+	0.312045i
$827$	7.00314			0.243523			0.121762	−	0.992559i	$-0.461146\pi$
$827$	7.00314			0.243523			0.121762	+	0.992559i	$0.461146\pi$
$828$		0			0
$829$	−13.7663			−0.478124			−0.239062	−	0.971004i	$-0.576840\pi$
$829$	−13.7663			−0.478124			−0.239062	+	0.971004i	$0.576840\pi$
$830$	−7.25450	+	3.66648i	−0.251807	+	0.127265i
$831$		0			0
$832$	25.4891	+	8.83915i	0.883676	+	0.306442i
$833$			0.939764i			0.0325609i
$834$		0			0
$835$		−	15.2213i		−	0.526755i
$836$	−12.1948	−	8.98266i	−0.421767	−	0.310672i
$837$		0			0
$838$	−3.60597	−	7.13477i	−0.124566	−	0.246466i
$839$	−45.6782			−1.57699			−0.788493	−	0.615044i	$-0.789138\pi$
$839$	−45.6782			−1.57699			−0.788493	+	0.615044i	$0.789138\pi$
$840$		0			0
$841$	28.3723			0.978355
$842$	−18.8860	−	37.3677i	−0.650853	−	1.28778i
$843$		0			0
$844$	−9.86141	−	7.26387i	−0.339444	−	0.250033i
$845$			1.28962i			0.0443643i
$846$		0			0
$847$			2.02163i			0.0694641i
$848$	32.5196	−	10.0974i	1.11673	−	0.346744i
$849$		0			0
$850$	−13.9307	+	7.04069i	−0.477819	+	0.241494i
$851$	10.2066			0.349877
$852$		0			0
$853$	4.39403			0.150449			0.0752244	−	0.997167i	$-0.476033\pi$
$853$	4.39403			0.150449			0.0752244	+	0.997167i	$0.476033\pi$
$854$	11.5569	−	5.84096i	0.395470	−	0.199874i
$855$		0			0
$856$	−36.9090	−	6.21803i	−1.26152	−	0.212528i
$857$		−	25.4458i		−	0.869211i	−0.900621	−	0.434605i	$-0.856888\pi$
$857$		−	25.4458i		−	0.869211i	0.900621	−	0.434605i	$-0.143112\pi$
$858$		0			0
$859$			35.1094i			1.19792i	0.800780	+	0.598958i	$0.204418\pi$
$859$			35.1094i			1.19792i	−0.800780	+	0.598958i	$0.795582\pi$
$860$	6.52818	−	8.86263i	0.222609	−	0.302213i
$861$		0			0
$862$	−9.35053	−	18.5010i	−0.318480	−	0.630145i
$863$	4.15335			0.141382			0.0706909	−	0.997498i	$-0.477480\pi$
$863$	4.15335			0.141382			0.0706909	+	0.997498i	$0.477480\pi$
$864$		0			0
$865$	−4.39403			−0.149402
$866$	9.16823	+	18.1402i	0.311549	+	0.616431i
$867$		0			0
$868$	5.48913	−	7.45202i	0.186313	−	0.252938i
$869$			34.8434i			1.18198i
$870$		0			0
$871$			23.4259i			0.793758i
$872$	−26.4663	−	4.45877i	−0.896264	−	0.150993i
$873$		0			0
$874$	6.00000	−	3.03245i	0.202953	−	0.102574i
$875$	20.1618			0.681592
$876$		0			0
$877$	27.3723			0.924296			0.462148	−	0.886803i	$-0.347079\pi$
$877$	27.3723			0.924296			0.462148	+	0.886803i	$0.347079\pi$
$878$	−41.5248	+	20.9870i	−1.40140	+	0.708277i
$879$		0			0
$880$	−10.3723	+	3.22060i	−0.349650	+	0.108566i
$881$			19.7899i			0.666740i	0.942796	+	0.333370i	$0.108186\pi$
