LMFDB - Embedded newform 136.3.t.b.41.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			41.1
Character	$\chi$	$=$	136.41
Dual form			136.3.t.b.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.07751 + 4.60583i) q^{3} +(1.22413 + 6.15412i) q^{5} +(0.478359 - 2.40487i) q^{7} +(-8.29839 - 20.0341i) q^{9} +O(q^{10})$	\(q+(-3.07751 + 4.60583i) q^{3} +(1.22413 + 6.15412i) q^{5} +(0.478359 - 2.40487i) q^{7} +(-8.29839 - 20.0341i) q^{9} +(-12.9251 + 8.63629i) q^{11} +(13.3302 - 13.3302i) q^{13} +(-32.1121 - 13.3013i) q^{15} +(-13.2281 + 10.6779i) q^{17} +(-5.91966 + 14.2913i) q^{19} +(9.60427 + 9.60427i) q^{21} +(-4.55826 - 6.82191i) q^{23} +(-13.2777 + 5.49982i) q^{25} +(68.9154 + 13.7081i) q^{27} +(7.84919 - 1.56130i) q^{29} +(22.3133 + 14.9092i) q^{31} -86.1092i q^{33} +15.3855 q^{35} +(-32.9559 + 49.3220i) q^{37} +(20.3728 + 102.421i) q^{39} +(-7.55399 + 37.9765i) q^{41} +(-15.2990 - 36.9351i) q^{43} +(113.134 - 75.5936i) q^{45} +(-3.87805 + 3.87805i) q^{47} +(39.7155 + 16.4507i) q^{49} +(-8.47083 - 93.7877i) q^{51} +(-29.7894 + 71.9180i) q^{53} +(-68.9708 - 68.9708i) q^{55} +(-47.6055 - 71.2467i) q^{57} +(30.3685 - 12.5790i) q^{59} +(-3.81937 - 0.759720i) q^{61} +(-52.1490 + 10.3731i) q^{63} +(98.3539 + 65.7180i) q^{65} +72.0359i q^{67} +45.4487 q^{69} +(-36.3241 + 54.3629i) q^{71} +(-11.8151 - 59.3983i) q^{73} +(15.5312 - 78.0807i) q^{75} +(14.5863 + 35.2145i) q^{77} +(75.3098 - 50.3204i) q^{79} +(-137.225 + 137.225i) q^{81} +(13.8781 + 5.74849i) q^{83} +(-81.9060 - 68.3362i) q^{85} +(-16.9649 + 40.9569i) q^{87} +(78.9020 + 78.9020i) q^{89} +(-25.6809 - 38.4342i) q^{91} +(-137.339 + 56.8876i) q^{93} +(-95.1970 - 18.9359i) q^{95} +(-132.790 + 26.4136i) q^{97} +(280.278 + 187.276i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−3.07751	+	4.60583i	−1.02584	+	1.53528i	−0.193429	+	0.981114i	$0.561961\pi$
$3$	−3.07751	+	4.60583i	−1.02584	+	1.53528i	−0.832409	+	0.554161i	$0.813039\pi$
$4$		0			0
$5$	1.22413	+	6.15412i	0.244826	+	1.23082i	0.886093	+	0.463507i	$0.153409\pi$
$5$	1.22413	+	6.15412i	0.244826	+	1.23082i	−0.641267	+	0.767318i	$0.721591\pi$
$6$		0			0
$7$	0.478359	−	2.40487i	0.0683370	−	0.343553i	−0.931457	−	0.363852i	$-0.881462\pi$
$7$	0.478359	−	2.40487i	0.0683370	−	0.343553i	0.999794	+	0.0202982i	$0.00646155\pi$
$8$		0			0
$9$	−8.29839	−	20.0341i	−0.922043	−	2.22601i
$10$		0			0
$11$	−12.9251	+	8.63629i	−1.17501	+	0.785117i	−0.980642	−	0.195811i	$-0.937266\pi$
$11$	−12.9251	+	8.63629i	−1.17501	+	0.785117i	−0.194369	+	0.980928i	$0.562266\pi$
$12$		0			0
$13$	13.3302	−	13.3302i	1.02540	−	1.02540i	0.0257343	−	0.999669i	$-0.491808\pi$
$13$	13.3302	−	13.3302i	1.02540	−	1.02540i	0.999669	−	0.0257343i	$-0.00819238\pi$
$14$		0			0
$15$	−32.1121	−	13.3013i	−2.14081	−	0.886751i
$16$		0			0
$17$	−13.2281	+	10.6779i	−0.778124	+	0.628111i
$17$	−13.2281	+	10.6779i	−0.778124	+	0.628111i
$18$		0			0
$19$	−5.91966	+	14.2913i	−0.311561	+	0.752175i	0.688086	+	0.725629i	$0.258451\pi$
$19$	−5.91966	+	14.2913i	−0.311561	+	0.752175i	−0.999648	+	0.0265465i	$0.991549\pi$
$20$		0			0
$21$	9.60427	+	9.60427i	0.457346	+	0.457346i
$22$		0			0
$23$	−4.55826	−	6.82191i	−0.198185	−	0.296605i	0.719044	−	0.694964i	$-0.244580\pi$
$23$	−4.55826	−	6.82191i	−0.198185	−	0.296605i	−0.917230	+	0.398359i	$0.869580\pi$
$24$		0			0
$25$	−13.2777	+	5.49982i	−0.531109	+	0.219993i
$26$		0			0
$27$	68.9154	+	13.7081i	2.55242	+	0.507709i
$28$		0			0
$29$	7.84919	−	1.56130i	0.270662	−	0.0538380i	−0.0578934	−	0.998323i	$-0.518438\pi$
$29$	7.84919	−	1.56130i	0.270662	−	0.0538380i	0.328555	+	0.944485i	$0.393438\pi$
$30$		0			0
$31$	22.3133	+	14.9092i	0.719783	+	0.480944i	0.860722	−	0.509075i	$-0.170012\pi$
$31$	22.3133	+	14.9092i	0.719783	+	0.480944i	−0.140940	+	0.990018i	$0.545012\pi$
$32$		0			0
$33$		−	86.1092i		−	2.60937i
$34$		0			0
$35$	15.3855			0.439585
$36$		0			0
$37$	−32.9559	+	49.3220i	−0.890700	+	1.33303i	0.0517428	+	0.998660i	$0.483522\pi$
$37$	−32.9559	+	49.3220i	−0.890700	+	1.33303i	−0.942443	+	0.334367i	$0.891478\pi$
$38$		0			0
$39$	20.3728	+	102.421i	0.522378	+	2.62617i
$40$		0			0
$41$	−7.55399	+	37.9765i	−0.184244	+	0.926256i	0.772431	+	0.635098i	$0.219040\pi$
$41$	−7.55399	+	37.9765i	−0.184244	+	0.926256i	−0.956675	+	0.291158i	$0.905960\pi$
$42$		0			0
$43$	−15.2990	−	36.9351i	−0.355792	−	0.858957i	−0.995882	−	0.0906575i	$-0.971103\pi$
$43$	−15.2990	−	36.9351i	−0.355792	−	0.858957i	0.640091	−	0.768300i	$-0.278897\pi$
$44$		0			0
$45$	113.134	−	75.5936i	2.51409	−	1.67986i
$46$		0			0
$47$	−3.87805	+	3.87805i	−0.0825118	+	0.0825118i	−0.747158	−	0.664646i	$-0.768582\pi$
$47$	−3.87805	+	3.87805i	−0.0825118	+	0.0825118i	0.664646	+	0.747158i	$0.268582\pi$
$48$		0			0
$49$	39.7155	+	16.4507i	0.810521	+	0.335729i
$50$		0			0
$51$	−8.47083	−	93.7877i	−0.166095	−	1.83897i
$52$		0			0
$53$	−29.7894	+	71.9180i	−0.562065	+	1.35694i	0.346047	+	0.938217i	$0.387524\pi$
$53$	−29.7894	+	71.9180i	−0.562065	+	1.35694i	−0.908112	+	0.418727i	$0.862476\pi$
$54$		0			0
$55$	−68.9708	−	68.9708i	−1.25401	−	1.25401i
$56$		0			0
$57$	−47.6055	−	71.2467i	−0.835185	−	1.24994i
$58$		0			0
$59$	30.3685	−	12.5790i	0.514720	−	0.213204i	−0.110176	−	0.993912i	$-0.535141\pi$
$59$	30.3685	−	12.5790i	0.514720	−	0.213204i	0.624896	+	0.780708i	$0.285141\pi$
$60$		0			0
$61$	−3.81937	−	0.759720i	−0.0626126	−	0.0124544i	0.163685	−	0.986513i	$-0.447662\pi$
$61$	−3.81937	−	0.759720i	−0.0626126	−	0.0124544i	−0.226297	+	0.974058i	$0.572662\pi$
$62$		0			0
$63$	−52.1490	+	10.3731i	−0.827762	+	0.164652i
$64$		0			0
$65$	98.3539	+	65.7180i	1.51314	+	1.01105i
$66$		0			0
$67$			72.0359i			1.07516i	0.843212	+	0.537581i	$0.180662\pi$
$67$			72.0359i			1.07516i	−0.843212	+	0.537581i	$0.819338\pi$
$68$		0			0
$69$	45.4487			0.658676
$70$		0			0
$71$	−36.3241	+	54.3629i	−0.511608	+	0.765675i	−0.993894	−	0.110339i	$-0.964806\pi$
$71$	−36.3241	+	54.3629i	−0.511608	+	0.765675i	0.482286	+	0.876014i	$0.339806\pi$
$72$		0			0
$73$	−11.8151	−	59.3983i	−0.161850	−	0.813675i	−0.973350	−	0.229323i	$-0.926349\pi$
$73$	−11.8151	−	59.3983i	−0.161850	−	0.813675i	0.811500	−	0.584352i	$-0.198651\pi$
$74$		0			0
$75$	15.5312	−	78.0807i	0.207083	−	1.04108i
$76$		0			0
$77$	14.5863	+	35.2145i	0.189433	+	0.457331i
$78$		0			0
$79$	75.3098	−	50.3204i	0.953288	−	0.636967i	0.0214225	−	0.999771i	$-0.493180\pi$
$79$	75.3098	−	50.3204i	0.953288	−	0.636967i	0.931866	+	0.362804i	$0.118180\pi$
$80$		0			0
$81$	−137.225	+	137.225i	−1.69413	+	1.69413i
$82$		0			0
$83$	13.8781	+	5.74849i	0.167206	+	0.0692589i	0.464716	−	0.885460i	$-0.346156\pi$
