LMFDB - Embedded newform 1360.2.bn.a.1327.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1360,2,Mod(783,1360)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1360, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 0, 3, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1360.783"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1360 = 2^{4} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1360.bn (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$10.8596546749$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1327.3
Character	$\chi$	$=$	1360.1327
Dual form			1360.2.bn.a.783.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.75921 - 1.75921i) q^{3} +(0.152427 - 2.23087i) q^{5} +(-3.52764 + 3.52764i) q^{7} +3.18965i q^{9} +0.109362i q^{11} +(-0.552044 + 0.552044i) q^{13} +(-4.19272 + 3.65642i) q^{15} +(0.707107 + 0.707107i) q^{17} +4.27687 q^{19} +12.4117 q^{21} +(-1.44065 - 1.44065i) q^{23} +(-4.95353 - 0.680089i) q^{25} +(0.333636 - 0.333636i) q^{27} -1.87634i q^{29} +8.59324i q^{31} +(0.192391 - 0.192391i) q^{33} +(7.33198 + 8.40739i) q^{35} +(7.20372 + 7.20372i) q^{37} +1.94232 q^{39} +7.43204 q^{41} +(-3.49344 - 3.49344i) q^{43} +(7.11569 + 0.486189i) q^{45} +(0.532434 - 0.532434i) q^{47} -17.8884i q^{49} -2.48790i q^{51} +(4.27220 - 4.27220i) q^{53} +(0.243973 + 0.0166698i) q^{55} +(-7.52392 - 7.52392i) q^{57} +12.2435 q^{59} -11.6072 q^{61} +(-11.2519 - 11.2519i) q^{63} +(1.14739 + 1.31568i) q^{65} +(-0.0701639 + 0.0701639i) q^{67} +5.06881i q^{69} -13.4448i q^{71} +(0.756996 - 0.756996i) q^{73} +(7.51789 + 9.91073i) q^{75} +(-0.385790 - 0.385790i) q^{77} -2.36101 q^{79} +8.39508 q^{81} +(-2.50801 - 2.50801i) q^{83} +(1.68524 - 1.46968i) q^{85} +(-3.30089 + 3.30089i) q^{87} +3.22396i q^{89} -3.89482i q^{91} +(15.1173 - 15.1173i) q^{93} +(0.651911 - 9.54113i) q^{95} +(4.52718 + 4.52718i) q^{97} -0.348828 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{13} - 16 q^{21} - 24 q^{25} + 8 q^{33} - 16 q^{41} + 24 q^{45} - 16 q^{53} + 32 q^{57} + 16 q^{61} + 56 q^{65} - 8 q^{73} + 40 q^{77} + 32 q^{81} + 56 q^{93} + 64 q^{97}+O(q^{100}) $ 32 * q + 8 * q^13 - 16 * q^21 - 24 * q^25 + 8 * q^33 - 16 * q^41 + 24 * q^45 - 16 * q^53 + 32 * q^57 + 16 * q^61 + 56 * q^65 - 8 * q^73 + 40 * q^77 + 32 * q^81 + 56 * q^93 + 64 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1360\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.75921	−	1.75921i	−1.01568	−	1.01568i	−0.999875	−	0.0158062i	$-0.994969\pi$
$3$	−1.75921	−	1.75921i	−1.01568	−	1.01568i	−0.0158062	−	0.999875i	$-0.505031\pi$
$4$		0			0
$5$	0.152427	−	2.23087i	0.0681674	−	0.997674i
$5$	0.152427	−	2.23087i	0.0681674	−	0.997674i
$6$		0			0
$7$	−3.52764	+	3.52764i	−1.33332	+	1.33332i	−0.430941	+	0.902380i	$0.641818\pi$
$7$	−3.52764	+	3.52764i	−1.33332	+	1.33332i	−0.902380	+	0.430941i	$0.858182\pi$
$8$		0			0
$9$			3.18965i			1.06322i
$10$		0			0
$11$			0.109362i			0.0329740i	0.999864	+	0.0164870i	$0.00524821\pi$
$11$			0.109362i			0.0329740i	−0.999864	+	0.0164870i	$0.994752\pi$
$12$		0			0
$13$	−0.552044	+	0.552044i	−0.153110	+	0.153110i	−0.779505	−	0.626396i	$-0.784529\pi$
$13$	−0.552044	+	0.552044i	−0.153110	+	0.153110i	0.626396	+	0.779505i	$0.284529\pi$
$14$		0			0
$15$	−4.19272	+	3.65642i	−1.08256	+	0.944082i
$16$		0			0
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$17$	0.707107	+	0.707107i	0.171499	+	0.171499i
$18$		0			0
$19$	4.27687			0.981181			0.490591	−	0.871390i	$-0.336781\pi$
$19$	4.27687			0.981181			0.490591	+	0.871390i	$0.336781\pi$
$20$		0			0
$21$	12.4117			2.70846
$22$		0			0
$23$	−1.44065	−	1.44065i	−0.300396	−	0.300396i	0.540773	−	0.841169i	$-0.318132\pi$
$23$	−1.44065	−	1.44065i	−0.300396	−	0.300396i	−0.841169	+	0.540773i	$0.818132\pi$
$24$		0			0
$25$	−4.95353	−	0.680089i	−0.990706	−	0.136018i
$26$		0			0
$27$	0.333636	−	0.333636i	0.0642082	−	0.0642082i
$28$		0			0
$29$		−	1.87634i		−	0.348428i	−0.984708	−	0.174214i	$-0.944261\pi$
$29$		−	1.87634i		−	0.348428i	0.984708	−	0.174214i	$-0.0557385\pi$
$30$		0			0
$31$			8.59324i			1.54339i	0.635991	+	0.771696i	$0.280591\pi$
$31$			8.59324i			1.54339i	−0.635991	+	0.771696i	$0.719409\pi$
$32$		0			0
$33$	0.192391	−	0.192391i	0.0334910	−	0.0334910i
$34$		0			0
$35$	7.33198	+	8.40739i	1.23933	+	1.42111i
$36$		0			0
$37$	7.20372	+	7.20372i	1.18428	+	1.18428i	0.978623	+	0.205661i	$0.0659345\pi$
$37$	7.20372	+	7.20372i	1.18428	+	1.18428i	0.205661	+	0.978623i	$0.434066\pi$
$38$		0			0
$39$	1.94232			0.311021
$40$		0			0
$41$	7.43204			1.16069			0.580345	−	0.814371i	$-0.302918\pi$
$41$	7.43204			1.16069			0.580345	+	0.814371i	$0.302918\pi$
$42$		0			0
$43$	−3.49344	−	3.49344i	−0.532745	−	0.532745i	0.388644	−	0.921388i	$-0.372944\pi$
$43$	−3.49344	−	3.49344i	−0.532745	−	0.532745i	−0.921388	+	0.388644i	$0.872944\pi$
$44$		0			0
$45$	7.11569	+	0.486189i	1.06074	+	0.0724768i
$46$		0			0
$47$	0.532434	−	0.532434i	0.0776634	−	0.0776634i	−0.667208	−	0.744871i	$-0.732511\pi$
$47$	0.532434	−	0.532434i	0.0776634	−	0.0776634i	0.744871	+	0.667208i	$0.232511\pi$
$48$		0			0
$49$		−	17.8884i		−	2.55549i
$50$		0			0
$51$		−	2.48790i		−	0.348376i
$52$		0			0
$53$	4.27220	−	4.27220i	0.586832	−	0.586832i	−0.349940	−	0.936772i	$-0.613798\pi$
$53$	4.27220	−	4.27220i	0.586832	−	0.586832i	0.936772	+	0.349940i	$0.113798\pi$
$54$		0			0
$55$	0.243973	+	0.0166698i	0.0328973	+	0.00224775i
$56$		0			0
$57$	−7.52392	−	7.52392i	−0.996567	−	0.996567i
$58$		0			0
$59$	12.2435			1.59396			0.796981	−	0.604005i	$-0.206429\pi$
$59$	12.2435			1.59396			0.796981	+	0.604005i	$0.206429\pi$
$60$		0			0
$61$	−11.6072			−1.48616			−0.743078	−	0.669205i	$-0.766635\pi$
$61$	−11.6072			−1.48616			−0.743078	+	0.669205i	$0.766635\pi$
$62$		0			0
$63$	−11.2519	−	11.2519i	−1.41761	−	1.41761i
$64$		0			0
$65$	1.14739	+	1.31568i	0.142316	+	0.163190i
$66$		0			0
$67$	−0.0701639	+	0.0701639i	−0.00857189	+	0.00857189i	−0.711380	−	0.702808i	$-0.751929\pi$
$67$	−0.0701639	+	0.0701639i	−0.00857189	+	0.00857189i	0.702808	+	0.711380i	$0.251929\pi$
$68$		0			0
$69$			5.06881i			0.610213i
$70$		0			0
$71$		−	13.4448i		−	1.59561i	−0.602917	−	0.797804i	$-0.705995\pi$
$71$		−	13.4448i		−	1.59561i	0.602917	−	0.797804i	$-0.294005\pi$
$72$		0			0
