LMFDB - Embedded newform 1148.2.k.b.337.10

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			337.10
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.10

$q$-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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.147004	+	0.147004i	0.0848728	+	0.0848728i	0.748269	−	0.663396i	$-0.230885\pi$
$3$	0.147004	+	0.147004i	0.0848728	+	0.0848728i	−0.663396	+	0.748269i	$0.730885\pi$
$4$		0			0
$5$			2.61619i			1.17000i	0.811034	+	0.584998i	$0.198905\pi$
$5$			2.61619i			1.17000i	−0.811034	+	0.584998i	$0.801095\pi$
$6$		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	−0.978112	−	0.208078i	$-0.933279\pi$
$11$	−3.93415	−	3.93415i	−1.18619	−	1.18619i	−0.208078	−	0.978112i	$-0.566721\pi$
$12$		0			0
$13$	−4.00823	−	4.00823i	−1.11168	−	1.11168i	−0.992923	−	0.118760i	$-0.962108\pi$
$13$	−4.00823	−	4.00823i	−1.11168	−	1.11168i	−0.118760	−	0.992923i	$-0.537892\pi$
$14$		0			0
$15$	−0.384591	+	0.384591i	−0.0993010	+	0.0993010i
$16$		0			0
$17$	−3.80906	+	3.80906i	−0.923834	+	0.923834i	−0.997298	−	0.0734642i	$-0.976595\pi$
$17$	−3.80906	+	3.80906i	−0.923834	+	0.923834i	0.0734642	+	0.997298i	$0.476595\pi$
$18$		0			0
$19$	2.63624	−	2.63624i	0.604796	−	0.604796i	−0.336785	−	0.941581i	$-0.609340\pi$
$19$	2.63624	−	2.63624i	0.604796	−	0.604796i	0.941581	+	0.336785i	$0.109340\pi$
$20$		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	0.0647858	−	0.997899i	$-0.479364\pi$
$29$	−5.02497	−	5.02497i	−0.933113	−	0.933113i	−0.997899	+	0.0647858i	$0.979364\pi$
$30$		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	$0.144436\pi$
$43$			5.74887i			0.876695i	−0.898806	+	0.438347i	$0.855564\pi$
$44$		0			0
$45$	7.73551			1.15314
$46$		0			0
$47$	3.50887	−	3.50887i	0.511822	−	0.511822i	−0.403263	−	0.915084i	$-0.632124\pi$
$47$	3.50887	−	3.50887i	0.511822	−	0.511822i	0.915084	+	0.403263i	$0.132124\pi$
$48$		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	0.253889	−	0.967233i	$-0.418290\pi$
$53$	−5.19323	−	5.19323i	−0.713345	−	0.713345i	−0.967233	+	0.253889i	$0.918290\pi$
$54$		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	$-0.974272\pi$
$61$		−	1.26120i		−	0.161480i	0.996735	−	0.0807398i	$-0.0257283\pi$
$62$		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	−0.981255	−	0.192716i	$-0.938270\pi$
$67$	−6.45447	+	6.45447i	−0.788539	+	0.788539i	0.192716	+	0.981255i	$0.438270\pi$
$68$		0			0
$69$	−0.962978	−	0.962978i	−0.115929	−	0.115929i
$70$		0			0
$71$	7.03066	+	7.03066i	0.834386	+	0.834386i	0.988113	−	0.153728i	$-0.0491279\pi$
$71$	7.03066	+	7.03066i	0.834386	+	0.834386i	−0.153728	+	0.988113i	$0.549128\pi$
$72$		0			0
$73$			8.69496i			1.01767i	0.860865	+	0.508834i	$0.169923\pi$
$73$			8.69496i			1.01767i	−0.860865	+	0.508834i	$0.830077\pi$
$74$		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	0.0609974	−	0.998138i	$-0.480572\pi$
$79$	−8.32949	−	8.32949i	−0.937140	−	0.937140i	−0.998138	+	0.0609974i	$0.980572\pi$
$80$		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	0.265287	−	0.964169i	$-0.414533\pi$
$89$	−6.59324	−	6.59324i	−0.698882	−	0.698882i	−0.964169	+	0.265287i	$0.914533\pi$
$90$		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	−0.952499	−	0.304541i	$-0.901497\pi$
$97$	−6.38165	+	6.38165i	−0.647958	+	0.647958i	0.304541	+	0.952499i	$0.401497\pi$
