LMFDB - Embedded newform 1380.2.t.a.1057.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1380,2,Mod(1057,1380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1380.1057");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1380.t (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.0193554789$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1057.18
Character	$\chi$	$=$	1380.1057
Dual form			1380.2.t.a.1333.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{3} +(1.86909 + 1.22740i) q^{5} +(-0.329148 + 0.329148i) q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{3} +(1.86909 + 1.22740i) q^{5} +(-0.329148 + 0.329148i) q^{7} -1.00000i q^{9} +2.84474i q^{11} +(-3.80782 + 3.80782i) q^{13} +(2.18955 - 0.453738i) q^{15} +(3.63814 - 3.63814i) q^{17} +3.13095 q^{19} +0.465486i q^{21} +(-0.0646993 + 4.79540i) q^{23} +(1.98696 + 4.58824i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.87883i q^{29} +4.47842 q^{31} +(2.01154 + 2.01154i) q^{33} +(-1.01920 + 0.211209i) q^{35} +(-2.51831 + 2.51831i) q^{37} +5.38507i q^{39} +1.80071 q^{41} +(-1.58312 - 1.58312i) q^{43} +(1.22740 - 1.86909i) q^{45} +(1.81938 + 1.81938i) q^{47} +6.78332i q^{49} -5.14511i q^{51} +(3.43611 + 3.43611i) q^{53} +(-3.49165 + 5.31707i) q^{55} +(2.21392 - 2.21392i) q^{57} -13.1712i q^{59} -1.84893i q^{61} +(0.329148 + 0.329148i) q^{63} +(-11.7909 + 2.44341i) q^{65} +(10.9475 - 10.9475i) q^{67} +(3.34511 + 3.43661i) q^{69} -11.9375 q^{71} +(-6.01737 + 6.01737i) q^{73} +(4.64937 + 1.83938i) q^{75} +(-0.936342 - 0.936342i) q^{77} +16.4583 q^{79} -1.00000 q^{81} +(-5.51052 - 5.51052i) q^{83} +(11.2655 - 2.33453i) q^{85} +(2.03564 + 2.03564i) q^{87} +2.89968 q^{89} -2.50667i q^{91} +(3.16672 - 3.16672i) q^{93} +(5.85201 + 3.84294i) q^{95} +(-7.16316 + 7.16316i) q^{97} +2.84474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) $ 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1380\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$691$	$1201$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$	$-1$

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
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$		0			0
$5$	1.86909	+	1.22740i	0.835881	+	0.548911i
$5$	1.86909	+	1.22740i	0.835881	+	0.548911i
$6$		0			0
$7$	−0.329148	+	0.329148i	−0.124406	+	0.124406i	−0.766569	−	0.642162i	$-0.778037\pi$
$7$	−0.329148	+	0.329148i	−0.124406	+	0.124406i	0.642162	+	0.766569i	$0.278037\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$			2.84474i			0.857723i	0.903370	+	0.428861i	$0.141085\pi$
$11$			2.84474i			0.857723i	−0.903370	+	0.428861i	$0.858915\pi$
$12$		0			0
$13$	−3.80782	+	3.80782i	−1.05610	+	1.05610i	−0.0577699	+	0.998330i	$0.518399\pi$
$13$	−3.80782	+	3.80782i	−1.05610	+	1.05610i	−0.998330	+	0.0577699i	$0.981601\pi$
$14$		0			0
$15$	2.18955	−	0.453738i	0.565339	−	0.117155i
$16$		0			0
$17$	3.63814	−	3.63814i	0.882379	−	0.882379i	−0.111397	−	0.993776i	$-0.535533\pi$
$17$	3.63814	−	3.63814i	0.882379	−	0.882379i	0.993776	+	0.111397i	$0.0355326\pi$
$18$		0			0
$19$	3.13095			0.718289			0.359145	−	0.933282i	$-0.383069\pi$
$19$	3.13095			0.718289			0.359145	+	0.933282i	$0.383069\pi$
$20$		0			0
$21$			0.465486i			0.101577i
$22$		0			0
$23$	−0.0646993	+	4.79540i	−0.0134907	+	0.999909i
$23$	−0.0646993	+	4.79540i	−0.0134907	+	0.999909i
$24$		0			0
$25$	1.98696	+	4.58824i	0.397393	+	0.917649i
$26$		0			0
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			2.87883i			0.534585i	0.963615	+	0.267293i	$0.0861290\pi$
$29$			2.87883i			0.534585i	−0.963615	+	0.267293i	$0.913871\pi$
$30$		0			0
$31$	4.47842			0.804348			0.402174	−	0.915563i	$-0.368255\pi$
$31$	4.47842			0.804348			0.402174	+	0.915563i	$0.368255\pi$
$32$		0			0
$33$	2.01154	+	2.01154i	0.350164	+	0.350164i
$34$		0			0
$35$	−1.01920	+	0.211209i	−0.172277	+	0.0357008i
$36$		0			0
$37$	−2.51831	+	2.51831i	−0.414008	+	0.414008i	−0.883132	−	0.469124i	$-0.844570\pi$
$37$	−2.51831	+	2.51831i	−0.414008	+	0.414008i	0.469124	+	0.883132i	$0.344570\pi$
$38$		0			0
$39$			5.38507i			0.862302i
$40$		0			0
$41$	1.80071			0.281224			0.140612	−	0.990065i	$-0.455093\pi$
$41$	1.80071			0.281224			0.140612	+	0.990065i	$0.455093\pi$
$42$		0			0
$43$	−1.58312	−	1.58312i	−0.241423	−	0.241423i	0.576016	−	0.817439i	$-0.304607\pi$
$43$	−1.58312	−	1.58312i	−0.241423	−	0.241423i	−0.817439	+	0.576016i	$0.804607\pi$
$44$		0			0
$45$	1.22740	−	1.86909i	0.182970	−	0.278627i
$46$		0			0
$47$	1.81938	+	1.81938i	0.265384	+	0.265384i	0.827237	−	0.561853i	$-0.189911\pi$
$47$	1.81938	+	1.81938i	0.265384	+	0.265384i	−0.561853	+	0.827237i	$0.689911\pi$
$48$		0			0
$49$			6.78332i			0.969046i
$50$		0			0
$51$		−	5.14511i		−	0.720459i
$52$		0			0
$53$	3.43611	+	3.43611i	0.471986	+	0.471986i	0.902557	−	0.430570i	$-0.141688\pi$
$53$	3.43611	+	3.43611i	0.471986	+	0.471986i	−0.430570	+	0.902557i	$0.641688\pi$
$54$		0			0
$55$	−3.49165	+	5.31707i	−0.470814	+	0.716954i
$56$		0			0
$57$	2.21392	−	2.21392i	0.293240	−	0.293240i
$58$		0			0
$59$		−	13.1712i		−	1.71475i	−0.514695	−	0.857373i	$-0.672095\pi$
$59$		−	13.1712i		−	1.71475i	0.514695	−	0.857373i	$-0.327905\pi$
$60$		0			0
$61$		−	1.84893i		−	0.236731i	−0.992970	−	0.118365i	$-0.962235\pi$
$61$		−	1.84893i		−	0.236731i	0.992970	−	0.118365i	$-0.0377654\pi$
$62$		0			0
$63$	0.329148	+	0.329148i	0.0414688	+	0.0414688i
$64$		0			0
$65$	−11.7909	+	2.44341i	−1.46248	+	0.303068i
$66$		0			0
$67$	10.9475	−	10.9475i	1.33745	−	1.33745i	0.438919	−	0.898527i	$-0.355362\pi$
$67$	10.9475	−	10.9475i	1.33745	−	1.33745i	0.898527	−	0.438919i	$-0.144638\pi$
$68$		0			0
$69$	3.34511	+	3.43661i	0.402704	+	0.413719i
$70$		0			0
$71$	−11.9375			−1.41672			−0.708359	−	0.705852i	$-0.750564\pi$
$71$	−11.9375			−1.41672			−0.708359	+	0.705852i	$0.750564\pi$
$72$		0			0
$73$	−6.01737	+	6.01737i	−0.704280	+	0.704280i	−0.965326	−	0.261047i	$-0.915932\pi$
$73$	−6.01737	+	6.01737i	−0.704280	+	0.704280i	0.261047	+	0.965326i	$0.415932\pi$
$74$		0			0
$75$	4.64937	+	1.83938i	0.536863	+	0.212394i
$76$		0			0
$77$	−0.936342	−	0.936342i	−0.106706	−	0.106706i
$78$		0			0
$79$	16.4583			1.85170			0.925852	−	0.377887i	$-0.123349\pi$
