LMFDB - Embedded newform 1148.2.k.b.729.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			729.10
Character	$\chi$	$=$	1148.729
Dual form			1148.2.k.b.337.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.147004 - 0.147004i) q^{3} -2.61619i q^{5} +(0.707107 - 0.707107i) q^{7} +2.95678i q^{9} +O(q^{10})$	\(q+(0.147004 - 0.147004i) q^{3} -2.61619i q^{5} +(0.707107 - 0.707107i) q^{7} +2.95678i q^{9} +(-3.93415 + 3.93415i) q^{11} +(-4.00823 + 4.00823i) q^{13} +(-0.384591 - 0.384591i) q^{15} +(-3.80906 - 3.80906i) q^{17} +(2.63624 + 2.63624i) q^{19} -0.207895i q^{21} -6.55069 q^{23} -1.84446 q^{25} +(0.875671 + 0.875671i) q^{27} +(-5.02497 + 5.02497i) q^{29} +5.50289 q^{31} +1.15667i q^{33} +(-1.84993 - 1.84993i) q^{35} +3.96807 q^{37} +1.17845i q^{39} +(-0.0213092 + 6.40309i) q^{41} -5.74887i q^{43} +7.73551 q^{45} +(3.50887 + 3.50887i) q^{47} -1.00000i q^{49} -1.11990 q^{51} +(-5.19323 + 5.19323i) q^{53} +(10.2925 + 10.2925i) q^{55} +0.775077 q^{57} +6.18269 q^{59} +1.26120i q^{61} +(2.09076 + 2.09076i) q^{63} +(10.4863 + 10.4863i) q^{65} +(-6.45447 - 6.45447i) q^{67} +(-0.962978 + 0.962978i) q^{69} +(7.03066 - 7.03066i) q^{71} -8.69496i q^{73} +(-0.271144 + 0.271144i) q^{75} +5.56373i q^{77} +(-8.32949 + 8.32949i) q^{79} -8.61288 q^{81} -17.0514 q^{83} +(-9.96524 + 9.96524i) q^{85} +1.47738i q^{87} +(-6.59324 + 6.59324i) q^{89} +5.66849i q^{91} +(0.808947 - 0.808947i) q^{93} +(6.89692 - 6.89692i) q^{95} +(-6.38165 - 6.38165i) q^{97} +(-11.6324 - 11.6324i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.147004	−	0.147004i	0.0848728	−	0.0848728i	−0.663396	−	0.748269i	$-0.730885\pi$
$3$	0.147004	−	0.147004i	0.0848728	−	0.0848728i	0.748269	+	0.663396i	$0.230885\pi$
$4$		0			0
$5$		−	2.61619i		−	1.17000i	−0.811034	−	0.584998i	$-0.801095\pi$
$5$		−	2.61619i		−	1.17000i	0.811034	−	0.584998i	$-0.198905\pi$
$6$		0			0
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$		0			0
$9$			2.95678i			0.985593i
$10$		0			0
$11$	−3.93415	+	3.93415i	−1.18619	+	1.18619i	−0.208078	+	0.978112i	$0.566721\pi$
$11$	−3.93415	+	3.93415i	−1.18619	+	1.18619i	−0.978112	+	0.208078i	$0.933279\pi$
$12$		0			0
$13$	−4.00823	+	4.00823i	−1.11168	+	1.11168i	−0.118760	+	0.992923i	$0.537892\pi$
$13$	−4.00823	+	4.00823i	−1.11168	+	1.11168i	−0.992923	+	0.118760i	$0.962108\pi$
$14$		0			0
$15$	−0.384591	−	0.384591i	−0.0993010	−	0.0993010i
$16$		0			0
$17$	−3.80906	−	3.80906i	−0.923834	−	0.923834i	0.0734642	−	0.997298i	$-0.476595\pi$
$17$	−3.80906	−	3.80906i	−0.923834	−	0.923834i	−0.997298	+	0.0734642i	$0.976595\pi$
$18$		0			0
$19$	2.63624	+	2.63624i	0.604796	+	0.604796i	0.941581	−	0.336785i	$-0.109340\pi$
$19$	2.63624	+	2.63624i	0.604796	+	0.604796i	−0.336785	+	0.941581i	$0.609340\pi$
$20$		0			0
$21$		−	0.207895i		−	0.0453664i
$22$		0			0
$23$	−6.55069			−1.36591			−0.682957	−	0.730459i	$-0.739306\pi$
$23$	−6.55069			−1.36591			−0.682957	+	0.730459i	$0.739306\pi$
$24$		0			0
$25$	−1.84446			−0.368893
$26$		0			0
$27$	0.875671	+	0.875671i	0.168523	+	0.168523i
$28$		0			0
$29$	−5.02497	+	5.02497i	−0.933113	+	0.933113i	−0.997899	−	0.0647858i	$-0.979364\pi$
$29$	−5.02497	+	5.02497i	−0.933113	+	0.933113i	0.0647858	+	0.997899i	$0.479364\pi$
$30$		0			0
$31$	5.50289			0.988348			0.494174	−	0.869363i	$-0.335471\pi$
$31$	5.50289			0.988348			0.494174	+	0.869363i	$0.335471\pi$
$32$		0			0
$33$			1.15667i			0.201351i
$34$		0			0
$35$	−1.84993	−	1.84993i	−0.312695	−	0.312695i
$36$		0			0
$37$	3.96807			0.652347			0.326173	−	0.945310i	$-0.394241\pi$
$37$	3.96807			0.652347			0.326173	+	0.945310i	$0.394241\pi$
$38$		0			0
$39$			1.17845i			0.188703i
$40$		0			0
$41$	−0.0213092	+	6.40309i	−0.00332794	+	0.999994i
$41$	−0.0213092	+	6.40309i	−0.00332794	+	0.999994i
$42$		0			0
$43$		−	5.74887i		−	0.876695i	−0.898806	−	0.438347i	$-0.855564\pi$
$43$		−	5.74887i		−	0.876695i	0.898806	−	0.438347i	$-0.144436\pi$
$44$		0			0
$45$	7.73551			1.15314
$46$		0			0
$47$	3.50887	+	3.50887i	0.511822	+	0.511822i	0.915084	−	0.403263i	$-0.132124\pi$
$47$	3.50887	+	3.50887i	0.511822	+	0.511822i	−0.403263	+	0.915084i	$0.632124\pi$
$48$		0			0
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	−1.11990			−0.156817
$52$		0			0
$53$	−5.19323	+	5.19323i	−0.713345	+	0.713345i	−0.967233	−	0.253889i	$-0.918290\pi$
$53$	−5.19323	+	5.19323i	−0.713345	+	0.713345i	0.253889	+	0.967233i	$0.418290\pi$
$54$		0			0
$55$	10.2925	+	10.2925i	1.38784	+	1.38784i
$56$		0			0
$57$	0.775077			0.102662
$58$		0			0
$59$	6.18269			0.804917			0.402459	−	0.915438i	$-0.368156\pi$
$59$	6.18269			0.804917			0.402459	+	0.915438i	$0.368156\pi$
$60$		0			0
$61$			1.26120i			0.161480i	0.996735	+	0.0807398i	$0.0257283\pi$
$61$			1.26120i			0.161480i	−0.996735	+	0.0807398i	$0.974272\pi$
$62$		0			0
$63$	2.09076	+	2.09076i	0.263411	+	0.263411i
$64$		0			0
$65$	10.4863	+	10.4863i	1.30067	+	1.30067i
$66$		0			0
$67$	−6.45447	−	6.45447i	−0.788539	−	0.788539i	0.192716	−	0.981255i	$-0.438270\pi$
$67$	−6.45447	−	6.45447i	−0.788539	−	0.788539i	−0.981255	+	0.192716i	$0.938270\pi$
$68$		0			0
$69$	−0.962978	+	0.962978i	−0.115929	+	0.115929i
$70$		0			0
$71$	7.03066	−	7.03066i	0.834386	−	0.834386i	−0.153728	−	0.988113i	$-0.549128\pi$
$71$	7.03066	−	7.03066i	0.834386	−	0.834386i	0.988113	+	0.153728i	$0.0491279\pi$
$72$		0			0
$73$		−	8.69496i		−	1.01767i	−0.860865	−	0.508834i	$-0.830077\pi$
$73$		−	8.69496i		−	1.01767i	0.860865	−	0.508834i	$-0.169923\pi$
$74$		0			0
$75$	−0.271144	+	0.271144i	−0.0313090	+	0.0313090i
$76$		0			0
$77$			5.56373i			0.634045i
$78$		0			0
$79$	−8.32949	+	8.32949i	−0.937140	+	0.937140i	−0.998138	−	0.0609974i	$-0.980572\pi$
$79$	−8.32949	+	8.32949i	−0.937140	+	0.937140i	0.0609974	+	0.998138i	$0.480572\pi$
$80$		0			0
$81$	−8.61288			−0.956987
$82$		0			0
$83$	−17.0514			−1.87164			−0.935820	−	0.352479i	$-0.885339\pi$
$83$	−17.0514			−1.87164			−0.935820	+	0.352479i	$0.885339\pi$
$84$		0			0
$85$	−9.96524	+	9.96524i	−1.08088	+	1.08088i