$98$		0			0
$99$	−11.6324	+	11.6324i	−1.16910	+	1.16910i
$100$		0			0
$101$	4.56995	−	4.56995i	0.454727	−	0.454727i	−0.442193	−	0.896920i	$-0.645799\pi$
$101$	4.56995	−	4.56995i	0.454727	−	0.454727i	0.896920	+	0.442193i	$0.145799\pi$
$102$		0			0
$103$			1.23098i			0.121292i	0.998159	+	0.0606459i	$0.0193161\pi$
$103$			1.23098i			0.121292i	−0.998159	+	0.0606459i	$0.980684\pi$
$104$		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	−0.470288	−	0.882513i	$-0.655850\pi$
$109$	4.30375	−	4.30375i	0.412225	−	0.412225i	0.882513	+	0.470288i	$0.155850\pi$
$110$		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	$-0.982043\pi$
$131$		−	1.29068i		−	0.112767i	0.998409	−	0.0563836i	$-0.0179570\pi$
$132$		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	−0.555901	−	0.831248i	$-0.687627\pi$
$137$	3.22286	−	3.22286i	0.275347	−	0.275347i	0.831248	+	0.555901i	$0.187627\pi$
$138$		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	−0.0479289	−	0.998851i	$-0.515262\pi$
$149$	11.6075	−	11.6075i	0.950922	−	0.950922i	0.998851	+	0.0479289i	$0.0152621\pi$
$150$		0			0
$151$	2.69241	+	2.69241i	0.219105	+	0.219105i	0.808121	−	0.589016i	$-0.200485\pi$
$151$	2.69241	+	2.69241i	0.219105	+	0.219105i	−0.589016	+	0.808121i	$0.700485\pi$
$152$		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	0.154172	−	0.988044i	$-0.450729\pi$
$157$	−10.4484	−	10.4484i	−0.833872	−	0.833872i	−0.988044	+	0.154172i	$0.950729\pi$
$158$		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	0.869038	−	0.494746i	$-0.164739\pi$
$167$	4.83692	+	4.83692i	0.374292	+	0.374292i	−0.494746	+	0.869038i	$0.664739\pi$
$168$		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	$-0.776775\pi$
$173$		−	16.9725i		−	1.29039i	0.764016	−	0.645197i	$-0.223225\pi$
$174$		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	−0.795714	−	0.605673i	$-0.792904\pi$
$179$	−2.54257	+	2.54257i	−0.190041	+	0.190041i	0.605673	+	0.795714i	$0.292904\pi$
$180$		0			0
$181$	8.26228	−	8.26228i	0.614131	−	0.614131i	−0.329889	−	0.944020i	$-0.607011\pi$
$181$	8.26228	−	8.26228i	0.614131	−	0.614131i	0.944020	+	0.329889i	$0.107011\pi$
$182$		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	−0.654524	−	0.756041i	$-0.727131\pi$
$191$	1.40300	−	1.40300i	0.101518	−	0.101518i	0.756041	+	0.654524i	$0.227131\pi$
$192$		0			0
$193$	−7.76154	−	7.76154i	−0.558688	−	0.558688i	0.370246	−	0.928934i	$-0.379273\pi$
$193$	−7.76154	−	7.76154i	−0.558688	−	0.558688i	−0.928934	+	0.370246i	$0.879273\pi$
$194$		0			0
$195$	3.08306			0.220782
$196$		0			0
$197$		−	18.3831i		−	1.30974i	−0.755742	−	0.654870i	$-0.772723\pi$
$197$		−	18.3831i		−	1.30974i	0.755742	−	0.654870i	$-0.227277\pi$
$198$		0			0
$199$	−7.84594	+	7.84594i	−0.556184	+	0.556184i	−0.928219	−	0.372035i	$-0.878660\pi$
$199$	−7.84594	+	7.84594i	−0.556184	+	0.556184i	0.372035	+	0.928219i	$0.378660\pi$
$200$		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	−0.922687	−	0.385549i	$-0.874012\pi$
$211$	−7.80238	+	7.80238i	−0.537138	+	0.537138i	0.385549	+	0.922687i	$0.374012\pi$
$212$		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	−0.979210	−	0.202849i	$-0.934980\pi$
$227$	−11.6971	+	11.6971i	−0.776361	+	0.776361i	0.202849	+	0.979210i	$0.434980\pi$
$228$		0			0
$229$	11.7017	−	11.7017i	0.773269	−	0.773269i	−0.205408	−	0.978676i	$-0.565852\pi$
