LMFDB - Embedded newform 135.3.h.a.44.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [135,3,Mod(44,135)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(135, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("135.44"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	135.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.67848356886$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{18} - 19 x^{16} + 66 x^{14} + 109 x^{12} - 813 x^{10} + 981 x^{8} + 5346 x^{6} + \cdots + 59049 $ x^20 - 3x^18 - 19x^16 + 66x^14 + 109x^12 - 813x^10 + 981x^8 + 5346x^6 - 13851x^4 - 19683*x^2 + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{12} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			44.9
Root			$0.346576 + 1.69702i$ of defining polynomial
Character	$\chi$	$=$	135.44
Dual form			135.3.h.a.89.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42081 + 2.46092i) q^{2} +(-2.03740 + 3.52889i) q^{4} +(-3.58357 + 3.48684i) q^{5} +(-8.42581 + 4.86464i) q^{7} -0.212574 q^{8} +(-13.6724 - 3.86473i) q^{10} +(-0.370966 + 0.214177i) q^{11} +(16.2396 + 9.37595i) q^{13} +(-23.9429 - 13.8235i) q^{14} +(7.84759 + 13.5924i) q^{16} +2.85718 q^{17} +0.530568 q^{19} +(-5.00347 - 19.7501i) q^{20} +(-1.05414 - 0.608611i) q^{22} +(10.8863 - 18.8557i) q^{23} +(0.683961 - 24.9906i) q^{25} +53.2858i q^{26} -39.6450i q^{28} +(21.0633 - 12.1609i) q^{29} +(6.33163 - 10.9667i) q^{31} +(-22.7250 + 39.3609i) q^{32} +(4.05951 + 7.03128i) q^{34} +(13.2323 - 46.8122i) q^{35} +14.5875i q^{37} +(0.753837 + 1.30568i) q^{38} +(0.761774 - 0.741210i) q^{40} +(33.1200 + 19.1218i) q^{41} +(-50.0269 + 28.8831i) q^{43} -1.74546i q^{44} +61.8697 q^{46} +(24.7850 + 42.9289i) q^{47} +(22.8295 - 39.5418i) q^{49} +(62.4716 - 33.8238i) q^{50} +(-66.1734 + 38.2052i) q^{52} -44.5876 q^{53} +(0.582582 - 2.06102i) q^{55} +(1.79111 - 1.03410i) q^{56} +(59.8538 + 34.5566i) q^{58} +(54.6329 + 31.5423i) q^{59} +(11.0823 + 19.1951i) q^{61} +35.9842 q^{62} -66.3710 q^{64} +(-90.8883 + 23.0255i) q^{65} +(-28.1839 - 16.2720i) q^{67} +(-5.82123 + 10.0827i) q^{68} +(134.001 - 33.9477i) q^{70} -89.8896i q^{71} -144.328i q^{73} +(-35.8987 + 20.7261i) q^{74} +(-1.08098 + 1.87232i) q^{76} +(2.08379 - 3.60923i) q^{77} +(-25.1240 - 43.5160i) q^{79} +(-75.5169 - 21.3462i) q^{80} +108.674i q^{82} +(-38.2556 - 66.2606i) q^{83} +(-10.2389 + 9.96251i) q^{85} +(-142.158 - 82.0747i) q^{86} +(0.0788577 - 0.0455285i) q^{88} +28.9588i q^{89} -182.443 q^{91} +(44.3598 + 76.8334i) q^{92} +(-70.4296 + 121.988i) q^{94} +(-1.90133 + 1.85000i) q^{95} +(19.9099 - 11.4950i) q^{97} +129.746 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) $ 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	1.42081	+	2.46092i	0.710405	+	1.23046i	0.964705	+	0.263332i	$0.0848216\pi$
$2$	1.42081	+	2.46092i	0.710405	+	1.23046i	−0.254300	+	0.967125i	$0.581845\pi$
$3$		0			0
$3$		0			0
$4$	−2.03740	+	3.52889i	−0.509351	+	0.882222i
$5$	−3.58357	+	3.48684i	−0.716714	+	0.697367i
$5$	−3.58357	+	3.48684i	−0.716714	+	0.697367i
$6$		0			0
$7$	−8.42581	+	4.86464i	−1.20369	+	0.694949i	−0.961373	−	0.275249i	$-0.911240\pi$
$7$	−8.42581	+	4.86464i	−1.20369	+	0.694949i	−0.242314	+	0.970198i	$0.577906\pi$
$8$	−0.212574			−0.0265717
$9$		0			0
$10$	−13.6724	−	3.86473i	−1.36724	−	0.386473i
$11$	−0.370966	+	0.214177i	−0.0337242	+	0.0194707i	−0.516767	−	0.856126i	$-0.672865\pi$
$11$	−0.370966	+	0.214177i	−0.0337242	+	0.0194707i	0.483043	+	0.875597i	$0.339531\pi$
$12$		0			0
$13$	16.2396	+	9.37595i	1.24920	+	0.721227i	0.970950	−	0.239281i	$-0.0769117\pi$
$13$	16.2396	+	9.37595i	1.24920	+	0.721227i	0.278252	+	0.960508i	$0.410245\pi$
$14$	−23.9429	−	13.8235i	−1.71021	−	0.987391i
$15$		0			0
$16$	7.84759	+	13.5924i	0.490474	+	0.849526i
$17$	2.85718			0.168069			0.0840347	−	0.996463i	$-0.473219\pi$
$17$	2.85718			0.168069			0.0840347	+	0.996463i	$0.473219\pi$
$18$		0			0
$19$	0.530568			0.0279246			0.0139623	−	0.999903i	$-0.495556\pi$
$19$	0.530568			0.0279246			0.0139623	+	0.999903i	$0.495556\pi$
$20$	−5.00347	−	19.7501i	−0.250173	−	0.987505i
$21$		0			0
$22$	−1.05414	−	0.608611i	−0.0479157	−	0.0276641i
$23$	10.8863	−	18.8557i	0.473319	−	0.819813i	−0.526214	−	0.850352i	$-0.676389\pi$
$23$	10.8863	−	18.8557i	0.473319	−	0.819813i	0.999534	+	0.0305388i	$0.00972230\pi$
$24$		0			0
$25$	0.683961	−	24.9906i	0.0273584	−	0.999626i
$26$			53.2858i			2.04945i
$27$		0			0
$28$		−	39.6450i		−	1.41589i
$29$	21.0633	−	12.1609i	0.726320	−	0.419341i	−0.0907547	−	0.995873i	$-0.528928\pi$
$29$	21.0633	−	12.1609i	0.726320	−	0.419341i	0.817074	+	0.576532i	$0.195595\pi$
