LMFDB - Embedded newform 1360.2.bn.b.783.13

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 = [64] 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:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			783.13
Character	$\chi$	$=$	1360.783
Dual form			1360.2.bn.b.1327.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.552078 + 0.552078i) q^{3} +(-1.19559 - 1.88960i) q^{5} +(-0.0505973 - 0.0505973i) q^{7} +2.39042i q^{9} +1.39538i q^{11} +(-2.69118 - 2.69118i) q^{13} +(1.70326 + 0.383147i) q^{15} +(-0.707107 + 0.707107i) q^{17} +8.01896 q^{19} +0.0558673 q^{21} +(1.11975 - 1.11975i) q^{23} +(-2.14115 + 4.51835i) q^{25} +(-2.97593 - 2.97593i) q^{27} -6.96154i q^{29} -3.14333i q^{31} +(-0.770361 - 0.770361i) q^{33} +(-0.0351150 + 0.156102i) q^{35} +(1.35614 - 1.35614i) q^{37} +2.97148 q^{39} -3.20257 q^{41} +(5.13403 - 5.13403i) q^{43} +(4.51693 - 2.85795i) q^{45} +(-4.19264 - 4.19264i) q^{47} -6.99488i q^{49} -0.780756i q^{51} +(-3.79203 - 3.79203i) q^{53} +(2.63671 - 1.66830i) q^{55} +(-4.42709 + 4.42709i) q^{57} +6.65494 q^{59} -4.87020 q^{61} +(0.120949 - 0.120949i) q^{63} +(-1.86771 + 8.30278i) q^{65} +(-2.17959 - 2.17959i) q^{67} +1.23637i q^{69} -2.81612i q^{71} +(-3.28017 - 3.28017i) q^{73} +(-1.31240 - 3.67656i) q^{75} +(0.0706027 - 0.0706027i) q^{77} +0.169138 q^{79} -3.88537 q^{81} +(12.4474 - 12.4474i) q^{83} +(2.18155 + 0.490739i) q^{85} +(3.84331 + 3.84331i) q^{87} +0.766728i q^{89} +0.272333i q^{91} +(1.73536 + 1.73536i) q^{93} +(-9.58736 - 15.1526i) q^{95} +(2.92067 - 2.92067i) q^{97} -3.33556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{13} + 64 q^{21} + 24 q^{25} - 56 q^{33} - 32 q^{41} - 24 q^{45} + 64 q^{53} + 64 q^{57} - 16 q^{61} + 40 q^{65} + 56 q^{73} - 40 q^{77} - 176 q^{81} - 104 q^{93} - 16 q^{97}+O(q^{100}) $ 64 * q - 8 * q^13 + 64 * q^21 + 24 * q^25 - 56 * q^33 - 32 * q^41 - 24 * q^45 + 64 * q^53 + 64 * q^57 - 16 * q^61 + 40 * q^65 + 56 * q^73 - 40 * q^77 - 176 * q^81 - 104 * q^93 - 16 * q^97

Character values

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

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.552078	+	0.552078i	−0.318742	+	0.318742i	−0.848284	−	0.529542i	$-0.822364\pi$
$3$	−0.552078	+	0.552078i	−0.318742	+	0.318742i	0.529542	+	0.848284i	$0.322364\pi$
$4$		0			0
$5$	−1.19559	−	1.88960i	−0.534682	−	0.845053i
$5$	−1.19559	−	1.88960i	−0.534682	−	0.845053i
$6$		0			0
$7$	−0.0505973	−	0.0505973i	−0.0191240	−	0.0191240i	0.697480	−	0.716604i	$-0.254305\pi$
$7$	−0.0505973	−	0.0505973i	−0.0191240	−	0.0191240i	−0.716604	+	0.697480i	$0.754305\pi$
$8$		0			0
$9$			2.39042i			0.796807i
$10$		0			0
$11$			1.39538i			0.420724i	0.977624	+	0.210362i	$0.0674643\pi$
$11$			1.39538i			0.420724i	−0.977624	+	0.210362i	$0.932536\pi$
$12$		0			0
$13$	−2.69118	−	2.69118i	−0.746399	−	0.746399i	0.227402	−	0.973801i	$-0.426977\pi$
$13$	−2.69118	−	2.69118i	−0.746399	−	0.746399i	−0.973801	+	0.227402i	$0.926977\pi$
$14$		0			0
$15$	1.70326	+	0.383147i	0.439780	+	0.0989282i
$16$		0			0
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$	8.01896			1.83968			0.919838	−	0.392298i	$-0.128320\pi$
$19$	8.01896			1.83968			0.919838	+	0.392298i	$0.128320\pi$
$20$		0			0
$21$	0.0558673			0.0121912
$22$		0			0
$23$	1.11975	−	1.11975i	0.233483	−	0.233483i	−0.580662	−	0.814145i	$-0.697206\pi$
$23$	1.11975	−	1.11975i	0.233483	−	0.233483i	0.814145	+	0.580662i	$0.197206\pi$
$24$		0			0
$25$	−2.14115	+	4.51835i	−0.428229	+	0.903670i
$26$		0			0
$27$	−2.97593	−	2.97593i	−0.572718	−	0.572718i
$28$		0			0
$29$		−	6.96154i		−	1.29273i	−0.763030	−	0.646363i	$-0.776289\pi$
$29$		−	6.96154i		−	1.29273i	0.763030	−	0.646363i	$-0.223711\pi$
$30$		0			0
$31$		−	3.14333i		−	0.564559i	−0.959332	−	0.282279i	$-0.908909\pi$
$31$		−	3.14333i		−	0.564559i	0.959332	−	0.282279i	$-0.0910905\pi$
$32$		0			0
$33$	−0.770361	−	0.770361i	−0.134103	−	0.134103i
$34$		0			0
$35$	−0.0351150	+	0.156102i	−0.00593552	+	0.0263860i
$36$		0			0
$37$	1.35614	−	1.35614i	0.222949	−	0.222949i	−0.586790	−	0.809739i	$-0.699609\pi$
$37$	1.35614	−	1.35614i	0.222949	−	0.222949i	0.809739	+	0.586790i	$0.199609\pi$
$38$		0			0
$39$	2.97148			0.475818
$40$		0			0
$41$	−3.20257			−0.500158			−0.250079	−	0.968225i	$-0.580457\pi$
$41$	−3.20257			−0.500158			−0.250079	+	0.968225i	$0.580457\pi$
$42$		0			0
$43$	5.13403	−	5.13403i	0.782933	−	0.782933i	−0.197392	−	0.980325i	$-0.563247\pi$
$43$	5.13403	−	5.13403i	0.782933	−	0.782933i	0.980325	+	0.197392i	$0.0632471\pi$
$44$		0			0
$45$	4.51693	−	2.85795i	0.673344	−	0.426039i
$46$		0			0
$47$	−4.19264	−	4.19264i	−0.611560	−	0.611560i	0.331792	−	0.943352i	$-0.392347\pi$
$47$	−4.19264	−	4.19264i	−0.611560	−	0.611560i	−0.943352	+	0.331792i	$0.892347\pi$
$48$		0			0
$49$		−	6.99488i		−	0.999269i
$50$		0			0
$51$		−	0.780756i		−	0.109328i
$52$		0			0
$53$	−3.79203	−	3.79203i	−0.520875	−	0.520875i	0.396961	−	0.917836i	$-0.370065\pi$
$53$	−3.79203	−	3.79203i	−0.520875	−	0.520875i	−0.917836	+	0.396961i	$0.870065\pi$
$54$		0			0
$55$	2.63671	−	1.66830i	0.355534	−	0.224954i
$56$		0			0
$57$	−4.42709	+	4.42709i	−0.586383	+	0.586383i
$58$		0			0
$59$	6.65494			0.866399			0.433200	−	0.901298i	$-0.357384\pi$
$59$	6.65494			0.866399			0.433200	+	0.901298i	$0.357384\pi$
$60$		0			0
$61$	−4.87020			−0.623565			−0.311783	−	0.950153i	$-0.600926\pi$
$61$	−4.87020			−0.623565			−0.311783	+	0.950153i	$0.600926\pi$
$62$		0			0
$63$	0.120949	−	0.120949i	0.0152381	−	0.0152381i
$64$		0			0
$65$	−1.86771	+	8.30278i	−0.231660	+	1.02983i
$66$		0			0
$67$	−2.17959	−	2.17959i	−0.266280	−	0.266280i	0.561320	−	0.827599i	$-0.310294\pi$
$67$	−2.17959	−	2.17959i	−0.266280	−	0.266280i	−0.827599	+	0.561320i	$0.810294\pi$
$68$		0			0
$69$			1.23637i			0.148842i
$70$		0			0
$71$		−	2.81612i		−	0.334212i	−0.985939	−	0.167106i	$-0.946558\pi$
$71$		−	2.81612i		−	0.334212i	0.985939	−	0.167106i	$-0.0534423\pi$
$72$		0			0
$73$	−3.28017	−	3.28017i	−0.383915	−	0.383915i	0.488595	−	0.872511i	$-0.337509\pi$
$73$	−3.28017	−	3.28017i	−0.383915	−	0.383915i	−0.872511	+	0.488595i	$0.837509\pi$
$74$		0			0
$75$	−1.31240	−	3.67656i	−0.151543	−	0.424533i
$76$		0			0
$77$	0.0706027	−	0.0706027i	0.00804593	−	0.00804593i
$78$		0			0