$229$	11.7017	−	11.7017i	0.773269	−	0.773269i	0.978676	+	0.205408i	$0.0658521\pi$
$230$		0			0
$231$	0.817890	−	0.817890i	0.0538132	−	0.0538132i
$232$		0			0
$233$	0.269706	+	0.269706i	0.0176690	+	0.0176690i	0.715886	−	0.698217i	$-0.246023\pi$
$233$	0.269706	+	0.269706i	0.0176690	+	0.0176690i	−0.698217	+	0.715886i	$0.746023\pi$
$234$		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	0.941914	+	0.335854i	$0.109025\pi$
$239$	19.7538	+	19.7538i	1.27777	+	1.27777i	0.335854	+	0.941914i	$0.390975\pi$
$240$		0			0
$241$			4.20799i			0.271061i	0.990773	+	0.135530i	$0.0432738\pi$
$241$			4.20799i			0.271061i	−0.990773	+	0.135530i	$0.956726\pi$
$242$		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	$0.0142512\pi$
$251$			1.41815i			0.0895131i	−0.998998	+	0.0447565i	$0.985749\pi$
$252$		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	0.431742	−	0.901997i	$-0.357899\pi$
$257$	−7.53877	−	7.53877i	−0.470255	−	0.470255i	−0.901997	+	0.431742i	$0.857899\pi$
$258$		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	−0.733199	−	0.680014i	$-0.761974\pi$
$263$	−0.862520	+	0.862520i	−0.0531853	+	0.0531853i	0.680014	+	0.733199i	$0.261974\pi$
$264$		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	−0.866359	−	0.499421i	$-0.833546\pi$
$281$	−6.15101	+	6.15101i	−0.366938	+	0.366938i	0.499421	+	0.866359i	$0.333546\pi$
$282$		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	−0.0610587	−	0.998134i	$-0.519448\pi$
$293$	16.0401	−	16.0401i	0.937076	−	0.937076i	0.998134	+	0.0610587i	$0.0194477\pi$
$294$		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	$-0.887195\pi$
$307$		−	12.1604i		−	0.694030i	0.937860	−	0.347015i	$-0.112805\pi$
$308$		0			0
$309$	−0.180959	+	0.180959i	−0.0102944	+	0.0102944i
$310$		0			0
$311$	−13.8654	+	13.8654i	−0.786233	+	0.786233i	−0.980874	−	0.194642i	$-0.937646\pi$
$311$	−13.8654	+	13.8654i	−0.786233	+	0.786233i	0.194642	+	0.980874i	$0.437646\pi$
$312$		0			0
$313$	−0.416709	+	0.416709i	−0.0235538	+	0.0235538i	−0.718786	−	0.695232i	$-0.755302\pi$
$313$	−0.416709	+	0.416709i	−0.0235538	+	0.0235538i	0.695232	+	0.718786i	$0.255302\pi$
$314$		0			0
$315$	5.46983	+	5.46983i	0.308190	+	0.308190i
$316$		0			0
$317$	−3.09378	−	3.09378i	−0.173764	−	0.173764i	0.614867	−	0.788631i	$-0.289210\pi$
$317$	−3.09378	−	3.09378i	−0.173764	−	0.173764i	−0.788631	+	0.614867i	$0.789210\pi$
$318$		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	0.480314	−	0.877097i	$-0.340523\pi$
$331$	−7.21883	−	7.21883i	−0.396783	−	0.396783i	−0.877097	+	0.480314i	$0.840523\pi$
$332$		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	$0.218364\pi$
$337$			23.2574i			1.26691i	−0.773779	+	0.633456i	$0.781636\pi$
$338$		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	−0.967683	−	0.252171i	$-0.918856\pi$
$347$	−13.3285	+	13.3285i	−0.715512	+	0.715512i	0.252171	+	0.967683i	$0.418856\pi$
$348$		0			0
$349$		−	20.2304i		−	1.08291i	−0.840730	−	0.541454i	$-0.817874\pi$
$349$		−	20.2304i		−	1.08291i	0.840730	−	0.541454i	$-0.182126\pi$
$350$		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	$-0.969001\pi$
$367$		−	3.72546i		−	0.194467i	0.995262	−	0.0972337i	$-0.0309994\pi$
$368$		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	−0.671805	−	0.740728i	$-0.734481\pi$
$383$	1.34885	−	1.34885i	0.0689230	−	0.0689230i	0.740728	+	0.671805i	$0.234481\pi$
