LMFDB - Embedded newform 1920.2.y.j.223.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(223,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0, 3]))

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

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

chi := DirichletCharacter("1920.223");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.y (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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 14 x^{14} - 10 x^{13} - 26 x^{12} + 78 x^{11} - 66 x^{10} - 74 x^{9} + 233 x^{8} + \cdots + 256 $ x^16 - 6x^15 + 14x^14 - 10x^13 - 26x^12 + 78x^11 - 66x^10 - 74x^9 + 233x^8 - 148x^7 - 264x^6 + 624x^5 - 416x^4 - 320x^3 + 896x^2 - 768*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			223.1
Root			$0.237728 + 1.39409i$ of defining polynomial
Character	$\chi$	$=$	1920.223
Dual form			1920.2.y.j.1567.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-2.23531 - 0.0583995i) q^{5} +(-0.747384 + 0.747384i) q^{7} +1.00000 q^{9} +(-0.920311 - 0.920311i) q^{11} -0.996441i q^{13} +(-2.23531 - 0.0583995i) q^{15} +(-0.982332 + 0.982332i) q^{17} +(-1.03458 - 1.03458i) q^{19} +(-0.747384 + 0.747384i) q^{21} +(4.77394 + 4.77394i) q^{23} +(4.99318 + 0.261081i) q^{25} +1.00000 q^{27} +(2.95516 - 2.95516i) q^{29} -10.4545i q^{31} +(-0.920311 - 0.920311i) q^{33} +(1.71428 - 1.62698i) q^{35} -8.22694i q^{37} -0.996441i q^{39} -5.70040i q^{41} -5.22869i q^{43} +(-2.23531 - 0.0583995i) q^{45} +(-0.0548243 - 0.0548243i) q^{47} +5.88283i q^{49} +(-0.982332 + 0.982332i) q^{51} -5.13957 q^{53} +(2.00343 + 2.11092i) q^{55} +(-1.03458 - 1.03458i) q^{57} +(-2.30403 + 2.30403i) q^{59} +(-10.8244 - 10.8244i) q^{61} +(-0.747384 + 0.747384i) q^{63} +(-0.0581916 + 2.22735i) q^{65} -8.99029i q^{67} +(4.77394 + 4.77394i) q^{69} +14.1421 q^{71} +(6.35840 - 6.35840i) q^{73} +(4.99318 + 0.261081i) q^{75} +1.37565 q^{77} +8.76588 q^{79} +1.00000 q^{81} +12.3589 q^{83} +(2.25318 - 2.13845i) q^{85} +(2.95516 - 2.95516i) q^{87} -18.0456 q^{89} +(0.744724 + 0.744724i) q^{91} -10.4545i q^{93} +(2.25218 + 2.37302i) q^{95} +(1.29787 - 1.29787i) q^{97} +(-0.920311 - 0.920311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) $ 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−2.23531	−	0.0583995i	−0.999659	−	0.0261170i
$5$	−2.23531	−	0.0583995i	−0.999659	−	0.0261170i
$6$		0			0
$7$	−0.747384	+	0.747384i	−0.282485	+	0.282485i	−0.834099	−	0.551615i	$-0.814012\pi$
$7$	−0.747384	+	0.747384i	−0.282485	+	0.282485i	0.551615	+	0.834099i	$0.314012\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−0.920311	−	0.920311i	−0.277484	−	0.277484i	0.554620	−	0.832104i	$-0.312864\pi$
$11$	−0.920311	−	0.920311i	−0.277484	−	0.277484i	−0.832104	+	0.554620i	$0.812864\pi$
$12$		0			0
$13$		−	0.996441i		−	0.276363i	−0.990407	−	0.138182i	$-0.955874\pi$
$13$		−	0.996441i		−	0.276363i	0.990407	−	0.138182i	$-0.0441257\pi$
$14$		0			0
$15$	−2.23531	−	0.0583995i	−0.577153	−	0.0150787i
$16$		0			0
$17$	−0.982332	+	0.982332i	−0.238251	+	0.238251i	−0.816125	−	0.577875i	$-0.803882\pi$
$17$	−0.982332	+	0.982332i	−0.238251	+	0.238251i	0.577875	+	0.816125i	$0.303882\pi$
$18$		0			0
$19$	−1.03458	−	1.03458i	−0.237349	−	0.237349i	0.578403	−	0.815751i	$-0.303676\pi$
$19$	−1.03458	−	1.03458i	−0.237349	−	0.237349i	−0.815751	+	0.578403i	$0.803676\pi$
$20$		0			0
$21$	−0.747384	+	0.747384i	−0.163093	+	0.163093i
$22$		0			0
$23$	4.77394	+	4.77394i	0.995436	+	0.995436i	0.999990	−	0.00455400i	$-0.00144959\pi$
$23$	4.77394	+	4.77394i	0.995436	+	0.995436i	−0.00455400	+	0.999990i	$0.501450\pi$
$24$		0			0
$25$	4.99318	+	0.261081i	0.998636	+	0.0522163i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	2.95516	−	2.95516i	0.548760	−	0.548760i	−0.377322	−	0.926082i	$-0.623155\pi$
$29$	2.95516	−	2.95516i	0.548760	−	0.548760i	0.926082	+	0.377322i	$0.123155\pi$
$30$		0			0
$31$		−	10.4545i		−	1.87768i	−0.344351	−	0.938841i	$-0.611901\pi$
$31$		−	10.4545i		−	1.87768i	0.344351	−	0.938841i	$-0.388099\pi$
$32$		0			0
$33$	−0.920311	−	0.920311i	−0.160206	−	0.160206i
$34$		0			0
$35$	1.71428	−	1.62698i	0.289766	−	0.275011i
$36$		0			0
$37$		−	8.22694i		−	1.35250i	−0.736672	−	0.676251i	$-0.763604\pi$
$37$		−	8.22694i		−	1.35250i	0.736672	−	0.676251i	$-0.236396\pi$
$38$		0			0
$39$		−	0.996441i		−	0.159558i
$40$		0			0
$41$		−	5.70040i		−	0.890253i	−0.895468	−	0.445127i	$-0.853159\pi$
$41$		−	5.70040i		−	0.890253i	0.895468	−	0.445127i	$-0.146841\pi$
$42$		0			0
$43$		−	5.22869i		−	0.797368i	−0.917088	−	0.398684i	$-0.869467\pi$
$43$		−	5.22869i		−	0.797368i	0.917088	−	0.398684i	$-0.130533\pi$
$44$		0			0
$45$	−2.23531	−	0.0583995i	−0.333220	−	0.00870568i
$46$		0			0
$47$	−0.0548243	−	0.0548243i	−0.00799695	−	0.00799695i	0.703097	−	0.711094i	$-0.251800\pi$
$47$	−0.0548243	−	0.0548243i	−0.00799695	−	0.00799695i	−0.711094	+	0.703097i	$0.751800\pi$
$48$		0			0
$49$			5.88283i			0.840405i
$50$		0			0
$51$	−0.982332	+	0.982332i	−0.137554	+	0.137554i
$52$		0			0
$53$	−5.13957			−0.705974			−0.352987	−	0.935628i	$-0.614834\pi$
$53$	−5.13957			−0.705974			−0.352987	+	0.935628i	$0.614834\pi$
$54$		0			0
$55$	2.00343	+	2.11092i	0.270142	+	0.284637i
$56$		0			0
$57$	−1.03458	−	1.03458i	−0.137033	−	0.137033i
$58$		0			0
$59$	−2.30403	+	2.30403i	−0.299959	+	0.299959i	−0.840998	−	0.541039i	$-0.818031\pi$
$59$	−2.30403	+	2.30403i	−0.299959	+	0.299959i	0.541039	+	0.840998i	$0.318031\pi$
$60$		0			0
$61$	−10.8244	−	10.8244i	−1.38592	−	1.38592i	−0.833689	−	0.552234i	$-0.813776\pi$
$61$	−10.8244	−	10.8244i	−1.38592	−	1.38592i	−0.552234	−	0.833689i	$-0.686224\pi$
$62$		0			0
$63$	−0.747384	+	0.747384i	−0.0941615	+	0.0941615i
$64$		0			0
$65$	−0.0581916	+	2.22735i	−0.00721778	+	0.276269i
$66$		0			0
$67$		−	8.99029i		−	1.09834i	−0.835711	−	0.549169i	$-0.814944\pi$
$67$		−	8.99029i		−	1.09834i	0.835711	−	0.549169i	$-0.185056\pi$
$68$		0			0
$69$	4.77394	+	4.77394i	0.574715	+	0.574715i
$70$		0			0
$71$	14.1421			1.67836			0.839180	−	0.543853i	$-0.183035\pi$
$71$	14.1421			1.67836			0.839180	+	0.543853i	$0.183035\pi$
$72$		0			0
$73$	6.35840	−	6.35840i	0.744195	−	0.744195i	−0.229188	−	0.973382i	$-0.573607\pi$
$73$	6.35840	−	6.35840i	0.744195	−	0.744195i	0.973382	+	0.229188i	$0.0736070\pi$
$74$		0			0
$75$	4.99318	+	0.261081i	0.576563	+	0.0301471i
$76$		0			0
$77$	1.37565			0.156770
$78$		0			0
$79$	8.76588			0.986238			0.493119	−	0.869962i	$-0.335857\pi$
