LMFDB - Embedded newform 1792.2.m.g.1345.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1792,2,Mod(449,1792)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1792, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1792.449");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1792 = 2^{8} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1792.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.3091920422$
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} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1345.2
Root			$-1.09227 + 0.838128i$ of defining polynomial
Character	$\chi$	$=$	1792.1345
Dual form			1792.2.m.g.449.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26274 - 1.26274i) q^{3} +(-2.95746 + 2.95746i) q^{5} +1.00000i q^{7} +0.189043i q^{9} +O(q^{10})$	\(q+(-1.26274 - 1.26274i) q^{3} +(-2.95746 + 2.95746i) q^{5} +1.00000i q^{7} +0.189043i q^{9} +(-3.18454 + 3.18454i) q^{11} +(-3.42541 - 3.42541i) q^{13} +7.46903 q^{15} -5.13834 q^{17} +(-1.50497 - 1.50497i) q^{19} +(1.26274 - 1.26274i) q^{21} +7.11888i q^{23} -12.4932i q^{25} +(-3.54952 + 3.54952i) q^{27} +(3.84618 + 3.84618i) q^{29} +0.831138 q^{31} +8.04251 q^{33} +(-2.95746 - 2.95746i) q^{35} +(5.64619 - 5.64619i) q^{37} +8.65084i q^{39} -2.22639i q^{41} +(1.61789 - 1.61789i) q^{43} +(-0.559087 - 0.559087i) q^{45} +7.83759 q^{47} -1.00000 q^{49} +(6.48840 + 6.48840i) q^{51} +(-5.58781 + 5.58781i) q^{53} -18.8363i q^{55} +3.80079i q^{57} +(1.85835 - 1.85835i) q^{59} +(1.65017 + 1.65017i) q^{61} -0.189043 q^{63} +20.2611 q^{65} +(5.77581 + 5.77581i) q^{67} +(8.98933 - 8.98933i) q^{69} -6.04851i q^{71} -7.67177i q^{73} +(-15.7757 + 15.7757i) q^{75} +(-3.18454 - 3.18454i) q^{77} -1.90198 q^{79} +9.53139 q^{81} +(-7.97920 - 7.97920i) q^{83} +(15.1964 - 15.1964i) q^{85} -9.71349i q^{87} +2.49938i q^{89} +(3.42541 - 3.42541i) q^{91} +(-1.04951 - 1.04951i) q^{93} +8.90180 q^{95} -1.98784 q^{97} +(-0.602015 - 0.602015i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 - 4 * q^5	$ 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times$.

$n$	$1023$	$1025$	$1541$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.26274	−	1.26274i	−0.729045	−	0.729045i	0.241384	−	0.970430i	$-0.422399\pi$
$3$	−1.26274	−	1.26274i	−0.729045	−	0.729045i	−0.970430	+	0.241384i	$0.922399\pi$
$4$		0			0
$5$	−2.95746	+	2.95746i	−1.32262	+	1.32262i	−0.410967	+	0.911650i	$0.634809\pi$
$5$	−2.95746	+	2.95746i	−1.32262	+	1.32262i	−0.911650	+	0.410967i	$0.865191\pi$
$6$		0			0
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		0			0
$9$			0.189043i			0.0630143i
$10$		0			0
$11$	−3.18454	+	3.18454i	−0.960175	+	0.960175i	−0.999237	−	0.0390622i	$-0.987563\pi$
$11$	−3.18454	+	3.18454i	−0.960175	+	0.960175i	0.0390622	+	0.999237i	$0.487563\pi$
$12$		0			0
$13$	−3.42541	−	3.42541i	−0.950039	−	0.950039i	0.0487712	−	0.998810i	$-0.484469\pi$
$13$	−3.42541	−	3.42541i	−0.950039	−	0.950039i	−0.998810	+	0.0487712i	$0.984469\pi$
$14$		0			0
$15$	7.46903			1.92850
$16$		0			0
$17$	−5.13834			−1.24623			−0.623115	−	0.782130i	$-0.714133\pi$
$17$	−5.13834			−1.24623			−0.623115	+	0.782130i	$0.714133\pi$
$18$		0			0
$19$	−1.50497	−	1.50497i	−0.345265	−	0.345265i	0.513078	−	0.858342i	$-0.328505\pi$
$19$	−1.50497	−	1.50497i	−0.345265	−	0.345265i	−0.858342	+	0.513078i	$0.828505\pi$
$20$		0			0
$21$	1.26274	−	1.26274i	0.275553	−	0.275553i
$22$		0			0
$23$			7.11888i			1.48439i	0.670184	+	0.742195i	$0.266215\pi$
$23$			7.11888i			1.48439i	−0.670184	+	0.742195i	$0.733785\pi$
$24$		0			0
$25$		−	12.4932i		−	2.49863i
$26$		0			0
$27$	−3.54952	+	3.54952i	−0.683105	+	0.683105i
$28$		0			0
$29$	3.84618	+	3.84618i	0.714218	+	0.714218i	0.967415	−	0.253197i	$-0.0814820\pi$
$29$	3.84618	+	3.84618i	0.714218	+	0.714218i	−0.253197	+	0.967415i	$0.581482\pi$
$30$		0			0
$31$	0.831138			0.149277			0.0746384	−	0.997211i	$-0.476220\pi$
$31$	0.831138			0.149277			0.0746384	+	0.997211i	$0.476220\pi$
$32$		0			0
$33$	8.04251			1.40002
$34$		0			0
$35$	−2.95746	−	2.95746i	−0.499902	−	0.499902i
$36$		0			0
$37$	5.64619	−	5.64619i	0.928229	−	0.928229i	−0.0693630	−	0.997591i	$-0.522097\pi$
$37$	5.64619	−	5.64619i	0.928229	−	0.928229i	0.997591	+	0.0693630i	$0.0220967\pi$
$38$		0			0
$39$			8.65084i			1.38524i
$40$		0			0
$41$		−	2.22639i		−	0.347704i	−0.984772	−	0.173852i	$-0.944379\pi$
$41$		−	2.22639i		−	0.347704i	0.984772	−	0.173852i	$-0.0556214\pi$
$42$		0			0
$43$	1.61789	−	1.61789i	0.246726	−	0.246726i	−0.572900	−	0.819626i	$-0.694182\pi$
$43$	1.61789	−	1.61789i	0.246726	−	0.246726i	0.819626	+	0.572900i	$0.194182\pi$
$44$		0			0
$45$	−0.559087	−	0.559087i	−0.0833438	−	0.0833438i
$46$		0			0
$47$	7.83759			1.14323			0.571615	−	0.820522i	$-0.306317\pi$
$47$	7.83759			1.14323			0.571615	+	0.820522i	$0.306317\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	6.48840	+	6.48840i	0.908558	+	0.908558i
$52$		0			0
$53$	−5.58781	+	5.58781i	−0.767544	+	0.767544i	−0.977674	−	0.210129i	$-0.932612\pi$
$53$	−5.58781	+	5.58781i	−0.767544	+	0.767544i	0.210129	+	0.977674i	$0.432612\pi$
$54$		0			0
$55$		−	18.8363i		−	2.53989i
$56$		0			0
$57$			3.80079i			0.503427i
$58$		0			0
$59$	1.85835	−	1.85835i	0.241937	−	0.241937i	−0.575714	−	0.817651i	$-0.695276\pi$
$59$	1.85835	−	1.85835i	0.241937	−	0.241937i	0.817651	+	0.575714i	$0.195276\pi$
$60$		0			0
$61$	1.65017	+	1.65017i	0.211283	+	0.211283i	0.804812	−	0.593529i	$-0.202266\pi$
$61$	1.65017	+	1.65017i	0.211283	+	0.211283i	−0.593529	+	0.804812i	$0.702266\pi$
$62$		0			0
$63$	−0.189043			−0.0238172
$64$		0			0
$65$	20.2611			2.51307
$66$		0			0
$67$	5.77581	+	5.77581i	0.705627	+	0.705627i	0.965613	−	0.259985i	$-0.0837178\pi$
$67$	5.77581	+	5.77581i	0.705627	+	0.705627i	−0.259985	+	0.965613i	$0.583718\pi$
$68$		0			0
$69$	8.98933	−	8.98933i	1.08219	−	1.08219i
$70$		0			0
$71$		−	6.04851i		−	0.717826i	−0.933371	−	0.358913i	$-0.883147\pi$
$71$		−	6.04851i		−	0.717826i	0.933371	−	0.358913i	$-0.116853\pi$
$72$		0			0
$73$		−	7.67177i		−	0.897913i	−0.893554	−	0.448957i	$-0.851796\pi$
$73$		−	7.67177i		−	0.897913i	0.893554	−	0.448957i	$-0.148204\pi$
$74$		0			0
$75$	−15.7757	+	15.7757i	−1.82162	+	1.82162i
$76$		0			0
$77$	−3.18454	−	3.18454i	−0.362912	−	0.362912i
$78$		0			0