$30$		0			0
$31$	6.33163	−	10.9667i	0.204246	−	0.353765i	−0.745646	−	0.666342i	$-0.767859\pi$
$31$	6.33163	−	10.9667i	0.204246	−	0.353765i	0.949892	+	0.312577i	$0.101192\pi$
$32$	−22.7250	+	39.3609i	−0.710157	+	1.23003i
$33$		0			0
$34$	4.05951	+	7.03128i	0.119397	+	0.206802i
$35$	13.2323	−	46.8122i	0.378065	−	1.33749i
$36$		0			0
$37$			14.5875i			0.394257i	0.980378	+	0.197129i	$0.0631617\pi$
$37$			14.5875i			0.394257i	−0.980378	+	0.197129i	$0.936838\pi$
$38$	0.753837	+	1.30568i	0.0198378	+	0.0343601i
$39$		0			0
$40$	0.761774	−	0.741210i	0.0190443	−	0.0185303i
$41$	33.1200	+	19.1218i	0.807804	+	0.466386i	0.846193	−	0.532877i	$-0.178889\pi$
$41$	33.1200	+	19.1218i	0.807804	+	0.466386i	−0.0383889	+	0.999263i	$0.512223\pi$
$42$		0			0
$43$	−50.0269	+	28.8831i	−1.16342	+	0.671699i	−0.952121	−	0.305723i	$-0.901102\pi$
$43$	−50.0269	+	28.8831i	−1.16342	+	0.671699i	−0.211297	+	0.977422i	$0.567769\pi$
$44$		−	1.74546i		−	0.0396696i
$45$		0			0
$46$	61.8697			1.34499
$47$	24.7850	+	42.9289i	0.527341	+	0.913381i	0.999492	+	0.0318635i	$0.0101442\pi$
$47$	24.7850	+	42.9289i	0.527341	+	0.913381i	−0.472152	+	0.881517i	$0.656522\pi$
$48$		0			0
$49$	22.8295	−	39.5418i	0.465908	−	0.806976i
$50$	62.4716	−	33.8238i	1.24943	−	0.676476i
$51$		0			0
$52$	−66.1734	+	38.2052i	−1.27256	+	0.734716i
$53$	−44.5876			−0.841275			−0.420637	−	0.907229i	$-0.638193\pi$
$53$	−44.5876			−0.841275			−0.420637	+	0.907229i	$0.638193\pi$
$54$		0			0
$55$	0.582582	−	2.06102i	0.0105924	−	0.0374730i
$56$	1.79111	−	1.03410i	0.0319840	−	0.0184660i
$57$		0			0
$58$	59.8538	+	34.5566i	1.03196	+	0.595804i
$59$	54.6329	+	31.5423i	0.925981	+	0.534615i	0.885538	−	0.464567i	$-0.153790\pi$
$59$	54.6329	+	31.5423i	0.925981	+	0.534615i	0.0404426	+	0.999182i	$0.487123\pi$
$60$		0			0
$61$	11.0823	+	19.1951i	0.181677	+	0.314673i	0.942452	−	0.334343i	$-0.108514\pi$
$61$	11.0823	+	19.1951i	0.181677	+	0.314673i	−0.760775	+	0.649016i	$0.775181\pi$
$62$	35.9842			0.580390
$63$		0			0
$64$	−66.3710			−1.03705
$65$	−90.8883	+	23.0255i	−1.39828	+	0.354239i
$66$		0			0
$67$	−28.1839	−	16.2720i	−0.420655	−	0.242866i	0.274702	−	0.961529i	$-0.411421\pi$
$67$	−28.1839	−	16.2720i	−0.420655	−	0.242866i	−0.695358	+	0.718664i	$0.744754\pi$
$68$	−5.82123	+	10.0827i	−0.0856063	+	0.148274i
$69$		0			0
$70$	134.001	−	33.9477i	1.91431	−	0.484968i
$71$		−	89.8896i		−	1.26605i	−0.774131	−	0.633025i	$-0.781813\pi$
$71$		−	89.8896i		−	1.26605i	0.774131	−	0.633025i	$-0.218187\pi$
$72$		0			0
$73$		−	144.328i		−	1.97709i	−0.150926	−	0.988545i	$-0.548225\pi$
$73$		−	144.328i		−	1.97709i	0.150926	−	0.988545i	$-0.451775\pi$
$74$	−35.8987	+	20.7261i	−0.485117	+	0.280082i
$75$		0			0
$76$	−1.08098	+	1.87232i	−0.0142234	+	0.0246357i
$77$	2.08379	−	3.60923i	0.0270622	−	0.0468732i
$78$		0			0
$79$	−25.1240	−	43.5160i	−0.318025	−	0.550836i	0.662051	−	0.749459i	$-0.269686\pi$
$79$	−25.1240	−	43.5160i	−0.318025	−	0.550836i	−0.980076	+	0.198623i	$0.936353\pi$
$80$	−75.5169	−	21.3462i	−0.943961	−	0.266827i
$81$		0			0
$82$			108.674i			1.32529i
$83$	−38.2556	−	66.2606i	−0.460911	−	0.798321i	0.538096	−	0.842884i	$-0.319144\pi$
$83$	−38.2556	−	66.2606i	−0.460911	−	0.798321i	−0.999007	+	0.0445628i	$0.985811\pi$
$84$		0			0
$85$	−10.2389	+	9.96251i	−0.120458	+	0.117206i
$86$	−142.158	−	82.0747i	−1.65300	−	0.954357i
$87$		0			0
$88$	0.0788577	−	0.0455285i	0.000896110	−	0.000517369i
$89$			28.9588i			0.325379i	0.986677	+	0.162690i	$0.0520169\pi$
$89$			28.9588i			0.325379i	−0.986677	+	0.162690i	$0.947983\pi$
$90$		0			0
$91$	−182.443			−2.00486
$92$	44.3598	+	76.8334i	0.482171	+	0.835145i
$93$		0			0
$94$	−70.4296	+	121.988i	−0.749251	+	1.29774i
$95$	−1.90133	+	1.85000i	−0.0200140	+	0.0194737i
$96$		0			0
$97$	19.9099	−	11.4950i	0.205257	−	0.118505i	−0.393848	−	0.919175i	$-0.628857\pi$
$97$	19.9099	−	11.4950i	0.205257	−	0.118505i	0.599105	+	0.800670i	$0.295523\pi$
$98$	129.746			1.32393
$99$		0			0
$100$	86.7956	+	53.3296i	0.867956	+	0.533296i
$101$	49.7337	−	28.7138i	0.492413	−	0.284295i	−0.233162	−	0.972438i	$-0.574907\pi$
$101$	49.7337	−	28.7138i	0.492413	−	0.284295i	0.725575	+	0.688143i	$0.241574\pi$
$102$		0			0
$103$	74.6430	+	43.0952i	0.724689	+	0.418400i	0.816476	−	0.577379i	$-0.195924\pi$
$103$	74.6430	+	43.0952i	0.724689	+	0.418400i	−0.0917868	+	0.995779i	$0.529258\pi$
$104$	−3.45212	−	1.99308i	−0.0331935	−	0.0191643i
$105$		0			0
$106$	−63.3504	−	109.726i	−0.597646	−	1.03515i
$107$	−97.0919			−0.907401			−0.453701	−	0.891154i	$-0.649896\pi$
$107$	−97.0919			−0.907401			−0.453701	+	0.891154i	$0.649896\pi$
$108$		0			0
