LMFDB - Embedded newform 432.2.u.e.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	432.193
Dual form			432.2.u.e.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70050 - 0.329088i) q^{3} +(0.198034 - 1.12311i) q^{5} +(-0.914338 + 0.767221i) q^{7} +(2.78340 - 1.11923i) q^{9} +O(q^{10})$	\(q+(1.70050 - 0.329088i) q^{3} +(0.198034 - 1.12311i) q^{5} +(-0.914338 + 0.767221i) q^{7} +(2.78340 - 1.11923i) q^{9} +(0.411958 + 2.33633i) q^{11} +(4.28496 - 1.55960i) q^{13} +(-0.0328444 - 1.97501i) q^{15} +(2.15278 - 3.72872i) q^{17} +(0.315991 + 0.547312i) q^{19} +(-1.30235 + 1.60556i) q^{21} +(-1.05775 - 0.887560i) q^{23} +(3.47631 + 1.26527i) q^{25} +(4.36485 - 2.81924i) q^{27} +(-9.61862 - 3.50089i) q^{29} +(-3.28435 - 2.75590i) q^{31} +(1.46939 + 3.83736i) q^{33} +(0.680600 + 1.17883i) q^{35} +(-4.23589 + 7.33678i) q^{37} +(6.77333 - 4.06223i) q^{39} +(-3.43000 + 1.24842i) q^{41} +(1.34522 + 7.62909i) q^{43} +(-0.705806 - 3.34770i) q^{45} +(-1.89320 + 1.58858i) q^{47} +(-0.968151 + 5.49066i) q^{49} +(2.43372 - 7.04914i) q^{51} +1.65993 q^{53} +2.70553 q^{55} +(0.717456 + 0.826715i) q^{57} +(2.05606 - 11.6605i) q^{59} +(1.11147 - 0.932633i) q^{61} +(-1.68627 + 3.15884i) q^{63} +(-0.903027 - 5.12132i) q^{65} +(-14.0501 + 5.11383i) q^{67} +(-2.09079 - 1.16120i) q^{69} +(-3.74388 + 6.48459i) q^{71} +(5.22698 + 9.05339i) q^{73} +(6.32786 + 1.00759i) q^{75} +(-2.16915 - 1.82013i) q^{77} +(13.0535 + 4.75107i) q^{79} +(6.49465 - 6.23053i) q^{81} +(-4.64588 - 1.69096i) q^{83} +(-3.76143 - 3.15621i) q^{85} +(-17.5086 - 2.78789i) q^{87} +(4.93727 + 8.55160i) q^{89} +(-2.72135 + 4.71351i) q^{91} +(-6.49197 - 3.60556i) q^{93} +(0.677266 - 0.246505i) q^{95} +(-1.74722 - 9.90896i) q^{97} +(3.76153 + 6.04187i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) $ 24 * q + 3 * q^7 + 6 * q^9	$ 24 q + 3 q^{7} + 6 q^{9} - 6 q^{11} + 12 q^{13} + 3 q^{15} + 6 q^{17} - 9 q^{19} - 18 q^{21} - 24 q^{23} - 24 q^{25} - 9 q^{29} + 27 q^{31} + 21 q^{33} + 18 q^{35} + 15 q^{37} + 15 q^{39} - 6 q^{41} - 39 q^{43} - 69 q^{45} + 36 q^{47} + 3 q^{49} + 36 q^{51} - 18 q^{53} + 54 q^{55} + 27 q^{57} + 30 q^{59} + 12 q^{61} - 18 q^{63} - 18 q^{65} - 54 q^{67} - 57 q^{69} + 36 q^{73} + 51 q^{75} - 24 q^{77} + 45 q^{79} + 18 q^{81} - 33 q^{83} - 57 q^{85} - 90 q^{87} + 9 q^{89} - 39 q^{91} + 42 q^{93} - 87 q^{95} + 57 q^{97} + 24 q^{99}+O(q^{100}) $ 24 * q + 3 * q^7 + 6 * q^9 - 6 * q^11 + 12 * q^13 + 3 * q^15 + 6 * q^17 - 9 * q^19 - 18 * q^21 - 24 * q^23 - 24 * q^25 - 9 * q^29 + 27 * q^31 + 21 * q^33 + 18 * q^35 + 15 * q^37 + 15 * q^39 - 6 * q^41 - 39 * q^43 - 69 * q^45 + 36 * q^47 + 3 * q^49 + 36 * q^51 - 18 * q^53 + 54 * q^55 + 27 * q^57 + 30 * q^59 + 12 * q^61 - 18 * q^63 - 18 * q^65 - 54 * q^67 - 57 * q^69 + 36 * q^73 + 51 * q^75 - 24 * q^77 + 45 * q^79 + 18 * q^81 - 33 * q^83 - 57 * q^85 - 90 * q^87 + 9 * q^89 - 39 * q^91 + 42 * q^93 - 87 * q^95 + 57 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{9}\right)$

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			0
$2$		0			0
$3$	1.70050	−	0.329088i	0.981784	−	0.189999i
$3$	1.70050	−	0.329088i	0.981784	−	0.189999i
$4$		0			0
$5$	0.198034	−	1.12311i	0.0885634	−	0.502268i	−0.907967	−	0.419041i	$-0.862366\pi$
$5$	0.198034	−	1.12311i	0.0885634	−	0.502268i	0.996531	−	0.0832270i	$-0.0265226\pi$
$6$		0			0
$7$	−0.914338	+	0.767221i	−0.345587	+	0.289982i	−0.799015	−	0.601311i	$-0.794645\pi$
$7$	−0.914338	+	0.767221i	−0.345587	+	0.289982i	0.453428	+	0.891293i	$0.350201\pi$
$8$		0			0
$9$	2.78340	−	1.11923i	0.927801	−	0.373077i
$10$		0			0
$11$	0.411958	+	2.33633i	0.124210	+	0.704430i	0.981774	+	0.190053i	$0.0608658\pi$
$11$	0.411958	+	2.33633i	0.124210	+	0.704430i	−0.857564	+	0.514377i	$0.828023\pi$
$12$		0			0
$13$	4.28496	−	1.55960i	1.18843	−	0.432555i	0.329261	−	0.944239i	$-0.393200\pi$
$13$	4.28496	−	1.55960i	1.18843	−	0.432555i	0.859174	+	0.511684i	$0.170978\pi$
$14$		0			0
$15$	−0.0328444	−	1.97501i	−0.00848039	−	0.509946i
$16$		0			0
$17$	2.15278	−	3.72872i	0.522125	−	0.904348i	−0.477543	−	0.878608i	$-0.658473\pi$
$17$	2.15278	−	3.72872i	0.522125	−	0.904348i	0.999669	−	0.0257394i	$-0.00819402\pi$
$18$		0			0
$19$	0.315991	+	0.547312i	0.0724933	+	0.125562i	0.899993	−	0.435903i	$-0.143571\pi$
$19$	0.315991	+	0.547312i	0.0724933	+	0.125562i	−0.827500	+	0.561465i	$0.810238\pi$
$20$		0			0
$21$	−1.30235	+	1.60556i	−0.284196	+	0.350361i
$22$		0			0
$23$	−1.05775	−	0.887560i	−0.220557	−	0.185069i	0.525814	−	0.850600i	$-0.323761\pi$
$23$	−1.05775	−	0.887560i	−0.220557	−	0.185069i	−0.746371	+	0.665531i	$0.768205\pi$
$24$		0			0
$25$	3.47631	+	1.26527i	0.695263	+	0.253055i
$26$		0			0
$27$	4.36485	−	2.81924i	0.840016	−	0.542562i
$28$		0			0
$29$	−9.61862	−	3.50089i	−1.78613	−	0.650099i	−0.999464	−	0.0327235i	$-0.989582\pi$
$29$	−9.61862	−	3.50089i	−1.78613	−	0.650099i	−0.786668	−	0.617376i	$-0.788196\pi$
$30$		0			0
$31$	−3.28435	−	2.75590i	−0.589887	−	0.494974i	0.298290	−	0.954475i	$-0.403584\pi$
$31$	−3.28435	−	2.75590i	−0.589887	−	0.494974i	−0.888177	+	0.459501i	$0.848028\pi$
$32$		0			0
$33$	1.46939	+	3.83736i	0.255789	+	0.667998i
$34$		0			0
$35$	0.680600	+	1.17883i	0.115042	+	0.199259i
$36$		0			0
$37$	−4.23589	+	7.33678i	−0.696377	+	1.20616i	0.273338	+	0.961918i	$0.411872\pi$
$37$	−4.23589	+	7.33678i	−0.696377	+	1.20616i	−0.969714	+	0.244242i	$0.921461\pi$
$38$		0			0
$39$	6.77333	−	4.06223i	1.08460	−	0.650477i
$40$		0			0
$41$	−3.43000	+	1.24842i	−0.535676	+	0.194970i	−0.595671	−	0.803229i	$-0.703114\pi$
$41$	−3.43000	+	1.24842i	−0.535676	+	0.194970i	0.0599952	+	0.998199i	$0.480891\pi$
$42$		0			0
$43$	1.34522	+	7.62909i	0.205143	+	1.16343i	0.897214	+	0.441596i	$0.145588\pi$
$43$	1.34522	+	7.62909i	0.205143	+	1.16343i	−0.692071	+	0.721830i	$0.743301\pi$
$44$		0			0
$45$	−0.705806	−	3.34770i	−0.105215	−	0.499046i
$46$		0			0
$47$	−1.89320	+	1.58858i	−0.276151	+	0.231718i	−0.770336	−	0.637639i	$-0.779911\pi$
$47$	−1.89320	+	1.58858i	−0.276151	+	0.231718i	0.494184	+	0.869357i	$0.335467\pi$
$48$		0			0
$49$	−0.968151	+	5.49066i	−0.138307	+	0.784379i
$50$		0			0
$51$	2.43372	−	7.04914i	0.340789	−	0.987078i
$52$		0			0
$53$	1.65993			0.228010			0.114005	−	0.993480i	$-0.463632\pi$
$53$	1.65993			0.228010			0.114005	+	0.993480i	$0.463632\pi$
$54$		0			0
$55$	2.70553			0.364813
$56$		0			0
$57$	0.717456	+	0.826715i	0.0950294	+	0.109501i
$58$		0			0
$59$	2.05606	−	11.6605i	0.267676	−	1.51807i	−0.493629	−	0.869672i	$-0.664330\pi$
$59$	2.05606	−	11.6605i	0.267676	−	1.51807i	0.761305	−	0.648394i	$-0.224559\pi$
$60$		0			0
$61$	1.11147	−	0.932633i	0.142309	−	0.119411i	−0.568854	−	0.822438i	$-0.692613\pi$
$61$	1.11147	−	0.932633i	0.142309	−	0.119411i	0.711163	+	0.703027i	$0.248169\pi$
$62$		0			0
$63$	−1.68627	+	3.15884i	−0.212451	+	0.397976i
$64$		0			0
$65$	−0.903027	−	5.12132i	−0.112007	−	0.635222i
$66$		0			0
$67$	−14.0501	+	5.11383i	−1.71650	+	0.624754i	−0.997527	−	0.0702852i	$-0.977609\pi$
$67$	−14.0501	+	5.11383i	−1.71650	+	0.624754i	−0.718972	+	0.695040i	$0.755387\pi$