$79$	0.169138			0.0190296			0.00951478	−	0.999955i	$-0.496971\pi$
$79$	0.169138			0.0190296			0.00951478	+	0.999955i	$0.496971\pi$
$80$		0			0
$81$	−3.88537			−0.431708
$82$		0			0
$83$	12.4474	−	12.4474i	1.36628	−	1.36628i	0.500604	−	0.865677i	$-0.333111\pi$
$83$	12.4474	−	12.4474i	1.36628	−	1.36628i	0.865677	−	0.500604i	$-0.166889\pi$
$84$		0			0
$85$	2.18155	+	0.490739i	0.236623	+	0.0532281i
$86$		0			0
$87$	3.84331	+	3.84331i	0.412046	+	0.412046i
$88$		0			0
$89$			0.766728i			0.0812730i	0.999174	+	0.0406365i	$0.0129386\pi$
$89$			0.766728i			0.0812730i	−0.999174	+	0.0406365i	$0.987061\pi$
$90$		0			0
$91$			0.272333i			0.0285483i
$92$		0			0
$93$	1.73536	+	1.73536i	0.179949	+	0.179949i
$94$		0			0
$95$	−9.58736	−	15.1526i	−0.983643	−	1.55462i
$96$		0			0
$97$	2.92067	−	2.92067i	0.296549	−	0.296549i	−0.543112	−	0.839660i	$-0.682754\pi$
$97$	2.92067	−	2.92067i	0.296549	−	0.296549i	0.839660	+	0.543112i	$0.182754\pi$
$98$		0			0
$99$	−3.33556			−0.335236
$100$		0			0
$101$	0.434444			0.0432288			0.0216144	−	0.999766i	$-0.493119\pi$
$101$	0.434444			0.0432288			0.0216144	+	0.999766i	$0.493119\pi$
$102$		0			0
$103$	3.06745	−	3.06745i	0.302244	−	0.302244i	−0.539647	−	0.841891i	$-0.681442\pi$
$103$	3.06745	−	3.06745i	0.302244	−	0.302244i	0.841891	+	0.539647i	$0.181442\pi$
$104$		0			0
$105$	−0.0667942	−	0.105567i	−0.00651845	−	0.0103022i
$106$		0			0
$107$	−4.01104	−	4.01104i	−0.387762	−	0.387762i	0.486127	−	0.873888i	$-0.338409\pi$
$107$	−4.01104	−	4.01104i	−0.387762	−	0.387762i	−0.873888	+	0.486127i	$0.838409\pi$
$108$		0			0
$109$		−	10.1492i		−	0.972121i	−0.873925	−	0.486060i	$-0.838434\pi$
$109$		−	10.1492i		−	0.972121i	0.873925	−	0.486060i	$-0.161566\pi$
$110$		0			0
$111$			1.49739i			0.142126i
$112$		0			0
$113$	−2.82305	−	2.82305i	−0.265570	−	0.265570i	0.561742	−	0.827312i	$-0.310131\pi$
$113$	−2.82305	−	2.82305i	−0.265570	−	0.265570i	−0.827312	+	0.561742i	$0.810131\pi$
$114$		0			0
$115$	−3.45462	−	0.777115i	−0.322145	−	0.0724664i
$116$		0			0
$117$	6.43305	−	6.43305i	0.594736	−	0.594736i
$118$		0			0
$119$	0.0715554			0.00655947
$120$		0			0
$121$	9.05290			0.822991
$122$		0			0
$123$	1.76807	−	1.76807i	0.159422	−	0.159422i
$124$		0			0
$125$	11.0978	−	1.35618i	0.992616	−	0.121300i
$126$		0			0
$127$	13.2399	+	13.2399i	1.17485	+	1.17485i	0.981040	+	0.193808i	$0.0620838\pi$
$127$	13.2399	+	13.2399i	1.17485	+	1.17485i	0.193808	+	0.981040i	$0.437916\pi$
$128$		0			0
$129$			5.66877i			0.499108i
$130$		0			0
$131$			17.7183i			1.54806i	0.633151	+	0.774029i	$0.281761\pi$
$131$			17.7183i			1.54806i	−0.633151	+	0.774029i	$0.718239\pi$
$132$		0			0
$133$	−0.405738	−	0.405738i	−0.0351819	−	0.0351819i
$134$		0			0
$135$	−2.06533	+	9.18129i	−0.177755	+	0.790200i
$136$		0			0
$137$	1.66803	−	1.66803i	0.142509	−	0.142509i	−0.632253	−	0.774762i	$-0.717870\pi$
$137$	1.66803	−	1.66803i	0.142509	−	0.142509i	0.774762	+	0.632253i	$0.217870\pi$
$138$		0			0
$139$	16.5560			1.40426			0.702132	−	0.712047i	$-0.252232\pi$
$139$	16.5560			1.40426			0.702132	+	0.712047i	$0.252232\pi$
$140$		0			0
$141$	4.62933			0.389860
$142$		0			0
$143$	3.75523	−	3.75523i	0.314028	−	0.314028i
$144$		0			0
$145$	−13.1545	+	8.32312i	−1.09242	+	0.691198i
$146$		0			0
$147$	3.86172	+	3.86172i	0.318509	+	0.318509i
$148$		0			0
$149$			15.0097i			1.22964i	0.788666	+	0.614822i	$0.210772\pi$
$149$			15.0097i			1.22964i	−0.788666	+	0.614822i	$0.789228\pi$
$150$		0			0
$151$			9.64249i			0.784695i	0.919817	+	0.392347i	$0.128337\pi$
$151$			9.64249i			0.784695i	−0.919817	+	0.392347i	$0.871663\pi$
$152$		0			0
$153$	−1.69028	−	1.69028i	−0.136651	−	0.136651i
$154$		0			0
$155$	−5.93963	+	3.75812i	−0.477082	+	0.301860i
$156$		0			0
$157$	10.0027	−	10.0027i	0.798299	−	0.798299i	−0.184529	−	0.982827i	$-0.559076\pi$
$157$	10.0027	−	10.0027i	0.798299	−	0.798299i	0.982827	+	0.184529i	$0.0590758\pi$
$158$		0			0
$159$	4.18699			0.332050
$160$		0			0
$161$	−0.113312			−0.00893026
$162$		0			0
$163$	−6.03164	+	6.03164i	−0.472435	+	0.472435i	−0.902702	−	0.430267i	$-0.858419\pi$
$163$	−6.03164	+	6.03164i	−0.472435	+	0.472435i	0.430267	+	0.902702i	$0.358419\pi$
$164$		0			0
$165$	−0.534638	+	2.37670i	−0.0416215	+	0.185026i
$166$		0			0
$167$	−16.6625	−	16.6625i	−1.28938	−	1.28938i	−0.935161	−	0.354222i	$-0.884746\pi$
$167$	−16.6625	−	16.6625i	−1.28938	−	1.28938i	−0.354222	−	0.935161i	$-0.615254\pi$
$168$		0			0
$169$			1.48491i			0.114224i
$170$		0			0
$171$			19.1687i			1.46587i
$172$		0			0
$173$	−1.36499	−	1.36499i	−0.103779	−	0.103779i	0.653311	−	0.757090i	$-0.273379\pi$
$173$	−1.36499	−	1.36499i	−0.103779	−	0.103779i	−0.757090	+	0.653311i	$0.773379\pi$
$174$		0			0
$175$	0.336953	−	0.120280i	0.0254712	−	0.00909232i
$176$		0			0
$177$	−3.67405	+	3.67405i	−0.276158	+	0.276158i
$178$		0			0
$179$	−20.3879			−1.52387			−0.761933	−	0.647655i	$-0.775750\pi$
$179$	−20.3879			−1.52387			−0.761933	+	0.647655i	$0.775750\pi$
$180$		0			0
$181$	16.7847			1.24760			0.623798	−	0.781586i	$-0.285589\pi$
$181$	16.7847			1.24760			0.623798	+	0.781586i	$0.285589\pi$
$182$		0			0
$183$	2.68873	−	2.68873i	0.198757	−	0.198757i
$184$		0			0
$185$	−4.18395	−	0.941177i	−0.307610	−	0.0691967i
$186$		0			0
$187$	−0.986686	−	0.986686i	−0.0721536	−	0.0721536i
$188$		0			0
$189$			0.301148i			0.0219053i
$190$		0			0
$191$			16.8497i			1.21920i	0.792708	+	0.609602i	$0.208671\pi$
$191$			16.8497i			1.21920i	−0.792708	+	0.609602i	$0.791329\pi$
$192$		0			0
$193$	−19.3056	−	19.3056i	−1.38965	−	1.38965i	−0.826044	−	0.563606i	$-0.809414\pi$
$193$	−19.3056	−	19.3056i	−1.38965	−	1.38965i	−0.563606	−	0.826044i	$-0.690586\pi$
$194$		0			0
$195$	−3.55266	−	5.61490i	−0.254412	−	0.402092i
$196$		0			0
$197$	−7.50894	+	7.50894i	−0.534990	+	0.534990i	−0.922053	−	0.387063i	$-0.873490\pi$
$197$	−7.50894	+	7.50894i	−0.534990	+	0.534990i	0.387063	+	0.922053i	$0.373490\pi$
$198$		0			0
$199$	12.2656			0.869485			0.434742	−	0.900555i	$-0.356839\pi$
$199$	12.2656			0.869485			0.434742	+	0.900555i	$0.356839\pi$
$200$		0			0
$201$	2.40661			0.169749
$202$		0			0
$203$	−0.352235	+	0.352235i	−0.0247221	+	0.0247221i
$204$		0			0
$205$	3.82895	+	6.05157i	0.267426	+	0.422660i
$206$		0			0
$207$	2.67667	+	2.67667i	0.186041	+	0.186041i