$109$	164.495			1.50913			0.754565	−	0.656225i	$-0.227848\pi$
$109$	164.495			1.50913			0.754565	+	0.656225i	$0.227848\pi$
$110$	5.89973	−	1.49463i	0.0536339	−	0.0135875i
$111$		0			0
$112$	−132.245	−	76.3514i	−1.18075	−	0.681709i
$113$	−21.4024	+	37.0700i	−0.189401	+	0.328053i	−0.945051	−	0.326924i	$-0.893988\pi$
$113$	−21.4024	+	37.0700i	−0.189401	+	0.328053i	0.755649	+	0.654976i	$0.227321\pi$
$114$		0			0
$115$	26.7347	+	105.530i	0.232476	+	0.917649i
$116$			99.1065i			0.854366i
$117$		0			0
$118$			179.262i			1.51917i
$119$	−24.0740	+	13.8992i	−0.202303	+	0.116800i
$120$		0			0
$121$	−60.4083	+	104.630i	−0.499242	+	0.864712i
$122$	−31.4916	+	54.5451i	−0.258128	+	0.447091i
$123$		0			0
$124$	25.8002	+	44.6872i	0.208066	+	0.360381i
$125$	84.6872	+	91.9406i	0.677498	+	0.735525i
$126$		0			0
$127$			78.7223i			0.619861i	0.950759	+	0.309931i	$0.100306\pi$
$127$			78.7223i			0.619861i	−0.950759	+	0.309931i	$0.899694\pi$
$128$	−3.40059	−	5.88999i	−0.0265671	−	0.0460155i
$129$		0			0
$130$	−185.799	−	190.953i	−1.42922	−	1.46887i
$131$	−158.295	−	91.3914i	−1.20836	−	0.697644i	−0.245956	−	0.969281i	$-0.579102\pi$
$131$	−158.295	−	91.3914i	−1.20836	−	0.697644i	−0.962400	+	0.271637i	$0.912435\pi$
$132$		0			0
$133$	−4.47047	+	2.58103i	−0.0336125	+	0.0194062i
$134$		−	92.4776i		−	0.690132i
$135$		0			0
$136$	−0.607362			−0.00446589
$137$	−2.78196	−	4.81850i	−0.0203063	−	0.0351715i	0.855694	−	0.517483i	$-0.173131\pi$
$137$	−2.78196	−	4.81850i	−0.0203063	−	0.0351715i	−0.876000	+	0.482311i	$0.839797\pi$
$138$		0			0
$139$	84.9601	−	147.155i	0.611224	−	1.05867i	−0.379810	−	0.925064i	$-0.624011\pi$
$139$	84.9601	−	147.155i	0.611224	−	1.05867i	0.991034	−	0.133607i	$-0.0426559\pi$
$140$	138.235	+	142.071i	0.987396	+	1.01479i
$141$		0			0
$142$	221.211	−	127.716i	1.55782	−	0.899409i
$143$	−8.03247			−0.0561711
$144$		0			0
$145$	−33.0787	+	117.024i	−0.228129	+	0.807059i
$146$	355.178	−	205.062i	2.43273	−	1.40454i
$147$		0			0
$148$	−51.4777	−	29.7207i	−0.347822	−	0.200815i
$149$	69.9180	+	40.3672i	0.469249	+	0.270921i	0.715925	−	0.698177i	$-0.246005\pi$
$149$	69.9180	+	40.3672i	0.469249	+	0.270921i	−0.246677	+	0.969098i	$0.579339\pi$
$150$		0			0
$151$	−44.1372	−	76.4478i	−0.292299	−	0.506277i	0.682054	−	0.731302i	$-0.261087\pi$
$151$	−44.1372	−	76.4478i	−0.292299	−	0.506277i	−0.974353	+	0.225025i	$0.927754\pi$
$152$	−0.112785			−0.000742006
$153$		0			0
$154$	11.8427			0.0769006
$155$	15.5492	+	61.3773i	0.100318	+	0.395983i
$156$		0			0
$157$	54.3401	+	31.3732i	0.346115	+	0.199830i	0.662973	−	0.748643i	$-0.269294\pi$
$157$	54.3401	+	31.3732i	0.346115	+	0.199830i	−0.316858	+	0.948473i	$0.602628\pi$
$158$	71.3929	−	123.656i	0.451854	−	0.782633i
$159$		0			0
$160$	−55.8082	−	220.291i	−0.348801	−	1.37682i
$161$			211.833i			1.31573i
$162$		0			0
$163$		−	241.437i		−	1.48121i	−0.671941	−	0.740605i	$-0.734539\pi$
$163$		−	241.437i		−	1.48121i	0.671941	−	0.740605i	$-0.265461\pi$
$164$	−134.957	+	77.9177i	−0.822911	+	0.475108i
$165$		0			0
$166$	108.708	−	188.288i	0.654867	−	1.13426i
$167$	66.5872	−	115.332i	0.398726	−	0.690613i	−0.594843	−	0.803842i	$-0.702786\pi$
$167$	66.5872	−	115.332i	0.398726	−	0.690613i	0.993569	+	0.113229i	$0.0361193\pi$
$168$		0			0
$169$	91.3170	+	158.166i	0.540338	+	0.935892i
$170$	−39.0644	−	11.0422i	−0.229791	−	0.0649543i
$171$		0			0
$172$		−	235.386i		−	1.36852i
$173$	33.5211	+	58.0603i	0.193764	+	0.335609i	0.946495	−	0.322720i	$-0.104597\pi$
$173$	33.5211	+	58.0603i	0.193764	+	0.335609i	−0.752731	+	0.658328i	$0.771264\pi$
$174$		0			0
$175$	115.808	+	213.894i	0.661758	+	1.22225i
$176$	−5.82238	−	3.36155i	−0.0330817	−	0.0190997i
$177$		0			0
$178$	−71.2651	+	41.1449i	−0.400366	+	0.231151i
$179$		−	37.9613i		−	0.212074i	−0.994362	−	0.106037i	$-0.966184\pi$
$179$		−	37.9613i		−	0.212074i	0.994362	−	0.106037i	$-0.0338162\pi$
$180$		0			0
$181$	278.012			1.53598			0.767990	−	0.640462i	$-0.221257\pi$
$181$	278.012			1.53598			0.767990	+	0.640462i	$0.221257\pi$
$182$	−259.216	−	448.976i	−1.42427	−	2.46690i
$183$		0			0
$184$	−2.31415	+	4.00823i	−0.0125769	+	0.0217839i
$185$	−50.8643	−	52.2754i	−0.274942	−	0.282570i
$186$		0			0
$187$	−1.05992	+	0.611943i	−0.00566800	+	0.00327242i
$188$	−201.988			−1.07441
$189$		0			0
$190$	−7.25413	−	2.05051i	−0.0381796	−	0.0107921i
$191$	−50.4943	+	29.1529i	−0.264368	+	0.152633i	−0.626326	−	0.779562i	$-0.715442\pi$
$191$	−50.4943	+	29.1529i	−0.264368	+	0.152633i	0.361957	+	0.932195i	$0.382109\pi$
$192$		0			0
$193$	−109.611	−	63.2837i	−0.567930	−	0.327895i	0.188392	−	0.982094i	$-0.439672\pi$