$68$		0			0
$69$	−2.09079	−	1.16120i	−0.251702	−	0.139792i
$70$		0			0
$71$	−3.74388	+	6.48459i	−0.444317	+	0.769579i	−0.998004	−	0.0631453i	$-0.979887\pi$
$71$	−3.74388	+	6.48459i	−0.444317	+	0.769579i	0.553688	+	0.832724i	$0.313220\pi$
$72$		0			0
$73$	5.22698	+	9.05339i	0.611772	+	1.05962i	0.990942	+	0.134292i	$0.0428761\pi$
$73$	5.22698	+	9.05339i	0.611772	+	1.05962i	−0.379170	+	0.925327i	$0.623791\pi$
$74$		0			0
$75$	6.32786	+	1.00759i	0.730678	+	0.116346i
$76$		0			0
$77$	−2.16915	−	1.82013i	−0.247198	−	0.207423i
$78$		0			0
$79$	13.0535	+	4.75107i	1.46863	+	0.534537i	0.947728	−	0.319080i	$-0.103374\pi$
$79$	13.0535	+	4.75107i	1.46863	+	0.534537i	0.520901	+	0.853617i	$0.325596\pi$
$80$		0			0
$81$	6.49465	−	6.23053i	0.721628	−	0.692281i
$82$		0			0
$83$	−4.64588	−	1.69096i	−0.509951	−	0.185607i	0.0742132	−	0.997242i	$-0.476355\pi$
$83$	−4.64588	−	1.69096i	−0.509951	−	0.185607i	−0.584164	+	0.811635i	$0.698578\pi$
$84$		0			0
$85$	−3.76143	−	3.15621i	−0.407984	−	0.342339i
$86$		0			0
$87$	−17.5086	−	2.78789i	−1.87712	−	0.298893i
$88$		0			0
$89$	4.93727	+	8.55160i	0.523349	+	0.906468i	0.999631	+	0.0271749i	$0.00865110\pi$
$89$	4.93727	+	8.55160i	0.523349	+	0.906468i	−0.476281	+	0.879293i	$0.658016\pi$
$90$		0			0
$91$	−2.72135	+	4.71351i	−0.285275	+	0.494110i
$92$		0			0
$93$	−6.49197	−	3.60556i	−0.673186	−	0.373880i
$94$		0			0
$95$	0.677266	−	0.246505i	0.0694861	−	0.0252909i
$96$		0			0
$97$	−1.74722	−	9.90896i	−0.177403	−	1.00610i	−0.935334	−	0.353767i	$-0.884901\pi$
$97$	−1.74722	−	9.90896i	−0.177403	−	1.00610i	0.757931	−	0.652335i	$-0.226211\pi$
$98$		0			0
$99$	3.76153	+	6.04187i	0.378048	+	0.607231i
$100$		0			0
$101$	−10.4102	+	8.73519i	−1.03585	+	0.869184i	−0.991536	−	0.129833i	$-0.958556\pi$
$101$	−10.4102	+	8.73519i	−1.03585	+	0.869184i	−0.0443174	+	0.999018i	$0.514111\pi$
$102$		0			0
$103$	2.18377	−	12.3848i	0.215173	−	1.22031i	−0.665433	−	0.746457i	$-0.731753\pi$
$103$	2.18377	−	12.3848i	0.215173	−	1.22031i	0.880606	−	0.473849i	$-0.157136\pi$
$104$		0			0
$105$	1.54530	+	1.78063i	0.150806	+	0.173772i
$106$		0			0
$107$	−13.2261			−1.27862			−0.639309	−	0.768950i	$-0.720780\pi$
$107$	−13.2261			−1.27862			−0.639309	+	0.768950i	$0.720780\pi$
$108$		0			0
$109$	−17.0147			−1.62972			−0.814858	−	0.579660i	$-0.803185\pi$
$109$	−17.0147			−1.62972			−0.814858	+	0.579660i	$0.803185\pi$
$110$		0			0
$111$	−4.78869	+	13.8702i	−0.454522	+	1.31650i
$112$		0			0
$113$	−0.692260	+	3.92600i	−0.0651224	+	0.369327i	0.934778	+	0.355232i	$0.115598\pi$
$113$	−0.692260	+	3.92600i	−0.0651224	+	0.369327i	−0.999901	+	0.0140956i	$0.995513\pi$
$114$		0			0
$115$	−1.20629	+	1.01220i	−0.112488	+	0.0943882i
$116$		0			0
$117$	10.1812	−	9.13685i	0.941254	−	0.844702i
$118$		0			0
$119$	0.892385	+	5.06097i	0.0818048	+	0.463938i
$120$		0			0
$121$	5.04789	−	1.83728i	0.458899	−	0.167026i
$122$		0			0
$123$	−5.42187	+	3.25171i	−0.488874	+	0.293196i
$124$		0			0
$125$	4.96054	−	8.59192i	0.443685	−	0.768484i
$126$		0			0
$127$	3.53147	+	6.11669i	0.313368	+	0.542769i	0.979089	−	0.203432i	$-0.0652095\pi$
$127$	3.53147	+	6.11669i	0.313368	+	0.542769i	−0.665722	+	0.746200i	$0.731876\pi$
$128$		0			0
$129$	4.79818	+	12.5306i	0.422457	+	1.10326i
$130$		0			0
$131$	−14.8402	−	12.4524i	−1.29659	−	1.08797i	−0.990723	−	0.135895i	$-0.956609\pi$
$131$	−14.8402	−	12.4524i	−1.29659	−	1.08797i	−0.305868	−	0.952074i	$-0.598947\pi$
$132$		0			0
$133$	−0.708832	−	0.257994i	−0.0614635	−	0.0223709i
$134$		0			0
$135$	−2.30191	−	5.46049i	−0.198117	−	0.469964i
$136$		0			0
$137$	−0.787129	−	0.286491i	−0.0672490	−	0.0244766i	0.308177	−	0.951329i	$-0.400281\pi$
$137$	−0.787129	−	0.286491i	−0.0672490	−	0.0244766i	−0.375426	+	0.926853i	$0.622503\pi$
$138$		0			0
$139$	5.06287	+	4.24825i	0.429427	+	0.360332i	0.831735	−	0.555172i	$-0.187348\pi$
$139$	5.06287	+	4.24825i	0.429427	+	0.360332i	−0.402309	+	0.915504i	$0.631792\pi$
$140$		0			0
$141$	−2.69660	+	3.32441i	−0.227095	+	0.279966i
$142$		0			0
$143$	5.40896	+	9.36860i	0.452320	+	0.783442i
$144$		0			0
$145$	−5.83668	+	10.1094i	−0.484710	+	0.839543i
$146$		0			0
$147$	0.160570	+	9.65547i	0.0132436	+	0.796370i
$148$		0			0
$149$	1.59654	−	0.581093i	0.130794	−	0.0476050i	−0.275794	−	0.961217i	$-0.588941\pi$
$149$	1.59654	−	0.581093i	0.130794	−	0.0476050i	0.406588	+	0.913612i	$0.366719\pi$
$150$		0			0
$151$	−0.798448	−	4.52822i	−0.0649768	−	0.368502i	−0.999907	−	0.0136689i	$-0.995649\pi$
$151$	−0.798448	−	4.52822i	−0.0649768	−	0.368502i	0.934930	−	0.354833i	$-0.115462\pi$
$152$		0			0
$153$	1.81875	−	12.7880i	0.147037	−	1.03385i
$154$		0			0
$155$	−3.74558	+	3.14291i	−0.300852	+	0.252445i
$156$		0			0
$157$	−0.688501	+	3.90468i	−0.0549483	+	0.311627i	−0.999878	−	0.0156472i	$-0.995019\pi$
$157$	−0.688501	+	3.90468i	−0.0549483	+	0.311627i	0.944929	+	0.327275i	$0.106130\pi$
$158$		0			0
$159$	2.82272	−	0.546265i	0.223856	−	0.0433216i
$160$		0			0
$161$	1.64810			0.129888
$162$		0			0
$163$	0.198971			0.0155846			0.00779232	−	0.999970i	$-0.497520\pi$
$163$	0.198971			0.0155846			0.00779232	+	0.999970i	$0.497520\pi$
$164$		0			0
$165$	4.60075	−	0.890358i	0.358168	−	0.0693143i
$166$		0			0
$167$	2.16205	−	12.2616i	0.167305	−	0.948833i	−0.779351	−	0.626587i	$-0.784451\pi$
$167$	2.16205	−	12.2616i	0.167305	−	0.948833i	0.946656	−	0.322246i	$-0.104438\pi$
$168$		0			0
$169$	5.96998	−	5.00941i	0.459229	−	0.385339i
$170$		0			0
$171$	1.49210	+	1.16972i	0.114104	+	0.0894510i
$172$		0			0
$173$	1.31349	+	7.44915i	0.0998625	+	0.566348i	0.993148	+	0.116860i	$0.0372827\pi$
$173$	1.31349	+	7.44915i	0.0998625	+	0.566348i	−0.893286	+	0.449489i	$0.851606\pi$
$174$		0			0
$175$	−4.14927	+	1.51021i	−0.313655	+	0.114161i
$176$		0			0
$177$	−0.341003	−	20.5053i	−0.0256313	−	1.54127i
$178$		0			0
$179$	10.9620	−	18.9868i	0.819342	−	1.41914i	−0.0868264	−	0.996223i	$-0.527673\pi$
$179$	10.9620	−	18.9868i	0.819342	−	1.41914i	0.906168	−	0.422918i	$-0.138994\pi$
$180$		0			0
$181$	−2.50399	−	4.33703i	−0.186120	−	0.322369i	0.757833	−	0.652448i	$-0.226258\pi$
$181$	−2.50399	−	4.33703i	−0.186120	−	0.322369i	−0.943953	+	0.330079i	$0.892925\pi$
$182$		0			0
$183$	1.58313	−	1.95171i	0.117029	−	0.144275i
$184$		0			0
$185$	7.40113	+	6.21029i	0.544142	+	0.456590i
$186$		0			0
$187$	9.59838	+	3.49352i	0.701903	+	0.255472i
$188$		0			0
$189$	−1.82797	+	5.92654i	−0.132965	+	0.431092i
$190$		0			0
$191$	10.5170	+	3.82786i	0.760980	+	0.276974i	0.693219	−	0.720727i	$-0.256192\pi$
$191$	10.5170	+	3.82786i	0.760980	+	0.276974i	0.0677616	+	0.997702i	$0.478414\pi$
$192$		0			0
$193$	−20.0129	−	16.7928i	−1.44056	−	1.20878i	−0.939122	−	0.343583i	$-0.888359\pi$
$193$	−20.0129	−	16.7928i	−1.44056	−	1.20878i	−0.501440	−	0.865192i	$-0.667196\pi$
$194$		0			0
$195$	−3.22096	−	8.41163i	−0.230658	−	0.602369i
$196$		0			0
$197$	11.6768	+	20.2248i	0.831936	+	1.44096i	0.896501	+	0.443042i	$0.146101\pi$
$197$	11.6768	+	20.2248i	0.831936	+	1.44096i	−0.0645650	+	0.997914i	$0.520566\pi$
$198$		0			0
