LMFDB - Embedded newform 416.2.w.d.225.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(225,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("416.225");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.w (of order $6$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.18092737797525504.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 12x^{10} + 108x^{8} - 430x^{6} + 1284x^{4} - 36x^{2} + 1 $ x^12 - 12x^10 + 108x^8 - 430x^6 + 1284x^4 - 36*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			225.3
Root			$2.04509 - 1.18073i$ of defining polynomial
Character	$\chi$	$=$	416.225
Dual form			416.2.w.d.257.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.515266 + 0.892467i) q^{3} +0.701519i q^{5} +(-2.54439 + 1.46900i) q^{7} +(0.969002 + 1.67836i) q^{9} +(-2.54439 - 1.46900i) q^{11} +(-3.33047 - 1.38129i) q^{13} +(-0.626082 - 0.361469i) q^{15} +(-0.500000 - 0.866025i) q^{17} +(-1.54580 + 0.892467i) q^{19} -3.02771i q^{21} +(-2.94884 + 5.10753i) q^{23} +4.50787 q^{25} -5.08877 q^{27} +(-2.86147 + 4.95621i) q^{29} +0.722938i q^{31} +(2.62207 - 1.51385i) q^{33} +(-1.03053 - 1.78493i) q^{35} +(-6.79947 - 3.92568i) q^{37} +(2.94884 - 2.26060i) q^{39} +(3.28493 + 1.89656i) q^{41} +(3.57492 + 6.19194i) q^{43} +(-1.17740 + 0.679773i) q^{45} -5.15307i q^{47} +(0.815932 - 1.41324i) q^{49} +1.03053 q^{51} -3.21507 q^{53} +(1.03053 - 1.78493i) q^{55} -1.83943i q^{57} +(5.63598 - 3.25394i) q^{59} +(3.07653 + 5.32871i) q^{61} +(-4.93103 - 2.84693i) q^{63} +(0.969002 - 2.33639i) q^{65} +(10.4712 + 6.04554i) q^{67} +(-3.03887 - 5.26348i) q^{69} +(-1.91830 + 1.10753i) q^{71} +10.9430i q^{73} +(-2.32275 + 4.02313i) q^{75} +8.63186 q^{77} +14.2997 q^{79} +(-0.284934 + 0.493520i) q^{81} -13.8760i q^{83} +(0.607533 - 0.350759i) q^{85} +(-2.94884 - 5.10753i) q^{87} +(6.83714 + 3.94742i) q^{89} +(10.5031 - 1.37793i) q^{91} +(-0.645198 - 0.372505i) q^{93} +(-0.626082 - 1.08441i) q^{95} +(-1.59299 + 0.919716i) q^{97} -5.69386i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{9} + 12 q^{13} - 6 q^{17} - 12 q^{25} - 6 q^{29} - 30 q^{33} - 6 q^{37} + 30 q^{41} + 24 q^{49} - 48 q^{53} + 18 q^{61} - 12 q^{65} + 6 q^{69} + 132 q^{77} + 6 q^{81} + 12 q^{85} + 30 q^{89}+ \cdots - 90 q^{97}+O(q^{100}) $ 12 * q - 12 * q^9 + 12 * q^13 - 6 * q^17 - 12 * q^25 - 6 * q^29 - 30 * q^33 - 6 * q^37 + 30 * q^41 + 24 * q^49 - 48 * q^53 + 18 * q^61 - 12 * q^65 + 6 * q^69 + 132 * q^77 + 6 * q^81 + 12 * q^85 + 30 * q^89 - 36 * q^93 - 90 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.515266	+	0.892467i	−0.297489	+	0.515266i	−0.975561	−	0.219730i	$-0.929482\pi$
$3$	−0.515266	+	0.892467i	−0.297489	+	0.515266i	0.678072	+	0.734996i	$0.262816\pi$
$4$		0			0
$5$			0.701519i			0.313729i	0.987620	+	0.156864i	$0.0501385\pi$
$5$			0.701519i			0.313729i	−0.987620	+	0.156864i	$0.949861\pi$
$6$		0			0
$7$	−2.54439	+	1.46900i	−0.961687	+	0.555230i	−0.896692	−	0.442655i	$-0.854037\pi$
$7$	−2.54439	+	1.46900i	−0.961687	+	0.555230i	−0.0649954	+	0.997886i	$0.520703\pi$
$8$		0			0
$9$	0.969002	+	1.67836i	0.323001	+	0.559453i
$10$		0			0
$11$	−2.54439	−	1.46900i	−0.767161	−	0.442921i	0.0646998	−	0.997905i	$-0.479391\pi$
$11$	−2.54439	−	1.46900i	−0.767161	−	0.442921i	−0.831861	+	0.554984i	$0.812724\pi$
$12$		0			0
$13$	−3.33047	−	1.38129i	−0.923706	−	0.383101i
$13$	−3.33047	−	1.38129i	−0.923706	−	0.383101i
$14$		0			0
$15$	−0.626082	−	0.361469i	−0.161654	−	0.0933308i
$16$		0			0
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	0.799000	−	0.601331i	$-0.205363\pi$
$17$	−0.500000	−	0.866025i	−0.121268	−	0.210042i	−0.920268	+	0.391289i	$0.872029\pi$
$18$		0			0
$19$	−1.54580	+	0.892467i	−0.354630	+	0.204746i	−0.666723	−	0.745306i	$-0.732303\pi$
$19$	−1.54580	+	0.892467i	−0.354630	+	0.204746i	0.312092	+	0.950052i	$0.398970\pi$
$20$		0			0
$21$		−	3.02771i		−	0.660700i
$22$		0			0
$23$	−2.94884	+	5.10753i	−0.614875	+	1.06499i	0.375532	+	0.926810i	$0.377460\pi$
$23$	−2.94884	+	5.10753i	−0.614875	+	1.06499i	−0.990406	+	0.138185i	$0.955873\pi$
$24$		0			0
$25$	4.50787			0.901574
$26$		0			0
$27$	−5.08877			−0.979334
$28$		0			0
$29$	−2.86147	+	4.95621i	−0.531361	+	0.920345i	0.467969	+	0.883745i	$0.344986\pi$
$29$	−2.86147	+	4.95621i	−0.531361	+	0.920345i	−0.999330	+	0.0365999i	$0.988347\pi$
$30$		0			0
$31$			0.722938i			0.129843i	0.997890	+	0.0649217i	$0.0206798\pi$
$31$			0.722938i			0.129843i	−0.997890	+	0.0649217i	$0.979320\pi$
$32$		0			0
$33$	2.62207	−	1.51385i	0.456444	−	0.263528i
$34$		0			0
$35$	−1.03053	−	1.78493i	−0.174192	−	0.301709i
$36$		0			0
$37$	−6.79947	−	3.92568i	−1.11783	−	0.645377i	−0.176981	−	0.984214i	$-0.556633\pi$
$37$	−6.79947	−	3.92568i	−1.11783	−	0.645377i	−0.940845	+	0.338837i	$0.889967\pi$
$38$		0			0
$39$	2.94884	−	2.26060i	0.472192	−	0.361986i
$40$		0			0
$41$	3.28493	+	1.89656i	0.513021	+	0.296193i	0.734074	−	0.679069i	$-0.237616\pi$
$41$	3.28493	+	1.89656i	0.513021	+	0.296193i	−0.221054	+	0.975262i	$0.570950\pi$
$42$		0			0
$43$	3.57492	+	6.19194i	0.545170	+	0.944262i	0.998596	+	0.0529681i	$0.0168682\pi$
$43$	3.57492	+	6.19194i	0.545170	+	0.944262i	−0.453426	+	0.891294i	$0.649798\pi$
$44$		0			0
$45$	−1.17740	+	0.679773i	−0.175517	+	0.101335i
$46$		0			0
$47$		−	5.15307i		−	0.751652i	−0.926690	−	0.375826i	$-0.877359\pi$
$47$		−	5.15307i		−	0.751652i	0.926690	−	0.375826i	$-0.122641\pi$
$48$		0			0
$49$	0.815932	−	1.41324i	0.116562	−	0.201891i
$50$		0			0
$51$	1.03053			0.144303
$52$		0			0
$53$	−3.21507			−0.441623			−0.220812	−	0.975316i	$-0.570871\pi$
$53$	−3.21507			−0.441623			−0.220812	+	0.975316i	$0.570871\pi$
$54$		0			0
$55$	1.03053	−	1.78493i	0.138957	−	0.240680i
$56$		0			0
$57$		−	1.83943i		−	0.243639i
$58$		0			0
$59$	5.63598	−	3.25394i	0.733742	−	0.423626i	−0.0860473	−	0.996291i	$-0.527424\pi$
$59$	5.63598	−	3.25394i	0.733742	−	0.423626i	0.819790	+	0.572665i	$0.194090\pi$
$60$		0			0
$61$	3.07653	+	5.32871i	0.393910	+	0.682272i	0.992961	−	0.118439i	$-0.0377889\pi$
$61$	3.07653	+	5.32871i	0.393910	+	0.682272i	−0.599051	+	0.800711i	$0.704456\pi$
$62$		0			0
$63$	−4.93103	−	2.84693i	−0.621251	−	0.358680i
$64$		0			0
$65$	0.969002	−	2.33639i	0.120190	−	0.289793i
$66$		0			0
$67$	10.4712	+	6.04554i	1.27926	+	0.738580i	0.976712	−	0.214555i	$-0.0688301\pi$
$67$	10.4712	+	6.04554i	1.27926	+	0.738580i	0.302546	+	0.953135i	$0.402163\pi$
$68$		0			0
$69$	−3.03887	−	5.26348i	−0.365837	−	0.633648i
$70$		0			0
$71$	−1.91830	+	1.10753i	−0.227661	+	0.131440i	−0.609492	−	0.792792i	$-0.708627\pi$