$208$		0			0
$209$			11.1895i			0.773997i
$210$		0			0
$211$		−	18.2075i		−	1.25346i	−0.779238	−	0.626728i	$-0.784394\pi$
$211$		−	18.2075i		−	1.25346i	0.779238	−	0.626728i	$-0.215606\pi$
$212$		0			0
$213$	1.55472	+	1.55472i	0.106528	+	0.106528i
$214$		0			0
$215$	−15.8394	−	3.56307i	−1.08024	−	0.242999i
$216$		0			0
$217$	−0.159044	+	0.159044i	−0.0107966	+	0.0107966i
$218$		0			0
$219$	3.62182			0.244740
$220$		0			0
$221$	3.80590			0.256013
$222$		0			0
$223$	−6.35989	+	6.35989i	−0.425890	+	0.425890i	−0.887226	−	0.461336i	$-0.847370\pi$
$223$	−6.35989	+	6.35989i	−0.425890	+	0.425890i	0.461336	+	0.887226i	$0.347370\pi$
$224$		0			0
$225$	−10.8008	−	5.11824i	−0.720050	−	0.341216i
$226$		0			0
$227$	−7.70344	−	7.70344i	−0.511295	−	0.511295i	0.403628	−	0.914923i	$-0.367749\pi$
$227$	−7.70344	−	7.70344i	−0.511295	−	0.511295i	−0.914923	+	0.403628i	$0.867749\pi$
$228$		0			0
$229$		−	22.2730i		−	1.47184i	−0.677068	−	0.735920i	$-0.736750\pi$
$229$		−	22.2730i		−	1.47184i	0.677068	−	0.735920i	$-0.263250\pi$
$230$		0			0
$231$			0.0779564i			0.00512915i
$232$		0			0
$233$	18.5509	+	18.5509i	1.21531	+	1.21531i	0.969256	+	0.246056i	$0.0791348\pi$
$233$	18.5509	+	18.5509i	1.21531	+	1.21531i	0.246056	+	0.969256i	$0.420865\pi$
$234$		0			0
$235$	−2.90974	+	12.9351i	−0.189810	+	0.843791i
$236$		0			0
$237$	−0.0933776	+	0.0933776i	−0.00606552	+	0.00606552i
$238$		0			0
$239$	−11.0578			−0.715267			−0.357634	−	0.933862i	$-0.616416\pi$
$239$	−11.0578			−0.715267			−0.357634	+	0.933862i	$0.616416\pi$
$240$		0			0
$241$	−3.57959			−0.230582			−0.115291	−	0.993332i	$-0.536780\pi$
$241$	−3.57959			−0.230582			−0.115291	+	0.993332i	$0.536780\pi$
$242$		0			0
$243$	11.0728	−	11.0728i	0.710322	−	0.710322i
$244$		0			0
$245$	−13.2175	+	8.36298i	−0.844435	+	0.534291i
$246$		0			0
$247$	−21.5805	−	21.5805i	−1.37313	−	1.37313i
$248$		0			0
$249$			13.7439i			0.870983i
$250$		0			0
$251$			7.38558i			0.466174i	0.972456	+	0.233087i	$0.0748827\pi$
$251$			7.38558i			0.466174i	−0.972456	+	0.233087i	$0.925117\pi$
$252$		0			0
$253$	1.56248	+	1.56248i	0.0982321	+	0.0982321i
$254$		0			0
$255$	−1.47531	+	0.933461i	−0.0923877	+	0.0584556i
$256$		0			0
$257$	−15.1003	+	15.1003i	−0.941928	+	0.941928i	−0.998404	−	0.0564762i	$-0.982013\pi$
$257$	−15.1003	+	15.1003i	−0.941928	+	0.941928i	0.0564762	+	0.998404i	$0.482013\pi$
$258$		0			0
$259$	−0.137234			−0.00852733
$260$		0			0
$261$	16.6410			1.03005
$262$		0			0
$263$	−10.0135	+	10.0135i	−0.617456	+	0.617456i	−0.944878	−	0.327422i	$-0.893820\pi$
$263$	−10.0135	+	10.0135i	−0.617456	+	0.617456i	0.327422	+	0.944878i	$0.393820\pi$
$264$		0			0
$265$	−2.63170	+	11.6991i	−0.161664	+	0.718669i
$266$		0			0
$267$	−0.423294	−	0.423294i	−0.0259052	−	0.0259052i
$268$		0			0
$269$		−	19.9282i		−	1.21504i	−0.794303	−	0.607521i	$-0.792164\pi$
$269$		−	19.9282i		−	1.21504i	0.794303	−	0.607521i	$-0.207836\pi$
$270$		0			0
$271$			26.6293i			1.61761i	0.588076	+	0.808806i	$0.299886\pi$
$271$			26.6293i			1.61761i	−0.588076	+	0.808806i	$0.700114\pi$
$272$		0			0
$273$	−0.150349	−	0.150349i	−0.00909954	−	0.00909954i
$274$		0			0
$275$	−6.30484	−	2.98772i	−0.380196	−	0.180166i
$276$		0			0
$277$	−19.2536	+	19.2536i	−1.15684	+	1.15684i	−0.171686	+	0.985152i	$0.554921\pi$
$277$	−19.2536	+	19.2536i	−1.15684	+	1.15684i	−0.985152	+	0.171686i	$0.945079\pi$
$278$		0			0
$279$	7.51388			0.449844
$280$		0			0
$281$	−7.64833			−0.456261			−0.228131	−	0.973631i	$-0.573261\pi$
$281$	−7.64833			−0.456261			−0.228131	+	0.973631i	$0.573261\pi$
$282$		0			0
$283$	−6.83560	+	6.83560i	−0.406334	+	0.406334i	−0.880458	−	0.474124i	$-0.842765\pi$
$283$	−6.83560	+	6.83560i	−0.406334	+	0.406334i	0.474124	+	0.880458i	$0.342765\pi$
$284$		0			0
$285$	13.6584	+	3.07244i	0.809053	+	0.181996i
$286$		0			0
$287$	0.162042	+	0.162042i	0.00956502	+	0.00956502i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$		0			0
$291$			3.22487i			0.189045i
$292$		0			0
$293$	−4.39187	−	4.39187i	−0.256576	−	0.256576i	0.567084	−	0.823660i	$-0.308071\pi$
$293$	−4.39187	−	4.39187i	−0.256576	−	0.256576i	−0.823660	+	0.567084i	$0.808071\pi$
$294$		0			0
$295$	−7.95656	−	12.5751i	−0.463249	−	0.732153i
$296$		0			0
$297$	4.15257	−	4.15257i	0.240957	−	0.240957i
$298$		0			0
$299$	−6.02688			−0.348544
$300$		0			0
$301$	−0.519537			−0.0299456
$302$		0			0
$303$	−0.239847	+	0.239847i	−0.0137788	+	0.0137788i
$304$		0			0
$305$	5.82274	+	9.20271i	0.333409	+	0.526946i
$306$		0			0
$307$	11.5174	+	11.5174i	0.657333	+	0.657333i	0.954748	−	0.297415i	$-0.0961246\pi$
$307$	11.5174	+	11.5174i	0.657333	+	0.657333i	−0.297415	+	0.954748i	$0.596125\pi$
$308$		0			0
$309$			3.38694i			0.192676i
$310$		0			0
$311$			14.5438i			0.824701i	0.911025	+	0.412350i	$0.135292\pi$
$311$			14.5438i			0.824701i	−0.911025	+	0.412350i	$0.864708\pi$
$312$		0			0
$313$	10.9569	+	10.9569i	0.619318	+	0.619318i	0.945357	−	0.326038i	$-0.105714\pi$
$313$	10.9569	+	10.9569i	0.619318	+	0.619318i	−0.326038	+	0.945357i	$0.605714\pi$
$314$		0			0
$315$	−0.373149	−	0.0839396i	−0.0210246	−	0.00472946i
$316$		0			0
$317$	10.9973	−	10.9973i	0.617672	−	0.617672i	−0.327261	−	0.944934i	$-0.606126\pi$
$317$	10.9973	−	10.9973i	0.617672	−	0.617672i	0.944934	+	0.327261i	$0.106126\pi$
$318$		0			0
$319$	9.71403			0.543881
$320$		0			0
$321$	4.42881			0.247192
$322$		0			0
$323$	−5.67026	+	5.67026i	−0.315502	+	0.315502i
$324$		0			0
$325$	17.9219	−	6.39749i	0.994129	−	0.354869i
$326$		0			0
$327$	5.60317	+	5.60317i	0.309856	+	0.309856i
$328$		0			0
$329$			0.424273i			0.0233909i
$330$		0			0
$331$			26.6060i			1.46240i	0.682164	+	0.731199i	$0.261039\pi$
$331$			26.6060i			1.46240i	−0.682164	+	0.731199i	$0.738961\pi$
$332$		0			0
$333$	3.24175	+	3.24175i	0.177647	+	0.177647i
$334$		0			0
$335$	−1.51266	+	6.72444i	−0.0826454	+	0.367395i
$336$		0			0
$337$	8.15942	−	8.15942i	0.444472	−	0.444472i	−0.449040	−	0.893512i	$-0.648234\pi$
$337$	8.15942	−	8.15942i	0.444472	−	0.444472i	0.893512	+	0.449040i	$0.148234\pi$
$338$		0			0
$339$	3.11708			0.169297
$340$		0			0
$341$	4.38616			0.237524
$342$		0			0
$343$	−0.708103	+	0.708103i	−0.0382340	+	0.0382340i
$344$		0			0
$345$	2.33625	−	1.47819i	0.125779	−	0.0795832i
$346$		0			0