$199$	5.80878	−	10.0611i	0.411774	−	0.713213i	−0.583310	−	0.812250i	$-0.698243\pi$
$199$	5.80878	−	10.0611i	0.411774	−	0.713213i	0.995084	+	0.0990366i	$0.0315761\pi$
$200$		0			0
$201$	−22.2094	+	13.3198i	−1.56653	+	0.939507i
$202$		0			0
$203$	11.4806	−	4.17861i	0.805782	−	0.293281i
$204$		0			0
$205$	0.722849	+	4.09948i	0.0504860	+	0.286320i
$206$		0			0
$207$	−3.93753	−	1.28657i	−0.273677	−	0.0894226i
$208$		0			0
$209$	−1.14853	+	0.963728i	−0.0794453	+	0.0666625i
$210$		0			0
$211$	3.32920	−	18.8808i	0.229191	−	1.29981i	−0.625317	−	0.780371i	$-0.715030\pi$
$211$	3.32920	−	18.8808i	0.229191	−	1.29981i	0.854508	−	0.519438i	$-0.173859\pi$
$212$		0			0
$213$	−4.23246	+	12.2591i	−0.290004	+	0.839981i
$214$		0			0
$215$	8.83468			0.602520
$216$		0			0
$217$	5.11739			0.347391
$218$		0			0
$219$	11.8678	+	13.6752i	0.801954	+	0.924081i
$220$		0			0
$221$	3.40926	−	19.3349i	0.229332	−	1.30061i
$222$		0			0
$223$	16.1826	−	13.5788i	1.08367	−	0.909306i	0.0874488	−	0.996169i	$-0.472129\pi$
$223$	16.1826	−	13.5788i	1.08367	−	0.909306i	0.996220	+	0.0868627i	$0.0276841\pi$
$224$		0			0
$225$	11.0921	−	0.369025i	0.739474	−	0.0246017i
$226$		0			0
$227$	−1.77907	−	10.0896i	−0.118081	−	0.669672i	−0.985178	−	0.171533i	$-0.945128\pi$
$227$	−1.77907	−	10.0896i	−0.118081	−	0.669672i	0.867097	−	0.498139i	$-0.165983\pi$
$228$		0			0
$229$	19.4254	−	7.07026i	1.28367	−	0.467216i	0.392023	−	0.919956i	$-0.371775\pi$
$229$	19.4254	−	7.07026i	1.28367	−	0.467216i	0.891643	+	0.452739i	$0.149553\pi$
$230$		0			0
$231$	−4.28762	−	2.38129i	−0.282105	−	0.156678i
$232$		0			0
$233$	−1.51377	+	2.62193i	−0.0991705	+	0.171768i	−0.911342	−	0.411651i	$-0.864952\pi$
$233$	−1.51377	+	2.62193i	−0.0991705	+	0.171768i	0.812171	+	0.583419i	$0.198286\pi$
$234$		0			0
$235$	1.40923	+	2.44086i	0.0919279	+	0.159224i
$236$		0			0
$237$	23.7609	+	3.78345i	1.54344	+	0.245762i
$238$		0			0
$239$	17.5677	+	14.7410i	1.13636	+	0.953518i	0.999314	−	0.0370469i	$-0.0117951\pi$
$239$	17.5677	+	14.7410i	1.13636	+	0.953518i	0.137045	+	0.990565i	$0.456240\pi$
$240$		0			0
$241$	8.52682	+	3.10351i	0.549260	+	0.199914i	0.601718	−	0.798709i	$-0.294483\pi$
$241$	8.52682	+	3.10351i	0.549260	+	0.199914i	−0.0524574	+	0.998623i	$0.516705\pi$
$242$		0			0
$243$	8.99376	−	12.7323i	0.576950	−	0.816780i
$244$		0			0
$245$	5.97486	+	2.17467i	0.381720	+	0.138935i
$246$		0			0
$247$	2.20760	+	1.85239i	0.140466	+	0.117865i
$248$		0			0
$249$	−8.45679	−	1.34658i	−0.535927	−	0.0853358i
$250$		0			0
$251$	13.7186	+	23.7613i	0.865910	+	1.49980i	0.866141	+	0.499799i	$0.166593\pi$
$251$	13.7186	+	23.7613i	0.865910	+	1.49980i	−0.000231635		1.00000i	$0.500074\pi$
$252$		0			0
$253$	1.63788	−	2.83690i	0.102973	−	0.178354i
$254$		0			0
$255$	−7.43498	−	4.12930i	−0.465596	−	0.258587i
$256$		0			0
$257$	12.9073	−	4.69788i	0.805137	−	0.293046i	0.0935236	−	0.995617i	$-0.470187\pi$
$257$	12.9073	−	4.69788i	0.805137	−	0.293046i	0.711614	+	0.702571i	$0.247965\pi$
$258$		0			0
$259$	−1.75589	−	9.95816i	−0.109106	−	0.618770i
$260$		0			0
$261$	−30.6908	+	1.02106i	−1.89971	+	0.0632018i
$262$		0			0
$263$	−9.09012	+	7.62751i	−0.560521	+	0.470333i	−0.878485	−	0.477770i	$-0.841445\pi$
$263$	−9.09012	+	7.62751i	−0.560521	+	0.470333i	0.317964	+	0.948103i	$0.397001\pi$
$264$		0			0
$265$	0.328723	−	1.86428i	0.0201933	−	0.114522i
$266$		0			0
$267$	11.2101	+	12.9172i	0.686044	+	0.790520i
$268$		0			0
$269$	11.1134			0.677596			0.338798	−	0.940859i	$-0.389980\pi$
$269$	11.1134			0.677596			0.338798	+	0.940859i	$0.389980\pi$
$270$		0			0
$271$	−15.7733			−0.958159			−0.479079	−	0.877772i	$-0.659029\pi$
$271$	−15.7733			−0.958159			−0.479079	+	0.877772i	$0.659029\pi$
$272$		0			0
$273$	−3.07649	+	8.91089i	−0.186198	+	0.539312i
$274$		0			0
$275$	−1.52400	+	8.64306i	−0.0919009	+	0.521196i
$276$		0			0
$277$	10.3001	−	8.64284i	0.618875	−	0.519298i	−0.278575	−	0.960415i	$-0.589862\pi$
$277$	10.3001	−	8.64284i	0.618875	−	0.519298i	0.897450	+	0.441117i	$0.145418\pi$
$278$		0			0
$279$	−12.2262	−	3.99483i	−0.731961	−	0.239164i
$280$		0			0
$281$	−1.32457	−	7.51203i	−0.0790175	−	0.448130i	−0.998488	−	0.0549712i	$-0.982493\pi$
$281$	−1.32457	−	7.51203i	−0.0790175	−	0.448130i	0.919470	−	0.393159i	$-0.128618\pi$
$282$		0			0
$283$	−15.0838	+	5.49007i	−0.896641	+	0.326351i	−0.748906	−	0.662676i	$-0.769421\pi$
$283$	−15.0838	+	5.49007i	−0.896641	+	0.326351i	−0.147735	+	0.989027i	$0.547198\pi$
$284$		0			0
$285$	1.07057	−	0.642062i	0.0634151	−	0.0380325i
$286$		0			0
$287$	2.17837	−	3.77304i	0.128585	−	0.222716i
$288$		0			0
$289$	−0.768906	−	1.33178i	−0.0452297	−	0.0783402i
$290$		0			0
$291$	−6.23206	−	16.2752i	−0.365330	−	0.954069i
$292$		0			0
$293$	−14.2750	−	11.9781i	−0.833954	−	0.699770i	0.122241	−	0.992500i	$-0.460992\pi$
$293$	−14.2750	−	11.9781i	−0.833954	−	0.699770i	−0.956195	+	0.292730i	$0.905436\pi$
$294$		0			0
$295$	−12.6888	−	4.61834i	−0.738770	−	0.268890i
$296$		0			0
$297$	8.38480	+	9.03632i	0.486535	+	0.524341i
$298$		0			0
$299$	−5.91667	−	2.15349i	−0.342170	−	0.124540i
$300$		0			0
$301$	−7.08318	−	5.94349i	−0.408268	−	0.342577i
$302$		0			0
$303$	−14.8279	+	18.2801i	−0.851840	+	1.05016i
$304$		0			0
$305$	−0.827338	−	1.43299i	−0.0473732	−	0.0820528i
$306$		0			0
$307$	−14.7612	+	25.5671i	−0.842466	+	1.45919i	0.0453378	+	0.998972i	$0.485564\pi$
$307$	−14.7612	+	25.5671i	−0.842466	+	1.45919i	−0.887804	+	0.460222i	$0.847770\pi$
$308$		0			0
$309$	−0.362183	−	21.7789i	−0.0206039	−	1.23896i
$310$		0			0
$311$	−4.90751	+	1.78619i	−0.278279	+	0.101285i	−0.477390	−	0.878692i	$-0.658417\pi$
$311$	−4.90751	+	1.78619i	−0.278279	+	0.101285i	0.199110	+	0.979977i	$0.436195\pi$
$312$		0			0
$313$	−0.477999	−	2.71087i	−0.0270181	−	0.153227i	0.968314	−	0.249736i	$-0.0803437\pi$
$313$	−0.477999	−	2.71087i	−0.0270181	−	0.153227i	−0.995332	+	0.0965083i	$0.969233\pi$
$314$		0			0
$315$	3.21377	+	2.51942i	0.181075	+	0.141953i
$316$		0			0
$317$	1.43033	−	1.20019i	0.0803352	−	0.0674093i	−0.601736	−	0.798695i	$-0.705524\pi$
$317$	1.43033	−	1.20019i	0.0803352	−	0.0674093i	0.682071	+	0.731286i	$0.261080\pi$
$318$		0			0
$319$	4.21677	−	23.9145i	0.236094	−	1.33895i
$320$		0			0
$321$	−22.4910	+	4.35256i	−1.25533	+	0.242936i
$322$		0			0
$323$	2.72103			0.151402
$324$		0			0
$325$	16.8692			0.935735
$326$		0			0
$327$	−28.9336	+	5.59935i	−1.60003	+	0.309645i
$328$		0			0
$329$	0.512230	−	2.90500i	0.0282402	−	0.160158i
$330$		0			0
$331$	−8.02738	+	6.73577i	−0.441225	+	0.370231i	−0.836167	−	0.548474i	$-0.815209\pi$
$331$	−8.02738	+	6.73577i	−0.441225	+	0.370231i	0.394943	+	0.918706i	$0.370764\pi$
$332$		0			0
$333$	−3.57865	+	25.1622i	−0.196109	+	1.37888i
$334$		0			0
$335$	2.96097	+	16.7925i	0.161775	+	0.917473i
$336$		0			0
$337$	−15.4016	+	5.60572i	−0.838978	+	0.305363i	−0.725538	−	0.688182i	$-0.758409\pi$
$337$	−15.4016	+	5.60572i	−0.838978	+	0.305363i	−0.113439	+	0.993545i	$0.536187\pi$
$338$		0			0
$339$	0.114813	+	6.90398i	0.00623579	+	0.374973i
$340$		0			0
$341$	5.08567	−	8.80864i	0.275405	−	0.477015i
$342$		0			0