$79$	8.76588			0.986238			0.493119	+	0.869962i	$0.335857\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	12.3589			1.35657			0.678284	−	0.734800i	$-0.262724\pi$
$83$	12.3589			1.35657			0.678284	+	0.734800i	$0.262724\pi$
$84$		0			0
$85$	2.25318	−	2.13845i	0.244392	−	0.231947i
$86$		0			0
$87$	2.95516	−	2.95516i	0.316827	−	0.316827i
$88$		0			0
$89$	−18.0456			−1.91283			−0.956414	−	0.292014i	$-0.905675\pi$
$89$	−18.0456			−1.91283			−0.956414	+	0.292014i	$0.905675\pi$
$90$		0			0
$91$	0.744724	+	0.744724i	0.0780683	+	0.0780683i
$92$		0			0
$93$		−	10.4545i		−	1.08408i
$94$		0			0
$95$	2.25218	+	2.37302i	0.231069	+	0.243467i
$96$		0			0
$97$	1.29787	−	1.29787i	0.131779	−	0.131779i	−0.638141	−	0.769920i	$-0.720296\pi$
$97$	1.29787	−	1.29787i	0.131779	−	0.131779i	0.769920	+	0.638141i	$0.220296\pi$
$98$		0			0
$99$	−0.920311	−	0.920311i	−0.0924947	−	0.0924947i
$100$		0			0
$101$	−4.25125	+	4.25125i	−0.423015	+	0.423015i	−0.886241	−	0.463225i	$-0.846692\pi$
$101$	−4.25125	+	4.25125i	−0.423015	+	0.423015i	0.463225	+	0.886241i	$0.346692\pi$
$102$		0			0
$103$	5.92346	+	5.92346i	0.583656	+	0.583656i	0.935906	−	0.352250i	$-0.114583\pi$
$103$	5.92346	+	5.92346i	0.583656	+	0.583656i	−0.352250	+	0.935906i	$0.614583\pi$
$104$		0			0
$105$	1.71428	−	1.62698i	0.167296	−	0.158777i
$106$		0			0
$107$	−0.0554707			−0.00536256			−0.00268128	−	0.999996i	$-0.500853\pi$
$107$	−0.0554707			−0.00536256			−0.00268128	+	0.999996i	$0.500853\pi$
$108$		0			0
$109$	0.947769	−	0.947769i	0.0907798	−	0.0907798i	−0.660259	−	0.751038i	$-0.729553\pi$
$109$	0.947769	−	0.947769i	0.0907798	−	0.0907798i	0.751038	+	0.660259i	$0.229553\pi$
$110$		0			0
$111$		−	8.22694i		−	0.780867i
$112$		0			0
$113$	−10.8801	−	10.8801i	−1.02351	−	1.02351i	−0.999717	−	0.0237977i	$-0.992424\pi$
$113$	−10.8801	−	10.8801i	−1.02351	−	1.02351i	−0.0237977	−	0.999717i	$-0.507576\pi$
$114$		0			0
$115$	−10.3924	−	10.9500i	−0.969098	−	1.02109i
$116$		0			0
$117$		−	0.996441i		−	0.0921210i
$118$		0			0
$119$		−	1.46836i		−	0.134604i
$120$		0			0
$121$		−	9.30606i		−	0.846005i
$122$		0			0
$123$		−	5.70040i		−	0.513988i
$124$		0			0
$125$	−11.1460	−	0.875196i	−0.996931	−	0.0782799i
$126$		0			0
$127$	9.61338	+	9.61338i	0.853050	+	0.853050i	0.990508	−	0.137458i	$-0.0438931\pi$
$127$	9.61338	+	9.61338i	0.853050	+	0.853050i	−0.137458	+	0.990508i	$0.543893\pi$
$128$		0			0
$129$		−	5.22869i		−	0.460360i
$130$		0			0
$131$	5.60184	−	5.60184i	0.489435	−	0.489435i	−0.418693	−	0.908128i	$-0.637512\pi$
$131$	5.60184	−	5.60184i	0.489435	−	0.489435i	0.908128	+	0.418693i	$0.137512\pi$
$132$		0			0
$133$	1.54646			0.134095
$134$		0			0
$135$	−2.23531	−	0.0583995i	−0.192384	−	0.00502623i
$136$		0			0
$137$	−4.68373	−	4.68373i	−0.400158	−	0.400158i	0.478130	−	0.878289i	$-0.341315\pi$
$137$	−4.68373	−	4.68373i	−0.400158	−	0.400158i	−0.878289	+	0.478130i	$0.841315\pi$
$138$		0			0
$139$	−1.64971	+	1.64971i	−0.139926	+	0.139926i	−0.773600	−	0.633674i	$-0.781546\pi$
$139$	−1.64971	+	1.64971i	−0.139926	+	0.139926i	0.633674	+	0.773600i	$0.281546\pi$
$140$		0			0
$141$	−0.0548243	−	0.0548243i	−0.00461704	−	0.00461704i
$142$		0			0
$143$	−0.917036	+	0.917036i	−0.0766864	+	0.0766864i
$144$		0			0
$145$	−6.77827	+	6.43311i	−0.562905	+	0.534241i
$146$		0			0
$147$			5.88283i			0.485208i
$148$		0			0
$149$	12.0813	+	12.0813i	0.989742	+	0.989742i	0.999948	−	0.0102058i	$-0.00324866\pi$
$149$	12.0813	+	12.0813i	0.989742	+	0.989742i	−0.0102058	+	0.999948i	$0.503249\pi$
$150$		0			0
$151$	−12.6503			−1.02947			−0.514735	−	0.857350i	$-0.672110\pi$
$151$	−12.6503			−1.02947			−0.514735	+	0.857350i	$0.672110\pi$
$152$		0			0
$153$	−0.982332	+	0.982332i	−0.0794169	+	0.0794169i
$154$		0			0
$155$	−0.610537	+	23.3690i	−0.0490395	+	1.87704i
$156$		0			0
$157$	6.31279			0.503816			0.251908	−	0.967751i	$-0.418942\pi$
$157$	6.31279			0.503816			0.251908	+	0.967751i	$0.418942\pi$
$158$		0			0
$159$	−5.13957			−0.407595
$160$		0			0
$161$	−7.13593			−0.562390
$162$		0			0
$163$	14.6329			1.14613			0.573067	−	0.819508i	$-0.305753\pi$
$163$	14.6329			1.14613			0.573067	+	0.819508i	$0.305753\pi$
$164$		0			0
$165$	2.00343	+	2.11092i	0.155967	+	0.164335i
$166$		0			0
$167$	−5.31380	+	5.31380i	−0.411194	+	0.411194i	−0.882155	−	0.470960i	$-0.843908\pi$
$167$	−5.31380	+	5.31380i	−0.411194	+	0.411194i	0.470960	+	0.882155i	$0.343908\pi$
$168$		0			0
$169$	12.0071			0.923623
$170$		0			0
$171$	−1.03458	−	1.03458i	−0.0791163	−	0.0791163i
$172$		0			0
$173$			13.1537i			1.00006i	0.866008	+	0.500029i	$0.166678\pi$
$173$			13.1537i			1.00006i	−0.866008	+	0.500029i	$0.833322\pi$
$174$		0			0
$175$	−3.92695	+	3.53669i	−0.296849	+	0.267349i
$176$		0			0
$177$	−2.30403	+	2.30403i	−0.173181	+	0.173181i
$178$		0			0
$179$	12.2215	+	12.2215i	0.913479	+	0.913479i	0.996544	−	0.0830647i	$-0.0264708\pi$
$179$	12.2215	+	12.2215i	0.913479	+	0.913479i	−0.0830647	+	0.996544i	$0.526471\pi$
$180$		0			0
$181$	−7.77734	+	7.77734i	−0.578085	+	0.578085i	−0.934375	−	0.356290i	$-0.884041\pi$
$181$	−7.77734	+	7.77734i	−0.578085	+	0.578085i	0.356290	+	0.934375i	$0.384041\pi$
$182$		0			0
$183$	−10.8244	−	10.8244i	−0.800163	−	0.800163i
$184$		0			0
$185$	−0.480449	+	18.3897i	−0.0353233	+	1.35204i
$186$		0			0
$187$	1.80810			0.132222
$188$		0			0
$189$	−0.747384	+	0.747384i	−0.0543642	+	0.0543642i
$190$		0			0
$191$		−	18.2743i		−	1.32228i	−0.750262	−	0.661141i	$-0.770073\pi$
$191$		−	18.2743i		−	1.32228i	0.750262	−	0.661141i	$-0.229927\pi$
$192$		0			0
$193$	−11.3061	−	11.3061i	−0.813832	−	0.813832i	0.171374	−	0.985206i	$-0.445179\pi$
$193$	−11.3061	−	11.3061i	−0.813832	−	0.813832i	−0.985206	+	0.171374i	$0.945179\pi$
$194$		0			0
$195$	−0.0581916	+	2.22735i	−0.00416719	+	0.159504i
$196$		0			0
$197$		−	11.1767i		−	0.796305i	−0.917319	−	0.398153i	$-0.869651\pi$
$197$		−	11.1767i		−	0.796305i	0.917319	−	0.398153i	$-0.130349\pi$
$198$		0			0
$199$		−	18.8869i		−	1.33886i	−0.742877	−	0.669428i	$-0.766539\pi$
$199$		−	18.8869i		−	1.33886i	0.742877	−	0.669428i	$-0.233461\pi$
$200$		0			0
$201$		−	8.99029i		−	0.634126i
$202$		0			0
$203$			4.41728i			0.310032i
$204$		0			0
$205$	−0.332900	+	12.7421i	−0.0232508	+	0.889949i
$206$		0			0
$207$	4.77394	+	4.77394i	0.331812	+	0.331812i
$208$		0			0
$209$			1.90427i			0.131721i
$210$		0			0
$211$	−7.95311	+	7.95311i	−0.547514	+	0.547514i	−0.925721	−	0.378207i	$-0.876541\pi$