$86$		0			0
$87$			1.47738i			0.158392i
$88$		0			0
$89$	−6.59324	+	6.59324i	−0.698882	+	0.698882i	−0.964169	−	0.265287i	$-0.914533\pi$
$89$	−6.59324	+	6.59324i	−0.698882	+	0.698882i	0.265287	+	0.964169i	$0.414533\pi$
$90$		0			0
$91$			5.66849i			0.594220i
$92$		0			0
$93$	0.808947	−	0.808947i	0.0838839	−	0.0838839i
$94$		0			0
$95$	6.89692	−	6.89692i	0.707610	−	0.707610i
$96$		0			0
$97$	−6.38165	−	6.38165i	−0.647958	−	0.647958i	0.304541	−	0.952499i	$-0.401497\pi$
$97$	−6.38165	−	6.38165i	−0.647958	−	0.647958i	−0.952499	+	0.304541i	$0.901497\pi$
$98$		0			0
$99$	−11.6324	−	11.6324i	−1.16910	−	1.16910i
$100$		0			0
$101$	4.56995	+	4.56995i	0.454727	+	0.454727i	0.896920	−	0.442193i	$-0.145799\pi$
$101$	4.56995	+	4.56995i	0.454727	+	0.454727i	−0.442193	+	0.896920i	$0.645799\pi$
$102$		0			0
$103$		−	1.23098i		−	0.121292i	−0.998159	−	0.0606459i	$-0.980684\pi$
$103$		−	1.23098i		−	0.121292i	0.998159	−	0.0606459i	$-0.0193161\pi$
$104$		0			0
$105$	−0.543894			−0.0530786
$106$		0			0
$107$	8.18167			0.790952			0.395476	−	0.918476i	$-0.370580\pi$
$107$	8.18167			0.790952			0.395476	+	0.918476i	$0.370580\pi$
$108$		0			0
$109$	4.30375	+	4.30375i	0.412225	+	0.412225i	0.882513	−	0.470288i	$-0.155850\pi$
$109$	4.30375	+	4.30375i	0.412225	+	0.412225i	−0.470288	+	0.882513i	$0.655850\pi$
$110$		0			0
$111$	0.583322	−	0.583322i	0.0553665	−	0.0553665i
$112$		0			0
$113$	−19.3440			−1.81973			−0.909863	−	0.414908i	$-0.863814\pi$
$113$	−19.3440			−1.81973			−0.909863	+	0.414908i	$0.863814\pi$
$114$		0			0
$115$			17.1379i			1.59811i
$116$		0			0
$117$	−11.8515	−	11.8515i	−1.09567	−	1.09567i
$118$		0			0
$119$	−5.38683			−0.493810
$120$		0			0
$121$		−	19.9550i		−	1.81410i
$122$		0			0
$123$	0.938148	+	0.944413i	0.0845899	+	0.0851548i
$124$		0			0
$125$		−	8.25549i		−	0.738393i
$126$		0			0
$127$	5.00156			0.443817			0.221909	−	0.975067i	$-0.428771\pi$
$127$	5.00156			0.443817			0.221909	+	0.975067i	$0.428771\pi$
$128$		0			0
$129$	−0.845108	−	0.845108i	−0.0744076	−	0.0744076i
$130$		0			0
$131$			1.29068i			0.112767i	0.998409	+	0.0563836i	$0.0179570\pi$
$131$			1.29068i			0.112767i	−0.998409	+	0.0563836i	$0.982043\pi$
$132$		0			0
$133$	3.72821			0.323277
$134$		0			0
$135$	2.29092	−	2.29092i	0.197171	−	0.197171i
$136$		0			0
$137$	3.22286	+	3.22286i	0.275347	+	0.275347i	0.831248	−	0.555901i	$-0.187627\pi$
$137$	3.22286	+	3.22286i	0.275347	+	0.275347i	−0.555901	+	0.831248i	$0.687627\pi$
$138$		0			0
$139$	17.4218			1.47770			0.738850	−	0.673870i	$-0.235369\pi$
$139$	17.4218			1.47770			0.738850	+	0.673870i	$0.235369\pi$
$140$		0			0
$141$	1.03164			0.0868795
$142$		0			0
$143$		−	31.5379i		−	2.63734i
$144$		0			0
$145$	13.1463	+	13.1463i	1.09174	+	1.09174i
$146$		0			0
$147$	−0.147004	−	0.147004i	−0.0121247	−	0.0121247i
$148$		0			0
$149$	11.6075	+	11.6075i	0.950922	+	0.950922i	0.998851	−	0.0479289i	$-0.0152621\pi$
$149$	11.6075	+	11.6075i	0.950922	+	0.950922i	−0.0479289	+	0.998851i	$0.515262\pi$
$150$		0			0
$151$	2.69241	−	2.69241i	0.219105	−	0.219105i	−0.589016	−	0.808121i	$-0.700485\pi$
$151$	2.69241	−	2.69241i	0.219105	−	0.219105i	0.808121	+	0.589016i	$0.200485\pi$
$152$		0			0
$153$	11.2626	−	11.2626i	0.910524	−	0.910524i
$154$		0			0
$155$		−	14.3966i		−	1.15636i
$156$		0			0
$157$	−10.4484	+	10.4484i	−0.833872	+	0.833872i	−0.988044	−	0.154172i	$-0.950729\pi$
$157$	−10.4484	+	10.4484i	−0.833872	+	0.833872i	0.154172	+	0.988044i	$0.450729\pi$
$158$		0			0
$159$			1.52685i			0.121087i
$160$		0			0
$161$	−4.63204	+	4.63204i	−0.365056	+	0.365056i
$162$		0			0
$163$	−4.99749			−0.391434			−0.195717	−	0.980660i	$-0.562703\pi$
$163$	−4.99749			−0.391434			−0.195717	+	0.980660i	$0.562703\pi$
$164$		0			0
$165$	3.02608			0.235580
$166$		0			0
$167$	4.83692	−	4.83692i	0.374292	−	0.374292i	−0.494746	−	0.869038i	$-0.664739\pi$
$167$	4.83692	−	4.83692i	0.374292	−	0.374292i	0.869038	+	0.494746i	$0.164739\pi$
$168$		0			0
$169$		−	19.1318i		−	1.47168i
$170$		0			0
$171$	−7.79479	+	7.79479i	−0.596083	+	0.596083i
$172$		0			0
$173$			16.9725i			1.29039i	0.764016	+	0.645197i	$0.223225\pi$
$173$			16.9725i			1.29039i	−0.764016	+	0.645197i	$0.776775\pi$
$174$		0			0
$175$	−1.30423	+	1.30423i	−0.0985907	+	0.0985907i
$176$		0			0
$177$	0.908880	−	0.908880i	0.0683156	−	0.0683156i
$178$		0			0
$179$	−2.54257	−	2.54257i	−0.190041	−	0.190041i	0.605673	−	0.795714i	$-0.292904\pi$
$179$	−2.54257	−	2.54257i	−0.190041	−	0.190041i	−0.795714	+	0.605673i	$0.792904\pi$
$180$		0			0
$181$	8.26228	+	8.26228i	0.614131	+	0.614131i	0.944020	−	0.329889i	$-0.107011\pi$
$181$	8.26228	+	8.26228i	0.614131	+	0.614131i	−0.329889	+	0.944020i	$0.607011\pi$
$182$		0			0
$183$	0.185401	+	0.185401i	0.0137052	+	0.0137052i
$184$		0			0
$185$		−	10.3812i		−	0.763244i
$186$		0			0
$187$	29.9708			2.19169
$188$		0			0
$189$	1.23839			0.0900793
$190$		0			0
$191$	1.40300	+	1.40300i	0.101518	+	0.101518i	0.756041	−	0.654524i	$-0.227131\pi$
$191$	1.40300	+	1.40300i	0.101518	+	0.101518i	−0.654524	+	0.756041i	$0.727131\pi$
$192$		0			0
$193$	−7.76154	+	7.76154i	−0.558688	+	0.558688i	−0.928934	−	0.370246i	$-0.879273\pi$
$193$	−7.76154	+	7.76154i	−0.558688	+	0.558688i	0.370246	+	0.928934i	$0.379273\pi$
$194$		0			0
$195$	3.08306			0.220782
$196$		0			0
$197$			18.3831i			1.30974i	0.755742	+	0.654870i	$0.227277\pi$
$197$			18.3831i			1.30974i	−0.755742	+	0.654870i	$0.772723\pi$
$198$		0			0
$199$	−7.84594	−	7.84594i	−0.556184	−	0.556184i	0.372035	−	0.928219i	$-0.378660\pi$
$199$	−7.84594	−	7.84594i	−0.556184	−	0.556184i	−0.928219	+	0.372035i	$0.878660\pi$
$200$		0			0
$201$	−1.89767			−0.133851
$202$		0			0
$203$			7.10638i			0.498770i
$204$		0			0
$205$	16.7517	+	0.0557490i	1.16999	+	0.00389368i
$206$		0			0
$207$		−	19.3690i		−	1.34624i
$208$		0			0
$209$	−20.7428			−1.43481
$210$		0			0
$211$	−7.80238	−	7.80238i	−0.537138	−	0.537138i	0.385549	−	0.922687i	$-0.374012\pi$
$211$	−7.80238	−	7.80238i	−0.537138	−	0.537138i	−0.922687	+	0.385549i	$0.874012\pi$