$71$	−1.91830	+	1.10753i	−0.227661	+	0.131440i	0.381832	+	0.924232i	$0.375293\pi$
$72$		0			0
$73$			10.9430i			1.28078i	0.768052	+	0.640388i	$0.221226\pi$
$73$			10.9430i			1.28078i	−0.768052	+	0.640388i	$0.778774\pi$
$74$		0			0
$75$	−2.32275	+	4.02313i	−0.268208	+	0.464551i
$76$		0			0
$77$	8.63186			0.983692
$78$		0			0
$79$	14.2997			1.60884			0.804419	−	0.594062i	$-0.202477\pi$
$79$	14.2997			1.60884			0.804419	+	0.594062i	$0.202477\pi$
$80$		0			0
$81$	−0.284934	+	0.493520i	−0.0316593	+	0.0548356i
$82$		0			0
$83$		−	13.8760i		−	1.52309i	−0.648112	−	0.761545i	$-0.724441\pi$
$83$		−	13.8760i		−	1.52309i	0.648112	−	0.761545i	$-0.275559\pi$
$84$		0			0
$85$	0.607533	−	0.350759i	0.0658962	−	0.0380452i
$86$		0			0
$87$	−2.94884	−	5.10753i	−0.316148	−	0.547585i
$88$		0			0
$89$	6.83714	+	3.94742i	0.724735	+	0.418426i	0.816493	−	0.577355i	$-0.195915\pi$
$89$	6.83714	+	3.94742i	0.724735	+	0.418426i	−0.0917579	+	0.995781i	$0.529249\pi$
$90$		0			0
$91$	10.5031	−	1.37793i	1.10103	−	0.144446i
$92$		0			0
$93$	−0.645198	−	0.372505i	−0.0669039	−	0.0386270i
$94$		0			0
$95$	−0.626082	−	1.08441i	−0.0642347	−	0.111258i
$96$		0			0
$97$	−1.59299	+	0.919716i	−0.161744	+	0.0933830i	−0.578687	−	0.815550i	$-0.696435\pi$
$97$	−1.59299	+	0.919716i	−0.161744	+	0.0933830i	0.416943	+	0.908933i	$0.363101\pi$
$98$		0			0
$99$		−	5.69386i		−	0.572255i
$100$		0			0
$101$	0.861469	−	1.49211i	0.0857193	−	0.148470i	−0.819978	−	0.572395i	$-0.806014\pi$
$101$	0.861469	−	1.49211i	0.0857193	−	0.148470i	0.905698	+	0.423925i	$0.139348\pi$
$102$		0			0
$103$	17.1696			1.69177			0.845887	−	0.533362i	$-0.179072\pi$
$103$	17.1696			1.69177			0.845887	+	0.533362i	$0.179072\pi$
$104$		0			0
$105$	2.12399			0.207280
$106$		0			0
$107$	−2.57633	+	4.46234i	−0.249063	+	0.431390i	−0.963266	−	0.268549i	$-0.913456\pi$
$107$	−2.57633	+	4.46234i	−0.249063	+	0.431390i	0.714203	+	0.699939i	$0.246789\pi$
$108$		0			0
$109$			4.86714i			0.466187i	0.972454	+	0.233094i	$0.0748849\pi$
$109$			4.86714i			0.466187i	−0.972454	+	0.233094i	$0.925115\pi$
$110$		0			0
$111$	7.00707	−	4.04554i	0.665082	−	0.383985i
$112$		0			0
$113$	−10.3760	−	17.9718i	−0.976093	−	1.69064i	−0.676281	−	0.736644i	$-0.736410\pi$
$113$	−10.3760	−	17.9718i	−0.976093	−	1.69064i	−0.299811	−	0.953998i	$-0.596924\pi$
$114$		0			0
$115$	−3.58303	−	2.06866i	−0.334119	−	0.192904i
$116$		0			0
$117$	−0.908927	−	6.92820i	−0.0840303	−	0.640513i
$118$		0			0
$119$	2.54439	+	1.46900i	0.233243	+	0.134663i
$120$		0			0
$121$	−1.18407	−	2.05087i	−0.107643	−	0.186442i
$122$		0			0
$123$	−3.38523	+	1.95446i	−0.305236	+	0.176228i
$124$		0			0
$125$			6.66995i			0.596578i
$126$		0			0
$127$	−10.0987	+	17.4914i	−0.896112	+	1.55211i	−0.0636900	+	0.997970i	$0.520287\pi$
$127$	−10.0987	+	17.4914i	−0.896112	+	1.55211i	−0.832422	+	0.554142i	$0.813046\pi$
$128$		0			0
$129$	−7.36814			−0.648728
$130$		0			0
$131$	1.99717			0.174494			0.0872470	−	0.996187i	$-0.472193\pi$
$131$	1.99717			0.174494			0.0872470	+	0.996187i	$0.472193\pi$
$132$		0			0
$133$	2.62207	−	4.54156i	0.227362	−	0.393803i
$134$		0			0
$135$		−	3.56987i		−	0.307245i
$136$		0			0
$137$	−19.8839	+	11.4800i	−1.69879	+	0.980799i	−0.751888	+	0.659291i	$0.770856\pi$
$137$	−19.8839	+	11.4800i	−1.69879	+	0.980799i	−0.946907	+	0.321508i	$0.895810\pi$
$138$		0			0
$139$	−4.38382	−	7.59299i	−0.371831	−	0.644029i	0.618017	−	0.786165i	$-0.287936\pi$
$139$	−4.38382	−	7.59299i	−0.371831	−	0.644029i	−0.989847	+	0.142136i	$0.954603\pi$
$140$		0			0
$141$	4.59894	+	2.65520i	0.387301	+	0.223608i
$142$		0			0
$143$	6.44488	+	8.40701i	0.538948	+	0.703029i
$144$		0			0
$145$	−3.47687	−	2.00737i	−0.288739	−	0.166703i
$146$		0			0
$147$	0.840844	+	1.45639i	0.0693517	+	0.120121i
$148$		0			0
$149$	0.985462	−	0.568957i	0.0807322	−	0.0466107i	−0.459090	−	0.888390i	$-0.651825\pi$
$149$	0.985462	−	0.568957i	0.0807322	−	0.0466107i	0.539823	+	0.841779i	$0.318491\pi$
$150$		0			0
$151$			0.722938i			0.0588318i	0.999567	+	0.0294159i	$0.00936473\pi$
$151$			0.722938i			0.0588318i	−0.999567	+	0.0294159i	$0.990635\pi$
$152$		0			0
$153$	0.969002	−	1.67836i	0.0783391	−	0.135687i
$154$		0			0
$155$	−0.507154			−0.0407356
$156$		0			0
$157$	4.66094			0.371984			0.185992	−	0.982551i	$-0.440450\pi$
$157$	4.66094			0.371984			0.185992	+	0.982551i	$0.440450\pi$
$158$		0			0
$159$	1.65661	−	2.86934i	0.131378	−	0.227553i
$160$		0			0
$161$		−	17.3274i		−	1.36559i
$162$		0			0
$163$	9.47259	−	5.46900i	0.741950	−	0.428365i	−0.0808276	−	0.996728i	$-0.525756\pi$
$163$	9.47259	−	5.46900i	0.741950	−	0.428365i	0.822778	+	0.568363i	$0.192423\pi$
$164$		0			0
$165$	1.06200	+	1.83943i	0.0826763	+	0.143200i
$166$		0			0
$167$	−20.7446	−	11.9769i	−1.60526	−	0.926798i	−0.990411	−	0.138155i	$-0.955883\pi$
$167$	−20.7446	−	11.9769i	−1.60526	−	0.926798i	−0.614851	−	0.788643i	$-0.710784\pi$
$168$		0			0
$169$	9.18407	+	9.20070i	0.706467	+	0.707746i
$170$		0			0
$171$	−2.99576	−	1.72960i	−0.229092	−	0.132266i
$172$		0			0
$173$	6.12994	+	10.6174i	0.466051	+	0.807224i	0.999248	−	0.0387670i	$-0.0123430\pi$
$173$	6.12994	+	10.6174i	0.466051	+	0.807224i	−0.533197	+	0.845991i	$0.679010\pi$
$174$		0			0
$175$	−11.4698	+	6.62207i	−0.867033	+	0.500582i
$176$		0			0
$177$			6.70657i			0.504097i
$178$		0			0
$179$	−10.5031	+	18.1919i	−0.785040	+	1.35973i	0.143935	+	0.989587i	$0.454024\pi$
$179$	−10.5031	+	18.1919i	−0.785040	+	1.35973i	−0.928975	+	0.370142i	$0.879309\pi$
$180$		0			0
$181$	8.66094			0.643763			0.321881	−	0.946780i	$-0.395685\pi$
$181$	8.66094			0.643763			0.321881	+	0.946780i	$0.395685\pi$
$182$		0			0
$183$	−6.34094			−0.468735
$184$		0			0
$185$	2.75394	−	4.76996i	0.202473	−	0.350694i
$186$		0			0
$187$			2.93800i			0.214848i
$188$		0			0
$189$	12.9478	−	7.47541i	0.941814	−	0.543756i
$190$		0			0
$191$	−8.03761	−	13.9215i	−0.581581	−	1.00733i	−0.995292	−	0.0969195i	$-0.969101\pi$
$191$	−8.03761	−	13.9215i	−0.581581	−	1.00733i	0.413711	−	0.910408i	$-0.364232\pi$
$192$		0			0
$193$	−7.31401	−	4.22275i	−0.526474	−	0.303960i	0.213105	−	0.977029i	$-0.431642\pi$
$193$	−7.31401	−	4.22275i	−0.526474	−	0.303960i	−0.739579	+	0.673069i	$0.764976\pi$
$194$		0			0
$195$	1.58585	+	2.06866i	0.113565	+	0.148140i
$196$		0			0
$197$	6.83714	+	3.94742i	0.487126	+	0.281242i	0.723381	−	0.690449i	$-0.242587\pi$
$197$	6.83714	+	3.94742i	0.487126	+	0.281242i	−0.236255	+	0.971691i	$0.575920\pi$
$198$		0			0
$199$	8.03761	+	13.9215i	0.569771	+	0.986872i	0.996588	+	0.0825342i	$0.0263014\pi$
$199$	8.03761	+	13.9215i	0.569771	+	0.986872i	−0.426817	+	0.904338i	$0.640365\pi$