$79$	−1.90198			−0.213989			−0.106995	−	0.994260i	$-0.534123\pi$
$79$	−1.90198			−0.213989			−0.106995	+	0.994260i	$0.534123\pi$
$80$		0			0
$81$	9.53139			1.05904
$82$		0			0
$83$	−7.97920	−	7.97920i	−0.875831	−	0.875831i	0.117269	−	0.993100i	$-0.462586\pi$
$83$	−7.97920	−	7.97920i	−0.875831	−	0.875831i	−0.993100	+	0.117269i	$0.962586\pi$
$84$		0			0
$85$	15.1964	−	15.1964i	1.64829	−	1.64829i
$86$		0			0
$87$		−	9.71349i		−	1.04139i
$88$		0			0
$89$			2.49938i			0.264934i	0.991187	+	0.132467i	$0.0422898\pi$
$89$			2.49938i			0.264934i	−0.991187	+	0.132467i	$0.957710\pi$
$90$		0			0
$91$	3.42541	−	3.42541i	0.359081	−	0.359081i
$92$		0			0
$93$	−1.04951	−	1.04951i	−0.108830	−	0.108830i
$94$		0			0
$95$	8.90180			0.913306
$96$		0			0
$97$	−1.98784			−0.201834			−0.100917	−	0.994895i	$-0.532178\pi$
$97$	−1.98784			−0.201834			−0.100917	+	0.994895i	$0.532178\pi$
$98$		0			0
$99$	−0.602015	−	0.602015i	−0.0605047	−	0.0605047i
$100$		0			0
$101$	11.1341	−	11.1341i	1.10788	−	1.10788i	0.114451	−	0.993429i	$-0.463489\pi$
$101$	11.1341	−	11.1341i	1.10788	−	1.10788i	0.993429	−	0.114451i	$-0.0365110\pi$
$102$		0			0
$103$			15.2106i			1.49874i	0.662150	+	0.749371i	$0.269644\pi$
$103$			15.2106i			1.49874i	−0.662150	+	0.749371i	$0.730356\pi$
$104$		0			0
$105$			7.46903i			0.728903i
$106$		0			0
$107$	−0.897608	+	0.897608i	−0.0867751	+	0.0867751i	−0.749162	−	0.662387i	$-0.769544\pi$
$107$	−0.897608	+	0.897608i	−0.0867751	+	0.0867751i	0.662387	+	0.749162i	$0.269544\pi$
$108$		0			0
$109$	−2.84528	−	2.84528i	−0.272528	−	0.272528i	0.557589	−	0.830117i	$-0.311727\pi$
$109$	−2.84528	−	2.84528i	−0.272528	−	0.272528i	−0.830117	+	0.557589i	$0.811727\pi$
$110$		0			0
$111$	−14.2594			−1.35344
$112$		0			0
$113$	−1.66487			−0.156618			−0.0783089	−	0.996929i	$-0.524952\pi$
$113$	−1.66487			−0.156618			−0.0783089	+	0.996929i	$0.524952\pi$
$114$		0			0
$115$	−21.0538	−	21.0538i	−1.96328	−	1.96328i
$116$		0			0
$117$	0.647550	−	0.647550i	0.0598660	−	0.0598660i
$118$		0			0
$119$		−	5.13834i		−	0.471031i
$120$		0			0
$121$		−	9.28258i		−	0.843871i
$122$		0			0
$123$	−2.81136	+	2.81136i	−0.253492	+	0.253492i
$124$		0			0
$125$	22.1607	+	22.1607i	1.98212	+	1.98212i
$126$		0			0
$127$	−7.86069			−0.697523			−0.348762	−	0.937211i	$-0.613398\pi$
$127$	−7.86069			−0.697523			−0.348762	+	0.937211i	$0.613398\pi$
$128$		0			0
$129$	−4.08596			−0.359749
$130$		0			0
$131$	5.44479	+	5.44479i	0.475713	+	0.475713i	0.903758	−	0.428045i	$-0.140797\pi$
$131$	5.44479	+	5.44479i	0.475713	+	0.475713i	−0.428045	+	0.903758i	$0.640797\pi$
$132$		0			0
$133$	1.50497	−	1.50497i	0.130498	−	0.130498i
$134$		0			0
$135$		−	20.9951i		−	1.80697i
$136$		0			0
$137$		−	17.6977i		−	1.51201i	−0.654564	−	0.756007i	$-0.727148\pi$
$137$		−	17.6977i		−	1.51201i	0.654564	−	0.756007i	$-0.272852\pi$
$138$		0			0
$139$	11.4502	−	11.4502i	0.971194	−	0.971194i	−0.0284022	−	0.999597i	$-0.509042\pi$
$139$	11.4502	−	11.4502i	0.971194	−	0.971194i	0.999597	+	0.0284022i	$0.00904192\pi$
$140$		0			0
$141$	−9.89687	−	9.89687i	−0.833467	−	0.833467i
$142$		0			0
$143$	21.8167			1.82441
$144$		0			0
$145$	−22.7499			−1.88927
$146$		0			0
$147$	1.26274	+	1.26274i	0.104149	+	0.104149i
$148$		0			0
$149$	8.61299	−	8.61299i	0.705604	−	0.705604i	−0.260004	−	0.965608i	$-0.583724\pi$
$149$	8.61299	−	8.61299i	0.705604	−	0.705604i	0.965608	+	0.260004i	$0.0837239\pi$
$150$		0			0
$151$			17.7449i			1.44406i	0.691863	+	0.722029i	$0.256790\pi$
$151$			17.7449i			1.44406i	−0.691863	+	0.722029i	$0.743210\pi$
$152$		0			0
$153$		−	0.971366i		−	0.0785303i
$154$		0			0
$155$	−2.45806	+	2.45806i	−0.197436	+	0.197436i
$156$		0			0
$157$	−9.88456	−	9.88456i	−0.788873	−	0.788873i	0.192436	−	0.981310i	$-0.438361\pi$
$157$	−9.88456	−	9.88456i	−0.788873	−	0.788873i	−0.981310	+	0.192436i	$0.938361\pi$
$158$		0			0
$159$	14.1119			1.11915
$160$		0			0
$161$	−7.11888			−0.561047
$162$		0			0
$163$	9.61397	+	9.61397i	0.753024	+	0.753024i	0.975042	−	0.222019i	$-0.0712646\pi$
$163$	9.61397	+	9.61397i	0.753024	+	0.753024i	−0.222019	+	0.975042i	$0.571265\pi$
$164$		0			0
$165$	−23.7854	+	23.7854i	−1.85169	+	1.85169i
$166$		0			0
$167$		−	6.70735i		−	0.519030i	−0.965739	−	0.259515i	$-0.916437\pi$
$167$		−	6.70735i		−	0.519030i	0.965739	−	0.259515i	$-0.0835627\pi$
$168$		0			0
$169$			10.4669i			0.805147i
$170$		0			0
$171$	0.284505	−	0.284505i	0.0217566	−	0.0217566i
$172$		0			0
$173$	−14.7331	−	14.7331i	−1.12014	−	1.12014i	−0.991720	−	0.128417i	$-0.959010\pi$
$173$	−14.7331	−	14.7331i	−1.12014	−	1.12014i	−0.128417	−	0.991720i	$-0.540990\pi$
$174$		0			0
$175$	12.4932			0.944394
$176$		0			0
$177$	−4.69325			−0.352766
$178$		0			0
$179$	−15.8453	−	15.8453i	−1.18433	−	1.18433i	−0.978611	−	0.205719i	$-0.934047\pi$
$179$	−15.8453	−	15.8453i	−1.18433	−	1.18433i	−0.205719	−	0.978611i	$-0.565953\pi$
$180$		0			0
$181$	3.13208	−	3.13208i	0.232805	−	0.232805i	−0.581057	−	0.813863i	$-0.697361\pi$
$181$	3.13208	−	3.13208i	0.232805	−	0.232805i	0.813863	+	0.581057i	$0.197361\pi$
$182$		0			0
$183$		−	4.16749i		−	0.308070i
$184$		0			0
$185$			33.3968i			2.45538i
$186$		0			0
$187$	16.3632	−	16.3632i	1.19660	−	1.19660i
$188$		0			0
$189$	−3.54952	−	3.54952i	−0.258189	−	0.258189i
$190$		0			0
$191$	7.38976			0.534704			0.267352	−	0.963599i	$-0.413851\pi$
$191$	7.38976			0.534704			0.267352	+	0.963599i	$0.413851\pi$
$192$		0			0
$193$	0.139138			0.0100154			0.00500769	−	0.999987i	$-0.498406\pi$
$193$	0.139138			0.0100154			0.00500769	+	0.999987i	$0.498406\pi$
$194$		0			0
$195$	−25.5845	−	25.5845i	−1.83215	−	1.83215i
$196$		0			0
$197$	−7.35796	+	7.35796i	−0.524233	+	0.524233i	−0.918847	−	0.394614i	$-0.870878\pi$
$197$	−7.35796	+	7.35796i	−0.524233	+	0.524233i	0.394614	+	0.918847i	$0.370878\pi$
$198$		0			0
$199$			5.09550i			0.361211i	0.983556	+	0.180605i	$0.0578057\pi$
$199$			5.09550i			0.361211i	−0.983556	+	0.180605i	$0.942194\pi$
$200$		0			0
$201$		−	14.5867i		−	1.02887i
$202$		0			0
$203$	−3.84618	+	3.84618i	−0.269949	+	0.269949i
$204$		0			0
$205$	6.58447	+	6.58447i	0.459879	+	0.459879i
$206$		0			0
$207$	−1.34577			−0.0935378
$208$		0			0
$209$	9.58529			0.663029
$210$		0			0
$211$	8.88050	+	8.88050i	0.611359	+	0.611359i	0.943300	−	0.331941i	$-0.107704\pi$