$347$	−20.8221	−	20.8221i	−1.11779	−	1.11779i	−0.992065	−	0.125725i	$-0.959874\pi$
$347$	−20.8221	−	20.8221i	−1.11779	−	1.11779i	−0.125725	−	0.992065i	$-0.540126\pi$
$348$		0			0
$349$		−	15.2664i		−	0.817191i	−0.912716	−	0.408595i	$-0.866019\pi$
$349$		−	15.2664i		−	0.817191i	0.912716	−	0.408595i	$-0.133981\pi$
$350$		0			0
$351$			16.0175i			0.854953i
$352$		0			0
$353$	−18.5198	−	18.5198i	−0.985710	−	0.985710i	0.0141896	−	0.999899i	$-0.495483\pi$
$353$	−18.5198	−	18.5198i	−0.985710	−	0.985710i	−0.999899	+	0.0141896i	$0.995483\pi$
$354$		0			0
$355$	−5.32133	+	3.36692i	−0.282427	+	0.178697i
$356$		0			0
$357$	−0.0395042	+	0.0395042i	−0.00209078	+	0.00209078i
$358$		0			0
$359$	1.50488			0.0794248			0.0397124	−	0.999211i	$-0.487356\pi$
$359$	1.50488			0.0794248			0.0397124	+	0.999211i	$0.487356\pi$
$360$		0			0
$361$	45.3038			2.38441
$362$		0			0
$363$	−4.99791	+	4.99791i	−0.262322	+	0.262322i
$364$		0			0
$365$	−2.27647	+	10.1199i	−0.119156	+	0.529701i
$366$		0			0
$367$	5.69692	+	5.69692i	0.297377	+	0.297377i	0.839985	−	0.542609i	$-0.182563\pi$
$367$	5.69692	+	5.69692i	0.297377	+	0.297377i	−0.542609	+	0.839985i	$0.682563\pi$
$368$		0			0
$369$		−	7.65550i		−	0.398529i
$370$		0			0
$371$			0.383732i			0.0199224i
$372$		0			0
$373$	24.5492	+	24.5492i	1.27111	+	1.27111i	0.945506	+	0.325605i	$0.105568\pi$
$373$	24.5492	+	24.5492i	1.27111	+	1.27111i	0.325605	+	0.945506i	$0.394432\pi$
$374$		0			0
$375$	−5.37813	+	6.87556i	−0.277725	+	0.355052i
$376$		0			0
$377$	−18.7348	+	18.7348i	−0.964890	+	0.964890i
$378$		0			0
$379$	−17.0123			−0.873861			−0.436930	−	0.899495i	$-0.643934\pi$
$379$	−17.0123			−0.873861			−0.436930	+	0.899495i	$0.643934\pi$
$380$		0			0
$381$	−14.6189			−0.748947
$382$		0			0
$383$	21.8154	−	21.8154i	1.11471	−	1.11471i	0.122210	−	0.992504i	$-0.461002\pi$
$383$	21.8154	−	21.8154i	1.11471	−	1.11471i	0.992504	−	0.122210i	$-0.0389981\pi$
$384$		0			0
$385$	−0.217822	−	0.0489990i	−0.0111012	−	0.00249722i
$386$		0			0
$387$	12.2725	+	12.2725i	0.623846	+	0.623846i
$388$		0			0
$389$		−	16.9311i		−	0.858441i	−0.903200	−	0.429220i	$-0.858788\pi$
$389$		−	16.9311i		−	0.858441i	0.903200	−	0.429220i	$-0.141212\pi$
$390$		0			0
$391$			1.58356i			0.0800841i
$392$		0			0
$393$	−9.78190	−	9.78190i	−0.493431	−	0.493431i
$394$		0			0
$395$	−0.202220	−	0.319603i	−0.0101748	−	0.0160810i
$396$		0			0
$397$	−10.7199	+	10.7199i	−0.538018	+	0.538018i	−0.922947	−	0.384928i	$-0.874226\pi$
$397$	−10.7199	+	10.7199i	−0.538018	+	0.538018i	0.384928	+	0.922947i	$0.374226\pi$
$398$		0			0
$399$	0.447998			0.0224279
$400$		0			0
$401$	−5.54386			−0.276847			−0.138423	−	0.990373i	$-0.544203\pi$
$401$	−5.54386			−0.276847			−0.138423	+	0.990373i	$0.544203\pi$
$402$		0			0
$403$	−8.45927	+	8.45927i	−0.421386	+	0.421386i
$404$		0			0
$405$	4.64529	+	7.34178i	0.230826	+	0.364816i
$406$		0			0
$407$	1.89234	+	1.89234i	0.0937999	+	0.0937999i
$408$		0			0
$409$			7.11756i			0.351941i	0.984395	+	0.175970i	$0.0563063\pi$
$409$			7.11756i			0.351941i	−0.984395	+	0.175970i	$0.943694\pi$
$410$		0			0
$411$			1.84176i			0.0908473i
$412$		0			0
$413$	−0.336722	−	0.336722i	−0.0165690	−	0.0165690i
$414$		0			0
$415$	−38.4025	−	8.63862i	−1.88511	−	0.424053i
$416$		0			0
$417$	−9.14021	+	9.14021i	−0.447598	+	0.447598i
$418$		0			0
$419$	−20.4856			−1.00079			−0.500393	−	0.865798i	$-0.666811\pi$
$419$	−20.4856			−1.00079			−0.500393	+	0.865798i	$0.666811\pi$
$420$		0			0
$421$	14.2174			0.692912			0.346456	−	0.938066i	$-0.387385\pi$
$421$	14.2174			0.692912			0.346456	+	0.938066i	$0.387385\pi$
$422$		0			0
$423$	10.0222	−	10.0222i	0.487295	−	0.487295i
$424$		0			0
$425$	−1.68094	−	4.70898i	−0.0815374	−	0.228419i
$426$		0			0
$427$	0.246419	+	0.246419i	0.0119251	+	0.0119251i
$428$		0			0
$429$			4.14636i			0.200188i
$430$		0			0
$431$		−	16.4428i		−	0.792019i	−0.918246	−	0.396010i	$-0.870395\pi$
$431$		−	16.4428i		−	0.792019i	0.918246	−	0.396010i	$-0.129605\pi$
$432$		0			0
$433$	5.45348	+	5.45348i	0.262078	+	0.262078i	0.825898	−	0.563820i	$-0.190669\pi$
$433$	5.45348	+	5.45348i	0.262078	+	0.262078i	−0.563820	+	0.825898i	$0.690669\pi$
$434$		0			0
$435$	2.66730	−	11.8573i	0.127887	−	0.568515i
$436$		0			0
$437$	8.97921	−	8.97921i	0.429534	−	0.429534i
$438$		0			0
$439$	31.3846			1.49791			0.748953	−	0.662624i	$-0.230557\pi$
$439$	31.3846			1.49791			0.748953	+	0.662624i	$0.230557\pi$
$440$		0			0
$441$	16.7207			0.796224
$442$		0			0
$443$	−1.22924	+	1.22924i	−0.0584028	+	0.0584028i	−0.735705	−	0.677302i	$-0.763149\pi$
$443$	−1.22924	+	1.22924i	−0.0584028	+	0.0584028i	0.677302	+	0.735705i	$0.263149\pi$
$444$		0			0
$445$	1.44881	−	0.916690i	0.0686800	−	0.0434553i
$446$		0			0
$447$	−8.28654	−	8.28654i	−0.391940	−	0.391940i
$448$		0			0
$449$			11.7586i			0.554921i	0.960737	+	0.277461i	$0.0894928\pi$
$449$			11.7586i			0.554921i	−0.960737	+	0.277461i	$0.910507\pi$
$450$		0			0
$451$		−	4.46882i		−	0.210429i
$452$		0			0
$453$	−5.32341	−	5.32341i	−0.250115	−	0.250115i
$454$		0			0
$455$	0.514599	−	0.325598i	0.0241248	−	0.0152643i
$456$		0			0
$457$	−6.65086	+	6.65086i	−0.311114	+	0.311114i	−0.845341	−	0.534227i	$-0.820603\pi$
$457$	−6.65086	+	6.65086i	−0.311114	+	0.311114i	0.534227	+	0.845341i	$0.320603\pi$
$458$		0			0
$459$	4.20860			0.196441
$460$		0			0
$461$	2.20598			0.102743			0.0513713	−	0.998680i	$-0.483641\pi$
$461$	2.20598			0.102743			0.0513713	+	0.998680i	$0.483641\pi$
$462$		0			0
$463$	−5.83069	+	5.83069i	−0.270975	+	0.270975i	−0.829493	−	0.558517i	$-0.811370\pi$
$463$	−5.83069	+	5.83069i	−0.270975	+	0.270975i	0.558517	+	0.829493i	$0.311370\pi$
$464$		0			0
$465$	1.20436	−	5.35391i	0.0558508	−	0.248282i
$466$		0			0
$467$	3.11066	+	3.11066i	0.143944	+	0.143944i	0.775407	−	0.631462i	$-0.217545\pi$
$467$	3.11066	+	3.11066i	0.143944	+	0.143944i	−0.631462	+	0.775407i	$0.717545\pi$
$468$		0			0
$469$			0.220563i			0.0101847i
$470$		0			0
$471$			11.0445i			0.508903i
$472$		0			0
$473$	7.16395	+	7.16395i	0.329399	+	0.329399i
$474$		0			0
$475$	−17.1698	+	36.2325i	−0.787803	+	1.66246i
$476$		0			0
$477$	9.06453	−	9.06453i	0.415036	−	0.415036i
$478$		0			0
$479$	17.7850			0.812615			0.406308	−	0.913736i	$-0.366816\pi$