$200$		0			0
$201$	−10.7909	+	6.23012i	−0.761130	+	0.439439i
$202$		0			0
$203$		−	16.8140i		−	1.18011i
$204$		0			0
$205$	−1.33047	+	2.30444i	−0.0929241	+	0.160949i
$206$		0			0
$207$	−11.4297			−0.794420
$208$		0			0
$209$	5.24414			0.362745
$210$		0			0
$211$	−11.5017	+	19.9215i	−0.791810	+	1.37146i	0.133035	+	0.991111i	$0.457528\pi$
$211$	−11.5017	+	19.9215i	−0.791810	+	1.37146i	−0.924845	+	0.380344i	$0.875806\pi$
$212$		0			0
$213$		−	2.28270i		−	0.156408i
$214$		0			0
$215$	−4.34376	+	2.50787i	−0.296242	+	0.171035i
$216$		0			0
$217$	−1.06200	−	1.83943i	−0.0720930	−	0.124869i
$218$		0			0
$219$	−9.76622	−	5.63853i	−0.659940	−	0.381017i
$220$		0			0
$221$	0.469002	+	3.57492i	0.0315485	+	0.240475i
$222$		0			0
$223$	13.1903	+	7.61540i	0.883286	+	0.509965i	0.871740	−	0.489968i	$-0.162992\pi$
$223$	13.1903	+	7.61540i	0.883286	+	0.509965i	0.0115453	+	0.999933i	$0.496325\pi$
$224$		0			0
$225$	4.36814	+	7.56583i	0.291209	+	0.504389i
$226$		0			0
$227$	−25.5797	+	14.7685i	−1.69779	+	0.980218i	−0.749933	+	0.661513i	$0.769915\pi$
$227$	−25.5797	+	14.7685i	−1.69779	+	0.980218i	−0.947854	+	0.318705i	$0.896752\pi$
$228$		0			0
$229$		−	13.1114i		−	0.866425i	−0.901292	−	0.433213i	$-0.857380\pi$
$229$		−	13.1114i		−	0.866425i	0.901292	−	0.433213i	$-0.142620\pi$
$230$		0			0
$231$	−4.44771	+	7.70365i	−0.292638	+	0.506863i
$232$		0			0
$233$	−25.3219			−1.65889			−0.829446	−	0.558587i	$-0.811344\pi$
$233$	−25.3219			−1.65889			−0.829446	+	0.558587i	$0.811344\pi$
$234$		0			0
$235$	3.61497			0.235815
$236$		0			0
$237$	−7.36814	+	12.7620i	−0.478612	+	0.828980i
$238$		0			0
$239$		−	6.73627i		−	0.435733i	−0.975979	−	0.217867i	$-0.930090\pi$
$239$		−	6.73627i		−	0.435733i	0.975979	−	0.217867i	$-0.0699098\pi$
$240$		0			0
$241$	−18.0989	+	10.4494i	−1.16586	+	0.673107i	−0.952700	−	0.303911i	$-0.901707\pi$
$241$	−18.0989	+	10.4494i	−1.16586	+	0.673107i	−0.213155	+	0.977018i	$0.568374\pi$
$242$		0			0
$243$	−7.92679	−	13.7296i	−0.508504	−	0.880755i
$244$		0			0
$245$	0.991412	+	0.572392i	0.0633390	+	0.0365688i
$246$		0			0
$247$	6.38099	−	0.837137i	0.406013	−	0.0532658i
$248$		0			0
$249$	12.3839	+	7.14984i	0.784796	+	0.453102i
$250$		0			0
$251$	9.44064	+	16.3517i	0.595888	+	1.03211i	0.993421	+	0.114521i	$0.0365332\pi$
$251$	9.44064	+	16.3517i	0.595888	+	1.03211i	−0.397533	+	0.917588i	$0.630133\pi$
$252$		0			0
$253$	15.0059	−	8.66369i	0.943416	−	0.544681i
$254$		0			0
$255$			0.722938i			0.0452721i
$256$		0			0
$257$	10.5911	−	18.3443i	0.660653	−	1.14428i	−0.319791	−	0.947488i	$-0.603613\pi$
$257$	10.5911	−	18.3443i	0.660653	−	1.14428i	0.980444	−	0.196797i	$-0.0630538\pi$
$258$		0			0
$259$	23.0673			1.43333
$260$		0			0
$261$	−11.0911			−0.686520
$262$		0			0
$263$	−0.483321	+	0.837137i	−0.0298029	+	0.0516201i	−0.880542	−	0.473968i	$-0.842821\pi$
$263$	−0.483321	+	0.837137i	−0.0298029	+	0.0516201i	0.850739	+	0.525588i	$0.176155\pi$
$264$		0			0
$265$		−	2.25543i		−	0.138550i
$266$		0			0
$267$	−7.04589	+	4.06795i	−0.431201	+	0.248954i
$268$		0			0
$269$	7.31593	+	12.6716i	0.446060	+	0.772599i	0.998125	−	0.0612019i	$-0.0194934\pi$
$269$	7.31593	+	12.6716i	0.446060	+	0.772599i	−0.552065	+	0.833801i	$0.686160\pi$
$270$		0			0
$271$	−19.4924	−	11.2539i	−1.18408	−	0.683628i	−0.227124	−	0.973866i	$-0.572932\pi$
$271$	−19.4924	−	11.2539i	−1.18408	−	0.683628i	−0.956954	+	0.290238i	$0.906266\pi$
$272$		0			0
$273$	−4.18215	+	10.0837i	−0.253115	+	0.610293i
$274$		0			0
$275$	−11.4698	−	6.62207i	−0.691653	−	0.399326i
$276$		0			0
$277$	−8.16761	−	14.1467i	−0.490744	−	0.849994i	0.509199	−	0.860649i	$-0.329942\pi$
$277$	−8.16761	−	14.1467i	−0.490744	−	0.849994i	−0.999943	+	0.0106552i	$0.996608\pi$
$278$		0			0
$279$	−1.21335	+	0.700528i	−0.0726413	+	0.0419395i
$280$		0			0
$281$		−	16.2534i		−	0.969594i	−0.874627	−	0.484797i	$-0.838894\pi$
$281$		−	16.2534i		−	0.969594i	0.874627	−	0.484797i	$-0.161106\pi$
$282$		0			0
$283$	−3.57492	+	6.19194i	−0.212507	+	0.368073i	−0.952498	−	0.304544i	$-0.901496\pi$
$283$	−3.57492	+	6.19194i	−0.212507	+	0.368073i	0.739992	+	0.672616i	$0.234829\pi$
$284$		0			0
$285$	1.29040			0.0764365
$286$		0			0
$287$	−11.1442			−0.657820
$288$		0			0
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$		0			0
$291$		−	1.89559i		−	0.111122i
$292$		0			0
$293$	15.2296	−	8.79282i	0.889723	−	0.513682i	0.0158711	−	0.999874i	$-0.494948\pi$
$293$	15.2296	−	8.79282i	0.889723	−	0.513682i	0.873852	+	0.486192i	$0.161615\pi$
$294$		0			0
$295$	2.28270	+	3.95375i	0.132904	+	0.230196i
$296$		0			0
$297$	12.9478	+	7.47541i	0.751307	+	0.433768i
$298$		0			0
$299$	16.8760	−	12.9373i	0.975964	−	0.748183i
$300$		0			0
$301$	−18.1919	−	10.5031i	−1.04857	−	0.605390i
$302$		0			0
$303$	0.887771	+	1.53766i	0.0510011	+	0.0883365i
$304$		0			0
$305$	−3.73819	+	2.15825i	−0.214048	+	0.123581i
$306$		0			0
$307$			3.27706i			0.187032i	0.995618	+	0.0935159i	$0.0298106\pi$
$307$			3.27706i			0.187032i	−0.995618	+	0.0935159i	$0.970189\pi$
$308$		0			0
$309$	−8.84693	+	15.3233i	−0.503284	+	0.871714i
$310$		0			0
$311$	21.1640			1.20010			0.600050	−	0.799963i	$-0.295147\pi$
$311$	21.1640			1.20010			0.600050	+	0.799963i	$0.295147\pi$
$312$		0			0
$313$	10.1821			0.575529			0.287764	−	0.957701i	$-0.407088\pi$
$313$	10.1821			0.575529			0.287764	+	0.957701i	$0.407088\pi$
$314$		0			0
$315$	1.99717	−	3.45921i	0.112528	−	0.194904i
$316$		0			0
$317$			28.7706i			1.61592i	0.589238	+	0.807959i	$0.299428\pi$
$317$			28.7706i			1.61592i	−0.589238	+	0.807959i	$0.700572\pi$
$318$		0			0
$319$	14.5614	−	8.40701i	0.815280	−	0.470702i
$320$		0			0
$321$	−2.65499	−	4.59858i	−0.148187	−	0.256668i
$322$		0			0
$323$	1.54580	+	0.892467i	0.0860105	+	0.0496582i
$324$		0			0
$325$	−15.0133	−	6.22668i	−0.832790	−	0.345394i
$326$		0			0
$327$	−4.34376	−	2.50787i	−0.240211	−	0.138686i
$328$		0			0
$329$	7.56987	+	13.1114i	0.417340	+	0.722855i
$330$		0			0
$331$	3.79655	−	2.19194i	0.208677	−	0.120480i	−0.392019	−	0.919957i	$-0.628223\pi$
$331$	3.79655	−	2.19194i	0.208677	−	0.120480i	0.600697	+	0.799477i	$0.294890\pi$
$332$		0			0
$333$		−	15.2160i		−	0.833829i
$334$		0			0
$335$	−4.24106	+	7.34573i	−0.231714	+	0.401340i
$336$		0			0
$337$	1.22840			0.0669152			0.0334576	−	0.999440i	$-0.489348\pi$
$337$	1.22840			0.0669152			0.0334576	+	0.999440i	$0.489348\pi$
$338$		0			0
$339$	21.3856			1.16151
$340$		0			0
$341$	1.06200	−	1.83943i	0.0575103	−	0.0996108i
$342$		0			0
$343$		−	15.7716i		−	0.851586i
$344$		0			0
$345$	3.69243	−	2.13182i	0.198794	−	0.114774i
