LMFDB - Embedded newform 936.2.g.c.469.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(469,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.469"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.g (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			469.3
Root			$0.264658 + 1.38923i$ of defining polynomial
Character	$\chi$	$=$	936.469
Dual form			936.2.g.c.469.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.264658 - 1.38923i) q^{2} +(-1.85991 - 0.735342i) q^{4} +1.00000i q^{5} +3.24914 q^{7} +(-1.51380 + 2.38923i) q^{8} +(1.38923 + 0.264658i) q^{10} +1.05863i q^{11} +1.00000i q^{13} +(0.859912 - 4.51380i) q^{14} +(2.91855 + 2.73534i) q^{16} -1.00000 q^{17} +4.00000i q^{19} +(0.735342 - 1.85991i) q^{20} +(1.47068 + 0.280176i) q^{22} +2.94137 q^{23} +4.00000 q^{25} +(1.38923 + 0.264658i) q^{26} +(-6.04312 - 2.38923i) q^{28} +7.43965i q^{29} +5.05863 q^{31} +(4.57243 - 3.33060i) q^{32} +(-0.264658 + 1.38923i) q^{34} +3.24914i q^{35} -6.55691i q^{37} +(5.55691 + 1.05863i) q^{38} +(-2.38923 - 1.51380i) q^{40} +9.43965 q^{41} +0.307774i q^{43} +(0.778457 - 1.96896i) q^{44} +(0.778457 - 4.08623i) q^{46} -6.80605 q^{47} +3.55691 q^{49} +(1.05863 - 5.55691i) q^{50} +(0.735342 - 1.85991i) q^{52} -1.55691i q^{53} -1.05863 q^{55} +(-4.91855 + 7.76294i) q^{56} +(10.3354 + 1.96896i) q^{58} -5.67418i q^{59} -9.67418i q^{61} +(1.33881 - 7.02760i) q^{62} +(-3.41683 - 7.23362i) q^{64} -1.00000 q^{65} +1.50172i q^{67} +(1.85991 + 0.735342i) q^{68} +(4.51380 + 0.859912i) q^{70} +5.36641 q^{71} +3.55691 q^{73} +(-9.10905 - 1.73534i) q^{74} +(2.94137 - 7.43965i) q^{76} +3.43965i q^{77} -6.73281 q^{79} +(-2.73534 + 2.91855i) q^{80} +(2.49828 - 13.1138i) q^{82} +2.49828i q^{83} -1.00000i q^{85} +(0.427568 + 0.0814549i) q^{86} +(-2.52932 - 1.60256i) q^{88} -2.11727 q^{89} +3.24914i q^{91} +(-5.47068 - 2.16291i) q^{92} +(-1.80128 + 9.45517i) q^{94} -4.00000 q^{95} +7.67418 q^{97} +(0.941367 - 4.94137i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.264658	−	1.38923i	0.187142	−	0.982333i
$2$	0.264658	−	1.38923i	0.187142	−	0.982333i
$3$		0			0
$3$		0			0
$4$	−1.85991	−	0.735342i	−0.929956	−	0.367671i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$		0			0
$7$	3.24914			1.22806			0.614030	−	0.789283i	$-0.289547\pi$
$7$	3.24914			1.22806			0.614030	+	0.789283i	$0.289547\pi$
$8$	−1.51380	+	2.38923i	−0.535209	+	0.844720i
$9$		0			0
$10$	1.38923	+	0.264658i	0.439313	+	0.0836923i
$11$			1.05863i			0.319190i	0.987183	+	0.159595i	$0.0510188\pi$
$11$			1.05863i			0.319190i	−0.987183	+	0.159595i	$0.948981\pi$
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	0.859912	−	4.51380i	0.229821	−	1.20636i
$15$		0			0
$16$	2.91855	+	2.73534i	0.729636	+	0.683835i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		0			0
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$	0.735342	−	1.85991i	0.164427	−	0.415889i
$21$		0			0
$22$	1.47068	+	0.280176i	0.313551	+	0.0597337i
$23$	2.94137			0.613317			0.306659	−	0.951820i	$-0.400789\pi$
$23$	2.94137			0.613317			0.306659	+	0.951820i	$0.400789\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	1.38923	+	0.264658i	0.272450	+	0.0519038i
$27$		0			0
$28$	−6.04312	−	2.38923i	−1.14204	−	0.451522i
$29$			7.43965i			1.38151i	0.723090	+	0.690754i	$0.242721\pi$
$29$			7.43965i			1.38151i	−0.723090	+	0.690754i	$0.757279\pi$
$30$		0			0
$31$	5.05863			0.908557			0.454279	−	0.890860i	$-0.349897\pi$
$31$	5.05863			0.908557			0.454279	+	0.890860i	$0.349897\pi$
$32$	4.57243	−	3.33060i	0.808299	−	0.588772i
$33$		0			0
$34$	−0.264658	+	1.38923i	−0.0453885	+	0.238251i
$35$			3.24914i			0.549205i
$36$		0			0
$37$		−	6.55691i		−	1.07795i	−0.842322	−	0.538975i	$-0.818812\pi$
$37$		−	6.55691i		−	1.07795i	0.842322	−	0.538975i	$-0.181188\pi$
$38$	5.55691	+	1.05863i	0.901451	+	0.171733i
$39$		0			0
$40$	−2.38923	−	1.51380i	−0.377770	−	0.239353i
$41$	9.43965			1.47423			0.737113	−	0.675770i	$-0.236189\pi$
$41$	9.43965			1.47423			0.737113	+	0.675770i	$0.236189\pi$
$42$		0			0
$43$			0.307774i			0.0469350i	0.999725	+	0.0234675i	$0.00747063\pi$
$43$			0.307774i			0.0469350i	−0.999725	+	0.0234675i	$0.992529\pi$
$44$	0.778457	−	1.96896i	0.117357	−	0.296833i
$45$		0			0
$46$	0.778457	−	4.08623i	0.114777	−	0.602482i
$47$	−6.80605			−0.992765			−0.496383	−	0.868104i	$-0.665339\pi$
$47$	−6.80605			−0.992765			−0.496383	+	0.868104i	$0.665339\pi$
$48$		0			0
$49$	3.55691			0.508131
$50$	1.05863	−	5.55691i	0.149713	−	0.785866i
$51$		0			0
$52$	0.735342	−	1.85991i	0.101974	−	0.257923i
$53$		−	1.55691i		−	0.213859i	−0.994267	−	0.106929i	$-0.965898\pi$
$53$		−	1.55691i		−	0.213859i	0.994267	−	0.106929i	$-0.0341019\pi$
$54$		0			0
$55$	−1.05863			−0.142746
$56$	−4.91855	+	7.76294i	−0.657268	+	1.03737i
$57$		0			0
$58$	10.3354	+	1.96896i	1.35710	+	0.258538i
$59$		−	5.67418i		−	0.738715i	−0.929287	−	0.369358i	$-0.879578\pi$
$59$		−	5.67418i		−	0.738715i	0.929287	−	0.369358i	$-0.120422\pi$
$60$		0			0
$61$		−	9.67418i		−	1.23865i	−0.785134	−	0.619326i	$-0.787406\pi$
$61$		−	9.67418i		−	1.23865i	0.785134	−	0.619326i	$-0.212594\pi$
$62$	1.33881	−	7.02760i	0.170029	−	0.892506i
$63$		0			0
$64$	−3.41683	−	7.23362i	−0.427103	−	0.904203i
$65$	−1.00000			−0.124035
$66$		0			0
$67$			1.50172i			0.183464i	0.995784	+	0.0917321i	$0.0292403\pi$
$67$			1.50172i			0.183464i	−0.995784	+	0.0917321i	$0.970760\pi$
$68$	1.85991	+	0.735342i	0.225547	+	0.0891733i
$69$		0			0
$70$	4.51380	+	0.859912i	0.539502	+	0.102779i
$71$	5.36641			0.636875			0.318438	−	0.947944i	$-0.396842\pi$
$71$	5.36641			0.636875			0.318438	+	0.947944i	$0.396842\pi$
$72$		0			0
$73$	3.55691			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$73$	3.55691			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$74$	−9.10905	−	1.73534i	−1.05891	−	0.201729i
$75$		0			0
$76$	2.94137	−	7.43965i	0.337398	−	0.853386i
$77$			3.43965i			0.391984i
$78$		0			0
$79$	−6.73281			−0.757501			−0.378750	−	0.925499i	$-0.623646\pi$
$79$	−6.73281			−0.757501			−0.378750	+	0.925499i	$0.623646\pi$
$80$	−2.73534	+	2.91855i	−0.305821	+	0.326303i
$81$		0			0
$82$	2.49828	−	13.1138i	0.275889	−	1.44818i
$83$			2.49828i			0.274222i	0.990556	+	0.137111i	$0.0437817\pi$
$83$			2.49828i			0.274222i	−0.990556	+	0.137111i	$0.956218\pi$
$84$		0			0
$85$		−	1.00000i		−	0.108465i
$86$	0.427568	+	0.0814549i	0.0461058	+	0.00878350i
$87$		0			0
$88$	−2.52932	−	1.60256i	−0.269626	−	0.170833i
$89$	−2.11727			−0.224430			−0.112215	−	0.993684i	$-0.535795\pi$