$211$	8.88050	+	8.88050i	0.611359	+	0.611359i	−0.331941	+	0.943300i	$0.607704\pi$
$212$		0			0
$213$	−7.63772	+	7.63772i	−0.523328	+	0.523328i
$214$		0			0
$215$			9.56970i			0.652648i
$216$		0			0
$217$			0.831138i			0.0564213i
$218$		0			0
$219$	−9.68748	+	9.68748i	−0.654619	+	0.654619i
$220$		0			0
$221$	17.6009	+	17.6009i	1.18397	+	1.18397i
$222$		0			0
$223$	−9.66949			−0.647517			−0.323758	−	0.946140i	$-0.604946\pi$
$223$	−9.66949			−0.647517			−0.323758	+	0.946140i	$0.604946\pi$
$224$		0			0
$225$	2.36174			0.157450
$226$		0			0
$227$	2.11845	+	2.11845i	0.140606	+	0.140606i	0.773906	−	0.633300i	$-0.218300\pi$
$227$	2.11845	+	2.11845i	0.140606	+	0.140606i	−0.633300	+	0.773906i	$0.718300\pi$
$228$		0			0
$229$	−6.36091	+	6.36091i	−0.420341	+	0.420341i	−0.885321	−	0.464980i	$-0.846061\pi$
$229$	−6.36091	+	6.36091i	−0.420341	+	0.420341i	0.464980	+	0.885321i	$0.346061\pi$
$230$		0			0
$231$			8.04251i			0.529158i
$232$		0			0
$233$			7.53066i			0.493350i	0.969098	+	0.246675i	$0.0793380\pi$
$233$			7.53066i			0.493350i	−0.969098	+	0.246675i	$0.920662\pi$
$234$		0			0
$235$	−23.1794	+	23.1794i	−1.51206	+	1.51206i
$236$		0			0
$237$	2.40171	+	2.40171i	0.156008	+	0.156008i
$238$		0			0
$239$	−1.87072			−0.121007			−0.0605034	−	0.998168i	$-0.519271\pi$
$239$	−1.87072			−0.121007			−0.0605034	+	0.998168i	$0.519271\pi$
$240$		0			0
$241$	−14.4911			−0.933454			−0.466727	−	0.884401i	$-0.654567\pi$
$241$	−14.4911			−0.933454			−0.466727	+	0.884401i	$0.654567\pi$
$242$		0			0
$243$	−1.38715	−	1.38715i	−0.0889857	−	0.0889857i
$244$		0			0
$245$	2.95746	−	2.95746i	0.188945	−	0.188945i
$246$		0			0
$247$			10.3103i			0.656029i
$248$		0			0
$249$			20.1514i			1.27704i
$250$		0			0
$251$	4.48287	−	4.48287i	0.282956	−	0.282956i	−0.551330	−	0.834287i	$-0.685880\pi$
$251$	4.48287	−	4.48287i	0.282956	−	0.282956i	0.834287	+	0.551330i	$0.185880\pi$
$252$		0			0
$253$	−22.6704	−	22.6704i	−1.42527	−	1.42527i
$254$		0			0
$255$	−38.3784			−2.40335
$256$		0			0
$257$	12.1594			0.758483			0.379241	−	0.925298i	$-0.376185\pi$
$257$	12.1594			0.758483			0.379241	+	0.925298i	$0.376185\pi$
$258$		0			0
$259$	5.64619	+	5.64619i	0.350837	+	0.350837i
$260$		0			0
$261$	−0.727094	+	0.727094i	−0.0450060	+	0.0450060i
$262$		0			0
$263$			0.0299529i			0.00184698i	1.00000		0.000923488i	$0.000293955\pi$
$263$			0.0299529i			0.00184698i	−1.00000		0.000923488i	$0.999706\pi$
$264$		0			0
$265$		−	33.0514i		−	2.03033i
$266$		0			0
$267$	3.15607	−	3.15607i	0.193149	−	0.193149i
$268$		0			0
$269$	12.7719	+	12.7719i	0.778718	+	0.778718i	0.979613	−	0.200895i	$-0.0643849\pi$
$269$	12.7719	+	12.7719i	0.778718	+	0.778718i	−0.200895	+	0.979613i	$0.564385\pi$
$270$		0			0
$271$	10.0906			0.612958			0.306479	−	0.951877i	$-0.400849\pi$
$271$	10.0906			0.612958			0.306479	+	0.951877i	$0.400849\pi$
$272$		0			0
$273$	−8.65084			−0.523573
$274$		0			0
$275$	39.7849	+	39.7849i	2.39912	+	2.39912i
$276$		0			0
$277$	6.26957	−	6.26957i	0.376702	−	0.376702i	−0.493209	−	0.869911i	$-0.664176\pi$
$277$	6.26957	−	6.26957i	0.376702	−	0.376702i	0.869911	+	0.493209i	$0.164176\pi$
$278$		0			0
$279$			0.157121i			0.00940657i
$280$		0			0
$281$			11.6731i			0.696356i	0.937428	+	0.348178i	$0.113200\pi$
$281$			11.6731i			0.696356i	−0.937428	+	0.348178i	$0.886800\pi$
$282$		0			0
$283$	−8.87749	+	8.87749i	−0.527712	+	0.527712i	−0.919890	−	0.392178i	$-0.871722\pi$
$283$	−8.87749	+	8.87749i	−0.527712	+	0.527712i	0.392178	+	0.919890i	$0.371722\pi$
$284$		0			0
$285$	−11.2407	−	11.2407i	−0.665841	−	0.665841i
$286$		0			0
$287$	2.22639			0.131420
$288$		0			0
$289$	9.40252			0.553090
$290$		0			0
$291$	2.51013	+	2.51013i	0.147146	+	0.147146i
$292$		0			0
$293$	−17.1935	+	17.1935i	−1.00445	+	1.00445i	−0.00446326	+	0.999990i	$0.501421\pi$
$293$	−17.1935	+	17.1935i	−1.00445	+	1.00445i	−0.999990	+	0.00446326i	$0.998579\pi$
$294$		0			0
$295$			10.9920i			0.639980i
$296$		0			0
$297$		−	22.6072i		−	1.31180i
$298$		0			0
$299$	24.3851	−	24.3851i	1.41023	−	1.41023i
$300$		0			0
$301$	1.61789	+	1.61789i	0.0932536	+	0.0932536i
$302$		0			0
$303$	−28.1189			−1.61539
$304$		0			0
$305$	−9.76065			−0.558893
$306$		0			0
$307$	19.2712	+	19.2712i	1.09987	+	1.09987i	0.994426	+	0.105440i	$0.0336251\pi$
$307$	19.2712	+	19.2712i	1.09987	+	1.09987i	0.105440	+	0.994426i	$0.466375\pi$
$308$		0			0
$309$	19.2071	−	19.2071i	1.09265	−	1.09265i
$310$		0			0
$311$			5.78650i			0.328122i	0.986450	+	0.164061i	$0.0524595\pi$
$311$			5.78650i			0.328122i	−0.986450	+	0.164061i	$0.947541\pi$
$312$		0			0
$313$		−	3.03673i		−	0.171646i	−0.996310	−	0.0858231i	$-0.972648\pi$
$313$		−	3.03673i		−	0.171646i	0.996310	−	0.0858231i	$-0.0273520\pi$
$314$		0			0
$315$	0.559087	−	0.559087i	0.0315010	−	0.0315010i
$316$		0			0
$317$	3.32219	+	3.32219i	0.186593	+	0.186593i	0.794221	−	0.607629i	$-0.207879\pi$
$317$	3.32219	+	3.32219i	0.186593	+	0.186593i	−0.607629	+	0.794221i	$0.707879\pi$
$318$		0			0
$319$	−24.4966			−1.37155
$320$		0			0
$321$	2.26690			0.126526
$322$		0			0
$323$	7.73306	+	7.73306i	0.430279	+	0.430279i
$324$		0			0
$325$	−42.7942	+	42.7942i	−2.37380	+	2.37380i
$326$		0			0
$327$			7.18572i			0.397371i
$328$		0			0
$329$			7.83759i			0.432101i
$330$		0			0
$331$	25.5017	−	25.5017i	1.40170	−	1.40170i	0.606990	−	0.794710i	$-0.292377\pi$
$331$	25.5017	−	25.5017i	1.40170	−	1.40170i	0.794710	−	0.606990i	$-0.207623\pi$
$332$		0			0
$333$	1.06737	+	1.06737i	0.0584917	+	0.0584917i
$334$		0			0
$335$	−34.1634			−1.86655
$336$		0			0
$337$	31.3282			1.70656			0.853279	−	0.521454i	$-0.174610\pi$
$337$	31.3282			1.70656			0.853279	+	0.521454i	$0.174610\pi$
$338$		0			0
$339$	2.10230	+	2.10230i	0.114182	+	0.114182i
$340$		0			0
$341$	−2.64679	+	2.64679i	−0.143332	+	0.143332i
$342$		0			0
$343$		−	1.00000i		−	0.0539949i
$344$		0			0
$345$			53.1712i			2.86264i
$346$		0			0
$347$	24.1128	−	24.1128i	1.29444	−	1.29444i	0.362429	−	0.932011i	$-0.381947\pi$
$347$	24.1128	−	24.1128i	1.29444	−	1.29444i	0.932011	−	0.362429i	$-0.118053\pi$
$348$		0			0
$349$	20.9731	+	20.9731i	1.12266	+	1.12266i	0.991340	+	0.131324i	$0.0419228\pi$
$349$	20.9731	+	20.9731i	1.12266	+	1.12266i	0.131324	+	0.991340i	$0.458077\pi$