$346$		0			0
$347$	−3.60686	−	6.24727i	−0.193627	−	0.335371i	0.752823	−	0.658223i	$-0.228692\pi$
$347$	−3.60686	−	6.24727i	−0.193627	−	0.335371i	−0.946449	+	0.322852i	$0.895358\pi$
$348$		0			0
$349$	−23.1748	−	13.3800i	−1.24052	−	0.716213i	−0.271317	−	0.962490i	$-0.587459\pi$
$349$	−23.1748	−	13.3800i	−1.24052	−	0.716213i	−0.969199	+	0.246277i	$0.920793\pi$
$350$		0			0
$351$	16.9480	+	7.02908i	0.904617	+	0.375184i
$352$		0			0
$353$	−12.8548	−	7.42172i	−0.684192	−	0.395018i	0.117241	−	0.993104i	$-0.462595\pi$
$353$	−12.8548	−	7.42172i	−0.684192	−	0.395018i	−0.801433	+	0.598085i	$0.795928\pi$
$354$		0			0
$355$	−0.776955	−	1.34573i	−0.0412365	−	0.0714237i
$356$		0			0
$357$	−2.62207	+	1.51385i	−0.138775	+	0.0801216i
$358$		0			0
$359$		−	19.5699i		−	1.03286i	−0.856330	−	0.516429i	$-0.827261\pi$
$359$		−	19.5699i		−	1.03286i	0.856330	−	0.516429i	$-0.172739\pi$
$360$		0			0
$361$	−7.90701	+	13.6953i	−0.416158	+	0.720807i
$362$		0			0
$363$	2.44044			0.128090
$364$		0			0
$365$	−7.67668			−0.401816
$366$		0			0
$367$	−5.00990	+	8.67740i	−0.261515	+	0.452957i	−0.966645	−	0.256121i	$-0.917555\pi$
$367$	−5.00990	+	8.67740i	−0.261515	+	0.452957i	0.705130	+	0.709078i	$0.250889\pi$
$368$		0			0
$369$			7.35107i			0.382681i
$370$		0			0
$371$	8.18037	−	4.72294i	0.424704	−	0.245203i
$372$		0			0
$373$	12.7995	+	22.1693i	0.662732	+	1.14788i	0.979895	+	0.199514i	$0.0639363\pi$
$373$	12.7995	+	22.1693i	0.662732	+	1.14788i	−0.317163	+	0.948371i	$0.602730\pi$
$374$		0			0
$375$	−5.95271	−	3.43680i	−0.307397	−	0.177476i
$376$		0			0
$377$	16.3760	−	12.5540i	0.843407	−	0.646563i
$378$		0			0
$379$	20.4910	+	11.8305i	1.05255	+	0.607690i	0.923362	−	0.383930i	$-0.125429\pi$
$379$	20.4910	+	11.8305i	1.05255	+	0.607690i	0.129188	+	0.991620i	$0.458763\pi$
$380$		0			0
$381$	−10.4070	−	18.0255i	−0.533167	−	0.923472i
$382$		0			0
$383$	17.0657	−	9.85288i	0.872016	−	0.503459i	0.00399834	−	0.999992i	$-0.498727\pi$
$383$	17.0657	−	9.85288i	0.872016	−	0.503459i	0.868018	+	0.496533i	$0.165394\pi$
$384$		0			0
$385$			6.05541i			0.308612i
$386$		0			0
$387$	−6.92820	+	12.0000i	−0.352180	+	0.609994i
$388$		0			0
$389$	−4.35480			−0.220797			−0.110399	−	0.993887i	$-0.535213\pi$
$389$	−4.35480			−0.220797			−0.110399	+	0.993887i	$0.535213\pi$
$390$		0			0
$391$	5.89767			0.298258
$392$		0			0
$393$	−1.02908	+	1.78241i	−0.0519100	+	0.0899108i
$394$		0			0
$395$			10.0315i			0.504739i
$396$		0			0
$397$	27.6511	−	15.9644i	1.38777	−	0.801230i	0.394708	−	0.918807i	$-0.370846\pi$
$397$	27.6511	−	15.9644i	1.38777	−	0.801230i	0.993064	+	0.117577i	$0.0375126\pi$
$398$		0			0
$399$	2.70213	+	4.68022i	0.135276	+	0.234304i
$400$		0			0
$401$	15.0989	+	8.71738i	0.754005	+	0.435325i	0.827139	−	0.561997i	$-0.189967\pi$
$401$	15.0989	+	8.71738i	0.754005	+	0.435325i	−0.0731340	+	0.997322i	$0.523300\pi$
$402$		0			0
$403$	0.998587	−	2.40772i	0.0497432	−	0.119937i
$404$		0			0
$405$	−0.346214	−	0.199887i	−0.0172035	−	0.00993244i
$406$		0			0
$407$	11.5337	+	19.9769i	0.571702	+	0.990217i
$408$		0			0
$409$	23.4537	−	13.5410i	1.15971	−	0.669561i	0.208478	−	0.978027i	$-0.433149\pi$
$409$	23.4537	−	13.5410i	1.15971	−	0.669561i	0.951235	+	0.308466i	$0.0998157\pi$
$410$		0			0
$411$		−	23.6609i		−	1.16711i
$412$		0			0
$413$	−9.56007	+	16.5585i	−0.470421	+	0.814792i
$414$		0			0
$415$	9.73428			0.477837
$416$		0			0
$417$	9.03533			0.442462
$418$		0			0
$419$	19.6821	−	34.0904i	0.961532	−	1.66542i	0.242876	−	0.970057i	$-0.421909\pi$
$419$	19.6821	−	34.0904i	0.961532	−	1.66542i	0.718656	−	0.695366i	$-0.244758\pi$
$420$		0			0
$421$			18.4653i			0.899943i	0.893043	+	0.449972i	$0.148566\pi$
$421$			18.4653i			0.899943i	−0.893043	+	0.449972i	$0.851434\pi$
$422$		0			0
$423$	8.64871	−	4.99333i	0.420515	−	0.242784i
$424$		0			0
$425$	−2.25394	−	3.90393i	−0.109332	−	0.189368i
$426$		0			0
$427$	−15.6558	−	9.03887i	−0.757636	−	0.437422i
$428$		0			0
$429$	−10.8238	+	1.42000i	−0.522578	+	0.0685582i
$430$		0			0
$431$	6.88815	+	3.97687i	0.331790	+	0.191559i	0.656636	−	0.754208i	$-0.271979\pi$
$431$	6.88815	+	3.97687i	0.331790	+	0.191559i	−0.324845	+	0.945767i	$0.605312\pi$
$432$		0			0
$433$	12.2849	+	21.2781i	0.590376	+	1.02256i	0.994182	+	0.107717i	$0.0343540\pi$
$433$	12.2849	+	21.2781i	0.590376	+	1.02256i	−0.403805	+	0.914845i	$0.632313\pi$
$434$		0			0
$435$	3.58303	−	2.06866i	0.171793	−	0.0991848i
$436$		0			0
$437$		−	10.5270i		−	0.503572i
$438$		0			0
$439$	6.66651	−	11.5467i	0.318175	−	0.551096i	−0.661932	−	0.749564i	$-0.730263\pi$
$439$	6.66651	−	11.5467i	0.318175	−	0.551096i	0.980107	+	0.198468i	$0.0635966\pi$
$440$		0			0
$441$	3.16256			0.150598
$442$		0			0
$443$	6.62646			0.314833			0.157416	−	0.987532i	$-0.449684\pi$
$443$	6.62646			0.314833			0.157416	+	0.987532i	$0.449684\pi$
$444$		0			0
$445$	−2.76919	+	4.79638i	−0.131272	+	0.227370i
$446$		0			0
$447$			1.17266i			0.0554647i
$448$		0			0
$449$	10.7909	−	6.23012i	0.509253	−	0.294018i	−0.223273	−	0.974756i	$-0.571674\pi$
$449$	10.7909	−	6.23012i	0.509253	−	0.294018i	0.732527	+	0.680738i	$0.238341\pi$
$450$		0			0
$451$	−5.57209	−	9.65115i	−0.262380	−	0.454455i
$452$		0			0
$453$	−0.645198	−	0.372505i	−0.0303140	−	0.0175018i
$454$		0			0
$455$	0.966643	+	7.36814i	0.0453169	+	0.345424i
$456$		0			0
$457$	7.50000	+	4.33013i	0.350835	+	0.202555i	0.665053	−	0.746796i	$-0.268409\pi$
$457$	7.50000	+	4.33013i	0.350835	+	0.202555i	−0.314218	+	0.949351i	$0.601742\pi$
$458$		0			0
$459$	2.54439	+	4.40701i	0.118762	+	0.205701i
$460$		0			0
$461$	−10.2587	+	5.92285i	−0.477794	+	0.275855i	−0.719497	−	0.694496i	$-0.755628\pi$
$461$	−10.2587	+	5.92285i	−0.477794	+	0.275855i	0.241702	+	0.970350i	$0.422294\pi$
$462$		0			0
$463$			13.8760i			0.644873i	0.946591	+	0.322436i	$0.104502\pi$
$463$			13.8760i			0.644873i	−0.946591	+	0.322436i	$0.895498\pi$
$464$		0			0
$465$	0.261319	−	0.452618i	0.0121184	−	0.0209897i
$466$		0			0
$467$	−6.05541			−0.280211			−0.140106	−	0.990137i	$-0.544744\pi$
$467$	−6.05541			−0.280211			−0.140106	+	0.990137i	$0.544744\pi$
$468$		0			0
$469$	−35.5236			−1.64033
$470$		0			0
$471$	−2.40162	+	4.15974i	−0.110661	+	0.191671i
$472$		0			0
$473$		−	21.0062i		−	0.965868i
$474$		0			0
$475$	−6.96826	+	4.02313i	−0.319726	+	0.184594i
$476$		0			0
$477$	−3.11540	−	5.39604i	−0.142645	−	0.247068i
$478$		0			0
$479$	12.8409	+	7.41367i	0.586714	+	0.338739i	0.763797	−	0.645457i	$-0.223333\pi$
$479$	12.8409	+	7.41367i	0.586714	+	0.338739i	−0.177083	+	0.984196i	$0.556666\pi$
$480$		0			0