$212$		0			0
$213$		−	2.06707i		−	0.141633i
$214$		0			0
$215$	−15.0402			−1.02573
$216$		0			0
$217$	3.89113	−	3.89113i	0.264147	−	0.264147i
$218$		0			0
$219$	−1.27819	−	1.27819i	−0.0863724	−	0.0863724i
$220$		0			0
$221$	30.5352			2.05402
$222$		0			0
$223$	−8.29621			−0.555555			−0.277777	−	0.960645i	$-0.589598\pi$
$223$	−8.29621			−0.555555			−0.277777	+	0.960645i	$0.589598\pi$
$224$		0			0
$225$		−	5.45367i		−	0.363578i
$226$		0			0
$227$	−11.6971	−	11.6971i	−0.776361	−	0.776361i	0.202849	−	0.979210i	$-0.434980\pi$
$227$	−11.6971	−	11.6971i	−0.776361	−	0.776361i	−0.979210	+	0.202849i	$0.934980\pi$
$228$		0			0
$229$	11.7017	+	11.7017i	0.773269	+	0.773269i	0.978676	−	0.205408i	$-0.0658521\pi$
$229$	11.7017	+	11.7017i	0.773269	+	0.773269i	−0.205408	+	0.978676i	$0.565852\pi$
$230$		0			0
$231$	0.817890	+	0.817890i	0.0538132	+	0.0538132i
$232$		0			0
$233$	0.269706	−	0.269706i	0.0176690	−	0.0176690i	−0.698217	−	0.715886i	$-0.746023\pi$
$233$	0.269706	−	0.269706i	0.0176690	−	0.0176690i	0.715886	+	0.698217i	$0.246023\pi$
$234$		0			0
$235$	9.17989	−	9.17989i	0.598830	−	0.598830i
$236$		0			0
$237$			2.44894i			0.159076i
$238$		0			0
$239$	19.7538	−	19.7538i	1.27777	−	1.27777i	0.335854	−	0.941914i	$-0.390975\pi$
$239$	19.7538	−	19.7538i	1.27777	−	1.27777i	0.941914	−	0.335854i	$-0.109025\pi$
$240$		0			0
$241$		−	4.20799i		−	0.271061i	−0.990773	−	0.135530i	$-0.956726\pi$
$241$		−	4.20799i		−	0.271061i	0.990773	−	0.135530i	$-0.0432738\pi$
$242$		0			0
$243$	−3.89314	+	3.89314i	−0.249745	+	0.249745i
$244$		0			0
$245$	−2.61619			−0.167142
$246$		0			0
$247$	−21.1334			−1.34468
$248$		0			0
$249$	−2.50663	+	2.50663i	−0.158851	+	0.158851i
$250$		0			0
$251$		−	1.41815i		−	0.0895131i	−0.998998	−	0.0447565i	$-0.985749\pi$
$251$		−	1.41815i		−	0.0895131i	0.998998	−	0.0447565i	$-0.0142512\pi$
$252$		0			0
$253$	25.7714	−	25.7714i	1.62023	−	1.62023i
$254$		0			0
$255$			2.92986i			0.183475i
$256$		0			0
$257$	−7.53877	+	7.53877i	−0.470255	+	0.470255i	−0.901997	−	0.431742i	$-0.857899\pi$
$257$	−7.53877	+	7.53877i	−0.470255	+	0.470255i	0.431742	+	0.901997i	$0.357899\pi$
$258$		0			0
$259$	2.80585	−	2.80585i	0.174347	−	0.174347i
$260$		0			0
$261$	−14.8577	−	14.8577i	−0.919670	−	0.919670i
$262$		0			0
$263$	−0.862520	−	0.862520i	−0.0531853	−	0.0531853i	0.680014	−	0.733199i	$-0.261974\pi$
$263$	−0.862520	−	0.862520i	−0.0531853	−	0.0531853i	−0.733199	+	0.680014i	$0.761974\pi$
$264$		0			0
$265$	13.5865	+	13.5865i	0.834611	+	0.834611i
$266$		0			0
$267$			1.93847i			0.118632i
$268$		0			0
$269$	−28.7744			−1.75440			−0.877202	−	0.480121i	$-0.840593\pi$
$269$	−28.7744			−1.75440			−0.877202	+	0.480121i	$0.840593\pi$
$270$		0			0
$271$	21.4026			1.30012			0.650058	−	0.759884i	$-0.274744\pi$
$271$	21.4026			1.30012			0.650058	+	0.759884i	$0.274744\pi$
$272$		0			0
$273$	0.833292	+	0.833292i	0.0504331	+	0.0504331i
$274$		0			0
$275$	7.25639	−	7.25639i	0.437577	−	0.437577i
$276$		0			0
$277$	−6.24067			−0.374966			−0.187483	−	0.982268i	$-0.560033\pi$
$277$	−6.24067			−0.374966			−0.187483	+	0.982268i	$0.560033\pi$
$278$		0			0
$279$			16.2708i			0.974109i
$280$		0			0
$281$	−6.15101	−	6.15101i	−0.366938	−	0.366938i	0.499421	−	0.866359i	$-0.333546\pi$
$281$	−6.15101	−	6.15101i	−0.366938	−	0.366938i	−0.866359	+	0.499421i	$0.833546\pi$
$282$		0			0
$283$	14.6949			0.873521			0.436761	−	0.899578i	$-0.356126\pi$
$283$	14.6949			0.873521			0.436761	+	0.899578i	$0.356126\pi$
$284$		0			0
$285$		−	2.02775i		−	0.120114i
$286$		0			0
$287$	4.51260	+	4.54274i	0.266370	+	0.268149i
$288$		0			0
$289$			12.0179i			0.706937i
$290$		0			0
$291$	−1.87626			−0.109988
$292$		0			0
$293$	16.0401	+	16.0401i	0.937076	+	0.937076i	0.998134	−	0.0610587i	$-0.0194477\pi$
$293$	16.0401	+	16.0401i	0.937076	+	0.937076i	−0.0610587	+	0.998134i	$0.519448\pi$
$294$		0			0
$295$		−	16.1751i		−	0.941751i
$296$		0			0
$297$	−6.89004			−0.399801
$298$		0			0
$299$	26.2567	−	26.2567i	1.51846	−	1.51846i
$300$		0			0
$301$	−4.06507	−	4.06507i	−0.234307	−	0.234307i
$302$		0			0
$303$	1.34360			0.0771880
$304$		0			0
$305$	3.29953			0.188931
$306$		0			0
$307$			12.1604i			0.694030i	0.937860	+	0.347015i	$0.112805\pi$
$307$			12.1604i			0.694030i	−0.937860	+	0.347015i	$0.887195\pi$
$308$		0			0
$309$	−0.180959	−	0.180959i	−0.0102944	−	0.0102944i
$310$		0			0
$311$	−13.8654	−	13.8654i	−0.786233	−	0.786233i	0.194642	−	0.980874i	$-0.437646\pi$
$311$	−13.8654	−	13.8654i	−0.786233	−	0.786233i	−0.980874	+	0.194642i	$0.937646\pi$
$312$		0			0
$313$	−0.416709	−	0.416709i	−0.0235538	−	0.0235538i	0.695232	−	0.718786i	$-0.255302\pi$
$313$	−0.416709	−	0.416709i	−0.0235538	−	0.0235538i	−0.718786	+	0.695232i	$0.755302\pi$
$314$		0			0
$315$	5.46983	−	5.46983i	0.308190	−	0.308190i
$316$		0			0
$317$	−3.09378	+	3.09378i	−0.173764	+	0.173764i	−0.788631	−	0.614867i	$-0.789210\pi$
$317$	−3.09378	+	3.09378i	−0.173764	+	0.173764i	0.614867	+	0.788631i	$0.289210\pi$
$318$		0			0
$319$		−	39.5379i		−	2.21370i
$320$		0			0
$321$	1.20274	−	1.20274i	0.0671304	−	0.0671304i
$322$		0			0
$323$		−	20.0832i		−	1.11746i
$324$		0			0
$325$	7.39304	−	7.39304i	0.410092	−	0.410092i
$326$		0			0
$327$	1.26534			0.0699733
$328$		0			0
$329$	4.96229			0.273580
$330$		0			0
$331$	−7.21883	+	7.21883i	−0.396783	+	0.396783i	−0.877097	−	0.480314i	$-0.840523\pi$
$331$	−7.21883	+	7.21883i	−0.396783	+	0.396783i	0.480314	+	0.877097i	$0.340523\pi$
$332$		0			0
$333$			11.7327i			0.642949i
$334$		0			0
$335$	−16.8861	+	16.8861i	−0.922588	+	0.922588i
$336$		0			0
$337$		−	23.2574i		−	1.26691i	−0.773779	−	0.633456i	$-0.781636\pi$
$337$		−	23.2574i		−	1.26691i	0.773779	−	0.633456i	$-0.218364\pi$
$338$		0			0
$339$	−2.84364	+	2.84364i	−0.154445	+	0.154445i
$340$		0			0
$341$	−21.6492	+	21.6492i	−1.17237	+	1.17237i
$342$		0			0
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$		0			0
$345$	2.51934	+	2.51934i	0.135637	+	0.135637i
