LMFDB - Embedded newform 1472.2.j.c.369.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1472,2,Mod(369,1472)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1472, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("1472.369");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1472 = 2^{6} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1472.j (of order $4$, degree $2$, 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:	$11.7539791775$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	12.0.221124989353984.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 2 x^{10} + 2 x^{9} + 12 x^{8} - 8 x^{7} - 14 x^{6} - 16 x^{5} + 48 x^{4} + 16 x^{3} + \cdots + 64 $ x^12 - 2x^11 - 2x^10 + 2x^9 + 12x^8 - 8x^7 - 14x^6 - 16x^5 + 48x^4 + 16x^3 - 32x^2 - 64*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 368)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			369.6
Root			$-1.14441 - 0.830857i$ of defining polynomial
Character	$\chi$	$=$	1472.369
Dual form			1472.2.j.c.1105.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.70582 - 1.70582i) q^{3} +(-2.61219 - 2.61219i) q^{5} +1.66171i q^{7} -2.81967i q^{9} +(-3.35563 - 3.35563i) q^{11} +(1.50815 - 1.50815i) q^{13} -8.91186 q^{15} -0.812201 q^{17} +(3.81967 - 3.81967i) q^{19} +(2.83459 + 2.83459i) q^{21} -1.00000i q^{23} +8.64704i q^{25} +(0.307612 + 0.307612i) q^{27} +(-7.12138 + 7.12138i) q^{29} -10.7058 q^{31} -11.4482 q^{33} +(4.34071 - 4.34071i) q^{35} +(3.80475 + 3.80475i) q^{37} -5.14528i q^{39} +0.765711i q^{41} +(-3.75797 - 3.75797i) q^{43} +(-7.36550 + 7.36550i) q^{45} -2.18890 q^{47} +4.23871 q^{49} +(-1.38547 + 1.38547i) q^{51} +(-1.48798 - 1.48798i) q^{53} +17.5311i q^{55} -13.0314i q^{57} +(-9.46671 - 9.46671i) q^{59} +(0.442628 - 0.442628i) q^{61} +4.68548 q^{63} -7.87914 q^{65} +(7.97172 - 7.97172i) q^{67} +(-1.70582 - 1.70582i) q^{69} -2.88774i q^{71} +7.28135i q^{73} +(14.7503 + 14.7503i) q^{75} +(5.57609 - 5.57609i) q^{77} -1.36206 q^{79} +9.50847 q^{81} +(-6.09040 + 6.09040i) q^{83} +(2.12162 + 2.12162i) q^{85} +24.2956i q^{87} -4.98060i q^{89} +(2.50612 + 2.50612i) q^{91} +(-18.2621 + 18.2621i) q^{93} -19.9554 q^{95} -7.46120 q^{97} +(-9.46176 + 9.46176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 4 q^{5} + 4 q^{11} + 18 q^{13} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 14 q^{27} + 2 q^{29} - 20 q^{31} - 36 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{43} - 20 q^{45} + 16 q^{47} + 52 q^{49} + 4 q^{51}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q - 2 * q^3 - 4 * q^5 + 4 * q^11 + 18 * q^13 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 14 * q^27 + 2 * q^29 - 20 * q^31 - 36 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^43 - 20 * q^45 + 16 * q^47 + 52 * q^49 + 4 * q^51 - 16 * q^53 - 8 * q^59 + 12 * q^61 + 4 * q^63 - 52 * q^65 + 4 * q^67 + 2 * q^69 + 46 * q^75 - 12 * q^77 + 4 * q^79 + 48 * q^81 - 28 * q^83 - 8 * q^85 - 14 * q^93 - 48 * q^95 + 36 * q^97 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1472\mathbb{Z}\right)^\times$.

$n$	$645$	$833$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70582	−	1.70582i	0.984858	−	0.984858i	−0.0150292	−	0.999887i	$-0.504784\pi$
$3$	1.70582	−	1.70582i	0.984858	−	0.984858i	0.999887	+	0.0150292i	$0.00478414\pi$
$4$		0			0
$5$	−2.61219	−	2.61219i	−1.16821	−	1.16821i	−0.982630	−	0.185575i	$-0.940585\pi$
$5$	−2.61219	−	2.61219i	−1.16821	−	1.16821i	−0.185575	−	0.982630i	$-0.559415\pi$
$6$		0			0
$7$			1.66171i			0.628069i	0.949412	+	0.314034i	$0.101681\pi$
$7$			1.66171i			0.628069i	−0.949412	+	0.314034i	$0.898319\pi$
$8$		0			0
$9$		−	2.81967i		−	0.939890i
$10$		0			0
$11$	−3.35563	−	3.35563i	−1.01176	−	1.01176i	−0.999930	−	0.0118300i	$-0.996234\pi$
$11$	−3.35563	−	3.35563i	−1.01176	−	1.01176i	−0.0118300	−	0.999930i	$-0.503766\pi$
$12$		0			0
$13$	1.50815	−	1.50815i	0.418286	−	0.418286i	−0.466327	−	0.884613i	$-0.654423\pi$
$13$	1.50815	−	1.50815i	0.418286	−	0.418286i	0.884613	+	0.466327i	$0.154423\pi$
$14$		0			0
$15$	−8.91186			−2.30103
$16$		0			0
$17$	−0.812201			−0.196988			−0.0984938	−	0.995138i	$-0.531402\pi$
$17$	−0.812201			−0.196988			−0.0984938	+	0.995138i	$0.531402\pi$
$18$		0			0
$19$	3.81967	−	3.81967i	0.876292	−	0.876292i	−0.116857	−	0.993149i	$-0.537282\pi$
$19$	3.81967	−	3.81967i	0.876292	−	0.876292i	0.993149	+	0.116857i	$0.0372818\pi$
$20$		0			0
$21$	2.83459	+	2.83459i	0.618559	+	0.618559i
$22$		0			0
$23$		−	1.00000i		−	0.208514i
$23$		−	1.00000i		−	0.208514i
$24$		0			0
$25$			8.64704i			1.72941i
$26$		0			0
$27$	0.307612	+	0.307612i	0.0592000	+	0.0592000i
$28$		0			0
$29$	−7.12138	+	7.12138i	−1.32241	+	1.32241i	−0.410584	+	0.911823i	$0.634675\pi$
$29$	−7.12138	+	7.12138i	−1.32241	+	1.32241i	−0.911823	+	0.410584i	$0.865325\pi$
$30$		0			0
$31$	−10.7058			−1.92281			−0.961405	−	0.275136i	$-0.911277\pi$
$31$	−10.7058			−1.92281			−0.961405	+	0.275136i	$0.911277\pi$
$32$		0			0
$33$	−11.4482			−1.99288
$34$		0			0
$35$	4.34071	−	4.34071i	0.733713	−	0.733713i
$36$		0			0
$37$	3.80475	+	3.80475i	0.625497	+	0.625497i	0.946932	−	0.321435i	$-0.104165\pi$
$37$	3.80475	+	3.80475i	0.625497	+	0.625497i	−0.321435	+	0.946932i	$0.604165\pi$
$38$		0			0
$39$		−	5.14528i		−	0.823904i
$40$		0			0
$41$			0.765711i			0.119584i	0.998211	+	0.0597920i	$0.0190437\pi$
$41$			0.765711i			0.119584i	−0.998211	+	0.0597920i	$0.980956\pi$
$42$		0			0
$43$	−3.75797	−	3.75797i	−0.573086	−	0.573086i	0.359904	−	0.932989i	$-0.382810\pi$
$43$	−3.75797	−	3.75797i	−0.573086	−	0.573086i	−0.932989	+	0.359904i	$0.882810\pi$
$44$		0			0
$45$	−7.36550	+	7.36550i	−1.09798	+	1.09798i
$46$		0			0
$47$	−2.18890			−0.319284			−0.159642	−	0.987175i	$-0.551034\pi$
$47$	−2.18890			−0.319284			−0.159642	+	0.987175i	$0.551034\pi$
$48$		0			0
$49$	4.23871			0.605530
$50$		0			0
$51$	−1.38547	+	1.38547i	−0.194005	+	0.194005i
$52$		0			0
$53$	−1.48798	−	1.48798i	−0.204390	−	0.204390i	0.597488	−	0.801878i	$-0.296166\pi$
$53$	−1.48798	−	1.48798i	−0.204390	−	0.204390i	−0.801878	+	0.597488i	$0.796166\pi$
$54$		0			0
$55$			17.5311i			2.36389i
$56$		0			0
$57$		−	13.0314i		−	1.72605i
$58$		0			0
$59$	−9.46671	−	9.46671i	−1.23246	−	1.23246i	−0.963016	−	0.269444i	$-0.913160\pi$