$384$		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	$0.267880\pi$
$389$			29.4146i			1.49138i	−0.666294	+	0.745689i	$0.732120\pi$
$390$		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	0.966439	−	0.256898i	$-0.0827003\pi$
$397$	14.1375	+	14.1375i	0.709541	+	0.709541i	−0.256898	+	0.966439i	$0.582700\pi$
$398$		0			0
$399$	0.548062	+	0.548062i	0.0274374	+	0.0274374i
$400$		0			0
$401$		−	1.00724i		−	0.0502991i	−0.999684	−	0.0251495i	$-0.991994\pi$
$401$		−	1.00724i		−	0.0502991i	0.999684	−	0.0251495i	$-0.00800619\pi$
$402$		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	$0.196863\pi$
$419$			23.7358i			1.15957i	−0.814770	+	0.579784i	$0.803137\pi$
$420$		0			0
$421$	−10.3142	−	10.3142i	−0.502682	−	0.502682i	0.409589	−	0.912270i	$-0.365672\pi$
$421$	−10.3142	−	10.3142i	−0.502682	−	0.502682i	−0.912270	+	0.409589i	$0.865672\pi$
$422$		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	$-0.865204\pi$
$431$		−	17.0622i		−	0.821858i	0.911667	−	0.410929i	$-0.134796\pi$
$432$		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	0.533311	−	0.845919i	$-0.320947\pi$
$439$	−6.54986	−	6.54986i	−0.312608	−	0.312608i	−0.845919	+	0.533311i	$0.820947\pi$
$440$		0			0
$441$	2.95678			0.140799
$442$		0			0
$443$		−	34.2324i		−	1.62643i	−0.581962	−	0.813216i	$-0.697715\pi$
$443$		−	34.2324i		−	1.62643i	0.581962	−	0.813216i	$-0.302285\pi$
$444$		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	$0.363487\pi$
$449$			38.5413i			1.81887i	−0.415841	+	0.909437i	$0.636513\pi$
$450$		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	−0.283710	−	0.958910i	$-0.591565\pi$
$457$	14.4341	−	14.4341i	0.675200	−	0.675200i	0.958910	+	0.283710i	$0.0915653\pi$
$458$		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	−0.971065	−	0.238816i	$-0.923241\pi$
$463$	−26.0335	−	26.0335i	−1.20988	−	1.20988i	−0.238816	−	0.971065i	$-0.576759\pi$
$464$		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	0.880417	−	0.474200i	$-0.157263\pi$
$479$	8.89051	+	8.89051i	0.406218	+	0.406218i	−0.474200	+	0.880417i	$0.657263\pi$
$480$		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	$-0.958571\pi$
$487$		−	5.72829i		−	0.259573i	0.991542	−	0.129787i	$-0.0414293\pi$
$488$		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	0.995081	+	0.0990657i	$0.0315854\pi$
$499$	24.4414	+	24.4414i	1.09415	+	1.09415i	0.0990657	+	0.995081i	$0.468415\pi$
$500$		0			0
$501$			1.42209i			0.0635345i
$502$		0			0
$503$	18.0344	+	18.0344i	0.804114	+	0.804114i	0.983736	−	0.179622i	$-0.0574874\pi$
$503$	18.0344	+	18.0344i	0.804114	+	0.804114i	−0.179622	+	0.983736i	$0.557487\pi$
$504$		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	−0.590723	−	0.806874i	$-0.701157\pi$
$509$	4.87660	−	4.87660i	0.216151	−	0.216151i	0.806874	+	0.590723i	$0.201157\pi$
$510$		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	0.458128	−	0.888886i	$-0.348520\pi$
$521$	−9.83224	−	9.83224i	−0.430758	−	0.430758i	−0.888886	+	0.458128i	$0.848520\pi$
$522$		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	$-0.692172\pi$
$541$		−	38.2955i		−	1.64645i	0.567714	−	0.823226i	$-0.307828\pi$
$542$		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	−0.0362285	−	0.999344i	$-0.511534\pi$
$547$	22.5254	−	22.5254i	0.963115	−	0.963115i	0.999344	+	0.0362285i	$0.0115344\pi$