$73$	0.756996	−	0.756996i	0.0885997	−	0.0885997i	−0.661418	−	0.750018i	$-0.730045\pi$
$73$	0.756996	−	0.756996i	0.0885997	−	0.0885997i	0.750018	+	0.661418i	$0.230045\pi$
$74$		0			0
$75$	7.51789	+	9.91073i	0.868091	+	1.14439i
$76$		0			0
$77$	−0.385790	−	0.385790i	−0.0439649	−	0.0439649i
$78$		0			0
$79$	−2.36101			−0.265634			−0.132817	−	0.991141i	$-0.542402\pi$
$79$	−2.36101			−0.265634			−0.132817	+	0.991141i	$0.542402\pi$
$80$		0			0
$81$	8.39508			0.932787
$82$		0			0
$83$	−2.50801	−	2.50801i	−0.275290	−	0.275290i	0.555935	−	0.831226i	$-0.312360\pi$
$83$	−2.50801	−	2.50801i	−0.275290	−	0.275290i	−0.831226	+	0.555935i	$0.812360\pi$
$84$		0			0
$85$	1.68524	−	1.46968i	0.182790	−	0.159409i
$86$		0			0
$87$	−3.30089	+	3.30089i	−0.353892	+	0.353892i
$88$		0			0
$89$			3.22396i			0.341739i	0.985294	+	0.170869i	$0.0546576\pi$
$89$			3.22396i			0.341739i	−0.985294	+	0.170869i	$0.945342\pi$
$90$		0			0
$91$		−	3.89482i		−	0.408288i
$92$		0			0
$93$	15.1173	−	15.1173i	1.56759	−	1.56759i
$94$		0			0
$95$	0.651911	−	9.54113i	0.0668846	−	0.978899i
$96$		0			0
$97$	4.52718	+	4.52718i	0.459666	+	0.459666i	0.898546	−	0.438880i	$-0.144625\pi$
$97$	4.52718	+	4.52718i	0.459666	+	0.459666i	−0.438880	+	0.898546i	$0.644625\pi$
$98$		0			0
$99$	−0.348828			−0.0350585
$100$		0			0
$101$	13.0132			1.29486			0.647432	−	0.762123i	$-0.275843\pi$
$101$	13.0132			1.29486			0.647432	+	0.762123i	$0.275843\pi$
$102$		0			0
$103$	7.60481	+	7.60481i	0.749325	+	0.749325i	0.974352	−	0.225028i	$-0.0722473\pi$
$103$	7.60481	+	7.60481i	0.749325	+	0.749325i	−0.225028	+	0.974352i	$0.572247\pi$
$104$		0			0
$105$	1.89188	−	27.6889i	0.184629	−	2.70216i
$106$		0			0
$107$	4.23466	−	4.23466i	0.409380	−	0.409380i	−0.472142	−	0.881522i	$-0.656519\pi$
$107$	4.23466	−	4.23466i	0.409380	−	0.409380i	0.881522	+	0.472142i	$0.156519\pi$
$108$		0			0
$109$			10.1767i			0.974749i	0.873193	+	0.487374i	$0.162045\pi$
$109$			10.1767i			0.974749i	−0.873193	+	0.487374i	$0.837955\pi$
$110$		0			0
$111$		−	25.3457i		−	2.40571i
$112$		0			0
$113$	−11.2950	+	11.2950i	−1.06254	+	1.06254i	−0.0646354	+	0.997909i	$0.520588\pi$
$113$	−11.2950	+	11.2950i	−1.06254	+	1.06254i	−0.997909	+	0.0646354i	$0.979412\pi$
$114$		0			0
$115$	−3.43349	+	2.99430i	−0.320175	+	0.279220i
$116$		0			0
$117$	−1.76083	−	1.76083i	−0.162789	−	0.162789i
$118$		0			0
$119$	−4.98883			−0.457325
$120$		0			0
$121$	10.9880			0.998913
$122$		0			0
$123$	−13.0745	−	13.0745i	−1.17889	−	1.17889i
$124$		0			0
$125$	−2.27224	+	10.9470i	−0.203235	+	0.979130i
$126$		0			0
$127$	5.84996	−	5.84996i	0.519100	−	0.519100i	−0.398199	−	0.917299i	$-0.630365\pi$
$127$	5.84996	−	5.84996i	0.519100	−	0.519100i	0.917299	+	0.398199i	$0.130365\pi$
$128$		0			0
$129$			12.2914i			1.08220i
$130$		0			0
$131$		−	16.7142i		−	1.46033i	−0.683270	−	0.730165i	$-0.739443\pi$
$131$		−	16.7142i		−	1.46033i	0.683270	−	0.730165i	$-0.260557\pi$
$132$		0			0
$133$	−15.0872	+	15.0872i	−1.30823	+	1.30823i
$134$		0			0
$135$	−0.693442	−	0.795152i	−0.0596820	−	0.0684358i
$136$		0			0
$137$	9.45271	+	9.45271i	0.807600	+	0.807600i	0.984270	−	0.176670i	$-0.0565327\pi$
$137$	9.45271	+	9.45271i	0.807600	+	0.807600i	−0.176670	+	0.984270i	$0.556533\pi$
$138$		0			0
$139$	15.3612			1.30292			0.651460	−	0.758683i	$-0.274157\pi$
$139$	15.3612			1.30292			0.651460	+	0.758683i	$0.274157\pi$
$140$		0			0
$141$	−1.87333			−0.157763
$142$		0			0
$143$	−0.0603728	−	0.0603728i	−0.00504863	−	0.00504863i
$144$		0			0
$145$	−4.18587	−	0.286006i	−0.347618	−	0.0237515i
$146$		0			0
$147$	−31.4695	+	31.4695i	−2.59556	+	2.59556i
$148$		0			0
$149$			11.7109i			0.959397i	0.877433	+	0.479699i	$0.159254\pi$
$149$			11.7109i			0.959397i	−0.877433	+	0.479699i	$0.840746\pi$
$150$		0			0
$151$			15.5459i			1.26510i	0.774518	+	0.632552i	$0.217993\pi$
$151$			15.5459i			1.26510i	−0.774518	+	0.632552i	$0.782007\pi$
$152$		0			0
$153$	−2.25542	+	2.25542i	−0.182340	+	0.182340i
$154$		0			0
$155$	19.1704	+	1.30984i	1.53980	+	0.105209i
$156$		0			0
$157$	−14.1273	−	14.1273i	−1.12748	−	1.12748i	−0.990586	−	0.136893i	$-0.956288\pi$
$157$	−14.1273	−	14.1273i	−1.12748	−	1.12748i	−0.136893	−	0.990586i	$-0.543712\pi$
$158$		0			0
$159$	−15.0314			−1.19207
$160$		0			0
$161$	10.1642			0.801049
$162$		0			0
$163$	4.90171	+	4.90171i	0.383931	+	0.383931i	0.872516	−	0.488585i	$-0.162487\pi$
$163$	4.90171	+	4.90171i	0.383931	+	0.383931i	−0.488585	+	0.872516i	$0.662487\pi$
$164$		0			0
$165$	−0.399874	−	0.458525i	−0.0311301	−	0.0356961i
$166$		0			0
$167$	−5.13078	+	5.13078i	−0.397031	+	0.397031i	−0.877185	−	0.480153i	$-0.840581\pi$
$167$	−5.13078	+	5.13078i	−0.397031	+	0.397031i	0.480153	+	0.877185i	$0.340581\pi$
$168$		0			0
$169$			12.3905i			0.953115i
$170$		0			0
$171$			13.6417i			1.04321i
$172$		0			0
$173$	−12.3074	+	12.3074i	−0.935716	+	0.935716i	−0.998055	−	0.0623386i	$-0.980144\pi$
$173$	−12.3074	+	12.3074i	−0.935716	+	0.935716i	0.0623386	+	0.998055i	$0.480144\pi$
$174$		0			0
$175$	19.8734	−	15.0751i	1.50228	−	1.13957i
$176$		0			0
$177$	−21.5388	−	21.5388i	−1.61896	−	1.61896i
$178$		0			0
$179$	16.4309			1.22811			0.614053	−	0.789265i	$-0.289538\pi$
$179$	16.4309			1.22811			0.614053	+	0.789265i	$0.289538\pi$
$180$		0			0
$181$	12.0336			0.894450			0.447225	−	0.894421i	$-0.352412\pi$
$181$	12.0336			0.894450			0.447225	+	0.894421i	$0.352412\pi$
$182$		0			0
$183$	20.4196	+	20.4196i	1.50946	+	1.50946i
$184$		0			0
$185$	17.1686	−	14.9725i	1.26226	−	1.10080i
$186$		0			0
$187$	−0.0773308	+	0.0773308i	−0.00565499	+	0.00565499i
$188$		0			0
$189$			2.35389i			0.171220i
$190$		0			0
$191$		−	2.36391i		−	0.171046i	−0.996336	−	0.0855231i	$-0.972744\pi$
$191$		−	2.36391i		−	0.171046i	0.996336	−	0.0855231i	$-0.0272562\pi$
$192$		0			0
$193$	5.47309	−	5.47309i	0.393962	−	0.393962i	−0.482135	−	0.876097i	$-0.660139\pi$
$193$	5.47309	−	5.47309i	0.393962	−	0.393962i	0.876097	+	0.482135i	$0.160139\pi$
$194$		0			0
$195$	0.296063	−	4.33307i	0.0212015	−	0.310297i
$196$		0			0
$197$	17.6717	+	17.6717i	1.25906	+	1.25906i	0.951543	+	0.307515i	$0.0994975\pi$
$197$	17.6717	+	17.6717i	1.25906	+	1.25906i	0.307515	+	0.951543i	$0.400502\pi$
$198$		0			0
$199$	−8.09068			−0.573533			−0.286766	−	0.958001i	$-0.592580\pi$
$199$	−8.09068			−0.573533			−0.286766	+	0.958001i	$0.592580\pi$