$89$	−2.11727			−0.224430			−0.112215	+	0.993684i	$0.535795\pi$
$90$		0			0
$91$			3.24914i			0.340602i
$92$	−5.47068	−	2.16291i	−0.570358	−	0.225499i
$93$		0			0
$94$	−1.80128	+	9.45517i	−0.185788	+	0.975226i
$95$	−4.00000			−0.410391
$96$		0			0
$97$	7.67418			0.779195			0.389597	−	0.920985i	$-0.372614\pi$
$97$	7.67418			0.779195			0.389597	+	0.920985i	$0.372614\pi$
$98$	0.941367	−	4.94137i	0.0950924	−	0.499153i
$99$		0			0
$100$	−7.43965	−	2.94137i	−0.743965	−	0.294137i
$101$			3.11383i			0.309838i	0.987927	+	0.154919i	$0.0495116\pi$
$101$			3.11383i			0.309838i	−0.987927	+	0.154919i	$0.950488\pi$
$102$		0			0
$103$	−17.6121			−1.73537			−0.867686	−	0.497112i	$-0.834394\pi$
$103$	−17.6121			−1.73537			−0.867686	+	0.497112i	$0.834394\pi$
$104$	−2.38923	−	1.51380i	−0.234283	−	0.148440i
$105$		0			0
$106$	−2.16291	−	0.412050i	−0.210080	−	0.0400219i
$107$			10.9414i			1.05774i	0.848702	+	0.528871i	$0.177384\pi$
$107$			10.9414i			1.05774i	−0.848702	+	0.528871i	$0.822616\pi$
$108$		0			0
$109$			10.3224i			0.988705i	0.869262	+	0.494352i	$0.164595\pi$
$109$			10.3224i			0.988705i	−0.869262	+	0.494352i	$0.835405\pi$
$110$	−0.280176	+	1.47068i	−0.0267137	+	0.140224i
$111$		0			0
$112$	9.48276	+	8.88751i	0.896037	+	0.839791i
$113$	17.1138			1.60993			0.804967	−	0.593320i	$-0.202183\pi$
$113$	17.1138			1.60993			0.804967	+	0.593320i	$0.202183\pi$
$114$		0			0
$115$			2.94137i			0.274284i
$116$	5.47068	−	13.8371i	0.507940	−	1.28474i
$117$		0			0
$118$	−7.88273	−	1.50172i	−0.725664	−	0.138244i
$119$	−3.24914			−0.297848
$120$		0			0
$121$	9.87930			0.898118
$122$	−13.4396	−	2.56035i	−1.21677	−	0.231803i
$123$		0			0
$124$	−9.40861	−	3.71982i	−0.844918	−	0.334050i
$125$			9.00000i			0.804984i
$126$		0			0
$127$	−15.9379			−1.41426			−0.707131	−	0.707082i	$-0.750011\pi$
$127$	−15.9379			−1.41426			−0.707131	+	0.707082i	$0.750011\pi$
$128$	−10.9534	+	2.83231i	−0.968157	+	0.250344i
$129$		0			0
$130$	−0.264658	+	1.38923i	−0.0232121	+	0.121843i
$131$		−	7.69223i		−	0.672073i	−0.941849	−	0.336036i	$-0.890913\pi$
$131$		−	7.69223i		−	0.672073i	0.941849	−	0.336036i	$-0.109087\pi$
$132$		0			0
$133$			12.9966i			1.12694i
$134$	2.08623	+	0.397442i	0.180223	+	0.0343338i
$135$		0			0
$136$	1.51380	−	2.38923i	0.129807	−	0.204875i
$137$	−5.32238			−0.454722			−0.227361	−	0.973811i	$-0.573010\pi$
$137$	−5.32238			−0.454722			−0.227361	+	0.973811i	$0.573010\pi$
$138$		0			0
$139$			12.4802i			1.05856i	0.848447	+	0.529280i	$0.177538\pi$
$139$			12.4802i			1.05856i	−0.848447	+	0.529280i	$0.822462\pi$
$140$	2.38923	−	6.04312i	0.201927	−	0.510736i
$141$		0			0
$142$	1.42026	−	7.45517i	0.119186	−	0.625624i
$143$	−1.05863			−0.0885274
$144$		0			0
$145$	−7.43965			−0.617829
$146$	0.941367	−	4.94137i	0.0779081	−	0.408950i
$147$		0			0
$148$	−4.82157	+	12.1953i	−0.396331	+	1.00245i
$149$		−	9.11383i		−	0.746634i	−0.927704	−	0.373317i	$-0.878220\pi$
$149$		−	9.11383i		−	0.746634i	0.927704	−	0.373317i	$-0.121780\pi$
$150$		0			0
$151$	−15.4216			−1.25499			−0.627496	−	0.778620i	$-0.715920\pi$
$151$	−15.4216			−1.25499			−0.627496	+	0.778620i	$0.715920\pi$
$152$	−9.55691	−	6.05520i	−0.775168	−	0.491141i
$153$		0			0
$154$	4.77846	+	0.910331i	0.385059	+	0.0733566i
$155$			5.05863i			0.406319i
$156$		0			0
$157$			3.79145i			0.302590i	0.988489	+	0.151295i	$0.0483444\pi$
$157$			3.79145i			0.302590i	−0.988489	+	0.151295i	$0.951656\pi$
$158$	−1.78189	+	9.35342i	−0.141760	+	0.744118i
$159$		0			0
$160$	3.33060	+	4.57243i	0.263307	+	0.361482i
$161$	9.55691			0.753190
$162$		0			0
$163$			4.17246i			0.326812i	0.986559	+	0.163406i	$0.0522481\pi$
$163$			4.17246i			0.326812i	−0.986559	+	0.163406i	$0.947752\pi$
$164$	−17.5569	−	6.94137i	−1.37096	−	0.542030i
$165$		0			0
$166$	3.47068	+	0.661191i	0.269377	+	0.0513184i
$167$	−14.2897			−1.10577			−0.552886	−	0.833257i	$-0.686474\pi$
$167$	−14.2897			−1.10577			−0.552886	+	0.833257i	$0.686474\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−1.38923	−	0.264658i	−0.106549	−	0.0202984i
$171$		0			0
$172$	0.226319	−	0.572432i	0.0172566	−	0.0436475i
$173$			6.99656i			0.531939i	0.963981	+	0.265969i	$0.0856920\pi$
$173$			6.99656i			0.531939i	−0.963981	+	0.265969i	$0.914308\pi$
$174$		0			0
$175$	12.9966			0.982448
$176$	−2.89572	+	3.08967i	−0.218273	+	0.232893i
$177$		0			0
$178$	−0.560352	+	2.94137i	−0.0420002	+	0.220465i
$179$		−	17.7474i		−	1.32650i	−0.748396	−	0.663252i	$-0.769176\pi$
$179$		−	17.7474i		−	1.32650i	0.748396	−	0.663252i	$-0.230824\pi$
$180$		0			0
$181$		−	8.11727i		−	0.603352i	−0.953411	−	0.301676i	$-0.902454\pi$
$181$		−	8.11727i		−	0.603352i	0.953411	−	0.301676i	$-0.0975460\pi$
$182$	4.51380	+	0.859912i	0.334585	+	0.0637409i
$183$		0			0
$184$	−4.45264	+	7.02760i	−0.328253	+	0.518081i
$185$	6.55691			0.482074
$186$		0			0
$187$		−	1.05863i		−	0.0774149i
$188$	12.6587	+	5.00478i	0.923228	+	0.365011i
$189$		0			0
$190$	−1.05863	+	5.55691i	−0.0768013	+	0.403141i
$191$	19.9379			1.44266			0.721329	−	0.692593i	$-0.243532\pi$
$191$	19.9379			1.44266			0.721329	+	0.692593i	$0.243532\pi$
$192$		0			0
$193$	4.11727			0.296367			0.148184	−	0.988960i	$-0.452657\pi$
$193$	4.11727			0.296367			0.148184	+	0.988960i	$0.452657\pi$
$194$	2.03104	−	10.6612i	0.145820	−	0.765429i
$195$		0			0
$196$	−6.61555	−	2.61555i	−0.472539	−	0.186825i
$197$		−	10.7914i		−	0.768859i	−0.923154	−	0.384429i	$-0.874398\pi$
$197$		−	10.7914i		−	0.768859i	0.923154	−	0.384429i	$-0.125602\pi$
$198$		0			0
$199$	0.615547			0.0436350			0.0218175	−	0.999762i	$-0.493055\pi$
$199$	0.615547			0.0436350			0.0218175	+	0.999762i	$0.493055\pi$
$200$	−6.05520	+	9.55691i	−0.428167	+	0.675776i
$201$		0			0
$202$	4.32582	+	0.824101i	0.304364	+	0.0579835i
$203$			24.1725i			1.69657i
$204$		0			0
$205$			9.43965i			0.659294i
$206$	−4.66119	+	24.4672i	−0.324761	+	1.70471i
$207$		0			0
$208$	−2.73534	+	2.91855i	−0.189662	+	0.202365i
$209$	−4.23453			−0.292909
$210$		0			0
$211$			1.80949i			0.124571i	0.998058	+	0.0622853i	$0.0198389\pi$
$211$			1.80949i			0.124571i	−0.998058	+	0.0622853i	$0.980161\pi$
$212$	−1.14486	+	2.89572i	−0.0786296	+	0.198879i
$213$		0			0
$214$	15.2001	+	2.89572i	1.03905	+	0.197948i
$215$	−0.307774			−0.0209900
$216$		0			0
$217$	16.4362			1.11576
$218$	14.3401	+	2.73190i	0.971237	+	0.185028i
$219$		0			0
$220$	1.96896	+	0.778457i	0.132748	+	0.0524836i
$221$		−	1.00000i		−	0.0672673i
$222$		0			0
$223$	−6.80605			−0.455767			−0.227884	−	0.973688i	$-0.573181\pi$
$223$	−6.80605			−0.455767			−0.227884	+	0.973688i	$0.573181\pi$
