LMFDB - Embedded newform 432.2.k.c.325.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			325.3
Character	$\chi$	$=$	432.325
Dual form			432.2.k.c.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20402 - 0.741841i) q^{2} +(0.899344 + 1.78639i) q^{4} +(-0.431497 - 0.431497i) q^{5} -0.145064i q^{7} +(0.242383 - 2.81802i) q^{8} +O(q^{10})$	\(q+(-1.20402 - 0.741841i) q^{2} +(0.899344 + 1.78639i) q^{4} +(-0.431497 - 0.431497i) q^{5} -0.145064i q^{7} +(0.242383 - 2.81802i) q^{8} +(0.199430 + 0.839634i) q^{10} +(-2.42618 - 2.42618i) q^{11} +(0.201311 - 0.201311i) q^{13} +(-0.107614 + 0.174661i) q^{14} +(-2.38236 + 3.21315i) q^{16} +3.15345 q^{17} +(3.09482 - 3.09482i) q^{19} +(0.382756 - 1.15888i) q^{20} +(1.12134 + 4.72102i) q^{22} -5.99610i q^{23} -4.62762i q^{25} +(-0.391724 + 0.0930425i) q^{26} +(0.259141 - 0.130463i) q^{28} +(-0.395136 + 0.395136i) q^{29} +3.98888 q^{31} +(5.25207 - 2.10138i) q^{32} +(-3.79683 - 2.33936i) q^{34} +(-0.0625947 + 0.0625947i) q^{35} +(-5.29237 - 5.29237i) q^{37} +(-6.02209 + 1.43037i) q^{38} +(-1.32056 + 1.11138i) q^{40} +1.76918i q^{41} +(-8.07993 - 8.07993i) q^{43} +(2.15213 - 6.51607i) q^{44} +(-4.44815 + 7.21944i) q^{46} -5.91082 q^{47} +6.97896 q^{49} +(-3.43296 + 5.57176i) q^{50} +(0.540668 + 0.178572i) q^{52} +(7.91745 + 7.91745i) q^{53} +2.09378i q^{55} +(-0.408794 - 0.0351611i) q^{56} +(0.768882 - 0.182625i) q^{58} +(-6.18218 - 6.18218i) q^{59} +(-0.789321 + 0.789321i) q^{61} +(-4.80270 - 2.95911i) q^{62} +(-7.88250 - 1.36608i) q^{64} -0.173730 q^{65} +(6.34861 - 6.34861i) q^{67} +(2.83604 + 5.63328i) q^{68} +(0.121801 - 0.0289302i) q^{70} +3.39100i q^{71} -2.23764i q^{73} +(2.44604 + 10.2982i) q^{74} +(8.31185 + 2.74524i) q^{76} +(-0.351951 + 0.351951i) q^{77} -7.01161 q^{79} +(2.41445 - 0.358486i) q^{80} +(1.31245 - 2.13014i) q^{82} +(4.08882 - 4.08882i) q^{83} +(-1.36070 - 1.36070i) q^{85} +(3.73440 + 15.7225i) q^{86} +(-7.42509 + 6.24896i) q^{88} +14.1667i q^{89} +(-0.0292030 - 0.0292030i) q^{91} +(10.7114 - 5.39256i) q^{92} +(7.11676 + 4.38488i) q^{94} -2.67081 q^{95} +17.2398 q^{97} +(-8.40283 - 5.17727i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.20402	−	0.741841i	−0.851373	−	0.524561i
$2$	−1.20402	−	0.741841i	−0.851373	−	0.524561i
$3$		0			0
$3$		0			0
$4$	0.899344	+	1.78639i	0.449672	+	0.893194i
$5$	−0.431497	−	0.431497i	−0.192971	−	0.192971i	0.604007	−	0.796979i	$-0.293570\pi$
$5$	−0.431497	−	0.431497i	−0.192971	−	0.192971i	−0.796979	+	0.604007i	$0.793570\pi$
$6$		0			0
$7$		−	0.145064i		−	0.0548291i	−0.999624	−	0.0274145i	$-0.991273\pi$
$7$		−	0.145064i		−	0.0548291i	0.999624	−	0.0274145i	$-0.00872741\pi$
$8$	0.242383	−	2.81802i	0.0856954	−	0.996321i
$9$		0			0
$10$	0.199430	+	0.839634i	0.0630654	+	0.265516i
$11$	−2.42618	−	2.42618i	−0.731521	−	0.731521i	0.239400	−	0.970921i	$-0.423049\pi$
$11$	−2.42618	−	2.42618i	−0.731521	−	0.731521i	−0.970921	+	0.239400i	$0.923049\pi$
$12$		0			0
$13$	0.201311	−	0.201311i	0.0558337	−	0.0558337i	−0.678639	−	0.734472i	$-0.737430\pi$
$13$	0.201311	−	0.201311i	0.0558337	−	0.0558337i	0.734472	+	0.678639i	$0.237430\pi$
$14$	−0.107614	+	0.174661i	−0.0287612	+	0.0466800i
$15$		0			0
$16$	−2.38236	+	3.21315i	−0.595590	+	0.803289i
$17$	3.15345			0.764824			0.382412	−	0.923992i	$-0.375094\pi$
$17$	3.15345			0.764824			0.382412	+	0.923992i	$0.375094\pi$
$18$		0			0
$19$	3.09482	−	3.09482i	0.710000	−	0.710000i	−0.256535	−	0.966535i	$-0.582581\pi$
$19$	3.09482	−	3.09482i	0.710000	−	0.710000i	0.966535	+	0.256535i	$0.0825809\pi$
$20$	0.382756	−	1.15888i	0.0855869	−	0.259134i
$21$		0			0
$22$	1.12134	+	4.72102i	0.239070	+	1.00652i
$23$		−	5.99610i		−	1.25027i	−0.780516	−	0.625136i	$-0.785043\pi$
$23$		−	5.99610i		−	1.25027i	0.780516	−	0.625136i	$-0.214957\pi$
$24$		0			0
$25$		−	4.62762i		−	0.925524i
$26$	−0.391724	+	0.0930425i	−0.0768234	+	0.0182471i
$27$		0			0
$28$	0.259141	−	0.130463i	0.0489730	−	0.0246551i
$29$	−0.395136	+	0.395136i	−0.0733750	+	0.0733750i	−0.742842	−	0.669467i	$-0.766523\pi$
$29$	−0.395136	+	0.395136i	−0.0733750	+	0.0733750i	0.669467	+	0.742842i	$0.266523\pi$
$30$		0			0
$31$	3.98888			0.716424			0.358212	−	0.933640i	$-0.383387\pi$
$31$	3.98888			0.716424			0.358212	+	0.933640i	$0.383387\pi$
$32$	5.25207	−	2.10138i	0.928443	−	0.371475i
$33$		0			0
$34$	−3.79683	−	2.33936i	−0.651150	−	0.401196i
$35$	−0.0625947	+	0.0625947i	−0.0105804	+	0.0105804i
$36$		0			0
$37$	−5.29237	−	5.29237i	−0.870060	−	0.870060i	0.122419	−	0.992479i	$-0.460935\pi$
$37$	−5.29237	−	5.29237i	−0.870060	−	0.870060i	−0.992479	+	0.122419i	$0.960935\pi$
$38$	−6.02209	+	1.43037i	−0.976913	+	0.232037i
$39$		0			0
$40$	−1.32056	+	1.11138i	−0.208798	+	0.175725i
$41$			1.76918i			0.276300i	0.990411	+	0.138150i	$0.0441156\pi$
$41$			1.76918i			0.276300i	−0.990411	+	0.138150i	$0.955884\pi$
$42$		0			0
$43$	−8.07993	−	8.07993i	−1.23218	−	1.23218i	−0.963125	−	0.269053i	$-0.913289\pi$
$43$	−8.07993	−	8.07993i	−1.23218	−	1.23218i	−0.269053	−	0.963125i	$-0.586711\pi$
$44$	2.15213	−	6.51607i	0.324445	−	0.982334i
$45$		0			0
$46$	−4.44815	+	7.21944i	−0.655844	+	1.06445i
$47$	−5.91082			−0.862181			−0.431091	−	0.902309i	$-0.641871\pi$
$47$	−5.91082			−0.862181			−0.431091	+	0.902309i	$0.641871\pi$
$48$		0			0
$49$	6.97896			0.996994
$50$	−3.43296	+	5.57176i	−0.485494	+	0.787966i
$51$		0			0
$52$	0.540668	+	0.178572i	0.0749771	+	0.0247634i
$53$	7.91745	+	7.91745i	1.08755	+	1.08755i	0.995781	+	0.0917652i	$0.0292509\pi$
$53$	7.91745	+	7.91745i	1.08755	+	1.08755i	0.0917652	+	0.995781i	$0.470749\pi$
$54$		0			0
$55$			2.09378i			0.282325i
$56$	−0.408794	−	0.0351611i	−0.0546274	−	0.00469860i
$57$		0			0
$58$	0.768882	−	0.182625i	0.100959	−	0.0239799i
$59$	−6.18218	−	6.18218i	−0.804852	−	0.804852i	0.178998	−	0.983849i	$-0.442714\pi$
$59$	−6.18218	−	6.18218i	−0.804852	−	0.804852i	−0.983849	+	0.178998i	$0.942714\pi$
$60$		0			0
$61$	−0.789321	+	0.789321i	−0.101062	+	0.101062i	−0.755830	−	0.654768i	$-0.772766\pi$
$61$	−0.789321	+	0.789321i	−0.101062	+	0.101062i	0.654768	+	0.755830i	$0.272766\pi$
$62$	−4.80270	−	2.95911i	−0.609944	−	0.375808i
$63$		0			0
$64$	−7.88250	−	1.36608i	−0.985313	−	0.170760i
$65$	−0.173730			−0.0215486
$66$		0			0
$67$	6.34861	−	6.34861i	0.775607	−	0.775607i	−0.203474	−	0.979080i	$-0.565223\pi$
$67$	6.34861	−	6.34861i	0.775607	−	0.775607i	0.979080	+	0.203474i	$0.0652232\pi$
$68$	2.83604	+	5.63328i	0.343920	+	0.683136i
$69$		0			0
$70$	0.121801	−	0.0289302i	0.0145580	−	0.00345782i
$71$			3.39100i			0.402437i	0.979546	+	0.201219i	$0.0644902\pi$
$71$			3.39100i			0.402437i	−0.979546	+	0.201219i	$0.935510\pi$
$72$		0			0
$73$		−	2.23764i		−	0.261896i	−0.991389	−	0.130948i	$-0.958198\pi$
$73$		−	2.23764i		−	0.261896i	0.991389	−	0.130948i	$-0.0418021\pi$
$74$	2.44604	+	10.2982i	0.284346	+	1.19714i
$75$		0			0
$76$	8.31185	+	2.74524i	0.953435	+	0.314900i
$77$	−0.351951	+	0.351951i	−0.0401086	+	0.0401086i
$78$		0			0
$79$	−7.01161			−0.788867			−0.394434	−	0.918924i	$-0.629059\pi$
$79$	−7.01161			−0.788867			−0.394434	+	0.918924i	$0.629059\pi$
$80$	2.41445	−	0.358486i	0.269943	−	0.0400799i
$81$		0			0