$83$	13.8781	+	5.74849i	0.167206	+	0.0692589i	−0.297510	+	0.954719i	$0.596156\pi$
$84$		0			0
$85$	−81.9060	−	68.3362i	−0.963600	−	0.803955i
$86$		0			0
$87$	−16.9649	+	40.9569i	−0.194999	+	0.470769i
$88$		0			0
$89$	78.9020	+	78.9020i	0.886539	+	0.886539i	0.994189	−	0.107650i	$-0.0343326\pi$
$89$	78.9020	+	78.9020i	0.886539	+	0.886539i	−0.107650	+	0.994189i	$0.534333\pi$
$90$		0			0
$91$	−25.6809	−	38.4342i	−0.282208	−	0.422354i
$92$		0			0
$93$	−137.339	+	56.8876i	−1.47676	+	0.611695i
$94$		0			0
$95$	−95.1970	−	18.9359i	−1.00207	−	0.199325i
$96$		0			0
$97$	−132.790	+	26.4136i	−1.36897	+	0.272305i	−0.824209	−	0.566286i	$-0.808380\pi$
$97$	−132.790	+	26.4136i	−1.36897	+	0.272305i	−0.544761	+	0.838591i	$0.683380\pi$
$98$		0			0
$99$	280.278	+	187.276i	2.83109	+	1.89167i
$100$		0			0
$101$		−	60.0178i		−	0.594235i	−0.954841	−	0.297118i	$-0.903975\pi$
$101$		−	60.0178i		−	0.594235i	0.954841	−	0.297118i	$-0.0960254\pi$
$102$		0			0
$103$	−54.3537			−0.527706			−0.263853	−	0.964563i	$-0.584993\pi$
$103$	−54.3537			−0.527706			−0.263853	+	0.964563i	$0.584993\pi$
$104$		0			0
$105$	−47.3490	+	70.8628i	−0.450943	+	0.674883i
$106$		0			0
$107$	−25.6229	−	128.815i	−0.239466	−	1.20388i	−0.894077	−	0.447912i	$-0.852168\pi$
$107$	−25.6229	−	128.815i	−0.239466	−	1.20388i	0.654611	−	0.755966i	$-0.272832\pi$
$108$		0			0
$109$	−5.10438	+	25.6614i	−0.0468291	+	0.235426i	−0.997110	−	0.0759672i	$-0.975796\pi$
$109$	−5.10438	+	25.6614i	−0.0468291	+	0.235426i	0.950281	+	0.311393i	$0.100796\pi$
$110$		0			0
$111$	−125.746	−	303.578i	−1.13285	−	2.73494i
$112$		0			0
$113$	84.5779	−	56.5132i	0.748477	−	0.500117i	−0.121875	−	0.992545i	$-0.538891\pi$
$113$	84.5779	−	56.5132i	0.748477	−	0.500117i	0.870353	+	0.492429i	$0.163891\pi$
$114$		0			0
$115$	36.4030	−	36.4030i	0.316548	−	0.316548i
$116$		0			0
$117$	−377.679	−	156.440i	−3.22802	−	1.33709i
$118$		0			0
$119$	19.3512	+	36.9198i	0.162615	+	0.310250i
$120$		0			0
$121$	46.1685	−	111.461i	0.381558	−	0.921162i
$122$		0			0
$123$	−151.666	−	151.666i	−1.23305	−	1.23305i
$124$		0			0
$125$	37.0505	+	55.4500i	0.296404	+	0.443600i
$126$		0			0
$127$	147.283	−	61.0066i	1.15971	−	0.480367i	0.281930	−	0.959435i	$-0.409025\pi$
$127$	147.283	−	61.0066i	1.15971	−	0.480367i	0.877778	+	0.479068i	$0.159025\pi$
$128$		0			0
$129$	217.200	+	43.2037i	1.68372	+	0.334913i
$130$		0			0
$131$	198.943	−	39.5722i	1.51865	−	0.302078i	0.635843	−	0.771819i	$-0.280653\pi$
$131$	198.943	−	39.5722i	1.51865	−	0.302078i	0.882804	+	0.469741i	$0.155653\pi$
$132$		0			0
$133$	31.5371	+	21.0724i	0.237121	+	0.158439i
$134$		0			0
$135$			440.894i			3.26589i
$136$		0			0
$137$	99.1143			0.723462			0.361731	−	0.932283i	$-0.382186\pi$
$137$	99.1143			0.723462			0.361731	+	0.932283i	$0.382186\pi$
$138$		0			0
$139$	54.5251	−	81.6025i	0.392267	−	0.587068i	−0.581799	−	0.813332i	$-0.697651\pi$
$139$	54.5251	−	81.6025i	0.392267	−	0.587068i	0.974066	+	0.226264i	$0.0726512\pi$
$140$		0			0
$141$	−5.92687	−	29.7964i	−0.0420346	−	0.211322i
$142$		0			0
$143$	−57.1711	+	287.419i	−0.399798	+	2.00992i
$144$		0			0
$145$	19.2169	+	46.3936i	0.132530	+	0.319956i
$146$		0			0
$147$	−197.994	+	132.295i	−1.34690	+	0.899969i
$148$		0			0
$149$	−50.2945	+	50.2945i	−0.337547	+	0.337547i	−0.855443	−	0.517896i	$-0.826715\pi$
$149$	−50.2945	+	50.2945i	−0.337547	+	0.337547i	0.517896	+	0.855443i	$0.326715\pi$
$150$		0			0
$151$	147.257	+	60.9959i	0.975213	+	0.403947i	0.812650	−	0.582752i	$-0.198024\pi$
$151$	147.257	+	60.9959i	0.975213	+	0.403947i	0.162563	+	0.986698i	$0.448024\pi$
$152$		0			0
$153$	323.694	+	176.404i	2.11564	+	1.15296i
$154$		0			0
$155$	−64.4390	+	155.569i	−0.415735	+	1.00367i
$156$		0			0
$157$	68.9297	+	68.9297i	0.439043	+	0.439043i	0.891690	−	0.452647i	$-0.149520\pi$
$157$	68.9297	+	68.9297i	0.439043	+	0.439043i	−0.452647	+	0.891690i	$0.649520\pi$
$158$		0			0
$159$	−239.565	−	358.534i	−1.50670	−	2.25493i
$160$		0			0
$161$	−18.5863	+	7.69871i	−0.115443	+	0.0478181i
$162$		0			0
$163$	16.1335	+	3.20915i	0.0989784	+	0.0196880i	0.244331	−	0.969692i	$-0.421432\pi$
$163$	16.1335	+	3.20915i	0.0989784	+	0.0196880i	−0.145353	+	0.989380i	$0.546432\pi$
$164$		0			0
$165$	529.926	−	105.409i	3.21167	−	0.638842i
$166$		0			0
$167$	−184.179	−	123.065i	−1.10287	−	0.736915i	−0.135626	−	0.990760i	$-0.543305\pi$
$167$	−184.179	−	123.065i	−1.10287	−	0.736915i	−0.967245	+	0.253845i	$0.918305\pi$
$168$		0			0
$169$		−	186.391i		−	1.10290i
$170$		0			0
$171$	335.437			1.96162
$172$		0			0
$173$	121.925	−	182.473i	0.704767	−	1.05476i	−0.290433	−	0.956895i	$-0.593799\pi$
$173$	121.925	−	182.473i	0.704767	−	1.05476i	0.995200	−	0.0978630i	$-0.0312007\pi$
$174$		0			0
$175$	6.87484	+	34.5622i	0.0392848	+	0.197498i
$176$		0			0
$177$	−35.5226	+	178.584i	−0.200692	+	1.00895i
$178$		0			0
$179$	116.962	+	282.371i	0.653417	+	1.57749i	0.807786	+	0.589476i	$0.200666\pi$
$179$	116.962	+	282.371i	0.653417	+	1.57749i	−0.154369	+	0.988013i	$0.549334\pi$
$180$		0			0
$181$	−10.2661	+	6.85962i	−0.0567190	+	0.0378984i	−0.583606	−	0.812037i	$-0.698359\pi$
$181$	−10.2661	+	6.85962i	−0.0567190	+	0.0378984i	0.526887	+	0.849935i	$0.323359\pi$
$182$		0			0
$183$	15.2533	−	15.2533i	0.0833514	−	0.0833514i
$184$		0			0
$185$	−343.876	−	142.438i	−1.85879	−	0.769936i
$186$		0			0
$187$	78.7574	−	252.255i	0.421163	−	1.34896i
$188$		0			0
$189$	65.9326	−	159.175i	0.348850	−	0.842198i
$190$		0			0
$191$	69.2166	+	69.2166i	0.362391	+	0.362391i	0.864692	−	0.502302i	$-0.167513\pi$
$191$	69.2166	+	69.2166i	0.362391	+	0.362391i	−0.502302	+	0.864692i	$0.667513\pi$
$192$		0			0
$193$	−81.7961	−	122.416i	−0.423814	−	0.634282i	0.556704	−	0.830711i	$-0.312066\pi$
$193$	−81.7961	−	122.416i	−0.423814	−	0.634282i	−0.980518	+	0.196428i	$0.937066\pi$
$194$		0			0
$195$	−605.371	+	250.753i	−3.10447	+	1.28591i
$196$		0			0
$197$	174.139	+	34.6385i	0.883956	+	0.175830i	0.616137	−	0.787639i	$-0.288697\pi$
$197$	174.139	+	34.6385i	0.883956	+	0.175830i	0.267819	+	0.963469i	$0.413697\pi$
$198$		0			0
$199$	130.328	−	25.9238i	0.654914	−	0.130271i	0.143562	−	0.989641i	$-0.454145\pi$
$199$	130.328	−	25.9238i	0.654914	−	0.130271i	0.511353	+	0.859371i	$0.329145\pi$
$200$		0			0
$201$	−331.785	−	221.692i	−1.65067	−	1.10294i
$202$		0			0
$203$		−	19.6232i		−	0.0966659i
$204$		0			0
$205$	−242.959			−1.18517
$206$		0			0
$207$	−98.8446	+	147.931i	−0.477510	+	0.714644i
$208$		0			0
$209$	−46.9117	−	235.841i	−0.224458	−	1.12843i
$210$		0			0
$211$	−30.0296	+	150.969i	−0.142320	+	0.715492i	0.842053	+	0.539395i	$0.181347\pi$
$211$	−30.0296	+	150.969i	−0.142320	+	0.715492i	−0.984373	+	0.176097i	$0.943653\pi$