$193$	−109.611	−	63.2837i	−0.567930	−	0.327895i	−0.756322	+	0.654199i	$0.773006\pi$
$194$	56.5764	+	32.6644i	0.291631	+	0.168373i
$195$		0			0
$196$	93.0258	+	161.125i	0.474621	+	0.822068i
$197$	335.557			1.70333			0.851667	−	0.524083i	$-0.175592\pi$
$197$	335.557			1.70333			0.851667	+	0.524083i	$0.175592\pi$
$198$		0			0
$199$	−127.161			−0.638998			−0.319499	−	0.947587i	$-0.603515\pi$
$199$	−127.161			−0.638998			−0.319499	+	0.947587i	$0.603515\pi$
$200$	−0.145392	+	5.31236i	−0.000726961	+	0.0265618i
$201$		0			0
$202$	141.324	+	81.5937i	0.699626	+	0.403929i
$203$	−118.317	+	204.931i	−0.582841	+	1.00951i
$204$		0			0
$205$	−185.362	+	46.9594i	−0.904206	+	0.229070i
$206$			244.920i			1.18893i
$207$		0			0
$208$			294.314i			1.41497i
$209$	−0.196823	+	0.113636i	−0.000941736	+	0.000543712i
$210$		0			0
$211$	−48.8580	+	84.6246i	−0.231555	+	0.401064i	−0.958266	−	0.285879i	$-0.907715\pi$
$211$	−48.8580	+	84.6246i	−0.231555	+	0.401064i	0.726711	+	0.686943i	$0.241048\pi$
$212$	90.8428	−	157.344i	0.428504	−	0.742191i
$213$		0			0
$214$	−137.949	−	238.935i	−0.644623	−	1.11652i
$215$	78.5646	−	277.940i	0.365417	−	1.29275i
$216$		0			0
$217$			123.204i			0.567762i
$218$	233.716	+	404.809i	1.07209	+	1.85692i
$219$		0			0
$220$	6.08614	+	6.25499i	0.0276643	+	0.0284318i
$221$	46.3995	+	26.7888i	0.209953	+	0.121216i
$222$		0			0
$223$	−80.9094	+	46.7130i	−0.362822	+	0.209476i	−0.670318	−	0.742074i	$-0.733842\pi$
$223$	−80.9094	+	46.7130i	−0.362822	+	0.209476i	0.307496	+	0.951549i	$0.400509\pi$
$224$		−	442.196i		−	1.97409i
$225$		0			0
$226$	−121.635			−0.538207
$227$	98.9949	+	171.464i	0.436101	+	0.755349i	0.997385	−	0.0722743i	$-0.0230257\pi$
$227$	98.9949	+	171.464i	0.436101	+	0.755349i	−0.561284	+	0.827623i	$0.689692\pi$
$228$		0			0
$229$	−90.6197	+	156.958i	−0.395719	+	0.685406i	−0.993193	−	0.116483i	$-0.962838\pi$
$229$	−90.6197	+	156.958i	−0.395719	+	0.685406i	0.597473	+	0.801889i	$0.296171\pi$
$230$	−221.715	+	215.730i	−0.963976	+	0.937955i
$231$		0			0
$232$	−4.47750	+	2.58509i	−0.0192996	+	0.0111426i
$233$	−178.525			−0.766202			−0.383101	−	0.923706i	$-0.625144\pi$
$233$	−178.525			−0.766202			−0.383101	+	0.923706i	$0.625144\pi$
$234$		0			0
$235$	−238.505	−	67.4175i	−1.01491	−	0.286883i
$236$	−222.618	+	128.529i	−0.943298	+	0.544613i
$237$		0			0
$238$	−68.4093	−	39.4961i	−0.287434	−	0.165950i
$239$	−13.2157	−	7.63006i	−0.0552956	−	0.0319250i	0.472097	−	0.881546i	$-0.343497\pi$
$239$	−13.2157	−	7.63006i	−0.0552956	−	0.0319250i	−0.527393	+	0.849621i	$0.676830\pi$
$240$		0			0
$241$	159.583	+	276.406i	0.662170	+	1.14691i	0.980044	+	0.198779i	$0.0636976\pi$
$241$	159.583	+	276.406i	0.662170	+	1.14691i	−0.317874	+	0.948133i	$0.602969\pi$
$242$	−343.315			−1.41866
$243$		0			0
$244$	−90.3163			−0.370149
$245$	56.0648	+	221.304i	0.228836	+	0.903280i
$246$		0			0
$247$	8.61623	+	4.97458i	0.0348835	+	0.0201400i
$248$	−1.34594	+	2.33123i	−0.00542717	+	0.00940014i
$249$		0			0
$250$	−105.934	+	339.038i	−0.423734	+	1.35615i
$251$			95.3404i			0.379842i	0.981799	+	0.189921i	$0.0608232\pi$
$251$			95.3404i			0.379842i	−0.981799	+	0.189921i	$0.939177\pi$
$252$		0			0
$253$			9.32644i			0.0368634i
$254$	−193.729	+	111.850i	−0.762713	+	0.440352i
$255$		0			0
$256$	−123.079	+	213.179i	−0.480777	+	0.832730i
$257$	3.96637	−	6.86996i	0.0154334	−	0.0267313i	−0.858206	−	0.513306i	$-0.828421\pi$
$257$	3.96637	−	6.86996i	0.0154334	−	0.0267313i	0.873639	+	0.486575i	$0.161754\pi$
$258$		0			0
$259$	−70.9631	−	122.912i	−0.273989	−	0.474562i
$260$	103.922	−	367.647i	0.399699	−	1.41403i
$261$		0			0
$262$		−	519.399i		−	1.98244i
$263$	−205.189	−	355.399i	−0.780188	−	1.35133i	−0.931832	−	0.362890i	$-0.881790\pi$
$263$	−205.189	−	355.399i	−0.780188	−	1.35133i	0.151644	−	0.988435i	$-0.451543\pi$
$264$		0			0
$265$	159.783	−	155.469i	0.602953	−	0.586677i
$266$	−12.7034	−	7.33429i	−0.0477570	−	0.0275725i
$267$		0			0
$268$	114.844	−	66.3052i	0.428522	−	0.247408i
$269$			201.081i			0.747513i	0.927527	+	0.373757i	$0.121930\pi$
$269$			201.081i			0.747513i	−0.927527	+	0.373757i	$0.878070\pi$
$270$		0			0
$271$	121.070			0.446751			0.223376	−	0.974732i	$-0.428292\pi$
$271$	121.070			0.446751			0.223376	+	0.974732i	$0.428292\pi$
$272$	22.4220	+	38.8360i	0.0824337	+	0.142779i
$273$		0			0
$274$	7.90527	−	13.6923i	0.0288514	−	0.0499720i
$275$	5.09870	+	9.41717i	0.0185407	+	0.0342443i
$276$		0			0
$277$	290.125	−	167.504i	1.04738	−	0.604707i	0.125468	−	0.992098i	$-0.459957\pi$
$277$	290.125	−	167.504i	1.04738	−	0.604707i	0.921916	+	0.387391i	$0.126624\pi$
$278$	482.849			1.73687
$279$		0			0