$79$	16.4583			1.85170			0.925852	+	0.377887i	$0.123349\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−5.51052	−	5.51052i	−0.604858	−	0.604858i	0.336740	−	0.941598i	$-0.390676\pi$
$83$	−5.51052	−	5.51052i	−0.604858	−	0.604858i	−0.941598	+	0.336740i	$0.890676\pi$
$84$		0			0
$85$	11.2655	−	2.33453i	1.22191	−	0.253215i
$86$		0			0
$87$	2.03564	+	2.03564i	0.218243	+	0.218243i
$88$		0			0
$89$	2.89968			0.307366			0.153683	−	0.988120i	$-0.450887\pi$
$89$	2.89968			0.307366			0.153683	+	0.988120i	$0.450887\pi$
$90$		0			0
$91$		−	2.50667i		−	0.262771i
$92$		0			0
$93$	3.16672	−	3.16672i	0.328374	−	0.328374i
$94$		0			0
$95$	5.85201	+	3.84294i	0.600404	+	0.394277i
$96$		0			0
$97$	−7.16316	+	7.16316i	−0.727309	+	0.727309i	−0.970083	−	0.242774i	$-0.921943\pi$
$97$	−7.16316	+	7.16316i	−0.727309	+	0.727309i	0.242774	+	0.970083i	$0.421943\pi$
$98$		0			0
$99$	2.84474			0.285908
$100$		0			0
$101$	−17.8790			−1.77903			−0.889513	−	0.456911i	$-0.848956\pi$
$101$	−17.8790			−1.77903			−0.889513	+	0.456911i	$0.848956\pi$
$102$		0			0
$103$	−8.23939	−	8.23939i	−0.811851	−	0.811851i	0.173060	−	0.984911i	$-0.444635\pi$
$103$	−8.23939	−	8.23939i	−0.811851	−	0.811851i	−0.984911	+	0.173060i	$0.944635\pi$
$104$		0			0
$105$	−0.571339	+	0.870033i	−0.0557569	+	0.0849065i
$106$		0			0
$107$	−6.28144	+	6.28144i	−0.607250	+	0.607250i	−0.942226	−	0.334976i	$-0.891272\pi$
$107$	−6.28144	+	6.28144i	−0.607250	+	0.607250i	0.334976	+	0.942226i	$0.391272\pi$
$108$		0			0
$109$	17.4238			1.66890			0.834448	−	0.551087i	$-0.185787\pi$
$109$	17.4238			1.66890			0.834448	+	0.551087i	$0.185787\pi$
$110$		0			0
$111$			3.56143i			0.338036i
$112$		0			0
$113$	10.3193	+	10.3193i	0.970761	+	0.970761i	0.999585	−	0.0288239i	$-0.00917621\pi$
$113$	10.3193	+	10.3193i	0.970761	+	0.970761i	−0.0288239	+	0.999585i	$0.509176\pi$
$114$		0			0
$115$	−6.00681	+	8.88359i	−0.560138	+	0.828399i
$116$		0			0
$117$	3.80782	+	3.80782i	0.352033	+	0.352033i
$118$		0			0
$119$			2.39497i			0.219547i
$120$		0			0
$121$	2.90743			0.264312
$122$		0			0
$123$	1.27330	−	1.27330i	0.114809	−	0.114809i
$124$		0			0
$125$	−1.91782	+	11.0146i	−0.171535	+	0.985178i
$126$		0			0
$127$	−0.0859341	−	0.0859341i	−0.00762542	−	0.00762542i	0.703284	−	0.710909i	$-0.251716\pi$
$127$	−0.0859341	−	0.0859341i	−0.00762542	−	0.00762542i	−0.710909	+	0.703284i	$0.751716\pi$
$128$		0			0
$129$	−2.23886			−0.197121
$130$		0			0
$131$	20.2035			1.76519			0.882595	−	0.470134i	$-0.155794\pi$
$131$	20.2035			1.76519			0.882595	+	0.470134i	$0.155794\pi$
$132$		0			0
$133$	−1.03055	+	1.03055i	−0.0893597	+	0.0893597i
$134$		0			0
$135$	−0.453738	−	2.18955i	−0.0390516	−	0.188446i
$136$		0			0
$137$	3.00234	−	3.00234i	0.256507	−	0.256507i	−0.567125	−	0.823632i	$-0.691944\pi$
$137$	3.00234	−	3.00234i	0.256507	−	0.256507i	0.823632	+	0.567125i	$0.191944\pi$
$138$		0			0
$139$		−	16.4941i		−	1.39901i	−0.714625	−	0.699507i	$-0.753403\pi$
$139$		−	16.4941i		−	1.39901i	0.714625	−	0.699507i	$-0.246597\pi$
$140$		0			0
$141$	2.57299			0.216685
$142$		0			0
$143$	−10.8323	−	10.8323i	−0.905841	−	0.905841i
$144$		0			0
$145$	−3.53348	+	5.38078i	−0.293440	+	0.446849i
$146$		0			0
$147$	4.79653	+	4.79653i	0.395611	+	0.395611i
$148$		0			0
$149$	−14.6623			−1.20118			−0.600591	−	0.799556i	$-0.705068\pi$
$149$	−14.6623			−1.20118			−0.600591	+	0.799556i	$0.705068\pi$
$150$		0			0
$151$	1.98463			0.161507			0.0807534	−	0.996734i	$-0.474267\pi$
$151$	1.98463			0.161507			0.0807534	+	0.996734i	$0.474267\pi$
$152$		0			0
$153$	−3.63814	−	3.63814i	−0.294126	−	0.294126i
$154$		0			0
$155$	8.37055	+	5.49683i	0.672339	+	0.441516i
$156$		0			0
$157$	15.3801	−	15.3801i	1.22747	−	1.22747i	0.262546	−	0.964919i	$-0.415438\pi$
$157$	15.3801	−	15.3801i	1.22747	−	1.22747i	0.964919	−	0.262546i	$-0.0845623\pi$
$158$		0			0
$159$	4.85940			0.385375
$160$		0			0
$161$	−1.55710	−	1.59969i	−0.122717	−	0.126073i
$162$		0			0
$163$	3.87670	−	3.87670i	0.303646	−	0.303646i	−0.538792	−	0.842439i	$-0.681119\pi$
$163$	3.87670	−	3.87670i	0.303646	−	0.303646i	0.842439	+	0.538792i	$0.181119\pi$
$164$		0			0
$165$	1.29077	+	6.22871i	0.100486	+	0.484904i
$166$		0			0
$167$	−5.00124	−	5.00124i	−0.387008	−	0.387008i	0.486611	−	0.873619i	$-0.338233\pi$
$167$	−5.00124	−	5.00124i	−0.387008	−	0.387008i	−0.873619	+	0.486611i	$0.838233\pi$
$168$		0			0
$169$		−	15.9990i		−	1.23069i
$170$		0			0
$171$		−	3.13095i		−	0.239430i
$172$		0			0
$173$	−2.68479	+	2.68479i	−0.204121	+	0.204121i	−0.801763	−	0.597642i	$-0.796104\pi$
$173$	−2.68479	+	2.68479i	−0.204121	+	0.204121i	0.597642	+	0.801763i	$0.296104\pi$
$174$		0			0
$175$	−2.16422	−	0.856207i	−0.163599	−	0.0647231i
$176$		0			0
$177$	−9.31346	−	9.31346i	−0.700042	−	0.700042i
$178$		0			0
$179$		−	16.4219i		−	1.22743i	−0.789526	−	0.613717i	$-0.789674\pi$
$179$		−	16.4219i		−	1.22743i	0.789526	−	0.613717i	$-0.210326\pi$
$180$		0			0
$181$			13.7603i			1.02279i	0.859345	+	0.511397i	$0.170872\pi$
$181$			13.7603i			1.02279i	−0.859345	+	0.511397i	$0.829128\pi$
$182$		0			0
$183$	−1.30739	−	1.30739i	−0.0966449	−	0.0966449i
$184$		0			0
$185$	−7.79793	+	1.61596i	−0.573315	+	0.118808i
$186$		0			0
$187$	10.3496	+	10.3496i	0.756836	+	0.756836i
$188$		0			0
$189$	0.465486			0.0338591
$190$		0			0
$191$		−	1.45967i		−	0.105618i	−0.998605	−	0.0528089i	$-0.983183\pi$
$191$		−	1.45967i		−	0.105618i	0.998605	−	0.0528089i	$-0.0168174\pi$
$192$		0			0
$193$	16.3178	−	16.3178i	1.17458	−	1.17458i	0.193476	−	0.981105i	$-0.438024\pi$
$193$	16.3178	−	16.3178i	1.17458	−	1.17458i	0.981105	−	0.193476i	$-0.0619762\pi$
$194$		0			0
$195$	−6.60966	+	10.0652i	−0.473327	+	0.720781i
$196$		0			0
$197$	−15.5863	−	15.5863i	−1.11048	−	1.11048i	−0.993086	−	0.117390i	$-0.962547\pi$
$197$	−15.5863	−	15.5863i	−1.11048	−	1.11048i	−0.117390	−	0.993086i	$-0.537453\pi$
$198$		0			0
$199$	2.69626			0.191133			0.0955663	−	0.995423i	$-0.469534\pi$
$199$	2.69626			0.191133			0.0955663	+	0.995423i	$0.469534\pi$
$200$		0			0
$201$		−	15.4821i		−	1.09202i
$202$		0			0
$203$	−0.947561	−	0.947561i	−0.0665058	−	0.0665058i
$204$		0			0
$205$	3.36569	+	2.21020i	0.235070	+	0.154367i
$206$		0			0
$207$	4.79540	+	0.0646993i	0.333303	+	0.00449691i
$208$		0			0
$209$			8.90675i			0.616093i
$210$		0			0
$211$	−2.39972			−0.165203			−0.0826017	−	0.996583i	$-0.526323\pi$