$82$	1.31245	−	2.13014i	0.144936	−	0.235235i
$83$	4.08882	−	4.08882i	0.448807	−	0.448807i	−0.446151	−	0.894958i	$-0.647206\pi$
$83$	4.08882	−	4.08882i	0.448807	−	0.448807i	0.894958	+	0.446151i	$0.147206\pi$
$84$		0			0
$85$	−1.36070	−	1.36070i	−0.147589	−	0.147589i
$86$	3.73440	+	15.7225i	0.402691	+	1.69540i
$87$		0			0
$88$	−7.42509	+	6.24896i	−0.791518	+	0.666142i
$89$			14.1667i			1.50167i	0.660489	+	0.750835i	$0.270349\pi$
$89$			14.1667i			1.50167i	−0.660489	+	0.750835i	$0.729651\pi$
$90$		0			0
$91$	−0.0292030	−	0.0292030i	−0.00306131	−	0.00306131i
$92$	10.7114	−	5.39256i	1.11674	−	0.562213i
$93$		0			0
$94$	7.11676	+	4.38488i	0.734038	+	0.452266i
$95$	−2.67081			−0.274019
$96$		0			0
$97$	17.2398			1.75044			0.875219	−	0.483727i	$-0.160717\pi$
$97$	17.2398			1.75044			0.875219	+	0.483727i	$0.160717\pi$
$98$	−8.40283	−	5.17727i	−0.848814	−	0.522984i
$99$		0			0
$100$	8.26672	−	4.16183i	0.826672	−	0.416183i
$101$	10.9005	+	10.9005i	1.08464	+	1.08464i	0.996069	+	0.0885752i	$0.0282314\pi$
$101$	10.9005	+	10.9005i	1.08464	+	1.08464i	0.0885752	+	0.996069i	$0.471769\pi$
$102$		0			0
$103$			16.0259i			1.57908i	0.613698	+	0.789541i	$0.289681\pi$
$103$			16.0259i			1.57908i	−0.613698	+	0.789541i	$0.710319\pi$
$104$	−0.518505	−	0.616094i	−0.0508436	−	0.0604130i
$105$		0			0
$106$	−3.65931	−	15.4063i	−0.355423	−	1.49639i
$107$	2.05995	+	2.05995i	0.199143	+	0.199143i	0.799632	−	0.600490i	$-0.205028\pi$
$107$	2.05995	+	2.05995i	0.199143	+	0.199143i	−0.600490	+	0.799632i	$0.705028\pi$
$108$		0			0
$109$	−11.7881	+	11.7881i	−1.12909	+	1.12909i	−0.138765	+	0.990325i	$0.544313\pi$
$109$	−11.7881	+	11.7881i	−1.12909	+	1.12909i	−0.990325	+	0.138765i	$0.955687\pi$
$110$	1.55325	−	2.52096i	0.148097	−	0.240364i
$111$		0			0
$112$	0.466113	+	0.345595i	0.0440436	+	0.0326556i
$113$	12.0717			1.13561			0.567807	−	0.823162i	$-0.307792\pi$
$113$	12.0717			1.13561			0.567807	+	0.823162i	$0.307792\pi$
$114$		0			0
$115$	−2.58730	+	2.58730i	−0.241267	+	0.241267i
$116$	−1.06123	−	0.350503i	−0.0985328	−	0.0325434i
$117$		0			0
$118$	2.85730	+	12.0297i	0.263036	+	1.10742i
$119$		−	0.457452i		−	0.0419346i
$120$		0			0
$121$			0.772692i			0.0702448i
$122$	1.53591	−	0.364811i	0.139055	−	0.0330284i
$123$		0			0
$124$	3.58738	+	7.12568i	0.322156	+	0.639905i
$125$	−4.15429	+	4.15429i	−0.371571	+	0.371571i
$126$		0			0
$127$	13.2608			1.17671			0.588355	−	0.808603i	$-0.299776\pi$
$127$	13.2608			1.17671			0.588355	+	0.808603i	$0.299776\pi$
$128$	8.47730	+	7.49236i	0.749294	+	0.662237i
$129$		0			0
$130$	0.209175	+	0.128880i	0.0183459	+	0.0113035i
$131$	−7.63558	+	7.63558i	−0.667124	+	0.667124i	−0.957049	−	0.289926i	$-0.906369\pi$
$131$	−7.63558	+	7.63558i	−0.667124	+	0.667124i	0.289926	+	0.957049i	$0.406369\pi$
$132$		0			0
$133$	−0.448947	−	0.448947i	−0.0389286	−	0.0389286i
$134$	−12.3535	+	2.93422i	−1.06718	+	0.253478i
$135$		0			0
$136$	0.764343	−	8.88649i	0.0655419	−	0.762010i
$137$		−	2.10201i		−	0.179586i	−0.995960	−	0.0897932i	$-0.971379\pi$
$137$		−	2.10201i		−	0.179586i	0.995960	−	0.0897932i	$-0.0286206\pi$
$138$		0			0
$139$	−5.44119	−	5.44119i	−0.461516	−	0.461516i	0.437636	−	0.899152i	$-0.355816\pi$
$139$	−5.44119	−	5.44119i	−0.461516	−	0.461516i	−0.899152	+	0.437636i	$0.855816\pi$
$140$	−0.168113	−	0.0555242i	−0.0142081	−	0.00469265i
$141$		0			0
$142$	2.51558	−	4.08284i	0.211103	−	0.342624i
$143$	−0.976834			−0.0816869
$144$		0			0
$145$	0.341000			0.0283185
$146$	−1.65997	+	2.69417i	−0.137380	+	0.222971i
$147$		0			0
$148$	4.69456	−	14.2139i	0.385890	−	1.16837i
$149$	−15.0912	−	15.0912i	−1.23632	−	1.23632i	−0.961495	−	0.274824i	$-0.911380\pi$
$149$	−15.0912	−	15.0912i	−1.23632	−	1.23632i	−0.274824	−	0.961495i	$-0.588620\pi$
$150$		0			0
$151$			15.1659i			1.23418i	0.786892	+	0.617090i	$0.211689\pi$
$151$			15.1659i			1.23418i	−0.786892	+	0.617090i	$0.788311\pi$
$152$	−7.97113	−	9.47140i	−0.646544	−	0.768232i
$153$		0			0
$154$	0.684850	−	0.162666i	0.0551868	−	0.0131080i
$155$	−1.72119	−	1.72119i	−0.138249	−	0.138249i
$156$		0			0
$157$	−11.6066	+	11.6066i	−0.926306	+	0.926306i	−0.997465	−	0.0711592i	$-0.977330\pi$
$157$	−11.6066	+	11.6066i	−0.926306	+	0.926306i	0.0711592	+	0.997465i	$0.477330\pi$
$158$	8.44214	+	5.20150i	0.671620	+	0.413809i
$159$		0			0
$160$	−3.17299	−	1.35951i	−0.250847	−	0.107479i
$161$	−0.869818			−0.0685513
$162$		0			0
$163$	5.06506	−	5.06506i	0.396726	−	0.396726i	−0.480351	−	0.877077i	$-0.659491\pi$
$163$	5.06506	−	5.06506i	0.396726	−	0.396726i	0.877077	+	0.480351i	$0.159491\pi$
$164$	−3.16045	+	1.59111i	−0.246790	+	0.124245i
$165$		0			0
$166$	−7.95630	+	1.88978i	−0.617528	+	0.146676i
$167$		−	22.6665i		−	1.75399i	−0.480501	−	0.876994i	$-0.659545\pi$
$167$		−	22.6665i		−	1.75399i	0.480501	−	0.876994i	$-0.340455\pi$
$168$		0			0
$169$			12.9189i			0.993765i
$170$	0.628893	+	2.64774i	0.0482339	+	0.203073i
$171$		0			0
$172$	7.16725	−	21.7005i	0.546498	−	1.65465i
$173$	7.67777	−	7.67777i	0.583730	−	0.583730i	−0.352196	−	0.935926i	$-0.614565\pi$
$173$	7.67777	−	7.67777i	0.583730	−	0.583730i	0.935926	+	0.352196i	$0.114565\pi$
$174$		0			0
$175$	−0.671301			−0.0507456
$176$	13.5757	−	2.01566i	1.02331	−	0.151936i
$177$		0			0
$178$	10.5095	−	17.0571i	0.787717	−	1.27848i
$179$	−2.05995	+	2.05995i	−0.153968	+	0.153968i	−0.779888	−	0.625920i	$-0.784724\pi$
$179$	−2.05995	+	2.05995i	−0.153968	+	0.153968i	0.625920	+	0.779888i	$0.284724\pi$
$180$		0			0
$181$	−7.82518	−	7.82518i	−0.581641	−	0.581641i	0.353713	−	0.935354i	$-0.384919\pi$
$181$	−7.82518	−	7.82518i	−0.581641	−	0.581641i	−0.935354	+	0.353713i	$0.884919\pi$
$182$	0.0134971	+	0.0568251i	0.00100047	+	0.00421216i
$183$		0			0
$184$	−16.8971	−	1.45335i	−1.24567	−	0.107143i
$185$			4.56728i			0.335793i
$186$		0			0
$187$	−7.65083	−	7.65083i	−0.559484	−	0.559484i
$188$	−5.31586	−	10.5590i	−0.387699	−	0.770095i
$189$		0			0
$190$	3.21571	+	1.98131i	0.233292	+	0.143740i
$191$	−3.78274			−0.273710			−0.136855	−	0.990591i	$-0.543699\pi$
$191$	−3.78274			−0.273710			−0.136855	+	0.990591i	$0.543699\pi$
$192$		0			0
$193$	−4.43287			−0.319085			−0.159542	−	0.987191i	$-0.551002\pi$
$193$	−4.43287			−0.319085			−0.159542	+	0.987191i	$0.551002\pi$
$194$	−20.7571	−	12.7892i	−1.49028	−	0.918211i
$195$		0			0
$196$	6.27649	+	12.4671i	0.448320	+	0.890509i
$197$	2.97523	+	2.97523i	0.211976	+	0.211976i	0.805106	−	0.593130i	$-0.202108\pi$
$197$	2.97523	+	2.97523i	0.211976	+	0.211976i	−0.593130	+	0.805106i	$0.702108\pi$
$198$		0			0
$199$			19.0589i			1.35105i	0.737338	+	0.675524i	$0.236083\pi$
$199$			19.0589i			1.35105i	−0.737338	+	0.675524i	$0.763917\pi$
$200$	−13.0407	−	1.12166i	−0.922120	−	0.0793132i
$201$		0			0
$202$	−5.03804	−	21.2110i	−0.354475	−	1.49240i
$203$	0.0573201	+	0.0573201i	0.00402308	+	0.00402308i
$204$		0			0
$205$	0.763398	−	0.763398i	0.0533180	−	0.0533180i
$206$	11.8887	−	19.2956i	0.828324	−	1.34439i
$207$		0			0
$208$	0.167248	+	1.12644i	0.0115966	+	0.0781045i
$209$	−15.0172			−1.03876
$210$		0			0
$211$	−3.44175	+	3.44175i	−0.236940	+	0.236940i	−0.815582	−	0.578642i	$-0.803583\pi$
$211$	−3.44175	+	3.44175i	−0.236940	+	0.236940i	0.578642	+	0.815582i	$0.303583\pi$