$280$	−2.81284	+	9.95105i	−0.0100458	+	0.0355395i
$281$	−120.265	+	69.4349i	−0.427989	+	0.247099i	−0.698489	−	0.715620i	$-0.746144\pi$
$281$	−120.265	+	69.4349i	−0.427989	+	0.247099i	0.270501	+	0.962720i	$0.412811\pi$
$282$		0			0
$283$	83.8352	+	48.4023i	0.296237	+	0.171033i	0.640751	−	0.767748i	$-0.278623\pi$
$283$	83.8352	+	48.4023i	0.296237	+	0.171033i	−0.344514	+	0.938781i	$0.611956\pi$
$284$	317.210	+	183.141i	1.11694	+	0.644864i
$285$		0			0
$286$	−11.4126	−	19.7672i	−0.0399042	−	0.0691162i
$287$	−372.083			−1.29646
$288$		0			0
$289$	−280.837			−0.971753
$290$	−334.984	+	84.8643i	−1.15512	+	0.292636i
$291$		0			0
$292$	509.316	+	294.054i	1.74423	+	1.00703i
$293$	192.539	−	333.488i	0.657131	−	1.13818i	−0.324224	−	0.945980i	$-0.605103\pi$
$293$	192.539	−	333.488i	0.657131	−	1.13818i	0.981355	−	0.192204i	$-0.0615635\pi$
$294$		0			0
$295$	−305.764	+	77.4617i	−1.03649	+	0.262582i
$296$		−	3.10093i		−	0.0104761i
$297$		0			0
$298$			229.417i			0.769854i
$299$	353.580	−	204.140i	1.18254	−	0.682742i
$300$		0			0
$301$	281.012	−	486.726i	0.933593	−	1.61703i
$302$	125.421	−	217.236i	0.415302	−	0.719324i
$303$		0			0
$304$	4.16368	+	7.21171i	0.0136963	+	0.0237227i
$305$	−106.644	−	30.1448i	−0.349653	−	0.0988354i
$306$		0			0
$307$		−	207.311i		−	0.675281i	−0.941275	−	0.337641i	$-0.890371\pi$
$307$		−	207.311i		−	0.675281i	0.941275	−	0.337641i	$-0.109629\pi$
$308$	8.49105	+	14.7069i	0.0275684	+	0.0477498i
$309$		0			0
$310$	−128.952	+	125.471i	−0.415974	+	0.404745i
$311$	−140.437	−	81.0816i	−0.451567	−	0.260712i	0.256925	−	0.966431i	$-0.417291\pi$
$311$	−140.437	−	81.0816i	−0.451567	−	0.260712i	−0.708492	+	0.705719i	$0.750624\pi$
$312$		0			0
$313$	196.427	−	113.407i	0.627561	−	0.362322i	−0.152246	−	0.988343i	$-0.548651\pi$
$313$	196.427	−	113.407i	0.627561	−	0.362322i	0.779807	+	0.626020i	$0.215317\pi$
$314$			178.302i			0.567840i
$315$		0			0
$316$	204.751			0.647946
$317$	−244.388	−	423.293i	−0.770941	−	1.33531i	−0.937048	−	0.349200i	$-0.886453\pi$
$317$	−244.388	−	423.293i	−0.770941	−	1.33531i	0.166108	−	0.986108i	$-0.446880\pi$
$318$		0			0
$319$	−5.20917	+	9.02255i	−0.0163297	+	0.0282839i
$320$	237.845	−	231.425i	0.743267	−	0.723203i
$321$		0			0
$322$	−521.302	+	300.974i	−1.61895	+	0.934702i
$323$	1.51593			0.00469328
$324$		0			0
$325$	245.418	−	399.426i	0.755134	−	1.22900i
$326$	594.157	−	343.036i	1.82257	−	1.05226i
$327$		0			0
$328$	−7.04044	−	4.06480i	−0.0214647	−	0.0123927i
$329$	−417.667	−	241.140i	−1.26951	−	0.732950i
$330$		0			0
$331$	−118.823	−	205.808i	−0.358982	−	0.621775i	0.628809	−	0.777560i	$-0.283543\pi$
$331$	−118.823	−	205.808i	−0.358982	−	0.621775i	−0.987791	+	0.155785i	$0.950209\pi$
$332$	311.768			0.939061
$333$		0			0
$334$	378.431			1.13303
$335$	157.737	−	39.9608i	0.470856	−	0.119286i
$336$		0			0
$337$	−244.250	−	141.018i	−0.724777	−	0.418450i	0.0917314	−	0.995784i	$-0.470760\pi$
$337$	−244.250	−	141.018i	−0.724777	−	0.418450i	−0.816508	+	0.577334i	$0.804093\pi$
$338$	−259.488	+	449.447i	−0.767717	+	1.32973i
$339$		0			0
$340$	−14.2958	−	56.4296i	−0.0420465	−	0.165969i
$341$			5.42437i			0.0159072i
$342$		0			0
$343$		−	32.5057i		−	0.0947688i
$344$	10.6344	−	6.13979i	0.0309140	−	0.0178482i
$345$		0			0
$346$	−95.2543	+	164.985i	−0.275302	+	0.476836i
$347$	−219.985	+	381.026i	−0.633963	+	1.09806i	0.352771	+	0.935710i	$0.385240\pi$
$347$	−219.985	+	381.026i	−0.633963	+	1.09806i	−0.986734	+	0.162347i	$0.948094\pi$
$348$		0			0
$349$	48.6291	+	84.2280i	0.139338	+	0.241341i	0.927246	−	0.374452i	$-0.122169\pi$
$349$	48.6291	+	84.2280i	0.139338	+	0.241341i	−0.787908	+	0.615793i	$0.788836\pi$
$350$	−361.833	+	588.895i	−1.03381	+	1.68256i
$351$		0			0
$352$		−	19.4687i		−	0.0553089i
$353$	−49.0978	−	85.0399i	−0.139087	−	0.240906i	0.788064	−	0.615593i	$-0.211084\pi$
$353$	−49.0978	−	85.0399i	−0.139087	−	0.240906i	−0.927151	+	0.374687i	$0.877750\pi$
$354$		0			0
$355$	313.430	+	322.126i	0.882902	+	0.907396i
$356$	−102.192	−	59.0007i	−0.287057	−	0.165732i
$357$		0			0
$358$	93.4195	−	53.9358i	0.260948	−	0.150659i
$359$			500.068i			1.39295i	0.717582	+	0.696474i	$0.245249\pi$
$359$			500.068i			1.39295i	−0.717582	+	0.696474i	$0.754751\pi$
$360$		0			0
$361$	−360.718			−0.999220
$362$	395.003	+	684.165i	1.09117	+	1.88996i
$363$		0			0
$364$	371.709	−	643.819i	1.02118	−	1.76873i
$365$	503.246	+	517.208i	1.37876	+	1.41701i
$366$		0			0
$367$	−296.023	+	170.909i	−0.806603	+	0.465692i	−0.845775	−	0.533540i	$-0.820861\pi$
$367$	−296.023	+	170.909i	−0.806603	+	0.465692i	0.0391718	+	0.999232i	$0.487528\pi$
$368$	341.726			0.928604
