LMFDB - Embedded newform 740.2.bf.a.97.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(97,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("740.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.bf (of order $12$, degree $4$, 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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$19$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.15
Character	$\chi$	$=$	740.97
Dual form			740.2.bf.a.473.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.405966 - 1.51509i) q^{3} +(-1.67270 + 1.48394i) q^{5} +(0.553968 - 2.06744i) q^{7} +(0.467396 + 0.269851i) q^{9} +6.12528i q^{11} +(1.98176 + 3.43251i) q^{13} +(1.56924 + 3.13671i) q^{15} +(2.12758 + 1.22836i) q^{17} +(-1.51854 - 0.406892i) q^{19} +(-2.90746 - 1.67862i) q^{21} +7.58124 q^{23} +(0.595841 - 4.96437i) q^{25} +(3.92596 - 3.92596i) q^{27} +(-4.95913 - 4.95913i) q^{29} +(7.17941 - 7.17941i) q^{31} +(9.28032 + 2.48666i) q^{33} +(2.14133 + 4.28026i) q^{35} +(-0.351904 + 6.07257i) q^{37} +(6.00508 - 1.60906i) q^{39} +(-6.05085 + 3.49346i) q^{41} -5.60574 q^{43} +(-1.18226 + 0.242208i) q^{45} +(5.21111 + 5.21111i) q^{47} +(2.09476 + 1.20941i) q^{49} +(2.72480 - 2.72480i) q^{51} +(0.278176 + 1.03817i) q^{53} +(-9.08954 - 10.2457i) q^{55} +(-1.23295 + 2.13554i) q^{57} +(1.14862 + 4.28673i) q^{59} +(1.49732 + 0.401206i) q^{61} +(0.816824 - 0.816824i) q^{63} +(-8.40853 - 2.80074i) q^{65} +(2.08749 + 0.559341i) q^{67} +(3.07773 - 11.4862i) q^{69} +(7.91056 + 13.7015i) q^{71} +(-0.464143 - 0.464143i) q^{73} +(-7.27956 - 2.91812i) q^{75} +(12.6636 + 3.39321i) q^{77} +(-2.38849 - 0.639993i) q^{79} +(-3.54481 - 6.13978i) q^{81} +(-2.65414 - 9.90537i) q^{83} +(-5.38162 + 1.10253i) q^{85} +(-9.52675 + 5.50027i) q^{87} +(-3.51683 + 0.942333i) q^{89} +(8.19433 - 2.19566i) q^{91} +(-7.96284 - 13.7920i) q^{93} +(3.14386 - 1.57282i) q^{95} -9.70531i q^{97} +(-1.65291 + 2.86293i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 2 q^{3} + 8 q^{13} + 2 q^{15} + 12 q^{19} - 4 q^{23} + 2 q^{25} + 28 q^{27} - 6 q^{29} + 16 q^{31} - 6 q^{33} + 20 q^{35} - 22 q^{37} + 8 q^{39} + 54 q^{41} - 16 q^{43} + 38 q^{45} + 8 q^{47} - 36 q^{49}+ \cdots - 70 q^{95}+O(q^{100}) $ 76 * q - 2 * q^3 + 8 * q^13 + 2 * q^15 + 12 * q^19 - 4 * q^23 + 2 * q^25 + 28 * q^27 - 6 * q^29 + 16 * q^31 - 6 * q^33 + 20 * q^35 - 22 * q^37 + 8 * q^39 + 54 * q^41 - 16 * q^43 + 38 * q^45 + 8 * q^47 - 36 * q^49 - 24 * q^53 + 18 * q^55 - 16 * q^59 - 28 * q^61 - 6 * q^65 - 34 * q^67 + 64 * q^69 - 8 * q^71 + 4 * q^73 + 24 * q^75 - 2 * q^77 - 40 * q^79 + 2 * q^81 - 62 * q^83 + 108 * q^87 - 2 * q^89 - 20 * q^91 - 30 * q^93 - 70 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	0.405966	−	1.51509i	0.234385	−	0.874736i	−0.744040	−	0.668135i	$-0.767093\pi$
$3$	0.405966	−	1.51509i	0.234385	−	0.874736i	0.978425	−	0.206601i	$-0.0662403\pi$
$4$		0			0
$5$	−1.67270	+	1.48394i	−0.748054	+	0.663638i
$5$	−1.67270	+	1.48394i	−0.748054	+	0.663638i
$6$		0			0
$7$	0.553968	−	2.06744i	0.209380	−	0.781418i	−0.778689	−	0.627410i	$-0.784115\pi$
$7$	0.553968	−	2.06744i	0.209380	−	0.781418i	0.988070	−	0.154008i	$-0.0492182\pi$
$8$		0			0
$9$	0.467396	+	0.269851i	0.155799	+	0.0899505i
$10$		0			0
$11$			6.12528i			1.84684i	0.383791	+	0.923420i	$0.374618\pi$
$11$			6.12528i			1.84684i	−0.383791	+	0.923420i	$0.625382\pi$
$12$		0			0
$13$	1.98176	+	3.43251i	0.549641	+	0.952007i	0.998299	+	0.0583030i	$0.0185689\pi$
$13$	1.98176	+	3.43251i	0.549641	+	0.952007i	−0.448658	+	0.893704i	$0.648098\pi$
$14$		0			0
$15$	1.56924	+	3.13671i	0.405176	+	0.809896i
$16$		0			0
$17$	2.12758	+	1.22836i	0.516015	+	0.297921i	0.735303	−	0.677739i	$-0.237040\pi$
$17$	2.12758	+	1.22836i	0.516015	+	0.297921i	−0.219288	+	0.975660i	$0.570373\pi$
$18$		0			0
$19$	−1.51854	−	0.406892i	−0.348377	−	0.0933474i	0.0803872	−	0.996764i	$-0.474384\pi$
$19$	−1.51854	−	0.406892i	−0.348377	−	0.0933474i	−0.428764	+	0.903416i	$0.641051\pi$
$20$		0			0
$21$	−2.90746	−	1.67862i	−0.634459	−	0.366305i
$22$		0			0
$23$	7.58124			1.58080			0.790399	−	0.612592i	$-0.209873\pi$
$23$	7.58124			1.58080			0.790399	+	0.612592i	$0.209873\pi$
$24$		0			0
$25$	0.595841	−	4.96437i	0.119168	−	0.992874i
$26$		0			0
$27$	3.92596	−	3.92596i	0.755551	−	0.755551i
$28$		0			0
$29$	−4.95913	−	4.95913i	−0.920887	−	0.920887i	0.0762050	−	0.997092i	$-0.475720\pi$
$29$	−4.95913	−	4.95913i	−0.920887	−	0.920887i	−0.997092	+	0.0762050i	$0.975720\pi$
$30$		0			0
$31$	7.17941	−	7.17941i	1.28946	−	1.28946i	0.354347	−	0.935114i	$-0.384703\pi$
$31$	7.17941	−	7.17941i	1.28946	−	1.28946i	0.935114	−	0.354347i	$-0.115297\pi$
$32$		0			0
$33$	9.28032	+	2.48666i	1.61550	+	0.432871i
$34$		0			0
$35$	2.14133	+	4.28026i	0.361951	+	0.723495i
$36$		0			0
$37$	−0.351904	+	6.07257i	−0.0578527	+	0.998325i
$37$	−0.351904	+	6.07257i	−0.0578527	+	0.998325i
$38$		0			0
$39$	6.00508	−	1.60906i	0.961582	−	0.257655i
$40$		0			0
$41$	−6.05085	+	3.49346i	−0.944984	+	0.545587i	−0.891519	−	0.452983i	$-0.850360\pi$
$41$	−6.05085	+	3.49346i	−0.944984	+	0.545587i	−0.0534647	+	0.998570i	$0.517026\pi$
$42$		0			0
$43$	−5.60574			−0.854867			−0.427434	−	0.904047i	$-0.640582\pi$
$43$	−5.60574			−0.854867			−0.427434	+	0.904047i	$0.640582\pi$
$44$		0			0
$45$	−1.18226	+	0.242208i	−0.176240	+	0.0361063i
$46$		0			0
$47$	5.21111	+	5.21111i	0.760119	+	0.760119i	0.976344	−	0.216225i	$-0.0693744\pi$
$47$	5.21111	+	5.21111i	0.760119	+	0.760119i	−0.216225	+	0.976344i	$0.569374\pi$
$48$		0			0
$49$	2.09476	+	1.20941i	0.299251	+	0.172773i
$50$		0			0
$51$	2.72480	−	2.72480i	0.381548	−	0.381548i
$52$		0			0
$53$	0.278176	+	1.03817i	0.0382104	+	0.142603i	0.982396	−	0.186811i	$-0.0598153\pi$
$53$	0.278176	+	1.03817i	0.0382104	+	0.142603i	−0.944185	+	0.329415i	$0.893149\pi$
$54$		0			0
$55$	−9.08954	−	10.2457i	−1.22563	−	1.38154i
$56$		0			0
$57$	−1.23295	+	2.13554i	−0.163309	+	0.282859i
$58$		0			0
$59$	1.14862	+	4.28673i	0.149538	+	0.558084i	0.999511	+	0.0312581i	$0.00995138\pi$
$59$	1.14862	+	4.28673i	0.149538	+	0.558084i	−0.849973	+	0.526826i	$0.823382\pi$
$60$		0			0
$61$	1.49732	+	0.401206i	0.191712	+	0.0513692i	0.353398	−	0.935473i	$-0.385026\pi$
$61$	1.49732	+	0.401206i	0.191712	+	0.0513692i	−0.161685	+	0.986842i	$0.551693\pi$
$62$		0			0
$63$	0.816824	−	0.816824i	0.102910	−	0.102910i
$64$		0			0
$65$	−8.40853	−	2.80074i	−1.04295	−	0.347389i
$66$		0			0
$67$	2.08749	+	0.559341i	0.255028	+	0.0683344i	0.384068	−	0.923305i	$-0.374523\pi$
$67$	2.08749	+	0.559341i	0.255028	+	0.0683344i	−0.129040	+	0.991639i	$0.541190\pi$
$68$		0			0
$69$	3.07773	−	11.4862i	0.370515	−	1.38278i
$70$		0			0
$71$	7.91056	+	13.7015i	0.938811	+	1.62607i	0.767693	+	0.640818i	$0.221405\pi$
$71$	7.91056	+	13.7015i	0.938811	+	1.62607i	0.171118	+	0.985250i	$0.445262\pi$
$72$		0			0