$200$		0			0
$201$	0.246866			0.0174126
$202$		0			0
$203$	6.61906	+	6.61906i	0.464567	+	0.464567i
$204$		0			0
$205$	1.13284	−	16.5799i	0.0791213	−	1.15799i
$206$		0			0
$207$	4.59517	−	4.59517i	0.319386	−	0.319386i
$208$		0			0
$209$			0.467728i			0.0323534i
$210$		0			0
$211$			14.2747i			0.982713i	0.870959	+	0.491356i	$0.163499\pi$
$211$			14.2747i			0.982713i	−0.870959	+	0.491356i	$0.836501\pi$
$212$		0			0
$213$	−23.6523	+	23.6523i	−1.62063	+	1.62063i
$214$		0			0
$215$	−8.32589	+	7.26090i	−0.567821	+	0.495190i
$216$		0			0
$217$	−30.3138	−	30.3138i	−2.05784	−	2.05784i
$218$		0			0
$219$	−2.66343			−0.179978
$220$		0			0
$221$	−0.780708			−0.0525161
$222$		0			0
$223$	6.75233	+	6.75233i	0.452169	+	0.452169i	0.896074	−	0.443905i	$-0.146407\pi$
$223$	6.75233	+	6.75233i	0.452169	+	0.452169i	−0.443905	+	0.896074i	$0.646407\pi$
$224$		0			0
$225$	2.16925	−	15.8000i	0.144616	−	1.05334i
$226$		0			0
$227$	−17.7157	+	17.7157i	−1.17583	+	1.17583i	−0.195034	+	0.980797i	$0.562482\pi$
$227$	−17.7157	+	17.7157i	−1.17583	+	1.17583i	−0.980797	+	0.195034i	$0.937518\pi$
$228$		0			0
$229$			17.4226i			1.15132i	0.817689	+	0.575660i	$0.195255\pi$
$229$			17.4226i			1.15132i	−0.817689	+	0.575660i	$0.804745\pi$
$230$		0			0
$231$			1.35737i			0.0893086i
$232$		0			0
$233$	9.47429	−	9.47429i	0.620681	−	0.620681i	−0.325024	−	0.945706i	$-0.605372\pi$
$233$	9.47429	−	9.47429i	0.620681	−	0.620681i	0.945706	+	0.325024i	$0.105372\pi$
$234$		0			0
$235$	−1.10663	−	1.26895i	−0.0721887	−	0.0827769i
$236$		0			0
$237$	4.15352	+	4.15352i	0.269800	+	0.269800i
$238$		0			0
$239$	5.61969			0.363507			0.181754	−	0.983344i	$-0.441823\pi$
$239$	5.61969			0.363507			0.181754	+	0.983344i	$0.441823\pi$
$240$		0			0
$241$	−27.8044			−1.79104			−0.895519	−	0.445023i	$-0.853196\pi$
$241$	−27.8044			−1.79104			−0.895519	+	0.445023i	$0.853196\pi$
$242$		0			0
$243$	−15.7696	−	15.7696i	−1.01162	−	1.01162i
$244$		0			0
$245$	−39.9067	−	2.72668i	−2.54954	−	0.174201i
$246$		0			0
$247$	−2.36102	+	2.36102i	−0.150228	+	0.150228i
$248$		0			0
$249$			8.82425i			0.559214i
$250$		0			0
$251$			1.27835i			0.0806889i	0.999186	+	0.0403444i	$0.0128455\pi$
$251$			1.27835i			0.0806889i	−0.999186	+	0.0403444i	$0.987154\pi$
$252$		0			0
$253$	0.157553	−	0.157553i	0.00990525	−	0.00990525i
$254$		0			0
$255$	−5.55018	−	0.379223i	−0.347565	−	0.0237479i
$256$		0			0
$257$	−14.3886	−	14.3886i	−0.897536	−	0.897536i	0.0976820	−	0.995218i	$-0.468857\pi$
$257$	−14.3886	−	14.3886i	−0.897536	−	0.897536i	−0.995218	+	0.0976820i	$0.968857\pi$
$258$		0			0
$259$	−50.8242			−3.15806
$260$		0			0
$261$	5.98488			0.370455
$262$		0			0
$263$	16.7118	+	16.7118i	1.03049	+	1.03049i	0.999520	+	0.0309740i	$0.00986089\pi$
$263$	16.7118	+	16.7118i	1.03049	+	1.03049i	0.0309740	+	0.999520i	$0.490139\pi$
$264$		0			0
$265$	−8.87951	−	10.1819i	−0.545464	−	0.625469i
$266$		0			0
$267$	5.67162	−	5.67162i	0.347098	−	0.347098i
$268$		0			0
$269$		−	6.02653i		−	0.367444i	−0.982978	−	0.183722i	$-0.941185\pi$
$269$		−	6.02653i		−	0.367444i	0.982978	−	0.183722i	$-0.0588147\pi$
$270$		0			0
$271$			3.35799i			0.203983i	0.994785	+	0.101992i	$0.0325215\pi$
$271$			3.35799i			0.203983i	−0.994785	+	0.101992i	$0.967478\pi$
$272$		0			0
$273$	−6.85181	+	6.85181i	−0.414691	+	0.414691i
$274$		0			0
$275$	0.0743761	−	0.541730i	0.00448505	−	0.0326675i
$276$		0			0
$277$	0.388962	+	0.388962i	0.0233705	+	0.0233705i	0.718695	−	0.695325i	$-0.244740\pi$
$277$	0.388962	+	0.388962i	0.0233705	+	0.0233705i	−0.695325	+	0.718695i	$0.744740\pi$
$278$		0			0
$279$	−27.4094			−1.64096
$280$		0			0
$281$	−10.0143			−0.597404			−0.298702	−	0.954346i	$-0.596554\pi$
$281$	−10.0143			−0.597404			−0.298702	+	0.954346i	$0.596554\pi$
$282$		0			0
$283$	3.18556	+	3.18556i	0.189362	+	0.189362i	0.795420	−	0.606058i	$-0.207250\pi$
$283$	3.18556	+	3.18556i	0.189362	+	0.189362i	−0.606058	+	0.795420i	$0.707250\pi$
$284$		0			0
$285$	−17.9317	+	15.6380i	−1.06218	+	0.926316i
$286$		0			0
$287$	−26.2175	+	26.2175i	−1.54757	+	1.54757i
$288$		0			0
$289$			1.00000i			0.0588235i
$290$		0			0
$291$		−	15.9285i		−	0.933748i
$292$		0			0
$293$	−6.89671	+	6.89671i	−0.402910	+	0.402910i	−0.879257	−	0.476347i	$-0.841961\pi$
$293$	−6.89671	+	6.89671i	−0.402910	+	0.402910i	0.476347	+	0.879257i	$0.341961\pi$
$294$		0			0
$295$	1.86623	−	27.3135i	0.108656	−	1.59025i
$296$		0			0
$297$	0.0364872	+	0.0364872i	0.00211720	+	0.00211720i
$298$		0			0
$299$	1.59060			0.0919870
$300$		0			0
$301$	24.6472			1.42064
$302$		0			0
$303$	−22.8930	−	22.8930i	−1.31517	−	1.31517i
$304$		0			0
$305$	−1.76926	+	25.8942i	−0.101307	+	1.48270i
$306$		0			0
$307$	15.0648	−	15.0648i	0.859796	−	0.859796i	−0.131518	−	0.991314i	$-0.541985\pi$
$307$	15.0648	−	15.0648i	0.859796	−	0.859796i	0.991314	+	0.131518i	$0.0419851\pi$
$308$		0			0
$309$		−	26.7570i		−	1.52215i
$310$		0			0
$311$			7.85414i			0.445367i	0.974891	+	0.222684i	$0.0714817\pi$
$311$			7.85414i			0.445367i	−0.974891	+	0.222684i	$0.928518\pi$
$312$		0			0
$313$	7.07894	−	7.07894i	0.400125	−	0.400125i	−0.478152	−	0.878277i	$-0.658693\pi$
$313$	7.07894	−	7.07894i	0.400125	−	0.400125i	0.878277	+	0.478152i	$0.158693\pi$
$314$		0			0
$315$	−26.8166	+	23.3864i	−1.51095	+	1.31768i
$316$		0			0
$317$	15.0732	+	15.0732i	0.846593	+	0.846593i	0.989706	−	0.143114i	$-0.0457114\pi$
$317$	15.0732	+	15.0732i	0.846593	+	0.846593i	−0.143114	+	0.989706i	$0.545711\pi$
$318$		0			0
$319$	0.205201			0.0114891
$320$		0			0
$321$	−14.8993			−0.831599
$322$		0			0
$323$	3.02420	+	3.02420i	0.168271	+	0.168271i
$324$		0			0
$325$	3.11001	−	2.35913i	0.172512	−	0.130861i
$326$		0			0
$327$	17.9029	−	17.9029i	0.990034	−	0.990034i
$328$		0			0
$329$			3.75646i			0.207101i
$330$		0			0
$331$		−	18.7357i		−	1.02981i	−0.857248	−	0.514904i	$-0.827828\pi$
$331$		−	18.7357i		−	1.02981i	0.857248	−	0.514904i	$-0.172172\pi$
$332$		0			0
$333$	−22.9774	+	22.9774i	−1.25915	+	1.25915i
$334$		0			0
$335$	0.145832	+	0.167221i	0.00796763	+	0.00913627i
$336$		0			0
$337$	5.24836	+	5.24836i	0.285896	+	0.285896i	0.835455	−	0.549559i	$-0.185204\pi$
$337$	5.24836	+	5.24836i	0.285896	+	0.285896i	−0.549559	+	0.835455i	$0.685204\pi$
$338$		0			0
$339$	39.7406			2.15841