$59$	−9.46671	−	9.46671i	−1.23246	−	1.23246i	−0.269444	−	0.963016i	$-0.586840\pi$
$60$		0			0
$61$	0.442628	−	0.442628i	0.0566727	−	0.0566727i	−0.678202	−	0.734875i	$-0.737241\pi$
$61$	0.442628	−	0.442628i	0.0566727	−	0.0566727i	0.734875	+	0.678202i	$0.237241\pi$
$62$		0			0
$63$	4.68548			0.590316
$64$		0			0
$65$	−7.87914			−0.977287
$66$		0			0
$67$	7.97172	−	7.97172i	0.973901	−	0.973901i	−0.0257672	−	0.999668i	$-0.508203\pi$
$67$	7.97172	−	7.97172i	0.973901	−	0.973901i	0.999668	+	0.0257672i	$0.00820286\pi$
$68$		0			0
$69$	−1.70582	−	1.70582i	−0.205357	−	0.205357i
$70$		0			0
$71$		−	2.88774i		−	0.342712i	−0.985209	−	0.171356i	$-0.945185\pi$
$71$		−	2.88774i		−	0.342712i	0.985209	−	0.171356i	$-0.0548149\pi$
$72$		0			0
$73$			7.28135i			0.852218i	0.904672	+	0.426109i	$0.140116\pi$
$73$			7.28135i			0.852218i	−0.904672	+	0.426109i	$0.859884\pi$
$74$		0			0
$75$	14.7503	+	14.7503i	1.70322	+	1.70322i
$76$		0			0
$77$	5.57609	−	5.57609i	0.635455	−	0.635455i
$78$		0			0
$79$	−1.36206			−0.153243			−0.0766217	−	0.997060i	$-0.524413\pi$
$79$	−1.36206			−0.153243			−0.0766217	+	0.997060i	$0.524413\pi$
$80$		0			0
$81$	9.50847			1.05650
$82$		0			0
$83$	−6.09040	+	6.09040i	−0.668508	+	0.668508i	−0.957371	−	0.288863i	$-0.906723\pi$
$83$	−6.09040	+	6.09040i	−0.668508	+	0.668508i	0.288863	+	0.957371i	$0.406723\pi$
$84$		0			0
$85$	2.12162	+	2.12162i	0.230122	+	0.230122i
$86$		0			0
$87$			24.2956i			2.60477i
$88$		0			0
$89$		−	4.98060i		−	0.527942i	−0.964531	−	0.263971i	$-0.914968\pi$
$89$		−	4.98060i		−	0.527942i	0.964531	−	0.263971i	$-0.0850324\pi$
$90$		0			0
$91$	2.50612	+	2.50612i	0.262712	+	0.262712i
$92$		0			0
$93$	−18.2621	+	18.2621i	−1.89370	+	1.89370i
$94$		0			0
$95$	−19.9554			−2.04738
$96$		0			0
$97$	−7.46120			−0.757571			−0.378785	−	0.925485i	$-0.623658\pi$
$97$	−7.46120			−0.757571			−0.378785	+	0.925485i	$0.623658\pi$
$98$		0			0
$99$	−9.46176	+	9.46176i	−0.950943	+	0.950943i
$100$		0			0
$101$	−4.78167	−	4.78167i	−0.475794	−	0.475794i	0.427989	−	0.903784i	$-0.359222\pi$
$101$	−4.78167	−	4.78167i	−0.475794	−	0.475794i	−0.903784	+	0.427989i	$0.859222\pi$
$102$		0			0
$103$		−	2.63340i		−	0.259477i	−0.991548	−	0.129738i	$-0.958586\pi$
$103$		−	2.63340i		−	0.259477i	0.991548	−	0.129738i	$-0.0414137\pi$
$104$		0			0
$105$		−	14.8090i		−	1.44521i
$106$		0			0
$107$	−2.82518	−	2.82518i	−0.273121	−	0.273121i	0.557234	−	0.830355i	$-0.311862\pi$
$107$	−2.82518	−	2.82518i	−0.273121	−	0.273121i	−0.830355	+	0.557234i	$0.811862\pi$
$108$		0			0
$109$	3.66953	−	3.66953i	0.351477	−	0.351477i	−0.509182	−	0.860659i	$-0.670052\pi$
$109$	3.66953	−	3.66953i	0.351477	−	0.351477i	0.860659	+	0.509182i	$0.170052\pi$
$110$		0			0
$111$	12.9805			1.23205
$112$		0			0
$113$	12.9321			1.21655			0.608273	−	0.793728i	$-0.291863\pi$
$113$	12.9321			1.21655			0.608273	+	0.793728i	$0.291863\pi$
$114$		0			0
$115$	−2.61219	+	2.61219i	−0.243588	+	0.243588i
$116$		0			0
$117$	−4.25249	−	4.25249i	−0.393143	−	0.393143i
$118$		0			0
$119$		−	1.34965i		−	0.123722i
$120$		0			0
$121$			11.5205i			1.04732i
$122$		0			0
$123$	1.30617	+	1.30617i	0.117773	+	0.117773i
$124$		0			0
$125$	9.52674	−	9.52674i	0.852097	−	0.852097i
$126$		0			0
$127$	16.2134			1.43870			0.719352	−	0.694646i	$-0.244439\pi$
$127$	16.2134			1.43870			0.719352	+	0.694646i	$0.244439\pi$
$128$		0			0
$129$	−12.8209			−1.12882
$130$		0			0
$131$	−4.32736	+	4.32736i	−0.378083	+	0.378083i	−0.870410	−	0.492327i	$-0.836146\pi$
$131$	−4.32736	+	4.32736i	−0.378083	+	0.378083i	0.492327	+	0.870410i	$0.336146\pi$
$132$		0			0
$133$	6.34720	+	6.34720i	0.550372	+	0.550372i
$134$		0			0
$135$		−	1.60708i		−	0.138315i
$136$		0			0
$137$		−	11.7584i		−	1.00459i	−0.864698	−	0.502293i	$-0.832490\pi$
$137$		−	11.7584i		−	1.00459i	0.864698	−	0.502293i	$-0.167510\pi$
$138$		0			0
$139$	7.86498	+	7.86498i	0.667099	+	0.667099i	0.957044	−	0.289944i	$-0.0936368\pi$
$139$	7.86498	+	7.86498i	0.667099	+	0.667099i	−0.289944	+	0.957044i	$0.593637\pi$
$140$		0			0
$141$	−3.73387	+	3.73387i	−0.314449	+	0.314449i
$142$		0			0
$143$	−10.1216			−0.846410
$144$		0			0
$145$	37.2047			3.08968
$146$		0			0
$147$	7.23049	−	7.23049i	0.596360	−	0.596360i
$148$		0			0
$149$	−0.992711	−	0.992711i	−0.0813261	−	0.0813261i	0.665274	−	0.746600i	$-0.268315\pi$
$149$	−0.992711	−	0.992711i	−0.0813261	−	0.0813261i	−0.746600	+	0.665274i	$0.768315\pi$
$150$		0			0
$151$		−	20.4191i		−	1.66168i	−0.556508	−	0.830842i	$-0.687859\pi$
$151$		−	20.4191i		−	1.66168i	0.556508	−	0.830842i	$-0.312141\pi$
$152$		0			0
$153$			2.29014i			0.185147i
$154$		0			0
$155$	27.9654	+	27.9654i	2.24624	+	2.24624i
$156$		0			0
$157$	12.4153	−	12.4153i	0.990847	−	0.990847i	−0.00911182	−	0.999958i	$-0.502900\pi$
$157$	12.4153	−	12.4153i	0.990847	−	0.990847i	0.999958	+	0.00911182i	$0.00290042\pi$
$158$		0			0
$159$	−5.07647			−0.402590
$160$		0			0
$161$	1.66171			0.130961
$162$		0			0
$163$	5.10777	−	5.10777i	0.400072	−	0.400072i	−0.478187	−	0.878258i	$-0.658706\pi$
$163$	5.10777	−	5.10777i	0.400072	−	0.400072i	0.878258	+	0.478187i	$0.158706\pi$
$164$		0			0
$165$	29.9049	+	29.9049i	2.32809	+	2.32809i
$166$		0			0
$167$		−	21.0732i		−	1.63069i	−0.578972	−	0.815347i	$-0.696546\pi$
$167$		−	21.0732i		−	1.63069i	0.578972	−	0.815347i	$-0.303454\pi$
$168$		0			0
$169$			8.45096i			0.650074i
$170$		0			0
$171$	−10.7702	−	10.7702i	−0.823618	−	0.823618i
$172$		0			0
$173$	0.742883	−	0.742883i	0.0564804	−	0.0564804i	−0.678302	−	0.734783i	$-0.737284\pi$
$173$	0.742883	−	0.742883i	0.0564804	−	0.0564804i	0.734783	+	0.678302i	$0.237284\pi$
$174$		0			0
$175$	−14.3689			−1.08619
$176$		0			0
$177$	−32.2971			−2.42760
$178$		0			0
$179$	5.87835	−	5.87835i	0.439369	−	0.439369i	−0.452431	−	0.891799i	$-0.649443\pi$
$179$	5.87835	−	5.87835i	0.439369	−	0.439369i	0.891799	+	0.452431i	$0.149443\pi$
$180$		0			0
$181$	−12.5257	−	12.5257i	−0.931028	−	0.931028i	0.0667421	−	0.997770i	$-0.478740\pi$
$181$	−12.5257	−	12.5257i	−0.931028	−	0.931028i	−0.997770	+	0.0667421i	$0.978740\pi$
$182$		0			0
$183$		−	1.51009i		−	0.111629i
$184$		0			0
$185$		−	19.8774i		−	1.46142i
$186$		0			0
$187$	2.72544	+	2.72544i	0.199304	+	0.199304i
$188$		0			0
$189$	−0.511163	+	0.511163i	−0.0371817	+	0.0371817i