$479$	17.7850			0.812615			0.406308	+	0.913736i	$0.366816\pi$
$480$		0			0
$481$	−7.29926			−0.332817
$482$		0			0
$483$	0.0625572	−	0.0625572i	0.00284645	−	0.00284645i
$484$		0			0
$485$	−9.01079	−	2.02697i	−0.409159	−	0.0920400i
$486$		0			0
$487$	10.8029	+	10.8029i	0.489525	+	0.489525i	0.908156	−	0.418631i	$-0.137490\pi$
$487$	10.8029	+	10.8029i	0.489525	+	0.489525i	−0.418631	+	0.908156i	$0.637490\pi$
$488$		0			0
$489$		−	6.65988i		−	0.301170i
$490$		0			0
$491$		−	38.4004i		−	1.73299i	−0.499189	−	0.866493i	$-0.666369\pi$
$491$		−	38.4004i		−	1.73299i	0.499189	−	0.866493i	$-0.333631\pi$
$492$		0			0
$493$	4.92255	+	4.92255i	0.221701	+	0.221701i
$494$		0			0
$495$	3.98794	+	6.30285i	0.179245	+	0.283292i
$496$		0			0
$497$	−0.142488	+	0.142488i	−0.00639147	+	0.00639147i
$498$		0			0
$499$	21.0618			0.942854			0.471427	−	0.881905i	$-0.343739\pi$
$499$	21.0618			0.942854			0.471427	+	0.881905i	$0.343739\pi$
$500$		0			0
$501$	18.3980			0.821962
$502$		0			0
$503$	11.0384	−	11.0384i	0.492178	−	0.492178i	−0.416814	−	0.908992i	$-0.636853\pi$
$503$	11.0384	−	11.0384i	0.492178	−	0.492178i	0.908992	+	0.416814i	$0.136853\pi$
$504$		0			0
$505$	−0.519415	−	0.820923i	−0.0231137	−	0.0365306i
$506$		0			0
$507$	−0.819786	−	0.819786i	−0.0364080	−	0.0364080i
$508$		0			0
$509$		−	22.7065i		−	1.00645i	−0.864156	−	0.503224i	$-0.832147\pi$
$509$		−	22.7065i		−	1.00645i	0.864156	−	0.503224i	$-0.167853\pi$
$510$		0			0
$511$			0.331936i			0.0146840i
$512$		0			0
$513$	−23.8639	−	23.8639i	−1.05362	−	1.05362i
$514$		0			0
$515$	−9.46363	−	2.12884i	−0.417017	−	0.0938077i
$516$		0			0
$517$	5.85035	−	5.85035i	0.257298	−	0.257298i
$518$		0			0
$519$	1.50717			0.0661573
$520$		0			0
$521$	17.1794			0.752645			0.376322	−	0.926489i	$-0.377189\pi$
$521$	17.1794			0.752645			0.376322	+	0.926489i	$0.377189\pi$
$522$		0			0
$523$	21.3116	−	21.3116i	0.931889	−	0.931889i	−0.0659348	−	0.997824i	$-0.521003\pi$
$523$	21.3116	−	21.3116i	0.931889	−	0.931889i	0.997824	+	0.0659348i	$0.0210029\pi$
$524$		0			0
$525$	−0.119620	+	0.252428i	−0.00522065	+	0.0110169i
$526$		0			0
$527$	2.22267	+	2.22267i	0.0968211	+	0.0968211i
$528$		0			0
$529$			20.4923i			0.890971i
$530$		0			0
$531$			15.9081i			0.690353i
$532$		0			0
$533$	8.61871	+	8.61871i	0.373318	+	0.373318i
$534$		0			0
$535$	−2.78370	+	12.3748i	−0.120350	+	0.535009i
$536$		0			0
$537$	11.2557	−	11.2557i	0.485721	−	0.485721i
$538$		0			0
$539$	9.76055			0.420417
$540$		0			0
$541$	−38.5479			−1.65730			−0.828651	−	0.559765i	$-0.810891\pi$
$541$	−38.5479			−1.65730			−0.828651	+	0.559765i	$0.810891\pi$
$542$		0			0
$543$	−9.26645	+	9.26645i	−0.397661	+	0.397661i
$544$		0			0
$545$	−19.1780	+	12.1343i	−0.821494	+	0.519776i
$546$		0			0
$547$	−24.9281	−	24.9281i	−1.06585	−	1.06585i	−0.997673	−	0.0681753i	$-0.978282\pi$
$547$	−24.9281	−	24.9281i	−1.06585	−	1.06585i	−0.0681753	−	0.997673i	$-0.521718\pi$
$548$		0			0
$549$		−	11.6418i		−	0.496861i
$550$		0			0
$551$		−	55.8243i		−	2.37820i
$552$		0			0
$553$	−0.00855795	−	0.00855795i	−0.000363921	−	0.000363921i
$554$		0			0
$555$	2.82947	−	1.79026i	0.120104	−	0.0759925i
$556$		0			0
$557$	1.65212	−	1.65212i	0.0700028	−	0.0700028i	−0.671239	−	0.741241i	$-0.734237\pi$
$557$	1.65212	−	1.65212i	0.0700028	−	0.0700028i	0.741241	+	0.671239i	$0.234237\pi$
$558$		0			0
$559$	−27.6332			−1.16876
$560$		0			0
$561$	1.08946			0.0459968
$562$		0			0
$563$	19.3443	−	19.3443i	0.815266	−	0.815266i	−0.170152	−	0.985418i	$-0.554426\pi$
$563$	19.3443	−	19.3443i	0.815266	−	0.815266i	0.985418	+	0.170152i	$0.0544259\pi$
$564$		0			0
$565$	−1.95922	+	8.70962i	−0.0824251	+	0.366416i
$566$		0			0
$567$	0.196589	+	0.196589i	0.00825597	+	0.00825597i
$568$		0			0
$569$			34.1227i			1.43050i	0.698871	+	0.715248i	$0.253686\pi$
$569$			34.1227i			1.43050i	−0.698871	+	0.715248i	$0.746314\pi$
$570$		0			0
$571$			9.90202i			0.414387i	0.978300	+	0.207193i	$0.0664329\pi$
$571$			9.90202i			0.414387i	−0.978300	+	0.207193i	$0.933567\pi$
$572$		0			0
$573$	−9.30236	−	9.30236i	−0.388612	−	0.388612i
$574$		0			0
$575$	2.66187	+	7.45695i	0.111008	+	0.310976i
$576$		0			0
$577$	10.8397	−	10.8397i	0.451263	−	0.451263i	−0.444510	−	0.895774i	$-0.646622\pi$
$577$	10.8397	−	10.8397i	0.451263	−	0.451263i	0.895774	+	0.444510i	$0.146622\pi$
$578$		0			0
$579$	21.3164			0.885880
$580$		0			0
$581$	−1.25961			−0.0522574
$582$		0			0
$583$	5.29133	−	5.29133i	0.219145	−	0.219145i
$584$		0			0
$585$	−19.8471	−	4.46460i	−0.820578	−	0.184589i
$586$		0			0
$587$	−9.83793	−	9.83793i	−0.406055	−	0.406055i	0.474305	−	0.880360i	$-0.342699\pi$
$587$	−9.83793	−	9.83793i	−0.406055	−	0.406055i	−0.880360	+	0.474305i	$0.842699\pi$
$588$		0			0
$589$		−	25.2063i		−	1.03861i
$590$		0			0
$591$		−	8.29104i		−	0.341048i
$592$		0			0
$593$	−1.70099	−	1.70099i	−0.0698514	−	0.0698514i	0.671318	−	0.741169i	$-0.265728\pi$
$593$	−1.70099	−	1.70099i	−0.0698514	−	0.0698514i	−0.741169	+	0.671318i	$0.765728\pi$
$594$		0			0
$595$	−0.0855507	−	0.135211i	−0.00350723	−	0.00554310i
$596$		0			0
$597$	−6.77156	+	6.77156i	−0.277142	+	0.277142i
$598$		0			0
$599$	−1.09110			−0.0445811			−0.0222905	−	0.999752i	$-0.507096\pi$
$599$	−1.09110			−0.0445811			−0.0222905	+	0.999752i	$0.507096\pi$
$600$		0			0
$601$	−26.6612			−1.08753			−0.543766	−	0.839237i	$-0.683002\pi$
$601$	−26.6612			−1.08753			−0.543766	+	0.839237i	$0.683002\pi$
$602$		0			0
$603$	5.21014	−	5.21014i	0.212173	−	0.212173i
$604$		0			0
$605$	−10.8235	−	17.1063i	−0.440039	−	0.695471i
$606$		0			0
$607$	−3.06268	−	3.06268i	−0.124310	−	0.124310i	0.642215	−	0.766525i	$-0.278016\pi$
$607$	−3.06268	−	3.06268i	−0.124310	−	0.124310i	−0.766525	+	0.642215i	$0.778016\pi$
$608$		0			0
$609$		−	0.388923i		−	0.0157599i
$610$		0			0
$611$			22.5663i			0.912936i
$612$		0			0
$613$	−4.53968	−	4.53968i	−0.183356	−	0.183356i	0.609460	−	0.792816i	$-0.291386\pi$
$613$	−4.53968	−	4.53968i	−0.183356	−	0.183356i	−0.792816	+	0.609460i	$0.791386\pi$
$614$		0			0
$615$	−5.45482	−	1.22706i	−0.219960	−	0.0494798i
$616$		0			0
$617$	−3.79642	+	3.79642i	−0.152838	+	0.152838i	−0.779384	−	0.626546i	$-0.784468\pi$
$617$	−3.79642	+	3.79642i	−0.152838	+	0.152838i	0.626546	+	0.779384i	$0.284468\pi$
$618$		0			0