$346$		0			0
$347$	−13.3285	−	13.3285i	−0.715512	−	0.715512i	0.252171	−	0.967683i	$-0.418856\pi$
$347$	−13.3285	−	13.3285i	−0.715512	−	0.715512i	−0.967683	+	0.252171i	$0.918856\pi$
$348$		0			0
$349$			20.2304i			1.08291i	0.840730	+	0.541454i	$0.182126\pi$
$349$			20.2304i			1.08291i	−0.840730	+	0.541454i	$0.817874\pi$
$350$		0			0
$351$	−7.01978			−0.374688
$352$		0			0
$353$	16.4554			0.875830			0.437915	−	0.899016i	$-0.355717\pi$
$353$	16.4554			0.875830			0.437915	+	0.899016i	$0.355717\pi$
$354$		0			0
$355$	−18.3936	−	18.3936i	−0.976229	−	0.976229i
$356$		0			0
$357$	−0.791886	+	0.791886i	−0.0419110	+	0.0419110i
$358$		0			0
$359$	8.63094			0.455524			0.227762	−	0.973717i	$-0.426859\pi$
$359$	8.63094			0.455524			0.227762	+	0.973717i	$0.426859\pi$
$360$		0			0
$361$		−	5.10043i		−	0.268444i
$362$		0			0
$363$	−2.93347	−	2.93347i	−0.153967	−	0.153967i
$364$		0			0
$365$	−22.7477			−1.19067
$366$		0			0
$367$			3.72546i			0.194467i	0.995262	+	0.0972337i	$0.0309994\pi$
$367$			3.72546i			0.194467i	−0.995262	+	0.0972337i	$0.969001\pi$
$368$		0			0
$369$	−18.9325	−	0.0630066i	−0.985588	−	0.00327999i
$370$		0			0
$371$			7.34433i			0.381299i
$372$		0			0
$373$	−23.7762			−1.23108			−0.615542	−	0.788104i	$-0.711063\pi$
$373$	−23.7762			−1.23108			−0.615542	+	0.788104i	$0.711063\pi$
$374$		0			0
$375$	−1.21359	−	1.21359i	−0.0626695	−	0.0626695i
$376$		0			0
$377$		−	40.2825i		−	2.07465i
$378$		0			0
$379$	33.9921			1.74606			0.873029	−	0.487669i	$-0.162153\pi$
$379$	33.9921			1.74606			0.873029	+	0.487669i	$0.162153\pi$
$380$		0			0
$381$	0.735250	−	0.735250i	0.0376680	−	0.0376680i
$382$		0			0
$383$	1.34885	+	1.34885i	0.0689230	+	0.0689230i	0.740728	−	0.671805i	$-0.234481\pi$
$383$	1.34885	+	1.34885i	0.0689230	+	0.0689230i	−0.671805	+	0.740728i	$0.734481\pi$
$384$		0			0
$385$	14.5558			0.741831
$386$		0			0
$387$	16.9981			0.864065
$388$		0			0
$389$		−	29.4146i		−	1.49138i	−0.666294	−	0.745689i	$-0.732120\pi$
$389$		−	29.4146i		−	1.49138i	0.666294	−	0.745689i	$-0.267880\pi$
$390$		0			0
$391$	24.9520	+	24.9520i	1.26188	+	1.26188i
$392$		0			0
$393$	0.189735	+	0.189735i	0.00957088	+	0.00957088i
$394$		0			0
$395$	21.7915	+	21.7915i	1.09645	+	1.09645i
$396$		0			0
$397$	14.1375	−	14.1375i	0.709541	−	0.709541i	−0.256898	−	0.966439i	$-0.582700\pi$
$397$	14.1375	−	14.1375i	0.709541	−	0.709541i	0.966439	+	0.256898i	$0.0827003\pi$
$398$		0			0
$399$	0.548062	−	0.548062i	0.0274374	−	0.0274374i
$400$		0			0
$401$			1.00724i			0.0502991i	0.999684	+	0.0251495i	$0.00800619\pi$
$401$			1.00724i			0.0502991i	−0.999684	+	0.0251495i	$0.991994\pi$
$402$		0			0
$403$	−22.0568	+	22.0568i	−1.09873	+	1.09873i
$404$		0			0
$405$			22.5330i			1.11967i
$406$		0			0
$407$	−15.6110	+	15.6110i	−0.773807	+	0.773807i
$408$		0			0
$409$	−5.37330			−0.265692			−0.132846	−	0.991137i	$-0.542412\pi$
$409$	−5.37330			−0.265692			−0.132846	+	0.991137i	$0.542412\pi$
$410$		0			0
$411$	0.947546			0.0467390
$412$		0			0
$413$	4.37182	−	4.37182i	0.215123	−	0.215123i
$414$		0			0
$415$			44.6099i			2.18981i
$416$		0			0
$417$	2.56108	−	2.56108i	0.125417	−	0.125417i
$418$		0			0
$419$		−	23.7358i		−	1.15957i	−0.814770	−	0.579784i	$-0.803137\pi$
$419$		−	23.7358i		−	1.15957i	0.814770	−	0.579784i	$-0.196863\pi$
$420$		0			0
$421$	−10.3142	+	10.3142i	−0.502682	+	0.502682i	−0.912270	−	0.409589i	$-0.865672\pi$
$421$	−10.3142	+	10.3142i	−0.502682	+	0.502682i	0.409589	+	0.912270i	$0.365672\pi$
$422$		0			0
$423$	−10.3750	+	10.3750i	−0.504448	+	0.504448i
$424$		0			0
$425$	7.02568	+	7.02568i	0.340796	+	0.340796i
$426$		0			0
$427$	0.891801	+	0.891801i	0.0431573	+	0.0431573i
$428$		0			0
$429$	−4.63621	−	4.63621i	−0.223838	−	0.223838i
$430$		0			0
$431$			17.0622i			0.821858i	0.911667	+	0.410929i	$0.134796\pi$
$431$			17.0622i			0.821858i	−0.911667	+	0.410929i	$0.865204\pi$
$432$		0			0
$433$	5.09967			0.245074			0.122537	−	0.992464i	$-0.460897\pi$
$433$	5.09967			0.245074			0.122537	+	0.992464i	$0.460897\pi$
$434$		0			0
$435$	3.86512			0.185318
$436$		0			0
$437$	−17.2692	−	17.2692i	−0.826099	−	0.826099i
$438$		0			0
$439$	−6.54986	+	6.54986i	−0.312608	+	0.312608i	−0.845919	−	0.533311i	$-0.820947\pi$
$439$	−6.54986	+	6.54986i	−0.312608	+	0.312608i	0.533311	+	0.845919i	$0.320947\pi$
$440$		0			0
$441$	2.95678			0.140799
$442$		0			0
$443$			34.2324i			1.62643i	0.581962	+	0.813216i	$0.302285\pi$
$443$			34.2324i			1.62643i	−0.581962	+	0.813216i	$0.697715\pi$
$444$		0			0
$445$	17.2492	+	17.2492i	0.817690	+	0.817690i
$446$		0			0
$447$	3.41269			0.161415
$448$		0			0
$449$		−	38.5413i		−	1.81887i	−0.415841	−	0.909437i	$-0.636513\pi$
$449$		−	38.5413i		−	1.81887i	0.415841	−	0.909437i	$-0.363487\pi$
$450$		0			0
$451$	−25.1069	−	25.2745i	−1.18224	−	1.19013i
$452$		0			0
$453$		−	0.791589i		−	0.0371921i
$454$		0			0
$455$	14.8299			0.695235
$456$		0			0
$457$	14.4341	+	14.4341i	0.675200	+	0.675200i	0.958910	−	0.283710i	$-0.0915653\pi$
$457$	14.4341	+	14.4341i	0.675200	+	0.675200i	−0.283710	+	0.958910i	$0.591565\pi$
$458$		0			0
$459$		−	6.67097i		−	0.311374i
$460$		0			0
$461$	−5.54610			−0.258308			−0.129154	−	0.991625i	$-0.541226\pi$
$461$	−5.54610			−0.258308			−0.129154	+	0.991625i	$0.541226\pi$
$462$		0			0
$463$	−26.0335	+	26.0335i	−1.20988	+	1.20988i	−0.238816	+	0.971065i	$0.576759\pi$
$463$	−26.0335	+	26.0335i	−1.20988	+	1.20988i	−0.971065	+	0.238816i	$0.923241\pi$
$464$		0			0
$465$	−2.11636	−	2.11636i	−0.0981439	−	0.0981439i
$466$		0			0
$467$	35.6276			1.64865			0.824324	−	0.566118i	$-0.191555\pi$
$467$	35.6276			1.64865			0.824324	+	0.566118i	$0.191555\pi$
$468$		0			0
$469$	−9.12800			−0.421492
$470$		0			0
$471$			3.07191i			0.141546i
$472$		0			0
$473$	22.6169	+	22.6169i	1.03993	+	1.03993i
$474$		0			0
$475$	−4.86246	−	4.86246i	−0.223105	−	0.223105i
$476$		0			0
$477$	−15.3552	−	15.3552i	−0.703068	−	0.703068i
$478$		0			0
$479$	8.89051	−	8.89051i	0.406218	−	0.406218i	−0.474200	−	0.880417i	$-0.657263\pi$