$343$	−7.50487	−	12.9988i	−0.405225	−	0.701870i
$344$		0			0
$345$	−1.71820	+	2.11823i	−0.0925048	+	0.114041i
$346$		0			0
$347$	−1.53372	−	1.28694i	−0.0823344	−	0.0690868i	0.600692	−	0.799481i	$-0.294892\pi$
$347$	−1.53372	−	1.28694i	−0.0823344	−	0.0690868i	−0.683026	+	0.730394i	$0.739336\pi$
$348$		0			0
$349$	12.2727	+	4.46688i	0.656941	+	0.239107i	0.648915	−	0.760861i	$-0.275223\pi$
$349$	12.2727	+	4.46688i	0.656941	+	0.239107i	0.00802564	+	0.999968i	$0.497445\pi$
$350$		0			0
$351$	14.3063	−	18.8877i	0.763616	−	1.00815i
$352$		0			0
$353$	6.31603	+	2.29885i	0.336168	+	0.122355i	0.504588	−	0.863360i	$-0.331644\pi$
$353$	6.31603	+	2.29885i	0.336168	+	0.122355i	−0.168420	+	0.985715i	$0.553867\pi$
$354$		0			0
$355$	6.54147	+	5.48894i	0.347185	+	0.291323i
$356$		0			0
$357$	3.18301	+	8.31250i	0.168463	+	0.439944i
$358$		0			0
$359$	14.0814	+	24.3898i	0.743190	+	1.28724i	0.951036	+	0.309081i	$0.100022\pi$
$359$	14.0814	+	24.3898i	0.743190	+	1.28724i	−0.207845	+	0.978162i	$0.566645\pi$
$360$		0			0
$361$	9.30030	−	16.1086i	0.489489	−	0.847821i
$362$		0			0
$363$	7.97931	−	4.78550i	0.418805	−	0.251174i
$364$		0			0
$365$	11.2030	−	4.07757i	0.586394	−	0.213430i
$366$		0			0
$367$	−0.954081	−	5.41086i	−0.0498026	−	0.282445i	0.949728	−	0.313076i	$-0.101359\pi$
$367$	−0.954081	−	5.41086i	−0.0498026	−	0.282445i	−0.999531	+	0.0306311i	$0.990248\pi$
$368$		0			0
$369$	−8.14980	+	7.31380i	−0.424261	+	0.380741i
$370$		0			0
$371$	−1.51774	+	1.27354i	−0.0787972	+	0.0661187i
$372$		0			0
$373$	1.24856	−	7.08093i	0.0646480	−	0.366637i	−0.935271	−	0.353932i	$-0.884845\pi$
$373$	1.24856	−	7.08093i	0.0646480	−	0.366637i	0.999919	−	0.0127053i	$-0.00404432\pi$
$374$		0			0
$375$	5.60791	−	16.2430i	0.289591	−	0.838785i
$376$		0			0
$377$	−46.6754			−2.40391
$378$		0			0
$379$	−5.91330			−0.303746			−0.151873	−	0.988400i	$-0.548530\pi$
$379$	−5.91330			−0.303746			−0.151873	+	0.988400i	$0.548530\pi$
$380$		0			0
$381$	8.01820	+	9.23927i	0.410785	+	0.473342i
$382$		0			0
$383$	−3.03220	+	17.1965i	−0.154938	+	0.878699i	0.803904	+	0.594759i	$0.202753\pi$
$383$	−3.03220	+	17.1965i	−0.154938	+	0.878699i	−0.958842	+	0.283940i	$0.908358\pi$
$384$		0			0
$385$	−2.47377	+	2.07574i	−0.126075	+	0.105789i
$386$		0			0
$387$	12.2830	+	19.7292i	0.624379	+	1.00289i
$388$		0			0
$389$	5.41147	+	30.6899i	0.274372	+	1.55604i	0.740949	+	0.671561i	$0.234376\pi$
$389$	5.41147	+	30.6899i	0.274372	+	1.55604i	−0.466577	+	0.884481i	$0.654513\pi$
$390$		0			0
$391$	−5.58657	+	2.03334i	−0.282525	+	0.102831i
$392$		0			0
$393$	−29.3336	−	16.2915i	−1.47969	−	0.821800i
$394$		0			0
$395$	7.92098	−	13.7195i	0.398548	−	0.690305i
$396$		0			0
$397$	−4.81102	−	8.33293i	−0.241458	−	0.418218i	0.719672	−	0.694315i	$-0.244292\pi$
$397$	−4.81102	−	8.33293i	−0.241458	−	0.418218i	−0.961130	+	0.276097i	$0.910959\pi$
$398$		0			0
$399$	−1.29027	−	0.205450i	−0.0645943	−	0.0102854i
$400$		0			0
$401$	−10.8326	−	9.08963i	−0.540954	−	0.453914i	0.330910	−	0.943662i	$-0.392644\pi$
$401$	−10.8326	−	9.08963i	−0.540954	−	0.453914i	−0.871864	+	0.489748i	$0.837089\pi$
$402$		0			0
$403$	−18.3714	−	6.68665i	−0.915146	−	0.333086i
$404$		0			0
$405$	−5.71139	−	8.52804i	−0.283801	−	0.423762i
$406$		0			0
$407$	−18.8862	−	6.87400i	−0.936152	−	0.340731i
$408$		0			0
$409$	−17.0059	−	14.2696i	−0.840887	−	0.705588i	0.116876	−	0.993146i	$-0.462712\pi$
$409$	−17.0059	−	14.2696i	−0.840887	−	0.705588i	−0.957763	+	0.287559i	$0.907156\pi$
$410$		0			0
$411$	−1.43279	−	0.228144i	−0.0706745	−	0.0112535i
$412$		0			0
$413$	7.06623	+	12.2391i	0.347707	+	0.602246i
$414$		0			0
$415$	−2.81917	+	4.88294i	−0.138388	+	0.239694i
$416$		0			0
$417$	10.0075	+	5.55802i	0.490067	+	0.272177i
$418$		0			0
$419$	4.05078	−	1.47436i	0.197893	−	0.0720273i	−0.241172	−	0.970482i	$-0.577532\pi$
$419$	4.05078	−	1.47436i	0.197893	−	0.0720273i	0.439065	+	0.898455i	$0.355310\pi$
$420$		0			0
$421$	6.47173	+	36.7030i	0.315413	+	1.78879i	0.569896	+	0.821717i	$0.306983\pi$
$421$	6.47173	+	36.7030i	0.315413	+	1.78879i	−0.254483	+	0.967077i	$0.581905\pi$
$422$		0			0
$423$	−3.49154	+	6.54059i	−0.169765	+	0.318014i
$424$		0			0
$425$	12.2016	−	10.2383i	0.591864	−	0.496633i
$426$		0			0
$427$	−0.300723	+	1.70548i	−0.0145530	+	0.0825342i
$428$		0			0
$429$	12.2810	+	14.1513i	0.592934	+	0.683230i
$430$		0			0
$431$	−4.91915			−0.236947			−0.118474	−	0.992957i	$-0.537800\pi$
$431$	−4.91915			−0.236947			−0.118474	+	0.992957i	$0.537800\pi$
$432$		0			0
$433$	9.70964			0.466616			0.233308	−	0.972403i	$-0.425045\pi$
$433$	9.70964			0.466616			0.233308	+	0.972403i	$0.425045\pi$
$434$		0			0
$435$	−6.59839	+	19.1119i	−0.316368	+	0.916345i
$436$		0			0
$437$	0.151532	−	0.859381i	0.00724876	−	0.0411098i
$438$		0			0
$439$	9.51776	−	7.98635i	0.454258	−	0.381168i	−0.386755	−	0.922182i	$-0.626404\pi$
$439$	9.51776	−	7.98635i	0.454258	−	0.381168i	0.841013	+	0.541015i	$0.181960\pi$
$440$		0			0
$441$	3.45055	+	16.3663i	0.164312	+	0.779347i
$442$		0			0
$443$	−2.91461	−	16.5296i	−0.138477	−	0.785344i	−0.972375	−	0.233425i	$-0.925007\pi$
$443$	−2.91461	−	16.5296i	−0.138477	−	0.785344i	0.833897	−	0.551919i	$-0.186104\pi$
$444$		0			0
$445$	10.5821	−	3.85157i	0.501640	−	0.182582i
$446$		0			0
$447$	2.52368	−	1.51355i	0.119366	−	0.0715885i
$448$		0			0
$449$	3.14353	−	5.44475i	0.148352	−	0.256954i	−0.782266	−	0.622944i	$-0.785936\pi$
$449$	3.14353	−	5.44475i	0.148352	−	0.256954i	0.930619	+	0.365990i	$0.119270\pi$
$450$		0			0
$451$	−4.32973	−	7.49931i	−0.203879	−	0.353129i
$452$		0			0
$453$	−2.84795	−	7.43749i	−0.133808	−	0.349444i
$454$		0			0
$455$	4.75486	+	3.98980i	0.222911	+	0.187045i
$456$		0			0
$457$	−13.0245	−	4.74051i	−0.609258	−	0.221752i	0.0189203	−	0.999821i	$-0.493977\pi$
$457$	−13.0245	−	4.74051i	−0.609258	−	0.221752i	−0.628179	+	0.778069i	$0.716199\pi$
$458$		0			0
$459$	−1.11559	−	22.3445i	−0.0520712	−	1.04295i
$460$		0			0
$461$	−8.34472	−	3.03723i	−0.388652	−	0.141458i	0.140301	−	0.990109i	$-0.455193\pi$
$461$	−8.34472	−	3.03723i	−0.388652	−	0.141458i	−0.528953	+	0.848651i	$0.677415\pi$
$462$		0			0
$463$	24.3113	+	20.3996i	1.12984	+	0.948049i	0.999059	−	0.0433620i	$-0.0138069\pi$
$463$	24.3113	+	20.3996i	1.12984	+	0.948049i	0.130782	+	0.991411i	$0.458251\pi$
$464$		0			0
$465$	−5.33506	+	6.57715i	−0.247408	+	0.305008i
$466$		0			0
$467$	−8.88903	−	15.3963i	−0.411335	−	0.712454i	0.583701	−	0.811969i	$-0.301604\pi$
$467$	−8.88903	−	15.3963i	−0.411335	−	0.712454i	−0.995036	+	0.0995151i	$0.968271\pi$
$468$		0			0
$469$	8.92314	−	15.4553i	0.412032	−	0.713661i
$470$		0			0
$471$	0.114190	+	6.86649i	0.00526158	+	0.316391i
$472$		0			0
$473$	−17.2699	+	6.28573i	−0.794071	+	0.289018i
$474$		0			0
$475$	0.405983	+	2.30244i	0.0186278	+	0.105643i
$476$		0			0
$477$	4.62026	−	1.85785i	0.211547	−	0.0850650i
$478$		0			0
$479$	9.15931	−	7.68557i	0.418499	−	0.351163i	−0.409093	−	0.912493i	$-0.634155\pi$
$479$	9.15931	−	7.68557i	0.418499	−	0.351163i	0.827592	+	0.561330i	$0.189710\pi$
$480$		0			0
$481$	−6.70821	+	38.0441i	−0.305868	+	1.73466i