$211$	−2.39972			−0.165203			−0.0826017	+	0.996583i	$0.526323\pi$
$212$		0			0
$213$	−8.44108	+	8.44108i	−0.578373	+	0.578373i
$214$		0			0
$215$	−1.01586	−	4.90210i	−0.0692810	−	0.334321i
$216$		0			0
$217$	−1.47406	+	1.47406i	−0.100066	+	0.100066i
$218$		0			0
$219$			8.50984i			0.575042i
$220$		0			0
$221$			27.7068i			1.86376i
$222$		0			0
$223$	−20.5306	+	20.5306i	−1.37483	+	1.37483i	−0.521704	+	0.853127i	$0.674703\pi$
$223$	−20.5306	+	20.5306i	−1.37483	+	1.37483i	−0.853127	+	0.521704i	$0.825297\pi$
$224$		0			0
$225$	4.58824	−	1.98696i	0.305883	−	0.132464i
$226$		0			0
$227$	−13.9134	+	13.9134i	−0.923462	+	0.923462i	−0.997272	−	0.0738102i	$-0.976484\pi$
$227$	−13.9134	+	13.9134i	−0.923462	+	0.923462i	0.0738102	+	0.997272i	$0.476484\pi$
$228$		0			0
$229$	−3.49517			−0.230967			−0.115484	−	0.993309i	$-0.536842\pi$
$229$	−3.49517			−0.230967			−0.115484	+	0.993309i	$0.536842\pi$
$230$		0			0
$231$	−1.32419			−0.0871252
$232$		0			0
$233$	−15.7280	+	15.7280i	−1.03038	+	1.03038i	−0.0308524	+	0.999524i	$0.509822\pi$
$233$	−15.7280	+	15.7280i	−1.03038	+	1.03038i	−0.999524	+	0.0308524i	$0.990178\pi$
$234$		0			0
$235$	1.16746	+	5.63369i	0.0761570	+	0.367501i
$236$		0			0
$237$	11.6378	−	11.6378i	0.755955	−	0.755955i
$238$		0			0
$239$		−	0.592668i		−	0.0383365i	−0.999816	−	0.0191683i	$-0.993898\pi$
$239$		−	0.592668i		−	0.0383365i	0.999816	−	0.0191683i	$-0.00610182\pi$
$240$		0			0
$241$		−	1.77380i		−	0.114261i	−0.998367	−	0.0571304i	$-0.981805\pi$
$241$		−	1.77380i		−	0.114261i	0.998367	−	0.0571304i	$-0.0181951\pi$
$242$		0			0
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$		0			0
$245$	−8.32587	+	12.6786i	−0.531920	+	0.810007i
$246$		0			0
$247$	−11.9221	+	11.9221i	−0.758585	+	0.758585i
$248$		0			0
$249$	−7.79305			−0.493864
$250$		0			0
$251$		−	15.1243i		−	0.954639i	−0.878730	−	0.477320i	$-0.841608\pi$
$251$		−	15.1243i		−	0.954639i	0.878730	−	0.477320i	$-0.158392\pi$
$252$		0			0
$253$	−13.6417	−	0.184053i	−0.857645	−	0.0115713i
$254$		0			0
$255$	6.31512	−	9.61665i	0.395468	−	0.602218i
$256$		0			0
$257$	−15.9357	−	15.9357i	−0.994040	−	0.994040i	0.00594195	−	0.999982i	$-0.498109\pi$
$257$	−15.9357	−	15.9357i	−0.994040	−	0.994040i	−0.999982	+	0.00594195i	$0.998109\pi$
$258$		0			0
$259$		−	1.65780i		−	0.103010i
$260$		0			0
$261$	2.87883			0.178195
$262$		0			0
$263$	−14.1295	−	14.1295i	−0.871264	−	0.871264i	0.121346	−	0.992610i	$-0.461279\pi$
$263$	−14.1295	−	14.1295i	−0.871264	−	0.871264i	−0.992610	+	0.121346i	$0.961279\pi$
$264$		0			0
$265$	2.20489	+	10.6399i	0.135446	+	0.653603i
$266$		0			0
$267$	2.05038	−	2.05038i	0.125482	−	0.125482i
$268$		0			0
$269$		−	7.51057i		−	0.457927i	−0.973435	−	0.228964i	$-0.926466\pi$
$269$		−	7.51057i		−	0.457927i	0.973435	−	0.228964i	$-0.0735337\pi$
$270$		0			0
$271$	20.0922			1.22051			0.610256	−	0.792204i	$-0.291066\pi$
$271$	20.0922			1.22051			0.610256	+	0.792204i	$0.291066\pi$
$272$		0			0
$273$	−1.77249	−	1.77249i	−0.107276	−	0.107276i
$274$		0			0
$275$	−13.0524	+	5.65240i	−0.787088	+	0.340853i
$276$		0			0
$277$	−0.397718	−	0.397718i	−0.0238966	−	0.0238966i	0.695058	−	0.718954i	$-0.255379\pi$
$277$	−0.397718	−	0.397718i	−0.0238966	−	0.0238966i	−0.718954	+	0.695058i	$0.755379\pi$
$278$		0			0
$279$		−	4.47842i		−	0.268116i
$280$		0			0
$281$		−	2.45255i		−	0.146307i	−0.997321	−	0.0731534i	$-0.976694\pi$
$281$		−	2.45255i		−	0.146307i	0.997321	−	0.0731534i	$-0.0233063\pi$
$282$		0			0
$283$	−7.70214	−	7.70214i	−0.457845	−	0.457845i	0.440103	−	0.897948i	$-0.354942\pi$
$283$	−7.70214	−	7.70214i	−0.457845	−	0.457845i	−0.897948	+	0.440103i	$0.854942\pi$
$284$		0			0
$285$	6.85536	−	1.42063i	0.406077	−	0.0841509i
$286$		0			0
$287$	−0.592702	+	0.592702i	−0.0349861	+	0.0349861i
$288$		0			0
$289$		−	9.47213i		−	0.557184i
$290$		0			0
$291$			10.1302i			0.593845i
$292$		0			0
$293$	−10.8183	−	10.8183i	−0.632009	−	0.632009i	0.316562	−	0.948572i	$-0.397471\pi$
$293$	−10.8183	−	10.8183i	−0.632009	−	0.632009i	−0.948572	+	0.316562i	$0.897471\pi$
$294$		0			0
$295$	16.1664	−	24.6181i	0.941244	−	1.43332i
$296$		0			0
$297$	2.01154	−	2.01154i	0.116721	−	0.116721i
$298$		0			0
$299$	−18.0136	−	18.5064i	−1.04176	−	1.07025i
$300$		0			0
$301$	1.04216			0.0600691
$302$		0			0
$303$	−12.6423	+	12.6423i	−0.726284	+	0.726284i
$304$		0			0
$305$	2.26938	−	3.45580i	0.129944	−	0.197879i
$306$		0			0
$307$	−9.00763	−	9.00763i	−0.514092	−	0.514092i	0.401685	−	0.915778i	$-0.368425\pi$
$307$	−9.00763	−	9.00763i	−0.514092	−	0.514092i	−0.915778	+	0.401685i	$0.868425\pi$
$308$		0			0
$309$	−11.6523			−0.662874
$310$		0			0
$311$	0.886610			0.0502751			0.0251375	−	0.999684i	$-0.491998\pi$
$311$	0.886610			0.0502751			0.0251375	+	0.999684i	$0.491998\pi$
$312$		0			0
$313$	3.78768	+	3.78768i	0.214093	+	0.214093i	0.806003	−	0.591911i	$-0.201626\pi$
$313$	3.78768	+	3.78768i	0.214093	+	0.214093i	−0.591911	+	0.806003i	$0.701626\pi$
$314$		0			0
$315$	0.211209	+	1.01920i	0.0119003	+	0.0574256i
$316$		0			0
$317$	−15.7370	−	15.7370i	−0.883879	−	0.883879i	0.110047	−	0.993926i	$-0.464900\pi$
$317$	−15.7370	−	15.7370i	−0.883879	−	0.883879i	−0.993926	+	0.110047i	$0.964900\pi$
$318$		0			0
$319$	−8.18953			−0.458526
$320$		0			0
$321$			8.88330i			0.495818i
$322$		0			0
$323$	11.3908	−	11.3908i	0.633803	−	0.633803i
$324$		0			0
$325$	−25.0372	−	9.90521i	−1.38881	−	0.549442i
$326$		0			0
$327$	12.3205	−	12.3205i	0.681324	−	0.681324i
$328$		0			0
$329$	−1.19769			−0.0660308
$330$		0			0
$331$	12.8253			0.704942			0.352471	−	0.935823i	$-0.385342\pi$
$331$	12.8253			0.704942			0.352471	+	0.935823i	$0.385342\pi$
$332$		0			0
$333$	2.51831	+	2.51831i	0.138003	+	0.138003i
$334$		0			0
$335$	33.8987	−	7.02480i	1.85208	−	0.383806i
$336$		0			0
$337$	−6.24274	+	6.24274i	−0.340064	+	0.340064i	−0.856391	−	0.516327i	$-0.827299\pi$
$337$	−6.24274	+	6.24274i	−0.340064	+	0.340064i	0.516327	+	0.856391i	$0.327299\pi$
$338$		0			0
$339$	14.5937			0.792623
$340$		0			0
$341$			12.7400i			0.689908i
$342$		0			0
$343$	−4.53675	−	4.53675i	−0.244962	−	0.244962i
$344$		0			0
$345$	2.03419	+	10.5291i	0.109517	+	0.566868i
$346$		0			0
$347$	−2.94232	−	2.94232i	−0.157952	−	0.157952i	0.623707	−	0.781659i	$-0.285626\pi$