$548$		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	−0.135634	+	0.990759i	$0.543307\pi$
$557$	−26.5838	+	26.5838i	−1.12639	+	1.12639i	−0.990759	+	0.135634i	$0.956693\pi$
$558$		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	0.664561	−	0.747234i	$-0.268618\pi$
$563$	−1.96161	−	1.96161i	−0.0826722	−	0.0826722i	−0.747234	+	0.664561i	$0.768618\pi$
$564$		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	$-0.757252\pi$
$569$		−	32.9570i		−	1.38163i	0.723031	−	0.690816i	$-0.242748\pi$
$570$		0			0
$571$	−28.9481	−	28.9481i	−1.21144	−	1.21144i	−0.970553	−	0.240886i	$-0.922562\pi$
$571$	−28.9481	−	28.9481i	−1.21144	−	1.21144i	−0.240886	−	0.970553i	$-0.577438\pi$
$572$		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	0.962302	−	0.271985i	$-0.0876801\pi$
$577$	16.5820	+	16.5820i	0.690317	+	0.690317i	−0.271985	+	0.962302i	$0.587680\pi$
$578$		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	0.859544	−	0.511062i	$-0.170748\pi$
$587$	8.44304	+	8.44304i	0.348481	+	0.348481i	−0.511062	+	0.859544i	$0.670748\pi$
$588$		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	−0.0647527	−	0.997901i	$-0.520626\pi$
$593$	22.7237	−	22.7237i	0.933149	−	0.933149i	0.997901	+	0.0647527i	$0.0206259\pi$
$594$		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	−0.312195	−	0.950018i	$-0.601064\pi$
$601$	15.6364	−	15.6364i	0.637823	−	0.637823i	0.950018	+	0.312195i	$0.101064\pi$
$602$		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	$-0.864692\pi$
$607$		−	20.3207i		−	0.824793i	0.911005	−	0.412396i	$-0.135308\pi$
$608$		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	$0.263094\pi$
$613$			36.4246i			1.47118i	−0.677428	+	0.735589i	$0.736906\pi$
$614$		0			0
$615$	2.47077	+	2.45437i	0.0996309	+	0.0989699i
$616$		0			0
$617$		−	1.60897i		−	0.0647748i	−0.999475	−	0.0323874i	$-0.989689\pi$
$617$		−	1.60897i		−	0.0647748i	0.999475	−	0.0323874i	$-0.0103110\pi$
$618$		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	−0.911956	−	0.410289i	$-0.865428\pi$
$641$	−12.7012	+	12.7012i	−0.501667	+	0.501667i	0.410289	+	0.911956i	$0.365428\pi$
$642$		0			0
$643$	−26.9035	−	26.9035i	−1.06097	−	1.06097i	−0.998016	−	0.0629561i	$-0.979947\pi$
$643$	−26.9035	−	26.9035i	−1.06097	−	1.06097i	−0.0629561	−	0.998016i	$-0.520053\pi$
$644$		0			0
$645$	−2.21096	−	2.21096i	−0.0870566	−	0.0870566i
$646$		0			0
$647$		−	36.0313i		−	1.41653i	−0.705944	−	0.708267i	$-0.749477\pi$
$647$		−	36.0313i		−	1.41653i	0.705944	−	0.708267i	$-0.250523\pi$
$648$		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	0.956681	+	0.291137i	$0.0940335\pi$
$653$	31.8866	+	31.8866i	1.24782	+	1.24782i	0.291137	+	0.956681i	$0.405967\pi$
$654$		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	0.443159	−	0.896443i	$-0.353858\pi$
$659$	−11.6363	−	11.6363i	−0.453284	−	0.453284i	−0.896443	+	0.443159i	$0.853858\pi$
$660$		0			0
$661$		−	48.9963i		−	1.90573i	−0.303387	−	0.952867i	$-0.598118\pi$
$661$		−	48.9963i		−	1.90573i	0.303387	−	0.952867i	$-0.401882\pi$
$662$		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	−0.642612	−	0.766192i	$-0.722149\pi$
$673$	3.20595	−	3.20595i	0.123580	−	0.123580i	0.766192	+	0.642612i	$0.222149\pi$
$674$		0			0
$675$	−1.61514	+	1.61514i	−0.0621669	+	0.0621669i
$676$		0			0
$677$		−	22.6084i		−	0.868910i	−0.900694	−	0.434455i	$-0.856941\pi$