$881$			19.7899i			0.666740i	−0.942796	+	0.333370i	$0.891814\pi$
$882$		0			0
$883$			34.7921i			1.17085i	0.810727	+	0.585424i	$0.199072\pi$
$883$			34.7921i			1.17085i	−0.810727	+	0.585424i	$0.800928\pi$
$884$	13.7081	+	10.0974i	0.461055	+	0.339611i
$885$		0			0
$886$	−3.30298	−	6.53528i	−0.110966	−	0.219557i
$887$	−5.50371			−0.184797			−0.0923983	−	0.995722i	$-0.529453\pi$
$887$	−5.50371			−0.184797			−0.0923983	+	0.995722i	$0.529453\pi$
$888$		0			0
$889$	44.2337			1.48355
$890$	2.70071	+	5.34363i	0.0905281	+	0.179119i
$891$		0			0
$892$	2.74456	+	2.02163i	0.0918948	+	0.0676893i
$893$		−	25.5383i		−	0.854608i
$894$		0			0
$895$		−	14.9040i		−	0.498187i
$896$	30.4429	−	4.10891i	1.01703	−	0.137269i
$897$		0			0
$898$	−4.81386	+	2.43296i	−0.160641	+	0.0811890i
$899$	1.35036			0.0450369
$900$		0			0
$901$	21.4891			0.715907
$902$	−0.637910	+	0.322405i	−0.0212401	+	0.0107349i
$903$		0			0
$904$	7.48913	−	44.4539i	0.249085	−	1.47852i
$905$			3.16915i			0.105346i
$906$		0			0
$907$		−	24.6249i		−	0.817657i	−0.912611	−	0.408828i	$-0.865938\pi$
$907$		−	24.6249i		−	0.817657i	0.912611	−	0.408828i	$-0.134062\pi$
$908$	22.4014	−	30.4121i	0.743417	−	1.00926i
$909$		0			0
$910$	−4.62772	−	9.15640i	−0.153407	−	0.303532i
$911$	13.1586			0.435965			0.217983	−	0.975953i	$-0.430052\pi$
$911$	13.1586			0.435965			0.217983	+	0.975953i	$0.430052\pi$
$912$		0			0
$913$	24.8614			0.822792
$914$	3.81359	+	7.54556i	0.126142	+	0.249585i
$915$		0			0
$916$	−11.1168	+	15.0922i	−0.367311	+	0.498660i
$917$		−	19.6974i		−	0.650464i
$918$		0			0
$919$		−	46.0993i		−	1.52067i	−0.649529	−	0.760337i	$-0.725034\pi$
$919$		−	46.0993i		−	1.52067i	0.649529	−	0.760337i	$-0.274966\pi$
$920$	0.800857	−	4.75372i	0.0264035	−	0.156726i
$921$		0			0
$922$	−28.8614	+	14.5868i	−0.950500	+	0.480390i
$923$	−5.90414			−0.194337
$924$		0			0
$925$	20.7446			0.682077
$926$	26.5409	−	13.4140i	0.872187	−	0.440811i
$927$		0			0
$928$	3.11684	+	3.22060i	0.102315	+	0.105721i
$929$			35.1383i			1.15285i	0.817149	+	0.576426i	$0.195553\pi$
$929$			35.1383i			1.15285i	−0.817149	+	0.576426i	$0.804447\pi$
$930$		0			0
$931$		−	0.822662i		−	0.0269617i
$932$	45.1894	+	33.2863i	1.48023	+	1.09033i
$933$		0			0
$934$	−15.5584	−	30.7839i	−0.509087	−	1.00728i
$935$	−6.85407			−0.224152
$936$		0			0
$937$	−11.7228			−0.382968			−0.191484	−	0.981496i	$-0.561330\pi$
$937$	−11.7228			−0.382968			−0.191484	+	0.981496i	$0.561330\pi$
$938$	12.0319	+	23.8063i	0.392855	+	0.777303i
$939$		0			0
$940$	−14.7446	−	10.8608i	−0.480915	−	0.354240i
