LMFDB - Embedded newform 1160.2.bl.c.737.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1160,2,Mod(713,1160)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1160.713"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1160, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1160 = 2^{3} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1160.bl (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [42,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.26264663447$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			737.7
Character	$\chi$	$=$	1160.737
Dual form			1160.2.bl.c.713.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.70895 q^{3} +(-1.82020 + 1.29879i) q^{5} +(1.24431 + 1.24431i) q^{7} -0.0795021 q^{9} +(-2.03329 - 2.03329i) q^{11} +(-2.26136 - 2.26136i) q^{13} +(3.11063 - 2.21956i) q^{15} +1.14490i q^{17} +(2.14303 - 2.14303i) q^{19} +(-2.12645 - 2.12645i) q^{21} +(-4.92034 + 4.92034i) q^{23} +(1.62629 - 4.72813i) q^{25} +5.26270 q^{27} +(-5.07745 - 1.79431i) q^{29} +(5.72978 + 5.72978i) q^{31} +(3.47479 + 3.47479i) q^{33} +(-3.88098 - 0.648798i) q^{35} +5.71262 q^{37} +(3.86454 + 3.86454i) q^{39} +(4.87222 - 4.87222i) q^{41} +4.09667 q^{43} +(0.144710 - 0.103257i) q^{45} +4.43658 q^{47} -3.90341i q^{49} -1.95657i q^{51} +(4.75857 - 4.75857i) q^{53} +(6.34183 + 1.06019i) q^{55} +(-3.66232 + 3.66232i) q^{57} +7.13518i q^{59} +(-7.52807 - 7.52807i) q^{61} +(-0.0989249 - 0.0989249i) q^{63} +(7.05317 + 1.17910i) q^{65} +(4.81206 - 4.81206i) q^{67} +(8.40860 - 8.40860i) q^{69} -0.429835i q^{71} +6.67557i q^{73} +(-2.77924 + 8.08012i) q^{75} -5.06007i q^{77} +(4.85454 - 4.85454i) q^{79} -8.75517 q^{81} +(11.9524 - 11.9524i) q^{83} +(-1.48698 - 2.08394i) q^{85} +(8.67708 + 3.06637i) q^{87} +(5.43313 - 5.43313i) q^{89} -5.62765i q^{91} +(-9.79189 - 9.79189i) q^{93} +(-1.11740 + 6.68409i) q^{95} +2.84180 q^{97} +(0.161651 + 0.161651i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 8 q^{3} - 2 q^{5} + 4 q^{7} + 34 q^{9} + 2 q^{11} + 4 q^{13} - 4 q^{15} + 8 q^{19} + 4 q^{21} - 20 q^{23} + 4 q^{25} - 8 q^{27} + 20 q^{29} + 2 q^{31} - 10 q^{33} + 16 q^{35} - 12 q^{37} + 10 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) $ 42 * q - 8 * q^3 - 2 * q^5 + 4 * q^7 + 34 * q^9 + 2 * q^11 + 4 * q^13 - 4 * q^15 + 8 * q^19 + 4 * q^21 - 20 * q^23 + 4 * q^25 - 8 * q^27 + 20 * q^29 + 2 * q^31 - 10 * q^33 + 16 * q^35 - 12 * q^37 + 10 * q^39 - 30 * q^41 + 4 * q^43 - 32 * q^45 - 4 * q^47 + 16 * q^53 + 2 * q^55 + 40 * q^57 + 26 * q^61 + 80 * q^63 + 8 * q^65 + 44 * q^67 + 12 * q^69 + 4 * q^75 - 42 * q^79 + 114 * q^81 - 68 * q^83 + 30 * q^85 - 32 * q^87 + 18 * q^89 + 6 * q^93 - 26 * q^95 - 24 * q^97 + 60 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1160\mathbb{Z}\right)^\times$.

$n$	$321$	$581$	$697$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.70895			−0.986661			−0.493330	−	0.869842i	$-0.664221\pi$
$3$	−1.70895			−0.986661			−0.493330	+	0.869842i	$0.664221\pi$
$4$		0			0
$5$	−1.82020	+	1.29879i	−0.814020	+	0.580837i
$5$	−1.82020	+	1.29879i	−0.814020	+	0.580837i
$6$		0			0
$7$	1.24431	+	1.24431i	0.470303	+	0.470303i	0.902013	−	0.431709i	$-0.142089\pi$
$7$	1.24431	+	1.24431i	0.470303	+	0.470303i	−0.431709	+	0.902013i	$0.642089\pi$
$8$		0			0
$9$	−0.0795021			−0.0265007
$10$		0			0
$11$	−2.03329	−	2.03329i	−0.613061	−	0.613061i	0.330682	−	0.943742i	$-0.392721\pi$
$11$	−2.03329	−	2.03329i	−0.613061	−	0.613061i	−0.943742	+	0.330682i	$0.892721\pi$
$12$		0			0
$13$	−2.26136	−	2.26136i	−0.627188	−	0.627188i	0.320171	−	0.947360i	$-0.396260\pi$
$13$	−2.26136	−	2.26136i	−0.627188	−	0.627188i	−0.947360	+	0.320171i	$0.896260\pi$
$14$		0			0
$15$	3.11063	−	2.21956i	0.803162	−	0.573089i
$16$		0			0
$17$			1.14490i			0.277678i	0.990315	+	0.138839i	$0.0443370\pi$
$17$			1.14490i			0.277678i	−0.990315	+	0.138839i	$0.955663\pi$
$18$		0			0
$19$	2.14303	−	2.14303i	0.491644	−	0.491644i	−0.417180	−	0.908824i	$-0.636981\pi$
$19$	2.14303	−	2.14303i	0.491644	−	0.491644i	0.908824	+	0.417180i	$0.136981\pi$
$20$		0			0
$21$	−2.12645	−	2.12645i	−0.464030	−	0.464030i
$22$		0			0
$23$	−4.92034	+	4.92034i	−1.02596	+	1.02596i	−0.0263081	+	0.999654i	$0.508375\pi$
$23$	−4.92034	+	4.92034i	−1.02596	+	1.02596i	−0.999654	+	0.0263081i	$0.991625\pi$
$24$		0			0
$25$	1.62629	−	4.72813i	0.325257	−	0.945626i
$26$		0			0
$27$	5.26270			1.01281
$28$		0			0
$29$	−5.07745	−	1.79431i	−0.942858	−	0.333194i
$29$	−5.07745	−	1.79431i	−0.942858	−	0.333194i
$30$		0			0
$31$	5.72978	+	5.72978i	1.02910	+	1.02910i	0.999564	+	0.0295358i	$0.00940291\pi$
$31$	5.72978	+	5.72978i	1.02910	+	1.02910i	0.0295358	+	0.999564i	$0.490597\pi$
$32$		0			0
$33$	3.47479	+	3.47479i	0.604883	+	0.604883i
$34$		0			0
$35$	−3.88098	−	0.648798i	−0.656006	−	0.109667i
$36$		0			0
$37$	5.71262			0.939149			0.469574	−	0.882893i	$-0.344407\pi$
$37$	5.71262			0.939149			0.469574	+	0.882893i	$0.344407\pi$
$38$		0			0
$39$	3.86454	+	3.86454i	0.618822	+	0.618822i
$40$		0			0
$41$	4.87222	−	4.87222i	0.760912	−	0.760912i	−0.215575	−	0.976487i	$-0.569163\pi$
$41$	4.87222	−	4.87222i	0.760912	−	0.760912i	0.976487	+	0.215575i	$0.0691625\pi$
$42$		0			0
$43$	4.09667			0.624736			0.312368	−	0.949961i	$-0.398878\pi$
$43$	4.09667			0.624736			0.312368	+	0.949961i	$0.398878\pi$
$44$		0			0
$45$	0.144710	−	0.103257i	0.0215721	−	0.0153926i
$46$		0			0
$47$	4.43658			0.647141			0.323571	−	0.946204i	$-0.395117\pi$
$47$	4.43658			0.647141			0.323571	+	0.946204i	$0.395117\pi$
$48$		0			0
$49$		−	3.90341i		−	0.557630i
$50$		0			0
$51$		−	1.95657i		−	0.273974i
$52$		0			0
$53$	4.75857	−	4.75857i	0.653640	−	0.653640i	−0.300228	−	0.953868i	$-0.597063\pi$
$53$	4.75857	−	4.75857i	0.653640	−	0.653640i	0.953868	+	0.300228i	$0.0970627\pi$
$54$		0			0
$55$	6.34183	+	1.06019i	0.855132	+	0.142955i
$56$		0			0
$57$	−3.66232	+	3.66232i	−0.485086	+	0.485086i
$58$		0			0
$59$			7.13518i			0.928922i	0.885594	+	0.464461i	$0.153752\pi$
$59$			7.13518i			0.928922i	−0.885594	+	0.464461i	$0.846248\pi$
$60$		0			0
$61$	−7.52807	−	7.52807i	−0.963870	−	0.963870i	0.0354995	−	0.999370i	$-0.488698\pi$
$61$	−7.52807	−	7.52807i	−0.963870	−	0.963870i	−0.999370	+	0.0354995i	$0.988698\pi$
$62$		0			0
$63$	−0.0989249	−	0.0989249i	−0.0124634	−	0.0124634i
$64$		0			0
$65$	7.05317	+	1.17910i	0.874838	+	0.146250i
$66$		0			0