$481$	17.2229	+	22.4664i	0.785298	+	1.02438i
$482$		0			0
$483$	15.4641	+	8.92821i	0.703642	+	0.406248i
$484$		0			0
$485$	−0.645198	−	1.11752i	−0.0292969	−	0.0507438i
$486$		0			0
$487$	−19.9995	+	11.5467i	−0.906266	+	0.523233i	−0.879228	−	0.476402i	$-0.841941\pi$
$487$	−19.9995	+	11.5467i	−0.906266	+	0.523233i	−0.0270380	+	0.999634i	$0.508608\pi$
$488$		0			0
$489$			11.2720i			0.509736i
$490$		0			0
$491$	−7.41152	+	12.8371i	−0.334477	+	0.579332i	−0.983384	−	0.181536i	$-0.941893\pi$
$491$	−7.41152	+	12.8371i	−0.334477	+	0.579332i	0.648907	+	0.760868i	$0.275226\pi$
$492$		0			0
$493$	5.72294			0.257748
$494$		0			0
$495$	3.99435			0.179533
$496$		0			0
$497$	3.25394	−	5.63598i	0.145959	−	0.252808i
$498$		0			0
$499$		−	23.6147i		−	1.05714i	−0.848890	−	0.528569i	$-0.822729\pi$
$499$		−	23.6147i		−	1.05714i	0.848890	−	0.528569i	$-0.177271\pi$
$500$		0			0
$501$	21.3779	−	12.3426i	0.955095	−	0.551425i
$502$		0			0
$503$	−2.76602	−	4.79088i	−0.123331	−	0.213615i	0.797749	−	0.602990i	$-0.206024\pi$
$503$	−2.76602	−	4.79088i	−0.123331	−	0.213615i	−0.921079	+	0.389375i	$0.872691\pi$
$504$		0			0
$505$	1.04674	+	0.604336i	0.0465794	+	0.0268926i
$506$		0			0
$507$	−12.9436	+	3.45567i	−0.574844	+	0.153472i
$508$		0			0
$509$	−23.5844	−	13.6165i	−1.04536	−	0.603539i	−0.124014	−	0.992281i	$-0.539577\pi$
$509$	−23.5844	−	13.6165i	−1.04536	−	0.603539i	−0.921347	+	0.388741i	$0.872910\pi$
$510$		0			0
$511$	−16.0752	−	27.8431i	−0.711126	−	1.23171i
$512$		0			0
$513$	7.86621	−	4.54156i	0.347302	−	0.200515i
$514$		0			0
$515$			12.0448i			0.530758i
$516$		0			0
$517$	−7.56987	+	13.1114i	−0.332922	+	0.576639i
$518$		0			0
$519$	−12.6342			−0.554580
$520$		0			0
$521$	−27.1359			−1.18885			−0.594423	−	0.804153i	$-0.702619\pi$
$521$	−27.1359			−1.18885			−0.594423	+	0.804153i	$0.702619\pi$
$522$		0			0
$523$	−7.41152	+	12.8371i	−0.324083	+	0.561329i	−0.981326	−	0.192350i	$-0.938389\pi$
$523$	−7.41152	+	12.8371i	−0.324083	+	0.561329i	0.657243	+	0.753679i	$0.271722\pi$
$524$		0			0
$525$		−	13.6485i		−	0.595670i
$526$		0			0
$527$	0.626082	−	0.361469i	0.0272726	−	0.0157458i
$528$		0			0
$529$	−5.89126	−	10.2040i	−0.256142	−	0.443651i
$530$		0			0
$531$	10.9226	+	6.30614i	0.473998	+	0.273663i
$532$		0			0
$533$	−8.32068	−	10.8539i	−0.360409	−	0.470134i
$534$		0			0
$535$	−3.13041	−	1.80734i	−0.135339	−	0.0781383i
$536$		0			0
$537$	−10.8238	−	18.7474i	−0.467082	−	0.809009i
$538$		0			0
$539$	−4.15209	+	2.39721i	−0.178843	+	0.103255i
$540$		0			0
$541$		−	12.1951i		−	0.524309i	−0.965026	−	0.262154i	$-0.915567\pi$
$541$		−	12.1951i		−	0.524309i	0.965026	−	0.262154i	$-0.0844330\pi$
$542$		0			0
$543$	−4.46269	+	7.72960i	−0.191512	+	0.331709i
$544$		0			0
$545$	−3.41439			−0.146256
$546$		0			0
$547$	−30.5965			−1.30821			−0.654106	−	0.756403i	$-0.726955\pi$
$547$	−30.5965			−1.30821			−0.654106	+	0.756403i	$0.726955\pi$
$548$		0			0
$549$	−5.96234	+	10.3271i	−0.254466	+	0.440748i
$550$		0			0
$551$		−	10.2151i		−	0.435176i
$552$		0			0
$553$	−36.3839	+	21.0062i	−1.54720	+	0.893276i
$554$		0			0
$555$	2.83802	+	4.91559i	0.120467	+	0.208655i
$556$		0			0
$557$	−11.2005	−	6.46663i	−0.474582	−	0.274000i	0.243574	−	0.969882i	$-0.421680\pi$
$557$	−11.2005	−	6.46663i	−0.474582	−	0.274000i	−0.718156	+	0.695882i	$0.755013\pi$
$558$		0			0
$559$	−3.35329	−	25.5601i	−0.141829	−	1.08108i
$560$		0			0
$561$	−2.62207	−	1.51385i	−0.110704	−	0.0639149i
$562$		0			0
$563$	−2.76602	−	4.79088i	−0.116574	−	0.201912i	0.801834	−	0.597547i	$-0.203858\pi$
$563$	−2.76602	−	4.79088i	−0.116574	−	0.201912i	−0.918408	+	0.395635i	$0.870524\pi$
$564$		0			0
$565$	12.6075	−	7.27896i	0.530403	−	0.306228i
$566$		0			0
$567$		−	1.67427i		−	0.0703129i
$568$		0			0
$569$	8.97687	−	15.5484i	0.376330	−	0.651823i	−0.614195	−	0.789154i	$-0.710519\pi$
$569$	8.97687	−	15.5484i	0.376330	−	0.651823i	0.990525	+	0.137331i	$0.0438525\pi$
$570$		0			0
$571$	1.61780			0.0677028			0.0338514	−	0.999427i	$-0.489223\pi$
$571$	1.61780			0.0677028			0.0338514	+	0.999427i	$0.489223\pi$
$572$		0			0
$573$	16.5660			0.692056
$574$		0			0
$575$	−13.2930	+	23.0241i	−0.554355	+	0.960171i
$576$		0			0
$577$			17.8712i			0.743986i	0.928236	+	0.371993i	$0.121325\pi$
$577$			17.8712i			0.743986i	−0.928236	+	0.371993i	$0.878675\pi$
$578$		0			0
$579$	7.53732	−	4.35168i	0.313240	−	0.180849i
$580$		0			0
$581$	20.3839	+	35.3059i	0.845666	+	1.46474i
$582$		0			0
$583$	8.18037	+	4.72294i	0.338796	+	0.195604i
$584$		0			0
$585$	4.86026	−	0.637629i	0.200947	−	0.0263627i
$586$		0			0
$587$	−6.88815	−	3.97687i	−0.284304	−	0.164143i	0.351066	−	0.936351i	$-0.385819\pi$
$587$	−6.88815	−	3.97687i	−0.284304	−	0.164143i	−0.635370	+	0.772208i	$0.719153\pi$
$588$		0			0
$589$	−0.645198	−	1.11752i	−0.0265849	−	0.0460464i
$590$		0			0
$591$	−7.04589	+	4.06795i	−0.289829	+	0.167333i
$592$		0			0
$593$			24.6716i			1.01314i	0.862199	+	0.506570i	$0.169087\pi$
$593$			24.6716i			1.01314i	−0.862199	+	0.506570i	$0.830913\pi$
$594$		0			0
$595$	−1.03053	+	1.78493i	−0.0422477	+	0.0731752i
$596$		0			0
$597$	−16.5660			−0.678002
$598$		0			0
$599$	−8.48211			−0.346570			−0.173285	−	0.984872i	$-0.555438\pi$
$599$	−8.48211			−0.346570			−0.173285	+	0.984872i	$0.555438\pi$
$600$		0			0
$601$	19.5448	−	33.8526i	0.797250	−	1.38088i	−0.124151	−	0.992263i	$-0.539621\pi$
$601$	19.5448	−	33.8526i	0.797250	−	1.38088i	0.921401	−	0.388614i	$-0.127046\pi$
$602$		0			0
$603$			23.4325i			0.954247i
$604$		0			0
$605$	1.43872	−	0.830646i	0.0584923	−	0.0337705i
$606$		0			0
$607$	−10.3203	−	17.8753i	−0.418888	−	0.725536i	0.576940	−	0.816787i	$-0.304247\pi$
$607$	−10.3203	−	17.8753i	−0.418888	−	0.725536i	−0.995828	+	0.0912511i	$0.970913\pi$
$608$		0			0
$609$	15.0059	+	8.66369i	0.608072	+	0.351070i
$610$		0			0
$611$	−7.11789	+	17.1621i	−0.287959	+	0.694306i
$612$		0			0
$613$	21.7995	+	12.5859i	0.880472	+	0.508341i	0.870814	−	0.491612i	$-0.163592\pi$
$613$	21.7995	+	12.5859i	0.880472	+	0.508341i	0.00965825	+	0.999953i	$0.496926\pi$
$614$		0			0
$615$	−1.37109	−	2.37480i	−0.0552878	−	0.0957613i
$616$		0			0
$617$	−15.0236	+	8.67389i	−0.604828	+	0.349198i	−0.770939	−	0.636910i	$-0.780212\pi$
$617$	−15.0236	+	8.67389i	−0.604828	+	0.349198i	0.166111	+	0.986107i	$0.446879\pi$
$618$		0			0
$619$			37.0157i			1.48779i	0.668297	+	0.743894i	$0.267023\pi$
$619$			37.0157i			1.48779i	−0.668297	+	0.743894i	$0.732977\pi$
$620$		0			0
$621$	15.0059	−	25.9911i	0.602168	−	1.04299i
$622$		0			0
$623$	−23.1951			−0.929291
$624$		0			0
$625$	17.8603			0.714411