$340$		0			0
$341$	−0.939777			−0.0508918
$342$		0			0
$343$	38.4104	+	38.4104i	2.07397	+	2.07397i
$344$		0			0
$345$	11.3078	+	0.772624i	0.608794	+	0.0415967i
$346$		0			0
$347$	10.8985	−	10.8985i	0.585060	−	0.585060i	−0.351229	−	0.936289i	$-0.614236\pi$
$347$	10.8985	−	10.8985i	0.585060	−	0.585060i	0.936289	+	0.351229i	$0.114236\pi$
$348$		0			0
$349$		−	9.69684i		−	0.519060i	−0.965735	−	0.259530i	$-0.916432\pi$
$349$		−	9.69684i		−	0.519060i	0.965735	−	0.259530i	$-0.0835676\pi$
$350$		0			0
$351$			0.368363i			0.0196618i
$352$		0			0
$353$	2.96119	−	2.96119i	0.157608	−	0.157608i	−0.623898	−	0.781506i	$-0.714452\pi$
$353$	2.96119	−	2.96119i	0.157608	−	0.157608i	0.781506	+	0.623898i	$0.214452\pi$
$354$		0			0
$355$	−29.9936	−	2.04936i	−1.59190	−	0.108769i
$356$		0			0
$357$	8.77641	+	8.77641i	0.464497	+	0.464497i
$358$		0			0
$359$	−16.4624			−0.868851			−0.434425	−	0.900708i	$-0.643049\pi$
$359$	−16.4624			−0.868851			−0.434425	+	0.900708i	$0.643049\pi$
$360$		0			0
$361$	−0.708384			−0.0372834
$362$		0			0
$363$	−19.3303	−	19.3303i	−1.01458	−	1.01458i
$364$		0			0
$365$	−1.57337	−	1.80414i	−0.0823540	−	0.0944332i
$366$		0			0
$367$	18.8652	−	18.8652i	0.984754	−	0.984754i	−0.0151317	−	0.999886i	$-0.504817\pi$
$367$	18.8652	−	18.8652i	0.984754	−	0.984754i	0.999886	+	0.0151317i	$0.00481675\pi$
$368$		0			0
$369$			23.7056i			1.23407i
$370$		0			0
$371$			30.1415i			1.56487i
$372$		0			0
$373$	1.88413	−	1.88413i	0.0975566	−	0.0975566i	−0.656644	−	0.754201i	$-0.728025\pi$
$373$	1.88413	−	1.88413i	0.0975566	−	0.0975566i	0.754201	+	0.656644i	$0.228025\pi$
$374$		0			0
$375$	23.2554	−	15.2607i	1.20091	−	0.788062i
$376$		0			0
$377$	1.03582	+	1.03582i	0.0533477	+	0.0533477i
$378$		0			0
$379$	18.9361			0.972684			0.486342	−	0.873768i	$-0.338331\pi$
$379$	18.9361			0.972684			0.486342	+	0.873768i	$0.338331\pi$
$380$		0			0
$381$	−20.5826			−1.05448
$382$		0			0
$383$	17.5530	+	17.5530i	0.896919	+	0.896919i	0.995162	−	0.0982437i	$-0.0313225\pi$
$383$	17.5530	+	17.5530i	0.896919	+	0.896919i	−0.0982437	+	0.995162i	$0.531322\pi$
$384$		0			0
$385$	−0.919452	+	0.801842i	−0.0468596	+	0.0408656i
$386$		0			0
$387$	11.1429	−	11.1429i	0.566423	−	0.566423i
$388$		0			0
$389$			9.17311i			0.465095i	0.972585	+	0.232547i	$0.0747061\pi$
$389$			9.17311i			0.465095i	−0.972585	+	0.232547i	$0.925294\pi$
$390$		0			0
$391$		−	2.03739i		−	0.103035i
$392$		0			0
$393$	−29.4039	+	29.4039i	−1.48323	+	1.48323i
$394$		0			0
$395$	−0.359882	+	5.26710i	−0.0181076	+	0.265017i
$396$		0			0
$397$	−11.2035	−	11.2035i	−0.562286	−	0.562286i	0.367670	−	0.929956i	$-0.380156\pi$
$397$	−11.2035	−	11.2035i	−0.562286	−	0.562286i	−0.929956	+	0.367670i	$0.880156\pi$
$398$		0			0
$399$	53.0833			2.65749
$400$		0			0
$401$	−4.64840			−0.232130			−0.116065	−	0.993242i	$-0.537028\pi$
$401$	−4.64840			−0.232130			−0.116065	+	0.993242i	$0.537028\pi$
$402$		0			0
$403$	−4.74385	−	4.74385i	−0.236308	−	0.236308i
$404$		0			0
$405$	1.27964	−	18.7283i	0.0635857	−	0.930617i
$406$		0			0
$407$	−0.787815	+	0.787815i	−0.0390506	+	0.0390506i
$408$		0			0
$409$			4.70539i			0.232667i	0.993210	+	0.116333i	$0.0371141\pi$
$409$			4.70539i			0.232667i	−0.993210	+	0.116333i	$0.962886\pi$
$410$		0			0
$411$		−	33.2586i		−	1.64053i
$412$		0			0
$413$	−43.1904	+	43.1904i	−2.12526	+	2.12526i
$414$		0			0
$415$	−5.97733	+	5.21276i	−0.293416	+	0.255884i
$416$		0			0
$417$	−27.0236	−	27.0236i	−1.32335	−	1.32335i
$418$		0			0
$419$	−25.7707			−1.25898			−0.629490	−	0.777008i	$-0.716736\pi$
$419$	−25.7707			−1.25898			−0.629490	+	0.777008i	$0.716736\pi$
$420$		0			0
$421$	35.8176			1.74564			0.872821	−	0.488040i	$-0.162288\pi$
$421$	35.8176			1.74564			0.872821	+	0.488040i	$0.162288\pi$
$422$		0			0
$423$	1.69828	+	1.69828i	0.0825731	+	0.0825731i
$424$		0			0
$425$	−3.02178	−	3.98357i	−0.146578	−	0.193232i
$426$		0			0
$427$	40.9461	−	40.9461i	1.98152	−	1.98152i
$428$		0			0
$429$			0.212417i			0.0102556i
$430$		0			0
$431$			31.9957i			1.54118i	0.637331	+	0.770591i	$0.280039\pi$
$431$			31.9957i			1.54118i	−0.637331	+	0.770591i	$0.719961\pi$
$432$		0			0
$433$	−0.524098	+	0.524098i	−0.0251865	+	0.0251865i	−0.719588	−	0.694401i	$-0.755669\pi$
$433$	−0.524098	+	0.524098i	−0.0251865	+	0.0251865i	0.694401	+	0.719588i	$0.255669\pi$
$434$		0			0
$435$	6.86069	+	7.86698i	0.328945	+	0.377193i
$436$		0			0
$437$	−6.16147	−	6.16147i	−0.294743	−	0.294743i
$438$		0			0
$439$	−39.8558			−1.90222			−0.951108	−	0.308859i	$-0.900053\pi$
$439$	−39.8558			−1.90222			−0.951108	+	0.308859i	$0.900053\pi$
$440$		0			0
$441$	57.0578			2.71704
$442$		0			0
$443$	−24.1179	−	24.1179i	−1.14588	−	1.14588i	−0.987356	−	0.158522i	$-0.949327\pi$
$443$	−24.1179	−	24.1179i	−1.14588	−	1.14588i	−0.158522	−	0.987356i	$-0.550673\pi$
$444$		0			0
$445$	7.19221	+	0.491418i	0.340944	+	0.0232954i
$446$		0			0
$447$	20.6020	−	20.6020i	0.974442	−	0.974442i
$448$		0			0
$449$			29.5450i			1.39432i	0.716917	+	0.697158i	$0.245552\pi$
$449$			29.5450i			1.39432i	−0.716917	+	0.697158i	$0.754448\pi$
$450$		0			0
$451$			0.812785i			0.0382726i
$452$		0			0
$453$	27.3485	−	27.3485i	1.28494	−	1.28494i
$454$		0			0
$455$	−8.68883	−	0.593676i	−0.407338	−	0.0278320i
$456$		0			0
$457$	−17.6876	−	17.6876i	−0.827393	−	0.827393i	0.159763	−	0.987155i	$-0.448927\pi$
$457$	−17.6876	−	17.6876i	−0.827393	−	0.827393i	−0.987155	+	0.159763i	$0.948927\pi$
$458$		0			0
$459$	0.471832			0.0220232
$460$		0			0
$461$	34.4158			1.60291			0.801453	−	0.598058i	$-0.204061\pi$
$461$	34.4158			1.60291			0.801453	+	0.598058i	$0.204061\pi$
$462$		0			0
$463$	11.4133	+	11.4133i	0.530421	+	0.530421i	0.920698	−	0.390276i	$-0.127621\pi$
$463$	11.4133	+	11.4133i	0.530421	+	0.530421i	−0.390276	+	0.920698i	$0.627621\pi$
$464$		0			0
$465$	−31.4205	−	36.0290i	−1.45709	−	1.67081i
$466$		0			0
$467$	0.283320	−	0.283320i	0.0131105	−	0.0131105i	−0.700521	−	0.713632i	$-0.747049\pi$
$467$	0.283320	−	0.283320i	0.0131105	−	0.0131105i	0.713632	+	0.700521i	$0.247049\pi$
$468$		0			0
$469$		−	0.495026i		−	0.0228582i
$470$		0			0
$471$			49.7057i			2.29032i
$472$		0			0
$473$	0.382051	−	0.382051i	0.0175667	−	0.0175667i
$474$		0			0
$475$	−21.1856	−	2.90865i	−0.972063	−	0.133458i
$476$		0			0
$477$	13.6268	+	13.6268i	0.623929	+	0.623929i