$67$	4.81206	−	4.81206i	0.587887	−	0.587887i	−0.349172	−	0.937059i	$-0.613537\pi$
$67$	4.81206	−	4.81206i	0.587887	−	0.587887i	0.937059	+	0.349172i	$0.113537\pi$
$68$		0			0
$69$	8.40860	−	8.40860i	1.01228	−	1.01228i
$70$		0			0
$71$		−	0.429835i		−	0.0510120i	−0.999675	−	0.0255060i	$-0.991880\pi$
$71$		−	0.429835i		−	0.0510120i	0.999675	−	0.0255060i	$-0.00811970\pi$
$72$		0			0
$73$			6.67557i			0.781316i	0.920536	+	0.390658i	$0.127752\pi$
$73$			6.67557i			0.781316i	−0.920536	+	0.390658i	$0.872248\pi$
$74$		0			0
$75$	−2.77924	+	8.08012i	−0.320919	+	0.933012i
$76$		0			0
$77$		−	5.06007i		−	0.576649i
$78$		0			0
$79$	4.85454	−	4.85454i	0.546178	−	0.546178i	−0.379155	−	0.925333i	$-0.623785\pi$
$79$	4.85454	−	4.85454i	0.546178	−	0.546178i	0.925333	+	0.379155i	$0.123785\pi$
$80$		0			0
$81$	−8.75517			−0.972797
$82$		0			0
$83$	11.9524	−	11.9524i	1.31194	−	1.31194i	0.391959	−	0.919983i	$-0.371797\pi$
$83$	11.9524	−	11.9524i	1.31194	−	1.31194i	0.919983	−	0.391959i	$-0.128203\pi$
$84$		0			0
$85$	−1.48698	−	2.08394i	−0.161286	−	0.226035i
$86$		0			0
$87$	8.67708	+	3.06637i	0.930281	+	0.328750i
$88$		0			0
$89$	5.43313	−	5.43313i	0.575911	−	0.575911i	−0.357863	−	0.933774i	$-0.616495\pi$
$89$	5.43313	−	5.43313i	0.575911	−	0.575911i	0.933774	+	0.357863i	$0.116495\pi$
$90$		0			0
$91$		−	5.62765i		−	0.589938i
$92$		0			0
$93$	−9.79189	−	9.79189i	−1.01537	−	1.01537i
$94$		0			0
$95$	−1.11740	+	6.68409i	−0.114643	+	0.685773i
$96$		0			0
$97$	2.84180			0.288542			0.144271	−	0.989538i	$-0.453916\pi$
$97$	2.84180			0.288542			0.144271	+	0.989538i	$0.453916\pi$
$98$		0			0
$99$	0.161651	+	0.161651i	0.0162465	+	0.0162465i
$100$		0			0
$101$	−12.4565	−	12.4565i	−1.23947	−	1.23947i	−0.960218	−	0.279253i	$-0.909913\pi$
$101$	−12.4565	−	12.4565i	−1.23947	−	1.23947i	−0.279253	−	0.960218i	$-0.590087\pi$
$102$		0			0
$103$	−0.387432	+	0.387432i	−0.0381748	+	0.0381748i	−0.725937	−	0.687762i	$-0.758593\pi$
$103$	−0.387432	+	0.387432i	−0.0381748	+	0.0381748i	0.687762	+	0.725937i	$0.258593\pi$
$104$		0			0
$105$	6.63239	+	1.10876i	0.647255	+	0.108204i
$106$		0			0
$107$	8.10940	+	8.10940i	0.783966	+	0.783966i	0.980497	−	0.196532i	$-0.0629679\pi$
$107$	8.10940	+	8.10940i	0.783966	+	0.783966i	−0.196532	+	0.980497i	$0.562968\pi$
$108$		0			0
$109$	11.2902			1.08141			0.540703	−	0.841214i	$-0.318158\pi$
$109$	11.2902			1.08141			0.540703	+	0.841214i	$0.318158\pi$
$110$		0			0
$111$	−9.76256			−0.926621
$112$		0			0
$113$		−	5.97851i		−	0.562411i	−0.959648	−	0.281205i	$-0.909266\pi$
$113$		−	5.97851i		−	0.562411i	0.959648	−	0.281205i	$-0.0907342\pi$
$114$		0			0
$115$	2.56553	−	15.3465i	0.239237	−	1.43107i
$116$		0			0
$117$	0.179783	+	0.179783i	0.0166209	+	0.0166209i
$118$		0			0
$119$	−1.42460	+	1.42460i	−0.130593	+	0.130593i
$120$		0			0
$121$		−	2.73145i		−	0.248314i
$122$		0			0
$123$	−8.32636	+	8.32636i	−0.750762	+	0.750762i
$124$		0			0
$125$	3.18067	+	10.7184i	0.284488	+	0.958680i
$126$		0			0
$127$			10.0059i			0.887883i	0.896056	+	0.443942i	$0.146420\pi$
$127$			10.0059i			0.887883i	−0.896056	+	0.443942i	$0.853580\pi$
$128$		0			0
$129$	−7.00098			−0.616402
$130$		0			0
$131$	−1.46901	+	1.46901i	−0.128348	+	0.128348i	−0.768363	−	0.640015i	$-0.778928\pi$
$131$	−1.46901	+	1.46901i	−0.128348	+	0.128348i	0.640015	+	0.768363i	$0.278928\pi$
$132$		0			0
$133$	5.33316			0.462444
$134$		0			0
$135$	−9.57920	+	6.83515i	−0.824446	+	0.588276i
$136$		0			0
$137$			17.0897i			1.46007i	0.683411	+	0.730034i	$0.260496\pi$
$137$			17.0897i			1.46007i	−0.683411	+	0.730034i	$0.739504\pi$
$138$		0			0
$139$		−	14.2352i		−	1.20742i	−0.797206	−	0.603708i	$-0.793689\pi$
$139$		−	14.2352i		−	1.20742i	0.797206	−	0.603708i	$-0.206311\pi$
$140$		0			0
$141$	−7.58187			−0.638509
$142$		0			0
$143$			9.19601i			0.769009i
$144$		0			0
$145$	11.5724	−	3.32853i	0.961037	−	0.276420i
$146$		0			0
$147$			6.67071i			0.550191i
$148$		0			0
$149$	−5.49541			−0.450201			−0.225101	−	0.974336i	$-0.572271\pi$
$149$	−5.49541			−0.450201			−0.225101	+	0.974336i	$0.572271\pi$
$150$		0			0
$151$			9.75739i			0.794045i	0.917809	+	0.397022i	$0.129957\pi$
$151$			9.75739i			0.794045i	−0.917809	+	0.397022i	$0.870043\pi$
$152$		0			0
$153$		−	0.0910216i		−	0.00735866i
$154$		0			0
$155$	−17.8712	−	2.98759i	−1.43545	−	0.239969i
$156$		0			0
$157$	−19.4741			−1.55420			−0.777102	−	0.629375i	$-0.783311\pi$
$157$	−19.4741			−1.55420			−0.777102	+	0.629375i	$0.783311\pi$
$158$		0			0
$159$	−8.13214	+	8.13214i	−0.644921	+	0.644921i
$160$		0			0
$161$	−12.2448			−0.965027
$162$		0			0
$163$			4.60847i			0.360963i	0.983578	+	0.180481i	$0.0577656\pi$
$163$			4.60847i			0.360963i	−0.983578	+	0.180481i	$0.942234\pi$
$164$		0			0
$165$	−10.8378	−	1.81180i	−0.843725	−	0.141049i
$166$		0			0
$167$	−5.23112	+	5.23112i	−0.404796	+	0.404796i	−0.879919	−	0.475123i	$-0.842404\pi$
$167$	−5.23112	+	5.23112i	−0.404796	+	0.404796i	0.475123	+	0.879919i	$0.342404\pi$
$168$		0			0
$169$		−	2.77250i		−	0.213269i
$170$		0			0
$171$	−0.170375	+	0.170375i	−0.0130289	+	0.0130289i
$172$		0			0
$173$	14.7626	+	14.7626i	1.12238	+	1.12238i	0.991383	+	0.130994i	$0.0418169\pi$
$173$	14.7626	+	14.7626i	1.12238	+	1.12238i	0.130994	+	0.991383i	$0.458183\pi$
$174$		0			0
$175$	7.90683	−	3.85964i	0.597700	−	0.291761i
$176$		0			0
$177$		−	12.1936i		−	0.916531i
$178$		0			0
$179$	−10.6268			−0.794281			−0.397141	−	0.917758i	$-0.629998\pi$
$179$	−10.6268			−0.794281			−0.397141	+	0.917758i	$0.629998\pi$
$180$		0			0
$181$	1.80363			0.134063			0.0670314	−	0.997751i	$-0.478647\pi$
$181$	1.80363			0.134063			0.0670314	+	0.997751i	$0.478647\pi$
$182$		0			0
$183$	12.8651	+	12.8651i	0.951013	+	0.951013i
$184$		0			0
$185$	−10.3981	+	7.41949i	−0.764486	+	0.545492i
$186$		0			0
$187$	2.32791	−	2.32791i	0.170233	−	0.170233i
$188$		0			0
$189$	6.54841	+	6.54841i	0.476327	+	0.476327i
$190$		0			0
$191$	−0.513771	−	0.513771i	−0.0371752	−	0.0371752i	0.688275	−	0.725450i	$-0.258368\pi$
$191$	−0.513771	−	0.513771i	−0.0371752	−	0.0371752i	−0.725450	+	0.688275i	$0.758368\pi$
$192$		0			0
$193$	6.44608			0.463999			0.232000	−	0.972716i	$-0.425473\pi$
$193$	6.44608			0.463999			0.232000	+	0.972716i	$0.425473\pi$
$194$		0			0
$195$	−12.0535	−	2.01503i	−0.863168	−	0.144299i
$196$		0			0
$197$	1.03684	+	1.03684i	0.0738717	+	0.0738717i	0.743077	−	0.669206i	$-0.233365\pi$
$197$	1.03684	+	1.03684i	0.0738717	+	0.0738717i	−0.669206	+	0.743077i	$0.733365\pi$