$479$	8.89051	−	8.89051i	0.406218	−	0.406218i	0.880417	+	0.474200i	$0.157263\pi$
$480$		0			0
$481$	−15.9049	+	15.9049i	−0.725203	+	0.725203i
$482$		0			0
$483$			1.36186i			0.0619666i
$484$		0			0
$485$	−16.6956	+	16.6956i	−0.758109	+	0.758109i
$486$		0			0
$487$			5.72829i			0.259573i	0.991542	+	0.129787i	$0.0414293\pi$
$487$			5.72829i			0.259573i	−0.991542	+	0.129787i	$0.958571\pi$
$488$		0			0
$489$	−0.734651	+	0.734651i	−0.0332221	+	0.0332221i
$490$		0			0
$491$	−3.18019			−0.143520			−0.0717600	−	0.997422i	$-0.522862\pi$
$491$	−3.18019			−0.143520			−0.0717600	+	0.997422i	$0.522862\pi$
$492$		0			0
$493$	38.2809			1.72408
$494$		0			0
$495$	−30.4326	+	30.4326i	−1.36784	+	1.36784i
$496$		0			0
$497$		−	9.94285i		−	0.445998i
$498$		0			0
$499$	24.4414	−	24.4414i	1.09415	−	1.09415i	0.0990657	−	0.995081i	$-0.468415\pi$
$499$	24.4414	−	24.4414i	1.09415	−	1.09415i	0.995081	−	0.0990657i	$-0.0315854\pi$
$500$		0			0
$501$		−	1.42209i		−	0.0635345i
$502$		0			0
$503$	18.0344	−	18.0344i	0.804114	−	0.804114i	−0.179622	−	0.983736i	$-0.557487\pi$
$503$	18.0344	−	18.0344i	0.804114	−	0.804114i	0.983736	+	0.179622i	$0.0574874\pi$
$504$		0			0
$505$	11.9559	−	11.9559i	0.532029	−	0.532029i
$506$		0			0
$507$	−2.81246	−	2.81246i	−0.124906	−	0.124906i
$508$		0			0
$509$	4.87660	+	4.87660i	0.216151	+	0.216151i	0.806874	−	0.590723i	$-0.201157\pi$
$509$	4.87660	+	4.87660i	0.216151	+	0.216151i	−0.590723	+	0.806874i	$0.701157\pi$
$510$		0			0
$511$	−6.14827	−	6.14827i	−0.271983	−	0.271983i
$512$		0			0
$513$			4.61697i			0.203844i
$514$		0			0
$515$	−3.22048			−0.141911
$516$		0			0
$517$	−27.6088			−1.21424
$518$		0			0
$519$	2.49502	+	2.49502i	0.109519	+	0.109519i
$520$		0			0
$521$	−9.83224	+	9.83224i	−0.430758	+	0.430758i	−0.888886	−	0.458128i	$-0.848520\pi$
$521$	−9.83224	+	9.83224i	−0.430758	+	0.430758i	0.458128	+	0.888886i	$0.348520\pi$
$522$		0			0
$523$	−7.21345			−0.315422			−0.157711	−	0.987485i	$-0.550411\pi$
$523$	−7.21345			−0.315422			−0.157711	+	0.987485i	$0.550411\pi$
$524$		0			0
$525$			0.383455i			0.0167354i
$526$		0			0
$527$	−20.9609	−	20.9609i	−0.913069	−	0.913069i
$528$		0			0
$529$	19.9116			0.865720
$530$		0			0
$531$			18.2808i			0.793321i
$532$		0			0
$533$	−25.5796	−	25.7505i	−1.10798	−	1.11538i
$534$		0			0
$535$		−	21.4048i		−	0.925412i
$536$		0			0
$537$	−0.747536			−0.0322586
$538$		0			0
$539$	3.93415	+	3.93415i	0.169456	+	0.169456i
$540$		0			0
$541$			38.2955i			1.64645i	0.567714	+	0.823226i	$0.307828\pi$
$541$			38.2955i			1.64645i	−0.567714	+	0.823226i	$0.692172\pi$
$542$		0			0
$543$	2.42918			0.104246
$544$		0			0
$545$	11.2594	−	11.2594i	0.482301	−	0.482301i
$546$		0			0
$547$	22.5254	+	22.5254i	0.963115	+	0.963115i	0.999344	−	0.0362285i	$-0.0115344\pi$
$547$	22.5254	+	22.5254i	0.963115	+	0.963115i	−0.0362285	+	0.999344i	$0.511534\pi$
$548$		0			0
$549$	−3.72908			−0.159153
$550$		0			0
$551$	−26.4941			−1.12869
$552$		0			0
$553$			11.7797i			0.500923i
$554$		0			0
$555$	−1.52608	−	1.52608i	−0.0647787	−	0.0647787i
$556$		0			0
$557$	−26.5838	−	26.5838i	−1.12639	−	1.12639i	−0.990759	−	0.135634i	$-0.956693\pi$
$557$	−26.5838	−	26.5838i	−1.12639	−	1.12639i	−0.135634	−	0.990759i	$-0.543307\pi$
$558$		0			0
$559$	23.0428	+	23.0428i	0.974607	+	0.974607i
$560$		0			0
$561$	4.40584	−	4.40584i	0.186015	−	0.186015i
$562$		0			0
$563$	−1.96161	+	1.96161i	−0.0826722	+	0.0826722i	−0.747234	−	0.664561i	$-0.768618\pi$
$563$	−1.96161	+	1.96161i	−0.0826722	+	0.0826722i	0.664561	+	0.747234i	$0.268618\pi$
$564$		0			0
$565$			50.6075i			2.12907i
$566$		0			0
$567$	−6.09023	+	6.09023i	−0.255766	+	0.255766i
$568$		0			0
$569$			32.9570i			1.38163i	0.723031	+	0.690816i	$0.242748\pi$
$569$			32.9570i			1.38163i	−0.723031	+	0.690816i	$0.757252\pi$
$570$		0			0
$571$	−28.9481	+	28.9481i	−1.21144	+	1.21144i	−0.240886	+	0.970553i	$0.577438\pi$
$571$	−28.9481	+	28.9481i	−1.21144	+	1.21144i	−0.970553	+	0.240886i	$0.922562\pi$
$572$		0			0
$573$	0.412494			0.0172322
$574$		0			0
$575$	12.0825			0.503876
$576$		0			0
$577$	16.5820	−	16.5820i	0.690317	−	0.690317i	−0.271985	−	0.962302i	$-0.587680\pi$
$577$	16.5820	−	16.5820i	0.690317	−	0.690317i	0.962302	+	0.271985i	$0.0876801\pi$
$578$		0			0
$579$			2.28195i			0.0948348i
$580$		0			0
$581$	−12.0572	+	12.0572i	−0.500217	+	0.500217i
$582$		0			0
$583$		−	40.8619i		−	1.69233i
$584$		0			0
$585$	−31.0057	+	31.0057i	−1.28193	+	1.28193i
$586$		0			0
$587$	8.44304	−	8.44304i	0.348481	−	0.348481i	−0.511062	−	0.859544i	$-0.670748\pi$
$587$	8.44304	−	8.44304i	0.348481	−	0.348481i	0.859544	+	0.511062i	$0.170748\pi$
$588$		0			0
$589$	14.5070	+	14.5070i	0.597749	+	0.597749i
$590$		0			0
$591$	2.70239	+	2.70239i	0.111161	+	0.111161i
$592$		0			0
$593$	22.7237	+	22.7237i	0.933149	+	0.933149i	0.997901	−	0.0647527i	$-0.0206259\pi$
$593$	22.7237	+	22.7237i	0.933149	+	0.933149i	−0.0647527	+	0.997901i	$0.520626\pi$
$594$		0			0
$595$			14.0930i			0.577756i
$596$		0			0
$597$	−2.30677			−0.0944099
$598$		0			0
$599$	21.0230			0.858975			0.429487	−	0.903073i	$-0.358694\pi$
$599$	21.0230			0.858975			0.429487	+	0.903073i	$0.358694\pi$
$600$		0			0
$601$	15.6364	+	15.6364i	0.637823	+	0.637823i	0.950018	−	0.312195i	$-0.101064\pi$
$601$	15.6364	+	15.6364i	0.637823	+	0.637823i	−0.312195	+	0.950018i	$0.601064\pi$
$602$		0			0
$603$	19.0844	−	19.0844i	0.777179	−	0.777179i
$604$		0			0
$605$	−52.2062			−2.12249
$606$		0			0
$607$			20.3207i			0.824793i	0.911005	+	0.412396i	$0.135308\pi$
$607$			20.3207i			0.824793i	−0.911005	+	0.412396i	$0.864692\pi$
$608$		0			0
$609$	1.04467	+	1.04467i	0.0423320	+	0.0423320i
$610$		0			0
$611$	−28.1287			−1.13797
$612$		0			0
$613$		−	36.4246i		−	1.47118i	−0.677428	−	0.735589i	$-0.736906\pi$
$613$		−	36.4246i		−	1.47118i	0.677428	−	0.735589i	$-0.263094\pi$
$614$		0			0
$615$	2.47077	−	2.45437i	0.0996309	−	0.0989699i
$616$		0			0
$617$			1.60897i			0.0647748i	0.999475	+	0.0323874i	$0.0103110\pi$