$190$		0			0
$191$	−1.64397			−0.118954			−0.0594768	−	0.998230i	$-0.518943\pi$
$191$	−1.64397			−0.118954			−0.0594768	+	0.998230i	$0.518943\pi$
$192$		0			0
$193$	−19.0438			−1.37080			−0.685401	−	0.728166i	$-0.740373\pi$
$193$	−19.0438			−1.37080			−0.685401	+	0.728166i	$0.740373\pi$
$194$		0			0
$195$	−13.4404	+	13.4404i	−0.962489	+	0.962489i
$196$		0			0
$197$	12.5735	+	12.5735i	0.895824	+	0.895824i	0.995064	−	0.0992395i	$-0.0316410\pi$
$197$	12.5735	+	12.5735i	0.895824	+	0.895824i	−0.0992395	+	0.995064i	$0.531641\pi$
$198$		0			0
$199$		−	15.8114i		−	1.12084i	−0.828209	−	0.560419i	$-0.810640\pi$
$199$		−	15.8114i		−	1.12084i	0.828209	−	0.560419i	$-0.189360\pi$
$200$		0			0
$201$		−	27.1967i		−	1.91831i
$202$		0			0
$203$	−11.8337	−	11.8337i	−0.830562	−	0.830562i
$204$		0			0
$205$	2.00018	−	2.00018i	0.139699	−	0.139699i
$206$		0			0
$207$	−2.81967			−0.195981
$208$		0			0
$209$	−25.6348			−1.77320
$210$		0			0
$211$	−8.18793	+	8.18793i	−0.563680	+	0.563680i	−0.930351	−	0.366671i	$-0.880498\pi$
$211$	−8.18793	+	8.18793i	−0.563680	+	0.563680i	0.366671	+	0.930351i	$0.380498\pi$
$212$		0			0
$213$	−4.92598	−	4.92598i	−0.337523	−	0.337523i
$214$		0			0
$215$			19.6331i			1.33896i
$216$		0			0
$217$		−	17.7899i		−	1.20766i
$218$		0			0
$219$	12.4207	+	12.4207i	0.839314	+	0.839314i
$220$		0			0
$221$	−1.22492	+	1.22492i	−0.0823972	+	0.0823972i
$222$		0			0
$223$	13.6729			0.915607			0.457804	−	0.889053i	$-0.348636\pi$
$223$	13.6729			0.915607			0.457804	+	0.889053i	$0.348636\pi$
$224$		0			0
$225$	24.3818			1.62545
$226$		0			0
$227$	10.5639	−	10.5639i	0.701148	−	0.701148i	−0.263509	−	0.964657i	$-0.584880\pi$
$227$	10.5639	−	10.5639i	0.701148	−	0.701148i	0.964657	+	0.263509i	$0.0848798\pi$
$228$		0			0
$229$	−18.5926	−	18.5926i	−1.22863	−	1.22863i	−0.964480	−	0.264155i	$-0.914907\pi$
$229$	−18.5926	−	18.5926i	−1.22863	−	1.22863i	−0.264155	−	0.964480i	$-0.585093\pi$
$230$		0			0
$231$		−	19.0237i		−	1.25167i
$232$		0			0
$233$			15.7207i			1.02990i	0.857220	+	0.514950i	$0.172189\pi$
$233$			15.7207i			1.02990i	−0.857220	+	0.514950i	$0.827811\pi$
$234$		0			0
$235$	5.71781	+	5.71781i	0.372989	+	0.372989i
$236$		0			0
$237$	−2.32343	+	2.32343i	−0.150923	+	0.150923i
$238$		0			0
$239$	3.11445			0.201457			0.100729	−	0.994914i	$-0.467883\pi$
$239$	3.11445			0.201457			0.100729	+	0.994914i	$0.467883\pi$
$240$		0			0
$241$	−11.6111			−0.747938			−0.373969	−	0.927441i	$-0.622003\pi$
$241$	−11.6111			−0.747938			−0.373969	+	0.927441i	$0.622003\pi$
$242$		0			0
$243$	15.2969	−	15.2969i	0.981299	−	0.981299i
$244$		0			0
$245$	−11.0723	−	11.0723i	−0.707383	−	0.707383i
$246$		0			0
$247$		−	11.5213i		−	0.733081i
$248$		0			0
$249$			20.7783i			1.31677i
$250$		0			0
$251$	−14.1075	−	14.1075i	−0.890454	−	0.890454i	0.104111	−	0.994566i	$-0.466800\pi$
$251$	−14.1075	−	14.1075i	−0.890454	−	0.890454i	−0.994566	+	0.104111i	$0.966800\pi$
$252$		0			0
$253$	−3.35563	+	3.35563i	−0.210967	+	0.210967i
$254$		0			0
$255$	7.23822			0.453275
$256$		0			0
$257$	8.50878			0.530763			0.265382	−	0.964143i	$-0.414502\pi$
$257$	8.50878			0.530763			0.265382	+	0.964143i	$0.414502\pi$
$258$		0			0
$259$	−6.32240	+	6.32240i	−0.392855	+	0.392855i
$260$		0			0
$261$	20.0799	+	20.0799i	1.24292	+	1.24292i
$262$		0			0
$263$			5.49050i			0.338559i	0.985568	+	0.169279i	$0.0541440\pi$
$263$			5.49050i			0.338559i	−0.985568	+	0.169279i	$0.945856\pi$
$264$		0			0
$265$			7.77377i			0.477539i
$266$		0			0
$267$	−8.49602	−	8.49602i	−0.519948	−	0.519948i
$268$		0			0
$269$	−1.16630	+	1.16630i	−0.0711108	+	0.0711108i	−0.741768	−	0.670657i	$-0.766012\pi$
$269$	−1.16630	+	1.16630i	−0.0711108	+	0.0711108i	0.670657	+	0.741768i	$0.266012\pi$
$270$		0			0
$271$	0.427919			0.0259942			0.0129971	−	0.999916i	$-0.495863\pi$
$271$	0.427919			0.0259942			0.0129971	+	0.999916i	$0.495863\pi$
$272$		0			0
$273$	8.54998			0.517468
$274$		0			0
$275$	29.0162	−	29.0162i	1.74974	−	1.74974i
$276$		0			0
$277$	14.2225	+	14.2225i	0.854549	+	0.854549i	0.990690	−	0.136141i	$-0.0434699\pi$
$277$	14.2225	+	14.2225i	0.854549	+	0.854549i	−0.136141	+	0.990690i	$0.543470\pi$
$278$		0			0
$279$			30.1867i			1.80723i
$280$		0			0
$281$		−	25.6942i		−	1.53279i	−0.642370	−	0.766395i	$-0.722049\pi$
$281$		−	25.6942i		−	1.53279i	0.642370	−	0.766395i	$-0.277951\pi$
$282$		0			0
$283$	−4.50559	−	4.50559i	−0.267830	−	0.267830i	0.560396	−	0.828225i	$-0.310649\pi$
$283$	−4.50559	−	4.50559i	−0.267830	−	0.267830i	−0.828225	+	0.560396i	$0.810649\pi$
$284$		0			0
$285$	−34.0404	+	34.0404i	−2.01638	+	2.01638i
$286$		0			0
$287$	−1.27239			−0.0751070
$288$		0			0
$289$	−16.3403			−0.961196
$290$		0			0
$291$	−12.7275	+	12.7275i	−0.746099	+	0.746099i
$292$		0			0
$293$	14.1998	+	14.1998i	0.829559	+	0.829559i	0.987456	−	0.157897i	$-0.0504713\pi$
$293$	14.1998	+	14.1998i	0.829559	+	0.829559i	−0.157897	+	0.987456i	$0.550471\pi$
$294$		0			0
$295$			49.4576i			2.87953i
$296$		0			0
$297$		−	2.06446i		−	0.119792i
$298$		0			0
$299$	−1.50815	−	1.50815i	−0.0872186	−	0.0872186i
$300$		0			0
$301$	6.24468	−	6.24468i	0.359937	−	0.359937i
$302$		0			0
$303$	−16.3134			−0.937179
$304$		0			0
$305$	−2.31245			−0.132411
$306$		0			0
$307$	−8.90060	+	8.90060i	−0.507984	+	0.507984i	−0.913907	−	0.405923i	$-0.866950\pi$
$307$	−8.90060	+	8.90060i	−0.507984	+	0.507984i	0.405923	+	0.913907i	$0.366950\pi$
$308$		0			0
$309$	−4.49212	−	4.49212i	−0.255548	−	0.255548i
$310$		0			0
$311$		−	4.52341i		−	0.256499i	−0.991742	−	0.128249i	$-0.959064\pi$
$311$		−	4.52341i		−	0.256499i	0.991742	−	0.128249i	$-0.0409358\pi$
$312$		0			0
$313$		−	10.0966i		−	0.570694i	−0.958424	−	0.285347i	$-0.907891\pi$
$313$		−	10.0966i		−	0.570694i	0.958424	−	0.285347i	$-0.0921089\pi$
$314$		0			0
$315$	−12.2394	−	12.2394i	−0.689610	−	0.689610i
$316$		0			0
$317$	13.8631	−	13.8631i	0.778627	−	0.778627i	−0.200970	−	0.979597i	$-0.564409\pi$
$317$	13.8631	−	13.8631i	0.778627	−	0.778627i	0.979597	+	0.200970i	$0.0644094\pi$
$318$		0			0
$319$	47.7934			2.67592
$320$		0			0
$321$	−9.63853			−0.537970
$322$		0			0
$323$	−3.10234	+	3.10234i	−0.172619	+	0.172619i
$324$		0			0
$325$	13.0410	+	13.0410i	0.723386	+	0.723386i
$326$		0			0