$482$		0			0
$483$	2.80259	−	0.542370i	0.127522	−	0.0246787i
$484$		0			0
$485$	−11.4748			−0.521045
$486$		0			0
$487$	11.8522			0.537076			0.268538	−	0.963269i	$-0.413460\pi$
$487$	11.8522			0.537076			0.268538	+	0.963269i	$0.413460\pi$
$488$		0			0
$489$	0.338351	−	0.0654791i	0.0153007	−	0.00296107i
$490$		0			0
$491$	−6.97821	+	39.5754i	−0.314922	+	1.78601i	0.257733	+	0.966216i	$0.417025\pi$
$491$	−6.97821	+	39.5754i	−0.314922	+	1.78601i	−0.572655	+	0.819796i	$0.694087\pi$
$492$		0			0
$493$	−33.7606	+	28.3285i	−1.52050	+	1.27585i
$494$		0			0
$495$	7.53057	−	3.02811i	0.338474	−	0.136103i
$496$		0			0
$497$	−1.55194	−	8.80149i	−0.0696140	−	0.394801i
$498$		0			0
$499$	21.4910	−	7.82207i	0.962068	−	0.350164i	0.187224	−	0.982317i	$-0.440051\pi$
$499$	21.4910	−	7.82207i	0.962068	−	0.350164i	0.774844	+	0.632153i	$0.217829\pi$
$500$		0			0
$501$	−0.358582	−	21.5624i	−0.0160203	−	0.963337i
$502$		0			0
$503$	21.6895	−	37.5674i	0.967089	−	1.67505i	0.263193	−	0.964743i	$-0.415224\pi$
$503$	21.6895	−	37.5674i	0.967089	−	1.67505i	0.703895	−	0.710304i	$-0.251442\pi$
$504$		0			0
$505$	7.74897	+	13.4216i	0.344825	+	0.597254i
$506$		0			0
$507$	8.50341	−	10.4831i	0.377650	−	0.465573i
$508$		0			0
$509$	6.04601	+	5.07320i	0.267984	+	0.224866i	0.766870	−	0.641802i	$-0.221813\pi$
$509$	6.04601	+	5.07320i	0.267984	+	0.224866i	−0.498886	+	0.866668i	$0.666257\pi$
$510$		0			0
$511$	−11.7252	−	4.26761i	−0.518691	−	0.188788i
$512$		0			0
$513$	2.92225	+	1.49808i	0.129021	+	0.0661420i
$514$		0			0
$515$	−13.4769	−	4.90520i	−0.593865	−	0.216149i
$516$		0			0
$517$	−4.49137	−	3.76871i	−0.197530	−	0.165748i
$518$		0			0
$519$	4.68501	+	12.2350i	0.205649	+	0.537058i
$520$		0			0
$521$	−1.20057	−	2.07945i	−0.0525978	−	0.0911021i	0.838528	−	0.544859i	$-0.183417\pi$
$521$	−1.20057	−	2.07945i	−0.0525978	−	0.0911021i	−0.891126	+	0.453757i	$0.850083\pi$
$522$		0			0
$523$	−1.19522	+	2.07018i	−0.0522633	+	0.0905227i	−0.890974	−	0.454055i	$-0.849977\pi$
$523$	−1.19522	+	2.07018i	−0.0522633	+	0.0905227i	0.838710	+	0.544578i	$0.183310\pi$
$524$		0			0
$525$	−6.55884	+	3.93359i	−0.286251	+	0.171676i
$526$		0			0
$527$	−17.3465	+	6.31359i	−0.755623	+	0.275024i
$528$		0			0
$529$	−3.66283	−	20.7729i	−0.159253	−	0.903171i
$530$		0			0
$531$	−7.32793	−	34.7570i	−0.318005	−	1.50833i
$532$		0			0
$533$	−12.7504	+	10.6988i	−0.552280	+	0.463418i
$534$		0			0
$535$	−2.61922	+	14.8543i	−0.113239	+	0.642209i
$536$		0			0
$537$	12.3926	−	35.8946i	0.534781	−	1.54896i
$538$		0			0
$539$	−13.2268			−0.569720
$540$		0			0
$541$	−20.2949			−0.872546			−0.436273	−	0.899814i	$-0.643702\pi$
$541$	−20.2949			−0.872546			−0.436273	+	0.899814i	$0.643702\pi$
$542$		0			0
$543$	−5.68529	−	6.55109i	−0.243979	−	0.281134i
$544$		0			0
$545$	−3.36950	+	19.1094i	−0.144333	+	0.818555i
$546$		0			0
$547$	4.27588	−	3.58789i	0.182823	−	0.153407i	−0.546783	−	0.837274i	$-0.684148\pi$
$547$	4.27588	−	3.58789i	0.182823	−	0.153407i	0.729606	+	0.683867i	$0.239703\pi$
$548$		0			0
$549$	2.04983	−	3.83988i	0.0874848	−	0.163882i
$550$		0			0
$551$	−1.12332	−	6.37064i	−0.0478548	−	0.271398i
$552$		0			0
$553$	−15.5804	+	5.67080i	−0.662546	+	0.241147i
$554$		0			0
$555$	14.6294	+	8.12497i	0.620982	+	0.344886i
$556$		0			0
$557$	7.32520	−	12.6876i	0.310379	−	0.537592i	−0.668066	−	0.744102i	$-0.732877\pi$
$557$	7.32520	−	12.6876i	0.310379	−	0.537592i	0.978444	+	0.206511i	$0.0662108\pi$
$558$		0			0
$559$	17.6625	+	30.5924i	0.747045	+	1.29392i
$560$		0			0
$561$	17.4717	+	2.78202i	0.737657	+	0.117457i
$562$		0			0
$563$	−5.20388	−	4.36658i	−0.219318	−	0.184029i	0.526509	−	0.850170i	$-0.323501\pi$
$563$	−5.20388	−	4.36658i	−0.219318	−	0.184029i	−0.745826	+	0.666140i	$0.767945\pi$
$564$		0			0
$565$	4.27223	+	1.55496i	0.179734	+	0.0654178i
$566$		0			0
$567$	−1.15811	+	10.6796i	−0.0486362	+	0.448503i
$568$		0			0
$569$	28.9288	+	10.5292i	1.21276	+	0.441407i	0.867659	−	0.497159i	$-0.165624\pi$
$569$	28.9288	+	10.5292i	1.21276	+	0.441407i	0.345098	+	0.938567i	$0.387846\pi$
$570$		0			0
$571$	−6.43293	−	5.39787i	−0.269210	−	0.225894i	0.498182	−	0.867073i	$-0.334001\pi$
$571$	−6.43293	−	5.39787i	−0.269210	−	0.225894i	−0.767391	+	0.641179i	$0.778446\pi$
$572$		0			0
$573$	19.1438	+	3.04827i	0.799743	+	0.127343i
$574$		0			0
$575$	−2.55407	−	4.42378i	−0.106512	−	0.184484i
$576$		0			0
$577$	−6.03816	+	10.4584i	−0.251372	+	0.435389i	−0.963904	−	0.266251i	$-0.914215\pi$
$577$	−6.03816	+	10.4584i	−0.251372	+	0.435389i	0.712532	+	0.701640i	$0.247548\pi$
$578$		0			0
$579$	−39.5583	−	21.9702i	−1.64399	−	0.913051i
$580$		0			0
$581$	5.54524	−	2.01830i	0.230055	−	0.0837333i
$582$		0			0
$583$	0.683823	+	3.87815i	0.0283211	+	0.160617i
$584$		0			0
$585$	−8.24542	−	13.2440i	−0.340906	−	0.547572i
$586$		0			0
$587$	16.6528	−	13.9733i	0.687334	−	0.576741i	−0.230805	−	0.973000i	$-0.574136\pi$
$587$	16.6528	−	13.9733i	0.687334	−	0.576741i	0.918139	+	0.396258i	$0.129692\pi$
$588$		0			0
$589$	0.470512	−	2.66840i	0.0193871	−	0.109950i
$590$		0			0
$591$	26.5121	+	30.5495i	1.09056	+	1.25664i
$592$		0			0
$593$	−35.4247			−1.45472			−0.727358	−	0.686258i	$-0.759252\pi$
$593$	−35.4247			−1.45472			−0.727358	+	0.686258i	$0.759252\pi$
$594$		0			0
$595$	5.86072			0.240266
$596$		0			0
$597$	6.56684	−	19.0205i	0.268763	−	0.778458i
$598$		0			0
$599$	5.24013	−	29.7183i	0.214106	−	1.21426i	−0.668345	−	0.743851i	$-0.732997\pi$
$599$	5.24013	−	29.7183i	0.214106	−	1.21426i	0.882451	−	0.470404i	$-0.155892\pi$
$600$		0			0
$601$	23.2204	−	19.4842i	0.947180	−	0.794779i	−0.0316401	−	0.999499i	$-0.510073\pi$
$601$	23.2204	−	19.4842i	0.947180	−	0.794779i	0.978820	+	0.204721i	$0.0656286\pi$
$602$		0			0
$603$	−33.3836	+	29.9592i	−1.35949	+	1.22003i
$604$		0			0
$605$	−1.06381	−	6.03316i	−0.0432500	−	0.245283i
$606$		0			0
$607$	13.1175	−	4.77438i	0.532423	−	0.193786i	−0.0617967	−	0.998089i	$-0.519683\pi$
$607$	13.1175	−	4.77438i	0.532423	−	0.193786i	0.594220	+	0.804302i	$0.297461\pi$
$608$		0			0
$609$	18.1477	−	10.8839i	0.735381	−	0.441036i
$610$		0			0
$611$	−5.63473	+	9.75964i	−0.227957	+	0.394833i
$612$		0			0
$613$	−8.86935	−	15.3622i	−0.358230	−	0.620472i	0.629436	−	0.777053i	$-0.283286\pi$
$613$	−8.86935	−	15.3622i	−0.358230	−	0.620472i	−0.987665	+	0.156581i	$0.949953\pi$
$614$		0			0
$615$	2.57830	+	6.73328i	0.103967	+	0.271512i
$616$		0			0
$617$	27.0469	+	22.6950i	1.08887	+	0.913667i	0.996627	−	0.0820698i	$-0.0261531\pi$
$617$	27.0469	+	22.6950i	1.08887	+	0.913667i	0.0922394	+	0.995737i	$0.470597\pi$
$618$		0			0
$619$	12.9143	+	4.70042i	0.519070	+	0.188926i	0.588251	−	0.808678i	$-0.299817\pi$
$619$	12.9143	+	4.70042i	0.519070	+	0.188926i	−0.0691816	+	0.997604i	$0.522039\pi$
$620$		0			0
$621$	−7.11917	−	0.892012i	−0.285682	−	0.0357952i
$622$		0			0
$623$	−11.0753	−	4.03108i	−0.443722	−	0.161502i
$624$		0			0
$625$	5.50231	+	4.61698i	0.220092	+	0.184679i
$626$		0			0
$627$	−1.63592	+	2.01679i	−0.0653323	+	0.0805427i
$628$		0			0
$629$	18.2379	+	31.5889i	0.727192	+	1.25953i