$369$		0			0
$370$	56.3769	−	199.446i	0.152370	−	0.539044i
$371$	375.686	−	216.902i	1.01263	−	0.584643i
$372$		0			0
$373$	−529.179	−	305.522i	−1.41871	−	0.819093i	−0.422525	−	0.906351i	$-0.638856\pi$
$373$	−529.179	−	305.522i	−1.41871	−	0.819093i	−0.996186	+	0.0872584i	$0.972189\pi$
$374$	−3.01188	−	1.73891i	−0.00805316	−	0.00464949i
$375$		0			0
$376$	−5.26865	−	9.12556i	−0.0140124	−	0.0242701i
$377$	456.080			1.20976
$378$		0			0
$379$	187.436			0.494555			0.247277	−	0.968945i	$-0.420464\pi$
$379$	187.436			0.494555			0.247277	+	0.968945i	$0.420464\pi$
$380$	−2.65468	−	10.4788i	−0.00698600	−	0.0275757i
$381$		0			0
$382$	−143.486	−	82.8415i	−0.375617	−	0.216863i
$383$	−73.9088	+	128.014i	−0.192973	+	0.334240i	−0.946234	−	0.323482i	$-0.895146\pi$
$383$	−73.9088	+	128.014i	−0.192973	+	0.334240i	0.753261	+	0.657722i	$0.228480\pi$
$384$		0			0
$385$	5.11739	+	20.1998i	0.0132919	+	0.0524670i
$386$		−	359.656i		−	0.931752i
$387$		0			0
$388$			93.6797i			0.241442i
$389$	397.890	−	229.722i	1.02285	−	0.590545i	0.107924	−	0.994159i	$-0.465580\pi$
$389$	397.890	−	229.722i	1.02285	−	0.590545i	0.914929	+	0.403615i	$0.132246\pi$
$390$		0			0
$391$	31.1042	−	53.8741i	0.0795505	−	0.137786i
$392$	−4.85295	+	8.40556i	−0.0123800	+	0.0214428i
$393$		0			0
$394$	476.763	+	825.777i	1.21006	+	2.09588i
$395$	241.767	+	68.3396i	0.612068	+	0.173012i
$396$		0			0
$397$			718.905i			1.81084i	0.424512	+	0.905422i	$0.360446\pi$
$397$			718.905i			1.81084i	−0.424512	+	0.905422i	$0.639554\pi$
$398$	−180.671	−	312.932i	−0.453948	−	0.786260i
$399$		0			0
$400$	345.051	−	186.820i	0.862627	−	0.467049i
$401$	65.5957	+	37.8717i	0.163580	+	0.0944431i	0.579555	−	0.814933i	$-0.303226\pi$
$401$	65.5957	+	37.8717i	0.163580	+	0.0944431i	−0.415975	+	0.909376i	$0.636560\pi$
$402$		0			0
$403$	205.647	−	118.730i	0.510289	−	0.294616i
$404$			234.006i			0.579223i
$405$		0			0
$406$	−672.422			−1.65621
$407$	−3.12432	−	5.41148i	−0.00767646	−	0.0132960i
$408$		0			0
$409$	−255.035	+	441.733i	−0.623556	+	1.08003i	0.365262	+	0.930905i	$0.380979\pi$
$409$	−255.035	+	441.733i	−0.623556	+	1.08003i	−0.988818	+	0.149126i	$0.952354\pi$
$410$	−378.928	−	389.441i	−0.924214	−	0.949855i
$411$		0			0
$412$	−304.156	+	175.604i	−0.738242	+	0.426224i
$413$	−613.768			−1.48612
$414$		0			0
$415$	368.132	+	104.059i	0.887064	+	0.250744i
$416$	−738.092	+	426.137i	−1.77426	+	1.02437i
$417$		0			0
$418$	−0.559296	−	0.322910i	−0.00133803	−	0.000772511i
$419$	−603.768	−	348.586i	−1.44097	−	0.831947i	−0.443060	−	0.896492i	$-0.646107\pi$
$419$	−603.768	−	348.586i	−1.44097	−	0.831947i	−0.997915	+	0.0645450i	$0.979440\pi$
$420$		0			0
$421$	−378.410	−	655.425i	−0.898836	−	1.55683i	−0.828984	−	0.559272i	$-0.811081\pi$
$421$	−378.410	−	655.425i	−0.898836	−	1.55683i	−0.0698516	−	0.997557i	$-0.522253\pi$
$422$	−277.672			−0.657990
$423$		0			0
$424$	9.47815			0.0223541
$425$	1.95420	−	71.4027i	0.00459812	−	0.168006i
$426$		0			0
$427$	−186.754	−	107.823i	−0.437364	−	0.252512i
$428$	197.815	−	342.626i	0.462186	−	0.800529i
$429$		0			0
$430$	795.613	−	201.560i	1.85026	−	0.468743i
$431$		−	497.875i		−	1.15516i	−0.816333	−	0.577581i	$-0.803997\pi$
$431$		−	497.875i		−	1.15516i	0.816333	−	0.577581i	$-0.196003\pi$
$432$		0			0
$433$			421.645i			0.973775i	0.873465	+	0.486888i	$0.161868\pi$
$433$			421.645i			0.973775i	−0.873465	+	0.486888i	$0.838132\pi$
$434$	−303.196	+	175.050i	−0.698608	+	0.403341i
$435$		0			0
$436$	−335.143	+	580.485i	−0.768677	+	1.33139i
$437$	5.77595	−	10.0042i	0.0132173	−	0.0228930i
$438$		0			0
$439$	−228.743	−	396.195i	−0.521055	−	0.902494i	−0.999700	−	0.0244857i	$-0.992205\pi$
$439$	−228.743	−	396.195i	−0.521055	−	0.902494i	0.478645	−	0.878009i	$-0.341128\pi$
$440$	−0.123842	+	0.438118i	−0.000281458	+	0.000995724i
$441$		0			0
$442$			152.247i			0.344450i
$443$	116.136	+	201.153i	0.262157	+	0.454069i	0.966815	−	0.255478i	$-0.0822328\pi$
$443$	116.136	+	201.153i	0.262157	+	0.454069i	−0.704658	+	0.709547i	$0.748899\pi$
$444$		0			0
$445$	−100.974	−	103.776i	−0.226909	−	0.233204i
$446$	−229.914	−	132.741i	−0.515502	−	0.297625i
$447$		0			0
$448$	559.230	−	322.871i	1.24828	−	0.720695i
$449$		−	678.345i		−	1.51079i	−0.655269	−	0.755395i	$-0.727445\pi$
$449$		−	678.345i		−	1.51079i	0.655269	−	0.755395i	$-0.272555\pi$
$450$		0			0
$451$	−16.3818			−0.0363234
$452$	−87.2105	−	151.053i	−0.192943	−	0.334188i
$453$		0			0
$454$	−281.306	+	487.236i	−0.619617	+	1.07321i
$455$	653.796	−	636.148i	1.43691	−	1.39813i
$456$		0			0
$457$	637.008	−	367.777i	1.39389	−	0.804763i	0.400147	−	0.916451i	$-0.368959\pi$