$73$	−0.464143	−	0.464143i	−0.0543238	−	0.0543238i	0.679423	−	0.733747i	$-0.262230\pi$
$73$	−0.464143	−	0.464143i	−0.0543238	−	0.0543238i	−0.733747	+	0.679423i	$0.762230\pi$
$74$		0			0
$75$	−7.27956	−	2.91812i	−0.840571	−	0.336955i
$76$		0			0
$77$	12.6636	+	3.39321i	1.44315	+	0.386692i
$78$		0			0
$79$	−2.38849	−	0.639993i	−0.268726	−	0.0720048i	0.121940	−	0.992537i	$-0.461088\pi$
$79$	−2.38849	−	0.639993i	−0.268726	−	0.0720048i	−0.390666	+	0.920533i	$0.627755\pi$
$80$		0			0
$81$	−3.54481	−	6.13978i	−0.393867	−	0.682198i
$82$		0			0
$83$	−2.65414	−	9.90537i	−0.291329	−	1.08726i	−0.944089	−	0.329691i	$-0.893056\pi$
$83$	−2.65414	−	9.90537i	−0.291329	−	1.08726i	0.652760	−	0.757565i	$-0.273611\pi$
$84$		0			0
$85$	−5.38162	+	1.10253i	−0.583719	+	0.119586i
$86$		0			0
$87$	−9.52675	+	5.50027i	−1.02137	+	0.589691i
$88$		0			0
$89$	−3.51683	+	0.942333i	−0.372784	+	0.0998871i	−0.440346	−	0.897828i	$-0.645144\pi$
$89$	−3.51683	+	0.942333i	−0.372784	+	0.0998871i	0.0675628	+	0.997715i	$0.478478\pi$
$90$		0			0
$91$	8.19433	−	2.19566i	0.858999	−	0.230168i
$92$		0			0
$93$	−7.96284	−	13.7920i	−0.825708	−	1.43017i
$94$		0			0
$95$	3.14386	−	1.57282i	0.322554	−	0.161368i
$96$		0			0
$97$		−	9.70531i		−	0.985425i	−0.870192	−	0.492713i	$-0.836005\pi$
$97$		−	9.70531i		−	0.985425i	0.870192	−	0.492713i	$-0.163995\pi$
$98$		0			0
$99$	−1.65291	+	2.86293i	−0.166124	+	0.287736i
$100$		0			0
$101$		−	4.91307i		−	0.488869i	−0.969666	−	0.244435i	$-0.921398\pi$
$101$		−	4.91307i		−	0.488869i	0.969666	−	0.244435i	$-0.0786023\pi$
$102$		0			0
$103$			7.27718i			0.717042i	0.933522	+	0.358521i	$0.116719\pi$
$103$			7.27718i			0.717042i	−0.933522	+	0.358521i	$0.883281\pi$
$104$		0			0
$105$	7.35427	−	1.50667i	0.717703	−	0.147035i
$106$		0			0
$107$	−3.23691	+	12.0803i	−0.312924	+	1.16785i	0.612982	+	0.790097i	$0.289970\pi$
$107$	−3.23691	+	12.0803i	−0.312924	+	1.16785i	−0.925907	+	0.377753i	$0.876697\pi$
$108$		0			0
$109$	−4.22836	−	15.7804i	−0.405003	−	1.51149i	−0.804050	−	0.594562i	$-0.797325\pi$
$109$	−4.22836	−	15.7804i	−0.405003	−	1.51149i	0.399046	−	0.916931i	$-0.369341\pi$
$110$		0			0
$111$	9.05762	+	2.99843i	0.859711	+	0.284598i
$112$		0			0
$113$	4.82461	+	2.78549i	0.453862	+	0.262037i	0.709460	−	0.704746i	$-0.248939\pi$
$113$	4.82461	+	2.78549i	0.453862	+	0.262037i	−0.255598	+	0.966783i	$0.582272\pi$
$114$		0			0
$115$	−12.6811	+	11.2501i	−1.18252	+	1.04908i
$116$		0			0
$117$			2.13912i			0.197762i
$118$		0			0
$119$	3.71817	−	3.71817i	0.340844	−	0.340844i
$120$		0			0
$121$	−26.5190			−2.41082
$122$		0			0
$123$	2.83645	+	10.5858i	0.255754	+	0.954488i
$124$		0			0
$125$	6.37017	+	9.18809i	0.569765	+	0.821808i
$126$		0			0
$127$	−9.04950	+	2.42481i	−0.803013	+	0.215167i	−0.636907	−	0.770941i	$-0.719786\pi$
$127$	−9.04950	+	2.42481i	−0.803013	+	0.215167i	−0.166107	+	0.986108i	$0.553120\pi$
$128$		0			0
$129$	−2.27574	+	8.49318i	−0.200368	+	0.747783i
$130$		0			0
$131$	−2.10337	−	7.84988i	−0.183772	−	0.685847i	−0.994890	−	0.100965i	$-0.967807\pi$
$131$	−2.10337	−	7.84988i	−0.183772	−	0.685847i	0.811118	−	0.584883i	$-0.198860\pi$
$132$		0			0
$133$	−1.68245	+	2.91408i	−0.145887	+	0.252683i
$134$		0			0
$135$	−0.741056	+	12.3928i	−0.0637800	+	1.06661i
$136$		0			0
$137$	1.01155	+	1.01155i	0.0864225	+	0.0864225i	0.748996	−	0.662574i	$-0.230536\pi$
$137$	1.01155	+	1.01155i	0.0864225	+	0.0864225i	−0.662574	+	0.748996i	$0.730536\pi$
$138$		0			0
$139$	−9.39209	+	16.2676i	−0.796627	+	1.37980i	0.125174	+	0.992135i	$0.460051\pi$
$139$	−9.39209	+	16.2676i	−0.796627	+	1.37980i	−0.921801	+	0.387663i	$0.873282\pi$
$140$		0			0
$141$	10.0108	−	5.77975i	0.843063	−	0.486743i
$142$		0			0
$143$	−21.0251	+	12.1388i	−1.75820	+	1.01510i
$144$		0			0
$145$	15.6542	+	0.936076i	1.30001	+	0.0777369i
$146$		0			0
$147$	2.68276	−	2.68276i	0.221271	−	0.221271i
$148$		0			0
$149$		−	9.42315i		−	0.771974i	−0.922504	−	0.385987i	$-0.873861\pi$
$149$		−	9.42315i		−	0.771974i	0.922504	−	0.385987i	$-0.126139\pi$
$150$		0			0
$151$	12.9950	−	7.50270i	1.05752	−	0.610561i	0.132776	−	0.991146i	$-0.457611\pi$
$151$	12.9950	−	7.50270i	1.05752	−	0.610561i	0.924746	+	0.380585i	$0.124277\pi$
$152$		0			0
$153$	0.662950	+	1.14826i	0.0535963	+	0.0928316i
$154$		0			0
$155$	−1.35517	+	22.6628i	−0.108850	+	1.82032i
$156$		0			0
$157$	5.37189	−	1.43939i	0.428724	−	0.114876i	−0.0380033	−	0.999278i	$-0.512100\pi$
$157$	5.37189	−	1.43939i	0.428724	−	0.114876i	0.466727	+	0.884401i	$0.345433\pi$
$158$		0			0
$159$	1.68584			0.133696
$160$		0			0
$161$	4.19977	−	15.6737i	0.330988	−	1.23526i
$162$		0			0
$163$	1.84098	+	1.06289i	0.144197	+	0.0832522i	0.570363	−	0.821393i	$-0.306803\pi$
$163$	1.84098	+	1.06289i	0.144197	+	0.0832522i	−0.426166	+	0.904645i	$0.640136\pi$
$164$		0			0
$165$	−19.2132	+	9.61202i	−1.49575	+	0.748295i
$166$		0			0
$167$	20.3149	−	11.7288i	1.57202	−	0.907604i	0.576094	−	0.817384i	$-0.304576\pi$
$167$	20.3149	−	11.7288i	1.57202	−	0.907604i	0.995922	−	0.0902197i	$-0.0287569\pi$
$168$		0			0
$169$	−1.35475	+	2.34649i	−0.104211	+	0.180499i
$170$		0			0
$171$	−0.599960	−	0.599960i	−0.0458801	−	0.0458801i
$172$		0			0
$173$	−20.8700	+	5.59210i	−1.58672	+	0.425159i	−0.940997	−	0.338415i	$-0.890109\pi$
$173$	−20.8700	+	5.59210i	−1.58672	+	0.425159i	−0.645720	+	0.763575i	$0.723442\pi$
$174$		0			0
$175$	−9.93345	−	3.98197i	−0.750898	−	0.301009i
$176$		0			0
$177$	6.96106			0.523226
$178$		0			0
$179$	−17.3309	−	17.3309i	−1.29537	−	1.29537i	−0.931417	−	0.363954i	$-0.881427\pi$
$179$	−17.3309	−	17.3309i	−1.29537	−	1.29537i	−0.363954	−	0.931417i	$-0.618573\pi$
$180$		0			0
$181$	8.14391	+	14.1057i	0.605332	+	1.04847i	0.991999	+	0.126246i	$0.0402929\pi$
$181$	8.14391	+	14.1057i	0.605332	+	1.04847i	−0.386667	+	0.922219i	$0.626374\pi$
$182$		0			0
$183$	1.21572	−	2.10570i	0.0898689	−	0.155657i
$184$		0			0
$185$	−8.42271	−	10.6798i	−0.619250	−	0.785194i
$186$		0			0
$187$	−7.52405	+	13.0320i	−0.550213	+	0.952997i
$188$		0			0
$189$	−5.94182	−	10.2915i	−0.432204	−	0.748599i
$190$		0			0
$191$	−7.45269	−	7.45269i	−0.539257	−	0.539257i	0.384053	−	0.923311i	$-0.374528\pi$
$191$	−7.45269	−	7.45269i	−0.539257	−	0.539257i	−0.923311	+	0.384053i	$0.874528\pi$
$192$		0			0
$193$	−26.1972			−1.88572			−0.942858	−	0.333194i	$-0.891874\pi$
$193$	−26.1972			−1.88572			−0.942858	+	0.333194i	$0.891874\pi$
$194$		0			0
$195$	−7.65694	+	11.6026i	−0.548325	+	0.830882i
$196$		0			0
$197$	17.3177	−	4.64027i	1.23384	−	0.330605i	0.417764	−	0.908556i	$-0.362814\pi$
$197$	17.3177	−	4.64027i	1.23384	−	0.330605i	0.816072	+	0.577950i	$0.196147\pi$
$198$		0			0
$199$	−17.2167	−	17.2167i	−1.22046	−	1.22046i	−0.967469	−	0.252990i	$-0.918586\pi$
$199$	−17.2167	−	17.2167i	−1.22046	−	1.22046i	−0.252990	−	0.967469i	$-0.581414\pi$
$200$		0			0