$212$		0			0
$213$	−138.598	−	334.605i	−0.650695	−	1.57092i
$214$		0			0
$215$	208.575	−	139.366i	0.970118	−	0.648212i
$216$		0			0
$217$	46.5286	−	46.5286i	0.214418	−	0.214418i
$218$		0			0
$219$	309.939	+	128.381i	1.41525	+	0.586215i
$220$		0			0
$221$	−33.9949	+	318.673i	−0.153823	+	1.44196i
$222$		0			0
$223$	70.6954	−	170.674i	0.317020	−	0.765353i	−0.682390	−	0.730988i	$-0.739059\pi$
$223$	70.6954	−	170.674i	0.317020	−	0.765353i	0.999409	−	0.0343644i	$-0.0109407\pi$
$224$		0			0
$225$	220.368	+	220.368i	0.979412	+	0.979412i
$226$		0			0
$227$	−57.1437	−	85.5217i	−0.251735	−	0.376747i	0.683983	−	0.729498i	$-0.260246\pi$
$227$	−57.1437	−	85.5217i	−0.251735	−	0.376747i	−0.935717	+	0.352751i	$0.885246\pi$
$228$		0			0
$229$	−224.457	+	92.9733i	−0.980164	+	0.405997i	−0.814486	−	0.580183i	$-0.802981\pi$
$229$	−224.457	+	92.9733i	−0.980164	+	0.405997i	−0.165677	+	0.986180i	$0.552981\pi$
$230$		0			0
$231$	−207.082	−	41.1911i	−0.896457	−	0.178316i
$232$		0			0
$233$	68.7073	−	13.6667i	0.294881	−	0.0586555i	−0.0454328	−	0.998967i	$-0.514467\pi$
$233$	68.7073	−	13.6667i	0.294881	−	0.0586555i	0.340314	+	0.940312i	$0.389467\pi$
$234$		0			0
$235$	−28.6133	−	19.1188i	−0.121759	−	0.0813564i
$236$		0			0
$237$			501.725i			2.11698i
$238$		0			0
$239$	−377.396			−1.57906			−0.789532	−	0.613710i	$-0.789676\pi$
$239$	−377.396			−1.57906			−0.789532	+	0.613710i	$0.789676\pi$
$240$		0			0
$241$	−183.989	+	275.358i	−0.763438	+	1.14257i	0.222415	+	0.974952i	$0.428606\pi$
$241$	−183.989	+	275.358i	−0.763438	+	1.14257i	−0.985853	+	0.167613i	$0.946394\pi$
$242$		0			0
$243$	−86.3489	−	434.105i	−0.355345	−	1.78644i
$244$		0			0
$245$	−52.6226	+	264.552i	−0.214786	+	1.07980i
$246$		0			0
$247$	111.596	+	269.417i	0.451807	+	1.09076i
$248$		0			0
$249$	−69.1865	+	46.2290i	−0.277858	+	0.185659i
$250$		0			0
$251$	−100.014	+	100.014i	−0.398461	+	0.398461i	−0.877690	−	0.479229i	$-0.840916\pi$
$251$	−100.014	+	100.014i	−0.398461	+	0.398461i	0.479229	+	0.877690i	$0.340916\pi$
$252$		0			0
$253$	117.832	+	48.8076i	0.465739	+	0.192915i
$254$		0			0
$255$	566.812	−	166.939i	2.22279	−	0.654663i
$256$		0			0
$257$	177.611	−	428.791i	0.691093	−	1.66845i	−0.0514731	−	0.998674i	$-0.516392\pi$
$257$	177.611	−	428.791i	0.691093	−	1.66845i	0.742566	−	0.669772i	$-0.233608\pi$
$258$		0			0
$259$	102.848	+	102.848i	0.397098	+	0.397098i
$260$		0			0
$261$	−96.4148	−	144.295i	−0.369406	−	0.552854i
$262$		0			0
$263$	−105.346	+	43.6357i	−0.400555	+	0.165915i	−0.573861	−	0.818953i	$-0.694555\pi$
$263$	−105.346	+	43.6357i	−0.400555	+	0.165915i	0.173306	+	0.984868i	$0.444555\pi$
$264$		0			0
$265$	−479.059	−	95.2907i	−1.80777	−	0.359587i
$266$		0			0
$267$	−606.231	+	120.587i	−2.27053	+	0.451636i
$268$		0			0
$269$	175.857	+	117.504i	0.653745	+	0.436818i	0.837711	−	0.546114i	$-0.183894\pi$
$269$	175.857	+	117.504i	0.653745	+	0.436818i	−0.183966	+	0.982933i	$0.558894\pi$
$270$		0			0
$271$			517.492i			1.90956i	0.297307	+	0.954782i	$0.403911\pi$
$271$			517.492i			1.90956i	−0.297307	+	0.954782i	$0.596089\pi$
$272$		0			0
$273$	256.055			0.937929
$274$		0			0
$275$	124.118	−	185.756i	0.451339	−	0.675477i
$276$		0			0
$277$	14.7887	+	74.3478i	0.0533888	+	0.268404i	0.998255	−	0.0590535i	$-0.0188083\pi$
$277$	14.7887	+	74.3478i	0.0533888	+	0.268404i	−0.944866	+	0.327457i	$0.893808\pi$
$278$		0			0
$279$	113.529	−	570.749i	0.406914	−	2.04569i
$280$		0			0
$281$	−23.6551	−	57.1084i	−0.0841818	−	0.203233i	0.876183	−	0.481978i	$-0.160081\pi$
$281$	−23.6551	−	57.1084i	−0.0841818	−	0.203233i	−0.960365	+	0.278745i	$0.910081\pi$
$282$		0			0
$283$	−336.839	+	225.069i	−1.19024	+	0.795295i	−0.983110	−	0.183017i	$-0.941413\pi$
$283$	−336.839	+	225.069i	−1.19024	+	0.795295i	−0.207134	+	0.978313i	$0.566413\pi$
$284$		0			0
$285$	380.186	−	380.186i	1.33398	−	1.33398i
$286$		0			0
$287$	87.7151	+	36.3328i	0.305628	+	0.126595i
$288$		0			0
$289$	60.9653	−	282.496i	0.210953	−	0.977496i
$290$		0			0
$291$	287.007	−	692.896i	0.986278	−	2.38109i
$292$		0			0
$293$	47.3988	+	47.3988i	0.161771	+	0.161771i	0.783351	−	0.621580i	$-0.213509\pi$
$293$	47.3988	+	47.3988i	0.161771	+	0.161771i	−0.621580	+	0.783351i	$0.713509\pi$
$294$		0			0
$295$	114.588	+	171.493i	0.388433	+	0.581332i
$296$		0			0
$297$	−1009.13	+	417.994i	−3.39774	+	1.40739i
$298$		0			0
$299$	−151.700	−	30.1751i	−0.507359	−	0.100920i
$300$		0			0
$301$	−96.1428	+	19.1240i	−0.319411	+	0.0635349i
$302$		0			0
$303$	276.431	+	184.706i	0.912315	+	0.609589i
$304$		0			0
$305$		−	24.4349i		−	0.0801143i
$306$		0			0
$307$	−6.15066			−0.0200347			−0.0100174	−	0.999950i	$-0.503189\pi$
$307$	−6.15066			−0.0200347			−0.0100174	+	0.999950i	$0.503189\pi$
$308$		0			0
$309$	167.274	−	250.344i	0.541341	−	0.810174i
$310$		0			0
$311$	23.4206	+	117.743i	0.0753074	+	0.378596i	0.999998	−	0.00212412i	$-0.000676128\pi$
$311$	23.4206	+	117.743i	0.0753074	+	0.378596i	−0.924690	+	0.380720i	$0.875676\pi$
$312$		0			0
$313$	10.7523	−	54.0556i	0.0343525	−	0.172702i	−0.959800	−	0.280684i	$-0.909439\pi$
$313$	10.7523	−	54.0556i	0.0343525	−	0.172702i	0.994153	+	0.107982i	$0.0344389\pi$
$314$		0			0
$315$	−127.675	−	308.234i	−0.405316	−	0.978519i
$316$		0			0
$317$	−256.442	+	171.349i	−0.808966	+	0.540534i	−0.889884	−	0.456187i	$-0.849215\pi$
$317$	−256.442	+	171.349i	−0.808966	+	0.540534i	0.0809180	+	0.996721i	$0.474215\pi$
$318$		0			0
$319$	−87.9679	+	87.9679i	−0.275761	+	0.275761i
$320$		0			0
$321$	672.154	+	278.415i	2.09394	+	0.867338i
$322$		0			0
$323$	−74.2954	−	252.257i	−0.230017	−	0.780980i
$324$		0			0
$325$	−103.682	+	250.309i	−0.319020	+	0.770182i
$326$		0			0
$327$	−102.483	−	102.483i	−0.313405	−	0.313405i
$328$		0			0
$329$	7.47112	+	11.1813i	0.0227086	+	0.0339858i
$330$		0			0
$331$	175.896	−	72.8584i	0.531407	−	0.220116i	−0.100812	−	0.994905i	$-0.532144\pi$
$331$	175.896	−	72.8584i	0.531407	−	0.220116i	0.632220	+	0.774789i	$0.282144\pi$
$332$		0			0
$333$	1261.60	+	250.948i	3.78859	+	0.753598i
$334$		0			0
$335$	−443.318	+	88.1814i	−1.32334	+	0.263228i
$336$		0			0
$337$	−12.1542	−	8.12117i	−0.0360658	−	0.0240984i	0.537407	−	0.843323i	$-0.319404\pi$
$337$	−12.1542	−	8.12117i	−0.0360658	−	0.0240984i	−0.573472	+	0.819225i	$0.694404\pi$
$338$		0			0
$339$			563.471i			1.66216i
$340$		0			0
$341$	−417.162			−1.22335
$342$		0			0
$343$	125.310	−	187.540i	0.365337	−	0.546765i
$344$		0			0
$345$	55.6351	+	279.697i	0.161261	+	0.810715i
$346$		0			0
$347$	26.8277	−	134.872i	0.0773131	−	0.388679i	−0.922682	−	0.385562i	$-0.874008\pi$