$677$		−	22.6084i		−	0.868910i	0.900694	−	0.434455i	$-0.143059\pi$
$678$		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	−0.423768	−	0.905771i	$-0.639293\pi$
$683$	12.5968	−	12.5968i	0.482003	−	0.482003i	0.905771	+	0.423768i	$0.139293\pi$
$684$		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	0.0346483	−	0.999400i	$-0.488969\pi$
$691$	27.1819	−	27.1819i	1.03405	−	1.03405i	0.999400	−	0.0346483i	$-0.0110311\pi$
$692$		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	−0.960016	−	0.279946i	$-0.909683\pi$
$709$	−33.0165	−	33.0165i	−1.23996	−	1.23996i	−0.279946	−	0.960016i	$-0.590317\pi$
$710$		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	−0.649906	−	0.760014i	$-0.725192\pi$
$719$	2.95246	−	2.95246i	0.110108	−	0.110108i	0.760014	+	0.649906i	$0.225192\pi$
$720$		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	0.975354	−	0.220647i	$-0.0708170\pi$
$727$	20.3491	+	20.3491i	0.754706	+	0.754706i	−0.220647	+	0.975354i	$0.570817\pi$
$728$		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	$0.282925\pi$
$733$			42.0371i			1.55268i	−0.630316	+	0.776338i	$0.717075\pi$
$734$		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	$-0.748503\pi$
$743$		−	38.7296i		−	1.42085i	0.703773	−	0.710425i	$-0.251497\pi$
$744$		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	0.826486	−	0.562958i	$-0.190337\pi$
$751$	7.22182	+	7.22182i	0.263528	+	0.263528i	−0.562958	+	0.826486i	$0.690337\pi$
$752$		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	−0.0285234	−	0.999593i	$-0.509081\pi$
$757$	26.7177	−	26.7177i	0.971070	−	0.971070i	0.999593	+	0.0285234i	$0.00908050\pi$
$758$		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	−0.880022	−	0.474932i	$-0.842473\pi$
$773$	−11.2627	+	11.2627i	−0.405090	+	0.405090i	0.474932	+	0.880022i	$0.342473\pi$
$774$		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	$-0.824528\pi$
$787$		−	29.3868i		−	1.04753i	0.851864	−	0.523764i	$-0.175472\pi$
$788$		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	0.549666	−	0.835384i	$-0.314755\pi$
$809$	−8.12665	−	8.12665i	−0.285718	−	0.285718i	−0.835384	+	0.549666i	$0.814755\pi$
$810$		0			0
$811$		−	52.4059i		−	1.84022i	−0.391662	−	0.920109i	$-0.628100\pi$
$811$		−	52.4059i		−	1.84022i	0.391662	−	0.920109i	$-0.371900\pi$
$812$		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	0.985988	+	0.166815i	$0.0533483\pi$
$823$	33.0716	+	33.0716i	1.15280	+	1.15280i	0.166815	+	0.985988i	$0.446652\pi$
$824$		0			0
$825$			2.13344i			0.0742768i
$826$		0			0
$827$	−19.3804	−	19.3804i	−0.673923	−	0.673923i	0.284695	−	0.958618i	$-0.408108\pi$
$827$	−19.3804	−	19.3804i	−0.673923	−	0.673923i	−0.958618	+	0.284695i	$0.908108\pi$
$828$		0			0
$829$		−	31.8105i		−	1.10483i	−0.833571	−	0.552413i	$-0.813707\pi$
$829$		−	31.8105i		−	1.10483i	0.833571	−	0.552413i	$-0.186293\pi$
$830$		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	−0.617105	−	0.786881i	$-0.711695\pi$
$839$	4.91765	−	4.91765i	0.169776	−	0.169776i	0.786881	+	0.617105i	$0.211695\pi$
$840$		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	$0.0978264\pi$
$853$			17.6706i			0.605031i	−0.953144	+	0.302516i	$0.902174\pi$
$854$		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	$-0.901803\pi$
$859$		−	17.7978i		−	0.607252i	0.952791	−	0.303626i	$-0.0981974\pi$