$211$	−7.95311	+	7.95311i	−0.547514	+	0.547514i	0.378207	+	0.925721i	$0.376541\pi$
$212$		0			0
$213$	14.1421			0.969002
$214$		0			0
$215$	−0.305353	+	11.6877i	−0.0208249	+	0.797096i
$216$		0			0
$217$	7.81352	+	7.81352i	0.530416	+	0.530416i
$218$		0			0
$219$	6.35840	−	6.35840i	0.429661	−	0.429661i
$220$		0			0
$221$	0.978836	+	0.978836i	0.0658437	+	0.0658437i
$222$		0			0
$223$	−4.22843	+	4.22843i	−0.283157	+	0.283157i	−0.834367	−	0.551210i	$-0.814166\pi$
$223$	−4.22843	+	4.22843i	−0.283157	+	0.283157i	0.551210	+	0.834367i	$0.314166\pi$
$224$		0			0
$225$	4.99318	+	0.261081i	0.332879	+	0.0174054i
$226$		0			0
$227$			15.7654i			1.04639i	0.852214	+	0.523193i	$0.175259\pi$
$227$			15.7654i			1.04639i	−0.852214	+	0.523193i	$0.824741\pi$
$228$		0			0
$229$	0.746140	+	0.746140i	0.0493063	+	0.0493063i	0.731330	−	0.682024i	$-0.238900\pi$
$229$	0.746140	+	0.746140i	0.0493063	+	0.0493063i	−0.682024	+	0.731330i	$0.738900\pi$
$230$		0			0
$231$	1.37565			0.0905112
$232$		0			0
$233$	−5.74517	+	5.74517i	−0.376379	+	0.376379i	−0.869794	−	0.493415i	$-0.835748\pi$
$233$	−5.74517	+	5.74517i	−0.376379	+	0.376379i	0.493415	+	0.869794i	$0.335748\pi$
$234$		0			0
$235$	0.119347	+	0.125751i	0.00778536	+	0.00820308i
$236$		0			0
$237$	8.76588			0.569405
$238$		0			0
$239$	−27.9736			−1.80946			−0.904729	−	0.425987i	$-0.859927\pi$
$239$	−27.9736			−1.80946			−0.904729	+	0.425987i	$0.859927\pi$
$240$		0			0
$241$	−7.01072			−0.451600			−0.225800	−	0.974174i	$-0.572500\pi$
$241$	−7.01072			−0.451600			−0.225800	+	0.974174i	$0.572500\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	0.343555	−	13.1499i	0.0219489	−	0.840118i
$246$		0			0
$247$	−1.03090	+	1.03090i	−0.0655945	+	0.0655945i
$248$		0			0
$249$	12.3589			0.783215
$250$		0			0
$251$	−5.41619	−	5.41619i	−0.341867	−	0.341867i	0.515202	−	0.857069i	$-0.327717\pi$
$251$	−5.41619	−	5.41619i	−0.341867	−	0.341867i	−0.857069	+	0.515202i	$0.827717\pi$
$252$		0			0
$253$		−	8.78702i		−	0.552435i
$254$		0			0
$255$	2.25318	−	2.13845i	0.141100	−	0.133915i
$256$		0			0
$257$	17.0268	−	17.0268i	1.06210	−	1.06210i	0.0641616	−	0.997940i	$-0.479563\pi$
$257$	17.0268	−	17.0268i	1.06210	−	1.06210i	0.997940	−	0.0641616i	$-0.0204373\pi$
$258$		0			0
$259$	6.14869	+	6.14869i	0.382061	+	0.382061i
$260$		0			0
$261$	2.95516	−	2.95516i	0.182920	−	0.182920i
$262$		0			0
$263$	−7.04662	−	7.04662i	−0.434513	−	0.434513i	0.455647	−	0.890160i	$-0.349408\pi$
$263$	−7.04662	−	7.04662i	−0.434513	−	0.434513i	−0.890160	+	0.455647i	$0.849408\pi$
$264$		0			0
$265$	11.4885	+	0.300148i	0.705734	+	0.0184380i
$266$		0			0
$267$	−18.0456			−1.10437
$268$		0			0
$269$	−13.1762	+	13.1762i	−0.803366	+	0.803366i	−0.983620	−	0.180254i	$-0.942308\pi$
$269$	−13.1762	+	13.1762i	−0.803366	+	0.803366i	0.180254	+	0.983620i	$0.442308\pi$
$270$		0			0
$271$		−	2.01115i		−	0.122169i	−0.998133	−	0.0610845i	$-0.980544\pi$
$271$		−	2.01115i		−	0.122169i	0.998133	−	0.0610845i	$-0.0194559\pi$
$272$		0			0
$273$	0.744724	+	0.744724i	0.0450727	+	0.0450727i
$274$		0			0
$275$	−4.35500	−	4.83555i	−0.262616	−	0.291595i
$276$		0			0
$277$		−	5.15280i		−	0.309602i	−0.987946	−	0.154801i	$-0.950526\pi$
$277$		−	5.15280i		−	0.309602i	0.987946	−	0.154801i	$-0.0494736\pi$
$278$		0			0
$279$		−	10.4545i		−	0.625894i
$280$		0			0
$281$			14.7480i			0.879791i	0.898049	+	0.439895i	$0.144984\pi$
$281$			14.7480i			0.879791i	−0.898049	+	0.439895i	$0.855016\pi$
$282$		0			0
$283$		−	7.82068i		−	0.464891i	−0.972609	−	0.232446i	$-0.925327\pi$
$283$		−	7.82068i		−	0.464891i	0.972609	−	0.232446i	$-0.0746728\pi$
$284$		0			0
$285$	2.25218	+	2.37302i	0.133408	+	0.140566i
$286$		0			0
$287$	4.26039	+	4.26039i	0.251483	+	0.251483i
$288$		0			0
$289$			15.0700i			0.886473i
$290$		0			0
$291$	1.29787	−	1.29787i	0.0760826	−	0.0760826i
$292$		0			0
$293$	−19.1115			−1.11651			−0.558254	−	0.829670i	$-0.688529\pi$
$293$	−19.1115			−1.11651			−0.558254	+	0.829670i	$0.688529\pi$
$294$		0			0
$295$	5.28476	−	5.01565i	0.307690	−	0.292022i
$296$		0			0
$297$	−0.920311	−	0.920311i	−0.0534019	−	0.0534019i
$298$		0			0
$299$	4.75695	−	4.75695i	0.275102	−	0.275102i
$300$		0			0
$301$	3.90784	+	3.90784i	0.225244	+	0.225244i
$302$		0			0
$303$	−4.25125	+	4.25125i	−0.244228	+	0.244228i
$304$		0			0
$305$	23.5637	+	24.8280i	1.34925	+	1.42165i
$306$		0			0
$307$		−	3.29048i		−	0.187798i	−0.995582	−	0.0938988i	$-0.970067\pi$
$307$		−	3.29048i		−	0.187798i	0.995582	−	0.0938988i	$-0.0299330\pi$
$308$		0			0
$309$	5.92346	+	5.92346i	0.336974	+	0.336974i
$310$		0			0
$311$	10.6744			0.605292			0.302646	−	0.953103i	$-0.402130\pi$
$311$	10.6744			0.605292			0.302646	+	0.953103i	$0.402130\pi$
$312$		0			0
$313$	−21.5451	+	21.5451i	−1.21780	+	1.21780i	−0.249401	+	0.968400i	$0.580234\pi$
$313$	−21.5451	+	21.5451i	−1.21780	+	1.21780i	−0.968400	+	0.249401i	$0.919766\pi$
$314$		0			0
$315$	1.71428	−	1.62698i	0.0965886	−	0.0916702i
$316$		0			0
$317$	16.1238			0.905603			0.452801	−	0.891611i	$-0.350425\pi$
$317$	16.1238			0.905603			0.452801	+	0.891611i	$0.350425\pi$
$318$		0			0
$319$	−5.43934			−0.304544
$320$		0			0
$321$	−0.0554707			−0.00309607
$322$		0			0
$323$	2.03260			0.113097
$324$		0			0
$325$	0.260152	−	4.97541i	0.0144306	−	0.275986i
$326$		0			0
$327$	0.947769	−	0.947769i	0.0524117	−	0.0524117i
$328$		0			0
$329$	0.0819496			0.00451803
$330$		0			0
$331$	1.97876	+	1.97876i	0.108762	+	0.108762i	0.759394	−	0.650631i	$-0.225496\pi$
$331$	1.97876	+	1.97876i	0.108762	+	0.108762i	−0.650631	+	0.759394i	$0.725496\pi$
$332$		0			0
$333$		−	8.22694i		−	0.450834i
$334$		0			0
$335$	−0.525028	+	20.0960i	−0.0286854	+	1.09796i
$336$		0			0
$337$	25.2423	−	25.2423i	1.37503	−	1.37503i	0.522229	−	0.852806i	$-0.325101\pi$
$337$	25.2423	−	25.2423i	1.37503	−	1.37503i	0.852806	−	0.522229i	$-0.174899\pi$
$338$		0			0
$339$	−10.8801	−	10.8801i	−0.590926	−	0.590926i
$340$		0			0
$341$	−9.62138	+	9.62138i	−0.521027	+	0.521027i
$342$		0			0
$343$	−9.62842	−	9.62842i	−0.519886	−	0.519886i
$344$		0			0
$345$	−10.3924	−	10.9500i	−0.559509	−	0.589529i
$346$		0			0
$347$	24.1967			1.29895			0.649475	−	0.760383i	$-0.274989\pi$
$347$	24.1967			1.29895			0.649475	+	0.760383i	$0.274989\pi$
$348$		0			0
$349$	−2.28867	+	2.28867i	−0.122510	+	0.122510i	−0.765704	−	0.643194i	$-0.777609\pi$
$349$	−2.28867	+	2.28867i	−0.122510	+	0.122510i	0.643194	+	0.765704i	$0.277609\pi$