$198$		0			0
$199$		−	25.8568i		−	1.83294i	−0.400108	−	0.916468i	$-0.631027\pi$
$199$		−	25.8568i		−	1.83294i	0.400108	−	0.916468i	$-0.368973\pi$
$200$		0			0
$201$	−8.22356	+	8.22356i	−0.580045	+	0.580045i
$202$		0			0
$203$	−4.08523	−	8.55056i	−0.286727	−	0.600132i
$204$		0			0
$205$	−2.54044	+	15.1964i	−0.177432	+	1.06136i
$206$		0			0
$207$	0.391177	−	0.391177i	0.0271887	−	0.0271887i
$208$		0			0
$209$	−8.71480			−0.602815
$210$		0			0
$211$	7.25757	−	7.25757i	0.499632	−	0.499632i	−0.411692	−	0.911323i	$-0.635062\pi$
$211$	7.25757	−	7.25757i	0.499632	−	0.499632i	0.911323	+	0.411692i	$0.135062\pi$
$212$		0			0
$213$			0.734565i			0.0503316i
$214$		0			0
$215$	−7.45677	+	5.32071i	−0.508547	+	0.362869i
$216$		0			0
$217$			14.2592i			0.967978i
$218$		0			0
$219$		−	11.4082i		−	0.770894i
$220$		0			0
$221$	2.58902	−	2.58902i	0.174156	−	0.174156i
$222$		0			0
$223$	11.0343	−	11.0343i	0.738914	−	0.738914i	−0.233454	−	0.972368i	$-0.575003\pi$
$223$	11.0343	−	11.0343i	0.738914	−	0.738914i	0.972368	+	0.233454i	$0.0750028\pi$
$224$		0			0
$225$	−0.129293	+	0.375896i	−0.00861954	+	0.0250597i
$226$		0			0
$227$	4.64245	+	4.64245i	0.308130	+	0.308130i	0.844184	−	0.536054i	$-0.180086\pi$
$227$	4.64245	+	4.64245i	0.308130	+	0.308130i	−0.536054	+	0.844184i	$0.680086\pi$
$228$		0			0
$229$	11.4348	+	11.4348i	0.755634	+	0.755634i	0.975525	−	0.219891i	$-0.0705700\pi$
$229$	11.4348	+	11.4348i	0.755634	+	0.755634i	−0.219891	+	0.975525i	$0.570570\pi$
$230$		0			0
$231$			8.64739i			0.568957i
$232$		0			0
$233$	15.1974	−	15.1974i	0.995617	−	0.995617i	−0.00437330	−	0.999990i	$-0.501392\pi$
$233$	15.1974	−	15.1974i	0.995617	−	0.995617i	0.999990	+	0.00437330i	$0.00139207\pi$
$234$		0			0
$235$	−8.07548	+	5.76219i	−0.526786	+	0.375884i
$236$		0			0
$237$	−8.29615	+	8.29615i	−0.538893	+	0.538893i
$238$		0			0
$239$		−	10.0305i		−	0.648817i	−0.945917	−	0.324408i	$-0.894835\pi$
$239$		−	10.0305i		−	0.648817i	0.945917	−	0.324408i	$-0.105165\pi$
$240$		0			0
$241$			3.99577i			0.257390i	0.991684	+	0.128695i	$0.0410789\pi$
$241$			3.99577i			0.257390i	−0.991684	+	0.128695i	$0.958921\pi$
$242$		0			0
$243$	−0.825990			−0.0529873
$244$		0			0
$245$	5.06971	+	7.10500i	0.323892	+	0.453922i
$246$		0			0
$247$	−9.69232			−0.616707
$248$		0			0
$249$	−20.4259	+	20.4259i	−1.29444	+	1.29444i
$250$		0			0
$251$	−17.7882	−	17.7882i	−1.12278	−	1.12278i	−0.991321	−	0.131460i	$-0.958033\pi$
$251$	−17.7882	−	17.7882i	−1.12278	−	1.12278i	−0.131460	−	0.991321i	$-0.541967\pi$
$252$		0			0
$253$	20.0090			1.25795
$254$		0			0
$255$	2.54117	+	3.56135i	0.159134	+	0.223020i
$256$		0			0
$257$	−17.9083	−	17.9083i	−1.11709	−	1.11709i	−0.992166	−	0.124926i	$-0.960131\pi$
$257$	−17.9083	−	17.9083i	−1.11709	−	1.11709i	−0.124926	−	0.992166i	$-0.539869\pi$
$258$		0			0
$259$	7.10824	+	7.10824i	0.441685	+	0.441685i
$260$		0			0
$261$	0.403668	+	0.142651i	0.0249864	+	0.00882989i
$262$		0			0
$263$	−6.44568			−0.397458			−0.198729	−	0.980055i	$-0.563681\pi$
$263$	−6.44568			−0.397458			−0.198729	+	0.980055i	$0.563681\pi$
$264$		0			0
$265$	−2.48118	+	14.8420i	−0.152418	+	0.911734i
$266$		0			0
$267$	−9.28494	+	9.28494i	−0.568229	+	0.568229i
$268$		0			0
$269$	−17.3354	−	17.3354i	−1.05696	−	1.05696i	−0.998277	−	0.0586816i	$-0.981310\pi$
$269$	−17.3354	−	17.3354i	−1.05696	−	1.05696i	−0.0586816	−	0.998277i	$-0.518690\pi$
$270$		0			0
$271$	−15.5018	+	15.5018i	−0.941669	+	0.941669i	−0.998390	−	0.0567213i	$-0.981935\pi$
$271$	−15.5018	+	15.5018i	−0.941669	+	0.941669i	0.0567213	+	0.998390i	$0.481935\pi$
$272$		0			0
$273$			9.61735i			0.582068i
$274$		0			0
$275$	−12.9204	+	6.30695i	−0.779128	+	0.380323i
$276$		0			0
$277$	4.40524	+	4.40524i	0.264685	+	0.264685i	0.826954	−	0.562269i	$-0.190072\pi$
$277$	4.40524	+	4.40524i	0.264685	+	0.264685i	−0.562269	+	0.826954i	$0.690072\pi$
$278$		0			0
$279$	−0.455530	−	0.455530i	−0.0272719	−	0.0272719i
$280$		0			0
$281$	−9.80190			−0.584732			−0.292366	−	0.956306i	$-0.594443\pi$
$281$	−9.80190			−0.584732			−0.292366	+	0.956306i	$0.594443\pi$
$282$		0			0
$283$	−10.1118	−	10.1118i	−0.601085	−	0.601085i	0.339515	−	0.940601i	$-0.389737\pi$
$283$	−10.1118	−	10.1118i	−0.601085	−	0.601085i	−0.940601	+	0.339515i	$0.889737\pi$
$284$		0			0
$285$	1.90958	−	11.4228i	0.113114	−	0.676626i
$286$		0			0
$287$	12.1251			0.715719
$288$		0			0
$289$	15.6892			0.922895
$290$		0			0
$291$	−4.85649			−0.284693
$292$		0			0
$293$	−16.3980			−0.957984			−0.478992	−	0.877819i	$-0.658998\pi$
$293$	−16.3980			−0.957984			−0.478992	+	0.877819i	$0.658998\pi$
$294$		0			0
$295$	−9.26711	−	12.9875i	−0.539552	−	0.756161i
$296$		0			0
$297$	−10.7006	−	10.7006i	−0.620913	−	0.620913i
$298$		0			0
$299$	22.2533			1.28694
$300$		0			0
$301$	5.09750	+	5.09750i	0.293815	+	0.293815i
$302$		0			0
$303$	21.2875	+	21.2875i	1.22294	+	1.22294i
$304$		0			0
$305$	23.4800	+	3.92524i	1.34446	+	0.224758i
$306$		0			0
$307$		−	7.71576i		−	0.440362i	−0.975459	−	0.220181i	$-0.929335\pi$
$307$		−	7.71576i		−	0.440362i	0.975459	−	0.220181i	$-0.0706647\pi$
$308$		0			0
$309$	0.662100	−	0.662100i	0.0376656	−	0.0376656i
$310$		0			0
$311$	19.4387	+	19.4387i	1.10227	+	1.10227i	0.994137	+	0.108132i	$0.0344868\pi$
$311$	19.4387	+	19.4387i	1.10227	+	1.10227i	0.108132	+	0.994137i	$0.465513\pi$
$312$		0			0
$313$	3.79941	−	3.79941i	0.214755	−	0.214755i	−0.591529	−	0.806284i	$-0.701475\pi$
$313$	3.79941	−	3.79941i	0.214755	−	0.214755i	0.806284	+	0.591529i	$0.201475\pi$
$314$		0			0
$315$	0.308546	+	0.0515808i	0.0173846	+	0.00290625i
$316$		0			0
$317$	−9.67291			−0.543285			−0.271642	−	0.962398i	$-0.587567\pi$
$317$	−9.67291			−0.543285			−0.271642	+	0.962398i	$0.587567\pi$
$318$		0			0
$319$	6.67558	+	13.9723i	0.373761	+	0.782298i
$320$		0			0
$321$	−13.8585	−	13.8585i	−0.773508	−	0.773508i
$322$		0			0
$323$	2.45354	+	2.45354i	0.136519	+	0.136519i
$324$		0			0
$325$	−14.3696	+	7.01438i	−0.797083	+	0.389088i
$326$		0			0
$327$	−19.2943			−1.06698
$328$		0			0
$329$	5.52046	+	5.52046i	0.304353	+	0.304353i
$330$		0			0
$331$	−15.0790	+	15.0790i	−0.828815	+	0.828815i	−0.987353	−	0.158538i	$-0.949322\pi$
$331$	−15.0790	+	15.0790i	−0.828815	+	0.828815i	0.158538	+	0.987353i	$0.449322\pi$
$332$		0			0
$333$	−0.454165			−0.0248881
$334$		0			0
$335$	−2.50908	+	15.0088i	−0.137085	+	0.820018i
$336$		0			0