$457$	637.008	−	367.777i	1.39389	−	0.804763i	0.993743	+	0.111688i	$0.0356258\pi$
$458$	−515.014			−1.12448
$459$		0			0
$460$	−426.872	−	120.663i	−0.927982	−	0.262310i
$461$	−344.752	+	199.043i	−0.747835	+	0.431763i	−0.824911	−	0.565263i	$-0.808775\pi$
$461$	−344.752	+	199.043i	−0.747835	+	0.431763i	0.0770763	+	0.997025i	$0.475441\pi$
$462$		0			0
$463$	−139.076	−	80.2955i	−0.300380	−	0.173424i	0.342234	−	0.939615i	$-0.388817\pi$
$463$	−139.076	−	80.2955i	−0.300380	−	0.173424i	−0.642613	+	0.766191i	$0.722150\pi$
$464$	330.592	+	190.867i	0.712482	+	0.411352i
$465$		0			0
$466$	−253.650	−	439.335i	−0.544314	−	0.942780i
$467$	406.660			0.870792			0.435396	−	0.900239i	$-0.356608\pi$
$467$	406.660			0.870792			0.435396	+	0.900239i	$0.356608\pi$
$468$		0			0
$469$	316.630			0.675117
$470$	−172.961	−	682.728i	−0.368003	−	1.45261i
$471$		0			0
$472$	−11.6135	−	6.70507i	−0.0246049	−	0.0142057i
$473$	12.3722	−	21.4293i	0.0261569	−	0.0453050i
$474$		0			0
$475$	0.362888	−	13.2592i	0.000763975	−	0.0279142i
$476$		−	113.273i		−	0.237968i
$477$		0			0
$478$		−	43.3635i		−	0.0907186i
$479$	−731.450	+	422.303i	−1.52704	+	0.881635i	−0.527552	+	0.849523i	$0.676890\pi$
$479$	−731.450	+	422.303i	−1.52704	+	0.881635i	−0.999484	+	0.0321123i	$0.989777\pi$
$480$		0			0
$481$	−136.772	+	236.896i	−0.284349	+	0.492507i
$482$	−453.474	+	785.440i	−0.940818	+	1.62954i
$483$		0			0
$484$	−246.152	−	426.348i	−0.508579	−	0.880884i
$485$	−31.2674	+	110.616i	−0.0644689	+	0.228073i
$486$		0			0
$487$			225.518i			0.463075i	0.972826	+	0.231538i	$0.0743757\pi$
$487$			225.518i			0.463075i	−0.972826	+	0.231538i	$0.925624\pi$
$488$	−2.35580	−	4.08037i	−0.00482746	−	0.00836141i
$489$		0			0
$490$	−464.952	+	452.401i	−0.948882	+	0.923268i
$491$	662.639	+	382.575i	1.34957	+	0.779175i	0.988189	−	0.153243i	$-0.0489717\pi$
$491$	662.639	+	382.575i	1.34957	+	0.779175i	0.361382	+	0.932418i	$0.382305\pi$
$492$		0			0
$493$	60.1815	−	34.7458i	0.122072	−	0.0704783i
$494$			28.2718i			0.0572303i
$495$		0			0
$496$	198.752			0.400710
$497$	437.281	+	757.392i	0.879841	+	1.52393i
$498$		0			0
$499$	102.024	−	176.711i	0.204458	−	0.354131i	−0.745502	−	0.666503i	$-0.767790\pi$
$499$	102.024	−	176.711i	0.204458	−	0.354131i	0.949960	+	0.312372i	$0.101124\pi$
$500$	−496.990	+	111.532i	−0.993980	+	0.223063i
$501$		0			0
$502$	−234.625	+	135.461i	−0.467380	+	0.269842i
$503$	585.545			1.16411			0.582053	−	0.813151i	$-0.302250\pi$
$503$	585.545			1.16411			0.582053	+	0.813151i	$0.302250\pi$
$504$		0			0
$505$	−78.1041	+	276.311i	−0.154662	+	0.547151i
$506$	−22.9516	+	13.2511i	−0.0453588	+	0.0261879i
$507$		0			0
$508$	−277.802	−	160.389i	−0.546855	−	0.315727i
$509$	−10.3361	−	5.96756i	−0.0203067	−	0.0117241i	0.489812	−	0.871828i	$-0.337065\pi$
$509$	−10.3361	−	5.96756i	−0.0203067	−	0.0117241i	−0.510119	+	0.860104i	$0.670399\pi$
$510$		0			0
$511$	702.102	+	1216.08i	1.37398	+	2.37980i
$512$	−726.692			−1.41932
$513$		0			0
$514$	22.5418			0.0438557
$515$	−417.754	+	105.833i	−0.811173	+	0.205502i
$516$		0			0
$517$	−18.3888	−	10.6168i	−0.0355683	−	0.0205354i
$518$	201.650	−	349.268i	0.389286	−	0.674263i
$519$		0			0
$520$	19.3205	−	4.89462i	0.0371548	−	0.00941274i
$521$		−	541.869i		−	1.04006i	−0.854149	−	0.520028i	$-0.825922\pi$
$521$		−	541.869i		−	1.04006i	0.854149	−	0.520028i	$-0.174078\pi$
$522$		0			0
$523$		−	356.100i		−	0.680880i	−0.940266	−	0.340440i	$-0.889424\pi$
$523$		−	356.100i		−	0.680880i	0.940266	−	0.340440i	$-0.110576\pi$
$524$	645.020	−	372.402i	1.23095	−	0.710692i
$525$		0			0
$526$	583.071	−	1009.91i	1.10850	−	1.91998i
$527$	18.0906	−	31.3338i	0.0343275	−	0.0594570i
$528$		0			0
$529$	27.4749	+	47.5879i	0.0519374	+	0.0899582i
$530$	609.618	+	172.319i	1.15022	+	0.325130i
$531$		0			0
$532$		−	21.0344i		−	0.0395383i
$533$	358.571	+	621.062i	0.672740	+	1.16522i
$534$		0			0
$535$	347.936	−	338.544i	0.650347	−	0.632792i
$536$	5.99116	+	3.45900i	0.0111775	+	0.00645336i
$537$		0			0
$538$	−494.843	+	285.698i	−0.919783	+	0.531037i
$539$			19.5582i			0.0362862i
$540$		0			0
$541$	378.892			0.700355			0.350178	−	0.936683i	$-0.386121\pi$
$541$	378.892			0.700355			0.350178	+	0.936683i	$0.386121\pi$
$542$	172.017	+	297.942i	0.317375	+	0.549709i
$543$		0			0
$544$	−64.9294	+	112.461i	−0.119356	+	0.206730i
$545$	−589.480	+	573.568i	−1.08161	+	1.05242i
$546$		0			0
$547$	−484.407	+	279.673i	−0.885571	+	0.511285i	−0.872491	−	0.488630i	$-0.837497\pi$
$547$	−484.407	+	279.673i	−0.885571	+	0.511285i	−0.0130799	+	0.999914i	$0.504164\pi$
$548$	22.6719			0.0413721
$549$		0			0
$550$	−15.9306	+	25.9275i	−0.0289647	+	0.0471409i