$224$	14.8565	−	10.8216i	0.992640	−	0.723047i
$225$		0			0
$226$	4.52932	−	23.7750i	0.301286	−	1.58149i
$227$			6.67074i			0.442753i	0.975188	+	0.221376i	$0.0710549\pi$
$227$			6.67074i			0.442753i	−0.975188	+	0.221376i	$0.928945\pi$
$228$		0			0
$229$		−	18.1138i		−	1.19700i	−0.801124	−	0.598498i	$-0.795765\pi$
$229$		−	18.1138i		−	1.19700i	0.801124	−	0.598498i	$-0.204235\pi$
$230$	4.08623	+	0.778457i	0.269438	+	0.0513299i
$231$		0			0
$232$	−17.7750	−	11.2621i	−1.16699	−	0.739395i
$233$	−11.4362			−0.749211			−0.374606	−	0.927184i	$-0.622222\pi$
$233$	−11.4362			−0.749211			−0.374606	+	0.927184i	$0.622222\pi$
$234$		0			0
$235$		−	6.80605i		−	0.443978i
$236$	−4.17246	+	10.5535i	−0.271604	+	0.686973i
$237$		0			0
$238$	−0.859912	+	4.51380i	−0.0557398	+	0.292586i
$239$	−16.8613			−1.09066			−0.545332	−	0.838220i	$-0.683596\pi$
$239$	−16.8613			−1.09066			−0.545332	+	0.838220i	$0.683596\pi$
$240$		0			0
$241$	−5.23109			−0.336964			−0.168482	−	0.985705i	$-0.553887\pi$
$241$	−5.23109			−0.336964			−0.168482	+	0.985705i	$0.553887\pi$
$242$	2.61464	−	13.7246i	0.168075	−	0.882251i
$243$		0			0
$244$	−7.11383	+	17.9931i	−0.455416	+	1.15189i
$245$			3.55691i			0.227243i
$246$		0			0
$247$	−4.00000			−0.254514
$248$	−7.65775	+	12.0862i	−0.486268	+	0.767476i
$249$		0			0
$250$	12.5031	+	2.38192i	0.790763	+	0.150646i
$251$		−	2.05520i		−	0.129723i	−0.997894	−	0.0648614i	$-0.979339\pi$
$251$		−	2.05520i		−	0.129723i	0.997894	−	0.0648614i	$-0.0206605\pi$
$252$		0			0
$253$			3.11383i			0.195765i
$254$	−4.21811	+	22.1414i	−0.264667	+	1.38928i
$255$		0			0
$256$	1.03581	+	15.9664i	0.0647382	+	0.997902i
$257$	21.2277			1.32414			0.662072	−	0.749440i	$-0.269677\pi$
$257$	21.2277			1.32414			0.662072	+	0.749440i	$0.269677\pi$
$258$		0			0
$259$		−	21.3043i		−	1.32379i
$260$	1.85991	+	0.735342i	0.115347	+	0.0456040i
$261$		0			0
$262$	−10.6863	−	2.03581i	−0.660199	−	0.125773i
$263$	−23.5569			−1.45258			−0.726291	−	0.687388i	$-0.758757\pi$
$263$	−23.5569			−1.45258			−0.726291	+	0.687388i	$0.758757\pi$
$264$		0			0
$265$	1.55691			0.0956405
$266$	18.0552	+	3.43965i	1.10704	+	0.210898i
$267$		0			0
$268$	1.10428	−	2.79307i	0.0674544	−	0.170614i
$269$		−	6.32582i		−	0.385692i	−0.981229	−	0.192846i	$-0.938228\pi$
$269$		−	6.32582i		−	0.385692i	0.981229	−	0.192846i	$-0.0617718\pi$
$270$		0			0
$271$	3.45769			0.210040			0.105020	−	0.994470i	$-0.466509\pi$
$271$	3.45769			0.210040			0.105020	+	0.994470i	$0.466509\pi$
$272$	−2.91855	−	2.73534i	−0.176963	−	0.165854i
$273$		0			0
$274$	−1.40861	+	7.39400i	−0.0850974	+	0.446688i
$275$			4.23453i			0.255352i
$276$		0			0
$277$			28.5535i			1.71561i	0.513974	+	0.857806i	$0.328173\pi$
$277$			28.5535i			1.71561i	−0.513974	+	0.857806i	$0.671827\pi$
$278$	17.3379	+	3.30300i	1.03986	+	0.198101i
$279$		0			0
$280$	−7.76294	−	4.91855i	−0.463924	−	0.293939i
$281$	−24.9966			−1.49117			−0.745585	−	0.666411i	$-0.767830\pi$
$281$	−24.9966			−1.49117			−0.745585	+	0.666411i	$0.767830\pi$
$282$		0			0
$283$		−	21.8207i		−	1.29710i	−0.761170	−	0.648552i	$-0.775375\pi$
$283$		−	21.8207i		−	1.29710i	0.761170	−	0.648552i	$-0.224625\pi$
$284$	−9.98104	−	3.94614i	−0.592266	−	0.234160i
$285$		0			0
$286$	−0.280176	+	1.47068i	−0.0165672	+	0.0869633i
$287$	30.6707			1.81044
$288$		0			0
$289$	−16.0000			−0.941176
$290$	−1.96896	+	10.3354i	−0.115622	+	0.606914i
$291$		0			0
$292$	−6.61555	−	2.61555i	−0.387146	−	0.153063i
$293$		−	27.4362i		−	1.60284i	−0.598102	−	0.801420i	$-0.704078\pi$
$293$		−	27.4362i		−	1.60284i	0.598102	−	0.801420i	$-0.295922\pi$
$294$		0			0
$295$	5.67418			0.330364
$296$	15.6660	+	9.92585i	0.910566	+	0.576928i
$297$		0			0
$298$	−12.6612	−	2.41205i	−0.733443	−	0.139726i
$299$			2.94137i			0.170104i
$300$		0			0
$301$			1.00000i			0.0576390i
$302$	−4.08145	+	21.4241i	−0.234861	+	1.23282i
$303$		0			0
$304$	−10.9414	+	11.6742i	−0.627530	+	0.669560i
$305$	9.67418			0.553942
$306$		0			0
$307$		−	26.6707i		−	1.52218i	−0.648646	−	0.761090i	$-0.724665\pi$
$307$		−	26.6707i		−	1.52218i	0.648646	−	0.761090i	$-0.275335\pi$
$308$	2.52932	−	6.39744i	0.144121	−	0.364528i
$309$		0			0
$310$	7.02760	+	1.33881i	0.399141	+	0.0760393i
$311$	−6.87930			−0.390089			−0.195045	−	0.980794i	$-0.562485\pi$
$311$	−6.87930			−0.390089			−0.195045	+	0.980794i	$0.562485\pi$
$312$		0			0
$313$	17.6707			0.998809			0.499405	−	0.866369i	$-0.333552\pi$
$313$	17.6707			0.998809			0.499405	+	0.866369i	$0.333552\pi$
$314$	5.26719	+	1.00344i	0.297245	+	0.0566273i
$315$		0			0
$316$	12.5224	+	4.95092i	0.704442	+	0.278511i
$317$		−	1.11383i		−	0.0625588i	−0.999511	−	0.0312794i	$-0.990042\pi$
$317$		−	1.11383i		−	0.0625588i	0.999511	−	0.0312794i	$-0.00995817\pi$
$318$		0			0
$319$	−7.87586			−0.440963
$320$	7.23362	−	3.41683i	0.404372	−	0.191006i
$321$		0			0
$322$	2.52932	−	13.2767i	0.140953	−	0.739884i
$323$		−	4.00000i		−	0.222566i
$324$		0			0
$325$			4.00000i			0.221880i
$326$	5.79650	+	1.10428i	0.321039	+	0.0611602i
$327$		0			0
$328$	−14.2897	+	22.5535i	−0.789018	+	1.24531i
$329$	−22.1138			−1.21917
$330$		0			0
$331$			18.4983i			1.01676i	0.861134	+	0.508379i	$0.169755\pi$
$331$			18.4983i			1.01676i	−0.861134	+	0.508379i	$0.830245\pi$
$332$	1.83709	−	4.64658i	0.100823	−	0.255014i
$333$		0			0
$334$	−3.78189	+	19.8517i	−0.206936	+	1.08624i
$335$	−1.50172			−0.0820477
$336$		0			0
$337$	−17.4362			−0.949811			−0.474905	−	0.880037i	$-0.657518\pi$
$337$	−17.4362			−0.949811			−0.474905	+	0.880037i	$0.657518\pi$
$338$	−0.264658	+	1.38923i	−0.0143955	+	0.0755641i
$339$		0			0
$340$	−0.735342	+	1.85991i	−0.0398795	+	0.100868i
$341$			5.35524i			0.290002i
$342$		0			0
$343$	−11.1871			−0.604045
$344$	−0.735342	−	0.465907i	−0.0396470	−	0.0251200i
$345$		0			0
$346$	9.71982	+	1.85170i	0.522541	+	0.0995479i
$347$			8.98539i			0.482361i	0.970480	+	0.241181i	$0.0775346\pi$
$347$			8.98539i			0.482361i	−0.970480	+	0.241181i	$0.922465\pi$
$348$		0			0
$349$			10.9931i			0.588448i	0.955736	+	0.294224i	$0.0950612\pi$
$349$			10.9931i			0.588448i	−0.955736	+	0.294224i	$0.904939\pi$
$350$	3.43965	−	18.0552i	0.183857	−	0.965091i
$351$		0			0
$352$	3.52588	+	4.84053i	0.187930	+	0.258001i
$353$	−23.2311			−1.23647			−0.618233	−	0.785995i	$-0.712151\pi$
$353$	−23.2311			−1.23647			−0.618233	+	0.785995i	$0.712151\pi$
$354$		0			0
$355$			5.36641i			0.284819i
$356$	3.93793	+	1.55691i	0.208710	+	0.0825163i
$357$		0			0
$358$	−24.6552	−	4.69700i	−1.30307	−	0.248244i