$337$	−7.46187			−0.406474			−0.203237	−	0.979130i	$-0.565146\pi$
$337$	−7.46187			−0.406474			−0.203237	+	0.979130i	$0.565146\pi$
$338$		0			0
$339$			10.2170i			0.554909i
$340$		0			0
$341$		−	23.3006i		−	1.26180i
$342$		0			0
$343$	13.5672	−	13.5672i	0.732558	−	0.732558i
$344$		0			0
$345$	−4.38436	+	26.2264i	−0.236046	+	1.41198i
$346$		0			0
$347$	2.76542	−	2.76542i	0.148456	−	0.148456i	−0.628972	−	0.777428i	$-0.716524\pi$
$347$	2.76542	−	2.76542i	0.148456	−	0.148456i	0.777428	+	0.628972i	$0.216524\pi$
$348$		0			0
$349$		−	24.5732i		−	1.31538i	−0.753291	−	0.657688i	$-0.771535\pi$
$349$		−	24.5732i		−	1.31538i	0.753291	−	0.657688i	$-0.228465\pi$
$350$		0			0
$351$	−11.9009	−	11.9009i	−0.635221	−	0.635221i
$352$		0			0
$353$	−19.1964	−	19.1964i	−1.02172	−	1.02172i	−0.999759	−	0.0219603i	$-0.993009\pi$
$353$	−19.1964	−	19.1964i	−1.02172	−	1.02172i	−0.0219603	−	0.999759i	$-0.506991\pi$
$354$		0			0
$355$	0.558266	+	0.782388i	0.0296297	+	0.0415248i
$356$		0			0
$357$	2.43457	−	2.43457i	0.128851	−	0.128851i
$358$		0			0
$359$	17.0947	−	17.0947i	0.902222	−	0.902222i	−0.0934058	−	0.995628i	$-0.529775\pi$
$359$	17.0947	−	17.0947i	0.902222	−	0.902222i	0.995628	+	0.0934058i	$0.0297754\pi$
$360$		0			0
$361$			9.81486i			0.516572i
$362$		0			0
$363$			4.66790i			0.245001i
$364$		0			0
$365$	−8.67016	−	12.1509i	−0.453817	−	0.636007i
$366$		0			0
$367$		−	30.7491i		−	1.60509i	−0.596591	−	0.802545i	$-0.703479\pi$
$367$		−	30.7491i		−	1.60509i	0.596591	−	0.802545i	$-0.296521\pi$
$368$		0			0
$369$	−0.387351	+	0.387351i	−0.0201647	+	0.0201647i
$370$		0			0
$371$	11.8422			0.614818
$372$		0			0
$373$	−18.1021	+	18.1021i	−0.937292	+	0.937292i	−0.998147	−	0.0608545i	$-0.980617\pi$
$373$	−18.1021	+	18.1021i	−0.937292	+	0.937292i	0.0608545	+	0.998147i	$0.480617\pi$
$374$		0			0
$375$	−5.43560	−	18.3171i	−0.280693	−	0.945891i
$376$		0			0
$377$	7.42436	+	15.5395i	0.382374	+	0.800325i
$378$		0			0
$379$	2.45786	−	2.45786i	0.126252	−	0.126252i	−0.641157	−	0.767409i	$-0.721545\pi$
$379$	2.45786	−	2.45786i	0.126252	−	0.126252i	0.767409	+	0.641157i	$0.221545\pi$
$380$		0			0
$381$		−	17.0996i		−	0.876039i
$382$		0			0
$383$	13.7759	+	13.7759i	0.703914	+	0.703914i	0.965248	−	0.261334i	$-0.0841626\pi$
$383$	13.7759	+	13.7759i	0.703914	+	0.703914i	−0.261334	+	0.965248i	$0.584163\pi$
$384$		0			0
$385$	6.57197	+	9.21037i	0.334939	+	0.469404i
$386$		0			0
$387$	−0.325693			−0.0165559
$388$		0			0
$389$	21.4018	+	21.4018i	1.08511	+	1.08511i	0.996024	+	0.0890895i	$0.0283957\pi$
$389$	21.4018	+	21.4018i	1.08511	+	1.08511i	0.0890895	+	0.996024i	$0.471604\pi$
$390$		0			0
$391$	−5.63328	−	5.63328i	−0.284887	−	0.284887i
$392$		0			0
$393$	2.51046	−	2.51046i	0.126636	−	0.126636i
$394$		0			0
$395$	−2.53122	+	15.1413i	−0.127360	+	0.761840i
$396$		0			0
$397$	11.7919	+	11.7919i	0.591819	+	0.591819i	0.938123	−	0.346304i	$-0.112563\pi$
$397$	11.7919	+	11.7919i	0.591819	+	0.591819i	−0.346304	+	0.938123i	$0.612563\pi$
$398$		0			0
$399$	−9.11409			−0.456275
$400$		0			0
$401$	12.5541			0.626921			0.313461	−	0.949601i	$-0.398512\pi$
$401$	12.5541			0.626921			0.313461	+	0.949601i	$0.398512\pi$
$402$		0			0
$403$		−	25.9142i		−	1.29088i
$404$		0			0
$405$	15.9362	−	11.3711i	0.791876	−	0.565036i
$406$		0			0
$407$	−11.6154	−	11.6154i	−0.575755	−	0.575755i
$408$		0			0
$409$	4.61147	−	4.61147i	0.228023	−	0.228023i	−0.583844	−	0.811866i	$-0.698452\pi$
$409$	4.61147	−	4.61147i	0.228023	−	0.228023i	0.811866	+	0.583844i	$0.198452\pi$
$410$		0			0
$411$		−	29.2053i		−	1.44059i
$412$		0			0
$413$	−8.87835	+	8.87835i	−0.436875	+	0.436875i
$414$		0			0
$415$	−6.23212	+	37.2793i	−0.305923	+	1.82997i
$416$		0			0
$417$			24.3272i			1.19131i
$418$		0			0
$419$	−21.4262			−1.04674			−0.523368	−	0.852106i	$-0.675325\pi$
$419$	−21.4262			−1.04674			−0.523368	+	0.852106i	$0.675325\pi$
$420$		0			0
$421$	12.5331	−	12.5331i	0.610825	−	0.610825i	−0.332336	−	0.943161i	$-0.607837\pi$
$421$	12.5331	−	12.5331i	0.610825	−	0.610825i	0.943161	+	0.332336i	$0.107837\pi$
$422$		0			0
$423$	−0.352717			−0.0171497
$424$		0			0
$425$	5.41321	+	1.86193i	0.262579	+	0.0903168i
$426$		0			0
$427$		−	18.7344i		−	0.906623i
$428$		0			0
$429$		−	15.7155i		−	0.758751i
$430$		0			0
$431$	25.4498			1.22587			0.612936	−	0.790132i	$-0.289988\pi$
$431$	25.4498			1.22587			0.612936	+	0.790132i	$0.289988\pi$
$432$		0			0
$433$		−	32.5610i		−	1.56478i	−0.622787	−	0.782391i	$-0.714000\pi$
$433$		−	32.5610i		−	1.56478i	0.622787	−	0.782391i	$-0.286000\pi$
$434$		0			0
$435$	−19.7766	+	5.68829i	−0.948217	+	0.272732i
$436$		0			0
$437$			21.0889i			1.00882i
$438$		0			0
$439$	21.1677			1.01028			0.505140	−	0.863037i	$-0.331441\pi$
$439$	21.1677			1.01028			0.505140	+	0.863037i	$0.331441\pi$
$440$		0			0
$441$			0.310329i			0.0147776i
$442$		0			0
$443$			36.7379i			1.74547i	0.488194	+	0.872735i	$0.337656\pi$
$443$			36.7379i			1.74547i	−0.488194	+	0.872735i	$0.662344\pi$
$444$		0			0
$445$	−2.83291	+	16.9459i	−0.134293	+	0.803314i
$446$		0			0
$447$	9.39136			0.444196
$448$		0			0
$449$	1.33479	−	1.33479i	0.0629927	−	0.0629927i	−0.674909	−	0.737901i	$-0.735817\pi$
$449$	1.33479	−	1.33479i	0.0629927	−	0.0629927i	0.737901	+	0.674909i	$0.235817\pi$
$450$		0			0
$451$	−19.8133			−0.932971
$452$		0			0
$453$		−	16.6749i		−	0.783453i
$454$		0			0
$455$	7.30913	+	10.2435i	0.342657	+	0.480221i
$456$		0			0
$457$	3.45211	−	3.45211i	0.161483	−	0.161483i	−0.621740	−	0.783223i	$-0.713574\pi$
$457$	3.45211	−	3.45211i	0.161483	−	0.161483i	0.783223	+	0.621740i	$0.213574\pi$
$458$		0			0
$459$			6.02525i			0.281234i
$460$		0			0
$461$	15.1152	−	15.1152i	0.703985	−	0.703985i	−0.261279	−	0.965263i	$-0.584144\pi$
$461$	15.1152	−	15.1152i	0.703985	−	0.703985i	0.965263	+	0.261279i	$0.0841442\pi$
$462$		0			0
$463$	23.3083	+	23.3083i	1.08323	+	1.08323i	0.996206	+	0.0870237i	$0.0277356\pi$
$463$	23.3083	+	23.3083i	1.08323	+	1.08323i	0.0870237	+	0.996206i	$0.472264\pi$
$464$		0			0
$465$	30.5409	+	5.10563i	1.41630	+	0.236768i
$466$		0			0
$467$		−	30.6280i		−	1.41730i	−0.705563	−	0.708648i	$-0.749306\pi$
$467$		−	30.6280i		−	1.41730i	0.705563	−	0.708648i	$-0.250694\pi$
$468$		0			0
$469$	11.9754			0.552970
$470$		0			0
$471$	33.2802			1.53347
$472$		0			0
$473$	−8.32972	−	8.32972i	−0.383001	−	0.383001i
$474$		0			0
$475$	−6.64733	−	13.6177i	−0.305001	−	0.624822i
$476$		0			0