$201$	1.69490	−	2.93566i	0.119549	−	0.207065i
$202$		0			0
$203$	−12.9999	+	7.50549i	−0.912413	+	0.526782i
$204$		0			0
$205$	4.93716	−	14.8226i	0.344826	−	1.03526i
$206$		0			0
$207$	3.54344	+	2.04581i	0.246286	+	0.142194i
$208$		0			0
$209$	2.49232	−	9.30148i	0.172398	−	0.643397i
$210$		0			0
$211$	−8.01500			−0.551776			−0.275888	−	0.961190i	$-0.588972\pi$
$211$	−8.01500			−0.551776			−0.275888	+	0.961190i	$0.588972\pi$
$212$		0			0
$213$	23.9704	−	6.42284i	1.64242	−	0.440086i
$214$		0			0
$215$	9.37671	−	8.31859i	0.639487	−	0.567323i
$216$		0			0
$217$	−10.8658	−	18.8202i	−0.737620	−	1.27760i
$218$		0			0
$219$	−0.891643	+	0.514791i	−0.0602517	+	0.0347863i
$220$		0			0
$221$			9.73727i			0.654999i
$222$		0			0
$223$	16.5105	−	16.5105i	1.10563	−	1.10563i	0.111909	−	0.993718i	$-0.464303\pi$
$223$	16.5105	−	16.5105i	1.10563	−	1.10563i	0.993718	−	0.111909i	$-0.0356966\pi$
$224$		0			0
$225$	1.61814	−	2.15954i	0.107876	−	0.143969i
$226$		0			0
$227$	8.24129	−	4.75811i	0.546993	−	0.315807i	−0.200915	−	0.979609i	$-0.564392\pi$
$227$	8.24129	−	4.75811i	0.546993	−	0.315807i	0.747908	+	0.663802i	$0.231058\pi$
$228$		0			0
$229$	0.0183277	−	0.0105815i	0.00121113	−	0.000699247i	−0.499394	−	0.866375i	$-0.666444\pi$
$229$	0.0183277	−	0.0105815i	0.00121113	−	0.000699247i	0.500605	+	0.865676i	$0.333111\pi$
$230$		0			0
$231$	10.2820	−	17.8090i	0.676507	−	1.17174i
$232$		0			0
$233$	−13.6444	−	13.6444i	−0.893872	−	0.893872i	0.101013	−	0.994885i	$-0.467792\pi$
$233$	−13.6444	−	13.6444i	−0.893872	−	0.893872i	−0.994885	+	0.101013i	$0.967792\pi$
$234$		0			0
$235$	−16.4496	−	0.983640i	−1.07305	−	0.0641656i
$236$		0			0
$237$	−1.93929	+	3.35895i	−0.125970	+	0.218187i
$238$		0			0
$239$	3.44061	+	12.8405i	0.222555	+	0.830585i	0.983369	+	0.181616i	$0.0581329\pi$
$239$	3.44061	+	12.8405i	0.222555	+	0.830585i	−0.760815	+	0.648969i	$0.775200\pi$
$240$		0			0
$241$	−3.45609	+	12.8983i	−0.222627	+	0.830854i	0.760715	+	0.649086i	$0.224849\pi$
$241$	−3.45609	+	12.8983i	−0.222627	+	0.830854i	−0.983341	+	0.181768i	$0.941818\pi$
$242$		0			0
$243$	5.34749	−	1.43286i	0.343042	−	0.0919178i
$244$		0			0
$245$	−5.29859	+	1.08552i	−0.338515	+	0.0693513i
$246$		0			0
$247$	−1.61272	−	6.01877i	−0.102615	−	0.382965i
$248$		0			0
$249$	−16.0850			−1.01934
$250$		0			0
$251$	15.4889	−	15.4889i	0.977651	−	0.977651i	−0.0221046	−	0.999756i	$-0.507037\pi$
$251$	15.4889	−	15.4889i	0.977651	−	0.977651i	0.999756	+	0.0221046i	$0.00703670\pi$
$252$		0			0
$253$			46.4372i			2.91948i
$254$		0			0
$255$	−0.514328	+	8.60121i	−0.0322085	+	0.538629i
$256$		0			0
$257$	−9.19404	−	5.30818i	−0.573508	−	0.331115i	0.185041	−	0.982731i	$-0.440758\pi$
$257$	−9.19404	−	5.30818i	−0.573508	−	0.331115i	−0.758549	+	0.651616i	$0.774092\pi$
$258$		0			0
$259$	12.3597	+	4.09155i	0.767996	+	0.254237i
$260$		0			0
$261$	−0.979651	−	3.65611i	−0.0606389	−	0.226307i
$262$		0			0
$263$	−2.64085	+	9.85577i	−0.162842	+	0.607733i	0.835464	+	0.549545i	$0.185199\pi$
$263$	−2.64085	+	9.85577i	−0.162842	+	0.607733i	−0.998306	+	0.0581879i	$0.981468\pi$
$264$		0			0
$265$	−2.00588	−	1.32374i	−0.123220	−	0.0813169i
$266$		0			0
$267$			5.71086i			0.349499i
$268$		0			0
$269$		−	17.2415i		−	1.05124i	−0.850721	−	0.525618i	$-0.823834\pi$
$269$		−	17.2415i		−	1.05124i	0.850721	−	0.525618i	$-0.176166\pi$
$270$		0			0
$271$	−0.552841	+	0.957549i	−0.0335827	+	0.0581670i	−0.882328	−	0.470634i	$-0.844025\pi$
$271$	−0.552841	+	0.957549i	−0.0335827	+	0.0581670i	0.848746	+	0.528801i	$0.177358\pi$
$272$		0			0
$273$		−	13.3065i		−	0.805345i
$274$		0			0
$275$	30.4081	+	3.64969i	1.83368	+	0.220085i
$276$		0			0
$277$	−9.20058	−	15.9359i	−0.552809	−	0.957494i	−0.998070	−	0.0620930i	$-0.980222\pi$
$277$	−9.20058	−	15.9359i	−0.552809	−	0.957494i	0.445261	−	0.895401i	$-0.353111\pi$
$278$		0			0
$279$	5.29301	−	1.41826i	0.316884	−	0.0849088i
$280$		0			0
$281$	−11.5682	+	3.09969i	−0.690100	+	0.184912i	−0.586792	−	0.809738i	$-0.699609\pi$
$281$	−11.5682	+	3.09969i	−0.690100	+	0.184912i	−0.103308	+	0.994649i	$0.532943\pi$
$282$		0			0
$283$	−5.44518	+	3.14378i	−0.323683	+	0.186878i	−0.653033	−	0.757330i	$-0.726504\pi$
$283$	−5.44518	+	3.14378i	−0.323683	+	0.186878i	0.329350	+	0.944208i	$0.393170\pi$
$284$		0			0
$285$	−1.10665	−	5.40174i	−0.0655524	−	0.319971i
$286$		0			0
$287$	3.87053	+	14.4450i	0.228470	+	0.852662i
$288$		0			0
$289$	−5.48226	−	9.49555i	−0.322486	−	0.558562i
$290$		0			0
$291$	−14.7044	−	3.94003i	−0.861987	−	0.230969i
$292$		0			0
$293$	19.9417	+	5.34337i	1.16501	+	0.312163i	0.788965	−	0.614438i	$-0.210617\pi$
$293$	19.9417	+	5.34337i	1.16501	+	0.312163i	0.376044	+	0.926602i	$0.377284\pi$
$294$		0			0
$295$	−8.28255	−	5.46591i	−0.482229	−	0.318238i
$296$		0			0
$297$	24.0476	+	24.0476i	1.39538	+	1.39538i
$298$		0			0
$299$	15.0242	+	26.0227i	0.868872	+	1.50493i
$300$		0			0
$301$	−3.10540	+	11.5895i	−0.178992	+	0.668009i
$302$		0			0
$303$	−7.44373	−	1.99454i	−0.427631	−	0.114583i
$304$		0			0
$305$	−3.09993	+	1.55084i	−0.177502	+	0.0888008i
$306$		0			0
$307$	2.93707	−	2.93707i	0.167627	−	0.167627i	−0.618308	−	0.785936i	$-0.712182\pi$
$307$	2.93707	−	2.93707i	0.167627	−	0.167627i	0.785936	+	0.618308i	$0.212182\pi$
$308$		0			0
$309$	11.0256	+	2.95429i	0.627223	+	0.168064i
$310$		0			0
$311$	3.22003	+	12.0173i	0.182591	+	0.681439i	0.995133	+	0.0985370i	$0.0314163\pi$
$311$	3.22003	+	12.0173i	0.182591	+	0.681439i	−0.812542	+	0.582902i	$0.801917\pi$
$312$		0			0
$313$	−2.28242	+	3.95327i	−0.129010	+	0.223452i	−0.923293	−	0.384095i	$-0.874513\pi$
$313$	−2.28242	+	3.95327i	−0.129010	+	0.223452i	0.794283	+	0.607548i	$0.207847\pi$
$314$		0			0
$315$	−0.154182	+	2.57842i	−0.00868718	+	0.145277i
$316$		0			0
$317$	5.34258	+	19.9388i	0.300069	+	1.11987i	0.937107	+	0.349041i	$0.113493\pi$
$317$	5.34258	+	19.9388i	0.300069	+	1.11987i	−0.637038	+	0.770832i	$0.719841\pi$
$318$		0			0
$319$	30.3760	−	30.3760i	1.70073	−	1.70073i
$320$		0			0
$321$	16.9887	+	9.80841i	0.948215	+	0.547452i
$322$		0			0
$323$	−2.73101	−	2.73101i	−0.151958	−	0.151958i
$324$		0			0
$325$	18.2211	−	7.79296i	1.01072	−	0.432276i
$326$		0			0
$327$	−25.6253			−1.41708
$328$		0			0
$329$	13.6604	−	7.88686i	0.753125	−	0.434817i
$330$		0			0
$331$	5.17952	−	1.38785i	0.284692	−	0.0762830i	−0.113647	−	0.993521i	$-0.536253\pi$
$331$	5.17952	−	1.38785i	0.284692	−	0.0762830i	0.398339	+	0.917238i	$0.369587\pi$
$332$		0			0
$333$	−1.80317	+	2.74334i	−0.0988132	+	0.150334i
$334$		0			0
$335$	−4.32177	+	2.16210i	−0.236124	+	0.118128i
$336$		0			0
$337$	2.01791	+	0.540698i	0.109923	+	0.0294537i	0.313361	−	0.949634i	$-0.398545\pi$
$337$	2.01791	+	0.540698i	0.109923	+	0.0294537i	−0.203438	+	0.979088i	$0.565212\pi$
$338$		0			0
$339$	6.17889	−	6.17889i	0.335591	−	0.335591i
$340$		0			0
$341$	43.9759	+	43.9759i	2.38143	+	2.38143i