$327$		−	12.5191i		−	0.692310i
$328$		0			0
$329$		−	3.63732i		−	0.200532i
$330$		0			0
$331$	−7.42842	−	7.42842i	−0.408303	−	0.408303i	0.472843	−	0.881146i	$-0.343228\pi$
$331$	−7.42842	−	7.42842i	−0.408303	−	0.408303i	−0.881146	+	0.472843i	$0.843228\pi$
$332$		0			0
$333$	10.7281	−	10.7281i	0.587898	−	0.587898i
$334$		0			0
$335$	−41.6472			−2.27543
$336$		0			0
$337$	27.7241			1.51023			0.755113	−	0.655595i	$-0.227582\pi$
$337$	27.7241			1.51023			0.755113	+	0.655595i	$0.227582\pi$
$338$		0			0
$339$	22.0598	−	22.0598i	1.19812	−	1.19812i
$340$		0			0
$341$	35.9245	+	35.9245i	1.94542	+	1.94542i
$342$		0			0
$343$			18.6755i			1.00838i
$344$		0			0
$345$			8.91186i			0.479798i
$346$		0			0
$347$	7.58296	+	7.58296i	0.407075	+	0.407075i	0.880717	−	0.473643i	$-0.157061\pi$
$347$	7.58296	+	7.58296i	0.407075	+	0.407075i	−0.473643	+	0.880717i	$0.657061\pi$
$348$		0			0
$349$	23.1963	−	23.1963i	1.24167	−	1.24167i	0.282364	−	0.959307i	$-0.408882\pi$
$349$	23.1963	−	23.1963i	1.24167	−	1.24167i	0.959307	−	0.282364i	$-0.0911184\pi$
$350$		0			0
$351$	0.927851			0.0495250
$352$		0			0
$353$	−14.5140			−0.772500			−0.386250	−	0.922394i	$-0.626230\pi$
$353$	−14.5140			−0.772500			−0.386250	+	0.922394i	$0.626230\pi$
$354$		0			0
$355$	−7.54333	+	7.54333i	−0.400358	+	0.400358i
$356$		0			0
$357$	−2.30226	−	2.30226i	−0.121848	−	0.121848i
$358$		0			0
$359$			5.94898i			0.313975i	0.987601	+	0.156988i	$0.0501783\pi$
$359$			5.94898i			0.313975i	−0.987601	+	0.156988i	$0.949822\pi$
$360$		0			0
$361$		−	10.1798i		−	0.535776i
$362$		0			0
$363$	19.6519	+	19.6519i	1.03146	+	1.03146i
$364$		0			0
$365$	19.0203	−	19.0203i	0.995566	−	0.995566i
$366$		0			0
$367$	−22.5189			−1.17548			−0.587738	−	0.809052i	$-0.699981\pi$
$367$	−22.5189			−1.17548			−0.587738	+	0.809052i	$0.699981\pi$
$368$		0			0
$369$	2.15905			0.112396
$370$		0			0
$371$	2.47260	−	2.47260i	0.128371	−	0.128371i
$372$		0			0
$373$	−3.70962	−	3.70962i	−0.192077	−	0.192077i	0.604516	−	0.796593i	$-0.293366\pi$
$373$	−3.70962	−	3.70962i	−0.192077	−	0.192077i	−0.796593	+	0.604516i	$0.793366\pi$
$374$		0			0
$375$		−	32.5019i		−	1.67839i
$376$		0			0
$377$			21.4802i			1.10629i
$378$		0			0
$379$	5.06716	+	5.06716i	0.260282	+	0.260282i	0.825169	−	0.564886i	$-0.191080\pi$
$379$	5.06716	+	5.06716i	0.260282	+	0.260282i	−0.564886	+	0.825169i	$0.691080\pi$
$380$		0			0
$381$	27.6571	−	27.6571i	1.41692	−	1.41692i
$382$		0			0
$383$	15.1644			0.774864			0.387432	−	0.921898i	$-0.373362\pi$
$383$	15.1644			0.774864			0.387432	+	0.921898i	$0.373362\pi$
$384$		0			0
$385$	−29.1316			−1.48468
$386$		0			0
$387$	−10.5962	+	10.5962i	−0.538637	+	0.538637i
$388$		0			0
$389$	−24.4010	−	24.4010i	−1.23718	−	1.23718i	−0.961149	−	0.276029i	$-0.910982\pi$
$389$	−24.4010	−	24.4010i	−1.23718	−	1.23718i	−0.276029	−	0.961149i	$-0.589018\pi$
$390$		0			0
$391$			0.812201i			0.0410748i
$392$		0			0
$393$			14.7634i			0.744716i
$394$		0			0
$395$	3.55794	+	3.55794i	0.179020	+	0.179020i
$396$		0			0
$397$	−15.6879	+	15.6879i	−0.787352	+	0.787352i	−0.981059	−	0.193707i	$-0.937949\pi$
$397$	−15.6879	+	15.6879i	−0.787352	+	0.787352i	0.193707	+	0.981059i	$0.437949\pi$
$398$		0			0
$399$	21.6544			1.08408
$400$		0			0
$401$	22.7601			1.13659			0.568293	−	0.822826i	$-0.307604\pi$
$401$	22.7601			1.13659			0.568293	+	0.822826i	$0.307604\pi$
$402$		0			0
$403$	−16.1459	+	16.1459i	−0.804284	+	0.804284i
$404$		0			0
$405$	−24.8379	−	24.8379i	−1.23421	−	1.23421i
$406$		0			0
$407$		−	25.5346i		−	1.26571i
$408$		0			0
$409$			19.7572i			0.976929i	0.872584	+	0.488465i	$0.162443\pi$
$409$			19.7572i			0.976929i	−0.872584	+	0.488465i	$0.837557\pi$
$410$		0			0
$411$	−20.0577	−	20.0577i	−0.989374	−	0.989374i
$412$		0			0
$413$	15.7310	−	15.7310i	0.774070	−	0.774070i
$414$		0			0
$415$	31.8185			1.56191
$416$		0			0
$417$	26.8326			1.31400
$418$		0			0
$419$	−13.2965	+	13.2965i	−0.649578	+	0.649578i	−0.952891	−	0.303313i	$-0.901907\pi$
$419$	−13.2965	+	13.2965i	−0.649578	+	0.649578i	0.303313	+	0.952891i	$0.401907\pi$
$420$		0			0
$421$	10.7611	+	10.7611i	0.524465	+	0.524465i	0.918917	−	0.394451i	$-0.129065\pi$
$421$	10.7611	+	10.7611i	0.524465	+	0.524465i	−0.394451	+	0.918917i	$0.629065\pi$
$422$		0			0
$423$			6.17197i			0.300091i
$424$		0			0
$425$		−	7.02313i		−	0.340672i
$426$		0			0
$427$	0.735521	+	0.735521i	0.0355943	+	0.0355943i
$428$		0			0
$429$	−17.2656	+	17.2656i	−0.833593	+	0.833593i
$430$		0			0
$431$	30.6031			1.47410			0.737050	−	0.675838i	$-0.236218\pi$
$431$	30.6031			1.47410			0.737050	+	0.675838i	$0.236218\pi$
$432$		0			0
$433$	−18.9640			−0.911352			−0.455676	−	0.890146i	$-0.650602\pi$
$433$	−18.9640			−0.911352			−0.455676	+	0.890146i	$0.650602\pi$
$434$		0			0
$435$	63.4647	−	63.4647i	3.04290	−	3.04290i
$436$		0			0
$437$	−3.81967	−	3.81967i	−0.182720	−	0.182720i
$438$		0			0
$439$			9.69923i			0.462919i	0.972845	+	0.231460i	$0.0743501\pi$
$439$			9.69923i			0.462919i	−0.972845	+	0.231460i	$0.925650\pi$
$440$		0			0
$441$		−	11.9518i		−	0.569131i
$442$		0			0
$443$	7.91936	+	7.91936i	0.376260	+	0.376260i	0.869751	−	0.493491i	$-0.164279\pi$
$443$	7.91936	+	7.91936i	0.376260	+	0.376260i	−0.493491	+	0.869751i	$0.664279\pi$
$444$		0			0
$445$	−13.0103	+	13.0103i	−0.616745	+	0.616745i
$446$		0			0
$447$	−3.38678			−0.160189
$448$		0			0
$449$	34.5114			1.62869			0.814346	−	0.580380i	$-0.197096\pi$
$449$	34.5114			1.62869			0.814346	+	0.580380i	$0.197096\pi$
$450$		0			0
$451$	2.56944	−	2.56944i	0.120990	−	0.120990i
$452$		0			0
$453$	−34.8314	−	34.8314i	−1.63652	−	1.63652i
$454$		0			0
$455$		−	13.0929i		−	0.613804i
$456$		0			0
$457$			33.1088i			1.54877i	0.632717	+	0.774383i	$0.281939\pi$
$457$			33.1088i			1.54877i	−0.632717	+	0.774383i	$0.718061\pi$
$458$		0			0
$459$	−0.249843	−	0.249843i	−0.0116617	−	0.0116617i
$460$		0			0
$461$	9.64848	−	9.64848i	0.449374	−	0.449374i	−0.445772	−	0.895147i	$-0.647071\pi$
$461$	9.64848	−	9.64848i	0.449374	−	0.449374i	0.895147	+	0.445772i	$0.147071\pi$
$462$		0			0
$463$	−26.3833			−1.22613			−0.613067	−	0.790031i	$-0.710065\pi$
$463$	−26.3833			−1.22613			−0.613067	+	0.790031i	$0.710065\pi$
$464$		0			0
$465$	95.4082			4.42445
$466$		0			0