$478$		0			0
$479$	4.18997			0.191445			0.0957223	−	0.995408i	$-0.469484\pi$
$479$	4.18997			0.191445			0.0957223	+	0.995408i	$0.469484\pi$
$480$		0			0
$481$	−7.95354			−0.362650
$482$		0			0
$483$	−17.8809	−	17.8809i	−0.813610	−	0.813610i
$484$		0			0
$485$	10.7896	−	9.40948i	0.489931	−	0.427262i
$486$		0			0
$487$	2.95223	−	2.95223i	0.133778	−	0.133778i	−0.637047	−	0.770825i	$-0.719844\pi$
$487$	2.95223	−	2.95223i	0.133778	−	0.133778i	0.770825	+	0.637047i	$0.219844\pi$
$488$		0			0
$489$		−	17.2463i		−	0.779904i
$490$		0			0
$491$		−	16.8566i		−	0.760725i	−0.924837	−	0.380363i	$-0.875799\pi$
$491$		−	16.8566i		−	0.760725i	0.924837	−	0.380363i	$-0.124201\pi$
$492$		0			0
$493$	1.32678	−	1.32678i	0.0597550	−	0.0597550i
$494$		0			0
$495$	−0.0531707	+	0.778188i	−0.00238985	+	0.0349769i
$496$		0			0
$497$	47.4285	+	47.4285i	2.12746	+	2.12746i
$498$		0			0
$499$	28.6700			1.28345			0.641724	−	0.766936i	$-0.278220\pi$
$499$	28.6700			1.28345			0.641724	+	0.766936i	$0.278220\pi$
$500$		0			0
$501$	18.0522			0.806515
$502$		0			0
$503$	−21.0768	−	21.0768i	−0.939766	−	0.939766i	0.0585200	−	0.998286i	$-0.481362\pi$
$503$	−21.0768	−	21.0768i	−0.939766	−	0.939766i	−0.998286	+	0.0585200i	$0.981362\pi$
$504$		0			0
$505$	1.98357	−	29.0308i	0.0882675	−	1.29185i
$506$		0			0
$507$	21.7975	−	21.7975i	0.968061	−	0.968061i
$508$		0			0
$509$			31.5330i			1.39768i	0.715280	+	0.698838i	$0.246299\pi$
$509$			31.5330i			1.39768i	−0.715280	+	0.698838i	$0.753701\pi$
$510$		0			0
$511$			5.34081i			0.236264i
$512$		0			0
$513$	1.42692	−	1.42692i	0.0629999	−	0.0629999i
$514$		0			0
$515$	18.1245	−	15.8061i	0.798661	−	0.696502i
$516$		0			0
$517$	0.0582282	+	0.0582282i	0.00256087	+	0.00256087i
$518$		0			0
$519$	43.3027			1.90078
$520$		0			0
$521$	15.2951			0.670090			0.335045	−	0.942202i	$-0.391248\pi$
$521$	15.2951			0.670090			0.335045	+	0.942202i	$0.391248\pi$
$522$		0			0
$523$	3.43425	+	3.43425i	0.150169	+	0.150169i	0.778194	−	0.628024i	$-0.216136\pi$
$523$	3.43425	+	3.43425i	0.150169	+	0.150169i	−0.628024	+	0.778194i	$0.716136\pi$
$524$		0			0
$525$	−61.4818	−	8.44107i	−2.68329	−	0.368398i
$526$		0			0
$527$	−6.07634	+	6.07634i	−0.264690	+	0.264690i
$528$		0			0
$529$		−	18.8491i		−	0.819524i
$530$		0			0
$531$			39.0523i			1.69473i
$532$		0			0
$533$	−4.10282	+	4.10282i	−0.177713	+	0.177713i
$534$		0			0
$535$	−8.80148	−	10.0924i	−0.380521	−	0.436334i
$536$		0			0
$537$	−28.9055	−	28.9055i	−1.24736	−	1.24736i
$538$		0			0
$539$	1.95632			0.0842646
$540$		0			0
$541$	−12.4383			−0.534766			−0.267383	−	0.963590i	$-0.586159\pi$
$541$	−12.4383			−0.534766			−0.267383	+	0.963590i	$0.586159\pi$
$542$		0			0
$543$	−21.1696	−	21.1696i	−0.908476	−	0.908476i
$544$		0			0
$545$	22.7028	+	1.55120i	0.972481	+	0.0664461i
$546$		0			0
$547$	10.5055	−	10.5055i	0.449183	−	0.449183i	−0.445900	−	0.895083i	$-0.647116\pi$
$547$	10.5055	−	10.5055i	0.449183	−	0.449183i	0.895083	+	0.445900i	$0.147116\pi$
$548$		0			0
$549$		−	37.0231i		−	1.58011i
$550$		0			0
$551$		−	8.02488i		−	0.341871i
$552$		0			0
$553$	8.32878	−	8.32878i	0.354176	−	0.354176i
$554$		0			0
$555$	−56.5430	−	3.86338i	−2.40011	−	0.163991i
$556$		0			0
$557$	−5.15060	−	5.15060i	−0.218238	−	0.218238i	0.589518	−	0.807755i	$-0.299318\pi$
$557$	−5.15060	−	5.15060i	−0.218238	−	0.218238i	−0.807755	+	0.589518i	$0.799318\pi$
$558$		0			0
$559$	3.85707			0.163137
$560$		0			0
$561$	0.272083			0.0114873
$562$		0			0
$563$	21.4026	+	21.4026i	0.902010	+	0.902010i	0.995610	−	0.0935998i	$-0.0298374\pi$
$563$	21.4026	+	21.4026i	0.902010	+	0.902010i	−0.0935998	+	0.995610i	$0.529837\pi$
$564$		0			0
$565$	23.4760	+	26.9193i	0.987642	+	1.13250i
$566$		0			0
$567$	−29.6148	+	29.6148i	−1.24370	+	1.24370i
$568$		0			0
$569$			3.07975i			0.129110i	0.997914	+	0.0645550i	$0.0205628\pi$
$569$			3.07975i			0.129110i	−0.997914	+	0.0645550i	$0.979437\pi$
$570$		0			0
$571$			29.2676i			1.22481i	0.790544	+	0.612406i	$0.209798\pi$
$571$			29.2676i			1.22481i	−0.790544	+	0.612406i	$0.790202\pi$
$572$		0			0
$573$	−4.15861	+	4.15861i	−0.173728	+	0.173728i
$574$		0			0
$575$	6.15653	+	8.11607i	0.256745	+	0.338464i
$576$		0			0
$577$	7.25982	+	7.25982i	0.302230	+	0.302230i	0.841886	−	0.539656i	$-0.181446\pi$
$577$	7.25982	+	7.25982i	0.302230	+	0.302230i	−0.539656	+	0.841886i	$0.681446\pi$
$578$		0			0
$579$	−19.2566			−0.800279
$580$		0			0
$581$	17.6947			0.734101
$582$		0			0
$583$	0.467217	+	0.467217i	0.0193502	+	0.0193502i
$584$		0			0
$585$	−4.19657	+	3.65977i	−0.173507	+	0.151313i
$586$		0			0
$587$	9.66688	−	9.66688i	0.398995	−	0.398995i	−0.478884	−	0.877878i	$-0.658958\pi$
$587$	9.66688	−	9.66688i	0.398995	−	0.398995i	0.877878	+	0.478884i	$0.158958\pi$
$588$		0			0
$589$			36.7522i			1.51435i
$590$		0			0
$591$		−	62.1766i		−	2.55760i
$592$		0			0
$593$	−26.1809	+	26.1809i	−1.07512	+	1.07512i	−0.0781823	+	0.996939i	$0.524912\pi$
$593$	−26.1809	+	26.1809i	−1.07512	+	1.07512i	−0.996939	+	0.0781823i	$0.975088\pi$
$594$		0			0
$595$	−0.760433	+	11.1294i	−0.0311747	+	0.456261i
$596$		0			0
$597$	14.2332	+	14.2332i	0.582527	+	0.582527i
$598$		0			0
$599$	−33.1930			−1.35623			−0.678114	−	0.734957i	$-0.737202\pi$
$599$	−33.1930			−1.35623			−0.678114	+	0.734957i	$0.737202\pi$
$600$		0			0
$601$	−36.9553			−1.50744			−0.753720	−	0.657196i	$-0.771742\pi$
$601$	−36.9553			−1.50744			−0.753720	+	0.657196i	$0.771742\pi$
$602$		0			0
$603$	−0.223798	−	0.223798i	−0.00911378	−	0.00911378i
$604$		0			0
$605$	1.67487	−	24.5129i	0.0680933	−	0.996589i
$606$		0			0
$607$	−24.5130	+	24.5130i	−0.994953	+	0.994953i	−0.999987	−	0.00503385i	$-0.998398\pi$
$607$	−24.5130	+	24.5130i	−0.994953	+	0.994953i	0.00503385	+	0.999987i	$0.498398\pi$
$608$		0			0
$609$		−	23.2886i		−	0.943703i
$610$		0			0
$611$			0.587854i			0.0237820i
$612$		0			0
$613$	32.3391	−	32.3391i	1.30616	−	1.30616i	0.382002	−	0.924162i	$-0.375235\pi$
$613$	32.3391	−	32.3391i	1.30616	−	1.30616i	0.924162	−	0.382002i	$-0.124765\pi$
$614$		0			0
$615$	−31.1605	+	27.1746i	−1.25651	+	1.09579i
$616$		0			0
$617$	−7.36012	−	7.36012i	−0.296307	−	0.296307i	0.543258	−	0.839566i	$-0.317190\pi$
$617$	−7.36012	−	7.36012i	−0.296307	−	0.296307i	−0.839566	+	0.543258i	$0.817190\pi$
$618$		0			0