$350$		0			0
$351$		−	0.996441i		−	0.0531861i
$352$		0			0
$353$	−9.70578	−	9.70578i	−0.516587	−	0.516587i	0.399950	−	0.916537i	$-0.369027\pi$
$353$	−9.70578	−	9.70578i	−0.516587	−	0.516587i	−0.916537	+	0.399950i	$0.869027\pi$
$354$		0			0
$355$	−31.6120	−	0.825893i	−1.67779	−	0.0438338i
$356$		0			0
$357$		−	1.46836i		−	0.0777138i
$358$		0			0
$359$			27.1463i			1.43273i	0.697726	+	0.716365i	$0.254195\pi$
$359$			27.1463i			1.43273i	−0.697726	+	0.716365i	$0.745805\pi$
$360$		0			0
$361$		−	16.8593i		−	0.887331i
$362$		0			0
$363$		−	9.30606i		−	0.488441i
$364$		0			0
$365$	−14.5843	+	13.8416i	−0.763377	+	0.724505i
$366$		0			0
$367$	16.3750	+	16.3750i	0.854769	+	0.854769i	0.990716	−	0.135947i	$-0.0434078\pi$
$367$	16.3750	+	16.3750i	0.854769	+	0.854769i	−0.135947	+	0.990716i	$0.543408\pi$
$368$		0			0
$369$		−	5.70040i		−	0.296751i
$370$		0			0
$371$	3.84123	−	3.84123i	0.199427	−	0.199427i
$372$		0			0
$373$	29.7473			1.54026			0.770129	−	0.637888i	$-0.220192\pi$
$373$	29.7473			1.54026			0.770129	+	0.637888i	$0.220192\pi$
$374$		0			0
$375$	−11.1460	−	0.875196i	−0.575579	−	0.0451949i
$376$		0			0
$377$	−2.94464	−	2.94464i	−0.151657	−	0.151657i
$378$		0			0
$379$	−11.0584	+	11.0584i	−0.568031	+	0.568031i	−0.931576	−	0.363546i	$-0.881566\pi$
$379$	−11.0584	+	11.0584i	−0.568031	+	0.568031i	0.363546	+	0.931576i	$0.381566\pi$
$380$		0			0
$381$	9.61338	+	9.61338i	0.492509	+	0.492509i
$382$		0			0
$383$	16.2297	−	16.2297i	0.829298	−	0.829298i	−0.158122	−	0.987420i	$-0.550544\pi$
$383$	16.2297	−	16.2297i	0.829298	−	0.829298i	0.987420	+	0.158122i	$0.0505439\pi$
$384$		0			0
$385$	−3.07500	−	0.0803373i	−0.156717	−	0.00409437i
$386$		0			0
$387$		−	5.22869i		−	0.265789i
$388$		0			0
$389$	−12.6341	−	12.6341i	−0.640575	−	0.640575i	0.310122	−	0.950697i	$-0.399630\pi$
$389$	−12.6341	−	12.6341i	−0.640575	−	0.640575i	−0.950697	+	0.310122i	$0.899630\pi$
$390$		0			0
$391$	−9.37920			−0.474326
$392$		0			0
$393$	5.60184	−	5.60184i	0.282576	−	0.282576i
$394$		0			0
$395$	−19.5944	−	0.511923i	−0.985902	−	0.0257576i
$396$		0			0
$397$	5.42044			0.272044			0.136022	−	0.990706i	$-0.456568\pi$
$397$	5.42044			0.272044			0.136022	+	0.990706i	$0.456568\pi$
$398$		0			0
$399$	1.54646			0.0774197
$400$		0			0
$401$	15.7550			0.786765			0.393382	−	0.919375i	$-0.371305\pi$
$401$	15.7550			0.786765			0.393382	+	0.919375i	$0.371305\pi$
$402$		0			0
$403$	−10.4173			−0.518922
$404$		0			0
$405$	−2.23531	−	0.0583995i	−0.111073	−	0.00290189i
$406$		0			0
$407$	−7.57135	+	7.57135i	−0.375298	+	0.375298i
$408$		0			0
$409$	−30.9442			−1.53009			−0.765046	−	0.643976i	$-0.777284\pi$
$409$	−30.9442			−1.53009			−0.765046	+	0.643976i	$0.777284\pi$
$410$		0			0
$411$	−4.68373	−	4.68373i	−0.231032	−	0.231032i
$412$		0			0
$413$		−	3.44398i		−	0.169467i
$414$		0			0
$415$	−27.6260	−	0.721754i	−1.35610	−	0.0354295i
$416$		0			0
$417$	−1.64971	+	1.64971i	−0.0807864	+	0.0807864i
$418$		0			0
$419$	−15.2385	−	15.2385i	−0.744451	−	0.744451i	0.228980	−	0.973431i	$-0.426461\pi$
$419$	−15.2385	−	15.2385i	−0.744451	−	0.744451i	−0.973431	+	0.228980i	$0.926461\pi$
$420$		0			0
$421$	−14.4008	+	14.4008i	−0.701852	+	0.701852i	−0.964808	−	0.262956i	$-0.915303\pi$
$421$	−14.4008	+	14.4008i	−0.701852	+	0.701852i	0.262956	+	0.964808i	$0.415303\pi$
$422$		0			0
$423$	−0.0548243	−	0.0548243i	−0.00266565	−	0.00266565i
$424$		0			0
$425$	−5.16143	+	4.64849i	−0.250366	+	0.225485i
$426$		0			0
$427$	16.1800			0.783004
$428$		0			0
$429$	−0.917036	+	0.917036i	−0.0442749	+	0.0442749i
$430$		0			0
$431$			4.47310i			0.215461i	0.994180	+	0.107731i	$0.0343584\pi$
$431$			4.47310i			0.215461i	−0.994180	+	0.107731i	$0.965642\pi$
$432$		0			0
$433$	20.8589	+	20.8589i	1.00242	+	1.00242i	0.999997	+	0.00241793i	$0.000769652\pi$
$433$	20.8589	+	20.8589i	1.00242	+	1.00242i	0.00241793	+	0.999997i	$0.499230\pi$
$434$		0			0
$435$	−6.77827	+	6.43311i	−0.324993	+	0.308444i
$436$		0			0
$437$		−	9.87805i		−	0.472531i
$438$		0			0
$439$			0.257771i			0.0123027i	0.999981	+	0.00615136i	$0.00195805\pi$
$439$			0.257771i			0.0123027i	−0.999981	+	0.00615136i	$0.998042\pi$
$440$		0			0
$441$			5.88283i			0.280135i
$442$		0			0
$443$			27.8275i			1.32212i	0.750331	+	0.661062i	$0.229894\pi$
$443$			27.8275i			1.32212i	−0.750331	+	0.661062i	$0.770106\pi$
$444$		0			0
$445$	40.3374	+	1.05385i	1.91218	+	0.0499574i
$446$		0			0
$447$	12.0813	+	12.0813i	0.571428	+	0.571428i
$448$		0			0
$449$		−	7.32170i		−	0.345533i	−0.984963	−	0.172766i	$-0.944729\pi$
$449$		−	7.32170i		−	0.345533i	0.984963	−	0.172766i	$-0.0552705\pi$
$450$		0			0
$451$	−5.24614	+	5.24614i	−0.247031	+	0.247031i
$452$		0			0
$453$	−12.6503			−0.594364
$454$		0			0
$455$	−1.62119	−	1.70818i	−0.0760027	−	0.0800806i
$456$		0			0
$457$	13.1962	+	13.1962i	0.617293	+	0.617293i	0.944836	−	0.327543i	$-0.106221\pi$
$457$	13.1962	+	13.1962i	0.617293	+	0.617293i	−0.327543	+	0.944836i	$0.606221\pi$
$458$		0			0
$459$	−0.982332	+	0.982332i	−0.0458514	+	0.0458514i
$460$		0			0
$461$	19.6030	+	19.6030i	0.913002	+	0.913002i	0.996507	−	0.0835057i	$-0.0266117\pi$
$461$	19.6030	+	19.6030i	0.913002	+	0.913002i	−0.0835057	+	0.996507i	$0.526612\pi$
$462$		0			0
$463$	17.2918	−	17.2918i	0.803619	−	0.803619i	−0.180040	−	0.983659i	$-0.557623\pi$
$463$	17.2918	−	17.2918i	0.803619	−	0.803619i	0.983659	+	0.180040i	$0.0576227\pi$
$464$		0			0
$465$	−0.610537	+	23.3690i	−0.0283130	+	1.08371i
$466$		0			0
$467$			31.3895i			1.45253i	0.687413	+	0.726267i	$0.258746\pi$
$467$			31.3895i			1.45253i	−0.687413	+	0.726267i	$0.741254\pi$
$468$		0			0
$469$	6.71920	+	6.71920i	0.310264	+	0.310264i
$470$		0			0
$471$	6.31279			0.290878
$472$		0			0
$473$	−4.81202	+	4.81202i	−0.221257	+	0.221257i
$474$		0			0
$475$	−4.89573	−	5.43595i	−0.224632	−	0.249419i
$476$		0			0
$477$	−5.13957			−0.235325
$478$		0			0
$479$	−10.4863			−0.479133			−0.239566	−	0.970880i	$-0.577005\pi$
$479$	−10.4863			−0.479133			−0.239566	+	0.970880i	$0.577005\pi$
$480$		0			0
$481$	−8.19767			−0.373781
$482$		0			0
$483$	−7.13593			−0.324696
$484$		0			0
$485$	−2.97694	+	2.82535i	−0.135176	+	0.128292i
$486$		0			0
$487$	−4.72750	+	4.72750i	−0.214224	+	0.214224i	−0.806059	−	0.591835i	$-0.798404\pi$
$487$	−4.72750	+	4.72750i	−0.214224	+	0.214224i	0.591835	+	0.806059i	$0.298404\pi$
$488$		0			0
$489$	14.6329			0.661721
$490$		0			0