$347$	−2.94232	−	2.94232i	−0.157952	−	0.157952i	−0.781659	+	0.623707i	$0.785626\pi$
$348$		0			0
$349$		−	19.2765i		−	1.03185i	−0.856635	−	0.515923i	$-0.827449\pi$
$349$		−	19.2765i		−	1.03185i	0.856635	−	0.515923i	$-0.172551\pi$
$350$		0			0
$351$	5.38507			0.287434
$352$		0			0
$353$	−2.11303	+	2.11303i	−0.112465	+	0.112465i	−0.761100	−	0.648635i	$-0.775340\pi$
$353$	−2.11303	+	2.11303i	−0.112465	+	0.112465i	0.648635	+	0.761100i	$0.275340\pi$
$354$		0			0
$355$	−22.3122	−	14.6521i	−1.18421	−	0.777653i
$356$		0			0
$357$	1.69350	+	1.69350i	0.0896297	+	0.0896297i
$358$		0			0
$359$	−0.00848136			−0.000447629			−0.000223815	−	1.00000i	$-0.500071\pi$
$359$	−0.00848136			−0.000447629			−0.000223815		1.00000i	$0.500071\pi$
$360$		0			0
$361$	−9.19716			−0.484061
$362$		0			0
$363$	2.05586	−	2.05586i	0.107905	−	0.107905i
$364$		0			0
$365$	−18.6327	+	3.86124i	−0.975281	+	0.202107i
$366$		0			0
$367$	14.0010	−	14.0010i	0.730848	−	0.730848i	−0.239940	−	0.970788i	$-0.577128\pi$
$367$	14.0010	−	14.0010i	0.730848	−	0.730848i	0.970788	+	0.239940i	$0.0771277\pi$
$368$		0			0
$369$		−	1.80071i		−	0.0937415i
$370$		0			0
$371$	−2.26198			−0.117436
$372$		0			0
$373$	−10.5769	−	10.5769i	−0.547650	−	0.547650i	0.378111	−	0.925760i	$-0.376574\pi$
$373$	−10.5769	−	10.5769i	−0.547650	−	0.547650i	−0.925760	+	0.378111i	$0.876574\pi$
$374$		0			0
$375$	6.43241	+	9.14462i	0.332168	+	0.472226i
$376$		0			0
$377$	−10.9621	−	10.9621i	−0.564575	−	0.564575i
$378$		0			0
$379$	12.6867			0.651674			0.325837	−	0.945426i	$-0.394354\pi$
$379$	12.6867			0.651674			0.325837	+	0.945426i	$0.394354\pi$
$380$		0			0
$381$	−0.121529			−0.00622613
$382$		0			0
$383$	−3.22031	−	3.22031i	−0.164550	−	0.164550i	0.620029	−	0.784579i	$-0.287121\pi$
$383$	−3.22031	−	3.22031i	−0.164550	−	0.164550i	−0.784579	+	0.620029i	$0.787121\pi$
$384$		0			0
$385$	−0.600835	−	2.89937i	−0.0306214	−	0.147766i
$386$		0			0
$387$	−1.58312	+	1.58312i	−0.0804743	+	0.0804743i
$388$		0			0
$389$	10.2351			0.518941			0.259470	−	0.965751i	$-0.416452\pi$
$389$	10.2351			0.518941			0.259470	+	0.965751i	$0.416452\pi$
$390$		0			0
$391$	17.2109	+	17.6817i	0.870394	+	0.894202i
$392$		0			0
$393$	14.2860	−	14.2860i	0.720636	−	0.720636i
$394$		0			0
$395$	30.7620	+	20.2010i	1.54780	+	1.01642i
$396$		0			0
$397$	5.37503	+	5.37503i	0.269765	+	0.269765i	0.829006	−	0.559240i	$-0.188907\pi$
$397$	5.37503	+	5.37503i	0.269765	+	0.269765i	−0.559240	+	0.829006i	$0.688907\pi$
$398$		0			0
$399$			1.45741i			0.0729619i
$400$		0			0
$401$			30.0071i			1.49848i	0.662296	+	0.749242i	$0.269582\pi$
$401$			30.0071i			1.49848i	−0.662296	+	0.749242i	$0.730418\pi$
$402$		0			0
$403$	−17.0530	+	17.0530i	−0.849472	+	0.849472i
$404$		0			0
$405$	−1.86909	−	1.22740i	−0.0928756	−	0.0609902i
$406$		0			0
$407$	−7.16396	−	7.16396i	−0.355104	−	0.355104i
$408$		0			0
$409$		−	14.4411i		−	0.714066i	−0.934092	−	0.357033i	$-0.883788\pi$
$409$		−	14.4411i		−	0.714066i	0.934092	−	0.357033i	$-0.116212\pi$
$410$		0			0
$411$		−	4.24594i		−	0.209437i
$412$		0			0
$413$	4.33528	+	4.33528i	0.213325	+	0.213325i
$414$		0			0
$415$	−3.53600	−	17.0632i	−0.173576	−	0.837602i
$416$		0			0
$417$	−11.6631	−	11.6631i	−0.571145	−	0.571145i
$418$		0			0
$419$	6.40138			0.312728			0.156364	−	0.987700i	$-0.450023\pi$
$419$	6.40138			0.312728			0.156364	+	0.987700i	$0.450023\pi$
$420$		0			0
$421$			26.5834i			1.29559i	0.761813	+	0.647797i	$0.224310\pi$
$421$			26.5834i			1.29559i	−0.761813	+	0.647797i	$0.775690\pi$
$422$		0			0
$423$	1.81938	−	1.81938i	0.0884613	−	0.0884613i
$424$		0			0
$425$	23.9215	+	9.46382i	1.16036	+	0.459063i
$426$		0			0
$427$	0.608571	+	0.608571i	0.0294508	+	0.0294508i
$428$		0			0
$429$	−15.3192			−0.739616
$430$		0			0
$431$		−	23.7767i		−	1.14528i	−0.819806	−	0.572642i	$-0.805919\pi$
$431$		−	23.7767i		−	1.14528i	0.819806	−	0.572642i	$-0.194081\pi$
$432$		0			0
$433$	−16.5972	−	16.5972i	−0.797610	−	0.797610i	0.185108	−	0.982718i	$-0.440737\pi$
$433$	−16.5972	−	16.5972i	−0.797610	−	0.797610i	−0.982718	+	0.185108i	$0.940737\pi$
$434$		0			0
$435$	1.30623	+	6.30334i	0.0626292	+	0.302222i
$436$		0			0
$437$	−0.202570	+	15.0141i	−0.00969025	+	0.718224i
$438$		0			0
$439$			20.1119i			0.959887i	0.877299	+	0.479944i	$0.159343\pi$
$439$			20.1119i			0.959887i	−0.877299	+	0.479944i	$0.840657\pi$
$440$		0			0
$441$	6.78332			0.323015
$442$		0			0
$443$	−0.415363	+	0.415363i	−0.0197345	+	0.0197345i	−0.716905	−	0.697171i	$-0.754442\pi$
$443$	−0.415363	+	0.415363i	−0.0197345	+	0.0197345i	0.697171	+	0.716905i	$0.254442\pi$
$444$		0			0
$445$	5.41975	+	3.55908i	0.256921	+	0.168717i
$446$		0			0
$447$	−10.3678	+	10.3678i	−0.490381	+	0.490381i
$448$		0			0
$449$		−	9.50416i		−	0.448529i	−0.974528	−	0.224265i	$-0.928002\pi$
$449$		−	9.50416i		−	0.448529i	0.974528	−	0.224265i	$-0.0719980\pi$
$450$		0			0
$451$			5.12257i			0.241213i
$452$		0			0
$453$	1.40335	−	1.40335i	0.0659349	−	0.0659349i
$454$		0			0
$455$	3.07670	−	4.68519i	0.144238	−	0.219645i
$456$		0			0
$457$	−22.0195	+	22.0195i	−1.03003	+	1.03003i	−0.0304930	+	0.999535i	$0.509708\pi$
$457$	−22.0195	+	22.0195i	−1.03003	+	1.03003i	−0.999535	+	0.0304930i	$0.990292\pi$
$458$		0			0
$459$	−5.14511			−0.240153
$460$		0			0
$461$	7.74069			0.360520			0.180260	−	0.983619i	$-0.442306\pi$
$461$	7.74069			0.360520			0.180260	+	0.983619i	$0.442306\pi$
$462$		0			0
$463$	4.33354	−	4.33354i	0.201397	−	0.201397i	−0.599201	−	0.800598i	$-0.704515\pi$
$463$	4.33354	−	4.33354i	0.201397	−	0.201397i	0.800598	+	0.599201i	$0.204515\pi$
$464$		0			0
$465$	9.80572	−	2.03203i	0.454729	−	0.0942332i
$466$		0			0
$467$	14.6342	−	14.6342i	0.677192	−	0.677192i	−0.282172	−	0.959364i	$-0.591055\pi$
$467$	14.6342	−	14.6342i	0.677192	−	0.677192i	0.959364	+	0.282172i	$0.0910548\pi$
$468$		0			0
$469$			7.20667i			0.332773i
$470$		0			0
$471$		−	21.7507i		−	1.00222i
$472$		0			0
$473$	4.50356	−	4.50356i	0.207074	−	0.207074i
$474$		0			0
$475$	6.22108	+	14.3656i	0.285443	+	0.659137i
$476$		0			0
$477$	3.43611	−	3.43611i	0.157329	−	0.157329i
$478$		0			0
$479$	26.7491			1.22220			0.611098	−	0.791555i	$-0.290728\pi$
$479$	26.7491			1.22220			0.611098	+	0.791555i	$0.290728\pi$
$480$		0			0
$481$		−	19.1786i		−	0.874468i
$482$		0			0