$626$		0			0
$627$	−2.70213	+	4.68022i	−0.107913	+	0.186910i
$628$		0			0
$629$			7.85135i			0.313054i
$630$		0			0
$631$	−34.6010	+	19.9769i	−1.37744	+	0.795267i	−0.991851	−	0.127403i	$-0.959336\pi$
$631$	−34.6010	+	19.9769i	−1.37744	+	0.795267i	−0.385591	+	0.922670i	$0.626003\pi$
$632$		0			0
$633$	−11.8529	−	20.5298i	−0.471110	−	0.815986i
$634$		0			0
$635$	−12.2706	−	7.08441i	−0.486942	−	0.281136i
$636$		0			0
$637$	−4.66953	+	3.57970i	−0.185013	+	0.141833i
$638$		0			0
$639$	−3.71768	−	2.14640i	−0.147069	−	0.0849104i
$640$		0			0
$641$	8.77706	+	15.2023i	0.346673	+	0.600455i	0.985656	−	0.168765i	$-0.0539780\pi$
$641$	8.77706	+	15.2023i	0.346673	+	0.600455i	−0.638983	+	0.769221i	$0.720645\pi$
$642$		0			0
$643$	−1.13448	+	0.654991i	−0.0447394	+	0.0258303i	−0.522203	−	0.852821i	$-0.674890\pi$
$643$	−1.13448	+	0.654991i	−0.0447394	+	0.0258303i	0.477463	+	0.878652i	$0.341556\pi$
$644$		0			0
$645$		−	5.16888i		−	0.203525i
$646$		0			0
$647$	−13.3480	+	23.1194i	−0.524764	+	0.908919i	0.474820	+	0.880083i	$0.342513\pi$
$647$	−13.3480	+	23.1194i	−0.524764	+	0.908919i	−0.999584	+	0.0288356i	$0.990820\pi$
$648$		0			0
$649$	−19.1201			−0.750532
$650$		0			0
$651$	2.18884			0.0857875
$652$		0			0
$653$	−6.56007	+	11.3624i	−0.256716	+	0.444644i	−0.965360	−	0.260921i	$-0.915974\pi$
$653$	−6.56007	+	11.3624i	−0.256716	+	0.444644i	0.708645	+	0.705566i	$0.249307\pi$
$654$		0			0
$655$			1.40106i			0.0547438i
$656$		0			0
$657$	−18.3662	+	10.6037i	−0.716534	+	0.413691i
$658$		0			0
$659$	21.9328	+	37.9888i	0.854382	+	1.47983i	0.877217	+	0.480093i	$0.159397\pi$
$659$	21.9328	+	37.9888i	0.854382	+	1.47983i	−0.0228358	+	0.999739i	$0.507269\pi$
$660$		0			0
$661$	14.6597	+	8.46380i	0.570198	+	0.329204i	0.757228	−	0.653150i	$-0.226553\pi$
$661$	14.6597	+	8.46380i	0.570198	+	0.329204i	−0.187031	+	0.982354i	$0.559886\pi$
$662$		0			0
$663$	−3.43216	−	1.42347i	−0.133294	−	0.0552828i
$664$		0			0
$665$	3.18599	+	1.83943i	0.123547	+	0.0713301i
$666$		0			0
$667$	−16.8760	−	29.2301i	−0.653441	−	1.13179i
$668$		0			0
$669$	−13.5930	+	7.84792i	−0.525536	+	0.303418i
$670$		0			0
$671$		−	18.0777i		−	0.697883i
$672$		0			0
$673$	9.57774	−	16.5891i	0.369195	−	0.639464i	−0.620245	−	0.784408i	$-0.712967\pi$
$673$	9.57774	−	16.5891i	0.369195	−	0.639464i	0.989440	+	0.144944i	$0.0463002\pi$
$674$		0			0
$675$	−22.9395			−0.882943
$676$		0			0
$677$	36.2136			1.39180			0.695901	−	0.718137i	$-0.255005\pi$
$677$	36.2136			1.39180			0.695901	+	0.718137i	$0.255005\pi$
$678$		0			0
$679$	2.70213	−	4.68022i	0.103698	−	0.179611i
$680$		0			0
$681$		−	30.4388i		−	1.16642i
$682$		0			0
$683$	4.13024	−	2.38460i	0.158039	−	0.0912440i	−0.418895	−	0.908035i	$-0.637582\pi$
$683$	4.13024	−	2.38460i	0.158039	−	0.0912440i	0.576934	+	0.816791i	$0.304249\pi$
$684$		0			0
$685$	−8.05341	−	13.9489i	−0.307705	−	0.532961i
$686$		0			0
$687$	11.7015	+	6.75586i	0.446440	+	0.257752i
$688$		0			0
$689$	10.7077	+	4.44094i	0.407930	+	0.169186i
$690$		0			0
$691$	−25.0883	−	14.4847i	−0.954404	−	0.551026i	−0.0599581	−	0.998201i	$-0.519097\pi$
$691$	−25.0883	−	14.4847i	−0.954404	−	0.551026i	−0.894446	+	0.447175i	$0.852430\pi$
$692$		0			0
$693$	8.36429	+	14.4874i	0.317733	+	0.550330i
$694$		0			0
$695$	5.32663	−	3.07533i	0.202050	−	0.116654i
$696$		0			0
$697$		−	3.79312i		−	0.143674i
$698$		0			0
$699$	13.0475	−	22.5989i	0.493502	−	0.854771i
$700$		0			0
$701$	39.0157			1.47360			0.736802	−	0.676108i	$-0.236335\pi$
$701$	39.0157			1.47360			0.736802	+	0.676108i	$0.236335\pi$
$702$		0			0
$703$	14.0141			0.528554
$704$		0			0
$705$	−1.86267	+	3.22625i	−0.0701523	+	0.121507i
$706$		0			0
$707$			5.06200i			0.190376i
$708$		0			0
$709$	−24.4275	+	14.1032i	−0.917394	+	0.529658i	−0.882803	−	0.469744i	$-0.844346\pi$
$709$	−24.4275	+	14.1032i	−0.917394	+	0.529658i	−0.0345911	+	0.999402i	$0.511013\pi$
$710$		0			0
$711$	13.8564	+	24.0000i	0.519656	+	0.900070i
$712$		0			0
$713$	−3.69243	−	2.13182i	−0.138282	−	0.0798374i
$714$		0			0
$715$	−5.89767	+	4.52120i	−0.220560	+	0.169083i
$716$		0			0
$717$	6.01190	+	3.47097i	0.224519	+	0.129626i
$718$		0			0
$719$	4.60545	+	7.97687i	0.171754	+	0.297487i	0.939033	−	0.343826i	$-0.111723\pi$
$719$	4.60545	+	7.97687i	0.171754	+	0.297487i	−0.767279	+	0.641313i	$0.778390\pi$
$720$		0			0
$721$	−43.6862	+	25.2222i	−1.62696	+	0.939325i
$722$		0			0
$723$		−	21.5369i		−	0.800968i
$724$		0			0
$725$	−12.8991	+	22.3420i	−0.479062	+	0.829759i
$726$		0			0
$727$	−12.2386			−0.453905			−0.226952	−	0.973906i	$-0.572876\pi$
$727$	−12.2386			−0.453905			−0.226952	+	0.973906i	$0.572876\pi$
$728$		0			0
$729$	14.6280			0.541779
$730$		0			0
$731$	3.57492	−	6.19194i	0.132223	−	0.229017i
$732$		0			0
$733$		−	6.66995i		−	0.246360i	−0.992384	−	0.123180i	$-0.960691\pi$
$733$		−	6.66995i		−	0.246360i	0.992384	−	0.123180i	$-0.0393093\pi$
$734$		0			0
$735$	−1.02168	+	0.589868i	−0.0376853	+	0.0217576i
$736$		0			0
$737$	−17.7618	−	30.7644i	−0.654265	−	1.13322i
$738$		0			0
$739$	−17.8107	−	10.2830i	−0.655177	−	0.378267i	0.135260	−	0.990810i	$-0.456813\pi$
$739$	−17.8107	−	10.2830i	−0.655177	−	0.378267i	−0.790437	+	0.612543i	$0.790146\pi$
$740$		0			0
$741$	−2.54079	+	6.12617i	−0.0933383	+	0.225051i
$742$		0			0
$743$	−0.0400566	−	0.0231267i	−0.00146953	−	0.000848436i	0.499265	−	0.866449i	$-0.333603\pi$
$743$	−0.0400566	−	0.0231267i	−0.00146953	−	0.000848436i	−0.500735	+	0.865601i	$0.666937\pi$
$744$		0			0
$745$	0.399134	+	0.691320i	0.0146231	+	0.0253280i
$746$		0			0
$747$	23.2889	−	13.4459i	0.852098	−	0.491959i
$748$		0			0
$749$		−	15.1385i		−	0.553150i
$750$		0			0
$751$	19.4924	−	33.7618i	0.711287	−	1.23199i	−0.253087	−	0.967444i	$-0.581446\pi$
$751$	19.4924	−	33.7618i	0.711287	−	1.23199i	0.964374	−	0.264542i	$-0.0852209\pi$
$752$		0			0
$753$	−19.4578			−0.709081
$754$		0			0
$755$	−0.507154			−0.0184572
$756$		0			0
$757$	−0.129943	+	0.225068i	−0.00472285	+	0.00818022i	−0.868377	−	0.495904i	$-0.834837\pi$
$757$	−0.129943	+	0.225068i	−0.00472285	+	0.00818022i	0.863654	+	0.504085i	$0.168170\pi$
$758$		0			0
$759$			17.8564i			0.648147i
$760$		0			0
$761$	−29.5467	+	17.0588i	−1.07107	+	0.618382i	−0.928473	−	0.371399i	$-0.878878\pi$
$761$	−29.5467	+	17.0588i	−1.07107	+	0.618382i	−0.142595	+	0.989781i	$0.545545\pi$
$762$		0			0
$763$	−7.14984	−	12.3839i	−0.258841	−	0.448327i
$764$		0			0
$765$	1.17740	+	0.679773i	0.0425690	+	0.0245772i
$766$		0			0
$767$	−23.2651	+	3.05220i	−0.840054	+	0.110209i
$768$		0			0
$769$	2.36075	+	1.36298i	0.0851309	+	0.0491503i	0.541961	−	0.840404i	$-0.317682\pi$