$619$	24.4713			0.983584			0.491792	−	0.870713i	$-0.336342\pi$
$619$	24.4713			0.983584			0.491792	+	0.870713i	$0.336342\pi$
$620$		0			0
$621$	−6.66458			−0.267440
$622$		0			0
$623$	0.0387944	−	0.0387944i	0.00155426	−	0.00155426i
$624$		0			0
$625$	−15.8310	−	19.3489i	−0.633239	−	0.773956i
$626$		0			0
$627$	−6.17750	−	6.17750i	−0.246705	−	0.246705i
$628$		0			0
$629$			1.91788i			0.0764708i
$630$		0			0
$631$			14.8529i			0.591284i	0.955299	+	0.295642i	$0.0955335\pi$
$631$			14.8529i			0.591284i	−0.955299	+	0.295642i	$0.904466\pi$
$632$		0			0
$633$	10.0520	+	10.0520i	0.399530	+	0.399530i
$634$		0			0
$635$	9.18859	−	40.8474i	0.364638	−	1.62098i
$636$		0			0
$637$	−18.8245	+	18.8245i	−0.745853	+	0.745853i
$638$		0			0
$639$	6.73172			0.266303
$640$		0			0
$641$	16.9651			0.670081			0.335040	−	0.942204i	$-0.391250\pi$
$641$	16.9651			0.670081			0.335040	+	0.942204i	$0.391250\pi$
$642$		0			0
$643$	34.9211	−	34.9211i	1.37715	−	1.37715i	0.527758	−	0.849395i	$-0.323033\pi$
$643$	34.9211	−	34.9211i	1.37715	−	1.37715i	0.849395	−	0.527758i	$-0.176967\pi$
$644$		0			0
$645$	10.7117	−	6.77751i	0.421772	−	0.266864i
$646$		0			0
$647$	33.1183	+	33.1183i	1.30201	+	1.30201i	0.927033	+	0.374981i	$0.122351\pi$
$647$	33.1183	+	33.1183i	1.30201	+	1.30201i	0.374981	+	0.927033i	$0.377649\pi$
$648$		0			0
$649$			9.28620i			0.364515i
$650$		0			0
$651$		−	0.175609i		−	0.00688268i
$652$		0			0
$653$	−27.5635	−	27.5635i	−1.07864	−	1.07864i	−0.996631	−	0.0820105i	$-0.973866\pi$
$653$	−27.5635	−	27.5635i	−1.07864	−	1.07864i	−0.0820105	−	0.996631i	$-0.526134\pi$
$654$		0			0
$655$	33.4805	−	21.1838i	1.30819	−	0.827719i
$656$		0			0
$657$	7.84099	−	7.84099i	0.305906	−	0.305906i
$658$		0			0
$659$	−18.6950			−0.728255			−0.364128	−	0.931349i	$-0.618633\pi$
$659$	−18.6950			−0.728255			−0.364128	+	0.931349i	$0.618633\pi$
$660$		0			0
$661$	−28.1731			−1.09581			−0.547903	−	0.836542i	$-0.684574\pi$
$661$	−28.1731			−1.09581			−0.547903	+	0.836542i	$0.684574\pi$
$662$		0			0
$663$	−2.10116	+	2.10116i	−0.0816021	+	0.0816021i
$664$		0			0
$665$	−0.281586	+	1.25178i	−0.0109194	+	0.0485418i
$666$		0			0
$667$	−7.79516	−	7.79516i	−0.301830	−	0.301830i
$668$		0			0
$669$		−	7.02231i		−	0.271498i
$670$		0			0
$671$		−	6.79580i		−	0.262349i
$672$		0			0
$673$	−21.9967	−	21.9967i	−0.847912	−	0.847912i	0.141961	−	0.989872i	$-0.454659\pi$
$673$	−21.9967	−	21.9967i	−0.847912	−	0.847912i	−0.989872	+	0.141961i	$0.954659\pi$
$674$		0			0
$675$	19.8182	−	7.07440i	0.762803	−	0.272294i
$676$		0			0
$677$	−18.0200	+	18.0200i	−0.692563	+	0.692563i	−0.962795	−	0.270232i	$-0.912900\pi$
$677$	−18.0200	+	18.0200i	−0.692563	+	0.692563i	0.270232	+	0.962795i	$0.412900\pi$
$678$		0			0
$679$	−0.295556			−0.0113424
$680$		0			0
$681$	8.50580			0.325943
$682$		0			0
$683$	11.7524	−	11.7524i	0.449693	−	0.449693i	−0.445559	−	0.895252i	$-0.646995\pi$
$683$	11.7524	−	11.7524i	0.449693	−	0.449693i	0.895252	+	0.445559i	$0.146995\pi$
$684$		0			0
$685$	−5.14616	−	1.15763i	−0.196625	−	0.0442306i
$686$		0			0
$687$	12.2964	+	12.2964i	0.469138	+	0.469138i
$688$		0			0
$689$			20.4101i			0.777561i
$690$		0			0
$691$			30.1130i			1.14555i	0.819712	+	0.572776i	$0.194134\pi$
$691$			30.1130i			1.14555i	−0.819712	+	0.572776i	$0.805866\pi$
$692$		0			0
$693$	0.168770	+	0.168770i	0.00641105	+	0.00641105i
$694$		0			0
$695$	−19.7942	−	31.2842i	−0.750835	−	1.18668i
$696$		0			0
$697$	2.26456	−	2.26456i	0.0857764	−	0.0857764i
$698$		0			0
$699$	−20.4831			−0.774743
$700$		0			0
$701$	−18.8598			−0.712324			−0.356162	−	0.934424i	$-0.615915\pi$
$701$	−18.8598			−0.712324			−0.356162	+	0.934424i	$0.615915\pi$
$702$		0			0
$703$	10.8749	−	10.8749i	0.410153	−	0.410153i
$704$		0			0
$705$	−5.53477	−	8.74757i	−0.208451	−	0.329453i
$706$		0			0
$707$	−0.0219817	−	0.0219817i	−0.000826706	−	0.000826706i
$708$		0			0
$709$		−	33.1192i		−	1.24382i	−0.783090	−	0.621909i	$-0.786358\pi$
$709$		−	33.1192i		−	1.24382i	0.783090	−	0.621909i	$-0.213642\pi$
$710$		0			0
$711$			0.404312i			0.0151629i
$712$		0			0
$713$	−3.51973	−	3.51973i	−0.131815	−	0.131815i
$714$		0			0
$715$	−11.5856	−	2.60617i	−0.433276	−	0.0974652i
$716$		0			0
$717$	6.10475	−	6.10475i	0.227986	−	0.227986i
$718$		0			0
$719$	−4.64634			−0.173279			−0.0866396	−	0.996240i	$-0.527613\pi$
$719$	−4.64634			−0.173279			−0.0866396	+	0.996240i	$0.527613\pi$
$720$		0			0
$721$	−0.310409			−0.0115602
$722$		0			0
$723$	1.97622	−	1.97622i	0.0734962	−	0.0734962i
$724$		0			0
$725$	31.4547	+	14.9057i	1.16820	+	0.553583i
$726$		0			0
$727$	−18.5017	−	18.5017i	−0.686192	−	0.686192i	0.275196	−	0.961388i	$-0.411257\pi$
$727$	−18.5017	−	18.5017i	−0.686192	−	0.686192i	−0.961388	+	0.275196i	$0.911257\pi$
$728$		0			0
$729$			0.570016i			0.0211117i
$730$		0			0
$731$			7.26062i			0.268544i
$732$		0			0
$733$	10.8358	+	10.8358i	0.400230	+	0.400230i	0.878314	−	0.478084i	$-0.158668\pi$
$733$	10.8358	+	10.8358i	0.400230	+	0.400230i	−0.478084	+	0.878314i	$0.658668\pi$
$734$		0			0
$735$	2.68007	−	11.9141i	0.0988559	−	0.439458i
$736$		0			0
$737$	3.04137	−	3.04137i	0.112030	−	0.112030i
$738$		0			0
$739$	14.1025			0.518769			0.259385	−	0.965774i	$-0.416480\pi$
$739$	14.1025			0.518769			0.259385	+	0.965774i	$0.416480\pi$
$740$		0			0
$741$	23.8282			0.875351
$742$		0			0
$743$	−27.1941	+	27.1941i	−0.997654	+	0.997654i	−0.999997	−	0.00234369i	$-0.999254\pi$
$743$	−27.1941	+	27.1941i	−0.997654	+	0.997654i	0.00234369	+	0.999997i	$0.499254\pi$
$744$		0			0
$745$	28.3623	−	17.9454i	1.03911	−	0.657469i
$746$		0			0
$747$	29.7545	+	29.7545i	1.08866	+	1.08866i
$748$		0			0
$749$			0.405895i			0.0148311i
$750$		0			0
$751$		−	23.4192i		−	0.854580i	−0.904115	−	0.427290i	$-0.859468\pi$
$751$		−	23.4192i		−	0.854580i	0.904115	−	0.427290i	$-0.140532\pi$
$752$		0			0
$753$	−4.07742	−	4.07742i	−0.148589	−	0.148589i
$754$		0			0
$755$	18.2204	−	11.5284i	0.663109	−	0.419562i
$756$		0			0
$757$	−8.50542	+	8.50542i	−0.309135	+	0.309135i	−0.844574	−	0.535439i	$-0.820146\pi$
$757$	−8.50542	+	8.50542i	−0.309135	+	0.309135i	0.535439	+	0.844574i	$0.320146\pi$
$758$		0			0
$759$	−1.72522			−0.0626215
$760$		0			0
$761$	−17.0043			−0.616406			−0.308203	−	0.951321i	$-0.599728\pi$