$491$	−3.00877	−	3.00877i	−0.135784	−	0.135784i	0.635948	−	0.771732i	$-0.280609\pi$
$491$	−3.00877	−	3.00877i	−0.135784	−	0.135784i	−0.771732	+	0.635948i	$0.780609\pi$
$492$		0			0
$493$			5.80590i			0.261485i
$494$		0			0
$495$	2.00343	+	2.11092i	0.0900475	+	0.0948789i
$496$		0			0
$497$	−10.5696	+	10.5696i	−0.474111	+	0.474111i
$498$		0			0
$499$	−8.75769	−	8.75769i	−0.392048	−	0.392048i	0.483369	−	0.875417i	$-0.339413\pi$
$499$	−8.75769	−	8.75769i	−0.392048	−	0.392048i	−0.875417	+	0.483369i	$0.839413\pi$
$500$		0			0
$501$	−5.31380	+	5.31380i	−0.237403	+	0.237403i
$502$		0			0
$503$	3.79393	+	3.79393i	0.169163	+	0.169163i	0.786611	−	0.617448i	$-0.211834\pi$
$503$	3.79393	+	3.79393i	0.169163	+	0.169163i	−0.617448	+	0.786611i	$0.711834\pi$
$504$		0			0
$505$	9.75112	−	9.25457i	0.433919	−	0.411823i
$506$		0			0
$507$	12.0071			0.533254
$508$		0			0
$509$	9.92183	−	9.92183i	0.439777	−	0.439777i	−0.452160	−	0.891937i	$-0.649346\pi$
$509$	9.92183	−	9.92183i	0.439777	−	0.439777i	0.891937	+	0.452160i	$0.149346\pi$
$510$		0			0
$511$			9.50433i			0.420447i
$512$		0			0
$513$	−1.03458	−	1.03458i	−0.0456778	−	0.0456778i
$514$		0			0
$515$	−12.8948	−	13.5867i	−0.568214	−	0.598701i
$516$		0			0
$517$			0.100911i			0.00443805i
$518$		0			0
$519$			13.1537i			0.577384i
$520$		0			0
$521$			31.9555i			1.39999i	0.714146	+	0.699997i	$0.246815\pi$
$521$			31.9555i			1.39999i	−0.714146	+	0.699997i	$0.753185\pi$
$522$		0			0
$523$		−	24.3222i		−	1.06354i	−0.846890	−	0.531768i	$-0.821528\pi$
$523$		−	24.3222i		−	1.06354i	0.846890	−	0.531768i	$-0.178472\pi$
$524$		0			0
$525$	−3.92695	+	3.53669i	−0.171386	+	0.154354i
$526$		0			0
$527$	10.2698	+	10.2698i	0.447359	+	0.447359i
$528$		0			0
$529$			22.5810i			0.981784i
$530$		0			0
$531$	−2.30403	+	2.30403i	−0.0999862	+	0.0999862i
$532$		0			0
$533$	−5.68011			−0.246033
$534$		0			0
$535$	0.123994	+	0.00323946i	0.00536073	+	0.000140054i
$536$		0			0
$537$	12.2215	+	12.2215i	0.527398	+	0.527398i
$538$		0			0
$539$	5.41404	−	5.41404i	0.233199	−	0.233199i
$540$		0			0
$541$	−24.3708	−	24.3708i	−1.04778	−	1.04778i	−0.998800	−	0.0489835i	$-0.984402\pi$
$541$	−24.3708	−	24.3708i	−1.04778	−	1.04778i	−0.0489835	−	0.998800i	$-0.515598\pi$
$542$		0			0
$543$	−7.77734	+	7.77734i	−0.333758	+	0.333758i
$544$		0			0
$545$	−2.17390	+	2.06320i	−0.0931197	+	0.0883779i
$546$		0			0
$547$			46.2500i			1.97751i	0.149550	+	0.988754i	$0.452218\pi$
$547$			46.2500i			1.97751i	−0.149550	+	0.988754i	$0.547782\pi$
$548$		0			0
$549$	−10.8244	−	10.8244i	−0.461974	−	0.461974i
$550$		0			0
$551$	−6.11470			−0.260495
$552$		0			0
$553$	−6.55147	+	6.55147i	−0.278597	+	0.278597i
$554$		0			0
$555$	−0.480449	+	18.3897i	−0.0203939	+	0.780601i
$556$		0			0
$557$	3.18081			0.134775			0.0673876	−	0.997727i	$-0.478534\pi$
$557$	3.18081			0.134775			0.0673876	+	0.997727i	$0.478534\pi$
$558$		0			0
$559$	−5.21008			−0.220363
$560$		0			0
$561$	1.80810			0.0763382
$562$		0			0
$563$	−26.5795			−1.12019			−0.560096	−	0.828427i	$-0.689236\pi$
$563$	−26.5795			−1.12019			−0.560096	+	0.828427i	$0.689236\pi$
$564$		0			0
$565$	23.6850	+	24.9558i	0.996434	+	1.04990i
$566$		0			0
$567$	−0.747384	+	0.747384i	−0.0313872	+	0.0313872i
$568$		0			0
$569$	−6.17442			−0.258845			−0.129423	−	0.991590i	$-0.541312\pi$
$569$	−6.17442			−0.258845			−0.129423	+	0.991590i	$0.541312\pi$
$570$		0			0
$571$	−22.1640	−	22.1640i	−0.927533	−	0.927533i	0.0700130	−	0.997546i	$-0.477696\pi$
$571$	−22.1640	−	22.1640i	−0.927533	−	0.927533i	−0.997546	+	0.0700130i	$0.977696\pi$
$572$		0			0
$573$		−	18.2743i		−	0.763419i
$574$		0			0
$575$	22.5908	+	25.0835i	0.942100	+	1.04606i
$576$		0			0
$577$	16.5888	−	16.5888i	0.690601	−	0.690601i	−0.271764	−	0.962364i	$-0.587607\pi$
$577$	16.5888	−	16.5888i	0.690601	−	0.690601i	0.962364	+	0.271764i	$0.0876068\pi$
$578$		0			0
$579$	−11.3061	−	11.3061i	−0.469866	−	0.469866i
$580$		0			0
$581$	−9.23686	+	9.23686i	−0.383209	+	0.383209i
$582$		0			0
$583$	4.73000	+	4.73000i	0.195897	+	0.195897i
$584$		0			0
$585$	−0.0581916	+	2.22735i	−0.00240593	+	0.0920896i
$586$		0			0
$587$	4.69495			0.193781			0.0968907	−	0.995295i	$-0.469110\pi$
$587$	4.69495			0.193781			0.0968907	+	0.995295i	$0.469110\pi$
$588$		0			0
$589$	−10.8160	+	10.8160i	−0.445666	+	0.445666i
$590$		0			0
$591$		−	11.1767i		−	0.459747i
$592$		0			0
$593$	16.7482	+	16.7482i	0.687765	+	0.687765i	0.961738	−	0.273972i	$-0.0883376\pi$
$593$	16.7482	+	16.7482i	0.687765	+	0.687765i	−0.273972	+	0.961738i	$0.588338\pi$
$594$		0			0
$595$	−0.0857514	+	3.28223i	−0.00351546	+	0.134558i
$596$		0			0
$597$		−	18.8869i		−	0.772989i
$598$		0			0
$599$			3.09289i			0.126372i	0.998002	+	0.0631860i	$0.0201261\pi$
$599$			3.09289i			0.126372i	−0.998002	+	0.0631860i	$0.979874\pi$
$600$		0			0
$601$		−	23.3900i		−	0.954099i	−0.878876	−	0.477050i	$-0.841706\pi$
$601$		−	23.3900i		−	0.954099i	0.878876	−	0.477050i	$-0.158294\pi$
$602$		0			0
$603$		−	8.99029i		−	0.366113i
$604$		0			0
$605$	−0.543469	+	20.8019i	−0.0220952	+	0.845716i
$606$		0			0
$607$	−25.7183	−	25.7183i	−1.04387	−	1.04387i	−0.998992	−	0.0448798i	$-0.985710\pi$
$607$	−25.7183	−	25.7183i	−1.04387	−	1.04387i	−0.0448798	−	0.998992i	$-0.514290\pi$
$608$		0			0
$609$			4.41728i			0.178997i
$610$		0			0
$611$	−0.0546292	+	0.0546292i	−0.00221006	+	0.00221006i
$612$		0			0
$613$	−35.2830			−1.42507			−0.712533	−	0.701639i	$-0.752452\pi$
$613$	−35.2830			−1.42507			−0.712533	+	0.701639i	$0.752452\pi$
$614$		0			0
$615$	−0.332900	+	12.7421i	−0.0134238	+	0.513813i
$616$		0			0
$617$	4.50814	+	4.50814i	0.181491	+	0.181491i	0.792005	−	0.610514i	$-0.209037\pi$
$617$	4.50814	+	4.50814i	0.181491	+	0.181491i	−0.610514	+	0.792005i	$0.709037\pi$
$618$		0			0
$619$	1.70323	−	1.70323i	0.0684586	−	0.0684586i	−0.672048	−	0.740507i	$-0.734585\pi$
$619$	1.70323	−	1.70323i	0.0684586	−	0.0684586i	0.740507	+	0.672048i	$0.234585\pi$
$620$		0			0
$621$	4.77394	+	4.77394i	0.191572	+	0.191572i
$622$		0			0
$623$	13.4870	−	13.4870i	0.540344	−	0.540344i
$624$		0			0
$625$	24.8637	+	2.60725i	0.994547	+	0.104290i
$626$		0			0
$627$			1.90427i			0.0760492i
$628$		0			0
$629$	8.08159	+	8.08159i	0.322234	+	0.322234i
$630$		0			0
$631$	−16.8799			−0.671980			−0.335990	−	0.941866i	$-0.609071\pi$
$631$	−16.8799			−0.671980			−0.335990	+	0.941866i	$0.609071\pi$
$632$		0			0
$633$	−7.95311	+	7.95311i	−0.316108	+	0.316108i
$634$		0			0