$347$	26.8277	−	134.872i	0.0773131	−	0.388679i	0.999995	−	0.00311754i	$-0.000992347\pi$
$348$		0			0
$349$	−81.5428	−	196.862i	−0.233647	−	0.564074i	0.762954	−	0.646453i	$-0.223748\pi$
$349$	−81.5428	−	196.862i	−0.233647	−	0.564074i	−0.996601	+	0.0823790i	$0.973748\pi$
$350$		0			0
$351$	1101.39	−	735.926i	3.13787	−	2.09666i
$352$		0			0
$353$	39.1786	−	39.1786i	0.110987	−	0.110987i	−0.649432	−	0.760420i	$-0.724993\pi$
$353$	39.1786	−	39.1786i	0.110987	−	0.110987i	0.760420	+	0.649432i	$0.224993\pi$
$354$		0			0
$355$	−379.022	−	156.996i	−1.06767	−	0.442242i
$356$		0			0
$357$	−229.600	−	24.4929i	−0.643136	−	0.0686076i
$358$		0			0
$359$	215.678	−	520.693i	0.600775	−	1.45040i	−0.272010	−	0.962295i	$-0.587688\pi$
$359$	215.678	−	520.693i	0.600775	−	1.45040i	0.872785	−	0.488105i	$-0.162312\pi$
$360$		0			0
$361$	86.0658	+	86.0658i	0.238410	+	0.238410i
$362$		0			0
$363$	371.284	+	555.666i	1.02282	+	1.53076i
$364$		0			0
$365$	351.081	−	145.423i	0.961867	−	0.398418i
$366$		0			0
$367$	477.111	+	94.9034i	1.30003	+	0.258592i	0.796107	−	0.605156i	$-0.206889\pi$
$367$	477.111	+	94.9034i	1.30003	+	0.258592i	0.503924	+	0.863748i	$0.331889\pi$
$368$		0			0
$369$	823.510	−	163.806i	2.23173	−	0.443920i
$370$		0			0
$371$	158.704	+	106.042i	0.427773	+	0.285829i
$372$		0			0
$373$			140.669i			0.377128i	0.982061	+	0.188564i	$0.0603833\pi$
$373$			140.669i			0.377128i	−0.982061	+	0.188564i	$0.939617\pi$
$374$		0			0
$375$	−369.417			−0.985111
$376$		0			0
$377$	83.8191	−	125.444i	0.222332	−	0.332743i
$378$		0			0
$379$	38.4604	+	193.353i	0.101479	+	0.510167i	0.997773	+	0.0667069i	$0.0212492\pi$
$379$	38.4604	+	193.353i	0.101479	+	0.510167i	−0.896294	+	0.443460i	$0.853751\pi$
$380$		0			0
$381$	−172.280	+	866.108i	−0.452178	+	2.27325i
$382$		0			0
$383$	14.3601	+	34.6683i	0.0374937	+	0.0905177i	0.941517	−	0.336965i	$-0.109400\pi$
$383$	14.3601	+	34.6683i	0.0374937	+	0.0905177i	−0.904023	+	0.427483i	$0.859400\pi$
$384$		0			0
$385$	−198.859	+	132.873i	−0.516517	+	0.345125i
$386$		0			0
$387$	−613.004	+	613.004i	−1.58399	+	1.58399i
$388$		0			0
$389$	−494.589	−	204.866i	−1.27144	−	0.526647i	−0.358037	−	0.933708i	$-0.616554\pi$
$389$	−494.589	−	204.866i	−1.27144	−	0.526647i	−0.913401	+	0.407061i	$0.866554\pi$
$390$		0			0
$391$	133.141	+	41.5684i	0.340513	+	0.106313i
$392$		0			0
$393$	−429.987	+	1038.08i	−1.09411	+	2.64142i
$394$		0			0
$395$	401.867	+	401.867i	1.01738	+	1.01738i
$396$		0			0
$397$	−211.412	−	316.401i	−0.532525	−	0.796980i	0.463496	−	0.886099i	$-0.346595\pi$
$397$	−211.412	−	316.401i	−0.532525	−	0.796980i	−0.996021	+	0.0891193i	$0.971595\pi$
$398$		0			0
$399$	−194.112	+	80.4038i	−0.486496	+	0.201513i
$400$		0			0
$401$	−512.019	−	101.847i	−1.27686	−	0.253983i	−0.490329	−	0.871538i	$-0.663123\pi$
$401$	−512.019	−	101.847i	−1.27686	−	0.253983i	−0.786528	+	0.617555i	$0.788123\pi$
$402$		0			0
$403$	496.185	−	98.6973i	1.23123	−	0.244907i
$404$		0			0
$405$	−1012.48	−	676.517i	−2.49995	−	1.67041i
$406$		0			0
$407$		−	922.109i		−	2.26563i
$408$		0			0
$409$	596.576			1.45862			0.729310	−	0.684183i	$-0.239841\pi$
$409$	596.576			1.45862			0.729310	+	0.684183i	$0.239841\pi$
$410$		0			0
$411$	−305.026	+	456.503i	−0.742155	+	1.11071i
$412$		0			0
$413$	−15.7239	−	79.0496i	−0.0380725	−	0.191403i
$414$		0			0
$415$	−18.3883	+	92.4443i	−0.0443092	+	0.222757i
$416$		0			0
$417$	208.045	+	502.266i	0.498910	+	1.20447i
$418$		0			0
$419$	179.020	−	119.617i	0.427254	−	0.285482i	−0.323293	−	0.946299i	$-0.604790\pi$
$419$	179.020	−	119.617i	0.427254	−	0.285482i	0.750547	+	0.660817i	$0.229790\pi$
$420$		0			0
$421$	353.691	−	353.691i	0.840122	−	0.840122i	−0.148753	−	0.988874i	$-0.547526\pi$
$421$	353.691	−	353.691i	0.840122	−	0.840122i	0.988874	+	0.148753i	$0.0475259\pi$
$422$		0			0
$423$	109.875	+	45.5116i	0.259751	+	0.107593i
$424$		0			0
$425$	116.913	−	214.530i	0.275089	−	0.504777i
$426$		0			0
$427$	−3.65406	+	8.82168i	−0.00855752	+	0.0206597i
$428$		0			0
$429$	−1147.86	−	1147.86i	−2.67565	−	2.67565i
$430$		0			0
$431$	−116.770	−	174.759i	−0.270929	−	0.405473i	0.670910	−	0.741539i	$-0.265904\pi$
$431$	−116.770	−	174.759i	−0.270929	−	0.405473i	−0.941839	+	0.336065i	$0.890904\pi$
$432$		0			0
$433$	675.636	−	279.857i	1.56036	−	0.646322i	0.575208	−	0.818007i	$-0.304921\pi$
$433$	675.636	−	279.857i	1.56036	−	0.646322i	0.985152	+	0.171685i	$0.0549212\pi$
$434$		0			0
$435$	−272.821	−	54.2675i	−0.627175	−	0.124753i
$436$		0			0
$437$	124.478	−	24.7601i	0.284846	−	0.0566593i
$438$		0			0
$439$	114.753	+	76.6758i	0.261397	+	0.174660i	0.679362	−	0.733803i	$-0.262256\pi$
$439$	114.753	+	76.6758i	0.261397	+	0.174660i	−0.417965	+	0.908463i	$0.637256\pi$
$440$		0			0
$441$		−	932.178i		−	2.11378i
$442$		0			0
$443$	−298.086			−0.672881			−0.336441	−	0.941705i	$-0.609223\pi$
$443$	−298.086			−0.672881			−0.336441	+	0.941705i	$0.609223\pi$
$444$		0			0
$445$	−388.986	+	582.159i	−0.874126	+	1.30822i
$446$		0			0
$447$	−76.8656	−	386.430i	−0.171959	−	0.864496i
$448$		0			0
$449$	13.6109	−	68.4264i	0.0303137	−	0.152397i	−0.962664	−	0.270699i	$-0.912745\pi$
$449$	13.6109	−	68.4264i	0.0303137	−	0.152397i	0.992978	+	0.118302i	$0.0377451\pi$
$450$		0			0
$451$	−230.340	−	556.089i	−0.510731	−	1.23301i
$452$		0			0
$453$	−734.123	+	490.525i	−1.62058	+	1.08284i
$454$		0			0
$455$	205.092	−	205.092i	0.450751	−	0.450751i
$456$		0			0
$457$	−261.616	−	108.365i	−0.572463	−	0.237122i	0.0776226	−	0.996983i	$-0.475267\pi$
$457$	−261.616	−	108.365i	−0.572463	−	0.237122i	−0.650086	+	0.759861i	$0.725267\pi$
$458$		0			0
$459$	−1057.99	+	554.539i	−2.30500	+	1.20815i
$460$		0			0
$461$	−33.4162	+	80.6738i	−0.0724863	+	0.174997i	−0.955970	−	0.293465i	$-0.905192\pi$
$461$	−33.4162	+	80.6738i	−0.0724863	+	0.174997i	0.883484	+	0.468462i	$0.155192\pi$
$462$		0			0
$463$	262.432	+	262.432i	0.566808	+	0.566808i	0.931233	−	0.364425i	$-0.118734\pi$
$463$	262.432	+	262.432i	0.566808	+	0.566808i	−0.364425	+	0.931233i	$0.618734\pi$
$464$		0			0
$465$	−518.214	−	775.562i	−1.11444	−	1.66788i
$466$		0			0
$467$	−470.768	+	194.999i	−1.00807	+	0.417556i	−0.824750	−	0.565498i	$-0.808684\pi$
$467$	−470.768	+	194.999i	−1.00807	+	0.417556i	−0.183319	+	0.983053i	$0.558684\pi$
$468$		0			0
$469$	173.237	+	34.4590i	0.369376	+	0.0734734i
$470$		0			0
$471$	−529.610	+	105.346i	−1.12444	+	0.223665i
$472$		0			0
$473$	516.724	+	345.264i	1.09244	+	0.729946i
$474$		0			0
$475$		−	222.314i		−	0.468029i
$476$		0			0
$477$	1688.02			3.53882
$478$		0			0
$479$	156.924	−	234.853i	0.327607	−	0.490298i	−0.630705	−	0.776023i	$-0.717234\pi$
$479$	156.924	−	234.853i	0.327607	−	0.490298i	0.958312	+	0.285725i	$0.0922342\pi$