$761$	−17.0043			−0.616406			−0.308203	+	0.951321i	$0.599728\pi$
$762$		0			0
$763$	−0.513524	+	0.513524i	−0.0185908	+	0.0185908i
$764$		0			0
$765$	−1.17307	+	5.21483i	−0.0424125	+	0.188543i
$766$		0			0
$767$	−17.9096	−	17.9096i	−0.646680	−	0.646680i
$768$		0			0
$769$		−	6.51142i		−	0.234808i	−0.993084	−	0.117404i	$-0.962543\pi$
$769$		−	6.51142i		−	0.234808i	0.993084	−	0.117404i	$-0.0374572\pi$
$770$		0			0
$771$		−	16.6730i		−	0.600464i
$772$		0			0
$773$	15.8647	+	15.8647i	0.570612	+	0.570612i	0.932299	−	0.361687i	$-0.117799\pi$
$773$	15.8647	+	15.8647i	0.570612	+	0.570612i	−0.361687	+	0.932299i	$0.617799\pi$
$774$		0			0
$775$	14.2027	+	6.73033i	0.510175	+	0.241761i
$776$		0			0
$777$	0.0757641	−	0.0757641i	0.00271802	−	0.00271802i
$778$		0			0
$779$	−25.6813			−0.920129
$780$		0			0
$781$	3.92957			0.140611
$782$		0			0
$783$	−20.7171	+	20.7171i	−0.740368	+	0.740368i
$784$		0			0
$785$	−30.8600	−	6.94194i	−1.10144	−	0.247768i
$786$		0			0
$787$	10.2669	+	10.2669i	0.365974	+	0.365974i	0.866007	−	0.500032i	$-0.166679\pi$
$787$	10.2669	+	10.2669i	0.365974	+	0.365974i	−0.500032	+	0.866007i	$0.666679\pi$
$788$		0			0
$789$		−	11.0564i		−	0.393619i
$790$		0			0
$791$			0.285677i			0.0101575i
$792$		0			0
$793$	13.1066	+	13.1066i	0.465429	+	0.465429i
$794$		0			0
$795$	−5.00590	−	7.91171i	−0.177541	−	0.280600i
$796$		0			0
$797$	−36.1862	+	36.1862i	−1.28178	+	1.28178i	−0.342127	+	0.939654i	$0.611147\pi$
$797$	−36.1862	+	36.1862i	−1.28178	+	1.28178i	−0.939654	+	0.342127i	$0.888853\pi$
$798$		0			0
$799$	5.92930			0.209763
$800$		0			0
$801$	−1.83280			−0.0647589
$802$		0			0
$803$	4.57710	−	4.57710i	0.161522	−	0.161522i
$804$		0			0
$805$	0.135475	+	0.214115i	0.00477486	+	0.00754655i
$806$		0			0
$807$	11.0019	+	11.0019i	0.387285	+	0.387285i
$808$		0			0
$809$		−	30.1038i		−	1.05839i	−0.848499	−	0.529196i	$-0.822494\pi$
$809$		−	30.1038i		−	1.05839i	0.848499	−	0.529196i	$-0.177506\pi$
$810$		0			0
$811$			17.2830i			0.606889i	0.952849	+	0.303444i	$0.0981366\pi$
$811$			17.2830i			0.606889i	−0.952849	+	0.303444i	$0.901863\pi$
$812$		0			0
$813$	−14.7014	−	14.7014i	−0.515601	−	0.515601i
$814$		0			0
$815$	18.6087	+	4.18602i	0.651835	+	0.146630i
$816$		0			0
$817$	41.1696	−	41.1696i	1.44034	−	1.44034i
$818$		0			0
$819$	−0.650990			−0.0227474
$820$		0			0
$821$	19.4223			0.677844			0.338922	−	0.940814i	$-0.389938\pi$
$821$	19.4223			0.677844			0.338922	+	0.940814i	$0.389938\pi$
$822$		0			0
$823$	27.6292	−	27.6292i	0.963093	−	0.963093i	−0.0362495	−	0.999343i	$-0.511541\pi$
$823$	27.6292	−	27.6292i	0.963093	−	0.963093i	0.999343	+	0.0362495i	$0.0115411\pi$
$824$		0			0
$825$	5.13022	−	1.83131i	0.178611	−	0.0637579i
$826$		0			0
$827$	35.1150	+	35.1150i	1.22107	+	1.22107i	0.967253	+	0.253815i	$0.0816854\pi$
$827$	35.1150	+	35.1150i	1.22107	+	1.22107i	0.253815	+	0.967253i	$0.418315\pi$
$828$		0			0
$829$			12.6190i			0.438275i	0.975694	+	0.219137i	$0.0703243\pi$
$829$			12.6190i			0.438275i	−0.975694	+	0.219137i	$0.929676\pi$
$830$		0			0
$831$		−	21.2590i		−	0.737466i
$832$		0			0
$833$	4.94613	+	4.94613i	0.171373	+	0.171373i
$834$		0			0
$835$	−11.5639	+	51.4069i	−0.400187	+	1.77901i
$836$		0			0
$837$	−9.35434	+	9.35434i	−0.323333	+	0.323333i
$838$		0			0
$839$	−1.11833			−0.0386090			−0.0193045	−	0.999814i	$-0.506145\pi$
$839$	−1.11833			−0.0386090			−0.0193045	+	0.999814i	$0.506145\pi$
$840$		0			0
$841$	−19.4631			−0.671140
$842$		0			0
$843$	4.22248	−	4.22248i	0.145430	−	0.145430i
$844$		0			0
$845$	2.80588	−	1.77534i	0.0965252	−	0.0610735i
$846$		0			0
$847$	−0.458052	−	0.458052i	−0.0157389	−	0.0157389i
$848$		0			0
$849$		−	7.54756i		−	0.259032i
$850$		0			0
$851$		−	3.03708i		−	0.104110i
$852$		0			0
$853$	16.8257	+	16.8257i	0.576100	+	0.576100i	0.933826	−	0.357726i	$-0.116448\pi$
$853$	16.8257	+	16.8257i	0.576100	+	0.576100i	−0.357726	+	0.933826i	$0.616448\pi$
$854$		0			0
$855$	36.2211	−	22.9178i	1.23873	−	0.783773i
$856$		0			0
$857$	5.66521	−	5.66521i	0.193520	−	0.193520i	−0.603695	−	0.797215i	$-0.706306\pi$
$857$	5.66521	−	5.66521i	0.193520	−	0.193520i	0.797215	+	0.603695i	$0.206306\pi$
$858$		0			0
$859$	48.2158			1.64510			0.822550	−	0.568693i	$-0.192551\pi$
$859$	48.2158			1.64510			0.822550	+	0.568693i	$0.192551\pi$
$860$		0			0
$861$	−0.178919			−0.00609755
$862$		0			0
$863$	−3.50464	+	3.50464i	−0.119299	+	0.119299i	−0.764236	−	0.644937i	$-0.776884\pi$
$863$	−3.50464	+	3.50464i	−0.119299	+	0.119299i	0.644937	+	0.764236i	$0.276884\pi$
$864$		0			0
$865$	−0.947319	+	4.21126i	−0.0322098	+	0.143187i
$866$		0			0
$867$	0.552078	+	0.552078i	0.0187495	+	0.0187495i
$868$		0			0
$869$			0.236013i			0.00800620i
$870$		0			0
$871$			11.7314i			0.397502i
$872$		0			0
$873$	6.98162	+	6.98162i	0.236292	+	0.236292i
$874$		0			0
$875$	−0.630137	−	0.492899i	−0.0213025	−	0.0166630i
$876$		0			0
$877$	−27.5813	+	27.5813i	−0.931353	+	0.931353i	−0.997791	−	0.0664376i	$-0.978837\pi$
$877$	−27.5813	+	27.5813i	−0.931353	+	0.931353i	0.0664376	+	0.997791i	$0.478837\pi$
$878$		0			0
$879$	4.84930			0.163563
$880$		0			0
$881$	21.2061			0.714452			0.357226	−	0.934018i	$-0.383723\pi$
$881$	21.2061			0.714452			0.357226	+	0.934018i	$0.383723\pi$
$882$		0			0
$883$	−37.5979	+	37.5979i	−1.26527	+	1.26527i	−0.316766	+	0.948504i	$0.602597\pi$
$883$	−37.5979	+	37.5979i	−1.26527	+	1.26527i	−0.948504	+	0.316766i	$0.897403\pi$
$884$		0			0
$885$	11.3351	+	2.54982i	0.381025	+	0.0857114i
$886$		0			0
$887$	−17.2112	−	17.2112i	−0.577896	−	0.577896i	0.356427	−	0.934323i	$-0.383995\pi$
$887$	−17.2112	−	17.2112i	−0.577896	−	0.577896i	−0.934323	+	0.356427i	$0.883995\pi$
$888$		0			0
$889$		−	1.33980i		−	0.0449355i
$890$		0			0
$891$		−	5.42158i		−	0.181630i
$892$		0			0
$893$	−33.6207	−	33.6207i	−1.12507	−	1.12507i
$894$		0			0
$895$	24.3756	+	38.5250i	0.814785	+	1.28775i
$896$		0			0
$897$	3.32731	−	3.32731i	0.111096	−	0.111096i
$898$		0			0
$899$	−21.8824			−0.729820
$900$		0			0
$901$	5.36273			0.178659
$902$		0			0
$903$	0.286825	−	0.286825i	0.00954493	−	0.00954493i
$904$		0			0
$905$	−20.0675	−	31.7163i	−0.667067	−	1.05428i
$906$		0			0
$907$	−14.2977	−	14.2977i	−0.474746	−	0.474746i	0.428701	−	0.903447i	$-0.358971\pi$