$635$	−20.9274	−	22.0503i	−0.830480	−	0.875038i
$636$		0			0
$637$	5.86190			0.232257
$638$		0			0
$639$	14.1421			0.559454
$640$		0			0
$641$	−36.2647			−1.43237			−0.716185	−	0.697911i	$-0.754113\pi$
$641$	−36.2647			−1.43237			−0.716185	+	0.697911i	$0.754113\pi$
$642$		0			0
$643$	43.9474			1.73312			0.866559	−	0.499074i	$-0.166327\pi$
$643$	43.9474			1.73312			0.866559	+	0.499074i	$0.166327\pi$
$644$		0			0
$645$	−0.305353	+	11.6877i	−0.0120233	+	0.460203i
$646$		0			0
$647$	2.77825	−	2.77825i	0.109224	−	0.109224i	−0.650382	−	0.759607i	$-0.725391\pi$
$647$	2.77825	−	2.77825i	0.109224	−	0.109224i	0.759607	+	0.650382i	$0.225391\pi$
$648$		0			0
$649$	4.24084			0.166468
$650$		0			0
$651$	7.81352	+	7.81352i	0.306236	+	0.306236i
$652$		0			0
$653$		−	15.8532i		−	0.620384i	−0.950674	−	0.310192i	$-0.899607\pi$
$653$		−	15.8532i		−	0.620384i	0.950674	−	0.310192i	$-0.100393\pi$
$654$		0			0
$655$	−12.8490	+	12.1947i	−0.502051	+	0.476486i
$656$		0			0
$657$	6.35840	−	6.35840i	0.248065	−	0.248065i
$658$		0			0
$659$	3.02357	+	3.02357i	0.117781	+	0.117781i	0.763541	−	0.645759i	$-0.223459\pi$
$659$	3.02357	+	3.02357i	0.117781	+	0.117781i	−0.645759	+	0.763541i	$0.723459\pi$
$660$		0			0
$661$	14.5980	−	14.5980i	0.567797	−	0.567797i	−0.363714	−	0.931511i	$-0.618491\pi$
$661$	14.5980	−	14.5980i	0.567797	−	0.567797i	0.931511	+	0.363714i	$0.118491\pi$
$662$		0			0
$663$	0.978836	+	0.978836i	0.0380149	+	0.0380149i
$664$		0			0
$665$	−3.45680	−	0.0903123i	−0.134049	−	0.00350216i
$666$		0			0
$667$	28.2155			1.09251
$668$		0			0
$669$	−4.22843	+	4.22843i	−0.163480	+	0.163480i
$670$		0			0
$671$			19.9236i			0.769143i
$672$		0			0
$673$	−11.2973	−	11.2973i	−0.435481	−	0.435481i	0.455007	−	0.890488i	$-0.349637\pi$
$673$	−11.2973	−	11.2973i	−0.435481	−	0.435481i	−0.890488	+	0.455007i	$0.849637\pi$
$674$		0			0
$675$	4.99318	+	0.261081i	0.192188	+	0.0100490i
$676$		0			0
$677$			9.23434i			0.354905i	0.984129	+	0.177452i	$0.0567855\pi$
$677$			9.23434i			0.354905i	−0.984129	+	0.177452i	$0.943214\pi$
$678$		0			0
$679$			1.94002i			0.0744510i
$680$		0			0
$681$			15.7654i			0.604131i
$682$		0			0
$683$			10.8971i			0.416967i	0.978026	+	0.208483i	$0.0668527\pi$
$683$			10.8971i			0.416967i	−0.978026	+	0.208483i	$0.933147\pi$
$684$		0			0
$685$	10.1960	+	10.7431i	0.389571	+	0.410473i
$686$		0			0
$687$	0.746140	+	0.746140i	0.0284670	+	0.0284670i
$688$		0			0
$689$			5.12128i			0.195105i
$690$		0			0
$691$	−12.7458	+	12.7458i	−0.484873	+	0.484873i	−0.906684	−	0.421811i	$-0.861395\pi$
$691$	−12.7458	+	12.7458i	−0.484873	+	0.484873i	0.421811	+	0.906684i	$0.361395\pi$
$692$		0			0
$693$	1.37565			0.0522567
$694$		0			0
$695$	3.78394	−	3.59125i	0.143533	−	0.136224i
$696$		0			0
$697$	5.59969	+	5.59969i	0.212103	+	0.212103i
$698$		0			0
$699$	−5.74517	+	5.74517i	−0.217302	+	0.217302i
$700$		0			0
$701$	−28.0269	−	28.0269i	−1.05856	−	1.05856i	−0.998175	−	0.0603853i	$-0.980767\pi$
$701$	−28.0269	−	28.0269i	−1.05856	−	1.05856i	−0.0603853	−	0.998175i	$-0.519233\pi$
$702$		0			0
$703$	−8.51143	+	8.51143i	−0.321015	+	0.321015i
$704$		0			0
$705$	0.119347	+	0.125751i	0.00449488	+	0.00473605i
$706$		0			0
$707$		−	6.35463i		−	0.238991i
$708$		0			0
$709$	−6.39995	−	6.39995i	−0.240355	−	0.240355i	0.576642	−	0.816997i	$-0.304363\pi$
$709$	−6.39995	−	6.39995i	−0.240355	−	0.240355i	−0.816997	+	0.576642i	$0.804363\pi$
$710$		0			0
$711$	8.76588			0.328746
$712$		0			0
$713$	49.9091	−	49.9091i	1.86911	−	1.86911i
$714$		0			0
$715$	2.10341	−	1.99630i	0.0786630	−	0.0746574i
$716$		0			0
$717$	−27.9736			−1.04469
$718$		0			0
$719$	−11.7136			−0.436843			−0.218422	−	0.975854i	$-0.570091\pi$
$719$	−11.7136			−0.436843			−0.218422	+	0.975854i	$0.570091\pi$
$720$		0			0
$721$	−8.85420			−0.329748
$722$		0			0
$723$	−7.01072			−0.260732
$724$		0			0
$725$	15.5272	−	13.9841i	0.576665	−	0.519357i
$726$		0			0
$727$	7.19783	−	7.19783i	0.266953	−	0.266953i	−0.560918	−	0.827871i	$-0.689552\pi$
$727$	7.19783	−	7.19783i	0.266953	−	0.266953i	0.827871	+	0.560918i	$0.189552\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.13631	+	5.13631i	0.189973	+	0.189973i
$732$		0			0
$733$			10.6158i			0.392103i	0.980594	+	0.196052i	$0.0628120\pi$
$733$			10.6158i			0.392103i	−0.980594	+	0.196052i	$0.937188\pi$
$734$		0			0
$735$	0.343555	−	13.1499i	0.0126722	−	0.485043i
$736$		0			0
$737$	−8.27386	+	8.27386i	−0.304772	+	0.304772i
$738$		0			0
$739$	30.4725	+	30.4725i	1.12095	+	1.12095i	0.991599	+	0.129349i	$0.0412888\pi$
$739$	30.4725	+	30.4725i	1.12095	+	1.12095i	0.129349	+	0.991599i	$0.458711\pi$
$740$		0			0
$741$	−1.03090	+	1.03090i	−0.0378710	+	0.0378710i
$742$		0			0
$743$	−6.20995	−	6.20995i	−0.227821	−	0.227821i	0.583961	−	0.811782i	$-0.301502\pi$
$743$	−6.20995	−	6.20995i	−0.227821	−	0.227821i	−0.811782	+	0.583961i	$0.801502\pi$
$744$		0			0
$745$	−26.2999	−	27.7110i	−0.963555	−	1.01525i
$746$		0			0
$747$	12.3589			0.452189
$748$		0			0
$749$	0.0414579	−	0.0414579i	0.00151484	−	0.00151484i
$750$		0			0
$751$		−	11.3219i		−	0.413143i	−0.978432	−	0.206571i	$-0.933769\pi$
$751$		−	11.3219i		−	0.413143i	0.978432	−	0.206571i	$-0.0662305\pi$
$752$		0			0
$753$	−5.41619	−	5.41619i	−0.197377	−	0.197377i
$754$		0			0
$755$	28.2774	+	0.738773i	1.02912	+	0.0268867i
$756$		0			0
$757$			11.1139i			0.403942i	0.979391	+	0.201971i	$0.0647348\pi$
$757$			11.1139i			0.403942i	−0.979391	+	0.201971i	$0.935265\pi$
$758$		0			0
$759$		−	8.78702i		−	0.318949i
$760$		0			0
$761$		−	4.08171i		−	0.147962i	−0.997260	−	0.0739810i	$-0.976430\pi$
$761$		−	4.08171i		−	0.147962i	0.997260	−	0.0739810i	$-0.0235704\pi$
$762$		0			0
$763$			1.41669i			0.0512878i
$764$		0			0
$765$	2.25318	−	2.13845i	0.0814639	−	0.0773156i
$766$		0			0
$767$	2.29583	+	2.29583i	0.0828975	+	0.0828975i
$768$		0			0
$769$		−	31.6143i		−	1.14004i	−0.821631	−	0.570020i	$-0.806935\pi$
$769$		−	31.6143i		−	1.14004i	0.821631	−	0.570020i	$-0.193065\pi$
$770$		0			0
$771$	17.0268	−	17.0268i	0.613204	−	0.613204i
$772$		0			0
$773$	−22.3964			−0.805542			−0.402771	−	0.915301i	$-0.631953\pi$
$773$	−22.3964			−0.805542			−0.402771	+	0.915301i	$0.631953\pi$
$774$		0			0
$775$	2.72947	−	52.2011i	0.0980455	−	1.87512i
$776$		0			0
$777$	6.14869	+	6.14869i	0.220583	+	0.220583i
$778$		0			0
$779$	−5.89752	+	5.89752i	−0.211301	+	0.211301i
$780$		0			0
$781$	−13.0151	−	13.0151i	−0.465719	−	0.465719i