$483$	−2.23219	−	0.0301166i	−0.101568	−	0.00137035i
$484$		0			0
$485$	−22.1807	+	4.59648i	−1.00717	+	0.208715i
$486$		0			0
$487$	21.0336	+	21.0336i	0.953124	+	0.953124i	0.998949	−	0.0458258i	$-0.0145919\pi$
$487$	21.0336	+	21.0336i	0.953124	+	0.953124i	−0.0458258	+	0.998949i	$0.514592\pi$
$488$		0			0
$489$		−	5.48248i		−	0.247926i
$490$		0			0
$491$	−5.98779			−0.270225			−0.135113	−	0.990830i	$-0.543140\pi$
$491$	−5.98779			−0.270225			−0.135113	+	0.990830i	$0.543140\pi$
$492$		0			0
$493$	10.4736	+	10.4736i	0.471707	+	0.471707i
$494$		0			0
$495$	5.31707	+	3.49165i	0.238985	+	0.156938i
$496$		0			0
$497$	3.92920	−	3.92920i	0.176249	−	0.176249i
$498$		0			0
$499$		−	29.2040i		−	1.30735i	−0.756776	−	0.653674i	$-0.773227\pi$
$499$		−	29.2040i		−	1.30735i	0.756776	−	0.653674i	$-0.226773\pi$
$500$		0			0
$501$	−7.07282			−0.315990
$502$		0			0
$503$	−11.0743	−	11.0743i	−0.493780	−	0.493780i	0.415715	−	0.909495i	$-0.363531\pi$
$503$	−11.0743	−	11.0743i	−0.493780	−	0.493780i	−0.909495	+	0.415715i	$0.863531\pi$
$504$		0			0
$505$	−33.4173	−	21.9447i	−1.48705	−	0.976527i
$506$		0			0
$507$	−11.3130	−	11.3130i	−0.502429	−	0.502429i
$508$		0			0
$509$			42.5995i			1.88819i	0.329675	+	0.944095i	$0.393061\pi$
$509$			42.5995i			1.88819i	−0.329675	+	0.944095i	$0.606939\pi$
$510$		0			0
$511$		−	3.96121i		−	0.175234i
$512$		0			0
$513$	−2.21392	−	2.21392i	−0.0977468	−	0.0977468i
$514$		0			0
$515$	−5.28707	−	25.5132i	−0.232976	−	1.12424i
$516$		0			0
$517$	−5.17567	+	5.17567i	−0.227626	+	0.227626i
$518$		0			0
$519$			3.79687i			0.166664i
$520$		0			0
$521$		−	1.87583i		−	0.0821816i	−0.999155	−	0.0410908i	$-0.986917\pi$
$521$		−	1.87583i		−	0.0821816i	0.999155	−	0.0410908i	$-0.0130833\pi$
$522$		0			0
$523$	1.97798	+	1.97798i	0.0864908	+	0.0864908i	0.749029	−	0.662538i	$-0.230521\pi$
$523$	1.97798	+	1.97798i	0.0864908	+	0.0864908i	−0.662538	+	0.749029i	$0.730521\pi$
$524$		0			0
$525$	−2.13576	+	0.924903i	−0.0932123	+	0.0403661i
$526$		0			0
$527$	16.2931	−	16.2931i	0.709740	−	0.709740i
$528$		0			0
$529$	−22.9916	−	0.620517i	−0.999636	−	0.0269790i
$530$		0			0
$531$	−13.1712			−0.571582
$532$		0			0
$533$	−6.85680	+	6.85680i	−0.297001	+	0.297001i
$534$		0			0
$535$	−19.4504	+	4.03069i	−0.840915	+	0.174262i
$536$		0			0
$537$	−11.6121	−	11.6121i	−0.501098	−	0.501098i
$538$		0			0
$539$	−19.2968			−0.831173
$540$		0			0
$541$	25.7295			1.10620			0.553099	−	0.833115i	$-0.313445\pi$
$541$	25.7295			1.10620			0.553099	+	0.833115i	$0.313445\pi$
$542$		0			0
$543$	9.72999	+	9.72999i	0.417554	+	0.417554i
$544$		0			0
$545$	32.5665	+	21.3860i	1.39500	+	0.916076i
$546$		0			0
$547$	−12.1960	−	12.1960i	−0.521461	−	0.521461i	0.396551	−	0.918013i	$-0.370207\pi$
$547$	−12.1960	−	12.1960i	−0.521461	−	0.521461i	−0.918013	+	0.396551i	$0.870207\pi$
$548$		0			0
$549$	−1.84893			−0.0789103
$550$		0			0
$551$			9.01347i			0.383987i
$552$		0			0
$553$	−5.41722	+	5.41722i	−0.230364	+	0.230364i
$554$		0			0
$555$	−4.37131	+	6.65662i	−0.185552	+	0.282558i
$556$		0			0
$557$	23.3789	−	23.3789i	0.990596	−	0.990596i	−0.00936035	−	0.999956i	$-0.502980\pi$
$557$	23.3789	−	23.3789i	0.990596	−	0.990596i	0.999956	+	0.00936035i	$0.00297954\pi$
$558$		0			0
$559$	12.0565			0.509934
$560$		0			0
$561$	14.6365			0.617954
$562$		0			0
$563$	−14.7091	−	14.7091i	−0.619915	−	0.619915i	0.325595	−	0.945509i	$-0.394436\pi$
$563$	−14.7091	−	14.7091i	−0.619915	−	0.619915i	−0.945509	+	0.325595i	$0.894436\pi$
$564$		0			0
$565$	6.62173	+	31.9537i	0.278578	+	1.34430i
$566$		0			0
$567$	0.329148	−	0.329148i	0.0138229	−	0.0138229i
$568$		0			0
$569$	39.2727			1.64640			0.823200	−	0.567752i	$-0.192187\pi$
$569$	39.2727			1.64640			0.823200	+	0.567752i	$0.192187\pi$
$570$		0			0
$571$			3.91169i			0.163699i	0.996645	+	0.0818495i	$0.0260827\pi$
$571$			3.91169i			0.163699i	−0.996645	+	0.0818495i	$0.973917\pi$
$572$		0			0
$573$	−1.03214	−	1.03214i	−0.0431183	−	0.0431183i
$574$		0			0
$575$	−22.1310	+	9.23142i	−0.922926	+	0.384977i
$576$		0			0
$577$	16.4799	+	16.4799i	0.686067	+	0.686067i	0.961360	−	0.275293i	$-0.0887750\pi$
$577$	16.4799	+	16.4799i	0.686067	+	0.686067i	−0.275293	+	0.961360i	$0.588775\pi$
$578$		0			0
$579$		−	23.0769i		−	0.959042i
$580$		0			0
$581$	3.62755			0.150496
$582$		0			0
$583$	−9.77487	+	9.77487i	−0.404834	+	0.404834i
$584$		0			0
$585$	2.44341	+	11.7909i	0.101023	+	0.487493i
$586$		0			0
$587$	12.2594	+	12.2594i	0.506000	+	0.506000i	0.913296	−	0.407296i	$-0.133528\pi$
$587$	12.2594	+	12.2594i	0.506000	+	0.506000i	−0.407296	+	0.913296i	$0.633528\pi$
$588$		0			0
$589$	14.0217			0.577755
$590$		0			0
$591$	−22.0423			−0.906699
$592$		0			0
$593$	−5.46260	+	5.46260i	−0.224322	+	0.224322i	−0.810316	−	0.585994i	$-0.800704\pi$
$593$	−5.46260	+	5.46260i	−0.224322	+	0.224322i	0.585994	+	0.810316i	$0.300704\pi$
$594$		0			0
$595$	−2.93960	+	4.47641i	−0.120512	+	0.183515i
$596$		0			0
$597$	1.90654	−	1.90654i	0.0780295	−	0.0780295i
$598$		0			0
$599$			21.6732i			0.885545i	0.896634	+	0.442772i	$0.146005\pi$
$599$			21.6732i			0.885545i	−0.896634	+	0.442772i	$0.853995\pi$
$600$		0			0
$601$	−8.96958			−0.365877			−0.182938	−	0.983124i	$-0.558561\pi$
$601$	−8.96958			−0.365877			−0.182938	+	0.983124i	$0.558561\pi$
$602$		0			0
$603$	−10.9475	−	10.9475i	−0.445815	−	0.445815i
$604$		0			0
$605$	5.43423	+	3.56859i	0.220933	+	0.145084i
$606$		0			0
$607$	19.9310	+	19.9310i	0.808975	+	0.808975i	0.984479	−	0.175503i	$-0.0561553\pi$
$607$	19.9310	+	19.9310i	0.808975	+	0.808975i	−0.175503	+	0.984479i	$0.556155\pi$
$608$		0			0
$609$	−1.34005			−0.0543017
$610$		0			0
$611$	−13.8558			−0.560544
$612$		0			0
$613$	4.96870	+	4.96870i	0.200684	+	0.200684i	0.800293	−	0.599609i	$-0.204677\pi$
$613$	4.96870	+	4.96870i	0.200684	+	0.200684i	−0.599609	+	0.800293i	$0.704677\pi$
$614$		0			0
$615$	3.94275	−	0.817053i	0.158987	−	0.0329468i
$616$		0			0
$617$	31.2236	−	31.2236i	1.25701	−	1.25701i	0.304504	−	0.952511i	$-0.401509\pi$
$617$	31.2236	−	31.2236i	1.25701	−	1.25701i	0.952511	−	0.304504i	$-0.0984906\pi$
$618$		0			0
$619$	20.1489			0.809851			0.404926	−	0.914350i	$-0.367297\pi$
$619$	20.1489			0.809851			0.404926	+	0.914350i	$0.367297\pi$
$620$		0			0
$621$	3.43661	−	3.34511i	0.137906	−	0.134235i