$630$		0			0
$631$	10.3780	−	17.9752i	0.413140	−	0.715580i	−0.582091	−	0.813124i	$-0.697765\pi$
$631$	10.3780	−	17.9752i	0.413140	−	0.715580i	0.995231	+	0.0975436i	$0.0310985\pi$
$632$		0			0
$633$	−0.552156	−	33.2024i	−0.0219462	−	1.31968i
$634$		0			0
$635$	7.56904	−	2.75491i	0.300368	−	0.109325i
$636$		0			0
$637$	4.41473	+	25.0372i	0.174918	+	0.992009i
$638$		0			0
$639$	−3.16298	+	22.2395i	−0.125125	+	0.879780i
$640$		0			0
$641$	26.3237	−	22.0882i	1.03973	−	0.872433i	0.0477494	−	0.998859i	$-0.484795\pi$
$641$	26.3237	−	22.0882i	1.03973	−	0.872433i	0.991976	+	0.126426i	$0.0403507\pi$
$642$		0			0
$643$	−8.00872	+	45.4197i	−0.315833	+	1.79118i	0.251677	+	0.967811i	$0.419018\pi$
$643$	−8.00872	+	45.4197i	−0.315833	+	1.79118i	−0.567510	+	0.823367i	$0.692093\pi$
$644$		0			0
$645$	15.0234	−	2.90739i	0.591545	−	0.114478i
$646$		0			0
$647$	−43.6178			−1.71479			−0.857395	−	0.514658i	$-0.827919\pi$
$647$	−43.6178			−1.71479			−0.857395	+	0.514658i	$0.827919\pi$
$648$		0			0
$649$	28.0898			1.10262
$650$		0			0
$651$	8.70212	−	1.68407i	0.341063	−	0.0660040i
$652$		0			0
$653$	6.14019	−	34.8228i	0.240284	−	1.36272i	−0.590910	−	0.806738i	$-0.701231\pi$
$653$	6.14019	−	34.8228i	0.240284	−	1.36272i	0.831194	−	0.555982i	$-0.187658\pi$
$654$		0			0
$655$	−16.9242	+	14.2011i	−0.661283	+	0.554882i
$656$		0			0
$657$	24.6816	+	19.3490i	0.962921	+	0.754878i
$658$		0			0
$659$	2.03059	+	11.5160i	0.0791004	+	0.448601i	0.998474	+	0.0552162i	$0.0175848\pi$
$659$	2.03059	+	11.5160i	0.0791004	+	0.448601i	−0.919374	+	0.393385i	$0.871304\pi$
$660$		0			0
$661$	27.7985	−	10.1178i	1.08124	−	0.393538i	0.260869	−	0.965374i	$-0.415991\pi$
$661$	27.7985	−	10.1178i	1.08124	−	0.393538i	0.820368	+	0.571836i	$0.193769\pi$
$662$		0			0
$663$	−0.565435	−	34.0009i	−0.0219597	−	1.32049i
$664$		0			0
$665$	−0.430127	+	0.745001i	−0.0166796	+	0.0288899i
$666$		0			0
$667$	7.06687	+	12.2402i	0.273630	+	0.473941i
$668$		0			0
$669$	23.0499	−	28.4163i	0.891162	−	1.09864i
$670$		0			0
$671$	2.63682	+	2.21255i	0.101793	+	0.0854147i
$672$		0			0
$673$	−25.1603	−	9.15759i	−0.969857	−	0.352999i	−0.191968	−	0.981401i	$-0.561487\pi$
$673$	−25.1603	−	9.15759i	−0.969857	−	0.352999i	−0.777889	+	0.628402i	$0.783709\pi$
$674$		0			0
$675$	18.7407	−	4.27781i	0.721330	−	0.164653i
$676$		0			0
$677$	−13.1243	−	4.77687i	−0.504409	−	0.183590i	0.0772669	−	0.997010i	$-0.475381\pi$
$677$	−13.1243	−	4.77687i	−0.504409	−	0.183590i	−0.581676	+	0.813421i	$0.697603\pi$
$678$		0			0
$679$	9.19990	+	7.71964i	0.353060	+	0.296252i
$680$		0			0
$681$	−6.34569	−	16.5719i	−0.243167	−	0.635038i
$682$		0			0
$683$	−11.5505	−	20.0061i	−0.441968	−	0.765511i	0.555868	−	0.831271i	$-0.312386\pi$
$683$	−11.5505	−	20.0061i	−0.441968	−	0.765511i	−0.997835	+	0.0657599i	$0.979053\pi$
$684$		0			0
$685$	−0.477638	+	0.827294i	−0.0182496	+	0.0316093i
$686$		0			0
$687$	30.7061	−	18.4157i	1.17151	−	0.702601i
$688$		0			0
$689$	7.11276	−	2.58883i	0.270974	−	0.0986266i
$690$		0			0
$691$	0.480777	+	2.72662i	0.0182896	+	0.103726i	0.992586	−	0.121544i	$-0.0387847\pi$
$691$	0.480777	+	2.72662i	0.0182896	+	0.103726i	−0.974296	+	0.225270i	$0.927674\pi$
$692$		0			0
$693$	−8.07476	−	2.63838i	−0.306735	−	0.100224i
$694$		0			0
$695$	5.77386	−	4.84484i	0.219015	−	0.183775i
$696$		0			0
$697$	−2.72902	+	15.4771i	−0.103369	+	0.586236i
$698$		0			0
$699$	−1.71132	+	4.95676i	−0.0647282	+	0.187482i
$700$		0			0
$701$	−13.5645			−0.512325			−0.256162	−	0.966634i	$-0.582458\pi$
$701$	−13.5645			−0.512325			−0.256162	+	0.966634i	$0.582458\pi$
$702$		0			0
$703$	−5.35401			−0.201930
$704$		0			0
$705$	3.19965	+	3.68691i	0.120506	+	0.138857i
$706$		0			0
$707$	2.81662	−	15.9738i	0.105930	−	0.600758i
$708$		0			0
$709$	−6.79940	+	5.70537i	−0.255357	+	0.214270i	−0.761475	−	0.648194i	$-0.775524\pi$
$709$	−6.79940	+	5.70537i	−0.255357	+	0.214270i	0.506118	+	0.862464i	$0.331080\pi$
$710$		0			0
$711$	41.6506	−	1.38568i	1.56202	−	0.0519670i
$712$		0			0
$713$	1.02801	+	5.83012i	0.0384992	+	0.218340i
$714$		0			0
$715$	11.5931	−	4.21954i	0.433557	−	0.157802i
$716$		0			0
$717$	34.7249	+	19.2858i	1.29683	+	0.720242i
$718$		0			0
$719$	−1.35498	+	2.34689i	−0.0505321	+	0.0875241i	−0.890185	−	0.455599i	$-0.849425\pi$
$719$	−1.35498	+	2.34689i	−0.0505321	+	0.0875241i	0.839653	+	0.543123i	$0.182758\pi$
$720$		0			0
$721$	7.50514	+	12.9993i	0.279506	+	0.484119i
$722$		0			0
$723$	15.5212	+	2.47144i	0.577239	+	0.0919138i
$724$		0			0
$725$	−29.0077	−	24.3404i	−1.07732	−	0.903979i
$726$		0			0
$727$	3.06279	+	1.11476i	0.113592	+	0.0413443i	0.398191	−	0.917302i	$-0.369638\pi$
$727$	3.06279	+	1.11476i	0.113592	+	0.0413443i	−0.284599	+	0.958647i	$0.591860\pi$
$728$		0			0
$729$	11.1038	−	24.6111i	0.411253	−	0.911521i
$730$		0			0
$731$	31.3427	+	11.4078i	1.15925	+	0.421933i
$732$		0			0
$733$	22.5186	+	18.8953i	0.831743	+	0.697915i	0.955690	−	0.294374i	$-0.0951110\pi$
$733$	22.5186	+	18.8953i	0.831743	+	0.697915i	−0.123948	+	0.992289i	$0.539555\pi$
$734$		0			0
$735$	10.8759	+	1.73177i	0.401164	+	0.0638774i
$736$		0			0
$737$	−17.7357	−	30.7191i	−0.653302	−	1.13155i
$738$		0			0
$739$	17.6301	−	30.5362i	0.648533	−	1.12329i	−0.334941	−	0.942239i	$-0.608716\pi$
$739$	17.6301	−	30.5362i	0.648533	−	1.12329i	0.983473	−	0.181053i	$-0.0579504\pi$
$740$		0			0
$741$	4.36362	+	2.42350i	0.160302	+	0.0890295i
$742$		0			0
$743$	−34.7819	+	12.6596i	−1.27602	+	0.464435i	−0.889116	−	0.457683i	$-0.848680\pi$
$743$	−34.7819	+	12.6596i	−1.27602	+	0.464435i	−0.386909	+	0.922118i	$0.626457\pi$
$744$		0			0
$745$	−0.336460	−	1.90816i	−0.0123269	−	0.0699095i
$746$		0			0
$747$	−14.8239	+	0.493179i	−0.542379	+	0.0180445i
$748$		0			0
$749$	12.0932	−	10.1474i	0.441874	−	0.370776i
$750$		0			0
$751$	−1.74520	+	9.89752i	−0.0636833	+	0.361166i	0.936268	+	0.351287i	$0.114256\pi$
$751$	−1.74520	+	9.89752i	−0.0636833	+	0.361166i	−0.999951	+	0.00987905i	$0.996855\pi$
$752$		0			0
$753$	31.1480	+	35.8915i	1.13510	+	1.30796i
$754$		0			0
$755$	−5.24379			−0.190841
$756$		0			0
$757$	−27.8074			−1.01068			−0.505339	−	0.862921i	$-0.668632\pi$
$757$	−27.8074			−1.01068			−0.505339	+	0.862921i	$0.668632\pi$
$758$		0			0
$759$	1.85163	−	5.36315i	0.0672099	−	0.194670i
$760$		0			0
$761$	−7.95439	+	45.1116i	−0.288346	+	1.63529i	0.404735	+	0.914434i	$0.367364\pi$
$761$	−7.95439	+	45.1116i	−0.288346	+	1.63529i	−0.693081	+	0.720860i	$0.743747\pi$
$762$		0			0
$763$	15.5572	−	13.0541i	0.563209	−	0.472589i
$764$		0			0
$765$	−14.0021	−	4.57510i	−0.506246	−	0.165413i
$766$		0			0
$767$	−9.37555	−	53.1714i	−0.338531	−	1.91991i
$768$		0			0
$769$	−17.5588	+	6.39088i	−0.633186	+	0.230461i	−0.638618	−	0.769524i	$-0.720493\pi$
$769$	−17.5588	+	6.39088i	−0.633186	+	0.230461i	0.00543126	+	0.999985i	$0.498271\pi$
$770$		0			0
$771$	20.4029	−	12.2364i	0.734792	−	0.440683i
$772$		0			0
$773$	−0.423858	+	0.734144i	−0.0152451	+	0.0264053i	−0.873547	−	0.486739i	$-0.838186\pi$
$773$	−0.423858	+	0.734144i	−0.0152451	+	0.0264053i	0.858302	+	0.513145i	$0.171520\pi$