$619$	−31.4305			−1.26330			−0.631649	−	0.775254i	$-0.717622\pi$
$619$	−31.4305			−1.26330			−0.631649	+	0.775254i	$0.717622\pi$
$620$		0			0
$621$	−0.961304			−0.0385758
$622$		0			0
$623$	−11.3729	−	11.3729i	−0.455647	−	0.455647i
$624$		0			0
$625$	24.0750	+	6.73768i	0.962998	+	0.269507i
$626$		0			0
$627$	0.822833	−	0.822833i	0.0328608	−	0.0328608i
$628$		0			0
$629$			10.1876i			0.406206i
$630$		0			0
$631$			20.0645i			0.798756i	0.916786	+	0.399378i	$0.130774\pi$
$631$			20.0645i			0.798756i	−0.916786	+	0.399378i	$0.869226\pi$
$632$		0			0
$633$	25.1123	−	25.1123i	0.998123	−	0.998123i
$634$		0			0
$635$	−12.1588	−	13.9422i	−0.482507	−	0.553278i
$636$		0			0
$637$	9.87520	+	9.87520i	0.391270	+	0.391270i
$638$		0			0
$639$	42.8843			1.69648
$640$		0			0
$641$	−3.43110			−0.135520			−0.0677601	−	0.997702i	$-0.521585\pi$
$641$	−3.43110			−0.135520			−0.0677601	+	0.997702i	$0.521585\pi$
$642$		0			0
$643$	1.14597	+	1.14597i	0.0451928	+	0.0451928i	0.729342	−	0.684149i	$-0.239826\pi$
$643$	1.14597	+	1.14597i	0.0451928	+	0.0451928i	−0.684149	+	0.729342i	$0.739826\pi$
$644$		0			0
$645$	27.4205	+	1.87354i	1.07968	+	0.0737706i
$646$		0			0
$647$	30.0909	−	30.0909i	1.18300	−	1.18300i	0.204033	−	0.978964i	$-0.434595\pi$
$647$	30.0909	−	30.0909i	1.18300	−	1.18300i	0.978964	−	0.204033i	$-0.0654050\pi$
$648$		0			0
$649$			1.33897i			0.0525592i
$650$		0			0
$651$			106.657i			4.18021i
$652$		0			0
$653$	29.4673	−	29.4673i	1.15314	−	1.15314i	0.167224	−	0.985919i	$-0.446520\pi$
$653$	29.4673	−	29.4673i	1.15314	−	1.15314i	0.985919	−	0.167224i	$-0.0534804\pi$
$654$		0			0
$655$	−37.2873	−	2.54770i	−1.45693	−	0.0995470i
$656$		0			0
$657$	2.41455	+	2.41455i	0.0942007	+	0.0942007i
$658$		0			0
$659$	−16.5893			−0.646228			−0.323114	−	0.946360i	$-0.604730\pi$
$659$	−16.5893			−0.646228			−0.323114	+	0.946360i	$0.604730\pi$
$660$		0			0
$661$	0.00772812			0.000300589			0.000150295	−	1.00000i	$-0.499952\pi$
$661$	0.00772812			0.000300589			0.000150295		1.00000i	$0.499952\pi$
$662$		0			0
$663$	1.37343	+	1.37343i	0.0533396	+	0.0533396i
$664$		0			0
$665$	31.3579	+	35.9573i	1.21601	+	1.39436i
$666$		0			0
$667$	−2.70315	+	2.70315i	−0.104667	+	0.104667i
$668$		0			0
$669$		−	23.7575i		−	0.918519i
$670$		0			0
$671$		−	1.26940i		−	0.0490045i
$672$		0			0
$673$	34.9745	−	34.9745i	1.34817	−	1.34817i	0.460520	−	0.887649i	$-0.347663\pi$
$673$	34.9745	−	34.9745i	1.34817	−	1.34817i	0.887649	−	0.460520i	$-0.152337\pi$
$674$		0			0
$675$	−1.87958	+	1.42577i	−0.0723450	+	0.0548780i
$676$		0			0
$677$	−20.4495	−	20.4495i	−0.785939	−	0.785939i	0.194886	−	0.980826i	$-0.437566\pi$
$677$	−20.4495	−	20.4495i	−0.785939	−	0.785939i	−0.980826	+	0.194886i	$0.937566\pi$
$678$		0			0
$679$	−31.9405			−1.22576
$680$		0			0
$681$	62.3312			2.38854
$682$		0			0
$683$	10.5327	+	10.5327i	0.403022	+	0.403022i	0.879297	−	0.476274i	$-0.158013\pi$
$683$	10.5327	+	10.5327i	0.403022	+	0.403022i	−0.476274	+	0.879297i	$0.658013\pi$
$684$		0			0
$685$	22.5286	−	19.6469i	0.860773	−	0.750669i
$686$		0			0
$687$	30.6501	−	30.6501i	1.16937	−	1.16937i
$688$		0			0
$689$			4.71688i			0.179699i
$690$		0			0
$691$		−	30.8502i		−	1.17360i	−0.809733	−	0.586798i	$-0.800388\pi$
$691$		−	30.8502i		−	1.17360i	0.809733	−	0.586798i	$-0.199612\pi$
$692$		0			0
$693$	1.23054	−	1.23054i	0.0467442	−	0.0467442i
$694$		0			0
$695$	2.34146	−	34.2688i	0.0888167	−	1.29989i
$696$		0			0
$697$	5.25525	+	5.25525i	0.199057	+	0.199057i
$698$		0			0
$699$	−33.3346			−1.26083
$700$		0			0
$701$	−15.0793			−0.569539			−0.284770	−	0.958596i	$-0.591917\pi$
$701$	−15.0793			−0.569539			−0.284770	+	0.958596i	$0.591917\pi$
$702$		0			0
$703$	30.8094	+	30.8094i	1.16200	+	1.16200i
$704$		0			0
$705$	−0.285546	+	4.17914i	−0.0107543	+	0.157396i
$706$		0			0
$707$	−45.9059	+	45.9059i	−1.72647	+	1.72647i
$708$		0			0
$709$		−	23.0503i		−	0.865673i	−0.901473	−	0.432836i	$-0.857513\pi$
$709$		−	23.0503i		−	0.865673i	0.901473	−	0.432836i	$-0.142487\pi$
$710$		0			0
$711$		−	7.53080i		−	0.282427i
$712$		0			0
$713$	12.3799	−	12.3799i	0.463629	−	0.463629i
$714$		0			0
$715$	−0.143886	+	0.125481i	−0.00538104	+	0.00469273i
$716$		0			0
$717$	−9.88622	−	9.88622i	−0.369208	−	0.369208i
$718$		0			0
$719$	−18.9075			−0.705131			−0.352565	−	0.935787i	$-0.614691\pi$
$719$	−18.9075			−0.705131			−0.352565	+	0.935787i	$0.614691\pi$
$720$		0			0
$721$	−53.6540			−1.99818
$722$		0			0
$723$	48.9138	+	48.9138i	1.81912	+	1.81912i
$724$		0			0
$725$	−1.27608	+	9.29453i	−0.0473924	+	0.345190i
$726$		0			0
$727$	−8.98596	+	8.98596i	−0.333271	+	0.333271i	−0.853827	−	0.520556i	$-0.825725\pi$
$727$	−8.98596	+	8.98596i	−0.333271	+	0.333271i	0.520556	+	0.853827i	$0.325725\pi$
$728$		0			0
$729$			30.2990i			1.12218i
$730$		0			0
$731$		−	4.94047i		−	0.182730i
$732$		0			0
$733$	−2.40490	+	2.40490i	−0.0888272	+	0.0888272i	−0.750124	−	0.661297i	$-0.770006\pi$
$733$	−2.40490	+	2.40490i	−0.0888272	+	0.0888272i	0.661297	+	0.750124i	$0.270006\pi$
$734$		0			0
$735$	65.4075	+	75.0011i	2.41259	+	2.76646i
$736$		0			0
$737$	−0.00767329	−	0.00767329i	−0.000282649	−	0.000282649i
$738$		0			0
$739$	31.2816			1.15071			0.575357	−	0.817903i	$-0.304863\pi$
$739$	31.2816			1.15071			0.575357	+	0.817903i	$0.304863\pi$
$740$		0			0
$741$	8.30707			0.305168
$742$		0			0
$743$	28.1502	+	28.1502i	1.03273	+	1.03273i	0.999446	+	0.0332849i	$0.0105969\pi$
$743$	28.1502	+	28.1502i	1.03273	+	1.03273i	0.0332849	+	0.999446i	$0.489403\pi$
$744$		0			0
$745$	26.1255	+	1.78506i	0.957165	+	0.0653996i
$746$		0			0
$747$	7.99969	−	7.99969i	0.292693	−	0.292693i
$748$		0			0
$749$			29.8767i			1.09167i
$750$		0			0
$751$		−	27.9186i		−	1.01877i	−0.860540	−	0.509383i	$-0.829874\pi$
$751$		−	27.9186i		−	1.01877i	0.860540	−	0.509383i	$-0.170126\pi$
$752$		0			0
$753$	2.24889	−	2.24889i	0.0819542	−	0.0819542i
$754$		0			0
$755$	34.6807	+	2.36961i	1.26216	+	0.0862389i
$756$		0			0
$757$	−21.2982	−	21.2982i	−0.774096	−	0.774096i	0.204724	−	0.978820i	$-0.434370\pi$
$757$	−21.2982	−	21.2982i	−0.774096	−	0.774096i	−0.978820	+	0.204724i	$0.934370\pi$
$758$		0			0
$759$	−0.554337			−0.0201212
$760$		0			0
$761$	−38.5324			−1.39680			−0.698398	−	0.715709i	$-0.746104\pi$
$761$	−38.5324			−1.39680			−0.698398	+	0.715709i	$0.746104\pi$