$342$		0			0
$343$	14.2551	−	14.2551i	0.769703	−	0.769703i
$344$		0			0
$345$	11.8968	+	23.7802i	0.640501	+	1.28028i
$346$		0			0
$347$	−4.93120			−0.264721			−0.132360	−	0.991202i	$-0.542256\pi$
$347$	−4.93120			−0.264721			−0.132360	+	0.991202i	$0.542256\pi$
$348$		0			0
$349$	−10.4303	−	6.02195i	−0.558323	−	0.322348i	0.194149	−	0.980972i	$-0.437805\pi$
$349$	−10.4303	−	6.02195i	−0.558323	−	0.322348i	−0.752472	+	0.658624i	$0.771139\pi$
$350$		0			0
$351$	21.2562	+	5.69558i	1.13457	+	0.304008i
$352$		0			0
$353$	5.33767	+	3.08170i	0.284095	+	0.164023i	0.635276	−	0.772285i	$-0.280886\pi$
$353$	5.33767	+	3.08170i	0.284095	+	0.164023i	−0.351181	+	0.936308i	$0.614220\pi$
$354$		0			0
$355$	−33.5642	−	11.1797i	−1.78140	−	0.593355i
$356$		0			0
$357$	−4.12390	−	7.14281i	−0.218260	−	0.378038i
$358$		0			0
$359$		−	20.4873i		−	1.08128i	−0.841254	−	0.540639i	$-0.818182\pi$
$359$		−	20.4873i		−	1.08128i	0.841254	−	0.540639i	$-0.181818\pi$
$360$		0			0
$361$	−14.3141	−	8.26424i	−0.753372	−	0.434960i
$362$		0			0
$363$	−10.7658	+	40.1786i	−0.565059	+	2.10883i
$364$		0			0
$365$	1.46513	+	0.0876108i	0.0766885	+	0.00458576i
$366$		0			0
$367$	−3.25916	+	12.1634i	−0.170127	+	0.634923i	0.827203	+	0.561903i	$0.189930\pi$
$367$	−3.25916	+	12.1634i	−0.170127	+	0.634923i	−0.997330	+	0.0730201i	$0.976736\pi$
$368$		0			0
$369$	−3.77086			−0.196303
$370$		0			0
$371$	2.30045			0.119433
$372$		0			0
$373$	−0.470315	+	1.75524i	−0.0243520	+	0.0908828i	−0.977032	−	0.213091i	$-0.931647\pi$
$373$	−0.470315	+	1.75524i	−0.0243520	+	0.0908828i	0.952680	+	0.303974i	$0.0983136\pi$
$374$		0			0
$375$	16.5068	−	5.92130i	0.852409	−	0.305775i
$376$		0			0
$377$	7.19445	−	26.8501i	0.370533	−	1.38285i
$378$		0			0
$379$	−2.90970	−	1.67992i	−0.149461	−	0.0862916i	0.423404	−	0.905941i	$-0.360835\pi$
$379$	−2.90970	−	1.67992i	−0.149461	−	0.0862916i	−0.572866	+	0.819649i	$0.694168\pi$
$380$		0			0
$381$			14.6952i			0.752856i
$382$		0			0
$383$	−3.43353	−	5.94705i	−0.175445	−	0.303880i	0.764870	−	0.644185i	$-0.222803\pi$
$383$	−3.43353	−	5.94705i	−0.175445	−	0.303880i	−0.940315	+	0.340305i	$0.889470\pi$
$384$		0			0
$385$	−26.2177	+	13.1163i	−1.33618	+	0.668466i
$386$		0			0
$387$	−2.62010	−	1.51272i	−0.133187	−	0.0768957i
$388$		0			0
$389$	−13.0506	−	3.49690i	−0.661692	−	0.177300i	−0.0876825	−	0.996148i	$-0.527946\pi$
$389$	−13.0506	−	3.49690i	−0.661692	−	0.177300i	−0.574009	+	0.818849i	$0.694613\pi$
$390$		0			0
$391$	16.1297	+	9.31250i	0.815715	+	0.470953i
$392$		0			0
$393$	−12.7472			−0.643009
$394$		0			0
$395$	4.94493	−	2.47386i	0.248806	−	0.124473i
$396$		0			0
$397$	20.9695	−	20.9695i	1.05243	−	1.05243i	0.0538814	−	0.998547i	$-0.482841\pi$
$397$	20.9695	−	20.9695i	1.05243	−	1.05243i	0.998547	−	0.0538814i	$-0.0171593\pi$
$398$		0			0
$399$	3.73207	+	3.73207i	0.186837	+	0.186837i
$400$		0			0
$401$	−3.95683	+	3.95683i	−0.197595	+	0.197595i	−0.798968	−	0.601373i	$-0.794620\pi$
$401$	−3.95683	+	3.95683i	−0.197595	+	0.197595i	0.601373	+	0.798968i	$0.294620\pi$
$402$		0			0
$403$	38.8713	+	10.4155i	1.93632	+	0.518834i
$404$		0			0
$405$	15.0405	+	5.00973i	0.747367	+	0.248935i
$406$		0			0
$407$	−37.1962	−	2.15551i	−1.84375	−	0.106845i
$408$		0			0
$409$	13.2096	−	3.53951i	0.653174	−	0.175017i	0.0830106	−	0.996549i	$-0.473546\pi$
$409$	13.2096	−	3.53951i	0.653174	−	0.175017i	0.570164	+	0.821531i	$0.306880\pi$
$410$		0			0
$411$	1.94324	−	1.12193i	0.0958530	−	0.0553408i
$412$		0			0
$413$	9.49884			0.467407
$414$		0			0
$415$	19.1385	+	12.6301i	0.939474	+	0.619988i
$416$		0			0
$417$	20.8339	+	20.8339i	1.02024	+	1.02024i
$418$		0			0
$419$	−9.95188	−	5.74572i	−0.486181	−	0.280697i	0.236808	−	0.971557i	$-0.423899\pi$
$419$	−9.95188	−	5.74572i	−0.486181	−	0.280697i	−0.722989	+	0.690860i	$0.757232\pi$
$420$		0			0
$421$	0.0426691	−	0.0426691i	0.00207957	−	0.00207957i	−0.706066	−	0.708146i	$-0.749532\pi$
$421$	0.0426691	−	0.0426691i	0.00207957	−	0.00207957i	0.708146	+	0.706066i	$0.249532\pi$
$422$		0			0
$423$	1.02943	+	3.84188i	0.0500526	+	0.186799i
$424$		0			0
$425$	7.36574	−	9.83021i	0.357291	−	0.476835i
$426$		0			0
$427$	1.65894	−	2.87336i	0.0802816	−	0.139052i
$428$		0			0
$429$	9.85591	+	36.7828i	0.475848	+	1.77589i
$430$		0			0
$431$	−18.9778	−	5.08508i	−0.914128	−	0.244940i	−0.229054	−	0.973414i	$-0.573563\pi$
$431$	−18.9778	−	5.08508i	−0.914128	−	0.244940i	−0.685074	+	0.728474i	$0.740230\pi$
$432$		0			0
$433$	13.9360	−	13.9360i	0.669720	−	0.669720i	−0.287931	−	0.957651i	$-0.592967\pi$
$433$	13.9360	−	13.9360i	0.669720	−	0.669720i	0.957651	+	0.287931i	$0.0929673\pi$
$434$		0			0
$435$	7.77331	−	23.3374i	0.372702	−	1.11894i
$436$		0			0
$437$	−11.5124	−	3.08474i	−0.550714	−	0.147563i
$438$		0			0
$439$	−0.204787	+	0.764276i	−0.00977395	+	0.0364769i	−0.970641	−	0.240534i	$-0.922677\pi$
$439$	−0.204787	+	0.764276i	−0.00977395	+	0.0364769i	0.960867	+	0.277011i	$0.0893440\pi$
$440$		0			0
$441$	0.652722	+	1.13055i	0.0310820	+	0.0538356i
$442$		0			0
$443$	18.1047	+	18.1047i	0.860180	+	0.860180i	0.991359	−	0.131179i	$-0.0418763\pi$
$443$	18.1047	+	18.1047i	0.860180	+	0.860180i	−0.131179	+	0.991359i	$0.541876\pi$
$444$		0			0
$445$	4.48424	−	6.79501i	0.212573	−	0.322114i
$446$		0			0
$447$	−14.2769	−	3.82548i	−0.675274	−	0.180939i
$448$		0			0
$449$	−26.0341	−	6.97581i	−1.22862	−	0.329209i	−0.414580	−	0.910013i	$-0.636072\pi$
$449$	−26.0341	−	6.97581i	−1.22862	−	0.329209i	−0.814043	+	0.580804i	$0.802738\pi$
$450$		0			0
$451$	−21.3984	−	37.0631i	−1.00761	−	1.74523i
$452$		0			0
$453$	−6.09168	−	22.7345i	−0.286212	−	1.06816i
$454$		0			0
$455$	−10.4484	+	15.8326i	−0.489829	+	0.742243i
$456$		0			0
$457$	−12.1007	+	6.98637i	−0.566049	+	0.326808i	−0.755570	−	0.655068i	$-0.772640\pi$
$457$	−12.1007	+	6.98637i	−0.566049	+	0.326808i	0.189521	+	0.981877i	$0.439307\pi$
$458$		0			0
$459$	13.1753	−	3.53031i	0.614970	−	0.164781i
$460$		0			0
$461$	−4.96919	+	1.33149i	−0.231438	+	0.0620137i	−0.372674	−	0.927962i	$-0.621559\pi$
$461$	−4.96919	+	1.33149i	−0.231438	+	0.0620137i	0.141236	+	0.989976i	$0.454892\pi$
$462$		0			0
$463$	1.23913	+	2.14623i	0.0575871	+	0.0997438i	0.893382	−	0.449298i	$-0.148326\pi$
$463$	1.23913	+	2.14623i	0.0575871	+	0.0997438i	−0.835795	+	0.549042i	$0.814993\pi$
$464$		0			0
$465$	33.7860	+	11.2535i	1.56679	+	0.521871i
$466$		0			0
$467$		−	6.14752i		−	0.284473i	−0.989833	−	0.142237i	$-0.954571\pi$
$467$		−	6.14752i		−	0.284473i	0.989833	−	0.142237i	$-0.0454294\pi$
$468$		0			0
$469$	2.31281	−	4.00590i	0.106795	−	0.184975i
$470$		0			0
$471$		−	8.72323i		−	0.401945i
$472$		0			0
$473$		−	34.3367i		−	1.57880i
$474$		0			0
$475$	−2.92477	+	7.29616i	−0.134198	+	0.334771i
$476$		0			0
$477$	−0.150132	+	0.560302i	−0.00687409	+	0.0256545i
$478$		0			0