$359$	11.2863			0.595668			0.297834	−	0.954618i	$-0.403736\pi$
$359$	11.2863			0.595668			0.297834	+	0.954618i	$0.403736\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−11.2767	−	2.14830i	−0.592692	−	0.112912i
$363$		0			0
$364$	2.38923	−	6.04312i	0.125230	−	0.316745i
$365$			3.55691i			0.186177i
$366$		0			0
$367$	13.6121			0.710546			0.355273	−	0.934763i	$-0.384388\pi$
$367$	13.6121			0.710546			0.355273	+	0.934763i	$0.384388\pi$
$368$	8.58451	+	8.04564i	0.447499	+	0.419408i
$369$		0			0
$370$	1.73534	−	9.10905i	0.0902161	−	0.473557i
$371$		−	5.05863i		−	0.262631i
$372$		0			0
$373$		−	33.1070i		−	1.71421i	−0.515139	−	0.857107i	$-0.672260\pi$
$373$		−	33.1070i		−	1.71421i	0.515139	−	0.857107i	$-0.327740\pi$
$374$	−1.47068	−	0.280176i	−0.0760472	−	0.0144876i
$375$		0			0
$376$	10.3030	−	16.2612i	0.531337	−	0.838608i
$377$	−7.43965			−0.383161
$378$		0			0
$379$			33.1690i			1.70378i	0.523722	+	0.851889i	$0.324543\pi$
$379$			33.1690i			1.70378i	−0.523722	+	0.851889i	$0.675457\pi$
$380$	7.43965	+	2.94137i	0.381646	+	0.150889i
$381$		0			0
$382$	5.27674	−	27.6983i	0.269981	−	1.41717i
$383$	−33.0698			−1.68979			−0.844894	−	0.534934i	$-0.820337\pi$
$383$	−33.0698			−1.68979			−0.844894	+	0.534934i	$0.820337\pi$
$384$		0			0
$385$	−3.43965			−0.175301
$386$	1.08967	−	5.71982i	0.0554627	−	0.291131i
$387$		0			0
$388$	−14.2733	−	5.64315i	−0.724617	−	0.286487i
$389$		−	19.5569i		−	0.991575i	−0.868444	−	0.495787i	$-0.834880\pi$
$389$		−	19.5569i		−	0.991575i	0.868444	−	0.495787i	$-0.165120\pi$
$390$		0			0
$391$	−2.94137			−0.148751
$392$	−5.38445	+	8.49828i	−0.271956	+	0.429228i
$393$		0			0
$394$	−14.9918	−	2.85605i	−0.755275	−	0.143886i
$395$		−	6.73281i		−	0.338765i
$396$		0			0
$397$		−	34.2208i		−	1.71749i	−0.512402	−	0.858746i	$-0.671244\pi$
$397$		−	34.2208i		−	1.71749i	0.512402	−	0.858746i	$-0.328756\pi$
$398$	0.162910	−	0.855136i	0.00816593	−	0.0428641i
$399$		0			0
$400$	11.6742	+	10.9414i	0.583709	+	0.547068i
$401$	32.6707			1.63150			0.815750	−	0.578405i	$-0.196325\pi$
$401$	32.6707			1.63150			0.815750	+	0.578405i	$0.196325\pi$
$402$		0			0
$403$			5.05863i			0.251988i
$404$	2.28973	−	5.79145i	0.113918	−	0.288135i
$405$		0			0
$406$	33.5811	+	6.39744i	1.66660	+	0.317500i
$407$	6.94137			0.344071
$408$		0			0
$409$	−6.20855			−0.306993			−0.153497	−	0.988149i	$-0.549053\pi$
$409$	−6.20855			−0.306993			−0.153497	+	0.988149i	$0.549053\pi$
$410$	13.1138	+	2.49828i	0.647646	+	0.123381i
$411$		0			0
$412$	32.7570	+	12.9509i	1.61382	+	0.638046i
$413$		−	18.4362i		−	0.907187i
$414$		0			0
$415$	−2.49828			−0.122636
$416$	3.33060	+	4.57243i	0.163296	+	0.224182i
$417$		0			0
$418$	−1.12070	+	5.88273i	−0.0548154	+	0.287734i
$419$		−	0.369845i		−	0.0180681i	−0.999959	−	0.00903405i	$-0.997124\pi$
$419$		−	0.369845i		−	0.0180681i	0.999959	−	0.00903405i	$-0.00287567\pi$
$420$		0			0
$421$		−	3.87930i		−	0.189065i	−0.995522	−	0.0945327i	$-0.969864\pi$
$421$		−	3.87930i		−	0.189065i	0.995522	−	0.0945327i	$-0.0301357\pi$
$422$	2.51380	+	0.478897i	0.122370	+	0.0233124i
$423$		0			0
$424$	3.71982	+	2.35685i	0.180651	+	0.114459i
$425$	−4.00000			−0.194029
$426$		0			0
$427$		−	31.4328i		−	1.52114i
$428$	8.04564	−	20.3500i	0.388901	−	0.983653i
$429$		0			0
$430$	−0.0814549	+	0.427568i	−0.00392810	+	0.0206192i
$431$	−0.516327			−0.0248706			−0.0124353	−	0.999923i	$-0.503958\pi$
$431$	−0.516327			−0.0248706			−0.0124353	+	0.999923i	$0.503958\pi$
$432$		0			0
$433$	30.7846			1.47941			0.739706	−	0.672930i	$-0.234965\pi$
$433$	30.7846			1.47941			0.739706	+	0.672930i	$0.234965\pi$
$434$	4.34998	−	22.8337i	0.208806	−	1.09605i
$435$		0			0
$436$	7.59048	−	19.1987i	0.363518	−	0.919452i
$437$			11.7655i			0.562819i
$438$		0			0
$439$	30.4362			1.45264			0.726321	−	0.687356i	$-0.241229\pi$
$439$	30.4362			1.45264			0.726321	+	0.687356i	$0.241229\pi$
$440$	1.60256	−	2.52932i	0.0763989	−	0.120580i
$441$		0			0
$442$	−1.38923	−	0.264658i	−0.0660789	−	0.0125885i
$443$		−	3.45769i		−	0.164280i	−0.996621	−	0.0821400i	$-0.973825\pi$
$443$		−	3.45769i		−	0.164280i	0.996621	−	0.0821400i	$-0.0261755\pi$
$444$		0			0
$445$		−	2.11727i		−	0.100368i
$446$	−1.80128	+	9.45517i	−0.0852930	+	0.447715i
$447$		0			0
$448$	−11.1017	−	23.5031i	−0.524508	−	1.11042i
$449$	−14.7880			−0.697889			−0.348945	−	0.937143i	$-0.613460\pi$
$449$	−14.7880			−0.697889			−0.348945	+	0.937143i	$0.613460\pi$
$450$		0			0
$451$			9.99312i			0.470558i
$452$	−31.8302	−	12.5845i	−1.49717	−	0.591926i
$453$		0			0
$454$	9.26719	+	1.76547i	0.434931	+	0.0828575i
$455$	−3.24914			−0.152322
$456$		0			0
$457$	31.8759			1.49109			0.745545	−	0.666455i	$-0.232189\pi$
$457$	31.8759			1.49109			0.745545	+	0.666455i	$0.232189\pi$
$458$	−25.1642	−	4.79397i	−1.17585	−	0.224008i
$459$		0			0
$460$	2.16291	−	5.47068i	0.100846	−	0.255072i
$461$		−	18.5569i		−	0.864282i	−0.901806	−	0.432141i	$-0.857758\pi$
$461$		−	18.5569i		−	0.864282i	0.901806	−	0.432141i	$-0.142242\pi$
$462$		0			0
$463$	−24.8241			−1.15367			−0.576837	−	0.816859i	$-0.695713\pi$
$463$	−24.8241			−1.15367			−0.576837	+	0.816859i	$0.695713\pi$
$464$	−20.3500	+	21.7129i	−0.944724	+	1.00800i
$465$		0			0
$466$	−3.02669	+	15.8875i	−0.140209	+	0.735975i
$467$		−	40.2829i		−	1.86407i	−0.362371	−	0.932034i	$-0.618033\pi$
$467$		−	40.2829i		−	1.86407i	0.362371	−	0.932034i	$-0.381967\pi$
$468$		0			0
$469$			4.87930i			0.225305i
$470$	−9.45517	−	1.80128i	−0.436134	−	0.0830868i
$471$		0			0
$472$	13.5569	+	8.58957i	0.624008	+	0.395367i
$473$	−0.325819			−0.0149812
$474$		0			0
$475$			16.0000i			0.734130i
$476$	6.04312	+	2.38923i	0.276986	+	0.109510i
$477$		0			0
$478$	−4.46247	+	23.4241i	−0.204109	+	1.07139i
$479$	4.07324			0.186111			0.0930556	−	0.995661i	$-0.470337\pi$
$479$	4.07324			0.186111			0.0930556	+	0.995661i	$0.470337\pi$
$480$		0			0
$481$	6.55691			0.298970
$482$	−1.38445	+	7.26719i	−0.0630601	+	0.331011i
$483$		0			0
$484$	−18.3746	−	7.26466i	−0.835210	−	0.330212i
$485$			7.67418i			0.348467i
$486$		0			0
$487$	15.0518			0.682060			0.341030	−	0.940052i	$-0.389224\pi$
$487$	15.0518			0.682060			0.341030	+	0.940052i	$0.389224\pi$
$488$	23.1138	+	14.6448i	1.04631	+	0.662937i
$489$		0			0
$490$	4.94137	+	0.941367i	0.223228	+	0.0425266i
$491$			3.92676i			0.177212i	0.996067	+	0.0886061i	$0.0282412\pi$
$491$			3.92676i			0.177212i	−0.996067	+	0.0886061i	$0.971759\pi$
$492$		0			0
$493$		−	7.43965i		−	0.335065i
$494$	−1.05863	+	5.55691i	−0.0476302	+	0.250017i
$495$		0			0
$496$	14.7638	+	13.8371i	0.662916	+	0.621304i