$762$		0			0
$763$	−35.8996	−	35.8996i	−1.29965	−	1.29965i
$764$		0			0
$765$	4.68776	+	5.37534i	0.169486	+	0.194346i
$766$		0			0
$767$	−6.75893	+	6.75893i	−0.244051	+	0.244051i
$768$		0			0
$769$			6.50538i			0.234590i	0.993097	+	0.117295i	$0.0374223\pi$
$769$			6.50538i			0.234590i	−0.993097	+	0.117295i	$0.962578\pi$
$770$		0			0
$771$			50.6252i			1.82322i
$772$		0			0
$773$	−17.0779	+	17.0779i	−0.614248	+	0.614248i	−0.944050	−	0.329802i	$-0.893018\pi$
$773$	−17.0779	+	17.0779i	−0.614248	+	0.614248i	0.329802	+	0.944050i	$0.393018\pi$
$774$		0			0
$775$	5.84417	−	42.5669i	0.209929	−	1.52905i
$776$		0			0
$777$	89.4105	+	89.4105i	3.20758	+	3.20758i
$778$		0			0
$779$	31.7859			1.13885
$780$		0			0
$781$	1.47036			0.0526135
$782$		0			0
$783$	−0.626015	−	0.626015i	−0.0223720	−	0.0223720i
$784$		0			0
$785$	−33.6694	+	29.3627i	−1.20171	+	1.04800i
$786$		0			0
$787$	−5.62237	+	5.62237i	−0.200416	+	0.200416i	−0.800178	−	0.599762i	$-0.795262\pi$
$787$	−5.62237	+	5.62237i	−0.200416	+	0.200416i	0.599762	+	0.800178i	$0.295262\pi$
$788$		0			0
$789$		−	58.7992i		−	2.09331i
$790$		0			0
$791$		−	79.6893i		−	2.83343i
$792$		0			0
$793$	6.40771	−	6.40771i	0.227545	−	0.227545i
$794$		0			0
$795$	−2.29119	+	33.5331i	−0.0812602	+	1.18929i
$796$		0			0
$797$	−24.5999	−	24.5999i	−0.871374	−	0.871374i	0.121248	−	0.992622i	$-0.461310\pi$
$797$	−24.5999	−	24.5999i	−0.871374	−	0.871374i	−0.992622	+	0.121248i	$0.961310\pi$
$798$		0			0
$799$	0.752975			0.0266383
$800$		0			0
$801$	−10.2833			−0.363342
$802$		0			0
$803$	0.0827868	+	0.0827868i	0.00292148	+	0.00292148i
$804$		0			0
$805$	1.54929	−	22.6749i	0.0546055	−	0.799186i
$806$		0			0
$807$	−10.6019	+	10.6019i	−0.373206	+	0.373206i
$808$		0			0
$809$			1.78029i			0.0625916i	0.999510	+	0.0312958i	$0.00996339\pi$
$809$			1.78029i			0.0625916i	−0.999510	+	0.0312958i	$0.990037\pi$
$810$		0			0
$811$			32.9274i			1.15624i	0.815952	+	0.578119i	$0.196213\pi$
$811$			32.9274i			1.15624i	−0.815952	+	0.578119i	$0.803787\pi$
$812$		0			0
$813$	5.90742	−	5.90742i	0.207182	−	0.207182i
$814$		0			0
$815$	11.6822	−	10.1879i	0.409210	−	0.356867i
$816$		0			0
$817$	−14.9410	−	14.9410i	−0.522719	−	0.522719i
$818$		0			0
$819$	12.4231			0.434099
$820$		0			0
$821$	2.83836			0.0990596			0.0495298	−	0.998773i	$-0.484228\pi$
$821$	2.83836			0.0990596			0.0495298	+	0.998773i	$0.484228\pi$
$822$		0			0
$823$	−0.443760	−	0.443760i	−0.0154685	−	0.0154685i	0.699330	−	0.714799i	$-0.253482\pi$
$823$	−0.443760	−	0.443760i	−0.0154685	−	0.0154685i	−0.714799	+	0.699330i	$0.753482\pi$
$824$		0			0
$825$	−1.08386	+	0.822174i	−0.0377352	+	0.0286244i
$826$		0			0
$827$	3.17598	−	3.17598i	0.110440	−	0.110440i	−0.649728	−	0.760167i	$-0.725117\pi$
$827$	3.17598	−	3.17598i	0.110440	−	0.110440i	0.760167	+	0.649728i	$0.225117\pi$
$828$		0			0
$829$		−	12.5801i		−	0.436926i	−0.975845	−	0.218463i	$-0.929896\pi$
$829$		−	12.5801i		−	0.436926i	0.975845	−	0.218463i	$-0.0701043\pi$
$830$		0			0
$831$		−	1.36853i		−	0.0474739i
$832$		0			0
$833$	12.6490	−	12.6490i	0.438263	−	0.438263i
$834$		0			0
$835$	10.6640	+	12.2281i	0.369043	+	0.423172i
$836$		0			0
$837$	2.86701	+	2.86701i	0.0990985	+	0.0990985i
$838$		0			0
$839$	6.00678			0.207377			0.103688	−	0.994610i	$-0.466936\pi$
$839$	6.00678			0.207377			0.103688	+	0.994610i	$0.466936\pi$
$840$		0			0
$841$	25.4793			0.878598
$842$		0			0
$843$	17.6173	+	17.6173i	0.606772	+	0.606772i
$844$		0			0
$845$	27.6415	+	1.88865i	0.950898	+	0.0649714i
$846$		0			0
$847$	−38.7618	+	38.7618i	−1.33187	+	1.33187i
$848$		0			0
$849$		−	11.2081i		−	0.384663i
$850$		0			0
$851$		−	20.7561i		−	0.711509i
$852$		0			0
$853$	4.95951	−	4.95951i	0.169810	−	0.169810i	−0.617086	−	0.786896i	$-0.711687\pi$
$853$	4.95951	−	4.95951i	0.169810	−	0.169810i	0.786896	+	0.617086i	$0.211687\pi$
$854$		0			0
$855$	30.4329	+	2.07937i	1.04078	+	0.0711129i
$856$		0			0
$857$	−9.58425	−	9.58425i	−0.327392	−	0.327392i	0.524202	−	0.851594i	$-0.324364\pi$
$857$	−9.58425	−	9.58425i	−0.327392	−	0.327392i	−0.851594	+	0.524202i	$0.824364\pi$
$858$		0			0
$859$	−45.0588			−1.53739			−0.768693	−	0.639618i	$-0.779093\pi$
$859$	−45.0588			−1.53739			−0.768693	+	0.639618i	$0.779093\pi$
$860$		0			0
$861$	92.2444			3.14368
$862$		0			0
$863$	−22.3227	−	22.3227i	−0.759873	−	0.759873i	0.216426	−	0.976299i	$-0.430560\pi$
$863$	−22.3227	−	22.3227i	−0.759873	−	0.759873i	−0.976299	+	0.216426i	$0.930560\pi$
$864$		0			0
$865$	25.5802	+	29.3322i	0.869754	+	0.997325i
$866$		0			0
$867$	1.75921	−	1.75921i	0.0597460	−	0.0597460i
$868$		0			0
$869$		−	0.258206i		−	0.00875902i
$870$		0			0
$871$		−	0.0774672i		−	0.00262488i
$872$		0			0
$873$	−14.4401	+	14.4401i	−0.488724	+	0.488724i
$874$		0			0
$875$	−30.6014	−	46.6327i	−1.03452	−	1.57647i
$876$		0			0
$877$	2.22152	+	2.22152i	0.0750154	+	0.0750154i	0.743619	−	0.668604i	$-0.233108\pi$
$877$	2.22152	+	2.22152i	0.0750154	+	0.0750154i	−0.668604	+	0.743619i	$0.733108\pi$
$878$		0			0
$879$	24.2656			0.818457
$880$		0			0
$881$	51.2560			1.72686			0.863429	−	0.504470i	$-0.168312\pi$
$881$	51.2560			1.72686			0.863429	+	0.504470i	$0.168312\pi$
$882$		0			0
$883$	23.4708	+	23.4708i	0.789857	+	0.789857i	0.981470	−	0.191614i	$-0.0613721\pi$
$883$	23.4708	+	23.4708i	0.789857	+	0.789857i	−0.191614	+	0.981470i	$0.561372\pi$
$884$		0			0
$885$	−51.3333	+	44.7671i	−1.72555	+	1.50483i
$886$		0			0
$887$	−13.0504	+	13.0504i	−0.438188	+	0.438188i	−0.891402	−	0.453214i	$-0.850277\pi$
$887$	−13.0504	+	13.0504i	−0.438188	+	0.438188i	0.453214	+	0.891402i	$0.350277\pi$
$888$		0			0
$889$			41.2731i			1.38425i
$890$		0			0
$891$			0.918105i			0.0307577i
$892$		0			0
$893$	2.27715	−	2.27715i	0.0762019	−	0.0762019i
$894$		0			0
$895$	2.50452	−	36.6552i	0.0837169	−	1.22525i
$896$		0			0
$897$	−2.79821	−	2.79821i	−0.0934295	−	0.0934295i
$898$		0			0
$899$	16.1239			0.537762
$900$		0			0
$901$	6.04180			0.201282
$902$		0			0
$903$	−43.3596	−	43.3596i	−1.44292	−	1.44292i
$904$		0			0
$905$	1.83425	−	26.8454i	0.0609724	−	0.892370i
$906$		0			0
$907$	29.0168	−	29.0168i	0.963486	−	0.963486i	−0.0358701	−	0.999356i	$-0.511420\pi$
$907$	29.0168	−	29.0168i	0.963486	−	0.963486i	0.999356	+	0.0358701i	$0.0114203\pi$
$908$		0			0