$479$	5.52599	+	20.6233i	0.252489	+	0.942302i	0.969470	+	0.245209i	$0.0788567\pi$
$479$	5.52599	+	20.6233i	0.252489	+	0.942302i	−0.716981	+	0.697093i	$0.754477\pi$
$480$		0			0
$481$	−21.5416	+	10.8265i	−0.982210	+	0.493645i
$482$		0			0
$483$	−22.0421	−	12.7260i	−1.00295	−	0.579054i
$484$		0			0
$485$	14.4021	+	16.2341i	0.653966	+	0.737151i
$486$		0			0
$487$		−	21.8499i		−	0.990113i	−0.868861	−	0.495057i	$-0.835147\pi$
$487$		−	21.8499i		−	0.990113i	0.868861	−	0.495057i	$-0.164853\pi$
$488$		0			0
$489$	2.35775	−	2.35775i	0.106621	−	0.106621i
$490$		0			0
$491$	3.87041			0.174669			0.0873346	−	0.996179i	$-0.472165\pi$
$491$	3.87041			0.174669			0.0873346	+	0.996179i	$0.472165\pi$
$492$		0			0
$493$	−4.45936	−	16.6426i	−0.200840	−	0.749543i
$494$		0			0
$495$	−1.48359	−	7.24165i	−0.0666825	−	0.325488i
$496$		0			0
$497$	32.7092	−	8.76440i	1.46721	−	0.393137i
$498$		0			0
$499$	2.17573	−	8.11993i	0.0973990	−	0.363498i	−0.899973	−	0.435945i	$-0.856414\pi$
$499$	2.17573	−	8.11993i	0.0973990	−	0.363498i	0.997372	+	0.0724470i	$0.0230808\pi$
$500$		0			0
$501$	−9.52301	−	35.5404i	−0.425457	−	1.58783i
$502$		0			0
$503$	17.1762	−	29.7501i	0.765851	−	1.32649i	−0.173945	−	0.984755i	$-0.555651\pi$
$503$	17.1762	−	29.7501i	0.765851	−	1.32649i	0.939796	−	0.341737i	$-0.111015\pi$
$504$		0			0
$505$	7.29071	+	8.21809i	0.324432	+	0.365700i
$506$		0			0
$507$	3.00515	+	3.00515i	0.133463	+	0.133463i
$508$		0			0
$509$	−15.6825	+	27.1629i	−0.695114	+	1.20397i	0.275028	+	0.961436i	$0.411313\pi$
$509$	−15.6825	+	27.1629i	−0.695114	+	1.20397i	−0.970142	+	0.242537i	$0.922021\pi$
$510$		0			0
$511$	−1.21671	+	0.702466i	−0.0538240	+	0.0310753i
$512$		0			0
$513$	−7.55917	+	4.36429i	−0.333745	+	0.192688i
$514$		0			0
$515$	−10.7989	−	12.1725i	−0.475857	−	0.536386i
$516$		0			0
$517$	−31.9195	+	31.9195i	−1.40382	+	1.40382i
$518$		0			0
$519$			33.8901i			1.48761i
$520$		0			0
$521$	−7.45751	+	4.30560i	−0.326719	+	0.188632i	−0.654384	−	0.756163i	$-0.727072\pi$
$521$	−7.45751	+	4.30560i	−0.326719	+	0.188632i	0.327664	+	0.944794i	$0.393739\pi$
$522$		0			0
$523$	8.82687	+	15.2886i	0.385972	+	0.668523i	0.991904	−	0.126994i	$-0.0405328\pi$
$523$	8.82687	+	15.2886i	0.385972	+	0.668523i	−0.605932	+	0.795517i	$0.707199\pi$
$524$		0			0
$525$	−10.0657	+	13.4335i	−0.439302	+	0.586286i
$526$		0			0
$527$	24.0937	−	6.45589i	1.04954	−	0.281223i
$528$		0			0
$529$	34.4752			1.49892
$530$		0			0
$531$	−0.619916	+	2.31356i	−0.0269021	+	0.100400i
$532$		0			0
$533$	−23.9827	−	13.8464i	−1.03880	−	0.599754i
$534$		0			0
$535$	−12.5121	−	25.0101i	−0.540945	−	1.08128i
$536$		0			0
$537$	−33.2935	+	19.2220i	−1.43672	+	0.829492i
$538$		0			0
$539$	−7.40797	+	12.8310i	−0.319084	+	0.552669i
$540$		0			0
$541$	−29.9372	−	29.9372i	−1.28710	−	1.28710i	−0.936541	−	0.350559i	$-0.885992\pi$
$541$	−29.9372	−	29.9372i	−1.28710	−	1.28710i	−0.350559	−	0.936541i	$-0.614008\pi$
$542$		0			0
$543$	24.6775	−	6.61230i	1.05901	−	0.283761i
$544$		0			0
$545$	30.4900	+	20.1213i	1.30605	+	0.861902i
$546$		0			0
$547$	26.5354			1.13457			0.567285	−	0.823522i	$-0.307994\pi$
$547$	26.5354			1.13457			0.567285	+	0.823522i	$0.307994\pi$
$548$		0			0
$549$	0.591576	+	0.591576i	0.0252479	+	0.0252479i
$550$		0			0
$551$	5.51281	+	9.54847i	0.234854	+	0.406779i
$552$		0			0
$553$	−2.64629	+	4.58351i	−0.112532	+	0.194911i
$554$		0			0
$555$	−19.6001	+	8.42550i	−0.831980	+	0.357643i
$556$		0			0
$557$	18.9422	−	32.8088i	0.802605	−	1.39015i	−0.115290	−	0.993332i	$-0.536780\pi$
$557$	18.9422	−	32.8088i	0.802605	−	1.39015i	0.917896	−	0.396822i	$-0.129887\pi$
$558$		0			0
$559$	−11.1092	−	19.2418i	−0.469870	−	0.813840i
$560$		0			0
$561$	16.6902	+	16.6902i	0.704659	+	0.704659i
$562$		0			0
$563$	−1.60329			−0.0675706			−0.0337853	−	0.999429i	$-0.510756\pi$
$563$	−1.60329			−0.0675706			−0.0337853	+	0.999429i	$0.510756\pi$
$564$		0			0
$565$	−12.2036	+	2.50015i	−0.513411	+	0.105182i
$566$		0			0
$567$	−14.6573	+	3.92742i	−0.615550	+	0.164936i
$568$		0			0
$569$	8.13575	+	8.13575i	0.341068	+	0.341068i	0.856769	−	0.515700i	$-0.172468\pi$
$569$	8.13575	+	8.13575i	0.341068	+	0.341068i	−0.515700	+	0.856769i	$0.672468\pi$
$570$		0			0
$571$	10.4469	−	18.0945i	0.437187	−	0.757230i	−0.560284	−	0.828300i	$-0.689308\pi$
$571$	10.4469	−	18.0945i	0.437187	−	0.757230i	0.997471	+	0.0710702i	$0.0226414\pi$
$572$		0			0
$573$	−14.3170	+	8.26593i	−0.598101	+	0.345314i
$574$		0			0
$575$	4.51722	−	37.6361i	0.188381	−	1.56953i
$576$		0			0
$577$	30.6651	+	17.7045i	1.27660	+	0.737048i	0.976223	−	0.216771i	$-0.0695525\pi$
$577$	30.6651	+	17.7045i	1.27660	+	0.737048i	0.300382	+	0.953819i	$0.402886\pi$
$578$		0			0
$579$	−10.6352	+	39.6911i	−0.441983	+	1.64950i
$580$		0			0
$581$	−21.9490			−0.910600
$582$		0			0
$583$	−6.35906	+	1.70390i	−0.263365	+	0.0705685i
$584$		0			0
$585$	−3.17433	−	3.57811i	−0.131242	−	0.147937i
$586$		0			0
$587$	−9.00898	−	15.6040i	−0.371840	−	0.644046i	0.618008	−	0.786172i	$-0.287940\pi$
$587$	−9.00898	−	15.6040i	−0.371840	−	0.644046i	−0.989849	+	0.142125i	$0.954606\pi$
$588$		0			0
$589$	−13.8235	+	7.98099i	−0.569587	+	0.328851i
$590$		0			0
$591$		−	28.1216i		−	1.15677i
$592$		0			0
$593$	−11.2796	+	11.2796i	−0.463198	+	0.463198i	−0.899702	−	0.436504i	$-0.856216\pi$
$593$	−11.2796	+	11.2796i	−0.463198	+	0.463198i	0.436504	+	0.899702i	$0.356216\pi$
$594$		0			0
$595$	−0.701836	+	11.7369i	−0.0287725	+	0.481167i
$596$		0			0
$597$	−33.0742	+	19.0954i	−1.35364	+	0.781522i
$598$		0			0
$599$	−2.41752	+	1.39576i	−0.0987772	+	0.0570290i	−0.548575	−	0.836101i	$-0.684829\pi$
$599$	−2.41752	+	1.39576i	−0.0987772	+	0.0570290i	0.449798	+	0.893130i	$0.351496\pi$
$600$		0			0
$601$	−1.01460	+	1.75734i	−0.0413865	+	0.0716835i	−0.885977	−	0.463730i	$-0.846511\pi$
$601$	−1.01460	+	1.75734i	−0.0413865	+	0.0716835i	0.844590	+	0.535413i	$0.179844\pi$
$602$		0			0
$603$	0.824747	+	0.824747i	0.0335863	+	0.0335863i
$604$		0			0
$605$	44.3583	−	39.3526i	1.80342	−	1.59991i
$606$		0			0
$607$	9.30098	−	16.1098i	0.377515	−	0.653875i	−0.613185	−	0.789939i	$-0.710112\pi$
$607$	9.30098	−	16.1098i	0.377515	−	0.653875i	0.990700	+	0.136064i	$0.0434453\pi$
$608$		0			0
$609$	6.09395	+	22.7429i	0.246939	+	0.921590i
$610$		0			0
$611$	−7.56002	+	28.2144i	−0.305846	+	1.14143i
$612$		0			0
$613$	19.5983	−	5.25135i	0.791569	−	0.212100i	0.159690	−	0.987167i	$-0.448951\pi$
$613$	19.5983	−	5.25135i	0.791569	−	0.212100i	0.631879	+	0.775067i	$0.282284\pi$
$614$		0			0
$615$	−20.4532	−	13.4977i	−0.824753	−	0.544280i
$616$		0			0
$617$	9.56798	+	35.7082i	0.385192	+	1.43756i	0.837863	+	0.545880i	$0.183805\pi$
$617$	9.56798	+	35.7082i	0.385192	+	1.43756i	−0.452671	+	0.891678i	$0.649529\pi$
$618$		0			0
$619$	27.5880			1.10886			0.554429	−	0.832231i	$-0.312937\pi$
$619$	27.5880			1.10886			0.554429	+	0.832231i	$0.312937\pi$