$497$	17.4362			0.782121
$498$		0			0
$499$		−	32.3189i		−	1.44679i	−0.690432	−	0.723397i	$-0.742580\pi$
$499$		−	32.3189i		−	1.44679i	0.690432	−	0.723397i	$-0.257420\pi$
$500$	6.61808	−	16.7392i	0.295969	−	0.748600i
$501$		0			0
$502$	−2.85514	−	0.543924i	−0.127431	−	0.0242765i
$503$	16.1104			0.718327			0.359163	−	0.933275i	$-0.383062\pi$
$503$	16.1104			0.718327			0.359163	+	0.933275i	$0.383062\pi$
$504$		0			0
$505$	−3.11383			−0.138564
$506$	4.32582	+	0.824101i	0.192306	+	0.0366357i
$507$		0			0
$508$	29.6431	+	11.7198i	1.31520	+	0.519983i
$509$		−	16.2277i		−	0.719278i	−0.933091	−	0.359639i	$-0.882900\pi$
$509$		−	16.2277i		−	0.719278i	0.933091	−	0.359639i	$-0.117100\pi$
$510$		0			0
$511$	11.5569			0.511248
$512$	22.4552	+	2.78667i	0.992387	+	0.123155i
$513$		0			0
$514$	5.61808	−	29.4901i	0.247803	−	1.30075i
$515$		−	17.6121i		−	0.776082i
$516$		0			0
$517$		−	7.20512i		−	0.316881i
$518$	−29.5966	−	5.63837i	−1.30040	−	0.247736i
$519$		0			0
$520$	1.51380	−	2.38923i	0.0663845	−	0.104775i
$521$	8.32238			0.364610			0.182305	−	0.983242i	$-0.441644\pi$
$521$	8.32238			0.364610			0.182305	+	0.983242i	$0.441644\pi$
$522$		0			0
$523$		−	32.2829i		−	1.41163i	−0.708396	−	0.705815i	$-0.750581\pi$
$523$		−	32.2829i		−	1.41163i	0.708396	−	0.705815i	$-0.249419\pi$
$524$	−5.65641	+	14.3069i	−0.247102	+	0.624998i
$525$		0			0
$526$	−6.23453	+	32.7259i	−0.271839	+	1.42692i
$527$	−5.05863			−0.220358
$528$		0			0
$529$	−14.3484			−0.623842
$530$	0.412050	−	2.16291i	0.0178983	−	0.0939508i
$531$		0			0
$532$	9.55691	−	24.1725i	0.414345	−	1.04801i
$533$			9.43965i			0.408877i
$534$		0			0
$535$	−10.9414			−0.473037
$536$	−3.58795	−	2.27330i	−0.154976	−	0.0981916i
$537$		0			0
$538$	−8.78801	−	1.67418i	−0.378878	−	0.0721790i
$539$			3.76547i			0.162190i
$540$		0			0
$541$		−	2.32238i		−	0.0998470i	−0.998753	−	0.0499235i	$-0.984102\pi$
$541$		−	2.32238i		−	0.0998470i	0.998753	−	0.0499235i	$-0.0158977\pi$
$542$	0.915107	−	4.80353i	0.0393072	−	0.206329i
$543$		0			0
$544$	−4.57243	+	3.33060i	−0.196041	+	0.142798i
$545$	−10.3224			−0.442162
$546$		0			0
$547$			9.89390i			0.423033i	0.977374	+	0.211516i	$0.0678402\pi$
$547$			9.89390i			0.423033i	−0.977374	+	0.211516i	$0.932160\pi$
$548$	9.89916	+	3.91377i	0.422871	+	0.167188i
$549$		0			0
$550$	5.88273	+	1.12070i	0.250841	+	0.0477870i
$551$	−29.7586			−1.26776
$552$		0			0
$553$	−21.8759			−0.930256
$554$	39.6673	+	7.55691i	1.68530	+	0.321063i
$555$		0			0
$556$	9.17724	−	23.2121i	0.389202	−	0.984414i
$557$		−	30.3155i		−	1.28451i	−0.766491	−	0.642255i	$-0.777999\pi$
$557$		−	30.3155i		−	1.28451i	0.766491	−	0.642255i	$-0.222001\pi$
$558$		0			0
$559$	−0.307774			−0.0130174
$560$	−8.88751	+	9.48276i	−0.375566	+	0.400720i
$561$		0			0
$562$	−6.61555	+	34.7259i	−0.279060	+	1.46483i
$563$		−	38.7440i		−	1.63286i	−0.577441	−	0.816432i	$-0.695949\pi$
$563$		−	38.7440i		−	1.63286i	0.577441	−	0.816432i	$-0.304051\pi$
$564$		0			0
$565$			17.1138i			0.719984i
$566$	−30.3139	−	5.77502i	−1.27419	−	0.242742i
$567$		0			0
$568$	−8.12366	+	12.8216i	−0.340861	+	0.537981i
$569$	19.2345			0.806354			0.403177	−	0.915122i	$-0.367906\pi$
$569$	19.2345			0.806354			0.403177	+	0.915122i	$0.367906\pi$
$570$		0			0
$571$		−	10.8320i		−	0.453307i	−0.973976	−	0.226653i	$-0.927222\pi$
$571$		−	10.8320i		−	0.453307i	0.973976	−	0.226653i	$-0.0727784\pi$
$572$	1.96896	+	0.778457i	0.0823265	+	0.0325489i
$573$		0			0
$574$	8.11727	−	42.6087i	0.338808	−	1.77845i
$575$	11.7655			0.490654
$576$		0			0
$577$	−45.1329			−1.87891			−0.939454	−	0.342674i	$-0.888667\pi$
$577$	−45.1329			−1.87891			−0.939454	+	0.342674i	$0.888667\pi$
$578$	−4.23453	+	22.2277i	−0.176133	+	0.924549i
$579$		0			0
$580$	13.8371	+	5.47068i	0.574554	+	0.227158i
$581$			8.11727i			0.336761i
$582$		0			0
$583$	1.64820			0.0682615
$584$	−5.38445	+	8.49828i	−0.222810	+	0.351661i
$585$		0			0
$586$	−38.1152	−	7.26122i	−1.57452	−	0.299958i
$587$		−	5.05863i		−	0.208792i	−0.994536	−	0.104396i	$-0.966709\pi$
$587$		−	5.05863i		−	0.208792i	0.994536	−	0.104396i	$-0.0332910\pi$
$588$		0			0
$589$			20.2345i			0.833749i
$590$	1.50172	−	7.88273i	0.0618248	−	0.324527i
$591$		0			0
$592$	17.9354	−	19.1367i	0.737140	−	0.786511i
$593$	−29.4328			−1.20866			−0.604330	−	0.796734i	$-0.706559\pi$
$593$	−29.4328			−1.20866			−0.604330	+	0.796734i	$0.706559\pi$
$594$		0			0
$595$		−	3.24914i		−	0.133202i
$596$	−6.70178	+	16.9509i	−0.274516	+	0.694337i
$597$		0			0
$598$	4.08623	+	0.778457i	0.167098	+	0.0318335i
$599$	40.4293			1.65190			0.825949	−	0.563745i	$-0.190640\pi$
$599$	40.4293			1.65190			0.825949	+	0.563745i	$0.190640\pi$
$600$		0			0
$601$	−22.9931			−0.937909			−0.468955	−	0.883222i	$-0.655369\pi$
$601$	−22.9931			−0.937909			−0.468955	+	0.883222i	$0.655369\pi$
$602$	1.38923	+	0.264658i	0.0566207	+	0.0107867i
$603$		0			0
$604$	28.6828	+	11.3401i	1.16709	+	0.461424i
$605$			9.87930i			0.401650i
$606$		0			0
$607$	17.7846			0.721853			0.360927	−	0.932594i	$-0.382460\pi$
$607$	17.7846			0.721853			0.360927	+	0.932594i	$0.382460\pi$
$608$	13.3224	+	18.2897i	0.540294	+	0.741746i
$609$		0			0
$610$	2.56035	−	13.4396i	0.103666	−	0.544155i
$611$		−	6.80605i		−	0.275344i
$612$		0			0
$613$		−	24.2277i		−	0.978546i	−0.872131	−	0.489273i	$-0.837262\pi$
$613$		−	24.2277i		−	0.978546i	0.872131	−	0.489273i	$-0.162738\pi$
$614$	−37.0518	−	7.05863i	−1.49529	−	0.284863i
$615$		0			0
$616$	−8.21811	−	5.20693i	−0.331117	−	0.209793i
$617$	18.2277			0.733818			0.366909	−	0.930257i	$-0.380416\pi$
$617$	18.2277			0.733818			0.366909	+	0.930257i	$0.380416\pi$
$618$		0			0
$619$			43.1982i			1.73628i	0.496316	+	0.868142i	$0.334686\pi$
$619$			43.1982i			1.73628i	−0.496316	+	0.868142i	$0.665314\pi$
$620$	3.71982	−	9.40861i	0.149392	−	0.377859i
$621$		0			0
$622$	−1.82066	+	9.55691i	−0.0730019	+	0.383197i
$623$	−6.87930			−0.275613
$624$		0			0
$625$	11.0000			0.440000
$626$	4.67671	−	24.5487i	0.186919	−	0.981163i
$627$		0			0
$628$	2.78801	−	7.05176i	0.111254	−	0.281396i
$629$			6.55691i			0.261441i
$630$		0			0
$631$	−7.07668			−0.281718			−0.140859	−	0.990030i	$-0.544986\pi$
$631$	−7.07668			−0.281718			−0.140859	+	0.990030i	$0.544986\pi$
$632$	10.1921	−	16.0862i	0.405421	−	0.639876i
$633$		0			0
$634$	−1.54736	−	0.294784i	−0.0614536	−	0.0117074i
$635$		−	15.9379i		−	0.632477i
$636$		0			0
$637$			3.55691i			0.140930i
$638$	−2.08441	+	10.9414i	−0.0825226	+	0.433173i
$639$		0			0
$640$	−2.83231	−	10.9534i	−0.111957	−	0.432973i