$467$	9.91627	−	9.91627i	0.458870	−	0.458870i	−0.439414	−	0.898285i	$-0.644814\pi$
$467$	9.91627	−	9.91627i	0.458870	−	0.458870i	0.898285	+	0.439414i	$0.144814\pi$
$468$		0			0
$469$	13.2467	+	13.2467i	0.611677	+	0.611677i
$470$		0			0
$471$		−	42.3565i		−	1.95169i
$472$		0			0
$473$			25.2207i			1.15965i
$474$		0			0
$475$	33.0288	+	33.0288i	1.51547	+	1.51547i
$476$		0			0
$477$	−4.19561	+	4.19561i	−0.192104	+	0.192104i
$478$		0			0
$479$	6.32910			0.289184			0.144592	−	0.989491i	$-0.453813\pi$
$479$	6.32910			0.289184			0.144592	+	0.989491i	$0.453813\pi$
$480$		0			0
$481$	11.4763			0.523273
$482$		0			0
$483$	2.83459	−	2.83459i	0.128978	−	0.128978i
$484$		0			0
$485$	19.4901	+	19.4901i	0.884998	+	0.884998i
$486$		0			0
$487$		−	43.0783i		−	1.95207i	−0.217623	−	0.976033i	$-0.569830\pi$
$487$		−	43.0783i		−	1.95207i	0.217623	−	0.976033i	$-0.430170\pi$
$488$		0			0
$489$		−	17.4259i		−	0.788027i
$490$		0			0
$491$	−4.44148	−	4.44148i	−0.200441	−	0.200441i	0.599748	−	0.800189i	$-0.295268\pi$
$491$	−4.44148	−	4.44148i	−0.200441	−	0.200441i	−0.800189	+	0.599748i	$0.795268\pi$
$492$		0			0
$493$	5.78399	−	5.78399i	0.260498	−	0.260498i
$494$		0			0
$495$	49.4318			2.22179
$496$		0			0
$497$	4.79861			0.215247
$498$		0			0
$499$	7.83750	−	7.83750i	0.350855	−	0.350855i	−0.509573	−	0.860428i	$-0.670197\pi$
$499$	7.83750	−	7.83750i	0.350855	−	0.350855i	0.860428	+	0.509573i	$0.170197\pi$
$500$		0			0
$501$	−35.9472	−	35.9472i	−1.60600	−	1.60600i
$502$		0			0
$503$			2.51611i			0.112188i	0.998425	+	0.0560939i	$0.0178646\pi$
$503$			2.51611i			0.112188i	−0.998425	+	0.0560939i	$0.982135\pi$
$504$		0			0
$505$			24.9812i			1.11165i
$506$		0			0
$507$	14.4159	+	14.4159i	0.640230	+	0.640230i
$508$		0			0
$509$	−18.5730	+	18.5730i	−0.823235	+	0.823235i	−0.986571	−	0.163336i	$-0.947775\pi$
$509$	−18.5730	+	18.5730i	−0.823235	+	0.823235i	0.163336	+	0.986571i	$0.447775\pi$
$510$		0			0
$511$	−12.0995			−0.535252
$512$		0			0
$513$	2.34995			0.103753
$514$		0			0
$515$	−6.87893	+	6.87893i	−0.303122	+	0.303122i
$516$		0			0
$517$	7.34513	+	7.34513i	0.323038	+	0.323038i
$518$		0			0
$519$		−	2.53446i		−	0.111250i
$520$		0			0
$521$			26.4008i			1.15664i	0.815810	+	0.578320i	$0.196292\pi$
$521$			26.4008i			1.15664i	−0.815810	+	0.578320i	$0.803708\pi$
$522$		0			0
$523$	−29.1181	−	29.1181i	−1.27324	−	1.27324i	−0.944376	−	0.328869i	$-0.893333\pi$
$523$	−29.1181	−	29.1181i	−1.27324	−	1.27324i	−0.328869	−	0.944376i	$-0.606667\pi$
$524$		0			0
$525$	−24.5108	+	24.5108i	−1.06974	+	1.06974i
$526$		0			0
$527$	8.69523			0.378770
$528$		0			0
$529$	−1.00000			−0.0434783
$530$		0			0
$531$	−26.6930	+	26.6930i	−1.15838	+	1.15838i
$532$		0			0
$533$	1.15481	+	1.15481i	0.0500203	+	0.0500203i
$534$		0			0
$535$			14.7598i			0.638122i
$536$		0			0
$537$		−	20.0549i		−	0.865431i
$538$		0			0
$539$	−14.2235	−	14.2235i	−0.612651	−	0.612651i
$540$		0			0
$541$	−16.9801	+	16.9801i	−0.730031	+	0.730031i	−0.970626	−	0.240595i	$-0.922658\pi$
$541$	−16.9801	+	16.9801i	−0.730031	+	0.730031i	0.240595	+	0.970626i	$0.422658\pi$
$542$		0			0
$543$	−42.7333			−1.83386
$544$		0			0
$545$	−19.1710			−0.821194
$546$		0			0
$547$	1.44323	−	1.44323i	0.0617081	−	0.0617081i	−0.675579	−	0.737287i	$-0.736106\pi$
$547$	1.44323	−	1.44323i	0.0617081	−	0.0617081i	0.737287	+	0.675579i	$0.236106\pi$
$548$		0			0
$549$	−1.24806	−	1.24806i	−0.0532661	−	0.0532661i
$550$		0			0
$551$			54.4026i			2.31763i
$552$		0			0
$553$		−	2.26335i		−	0.0962473i
$554$		0			0
$555$	−33.9074	−	33.9074i	−1.43929	−	1.43929i
$556$		0			0
$557$	5.09710	−	5.09710i	0.215971	−	0.215971i	−0.590827	−	0.806798i	$-0.701198\pi$
$557$	5.09710	−	5.09710i	0.215971	−	0.215971i	0.806798	+	0.590827i	$0.201198\pi$
$558$		0			0
$559$	−11.3352			−0.479427
$560$		0			0
$561$	9.29826			0.392573
$562$		0			0
$563$	−6.95433	+	6.95433i	−0.293090	+	0.293090i	−0.838300	−	0.545210i	$-0.816450\pi$
$563$	−6.95433	+	6.95433i	−0.293090	+	0.293090i	0.545210	+	0.838300i	$0.316450\pi$
$564$		0			0
$565$	−33.7809	−	33.7809i	−1.42117	−	1.42117i
$566$		0			0
$567$			15.8004i			0.663553i
$568$		0			0
$569$			0.100497i			0.00421306i	0.999998	+	0.00210653i	$0.000670529\pi$
$569$			0.100497i			0.00421306i	−0.999998	+	0.00210653i	$0.999329\pi$
$570$		0			0
$571$	29.6374	+	29.6374i	1.24029	+	1.24029i	0.959881	+	0.280406i	$0.0904691\pi$
$571$	29.6374	+	29.6374i	1.24029	+	1.24029i	0.280406	+	0.959881i	$0.409531\pi$
$572$		0			0
$573$	−2.80432	+	2.80432i	−0.117152	+	0.117152i
$574$		0			0
$575$	8.64704			0.360606
$576$		0			0
$577$	11.2586			0.468702			0.234351	−	0.972152i	$-0.424703\pi$
$577$	11.2586			0.468702			0.234351	+	0.972152i	$0.424703\pi$
$578$		0			0
$579$	−32.4853	+	32.4853i	−1.35004	+	1.35004i
$580$		0			0
$581$	−10.1205	−	10.1205i	−0.419869	−	0.419869i
$582$		0			0
$583$			9.98622i			0.413587i
$584$		0			0
$585$			22.2166i			0.918542i
$586$		0			0
$587$	−2.71169	−	2.71169i	−0.111923	−	0.111923i	0.648927	−	0.760850i	$-0.275218\pi$
$587$	−2.71169	−	2.71169i	−0.111923	−	0.111923i	−0.760850	+	0.648927i	$0.775218\pi$
$588$		0			0
$589$	−40.8925	+	40.8925i	−1.68494	+	1.68494i
$590$		0			0
$591$	42.8963			1.76452
$592$		0			0
$593$	−11.6754			−0.479451			−0.239726	−	0.970841i	$-0.577058\pi$
$593$	−11.6754			−0.479451			−0.239726	+	0.970841i	$0.577058\pi$
$594$		0			0
$595$	−3.52553	+	3.52553i	−0.144532	+	0.144532i
$596$		0			0
$597$	−26.9714	−	26.9714i	−1.10387	−	1.10387i
$598$		0			0
$599$			29.4312i			1.20253i	0.799051	+	0.601263i	$0.205336\pi$
$599$			29.4312i			1.20253i	−0.799051	+	0.601263i	$0.794664\pi$
$600$		0			0
$601$		−	7.06623i		−	0.288237i	−0.989560	−	0.144119i	$-0.953965\pi$
$601$		−	7.06623i		−	0.288237i	0.989560	−	0.144119i	$-0.0460347\pi$
$602$		0			0
$603$	−22.4776	−	22.4776i	−0.915359	−	0.915359i
$604$		0			0
$605$	30.0937	−	30.0937i	1.22348	−	1.22348i
$606$		0			0
$607$	−0.575135			−0.0233440			−0.0116720	−	0.999932i	$-0.503715\pi$
$607$	−0.575135			−0.0233440			−0.0116720	+	0.999932i	$0.503715\pi$
$608$		0			0
$609$	−40.3724			−1.63597
$610$		0			0
$611$	−3.30119	+	3.30119i	−0.133552	+	0.133552i
$612$		0			0
$613$	−26.7943	−	26.7943i	−1.08221	−	1.08221i	−0.996303	−	0.0859064i	$-0.972621\pi$
$613$	−26.7943	−	26.7943i	−1.08221	−	1.08221i	−0.0859064	−	0.996303i	$-0.527379\pi$