$617$			1.60897i			0.0647748i	−0.999475	+	0.0323874i	$0.989689\pi$
$618$		0			0
$619$	17.0273			0.684383			0.342192	−	0.939630i	$-0.388831\pi$
$619$	17.0273			0.684383			0.342192	+	0.939630i	$0.388831\pi$
$620$		0			0
$621$	−5.73625	−	5.73625i	−0.230188	−	0.230188i
$622$		0			0
$623$			9.32425i			0.373568i
$624$		0			0
$625$	−30.8203			−1.23281
$626$		0			0
$627$	−3.04927	+	3.04927i	−0.121776	+	0.121776i
$628$		0			0
$629$	−15.1146	−	15.1146i	−0.602660	−	0.602660i
$630$		0			0
$631$	−21.9730			−0.874732			−0.437366	−	0.899284i	$-0.644089\pi$
$631$	−21.9730			−0.874732			−0.437366	+	0.899284i	$0.644089\pi$
$632$		0			0
$633$	−2.29396			−0.0911769
$634$		0			0
$635$		−	13.0851i		−	0.519265i
$636$		0			0
$637$	4.00823	+	4.00823i	0.158812	+	0.158812i
$638$		0			0
$639$	20.7881	+	20.7881i	0.822365	+	0.822365i
$640$		0			0
$641$	−12.7012	−	12.7012i	−0.501667	−	0.501667i	0.410289	−	0.911956i	$-0.365428\pi$
$641$	−12.7012	−	12.7012i	−0.501667	−	0.501667i	−0.911956	+	0.410289i	$0.865428\pi$
$642$		0			0
$643$	−26.9035	+	26.9035i	−1.06097	+	1.06097i	−0.0629561	+	0.998016i	$0.520053\pi$
$643$	−26.9035	+	26.9035i	−1.06097	+	1.06097i	−0.998016	+	0.0629561i	$0.979947\pi$
$644$		0			0
$645$	−2.21096	+	2.21096i	−0.0870566	+	0.0870566i
$646$		0			0
$647$			36.0313i			1.41653i	0.705944	+	0.708267i	$0.250523\pi$
$647$			36.0313i			1.41653i	−0.705944	+	0.708267i	$0.749477\pi$
$648$		0			0
$649$	−24.3236	+	24.3236i	−0.954785	+	0.954785i
$650$		0			0
$651$		−	1.14402i		−	0.0448378i
$652$		0			0
$653$	31.8866	−	31.8866i	1.24782	−	1.24782i	0.291137	−	0.956681i	$-0.405967\pi$
$653$	31.8866	−	31.8866i	1.24782	−	1.24782i	0.956681	−	0.291137i	$-0.0940335\pi$
$654$		0			0
$655$	3.37667			0.131937
$656$		0			0
$657$	25.7091			1.00301
$658$		0			0
$659$	−11.6363	+	11.6363i	−0.453284	+	0.453284i	−0.896443	−	0.443159i	$-0.853858\pi$
$659$	−11.6363	+	11.6363i	−0.453284	+	0.453284i	0.443159	+	0.896443i	$0.353858\pi$
$660$		0			0
$661$			48.9963i			1.90573i	0.303387	+	0.952867i	$0.401882\pi$
$661$			48.9963i			1.90573i	−0.303387	+	0.952867i	$0.598118\pi$
$662$		0			0
$663$	4.48880	−	4.48880i	0.174331	−	0.174331i
$664$		0			0
$665$		−	9.75372i		−	0.378233i
$666$		0			0
$667$	32.9170	−	32.9170i	1.27455	−	1.27455i
$668$		0			0
$669$	−1.21958	+	1.21958i	−0.0471515	+	0.0471515i
$670$		0			0
$671$	−4.96173	−	4.96173i	−0.191546	−	0.191546i
$672$		0			0
$673$	3.20595	+	3.20595i	0.123580	+	0.123580i	0.766192	−	0.642612i	$-0.222149\pi$
$673$	3.20595	+	3.20595i	0.123580	+	0.123580i	−0.642612	+	0.766192i	$0.722149\pi$
$674$		0			0
$675$	−1.61514	−	1.61514i	−0.0621669	−	0.0621669i
$676$		0			0
$677$			22.6084i			0.868910i	0.900694	+	0.434455i	$0.143059\pi$
$677$			22.6084i			0.868910i	−0.900694	+	0.434455i	$0.856941\pi$
$678$		0			0
$679$	−9.02502			−0.346348
$680$		0			0
$681$	−3.43903			−0.131784
$682$		0			0
$683$	12.5968	+	12.5968i	0.482003	+	0.482003i	0.905771	−	0.423768i	$-0.139293\pi$
$683$	12.5968	+	12.5968i	0.482003	+	0.482003i	−0.423768	+	0.905771i	$0.639293\pi$
$684$		0			0
$685$	8.43161	−	8.43161i	0.322155	−	0.322155i
$686$		0			0
$687$	3.44039			0.131259
$688$		0			0
$689$		−	41.6313i		−	1.58603i
$690$		0			0
$691$	27.1819	+	27.1819i	1.03405	+	1.03405i	0.999400	+	0.0346483i	$0.0110311\pi$
$691$	27.1819	+	27.1819i	1.03405	+	1.03405i	0.0346483	+	0.999400i	$0.488969\pi$
$692$		0			0
$693$	−16.4507			−0.624911
$694$		0			0
$695$		−	45.5788i		−	1.72890i
$696$		0			0
$697$	24.4709	−	24.3086i	0.926903	−	0.920754i
$698$		0			0
$699$		−	0.0792958i		−	0.00299924i
$700$		0			0
$701$	−21.3332			−0.805745			−0.402872	−	0.915256i	$-0.631988\pi$
$701$	−21.3332			−0.805745			−0.402872	+	0.915256i	$0.631988\pi$
$702$		0			0
$703$	10.4608	+	10.4608i	0.394537	+	0.394537i
$704$		0			0
$705$		−	2.69896i		−	0.101649i
$706$		0			0
$707$	6.46289			0.243062
$708$		0			0
$709$	−33.0165	+	33.0165i	−1.23996	+	1.23996i	−0.279946	+	0.960016i	$0.590317\pi$
$709$	−33.0165	+	33.0165i	−1.23996	+	1.23996i	−0.960016	+	0.279946i	$0.909683\pi$
$710$		0			0
$711$	−24.6285	−	24.6285i	−0.923639	−	0.923639i
$712$		0			0
$713$	−36.0477			−1.35000
$714$		0			0
$715$	−82.5093			−3.08567
$716$		0			0
$717$		−	5.80778i		−	0.216896i
$718$		0			0
$719$	2.95246	+	2.95246i	0.110108	+	0.110108i	0.760014	−	0.649906i	$-0.225192\pi$
$719$	2.95246	+	2.95246i	0.110108	+	0.110108i	−0.649906	+	0.760014i	$0.725192\pi$
$720$		0			0
$721$	−0.870433	−	0.870433i	−0.0324166	−	0.0324166i
$722$		0			0
$723$	−0.618592	−	0.618592i	−0.0230057	−	0.0230057i
$724$		0			0
$725$	9.26837	−	9.26837i	0.344219	−	0.344219i
$726$		0			0
$727$	20.3491	−	20.3491i	0.754706	−	0.754706i	−0.220647	−	0.975354i	$-0.570817\pi$
$727$	20.3491	−	20.3491i	0.754706	−	0.754706i	0.975354	+	0.220647i	$0.0708170\pi$
$728$		0			0
$729$		−	24.6940i		−	0.914594i
$730$		0			0
$731$	−21.8978	+	21.8978i	−0.809920	+	0.809920i
$732$		0			0
$733$		−	42.0371i		−	1.55268i	−0.630316	−	0.776338i	$-0.717075\pi$
$733$		−	42.0371i		−	1.55268i	0.630316	−	0.776338i	$-0.282925\pi$
$734$		0			0
$735$	−0.384591	+	0.384591i	−0.0141859	+	0.0141859i
$736$		0			0
$737$	50.7857			1.87071
$738$		0			0
$739$	−39.3349			−1.44696			−0.723478	−	0.690347i	$-0.757458\pi$
$739$	−39.3349			−1.44696			−0.723478	+	0.690347i	$0.757458\pi$
$740$		0			0
$741$	−3.10669	+	3.10669i	−0.114127	+	0.114127i
$742$		0			0
$743$			38.7296i			1.42085i	0.703773	+	0.710425i	$0.251497\pi$
$743$			38.7296i			1.42085i	−0.703773	+	0.710425i	$0.748503\pi$
$744$		0			0
$745$	30.3674	−	30.3674i	1.11258	−	1.11258i
$746$		0			0
$747$		−	50.4174i		−	1.84468i
$748$		0			0
$749$	5.78532	−	5.78532i	0.211391	−	0.211391i
$750$		0			0
$751$	7.22182	−	7.22182i	0.263528	−	0.263528i	−0.562958	−	0.826486i	$-0.690337\pi$
$751$	7.22182	−	7.22182i	0.263528	−	0.263528i	0.826486	+	0.562958i	$0.190337\pi$
$752$		0			0
$753$	−0.208474	−	0.208474i	−0.00759723	−	0.00759723i
$754$		0			0
$755$	−7.04385	−	7.04385i	−0.256352	−	0.256352i
$756$		0			0