$212$	−7.02312	+	21.2642i	−0.482350	+	1.46043i
$213$		0			0
$214$	−0.952072	−	4.00838i	−0.0650823	−	0.274007i
$215$			6.97293i			0.475550i
$216$		0			0
$217$		−	0.578643i		−	0.0392808i
$218$	22.9379	−	5.44823i	1.55355	−	0.369001i
$219$		0			0
$220$	−3.74030	+	1.88303i	−0.252171	+	0.126954i
$221$	0.634824	−	0.634824i	0.0427029	−	0.0427029i
$222$		0			0
$223$	−20.6369			−1.38195			−0.690975	−	0.722879i	$-0.742819\pi$
$223$	−20.6369			−1.38195			−0.690975	+	0.722879i	$0.742819\pi$
$224$	−0.304835	−	0.761886i	−0.0203676	−	0.0509056i
$225$		0			0
$226$	−14.5347	−	8.95531i	−0.966831	−	0.595698i
$227$	15.2341	−	15.2341i	1.01112	−	1.01112i	0.0111848	−	0.999937i	$-0.496440\pi$
$227$	15.2341	−	15.2341i	1.01112	−	1.01112i	0.999937	−	0.0111848i	$-0.00356030\pi$
$228$		0			0
$229$	−6.28300	−	6.28300i	−0.415192	−	0.415192i	0.468350	−	0.883543i	$-0.344848\pi$
$229$	−6.28300	−	6.28300i	−0.415192	−	0.415192i	−0.883543	+	0.468350i	$0.844848\pi$
$230$	5.03453	−	1.19580i	0.331967	−	0.0788489i
$231$		0			0
$232$	1.01773	+	1.20928i	0.0668172	+	0.0793930i
$233$		−	16.8057i		−	1.10098i	−0.834842	−	0.550490i	$-0.814441\pi$
$233$		−	16.8057i		−	1.10098i	0.834842	−	0.550490i	$-0.185559\pi$
$234$		0			0
$235$	2.55050	+	2.55050i	0.166376	+	0.166376i
$236$	5.48386	−	16.6037i	0.356969	−	1.08081i
$237$		0			0
$238$	−0.339357	+	0.550783i	−0.0219972	+	0.0357020i
$239$	13.6647			0.883899			0.441950	−	0.897040i	$-0.354287\pi$
$239$	13.6647			0.883899			0.441950	+	0.897040i	$0.354287\pi$
$240$		0			0
$241$	27.0347			1.74146			0.870730	−	0.491761i	$-0.163647\pi$
$241$	27.0347			1.74146			0.870730	+	0.491761i	$0.163647\pi$
$242$	0.573215	−	0.930340i	0.0368476	−	0.0598045i
$243$		0			0
$244$	−2.11991	−	0.700162i	−0.135713	−	0.0448233i
$245$	−3.01140	−	3.01140i	−0.192391	−	0.192391i
$246$		0			0
$247$		−	1.24604i		−	0.0792838i
$248$	0.966838	−	11.2408i	0.0613943	−	0.713788i
$249$		0			0
$250$	8.08368	−	1.92004i	0.511257	−	0.121434i
$251$	4.18483	+	4.18483i	0.264144	+	0.264144i	0.826735	−	0.562591i	$-0.190195\pi$
$251$	4.18483	+	4.18483i	0.264144	+	0.264144i	−0.562591	+	0.826735i	$0.690195\pi$
$252$		0			0
$253$	−14.5476	+	14.5476i	−0.914600	+	0.914600i
$254$	−15.9664	−	9.83744i	−1.00182	−	0.617256i
$255$		0			0
$256$	−4.64873	−	15.3098i	−0.290546	−	0.956861i
$257$	−2.12929			−0.132821			−0.0664106	−	0.997792i	$-0.521155\pi$
$257$	−2.12929			−0.132821			−0.0664106	+	0.997792i	$0.521155\pi$
$258$		0			0
$259$	−0.767732	+	0.767732i	−0.0477046	+	0.0477046i
$260$	−0.156243	−	0.310349i	−0.00968980	−	0.0192471i
$261$		0			0
$262$	14.8578	−	3.52903i	0.917918	−	0.218024i
$263$			22.3552i			1.37848i	0.724534	+	0.689239i	$0.242055\pi$
$263$			22.3552i			1.37848i	−0.724534	+	0.689239i	$0.757945\pi$
$264$		0			0
$265$		−	6.83271i		−	0.419730i
$266$	0.207495	+	0.873589i	0.0127224	+	0.0535632i
$267$		0			0
$268$	17.0507	+	5.63149i	1.04154	+	0.343998i
$269$	7.04997	−	7.04997i	0.429844	−	0.429844i	−0.458731	−	0.888575i	$-0.651696\pi$
$269$	7.04997	−	7.04997i	0.429844	−	0.429844i	0.888575	+	0.458731i	$0.151696\pi$
$270$		0			0
$271$	15.1344			0.919351			0.459676	−	0.888087i	$-0.347966\pi$
$271$	15.1344			0.919351			0.459676	+	0.888087i	$0.347966\pi$
$272$	−7.51265	+	10.1325i	−0.455521	+	0.614374i
$273$		0			0
$274$	−1.55935	+	2.53086i	−0.0942040	+	0.152895i
$275$	−11.2274	+	11.2274i	−0.677040	+	0.677040i
$276$		0			0
$277$	14.2724	+	14.2724i	0.857543	+	0.857543i	0.991048	−	0.133505i	$-0.0426232\pi$
$277$	14.2724	+	14.2724i	0.857543	+	0.857543i	−0.133505	+	0.991048i	$0.542623\pi$
$278$	2.51482	+	10.5878i	0.150829	+	0.635015i
$279$		0			0
$280$	0.161221	+	0.191565i	0.00963482	+	0.0114482i
$281$		−	20.3101i		−	1.21160i	−0.795618	−	0.605799i	$-0.792854\pi$
$281$		−	20.3101i		−	1.21160i	0.795618	−	0.605799i	$-0.207146\pi$
$282$		0			0
$283$	−4.91438	−	4.91438i	−0.292130	−	0.292130i	0.545791	−	0.837921i	$-0.316229\pi$
$283$	−4.91438	−	4.91438i	−0.292130	−	0.292130i	−0.837921	+	0.545791i	$0.816229\pi$
$284$	−6.05763	+	3.04967i	−0.359454	+	0.180965i
$285$		0			0
$286$	1.17613	+	0.724655i	0.0695461	+	0.0428498i
$287$	0.256645			0.0151493
$288$		0			0
$289$	−7.05576			−0.415045
$290$	−0.410572	−	0.252968i	−0.0241096	−	0.0148548i
$291$		0			0
$292$	3.99730	−	2.01241i	0.233924	−	0.117767i
$293$	−11.6160	−	11.6160i	−0.678611	−	0.678611i	0.281075	−	0.959686i	$-0.409309\pi$
$293$	−11.6160	−	11.6160i	−0.678611	−	0.678611i	−0.959686	+	0.281075i	$0.909309\pi$
$294$		0			0
$295$			5.33518i			0.310626i
$296$	−16.1968	+	13.6312i	−0.941419	+	0.792299i
$297$		0			0
$298$	6.97489	+	29.3654i	0.404044	+	1.70109i
$299$	−1.20708	−	1.20708i	−0.0698073	−	0.0698073i
$300$		0			0
$301$	−1.17211	+	1.17211i	−0.0675592	+	0.0675592i
$302$	11.2507	−	18.2601i	0.647403	−	1.05075i
$303$		0			0
$304$	2.57116	+	17.3171i	0.147466	+	0.993204i
$305$	0.681179			0.0390042
$306$		0			0
$307$	7.20459	−	7.20459i	0.411188	−	0.411188i	−0.470964	−	0.882152i	$-0.656094\pi$
$307$	7.20459	−	7.20459i	0.411188	−	0.411188i	0.882152	+	0.470964i	$0.156094\pi$
$308$	−0.945247	−	0.312196i	−0.0538605	−	0.0177890i
$309$		0			0
$310$	0.795503	+	3.34920i	0.0451815	+	0.190222i
$311$			2.76925i			0.157030i	0.996913	+	0.0785148i	$0.0250178\pi$
$311$			2.76925i			0.157030i	−0.996913	+	0.0785148i	$0.974982\pi$
$312$		0			0
$313$			0.232921i			0.0131655i	0.999978	+	0.00658273i	$0.00209536\pi$
$313$			0.232921i			0.0131655i	−0.999978	+	0.00658273i	$0.997905\pi$
$314$	22.5848	−	5.36436i	1.27454	−	0.302728i
$315$		0			0
$316$	−6.30585	−	12.5254i	−0.354732	−	0.704611i
$317$	−16.5035	+	16.5035i	−0.926931	+	0.926931i	−0.997506	−	0.0705754i	$-0.977516\pi$
$317$	−16.5035	+	16.5035i	−0.926931	+	0.926931i	0.0705754	+	0.997506i	$0.477516\pi$
$318$		0			0
$319$	1.91734			0.107351
$320$	2.81181	+	3.99073i	0.157185	+	0.223089i
$321$		0			0
$322$	1.04728	+	0.645267i	0.0583627	+	0.0359593i
$323$	9.75935	−	9.75935i	0.543025	−	0.543025i
$324$		0			0
$325$	−0.931592	−	0.931592i	−0.0516754	−	0.0516754i
$326$	−9.85592	+	2.34098i	−0.545869	+	0.129655i
$327$		0			0
$328$	4.98560	+	0.428821i	0.275284	+	0.0236777i
$329$			0.857447i			0.0472726i
$330$		0			0
$331$	1.73963	+	1.73963i	0.0956187	+	0.0956187i	0.753298	−	0.657679i	$-0.228462\pi$
$331$	1.73963	+	1.73963i	0.0956187	+	0.0956187i	−0.657679	+	0.753298i	$0.728462\pi$
$332$	10.9815	+	3.62696i	0.602687	+	0.199055i
$333$		0			0
$334$	−16.8150	+	27.2910i	−0.920073	+	1.49330i
$335$	−5.47881			−0.299340
$336$		0			0
$337$	3.38998			0.184664			0.0923319	−	0.995728i	$-0.470568\pi$
$337$	3.38998			0.184664			0.0923319	+	0.995728i	$0.470568\pi$
$338$	9.58380	−	15.5547i	0.521290	−	0.846065i
$339$		0			0
$340$	1.20700	−	3.65448i	0.0654589	−	0.198192i
$341$	−9.67774	−	9.67774i	−0.524079	−	0.524079i
$342$		0			0
$343$		−	2.02784i		−	0.109493i
$344$	−24.7279	+	20.8110i	−1.33324	+	1.12205i
$345$		0			0
$346$	−14.9399	+	3.54853i	−0.803173	+	0.190770i
$347$	20.0204	+	20.0204i	1.07475	+	1.07475i	0.996971	+	0.0777788i	$0.0247828\pi$
$347$	20.0204	+	20.0204i	1.07475	+	1.07475i	0.0777788	+	0.996971i	$0.475217\pi$
$348$		0			0
$349$	11.9303	−	11.9303i	0.638616	−	0.638616i	−0.311598	−	0.950214i	$-0.600864\pi$