$350$		0			0
$351$	24.3171			1.29795
$352$		0			0
$353$	−0.605671			−0.0322366			−0.0161183	−	0.999870i	$-0.505131\pi$
$353$	−0.605671			−0.0322366			−0.0161183	+	0.999870i	$0.505131\pi$
$354$		0			0
$355$	17.8882	+	17.8882i	0.949409	+	0.949409i
$356$		0			0
$357$	−6.48840	+	6.48840i	−0.343403	+	0.343403i
$358$		0			0
$359$			11.6214i			0.613354i	0.951814	+	0.306677i	$0.0992171\pi$
$359$			11.6214i			0.613354i	−0.951814	+	0.306677i	$0.900783\pi$
$360$		0			0
$361$		−	14.4701i		−	0.761585i
$362$		0			0
$363$	−11.7215	+	11.7215i	−0.615220	+	0.615220i
$364$		0			0
$365$	22.6890	+	22.6890i	1.18760	+	1.18760i
$366$		0			0
$367$	13.1299			0.685376			0.342688	−	0.939449i	$-0.388663\pi$
$367$	13.1299			0.685376			0.342688	+	0.939449i	$0.388663\pi$
$368$		0			0
$369$	0.420883			0.0219103
$370$		0			0
$371$	−5.58781	−	5.58781i	−0.290104	−	0.290104i
$372$		0			0
$373$	13.0674	−	13.0674i	0.676604	−	0.676604i	−0.282626	−	0.959230i	$-0.591206\pi$
$373$	13.0674	−	13.0674i	0.676604	−	0.676604i	0.959230	+	0.282626i	$0.0912056\pi$
$374$		0			0
$375$		−	55.9666i		−	2.89010i
$376$		0			0
$377$		−	26.3495i		−	1.35707i
$378$		0			0
$379$	2.92702	−	2.92702i	0.150351	−	0.150351i	−0.627924	−	0.778275i	$-0.716095\pi$
$379$	2.92702	−	2.92702i	0.150351	−	0.150351i	0.778275	+	0.627924i	$0.216095\pi$
$380$		0			0
$381$	9.92603	+	9.92603i	0.508526	+	0.508526i
$382$		0			0
$383$	−34.3667			−1.75606			−0.878029	−	0.478608i	$-0.841142\pi$
$383$	−34.3667			−1.75606			−0.878029	+	0.478608i	$0.841142\pi$
$384$		0			0
$385$	18.8363			0.959987
$386$		0			0
$387$	0.305851	+	0.305851i	0.0155473	+	0.0155473i
$388$		0			0
$389$	7.44858	−	7.44858i	0.377658	−	0.377658i	−0.492599	−	0.870257i	$-0.663953\pi$
$389$	7.44858	−	7.44858i	0.377658	−	0.377658i	0.870257	+	0.492599i	$0.163953\pi$
$390$		0			0
$391$		−	36.5792i		−	1.84989i
$392$		0			0
$393$		−	13.7507i		−	0.693633i
$394$		0			0
$395$	5.62503	−	5.62503i	0.283026	−	0.283026i
$396$		0			0
$397$	7.92582	+	7.92582i	0.397786	+	0.397786i	0.877451	−	0.479666i	$-0.159242\pi$
$397$	7.92582	+	7.92582i	0.397786	+	0.397786i	−0.479666	+	0.877451i	$0.659242\pi$
$398$		0			0
$399$	−3.80079			−0.190278
$400$		0			0
$401$	15.4031			0.769192			0.384596	−	0.923085i	$-0.374341\pi$
$401$	15.4031			0.769192			0.384596	+	0.923085i	$0.374341\pi$
$402$		0			0
$403$	−2.84699	−	2.84699i	−0.141819	−	0.141819i
$404$		0			0
$405$	−28.1887	+	28.1887i	−1.40071	+	1.40071i
$406$		0			0
$407$			35.9610i			1.78252i
$408$		0			0
$409$		−	22.6029i		−	1.11764i	−0.829289	−	0.558820i	$-0.811254\pi$
$409$		−	22.6029i		−	1.11764i	0.829289	−	0.558820i	$-0.188746\pi$
$410$		0			0
$411$	−22.3476	+	22.3476i	−1.10233	+	1.10233i
$412$		0			0
$413$	1.85835	+	1.85835i	0.0914436	+	0.0914436i
$414$		0			0
$415$	47.1964			2.31678
$416$		0			0
$417$	−28.9174			−1.41609
$418$		0			0
$419$	−9.01333	−	9.01333i	−0.440330	−	0.440330i	0.451793	−	0.892123i	$-0.350785\pi$
$419$	−9.01333	−	9.01333i	−0.440330	−	0.440330i	−0.892123	+	0.451793i	$0.850785\pi$
$420$		0			0
$421$	−21.8788	+	21.8788i	−1.06631	+	1.06631i	−0.0686687	+	0.997640i	$0.521875\pi$
$421$	−21.8788	+	21.8788i	−1.06631	+	1.06631i	−0.997640	+	0.0686687i	$0.978125\pi$
$422$		0			0
$423$			1.48164i			0.0720399i
$424$		0			0
$425$			64.1941i			3.11387i
$426$		0			0
$427$	−1.65017	+	1.65017i	−0.0798575	+	0.0798575i
$428$		0			0
$429$	−27.5489	−	27.5489i	−1.33007	−	1.33007i
$430$		0			0
$431$	−13.1089			−0.631434			−0.315717	−	0.948853i	$-0.602245\pi$
$431$	−13.1089			−0.631434			−0.315717	+	0.948853i	$0.602245\pi$
$432$		0			0
$433$	−35.1859			−1.69093			−0.845463	−	0.534033i	$-0.820676\pi$
$433$	−35.1859			−1.69093			−0.845463	+	0.534033i	$0.820676\pi$
$434$		0			0
$435$	28.7273	+	28.7273i	1.37737	+	1.37737i
$436$		0			0
$437$	10.7137	−	10.7137i	0.512507	−	0.512507i
$438$		0			0
$439$		−	4.82251i		−	0.230166i	−0.993356	−	0.115083i	$-0.963287\pi$
$439$		−	4.82251i		−	0.230166i	0.993356	−	0.115083i	$-0.0367134\pi$
$440$		0			0
$441$		−	0.189043i		−	0.00900204i
$442$		0			0
$443$	−12.5595	+	12.5595i	−0.596719	+	0.596719i	−0.939438	−	0.342719i	$-0.888652\pi$
$443$	−12.5595	+	12.5595i	−0.596719	+	0.596719i	0.342719	+	0.939438i	$0.388652\pi$
$444$		0			0
$445$	−7.39181	−	7.39181i	−0.350406	−	0.350406i
$446$		0			0
$447$	−21.7520			−1.02883
$448$		0			0
$449$	−29.9204			−1.41203			−0.706015	−	0.708197i	$-0.749509\pi$
$449$	−29.9204			−1.41203			−0.706015	+	0.708197i	$0.749509\pi$
$450$		0			0
$451$	7.09003	+	7.09003i	0.333856	+	0.333856i
$452$		0			0
$453$	22.4072	−	22.4072i	1.05278	−	1.05278i
$454$		0			0
$455$			20.2611i			0.949853i
$456$		0			0
$457$			29.1293i			1.36261i	0.732000	+	0.681305i	$0.238587\pi$
$457$			29.1293i			1.36261i	−0.732000	+	0.681305i	$0.761413\pi$
$458$		0			0
$459$	18.2386	−	18.2386i	0.851306	−	0.851306i
$460$		0			0
$461$	−7.15458	−	7.15458i	−0.333222	−	0.333222i	0.520587	−	0.853809i	$-0.325713\pi$
$461$	−7.15458	−	7.15458i	−0.333222	−	0.333222i	−0.853809	+	0.520587i	$0.825713\pi$
$462$		0			0
$463$	−40.1547			−1.86615			−0.933074	−	0.359686i	$-0.882884\pi$
$463$	−40.1547			−1.86615			−0.933074	+	0.359686i	$0.882884\pi$
$464$		0			0
$465$	6.20779			0.287880
$466$		0			0
$467$	−28.5054	−	28.5054i	−1.31907	−	1.31907i	−0.914510	−	0.404563i	$-0.867423\pi$
$467$	−28.5054	−	28.5054i	−1.31907	−	1.31907i	−0.404563	−	0.914510i	$-0.632577\pi$
$468$		0			0
$469$	−5.77581	+	5.77581i	−0.266702	+	0.266702i
$470$		0			0
$471$			24.9633i			1.15025i
$472$		0			0
$473$			10.3045i			0.473800i
$474$		0			0
$475$	−18.8019	+	18.8019i	−0.862689	+	0.862689i
$476$		0			0
$477$	−1.05634	−	1.05634i	−0.0483663	−	0.0483663i
$478$		0			0
$479$	−12.6994			−0.580249			−0.290124	−	0.956989i	$-0.593697\pi$
$479$	−12.6994			−0.580249			−0.290124	+	0.956989i	$0.593697\pi$
$480$		0			0
$481$	−38.6811			−1.76371
$482$		0			0
$483$	8.98933	+	8.98933i	0.409028	+	0.409028i
$484$		0			0
$485$	5.87895	−	5.87895i	0.266949	−	0.266949i
$486$		0			0
$487$		−	34.2373i		−	1.55144i	−0.631076	−	0.775721i	$-0.717386\pi$
$487$		−	34.2373i		−	1.55144i	0.631076	−	0.775721i	$-0.282614\pi$
$488$		0			0
$489$		−	24.2799i		−	1.09798i
$490$		0			0
$491$	21.4142	−	21.4142i	0.966412	−	0.966412i	−0.0330424	−	0.999454i	$-0.510520\pi$