$477$	−0.378316	+	0.378316i	−0.0173219	+	0.0173219i
$478$		0			0
$479$	2.93688	+	2.93688i	0.134189	+	0.134189i	0.771011	−	0.636822i	$-0.219751\pi$
$479$	2.93688	+	2.93688i	0.134189	+	0.134189i	−0.636822	+	0.771011i	$0.719751\pi$
$480$		0			0
$481$	−12.9183	−	12.9183i	−0.589023	−	0.589023i
$482$		0			0
$483$	20.9257			0.952154
$484$		0			0
$485$	−5.17267	+	3.69091i	−0.234879	+	0.167596i
$486$		0			0
$487$	−9.47313	−	9.47313i	−0.429269	−	0.429269i	0.459111	−	0.888379i	$-0.348168\pi$
$487$	−9.47313	−	9.47313i	−0.429269	−	0.429269i	−0.888379	+	0.459111i	$0.848168\pi$
$488$		0			0
$489$		−	7.87562i		−	0.356148i
$490$		0			0
$491$	−13.2066	+	13.2066i	−0.596004	+	0.596004i	−0.939247	−	0.343243i	$-0.888475\pi$
$491$	−13.2066	+	13.2066i	−0.596004	+	0.596004i	0.343243	+	0.939247i	$0.388475\pi$
$492$		0			0
$493$	2.05429	−	5.81315i	0.0925208	−	0.261811i
$494$		0			0
$495$	−0.504188	−	0.0842870i	−0.0226616	−	0.00378842i
$496$		0			0
$497$	0.534846	−	0.534846i	0.0239911	−	0.0239911i
$498$		0			0
$499$	−24.3088			−1.08821			−0.544105	−	0.839017i	$-0.683131\pi$
$499$	−24.3088			−1.08821			−0.544105	+	0.839017i	$0.683131\pi$
$500$		0			0
$501$	8.93971	−	8.93971i	0.399397	−	0.399397i
$502$		0			0
$503$		−	9.00114i		−	0.401341i	−0.979659	−	0.200670i	$-0.935688\pi$
$503$		−	9.00114i		−	0.401341i	0.979659	−	0.200670i	$-0.0643120\pi$
$504$		0			0
$505$	38.8518	+	6.49500i	1.72888	+	0.289024i
$506$		0			0
$507$			4.73805i			0.210424i
$508$		0			0
$509$			34.5917i			1.53325i	0.642095	+	0.766625i	$0.278065\pi$
$509$			34.5917i			1.53325i	−0.642095	+	0.766625i	$0.721935\pi$
$510$		0			0
$511$	−8.30644	+	8.30644i	−0.367455	+	0.367455i
$512$		0			0
$513$	11.2781	−	11.2781i	0.497941	−	0.497941i
$514$		0			0
$515$	0.202012	−	1.20840i	0.00890172	−	0.0532484i
$516$		0			0
$517$	−9.02086	−	9.02086i	−0.396737	−	0.396737i
$518$		0			0
$519$	−25.2284	−	25.2284i	−1.10741	−	1.10741i
$520$		0			0
$521$		−	3.78963i		−	0.166027i	−0.996548	−	0.0830134i	$-0.973546\pi$
$521$		−	3.78963i		−	0.166027i	0.996548	−	0.0830134i	$-0.0264544\pi$
$522$		0			0
$523$	30.1836	−	30.1836i	1.31983	−	1.31983i	0.405931	−	0.913904i	$-0.366947\pi$
$523$	30.1836	−	30.1836i	1.31983	−	1.31983i	0.913904	−	0.405931i	$-0.133053\pi$
$524$		0			0
$525$	−13.5124	+	6.59592i	−0.589728	+	0.287869i
$526$		0			0
$527$	−6.56000	+	6.56000i	−0.285758	+	0.285758i
$528$		0			0
$529$		−	25.4195i		−	1.10520i
$530$		0			0
$531$		−	0.567262i		−	0.0246171i
$532$		0			0
$533$	−22.0357			−0.954471
$534$		0			0
$535$	−25.2932	−	4.22835i	−1.09352	−	0.182808i
$536$		0			0
$537$	18.1606			0.783686
$538$		0			0
$539$	−7.93677	+	7.93677i	−0.341861	+	0.341861i
$540$		0			0
$541$	32.5239	+	32.5239i	1.39831	+	1.39831i	0.804900	+	0.593411i	$0.202219\pi$
$541$	32.5239	+	32.5239i	1.39831	+	1.39831i	0.593411	+	0.804900i	$0.297781\pi$
$542$		0			0
$543$	−3.08231			−0.132274
$544$		0			0
$545$	−20.5505	+	14.6636i	−0.880285	+	0.628120i
$546$		0			0
$547$	0.849175	+	0.849175i	0.0363081	+	0.0363081i	0.725028	−	0.688720i	$-0.241827\pi$
$547$	0.849175	+	0.849175i	0.0363081	+	0.0363081i	−0.688720	+	0.725028i	$0.741827\pi$
$548$		0			0
$549$	0.598497	+	0.598497i	0.0255432	+	0.0255432i
$550$		0			0
$551$	−14.7264	+	7.03586i	−0.627364	+	0.299738i
$552$		0			0
$553$	12.0811			0.513739
$554$		0			0
$555$	17.7698	−	12.6795i	0.754288	−	0.538216i
$556$		0			0
$557$	2.78919	−	2.78919i	0.118182	−	0.118182i	−0.645542	−	0.763724i	$-0.723369\pi$
$557$	2.78919	−	2.78919i	0.118182	−	0.118182i	0.763724	+	0.645542i	$0.223369\pi$
$558$		0			0
$559$	−9.26404	−	9.26404i	−0.391827	−	0.391827i
$560$		0			0
$561$	−3.97827	+	3.97827i	−0.167963	+	0.167963i
$562$		0			0
$563$		−	42.4801i		−	1.79032i	−0.445742	−	0.895161i	$-0.647060\pi$
$563$		−	42.4801i		−	1.79032i	0.445742	−	0.895161i	$-0.352940\pi$
$564$		0			0
$565$	7.76483	+	10.8821i	0.326669	+	0.457814i
$566$		0			0
$567$	−10.8941	−	10.8941i	−0.457510	−	0.457510i
$568$		0			0
$569$	8.10861	+	8.10861i	0.339930	+	0.339930i	0.856341	−	0.516411i	$-0.172732\pi$
$569$	8.10861	+	8.10861i	0.339930	+	0.339930i	−0.516411	+	0.856341i	$0.672732\pi$
$570$		0			0
$571$	19.9426			0.834573			0.417286	−	0.908775i	$-0.362981\pi$
$571$	19.9426			0.834573			0.417286	+	0.908775i	$0.362981\pi$
$572$		0			0
$573$	0.878008	+	0.878008i	0.0366793	+	0.0366793i
$574$		0			0
$575$	15.2621	+	31.2659i	0.636474	+	1.30388i
$576$		0			0
$577$	−0.358955			−0.0149435			−0.00747175	−	0.999972i	$-0.502378\pi$
$577$	−0.358955			−0.0149435			−0.00747175	+	0.999972i	$0.502378\pi$
$578$		0			0
$579$	−11.0160			−0.457810
$580$		0			0
$581$	29.7448			1.23402
$582$		0			0
$583$	−19.3511			−0.801441
$584$		0			0
$585$	−0.560742	−	0.0937412i	−0.0231838	−	0.00387572i
$586$		0			0
$587$	15.2260	+	15.2260i	0.628445	+	0.628445i	0.947677	−	0.319232i	$-0.103425\pi$
$587$	15.2260	+	15.2260i	0.628445	+	0.628445i	−0.319232	+	0.947677i	$0.603425\pi$
$588$		0			0
$589$	24.5582			1.01190
$590$		0			0
$591$	−1.77190	−	1.77190i	−0.0728863	−	0.0728863i
$592$		0			0
$593$	−16.2813	−	16.2813i	−0.668594	−	0.668594i	0.288796	−	0.957391i	$-0.406745\pi$
$593$	−16.2813	−	16.2813i	−0.668594	−	0.668594i	−0.957391	+	0.288796i	$0.906745\pi$
$594$		0			0
$595$	0.742806	−	4.44332i	0.0304521	−	0.182158i
$596$		0			0
$597$			44.1878i			1.80849i
$598$		0			0
$599$	14.3550	−	14.3550i	0.586530	−	0.586530i	−0.350160	−	0.936690i	$-0.613873\pi$
$599$	14.3550	−	14.3550i	0.586530	−	0.586530i	0.936690	+	0.350160i	$0.113873\pi$
$600$		0			0
$601$	−10.4458	−	10.4458i	−0.426092	−	0.426092i	0.461203	−	0.887295i	$-0.347418\pi$
$601$	−10.4458	−	10.4458i	−0.426092	−	0.426092i	−0.887295	+	0.461203i	$0.847418\pi$
$602$		0			0
$603$	−0.382569	+	0.382569i	−0.0155794	+	0.0155794i
$604$		0			0
$605$	3.54758	+	4.97179i	0.144230	+	0.202132i
$606$		0			0
$607$	−5.09856			−0.206944			−0.103472	−	0.994632i	$-0.532995\pi$
$607$	−5.09856			−0.206944			−0.103472	+	0.994632i	$0.532995\pi$
$608$		0			0
$609$	6.98144	+	14.6125i	0.282902	+	0.592126i
$610$		0			0
$611$	−10.0327	−	10.0327i	−0.405880	−	0.405880i
$612$		0			0
$613$	18.0020	+	18.0020i	0.727094	+	0.727094i	0.970040	−	0.242945i	$-0.0781136\pi$
$613$	18.0020	+	18.0020i	0.727094	+	0.727094i	−0.242945	+	0.970040i	$0.578114\pi$
$614$		0			0
$615$	4.34148	−	25.9699i	0.175065	−	1.04721i
$616$		0			0
$617$	27.6250			1.11214			0.556070	−	0.831135i	$-0.312309\pi$
$617$	27.6250			1.11214			0.556070	+	0.831135i	$0.312309\pi$