$349$	11.9303	−	11.9303i	0.638616	−	0.638616i	0.950214	+	0.311598i	$0.100864\pi$
$350$	0.808263	+	0.497999i	0.0432035	+	0.0266192i
$351$		0			0
$352$	−17.8408	−	7.64412i	−0.950917	−	0.407433i
$353$	−26.0718			−1.38766			−0.693830	−	0.720139i	$-0.744078\pi$
$353$	−26.0718			−1.38766			−0.693830	+	0.720139i	$0.744078\pi$
$354$		0			0
$355$	1.46320	−	1.46320i	0.0776588	−	0.0776588i
$356$	−25.3073	+	12.7408i	−1.34128	+	0.675260i
$357$		0			0
$358$	4.00838	−	0.952072i	0.211849	−	0.0503186i
$359$			11.3940i			0.601350i	0.953727	+	0.300675i	$0.0972120\pi$
$359$			11.3940i			0.601350i	−0.953727	+	0.300675i	$0.902788\pi$
$360$		0			0
$361$		−	0.155790i		−	0.00819949i
$362$	3.61666	+	15.2267i	0.190087	+	0.800299i
$363$		0			0
$364$	0.0259043	−	0.0784314i	0.00135776	−	0.00411092i
$365$	−0.965536	+	0.965536i	−0.0505384	+	0.0505384i
$366$		0			0
$367$	9.83069			0.513158			0.256579	−	0.966523i	$-0.417405\pi$
$367$	9.83069			0.513158			0.256579	+	0.966523i	$0.417405\pi$
$368$	19.2664	+	14.2849i	1.00433	+	0.744650i
$369$		0			0
$370$	3.38819	−	5.49911i	0.176144	−	0.285885i
$371$	1.14854	−	1.14854i	0.0596291	−	0.0596291i
$372$		0			0
$373$	−14.9304	−	14.9304i	−0.773067	−	0.773067i	0.205575	−	0.978641i	$-0.434094\pi$
$373$	−14.9304	−	14.9304i	−0.773067	−	0.773067i	−0.978641	+	0.205575i	$0.934094\pi$
$374$	3.53608	+	14.8875i	0.182846	+	0.769813i
$375$		0			0
$376$	−1.43268	+	16.6568i	−0.0738850	+	0.859009i
$377$			0.159091i			0.00819359i
$378$		0			0
$379$	2.32709	+	2.32709i	0.119534	+	0.119534i	0.764344	−	0.644809i	$-0.223063\pi$
$379$	2.32709	+	2.32709i	0.119534	+	0.119534i	−0.644809	+	0.764344i	$0.723063\pi$
$380$	−2.40198	−	4.77110i	−0.123219	−	0.244752i
$381$		0			0
$382$	4.55451	+	2.80619i	0.233029	+	0.143577i
$383$	28.7611			1.46962			0.734811	−	0.678272i	$-0.237271\pi$
$383$	28.7611			1.46962			0.734811	+	0.678272i	$0.237271\pi$
$384$		0			0
$385$	0.303732			0.0154796
$386$	5.33727	+	3.28848i	0.271660	+	0.167379i
$387$		0			0
$388$	15.5045	+	30.7970i	0.787123	+	1.56348i
$389$	16.6290	+	16.6290i	0.843125	+	0.843125i	0.989264	−	0.146139i	$-0.0466848\pi$
$389$	16.6290	+	16.6290i	0.843125	+	0.843125i	−0.146139	+	0.989264i	$0.546685\pi$
$390$		0			0
$391$		−	18.9084i		−	0.956238i
$392$	1.69158	−	19.6669i	0.0854378	−	0.993326i
$393$		0			0
$394$	−1.37510	−	5.78939i	−0.0692764	−	0.291665i
$395$	3.02549	+	3.02549i	0.152229	+	0.152229i
$396$		0			0
$397$	19.4919	−	19.4919i	0.978271	−	0.978271i	−0.0214976	−	0.999769i	$-0.506843\pi$
$397$	19.4919	−	19.4919i	0.978271	−	0.978271i	0.999769	+	0.0214976i	$0.00684343\pi$
$398$	14.1387	−	22.9473i	0.708707	−	1.15025i
$399$		0			0
$400$	14.8693	+	11.0247i	0.743463	+	0.551233i
$401$	34.7719			1.73643			0.868213	−	0.496192i	$-0.165269\pi$
$401$	34.7719			1.73643			0.868213	+	0.496192i	$0.165269\pi$
$402$		0			0
$403$	0.803006	−	0.803006i	0.0400006	−	0.0400006i
$404$	−9.66925	+	29.2759i	−0.481063	+	1.45653i
$405$		0			0
$406$	−0.0264923	−	0.111537i	−0.00131479	−	0.00553549i
$407$			25.6805i			1.27293i
$408$		0			0
$409$			0.194755i			0.00963004i	0.999988	+	0.00481502i	$0.00153267\pi$
$409$			0.194755i			0.00963004i	−0.999988	+	0.00481502i	$0.998467\pi$
$410$	−1.48547	+	0.352829i	−0.0733620	+	0.0174250i
$411$		0			0
$412$	−28.6285	+	14.4128i	−1.41043	+	0.710069i
$413$	−0.896813	+	0.896813i	−0.0441293	+	0.0441293i
$414$		0			0
$415$	−3.52863			−0.173214
$416$	0.634268	−	1.48033i	0.0310975	−	0.0725792i
$417$		0			0
$418$	18.0810	+	11.1403i	0.884371	+	0.544892i
$419$	−26.2018	+	26.2018i	−1.28004	+	1.28004i	−0.339400	+	0.940642i	$0.610224\pi$
$419$	−26.2018	+	26.2018i	−1.28004	+	1.28004i	−0.940642	+	0.339400i	$0.889776\pi$
$420$		0			0
$421$	3.73965	+	3.73965i	0.182259	+	0.182259i	0.792340	−	0.610080i	$-0.208863\pi$
$421$	3.73965	+	3.73965i	0.182259	+	0.182259i	−0.610080	+	0.792340i	$0.708863\pi$
$422$	6.69717	−	1.59072i	0.326013	−	0.0774348i
$423$		0			0
$424$	24.2306	−	20.3925i	1.17674	−	0.990348i
$425$		−	14.5930i		−	0.707863i
$426$		0			0
$427$	0.114502	+	0.114502i	0.00554115	+	0.00554115i
$428$	−1.82726	+	5.53247i	−0.0883241	+	0.267422i
$429$		0			0
$430$	5.17281	−	8.39557i	0.249455	−	0.404870i
$431$	15.9815			0.769803			0.384902	−	0.922958i	$-0.374235\pi$
$431$	15.9815			0.769803			0.384902	+	0.922958i	$0.374235\pi$
$432$		0			0
$433$	−16.4282			−0.789487			−0.394743	−	0.918791i	$-0.629166\pi$
$433$	−16.4282			−0.789487			−0.394743	+	0.918791i	$0.629166\pi$
$434$	−0.429261	+	0.696700i	−0.0206052	+	0.0334427i
$435$		0			0
$436$	−31.6595	−	10.4565i	−1.51622	−	0.500776i
$437$	−18.5568	−	18.5568i	−0.887694	−	0.887694i
$438$		0			0
$439$		−	16.7064i		−	0.797355i	−0.917091	−	0.398678i	$-0.869469\pi$
$439$		−	16.7064i		−	0.797355i	0.917091	−	0.398678i	$-0.130531\pi$
$440$	5.90031	+	0.507497i	0.281286	+	0.0241940i
$441$		0			0
$442$	−1.23528	+	0.293405i	−0.0587564	+	0.0139558i
$443$	14.0270	+	14.0270i	0.666443	+	0.666443i	0.956891	−	0.290448i	$-0.0938042\pi$
$443$	14.0270	+	14.0270i	0.666443	+	0.666443i	−0.290448	+	0.956891i	$0.593804\pi$
$444$		0			0
$445$	6.11290	−	6.11290i	0.289779	−	0.289779i
$446$	24.8473	+	15.3093i	1.17656	+	0.724917i
$447$		0			0
$448$	−0.198170	+	1.14347i	−0.00936263	+	0.0540238i
$449$	−36.1984			−1.70831			−0.854153	−	0.520022i	$-0.825924\pi$
$449$	−36.1984			−1.70831			−0.854153	+	0.520022i	$0.825924\pi$
$450$		0			0
$451$	4.29236	−	4.29236i	0.202119	−	0.202119i
$452$	10.8567	+	21.5648i	0.510654	+	1.01432i
$453$		0			0
$454$	−29.6435	+	7.04093i	−1.39124	+	0.330447i
$455$			0.0252020i			0.00118149i
$456$		0			0
$457$		−	26.1008i		−	1.22094i	−0.792037	−	0.610472i	$-0.790980\pi$
$457$		−	26.1008i		−	1.22094i	0.792037	−	0.610472i	$-0.209020\pi$
$458$	2.90389	+	12.2259i	0.135690	+	0.571277i
$459$		0			0
$460$	−6.94879	−	2.29504i	−0.323989	−	0.107007i
$461$	21.9138	−	21.9138i	1.02063	−	1.02063i	0.0208460	−	0.999783i	$-0.493364\pi$
$461$	21.9138	−	21.9138i	1.02063	−	1.02063i	0.999783	−	0.0208460i	$-0.00663598\pi$
$462$		0			0
$463$	−12.2790			−0.570654			−0.285327	−	0.958430i	$-0.592102\pi$
$463$	−12.2790			−0.570654			−0.285327	+	0.958430i	$0.592102\pi$
$464$	−0.328278	−	2.21099i	−0.0152399	−	0.102643i
$465$		0			0
$466$	−12.4672	+	20.2345i	−0.577531	+	0.937345i
$467$	2.75939	−	2.75939i	0.127690	−	0.127690i	−0.640374	−	0.768063i	$-0.721221\pi$
$467$	2.75939	−	2.75939i	0.127690	−	0.127690i	0.768063	+	0.640374i	$0.221221\pi$
$468$		0			0
$469$	−0.920956	−	0.920956i	−0.0425258	−	0.0425258i
$470$	−1.17880	−	4.96292i	−0.0543738	−	0.228923i
$471$		0			0
$472$	−18.9200	+	15.9231i	−0.870863	+	0.732919i
$473$			39.2067i			1.80273i
$474$		0			0
$475$	−14.3216	−	14.3216i	−0.657122	−	0.657122i
$476$	0.817186	−	0.411407i	0.0374557	−	0.0188568i
$477$		0			0
$478$	−16.4527	−	10.1371i	−0.752528	−	0.463659i
$479$	−9.23611			−0.422008			−0.211004	−	0.977485i	$-0.567673\pi$
$479$	−9.23611			−0.422008			−0.211004	+	0.977485i	$0.567673\pi$
$480$		0			0
$481$	−2.13082			−0.0971572
$482$	−32.5504	−	20.0555i	−1.48263	−	0.913501i
$483$		0			0
$484$	−1.38033	+	0.694917i	−0.0627422	+	0.0315871i
$485$	−7.43892	−	7.43892i	−0.337784	−	0.337784i
$486$		0			0