$491$	21.4142	−	21.4142i	0.966412	−	0.966412i	0.999454	+	0.0330424i	$0.0105196\pi$
$492$		0			0
$493$	−19.7630	−	19.7630i	−0.890080	−	0.890080i
$494$		0			0
$495$	3.56087			0.160049
$496$		0			0
$497$	6.04851			0.271313
$498$		0			0
$499$	−15.7099	−	15.7099i	−0.703270	−	0.703270i	0.261841	−	0.965111i	$-0.415670\pi$
$499$	−15.7099	−	15.7099i	−0.703270	−	0.703270i	−0.965111	+	0.261841i	$0.915670\pi$
$500$		0			0
$501$	−8.46966	+	8.46966i	−0.378397	+	0.378397i
$502$		0			0
$503$			28.6238i			1.27627i	0.769923	+	0.638137i	$0.220294\pi$
$503$			28.6238i			1.27627i	−0.769923	+	0.638137i	$0.779706\pi$
$504$		0			0
$505$			65.8571i			2.93060i
$506$		0			0
$507$	13.2170	−	13.2170i	0.586989	−	0.586989i
$508$		0			0
$509$	15.0347	+	15.0347i	0.666399	+	0.666399i	0.956881	−	0.290481i	$-0.0938154\pi$
$509$	15.0347	+	15.0347i	0.666399	+	0.666399i	−0.290481	+	0.956881i	$0.593815\pi$
$510$		0			0
$511$	7.67177			0.339379
$512$		0			0
$513$	10.6839			0.471704
$514$		0			0
$515$	−44.9847	−	44.9847i	−1.98226	−	1.98226i
$516$		0			0
$517$	−24.9591	+	24.9591i	−1.09770	+	1.09770i
$518$		0			0
$519$			37.2083i			1.63326i
$520$		0			0
$521$		−	23.7033i		−	1.03846i	−0.854635	−	0.519230i	$-0.826219\pi$
$521$		−	23.7033i		−	1.03846i	0.854635	−	0.519230i	$-0.173781\pi$
$522$		0			0
$523$	−13.9046	+	13.9046i	−0.608004	+	0.608004i	−0.942424	−	0.334420i	$-0.891459\pi$
$523$	−13.9046	+	13.9046i	−0.608004	+	0.608004i	0.334420	+	0.942424i	$0.391459\pi$
$524$		0			0
$525$	−15.7757	−	15.7757i	−0.688506	−	0.688506i
$526$		0			0
$527$	−4.27067			−0.186033
$528$		0			0
$529$	−27.6785			−1.20341
$530$		0			0
$531$	0.351308	+	0.351308i	0.0152455	+	0.0152455i
$532$		0			0
$533$	−7.62631	+	7.62631i	−0.330332	+	0.330332i
$534$		0			0
$535$		−	5.30928i		−	0.229540i
$536$		0			0
$537$			40.0170i			1.72686i
$538$		0			0
$539$	3.18454	−	3.18454i	0.137168	−	0.137168i
$540$		0			0
$541$	−8.66926	−	8.66926i	−0.372721	−	0.372721i	0.495747	−	0.868467i	$-0.334894\pi$
$541$	−8.66926	−	8.66926i	−0.372721	−	0.372721i	−0.868467	+	0.495747i	$0.834894\pi$
$542$		0			0
$543$	−7.91002			−0.339451
$544$		0			0
$545$	16.8296			0.720901
$546$		0			0
$547$	4.07284	+	4.07284i	0.174142	+	0.174142i	0.788796	−	0.614655i	$-0.210705\pi$
$547$	4.07284	+	4.07284i	0.174142	+	0.174142i	−0.614655	+	0.788796i	$0.710705\pi$
$548$		0			0
$549$	−0.311954	+	0.311954i	−0.0133139	+	0.0133139i
$550$		0			0
$551$		−	11.5768i		−	0.493188i
$552$		0			0
$553$		−	1.90198i		−	0.0808804i
$554$		0			0
$555$	42.1716	−	42.1716i	1.79008	−	1.79008i
$556$		0			0
$557$	−1.82388	−	1.82388i	−0.0772805	−	0.0772805i	0.667410	−	0.744690i	$-0.267403\pi$
$557$	−1.82388	−	1.82388i	−0.0772805	−	0.0772805i	−0.744690	+	0.667410i	$0.767403\pi$
$558$		0			0
$559$	−11.0839			−0.468798
$560$		0			0
$561$	−41.3252			−1.74475
$562$		0			0
$563$	−10.6911	−	10.6911i	−0.450577	−	0.450577i	0.444969	−	0.895546i	$-0.353215\pi$
$563$	−10.6911	−	10.6911i	−0.450577	−	0.450577i	−0.895546	+	0.444969i	$0.853215\pi$
$564$		0			0
$565$	4.92379	−	4.92379i	0.207145	−	0.207145i
$566$		0			0
$567$			9.53139i			0.400281i
$568$		0			0
$569$		−	11.0034i		−	0.461288i	−0.973038	−	0.230644i	$-0.925917\pi$
$569$		−	11.0034i		−	0.461288i	0.973038	−	0.230644i	$-0.0740833\pi$
$570$		0			0
$571$	28.9901	−	28.9901i	1.21320	−	1.21320i	0.243231	−	0.969968i	$-0.421793\pi$
$571$	28.9901	−	28.9901i	1.21320	−	1.21320i	0.969968	−	0.243231i	$-0.0782073\pi$
$572$		0			0
$573$	−9.33137	−	9.33137i	−0.389824	−	0.389824i
$574$		0			0
$575$	88.9373			3.70894
$576$		0			0
$577$	2.85596			0.118895			0.0594476	−	0.998231i	$-0.481066\pi$
$577$	2.85596			0.118895			0.0594476	+	0.998231i	$0.481066\pi$
$578$		0			0
$579$	−0.175696	−	0.175696i	−0.00730167	−	0.00730167i
$580$		0			0
$581$	7.97920	−	7.97920i	0.331033	−	0.331033i
$582$		0			0
$583$		−	35.5892i		−	1.47395i
$584$		0			0
$585$			3.83021i			0.158360i
$586$		0			0
$587$	−17.5561	+	17.5561i	−0.724617	+	0.724617i	−0.969542	−	0.244925i	$-0.921237\pi$
$587$	−17.5561	+	17.5561i	−0.724617	+	0.724617i	0.244925	+	0.969542i	$0.421237\pi$
$588$		0			0
$589$	−1.25084	−	1.25084i	−0.0515400	−	0.0515400i
$590$		0			0
$591$	18.5824			0.764379
$592$		0			0
$593$	7.72713			0.317315			0.158658	−	0.987334i	$-0.449283\pi$
$593$	7.72713			0.317315			0.158658	+	0.987334i	$0.449283\pi$
$594$		0			0
$595$	15.1964	+	15.1964i	0.622993	+	0.622993i
$596$		0			0
$597$	6.43431	−	6.43431i	0.263339	−	0.263339i
$598$		0			0
$599$		−	7.28771i		−	0.297768i	−0.988855	−	0.148884i	$-0.952432\pi$
$599$		−	7.28771i		−	0.297768i	0.988855	−	0.148884i	$-0.0475681\pi$
$600$		0			0
$601$		−	20.0313i		−	0.817095i	−0.912737	−	0.408547i	$-0.866035\pi$
$601$		−	20.0313i		−	0.817095i	0.912737	−	0.408547i	$-0.133965\pi$
$602$		0			0
$603$	−1.09188	+	1.09188i	−0.0444646	+	0.0444646i
$604$		0			0
$605$	27.4529	+	27.4529i	1.11612	+	1.11612i
$606$		0			0
$607$	17.2219			0.699014			0.349507	−	0.936934i	$-0.386349\pi$
$607$	17.2219			0.699014			0.349507	+	0.936934i	$0.386349\pi$
$608$		0			0
$609$	9.71349			0.393610
$610$		0			0
$611$	−26.8470	−	26.8470i	−1.08611	−	1.08611i
$612$		0			0
$613$	26.4453	−	26.4453i	1.06811	−	1.06811i	0.0706108	−	0.997504i	$-0.477505\pi$
$613$	26.4453	−	26.4453i	1.06811	−	1.06811i	0.997504	−	0.0706108i	$-0.0224948\pi$
$614$		0			0
$615$		−	16.6290i		−	0.670545i
$616$		0			0
$617$		−	22.1036i		−	0.889856i	−0.895566	−	0.444928i	$-0.853229\pi$
$617$		−	22.1036i		−	0.889856i	0.895566	−	0.444928i	$-0.146771\pi$
$618$		0			0
$619$	−21.5602	+	21.5602i	−0.866579	+	0.866579i	−0.992092	−	0.125513i	$-0.959942\pi$
$619$	−21.5602	+	21.5602i	−0.866579	+	0.866579i	0.125513	+	0.992092i	$0.459942\pi$
$620$		0			0
$621$	−25.2686	−	25.2686i	−1.01399	−	1.01399i
$622$		0			0
$623$	−2.49938			−0.100135
$624$		0			0
$625$	−68.6132			−2.74453
$626$		0			0
$627$	−12.1038	−	12.1038i	−0.483378	−	0.483378i
$628$		0			0
$629$	−29.0121	+	29.0121i	−1.15679	+	1.15679i
$630$		0			0
$631$		−	40.3151i		−	1.60492i	−0.596708	−	0.802458i	$-0.703525\pi$
$631$		−	40.3151i		−	1.60492i	0.596708	−	0.802458i	$-0.296475\pi$
$632$		0			0
$633$		−	22.4276i		−	0.891417i
$634$		0			0
$635$	23.2477	−	23.2477i	0.922556	−	0.922556i
$636$		0			0
$637$	3.42541	+	3.42541i	0.135720	+	0.135720i
$638$		0			0
$639$	1.14343			0.0452333