$757$	26.7177	+	26.7177i	0.971070	+	0.971070i	0.999593	−	0.0285234i	$-0.00908050\pi$
$757$	26.7177	+	26.7177i	0.971070	+	0.971070i	−0.0285234	+	0.999593i	$0.509081\pi$
$758$		0			0
$759$		−	7.57700i		−	0.275028i
$760$		0			0
$761$	45.2274			1.63949			0.819746	−	0.572728i	$-0.194115\pi$
$761$	45.2274			1.63949			0.819746	+	0.572728i	$0.194115\pi$
$762$		0			0
$763$	6.08642			0.220343
$764$		0			0
$765$	−29.4650	−	29.4650i	−1.06531	−	1.06531i
$766$		0			0
$767$	−24.7816	+	24.7816i	−0.894813	+	0.894813i
$768$		0			0
$769$	−16.2917			−0.587495			−0.293747	−	0.955883i	$-0.594902\pi$
$769$	−16.2917			−0.587495			−0.293747	+	0.955883i	$0.594902\pi$
$770$		0			0
$771$			2.21646i			0.0798238i
$772$		0			0
$773$	−11.2627	−	11.2627i	−0.405090	−	0.405090i	0.474932	−	0.880022i	$-0.342473\pi$
$773$	−11.2627	−	11.2627i	−0.405090	−	0.405090i	−0.880022	+	0.474932i	$0.842473\pi$
$774$		0			0
$775$	−10.1499			−0.364594
$776$		0			0
$777$		−	0.824943i		−	0.0295946i
$778$		0			0
$779$	−16.9363	+	16.8239i	−0.606805	+	0.602780i
$780$		0			0
$781$			55.3193i			1.97948i
$782$		0			0
$783$	−8.80044			−0.314502
$784$		0			0
$785$	27.3350	+	27.3350i	0.975627	+	0.975627i
$786$		0			0
$787$			29.3868i			1.04753i	0.851864	+	0.523764i	$0.175472\pi$
$787$			29.3868i			1.04753i	−0.851864	+	0.523764i	$0.824528\pi$
$788$		0			0
$789$	−0.253588			−0.00902797
$790$		0			0
$791$	−13.6782	+	13.6782i	−0.486342	+	0.486342i
$792$		0			0
$793$	−5.05517	−	5.05517i	−0.179514	−	0.179514i
$794$		0			0
$795$	3.99454			0.141672
$796$		0			0
$797$	−10.0350			−0.355457			−0.177728	−	0.984080i	$-0.556875\pi$
$797$	−10.0350			−0.355457			−0.177728	+	0.984080i	$0.556875\pi$
$798$		0			0
$799$		−	26.7310i		−	0.945676i
$800$		0			0
$801$	−19.4948	−	19.4948i	−0.688813	−	0.688813i
$802$		0			0
$803$	34.2073	+	34.2073i	1.20715	+	1.20715i
$804$		0			0
$805$	12.1183	+	12.1183i	0.427114	+	0.427114i
$806$		0			0
$807$	−4.22995	+	4.22995i	−0.148901	+	0.148901i
$808$		0			0
$809$	−8.12665	+	8.12665i	−0.285718	+	0.285718i	−0.835384	−	0.549666i	$-0.814755\pi$
$809$	−8.12665	+	8.12665i	−0.285718	+	0.285718i	0.549666	+	0.835384i	$0.314755\pi$
$810$		0			0
$811$			52.4059i			1.84022i	0.391662	+	0.920109i	$0.371900\pi$
$811$			52.4059i			1.84022i	−0.391662	+	0.920109i	$0.628100\pi$
$812$		0			0
$813$	3.14627	−	3.14627i	0.110345	−	0.110345i
$814$		0			0
$815$			13.0744i			0.457976i
$816$		0			0
$817$	15.1554	−	15.1554i	0.530222	−	0.530222i
$818$		0			0
$819$	−16.7605			−0.585659
$820$		0			0
$821$	41.1328			1.43554			0.717772	−	0.696278i	$-0.245162\pi$
$821$	41.1328			1.43554			0.717772	+	0.696278i	$0.245162\pi$
$822$		0			0
$823$	33.0716	−	33.0716i	1.15280	−	1.15280i	0.166815	−	0.985988i	$-0.446652\pi$
$823$	33.0716	−	33.0716i	1.15280	−	1.15280i	0.985988	−	0.166815i	$-0.0533483\pi$
$824$		0			0
$825$		−	2.13344i		−	0.0742768i
$826$		0			0
$827$	−19.3804	+	19.3804i	−0.673923	+	0.673923i	−0.958618	−	0.284695i	$-0.908108\pi$
$827$	−19.3804	+	19.3804i	−0.673923	+	0.673923i	0.284695	+	0.958618i	$0.408108\pi$
$828$		0			0
$829$			31.8105i			1.10483i	0.833571	+	0.552413i	$0.186293\pi$
$829$			31.8105i			1.10483i	−0.833571	+	0.552413i	$0.813707\pi$
$830$		0			0
$831$	−0.917404	+	0.917404i	−0.0318244	+	0.0318244i
$832$		0			0
$833$	−3.80906	+	3.80906i	−0.131976	+	0.131976i
$834$		0			0
$835$	−12.6543	−	12.6543i	−0.437921	−	0.437921i
$836$		0			0
$837$	4.81872	+	4.81872i	0.166559	+	0.166559i
$838$		0			0
$839$	4.91765	+	4.91765i	0.169776	+	0.169776i	0.786881	−	0.617105i	$-0.211695\pi$
$839$	4.91765	+	4.91765i	0.169776	+	0.169776i	−0.617105	+	0.786881i	$0.711695\pi$
$840$		0			0
$841$		−	21.5006i		−	0.741401i
$842$		0			0
$843$	−1.80845			−0.0622862
$844$		0			0
$845$	−50.0525			−1.72186
$846$		0			0
$847$	−14.1103	−	14.1103i	−0.484837	−	0.484837i
$848$		0			0
$849$	2.16021	−	2.16021i	0.0741382	−	0.0741382i
$850$		0			0
$851$	−25.9936			−0.891049
$852$		0			0
$853$		−	17.6706i		−	0.605031i	−0.953144	−	0.302516i	$-0.902174\pi$
$853$		−	17.6706i		−	0.605031i	0.953144	−	0.302516i	$-0.0978264\pi$
$854$		0			0
$855$	20.3927	+	20.3927i	0.697415	+	0.697415i
$856$		0			0
$857$	35.3343			1.20700			0.603498	−	0.797364i	$-0.293773\pi$
$857$	35.3343			1.20700			0.603498	+	0.797364i	$0.293773\pi$
$858$		0			0
$859$			17.7978i			0.607252i	0.952791	+	0.303626i	$0.0981974\pi$
$859$			17.7978i			0.607252i	−0.952791	+	0.303626i	$0.901803\pi$
$860$		0			0
$861$	1.33117	+	0.00443008i	0.0453662	+	0.000150977i
$862$		0			0
$863$			16.7423i			0.569915i	0.958540	+	0.284957i	$0.0919794\pi$
$863$			16.7423i			0.569915i	−0.958540	+	0.284957i	$0.908021\pi$
$864$		0			0
$865$	44.4033			1.50976
$866$		0			0
$867$	1.76668	+	1.76668i	0.0599998	+	0.0599998i
$868$		0			0
$869$		−	65.5389i		−	2.22325i
$870$		0			0
$871$	51.7420			1.75321
$872$		0			0
$873$	18.8691	−	18.8691i	0.638623	−	0.638623i
$874$		0			0
$875$	−5.83751	−	5.83751i	−0.197344	−	0.197344i
$876$		0			0
$877$	33.2758			1.12364			0.561822	−	0.827258i	$-0.310100\pi$
$877$	33.2758			1.12364			0.561822	+	0.827258i	$0.310100\pi$
$878$		0			0
$879$	4.71593			0.159065
$880$		0			0
$881$		−	11.9716i		−	0.403334i	−0.979454	−	0.201667i	$-0.935364\pi$
$881$		−	11.9716i		−	0.403334i	0.979454	−	0.201667i	$-0.0646359\pi$
$882$		0			0
$883$	−25.3070	−	25.3070i	−0.851649	−	0.851649i	0.138687	−	0.990336i	$-0.455712\pi$
$883$	−25.3070	−	25.3070i	−0.851649	−	0.851649i	−0.990336	+	0.138687i	$0.955712\pi$
$884$		0			0
$885$	−2.37781	−	2.37781i	−0.0799291	−	0.0799291i
$886$		0			0
$887$	−41.4254	−	41.4254i	−1.39093	−	1.39093i	−0.823252	−	0.567677i	$-0.807842\pi$
$887$	−41.4254	−	41.4254i	−1.39093	−	1.39093i	−0.567677	−	0.823252i	$-0.692158\pi$
$888$		0			0
$889$	3.53664	−	3.53664i	0.118615	−	0.118615i
$890$		0			0
$891$	33.8844	−	33.8844i	1.13517	−	1.13517i
$892$		0			0
$893$			18.5005i			0.619095i
$894$		0			0
$895$	−6.65185	+	6.65185i	−0.222347	+	0.222347i
$896$		0			0
$897$		−	7.71968i		−	0.257753i
$898$		0			0