$641$	28.2277			1.11493			0.557463	−	0.830202i	$-0.311775\pi$
$641$	28.2277			1.11493			0.557463	+	0.830202i	$0.311775\pi$
$642$		0			0
$643$			2.73281i			0.107772i	0.998547	+	0.0538858i	$0.0171607\pi$
$643$			2.73281i			0.107772i	−0.998547	+	0.0538858i	$0.982839\pi$
$644$	−17.7750	−	7.02760i	−0.700434	−	0.276926i
$645$		0			0
$646$	−5.55691	−	1.05863i	−0.218634	−	0.0416514i
$647$	14.5604			0.572427			0.286213	−	0.958166i	$-0.407603\pi$
$647$	14.5604			0.572427			0.286213	+	0.958166i	$0.407603\pi$
$648$		0			0
$649$	6.00688			0.235790
$650$	5.55691	+	1.05863i	0.217960	+	0.0415230i
$651$		0			0
$652$	3.06819	−	7.76041i	0.120159	−	0.303921i
$653$			29.3415i			1.14822i	0.818778	+	0.574111i	$0.194652\pi$
$653$			29.3415i			1.14822i	−0.818778	+	0.574111i	$0.805348\pi$
$654$		0			0
$655$	7.69223			0.300560
$656$	27.5500	+	25.8207i	1.07565	+	1.00813i
$657$		0			0
$658$	−5.85261	+	30.7212i	−0.228158	+	1.19764i
$659$			32.2829i			1.25756i	0.777583	+	0.628781i	$0.216446\pi$
$659$			32.2829i			1.25756i	−0.777583	+	0.628781i	$0.783554\pi$
$660$		0			0
$661$		−	24.4102i		−	0.949448i	−0.880135	−	0.474724i	$-0.842548\pi$
$661$		−	24.4102i		−	0.949448i	0.880135	−	0.474724i	$-0.157452\pi$
$662$	25.6983	+	4.89572i	0.998794	+	0.190278i
$663$		0			0
$664$	−5.96896	−	3.78189i	−0.231641	−	0.146766i
$665$	−12.9966			−0.503985
$666$		0			0
$667$			21.8827i			0.847303i
$668$	26.5776	+	10.5078i	1.02832	+	0.406560i
$669$		0			0
$670$	−0.397442	+	2.08623i	−0.0153545	+	0.0805981i
$671$	10.2414			0.395365
$672$		0			0
$673$	11.8793			0.457913			0.228957	−	0.973437i	$-0.426469\pi$
$673$	11.8793			0.457913			0.228957	+	0.973437i	$0.426469\pi$
$674$	−4.61464	+	24.2229i	−0.177749	+	0.933031i
$675$		0			0
$676$	1.85991	+	0.735342i	0.0715351	+	0.0282824i
$677$		−	8.76891i		−	0.337016i	−0.985700	−	0.168508i	$-0.946105\pi$
$677$		−	8.76891i		−	0.337016i	0.985700	−	0.168508i	$-0.0538950\pi$
$678$		0			0
$679$	24.9345			0.956898
$680$	2.38923	+	1.51380i	0.0916227	+	0.0580515i
$681$		0			0
$682$	7.43965	+	1.41731i	0.284879	+	0.0542715i
$683$		−	3.38445i		−	0.129502i	−0.997901	−	0.0647512i	$-0.979375\pi$
$683$		−	3.38445i		−	0.129502i	0.997901	−	0.0647512i	$-0.0206254\pi$
$684$		0			0
$685$		−	5.32238i		−	0.203358i
$686$	−2.96075	+	15.5414i	−0.113042	+	0.593373i
$687$		0			0
$688$	−0.841866	+	0.898251i	−0.0320958	+	0.0342455i
$689$	1.55691			0.0593137
$690$		0			0
$691$			11.2242i			0.426989i	0.976944	+	0.213495i	$0.0684846\pi$
$691$			11.2242i			0.426989i	−0.976944	+	0.213495i	$0.931515\pi$
$692$	5.14486	−	13.0130i	0.195578	−	0.494680i
$693$		0			0
$694$	12.4828	+	2.37806i	0.473839	+	0.0902699i
$695$	−12.4802			−0.473402
$696$		0			0
$697$	−9.43965			−0.357552
$698$	15.2720	+	2.90942i	0.578052	+	0.110123i
$699$		0			0
$700$	−24.1725	−	9.55691i	−0.913633	−	0.361217i
$701$			48.6707i			1.83827i	0.393944	+	0.919134i	$0.371110\pi$
$701$			48.6707i			1.83827i	−0.393944	+	0.919134i	$0.628890\pi$
$702$		0			0
$703$	26.2277			0.989195
$704$	7.65775	−	3.61717i	0.288612	−	0.136327i
$705$		0			0
$706$	−6.14830	+	32.2733i	−0.231394	+	1.21462i
$707$			10.1173i			0.380499i
$708$		0			0
$709$			11.7586i			0.441603i	0.975319	+	0.220802i	$0.0708673\pi$
$709$			11.7586i			0.441603i	−0.975319	+	0.220802i	$0.929133\pi$
$710$	7.45517	+	1.42026i	0.279787	+	0.0533016i
$711$		0			0
$712$	3.20512	−	5.05863i	0.120117	−	0.189580i
$713$	14.8793			0.557234
$714$		0			0
$715$		−	1.05863i		−	0.0395906i
$716$	−13.0504	+	33.0086i	−0.487717	+	1.23359i
$717$		0			0
$718$	2.98701	−	15.6792i	0.111474	−	0.585144i
$719$	38.7191			1.44398			0.721989	−	0.691905i	$-0.243228\pi$
$719$	38.7191			1.44398			0.721989	+	0.691905i	$0.243228\pi$
$720$		0			0
$721$	−57.2242			−2.13114
$722$	0.793975	−	4.16769i	0.0295487	−	0.155105i
$723$		0			0
$724$	−5.96896	+	15.0974i	−0.221835	+	0.561090i
$725$			29.7586i			1.10521i
$726$		0			0
$727$	−8.93449			−0.331362			−0.165681	−	0.986179i	$-0.552982\pi$
$727$	−8.93449			−0.331362			−0.165681	+	0.986179i	$0.552982\pi$
$728$	−7.76294	−	4.91855i	−0.287714	−	0.182293i
$729$		0			0
$730$	4.94137	+	0.941367i	0.182888	+	0.0348415i
$731$		−	0.307774i		−	0.0113834i
$732$		0			0
$733$		−	36.3484i		−	1.34256i	−0.741205	−	0.671279i	$-0.765745\pi$
$733$		−	36.3484i		−	1.34256i	0.741205	−	0.671279i	$-0.234255\pi$
$734$	3.60256	−	18.9103i	0.132973	−	0.697993i
$735$		0			0
$736$	13.4492	−	9.79650i	0.495744	−	0.361104i
$737$	−1.58977			−0.0585599
$738$		0			0
$739$		−	8.44309i		−	0.310584i	−0.987869	−	0.155292i	$-0.950368\pi$
$739$		−	8.44309i		−	0.310584i	0.987869	−	0.155292i	$-0.0496318\pi$
$740$	−12.1953	−	4.82157i	−0.448308	−	0.177245i
$741$		0			0
$742$	−7.02760	−	1.33881i	−0.257991	−	0.0491492i
$743$	−22.5354			−0.826745			−0.413372	−	0.910562i	$-0.635649\pi$
$743$	−22.5354			−0.826745			−0.413372	+	0.910562i	$0.635649\pi$
$744$		0			0
$745$	9.11383			0.333905
$746$	−45.9931	−	8.76203i	−1.68393	−	0.320801i
$747$		0			0
$748$	−0.778457	+	1.96896i	−0.0284632	+	0.0719925i
$749$			35.5500i			1.29897i
$750$		0			0
$751$	2.43621			0.0888986			0.0444493	−	0.999012i	$-0.485847\pi$
$751$	2.43621			0.0888986			0.0444493	+	0.999012i	$0.485847\pi$
$752$	−19.8638	−	18.6169i	−0.724357	−	0.678888i
$753$		0			0
$754$	−1.96896	+	10.3354i	−0.0717055	+	0.376392i
$755$		−	15.4216i		−	0.561250i
$756$		0			0
$757$			43.1329i			1.56769i	0.620955	+	0.783847i	$0.286745\pi$
$757$			43.1329i			1.56769i	−0.620955	+	0.783847i	$0.713255\pi$
$758$	46.0794	+	8.77846i	1.67368	+	0.318848i
$759$		0			0
$760$	6.05520	−	9.55691i	0.219645	−	0.346666i
$761$	−30.0191			−1.08819			−0.544096	−	0.839023i	$-0.683127\pi$
$761$	−30.0191			−1.08819			−0.544096	+	0.839023i	$0.683127\pi$
$762$		0			0
$763$			33.5389i			1.21419i
$764$	−37.0828	−	14.6612i	−1.34161	−	0.530423i
$765$		0			0
$766$	−8.75220	+	45.9415i	−0.316230	+	1.65993i
$767$	5.67418			0.204883
$768$		0			0
$769$	−35.3484			−1.27469			−0.637347	−	0.770577i	$-0.719968\pi$
$769$	−35.3484			−1.27469			−0.637347	+	0.770577i	$0.719968\pi$
$770$	−0.910331	+	4.77846i	−0.0328061	+	0.172204i
$771$		0			0
$772$	−7.65775	−	3.02760i	−0.275609	−	0.108966i
$773$			47.2277i			1.69866i	0.527862	+	0.849330i	$0.322994\pi$
$773$			47.2277i			1.69866i	−0.527862	+	0.849330i	$0.677006\pi$
$774$		0			0
$775$	20.2345			0.726846
$776$	−11.6172	+	18.3354i	−0.417032	+	0.658201i
$777$		0			0
$778$	−27.1690	−	5.17590i	−0.974057	−	0.185565i
$779$			37.7586i			1.35284i
$780$		0			0
$781$			5.68106i			0.203284i
$782$	−0.778457	+	4.08623i	−0.0278376	+	0.146123i
$783$		0			0