$941$		−	36.7229i		−	1.19713i	−0.801073	−	0.598567i	$-0.795737\pi$
$941$		−	36.7229i		−	1.19713i	0.801073	−	0.598567i	$-0.204263\pi$
$942$		0			0
$943$		−	0.317254i		−	0.0103312i
$944$	6.14162	+	19.7797i	0.199893	+	0.643775i
$945$		0			0
$946$	−30.0475	+	15.1863i	−0.976930	+	0.493748i
$947$	44.5514			1.44773			0.723864	−	0.689943i	$-0.242364\pi$
$947$	44.5514			1.44773			0.723864	+	0.689943i	$0.242364\pi$
$948$		0			0
$949$	−8.00000			−0.259691
$950$	12.1948	−	6.16337i	0.395653	−	0.199966i
$951$		0			0
$952$	19.1168	+	3.22060i	0.619580	+	0.104380i
$953$		−	32.8164i		−	1.06303i	−0.847050	−	0.531514i	$-0.821623\pi$
$953$		−	32.8164i		−	1.06303i	0.847050	−	0.531514i	$-0.178377\pi$
$954$		0			0
$955$			3.09150i			0.100039i
$956$	19.7613	−	26.8280i	0.639128	−	0.867678i
$957$		0			0
$958$	6.25544	+	12.3770i	0.202104	+	0.399883i
$959$	50.9305			1.64463
$960$		0			0
$961$	28.0951			0.906293
$962$	−10.2066	−	20.1947i	−0.329073	−	0.651103i
$963$		0			0
$964$	−19.5584	+	26.5525i	−0.629934	+	0.855197i
$965$			2.96677i			0.0955036i
$966$		0			0
$967$		−	56.2665i		−	1.80941i	−0.426041	−	0.904704i	$-0.640092\pi$
$967$		−	56.2665i		−	1.80941i	0.426041	−	0.904704i	$-0.359908\pi$
$968$	2.07668	+	0.349857i	0.0667469	+	0.0112448i
$969$		0			0
$970$	12.4891	−	6.31211i	0.401002	−	0.202669i
$971$	24.7156			0.793160			0.396580	−	0.918000i	$-0.370197\pi$
$971$	24.7156			0.793160			0.396580	+	0.918000i	$0.370197\pi$
$972$		0			0
$973$	25.3723			0.813398
$974$	22.6389	−	11.4419i	0.725397	−	0.366621i
$975$		0			0
$976$	−4.00000	−	12.8824i	−0.128037	−	0.412356i
$977$			21.5220i			0.688550i	0.938869	+	0.344275i	$0.111875\pi$
$977$			21.5220i			0.688550i	−0.938869	+	0.344275i	$0.888125\pi$
$978$		0			0
$979$		−	18.3128i		−	0.585280i
$980$	−0.474964	−	0.349857i	−0.0151722	−	0.0111758i
$981$		0			0
$982$	−15.8139	−	31.2893i	−0.504641	−	0.998481i
$983$	−16.8093			−0.536133			−0.268066	−	0.963400i	$-0.586385\pi$
$983$	−16.8093			−0.536133			−0.268066	+	0.963400i	$0.586385\pi$
$984$		0			0
$985$	8.46738			0.269793
$986$	1.27582	+	2.52434i	0.0406304	+	0.0803913i
$987$		0			0
$988$	−12.0000	−	8.83915i	−0.381771	−	0.281211i
$989$		−	14.9436i		−	0.475180i
$990$		0			0
$991$			16.2912i			0.517506i	0.965944	+	0.258753i	$0.0833116\pi$
$991$			16.2912i			0.517506i	−0.965944	+	0.258753i	$0.916688\pi$
$992$	−6.70500	−	6.92820i	−0.212884	−	0.219971i
$993$		0			0
$994$	−6.00000	+	3.03245i	−0.190308	+	0.0961834i
$995$	15.3098			0.485355
$996$		0			0
$997$	−52.8614			−1.67414			−0.837069	−	0.547098i	$-0.815733\pi$