$782$		0			0
$783$	2.95516	−	2.95516i	0.105609	−	0.105609i
$784$		0			0
$785$	−14.1110	−	0.368664i	−0.503644	−	0.0131582i
$786$		0			0
$787$		−	45.2339i		−	1.61242i	−0.591633	−	0.806208i	$-0.701516\pi$
$787$		−	45.2339i		−	1.61242i	0.591633	−	0.806208i	$-0.298484\pi$
$788$		0			0
$789$	−7.04662	−	7.04662i	−0.250866	−	0.250866i
$790$		0			0
$791$	16.2632			0.578254
$792$		0			0
$793$	−10.7859	+	10.7859i	−0.383018	+	0.383018i
$794$		0			0
$795$	11.4885	+	0.300148i	0.407456	+	0.0106452i
$796$		0			0
$797$	33.6337			1.19137			0.595684	−	0.803219i	$-0.296881\pi$
$797$	33.6337			1.19137			0.595684	+	0.803219i	$0.296881\pi$
$798$		0			0
$799$	0.107711			0.00381056
$800$		0			0
$801$	−18.0456			−0.637609
$802$		0			0
$803$	−11.7034			−0.413004
$804$		0			0
$805$	15.9510	+	0.416735i	0.562199	+	0.0146880i
$806$		0			0
$807$	−13.1762	+	13.1762i	−0.463823	+	0.463823i
$808$		0			0
$809$	7.75023			0.272483			0.136242	−	0.990676i	$-0.456498\pi$
$809$	7.75023			0.272483			0.136242	+	0.990676i	$0.456498\pi$
$810$		0			0
$811$	15.5679	+	15.5679i	0.546661	+	0.546661i	0.925474	−	0.378812i	$-0.123667\pi$
$811$	15.5679	+	15.5679i	0.546661	+	0.546661i	−0.378812	+	0.925474i	$0.623667\pi$
$812$		0			0
$813$		−	2.01115i		−	0.0705343i
$814$		0			0
$815$	−32.7089	−	0.854552i	−1.14574	−	0.0299336i
$816$		0			0
$817$	−5.40950	+	5.40950i	−0.189254	+	0.189254i
$818$		0			0
$819$	0.744724	+	0.744724i	0.0260228	+	0.0260228i
$820$		0			0
$821$	25.2360	−	25.2360i	0.880741	−	0.880741i	−0.112869	−	0.993610i	$-0.536004\pi$
$821$	25.2360	−	25.2360i	0.880741	−	0.880741i	0.993610	+	0.112869i	$0.0360041\pi$
$822$		0			0
$823$	24.2751	+	24.2751i	0.846178	+	0.846178i	0.989654	−	0.143476i	$-0.0458278\pi$
$823$	24.2751	+	24.2751i	0.846178	+	0.846178i	−0.143476	+	0.989654i	$0.545828\pi$
$824$		0			0
$825$	−4.35500	−	4.83555i	−0.151622	−	0.168352i
$826$		0			0
$827$	−8.03445			−0.279385			−0.139693	−	0.990195i	$-0.544611\pi$
$827$	−8.03445			−0.279385			−0.139693	+	0.990195i	$0.544611\pi$
$828$		0			0
$829$	−17.2385	+	17.2385i	−0.598718	+	0.598718i	−0.939971	−	0.341254i	$-0.889148\pi$
$829$	−17.2385	+	17.2385i	−0.598718	+	0.598718i	0.341254	+	0.939971i	$0.389148\pi$
$830$		0			0
$831$		−	5.15280i		−	0.178749i
$832$		0			0
$833$	−5.77890	−	5.77890i	−0.200227	−	0.200227i
$834$		0			0
$835$	12.1883	−	11.5676i	0.421793	−	0.400315i
$836$		0			0
$837$		−	10.4545i		−	0.361360i
$838$		0			0
$839$		−	23.0026i		−	0.794136i	−0.917789	−	0.397068i	$-0.870028\pi$
$839$		−	23.0026i		−	0.794136i	0.917789	−	0.397068i	$-0.129972\pi$
$840$		0			0
$841$			11.5340i			0.397726i
$842$		0			0
$843$			14.7480i			0.507947i
$844$		0			0
$845$	−26.8395	−	0.701209i	−0.923308	−	0.0241223i
$846$		0			0
$847$	6.95520	+	6.95520i	0.238983	+	0.238983i
$848$		0			0
$849$		−	7.82068i		−	0.268405i
$850$		0			0
$851$	39.2750	−	39.2750i	1.34633	−	1.34633i
$852$		0			0
$853$	17.9417			0.614312			0.307156	−	0.951659i	$-0.400623\pi$
$853$	17.9417			0.614312			0.307156	+	0.951659i	$0.400623\pi$
$854$		0			0
$855$	2.25218	+	2.37302i	0.0770230	+	0.0811556i
$856$		0			0
$857$	−27.5741	−	27.5741i	−0.941914	−	0.941914i	0.0564890	−	0.998403i	$-0.482009\pi$
$857$	−27.5741	−	27.5741i	−0.941914	−	0.941914i	−0.998403	+	0.0564890i	$0.982009\pi$
$858$		0			0
$859$	−22.0003	+	22.0003i	−0.750640	+	0.750640i	−0.974599	−	0.223959i	$-0.928102\pi$
$859$	−22.0003	+	22.0003i	−0.750640	+	0.750640i	0.223959	+	0.974599i	$0.428102\pi$
$860$		0			0
$861$	4.26039	+	4.26039i	0.145194	+	0.145194i
$862$		0			0
$863$	16.4456	−	16.4456i	0.559814	−	0.559814i	−0.369440	−	0.929254i	$-0.620451\pi$
$863$	16.4456	−	16.4456i	0.559814	−	0.559814i	0.929254	+	0.369440i	$0.120451\pi$
$864$		0			0
$865$	0.768171	−	29.4026i	0.0261186	−	0.999718i
$866$		0			0
$867$			15.0700i			0.511806i
$868$		0			0
$869$	−8.06733	−	8.06733i	−0.273665	−	0.273665i
$870$		0			0
$871$	−8.95830			−0.303540
$872$		0			0
$873$	1.29787	−	1.29787i	0.0439263	−	0.0439263i
$874$		0			0
$875$	8.98447	−	7.67626i	0.303731	−	0.259505i
$876$		0			0
$877$	−6.59281			−0.222623			−0.111312	−	0.993786i	$-0.535505\pi$
$877$	−6.59281			−0.222623			−0.111312	+	0.993786i	$0.535505\pi$
$878$		0			0
$879$	−19.1115			−0.644617
$880$		0			0
$881$	22.1698			0.746920			0.373460	−	0.927646i	$-0.378171\pi$
$881$	22.1698			0.746920			0.373460	+	0.927646i	$0.378171\pi$
$882$		0			0
$883$	38.7205			1.30305			0.651524	−	0.758628i	$-0.274130\pi$
$883$	38.7205			1.30305			0.651524	+	0.758628i	$0.274130\pi$
$884$		0			0
$885$	5.28476	−	5.01565i	0.177645	−	0.168599i
$886$		0			0
$887$	25.2413	−	25.2413i	0.847518	−	0.847518i	−0.142305	−	0.989823i	$-0.545451\pi$
$887$	25.2413	−	25.2413i	0.847518	−	0.847518i	0.989823	+	0.142305i	$0.0454512\pi$
$888$		0			0
$889$	−14.3698			−0.481947
$890$		0			0
$891$	−0.920311	−	0.920311i	−0.0308316	−	0.0308316i
$892$		0			0
$893$			0.113440i			0.00379613i
$894$		0			0
$895$	−26.6051	−	28.0326i	−0.889310	−	0.937025i
$896$		0			0
$897$	4.75695	−	4.75695i	0.158830	−	0.158830i
$898$		0			0
$899$	−30.8947	−	30.8947i	−1.03040	−	1.03040i
$900$		0			0
$901$	5.04877	−	5.04877i	0.168199	−	0.168199i
$902$		0			0
$903$	3.90784	+	3.90784i	0.130045	+	0.130045i
$904$		0			0
$905$	17.8389	−	16.9305i	0.592986	−	0.562790i
$906$		0			0
$907$	9.44895			0.313747			0.156874	−	0.987619i	$-0.449858\pi$
$907$	9.44895			0.313747			0.156874	+	0.987619i	$0.449858\pi$
$908$		0			0
$909$	−4.25125	+	4.25125i	−0.141005	+	0.141005i
$910$		0			0
$911$		−	36.1798i		−	1.19869i	−0.800490	−	0.599346i	$-0.795427\pi$
$911$		−	36.1798i		−	1.19869i	0.800490	−	0.599346i	$-0.204573\pi$
$912$		0			0
$913$	−11.3740	−	11.3740i	−0.376426	−	0.376426i
$914$		0			0
$915$	23.5637	+	24.8280i	0.778992	+	0.820788i
$916$		0			0
$917$			8.37345i			0.276516i
$918$		0			0
$919$			45.3587i			1.49624i	0.663561	+	0.748122i	$0.269044\pi$
$919$			45.3587i			1.49624i	−0.663561	+	0.748122i	$0.730956\pi$
$920$		0			0
$921$		−	3.29048i		−	0.108425i
$922$		0			0
$923$		−	14.0918i		−	0.463837i
$924$		0			0
$925$	2.14790	−	41.0786i	0.0706226	−	1.35066i
$926$		0			0
$927$	5.92346	+	5.92346i	0.194552	+	0.194552i
$928$		0			0
$929$			0.551101i			0.0180810i	0.999959	+	0.00904052i	$0.00287773\pi$
$929$			0.551101i			0.0180810i	−0.999959	+	0.00904052i	$0.997122\pi$
$930$		0			0
$931$	6.08626	−	6.08626i	0.199469	−	0.199469i
$932$		0			0
$933$	10.6744			0.349466
$934$		0			0
$935$	−4.04166	−	0.105592i	−0.132176	−	0.00345324i