$860$		0			0
$861$	1.33117	−	0.00443008i	0.0453662	−	0.000150977i
$862$		0			0
$863$		−	16.7423i		−	0.569915i	−0.958540	−	0.284957i	$-0.908021\pi$
$863$		−	16.7423i		−	0.569915i	0.958540	−	0.284957i	$-0.0919794\pi$
$864$		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	$0.0646359\pi$
$881$			11.9716i			0.403334i	−0.979454	+	0.201667i	$0.935364\pi$
$882$		0			0
$883$	−25.3070	+	25.3070i	−0.851649	+	0.851649i	−0.990336	−	0.138687i	$-0.955712\pi$
$883$	−25.3070	+	25.3070i	−0.851649	+	0.851649i	0.138687	+	0.990336i	$0.455712\pi$
$884$		0			0
$885$	−2.37781	+	2.37781i	−0.0799291	+	0.0799291i
$886$		0			0
$887$	−41.4254	+	41.4254i	−1.39093	+	1.39093i	−0.567677	+	0.823252i	$0.692158\pi$
$887$	−41.4254	+	41.4254i	−1.39093	+	1.39093i	−0.823252	+	0.567677i	$0.807842\pi$
$888$		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	$0.0507593\pi$
$907$			9.56439i			0.317580i	−0.987312	+	0.158790i	$0.949241\pi$
$908$		0			0
$909$	−13.5123	−	13.5123i	−0.448176	−	0.448176i
$910$		0			0
$911$		−	47.7805i		−	1.58304i	−0.611143	−	0.791520i	$-0.709290\pi$
$911$		−	47.7805i		−	1.58304i	0.611143	−	0.791520i	$-0.290710\pi$
$912$		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	−0.553258	−	0.833010i	$-0.686616\pi$
$919$	8.48066	−	8.48066i	0.279751	−	0.279751i	0.833010	+	0.553258i	$0.186616\pi$
$920$		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	−0.856691	−	0.515830i	$-0.827484\pi$
$929$	−10.3893	+	10.3893i	−0.340861	+	0.340861i	0.515830	+	0.856691i	$0.327484\pi$
$930$		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	−0.915883	−	0.401446i	$-0.868508\pi$
$937$	−15.7471	+	15.7471i	−0.514437	+	0.514437i	0.401446	+	0.915883i	$0.368508\pi$
$938$		0			0
$939$	−0.122516			−0.00399816
$940$		0			0
$941$		−	38.0283i		−	1.23969i	−0.784726	−	0.619843i	$-0.787196\pi$
$941$		−	38.0283i		−	1.23969i	0.784726	−	0.619843i	$-0.212804\pi$
$942$		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	−0.825264	−	0.564747i	$-0.808974\pi$
$967$	−8.10120	+	8.10120i	−0.260517	+	0.260517i	0.564747	+	0.825264i	$0.308974\pi$
$968$		0			0
$969$	−2.95232	+	2.95232i	−0.0948422	+	0.0948422i
$970$		0			0
$971$	−7.09729	−	7.09729i	−0.227763	−	0.227763i	0.583995	−	0.811757i	$-0.301489\pi$
$971$	−7.09729	−	7.09729i	−0.227763	−	0.227763i	−0.811757	+	0.583995i	$0.801489\pi$
$972$		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	−0.856811	−	0.515630i	$-0.827558\pi$
$977$	−42.8984	−	42.8984i	−1.37244	−	1.37244i	−0.515630	−	0.856811i	$-0.672442\pi$
$978$		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	0.926090	−	0.377303i	$-0.123148\pi$
$991$	17.2759	+	17.2759i	0.548787	+	0.548787i	−0.377303	+	0.926090i	$0.623148\pi$
$992$		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	0.749816	−	0.661646i	$-0.230142\pi$
$997$	2.78401	+	2.78401i	0.0881703	+	0.0881703i	−0.661646	+	0.749816i	$0.730142\pi$
$998$		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.337.10	✓	36
41.32	even	4	inner	1148.2.k.b.729.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.10	✓	36	1.1	even	1	trivial
1148.2.k.b.729.10	yes	36	41.32	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
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

Varieties

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Database

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