$640$		0			0
$641$	−0.875535			−0.0345815			−0.0172908	−	0.999851i	$-0.505504\pi$
$641$	−0.875535			−0.0345815			−0.0172908	+	0.999851i	$0.505504\pi$
$642$		0			0
$643$	−28.5976	−	28.5976i	−1.12778	−	1.12778i	−0.990538	−	0.137240i	$-0.956177\pi$
$643$	−28.5976	−	28.5976i	−1.12778	−	1.12778i	−0.137240	−	0.990538i	$-0.543823\pi$
$644$		0			0
$645$	12.0841	−	12.0841i	0.475810	−	0.475810i
$646$		0			0
$647$			3.32973i			0.130905i	0.997856	+	0.0654526i	$0.0208491\pi$
$647$			3.32973i			0.130905i	−0.997856	+	0.0654526i	$0.979151\pi$
$648$		0			0
$649$			11.8360i			0.464603i
$650$		0			0
$651$	1.04951	−	1.04951i	0.0411337	−	0.0411337i
$652$		0			0
$653$	−20.7599	−	20.7599i	−0.812397	−	0.812397i	0.172596	−	0.984993i	$-0.444785\pi$
$653$	−20.7599	−	20.7599i	−0.812397	−	0.812397i	−0.984993	+	0.172596i	$0.944785\pi$
$654$		0			0
$655$	−32.2055			−1.25837
$656$		0			0
$657$	1.45029			0.0565814
$658$		0			0
$659$	20.7066	+	20.7066i	0.806616	+	0.806616i	0.984120	−	0.177504i	$-0.0568022\pi$
$659$	20.7066	+	20.7066i	0.806616	+	0.806616i	−0.177504	+	0.984120i	$0.556802\pi$
$660$		0			0
$661$	9.70914	−	9.70914i	0.377642	−	0.377642i	−0.492609	−	0.870251i	$-0.663957\pi$
$661$	9.70914	−	9.70914i	0.377642	−	0.377642i	0.870251	+	0.492609i	$0.163957\pi$
$662$		0			0
$663$		−	44.4509i		−	1.72633i
$664$		0			0
$665$			8.90180i			0.345197i
$666$		0			0
$667$	−27.3805	+	27.3805i	−1.06018	+	1.06018i
$668$		0			0
$669$	12.2101	+	12.2101i	0.472069	+	0.472069i
$670$		0			0
$671$	−10.5101			−0.405737
$672$		0			0
$673$	49.3202			1.90115			0.950577	−	0.310490i	$-0.100493\pi$
$673$	49.3202			1.90115			0.950577	+	0.310490i	$0.100493\pi$
$674$		0			0
$675$	44.3447	+	44.3447i	1.70683	+	1.70683i
$676$		0			0
$677$	12.2329	−	12.2329i	0.470149	−	0.470149i	−0.431813	−	0.901963i	$-0.642126\pi$
$677$	12.2329	−	12.2329i	0.470149	−	0.470149i	0.901963	+	0.431813i	$0.142126\pi$
$678$		0			0
$679$		−	1.98784i		−	0.0762861i
$680$		0			0
$681$		−	5.35011i		−	0.205017i
$682$		0			0
$683$	3.79812	−	3.79812i	0.145331	−	0.145331i	−0.630698	−	0.776029i	$-0.717231\pi$
$683$	3.79812	−	3.79812i	0.145331	−	0.145331i	0.776029	+	0.630698i	$0.217231\pi$
$684$		0			0
$685$	52.3402	+	52.3402i	1.99981	+	1.99981i
$686$		0			0
$687$	16.0644			0.612895
$688$		0			0
$689$	38.2811			1.45839
$690$		0			0
$691$	31.7387	+	31.7387i	1.20740	+	1.20740i	0.971867	+	0.235531i	$0.0756830\pi$
$691$	31.7387	+	31.7387i	1.20740	+	1.20740i	0.235531	+	0.971867i	$0.424317\pi$
$692$		0			0
$693$	0.602015	−	0.602015i	0.0228686	−	0.0228686i
$694$		0			0
$695$			67.7271i			2.56904i
$696$		0			0
$697$			11.4399i			0.433319i
$698$		0			0
$699$	9.50930	−	9.50930i	0.359675	−	0.359675i
$700$		0			0
$701$	−6.08828	−	6.08828i	−0.229951	−	0.229951i	0.582721	−	0.812672i	$-0.301988\pi$
$701$	−6.08828	−	6.08828i	−0.229951	−	0.229951i	−0.812672	+	0.582721i	$0.801988\pi$
$702$		0			0
$703$	−16.9947			−0.640969
$704$		0			0
$705$	58.5392			2.20472
$706$		0			0
$707$	11.1341	+	11.1341i	0.418739	+	0.418739i
$708$		0			0
$709$	−2.17748	+	2.17748i	−0.0817769	+	0.0817769i	−0.746812	−	0.665035i	$-0.768417\pi$
$709$	−2.17748	+	2.17748i	−0.0817769	+	0.0817769i	0.665035	+	0.746812i	$0.268417\pi$
$710$		0			0
$711$		−	0.359556i		−	0.0134844i
$712$		0			0
$713$			5.91677i			0.221585i
$714$		0			0
$715$	−64.5221	+	64.5221i	−2.41299	+	2.41299i
$716$		0			0
$717$	2.36224	+	2.36224i	0.0882195	+	0.0882195i
$718$		0			0
$719$	42.5677			1.58751			0.793754	−	0.608239i	$-0.208124\pi$
$719$	42.5677			1.58751			0.793754	+	0.608239i	$0.208124\pi$
$720$		0			0
$721$	−15.2106			−0.566471
$722$		0			0
$723$	18.2986	+	18.2986i	0.680531	+	0.680531i
$724$		0			0
$725$	48.0510	−	48.0510i	1.78457	−	1.78457i
$726$		0			0
$727$			3.44163i			0.127643i	0.997961	+	0.0638214i	$0.0203288\pi$
$727$			3.44163i			0.127643i	−0.997961	+	0.0638214i	$0.979671\pi$
$728$		0			0
$729$		−	25.0909i		−	0.929294i
$730$		0			0
$731$	−8.31327	+	8.31327i	−0.307477	+	0.307477i
$732$		0			0
$733$	8.59144	+	8.59144i	0.317332	+	0.317332i	0.847742	−	0.530410i	$-0.177962\pi$
$733$	8.59144	+	8.59144i	0.317332	+	0.317332i	−0.530410	+	0.847742i	$0.677962\pi$
$734$		0			0
$735$	−7.46903			−0.275499
$736$		0			0
$737$	−36.7866			−1.35505
$738$		0			0
$739$	−19.7676	−	19.7676i	−0.727161	−	0.727161i	0.242892	−	0.970053i	$-0.421904\pi$
$739$	−19.7676	−	19.7676i	−0.727161	−	0.727161i	−0.970053	+	0.242892i	$0.921904\pi$
$740$		0			0
$741$	13.0193	−	13.0193i	0.478275	−	0.478275i
$742$		0			0
$743$		−	14.0786i		−	0.516495i	−0.966079	−	0.258248i	$-0.916855\pi$
$743$		−	14.0786i		−	0.516495i	0.966079	−	0.258248i	$-0.0831450\pi$
$744$		0			0
$745$			50.9452i			1.86649i
$746$		0			0
$747$	1.50841	−	1.50841i	0.0551899	−	0.0551899i
$748$		0			0
$749$	−0.897608	−	0.897608i	−0.0327979	−	0.0327979i
$750$		0			0
$751$	27.6318			1.00830			0.504148	−	0.863617i	$-0.331806\pi$
$751$	27.6318			1.00830			0.504148	+	0.863617i	$0.331806\pi$
$752$		0			0
$753$	−11.3214			−0.412576
$754$		0			0
$755$	−52.4798	−	52.4798i	−1.90994	−	1.90994i
$756$		0			0
$757$	−1.95221	+	1.95221i	−0.0709542	+	0.0709542i	−0.741693	−	0.670739i	$-0.765977\pi$
$757$	−1.95221	+	1.95221i	−0.0709542	+	0.0709542i	0.670739	+	0.741693i	$0.265977\pi$
$758$		0			0
$759$			57.2537i			2.07818i
$760$		0			0
$761$		−	34.5598i		−	1.25279i	−0.779505	−	0.626396i	$-0.784529\pi$
$761$		−	34.5598i		−	1.25279i	0.779505	−	0.626396i	$-0.215471\pi$
$762$		0			0
$763$	2.84528	−	2.84528i	0.103006	−	0.103006i
$764$		0			0
$765$	2.87278	+	2.87278i	0.103866	+	0.103866i
$766$		0			0
$767$	−12.7313			−0.459699
$768$		0			0
$769$	49.7370			1.79356			0.896781	−	0.442474i	$-0.145899\pi$
$769$	49.7370			1.79356			0.896781	+	0.442474i	$0.145899\pi$
$770$		0			0
$771$	−15.3542	−	15.3542i	−0.552968	−	0.552968i
$772$		0			0
$773$	−10.0261	+	10.0261i	−0.360614	+	0.360614i	−0.864039	−	0.503425i	$-0.832073\pi$
$773$	−10.0261	+	10.0261i	−0.360614	+	0.360614i	0.503425	+	0.864039i	$0.332073\pi$
$774$		0			0
$775$		−	10.3835i		−	0.372988i
$776$		0			0
$777$		−	14.2594i		−	0.511553i
$778$		0			0
$779$	−3.35066	+	3.35066i	−0.120050	+	0.120050i
$780$		0			0
$781$	19.2617	+	19.2617i	0.689238	+	0.689238i
$782$		0			0
$783$	−27.3042			−0.975772
$784$		0			0
$785$	58.4664			2.08675