$487$		−	31.5777i		−	1.43092i	−0.698652	−	0.715461i	$-0.746217\pi$
$487$		−	31.5777i		−	1.43092i	0.698652	−	0.715461i	$-0.253783\pi$
$488$	2.03301	+	2.41564i	0.0920299	+	0.109351i
$489$		0			0
$490$	1.39182	+	5.85977i	0.0628758	+	0.264717i
$491$	9.58359	+	9.58359i	0.432501	+	0.432501i	0.889478	−	0.456977i	$-0.151068\pi$
$491$	9.58359	+	9.58359i	0.432501	+	0.432501i	−0.456977	+	0.889478i	$0.651068\pi$
$492$		0			0
$493$	−1.24604	+	1.24604i	−0.0561189	+	0.0561189i
$494$	−0.924365	+	1.50026i	−0.0415892	+	0.0675001i
$495$		0			0
$496$	−9.50294	+	12.8169i	−0.426695	+	0.575495i
$497$	0.491912			0.0220653
$498$		0			0
$499$	8.34782	−	8.34782i	0.373700	−	0.373700i	−0.495123	−	0.868823i	$-0.664877\pi$
$499$	8.34782	−	8.34782i	0.373700	−	0.373700i	0.868823	+	0.495123i	$0.164877\pi$
$500$	−11.1573	−	3.68503i	−0.498970	−	0.164800i
$501$		0			0
$502$	−1.93415	−	8.14311i	−0.0863256	−	0.363445i
$503$		−	18.7022i		−	0.833888i	−0.908932	−	0.416944i	$-0.863101\pi$
$503$		−	18.7022i		−	0.833888i	0.908932	−	0.416944i	$-0.136899\pi$
$504$		0			0
$505$		−	9.40710i		−	0.418610i
$506$	28.3077	−	6.72365i	1.25843	−	0.298903i
$507$		0			0
$508$	11.9261	+	23.6890i	0.529134	+	1.05103i
$509$	−18.0996	+	18.0996i	−0.802251	+	0.802251i	−0.983447	−	0.181196i	$-0.942003\pi$
$509$	−18.0996	+	18.0996i	−0.802251	+	0.802251i	0.181196	+	0.983447i	$0.442003\pi$
$510$		0			0
$511$	−0.324602			−0.0143595
$512$	−5.76024	+	21.8819i	−0.254569	+	0.967055i
$513$		0			0
$514$	2.56371	+	1.57959i	0.113080	+	0.0696728i
$515$	6.91514	−	6.91514i	0.304717	−	0.304717i
$516$		0			0
$517$	14.3407	+	14.3407i	0.630703	+	0.630703i
$518$	1.49390	−	0.354832i	0.0656383	−	0.0155904i
$519$		0			0
$520$	−0.0421093	+	0.489576i	−0.00184661	+	0.0214693i
$521$		−	36.0316i		−	1.57857i	−0.614024	−	0.789287i	$-0.710450\pi$
$521$		−	36.0316i		−	1.57857i	0.614024	−	0.789287i	$-0.289550\pi$
$522$		0			0
$523$	7.68786	+	7.68786i	0.336167	+	0.336167i	0.854922	−	0.518756i	$-0.173605\pi$
$523$	7.68786	+	7.68786i	0.336167	+	0.336167i	−0.518756	+	0.854922i	$0.673605\pi$
$524$	−20.5071	−	6.77309i	−0.895858	−	0.295884i
$525$		0			0
$526$	16.5840	−	26.9161i	0.723096	−	1.17360i
$527$	12.5787			0.547938
$528$		0			0
$529$	−12.9532			−0.563182
$530$	−5.06878	+	8.22674i	−0.220174	+	0.357347i
$531$		0			0
$532$	0.398235	−	1.20575i	0.0172657	−	0.0522759i
$533$	0.356157	+	0.356157i	0.0154269	+	0.0154269i
$534$		0			0
$535$		−	1.77772i		−	0.0768577i
$536$	−16.3517	−	19.4293i	−0.706288	−	0.839219i
$537$		0			0
$538$	−13.7183	+	3.25837i	−0.591437	+	0.140478i
$539$	−16.9322	−	16.9322i	−0.729321	−	0.729321i
$540$		0			0
$541$	10.6750	−	10.6750i	0.458953	−	0.458953i	−0.439358	−	0.898312i	$-0.644794\pi$
$541$	10.6750	−	10.6750i	0.458953	−	0.458953i	0.898312	+	0.439358i	$0.144794\pi$
$542$	−18.2222	−	11.2273i	−0.782711	−	0.482255i
$543$		0			0
$544$	16.5621	−	6.62660i	0.710095	−	0.284113i
$545$	10.1730			0.435764
$546$		0			0
$547$	−22.5460	+	22.5460i	−0.963997	+	0.963997i	−0.999374	−	0.0353769i	$-0.988737\pi$
$547$	−22.5460	+	22.5460i	−0.963997	+	0.963997i	0.0353769	+	0.999374i	$0.488737\pi$
$548$	3.75500	−	1.89043i	0.160405	−	0.0807550i
$549$		0			0
$550$	21.8471	−	5.18913i	0.931562	−	0.221265i
$551$			2.44575i			0.104192i
$552$		0			0
$553$			1.01713i			0.0432529i
$554$	−6.59644	−	27.7721i	−0.280256	−	1.17992i
$555$		0			0
$556$	4.82657	−	14.6136i	0.204692	−	0.619754i
$557$	−5.21780	+	5.21780i	−0.221085	+	0.221085i	−0.808955	−	0.587870i	$-0.799967\pi$
$557$	−5.21780	+	5.21780i	−0.221085	+	0.221085i	0.587870	+	0.808955i	$0.299967\pi$
$558$		0			0
$559$	−3.25316			−0.137594
$560$	−0.0520034	−	0.350249i	−0.00219754	−	0.0148007i
$561$		0			0
$562$	−15.0668	+	24.4538i	−0.635557	+	1.03152i
$563$	−2.18674	+	2.18674i	−0.0921602	+	0.0921602i	−0.751684	−	0.659524i	$-0.770758\pi$
$563$	−2.18674	+	2.18674i	−0.0921602	+	0.0921602i	0.659524	+	0.751684i	$0.270758\pi$
$564$		0			0
$565$	−5.20892	−	5.20892i	−0.219141	−	0.219141i
$566$	2.27134	+	9.56272i	0.0954716	+	0.401951i
$567$		0			0
$568$	9.55590	+	0.821921i	0.400957	+	0.0344870i
$569$			9.40319i			0.394202i	0.980383	+	0.197101i	$0.0631527\pi$
$569$			9.40319i			0.394202i	−0.980383	+	0.197101i	$0.936847\pi$
$570$		0			0
$571$	28.5674	+	28.5674i	1.19551	+	1.19551i	0.975497	+	0.220014i	$0.0706102\pi$
$571$	28.5674	+	28.5674i	1.19551	+	1.19551i	0.220014	+	0.975497i	$0.429390\pi$
$572$	−0.878510	−	1.74500i	−0.0367323	−	0.0729623i
$573$		0			0
$574$	−0.309007	−	0.190390i	−0.0128977	−	0.00794672i
$575$	−27.7477			−1.15716
$576$		0			0
$577$	−8.70475			−0.362384			−0.181192	−	0.983448i	$-0.557995\pi$
$577$	−8.70475			−0.362384			−0.181192	+	0.983448i	$0.557995\pi$
$578$	8.49531	+	5.23425i	0.353358	+	0.217716i
$579$		0			0
$580$	0.306677	+	0.609158i	0.0127341	+	0.0252939i
$581$	−0.593141	−	0.593141i	−0.0246077	−	0.0246077i
$582$		0			0
$583$		−	38.4183i		−	1.59112i
$584$	−6.30573	−	0.542367i	−0.260933	−	0.0224433i
$585$		0			0
$586$	5.36869	+	22.6031i	0.221779	+	0.933724i
$587$	2.03359	+	2.03359i	0.0839353	+	0.0839353i	0.747828	−	0.663893i	$-0.231097\pi$
$587$	2.03359	+	2.03359i	0.0839353	+	0.0839353i	−0.663893	+	0.747828i	$0.731097\pi$
$588$		0			0
$589$	12.3449	−	12.3449i	0.508661	−	0.508661i
$590$	3.95786	−	6.42369i	0.162942	−	0.264459i
$591$		0			0
$592$	29.6135	−	4.39688i	1.21711	−	0.180710i
$593$	18.8849			0.775508			0.387754	−	0.921763i	$-0.373251\pi$
$593$	18.8849			0.775508			0.387754	+	0.921763i	$0.373251\pi$
$594$		0			0
$595$	−0.197389	+	0.197389i	−0.00809216	+	0.00809216i
$596$	13.3865	−	40.5309i	0.548334	−	1.66021i
$597$		0			0
$598$	0.557892	+	2.34882i	0.0228139	+	0.0960502i
$599$		−	6.48419i		−	0.264937i	−0.991187	−	0.132468i	$-0.957710\pi$
$599$		−	6.48419i		−	0.264937i	0.991187	−	0.132468i	$-0.0422903\pi$
$600$		0			0
$601$			11.1376i			0.454313i	0.973858	+	0.227156i	$0.0729429\pi$
$601$			11.1376i			0.454313i	−0.973858	+	0.227156i	$0.927057\pi$
$602$	2.28076	−	0.541728i	0.0929570	−	0.0220792i
$603$		0			0
$604$	−27.0921	+	13.6393i	−1.10236	+	0.554977i
$605$	0.333414	−	0.333414i	0.0135552	−	0.0135552i
$606$		0			0
$607$	22.1363			0.898486			0.449243	−	0.893410i	$-0.351694\pi$
$607$	22.1363			0.898486			0.449243	+	0.893410i	$0.351694\pi$
$608$	9.75079	−	22.7576i	0.395447	−	0.922942i
$609$		0			0
$610$	−0.820156	−	0.505327i	−0.0332071	−	0.0204601i
$611$	−1.18991	+	1.18991i	−0.0481387	+	0.0481387i
$612$		0			0
$613$	−2.82549	−	2.82549i	−0.114121	−	0.114121i	0.647740	−	0.761861i	$-0.275714\pi$
$613$	−2.82549	−	2.82549i	−0.114121	−	0.114121i	−0.761861	+	0.647740i	$0.775714\pi$
$614$	−14.0192	+	3.32984i	−0.565767	+	0.134381i
$615$		0			0
$616$	0.906500	+	1.07711i	0.0365239	+	0.0433982i
$617$		−	7.27869i		−	0.293029i	−0.989209	−	0.146514i	$-0.953194\pi$
$617$		−	7.27869i		−	0.293029i	0.989209	−	0.146514i	$-0.0468055\pi$
$618$		0			0
$619$	24.7397	+	24.7397i	0.994371	+	0.994371i	0.999984	−	0.00561374i	$-0.00178692\pi$
$619$	24.7397	+	24.7397i	0.994371	+	0.994371i	−0.00561374	+	0.999984i	$0.501787\pi$
$620$	1.52677	−	4.62265i	0.0613165	−	0.185650i
$621$		0			0
$622$	2.05434	−	3.33424i	0.0823715	−	0.133691i
$623$	2.05508			0.0823352