$480$		0			0
$481$	218.164	+	1096.78i	0.453563	+	2.28022i
$482$		0			0
$483$	21.7408	−	109.298i	0.0450120	−	0.226290i
$484$		0			0
$485$	−325.105	−	784.873i	−0.670319	−	1.61829i
$486$		0			0
$487$	−676.592	+	452.084i	−1.38931	+	0.928304i	−0.389332	+	0.921098i	$0.627294\pi$
$487$	−676.592	+	452.084i	−1.38931	+	0.928304i	−0.999974	+	0.00720678i	$0.997706\pi$
$488$		0			0
$489$	−64.4318	+	64.4318i	−0.131762	+	0.131762i
$490$		0			0
$491$	−250.853	−	103.907i	−0.510903	−	0.211623i	0.112313	−	0.993673i	$-0.464174\pi$
$491$	−250.853	−	103.907i	−0.510903	−	0.211623i	−0.623216	+	0.782050i	$0.714174\pi$
$492$		0			0
$493$	−87.1585	+	104.466i	−0.176792	+	0.211898i
$494$		0			0
$495$	−809.420	+	1954.11i	−1.63519	+	3.94770i
$496$		0			0
$497$	113.360	+	113.360i	0.228088	+	0.228088i
$498$		0			0
$499$	−62.1635	−	93.0342i	−0.124576	−	0.186441i	0.763939	−	0.645288i	$-0.223263\pi$
$499$	−62.1635	−	93.0342i	−0.124576	−	0.186441i	−0.888515	+	0.458847i	$0.848263\pi$
$500$		0			0
$501$	1133.63	−	469.565i	2.26273	−	0.937255i
$502$		0			0
$503$	398.056	+	79.1783i	0.791365	+	0.157412i	0.574192	−	0.818721i	$-0.305316\pi$
$503$	398.056	+	79.1783i	0.791365	+	0.157412i	0.217173	+	0.976133i	$0.430316\pi$
$504$		0			0
$505$	369.357	−	73.4696i	0.731400	−	0.145484i
$506$		0			0
$507$	858.483	+	573.620i	1.69326	+	1.13140i
$508$		0			0
$509$		−	512.236i		−	1.00636i	−0.864182	−	0.503179i	$-0.832164\pi$
$509$		−	512.236i		−	1.00636i	0.864182	−	0.503179i	$-0.167836\pi$
$510$		0			0
$511$	−148.497			−0.290601
$512$		0			0
$513$	−603.863	+	903.746i	−1.17712	+	1.76169i
$514$		0			0
$515$	−66.5361	−	334.500i	−0.129196	−	0.649514i
$516$		0			0
$517$	16.6323	−	83.6163i	0.0321708	−	0.161734i
$518$		0			0
$519$	465.215	+	1123.13i	0.896368	+	2.16402i
$520$		0			0
$521$	566.692	−	378.651i	1.08770	−	0.726778i	0.123604	−	0.992332i	$-0.460555\pi$
$521$	566.692	−	378.651i	1.08770	−	0.726778i	0.964096	+	0.265554i	$0.0855547\pi$
$522$		0			0
$523$	17.8649	−	17.8649i	0.0341585	−	0.0341585i	−0.689821	−	0.723980i	$-0.742311\pi$
$523$	17.8649	−	17.8649i	0.0341585	−	0.0341585i	0.723980	+	0.689821i	$0.242311\pi$
$524$		0			0
$525$	−180.345	−	74.7012i	−0.343514	−	0.142288i
$526$		0			0
$527$	−454.361	+	41.0376i	−0.862166	+	0.0778701i
$528$		0			0
$529$	176.679	−	426.540i	0.333986	−	0.806314i
$530$		0			0
$531$	−504.018	−	504.018i	−0.949187	−	0.949187i
$532$		0			0
$533$	405.539	+	606.932i	0.760861	+	1.13871i
$534$		0			0
$535$	761.377	−	315.373i	1.42313	−	0.589482i
$536$		0			0
$537$	−1660.50	−	330.294i	−3.09218	−	0.615073i
$538$		0			0
$539$	−655.401	+	130.367i	−1.21596	+	0.241869i
$540$		0			0
$541$	627.644	+	419.378i	1.16015	+	0.775191i	0.978108	−	0.208099i	$-0.0667277\pi$
$541$	627.644	+	419.378i	1.16015	+	0.775191i	0.182047	+	0.983290i	$0.441728\pi$
$542$		0			0
$543$		−	68.3946i		−	0.125957i
$544$		0			0
$545$	−164.172			−0.301233
$546$		0			0
$547$	186.953	−	279.794i	0.341778	−	0.511507i	−0.620269	−	0.784389i	$-0.712977\pi$
$547$	186.953	−	279.794i	0.341778	−	0.511507i	0.962048	+	0.272882i	$0.0879767\pi$
$548$		0			0
$549$	16.4743	+	82.8220i	0.0300079	+	0.150860i
$550$		0			0
$551$	−24.1515	+	121.418i	−0.0438321	+	0.220359i
$552$		0			0
$553$	−84.9890	−	205.182i	−0.153687	−	0.371034i
$554$		0			0
$555$	1714.33	−	1145.48i	3.08888	−	2.06392i
$556$		0			0
$557$	−152.552	+	152.552i	−0.273881	+	0.273881i	−0.830660	−	0.556780i	$-0.812037\pi$
$557$	−152.552	+	152.552i	−0.273881	+	0.273881i	0.556780	+	0.830660i	$0.312037\pi$
$558$		0			0
$559$	−696.294	−	288.415i	−1.24561	−	0.515947i
$560$		0			0
$561$	919.464	+	1139.06i	1.63897	+	2.03041i
$562$		0			0
$563$	164.288	−	396.626i	0.291808	−	0.704486i	−0.708191	−	0.706021i	$-0.750488\pi$
$563$	164.288	−	396.626i	0.291808	−	0.704486i	0.999999	+	0.00153466i	$0.000488498\pi$
$564$		0			0
$565$	451.323	+	451.323i	0.798803	+	0.798803i
$566$		0			0
$567$	264.365	+	395.651i	0.466253	+	0.697797i
$568$		0			0
$569$	167.920	−	69.5547i	0.295114	−	0.122240i	−0.230214	−	0.973140i	$-0.573943\pi$
$569$	167.920	−	69.5547i	0.295114	−	0.122240i	0.525328	+	0.850900i	$0.323943\pi$
$570$		0			0
$571$	−1060.77	−	211.000i	−1.85774	−	0.369528i	−0.866240	−	0.499628i	$-0.833470\pi$
$571$	−1060.77	−	211.000i	−1.85774	−	0.369528i	−0.991501	+	0.130100i	$0.958470\pi$
$572$		0			0
$573$	−531.815	+	105.785i	−0.928124	+	0.184615i
$574$		0			0
$575$	98.0426	+	65.5100i	0.170509	+	0.113930i
$576$		0			0
$577$		−	959.226i		−	1.66244i	−0.555946	−	0.831218i	$-0.687644\pi$
$577$		−	959.226i		−	1.66244i	0.555946	−	0.831218i	$-0.312356\pi$
$578$		0			0
$579$	815.558			1.40856
$580$		0			0
$581$	20.4631	−	30.6252i	0.0352205	−	0.0527112i
$582$		0			0
$583$	−236.073	−	1186.82i	−0.404928	−	2.03571i
$584$		0			0
$585$	500.420	−	2515.78i	0.855419	−	4.30048i
$586$		0			0
$587$	189.950	+	458.580i	0.323594	+	0.781226i	0.999040	+	0.0438160i	$0.0139515\pi$
$587$	189.950	+	458.580i	0.323594	+	0.781226i	−0.675445	+	0.737410i	$0.736048\pi$
$588$		0			0
$589$	−345.160	+	230.629i	−0.586010	+	0.391560i
$590$		0			0
$591$	−695.455	+	695.455i	−1.17674	+	1.17674i
$592$		0			0
$593$	−444.124	−	183.962i	−0.748944	−	0.310223i	−0.0246333	−	0.999697i	$-0.507842\pi$
$593$	−444.124	−	183.962i	−0.748944	−	0.310223i	−0.724311	+	0.689474i	$0.757842\pi$
$594$		0			0
$595$	−203.520	+	164.284i	−0.342051	+	0.276108i
$596$		0			0
$597$	−281.686	+	680.049i	−0.471835	+	1.13911i
$598$		0			0
$599$	53.9662	+	53.9662i	0.0900939	+	0.0900939i	0.750717	−	0.660624i	$-0.229708\pi$
$599$	53.9662	+	53.9662i	0.0900939	+	0.0900939i	−0.660624	+	0.750717i	$0.729708\pi$
$600$		0			0
$601$	50.7792	+	75.9964i	0.0844911	+	0.126450i	0.871308	−	0.490737i	$-0.163272\pi$
$601$	50.7792	+	75.9964i	0.0844911	+	0.126450i	−0.786817	+	0.617187i	$0.788272\pi$
$602$		0			0
$603$	1443.17	−	597.782i	2.39332	−	0.991346i
$604$		0			0
$605$	742.459	+	147.684i	1.22720	+	0.244106i
$606$		0			0
$607$	341.923	−	68.0127i	0.563300	−	0.112047i	0.0947766	−	0.995499i	$-0.469786\pi$
$607$	341.923	−	68.0127i	0.563300	−	0.112047i	0.468523	+	0.883451i	$0.344786\pi$
$608$		0			0
$609$	90.3809	+	60.3906i	0.148409	+	0.0991635i
$610$		0			0
$611$			103.391i			0.169216i
$612$		0			0
$613$	−1166.81			−1.90345			−0.951723	−	0.306960i	$-0.900688\pi$
$613$	−1166.81			−1.90345			−0.951723	+	0.306960i	$0.900688\pi$
$614$		0			0
$615$	747.710	−	1119.03i	1.21579	−	1.81956i
$616$		0			0
$617$	159.827	+	803.507i	0.259040	+	1.30228i	0.862975	+	0.505247i	$0.168599\pi$
$617$	159.827	+	803.507i	0.259040	+	1.30228i	−0.603935	+	0.797034i	$0.706401\pi$
$618$		0			0