$899$	−27.6518	+	27.6518i	−0.922241	+	0.922241i
$900$		0			0
$901$	39.5627			1.31802
$902$		0			0
$903$	−1.19516			−0.0397725
$904$		0			0
$905$	21.6157	−	21.6157i	0.718531	−	0.718531i
$906$		0			0
$907$		−	9.56439i		−	0.317580i	−0.987312	−	0.158790i	$-0.949241\pi$
$907$		−	9.56439i		−	0.317580i	0.987312	−	0.158790i	$-0.0507593\pi$
$908$		0			0
$909$	−13.5123	+	13.5123i	−0.448176	+	0.448176i
$910$		0			0
$911$			47.7805i			1.58304i	0.611143	+	0.791520i	$0.290710\pi$
$911$			47.7805i			1.58304i	−0.611143	+	0.791520i	$0.709290\pi$
$912$		0			0
$913$	67.0829	−	67.0829i	2.22012	−	2.22012i
$914$		0			0
$915$	0.485045	−	0.485045i	0.0160351	−	0.0160351i
$916$		0			0
$917$	0.912649	+	0.912649i	0.0301383	+	0.0301383i
$918$		0			0
$919$	8.48066	+	8.48066i	0.279751	+	0.279751i	0.833010	−	0.553258i	$-0.186616\pi$
$919$	8.48066	+	8.48066i	0.279751	+	0.279751i	−0.553258	+	0.833010i	$0.686616\pi$
$920$		0			0
$921$	1.78763	+	1.78763i	0.0589043	+	0.0589043i
$922$		0			0
$923$			56.3610i			1.85514i
$924$		0			0
$925$	−7.31896			−0.240646
$926$		0			0
$927$	3.63973			0.119544
$928$		0			0
$929$	−10.3893	−	10.3893i	−0.340861	−	0.340861i	0.515830	−	0.856691i	$-0.327484\pi$
$929$	−10.3893	−	10.3893i	−0.340861	−	0.340861i	−0.856691	+	0.515830i	$0.827484\pi$
$930$		0			0
$931$	2.63624	−	2.63624i	0.0863994	−	0.0863994i
$932$		0			0
$933$	−4.07653			−0.133460
$934$		0			0
$935$		−	78.4095i		−	2.56426i
$936$		0			0
$937$	−15.7471	−	15.7471i	−0.514437	−	0.514437i	0.401446	−	0.915883i	$-0.368508\pi$
$937$	−15.7471	−	15.7471i	−0.514437	−	0.514437i	−0.915883	+	0.401446i	$0.868508\pi$
$938$		0			0
$939$	−0.122516			−0.00399816
$940$		0			0
$941$			38.0283i			1.23969i	0.784726	+	0.619843i	$0.212804\pi$
$941$			38.0283i			1.23969i	−0.784726	+	0.619843i	$0.787196\pi$
$942$		0			0
$943$	0.139590	−	41.9447i	0.00454568	−	1.36591i
$944$		0			0
$945$		−	3.23986i		−	0.105392i
$946$		0			0
$947$	19.8569			0.645262			0.322631	−	0.946525i	$-0.395433\pi$
$947$	19.8569			0.645262			0.322631	+	0.946525i	$0.395433\pi$
$948$		0			0
$949$	34.8514	+	34.8514i	1.13132	+	1.13132i
$950$		0			0
$951$			0.909596i			0.0294957i
$952$		0			0
$953$	30.2985			0.981464			0.490732	−	0.871311i	$-0.336729\pi$
$953$	30.2985			0.981464			0.490732	+	0.871311i	$0.336729\pi$
$954$		0			0
$955$	3.67052	−	3.67052i	0.118775	−	0.118775i
$956$		0			0
$957$	−5.81224	−	5.81224i	−0.187883	−	0.187883i
$958$		0			0
$959$	4.55781			0.147179
$960$		0			0
$961$	−0.718223			−0.0231685
$962$		0			0
$963$			24.1914i			0.779557i
$964$		0			0
$965$	20.3057	+	20.3057i	0.653663	+	0.653663i
$966$		0			0
$967$	−8.10120	−	8.10120i	−0.260517	−	0.260517i	0.564747	−	0.825264i	$-0.308974\pi$
$967$	−8.10120	−	8.10120i	−0.260517	−	0.260517i	−0.825264	+	0.564747i	$0.808974\pi$
$968$		0			0
$969$	−2.95232	−	2.95232i	−0.0948422	−	0.0948422i
$970$		0			0
$971$	−7.09729	+	7.09729i	−0.227763	+	0.227763i	−0.811757	−	0.583995i	$-0.801489\pi$
$971$	−7.09729	+	7.09729i	−0.227763	+	0.227763i	0.583995	+	0.811757i	$0.301489\pi$
$972$		0			0
$973$	12.3191	−	12.3191i	0.394932	−	0.394932i
$974$		0			0
$975$		−	2.17361i		−	0.0696113i
$976$		0			0
$977$	−42.8984	+	42.8984i	−1.37244	+	1.37244i	−0.515630	+	0.856811i	$0.672442\pi$
$977$	−42.8984	+	42.8984i	−1.37244	+	1.37244i	−0.856811	+	0.515630i	$0.827558\pi$
$978$		0			0
$979$		−	51.8776i		−	1.65801i
$980$		0			0
$981$	−12.7252	+	12.7252i	−0.406286	+	0.406286i
$982$		0			0
$983$	−0.419561			−0.0133819			−0.00669095	−	0.999978i	$-0.502130\pi$
$983$	−0.419561			−0.0133819			−0.00669095	+	0.999978i	$0.502130\pi$
$984$		0			0
$985$	48.0937			1.53239
$986$		0			0
$987$	0.729478	−	0.729478i	0.0232195	−	0.0232195i
$988$		0			0
$989$			37.6591i			1.19749i
$990$		0			0
$991$	17.2759	−	17.2759i	0.548787	−	0.548787i	−0.377303	−	0.926090i	$-0.623148\pi$
$991$	17.2759	−	17.2759i	0.548787	−	0.548787i	0.926090	+	0.377303i	$0.123148\pi$
$992$		0			0
$993$			2.12239i			0.0673522i
$994$		0			0
$995$	−20.5265	+	20.5265i	−0.650734	+	0.650734i
$996$		0			0
$997$	2.78401	−	2.78401i	0.0881703	−	0.0881703i	−0.661646	−	0.749816i	$-0.730142\pi$
$997$	2.78401	−	2.78401i	0.0881703	−	0.0881703i	0.749816	+	0.661646i	$0.230142\pi$
$998$		0			0
$999$	3.47472	+	3.47472i	0.109935	+	0.109935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.729.10	yes	36
41.9	even	4	inner	1148.2.k.b.337.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.10	✓	36	41.9	even	4	inner
1148.2.k.b.729.10	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.147004 - 0.147004i) q^{3} -2.61619i q^{5} +(0.707107 - 0.707107i) q^{7} +2.95678i q^{9} +O(q^{10})\)	\(q+(0.147004 - 0.147004i) q^{3} -2.61619i q^{5} +(0.707107 - 0.707107i) q^{7} +2.95678i q^{9} +(-3.93415 + 3.93415i) q^{11} +(-4.00823 + 4.00823i) q^{13} +(-0.384591 - 0.384591i) q^{15} +(-3.80906 - 3.80906i) q^{17} +(2.63624 + 2.63624i) q^{19} -0.207895i q^{21} -6.55069 q^{23} -1.84446 q^{25} +(0.875671 + 0.875671i) q^{27} +(-5.02497 + 5.02497i) q^{29} +5.50289 q^{31} +1.15667i q^{33} +(-1.84993 - 1.84993i) q^{35} +3.96807 q^{37} +1.17845i q^{39} +(-0.0213092 + 6.40309i) q^{41} -5.74887i q^{43} +7.73551 q^{45} +(3.50887 + 3.50887i) q^{47} -1.00000i q^{49} -1.11990 q^{51} +(-5.19323 + 5.19323i) q^{53} +(10.2925 + 10.2925i) q^{55} +0.775077 q^{57} +6.18269 q^{59} +1.26120i q^{61} +(2.09076 + 2.09076i) q^{63} +(10.4863 + 10.4863i) q^{65} +(-6.45447 - 6.45447i) q^{67} +(-0.962978 + 0.962978i) q^{69} +(7.03066 - 7.03066i) q^{71} -8.69496i q^{73} +(-0.271144 + 0.271144i) q^{75} +5.56373i q^{77} +(-8.32949 + 8.32949i) q^{79} -8.61288 q^{81} -17.0514 q^{83} +(-9.96524 + 9.96524i) q^{85} +1.47738i q^{87} +(-6.59324 + 6.59324i) q^{89} +5.66849i q^{91} +(0.808947 - 0.808947i) q^{93} +(6.89692 - 6.89692i) q^{95} +(-6.38165 - 6.38165i) q^{97} +(-11.6324 - 11.6324i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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Database

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