$774$		0			0
$775$	−7.93047	−	13.7360i	−0.284871	−	0.493411i
$776$		0			0
$777$	−6.26301	−	16.3560i	−0.224684	−	0.586769i
$778$		0			0
$779$	−1.76712	−	1.48279i	−0.0633137	−	0.0531265i
$780$		0			0
$781$	−16.6925	−	6.07556i	−0.597303	−	0.217401i
$782$		0			0
$783$	−51.8537	+	11.8363i	−1.85310	+	0.422994i
$784$		0			0
$785$	4.24902	+	1.54652i	0.151654	+	0.0551976i
$786$		0			0
$787$	17.5874	+	14.7576i	0.626924	+	0.526051i	0.899971	−	0.435949i	$-0.143587\pi$
$787$	17.5874	+	14.7576i	0.626924	+	0.526051i	−0.273048	+	0.962000i	$0.588032\pi$
$788$		0			0
$789$	−12.9476	+	15.9620i	−0.460947	+	0.568264i
$790$		0			0
$791$	−2.37915	−	4.12081i	−0.0845929	−	0.146519i
$792$		0			0
$793$	3.30807	−	5.72975i	0.117473	−	0.203469i
$794$		0			0
$795$	−0.0545196	−	3.27839i	−0.00193361	−	0.116273i
$796$		0			0
$797$	−47.8731	+	17.4244i	−1.69575	+	0.617203i	−0.995330	−	0.0965275i	$-0.969226\pi$
$797$	−47.8731	+	17.4244i	−1.69575	+	0.617203i	−0.700421	+	0.713730i	$0.747004\pi$
$798$		0			0
$799$	1.84774	+	10.4791i	0.0653685	+	0.370723i
$800$		0			0
$801$	23.3136	+	18.2766i	0.823746	+	0.645772i
$802$		0			0
$803$	−18.9984	+	15.9416i	−0.670440	+	0.562566i
$804$		0			0
$805$	0.326379	−	1.85099i	0.0115034	−	0.0652388i
$806$		0			0
$807$	18.8983	−	3.65729i	0.665253	−	0.128743i
$808$		0			0
$809$	−17.5145			−0.615778			−0.307889	−	0.951422i	$-0.599622\pi$
$809$	−17.5145			−0.615778			−0.307889	+	0.951422i	$0.599622\pi$
$810$		0			0
$811$	−0.553503			−0.0194361			−0.00971806	−	0.999953i	$-0.503093\pi$
$811$	−0.553503			−0.0194361			−0.00971806	+	0.999953i	$0.503093\pi$
$812$		0			0
$813$	−26.8225	+	5.19080i	−0.940705	+	0.182049i
$814$		0			0
$815$	0.0394031	−	0.223466i	0.00138023	−	0.00782767i
$816$		0			0
$817$	−3.75042	+	3.14698i	−0.131211	+	0.110099i
$818$		0			0
$819$	−2.29910	+	16.1654i	−0.0803371	+	0.564865i
$820$		0			0
$821$	−4.88397	−	27.6984i	−0.170452	−	0.966680i	−0.943264	−	0.332045i	$-0.892261\pi$
$821$	−4.88397	−	27.6984i	−0.170452	−	0.966680i	0.772812	−	0.634635i	$-0.218850\pi$
$822$		0			0
$823$	−15.1516	+	5.51472i	−0.528151	+	0.192231i	−0.592312	−	0.805708i	$-0.701785\pi$
$823$	−15.1516	+	5.51472i	−0.528151	+	0.192231i	0.0641618	+	0.997940i	$0.479563\pi$
$824$		0			0
$825$	0.252760	+	15.1990i	0.00879997	+	0.529163i
$826$		0			0
$827$	−8.04607	+	13.9362i	−0.279789	+	0.484609i	−0.971332	−	0.237726i	$-0.923598\pi$
$827$	−8.04607	+	13.9362i	−0.279789	+	0.484609i	0.691543	+	0.722335i	$0.256931\pi$
$828$		0			0
$829$	−12.3056	−	21.3139i	−0.427391	−	0.740263i	0.569250	−	0.822165i	$-0.307234\pi$
$829$	−12.3056	−	21.3139i	−0.427391	−	0.740263i	−0.996640	+	0.0819022i	$0.973900\pi$
$830$		0			0
$831$	14.6711	−	18.0868i	0.508936	−	0.627424i
$832$		0			0
$833$	18.3889	+	15.4301i	0.637138	+	0.534622i
$834$		0			0
$835$	−13.3429	−	4.85643i	−0.461751	−	0.168064i
$836$		0			0
$837$	−22.1052	−	2.76972i	−0.764068	−	0.0957356i
$838$		0			0
$839$	49.9245	+	18.1710i	1.72359	+	0.627334i	0.998141	−	0.0609455i	$-0.0194116\pi$
$839$	49.9245	+	18.1710i	1.72359	+	0.627334i	0.725445	+	0.688280i	$0.241634\pi$
$840$		0			0
$841$	58.0463	+	48.7066i	2.00160	+	1.67954i
$842$		0			0
$843$	−4.72456	−	12.3383i	−0.162723	−	0.424954i
$844$		0			0
$845$	−4.44384	−	7.69695i	−0.152873	−	0.264783i
$846$		0			0
$847$	−3.20588	+	5.55274i	−0.110155	+	0.190794i
$848$		0			0
$849$	−23.8434	+	14.2998i	−0.818302	+	0.490767i
$850$		0			0
$851$	10.9924	−	4.00089i	0.376813	−	0.137149i
$852$		0			0
$853$	−3.07404	−	17.4338i	−0.105253	−	0.596921i	−0.991119	−	0.132979i	$-0.957546\pi$
$853$	−3.07404	−	17.4338i	−0.105253	−	0.596921i	0.885866	−	0.463942i	$-0.153565\pi$
$854$		0			0
$855$	1.60921	−	1.44414i	0.0550338	−	0.0493885i
$856$		0			0
$857$	−26.6198	+	22.3367i	−0.909315	+	0.763006i	−0.971989	−	0.235028i	$-0.924482\pi$
$857$	−26.6198	+	22.3367i	−0.909315	+	0.763006i	0.0626736	+	0.998034i	$0.480037\pi$
$858$		0			0
$859$	4.69075	−	26.6026i	0.160046	−	0.907667i	−0.793980	−	0.607944i	$-0.791995\pi$
$859$	4.69075	−	26.6026i	0.160046	−	0.907667i	0.954026	−	0.299723i	$-0.0968944\pi$
$860$		0			0
$861$	2.46265	−	7.13293i	0.0839268	−	0.243090i
$862$		0			0
$863$	−26.4896			−0.901717			−0.450858	−	0.892595i	$-0.648882\pi$
$863$	−26.4896			−0.901717			−0.450858	+	0.892595i	$0.648882\pi$
$864$		0			0
$865$	8.62630			0.293303
$866$		0			0
$867$	−1.74580	−	2.01166i	−0.0592904	−	0.0683196i
$868$		0			0
$869$	−5.72259	+	32.4544i	−0.194126	+	1.10094i
$870$		0			0
$871$	−52.2288	+	43.8252i	−1.76971	+	1.48496i
$872$		0			0
$873$	−15.9536	−	25.6251i	−0.539948	−	0.867277i
$874$		0			0
$875$	2.05628	+	11.6617i	0.0695150	+	0.394239i
$876$		0			0
$877$	−30.6921	+	11.1710i	−1.03640	+	0.377219i	−0.803514	−	0.595286i	$-0.797039\pi$
$877$	−30.6921	+	11.1710i	−1.03640	+	0.377219i	−0.232885	+	0.972504i	$0.574817\pi$
$878$		0			0
$879$	−28.2165	−	15.6711i	−0.951719	−	0.528573i
$880$		0			0
$881$	28.6351	−	49.5975i	0.964741	−	1.67098i	0.254433	−	0.967090i	$-0.418111\pi$
$881$	28.6351	−	49.5975i	0.964741	−	1.67098i	0.710309	−	0.703890i	$-0.248555\pi$
$882$		0			0
$883$	−25.5997	−	44.3400i	−0.861499	−	1.49216i	−0.870482	−	0.492201i	$-0.836192\pi$
$883$	−25.5997	−	44.3400i	−0.861499	−	1.49216i	0.00898207	−	0.999960i	$-0.497141\pi$
$884$		0			0
$885$	−23.0971	−	3.67776i	−0.776402	−	0.123627i
$886$		0			0
$887$	0.690832	+	0.579677i	0.0231959	+	0.0194637i	0.654312	−	0.756225i	$-0.272958\pi$
$887$	0.690832	+	0.579677i	0.0231959	+	0.0194637i	−0.631116	+	0.775688i	$0.717403\pi$
$888$		0			0
$889$	−7.92181	−	2.88330i	−0.265689	−	0.0967029i
$890$		0			0
$891$	17.2321	+	12.6069i	0.577297	+	0.422348i
$892$		0			0
$893$	−1.46768	−	0.534193i	−0.0491142	−	0.0178761i
$894$		0			0
$895$	−19.1534	−	16.0716i	−0.640226	−	0.537213i
$896$		0			0
$897$	−10.7700	−	1.71491i	−0.359599	−	0.0572590i
$898$		0			0
$899$	21.9428	+	38.0061i	0.731834	+	1.26757i
$900$		0			0
$901$	3.57347	−	6.18943i	0.119050	−	0.206200i
$902$		0			0
$903$	−14.0009	−	7.77592i	−0.465920	−	0.258766i
$904$		0			0
$905$	−5.36682	+	1.95336i	−0.178399	+	0.0649320i
$906$		0			0
$907$	4.97563	+	28.2182i	0.165213	+	0.936969i	0.948845	+	0.315743i	$0.102254\pi$
$907$	4.97563	+	28.2182i	0.165213	+	0.936969i	−0.783632	+	0.621226i	$0.786635\pi$
$908$		0			0
$909$	−19.1991	+	35.9649i	−0.636793	+	1.19288i
$910$		0			0
$911$	1.44517	−	1.21264i	0.0478807	−	0.0401767i	−0.618533	−	0.785759i	$-0.712273\pi$
$911$	1.44517	−	1.21264i	0.0478807	−	0.0401767i	0.666414	+	0.745582i	$0.267828\pi$
$912$		0			0
$913$	2.03674	−	11.5509i	0.0674061	−	0.382279i
$914$		0			0
$915$	−1.87847	−	2.16453i	−0.0621002	−	0.0715573i
$916$		0			0
$917$	23.1226			0.763577
$918$		0			0
$919$	0.605181			0.0199631			0.00998153	−	0.999950i	$-0.496823\pi$
$919$	0.605181			0.0199631			0.00998153	+	0.999950i	$0.496823\pi$
$920$		0			0
$921$	−16.6876	+	48.3347i	−0.549874	+	1.59268i
$922$		0			0
$923$	−5.92903	+	33.6252i	−0.195156	+	1.10679i
$924$		0			0
$925$	−24.0083	+	20.1454i	−0.789389	+	0.662376i
$926$		0			0
$927$	−7.78308	−	36.9159i	−0.255630	−	1.21248i
$928$		0			0