$619$	−71.4308	+	359.107i	−0.115397	+	0.580140i	0.879211	+	0.476433i	$0.158071\pi$
$619$	−71.4308	+	359.107i	−0.115397	+	0.580140i	−0.994608	+	0.103707i	$0.966929\pi$
$620$		0			0
$621$	−220.619	−	532.620i	−0.355263	−	0.857682i
$622$		0			0
$623$	227.493	−	152.006i	0.365157	−	0.243990i
$624$		0			0
$625$	−549.950	+	549.950i	−0.879920	+	0.879920i
$626$		0			0
$627$	1230.61	+	509.737i	1.96270	+	0.812978i
$628$		0			0
$629$	−90.7108	−	1004.34i	−0.144214	−	1.59672i
$630$		0			0
$631$	−58.7276	+	141.781i	−0.0930707	+	0.224692i	−0.963559	−	0.267497i	$-0.913803\pi$
$631$	−58.7276	+	141.781i	−0.0930707	+	0.224692i	0.870488	+	0.492190i	$0.163803\pi$
$632$		0			0
$633$	−602.920	−	602.920i	−0.952480	−	0.952480i
$634$		0			0
$635$	555.736	+	831.717i	0.875174	+	1.30979i
$636$		0			0
$637$	748.709	−	310.125i	1.17537	−	0.486853i
$638$		0			0
$639$	1390.54	+	276.596i	2.17612	+	0.432858i
$640$		0			0
$641$	−848.581	+	168.793i	−1.32384	+	0.263328i	−0.805881	−	0.592078i	$-0.798308\pi$
$641$	−848.581	+	168.793i	−1.32384	+	0.263328i	−0.517959	+	0.855406i	$0.673308\pi$
$642$		0			0
$643$	−228.667	−	152.790i	−0.355625	−	0.237621i	0.364905	−	0.931045i	$-0.381101\pi$
$643$	−228.667	−	152.790i	−0.355625	−	0.237621i	−0.720530	+	0.693424i	$0.756101\pi$
$644$		0			0
$645$			1389.56i			2.15436i
$646$		0			0
$647$	−801.930			−1.23946			−0.619730	−	0.784815i	$-0.712758\pi$
$647$	−801.930			−1.23946			−0.619730	+	0.784815i	$0.712758\pi$
$648$		0			0
$649$	−283.880	+	424.856i	−0.437411	+	0.654632i
$650$		0			0
$651$	71.1102	+	357.495i	0.109232	+	0.549148i
$652$		0			0
$653$	−120.152	+	604.046i	−0.184000	+	0.925032i	0.772881	+	0.634551i	$0.218815\pi$
$653$	−120.152	+	604.046i	−0.184000	+	0.925032i	−0.956881	+	0.290480i	$0.906185\pi$
$654$		0			0
$655$	487.064	+	1175.88i	0.743609	+	1.79523i
$656$		0			0
$657$	−1091.94	+	729.614i	−1.66202	+	1.11052i
$658$		0			0
$659$	429.342	−	429.342i	0.651506	−	0.651506i	−0.301850	−	0.953356i	$-0.597604\pi$
$659$	429.342	−	429.342i	0.651506	−	0.651506i	0.953356	+	0.301850i	$0.0976041\pi$
$660$		0			0
$661$	334.856	+	138.702i	0.506590	+	0.209836i	0.621315	−	0.783561i	$-0.286599\pi$
$661$	334.856	+	138.702i	0.506590	+	0.209836i	−0.114725	+	0.993397i	$0.536599\pi$
$662$		0			0
$663$	−1363.13	−	1137.29i	−2.05600	−	1.71538i
$664$		0			0
$665$	−91.0767	+	219.879i	−0.136957	+	0.330645i
$666$		0			0
$667$	−46.4297	−	46.4297i	−0.0696097	−	0.0696097i
$668$		0			0
$669$	568.527	+	850.861i	0.849817	+	1.27184i
$670$		0			0
$671$	55.9270	−	23.1657i	0.0833487	−	0.0345242i
$672$		0			0
$673$	396.015	+	78.7722i	0.588432	+	0.117046i	0.480321	−	0.877093i	$-0.340520\pi$
$673$	396.015	+	78.7722i	0.588432	+	0.117046i	0.108110	+	0.994139i	$0.465520\pi$
$674$		0			0
$675$	−990.433	+	197.009i	−1.46731	+	0.291866i
$676$		0			0
$677$	339.579	+	226.900i	0.501594	+	0.335155i	0.780491	−	0.625166i	$-0.214969\pi$
$677$	339.579	+	226.900i	0.501594	+	0.335155i	−0.278897	+	0.960321i	$0.589969\pi$
$678$		0			0
$679$			331.978i			0.488923i
$680$		0			0
$681$	569.759			0.836650
$682$		0			0
$683$	170.889	−	255.754i	0.250204	−	0.374457i	−0.685014	−	0.728530i	$-0.740204\pi$
$683$	170.889	−	255.754i	0.250204	−	0.374457i	0.935218	+	0.354074i	$0.115204\pi$
$684$		0			0
$685$	121.329	+	609.961i	0.177122	+	0.890455i
$686$		0			0
$687$	262.552	−	1319.94i	0.382172	−	1.92131i
$688$		0			0
$689$	561.585	+	1355.79i	0.815072	+	1.96776i
$690$		0			0
$691$	320.000	−	213.817i	0.463097	−	0.309431i	−0.302044	−	0.953294i	$-0.597669\pi$
$691$	320.000	−	213.817i	0.463097	−	0.309431i	0.765141	+	0.643862i	$0.222669\pi$
$692$		0			0
$693$	584.447	−	584.447i	0.843359	−	0.843359i
$694$		0			0
$695$	568.938	+	235.662i	0.818615	+	0.339082i
$696$		0			0
$697$	−305.584	−	583.017i	−0.438427	−	0.836467i
$698$		0			0
$699$	−148.501	+	358.513i	−0.212448	+	0.512895i
$700$		0			0
$701$	−169.350	−	169.350i	−0.241584	−	0.241584i	0.575921	−	0.817505i	$-0.304643\pi$
$701$	−169.350	−	169.350i	−0.241584	−	0.241584i	−0.817505	+	0.575921i	$0.804643\pi$
$702$		0			0
$703$	−509.789	−	762.953i	−0.725162	−	1.08528i
$704$		0			0
$705$	176.115	−	72.9494i	0.249809	−	0.103474i
$706$		0			0
$707$	−144.335	−	28.7100i	−0.204152	−	0.0406083i
$708$		0			0
$709$	568.332	−	113.048i	0.801596	−	0.159447i	0.222741	−	0.974878i	$-0.428500\pi$
$709$	568.332	−	113.048i	0.801596	−	0.159447i	0.578855	+	0.815430i	$0.303500\pi$
$710$		0			0
$711$	−1633.07	−	1091.18i	−2.29687	−	1.53472i
$712$		0			0
$713$		−	220.179i		−	0.308807i
$714$		0			0
$715$	−1838.79			−2.57174
$716$		0			0
$717$	1161.44	−	1738.22i	1.61986	−	2.42430i
$718$		0			0
$719$	191.884	+	964.668i	0.266877	+	1.34168i	0.848920	+	0.528522i	$0.177253\pi$
$719$	191.884	+	964.668i	0.266877	+	1.34168i	−0.582043	+	0.813158i	$0.697747\pi$
$720$		0			0
$721$	−26.0006	+	130.714i	−0.0360619	+	0.181295i
$722$		0			0
$723$	−702.025	−	1694.84i	−0.970989	−	2.34417i
$724$		0			0
$725$	−95.6326	+	63.8997i	−0.131907	+	0.0881375i
$726$		0			0
$727$	−394.581	+	394.581i	−0.542753	+	0.542753i	−0.924335	−	0.381582i	$-0.875379\pi$
$727$	−394.581	+	394.581i	−0.542753	+	0.542753i	0.381582	+	0.924335i	$0.375379\pi$
$728$		0			0
$729$	651.520	+	269.868i	0.893717	+	0.370190i
$730$		0			0
$731$	596.767	+	325.220i	0.816370	+	0.444898i
$732$		0			0
$733$	−211.757	+	511.226i	−0.288890	+	0.697443i	−0.999984	−	0.00565410i	$-0.998200\pi$
$733$	−211.757	+	511.226i	−0.288890	+	0.697443i	0.711094	+	0.703097i	$0.248200\pi$
$734$		0			0
$735$	−1056.53	−	1056.53i	−1.43746	−	1.43746i
$736$		0			0
$737$	−622.123	−	931.072i	−0.844129	−	1.26333i
$738$		0			0
$739$	556.230	−	230.398i	0.752679	−	0.311770i	0.0268451	−	0.999640i	$-0.491454\pi$
$739$	556.230	−	230.398i	0.752679	−	0.311770i	0.725834	+	0.687870i	$0.241454\pi$
$740$		0			0
$741$	−1584.33	−	315.143i	−2.13810	−	0.425294i
$742$		0			0
$743$	−269.538	+	53.6145i	−0.362770	+	0.0721595i	−0.373110	−	0.927787i	$-0.621709\pi$
$743$	−269.538	+	53.6145i	−0.362770	+	0.0721595i	0.0103398	+	0.999947i	$0.496709\pi$
$744$		0			0
$745$	−371.085	−	247.951i	−0.498101	−	0.332821i
$746$		0			0
$747$		−	325.738i		−	0.436061i
$748$		0			0
$749$	−322.041			−0.429961
$750$		0			0
$751$	−542.990	+	812.643i	−0.723023	+	1.08208i	0.269850	+	0.962902i	$0.413026\pi$
$751$	−542.990	+	812.643i	−0.723023	+	1.08208i	−0.992873	+	0.119178i	$0.961974\pi$
$752$		0			0
$753$	−152.852	−	768.439i	−0.202991	−	1.02050i
$754$		0			0
$755$	−195.114	+	980.906i	−0.258430	+	1.29921i
$756$		0			0
$757$	131.054	+	316.393i	0.173123	+	0.417957i	0.986496	−	0.163787i	$-0.0523708\pi$
$757$	131.054	+	316.393i	0.173123	+	0.417957i	−0.813372	+	0.581743i	$0.802371\pi$
$758$		0			0