$618$		0			0
$619$	24.0588	+	24.0588i	0.967006	+	0.967006i	0.999473	−	0.0324669i	$-0.0103363\pi$
$619$	24.0588	+	24.0588i	0.967006	+	0.967006i	−0.0324669	+	0.999473i	$0.510336\pi$
$620$		0			0
$621$	−25.8943	+	25.8943i	−1.03910	+	1.03910i
$622$		0			0
$623$	13.5210			0.541706
$624$		0			0
$625$	−19.7104	−	15.3786i	−0.788415	−	0.615143i
$626$		0			0
$627$	14.8931			0.594774
$628$		0			0
$629$			6.54035i			0.260781i
$630$		0			0
$631$			5.24104i			0.208642i	0.994544	+	0.104321i	$0.0332670\pi$
$631$			5.24104i			0.208642i	−0.994544	+	0.104321i	$0.966733\pi$
$632$		0			0
$633$	−12.4028	+	12.4028i	−0.492967	+	0.492967i
$634$		0			0
$635$	−12.9956	−	18.2128i	−0.515715	−	0.722755i
$636$		0			0
$637$	−8.82701	+	8.82701i	−0.349739	+	0.349739i
$638$		0			0
$639$			0.0341728i			0.00135185i
$640$		0			0
$641$	−23.1901	−	23.1901i	−0.915954	−	0.915954i	0.0807780	−	0.996732i	$-0.474260\pi$
$641$	−23.1901	−	23.1901i	−0.915954	−	0.915954i	−0.996732	+	0.0807780i	$0.974260\pi$
$642$		0			0
$643$	−18.2760	−	18.2760i	−0.720734	−	0.720734i	0.248020	−	0.968755i	$-0.420220\pi$
$643$	−18.2760	−	18.2760i	−0.720734	−	0.720734i	−0.968755	+	0.248020i	$0.920220\pi$
$644$		0			0
$645$	12.7432	−	9.09281i	0.501764	−	0.358029i
$646$		0			0
$647$	19.0496	−	19.0496i	0.748916	−	0.748916i	−0.225359	−	0.974276i	$-0.572356\pi$
$647$	19.0496	−	19.0496i	0.748916	−	0.748916i	0.974276	+	0.225359i	$0.0723556\pi$
$648$		0			0
$649$	14.5079	−	14.5079i	0.569485	−	0.569485i
$650$		0			0
$651$		−	24.3682i		−	0.955066i
$652$		0			0
$653$			28.9526i			1.13300i	0.824060	+	0.566502i	$0.191704\pi$
$653$			28.9526i			1.13300i	−0.824060	+	0.566502i	$0.808296\pi$
$654$		0			0
$655$	0.765963	−	4.58184i	0.0299287	−	0.179027i
$656$		0			0
$657$		−	0.530721i		−	0.0207054i
$658$		0			0
$659$	−4.90554	+	4.90554i	−0.191093	+	0.191093i	−0.796168	−	0.605075i	$-0.793143\pi$
$659$	−4.90554	+	4.90554i	−0.191093	+	0.191093i	0.605075	+	0.796168i	$0.293143\pi$
$660$		0			0
$661$	9.13285			0.355227			0.177613	−	0.984100i	$-0.443162\pi$
$661$	9.13285			0.355227			0.177613	+	0.984100i	$0.443162\pi$
$662$		0			0
$663$	−4.42450	+	4.42450i	−0.171833	+	0.171833i
$664$		0			0
$665$	−9.70745	+	6.92666i	−0.376439	+	0.268604i
$666$		0			0
$667$	33.8114	−	16.1542i	1.30918	−	0.625492i
$668$		0			0
$669$	−18.8571	+	18.8571i	−0.729057	+	0.729057i
$670$		0			0
$671$			30.6135i			1.18182i
$672$		0			0
$673$	−1.47121	−	1.47121i	−0.0567111	−	0.0567111i	0.678182	−	0.734894i	$-0.262768\pi$
$673$	−1.47121	−	1.47121i	−0.0567111	−	0.0567111i	−0.734894	+	0.678182i	$0.762768\pi$
$674$		0			0
$675$	8.55866	−	24.8827i	0.329423	−	0.957737i
$676$		0			0
$677$	10.6009			0.407424			0.203712	−	0.979031i	$-0.434699\pi$
$677$	10.6009			0.407424			0.203712	+	0.979031i	$0.434699\pi$
$678$		0			0
$679$	3.53607	+	3.53607i	0.135702	+	0.135702i
$680$		0			0
$681$	−7.93370	−	7.93370i	−0.304020	−	0.304020i
$682$		0			0
$683$	−16.7555	+	16.7555i	−0.641133	+	0.641133i	−0.950834	−	0.309701i	$-0.899771\pi$
$683$	−16.7555	+	16.7555i	−0.641133	+	0.641133i	0.309701	+	0.950834i	$0.399771\pi$
$684$		0			0
$685$	−22.1959	−	31.1067i	−0.848061	−	1.18852i
$686$		0			0
$687$	−19.5415	−	19.5415i	−0.745554	−	0.745554i
$688$		0			0
$689$	−21.5217			−0.819911
$690$		0			0
$691$	−9.00797			−0.342679			−0.171340	−	0.985212i	$-0.554810\pi$
$691$	−9.00797			−0.342679			−0.171340	+	0.985212i	$0.554810\pi$
$692$		0			0
$693$			0.402286i			0.0152816i
$694$		0			0
$695$	18.4886	+	25.9110i	0.701311	+	0.982860i
$696$		0			0
$697$	5.57818	+	5.57818i	0.211289	+	0.211289i
$698$		0			0
$699$	−25.9716	+	25.9716i	−0.982336	+	0.982336i
$700$		0			0
$701$		−	40.8403i		−	1.54252i	−0.636522	−	0.771259i	$-0.719627\pi$
$701$		−	40.8403i		−	1.54252i	0.636522	−	0.771259i	$-0.280373\pi$
$702$		0			0
$703$	12.2423	−	12.2423i	0.461727	−	0.461727i
$704$		0			0
$705$	13.8006	−	9.84727i	0.519759	−	0.370869i
$706$		0			0
$707$		−	30.9995i		−	1.16585i
$708$		0			0
$709$	−15.0474			−0.565118			−0.282559	−	0.959250i	$-0.591183\pi$
$709$	−15.0474			−0.565118			−0.282559	+	0.959250i	$0.591183\pi$
$710$		0			0
$711$	−0.385946	+	0.385946i	−0.0144741	+	0.0144741i
$712$		0			0
$713$	−56.3850			−2.11163
$714$		0			0
$715$	−11.9437	−	16.7386i	−0.446669	−	0.625989i
$716$		0			0
$717$			17.1415i			0.640162i
$718$		0			0
$719$			2.89098i			0.107815i	0.998546	+	0.0539077i	$0.0171677\pi$
$719$			2.89098i			0.107815i	−0.998546	+	0.0539077i	$0.982832\pi$
$720$		0			0
$721$	−0.964167			−0.0359075
$722$		0			0
$723$		−	6.82856i		−	0.253957i
$724$		0			0
$725$	−16.7411	+	21.0888i	−0.621749	+	0.783217i
$726$		0			0
$727$			5.56121i			0.206254i	0.994668	+	0.103127i	$0.0328848\pi$
$727$			5.56121i			0.206254i	−0.994668	+	0.103127i	$0.967115\pi$
$728$		0			0
$729$	27.6771			1.02508
$730$		0			0
$731$			4.69025i			0.173475i
$732$		0			0
$733$		−	6.33472i		−	0.233978i	−0.993133	−	0.116989i	$-0.962676\pi$
$733$		−	6.33472i		−	0.233978i	0.993133	−	0.116989i	$-0.0373242\pi$
$734$		0			0
$735$	−8.66386	−	12.1421i	−0.319571	−	0.447867i
$736$		0			0
$737$	−19.5687			−0.720821
$738$		0			0
$739$	−16.3799	+	16.3799i	−0.602544	+	0.602544i	−0.940987	−	0.338443i	$-0.890100\pi$
$739$	−16.3799	+	16.3799i	−0.602544	+	0.602544i	0.338443	+	0.940987i	$0.390100\pi$
$740$		0			0
$741$	16.5636			0.608481
$742$		0			0
$743$			29.7611i			1.09183i	0.837841	+	0.545914i	$0.183818\pi$
$743$			29.7611i			1.09183i	−0.837841	+	0.545914i	$0.816182\pi$
$744$		0			0
$745$	10.0028	−	7.13738i	0.366473	−	0.261493i
$746$		0			0
$747$	−0.950238	+	0.950238i	−0.0347674	+	0.0347674i
$748$		0			0
$749$			20.1812i			0.737403i
$750$		0			0
$751$	22.4774	−	22.4774i	0.820210	−	0.820210i	−0.165927	−	0.986138i	$-0.553062\pi$
$751$	22.4774	−	22.4774i	0.820210	−	0.820210i	0.986138	+	0.165927i	$0.0530618\pi$
$752$		0			0
$753$	30.3991	+	30.3991i	1.10780	+	1.10780i
$754$		0			0
$755$	−12.6728	−	17.7604i	−0.461211	−	0.646369i
$756$		0			0
$757$			24.0025i			0.872387i	0.899853	+	0.436193i	$0.143674\pi$
$757$			24.0025i			0.872387i	−0.899853	+	0.436193i	$0.856326\pi$
$758$		0			0
$759$	−34.1943			−1.24117
$760$		0			0
$761$	17.9463			0.650555			0.325277	−	0.945619i	$-0.394542\pi$
$761$	17.9463			0.650555			0.325277	+	0.945619i	$0.394542\pi$
$762$		0			0
$763$	14.0485	+	14.0485i	0.508588	+	0.508588i
$764$		0			0
$765$	0.118218	+	0.165678i	0.00427418	+	0.00599010i