$769$	2.36075	+	1.36298i	0.0851309	+	0.0491503i	−0.456830	+	0.889554i	$0.651015\pi$
$770$		0			0
$771$	10.9144	+	18.9044i	0.393074	+	0.680824i
$772$		0			0
$773$	39.3898	−	22.7417i	1.41675	−	0.817963i	0.420741	−	0.907181i	$-0.361770\pi$
$773$	39.3898	−	22.7417i	1.41675	−	0.817963i	0.996012	+	0.0892175i	$0.0284366\pi$
$774$		0			0
$775$			3.25891i			0.117063i
$776$		0			0
$777$	−11.8858	+	20.5868i	−0.426401	+	0.738548i
$778$		0			0
$779$	−6.77046			−0.242577
$780$		0			0
$781$	6.50787			0.232870
$782$		0			0
$783$	14.5614	−	25.2210i	0.520381	−	0.901326i
$784$		0			0
$785$			3.26974i			0.116702i
$786$		0			0
$787$	−31.9207	+	18.4294i	−1.13785	+	0.656938i	−0.945897	−	0.324467i	$-0.894815\pi$
$787$	−31.9207	+	18.4294i	−1.13785	+	0.656938i	−0.191952	+	0.981404i	$0.561482\pi$
$788$		0			0
$789$	−0.498078	−	0.862697i	−0.0177321	−	0.0307128i
$790$		0			0
$791$	52.8011	+	30.4847i	1.87739	+	1.08391i
$792$		0			0
$793$	−2.88580	−	21.9967i	−0.102478	−	0.781126i
$794$		0			0
$795$	2.01290	+	1.16215i	0.0713901	+	0.0412171i
$796$		0			0
$797$	−5.06795	−	8.77794i	−0.179516	−	0.310931i	0.762199	−	0.647343i	$-0.224120\pi$
$797$	−5.06795	−	8.77794i	−0.179516	−	0.310931i	−0.941715	+	0.336412i	$0.890786\pi$
$798$		0			0
$799$	−4.46269	+	2.57653i	−0.157879	+	0.0911512i
$800$		0			0
$801$			15.3002i			0.540607i
$802$		0			0
$803$	16.0752	−	27.8431i	0.567282	−	0.982561i
$804$		0			0
$805$	12.1555			0.428424
$806$		0			0
$807$	−15.0786			−0.530792
$808$		0			0
$809$	−9.63974	+	16.6965i	−0.338915	+	0.587018i	−0.984229	−	0.176899i	$-0.943393\pi$
$809$	−9.63974	+	16.6965i	−0.338915	+	0.587018i	0.645314	+	0.763918i	$0.276727\pi$
$810$		0			0
$811$		−	21.7653i		−	0.764285i	−0.924103	−	0.382142i	$-0.875186\pi$
$811$		−	21.7653i		−	0.764285i	0.924103	−	0.382142i	$-0.124814\pi$
$812$		0			0
$813$	20.0875	−	11.5975i	0.704501	−	0.406744i
$814$		0			0
$815$	3.83661	+	6.64520i	0.134390	+	0.232771i
$816$		0			0
$817$	−11.0522	−	6.38099i	−0.386668	−	0.223243i
$818$		0			0
$819$	12.4902	+	16.2928i	0.436443	+	0.569317i
$820$		0			0
$821$	38.7446	+	22.3692i	1.35220	+	0.780691i	0.988557	−	0.150848i	$-0.0482005\pi$
$821$	38.7446	+	22.3692i	1.35220	+	0.780691i	0.363640	+	0.931540i	$0.381534\pi$
$822$		0			0
$823$	−6.15936	−	10.6683i	−0.214702	−	0.371874i	0.738478	−	0.674277i	$-0.235545\pi$
$823$	−6.15936	−	10.6683i	−0.214702	−	0.371874i	−0.953180	+	0.302403i	$0.902211\pi$
$824$		0			0
$825$	11.8200	−	6.82426i	0.411518	−	0.237590i
$826$		0			0
$827$			43.6595i			1.51819i	0.650980	+	0.759095i	$0.274358\pi$
$827$			43.6595i			1.51819i	−0.650980	+	0.759095i	$0.725642\pi$
$828$		0			0
$829$	24.5224	−	42.4741i	0.851698	−	1.47519i	−0.0279759	−	0.999609i	$-0.508906\pi$
$829$	24.5224	−	42.4741i	0.851698	−	1.47519i	0.879674	−	0.475576i	$-0.157761\pi$
$830$		0			0
$831$	16.8340			0.583964
$832$		0			0
$833$	−1.63186			−0.0565408
$834$		0			0
$835$	8.40200	−	14.5527i	0.290763	−	0.503617i
$836$		0			0
$837$		−	3.67886i		−	0.127160i
$838$		0			0
$839$	34.4820	−	19.9082i	1.19045	−	0.687308i	0.232043	−	0.972706i	$-0.425459\pi$
$839$	34.4820	−	19.9082i	1.19045	−	0.687308i	0.958409	+	0.285398i	$0.0921257\pi$
$840$		0			0
$841$	−1.87601	−	3.24934i	−0.0646899	−	0.112046i
$842$		0			0
$843$	14.5056	+	8.37480i	0.499599	+	0.288444i
$844$		0			0
$845$	−6.45446	+	6.44279i	−0.222040	+	0.221639i
$846$		0			0
$847$	6.02545	+	3.47880i	0.207037	+	0.119533i
$848$		0			0
$849$	−3.68407	−	6.38099i	−0.126437	−	0.218995i
$850$		0			0
$851$	40.1011	−	23.1524i	1.37465	−	0.793652i
$852$		0			0
$853$			33.4230i			1.14438i	0.820121	+	0.572191i	$0.193906\pi$
$853$			33.4230i			1.14438i	−0.820121	+	0.572191i	$0.806094\pi$
$854$		0			0
$855$	1.21335	−	2.10158i	0.0414957	−	0.0718726i
$856$		0			0
$857$	−11.5345			−0.394012			−0.197006	−	0.980402i	$-0.563122\pi$
$857$	−11.5345			−0.394012			−0.197006	+	0.980402i	$0.563122\pi$
$858$		0			0
$859$	−3.61497			−0.123341			−0.0616707	−	0.998097i	$-0.519643\pi$
$859$	−3.61497			−0.123341			−0.0616707	+	0.998097i	$0.519643\pi$
$860$		0			0
$861$	5.74222	−	9.94582i	0.195694	−	0.338953i
$862$		0			0
$863$			46.8259i			1.59397i	0.603997	+	0.796986i	$0.293574\pi$
$863$			46.8259i			1.59397i	−0.603997	+	0.796986i	$0.706426\pi$
$864$		0			0
$865$	−7.44828	+	4.30027i	−0.253249	+	0.146214i
$866$		0			0
$867$	8.24426	+	14.2795i	0.279990	+	0.484956i
$868$		0			0
$869$	−36.3839	−	21.0062i	−1.23424	−	0.712588i
$870$		0			0
$871$	−26.5233	−	34.5982i	−0.898708	−	1.17232i
$872$		0			0
$873$	−3.08723	−	1.78241i	−0.104487	−	0.0603255i
$874$		0			0
$875$	−9.79817	−	16.9709i	−0.331239	−	0.573722i
$876$		0			0
$877$	−19.1080	+	11.0320i	−0.645232	+	0.372525i	−0.786627	−	0.617428i	$-0.788175\pi$
$877$	−19.1080	+	11.0320i	−0.645232	+	0.372525i	0.141395	+	0.989953i	$0.454841\pi$
$878$		0			0
$879$			18.1226i			0.611259i
$880$		0			0
$881$	16.2849	−	28.2063i	0.548653	−	0.950296i	−0.449714	−	0.893173i	$-0.648474\pi$
$881$	16.2849	−	28.2063i	0.548653	−	0.950296i	0.998367	−	0.0571228i	$-0.0181927\pi$
$882$		0			0
$883$	44.5807			1.50026			0.750130	−	0.661290i	$-0.229991\pi$
$883$	44.5807			1.50026			0.750130	+	0.661290i	$0.229991\pi$
$884$		0			0
$885$	−4.70478			−0.158150
$886$		0			0
$887$	19.7140	−	34.1457i	0.661932	−	1.14650i	−0.318175	−	0.948032i	$-0.603070\pi$
$887$	19.7140	−	34.1457i	0.661932	−	1.14650i	0.980107	−	0.198468i	$-0.0635966\pi$
$888$		0			0
$889$		−	59.3399i		−	1.99020i
$890$		0			0
$891$	1.44996	−	0.837137i	0.0485756	−	0.0280452i
$892$		0			0
$893$	4.59894	+	7.96561i	0.153898	+	0.266559i
$894$		0			0
$895$	−12.7620	−	7.36814i	−0.426586	−	0.246290i
$896$		0			0
$897$	2.85047	+	21.7274i	0.0951744	+	0.725457i
$898$		0			0
$899$	−3.58303	−	2.06866i	−0.119501	−	0.0689938i
$900$		0			0
$901$	1.60753	+	2.78433i	0.0535547	+	0.0927594i
$902$		0			0
$903$	18.7474	−	10.8238i	0.623874	−	0.360194i
$904$		0			0
$905$			6.07581i			0.201967i
$906$		0			0
$907$	29.3844	−	50.8953i	0.975693	−	1.68995i	0.298065	−	0.954545i	$-0.403659\pi$
$907$	29.3844	−	50.8953i	0.975693	−	1.68995i	0.677628	−	0.735405i	$-0.263008\pi$
$908$		0			0
$909$	3.33906			0.110750
$910$		0			0
$911$	9.86206			0.326745			0.163372	−	0.986564i	$-0.447763\pi$
$911$	9.86206			0.326745			0.163372	+	0.986564i	$0.447763\pi$
$912$		0			0
$913$	−20.3839	+	35.3059i	−0.674608	+	1.16846i
$914$		0			0
$915$		−	4.44828i		−	0.147056i
$916$		0			0
$917$	−5.08158	+	2.93385i	−0.167809	+	0.0968844i
$918$		0			0
$919$	−6.84933	−	11.8634i	−0.225939	−	0.391337i	0.730662	−	0.682739i	$-0.239212\pi$