$620$		0			0
$621$	29.7636	−	29.7636i	1.19437	−	1.19437i
$622$		0			0
$623$			7.79286i			0.312214i
$624$		0			0
$625$	−24.2899	−	5.91595i	−0.971598	−	0.236638i
$626$		0			0
$627$	−13.0808	−	7.55218i	−0.522395	−	0.301605i
$628$		0			0
$629$	−8.20802	+	12.4876i	−0.327275	+	0.497915i
$630$		0			0
$631$	1.39942	+	5.22271i	0.0557100	+	0.207913i	0.988170	−	0.153359i	$-0.0490092\pi$
$631$	1.39942	+	5.22271i	0.0557100	+	0.207913i	−0.932460	+	0.361272i	$0.882343\pi$
$632$		0			0
$633$	−3.25382	+	12.1434i	−0.129328	+	0.482658i
$634$		0			0
$635$	11.5388	−	17.4849i	0.457904	−	0.693867i
$636$		0			0
$637$			9.58704i			0.379852i
$638$		0			0
$639$			8.53871i			0.337786i
$640$		0			0
$641$	−23.9529	+	41.4876i	−0.946082	+	1.63866i	−0.192513	+	0.981295i	$0.561664\pi$
$641$	−23.9529	+	41.4876i	−0.946082	+	1.63866i	−0.753570	+	0.657368i	$0.771670\pi$
$642$		0			0
$643$		−	21.9328i		−	0.864943i	−0.901648	−	0.432472i	$-0.857642\pi$
$643$		−	21.9328i		−	0.864943i	0.901648	−	0.432472i	$-0.142358\pi$
$644$		0			0
$645$	−8.79675	−	17.5836i	−0.346372	−	0.692354i
$646$		0			0
$647$	−10.2229	−	17.7065i	−0.401902	−	0.696114i	0.592054	−	0.805899i	$-0.298317\pi$
$647$	−10.2229	−	17.7065i	−0.401902	−	0.696114i	−0.993955	+	0.109784i	$0.964984\pi$
$648$		0			0
$649$	−26.2574	+	7.03564i	−1.03069	+	0.276173i
$650$		0			0
$651$	−32.9253	+	8.82232i	−1.29045	+	0.345774i
$652$		0			0
$653$	32.3312	−	18.6664i	1.26522	−	0.730473i	0.291137	−	0.956681i	$-0.405966\pi$
$653$	32.3312	−	18.6664i	1.26522	−	0.730473i	0.974079	+	0.226209i	$0.0726331\pi$
$654$		0			0
$655$	15.1671	+	10.0092i	0.592626	+	0.391092i
$656$		0			0
$657$	−0.0916891	−	0.342188i	−0.00357713	−	0.0133500i
$658$		0			0
$659$	17.4183	+	30.1694i	0.678522	+	1.17523i	0.975426	+	0.220327i	$0.0707124\pi$
$659$	17.4183	+	30.1694i	0.678522	+	1.17523i	−0.296905	+	0.954907i	$0.595954\pi$
$660$		0			0
$661$	−35.2181	−	9.43666i	−1.36983	−	0.367044i	−0.502411	−	0.864629i	$-0.667553\pi$
$661$	−35.2181	−	9.43666i	−1.36983	−	0.367044i	−0.867415	+	0.497586i	$0.834220\pi$
$662$		0			0
$663$	14.7528	+	3.95300i	0.572952	+	0.153522i
$664$		0			0
$665$	−1.51010	−	7.37104i	−0.0585592	−	0.285837i
$666$		0			0
$667$	−37.5963	−	37.5963i	−1.45574	−	1.45574i
$668$		0			0
$669$	−18.3122	−	31.7176i	−0.707990	−	1.22627i
$670$		0			0
$671$	−2.45750	+	9.17150i	−0.0948706	+	0.354062i
$672$		0			0
$673$	−23.2764	−	6.23688i	−0.897238	−	0.240414i	−0.219408	−	0.975633i	$-0.570413\pi$
$673$	−23.2764	−	6.23688i	−0.897238	−	0.240414i	−0.677830	+	0.735219i	$0.737079\pi$
$674$		0			0
$675$	−17.1507	−	21.8292i	−0.660129	−	0.840205i
$676$		0			0
$677$	−30.4653	+	30.4653i	−1.17088	+	1.17088i	−0.188876	+	0.982001i	$0.560484\pi$
$677$	−30.4653	+	30.4653i	−1.17088	+	1.17088i	−0.982001	+	0.188876i	$0.939516\pi$
$678$		0			0
$679$	−20.0651	−	5.37644i	−0.770029	−	0.206329i
$680$		0			0
$681$	−3.86326	−	14.4179i	−0.148041	−	0.552495i
$682$		0			0
$683$	−9.95715	+	17.2463i	−0.381000	+	0.659911i	−0.991205	−	0.132332i	$-0.957753\pi$
$683$	−9.95715	+	17.2463i	−0.381000	+	0.659911i	0.610206	+	0.792243i	$0.291087\pi$
$684$		0			0
$685$	−3.19310	−	0.190938i	−0.122002	−	0.00729538i
$686$		0			0
$687$	−0.00859149	−	0.0320639i	−0.000327786	−	0.00122331i
$688$		0			0
$689$	−3.01224	+	3.01224i	−0.114757	+	0.114757i
$690$		0			0
$691$	9.11179	+	5.26070i	0.346629	+	0.200126i	0.663200	−	0.748443i	$-0.269198\pi$
$691$	9.11179	+	5.26070i	0.346629	+	0.200126i	−0.316571	+	0.948569i	$0.602531\pi$
$692$		0			0
$693$	5.00327	+	5.00327i	0.190059	+	0.190059i
$694$		0			0
$695$	−8.42998	−	41.1481i	−0.319767	−	1.56083i
$696$		0			0
$697$	−17.1649			−0.650168
$698$		0			0
$699$	−26.2115	+	15.1332i	−0.991412	+	0.572392i
$700$		0			0
$701$	24.4073	−	6.53992i	0.921852	−	0.247009i	0.233475	−	0.972363i	$-0.424990\pi$
$701$	24.4073	−	6.53992i	0.921852	−	0.247009i	0.688377	+	0.725353i	$0.258324\pi$
$702$		0			0
$703$	3.00526	−	9.07827i	0.113346	−	0.342393i
$704$		0			0
$705$	−8.16828	+	24.5233i	−0.307635	+	0.923599i
$706$		0			0
$707$	−10.1575	−	2.72169i	−0.382011	−	0.102360i
$708$		0			0
$709$	−31.0307	+	31.0307i	−1.16538	+	1.16538i	−0.182101	+	0.983280i	$0.558290\pi$
$709$	−31.0307	+	31.0307i	−1.16538	+	1.16538i	−0.983280	+	0.182101i	$0.941710\pi$
$710$		0			0
$711$	−0.943667	−	0.943667i	−0.0353903	−	0.0353903i
$712$		0			0
$713$	54.4289	−	54.4289i	2.03838	−	2.03838i
$714$		0			0
$715$	17.1553	−	51.5045i	0.641572	−	1.92616i
$716$		0			0
$717$	20.8513			0.778706
$718$		0			0
$719$	−21.0327	−	12.1432i	−0.784388	−	0.452867i	0.0535953	−	0.998563i	$-0.482932\pi$
$719$	−21.0327	−	12.1432i	−0.784388	−	0.452867i	−0.837983	+	0.545696i	$0.816265\pi$
$720$		0			0
$721$	15.0451	+	4.03133i	0.560310	+	0.150135i
$722$		0			0
$723$	18.1390	+	10.4726i	0.674597	+	0.389479i
$724$		0			0
$725$	−27.5738	+	21.6641i	−1.02407	+	0.804584i
$726$		0			0
$727$	13.8071	+	23.9146i	0.512077	+	0.886943i	0.999902	+	0.0140018i	$0.00445704\pi$
$727$	13.8071	+	23.9146i	0.512077	+	0.886943i	−0.487825	+	0.872941i	$0.662210\pi$
$728$		0			0
$729$		−	29.9524i		−	1.10935i
$730$		0			0
$731$	−11.9267	−	6.88587i	−0.441124	−	0.254683i
$732$		0			0
$733$	−0.418152	+	1.56056i	−0.0154448	+	0.0576407i	−0.973218	−	0.229883i	$-0.926166\pi$
$733$	−0.418152	+	1.56056i	−0.0154448	+	0.0576407i	0.957773	+	0.287524i	$0.0928322\pi$
$734$		0			0
$735$	−0.506393	+	8.46852i	−0.0186786	+	0.312366i
$736$		0			0
$737$	−3.42612	+	12.7865i	−0.126203	+	0.470995i
$738$		0			0
$739$	3.78461			0.139219			0.0696095	−	0.997574i	$-0.477825\pi$
$739$	3.78461			0.139219			0.0696095	+	0.997574i	$0.477825\pi$
$740$		0			0
$741$	−9.77367			−0.359045
$742$		0			0
$743$	−4.25835	+	15.8924i	−0.156224	+	0.583035i	0.842774	+	0.538268i	$0.180921\pi$
$743$	−4.25835	+	15.8924i	−0.156224	+	0.583035i	−0.998997	+	0.0447670i	$0.985745\pi$
$744$		0			0
$745$	13.9834	+	15.7621i	0.512312	+	0.577478i
$746$		0			0
$747$	1.43244	−	5.34596i	0.0524104	−	0.195598i
$748$		0			0
$749$	23.1822	+	13.3842i	0.847058	+	0.489049i
$750$		0			0
$751$		−	15.5864i		−	0.568755i	−0.958712	−	0.284377i	$-0.908213\pi$
$751$		−	15.5864i		−	0.568755i	0.958712	−	0.284377i	$-0.0917868\pi$
$752$		0			0
$753$	−17.1791	−	29.7550i	−0.626040	−	1.08433i
$754$		0			0
$755$	−10.6032	+	31.8336i	−0.385892	+	1.15854i
$756$		0			0
$757$	11.6521	+	6.72736i	0.423504	+	0.244510i	0.696575	−	0.717484i	$-0.254706\pi$
$757$	11.6521	+	6.72736i	0.423504	+	0.244510i	−0.273071	+	0.961994i	$0.588040\pi$
$758$		0			0
$759$	70.3564	+	18.8519i	2.55377	+	0.684282i
$760$		0			0
$761$	7.67383	+	4.43049i	0.278176	+	0.160605i	0.632597	−	0.774481i	$-0.281989\pi$
$761$	7.67383	+	4.43049i	0.278176	+	0.160605i	−0.354421	+	0.935086i	$0.615322\pi$
$762$		0			0
$763$	−34.9675			−1.26591
$764$		0			0
$765$	−2.81287	−	0.936920i	−0.101700	−	0.0338744i
$766$		0			0