$766$		0			0
$767$	16.1352	−	16.1352i	0.582609	−	0.582609i
$768$		0			0
$769$	19.2753	+	19.2753i	0.695085	+	0.695085i	0.963346	−	0.268261i	$-0.0864491\pi$
$769$	19.2753	+	19.2753i	0.695085	+	0.695085i	−0.268261	+	0.963346i	$0.586449\pi$
$770$		0			0
$771$	30.6044	+	30.6044i	1.10219	+	1.10219i
$772$		0			0
$773$	−8.38431			−0.301563			−0.150781	−	0.988567i	$-0.548179\pi$
$773$	−8.38431			−0.301563			−0.150781	+	0.988567i	$0.548179\pi$
$774$		0			0
$775$	36.4094	−	17.7729i	1.30786	−	0.638421i
$776$		0			0
$777$	−12.1476	−	12.1476i	−0.435793	−	0.435793i
$778$		0			0
$779$		−	20.8826i		−	0.748196i
$780$		0			0
$781$	−0.873980	+	0.873980i	−0.0312735	+	0.0312735i
$782$		0			0
$783$	−26.7211	−	9.44291i	−0.954934	−	0.337462i
$784$		0			0
$785$	35.4469	−	25.2928i	1.26515	−	0.902739i
$786$		0			0
$787$	8.84437	−	8.84437i	0.315268	−	0.315268i	−0.531678	−	0.846946i	$-0.678439\pi$
$787$	8.84437	−	8.84437i	0.315268	−	0.315268i	0.846946	+	0.531678i	$0.178439\pi$
$788$		0			0
$789$	11.0153			0.392156
$790$		0			0
$791$	7.43909	−	7.43909i	0.264504	−	0.264504i
$792$		0			0
$793$			34.0473i			1.20906i
$794$		0			0
$795$	4.24021	−	25.3641i	0.150385	−	0.899572i
$796$		0			0
$797$		−	22.7951i		−	0.807442i	−0.914882	−	0.403721i	$-0.867717\pi$
$797$		−	22.7951i		−	0.807442i	0.914882	−	0.403721i	$-0.132283\pi$
$798$		0			0
$799$			5.07942i			0.179697i
$800$		0			0
$801$	−0.431946	+	0.431946i	−0.0152620	+	0.0152620i
$802$		0			0
$803$	13.5734	−	13.5734i	0.478994	−	0.478994i
$804$		0			0
$805$	22.2881	−	15.9035i	0.785551	−	0.560523i
$806$		0			0
$807$	29.6253	+	29.6253i	1.04286	+	1.04286i
$808$		0			0
$809$	−17.6094	−	17.6094i	−0.619113	−	0.619113i	0.326191	−	0.945304i	$-0.394235\pi$
$809$	−17.6094	−	17.6094i	−0.619113	−	0.619113i	−0.945304	+	0.326191i	$0.894235\pi$
$810$		0			0
$811$		−	17.2999i		−	0.607482i	−0.952755	−	0.303741i	$-0.901764\pi$
$811$		−	17.2999i		−	0.607482i	0.952755	−	0.303741i	$-0.0982357\pi$
$812$		0			0
$813$	26.4918	−	26.4918i	0.929108	−	0.929108i
$814$		0			0
$815$	−5.98543	−	8.38835i	−0.209661	−	0.293831i
$816$		0			0
$817$	8.77927	−	8.77927i	0.307148	−	0.307148i
$818$		0			0
$819$			0.447410i			0.0156338i
$820$		0			0
$821$		−	27.8929i		−	0.973471i	−0.873549	−	0.486735i	$-0.838188\pi$
$821$		−	27.8929i		−	0.973471i	0.873549	−	0.486735i	$-0.161812\pi$
$822$		0			0
$823$	−22.9231			−0.799048			−0.399524	−	0.916723i	$-0.630825\pi$
$823$	−22.9231			−0.799048			−0.399524	+	0.916723i	$0.630825\pi$
$824$		0			0
$825$	22.0802	−	10.7782i	0.768735	−	0.375250i
$826$		0			0
$827$	−13.3541			−0.464367			−0.232183	−	0.972672i	$-0.574587\pi$
$827$	−13.3541			−0.464367			−0.232183	+	0.972672i	$0.574587\pi$
$828$		0			0
$829$	40.1431	−	40.1431i	1.39423	−	1.39423i	0.578651	−	0.815576i	$-0.303579\pi$
$829$	40.1431	−	40.1431i	1.39423	−	1.39423i	0.815576	−	0.578651i	$-0.196421\pi$
$830$		0			0
$831$	−7.52831	−	7.52831i	−0.261154	−	0.261154i
$832$		0			0
$833$	4.46899			0.154841
$834$		0			0
$835$	2.72758	−	16.3158i	0.0943917	−	0.564633i
$836$		0			0
$837$	30.1542	+	30.1542i	1.04228	+	1.04228i
$838$		0			0
$839$	−10.6523	−	10.6523i	−0.367758	−	0.367758i	0.498901	−	0.866659i	$-0.333737\pi$
$839$	−10.6523	−	10.6523i	−0.367758	−	0.367758i	−0.866659	+	0.498901i	$0.833737\pi$
$840$		0			0
$841$	22.5609	+	18.2210i	0.777963	+	0.628310i
$842$		0			0
$843$	16.7509			0.576932
$844$		0			0
$845$	3.60090	+	5.04652i	0.123875	+	0.173605i
$846$		0			0
$847$	3.39876	−	3.39876i	0.116783	−	0.116783i
$848$		0			0
$849$	17.2806	+	17.2806i	0.593067	+	0.593067i
$850$		0			0
$851$	−28.1080	+	28.1080i	−0.963531	+	0.963531i
$852$		0			0
$853$			27.2150i			0.931822i	0.884831	+	0.465911i	$0.154273\pi$
$853$			27.2150i			0.931822i	−0.884831	+	0.465911i	$0.845727\pi$
$854$		0			0
$855$	0.0888359	−	0.531399i	0.00303813	−	0.0181735i
$856$		0			0
$857$	41.0181	+	41.0181i	1.40115	+	1.40115i	0.796461	+	0.604690i	$0.206703\pi$
$857$	41.0181	+	41.0181i	1.40115	+	1.40115i	0.604690	+	0.796461i	$0.293297\pi$
$858$		0			0
$859$	19.1701	+	19.1701i	0.654076	+	0.654076i	0.953972	−	0.299896i	$-0.0969519\pi$
$859$	19.1701	+	19.1701i	0.654076	+	0.654076i	−0.299896	+	0.953972i	$0.596952\pi$
$860$		0			0
$861$	−20.7211			−0.706172
$862$		0			0
$863$	3.20896	+	3.20896i	0.109234	+	0.109234i	0.759612	−	0.650377i	$-0.225389\pi$
$863$	3.20896	+	3.20896i	0.109234	+	0.109234i	−0.650377	+	0.759612i	$0.725389\pi$
$864$		0			0
$865$	−46.0444	−	7.69740i	−1.56556	−	0.261720i
$866$		0			0
$867$	−26.8120			−0.910584
$868$		0			0
$869$	−19.7414			−0.669681
$870$		0			0
$871$	−21.7636			−0.737432
$872$		0			0
$873$	−0.225929			−0.00764655
$874$		0			0
$875$	−9.37919	+	17.2947i	−0.317074	+	0.584666i
$876$		0			0
$877$	−31.3620	−	31.3620i	−1.05902	−	1.05902i	−0.998145	−	0.0608744i	$-0.980611\pi$
$877$	−31.3620	−	31.3620i	−1.05902	−	1.05902i	−0.0608744	−	0.998145i	$-0.519389\pi$
$878$		0			0
$879$	28.0234			0.945205
$880$		0			0
$881$	12.6317	+	12.6317i	0.425574	+	0.425574i	0.887117	−	0.461544i	$-0.152704\pi$
$881$	12.6317	+	12.6317i	0.425574	+	0.425574i	−0.461544	+	0.887117i	$0.652704\pi$
$882$		0			0
$883$	−3.67000	−	3.67000i	−0.123505	−	0.123505i	0.642653	−	0.766158i	$-0.277834\pi$
$883$	−3.67000	−	3.67000i	−0.123505	−	0.123505i	−0.766158	+	0.642653i	$0.777834\pi$
$884$		0			0
$885$	15.8370	+	22.1949i	0.532355	+	0.746074i
$886$		0			0
$887$			19.9052i			0.668351i	0.942511	+	0.334175i	$0.108458\pi$
$887$			19.9052i			0.668351i	−0.942511	+	0.334175i	$0.891542\pi$
$888$		0			0
$889$	−12.4504	+	12.4504i	−0.417574	+	0.417574i
$890$		0			0
$891$	17.8018	+	17.8018i	0.596383	+	0.596383i
$892$		0			0
$893$	9.50771	−	9.50771i	0.318163	−	0.318163i
$894$		0			0
$895$	19.3429	−	13.8019i	0.646561	−	0.461348i
$896$		0			0
$897$	−38.0297			−1.26978
$898$		0			0
$899$	−18.8117	−	39.3737i	−0.627405	−	1.31319i
$900$		0			0
$901$	5.44806	+	5.44806i	0.181501	+	0.181501i
$902$		0			0
$903$	−8.71136	−	8.71136i	−0.289896	−	0.289896i
$904$		0			0
$905$	−3.28297	+	2.34254i	−0.109130	+	0.0778686i
$906$		0			0
$907$	35.2505			1.17047			0.585237	−	0.810862i	$-0.301001\pi$
$907$	35.2505			1.17047			0.585237	+	0.810862i	$0.301001\pi$
$908$		0			0
$909$	0.990320	+	0.990320i	0.0328468	+	0.0328468i
$910$		0			0
$911$	10.1463	−	10.1463i	0.336161	−	0.336161i	−0.518760	−	0.854920i	$-0.673606\pi$
$911$	10.1463	−	10.1463i	0.336161	−	0.336161i	0.854920	+	0.518760i	$0.173606\pi$