$614$		0			0
$615$		−	6.82391i		−	0.275167i
$616$		0			0
$617$			39.6599i			1.59665i	0.602229	+	0.798323i	$0.294279\pi$
$617$			39.6599i			1.59665i	−0.602229	+	0.798323i	$0.705721\pi$
$618$		0			0
$619$	14.8037	+	14.8037i	0.595011	+	0.595011i	0.938981	−	0.343970i	$-0.111772\pi$
$619$	14.8037	+	14.8037i	0.595011	+	0.595011i	−0.343970	+	0.938981i	$0.611772\pi$
$620$		0			0
$621$	0.307612	−	0.307612i	0.0123440	−	0.0123440i
$622$		0			0
$623$	8.27633			0.331584
$624$		0			0
$625$	−6.53605			−0.261442
$626$		0			0
$627$	−43.7284	+	43.7284i	−1.74634	+	1.74634i
$628$		0			0
$629$	−3.09022	−	3.09022i	−0.123215	−	0.123215i
$630$		0			0
$631$		−	14.6400i		−	0.582807i	−0.956600	−	0.291404i	$-0.905878\pi$
$631$		−	14.6400i		−	0.582807i	0.956600	−	0.291404i	$-0.0941223\pi$
$632$		0			0
$633$			27.9343i			1.11029i
$634$		0			0
$635$	−42.3523	−	42.3523i	−1.68070	−	1.68070i
$636$		0			0
$637$	6.39261	−	6.39261i	0.253284	−	0.253284i
$638$		0			0
$639$	−8.14248			−0.322112
$640$		0			0
$641$	43.2014			1.70635			0.853176	−	0.521622i	$-0.174673\pi$
$641$	43.2014			1.70635			0.853176	+	0.521622i	$0.174673\pi$
$642$		0			0
$643$	10.5494	−	10.5494i	0.416029	−	0.416029i	−0.467803	−	0.883833i	$-0.654954\pi$
$643$	10.5494	−	10.5494i	0.416029	−	0.416029i	0.883833	+	0.467803i	$0.154954\pi$
$644$		0			0
$645$	33.4905	+	33.4905i	1.31869	+	1.31869i
$646$		0			0
$647$			28.3175i			1.11328i	0.830755	+	0.556638i	$0.187909\pi$
$647$			28.3175i			1.11328i	−0.830755	+	0.556638i	$0.812091\pi$
$648$		0			0
$649$			63.5335i			2.49391i
$650$		0			0
$651$	−30.3464	−	30.3464i	−1.18937	−	1.18937i
$652$		0			0
$653$	10.8329	−	10.8329i	0.423926	−	0.423926i	−0.462627	−	0.886553i	$-0.653093\pi$
$653$	10.8329	−	10.8329i	0.423926	−	0.423926i	0.886553	+	0.462627i	$0.153093\pi$
$654$		0			0
$655$	22.6077			0.883358
$656$		0			0
$657$	20.5310			0.800991
$658$		0			0
$659$	−21.1434	+	21.1434i	−0.823630	+	0.823630i	−0.986627	−	0.162997i	$-0.947884\pi$
$659$	−21.1434	+	21.1434i	−0.823630	+	0.823630i	0.162997	+	0.986627i	$0.447884\pi$
$660$		0			0
$661$	3.71648	+	3.71648i	0.144554	+	0.144554i	0.775680	−	0.631126i	$-0.217407\pi$
$661$	3.71648	+	3.71648i	0.144554	+	0.144554i	−0.631126	+	0.775680i	$0.717407\pi$
$662$		0			0
$663$			4.17900i			0.162299i
$664$		0			0
$665$		−	33.1601i		−	1.28589i
$666$		0			0
$667$	7.12138	+	7.12138i	0.275741	+	0.275741i
$668$		0			0
$669$	23.3236	−	23.3236i	0.901743	−	0.901743i
$670$		0			0
$671$	−2.97059			−0.114678
$672$		0			0
$673$	−18.1480			−0.699552			−0.349776	−	0.936833i	$-0.613742\pi$
$673$	−18.1480			−0.699552			−0.349776	+	0.936833i	$0.613742\pi$
$674$		0			0
$675$	−2.65993	+	2.65993i	−0.102381	+	0.102381i
$676$		0			0
$677$	−8.16589	−	8.16589i	−0.313841	−	0.313841i	0.532555	−	0.846396i	$-0.321232\pi$
$677$	−8.16589	−	8.16589i	−0.313841	−	0.313841i	−0.846396	+	0.532555i	$0.821232\pi$
$678$		0			0
$679$		−	12.3984i		−	0.475806i
$680$		0			0
$681$		−	36.0402i		−	1.38106i
$682$		0			0
$683$	−4.85358	−	4.85358i	−0.185717	−	0.185717i	0.608125	−	0.793842i	$-0.291922\pi$
$683$	−4.85358	−	4.85358i	−0.185717	−	0.185717i	−0.793842	+	0.608125i	$0.791922\pi$
$684$		0			0
$685$	−30.7151	+	30.7151i	−1.17356	+	1.17356i
$686$		0			0
$687$	−63.4315			−2.42006
$688$		0			0
$689$	−4.48820			−0.170987
$690$		0			0
$691$	−10.8867	+	10.8867i	−0.414149	+	0.414149i	−0.883181	−	0.469032i	$-0.844603\pi$
$691$	−10.8867	+	10.8867i	−0.414149	+	0.414149i	0.469032	+	0.883181i	$0.344603\pi$
$692$		0			0
$693$	−15.7227	−	15.7227i	−0.597258	−	0.597258i
$694$		0			0
$695$		−	41.0896i		−	1.55862i
$696$		0			0
$697$		−	0.621911i		−	0.0235566i
$698$		0			0
$699$	26.8168	+	26.8168i	1.01430	+	1.01430i
$700$		0			0
$701$	−4.48997	+	4.48997i	−0.169584	+	0.169584i	−0.786797	−	0.617212i	$-0.788262\pi$
$701$	−4.48997	+	4.48997i	−0.169584	+	0.169584i	0.617212	+	0.786797i	$0.288262\pi$
$702$		0			0
$703$	29.0658			1.09624
$704$		0			0
$705$	19.5072			0.734682
$706$		0			0
$707$	7.94577	−	7.94577i	0.298832	−	0.298832i
$708$		0			0
$709$	8.56006	+	8.56006i	0.321480	+	0.321480i	0.849335	−	0.527855i	$-0.177003\pi$
$709$	8.56006	+	8.56006i	0.321480	+	0.321480i	−0.527855	+	0.849335i	$0.677003\pi$
$710$		0			0
$711$			3.84055i			0.144032i
$712$		0			0
$713$			10.7058i			0.400934i
$714$		0			0
$715$	26.4395	+	26.4395i	0.988780	+	0.988780i
$716$		0			0
$717$	5.31271	−	5.31271i	0.198407	−	0.198407i
$718$		0			0
$719$	17.5883			0.655932			0.327966	−	0.944689i	$-0.393637\pi$
$719$	17.5883			0.655932			0.327966	+	0.944689i	$0.393637\pi$
$720$		0			0
$721$	4.37596			0.162969
$722$		0			0
$723$	−19.8065	+	19.8065i	−0.736612	+	0.736612i
$724$		0			0
$725$	−61.5788	−	61.5788i	−2.28698	−	2.28698i
$726$		0			0
$727$			41.4212i			1.53623i	0.640315	+	0.768113i	$0.278804\pi$
$727$			41.4212i			1.53623i	−0.640315	+	0.768113i	$0.721196\pi$
$728$		0			0
$729$		−	23.6624i		−	0.876384i
$730$		0			0
$731$	3.05223	+	3.05223i	0.112891	+	0.112891i
$732$		0			0
$733$	24.4478	−	24.4478i	0.902998	−	0.902998i	−0.0926961	−	0.995694i	$-0.529549\pi$
$733$	24.4478	−	24.4478i	0.902998	−	0.902998i	0.995694	+	0.0926961i	$0.0295485\pi$
$734$		0			0
$735$	−37.7748			−1.39334
$736$		0			0
$737$	−53.5003			−1.97071
$738$		0			0
$739$	28.9582	−	28.9582i	1.06525	−	1.06525i	0.0675288	−	0.997717i	$-0.478489\pi$
$739$	28.9582	−	28.9582i	1.06525	−	1.06525i	0.997717	−	0.0675288i	$-0.0215114\pi$
$740$		0			0
$741$	−19.6533	−	19.6533i	−0.721981	−	0.721981i
$742$		0			0
$743$			27.0393i			0.991975i	0.868330	+	0.495987i	$0.165194\pi$
$743$			27.0393i			0.991975i	−0.868330	+	0.495987i	$0.834806\pi$
$744$		0			0
$745$			5.18629i			0.190011i
$746$		0			0
$747$	17.1729	+	17.1729i	0.628324	+	0.628324i
$748$		0			0
$749$	4.69465	−	4.69465i	0.171539	−	0.171539i
$750$		0			0
$751$	−8.86802			−0.323598			−0.161799	−	0.986824i	$-0.551730\pi$
$751$	−8.86802			−0.323598			−0.161799	+	0.986824i	$0.551730\pi$
$752$		0			0
$753$	−48.1297			−1.75394
$754$		0			0
$755$	−53.3385	+	53.3385i	−1.94119	+	1.94119i
$756$		0			0
$757$	−4.85766	−	4.85766i	−0.176555	−	0.176555i	0.613297	−	0.789852i	$-0.289843\pi$
$757$	−4.85766	−	4.85766i	−0.176555	−	0.176555i	−0.789852	+	0.613297i	$0.789843\pi$
$758$		0			0