$767$	−12.4379	+	12.4379i	−0.449107	+	0.449107i
$768$		0			0
$769$	33.7296	+	33.7296i	1.21632	+	1.21632i	0.968911	+	0.247411i	$0.0795798\pi$
$769$	33.7296	+	33.7296i	1.21632	+	1.21632i	0.247411	+	0.968911i	$0.420420\pi$
$770$		0			0
$771$	−11.7748	+	11.7748i	−0.424060	+	0.424060i
$772$		0			0
$773$	−37.3170	−	9.99907i	−1.34220	−	0.359642i	−0.484950	−	0.874542i	$-0.661162\pi$
$773$	−37.3170	−	9.99907i	−1.34220	−	0.359642i	−0.857250	+	0.514900i	$0.827829\pi$
$774$		0			0
$775$	−31.3635	−	39.9191i	−1.12661	−	1.43394i
$776$		0			0
$777$	11.2167	−	17.0650i	0.402397	−	0.612204i
$778$		0			0
$779$	10.6099	−	2.84292i	0.380140	−	0.101858i
$780$		0			0
$781$	−83.9254	+	48.4544i	−3.00309	+	1.73383i
$782$		0			0
$783$	−38.9387			−1.39155
$784$		0			0
$785$	−6.84958	+	10.3792i	−0.244472	+	0.370451i
$786$		0			0
$787$	8.45322	+	8.45322i	0.301325	+	0.301325i	0.841532	−	0.540207i	$-0.181654\pi$
$787$	8.45322	+	8.45322i	0.301325	+	0.301325i	−0.540207	+	0.841532i	$0.681654\pi$
$788$		0			0
$789$	13.8603	+	8.00222i	0.493438	+	0.284887i
$790$		0			0
$791$	8.43152	−	8.43152i	0.299790	−	0.299790i
$792$		0			0
$793$	1.59019	+	5.93466i	0.0564692	+	0.210746i
$794$		0			0
$795$	−2.81991	+	2.50169i	−0.100012	+	0.0887259i
$796$		0			0
$797$	−5.12625	+	8.87893i	−0.181581	+	0.314508i	−0.942419	−	0.334434i	$-0.891455\pi$
$797$	−5.12625	+	8.87893i	−0.181581	+	0.314508i	0.760838	+	0.648942i	$0.224788\pi$
$798$		0			0
$799$	4.68595	+	17.4882i	0.165777	+	0.618688i
$800$		0			0
$801$	−1.89805	−	0.508580i	−0.0670641	−	0.0179698i
$802$		0			0
$803$	2.84300	−	2.84300i	0.100327	−	0.100327i
$804$		0			0
$805$	16.2340	+	32.4496i	0.572172	+	1.14370i
$806$		0			0
$807$	−26.1224	−	6.99949i	−0.919554	−	0.246394i
$808$		0			0
$809$	−1.54603	+	5.76987i	−0.0543556	+	0.202858i	−0.987763	−	0.155959i	$-0.950153\pi$
$809$	−1.54603	+	5.76987i	−0.0543556	+	0.202858i	0.933408	+	0.358817i	$0.116820\pi$
$810$		0			0
$811$	−15.2338	−	26.3857i	−0.534932	−	0.926529i	−0.999167	−	0.0408168i	$-0.987004\pi$
$811$	−15.2338	−	26.3857i	−0.534932	−	0.926529i	0.464235	−	0.885712i	$-0.346329\pi$
$812$		0			0
$813$	1.22633	+	1.22633i	0.0430094	+	0.0430094i
$814$		0			0
$815$	−4.65668	+	0.954012i	−0.163116	+	0.0334176i
$816$		0			0
$817$	8.51255	+	2.28093i	0.297816	+	0.0797996i
$818$		0			0
$819$	4.42250	+	1.18501i	0.154535	+	0.0414075i
$820$		0			0
$821$	21.0393	+	36.4411i	0.734276	+	1.27180i	0.955040	+	0.296477i	$0.0958117\pi$
$821$	21.0393	+	36.4411i	0.734276	+	1.27180i	−0.220764	+	0.975327i	$0.570855\pi$
$822$		0			0
$823$	−11.0856	−	41.3719i	−0.386419	−	1.44214i	−0.835918	−	0.548854i	$-0.815064\pi$
$823$	−11.0856	−	41.3719i	−0.386419	−	1.44214i	0.449499	−	0.893281i	$-0.351603\pi$
$824$		0			0
$825$	17.8743	−	44.5893i	0.622303	−	1.55240i
$826$		0			0
$827$	22.2285	−	12.8336i	0.772961	−	0.446269i	−0.0609689	−	0.998140i	$-0.519419\pi$
$827$	22.2285	−	12.8336i	0.772961	−	0.446269i	0.833930	+	0.551870i	$0.186086\pi$
$828$		0			0
$829$	14.4577	−	3.87393i	0.502136	−	0.134547i	0.00114511	−	0.999999i	$-0.499636\pi$
$829$	14.4577	−	3.87393i	0.502136	−	0.134547i	0.500991	+	0.865452i	$0.332969\pi$
$830$		0			0
$831$	−27.8794	+	7.47025i	−0.967124	+	0.259140i
$832$		0			0
$833$	2.97118	+	5.14624i	0.102945	+	0.178307i
$834$		0			0
$835$	−16.5759	+	49.7649i	−0.573631	+	1.72219i
$836$		0			0
$837$		−	56.3721i		−	1.94851i
$838$		0			0
$839$	−21.3278	+	36.9407i	−0.736316	+	1.27534i	0.217828	+	0.975987i	$0.430103\pi$
$839$	−21.3278	+	36.9407i	−0.736316	+	1.27534i	−0.954144	+	0.299349i	$0.903230\pi$
$840$		0			0
$841$			20.1859i			0.696066i
$842$		0			0
$843$			18.7852i			0.646996i
$844$		0			0
$845$	−1.21597	−	5.93533i	−0.0418306	−	0.204182i
$846$		0			0
$847$	−14.6907	+	54.8264i	−0.504778	+	1.88386i
$848$		0			0
$849$	2.55254	+	9.52620i	0.0876028	+	0.326938i
$850$		0			0
$851$	−2.66787	+	46.0376i	−0.0914534	+	1.57815i
$852$		0			0
$853$	12.7726	+	7.37424i	0.437324	+	0.252489i	0.702462	−	0.711721i	$-0.252084\pi$
$853$	12.7726	+	7.37424i	0.437324	+	0.252489i	−0.265138	+	0.964211i	$0.585417\pi$
$854$		0			0
$855$	1.89386	+	0.113247i	0.0647686	+	0.00387298i
$856$		0			0
$857$		−	28.4190i		−	0.970775i	−0.874299	−	0.485387i	$-0.838679\pi$
$857$		−	28.4190i		−	0.970775i	0.874299	−	0.485387i	$-0.161321\pi$
$858$		0			0
$859$	29.9804	−	29.9804i	1.02292	−	1.02292i	0.0231882	−	0.999731i	$-0.492618\pi$
$859$	29.9804	−	29.9804i	1.02292	−	1.02292i	0.999731	−	0.0231882i	$-0.00738170\pi$
$860$		0			0
$861$	23.4568			0.799404
$862$		0			0
$863$	−9.38802	−	35.0366i	−0.319572	−	1.19266i	−0.919657	−	0.392723i	$-0.871533\pi$
$863$	−9.38802	−	35.0366i	−0.319572	−	1.19266i	0.600085	−	0.799936i	$-0.295133\pi$
$864$		0			0
$865$	26.6109	−	40.3237i	0.904797	−	1.37105i
$866$		0			0
$867$	−16.6122	+	4.45122i	−0.564180	+	0.151172i
$868$		0			0
$869$	3.92013	−	14.6301i	0.132981	−	0.496293i
$870$		0			0
$871$	2.21696	+	8.27381i	0.0751188	+	0.280347i
$872$		0			0
$873$	2.61899	−	4.53623i	0.0886395	−	0.153528i
$874$		0			0
$875$	22.5247	−	8.08001i	0.761473	−	0.273154i
$876$		0			0
$877$	6.04801	+	6.04801i	0.204227	+	0.204227i	0.801808	−	0.597581i	$-0.203872\pi$
$877$	6.04801	+	6.04801i	0.204227	+	0.204227i	−0.597581	+	0.801808i	$0.703872\pi$
$878$		0			0
$879$	16.1914	−	28.0442i	0.546121	−	0.945909i
$880$		0			0
$881$	−4.94232	+	2.85345i	−0.166511	+	0.0961352i	−0.580940	−	0.813947i	$-0.697315\pi$
$881$	−4.94232	+	2.85345i	−0.166511	+	0.0961352i	0.414429	+	0.910082i	$0.363981\pi$
$882$		0			0
$883$	−12.4918	+	7.21216i	−0.420383	+	0.242708i	−0.695241	−	0.718776i	$-0.744702\pi$
$883$	−12.4918	+	7.21216i	−0.420383	+	0.242708i	0.274858	+	0.961485i	$0.411369\pi$
$884$		0			0
$885$	−11.6438	+	10.3298i	−0.391401	+	0.347233i
$886$		0			0
$887$	25.5592	−	25.5592i	0.858192	−	0.858192i	−0.132933	−	0.991125i	$-0.542439\pi$
$887$	25.5592	−	25.5592i	0.858192	−	0.858192i	0.991125	+	0.132933i	$0.0424394\pi$
$888$		0			0
$889$			20.0525i			0.672541i
$890$		0			0
$891$	37.6079	−	21.7129i	1.25991	−	0.727410i
$892$		0			0
$893$	−5.79293	−	10.0336i	−0.193853	−	0.335763i
$894$		0			0
$895$	54.7073	+	3.27134i	1.82866	+	0.109349i
$896$		0			0
$897$	45.5259	−	12.1986i	1.52007	−	0.407301i
$898$		0			0
$899$	−71.2073			−2.37490
$900$		0			0
$901$	−0.683401	+	2.55049i	−0.0227674	+	0.0849691i
$902$		0			0
$903$	16.2984	+	9.40991i	0.542378	+	0.313142i
$904$		0			0
$905$	−34.5543	−	11.5094i	−1.14862	−	0.382587i
$906$		0			0
$907$	8.69782	−	5.02169i	0.288806	−	0.166742i	−0.348597	−	0.937273i	$-0.613342\pi$
$907$	8.69782	−	5.02169i	0.288806	−	0.166742i	0.637403	+	0.770530i	$0.280008\pi$
$908$		0			0
$909$	1.32580	−	2.29635i	0.0439740	−	0.0761652i
$910$		0			0
$911$	−30.0237	−	30.0237i	−0.994730	−	0.994730i	0.00525595	−	0.999986i	$-0.498327\pi$
$911$	−30.0237	−	30.0237i	−0.994730	−	0.994730i	−0.999986	+	0.00525595i	$0.998327\pi$