$759$	−587.429	+	392.508i	−0.773952	+	0.517138i
$760$		0			0
$761$	−336.551	+	336.551i	−0.442248	+	0.442248i	−0.892767	−	0.450519i	$-0.851239\pi$
$761$	−336.551	+	336.551i	−0.442248	+	0.442248i	0.450519	+	0.892767i	$0.351239\pi$
$762$		0			0
$763$	59.2708	+	24.5508i	0.0776812	+	0.0321766i
$764$		0			0
$765$	−689.366	+	2207.99i	−0.901132	+	2.88626i
$766$		0			0
$767$	237.137	−	572.500i	0.309175	−	0.746415i
$768$		0			0
$769$	330.011	+	330.011i	0.429143	+	0.429143i	0.888336	−	0.459193i	$-0.151861\pi$
$769$	330.011	+	330.011i	0.429143	+	0.429143i	−0.459193	+	0.888336i	$0.651861\pi$
$770$		0			0
$771$	1428.34	+	2137.66i	1.85258	+	2.77258i
$772$		0			0
$773$	−1081.14	+	447.823i	−1.39863	+	0.579331i	−0.949396	−	0.314083i	$-0.898303\pi$
$773$	−1081.14	+	447.823i	−1.39863	+	0.579331i	−0.449234	+	0.893414i	$0.648303\pi$
$774$		0			0
$775$	−378.268	−	75.2421i	−0.488088	−	0.0970866i
$776$		0			0
$777$	−790.219	+	157.184i	−1.01701	+	0.202297i
$778$		0			0
$779$	−498.017	−	332.765i	−0.639303	−	0.427169i
$780$		0			0
$781$		−	1016.35i		−	1.30135i
$782$		0			0
$783$	562.333			0.718177
$784$		0			0
$785$	−339.823	+	508.581i	−0.432895	+	0.647874i
$786$		0			0
$787$	−267.003	−	1342.32i	−0.339267	−	1.70561i	−0.654052	−	0.756449i	$-0.726932\pi$
$787$	−267.003	−	1342.32i	−0.339267	−	1.70561i	0.314785	−	0.949163i	$-0.398068\pi$
$788$		0			0
$789$	123.225	−	619.494i	0.156179	−	0.785164i
$790$		0			0
$791$	−95.4484	−	230.433i	−0.120668	−	0.291318i
$792$		0			0
$793$	−61.0404	+	40.7859i	−0.0769740	+	0.0514324i
$794$		0			0
$795$	1913.20	−	1913.20i	2.40654	−	2.40654i
$796$		0			0
$797$	582.398	+	241.237i	0.730737	+	0.302681i	0.716855	−	0.697222i	$-0.245581\pi$
$797$	582.398	+	241.237i	0.730737	+	0.302681i	0.0138823	+	0.999904i	$0.495581\pi$
$798$		0			0
$799$	9.88985	−	92.7087i	0.0123778	−	0.116031i
$800$		0			0
$801$	925.969	−	2235.49i	1.15602	−	2.79087i
$802$		0			0
$803$	665.692	+	665.692i	0.829006	+	0.829006i
$804$		0			0
$805$	−70.1309	−	104.958i	−0.0871191	−	0.130383i
$806$		0			0
$807$	−1082.41	+	448.348i	−1.34127	+	0.555573i
$808$		0			0
$809$	−240.875	−	47.9131i	−0.297745	−	0.0592251i	0.0439575	−	0.999033i	$-0.486003\pi$
$809$	−240.875	−	47.9131i	−0.297745	−	0.0592251i	−0.341702	+	0.939808i	$0.611003\pi$
$810$		0			0
$811$	595.515	−	118.455i	0.734297	−	0.146061i	0.186243	−	0.982504i	$-0.440369\pi$
$811$	595.515	−	118.455i	0.734297	−	0.146061i	0.548054	+	0.836443i	$0.315369\pi$
$812$		0			0
$813$	−2383.48	−	1592.59i	−2.93171	−	1.95890i
$814$		0			0
$815$			103.216i			0.126645i
$816$		0			0
$817$	618.418			0.756937
$818$		0			0
$819$	−556.883	+	833.435i	−0.679955	+	1.01763i
$820$		0			0
$821$	−0.700734	−	3.52283i	−0.000853512	−	0.00429090i	0.980356	−	0.197235i	$-0.0631963\pi$
$821$	−0.700734	−	3.52283i	−0.000853512	−	0.00429090i	−0.981210	+	0.192944i	$0.938196\pi$
$822$		0			0
$823$	−202.898	+	1020.04i	−0.246535	+	1.23941i	0.636931	+	0.770920i	$0.280203\pi$
$823$	−202.898	+	1020.04i	−0.246535	+	1.23941i	−0.883466	+	0.468494i	$0.844797\pi$
$824$		0			0
$825$	473.585	+	1143.33i	0.574042	+	1.38586i
$826$		0			0
$827$	−1159.89	+	775.013i	−1.40253	+	0.937138i	−0.402765	+	0.915303i	$0.631951\pi$
$827$	−1159.89	+	775.013i	−1.40253	+	0.937138i	−0.999762	+	0.0218347i	$0.993049\pi$
$828$		0			0
$829$	761.755	−	761.755i	0.918884	−	0.918884i	−0.0780639	−	0.996948i	$-0.524874\pi$
$829$	761.755	−	761.755i	0.918884	−	0.918884i	0.996948	+	0.0780639i	$0.0248738\pi$
$830$		0			0
$831$	−387.946	−	160.692i	−0.466842	−	0.193372i
$832$		0			0
$833$	−701.020	+	206.466i	−0.841560	+	0.247859i
$834$		0			0
$835$	531.896	−	1284.11i	0.637001	−	1.53786i
$836$		0			0
$837$	1333.35	+	1333.35i	1.59301	+	1.59301i
$838$		0			0
$839$	725.792	+	1086.22i	0.865068	+	1.29467i	0.954359	+	0.298660i	$0.0965398\pi$
$839$	725.792	+	1086.22i	0.865068	+	1.29467i	−0.0892913	+	0.996006i	$0.528460\pi$
$840$		0			0
$841$	−717.811	+	297.327i	−0.853520	+	0.353540i
$842$		0			0
$843$	335.830	+	66.8008i	0.398375	+	0.0792417i
$844$		0			0
$845$	1147.07	−	228.167i	1.35748	−	0.270020i
$846$		0			0
$847$	−245.964	−	164.348i	−0.290394	−	0.194035i
$848$		0			0
$849$		−	2244.07i		−	2.64320i
$850$		0			0
$851$	486.692			0.571906
$852$		0			0
$853$	543.784	−	813.830i	0.637495	−	0.954079i	−0.362262	−	0.932076i	$-0.617996\pi$
$853$	543.784	−	813.830i	0.637495	−	0.954079i	0.999758	−	0.0220032i	$-0.00700441\pi$
$854$		0			0
$855$	410.619	+	2064.32i	0.480256	+	2.41441i
$856$		0			0
$857$	−223.770	+	1124.97i	−0.261108	+	1.31268i	0.598252	+	0.801308i	$0.295862\pi$
$857$	−223.770	+	1124.97i	−0.261108	+	1.31268i	−0.859360	+	0.511371i	$0.829138\pi$
$858$		0			0
$859$	−179.676	−	433.776i	−0.209169	−	0.504978i	0.784124	−	0.620604i	$-0.213113\pi$
$859$	−179.676	−	433.776i	−0.209169	−	0.504978i	−0.993293	+	0.115626i	$0.963113\pi$
$860$		0			0
$861$	−437.287	+	292.186i	−0.507883	+	0.339356i
$862$		0			0
$863$	887.447	−	887.447i	1.02833	−	1.02833i	0.0287405	−	0.999587i	$-0.490850\pi$
$863$	887.447	−	887.447i	1.02833	−	1.02833i	0.999587	−	0.0287405i	$-0.00914965\pi$
$864$		0			0
$865$	1272.21	+	526.968i	1.47077	+	0.609212i
$866$		0			0
$867$	1113.51	+	1150.18i	1.28432	+	1.32662i
$868$		0			0
$869$	−538.806	+	1300.79i	−0.620030	+	1.49689i
$870$		0			0
$871$	960.256	+	960.256i	1.10248	+	1.10248i
$872$		0			0
$873$	1631.12	+	2441.14i	1.86840	+	2.79626i
$874$		0			0
$875$	151.074	−	62.5768i	0.172656	−	0.0715163i
$876$		0			0
$877$	1245.13	+	247.673i	1.41977	+	0.282409i	0.844499	−	0.535557i	$-0.179898\pi$
$877$	1245.13	+	247.673i	1.41977	+	0.282409i	0.575267	+	0.817966i	$0.304898\pi$
$878$		0			0
$879$	−364.181	+	72.4401i	−0.414313	+	0.0824119i
$880$		0			0
$881$	125.148	+	83.6210i	0.142052	+	0.0949160i	0.624565	−	0.780972i	$-0.285276\pi$
$881$	125.148	+	83.6210i	0.142052	+	0.0949160i	−0.482514	+	0.875888i	$0.660276\pi$
$882$		0			0
$883$			953.062i			1.07935i	0.841875	+	0.539673i	$0.181452\pi$
$883$			953.062i			1.07935i	−0.841875	+	0.539673i	$0.818548\pi$
$884$		0			0
$885$	−1142.51			−1.29097
$886$		0			0
$887$	506.134	−	757.482i	0.570613	−	0.853982i	−0.428150	−	0.903708i	$-0.640835\pi$
$887$	506.134	−	757.482i	0.570613	−	0.853982i	0.998763	+	0.0497252i	$0.0158346\pi$
$888$		0			0
$889$	−76.2590	−	383.380i	−0.0857807	−	0.431248i
$890$		0			0
$891$	588.533	−	2958.76i	0.660531	−	3.32072i
$892$		0			0
$893$	−32.4658	−	78.3793i	−0.0363558	−	0.0877708i
$894$		0			0
$895$	−1594.57	+	1065.46i	−1.78164	+	1.19045i
$896$		0			0
$897$	605.841	−	605.841i	0.675409	−	0.675409i
$898$		0			0
$899$	198.419	+	82.1878i	0.220711	+	0.0914213i
$900$		0			0