$929$	−4.47089	−	25.3557i	−0.146685	−	0.831892i	−0.965999	−	0.258547i	$-0.916756\pi$
$929$	−4.47089	−	25.3557i	−0.146685	−	0.831892i	0.819314	−	0.573346i	$-0.194355\pi$
$930$		0			0
$931$	−3.31103	+	1.20512i	−0.108515	+	0.0394961i
$932$		0			0
$933$	−7.75740	+	4.65241i	−0.253966	+	0.152313i
$934$		0			0
$935$	5.82440	−	10.0882i	0.190478	−	0.329918i
$936$		0			0
$937$	3.45488	+	5.98402i	0.112866	+	0.195489i	0.916925	−	0.399060i	$-0.130664\pi$
$937$	3.45488	+	5.98402i	0.112866	+	0.195489i	−0.804059	+	0.594550i	$0.797330\pi$
$938$		0			0
$939$	−1.70495	−	4.45252i	−0.0556390	−	0.145303i
$940$		0			0
$941$	−5.09908	−	4.27863i	−0.166225	−	0.139479i	0.555881	−	0.831262i	$-0.312381\pi$
$941$	−5.09908	−	4.27863i	−0.166225	−	0.139479i	−0.722106	+	0.691783i	$0.756826\pi$
$942$		0			0
$943$	4.73613	+	1.72381i	0.154230	+	0.0561350i
$944$		0			0
$945$	6.29413	+	3.22666i	0.204748	+	0.104963i
$946$		0			0
$947$	22.9907	+	8.36792i	0.747096	+	0.271921i	0.687383	−	0.726295i	$-0.258759\pi$
$947$	22.9907	+	8.36792i	0.747096	+	0.271921i	0.0597129	+	0.998216i	$0.480981\pi$
$948$		0			0
$949$	36.5171	+	30.6415i	1.18539	+	0.994664i
$950$		0			0
$951$	2.03731	−	2.51162i	0.0660641	−	0.0814450i
$952$		0			0
$953$	5.39493	+	9.34429i	0.174759	+	0.302691i	0.940078	−	0.340960i	$-0.110752\pi$
$953$	5.39493	+	9.34429i	0.174759	+	0.302691i	−0.765319	+	0.643651i	$0.777419\pi$
$954$		0			0
$955$	6.38180	−	11.0536i	0.206510	−	0.357686i
$956$		0			0
$957$	−0.699362	−	42.0543i	−0.0226072	−	1.35942i
$958$		0			0
$959$	0.939504	−	0.341952i	0.0303382	−	0.0110422i
$960$		0			0
$961$	−2.19110	−	12.4264i	−0.0706807	−	0.400850i
$962$		0			0
$963$	−36.8136	+	14.8031i	−1.18630	+	0.477022i
$964$		0			0
$965$	−22.8234	+	19.1511i	−0.734711	+	0.616495i
$966$		0			0
$967$	−6.61955	+	37.5414i	−0.212870	+	1.20725i	0.671693	+	0.740829i	$0.265567\pi$
$967$	−6.61955	+	37.5414i	−0.212870	+	1.20725i	−0.884564	+	0.466419i	$0.845544\pi$
$968$		0			0
$969$	4.62712	−	0.895460i	0.148644	−	0.0287663i
$970$		0			0
$971$	−38.6294			−1.23968			−0.619838	−	0.784730i	$-0.712802\pi$
$971$	−38.6294			−1.23968			−0.619838	+	0.784730i	$0.712802\pi$
$972$		0			0
$973$	−7.88852			−0.252894
$974$		0			0
$975$	28.6861	−	5.55146i	0.918689	−	0.177789i
$976$		0			0
$977$	0.965525	−	5.47577i	0.0308899	−	0.175185i	−0.965460	−	0.260553i	$-0.916095\pi$
$977$	0.965525	−	5.47577i	0.0308899	−	0.175185i	0.996350	+	0.0853673i	$0.0272064\pi$
$978$		0			0
$979$	−17.9454	+	15.0580i	−0.573538	+	0.481255i
$980$		0			0
$981$	−47.3589	+	19.0434i	−1.51205	+	0.608009i
$982$		0			0
$983$	7.81698	+	44.3323i	0.249323	+	1.41398i	0.810235	+	0.586105i	$0.199339\pi$
$983$	7.81698	+	44.3323i	0.249323	+	1.41398i	−0.560912	+	0.827875i	$0.689549\pi$
$984$		0			0
$985$	25.0270	−	9.10907i	0.797425	−	0.290239i
$986$		0			0
$987$	−0.0849547	−	5.10852i	−0.00270414	−	0.162606i
$988$		0			0
$989$	5.34837	−	9.26365i	0.170068	−	0.294567i
$990$		0			0
$991$	−12.2323	−	21.1869i	−0.388571	−	0.673025i	0.603687	−	0.797222i	$-0.293698\pi$
$991$	−12.2323	−	21.1869i	−0.388571	−	0.673025i	−0.992258	+	0.124197i	$0.960365\pi$
$992$		0			0
$993$	−11.4339	+	14.0959i	−0.362844	+	0.447320i
$994$		0			0
$995$	−10.1494	−	8.51632i	−0.321756	−	0.269985i
$996$		0			0
$997$	13.1021	+	4.76877i	0.414947	+	0.151028i	0.541053	−	0.840988i	$-0.318026\pi$
$997$	13.1021	+	4.76877i	0.414947	+	0.151028i	−0.126106	+	0.992017i	$0.540248\pi$
$998$		0			0
$999$	2.19508	+	43.9659i	0.0694492	+	1.39102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.e.193.4		24
4.3	odd	2		216.2.q.a.193.1	yes	24
12.11	even	2		648.2.q.a.145.2		24
27.7	even	9	inner	432.2.u.e.385.4		24
108.7	odd	18		216.2.q.a.169.1	✓	24
108.47	even	18		648.2.q.a.505.2		24
108.67	odd	18		5832.2.a.h.1.9		12
108.95	even	18		5832.2.a.i.1.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.q.a.169.1	✓	24	108.7	odd	18
216.2.q.a.193.1	yes	24	4.3	odd	2
432.2.u.e.193.4		24	1.1	even	1	trivial
432.2.u.e.385.4		24	27.7	even	9	inner
648.2.q.a.145.2		24	12.11	even	2
648.2.q.a.505.2		24	108.47	even	18
5832.2.a.h.1.9		12	108.67	odd	18
5832.2.a.i.1.4		12	108.95	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70050 - 0.329088i) q^{3} +(0.198034 - 1.12311i) q^{5} +(-0.914338 + 0.767221i) q^{7} +(2.78340 - 1.11923i) q^{9} +O(q^{10})\)	\(q+(1.70050 - 0.329088i) q^{3} +(0.198034 - 1.12311i) q^{5} +(-0.914338 + 0.767221i) q^{7} +(2.78340 - 1.11923i) q^{9} +(0.411958 + 2.33633i) q^{11} +(4.28496 - 1.55960i) q^{13} +(-0.0328444 - 1.97501i) q^{15} +(2.15278 - 3.72872i) q^{17} +(0.315991 + 0.547312i) q^{19} +(-1.30235 + 1.60556i) q^{21} +(-1.05775 - 0.887560i) q^{23} +(3.47631 + 1.26527i) q^{25} +(4.36485 - 2.81924i) q^{27} +(-9.61862 - 3.50089i) q^{29} +(-3.28435 - 2.75590i) q^{31} +(1.46939 + 3.83736i) q^{33} +(0.680600 + 1.17883i) q^{35} +(-4.23589 + 7.33678i) q^{37} +(6.77333 - 4.06223i) q^{39} +(-3.43000 + 1.24842i) q^{41} +(1.34522 + 7.62909i) q^{43} +(-0.705806 - 3.34770i) q^{45} +(-1.89320 + 1.58858i) q^{47} +(-0.968151 + 5.49066i) q^{49} +(2.43372 - 7.04914i) q^{51} +1.65993 q^{53} +2.70553 q^{55} +(0.717456 + 0.826715i) q^{57} +(2.05606 - 11.6605i) q^{59} +(1.11147 - 0.932633i) q^{61} +(-1.68627 + 3.15884i) q^{63} +(-0.903027 - 5.12132i) q^{65} +(-14.0501 + 5.11383i) q^{67} +(-2.09079 - 1.16120i) q^{69} +(-3.74388 + 6.48459i) q^{71} +(5.22698 + 9.05339i) q^{73} +(6.32786 + 1.00759i) q^{75} +(-2.16915 - 1.82013i) q^{77} +(13.0535 + 4.75107i) q^{79} +(6.49465 - 6.23053i) q^{81} +(-4.64588 - 1.69096i) q^{83} +(-3.76143 - 3.15621i) q^{85} +(-17.5086 - 2.78789i) q^{87} +(4.93727 + 8.55160i) q^{89} +(-2.72135 + 4.71351i) q^{91} +(-6.49197 - 3.60556i) q^{93} +(0.677266 - 0.246505i) q^{95} +(-1.74722 - 9.90896i) q^{97} +(3.76153 + 6.04187i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{7} + 6 q^{9}+O(q^{10}) \) 24 * q + 3 * q^7 + 6 * q^9	\( 24 q + 3 q^{7} + 6 q^{9} - 6 q^{11} + 12 q^{13} + 3 q^{15} + 6 q^{17} - 9 q^{19} - 18 q^{21} - 24 q^{23} - 24 q^{25} - 9 q^{29} + 27 q^{31} + 21 q^{33} + 18 q^{35} + 15 q^{37} + 15 q^{39} - 6 q^{41} - 39 q^{43} - 69 q^{45} + 36 q^{47} + 3 q^{49} + 36 q^{51} - 18 q^{53} + 54 q^{55} + 27 q^{57} + 30 q^{59} + 12 q^{61} - 18 q^{63} - 18 q^{65} - 54 q^{67} - 57 q^{69} + 36 q^{73} + 51 q^{75} - 24 q^{77} + 45 q^{79} + 18 q^{81} - 33 q^{83} - 57 q^{85} - 90 q^{87} + 9 q^{89} - 39 q^{91} + 42 q^{93} - 87 q^{95} + 57 q^{97} + 24 q^{99}+O(q^{100}) \) 24 * q + 3 * q^7 + 6 * q^9 - 6 * q^11 + 12 * q^13 + 3 * q^15 + 6 * q^17 - 9 * q^19 - 18 * q^21 - 24 * q^23 - 24 * q^25 - 9 * q^29 + 27 * q^31 + 21 * q^33 + 18 * q^35 + 15 * q^37 + 15 * q^39 - 6 * q^41 - 39 * q^43 - 69 * q^45 + 36 * q^47 + 3 * q^49 + 36 * q^51 - 18 * q^53 + 54 * q^55 + 27 * q^57 + 30 * q^59 + 12 * q^61 - 18 * q^63 - 18 * q^65 - 54 * q^67 - 57 * q^69 + 36 * q^73 + 51 * q^75 - 24 * q^77 + 45 * q^79 + 18 * q^81 - 33 * q^83 - 57 * q^85 - 90 * q^87 + 9 * q^89 - 39 * q^91 + 42 * q^93 - 87 * q^95 + 57 * q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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