$907$	−14.2977	−	14.2977i	−0.474746	−	0.474746i	−0.903447	+	0.428701i	$0.858971\pi$
$908$		0			0
$909$			1.03850i			0.0344450i
$910$		0			0
$911$		−	29.1425i		−	0.965533i	−0.875749	−	0.482766i	$-0.839632\pi$
$911$		−	29.1425i		−	0.965533i	0.875749	−	0.482766i	$-0.160368\pi$
$912$		0			0
$913$	17.3689	+	17.3689i	0.574827	+	0.574827i
$914$		0			0
$915$	−8.29522	−	1.86600i	−0.274232	−	0.0616882i
$916$		0			0
$917$	0.896500	−	0.896500i	0.0296050	−	0.0296050i
$918$		0			0
$919$	8.14767			0.268767			0.134383	−	0.990929i	$-0.457095\pi$
$919$	8.14767			0.268767			0.134383	+	0.990929i	$0.457095\pi$
$920$		0			0
$921$	−12.7170			−0.419040
$922$		0			0
$923$	−7.57870	+	7.57870i	−0.249456	+	0.249456i
$924$		0			0
$925$	3.22383	+	9.03124i	0.105999	+	0.296945i
$926$		0			0
$927$	7.33248	+	7.33248i	0.240830	+	0.240830i
$928$		0			0
$929$			4.50057i			0.147659i	0.997271	+	0.0738295i	$0.0235220\pi$
$929$			4.50057i			0.147659i	−0.997271	+	0.0738295i	$0.976478\pi$
$930$		0			0
$931$		−	56.0917i		−	1.83833i
$932$		0			0
$933$	−8.02929	−	8.02929i	−0.262867	−	0.262867i
$934$		0			0
$935$	−0.684770	+	3.04411i	−0.0223944	+	0.0995529i
$936$		0			0
$937$	27.7000	−	27.7000i	0.904919	−	0.904919i	−0.0909374	−	0.995857i	$-0.528986\pi$
$937$	27.7000	−	27.7000i	0.904919	−	0.904919i	0.995857	+	0.0909374i	$0.0289863\pi$
$938$		0			0
$939$	−12.0981			−0.394806
$940$		0			0
$941$	−58.9292			−1.92104			−0.960519	−	0.278216i	$-0.910257\pi$
$941$	−58.9292			−1.92104			−0.960519	+	0.278216i	$0.910257\pi$
$942$		0			0
$943$	−3.58607	+	3.58607i	−0.116779	+	0.116779i
$944$		0			0
$945$	0.569049	−	0.360049i	0.0185112	−	0.0117124i
$946$		0			0
$947$	−18.5943	−	18.5943i	−0.604234	−	0.604234i	0.337199	−	0.941433i	$-0.390520\pi$
$947$	−18.5943	−	18.5943i	−0.604234	−	0.604234i	−0.941433	+	0.337199i	$0.890520\pi$
$948$		0			0
$949$			17.6551i			0.573108i
$950$		0			0
$951$			12.1428i			0.393757i
$952$		0			0
$953$	14.5640	+	14.5640i	0.471773	+	0.471773i	0.902488	−	0.430715i	$-0.141739\pi$
$953$	14.5640	+	14.5640i	0.471773	+	0.471773i	−0.430715	+	0.902488i	$0.641739\pi$
$954$		0			0
$955$	31.8392	−	20.1453i	1.03029	−	0.651887i
$956$		0			0
$957$	−5.36290	+	5.36290i	−0.173358	+	0.173358i
$958$		0			0
$959$	−0.168795			−0.00545068
$960$		0			0
$961$	21.1195			0.681273
$962$		0			0
$963$	9.58807	−	9.58807i	0.308971	−	0.308971i
$964$		0			0
$965$	−13.3983	+	59.5614i	−0.431306	+	1.91735i
$966$		0			0
$967$	−23.0548	−	23.0548i	−0.741393	−	0.741393i	0.231453	−	0.972846i	$-0.425652\pi$
$967$	−23.0548	−	23.0548i	−0.741393	−	0.741393i	−0.972846	+	0.231453i	$0.925652\pi$
$968$		0			0
$969$		−	6.26085i		−	0.201128i
$970$		0			0
$971$			6.97371i			0.223797i	0.993720	+	0.111898i	$0.0356931\pi$
$971$			6.97371i			0.223797i	−0.993720	+	0.111898i	$0.964307\pi$
$972$		0			0
$973$	−0.837690	−	0.837690i	−0.0268551	−	0.0268551i
$974$		0			0
$975$	−6.36238	+	13.4262i	−0.203759	+	0.429983i
$976$		0			0
$977$	36.0919	−	36.0919i	1.15468	−	1.15468i	0.169081	−	0.985602i	$-0.445920\pi$
$977$	36.0919	−	36.0919i	1.15468	−	1.15468i	0.985602	−	0.169081i	$-0.0540798\pi$
$978$		0			0
$979$	−1.06988			−0.0341935
$980$		0			0
$981$	24.2609			0.774592
$982$		0			0
$983$	−8.59164	+	8.59164i	−0.274031	+	0.274031i	−0.830721	−	0.556690i	$-0.812071\pi$
$983$	−8.59164	+	8.59164i	−0.274031	+	0.274031i	0.556690	+	0.830721i	$0.312071\pi$
$984$		0			0
$985$	23.1665	+	5.21128i	0.738145	+	0.166045i
$986$		0			0
$987$	−0.234232	−	0.234232i	−0.00745568	−	0.00745568i
$988$		0			0
$989$		−	11.4976i		−	0.365604i
$990$		0			0
$991$		−	17.5035i		−	0.556016i	−0.960579	−	0.278008i	$-0.910326\pi$
$991$		−	17.5035i		−	0.556016i	0.960579	−	0.278008i	$-0.0896742\pi$
$992$		0			0
$993$	−14.6886	−	14.6886i	−0.466128	−	0.466128i
$994$		0			0
$995$	−14.6646	−	23.1770i	−0.464898	−	0.734761i
$996$		0			0
$997$	23.2041	−	23.2041i	0.734881	−	0.734881i	−0.236702	−	0.971582i	$-0.576066\pi$
$997$	23.2041	−	23.2041i	0.734881	−	0.734881i	0.971582	+	0.236702i	$0.0760664\pi$
$998$		0			0
$999$	−8.07158			−0.255374

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1360.2.bn.b.783.13	✓	64
4.3	odd	2	inner	1360.2.bn.b.783.20	yes	64
5.2	odd	4	inner	1360.2.bn.b.1327.20	yes	64
20.7	even	4	inner	1360.2.bn.b.1327.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1360.2.bn.b.783.13	✓	64	1.1	even	1	trivial
1360.2.bn.b.783.20	yes	64	4.3	odd	2	inner
1360.2.bn.b.1327.13	yes	64	20.7	even	4	inner
1360.2.bn.b.1327.20	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(-0.552078 + 0.552078i) q^{3} +(-1.19559 - 1.88960i) q^{5} +(-0.0505973 - 0.0505973i) q^{7} +2.39042i q^{9} +1.39538i q^{11} +(-2.69118 - 2.69118i) q^{13} +(1.70326 + 0.383147i) q^{15} +(-0.707107 + 0.707107i) q^{17} +8.01896 q^{19} +0.0558673 q^{21} +(1.11975 - 1.11975i) q^{23} +(-2.14115 + 4.51835i) q^{25} +(-2.97593 - 2.97593i) q^{27} -6.96154i q^{29} -3.14333i q^{31} +(-0.770361 - 0.770361i) q^{33} +(-0.0351150 + 0.156102i) q^{35} +(1.35614 - 1.35614i) q^{37} +2.97148 q^{39} -3.20257 q^{41} +(5.13403 - 5.13403i) q^{43} +(4.51693 - 2.85795i) q^{45} +(-4.19264 - 4.19264i) q^{47} -6.99488i q^{49} -0.780756i q^{51} +(-3.79203 - 3.79203i) q^{53} +(2.63671 - 1.66830i) q^{55} +(-4.42709 + 4.42709i) q^{57} +6.65494 q^{59} -4.87020 q^{61} +(0.120949 - 0.120949i) q^{63} +(-1.86771 + 8.30278i) q^{65} +(-2.17959 - 2.17959i) q^{67} +1.23637i q^{69} -2.81612i q^{71} +(-3.28017 - 3.28017i) q^{73} +(-1.31240 - 3.67656i) q^{75} +(0.0706027 - 0.0706027i) q^{77} +0.169138 q^{79} -3.88537 q^{81} +(12.4474 - 12.4474i) q^{83} +(2.18155 + 0.490739i) q^{85} +(3.84331 + 3.84331i) q^{87} +0.766728i q^{89} +0.272333i q^{91} +(1.73536 + 1.73536i) q^{93} +(-9.58736 - 15.1526i) q^{95} +(2.92067 - 2.92067i) q^{97} -3.33556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{13} + 64 q^{21} + 24 q^{25} - 56 q^{33} - 32 q^{41} - 24 q^{45} + 64 q^{53} + 64 q^{57} - 16 q^{61} + 40 q^{65} + 56 q^{73} - 40 q^{77} - 176 q^{81} - 104 q^{93} - 16 q^{97}+O(q^{100}) \) 64 * q - 8 * q^13 + 64 * q^21 + 24 * q^25 - 56 * q^33 - 32 * q^41 - 24 * q^45 + 64 * q^53 + 64 * q^57 - 16 * q^61 + 40 * q^65 + 56 * q^73 - 40 * q^77 - 176 * q^81 - 104 * q^93 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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