$912$		0			0
$913$	−48.6053			−1.60860
$914$		0			0
$915$	−40.1261	−	6.70802i	−1.32653	−	0.221760i
$916$		0			0
$917$	−3.65580			−0.120725
$918$		0			0
$919$			11.6645i			0.384777i	0.981319	+	0.192389i	$0.0616235\pi$
$919$			11.6645i			0.384777i	−0.981319	+	0.192389i	$0.938377\pi$
$920$		0			0
$921$			13.1858i			0.434487i
$922$		0			0
$923$	−0.972012	+	0.972012i	−0.0319942	+	0.0319942i
$924$		0			0
$925$	9.29035	−	27.0100i	0.305465	−	0.888083i
$926$		0			0
$927$	0.0308016	−	0.0308016i	0.00101166	−	0.00101166i
$928$		0			0
$929$		−	46.2322i		−	1.51683i	−0.651772	−	0.758415i	$-0.725974\pi$
$929$		−	46.2322i		−	1.51683i	0.651772	−	0.758415i	$-0.274026\pi$
$930$		0			0
$931$	−8.36511	−	8.36511i	−0.274155	−	0.274155i
$932$		0			0
$933$	−33.2197	−	33.2197i	−1.08756	−	1.08756i
$934$		0			0
$935$	−1.21380	+	7.26073i	−0.0396956	+	0.237451i
$936$		0			0
$937$	2.31766	−	2.31766i	0.0757148	−	0.0757148i	−0.668235	−	0.743950i	$-0.732950\pi$
$937$	2.31766	−	2.31766i	0.0757148	−	0.0757148i	0.743950	+	0.668235i	$0.232950\pi$
$938$		0			0
$939$	−6.49299	+	6.49299i	−0.211891	+	0.211891i
$940$		0			0
$941$			42.6993i			1.39196i	0.718062	+	0.695979i	$0.245029\pi$
$941$			42.6993i			1.39196i	−0.718062	+	0.695979i	$0.754971\pi$
$942$		0			0
$943$			47.9459i			1.56133i
$944$		0			0
$945$	−20.4245	−	3.41443i	−0.664408	−	0.111071i
$946$		0			0
$947$			23.7513i			0.771813i	0.922538	+	0.385906i	$0.126111\pi$
$947$			23.7513i			0.771813i	−0.922538	+	0.385906i	$0.873889\pi$
$948$		0			0
$949$	15.0959	−	15.0959i	0.490032	−	0.490032i
$950$		0			0
$951$	16.5305			0.536037
$952$		0			0
$953$	8.39659	−	8.39659i	0.271992	−	0.271992i	−0.557910	−	0.829902i	$-0.688396\pi$
$953$	8.39659	−	8.39659i	0.271992	−	0.271992i	0.829902	+	0.557910i	$0.188396\pi$
$954$		0			0
$955$	1.60245	+	0.267887i	0.0518541	+	0.00866863i
$956$		0			0
$957$	−11.4082	−	23.8779i	−0.368775	−	0.771862i
$958$		0			0
$959$	−21.2648	+	21.2648i	−0.686675	+	0.686675i
$960$		0			0
$961$			34.6608i			1.11809i
$962$		0			0
$963$	−0.644715	−	0.644715i	−0.0207756	−	0.0207756i
$964$		0			0
$965$	−11.7332	+	8.37211i	−0.377705	+	0.269508i
$966$		0			0
$967$	−17.9180			−0.576205			−0.288102	−	0.957600i	$-0.593024\pi$
$967$	−17.9180			−0.576205			−0.288102	+	0.957600i	$0.593024\pi$
$968$		0			0
$969$	−4.19297	−	4.19297i	−0.134698	−	0.134698i
$970$		0			0
$971$	31.9422	+	31.9422i	1.02507	+	1.02507i	0.999677	+	0.0253957i	$0.00808457\pi$
$971$	31.9422	+	31.9422i	1.02507	+	1.02507i	0.0253957	+	0.999677i	$0.491915\pi$
$972$		0			0
$973$	17.7130	−	17.7130i	0.567851	−	0.567851i
$974$		0			0
$975$	24.5569	−	11.9872i	0.786451	−	0.383898i
$976$		0			0
$977$	−36.9641	−	36.9641i	−1.18259	−	1.18259i	−0.979072	−	0.203514i	$-0.934764\pi$
$977$	−36.9641	−	36.9641i	−1.18259	−	1.18259i	−0.203514	−	0.979072i	$-0.565236\pi$
$978$		0			0
$979$	−22.0943			−0.706137
$980$		0			0
$981$	−0.897595			−0.0286580
$982$		0			0
$983$			38.4388i			1.22601i	0.790080	+	0.613004i	$0.210039\pi$
$983$			38.4388i			1.22601i	−0.790080	+	0.613004i	$0.789961\pi$
$984$		0			0
$985$	−3.23390	−	0.540622i	−0.103041	−	0.0172257i
$986$		0			0
$987$	−9.43417	−	9.43417i	−0.300293	−	0.300293i
$988$		0			0
$989$	−20.1570	+	20.1570i	−0.640955	+	0.640955i
$990$		0			0
$991$			32.7734i			1.04108i	0.853837	+	0.520541i	$0.174270\pi$
$991$			32.7734i			1.04108i	−0.853837	+	0.520541i	$0.825730\pi$
$992$		0			0
$993$	25.7692	−	25.7692i	0.817759	−	0.817759i
$994$		0			0
$995$	33.5825	+	47.0646i	1.06464	+	1.49205i
$996$		0			0
$997$		−	8.19170i		−	0.259434i	−0.991551	−	0.129717i	$-0.958593\pi$
$997$		−	8.19170i		−	0.259434i	0.991551	−	0.129717i	$-0.0414069\pi$
$998$		0			0
$999$	30.0638			0.951177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1160.2.bl.c.737.7	yes	42
5.3	odd	4		1160.2.s.d.273.7	yes	42
29.17	odd	4		1160.2.s.d.17.15	✓	42
145.133	even	4	inner	1160.2.bl.c.713.7	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1160.2.s.d.17.15	✓	42	29.17	odd	4
1160.2.s.d.273.7	yes	42	5.3	odd	4
1160.2.bl.c.713.7	yes	42	145.133	even	4	inner
1160.2.bl.c.737.7	yes	42	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1160 = 2^{3} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1160.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.70895 q^{3} +(-1.82020 + 1.29879i) q^{5} +(1.24431 + 1.24431i) q^{7} -0.0795021 q^{9} +(-2.03329 - 2.03329i) q^{11} +(-2.26136 - 2.26136i) q^{13} +(3.11063 - 2.21956i) q^{15} +1.14490i q^{17} +(2.14303 - 2.14303i) q^{19} +(-2.12645 - 2.12645i) q^{21} +(-4.92034 + 4.92034i) q^{23} +(1.62629 - 4.72813i) q^{25} +5.26270 q^{27} +(-5.07745 - 1.79431i) q^{29} +(5.72978 + 5.72978i) q^{31} +(3.47479 + 3.47479i) q^{33} +(-3.88098 - 0.648798i) q^{35} +5.71262 q^{37} +(3.86454 + 3.86454i) q^{39} +(4.87222 - 4.87222i) q^{41} +4.09667 q^{43} +(0.144710 - 0.103257i) q^{45} +4.43658 q^{47} -3.90341i q^{49} -1.95657i q^{51} +(4.75857 - 4.75857i) q^{53} +(6.34183 + 1.06019i) q^{55} +(-3.66232 + 3.66232i) q^{57} +7.13518i q^{59} +(-7.52807 - 7.52807i) q^{61} +(-0.0989249 - 0.0989249i) q^{63} +(7.05317 + 1.17910i) q^{65} +(4.81206 - 4.81206i) q^{67} +(8.40860 - 8.40860i) q^{69} -0.429835i q^{71} +6.67557i q^{73} +(-2.77924 + 8.08012i) q^{75} -5.06007i q^{77} +(4.85454 - 4.85454i) q^{79} -8.75517 q^{81} +(11.9524 - 11.9524i) q^{83} +(-1.48698 - 2.08394i) q^{85} +(8.67708 + 3.06637i) q^{87} +(5.43313 - 5.43313i) q^{89} -5.62765i q^{91} +(-9.79189 - 9.79189i) q^{93} +(-1.11740 + 6.68409i) q^{95} +2.84180 q^{97} +(0.161651 + 0.161651i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 8 q^{3} - 2 q^{5} + 4 q^{7} + 34 q^{9} + 2 q^{11} + 4 q^{13} - 4 q^{15} + 8 q^{19} + 4 q^{21} - 20 q^{23} + 4 q^{25} - 8 q^{27} + 20 q^{29} + 2 q^{31} - 10 q^{33} + 16 q^{35} - 12 q^{37} + 10 q^{39}+ \cdots + 60 q^{99}+O(q^{100}) \) 42 * q - 8 * q^3 - 2 * q^5 + 4 * q^7 + 34 * q^9 + 2 * q^11 + 4 * q^13 - 4 * q^15 + 8 * q^19 + 4 * q^21 - 20 * q^23 + 4 * q^25 - 8 * q^27 + 20 * q^29 + 2 * q^31 - 10 * q^33 + 16 * q^35 - 12 * q^37 + 10 * q^39 - 30 * q^41 + 4 * q^43 - 32 * q^45 - 4 * q^47 + 16 * q^53 + 2 * q^55 + 40 * q^57 + 26 * q^61 + 80 * q^63 + 8 * q^65 + 44 * q^67 + 12 * q^69 + 4 * q^75 - 42 * q^79 + 114 * q^81 - 68 * q^83 + 30 * q^85 - 32 * q^87 + 18 * q^89 + 6 * q^93 - 26 * q^95 - 24 * q^97 + 60 * q^99

Introduction

L-functions

Modular forms

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