$919$	−6.84933	−	11.8634i	−0.225939	−	0.391337i	−0.956601	+	0.291402i	$0.905878\pi$
$920$		0			0
$921$	−2.92467	−	1.68856i	−0.0963712	−	0.0556399i
$922$		0			0
$923$	7.91868	−	1.03887i	0.260646	−	0.0341948i
$924$		0			0
$925$	−30.6511	−	17.6964i	−1.00780	−	0.581856i
$926$		0			0
$927$	16.6374	+	28.8168i	0.546444	+	0.946469i
$928$		0			0
$929$	−7.31401	+	4.22275i	−0.239965	+	0.138544i	−0.615161	−	0.788402i	$-0.710909\pi$
$929$	−7.31401	+	4.22275i	−0.239965	+	0.138544i	0.375196	+	0.926946i	$0.377576\pi$
$930$		0			0
$931$			2.91277i			0.0954622i
$932$		0			0
$933$	−10.9051	+	18.8882i	−0.357016	+	0.618371i
$934$		0			0
$935$	−2.06106			−0.0674040
$936$		0			0
$937$	−10.6743			−0.348713			−0.174357	−	0.984683i	$-0.555785\pi$
$937$	−10.6743			−0.348713			−0.174357	+	0.984683i	$0.555785\pi$
$938$		0			0
$939$	−5.24651	+	9.08723i	−0.171214	+	0.296551i
$940$		0			0
$941$			25.9672i			0.846508i	0.906011	+	0.423254i	$0.139112\pi$
$941$			25.9672i			0.846508i	−0.906011	+	0.423254i	$0.860888\pi$
$942$		0			0
$943$	−19.3735	+	11.1853i	−0.630887	+	0.364243i
$944$		0			0
$945$	5.24414	+	9.08312i	0.170592	+	0.295474i
$946$		0			0
$947$	29.4164	+	16.9835i	0.955903	+	0.551891i	0.894910	−	0.446247i	$-0.147240\pi$
$947$	29.4164	+	16.9835i	0.955903	+	0.551891i	0.0609934	+	0.998138i	$0.480573\pi$
$948$		0			0
$949$	15.1154	−	36.4452i	0.490667	−	1.18306i
$950$		0			0
$951$	−25.6768	−	14.8245i	−0.832628	−	0.480718i
$952$		0			0
$953$	−2.17620	−	3.76928i	−0.0704939	−	0.122099i	0.828624	−	0.559806i	$-0.189124\pi$
$953$	−2.17620	−	3.76928i	−0.0704939	−	0.122099i	−0.899118	+	0.437707i	$0.855791\pi$
$954$		0			0
$955$	9.76622	−	5.63853i	0.316028	−	0.182459i
$956$		0			0
$957$			17.3274i			0.560115i
$958$		0			0
$959$	33.7282	−	58.4189i	1.08914	−	1.88644i
$960$		0			0
$961$	30.4774			0.983141
$962$		0			0
$963$	−9.98587			−0.321790
$964$		0			0
$965$	2.96234	−	5.13091i	0.0953609	−	0.165170i
$966$		0			0
$967$			19.0291i			0.611934i	0.952042	+	0.305967i	$0.0989797\pi$
$967$			19.0291i			0.611934i	−0.952042	+	0.305967i	$0.901020\pi$
$968$		0			0
$969$	−1.59299	+	0.919716i	−0.0511744	+	0.0295455i
$970$		0			0
$971$	17.6210	+	30.5205i	0.565485	+	0.979449i	0.997004	+	0.0773453i	$0.0246444\pi$
$971$	17.6210	+	30.5205i	0.565485	+	0.979449i	−0.431519	+	0.902104i	$0.642022\pi$
$972$		0			0
$973$	22.3082	+	12.8797i	0.715170	+	0.412903i
$974$		0			0
$975$	13.2930	−	10.1905i	0.425716	−	0.326357i
$976$		0			0
$977$	−4.61066	−	2.66197i	−0.147508	−	0.0851638i	0.424429	−	0.905461i	$-0.360475\pi$
$977$	−4.61066	−	2.66197i	−0.147508	−	0.0851638i	−0.571938	+	0.820297i	$0.693808\pi$
$978$		0			0
$979$	−11.5975	−	20.0875i	−0.370659	−	0.642000i
$980$		0			0
$981$	−8.16881	+	4.71627i	−0.260810	+	0.150579i
$982$		0			0
$983$		−	12.4750i		−	0.397889i	−0.980011	−	0.198945i	$-0.936249\pi$
$983$		−	12.4750i		−	0.397889i	0.980011	−	0.198945i	$-0.0637514\pi$
$984$		0			0
$985$	−2.76919	+	4.79638i	−0.0882338	+	0.152825i
$986$		0			0
$987$	−15.6020			−0.496617
$988$		0			0
$989$	−42.1674			−1.34084
$990$		0			0
$991$	−22.7029	+	39.3226i	−0.721182	+	1.24912i	0.239345	+	0.970935i	$0.423067\pi$
$991$	−22.7029	+	39.3226i	−0.721182	+	1.24912i	−0.960526	+	0.278189i	$0.910266\pi$
$992$		0			0
$993$			4.51773i			0.143366i
$994$		0			0
$995$	−9.76622	+	5.63853i	−0.309610	+	0.178753i
$996$		0			0
$997$	9.50667	+	16.4660i	0.301079	+	0.521484i	0.976381	−	0.216057i	$-0.0693198\pi$
$997$	9.50667	+	16.4660i	0.301079	+	0.521484i	−0.675302	+	0.737542i	$0.735986\pi$
$998$		0			0
$999$	34.6010	+	19.9769i	1.09473	+	0.632040i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.w.d.225.3	✓	12
4.3	odd	2	inner	416.2.w.d.225.4	yes	12
8.3	odd	2		832.2.w.j.641.3		12
8.5	even	2		832.2.w.j.641.4		12
13.6	odd	12		5408.2.a.bm.1.4		6
13.7	odd	12		5408.2.a.bn.1.4		6
13.10	even	6	inner	416.2.w.d.257.3	yes	12
52.7	even	12		5408.2.a.bm.1.3		6
52.19	even	12		5408.2.a.bn.1.3		6
52.23	odd	6	inner	416.2.w.d.257.4	yes	12
104.75	odd	6		832.2.w.j.257.3		12
104.101	even	6		832.2.w.j.257.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.w.d.225.3	✓	12	1.1	even	1	trivial
416.2.w.d.225.4	yes	12	4.3	odd	2	inner
416.2.w.d.257.3	yes	12	13.10	even	6	inner
416.2.w.d.257.4	yes	12	52.23	odd	6	inner
832.2.w.j.257.3		12	104.75	odd	6
832.2.w.j.257.4		12	104.101	even	6
832.2.w.j.641.3		12	8.3	odd	2
832.2.w.j.641.4		12	8.5	even	2
5408.2.a.bm.1.3		6	52.7	even	12
5408.2.a.bm.1.4		6	13.6	odd	12
5408.2.a.bn.1.3		6	52.19	even	12
5408.2.a.bn.1.4		6	13.7	odd	12

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.w (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.515266 + 0.892467i) q^{3} +0.701519i q^{5} +(-2.54439 + 1.46900i) q^{7} +(0.969002 + 1.67836i) q^{9} +(-2.54439 - 1.46900i) q^{11} +(-3.33047 - 1.38129i) q^{13} +(-0.626082 - 0.361469i) q^{15} +(-0.500000 - 0.866025i) q^{17} +(-1.54580 + 0.892467i) q^{19} -3.02771i q^{21} +(-2.94884 + 5.10753i) q^{23} +4.50787 q^{25} -5.08877 q^{27} +(-2.86147 + 4.95621i) q^{29} +0.722938i q^{31} +(2.62207 - 1.51385i) q^{33} +(-1.03053 - 1.78493i) q^{35} +(-6.79947 - 3.92568i) q^{37} +(2.94884 - 2.26060i) q^{39} +(3.28493 + 1.89656i) q^{41} +(3.57492 + 6.19194i) q^{43} +(-1.17740 + 0.679773i) q^{45} -5.15307i q^{47} +(0.815932 - 1.41324i) q^{49} +1.03053 q^{51} -3.21507 q^{53} +(1.03053 - 1.78493i) q^{55} -1.83943i q^{57} +(5.63598 - 3.25394i) q^{59} +(3.07653 + 5.32871i) q^{61} +(-4.93103 - 2.84693i) q^{63} +(0.969002 - 2.33639i) q^{65} +(10.4712 + 6.04554i) q^{67} +(-3.03887 - 5.26348i) q^{69} +(-1.91830 + 1.10753i) q^{71} +10.9430i q^{73} +(-2.32275 + 4.02313i) q^{75} +8.63186 q^{77} +14.2997 q^{79} +(-0.284934 + 0.493520i) q^{81} -13.8760i q^{83} +(0.607533 - 0.350759i) q^{85} +(-2.94884 - 5.10753i) q^{87} +(6.83714 + 3.94742i) q^{89} +(10.5031 - 1.37793i) q^{91} +(-0.645198 - 0.372505i) q^{93} +(-0.626082 - 1.08441i) q^{95} +(-1.59299 + 0.919716i) q^{97} -5.69386i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{9} + 12 q^{13} - 6 q^{17} - 12 q^{25} - 6 q^{29} - 30 q^{33} - 6 q^{37} + 30 q^{41} + 24 q^{49} - 48 q^{53} + 18 q^{61} - 12 q^{65} + 6 q^{69} + 132 q^{77} + 6 q^{81} + 12 q^{85} + 30 q^{89}+ \cdots - 90 q^{97}+O(q^{100}) \) 12 * q - 12 * q^9 + 12 * q^13 - 6 * q^17 - 12 * q^25 - 6 * q^29 - 30 * q^33 - 6 * q^37 + 30 * q^41 + 24 * q^49 - 48 * q^53 + 18 * q^61 - 12 * q^65 + 6 * q^69 + 132 * q^77 + 6 * q^81 + 12 * q^85 + 30 * q^89 - 36 * q^93 - 90 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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