$624$		0			0
$625$	−19.5530			−0.782119
$626$	0.172790	−	0.280442i	0.00690608	−	0.0112087i
$627$		0			0
$628$	−31.1722	−	10.2955i	−1.24390	−	0.410836i
$629$	−16.6892	−	16.6892i	−0.665442	−	0.665442i
$630$		0			0
$631$			16.3145i			0.649471i	0.945805	+	0.324736i	$0.105275\pi$
$631$			16.3145i			0.649471i	−0.945805	+	0.324736i	$0.894725\pi$
$632$	−1.69950	+	19.7589i	−0.0676023	+	0.785965i
$633$		0			0
$634$	32.1136	−	7.62765i	1.27540	−	0.302933i
$635$	−5.72201	−	5.72201i	−0.227071	−	0.227071i
$636$		0			0
$637$	1.40494	−	1.40494i	0.0556658	−	0.0556658i
$638$	−2.30853	−	1.42236i	−0.0913955	−	0.0563119i
$639$		0			0
$640$	−0.424999	−	6.89085i	−0.0167996	−	0.272385i
$641$	−14.6358			−0.578080			−0.289040	−	0.957317i	$-0.593336\pi$
$641$	−14.6358			−0.578080			−0.289040	+	0.957317i	$0.593336\pi$
$642$		0			0
$643$	−11.9564	+	11.9564i	−0.471515	+	0.471515i	−0.902405	−	0.430890i	$-0.858200\pi$
$643$	−11.9564	+	11.9564i	−0.471515	+	0.471515i	0.430890	+	0.902405i	$0.358200\pi$
$644$	−0.782266	−	1.55383i	−0.0308256	−	0.0612296i
$645$		0			0
$646$	−18.9904	+	4.51060i	−0.747166	+	0.177467i
$647$		−	16.0163i		−	0.629667i	−0.949147	−	0.314834i	$-0.898051\pi$
$647$		−	16.0163i		−	0.629667i	0.949147	−	0.314834i	$-0.101949\pi$
$648$		0			0
$649$			29.9982i			1.17753i
$650$	0.430565	+	1.81275i	0.0168882	+	0.0711019i
$651$		0			0
$652$	13.6034	+	4.49292i	0.532750	+	0.175957i
$653$	14.1903	−	14.1903i	0.555310	−	0.555310i	−0.372658	−	0.927969i	$-0.621554\pi$
$653$	14.1903	−	14.1903i	0.555310	−	0.555310i	0.927969	+	0.372658i	$0.121554\pi$
$654$		0			0
$655$	6.58946			0.257471
$656$	−5.68466	−	4.21483i	−0.221949	−	0.164562i
$657$		0			0
$658$	0.636089	−	1.03239i	0.0247973	−	0.0402466i
$659$	27.2275	−	27.2275i	1.06063	−	1.06063i	0.0625942	−	0.998039i	$-0.480063\pi$
$659$	27.2275	−	27.2275i	1.06063	−	1.06063i	0.998039	−	0.0625942i	$-0.0199374\pi$
$660$		0			0
$661$	32.4007	+	32.4007i	1.26024	+	1.26024i	0.950975	+	0.309267i	$0.100084\pi$
$661$	32.4007	+	32.4007i	1.26024	+	1.26024i	0.309267	+	0.950975i	$0.399916\pi$
$662$	−0.804027	−	3.38508i	−0.0312494	−	0.131565i
$663$		0			0
$664$	−10.5313	−	12.5135i	−0.408695	−	0.485617i
$665$			0.387438i			0.0150242i
$666$		0			0
$667$	2.36928	+	2.36928i	0.0917388	+	0.0917388i
$668$	40.4912	−	20.3850i	1.56665	−	0.788720i
$669$		0			0
$670$	6.59662	+	4.06441i	0.254850	+	0.157022i
$671$	3.83007			0.147858
$672$		0			0
$673$	−39.0948			−1.50700			−0.753498	−	0.657451i	$-0.771635\pi$
$673$	−39.0948			−1.50700			−0.753498	+	0.657451i	$0.771635\pi$
$674$	−4.08161	−	2.51482i	−0.157218	−	0.0968674i
$675$		0			0
$676$	−23.0782	+	11.6186i	−0.887625	+	0.446869i
$677$	31.1264	+	31.1264i	1.19628	+	1.19628i	0.975271	+	0.221014i	$0.0709366\pi$
$677$	31.1264	+	31.1264i	1.19628	+	1.19628i	0.221014	+	0.975271i	$0.429063\pi$
$678$		0			0
$679$		−	2.50088i		−	0.0959749i
$680$	−4.16430	+	3.50468i	−0.159694	+	0.134398i
$681$		0			0
$682$	4.47288	+	18.8316i	0.171275	+	0.721098i
$683$	−12.1168	−	12.1168i	−0.463637	−	0.463637i	0.436208	−	0.899846i	$-0.356321\pi$
$683$	−12.1168	−	12.1168i	−0.463637	−	0.463637i	−0.899846	+	0.436208i	$0.856321\pi$
$684$		0			0
$685$	−0.907009	+	0.907009i	−0.0346550	+	0.0346550i
$686$	−1.50434	+	2.44157i	−0.0574359	+	0.0932196i
$687$		0			0
$688$	45.2114	−	6.71278i	1.72367	−	0.255922i
$689$	3.18774			0.121443
$690$		0			0
$691$	10.5013	−	10.5013i	0.399488	−	0.399488i	−0.478565	−	0.878052i	$-0.658843\pi$
$691$	10.5013	−	10.5013i	0.399488	−	0.399488i	0.878052	+	0.478565i	$0.158843\pi$
$692$	20.6204	+	6.81051i	0.783871	+	0.258897i
$693$		0			0
$694$	−9.25306	−	38.9569i	−0.351241	−	1.47878i
$695$			4.69571i			0.178119i
$696$		0			0
$697$			5.57903i			0.211321i
$698$	−23.2148	+	5.51399i	−0.878693	+	0.208707i
$699$		0			0
$700$	−0.603731	−	1.19920i	−0.0228189	−	0.0453257i
$701$	19.5107	−	19.5107i	0.736908	−	0.736908i	−0.235071	−	0.971978i	$-0.575532\pi$
$701$	19.5107	−	19.5107i	0.736908	−	0.736908i	0.971978	+	0.235071i	$0.0755322\pi$
$702$		0			0
$703$	−32.7578			−1.23548
$704$	15.8100	+	22.4387i	0.595862	+	0.845691i
$705$		0			0
$706$	31.3910	+	19.3411i	1.18142	+	0.727912i
$707$	1.58128	−	1.58128i	0.0594701	−	0.0594701i
$708$		0			0
$709$	1.35461	+	1.35461i	0.0508736	+	0.0508736i	0.732086	−	0.681212i	$-0.238547\pi$
$709$	1.35461	+	1.35461i	0.0508736	+	0.0508736i	−0.681212	+	0.732086i	$0.738547\pi$
$710$	−2.84720	+	0.676267i	−0.106853	+	0.0253799i
$711$		0			0
$712$	39.9222	+	3.43378i	1.49615	+	0.128686i
$713$		−	23.9177i		−	0.895725i
$714$		0			0
$715$	0.421501	+	0.421501i	0.0157632	+	0.0157632i
$716$	−5.53247	−	1.82726i	−0.206758	−	0.0682880i
$717$		0			0
$718$	8.45251	−	13.7186i	0.315445	−	0.511974i
$719$	−47.1881			−1.75982			−0.879910	−	0.475140i	$-0.842397\pi$
$719$	−47.1881			−1.75982			−0.879910	+	0.475140i	$0.842397\pi$
$720$		0			0
$721$	2.32479			0.0865796
$722$	−0.115572	+	0.187575i	−0.00430113	+	0.00698083i
$723$		0			0
$724$	6.94127	−	21.0163i	0.257970	−	0.781066i
$725$	1.82854	+	1.82854i	0.0679103	+	0.0679103i
$726$		0			0
$727$			13.6590i			0.506585i	0.967390	+	0.253292i	$0.0815134\pi$
$727$			13.6590i			0.506585i	−0.967390	+	0.253292i	$0.918487\pi$
$728$	−0.0893731	+	0.0752164i	−0.00331239	+	0.00278771i
$729$		0			0
$730$	1.87880	−	0.446254i	0.0695376	−	0.0165166i
$731$	−25.4797	−	25.4797i	−0.942399	−	0.942399i
$732$		0			0
$733$	14.9287	−	14.9287i	0.551404	−	0.551404i	−0.375442	−	0.926846i	$-0.622509\pi$
$733$	14.9287	−	14.9287i	0.551404	−	0.551404i	0.926846	+	0.375442i	$0.122509\pi$
$734$	−11.8364	−	7.29280i	−0.436889	−	0.269182i
$735$		0			0
$736$	−12.6001	−	31.4919i	−0.464446	−	1.16081i
$737$	−30.8058			−1.13474
$738$		0			0
$739$	−28.4837	+	28.4837i	−1.04779	+	1.04779i	−0.0489898	+	0.998799i	$0.515600\pi$
$739$	−28.4837	+	28.4837i	−1.04779	+	1.04779i	−0.998799	+	0.0489898i	$0.984400\pi$
$740$	−8.15893	+	4.10756i	−0.299928	+	0.150997i
$741$		0			0
$742$	−2.23490	+	0.530834i	−0.0820457	+	0.0194875i
$743$		−	19.7331i		−	0.723937i	−0.932190	−	0.361968i	$-0.882105\pi$
$743$		−	19.7331i		−	0.723937i	0.932190	−	0.361968i	$-0.117895\pi$
$744$		0			0
$745$			13.0236i			0.477148i
$746$	6.90057	+	29.0525i	0.252648	+	1.06369i
$747$		0			0
$748$	6.78661	−	20.5481i	0.248143	−	0.751312i
$749$	0.298825	−	0.298825i	0.0109188	−	0.0109188i
$750$		0			0
$751$	−8.72525			−0.318389			−0.159194	−	0.987247i	$-0.550890\pi$
$751$	−8.72525			−0.318389			−0.159194	+	0.987247i	$0.550890\pi$
$752$	14.0817	−	18.9924i	0.513506	−	0.692580i
$753$		0			0
$754$	0.118020	−	0.191549i	0.00429803	−	0.00697580i
$755$	6.54402	−	6.54402i	0.238161	−	0.238161i
$756$		0			0
$757$	28.7284	+	28.7284i	1.04415	+	1.04415i	0.998979	+	0.0451715i	$0.0143834\pi$
$757$	28.7284	+	28.7284i	1.04415	+	1.04415i	0.0451715	+	0.998979i	$0.485617\pi$
$758$	−1.07554	−	4.52819i	−0.0390653	−	0.164471i
$759$		0			0
$760$	−0.647359	+	7.52640i	−0.0234822	+	0.273011i
$761$			41.3046i			1.49729i	0.662971	+	0.748645i	$0.269295\pi$
$761$			41.3046i			1.49729i	−0.662971	+	0.748645i	$0.730705\pi$
$762$		0			0
$763$	1.71002	+	1.71002i	0.0619070	+	0.0619070i
$764$	−3.40199	−	6.75744i	−0.123080	−	0.244476i
$765$		0			0