$784$	10.3810	+	9.72938i	0.370751	+	0.347478i
$785$	−3.79145			−0.135323
$786$		0			0
$787$		−	24.7880i		−	0.883597i	−0.897114	−	0.441799i	$-0.854341\pi$
$787$		−	24.7880i		−	0.883597i	0.897114	−	0.441799i	$-0.145659\pi$
$788$	−7.93540	+	20.0711i	−0.282687	+	0.715005i
$789$		0			0
$790$	−9.35342	−	1.78189i	−0.332780	−	0.0633970i
$791$	55.6052			1.97709
$792$		0			0
$793$	9.67418			0.343540
$794$	−47.5405	−	9.05681i	−1.68715	−	0.321414i
$795$		0			0
$796$	−1.14486	−	0.452638i	−0.0405786	−	0.0160433i
$797$		−	32.1104i		−	1.13741i	−0.822542	−	0.568704i	$-0.807445\pi$
$797$		−	32.1104i		−	1.13741i	0.822542	−	0.568704i	$-0.192555\pi$
$798$		0			0
$799$	6.80605			0.240781
$800$	18.2897	−	13.3224i	0.646640	−	0.471017i
$801$		0			0
$802$	8.64658	−	45.3871i	0.305321	−	1.60268i
$803$			3.76547i			0.132880i
$804$		0			0
$805$			9.55691i			0.336837i
$806$	7.02760	+	1.33881i	0.247537	+	0.0471575i
$807$		0			0
$808$	−7.43965	−	4.71371i	−0.261726	−	0.165828i
$809$	−4.55004			−0.159971			−0.0799854	−	0.996796i	$-0.525487\pi$
$809$	−4.55004			−0.159971			−0.0799854	+	0.996796i	$0.525487\pi$
$810$		0			0
$811$			48.3449i			1.69762i	0.528698	+	0.848810i	$0.322680\pi$
$811$			48.3449i			1.69762i	−0.528698	+	0.848810i	$0.677320\pi$
$812$	17.7750	−	44.9587i	0.623781	−	1.57774i
$813$		0			0
$814$	1.83709	−	9.64315i	0.0643900	−	0.337992i
$815$	−4.17246			−0.146155
$816$		0			0
$817$	−1.23109			−0.0430706
$818$	−1.64315	+	8.62510i	−0.0574512	+	0.301570i
$819$		0			0
$820$	6.94137	−	17.5569i	0.242403	−	0.613114i
$821$			24.3484i			0.849764i	0.905249	+	0.424882i	$0.139684\pi$
$821$			24.3484i			0.849764i	−0.905249	+	0.424882i	$0.860316\pi$
$822$		0			0
$823$	−28.4431			−0.991464			−0.495732	−	0.868476i	$-0.665100\pi$
$823$	−28.4431			−0.991464			−0.495732	+	0.868476i	$0.665100\pi$
$824$	26.6612	−	42.0794i	0.928787	−	1.46590i
$825$		0			0
$826$	−25.6121	−	4.87930i	−0.891159	−	0.169772i
$827$			34.6448i			1.20472i	0.798226	+	0.602358i	$0.205772\pi$
$827$			34.6448i			1.20472i	−0.798226	+	0.602358i	$0.794228\pi$
$828$		0			0
$829$			34.2208i			1.18854i	0.804267	+	0.594268i	$0.202558\pi$
$829$			34.2208i			1.18854i	−0.804267	+	0.594268i	$0.797442\pi$
$830$	−0.661191	+	3.47068i	−0.0229503	+	0.120469i
$831$		0			0
$832$	7.23362	−	3.41683i	0.250781	−	0.118457i
$833$	−3.55691			−0.123240
$834$		0			0
$835$		−	14.2897i		−	0.494516i
$836$	7.87586	+	3.11383i	0.272392	+	0.107694i
$837$		0			0
$838$	−0.513799	−	0.0978825i	−0.0177489	−	0.00338129i
$839$	−12.9345			−0.446548			−0.223274	−	0.974756i	$-0.571675\pi$
$839$	−12.9345			−0.446548			−0.223274	+	0.974756i	$0.571675\pi$
$840$		0			0
$841$	−26.3484			−0.908564
$842$	−5.38923	−	1.02669i	−0.185725	−	0.0353820i
$843$		0			0
$844$	1.33060	−	3.36550i	0.0458010	−	0.115845i
$845$		−	1.00000i		−	0.0344010i
$846$		0			0
$847$	32.0992			1.10294
$848$	4.25869	−	4.54392i	0.146244	−	0.156039i
$849$		0			0
$850$	−1.05863	+	5.55691i	−0.0363108	+	0.190601i
$851$		−	19.2863i		−	0.661126i
$852$		0			0
$853$			31.6448i			1.08350i	0.840541	+	0.541748i	$0.182237\pi$
$853$			31.6448i			1.08350i	−0.840541	+	0.541748i	$0.817763\pi$
$854$	−43.6673	−	8.31894i	−1.49426	−	0.284668i
$855$		0			0
$856$	−26.1414	−	16.5630i	−0.893496	−	0.566113i
$857$	−38.8724			−1.32786			−0.663928	−	0.747796i	$-0.731112\pi$
$857$	−38.8724			−1.32786			−0.663928	+	0.747796i	$0.731112\pi$
$858$		0			0
$859$		−	29.8207i		−	1.01747i	−0.860924	−	0.508734i	$-0.830114\pi$
$859$		−	29.8207i		−	1.01747i	0.860924	−	0.508734i	$-0.169886\pi$
$860$	0.572432	+	0.226319i	0.0195198	+	0.00771741i
$861$		0			0
$862$	−0.136650	+	0.717296i	−0.00465432	+	0.0244312i
$863$	−24.5163			−0.834545			−0.417273	−	0.908781i	$-0.637014\pi$
$863$	−24.5163			−0.834545			−0.417273	+	0.908781i	$0.637014\pi$
$864$		0			0
$865$	−6.99656			−0.237890
$866$	8.14739	−	42.7668i	0.276860	−	1.45328i
$867$		0			0
$868$	−30.5699	−	12.0862i	−1.03761	−	0.410233i
$869$		−	7.12758i		−	0.241787i
$870$		0			0
$871$	−1.50172			−0.0508838
$872$	−24.6625	−	15.6260i	−0.835179	−	0.529163i
$873$		0			0
$874$	16.3449	+	3.11383i	0.552875	+	0.105327i
$875$			29.2423i			0.988569i
$876$		0			0
$877$		−	4.34836i		−	0.146834i	−0.997301	−	0.0734169i	$-0.976610\pi$
$877$		−	4.34836i		−	0.146834i	0.997301	−	0.0734169i	$-0.0233904\pi$
$878$	8.05520	−	42.2829i	0.271850	−	1.42698i
$879$		0			0
$880$	−3.08967	−	2.89572i	−0.104153	−	0.0976148i
$881$	−27.6967			−0.933126			−0.466563	−	0.884488i	$-0.654508\pi$
$881$	−27.6967			−0.933126			−0.466563	+	0.884488i	$0.654508\pi$
$882$		0			0
$883$		−	14.0440i		−	0.472619i	−0.971678	−	0.236310i	$-0.924062\pi$
$883$		−	14.0440i		−	0.472619i	0.971678	−	0.236310i	$-0.0759379\pi$
$884$	−0.735342	+	1.85991i	−0.0247322	+	0.0625556i
$885$		0			0
$886$	−4.80353	−	0.915107i	−0.161378	−	0.0307436i
$887$	3.66730			0.123136			0.0615680	−	0.998103i	$-0.480390\pi$
$887$	3.66730			0.123136			0.0615680	+	0.998103i	$0.480390\pi$
$888$		0			0
$889$	−51.7846			−1.73680
$890$	−2.94137	−	0.560352i	−0.0985948	−	0.0187830i
$891$		0			0
$892$	12.6587	+	5.00478i	0.423843	+	0.167572i
$893$		−	27.2242i		−	0.911024i
$894$		0			0
$895$	17.7474			0.593231
$896$	−35.5893	+	9.20259i	−1.18895	+	0.307437i
$897$		0			0
$898$	−3.91377	+	20.5439i	−0.130604	+	0.685560i
$899$			37.6344i			1.25518i
$900$		0			0
$901$			1.55691i			0.0518683i
$902$	13.8827	+	2.64476i	0.462244	+	0.0880610i
$903$		0			0
$904$	−25.9069	+	40.8888i	−0.861650	+	1.35994i
$905$	8.11727			0.269827
$906$		0			0
$907$		−	9.39239i		−	0.311869i	−0.987767	−	0.155935i	$-0.950161\pi$
$907$		−	9.39239i		−	0.311869i	0.987767	−	0.155935i	$-0.0498389\pi$
$908$	4.90528	−	12.4070i	0.162787	−	0.411741i
$909$		0			0
$910$	−0.859912	+	4.51380i	−0.0285058	+	0.149631i
$911$	−3.64496			−0.120763			−0.0603815	−	0.998175i	$-0.519232\pi$
$911$	−3.64496			−0.120763			−0.0603815	+	0.998175i	$0.519232\pi$
$912$		0			0
$913$	−2.64476			−0.0875289
$914$	8.43621	−	44.2829i	0.279045	−	1.46475i
$915$		0			0
$916$	−13.3199	+	33.6901i	−0.440100	+	1.11315i
$917$		−	24.9931i		−	0.825346i
$918$		0			0
$919$	12.6516			0.417339			0.208670	−	0.977986i	$-0.433087\pi$
$919$	12.6516			0.417339			0.208670	+	0.977986i	$0.433087\pi$
$920$	−7.02760	−	4.45264i	−0.231693	−	0.146799i
$921$		0			0
$922$	−25.7798	−	4.91124i	−0.849012	−	0.161743i
$923$			5.36641i			0.176637i
$924$		0			0
$925$		−	26.2277i		−	0.862360i
$926$	−6.56990	+	34.4863i	−0.215900	+	1.13329i
$927$		0			0
$928$	24.7785	+	34.0173i	0.813393	+	1.11667i
$929$	−37.1070			−1.21744			−0.608720	−	0.793385i	$-0.708317\pi$