$786$		0			0
$787$	−9.26586	−	9.26586i	−0.330292	−	0.330292i	0.522405	−	0.852697i	$-0.325035\pi$
$787$	−9.26586	−	9.26586i	−0.330292	−	0.330292i	−0.852697	+	0.522405i	$0.825035\pi$
$788$		0			0
$789$	0.0378229	−	0.0378229i	0.00134653	−	0.00134653i
$790$		0			0
$791$		−	1.66487i		−	0.0591960i
$792$		0			0
$793$		−	11.3050i		−	0.401454i
$794$		0			0
$795$	−41.7355	+	41.7355i	−1.48021	+	1.48021i
$796$		0			0
$797$	21.3858	+	21.3858i	0.757525	+	0.757525i	0.975871	−	0.218346i	$-0.0700663\pi$
$797$	21.3858	+	21.3858i	0.757525	+	0.757525i	−0.218346	+	0.975871i	$0.570066\pi$
$798$		0			0
$799$	−40.2722			−1.42473
$800$		0			0
$801$	−0.472490			−0.0166946
$802$		0			0
$803$	24.4311	+	24.4311i	0.862153	+	0.862153i
$804$		0			0
$805$	21.0538	−	21.0538i	0.742050	−	0.742050i
$806$		0			0
$807$		−	32.2553i		−	1.13544i
$808$		0			0
$809$		−	1.36939i		−	0.0481450i	−0.999710	−	0.0240725i	$-0.992337\pi$
$809$		−	1.36939i		−	0.0481450i	0.999710	−	0.0240725i	$-0.00766326\pi$
$810$		0			0
$811$	21.0275	−	21.0275i	0.738375	−	0.738375i	−0.233889	−	0.972263i	$-0.575145\pi$
$811$	21.0275	−	21.0275i	0.738375	−	0.738375i	0.972263	+	0.233889i	$0.0751451\pi$
$812$		0			0
$813$	−12.7418	−	12.7418i	−0.446874	−	0.446874i
$814$		0			0
$815$	−56.8659			−1.99192
$816$		0			0
$817$	−4.86976			−0.170371
$818$		0			0
$819$	0.647550	+	0.647550i	0.0226272	+	0.0226272i
$820$		0			0
$821$	−12.8601	+	12.8601i	−0.448819	+	0.448819i	−0.894962	−	0.446142i	$-0.852797\pi$
$821$	−12.8601	+	12.8601i	−0.448819	+	0.448819i	0.446142	+	0.894962i	$0.352797\pi$
$822$		0			0
$823$		−	41.5715i		−	1.44909i	−0.689226	−	0.724546i	$-0.742049\pi$
$823$		−	41.5715i		−	1.44909i	0.689226	−	0.724546i	$-0.257951\pi$
$824$		0			0
$825$		−	100.476i		−	3.49814i
$826$		0			0
$827$	32.5770	−	32.5770i	1.13281	−	1.13281i	0.143104	−	0.989708i	$-0.454292\pi$
$827$	32.5770	−	32.5770i	1.13281	−	1.13281i	0.989708	−	0.143104i	$-0.0457083\pi$
$828$		0			0
$829$	−0.406541	−	0.406541i	−0.0141198	−	0.0141198i	0.700012	−	0.714131i	$-0.253178\pi$
$829$	−0.406541	−	0.406541i	−0.0141198	−	0.0141198i	−0.714131	+	0.700012i	$0.753178\pi$
$830$		0			0
$831$	−15.8337			−0.549265
$832$		0			0
$833$	5.13834			0.178033
$834$		0			0
$835$	19.8367	+	19.8367i	0.686478	+	0.686478i
$836$		0			0
$837$	−2.95014	+	2.95014i	−0.101972	+	0.101972i
$838$		0			0
$839$			28.6700i			0.989799i	0.868950	+	0.494899i	$0.164795\pi$
$839$			28.6700i			0.989799i	−0.868950	+	0.494899i	$0.835205\pi$
$840$		0			0
$841$			0.586242i			0.0202152i
$842$		0			0
$843$	14.7401	−	14.7401i	0.507675	−	0.507675i
$844$		0			0
$845$	−30.9555	−	30.9555i	−1.06490	−	1.06490i
$846$		0			0
$847$	9.28258			0.318953
$848$		0			0
$849$	22.4200			0.769452
$850$		0			0
$851$	40.1946	+	40.1946i	1.37785	+	1.37785i
$852$		0			0
$853$	−8.34697	+	8.34697i	−0.285795	+	0.285795i	−0.835415	−	0.549620i	$-0.814773\pi$
$853$	−8.34697	+	8.34697i	−0.285795	+	0.285795i	0.549620	+	0.835415i	$0.314773\pi$
$854$		0			0
$855$			1.68282i			0.0575513i
$856$		0			0
$857$		−	48.6998i		−	1.66355i	−0.555110	−	0.831777i	$-0.687324\pi$
$857$		−	48.6998i		−	1.66355i	0.555110	−	0.831777i	$-0.312676\pi$
$858$		0			0
$859$	0.0269889	−	0.0269889i	0.000920851	−	0.000920851i	−0.706646	−	0.707567i	$-0.749793\pi$
$859$	0.0269889	−	0.0269889i	0.000920851	−	0.000920851i	0.707567	+	0.706646i	$0.249793\pi$
$860$		0			0
$861$	−2.81136	−	2.81136i	−0.0958109	−	0.0958109i
$862$		0			0
$863$	1.64855			0.0561173			0.0280587	−	0.999606i	$-0.491067\pi$
$863$	1.64855			0.0561173			0.0280587	+	0.999606i	$0.491067\pi$
$864$		0			0
$865$	87.1452			2.96303
$866$		0			0
$867$	−11.8730	−	11.8730i	−0.403227	−	0.403227i
$868$		0			0
$869$	6.05692	−	6.05692i	0.205467	−	0.205467i
$870$		0			0
$871$		−	39.5690i		−	1.34075i
$872$		0			0
$873$		−	0.375786i		−	0.0127184i
$874$		0			0
$875$	−22.1607	+	22.1607i	−0.749169	+	0.749169i
$876$		0			0
$877$	−31.2724	−	31.2724i	−1.05599	−	1.05599i	−0.998336	−	0.0576583i	$-0.981637\pi$
$877$	−31.2724	−	31.2724i	−1.05599	−	1.05599i	−0.0576583	−	0.998336i	$-0.518363\pi$
$878$		0			0
$879$	43.4219			1.46458
$880$		0			0
$881$	−1.02249			−0.0344486			−0.0172243	−	0.999852i	$-0.505483\pi$
$881$	−1.02249			−0.0344486			−0.0172243	+	0.999852i	$0.505483\pi$
$882$		0			0
$883$	−7.56235	−	7.56235i	−0.254493	−	0.254493i	0.568317	−	0.822810i	$-0.307595\pi$
$883$	−7.56235	−	7.56235i	−0.254493	−	0.254493i	−0.822810	+	0.568317i	$0.807595\pi$
$884$		0			0
$885$	13.8801	−	13.8801i	0.466574	−	0.466574i
$886$		0			0
$887$			4.15374i			0.139469i	0.997566	+	0.0697344i	$0.0222152\pi$
$887$			4.15374i			0.139469i	−0.997566	+	0.0697344i	$0.977785\pi$
$888$		0			0
$889$		−	7.86069i		−	0.263639i
$890$		0			0
$891$	−30.3531	+	30.3531i	−1.01687	+	1.01687i
$892$		0			0
$893$	−11.7954	−	11.7954i	−0.394717	−	0.394717i
$894$		0			0
$895$	93.7235			3.13283
$896$		0			0
$897$	−61.5843			−2.05624
$898$		0			0
$899$	3.19671	+	3.19671i	0.106616	+	0.106616i
$900$		0			0
$901$	28.7120	−	28.7120i	0.956537	−	0.956537i
$902$		0			0
$903$		−	4.08596i		−	0.135972i
$904$		0			0
$905$			18.5260i			0.615825i
$906$		0			0
$907$	−3.43585	+	3.43585i	−0.114085	+	0.114085i	−0.761845	−	0.647759i	$-0.775706\pi$
$907$	−3.43585	+	3.43585i	−0.114085	+	0.114085i	0.647759	+	0.761845i	$0.275706\pi$
$908$		0			0
$909$	2.10481	+	2.10481i	0.0698123	+	0.0698123i
$910$		0			0
$911$	21.2511			0.704082			0.352041	−	0.935985i	$-0.385488\pi$
$911$	21.2511			0.704082			0.352041	+	0.935985i	$0.385488\pi$
$912$		0			0
$913$	50.8202			1.68190
$914$		0			0
$915$	12.3252	+	12.3252i	0.407458	+	0.407458i
$916$		0			0
$917$	−5.44479	+	5.44479i	−0.179803	+	0.179803i
$918$		0			0
$919$			14.2571i			0.470297i	0.971959	+	0.235149i	$0.0755577\pi$
$919$			14.2571i			0.470297i	−0.971959	+	0.235149i	$0.924442\pi$
$920$		0			0
$921$		−	48.6692i		−	1.60370i
$922$		0			0
$923$	−20.7186	+	20.7186i	−0.681962	+	0.681962i
$924$		0			0
$925$	−70.5388	−	70.5388i	−2.31930	−	2.31930i
$926$		0			0
$927$	−2.87545			−0.0944422
$928$		0			0
$929$	31.9394			1.04790			0.523948	−	0.851750i	$-0.324458\pi$
$929$	31.9394			1.04790			0.523948	+	0.851750i	$0.324458\pi$
$930$		0			0
$931$	1.50497	+	1.50497i	0.0493235	+	0.0493235i
$932$		0			0
$933$	7.30687	−	7.30687i	0.239216	−	0.239216i