$997$	−52.8614			−1.67414			−0.837069	+	0.547098i	$0.815733\pi$
$998$	−0.637910	+	0.322405i	−0.0201927	+	0.0102056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.2.b.b.323.3		8
3.2	odd	2	inner	324.2.b.b.323.6		8
4.3	odd	2	inner	324.2.b.b.323.5		8
8.3	odd	2		5184.2.c.j.5183.5		8
8.5	even	2		5184.2.c.j.5183.6		8
9.2	odd	6		108.2.h.a.71.3		8
9.4	even	3		108.2.h.a.35.4		8
9.5	odd	6		36.2.h.a.11.1	✓	8
9.7	even	3		36.2.h.a.23.2	yes	8
12.11	even	2	inner	324.2.b.b.323.4		8
24.5	odd	2		5184.2.c.j.5183.4		8
24.11	even	2		5184.2.c.j.5183.3		8
36.7	odd	6		36.2.h.a.23.1	yes	8
36.11	even	6		108.2.h.a.71.4		8
36.23	even	6		36.2.h.a.11.2	yes	8
36.31	odd	6		108.2.h.a.35.3		8
45.7	odd	12		900.2.o.a.599.2		16
45.14	odd	6		900.2.r.c.551.4		8
45.23	even	12		900.2.o.a.299.4		16
45.32	even	12		900.2.o.a.299.5		16
45.34	even	6		900.2.r.c.851.3		8
45.43	odd	12		900.2.o.a.599.7		16
72.5	odd	6		576.2.s.f.191.2		8
72.11	even	6		1728.2.s.f.1151.3		8
72.13	even	6		1728.2.s.f.575.3		8
72.29	odd	6		1728.2.s.f.1151.4		8
72.43	odd	6		576.2.s.f.383.2		8
72.59	even	6		576.2.s.f.191.3		8
72.61	even	6		576.2.s.f.383.3		8
72.67	odd	6		1728.2.s.f.575.4		8
180.7	even	12		900.2.o.a.599.4		16
180.23	odd	12		900.2.o.a.299.2		16
180.43	even	12		900.2.o.a.599.5		16
180.59	even	6		900.2.r.c.551.3		8
180.79	odd	6		900.2.r.c.851.4		8
180.167	odd	12		900.2.o.a.299.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.1	✓	8	9.5	odd	6
36.2.h.a.11.2	yes	8	36.23	even	6
36.2.h.a.23.1	yes	8	36.7	odd	6
36.2.h.a.23.2	yes	8	9.7	even	3
108.2.h.a.35.3		8	36.31	odd	6
108.2.h.a.35.4		8	9.4	even	3
108.2.h.a.71.3		8	9.2	odd	6
108.2.h.a.71.4		8	36.11	even	6
324.2.b.b.323.3		8	1.1	even	1	trivial
324.2.b.b.323.4		8	12.11	even	2	inner
324.2.b.b.323.5		8	4.3	odd	2	inner
324.2.b.b.323.6		8	3.2	odd	2	inner
576.2.s.f.191.2		8	72.5	odd	6
576.2.s.f.191.3		8	72.59	even	6
576.2.s.f.383.2		8	72.43	odd	6
576.2.s.f.383.3		8	72.61	even	6
900.2.o.a.299.2		16	180.23	odd	12
900.2.o.a.299.4		16	45.23	even	12
900.2.o.a.299.5		16	45.32	even	12
900.2.o.a.299.7		16	180.167	odd	12
900.2.o.a.599.2		16	45.7	odd	12
900.2.o.a.599.4		16	180.7	even	12
900.2.o.a.599.5		16	180.43	even	12
900.2.o.a.599.7		16	45.43	odd	12
900.2.r.c.551.3		8	180.59	even	6
900.2.r.c.551.4		8	45.14	odd	6
900.2.r.c.851.3		8	45.34	even	6
900.2.r.c.851.4		8	180.79	odd	6
1728.2.s.f.575.3		8	72.13	even	6
1728.2.s.f.575.4		8	72.67	odd	6
1728.2.s.f.1151.3		8	72.11	even	6
1728.2.s.f.1151.4		8	72.29	odd	6
5184.2.c.j.5183.3		8	24.11	even	2
5184.2.c.j.5183.4		8	24.5	odd	2