$766$	−34.6290	−	21.3361i	−1.25120	−	0.770906i
$767$	−2.48908			−0.0898756
$768$		0			0
$769$	7.72628			0.278617			0.139308	−	0.990249i	$-0.455512\pi$
$769$	7.72628			0.278617			0.139308	+	0.990249i	$0.455512\pi$
$770$	−0.365700	−	0.225321i	−0.0131789	−	0.00811999i
$771$		0			0
$772$	−3.98667	−	7.91881i	−0.143483	−	0.285004i
$773$	27.0058	+	27.0058i	0.971330	+	0.971330i	0.999600	−	0.0282699i	$-0.00899980\pi$
$773$	27.0058	+	27.0058i	0.971330	+	0.971330i	−0.0282699	+	0.999600i	$0.509000\pi$
$774$		0			0
$775$		−	18.4590i		−	0.663068i
$776$	4.17864	−	48.5822i	0.150005	−	1.74400i
$777$		0			0
$778$	−7.68564	−	32.3578i	−0.275544	−	1.16008i
$779$	5.47530	+	5.47530i	0.196173	+	0.196173i
$780$		0			0
$781$	8.22717	−	8.22717i	0.294391	−	0.294391i
$782$	−14.0270	+	22.7661i	−0.501605	+	0.814115i
$783$		0			0
$784$	−16.6264	+	22.4245i	−0.593799	+	0.800874i
$785$	10.0164			0.357501
$786$		0			0
$787$	−29.6837	+	29.6837i	−1.05811	+	1.05811i	−0.0599063	+	0.998204i	$0.519080\pi$
$787$	−29.6837	+	29.6837i	−1.05811	+	1.05811i	−0.998204	+	0.0599063i	$0.980920\pi$
$788$	−2.63915	+	7.99066i	−0.0940160	+	0.284656i
$789$		0			0
$790$	−1.39833	−	5.88718i	−0.0497502	−	0.209457i
$791$		−	1.75118i		−	0.0622646i
$792$		0			0
$793$			0.317798i			0.0112854i
$794$	−37.9286	+	9.00882i	−1.34604	+	0.319711i
$795$		0			0
$796$	−34.0466	+	17.1405i	−1.20675	+	0.607529i
$797$	−22.5646	+	22.5646i	−0.799279	+	0.799279i	−0.982982	−	0.183703i	$-0.941192\pi$
$797$	−22.5646	+	22.5646i	−0.799279	+	0.799279i	0.183703	+	0.982982i	$0.441192\pi$
$798$		0			0
$799$	−18.6395			−0.659416
$800$	−9.72440	−	24.3046i	−0.343810	−	0.859296i
$801$		0			0
$802$	−41.8662	−	25.7952i	−1.47835	−	0.910861i
$803$	−5.42892	+	5.42892i	−0.191583	+	0.191583i
$804$		0			0
$805$	0.375324	+	0.375324i	0.0132284	+	0.0132284i
$806$	−1.56254	+	0.371135i	−0.0550381	+	0.0130727i
$807$		0			0
$808$	33.3601	−	28.0759i	1.17360	−	0.987706i
$809$			12.6040i			0.443133i	0.975145	+	0.221566i	$0.0711169\pi$
$809$			12.6040i			0.443133i	−0.975145	+	0.221566i	$0.928883\pi$
$810$		0			0
$811$	−4.45783	−	4.45783i	−0.156536	−	0.156536i	0.624494	−	0.781030i	$-0.285305\pi$
$811$	−4.45783	−	4.45783i	−0.156536	−	0.156536i	−0.781030	+	0.624494i	$0.785305\pi$
$812$	−0.0508454	+	0.153946i	−0.00178432	+	0.00540246i
$813$		0			0
$814$	19.0508	−	30.9199i	0.667731	−	1.08374i
$815$	−4.37111			−0.153113
$816$		0			0
$817$	−50.0118			−1.74969
$818$	0.144478	−	0.234490i	0.00505154	−	0.00819876i
$819$		0			0
$820$	2.05028	+	0.677166i	0.0715989	+	0.0236477i
$821$	−0.309854	−	0.309854i	−0.0108140	−	0.0108140i	0.701679	−	0.712493i	$-0.252434\pi$
$821$	−0.309854	−	0.309854i	−0.0108140	−	0.0108140i	−0.712493	+	0.701679i	$0.752434\pi$
$822$		0			0
$823$		−	32.5835i		−	1.13579i	−0.823101	−	0.567895i	$-0.807758\pi$
$823$		−	32.5835i		−	1.13579i	0.823101	−	0.567895i	$-0.192242\pi$
$824$	45.1614	+	3.88442i	1.57327	+	0.135320i
$825$		0			0
$826$	1.74508	−	0.414491i	0.0607189	−	0.0144220i
$827$	−6.09935	−	6.09935i	−0.212095	−	0.212095i	0.593062	−	0.805157i	$-0.297919\pi$
$827$	−6.09935	−	6.09935i	−0.212095	−	0.212095i	−0.805157	+	0.593062i	$0.797919\pi$
$828$		0			0
$829$	12.6929	−	12.6929i	0.440843	−	0.440843i	−0.451452	−	0.892295i	$-0.649094\pi$
$829$	12.6929	−	12.6929i	0.440843	−	0.440843i	0.892295	+	0.451452i	$0.149094\pi$
$830$	4.24855	+	2.61768i	0.147469	+	0.0908610i
$831$		0			0
$832$	−1.86184	+	1.31183i	−0.0645478	+	0.0454794i
$833$	22.0078			0.762524
$834$		0			0
$835$	−9.78053	+	9.78053i	−0.338469	+	0.338469i
$836$	−13.5056	−	26.8265i	−0.467101	−	0.927813i
$837$		0			0
$838$	50.9852	−	12.1100i	1.76125	−	0.418334i
$839$			5.30930i			0.183297i	0.995791	+	0.0916487i	$0.0292137\pi$
$839$			5.30930i			0.183297i	−0.995791	+	0.0916487i	$0.970786\pi$
$840$		0			0
$841$			28.6877i			0.989232i
$842$	−1.72840	−	7.27685i	−0.0595646	−	0.250777i
$843$		0			0
$844$	−9.24361	−	3.05298i	−0.318178	−	0.105088i
$845$	5.57448	−	5.57448i	0.191768	−	0.191768i
$846$		0			0
$847$	0.112090			0.00385145
$848$	−44.3022	+	6.57779i	−1.52134	+	0.225882i
$849$		0			0
$850$	−10.8257	+	17.5703i	−0.371317	+	0.602655i
$851$	−31.7336	+	31.7336i	−1.08781	+	1.08781i
$852$		0			0
$853$	−20.6932	−	20.6932i	−0.708520	−	0.708520i	0.257704	−	0.966224i	$-0.417034\pi$
$853$	−20.6932	−	20.6932i	−0.708520	−	0.708520i	−0.966224	+	0.257704i	$0.917034\pi$
$854$	−0.0529209	−	0.222806i	−0.00181092	−	0.00762425i
$855$		0			0
$856$	6.30428	−	5.30568i	0.215476	−	0.181345i
$857$			35.7478i			1.22112i	0.791970	+	0.610560i	$0.209056\pi$
$857$			35.7478i			1.22112i	−0.791970	+	0.610560i	$0.790944\pi$
$858$		0			0
$859$	21.4421	+	21.4421i	0.731595	+	0.731595i	0.970936	−	0.239341i	$-0.0769314\pi$
$859$	21.4421	+	21.4421i	0.731595	+	0.731595i	−0.239341	+	0.970936i	$0.576931\pi$
$860$	−12.4564	+	6.27107i	−0.424758	+	0.213842i
$861$		0			0
$862$	−19.2421	−	11.8558i	−0.655390	−	0.403809i
$863$	39.2457			1.33594			0.667970	−	0.744188i	$-0.267163\pi$
$863$	39.2457			1.33594			0.667970	+	0.744188i	$0.267163\pi$
$864$		0			0
$865$	−6.62586			−0.225286
$866$	19.7799	+	12.1871i	0.672148	+	0.414134i
$867$		0			0
$868$	1.03368	−	0.520399i	0.0350854	−	0.0176635i
$869$	17.0114	+	17.0114i	0.577073	+	0.577073i
$870$		0			0
$871$		−	2.55609i		−	0.0866099i
$872$	30.3618	+	36.0762i	1.02818	+	1.22170i
$873$		0			0
$874$	8.57664	+	36.1091i	0.290109	+	1.22141i
$875$	0.602638	+	0.602638i	0.0203729	+	0.0203729i
$876$		0			0
$877$	−17.6404	+	17.6404i	−0.595675	+	0.595675i	−0.939159	−	0.343484i	$-0.888393\pi$
$877$	−17.6404	+	17.6404i	−0.595675	+	0.595675i	0.343484	+	0.939159i	$0.388393\pi$
$878$	−12.3935	+	20.1150i	−0.418261	+	0.678847i
$879$		0			0
$880$	−6.72763	−	4.98813i	−0.226788	−	0.168150i
$881$	45.9065			1.54663			0.773314	−	0.634023i	$-0.218598\pi$
$881$	45.9065			1.54663			0.773314	+	0.634023i	$0.218598\pi$
$882$		0			0
$883$	−28.7147	+	28.7147i	−0.966326	+	0.966326i	−0.999451	−	0.0331251i	$-0.989454\pi$
$883$	−28.7147	+	28.7147i	−0.966326	+	0.966326i	0.0331251	+	0.999451i	$0.489454\pi$
$884$	1.70497	+	0.563116i	0.0573443	+	0.0189397i
$885$		0			0
$886$	−6.48304	−	27.2947i	−0.217802	−	0.916982i
$887$		−	46.2815i		−	1.55398i	−0.629513	−	0.776990i	$-0.716746\pi$
$887$		−	46.2815i		−	1.55398i	0.629513	−	0.776990i	$-0.283254\pi$
$888$		0			0
$889$		−	1.92367i		−	0.0645179i
$890$	−11.8949	+	2.82528i	−0.398717	+	0.0947034i
$891$		0			0
$892$	−18.5597	−	36.8655i	−0.621425	−	1.23435i
$893$	−18.2929	+	18.2929i	−0.612148	+	0.612148i
$894$		0			0
$895$	1.77772			0.0594227
$896$	1.08687	−	1.22975i	0.0363098	−	0.0410831i
$897$		0			0
$898$	43.5837	+	26.8534i	1.45441	+	0.896110i
$899$	−1.57615	+	1.57615i	−0.0525676	+	0.0525676i
$900$		0			0
$901$	24.9673	+	24.9673i	0.831781	+	0.831781i
$902$	−8.35235	+	1.98385i	−0.278103	+	0.0660551i
$903$		0			0
$904$	2.92599	−	34.0184i	0.0973169	−	1.13144i
$905$			6.75308i			0.224480i
$906$		0			0
$907$	35.0957	+	35.0957i	1.16533	+	1.16533i	0.983291	+	0.182043i	$0.0582710\pi$
$907$	35.0957	+	35.0957i	1.16533	+	1.16533i	0.182043	+	0.983291i	$0.441729\pi$
$908$	40.9147	+	13.5133i	1.35780	+	0.448454i
$909$		0			0
$910$	0.0186959	−	0.0303438i	0.000619762	−	0.00100589i