$622$		0			0
$623$	−0.954425	+	0.954425i	−0.0382382	+	0.0382382i
$624$		0			0
$625$	−17.1040	+	18.2333i	−0.684158	+	0.729334i
$626$		0			0
$627$	6.29802	+	6.29802i	0.251519	+	0.251519i
$628$		0			0
$629$			18.3240i			0.730624i
$630$		0			0
$631$		−	18.1525i		−	0.722642i	−0.932442	−	0.361321i	$-0.882326\pi$
$631$		−	18.1525i		−	0.722642i	0.932442	−	0.361321i	$-0.117674\pi$
$632$		0			0
$633$	−1.69686	+	1.69686i	−0.0674440	+	0.0674440i
$634$		0			0
$635$	−0.0551424	−	0.266094i	−0.00218826	−	0.0105596i
$636$		0			0
$637$	−25.8297	−	25.8297i	−1.02341	−	1.02341i
$638$		0			0
$639$			11.9375i			0.472240i
$640$		0			0
$641$		−	9.46542i		−	0.373862i	−0.982373	−	0.186931i	$-0.940146\pi$
$641$		−	9.46542i		−	0.373862i	0.982373	−	0.186931i	$-0.0598540\pi$
$642$		0			0
$643$	2.67338	+	2.67338i	0.105428	+	0.105428i	0.757853	−	0.652425i	$-0.226248\pi$
$643$	2.67338	+	2.67338i	0.105428	+	0.105428i	−0.652425	+	0.757853i	$0.726248\pi$
$644$		0			0
$645$	−4.18463	−	2.74799i	−0.164770	−	0.108202i
$646$		0			0
$647$	4.97670	+	4.97670i	0.195654	+	0.195654i	0.798134	−	0.602480i	$-0.205821\pi$
$647$	4.97670	+	4.97670i	0.195654	+	0.195654i	−0.602480	+	0.798134i	$0.705821\pi$
$648$		0			0
$649$	37.4688			1.47078
$650$		0			0
$651$			2.08464i			0.0817035i
$652$		0			0
$653$	5.49740	−	5.49740i	0.215130	−	0.215130i	−0.591313	−	0.806442i	$-0.701390\pi$
$653$	5.49740	−	5.49740i	0.215130	−	0.215130i	0.806442	+	0.591313i	$0.201390\pi$
$654$		0			0
$655$	37.7621	+	24.7979i	1.47549	+	0.968933i
$656$		0			0
$657$	6.01737	+	6.01737i	0.234760	+	0.234760i
$658$		0			0
$659$	−16.6392			−0.648170			−0.324085	−	0.946028i	$-0.605056\pi$
$659$	−16.6392			−0.648170			−0.324085	+	0.946028i	$0.605056\pi$
$660$		0			0
$661$			30.6803i			1.19332i	0.802492	+	0.596662i	$0.203507\pi$
$661$			30.6803i			1.19332i	−0.802492	+	0.596662i	$0.796493\pi$
$662$		0			0
$663$	19.5917	+	19.5917i	0.760877	+	0.760877i
$664$		0			0
$665$	−3.19107	+	0.661283i	−0.123745	+	0.0256435i
$666$		0			0
$667$	−13.8051	−	0.186258i	−0.534537	−	0.00721195i
$668$		0			0
$669$			29.0346i			1.12254i
$670$		0			0
$671$	5.25972			0.203049
$672$		0			0
$673$	−19.0955	+	19.0955i	−0.736076	+	0.736076i	−0.971816	−	0.235740i	$-0.924249\pi$
$673$	−19.0955	+	19.0955i	−0.736076	+	0.736076i	0.235740	+	0.971816i	$0.424249\pi$
$674$		0			0
$675$	1.83938	−	4.64937i	0.0707979	−	0.178954i
$676$		0			0
$677$	−12.4530	+	12.4530i	−0.478606	+	0.478606i	−0.904686	−	0.426079i	$-0.859894\pi$
$677$	−12.4530	+	12.4530i	−0.478606	+	0.478606i	0.426079	+	0.904686i	$0.359894\pi$
$678$		0			0
$679$		−	4.71548i		−	0.180964i
$680$		0			0
$681$			19.6765i			0.754004i
$682$		0			0
$683$	−19.1818	+	19.1818i	−0.733970	+	0.733970i	−0.971404	−	0.237434i	$-0.923694\pi$
$683$	−19.1818	+	19.1818i	−0.733970	+	0.733970i	0.237434	+	0.971404i	$0.423694\pi$
$684$		0			0
$685$	9.29670	−	1.92655i	0.355209	−	0.0736096i
$686$		0			0
$687$	−2.47146	+	2.47146i	−0.0942920	+	0.0942920i
$688$		0			0
$689$	−26.1682			−0.996930
$690$		0			0
$691$	−2.23969			−0.0852017			−0.0426009	−	0.999092i	$-0.513564\pi$
$691$	−2.23969			−0.0852017			−0.0426009	+	0.999092i	$0.513564\pi$
$692$		0			0
$693$	−0.936342	+	0.936342i	−0.0355687	+	0.0355687i
$694$		0			0
$695$	20.2450	−	30.8290i	0.767935	−	1.16941i
$696$		0			0
$697$	6.55125	−	6.55125i	0.248146	−	0.248146i
$698$		0			0
$699$			22.2428i			0.841299i
$700$		0			0
$701$		−	15.4810i		−	0.584709i	−0.956310	−	0.292354i	$-0.905561\pi$
$701$		−	15.4810i		−	0.584709i	0.956310	−	0.292354i	$-0.0944387\pi$
$702$		0			0
$703$	−7.88471	+	7.88471i	−0.297378	+	0.297378i
$704$		0			0
$705$	4.80914	+	3.15810i	0.181123	+	0.118941i
$706$		0			0
$707$	5.88483	−	5.88483i	0.221322	−	0.221322i
$708$		0			0
$709$	52.5554			1.97376			0.986880	−	0.161456i	$-0.0516189\pi$
$709$	52.5554			1.97376			0.986880	+	0.161456i	$0.0516189\pi$
$710$		0			0
$711$		−	16.4583i		−	0.617235i
$712$		0			0
$713$	−0.289751	+	21.4758i	−0.0108513	+	0.804275i
$714$		0			0
$715$	−6.95089	−	33.5420i	−0.259948	−	1.25440i
$716$		0			0
$717$	−0.419080	−	0.419080i	−0.0156508	−	0.0156508i
$718$		0			0
$719$			0.993987i			0.0370694i	0.999828	+	0.0185347i	$0.00590012\pi$
$719$			0.993987i			0.0370694i	−0.999828	+	0.0185347i	$0.994100\pi$
$720$		0			0
$721$	5.42396			0.201999
$722$		0			0
$723$	−1.25427	−	1.25427i	−0.0466467	−	0.0466467i
$724$		0			0
$725$	−13.2088	+	5.72013i	−0.490561	+	0.212440i
$726$		0			0
$727$	−13.0232	+	13.0232i	−0.483003	+	0.483003i	−0.906089	−	0.423086i	$-0.860947\pi$
$727$	−13.0232	+	13.0232i	−0.483003	+	0.483003i	0.423086	+	0.906089i	$0.360947\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−11.5192			−0.426053
$732$		0			0
$733$	−28.4558	−	28.4558i	−1.05104	−	1.05104i	−0.998625	−	0.0524149i	$-0.983308\pi$
$733$	−28.4558	−	28.4558i	−1.05104	−	1.05104i	−0.0524149	−	0.998625i	$-0.516692\pi$
$734$		0			0
$735$	3.07785	+	14.8524i	0.113528	+	0.547840i
$736$		0			0
$737$	31.1427	+	31.1427i	1.14716	+	1.14716i
$738$		0			0
$739$		−	6.43780i		−	0.236818i	−0.992965	−	0.118409i	$-0.962221\pi$
$739$		−	6.43780i		−	0.236818i	0.992965	−	0.118409i	$-0.0377794\pi$
$740$		0			0
$741$			16.8604i			0.619382i
$742$		0			0
$743$	34.7251	+	34.7251i	1.27394	+	1.27394i	0.944003	+	0.329937i	$0.107028\pi$
$743$	34.7251	+	34.7251i	1.27394	+	1.27394i	0.329937	+	0.944003i	$0.392972\pi$
$744$		0			0
$745$	−27.4051	−	17.9965i	−1.00404	−	0.659343i
$746$		0			0
$747$	−5.51052	+	5.51052i	−0.201619	+	0.201619i
$748$		0			0
$749$		−	4.13505i		−	0.151091i
$750$		0			0
$751$			41.8204i			1.52605i	0.646371	+	0.763024i	$0.276286\pi$
$751$			41.8204i			1.52605i	−0.646371	+	0.763024i	$0.723714\pi$
$752$		0			0
$753$	−10.6945	−	10.6945i	−0.389730	−	0.389730i
$754$		0			0
$755$	3.70944	+	2.43594i	0.135000	+	0.0886530i
$756$		0			0
$757$	34.1006	−	34.1006i	1.23941	−	1.23941i	0.279162	−	0.960244i	$-0.409943\pi$
$757$	34.1006	−	34.1006i	1.23941	−	1.23941i	0.960244	−	0.279162i	$-0.0900567\pi$
$758$		0			0
$759$	−9.77627	+	9.51598i	−0.354856	+	0.345408i
$760$		0			0
$761$	36.7625			1.33264			0.666319	−	0.745667i	$-0.267869\pi$
$761$	36.7625			1.33264			0.666319	+	0.745667i	$0.267869\pi$
$762$		0			0
$763$	−5.73501	+	5.73501i	−0.207621	+	0.207621i
$764$		0			0