5184.2.c.j.5183.5		8	8.3	odd	2
5184.2.c.j.5183.6		8	8.5	even	2

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.637910 - 1.26217i) q^{2} +(-1.18614 + 1.61030i) q^{4} -0.792287i q^{5} +2.71519i q^{7} +(2.78912 + 0.469882i) q^{8} +O(q^{10})\)	\(q+(-0.637910 - 1.26217i) q^{2} +(-1.18614 + 1.61030i) q^{4} -0.792287i q^{5} +2.71519i q^{7} +(2.78912 + 0.469882i) q^{8} +(-1.00000 + 0.505408i) q^{10} +3.42703 q^{11} +3.37228 q^{13} +(3.42703 - 1.73205i) q^{14} +(-1.18614 - 3.82009i) q^{16} -2.52434i q^{17} +2.20979i q^{19} +(1.27582 + 0.939764i) q^{20} +(-2.18614 - 4.32550i) q^{22} +2.15121 q^{23} +4.37228 q^{25} +(-2.15121 - 4.25639i) q^{26} +(-4.37228 - 3.22060i) q^{28} -0.792287i q^{29} +1.70438i q^{31} +(-4.06494 + 3.93398i) q^{32} +(-3.18614 + 1.61030i) q^{34} +2.15121 q^{35} +4.74456 q^{37} +(2.78912 - 1.40965i) q^{38} +(0.372281 - 2.20979i) q^{40} -0.147477i q^{41} -6.94661i q^{43} +(-4.06494 + 5.51856i) q^{44} +(-1.37228 - 2.71519i) q^{46} -11.5569 q^{47} -0.372281 q^{49} +(-2.78912 - 5.51856i) q^{50} +(-4.00000 + 5.43039i) q^{52} +8.51278i q^{53} -2.71519i q^{55} +(-1.27582 + 7.57301i) q^{56} +(-1.00000 + 0.505408i) q^{58} -5.17782 q^{59} +3.37228 q^{61} +(2.15121 - 1.08724i) q^{62} +(7.55842 + 2.62112i) q^{64} -2.67181i q^{65} +6.94661i q^{67} +(4.06494 + 2.99422i) q^{68} +(-1.37228 - 2.71519i) q^{70} -1.75079 q^{71} -2.37228 q^{73} +(-3.02661 - 5.98844i) q^{74} +(-3.55842 - 2.62112i) q^{76} +9.30506i q^{77} +10.1672i q^{79} +(-3.02661 + 0.939764i) q^{80} +(-0.186141 + 0.0940770i) q^{82} +7.25450 q^{83} -2.00000 q^{85} +(-8.76780 + 4.43132i) q^{86} +(9.55842 + 1.61030i) q^{88} -5.34363i q^{89} +9.15640i q^{91} +(-2.55164 + 3.46410i) q^{92} +(7.37228 + 14.5868i) q^{94} +1.75079 q^{95} -12.4891 q^{97} +(0.237482 + 0.469882i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4}+O(q^{10}) \) 8 * q + 2 * q^4	\( 8 q + 2 q^{4} - 8 q^{10} + 4 q^{13} + 2 q^{16} - 6 q^{22} + 12 q^{25} - 12 q^{28} - 14 q^{34} - 8 q^{37} - 20 q^{40} + 12 q^{46} + 20 q^{49} - 32 q^{52} - 8 q^{58} + 4 q^{61} + 26 q^{64} + 12 q^{70} + 4 q^{73} + 6 q^{76} + 10 q^{82} - 16 q^{85} + 42 q^{88} + 36 q^{94} - 8 q^{97}+O(q^{100}) \) 8 * q + 2 * q^4 - 8 * q^10 + 4 * q^13 + 2 * q^16 - 6 * q^22 + 12 * q^25 - 12 * q^28 - 14 * q^34 - 8 * q^37 - 20 * q^40 + 12 * q^46 + 20 * q^49 - 32 * q^52 - 8 * q^58 + 4 * q^61 + 26 * q^64 + 12 * q^70 + 4 * q^73 + 6 * q^76 + 10 * q^82 - 16 * q^85 + 42 * q^88 + 36 * q^94 - 8 * q^97

Introduction

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