$934$		0			0
$935$			96.7873i			3.16528i
$936$		0			0
$937$			4.91109i			0.160438i	0.996777	+	0.0802191i	$0.0255620\pi$
$937$			4.91109i			0.160438i	−0.996777	+	0.0802191i	$0.974438\pi$
$938$		0			0
$939$	−3.83461	+	3.83461i	−0.125138	+	0.125138i
$940$		0			0
$941$	38.9550	+	38.9550i	1.26990	+	1.26990i	0.946140	+	0.323758i	$0.104947\pi$
$941$	38.9550	+	38.9550i	1.26990	+	1.26990i	0.323758	+	0.946140i	$0.395053\pi$
$942$		0			0
$943$	15.8494			0.516128
$944$		0			0
$945$	20.9951			0.682972
$946$		0			0
$947$	−34.6905	−	34.6905i	−1.12729	−	1.12729i	−0.990616	−	0.136672i	$-0.956359\pi$
$947$	−34.6905	−	34.6905i	−1.12729	−	1.12729i	−0.136672	−	0.990616i	$-0.543641\pi$
$948$		0			0
$949$	−26.2790	+	26.2790i	−0.853052	+	0.853052i
$950$		0			0
$951$		−	8.39014i		−	0.272069i
$952$		0			0
$953$			56.6312i			1.83446i	0.398354	+	0.917232i	$0.369582\pi$
$953$			56.6312i			1.83446i	−0.398354	+	0.917232i	$0.630418\pi$
$954$		0			0
$955$	−21.8549	+	21.8549i	−0.707209	+	0.707209i
$956$		0			0
$957$	30.9330	+	30.9330i	0.999921	+	0.999921i
$958$		0			0
$959$	17.6977			0.571487
$960$		0			0
$961$	−30.3092			−0.977716
$962$		0			0
$963$	−0.169687	−	0.169687i	−0.00546807	−	0.00546807i
$964$		0			0
$965$	−0.411496	+	0.411496i	−0.0132465	+	0.0132465i
$966$		0			0
$967$			47.2953i			1.52092i	0.649388	+	0.760458i	$0.275025\pi$
$967$			47.2953i			1.52092i	−0.649388	+	0.760458i	$0.724975\pi$
$968$		0			0
$969$		−	19.5298i		−	0.627386i
$970$		0			0
$971$	1.98079	−	1.98079i	0.0635665	−	0.0635665i	−0.674609	−	0.738175i	$-0.735688\pi$
$971$	1.98079	−	1.98079i	0.0635665	−	0.0635665i	0.738175	+	0.674609i	$0.235688\pi$
$972$		0			0
$973$	11.4502	+	11.4502i	0.367077	+	0.367077i
$974$		0			0
$975$	108.076			3.46121
$976$		0			0
$977$	22.0570			0.705665			0.352832	−	0.935687i	$-0.385219\pi$
$977$	22.0570			0.705665			0.352832	+	0.935687i	$0.385219\pi$
$978$		0			0
$979$	−7.95937	−	7.95937i	−0.254382	−	0.254382i
$980$		0			0
$981$	0.537880	−	0.537880i	0.0171732	−	0.0171732i
$982$		0			0
$983$		−	55.5608i		−	1.77212i	−0.463575	−	0.886058i	$-0.653434\pi$
$983$		−	55.5608i		−	1.77212i	0.463575	−	0.886058i	$-0.346566\pi$
$984$		0			0
$985$		−	43.5217i		−	1.38672i
$986$		0			0
$987$	9.89687	−	9.89687i	0.315021	−	0.315021i
$988$		0			0
$989$	11.5176	+	11.5176i	0.366237	+	0.366237i
$990$		0			0
$991$	13.9880			0.444345			0.222173	−	0.975007i	$-0.428685\pi$
$991$	13.9880			0.444345			0.222173	+	0.975007i	$0.428685\pi$
$992$		0			0
$993$	−64.4042			−2.04380
$994$		0			0
$995$	−15.0698	−	15.0698i	−0.477743	−	0.477743i
$996$		0			0
$997$	9.85983	−	9.85983i	0.312264	−	0.312264i	−0.533522	−	0.845786i	$-0.679132\pi$
$997$	9.85983	−	9.85983i	0.312264	−	0.312264i	0.845786	+	0.533522i	$0.179132\pi$
$998$		0			0
$999$			40.0825i			1.26816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1792.2.m.g.1345.2	yes	16
4.3	odd	2		1792.2.m.e.1345.7	yes	16
8.3	odd	2		1792.2.m.h.1345.2	yes	16
8.5	even	2		1792.2.m.f.1345.7	yes	16
16.3	odd	4		1792.2.m.h.449.2	yes	16
16.5	even	4	inner	1792.2.m.g.449.2	yes	16
16.11	odd	4		1792.2.m.e.449.7	✓	16
16.13	even	4		1792.2.m.f.449.7	yes	16
32.5	even	8		7168.2.a.ba.1.6		8
32.11	odd	8		7168.2.a.bf.1.6		8
32.21	even	8		7168.2.a.be.1.3		8
32.27	odd	8		7168.2.a.bb.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1792.2.m.e.449.7	✓	16	16.11	odd	4
1792.2.m.e.1345.7	yes	16	4.3	odd	2
1792.2.m.f.449.7	yes	16	16.13	even	4
1792.2.m.f.1345.7	yes	16	8.5	even	2
1792.2.m.g.449.2	yes	16	16.5	even	4	inner
1792.2.m.g.1345.2	yes	16	1.1	even	1	trivial
1792.2.m.h.449.2	yes	16	16.3	odd	4
1792.2.m.h.1345.2	yes	16	8.3	odd	2
7168.2.a.ba.1.6		8	32.5	even	8
7168.2.a.bb.1.3		8	32.27	odd	8
7168.2.a.be.1.3		8	32.21	even	8
7168.2.a.bf.1.6		8	32.11	odd	8

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:	\( N \)	\(=\)	\( 1792 = 2^{8} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1792.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26274 - 1.26274i) q^{3} +(-2.95746 + 2.95746i) q^{5} +1.00000i q^{7} +0.189043i q^{9} +O(q^{10})\)	\(q+(-1.26274 - 1.26274i) q^{3} +(-2.95746 + 2.95746i) q^{5} +1.00000i q^{7} +0.189043i q^{9} +(-3.18454 + 3.18454i) q^{11} +(-3.42541 - 3.42541i) q^{13} +7.46903 q^{15} -5.13834 q^{17} +(-1.50497 - 1.50497i) q^{19} +(1.26274 - 1.26274i) q^{21} +7.11888i q^{23} -12.4932i q^{25} +(-3.54952 + 3.54952i) q^{27} +(3.84618 + 3.84618i) q^{29} +0.831138 q^{31} +8.04251 q^{33} +(-2.95746 - 2.95746i) q^{35} +(5.64619 - 5.64619i) q^{37} +8.65084i q^{39} -2.22639i q^{41} +(1.61789 - 1.61789i) q^{43} +(-0.559087 - 0.559087i) q^{45} +7.83759 q^{47} -1.00000 q^{49} +(6.48840 + 6.48840i) q^{51} +(-5.58781 + 5.58781i) q^{53} -18.8363i q^{55} +3.80079i q^{57} +(1.85835 - 1.85835i) q^{59} +(1.65017 + 1.65017i) q^{61} -0.189043 q^{63} +20.2611 q^{65} +(5.77581 + 5.77581i) q^{67} +(8.98933 - 8.98933i) q^{69} -6.04851i q^{71} -7.67177i q^{73} +(-15.7757 + 15.7757i) q^{75} +(-3.18454 - 3.18454i) q^{77} -1.90198 q^{79} +9.53139 q^{81} +(-7.97920 - 7.97920i) q^{83} +(15.1964 - 15.1964i) q^{85} -9.71349i q^{87} +2.49938i q^{89} +(3.42541 - 3.42541i) q^{91} +(-1.04951 - 1.04951i) q^{93} +8.90180 q^{95} -1.98784 q^{97} +(-0.602015 - 0.602015i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} - 4 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 - 4 * q^5	\( 16 q + 4 q^{3} - 4 q^{5} - 8 q^{11} + 12 q^{13} - 8 q^{17} + 4 q^{19} - 4 q^{21} - 56 q^{27} + 8 q^{31} + 16 q^{33} - 4 q^{35} - 8 q^{37} - 24 q^{43} - 36 q^{45} + 40 q^{47} - 16 q^{49} + 24 q^{51} - 32 q^{53} - 4 q^{59} - 20 q^{61} - 24 q^{63} + 72 q^{65} + 32 q^{67} + 56 q^{69} - 28 q^{75} - 8 q^{77} - 40 q^{81} + 36 q^{83} - 12 q^{91} + 8 q^{93} + 80 q^{95} - 72 q^{97} - 8 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 - 4 * q^5 - 8 * q^11 + 12 * q^13 - 8 * q^17 + 4 * q^19 - 4 * q^21 - 56 * q^27 + 8 * q^31 + 16 * q^33 - 4 * q^35 - 8 * q^37 - 24 * q^43 - 36 * q^45 + 40 * q^47 - 16 * q^49 + 24 * q^51 - 32 * q^53 - 4 * q^59 - 20 * q^61 - 24 * q^63 + 72 * q^65 + 32 * q^67 + 56 * q^69 - 28 * q^75 - 8 * q^77 - 40 * q^81 + 36 * q^83 - 12 * q^91 + 8 * q^93 + 80 * q^95 - 72 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

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