$909$			41.5076i			1.37672i
$910$		0			0
$911$			4.32871i			0.143417i	0.997426	+	0.0717083i	$0.0228451\pi$
$911$			4.32871i			0.143417i	−0.997426	+	0.0717083i	$0.977155\pi$
$912$		0			0
$913$	0.274282	−	0.274282i	0.00907742	−	0.00907742i
$914$		0			0
$915$	48.6659	−	42.4409i	1.60885	−	1.40305i
$916$		0			0
$917$	58.9618	+	58.9618i	1.94709	+	1.94709i
$918$		0			0
$919$	−48.6191			−1.60380			−0.801899	−	0.597460i	$-0.796177\pi$
$919$	−48.6191			−1.60380			−0.801899	+	0.597460i	$0.796177\pi$
$920$		0			0
$921$	−53.0045			−1.74656
$922$		0			0
$923$	7.42214	+	7.42214i	0.244303	+	0.244303i
$924$		0			0
$925$	−30.7847	−	40.5830i	−1.01219	−	1.33436i
$926$		0			0
$927$	−24.2567	+	24.2567i	−0.796695	+	0.796695i
$928$		0			0
$929$		−	16.8326i		−	0.552259i	−0.961120	−	0.276129i	$-0.910948\pi$
$929$		−	16.8326i		−	0.552259i	0.961120	−	0.276129i	$-0.0890518\pi$
$930$		0			0
$931$		−	76.5065i		−	2.50740i
$932$		0			0
$933$	13.8171	−	13.8171i	0.452351	−	0.452351i
$934$		0			0
$935$	0.160727	+	0.184302i	0.00525635	+	0.00602732i
$936$		0			0
$937$	−3.14361	−	3.14361i	−0.102697	−	0.102697i	0.653891	−	0.756589i	$-0.273135\pi$
$937$	−3.14361	−	3.14361i	−0.102697	−	0.102697i	−0.756589	+	0.653891i	$0.773135\pi$
$938$		0			0
$939$	−24.9067			−0.812800
$940$		0			0
$941$	17.0461			0.555686			0.277843	−	0.960627i	$-0.410381\pi$
$941$	17.0461			0.555686			0.277843	+	0.960627i	$0.410381\pi$
$942$		0			0
$943$	−10.7070	−	10.7070i	−0.348667	−	0.348667i
$944$		0			0
$945$	5.25122	+	0.358797i	0.170822	+	0.0116717i
$946$		0			0
$947$	16.4471	−	16.4471i	0.534460	−	0.534460i	−0.387436	−	0.921896i	$-0.626639\pi$
$947$	16.4471	−	16.4471i	0.534460	−	0.534460i	0.921896	+	0.387436i	$0.126639\pi$
$948$		0			0
$949$			0.835791i			0.0271309i
$950$		0			0
$951$		−	53.0337i		−	1.71974i
$952$		0			0
$953$	20.8036	−	20.8036i	0.673896	−	0.673896i	−0.284716	−	0.958612i	$-0.591899\pi$
$953$	20.8036	−	20.8036i	0.673896	−	0.673896i	0.958612	+	0.284716i	$0.0918993\pi$
$954$		0			0
$955$	−5.27356	−	0.360323i	−0.170648	−	0.0116598i
$956$		0			0
$957$	−0.360992	−	0.360992i	−0.0116692	−	0.0116692i
$958$		0			0
$959$	−66.6914			−2.15358
$960$		0			0
$961$	−42.8438			−1.38206
$962$		0			0
$963$	13.5071	+	13.5071i	0.435260	+	0.435260i
$964$		0			0
$965$	−11.3755	−	13.0440i	−0.366190	−	0.419901i
$966$		0			0
$967$	−22.9821	+	22.9821i	−0.739053	+	0.739053i	−0.972395	−	0.233341i	$-0.925034\pi$
$967$	−22.9821	+	22.9821i	−0.739053	+	0.739053i	0.233341	+	0.972395i	$0.425034\pi$
$968$		0			0
$969$		−	10.6404i		−	0.341820i
$970$		0			0
$971$		−	8.44567i		−	0.271034i	−0.990775	−	0.135517i	$-0.956730\pi$
$971$		−	8.44567i		−	0.271034i	0.990775	−	0.135517i	$-0.0432696\pi$
$972$		0			0
$973$	−54.1887	+	54.1887i	−1.73721	+	1.73721i
$974$		0			0
$975$	−9.62137	−	1.32095i	−0.308130	−	0.0423044i
$976$		0			0
$977$	15.5180	+	15.5180i	0.496466	+	0.496466i	0.910336	−	0.413870i	$-0.135823\pi$
$977$	15.5180	+	15.5180i	0.496466	+	0.496466i	−0.413870	+	0.910336i	$0.635823\pi$
$978$		0			0
$979$	−0.352579			−0.0112685
$980$		0			0
$981$	−32.4600			−1.03637
$982$		0			0
$983$	−20.7889	−	20.7889i	−0.663063	−	0.663063i	0.293038	−	0.956101i	$-0.405334\pi$
$983$	−20.7889	−	20.7889i	−0.663063	−	0.663063i	−0.956101	+	0.293038i	$0.905334\pi$
$984$		0			0
$985$	42.1169	−	36.7296i	1.34196	−	1.17030i
$986$		0			0
$987$	6.60842	−	6.60842i	0.210348	−	0.210348i
$988$		0			0
$989$			10.0656i			0.320069i
$990$		0			0
$991$		−	7.30002i		−	0.231893i	−0.993255	−	0.115946i	$-0.963010\pi$
$991$		−	7.30002i		−	0.231893i	0.993255	−	0.115946i	$-0.0369901\pi$
$992$		0			0
$993$	−32.9601	+	32.9601i	−1.04596	+	1.04596i
$994$		0			0
$995$	−1.23324	+	18.0492i	−0.0390963	+	0.572199i
$996$		0			0
$997$	−13.5478	−	13.5478i	−0.429065	−	0.429065i	0.459245	−	0.888310i	$-0.348120\pi$
$997$	−13.5478	−	13.5478i	−0.429065	−	0.429065i	−0.888310	+	0.459245i	$0.848120\pi$
$998$		0			0
$999$	4.80684			0.152082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bn.a.1327.3	yes	32
4.3	odd	2	inner	1360.2.bn.a.1327.14	yes	32
5.3	odd	4	inner	1360.2.bn.a.783.14	yes	32
20.3	even	4	inner	1360.2.bn.a.783.3	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1360.2.bn.a.783.3	✓	32	20.3	even	4	inner
1360.2.bn.a.783.14	yes	32	5.3	odd	4	inner
1360.2.bn.a.1327.3	yes	32	1.1	even	1	trivial
1360.2.bn.a.1327.14	yes	32	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1360 = 2^{4} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1360.bn (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75921 - 1.75921i) q^{3} +(0.152427 - 2.23087i) q^{5} +(-3.52764 + 3.52764i) q^{7} +3.18965i q^{9} +0.109362i q^{11} +(-0.552044 + 0.552044i) q^{13} +(-4.19272 + 3.65642i) q^{15} +(0.707107 + 0.707107i) q^{17} +4.27687 q^{19} +12.4117 q^{21} +(-1.44065 - 1.44065i) q^{23} +(-4.95353 - 0.680089i) q^{25} +(0.333636 - 0.333636i) q^{27} -1.87634i q^{29} +8.59324i q^{31} +(0.192391 - 0.192391i) q^{33} +(7.33198 + 8.40739i) q^{35} +(7.20372 + 7.20372i) q^{37} +1.94232 q^{39} +7.43204 q^{41} +(-3.49344 - 3.49344i) q^{43} +(7.11569 + 0.486189i) q^{45} +(0.532434 - 0.532434i) q^{47} -17.8884i q^{49} -2.48790i q^{51} +(4.27220 - 4.27220i) q^{53} +(0.243973 + 0.0166698i) q^{55} +(-7.52392 - 7.52392i) q^{57} +12.2435 q^{59} -11.6072 q^{61} +(-11.2519 - 11.2519i) q^{63} +(1.14739 + 1.31568i) q^{65} +(-0.0701639 + 0.0701639i) q^{67} +5.06881i q^{69} -13.4448i q^{71} +(0.756996 - 0.756996i) q^{73} +(7.51789 + 9.91073i) q^{75} +(-0.385790 - 0.385790i) q^{77} -2.36101 q^{79} +8.39508 q^{81} +(-2.50801 - 2.50801i) q^{83} +(1.68524 - 1.46968i) q^{85} +(-3.30089 + 3.30089i) q^{87} +3.22396i q^{89} -3.89482i q^{91} +(15.1173 - 15.1173i) q^{93} +(0.651911 - 9.54113i) q^{95} +(4.52718 + 4.52718i) q^{97} -0.348828 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{13} - 16 q^{21} - 24 q^{25} + 8 q^{33} - 16 q^{41} + 24 q^{45} - 16 q^{53} + 32 q^{57} + 16 q^{61} + 56 q^{65} - 8 q^{73} + 40 q^{77} + 32 q^{81} + 56 q^{93} + 64 q^{97}+O(q^{100}) \) 32 * q + 8 * q^13 - 16 * q^21 - 24 * q^25 + 8 * q^33 - 16 * q^41 + 24 * q^45 - 16 * q^53 + 32 * q^57 + 16 * q^61 + 56 * q^65 - 8 * q^73 + 40 * q^77 + 32 * q^81 + 56 * q^93 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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