$912$		0			0
$913$	60.6731	−	16.2573i	2.00799	−	0.538038i
$914$		0			0
$915$	1.09119	+	5.32626i	0.0360735	+	0.176081i
$916$		0			0
$917$	−17.3943			−0.574412
$918$		0			0
$919$	2.42586	+	2.42586i	0.0800219	+	0.0800219i	0.745985	−	0.665963i	$-0.231979\pi$
$919$	2.42586	+	2.42586i	0.0800219	+	0.0800219i	−0.665963	+	0.745985i	$0.731979\pi$
$920$		0			0
$921$	−3.25757	−	5.64227i	−0.107340	−	0.185919i
$922$		0			0
$923$	−31.3537	+	54.3062i	−1.03202	+	1.78751i
$924$		0			0
$925$	29.9368	+	5.36527i	0.984317	+	0.176409i
$926$		0			0
$927$	−1.96376	+	3.40133i	−0.0644983	+	0.111714i
$928$		0			0
$929$	4.26647	+	7.38974i	0.139978	+	0.242450i	0.927488	−	0.373852i	$-0.121963\pi$
$929$	4.26647	+	7.38974i	0.139978	+	0.242450i	−0.787510	+	0.616302i	$0.788630\pi$
$930$		0			0
$931$	−2.68888	−	2.68888i	−0.0881245	−	0.0881245i
$932$		0			0
$933$	19.5145			0.638876
$934$		0			0
$935$	−6.75330	−	32.9639i	−0.220856	−	1.07804i
$936$		0			0
$937$	−9.04356	+	2.42321i	−0.295440	+	0.0791630i	−0.403495	−	0.914982i	$-0.632205\pi$
$937$	−9.04356	+	2.42321i	−0.295440	+	0.0791630i	0.108054	+	0.994145i	$0.465538\pi$
$938$		0			0
$939$	5.06297	+	5.06297i	0.165224	+	0.165224i
$940$		0			0
$941$	2.98104	−	5.16331i	0.0971791	−	0.168319i	−0.813337	−	0.581793i	$-0.802351\pi$
$941$	2.98104	−	5.16331i	0.0971791	−	0.168319i	0.910516	+	0.413474i	$0.135685\pi$
$942$		0			0
$943$	−45.8729	+	26.4848i	−1.49383	+	0.862462i
$944$		0			0
$945$	25.2109	+	8.39732i	0.820110	+	0.273165i
$946$		0			0
$947$	−32.5395	−	18.7867i	−1.05739	−	0.610485i	−0.132682	−	0.991159i	$-0.542359\pi$
$947$	−32.5395	−	18.7867i	−1.05739	−	0.610485i	−0.924709	+	0.380674i	$0.875692\pi$
$948$		0			0
$949$	0.673355	−	2.51299i	0.0218580	−	0.0815753i
$950$		0			0
$951$	32.3779			1.04993
$952$		0			0
$953$	−23.0281	+	6.17036i	−0.745953	+	0.199877i	−0.611722	−	0.791073i	$-0.709523\pi$
$953$	−23.0281	+	6.17036i	−0.745953	+	0.199877i	−0.134231	+	0.990950i	$0.542856\pi$
$954$		0			0
$955$	23.5254	+	1.40676i	0.761265	+	0.0455215i
$956$		0			0
$957$	−33.6907	−	58.3540i	−1.08907	−	1.88632i
$958$		0			0
$959$	2.65168	−	1.53095i	0.0856273	−	0.0494369i
$960$		0			0
$961$		−	72.0880i		−	2.32542i
$962$		0			0
$963$	−4.77282	+	4.77282i	−0.153802	+	0.153802i
$964$		0			0
$965$	43.8200	−	38.8751i	1.41062	−	1.25143i
$966$		0			0
$967$	6.74953	−	3.89684i	0.217050	−	0.125314i	−0.387533	−	0.921856i	$-0.626673\pi$
$967$	6.74953	−	3.89684i	0.217050	−	0.125314i	0.604584	+	0.796542i	$0.293340\pi$
$968$		0			0
$969$	−5.24642	+	3.02902i	−0.168539	+	0.0973062i
$970$		0			0
$971$	6.98253	−	12.0941i	0.224080	−	0.388118i	−0.731963	−	0.681344i	$-0.761396\pi$
$971$	6.98253	−	12.0941i	0.224080	−	0.388118i	0.956043	+	0.293226i	$0.0947290\pi$
$972$		0			0
$973$	28.4293	+	28.4293i	0.911401	+	0.911401i
$974$		0			0
$975$	−4.40987	−	30.7702i	−0.141229	−	0.985434i
$976$		0			0
$977$	−14.4009	+	24.9431i	−0.460726	+	0.798000i	−0.998997	−	0.0447713i	$-0.985744\pi$
$977$	−14.4009	+	24.9431i	−0.460726	+	0.798000i	0.538272	+	0.842771i	$0.319077\pi$
$978$		0			0
$979$	−5.77205	−	21.5416i	−0.184475	−	0.688472i
$980$		0			0
$981$	2.28206	−	8.51675i	0.0728605	−	0.271919i
$982$		0			0
$983$	12.1884	−	3.26586i	0.388748	−	0.104165i	−0.0591504	−	0.998249i	$-0.518839\pi$
$983$	12.1884	−	3.26586i	0.388748	−	0.104165i	0.447899	+	0.894084i	$0.352173\pi$
$984$		0			0
$985$	−22.0814	+	33.4602i	−0.703573	+	1.06613i
$986$		0			0
$987$	−6.40360	−	23.8986i	−0.203829	−	0.760699i
$988$		0			0
$989$	−42.4985			−1.35137
$990$		0			0
$991$	−13.0769	+	13.0769i	−0.415403	+	0.415403i	−0.883616	−	0.468213i	$-0.844898\pi$
$991$	−13.0769	+	13.0769i	−0.415403	+	0.415403i	0.468213	+	0.883616i	$0.344898\pi$
$992$		0			0
$993$		−	8.41084i		−	0.266910i
$994$		0			0
$995$	54.3469	+	3.24979i	1.72291	+	0.103025i
$996$		0			0
$997$	−9.04229	−	5.22057i	−0.286372	−	0.165337i	0.349933	−	0.936775i	$-0.386205\pi$
$997$	−9.04229	−	5.22057i	−0.286372	−	0.165337i	−0.636305	+	0.771438i	$0.719538\pi$
$998$		0			0
$999$	22.4591	+	25.2222i	0.710575	+	0.797996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.bf.a.97.15	✓	76
5.3	odd	4		740.2.bi.a.393.15	yes	76
37.29	odd	12		740.2.bi.a.177.15	yes	76
185.103	even	12	inner	740.2.bf.a.473.15	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.bf.a.97.15	✓	76	1.1	even	1	trivial
740.2.bf.a.473.15	yes	76	185.103	even	12	inner
740.2.bi.a.177.15	yes	76	37.29	odd	12
740.2.bi.a.393.15	yes	76	5.3	odd	4

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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.405966 - 1.51509i) q^{3} +(-1.67270 + 1.48394i) q^{5} +(0.553968 - 2.06744i) q^{7} +(0.467396 + 0.269851i) q^{9} +6.12528i q^{11} +(1.98176 + 3.43251i) q^{13} +(1.56924 + 3.13671i) q^{15} +(2.12758 + 1.22836i) q^{17} +(-1.51854 - 0.406892i) q^{19} +(-2.90746 - 1.67862i) q^{21} +7.58124 q^{23} +(0.595841 - 4.96437i) q^{25} +(3.92596 - 3.92596i) q^{27} +(-4.95913 - 4.95913i) q^{29} +(7.17941 - 7.17941i) q^{31} +(9.28032 + 2.48666i) q^{33} +(2.14133 + 4.28026i) q^{35} +(-0.351904 + 6.07257i) q^{37} +(6.00508 - 1.60906i) q^{39} +(-6.05085 + 3.49346i) q^{41} -5.60574 q^{43} +(-1.18226 + 0.242208i) q^{45} +(5.21111 + 5.21111i) q^{47} +(2.09476 + 1.20941i) q^{49} +(2.72480 - 2.72480i) q^{51} +(0.278176 + 1.03817i) q^{53} +(-9.08954 - 10.2457i) q^{55} +(-1.23295 + 2.13554i) q^{57} +(1.14862 + 4.28673i) q^{59} +(1.49732 + 0.401206i) q^{61} +(0.816824 - 0.816824i) q^{63} +(-8.40853 - 2.80074i) q^{65} +(2.08749 + 0.559341i) q^{67} +(3.07773 - 11.4862i) q^{69} +(7.91056 + 13.7015i) q^{71} +(-0.464143 - 0.464143i) q^{73} +(-7.27956 - 2.91812i) q^{75} +(12.6636 + 3.39321i) q^{77} +(-2.38849 - 0.639993i) q^{79} +(-3.54481 - 6.13978i) q^{81} +(-2.65414 - 9.90537i) q^{83} +(-5.38162 + 1.10253i) q^{85} +(-9.52675 + 5.50027i) q^{87} +(-3.51683 + 0.942333i) q^{89} +(8.19433 - 2.19566i) q^{91} +(-7.96284 - 13.7920i) q^{93} +(3.14386 - 1.57282i) q^{95} -9.70531i q^{97} +(-1.65291 + 2.86293i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 2 q^{3} + 8 q^{13} + 2 q^{15} + 12 q^{19} - 4 q^{23} + 2 q^{25} + 28 q^{27} - 6 q^{29} + 16 q^{31} - 6 q^{33} + 20 q^{35} - 22 q^{37} + 8 q^{39} + 54 q^{41} - 16 q^{43} + 38 q^{45} + 8 q^{47} - 36 q^{49}+ \cdots - 70 q^{95}+O(q^{100}) \) 76 * q - 2 * q^3 + 8 * q^13 + 2 * q^15 + 12 * q^19 - 4 * q^23 + 2 * q^25 + 28 * q^27 - 6 * q^29 + 16 * q^31 - 6 * q^33 + 20 * q^35 - 22 * q^37 + 8 * q^39 + 54 * q^41 - 16 * q^43 + 38 * q^45 + 8 * q^47 - 36 * q^49 - 24 * q^53 + 18 * q^55 - 16 * q^59 - 28 * q^61 - 6 * q^65 - 34 * q^67 + 64 * q^69 - 8 * q^71 + 4 * q^73 + 24 * q^75 - 2 * q^77 - 40 * q^79 + 2 * q^81 - 62 * q^83 + 108 * q^87 - 2 * q^89 - 20 * q^91 - 30 * q^93 - 70 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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