$759$			11.4482i			0.415544i
$760$		0			0
$761$		−	16.9685i		−	0.615109i	−0.951530	−	0.307554i	$-0.900489\pi$
$761$		−	16.9685i		−	0.615109i	0.951530	−	0.307554i	$-0.0995106\pi$
$762$		0			0
$763$	6.09770	+	6.09770i	0.220752	+	0.220752i
$764$		0			0
$765$	5.98227	−	5.98227i	0.216289	−	0.216289i
$766$		0			0
$767$	−28.5544			−1.03104
$768$		0			0
$769$	−31.9813			−1.15328			−0.576638	−	0.817000i	$-0.695636\pi$
$769$	−31.9813			−1.15328			−0.576638	+	0.817000i	$0.695636\pi$
$770$		0			0
$771$	14.5145	−	14.5145i	0.522726	−	0.522726i
$772$		0			0
$773$	21.7694	+	21.7694i	0.782991	+	0.782991i	0.980334	−	0.197344i	$-0.0632314\pi$
$773$	21.7694	+	21.7694i	0.782991	+	0.782991i	−0.197344	+	0.980334i	$0.563231\pi$
$774$		0			0
$775$		−	92.5731i		−	3.32532i
$776$		0			0
$777$			21.5698i			0.773813i
$778$		0			0
$779$	2.92476	+	2.92476i	0.104791	+	0.104791i
$780$		0			0
$781$	−9.69020	+	9.69020i	−0.346743	+	0.346743i
$782$		0			0
$783$	−4.38124			−0.156573
$784$		0			0
$785$	−64.8620			−2.31502
$786$		0			0
$787$	3.18657	−	3.18657i	0.113589	−	0.113589i	−0.648028	−	0.761617i	$-0.724406\pi$
$787$	3.18657	−	3.18657i	0.113589	−	0.113589i	0.761617	+	0.648028i	$0.224406\pi$
$788$		0			0
$789$	9.36582	+	9.36582i	0.333432	+	0.333432i
$790$		0			0
$791$			21.4894i			0.764074i
$792$		0			0
$793$		−	1.33510i		−	0.0474108i
$794$		0			0
$795$	13.2607	+	13.2607i	0.470308	+	0.470308i
$796$		0			0
$797$	26.7398	−	26.7398i	0.947171	−	0.947171i	−0.0515023	−	0.998673i	$-0.516401\pi$
$797$	26.7398	−	26.7398i	0.947171	−	0.947171i	0.998673	+	0.0515023i	$0.0164009\pi$
$798$		0			0
$799$	1.77783			0.0628949
$800$		0			0
$801$	−14.0436			−0.496208
$802$		0			0
$803$	24.4335	−	24.4335i	0.862240	−	0.862240i
$804$		0			0
$805$	−4.34071	−	4.34071i	−0.152990	−	0.152990i
$806$		0			0
$807$			3.97902i			0.140068i
$808$		0			0
$809$		−	9.52410i		−	0.334849i	−0.985885	−	0.167425i	$-0.946455\pi$
$809$		−	9.52410i		−	0.334849i	0.985885	−	0.167425i	$-0.0535451\pi$
$810$		0			0
$811$	−25.8962	−	25.8962i	−0.909340	−	0.909340i	0.0868788	−	0.996219i	$-0.472311\pi$
$811$	−25.8962	−	25.8962i	−0.909340	−	0.909340i	−0.996219	+	0.0868788i	$0.972311\pi$
$812$		0			0
$813$	0.729954	−	0.729954i	0.0256006	−	0.0256006i
$814$		0			0
$815$	−26.6849			−0.934732
$816$		0			0
$817$	−28.7084			−1.00438
$818$		0			0
$819$	7.06642	−	7.06642i	0.246921	−	0.246921i
$820$		0			0
$821$	−6.06470	−	6.06470i	−0.211659	−	0.211659i	0.593313	−	0.804972i	$-0.297820\pi$
$821$	−6.06470	−	6.06470i	−0.211659	−	0.211659i	−0.804972	+	0.593313i	$0.797820\pi$
$822$		0			0
$823$		−	29.8792i		−	1.04152i	−0.853703	−	0.520761i	$-0.825648\pi$
$823$		−	29.8792i		−	1.04152i	0.853703	−	0.520761i	$-0.174352\pi$
$824$		0			0
$825$		−	98.9932i		−	3.44650i
$826$		0			0
$827$	−18.3697	−	18.3697i	−0.638777	−	0.638777i	0.311477	−	0.950254i	$-0.399176\pi$
$827$	−18.3697	−	18.3697i	−0.638777	−	0.638777i	−0.950254	+	0.311477i	$0.899176\pi$
$828$		0			0
$829$	30.7996	−	30.7996i	1.06971	−	1.06971i	0.0723338	−	0.997380i	$-0.476955\pi$
$829$	30.7996	−	30.7996i	1.06971	−	1.06971i	0.997380	−	0.0723338i	$-0.0230447\pi$
$830$		0			0
$831$	48.5223			1.68322
$832$		0			0
$833$	−3.44268			−0.119282
$834$		0			0
$835$	−55.0472	+	55.0472i	−1.90499	+	1.90499i
$836$		0			0
$837$	−3.29322	−	3.29322i	−0.113830	−	0.113830i
$838$		0			0
$839$			22.5005i			0.776802i	0.921490	+	0.388401i	$0.126972\pi$
$839$			22.5005i			0.776802i	−0.921490	+	0.388401i	$0.873028\pi$
$840$		0			0
$841$		−	72.4280i		−	2.49752i
$842$		0			0
$843$	−43.8298	−	43.8298i	−1.50958	−	1.50958i
$844$		0			0
$845$	22.0755	−	22.0755i	0.759420	−	0.759420i
$846$		0			0
$847$	−19.1437			−0.657787
$848$		0			0
$849$	−15.3715			−0.527548
$850$		0			0
$851$	3.80475	−	3.80475i	0.130425	−	0.130425i
$852$		0			0
$853$	−7.30463	−	7.30463i	−0.250106	−	0.250106i	0.570908	−	0.821014i	$-0.306591\pi$
$853$	−7.30463	−	7.30463i	−0.250106	−	0.250106i	−0.821014	+	0.570908i	$0.806591\pi$
$854$		0			0
$855$			56.2676i			1.92431i
$856$		0			0
$857$			23.4068i			0.799561i	0.916611	+	0.399780i	$0.130914\pi$
$857$			23.4068i			0.799561i	−0.916611	+	0.399780i	$0.869086\pi$
$858$		0			0
$859$	26.9063	+	26.9063i	0.918030	+	0.918030i	0.996886	−	0.0788558i	$-0.0251267\pi$
$859$	26.9063	+	26.9063i	0.918030	+	0.918030i	−0.0788558	+	0.996886i	$0.525127\pi$
$860$		0			0
$861$	−2.17048	+	2.17048i	−0.0739697	+	0.0739697i
$862$		0			0
$863$	−31.7122			−1.07950			−0.539748	−	0.841827i	$-0.681481\pi$
$863$	−31.7122			−1.07950			−0.539748	+	0.841827i	$0.681481\pi$
$864$		0			0
$865$	−3.88110			−0.131961
$866$		0			0
$867$	−27.8737	+	27.8737i	−0.946641	+	0.946641i
$868$		0			0
$869$	4.57055	+	4.57055i	0.155045	+	0.155045i
$870$		0			0
$871$		−	24.0451i		−	0.814738i
$872$		0			0
$873$			21.0381i			0.712033i
$874$		0			0
$875$	15.8307	+	15.8307i	0.535176	+	0.535176i
$876$		0			0
$877$	−10.7834	+	10.7834i	−0.364128	+	0.364128i	−0.865330	−	0.501202i	$-0.832891\pi$
$877$	−10.7834	+	10.7834i	−0.364128	+	0.364128i	0.501202	+	0.865330i	$0.332891\pi$
$878$		0			0
$879$	48.4446			1.63400
$880$		0			0
$881$	−36.4108			−1.22671			−0.613355	−	0.789807i	$-0.710181\pi$
$881$	−36.4108			−1.22671			−0.613355	+	0.789807i	$0.710181\pi$
$882$		0			0
$883$	−38.0383	+	38.0383i	−1.28009	+	1.28009i	−0.339478	+	0.940614i	$0.610251\pi$
$883$	−38.0383	+	38.0383i	−1.28009	+	1.28009i	−0.940614	+	0.339478i	$0.889749\pi$
$884$		0			0
$885$	84.3659	+	84.3659i	2.83593	+	2.83593i
$886$		0			0
$887$		−	55.8616i		−	1.87565i	−0.347109	−	0.937825i	$-0.612837\pi$
$887$		−	55.8616i		−	1.87565i	0.347109	−	0.937825i	$-0.387163\pi$
$888$		0			0
$889$			26.9420i			0.903605i
$890$		0			0
$891$	−31.9069	−	31.9069i	−1.06892	−	1.06892i
$892$		0			0
$893$	−8.36087	+	8.36087i	−0.279786	+	0.279786i
$894$		0			0
$895$	−30.7107			−1.02655
$896$		0			0
$897$	−5.14528			−0.171796
$898$		0			0
$899$	76.2397	−	76.2397i	2.54274	−	2.54274i
$900$		0			0
$901$	1.20854	+	1.20854i	0.0402623	+	0.0402623i
$902$		0			0
$903$		−	21.3046i		−	0.708974i
$904$		0			0
$905$			65.4389i			2.17526i
$906$		0			0
$907$	3.28341	+	3.28341i	0.109024	+	0.109024i	0.759514	−	0.650491i	$-0.225437\pi$
$907$	3.28341	+	3.28341i	0.109024	+	0.109024i	−0.650491	+	0.759514i	$0.725437\pi$
$908$		0			0