$929$	−37.1070			−1.21744			−0.608720	+	0.793385i	$0.708317\pi$
$930$		0			0
$931$			14.2277i			0.466293i
$932$	21.2703	+	8.40952i	0.696733	+	0.275463i
$933$		0			0
$934$	−55.9621	−	10.6612i	−1.83114	−	0.348845i
$935$	1.05863			0.0346210
$936$		0			0
$937$	50.8724			1.66193			0.830965	−	0.556325i	$-0.187789\pi$
$937$	50.8724			1.66193			0.830965	+	0.556325i	$0.187789\pi$
$938$	6.77846	+	1.29135i	0.221324	+	0.0421639i
$939$		0			0
$940$	−5.00478	+	12.6587i	−0.163238	+	0.412880i
$941$		−	21.4622i		−	0.699647i	−0.936816	−	0.349824i	$-0.886241\pi$
$941$		−	21.4622i		−	0.699647i	0.936816	−	0.349824i	$-0.113759\pi$
$942$		0			0
$943$	27.7655			0.904168
$944$	15.5208	−	16.5604i	0.505160	−	0.538994i
$945$		0			0
$946$	−0.0862308	+	0.452638i	−0.00280361	+	0.0147165i
$947$		−	61.1690i		−	1.98773i	−0.110617	−	0.993863i	$-0.535283\pi$
$947$		−	61.1690i		−	1.98773i	0.110617	−	0.993863i	$-0.464717\pi$
$948$		0			0
$949$			3.55691i			0.115462i
$950$	22.2277	+	4.23453i	0.721160	+	0.137386i
$951$		0			0
$952$	4.91855	−	7.76294i	0.159411	−	0.251598i
$953$	−13.2345			−0.428709			−0.214354	−	0.976756i	$-0.568765\pi$
$953$	−13.2345			−0.428709			−0.214354	+	0.976756i	$0.568765\pi$
$954$		0			0
$955$			19.9379i			0.645176i
$956$	31.3604	+	12.3988i	1.01427	+	0.401005i
$957$		0			0
$958$	1.07802	−	5.65866i	0.0348291	−	0.182823i
$959$	−17.2932			−0.558425
$960$		0			0
$961$	−5.41023			−0.174524
$962$	1.73534	−	9.10905i	0.0559497	−	0.293688i
$963$		0			0
$964$	9.72938	+	3.84664i	0.313362	+	0.123892i
$965$			4.11727i			0.132539i
$966$		0			0
$967$	48.4441			1.55786			0.778929	−	0.627112i	$-0.215763\pi$
$967$	48.4441			1.55786			0.778929	+	0.627112i	$0.215763\pi$
$968$	−14.9553	+	23.6039i	−0.480680	+	0.758658i
$969$		0			0
$970$	10.6612	+	2.03104i	0.342310	+	0.0652126i
$971$		−	5.69910i		−	0.182893i	−0.995810	−	0.0914464i	$-0.970851\pi$
$971$		−	5.69910i		−	0.182893i	0.995810	−	0.0914464i	$-0.0291490\pi$
$972$		0			0
$973$			40.5500i			1.29997i
$974$	3.98357	−	20.9103i	0.127642	−	0.670010i
$975$		0			0
$976$	26.4622	−	28.2345i	0.847034	−	0.903765i
$977$	−2.65164			−0.0848334			−0.0424167	−	0.999100i	$-0.513506\pi$
$977$	−2.65164			−0.0848334			−0.0424167	+	0.999100i	$0.513506\pi$
$978$		0			0
$979$		−	2.24141i		−	0.0716357i
$980$	2.61555	−	6.61555i	0.0835506	−	0.211326i
$981$		0			0
$982$	5.45517	+	1.03925i	0.174081	+	0.0331638i
$983$	−27.2491			−0.869113			−0.434556	−	0.900645i	$-0.643095\pi$
$983$	−27.2491			−0.869113			−0.434556	+	0.900645i	$0.643095\pi$
$984$		0			0
$985$	10.7914			0.343844
$986$	−10.3354	−	1.96896i	−0.329145	−	0.0627046i
$987$		0			0
$988$	7.43965	+	2.94137i	0.236687	+	0.0935773i
$989$			0.905275i			0.0287861i
$990$		0			0
$991$	22.7552			0.722841			0.361421	−	0.932403i	$-0.382292\pi$
$991$	22.7552			0.722841			0.361421	+	0.932403i	$0.382292\pi$
$992$	23.1303	−	16.8483i	0.734386	−	0.534933i
$993$		0			0
$994$	4.61464	−	24.2229i	0.146367	−	0.768303i
$995$			0.615547i			0.0195142i
$996$		0			0
$997$		−	4.79488i		−	0.151856i	−0.997113	−	0.0759278i	$-0.975808\pi$
$997$		−	4.79488i		−	0.151856i	0.997113	−	0.0759278i	$-0.0241918\pi$
$998$	−44.8984	−	8.55348i	−1.42123	−	0.270756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.g.c.469.3		6
3.2	odd	2		104.2.b.c.53.4	yes	6
4.3	odd	2		3744.2.g.c.1873.4		6
8.3	odd	2		3744.2.g.c.1873.1		6
8.5	even	2	inner	936.2.g.c.469.4		6
12.11	even	2		416.2.b.c.209.1		6
24.5	odd	2		104.2.b.c.53.3	✓	6
24.11	even	2		416.2.b.c.209.6		6
48.5	odd	4		3328.2.a.bh.1.3		3
48.11	even	4		3328.2.a.bf.1.1		3
48.29	odd	4		3328.2.a.be.1.1		3
48.35	even	4		3328.2.a.bg.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.b.c.53.3	✓	6	24.5	odd	2
104.2.b.c.53.4	yes	6	3.2	odd	2
416.2.b.c.209.1		6	12.11	even	2
416.2.b.c.209.6		6	24.11	even	2
936.2.g.c.469.3		6	1.1	even	1	trivial
936.2.g.c.469.4		6	8.5	even	2	inner
3328.2.a.be.1.1		3	48.29	odd	4
3328.2.a.bf.1.1		3	48.11	even	4
3328.2.a.bg.1.3		3	48.35	even	4
3328.2.a.bh.1.3		3	48.5	odd	4
3744.2.g.c.1873.1		6	8.3	odd	2
3744.2.g.c.1873.4		6	4.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.264658 - 1.38923i) q^{2} +(-1.85991 - 0.735342i) q^{4} +1.00000i q^{5} +3.24914 q^{7} +(-1.51380 + 2.38923i) q^{8} +(1.38923 + 0.264658i) q^{10} +1.05863i q^{11} +1.00000i q^{13} +(0.859912 - 4.51380i) q^{14} +(2.91855 + 2.73534i) q^{16} -1.00000 q^{17} +4.00000i q^{19} +(0.735342 - 1.85991i) q^{20} +(1.47068 + 0.280176i) q^{22} +2.94137 q^{23} +4.00000 q^{25} +(1.38923 + 0.264658i) q^{26} +(-6.04312 - 2.38923i) q^{28} +7.43965i q^{29} +5.05863 q^{31} +(4.57243 - 3.33060i) q^{32} +(-0.264658 + 1.38923i) q^{34} +3.24914i q^{35} -6.55691i q^{37} +(5.55691 + 1.05863i) q^{38} +(-2.38923 - 1.51380i) q^{40} +9.43965 q^{41} +0.307774i q^{43} +(0.778457 - 1.96896i) q^{44} +(0.778457 - 4.08623i) q^{46} -6.80605 q^{47} +3.55691 q^{49} +(1.05863 - 5.55691i) q^{50} +(0.735342 - 1.85991i) q^{52} -1.55691i q^{53} -1.05863 q^{55} +(-4.91855 + 7.76294i) q^{56} +(10.3354 + 1.96896i) q^{58} -5.67418i q^{59} -9.67418i q^{61} +(1.33881 - 7.02760i) q^{62} +(-3.41683 - 7.23362i) q^{64} -1.00000 q^{65} +1.50172i q^{67} +(1.85991 + 0.735342i) q^{68} +(4.51380 + 0.859912i) q^{70} +5.36641 q^{71} +3.55691 q^{73} +(-9.10905 - 1.73534i) q^{74} +(2.94137 - 7.43965i) q^{76} +3.43965i q^{77} -6.73281 q^{79} +(-2.73534 + 2.91855i) q^{80} +(2.49828 - 13.1138i) q^{82} +2.49828i q^{83} -1.00000i q^{85} +(0.427568 + 0.0814549i) q^{86} +(-2.52932 - 1.60256i) q^{88} -2.11727 q^{89} +3.24914i q^{91} +(-5.47068 - 2.16291i) q^{92} +(-1.80128 + 9.45517i) q^{94} -4.00000 q^{95} +7.67418 q^{97} +(0.941367 - 4.94137i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} - 2 q^{4} + 2 q^{7} + 8 q^{8} - 4 q^{14} + 10 q^{16} - 6 q^{17} + 4 q^{20} + 8 q^{22} + 16 q^{23} + 24 q^{25} - 20 q^{28} + 32 q^{31} + 12 q^{32} - 2 q^{34} - 6 q^{40} + 20 q^{41} - 12 q^{44}+ \cdots + 4 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 - 2 * q^4 + 2 * q^7 + 8 * q^8 - 4 * q^14 + 10 * q^16 - 6 * q^17 + 4 * q^20 + 8 * q^22 + 16 * q^23 + 24 * q^25 - 20 * q^28 + 32 * q^31 + 12 * q^32 - 2 * q^34 - 6 * q^40 + 20 * q^41 - 12 * q^44 - 12 * q^46 + 10 * q^47 - 12 * q^49 + 8 * q^50 + 4 * q^52 - 8 * q^55 - 22 * q^56 + 12 * q^58 + 28 * q^62 + 22 * q^64 - 6 * q^65 + 2 * q^68 + 10 * q^70 + 18 * q^71 - 12 * q^73 - 28 * q^74 + 16 * q^76 - 12 * q^79 - 16 * q^80 - 20 * q^82 + 18 * q^86 - 16 * q^88 - 16 * q^89 - 32 * q^92 - 24 * q^95 + 16 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more