$901$	−373.875	−	1269.43i	−0.414956	−	1.40891i
$902$		0			0
$903$	207.799	−	501.671i	0.230121	−	0.555561i
$904$		0			0
$905$	−54.7820	−	54.7820i	−0.0605326	−	0.0605326i
$906$		0			0
$907$	−878.749	−	1315.14i	−0.968852	−	1.44999i	−0.891519	−	0.452984i	$-0.850359\pi$
$907$	−878.749	−	1315.14i	−0.968852	−	1.44999i	−0.0773333	−	0.997005i	$-0.524641\pi$
$908$		0			0
$909$	−1202.40	+	498.051i	−1.32277	+	0.547911i
$910$		0			0
$911$	−1743.00	−	346.704i	−1.91328	−	0.380575i	−0.913617	−	0.406576i	$-0.866723\pi$
$911$	−1743.00	−	346.704i	−1.91328	−	0.380575i	−0.999662	+	0.0260015i	$0.991723\pi$
$912$		0			0
$913$	−229.021	+	45.5552i	−0.250845	+	0.0498962i
$914$		0			0
$915$	112.543	+	75.1987i	0.122998	+	0.0821843i
$916$		0			0
$917$		−	497.362i		−	0.542379i
$918$		0			0
$919$	1587.59			1.72752			0.863760	−	0.503904i	$-0.168103\pi$
$919$	1587.59			1.72752			0.863760	+	0.503904i	$0.168103\pi$
$920$		0			0
$921$	18.9288	−	28.3289i	0.0205524	−	0.0307588i
$922$		0			0
$923$	240.461	+	1208.88i	0.260521	+	1.30973i
$924$		0			0
$925$	166.318	−	836.136i	0.179803	−	0.903931i
$926$		0			0
$927$	451.048	+	1088.93i	0.486568	+	1.17468i
$928$		0			0
$929$	282.825	−	188.977i	0.304440	−	0.203420i	−0.393961	−	0.919127i	$-0.628895\pi$
$929$	282.825	−	188.977i	0.304440	−	0.203420i	0.698401	+	0.715707i	$0.253895\pi$
$930$		0			0
$931$	−470.205	+	470.205i	−0.505054	+	0.505054i
$932$		0			0
$933$	−614.383	−	254.486i	−0.658502	−	0.272761i
$934$		0			0
$935$	1648.82	+	175.890i	1.76344	+	0.188118i
$936$		0			0
$937$	157.414	−	380.032i	0.167998	−	0.405584i	−0.817349	−	0.576143i	$-0.804557\pi$
$937$	157.414	−	380.032i	0.167998	−	0.405584i	0.985348	+	0.170559i	$0.0545573\pi$
$938$		0			0
$939$	215.880	+	215.880i	0.229904	+	0.229904i
$940$		0			0
$941$	−335.734	−	502.462i	−0.356784	−	0.533966i	0.609048	−	0.793133i	$-0.291552\pi$
$941$	−335.734	−	502.462i	−0.356784	−	0.533966i	−0.965832	+	0.259168i	$0.916552\pi$
$942$		0			0
$943$	293.505	−	121.574i	0.311246	−	0.128922i
$944$		0			0
$945$	1060.30	+	210.906i	1.12201	+	0.223181i
$946$		0			0
$947$	638.673	−	127.040i	0.674417	−	0.134150i	0.154011	−	0.988069i	$-0.450781\pi$
$947$	638.673	−	127.040i	0.674417	−	0.134150i	0.520405	+	0.853919i	$0.325781\pi$
$948$		0			0
$949$	−949.291	−	634.296i	−1.00031	−	0.668384i
$950$		0			0
$951$		−	1708.46i		−	1.79649i
$952$		0			0
$953$	215.789			0.226431			0.113216	−	0.993570i	$-0.463885\pi$
$953$	215.789			0.226431			0.113216	+	0.993570i	$0.463885\pi$
$954$		0			0
$955$	−341.237	+	510.698i	−0.357317	+	0.534762i
$956$		0			0
$957$	−134.442	−	675.887i	−0.140483	−	0.706256i
$958$		0			0
$959$	47.4122	−	238.357i	0.0494392	−	0.248548i
$960$		0			0
$961$	−92.1626	−	222.500i	−0.0959028	−	0.231530i
$962$		0			0
$963$	−2368.06	+	1582.29i	−2.45905	+	1.64308i
$964$		0			0
$965$	653.237	−	653.237i	0.676929	−	0.676929i
$966$		0			0
$967$	1462.82	+	605.921i	1.51274	+	0.626599i	0.976122	−	0.217223i	$-0.0697000\pi$
$967$	1462.82	+	605.921i	1.51274	+	0.626599i	0.536622	+	0.843823i	$0.319700\pi$
$968$		0			0
$969$	1390.50	+	434.132i	1.43498	+	0.448021i
$970$		0			0
$971$	4.39705	−	10.6154i	0.00452837	−	0.0109324i	−0.921599	−	0.388143i	$-0.873117\pi$
$971$	4.39705	−	10.6154i	0.00452837	−	0.0109324i	0.926128	+	0.377211i	$0.123117\pi$
$972$		0			0
$973$	−170.161	−	170.161i	−0.174883	−	0.174883i
$974$		0			0
$975$	−833.800	−	1247.87i	−0.855179	−	1.27987i
$976$		0			0
$977$	1398.66	−	579.346i	1.43159	−	0.592984i	0.473847	−	0.880607i	$-0.342865\pi$
$977$	1398.66	−	579.346i	1.43159	−	0.592984i	0.957744	+	0.287623i	$0.0928650\pi$
$978$		0			0
$979$	−1701.24	−	338.397i	−1.73773	−	0.345656i
$980$		0			0
$981$	556.461	−	110.687i	0.567239	−	0.112831i
$982$		0			0
$983$	−129.340	−	86.4222i	−0.131577	−	0.0879167i	0.488040	−	0.872821i	$-0.337712\pi$
$983$	−129.340	−	86.4222i	−0.131577	−	0.0879167i	−0.619617	+	0.784904i	$0.712712\pi$
$984$		0			0
$985$			1114.08i			1.13104i
$986$		0			0
$987$	−74.4917			−0.0754729
$988$		0			0
$989$	−182.231	+	272.729i	−0.184258	+	0.275762i
$990$		0			0
$991$	39.0976	+	196.557i	0.0394527	+	0.198342i	0.995485	−	0.0949194i	$-0.0302593\pi$
$991$	39.0976	+	196.557i	0.0394527	+	0.198342i	−0.956032	+	0.293262i	$0.905259\pi$
$992$		0			0
$993$	−205.749	+	1034.37i	−0.207199	+	1.04166i
$994$		0			0
$995$	319.077	+	770.320i	0.320680	+	0.774191i
$996$		0			0
$997$	1569.02	−	1048.39i	1.57374	−	1.05154i	0.607365	−	0.794423i	$-0.292227\pi$
$997$	1569.02	−	1048.39i	1.57374	−	1.05154i	0.966380	−	0.257119i	$-0.0827733\pi$
$998$		0			0
$999$	−2947.28	+	2947.28i	−2.95023	+	2.95023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.41.1	✓	40
4.3	odd	2		272.3.bh.g.177.5		40
17.5	odd	16	inner	136.3.t.b.73.1	yes	40
68.39	even	16		272.3.bh.g.209.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.41.1	✓	40	1.1	even	1	trivial
136.3.t.b.73.1	yes	40	17.5	odd	16	inner
272.3.bh.g.177.5		40	4.3	odd	2
272.3.bh.g.209.5		40	68.39	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.07751 + 4.60583i) q^{3} +(1.22413 + 6.15412i) q^{5} +(0.478359 - 2.40487i) q^{7} +(-8.29839 - 20.0341i) q^{9} +O(q^{10})\)	\(q+(-3.07751 + 4.60583i) q^{3} +(1.22413 + 6.15412i) q^{5} +(0.478359 - 2.40487i) q^{7} +(-8.29839 - 20.0341i) q^{9} +(-12.9251 + 8.63629i) q^{11} +(13.3302 - 13.3302i) q^{13} +(-32.1121 - 13.3013i) q^{15} +(-13.2281 + 10.6779i) q^{17} +(-5.91966 + 14.2913i) q^{19} +(9.60427 + 9.60427i) q^{21} +(-4.55826 - 6.82191i) q^{23} +(-13.2777 + 5.49982i) q^{25} +(68.9154 + 13.7081i) q^{27} +(7.84919 - 1.56130i) q^{29} +(22.3133 + 14.9092i) q^{31} -86.1092i q^{33} +15.3855 q^{35} +(-32.9559 + 49.3220i) q^{37} +(20.3728 + 102.421i) q^{39} +(-7.55399 + 37.9765i) q^{41} +(-15.2990 - 36.9351i) q^{43} +(113.134 - 75.5936i) q^{45} +(-3.87805 + 3.87805i) q^{47} +(39.7155 + 16.4507i) q^{49} +(-8.47083 - 93.7877i) q^{51} +(-29.7894 + 71.9180i) q^{53} +(-68.9708 - 68.9708i) q^{55} +(-47.6055 - 71.2467i) q^{57} +(30.3685 - 12.5790i) q^{59} +(-3.81937 - 0.759720i) q^{61} +(-52.1490 + 10.3731i) q^{63} +(98.3539 + 65.7180i) q^{65} +72.0359i q^{67} +45.4487 q^{69} +(-36.3241 + 54.3629i) q^{71} +(-11.8151 - 59.3983i) q^{73} +(15.5312 - 78.0807i) q^{75} +(14.5863 + 35.2145i) q^{77} +(75.3098 - 50.3204i) q^{79} +(-137.225 + 137.225i) q^{81} +(13.8781 + 5.74849i) q^{83} +(-81.9060 - 68.3362i) q^{85} +(-16.9649 + 40.9569i) q^{87} +(78.9020 + 78.9020i) q^{89} +(-25.6809 - 38.4342i) q^{91} +(-137.339 + 56.8876i) q^{93} +(-95.1970 - 18.9359i) q^{95} +(-132.790 + 26.4136i) q^{97} +(280.278 + 187.276i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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