$765$	−2.33453	−	11.2655i	−0.0844052	−	0.407304i
$766$		0			0
$767$	50.1537	+	50.1537i	1.81094	+	1.81094i
$768$		0			0
$769$	−13.2248			−0.476899			−0.238450	−	0.971155i	$-0.576639\pi$
$769$	−13.2248			−0.476899			−0.238450	+	0.971155i	$0.576639\pi$
$770$		0			0
$771$	−22.5365			−0.811631
$772$		0			0
$773$	22.2493	+	22.2493i	0.800250	+	0.800250i	0.983134	−	0.182884i	$-0.0585433\pi$
$773$	22.2493	+	22.2493i	0.800250	+	0.800250i	−0.182884	+	0.983134i	$0.558543\pi$
$774$		0			0
$775$	8.89846	+	20.5481i	0.319642	+	0.738109i
$776$		0			0
$777$	−1.17224	−	1.17224i	−0.0420538	−	0.0420538i
$778$		0			0
$779$	5.63795			0.202000
$780$		0			0
$781$		−	33.9591i		−	1.21515i
$782$		0			0
$783$	2.03564	−	2.03564i	0.0727478	−	0.0727478i
$784$		0			0
$785$	47.6243	−	9.86914i	1.69978	−	0.352245i
$786$		0			0
$787$	−5.58878	+	5.58878i	−0.199219	+	0.199219i	−0.799665	−	0.600446i	$-0.794990\pi$
$787$	−5.58878	+	5.58878i	−0.199219	+	0.199219i	0.600446	+	0.799665i	$0.294990\pi$
$788$		0			0
$789$	−19.9822			−0.711384
$790$		0			0
$791$	−6.79317			−0.241537
$792$		0			0
$793$	7.04038	+	7.04038i	0.250011	+	0.250011i
$794$		0			0
$795$	9.08263	+	5.96444i	0.322128	+	0.211537i
$796$		0			0
$797$	−7.06501	+	7.06501i	−0.250255	+	0.250255i	−0.821075	−	0.570820i	$-0.806625\pi$
$797$	−7.06501	+	7.06501i	−0.250255	+	0.250255i	0.570820	+	0.821075i	$0.306625\pi$
$798$		0			0
$799$	13.2383			0.468338
$800$		0			0
$801$		−	2.89968i		−	0.102455i
$802$		0			0
$803$	−17.1179	−	17.1179i	−0.604077	−	0.604077i
$804$		0			0
$805$	−0.946887	−	4.90115i	−0.0333734	−	0.172743i
$806$		0			0
$807$	−5.31077	−	5.31077i	−0.186948	−	0.186948i
$808$		0			0
$809$			20.1510i			0.708471i	0.935156	+	0.354236i	$0.115259\pi$
$809$			20.1510i			0.708471i	−0.935156	+	0.354236i	$0.884741\pi$
$810$		0			0
$811$	14.7105			0.516556			0.258278	−	0.966071i	$-0.416845\pi$
$811$	14.7105			0.516556			0.258278	+	0.966071i	$0.416845\pi$
$812$		0			0
$813$	14.2073	−	14.2073i	0.498272	−	0.498272i
$814$		0			0
$815$	12.0041	−	2.48761i	0.420487	−	0.0871371i
$816$		0			0
$817$	−4.95666	−	4.95666i	−0.173412	−	0.173412i
$818$		0			0
$819$	−2.50667			−0.0875903
$820$		0			0
$821$	21.9384			0.765656			0.382828	−	0.923820i	$-0.374950\pi$
$821$	21.9384			0.765656			0.382828	+	0.923820i	$0.374950\pi$
$822$		0			0
$823$	−11.5407	+	11.5407i	−0.402284	+	0.402284i	−0.879037	−	0.476753i	$-0.841814\pi$
$823$	−11.5407	+	11.5407i	−0.402284	+	0.402284i	0.476753	+	0.879037i	$0.341814\pi$
$824$		0			0
$825$	−5.23258	+	13.2263i	−0.182175	+	0.460480i
$826$		0			0
$827$	16.0237	−	16.0237i	0.557199	−	0.557199i	−0.371310	−	0.928509i	$-0.621091\pi$
$827$	16.0237	−	16.0237i	0.557199	−	0.557199i	0.928509	+	0.371310i	$0.121091\pi$
$828$		0			0
$829$		−	18.0698i		−	0.627591i	−0.949491	−	0.313796i	$-0.898399\pi$
$829$		−	18.0698i		−	0.627591i	0.949491	−	0.313796i	$-0.101601\pi$
$830$		0			0
$831$	−0.562459			−0.0195115
$832$		0			0
$833$	24.6787	+	24.6787i	0.855066	+	0.855066i
$834$		0			0
$835$	−3.20921	−	15.4863i	−0.111059	−	0.535925i
$836$		0			0
$837$	−3.16672	−	3.16672i	−0.109458	−	0.109458i
$838$		0			0
$839$	−3.29244			−0.113668			−0.0568338	−	0.998384i	$-0.518101\pi$
$839$	−3.29244			−0.113668			−0.0568338	+	0.998384i	$0.518101\pi$
$840$		0			0
$841$	20.7123			0.714219
$842$		0			0
$843$	−1.73421	−	1.73421i	−0.0597295	−	0.0597295i
$844$		0			0
$845$	19.6372	−	29.9035i	0.675542	−	1.02871i
$846$		0			0
$847$	−0.956974	+	0.956974i	−0.0328820	+	0.0328820i
$848$		0			0
$849$	−10.8925			−0.373829
$850$		0			0
$851$	−11.9134	−	12.2392i	−0.408385	−	0.419556i
$852$		0			0
$853$	9.80056	−	9.80056i	0.335565	−	0.335565i	−0.519130	−	0.854695i	$-0.673744\pi$
$853$	9.80056	−	9.80056i	0.335565	−	0.335565i	0.854695	+	0.519130i	$0.173744\pi$
$854$		0			0
$855$	3.84294	−	5.85201i	0.131426	−	0.200135i
$856$		0			0
$857$	−22.8702	−	22.8702i	−0.781230	−	0.781230i	0.198808	−	0.980038i	$-0.436293\pi$
$857$	−22.8702	−	22.8702i	−0.781230	−	0.781230i	−0.980038	+	0.198808i	$0.936293\pi$
$858$		0			0
$859$		−	24.6605i		−	0.841405i	−0.907199	−	0.420703i	$-0.861784\pi$
$859$		−	24.6605i		−	0.841405i	0.907199	−	0.420703i	$-0.138216\pi$
$860$		0			0
$861$			0.838207i			0.0285660i
$862$		0			0
$863$	2.21244	−	2.21244i	0.0753124	−	0.0753124i	−0.668447	−	0.743760i	$-0.733041\pi$
$863$	2.21244	−	2.21244i	0.0753124	−	0.0753124i	0.743760	+	0.668447i	$0.233041\pi$
$864$		0			0
$865$	−8.31343	+	1.72278i	−0.282665	+	0.0585764i
$866$		0			0
$867$	−6.69781	−	6.69781i	−0.227469	−	0.227469i
$868$		0			0
$869$			46.8197i			1.58825i
$870$		0			0
$871$			83.3720i			2.82495i
$872$		0			0
$873$	7.16316	+	7.16316i	0.242436	+	0.242436i
$874$		0			0
$875$	−2.99420	−	4.25669i	−0.101222	−	0.143902i
$876$		0			0
$877$	−12.9261	−	12.9261i	−0.436483	−	0.436483i	0.454344	−	0.890826i	$-0.349874\pi$
$877$	−12.9261	−	12.9261i	−0.436483	−	0.436483i	−0.890826	+	0.454344i	$0.849874\pi$
$878$		0			0
$879$	−15.2993			−0.516034
$880$		0			0
$881$		−	11.2206i		−	0.378031i	−0.981974	−	0.189015i	$-0.939470\pi$
$881$		−	11.2206i		−	0.378031i	0.981974	−	0.189015i	$-0.0605296\pi$
$882$		0			0
$883$	−18.4973	+	18.4973i	−0.622482	+	0.622482i	−0.946166	−	0.323683i	$-0.895079\pi$
$883$	−18.4973	+	18.4973i	−0.622482	+	0.622482i	0.323683	+	0.946166i	$0.395079\pi$
$884$		0			0
$885$	−5.97628	−	28.8390i	−0.200891	−	0.969413i
$886$		0			0
$887$	−10.6956	−	10.6956i	−0.359123	−	0.359123i	0.504367	−	0.863490i	$-0.331726\pi$
$887$	−10.6956	−	10.6956i	−0.359123	−	0.359123i	−0.863490	+	0.504367i	$0.831726\pi$
$888$		0			0
$889$	0.0565701			0.00189730
$890$		0			0
$891$		−	2.84474i		−	0.0953025i
$892$		0			0
$893$	5.69639	+	5.69639i	0.190622	+	0.190622i
$894$		0			0
$895$	20.1563	−	30.6940i	0.673752	−	1.02599i
$896$		0			0
$897$	−25.8236	−	0.348410i	−0.862223	−	0.0116331i
$898$		0			0
$899$			12.8926i			0.429993i
$900$		0			0
$901$	25.0021			0.832942
$902$		0			0
$903$	0.736918	−	0.736918i	0.0245231	−	0.0245231i
$904$		0			0
$905$	−16.8894	+	25.7192i	−0.561423	+	0.854934i
$906$		0			0
$907$	−30.4146	+	30.4146i	−1.00990	+	1.00990i	−0.00995040	+	0.999950i	$0.503167\pi$
$907$	−30.4146	+	30.4146i	−1.00990	+	1.00990i	−0.999950	+	0.00995040i	$0.996833\pi$
$908$		0			0
$909$			17.8790i			0.593008i
$910$		0			0