$936$		0			0
$937$	−10.4271	−	10.4271i	−0.340639	−	0.340639i	0.515969	−	0.856607i	$-0.327432\pi$
$937$	−10.4271	−	10.4271i	−0.340639	−	0.340639i	−0.856607	+	0.515969i	$0.827432\pi$
$938$		0			0
$939$	−21.5451	+	21.5451i	−0.703098	+	0.703098i
$940$		0			0
$941$	−7.44442	−	7.44442i	−0.242681	−	0.242681i	0.575277	−	0.817958i	$-0.304894\pi$
$941$	−7.44442	−	7.44442i	−0.242681	−	0.242681i	−0.817958	+	0.575277i	$0.804894\pi$
$942$		0			0
$943$	27.2134	−	27.2134i	0.886190	−	0.886190i
$944$		0			0
$945$	1.71428	−	1.62698i	0.0557655	−	0.0529258i
$946$		0			0
$947$		−	15.8341i		−	0.514539i	−0.966340	−	0.257270i	$-0.917177\pi$
$947$		−	15.8341i		−	0.514539i	0.966340	−	0.257270i	$-0.0828229\pi$
$948$		0			0
$949$	−6.33577	−	6.33577i	−0.205668	−	0.205668i
$950$		0			0
$951$	16.1238			0.522850
$952$		0			0
$953$	14.8928	−	14.8928i	0.482424	−	0.482424i	−0.423481	−	0.905905i	$-0.639192\pi$
$953$	14.8928	−	14.8928i	0.482424	−	0.482424i	0.905905	+	0.423481i	$0.139192\pi$
$954$		0			0
$955$	−1.06721	+	40.8486i	−0.0345341	+	1.32183i
$956$		0			0
$957$	−5.43934			−0.175829
$958$		0			0
$959$	7.00109			0.226077
$960$		0			0
$961$	−78.2963			−2.52569
$962$		0			0
$963$	−0.0554707			−0.00178752
$964$		0			0
$965$	24.6123	+	25.9329i	0.792300	+	0.834809i
$966$		0			0
$967$	27.8728	−	27.8728i	0.896330	−	0.896330i	−0.0987795	−	0.995109i	$-0.531494\pi$
$967$	27.8728	−	27.8728i	0.896330	−	0.896330i	0.995109	+	0.0987795i	$0.0314939\pi$
$968$		0			0
$969$	2.03260			0.0652966
$970$		0			0
$971$	−30.0958	−	30.0958i	−0.965819	−	0.965819i	0.0336155	−	0.999435i	$-0.489298\pi$
$971$	−30.0958	−	30.0958i	−0.965819	−	0.965819i	−0.999435	+	0.0336155i	$0.989298\pi$
$972$		0			0
$973$		−	2.46593i		−	0.0790540i
$974$		0			0
$975$	0.260152	−	4.97541i	0.00833154	−	0.159341i
$976$		0			0
$977$	−9.03427	+	9.03427i	−0.289032	+	0.289032i	−0.836697	−	0.547666i	$-0.815517\pi$
$977$	−9.03427	+	9.03427i	−0.289032	+	0.289032i	0.547666	+	0.836697i	$0.315517\pi$
$978$		0			0
$979$	16.6075	+	16.6075i	0.530780	+	0.530780i
$980$		0			0
$981$	0.947769	−	0.947769i	0.0302599	−	0.0302599i
$982$		0			0
$983$	−24.5191	−	24.5191i	−0.782039	−	0.782039i	0.198135	−	0.980175i	$-0.436511\pi$
$983$	−24.5191	−	24.5191i	−0.782039	−	0.782039i	−0.980175	+	0.198135i	$0.936511\pi$
$984$		0			0
$985$	−0.652712	+	24.9833i	−0.0207971	+	0.796034i
$986$		0			0
$987$	0.0819496			0.00260848
$988$		0			0
$989$	24.9615	−	24.9615i	0.793728	−	0.793728i
$990$		0			0
$991$			25.8872i			0.822334i	0.911560	+	0.411167i	$0.134879\pi$
$991$			25.8872i			0.822334i	−0.911560	+	0.411167i	$0.865121\pi$
$992$		0			0
$993$	1.97876	+	1.97876i	0.0627940	+	0.0627940i
$994$		0			0
$995$	−1.10298	+	42.2180i	−0.0349670	+	1.33840i
$996$		0			0
$997$			16.7546i			0.530624i	0.964163	+	0.265312i	$0.0854750\pi$
$997$			16.7546i			0.530624i	−0.964163	+	0.265312i	$0.914525\pi$
$998$		0			0
$999$		−	8.22694i		−	0.260289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.y.j.223.1		16
4.3	odd	2		1920.2.y.i.223.1		16
5.2	odd	4		1920.2.bc.j.607.3		16
8.3	odd	2		240.2.y.e.163.5	✓	16
8.5	even	2		960.2.y.e.943.8		16
16.3	odd	4		960.2.bc.e.463.6		16
16.5	even	4		1920.2.bc.i.1183.3		16
16.11	odd	4		1920.2.bc.j.1183.3		16
16.13	even	4		240.2.bc.e.43.8	yes	16
20.7	even	4		1920.2.bc.i.607.3		16
24.11	even	2		720.2.z.f.163.4		16
40.27	even	4		240.2.bc.e.67.8	yes	16
40.37	odd	4		960.2.bc.e.367.6		16
48.29	odd	4		720.2.bd.f.523.1		16
80.27	even	4	inner	1920.2.y.j.1567.1		16
80.37	odd	4		1920.2.y.i.1567.1		16
80.67	even	4		960.2.y.e.847.8		16
80.77	odd	4		240.2.y.e.187.5	yes	16
120.107	odd	4		720.2.bd.f.307.1		16
240.77	even	4		720.2.z.f.667.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.e.163.5	✓	16	8.3	odd	2
240.2.y.e.187.5	yes	16	80.77	odd	4
240.2.bc.e.43.8	yes	16	16.13	even	4
240.2.bc.e.67.8	yes	16	40.27	even	4
720.2.z.f.163.4		16	24.11	even	2
720.2.z.f.667.4		16	240.77	even	4
720.2.bd.f.307.1		16	120.107	odd	4
720.2.bd.f.523.1		16	48.29	odd	4
960.2.y.e.847.8		16	80.67	even	4
960.2.y.e.943.8		16	8.5	even	2
960.2.bc.e.367.6		16	40.37	odd	4
960.2.bc.e.463.6		16	16.3	odd	4
1920.2.y.i.223.1		16	4.3	odd	2
1920.2.y.i.1567.1		16	80.37	odd	4
1920.2.y.j.223.1		16	1.1	even	1	trivial
1920.2.y.j.1567.1		16	80.27	even	4	inner
1920.2.bc.i.607.3		16	20.7	even	4
1920.2.bc.i.1183.3		16	16.5	even	4
1920.2.bc.j.607.3		16	5.2	odd	4
1920.2.bc.j.1183.3		16	16.11	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-2.23531 - 0.0583995i) q^{5} +(-0.747384 + 0.747384i) q^{7} +1.00000 q^{9} +(-0.920311 - 0.920311i) q^{11} -0.996441i q^{13} +(-2.23531 - 0.0583995i) q^{15} +(-0.982332 + 0.982332i) q^{17} +(-1.03458 - 1.03458i) q^{19} +(-0.747384 + 0.747384i) q^{21} +(4.77394 + 4.77394i) q^{23} +(4.99318 + 0.261081i) q^{25} +1.00000 q^{27} +(2.95516 - 2.95516i) q^{29} -10.4545i q^{31} +(-0.920311 - 0.920311i) q^{33} +(1.71428 - 1.62698i) q^{35} -8.22694i q^{37} -0.996441i q^{39} -5.70040i q^{41} -5.22869i q^{43} +(-2.23531 - 0.0583995i) q^{45} +(-0.0548243 - 0.0548243i) q^{47} +5.88283i q^{49} +(-0.982332 + 0.982332i) q^{51} -5.13957 q^{53} +(2.00343 + 2.11092i) q^{55} +(-1.03458 - 1.03458i) q^{57} +(-2.30403 + 2.30403i) q^{59} +(-10.8244 - 10.8244i) q^{61} +(-0.747384 + 0.747384i) q^{63} +(-0.0581916 + 2.22735i) q^{65} -8.99029i q^{67} +(4.77394 + 4.77394i) q^{69} +14.1421 q^{71} +(6.35840 - 6.35840i) q^{73} +(4.99318 + 0.261081i) q^{75} +1.37565 q^{77} +8.76588 q^{79} +1.00000 q^{81} +12.3589 q^{83} +(2.25318 - 2.13845i) q^{85} +(2.95516 - 2.95516i) q^{87} -18.0456 q^{89} +(0.744724 + 0.744724i) q^{91} -10.4545i q^{93} +(2.25218 + 2.37302i) q^{95} +(1.29787 - 1.29787i) q^{97} +(-0.920311 - 0.920311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 4 q^{5} + 4 q^{7} + 16 q^{9} + 4 q^{15} - 8 q^{17} + 8 q^{19} + 4 q^{21} + 32 q^{25} + 16 q^{27} - 12 q^{29} - 20 q^{35} + 4 q^{45} + 32 q^{47} - 8 q^{51} - 16 q^{53} + 4 q^{55} + 8 q^{57}+ \cdots + 48 q^{97}+O(q^{100}) \) 16 * q + 16 * q^3 + 4 * q^5 + 4 * q^7 + 16 * q^9 + 4 * q^15 - 8 * q^17 + 8 * q^19 + 4 * q^21 + 32 * q^25 + 16 * q^27 - 12 * q^29 - 20 * q^35 + 4 * q^45 + 32 * q^47 - 8 * q^51 - 16 * q^53 + 4 * q^55 + 8 * q^57 - 24 * q^59 - 40 * q^61 + 4 * q^63 - 4 * q^65 + 8 * q^73 + 32 * q^75 + 72 * q^77 + 48 * q^79 + 16 * q^81 - 8 * q^83 + 8 * q^85 - 12 * q^87 - 40 * q^91 - 8 * q^95 + 48 * q^97

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