$911$	−50.7142			−1.68024			−0.840119	−	0.542403i	$-0.817515\pi$
$911$	−50.7142			−1.68024			−0.840119	+	0.542403i	$0.817515\pi$
$912$		0			0
$913$	−19.8404			−0.656623
$914$	−19.3627	+	31.4260i	−0.640460	+	1.03948i
$915$		0			0
$916$	5.57329	−	16.8745i	0.184147	−	0.557548i
$917$	1.10765	+	1.10765i	0.0365778	+	0.0365778i
$918$		0			0
$919$		−	28.7717i		−	0.949090i	−0.880231	−	0.474545i	$-0.842613\pi$
$919$		−	28.7717i		−	0.949090i	0.880231	−	0.474545i	$-0.157387\pi$
$920$	6.66394	+	7.91818i	0.219704	+	0.261055i
$921$		0			0
$922$	−42.6413	+	10.1282i	−1.40432	+	0.333554i
$923$	0.682645	+	0.682645i	0.0224695	+	0.0224695i
$924$		0			0
$925$	−24.4911	+	24.4911i	−0.805261	+	0.805261i
$926$	14.7842	+	9.10907i	0.485839	+	0.299343i
$927$		0			0
$928$	−1.24495	+	2.90562i	−0.0408675	+	0.0953815i
$929$	12.7259			0.417523			0.208761	−	0.977967i	$-0.433057\pi$
$929$	12.7259			0.417523			0.208761	+	0.977967i	$0.433057\pi$
$930$		0			0
$931$	21.5986	−	21.5986i	0.707865	−	0.707865i
$932$	30.0216	−	15.1141i	0.983389	−	0.495080i
$933$		0			0
$934$	−5.36941	+	1.27534i	−0.175692	+	0.0417305i
$935$			6.60262i			0.215929i
$936$		0			0
$937$		−	37.2582i		−	1.21717i	−0.793488	−	0.608586i	$-0.791737\pi$
$937$		−	37.2582i		−	1.21717i	0.793488	−	0.608586i	$-0.208263\pi$
$938$	0.425650	+	1.79205i	0.0138980	+	0.0585127i
$939$		0			0
$940$	−2.26240	+	6.84995i	−0.0737914	+	0.223421i
$941$	24.8783	−	24.8783i	0.811009	−	0.811009i	−0.173776	−	0.984785i	$-0.555597\pi$
$941$	24.8783	−	24.8783i	0.811009	−	0.811009i	0.984785	+	0.173776i	$0.0555969\pi$
$942$		0			0
$943$	10.6082			0.345451
$944$	34.5925	−	5.13613i	1.12589	−	0.167167i
$945$		0			0
$946$	29.0852	−	47.2058i	0.945640	−	1.53479i
$947$	−2.27042	+	2.27042i	−0.0737787	+	0.0737787i	−0.743033	−	0.669255i	$-0.766614\pi$
$947$	−2.27042	+	2.27042i	−0.0737787	+	0.0737787i	0.669255	+	0.743033i	$0.266614\pi$
$948$		0			0
$949$	−0.450462	−	0.450462i	−0.0146226	−	0.0146226i
$950$	6.61921	+	27.8680i	0.214756	+	0.904156i
$951$		0			0
$952$	−1.28911	−	0.110879i	−0.0417803	−	0.00359360i
$953$			25.8831i			0.838436i	0.907885	+	0.419218i	$0.137696\pi$
$953$			25.8831i			0.838436i	−0.907885	+	0.419218i	$0.862304\pi$
$954$		0			0
$955$	1.63224	+	1.63224i	0.0528181	+	0.0528181i
$956$	12.2893	+	24.4105i	0.397465	+	0.789493i
$957$		0			0
$958$	11.1205	+	6.85172i	0.359287	+	0.221369i
$959$	−0.304925			−0.00984656
$960$		0			0
$961$	−15.0888			−0.486737
$962$	2.56556	+	1.58073i	0.0827171	+	0.0509649i
$963$		0			0
$964$	24.3135	+	48.2945i	0.783086	+	1.55546i
$965$	1.91277	+	1.91277i	0.0615742	+	0.0615742i
$966$		0			0
$967$			50.4733i			1.62311i	0.584275	+	0.811555i	$0.301379\pi$
$967$			50.4733i			1.62311i	−0.584275	+	0.811555i	$0.698621\pi$
$968$	2.17746	+	0.187288i	0.0699864	+	0.00601966i
$969$		0			0
$970$	3.43814	+	14.4751i	0.110392	+	0.464769i
$971$	−0.328660	−	0.328660i	−0.0105472	−	0.0105472i	0.701814	−	0.712361i	$-0.252374\pi$
$971$	−0.328660	−	0.328660i	−0.0105472	−	0.0105472i	−0.712361	+	0.701814i	$0.752374\pi$
$972$		0			0
$973$	−0.789321	+	0.789321i	−0.0253045	+	0.0253045i
$974$	−23.4256	+	38.0203i	−0.750606	+	1.21825i
$975$		0			0
$976$	−0.655765	−	4.41666i	−0.0209905	−	0.141374i
$977$	26.5125			0.848210			0.424105	−	0.905613i	$-0.360589\pi$
$977$	26.5125			0.848210			0.424105	+	0.905613i	$0.360589\pi$
$978$		0			0
$979$	34.3710	−	34.3710i	1.09850	−	1.09850i
$980$	2.67124	−	8.08781i	0.0853296	−	0.258355i
$981$		0			0
$982$	−4.42937	−	18.6484i	−0.141347	−	0.595093i
$983$		−	4.92322i		−	0.157026i	−0.996913	−	0.0785131i	$-0.974983\pi$
$983$		−	4.92322i		−	0.157026i	0.996913	−	0.0785131i	$-0.0250172\pi$
$984$		0			0
$985$		−	2.56760i		−	0.0818106i
$986$	2.42463	−	0.575899i	0.0772159	−	0.0183404i
$987$		0			0
$988$	2.22591	−	1.12062i	0.0708158	−	0.0356517i
$989$	−48.4481	+	48.4481i	−1.54056	+	1.54056i
$990$		0			0
$991$	1.57207			0.0499385			0.0249693	−	0.999688i	$-0.492051\pi$
$991$	1.57207			0.0499385			0.0249693	+	0.999688i	$0.492051\pi$
$992$	20.9499	−	8.38216i	0.665159	−	0.266134i
$993$		0			0
$994$	−0.592273	−	0.364920i	−0.0187858	−	0.0115746i
$995$	8.22385	−	8.22385i	0.260714	−	0.260714i
$996$		0			0
$997$	2.35740	+	2.35740i	0.0746596	+	0.0746596i	0.743451	−	0.668791i	$-0.233188\pi$
$997$	2.35740	+	2.35740i	0.0746596	+	0.0746596i	−0.668791	+	0.743451i	$0.733188\pi$
$998$	−16.2437	+	3.85822i	−0.514186	+	0.122130i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.325.3	yes	24
3.2	odd	2	inner	432.2.k.c.325.10	yes	24
4.3	odd	2		1728.2.k.c.433.6		24
12.11	even	2		1728.2.k.c.433.7		24
16.3	odd	4		1728.2.k.c.1297.6		24
16.13	even	4	inner	432.2.k.c.109.3	✓	24
48.29	odd	4	inner	432.2.k.c.109.10	yes	24
48.35	even	4		1728.2.k.c.1297.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.3	✓	24	16.13	even	4	inner
432.2.k.c.109.10	yes	24	48.29	odd	4	inner
432.2.k.c.325.3	yes	24	1.1	even	1	trivial
432.2.k.c.325.10	yes	24	3.2	odd	2	inner
1728.2.k.c.433.6		24	4.3	odd	2
1728.2.k.c.433.7		24	12.11	even	2
1728.2.k.c.1297.6		24	16.3	odd	4
1728.2.k.c.1297.7		24	48.35	even	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20402 - 0.741841i) q^{2} +(0.899344 + 1.78639i) q^{4} +(-0.431497 - 0.431497i) q^{5} -0.145064i q^{7} +(0.242383 - 2.81802i) q^{8} +O(q^{10})\)	\(q+(-1.20402 - 0.741841i) q^{2} +(0.899344 + 1.78639i) q^{4} +(-0.431497 - 0.431497i) q^{5} -0.145064i q^{7} +(0.242383 - 2.81802i) q^{8} +(0.199430 + 0.839634i) q^{10} +(-2.42618 - 2.42618i) q^{11} +(0.201311 - 0.201311i) q^{13} +(-0.107614 + 0.174661i) q^{14} +(-2.38236 + 3.21315i) q^{16} +3.15345 q^{17} +(3.09482 - 3.09482i) q^{19} +(0.382756 - 1.15888i) q^{20} +(1.12134 + 4.72102i) q^{22} -5.99610i q^{23} -4.62762i q^{25} +(-0.391724 + 0.0930425i) q^{26} +(0.259141 - 0.130463i) q^{28} +(-0.395136 + 0.395136i) q^{29} +3.98888 q^{31} +(5.25207 - 2.10138i) q^{32} +(-3.79683 - 2.33936i) q^{34} +(-0.0625947 + 0.0625947i) q^{35} +(-5.29237 - 5.29237i) q^{37} +(-6.02209 + 1.43037i) q^{38} +(-1.32056 + 1.11138i) q^{40} +1.76918i q^{41} +(-8.07993 - 8.07993i) q^{43} +(2.15213 - 6.51607i) q^{44} +(-4.44815 + 7.21944i) q^{46} -5.91082 q^{47} +6.97896 q^{49} +(-3.43296 + 5.57176i) q^{50} +(0.540668 + 0.178572i) q^{52} +(7.91745 + 7.91745i) q^{53} +2.09378i q^{55} +(-0.408794 - 0.0351611i) q^{56} +(0.768882 - 0.182625i) q^{58} +(-6.18218 - 6.18218i) q^{59} +(-0.789321 + 0.789321i) q^{61} +(-4.80270 - 2.95911i) q^{62} +(-7.88250 - 1.36608i) q^{64} -0.173730 q^{65} +(6.34861 - 6.34861i) q^{67} +(2.83604 + 5.63328i) q^{68} +(0.121801 - 0.0289302i) q^{70} +3.39100i q^{71} -2.23764i q^{73} +(2.44604 + 10.2982i) q^{74} +(8.31185 + 2.74524i) q^{76} +(-0.351951 + 0.351951i) q^{77} -7.01161 q^{79} +(2.41445 - 0.358486i) q^{80} +(1.31245 - 2.13014i) q^{82} +(4.08882 - 4.08882i) q^{83} +(-1.36070 - 1.36070i) q^{85} +(3.73440 + 15.7225i) q^{86} +(-7.42509 + 6.24896i) q^{88} +14.1667i q^{89} +(-0.0292030 - 0.0292030i) q^{91} +(10.7114 - 5.39256i) q^{92} +(7.11676 + 4.38488i) q^{94} -2.67081 q^{95} +17.2398 q^{97} +(-8.40283 - 5.17727i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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