$911$			17.2794i			0.572492i	0.958156	+	0.286246i	$0.0924074\pi$
$911$			17.2794i			0.572492i	−0.958156	+	0.286246i	$0.907593\pi$
$912$		0			0
$913$	15.6760	−	15.6760i	0.518800	−	0.518800i
$914$		0			0
$915$	−0.838928	−	4.04831i	−0.0277341	−	0.133833i
$916$		0			0
$917$	−6.64995	+	6.64995i	−0.219601	+	0.219601i
$918$		0			0
$919$	49.0842			1.61914			0.809569	−	0.587025i	$-0.199701\pi$
$919$	49.0842			1.61914			0.809569	+	0.587025i	$0.199701\pi$
$920$		0			0
$921$	−12.7387			−0.419755
$922$		0			0
$923$	45.4558	−	45.4558i	1.49620	−	1.49620i
$924$		0			0
$925$	−16.5584	−	6.55084i	−0.544438	−	0.215390i
$926$		0			0
$927$	−8.23939	+	8.23939i	−0.270617	+	0.270617i
$928$		0			0
$929$			37.4523i			1.22877i	0.789006	+	0.614385i	$0.210596\pi$
$929$			37.4523i			1.22877i	−0.789006	+	0.614385i	$0.789404\pi$
$930$		0			0
$931$			21.2382i			0.696055i
$932$		0			0
$933$	0.626928	−	0.626928i	0.0205247	−	0.0205247i
$934$		0			0
$935$	6.64115	+	32.0474i	0.217189	+	1.04806i
$936$		0			0
$937$	16.9989	−	16.9989i	0.555331	−	0.555331i	−0.372643	−	0.927975i	$-0.621549\pi$
$937$	16.9989	−	16.9989i	0.555331	−	0.555331i	0.927975	+	0.372643i	$0.121549\pi$
$938$		0			0
$939$	5.35659			0.174806
$940$		0			0
$941$		−	35.4009i		−	1.15404i	−0.816731	−	0.577018i	$-0.804216\pi$
$941$		−	35.4009i		−	1.15404i	0.816731	−	0.577018i	$-0.195784\pi$
$942$		0			0
$943$	−0.116505	+	8.63514i	−0.00379392	+	0.281199i
$944$		0			0
$945$	0.870033	+	0.571339i	0.0283022	+	0.0185856i
$946$		0			0
$947$	14.1432	+	14.1432i	0.459592	+	0.459592i	0.898522	−	0.438929i	$-0.144642\pi$
$947$	14.1432	+	14.1432i	0.459592	+	0.459592i	−0.438929	+	0.898522i	$0.644642\pi$
$948$		0			0
$949$		−	45.8261i		−	1.48758i
$950$		0			0
$951$	−22.2555			−0.721684
$952$		0			0
$953$	−4.81511	−	4.81511i	−0.155977	−	0.155977i	0.624804	−	0.780781i	$-0.285179\pi$
$953$	−4.81511	−	4.81511i	−0.155977	−	0.155977i	−0.780781	+	0.624804i	$0.785179\pi$
$954$		0			0
$955$	1.79160	−	2.72824i	0.0579748	−	0.0882839i
$956$		0			0
$957$	−5.79088	+	5.79088i	−0.187192	+	0.187192i
$958$		0			0
$959$			1.97643i			0.0638221i
$960$		0			0
$961$	−10.9437			−0.353024
$962$		0			0
$963$	6.28144	+	6.28144i	0.202417	+	0.202417i
$964$		0			0
$965$	50.5279	−	10.4709i	1.62655	−	0.337069i
$966$		0			0
$967$	13.5076	+	13.5076i	0.434374	+	0.434374i	0.890113	−	0.455739i	$-0.150625\pi$
$967$	13.5076	+	13.5076i	0.434374	+	0.434374i	−0.455739	+	0.890113i	$0.650625\pi$
$968$		0			0
$969$		−	16.1091i		−	0.517498i
$970$		0			0
$971$		−	58.0358i		−	1.86246i	−0.364437	−	0.931228i	$-0.618738\pi$
$971$		−	58.0358i		−	1.86246i	0.364437	−	0.931228i	$-0.381262\pi$
$972$		0			0
$973$	5.42902	+	5.42902i	0.174046	+	0.174046i
$974$		0			0
$975$	−24.7080	+	10.6999i	−0.791290	+	0.342672i
$976$		0			0
$977$	30.8882	−	30.8882i	0.988200	−	0.988200i	−0.0117315	−	0.999931i	$-0.503734\pi$
$977$	30.8882	−	30.8882i	0.988200	−	0.988200i	0.999931	+	0.0117315i	$0.00373434\pi$
$978$		0			0
$979$			8.24886i			0.263635i
$980$		0			0
$981$		−	17.4238i		−	0.556299i
$982$		0			0
$983$	19.9983	+	19.9983i	0.637846	+	0.637846i	0.950024	−	0.312178i	$-0.101058\pi$
$983$	19.9983	+	19.9983i	0.637846	+	0.637846i	−0.312178	+	0.950024i	$0.601058\pi$
$984$		0			0
$985$	−10.0014	−	48.2627i	−0.318672	−	1.53778i
$986$		0			0
$987$	−0.846896	+	0.846896i	−0.0269570	+	0.0269570i
$988$		0			0
$989$	7.69410	−	7.48924i	0.244658	−	0.238144i
$990$		0			0
$991$	−56.7479			−1.80266			−0.901329	−	0.433136i	$-0.857407\pi$
$991$	−56.7479			−1.80266			−0.901329	+	0.433136i	$0.857407\pi$
$992$		0			0
$993$	9.06885	−	9.06885i	0.287791	−	0.287791i
$994$		0			0
$995$	5.03953	+	3.30939i	0.159764	+	0.104915i
$996$		0			0
$997$	21.2047	+	21.2047i	0.671558	+	0.671558i	0.958075	−	0.286517i	$-0.0924975\pi$
$997$	21.2047	+	21.2047i	0.671558	+	0.671558i	−0.286517	+	0.958075i	$0.592497\pi$
$998$		0			0
$999$	3.56143			0.112679

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1380.2.t.a.1057.18	yes	48
5.3	odd	4	inner	1380.2.t.a.1333.17	yes	48
23.22	odd	2	inner	1380.2.t.a.1057.17	✓	48
115.68	even	4	inner	1380.2.t.a.1333.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1380.2.t.a.1057.17	✓	48	23.22	odd	2	inner
1380.2.t.a.1057.18	yes	48	1.1	even	1	trivial
1380.2.t.a.1333.17	yes	48	5.3	odd	4	inner
1380.2.t.a.1333.18	yes	48	115.68	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1380 = 2^{2} \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1380.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.86909 + 1.22740i) q^{5} +(-0.329148 + 0.329148i) q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{3} +(1.86909 + 1.22740i) q^{5} +(-0.329148 + 0.329148i) q^{7} -1.00000i q^{9} +2.84474i q^{11} +(-3.80782 + 3.80782i) q^{13} +(2.18955 - 0.453738i) q^{15} +(3.63814 - 3.63814i) q^{17} +3.13095 q^{19} +0.465486i q^{21} +(-0.0646993 + 4.79540i) q^{23} +(1.98696 + 4.58824i) q^{25} +(-0.707107 - 0.707107i) q^{27} +2.87883i q^{29} +4.47842 q^{31} +(2.01154 + 2.01154i) q^{33} +(-1.01920 + 0.211209i) q^{35} +(-2.51831 + 2.51831i) q^{37} +5.38507i q^{39} +1.80071 q^{41} +(-1.58312 - 1.58312i) q^{43} +(1.22740 - 1.86909i) q^{45} +(1.81938 + 1.81938i) q^{47} +6.78332i q^{49} -5.14511i q^{51} +(3.43611 + 3.43611i) q^{53} +(-3.49165 + 5.31707i) q^{55} +(2.21392 - 2.21392i) q^{57} -13.1712i q^{59} -1.84893i q^{61} +(0.329148 + 0.329148i) q^{63} +(-11.7909 + 2.44341i) q^{65} +(10.9475 - 10.9475i) q^{67} +(3.34511 + 3.43661i) q^{69} -11.9375 q^{71} +(-6.01737 + 6.01737i) q^{73} +(4.64937 + 1.83938i) q^{75} +(-0.936342 - 0.936342i) q^{77} +16.4583 q^{79} -1.00000 q^{81} +(-5.51052 - 5.51052i) q^{83} +(11.2655 - 2.33453i) q^{85} +(2.03564 + 2.03564i) q^{87} +2.89968 q^{89} -2.50667i q^{91} +(3.16672 - 3.16672i) q^{93} +(5.85201 + 3.84294i) q^{95} +(-7.16316 + 7.16316i) q^{97} +2.84474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{13} - 16 q^{23} - 8 q^{25} + 8 q^{31} + 8 q^{35} - 24 q^{41} + 8 q^{47} - 32 q^{55} - 24 q^{71} + 8 q^{73} + 32 q^{75} + 40 q^{77} - 48 q^{81} + 24 q^{85} - 40 q^{87}+O(q^{100}) \) 48 * q - 8 * q^13 - 16 * q^23 - 8 * q^25 + 8 * q^31 + 8 * q^35 - 24 * q^41 + 8 * q^47 - 32 * q^55 - 24 * q^71 + 8 * q^73 + 32 * q^75 + 40 * q^77 - 48 * q^81 + 24 * q^85 - 40 * q^87

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more