$909$	−13.4827	+	13.4827i	−0.447194	+	0.447194i
$910$		0			0
$911$	7.38623			0.244717			0.122358	−	0.992486i	$-0.460954\pi$
$911$	7.38623			0.244717			0.122358	+	0.992486i	$0.460954\pi$
$912$		0			0
$913$	40.8742			1.35274
$914$		0			0
$915$	−3.94464	+	3.94464i	−0.130406	+	0.130406i
$916$		0			0
$917$	−7.19083	−	7.19083i	−0.237462	−	0.237462i
$918$		0			0
$919$			34.3845i			1.13424i	0.823635	+	0.567120i	$0.191942\pi$
$919$			34.3845i			1.13424i	−0.823635	+	0.567120i	$0.808058\pi$
$920$		0			0
$921$			30.3657i			1.00058i
$922$		0			0
$923$	−4.35515	−	4.35515i	−0.143352	−	0.143352i
$924$		0			0
$925$	−32.8998	+	32.8998i	−1.08174	+	1.08174i
$926$		0			0
$927$	−7.42532			−0.243880
$928$		0			0
$929$	16.1031			0.528325			0.264162	−	0.964478i	$-0.414905\pi$
$929$	16.1031			0.528325			0.264162	+	0.964478i	$0.414905\pi$
$930$		0			0
$931$	16.1905	−	16.1905i	0.530621	−	0.530621i
$932$		0			0
$933$	−7.71614	−	7.71614i	−0.252615	−	0.252615i
$934$		0			0
$935$		−	14.2387i		−	0.465657i
$936$		0			0
$937$		−	4.91883i		−	0.160691i	−0.996767	−	0.0803456i	$-0.974398\pi$
$937$		−	4.91883i		−	0.160691i	0.996767	−	0.0803456i	$-0.0256024\pi$
$938$		0			0
$939$	−17.2230	−	17.2230i	−0.562053	−	0.562053i
$940$		0			0
$941$	−3.21178	+	3.21178i	−0.104701	+	0.104701i	−0.757517	−	0.652816i	$-0.773588\pi$
$941$	−3.21178	+	3.21178i	−0.104701	+	0.104701i	0.652816	+	0.757517i	$0.273588\pi$
$942$		0			0
$943$	0.765711			0.0249350
$944$		0			0
$945$	2.67051			0.0868716
$946$		0			0
$947$	12.9780	−	12.9780i	0.421727	−	0.421727i	−0.464071	−	0.885798i	$-0.653612\pi$
$947$	12.9780	−	12.9780i	0.421727	−	0.421727i	0.885798	+	0.464071i	$0.153612\pi$
$948$		0			0
$949$	10.9814	+	10.9814i	0.356471	+	0.356471i
$950$		0			0
$951$		−	47.2959i		−	1.53367i
$952$		0			0
$953$		−	55.7029i		−	1.80439i	−0.431325	−	0.902197i	$-0.641954\pi$
$953$		−	55.7029i		−	1.80439i	0.431325	−	0.902197i	$-0.358046\pi$
$954$		0			0
$955$	4.29436	+	4.29436i	0.138962	+	0.138962i
$956$		0			0
$957$	81.5271	−	81.5271i	2.63540	−	2.63540i
$958$		0			0
$959$	19.5391			0.630949
$960$		0			0
$961$	83.6132			2.69720
$962$		0			0
$963$	−7.96609	+	7.96609i	−0.256704	+	0.256704i
$964$		0			0
$965$	49.7459	+	49.7459i	1.60138	+	1.60138i
$966$		0			0
$967$		−	0.819088i		−	0.0263401i	−0.999913	−	0.0131701i	$-0.995808\pi$
$967$		−	0.819088i		−	0.0263401i	0.999913	−	0.0131701i	$-0.00419228\pi$
$968$		0			0
$969$			10.5841i			0.340010i
$970$		0			0
$971$	−16.2383	−	16.2383i	−0.521112	−	0.521112i	0.396795	−	0.917907i	$-0.370122\pi$
$971$	−16.2383	−	16.2383i	−0.521112	−	0.521112i	−0.917907	+	0.396795i	$0.870122\pi$
$972$		0			0
$973$	−13.0694	+	13.0694i	−0.418984	+	0.418984i
$974$		0			0
$975$	44.4914			1.42487
$976$		0			0
$977$	−22.3995			−0.716622			−0.358311	−	0.933602i	$-0.616647\pi$
$977$	−22.3995			−0.716622			−0.358311	+	0.933602i	$0.616647\pi$
$978$		0			0
$979$	−16.7130	+	16.7130i	−0.534151	+	0.534151i
$980$		0			0
$981$	−10.3469	−	10.3469i	−0.330350	−	0.330350i
$982$		0			0
$983$			34.2716i			1.09309i	0.837429	+	0.546546i	$0.184058\pi$
$983$			34.2716i			1.09309i	−0.837429	+	0.546546i	$0.815942\pi$
$984$		0			0
$985$		−	65.6886i		−	2.09301i
$986$		0			0
$987$	−6.20463	−	6.20463i	−0.197496	−	0.197496i
$988$		0			0
$989$	−3.75797	+	3.75797i	−0.119497	+	0.119497i
$990$		0			0
$991$	−19.8594			−0.630856			−0.315428	−	0.948950i	$-0.602148\pi$
$991$	−19.8594			−0.630856			−0.315428	+	0.948950i	$0.602148\pi$
$992$		0			0
$993$	−25.3432			−0.804241
$994$		0			0
$995$	−41.3022	+	41.3022i	−1.30937	+	1.30937i
$996$		0			0
$997$	−21.4778	−	21.4778i	−0.680209	−	0.680209i	0.279838	−	0.960047i	$-0.409719\pi$
$997$	−21.4778	−	21.4778i	−0.680209	−	0.680209i	−0.960047	+	0.279838i	$0.909719\pi$
$998$		0			0
$999$			2.34077i			0.0740588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1472.2.j.c.369.6		12
4.3	odd	2		368.2.j.c.277.1	yes	12
16.3	odd	4		368.2.j.c.93.1	✓	12
16.13	even	4	inner	1472.2.j.c.1105.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
368.2.j.c.93.1	✓	12	16.3	odd	4
368.2.j.c.277.1	yes	12	4.3	odd	2
1472.2.j.c.369.6		12	1.1	even	1	trivial
1472.2.j.c.1105.6		12	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 1472 = 2^{6} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1472.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70582 - 1.70582i) q^{3} +(-2.61219 - 2.61219i) q^{5} +1.66171i q^{7} -2.81967i q^{9} +(-3.35563 - 3.35563i) q^{11} +(1.50815 - 1.50815i) q^{13} -8.91186 q^{15} -0.812201 q^{17} +(3.81967 - 3.81967i) q^{19} +(2.83459 + 2.83459i) q^{21} -1.00000i q^{23} +8.64704i q^{25} +(0.307612 + 0.307612i) q^{27} +(-7.12138 + 7.12138i) q^{29} -10.7058 q^{31} -11.4482 q^{33} +(4.34071 - 4.34071i) q^{35} +(3.80475 + 3.80475i) q^{37} -5.14528i q^{39} +0.765711i q^{41} +(-3.75797 - 3.75797i) q^{43} +(-7.36550 + 7.36550i) q^{45} -2.18890 q^{47} +4.23871 q^{49} +(-1.38547 + 1.38547i) q^{51} +(-1.48798 - 1.48798i) q^{53} +17.5311i q^{55} -13.0314i q^{57} +(-9.46671 - 9.46671i) q^{59} +(0.442628 - 0.442628i) q^{61} +4.68548 q^{63} -7.87914 q^{65} +(7.97172 - 7.97172i) q^{67} +(-1.70582 - 1.70582i) q^{69} -2.88774i q^{71} +7.28135i q^{73} +(14.7503 + 14.7503i) q^{75} +(5.57609 - 5.57609i) q^{77} -1.36206 q^{79} +9.50847 q^{81} +(-6.09040 + 6.09040i) q^{83} +(2.12162 + 2.12162i) q^{85} +24.2956i q^{87} -4.98060i q^{89} +(2.50612 + 2.50612i) q^{91} +(-18.2621 + 18.2621i) q^{93} -19.9554 q^{95} -7.46120 q^{97} +(-9.46176 + 9.46176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 4 q^{5} + 4 q^{11} + 18 q^{13} - 8 q^{17} + 8 q^{19} + 8 q^{21} - 14 q^{27} + 2 q^{29} - 20 q^{31} - 36 q^{33} - 4 q^{35} - 4 q^{37} - 20 q^{43} - 20 q^{45} + 16 q^{47} + 52 q^{49} + 4 q^{51}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q - 2 * q^3 - 4 * q^5 + 4 * q^11 + 18 * q^13 - 8 * q^17 + 8 * q^19 + 8 * q^21 - 14 * q^27 + 2 * q^29 - 20 * q^31 - 36 * q^33 - 4 * q^35 - 4 * q^37 - 20 * q^43 - 20 * q^45 + 16 * q^47 + 52 * q^49 + 4 * q^51 - 16 * q^53 - 8 * q^59 + 12 * q^61 + 4 * q^63 - 52 * q^65 + 4 * q^67 + 2 * q^69 + 46 * q^75 - 12 * q^77 + 4 * q^79 + 48 * q^81 - 28 * q^83 - 8 * q^85 - 14 * q^93 - 48 * q^95 + 36 * q^97 - 36 * q^99

Introduction

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