$551$	11.1755	−	6.45218i	0.0202822	−	0.0117099i
$552$		0			0
$553$	423.380	+	244.439i	0.765606	+	0.442023i
$554$	824.426	+	475.982i	1.48813	+	0.859174i
$555$		0			0
$556$	346.196	+	599.629i	0.622655	+	1.07847i
$557$	−471.971			−0.847345			−0.423673	−	0.905815i	$-0.639259\pi$
$557$	−471.971			−0.847345			−0.423673	+	0.905815i	$0.639259\pi$
$558$		0			0
$559$	−1083.23			−1.93779
$560$	740.132	−	187.504i	1.32167	−	0.334829i
$561$		0			0
$562$	−341.747	−	197.308i	−0.608090	−	0.351081i
$563$	247.289	−	428.316i	0.439234	−	0.760775i	−0.558397	−	0.829574i	$-0.688583\pi$
$563$	247.289	−	428.316i	0.439234	−	0.760775i	0.997631	+	0.0687990i	$0.0219167\pi$
$564$		0			0
$565$	−52.5600	−	207.469i	−0.0930265	−	0.367202i
$566$			275.082i			0.486010i
$567$		0			0
$568$			19.1082i			0.0336412i
$569$	−143.305	+	82.7370i	−0.251853	+	0.145408i	−0.620613	−	0.784117i	$-0.713116\pi$
$569$	−143.305	+	82.7370i	−0.251853	+	0.145408i	0.368759	+	0.929525i	$0.379783\pi$
$570$		0			0
$571$	−25.5302	+	44.2195i	−0.0447113	+	0.0774423i	−0.887515	−	0.460779i	$-0.847570\pi$
$571$	−25.5302	+	44.2195i	−0.0447113	+	0.0774423i	0.842804	+	0.538221i	$0.180903\pi$
$572$	16.3654	−	28.3457i	0.0286108	−	0.0495554i
$573$		0			0
$574$	−528.660	−	915.665i	−0.921010	−	1.59524i
$575$	−463.770	−	284.953i	−0.806557	−	0.495571i
$576$		0			0
$577$			707.833i			1.22675i	0.789793	+	0.613373i	$0.210188\pi$
$577$			707.833i			1.22675i	−0.789793	+	0.613373i	$0.789812\pi$
$578$	−399.015	−	691.115i	−0.690338	−	1.19570i
$579$		0			0
$580$	−345.568	−	355.155i	−0.595807	−	0.612337i
$581$	644.669	+	372.200i	1.10958	+	0.640619i
$582$		0			0
$583$	16.5405	−	9.54964i	0.0283713	−	0.0163802i
$584$			30.6803i			0.0525347i
$585$		0			0
$586$	1094.25			1.86732
$587$	−226.251	−	391.878i	−0.385436	−	0.667594i	0.606394	−	0.795164i	$-0.292615\pi$
$587$	−226.251	−	391.878i	−0.385436	−	0.667594i	−0.991830	+	0.127570i	$0.959282\pi$
$588$		0			0
$589$	3.35936	−	5.81859i	0.00570350	−	0.00987875i
$590$	−625.059	−	642.400i	−1.05942	−	1.08881i
$591$		0			0
$592$	−198.280	+	114.477i	−0.334932	+	0.193373i
$593$	−227.811			−0.384168			−0.192084	−	0.981379i	$-0.561525\pi$
$593$	−227.811			−0.384168			−0.192084	+	0.981379i	$0.561525\pi$
$594$		0			0
$595$	37.8070	−	133.751i	0.0635411	−	0.224791i
$596$	−284.903	+	164.489i	−0.478024	+	0.275988i
$597$		0			0
$598$	1004.74	+	580.088i	1.68017	+	0.970047i
$599$	484.611	+	279.790i	0.809033	+	0.467096i	0.846620	−	0.532198i	$-0.178634\pi$
$599$	484.611	+	279.790i	0.809033	+	0.467096i	−0.0375869	+	0.999293i	$0.511967\pi$
$600$		0			0
$601$	−335.271	−	580.707i	−0.557856	−	0.966235i	−0.997675	−	0.0681485i	$-0.978291\pi$
$601$	−335.271	−	580.707i	−0.557856	−	0.966235i	0.439819	−	0.898086i	$-0.355043\pi$
$602$	1597.06			2.65292
$603$		0			0
$604$	359.701			0.595532
$605$	−148.351	−	585.583i	−0.245208	−	0.967906i
$606$		0			0
$607$	−864.308	−	499.009i	−1.42390	−	0.822090i	−0.427272	−	0.904123i	$-0.640525\pi$
$607$	−864.308	−	499.009i	−1.42390	−	0.822090i	−0.996630	+	0.0820329i	$0.973859\pi$
$608$	−12.0572	+	20.8836i	−0.0198309	+	0.0343481i
$609$		0			0
$610$	−77.3373	−	305.272i	−0.126782	−	0.500446i
$611$			929.533i			1.52133i
$612$		0			0
$613$		−	229.314i		−	0.374086i	−0.982352	−	0.187043i	$-0.940110\pi$
$613$		−	229.314i		−	0.374086i	0.982352	−	0.187043i	$-0.0598903\pi$
$614$	510.176	−	294.550i	0.830905	−	0.479723i
$615$		0			0
$616$	−0.442960	+	0.767229i	−0.000719091	+	0.00124550i
$617$	248.717	−	430.791i	0.403108	−	0.698203i	−0.590992	−	0.806678i	$-0.701263\pi$
$617$	248.717	−	430.791i	0.403108	−	0.698203i	0.994099	+	0.108475i	$0.0345967\pi$
$618$		0			0
$619$	528.867	+	916.025i	0.854390	+	1.47985i	0.877210	+	0.480107i	$0.159402\pi$
$619$	528.867	+	916.025i	0.854390	+	1.47985i	−0.0228204	+	0.999740i	$0.507265\pi$
$620$	−248.274	−	70.1788i	−0.400441	−	0.113192i
$621$		0			0
$622$		−	460.806i		−	0.740846i
$623$	−140.874	−	244.001i	−0.226122	−	0.391655i
$624$		0			0
$625$	−624.064	−	34.1853i	−0.998503	−	0.0546964i
$626$	558.170	+	322.259i	0.891645	+	0.514792i
$627$		0			0
$628$	−221.425	+	127.840i	−0.352588	+	0.203567i
$629$			41.6792i			0.0662626i
$630$		0			0
$631$	638.591			1.01203			0.506015	−	0.862524i	$-0.331118\pi$
$631$	638.591			1.01203			0.506015	+	0.862524i	$0.331118\pi$
$632$	5.34071	+	9.25037i	0.00845048	+	0.0146367i
$633$		0			0
$634$	694.458	−	1202.84i	1.09536	−	1.89722i
$635$	−274.492	−	282.107i	−0.432271	−	0.444263i
$636$		0			0
$637$	741.485	−	428.097i	1.16403	−	0.672051i
$638$	−29.6050			−0.0464028
$639$		0			0
$640$	32.7237	+	9.24991i	0.0511307	+	0.0144530i
$641$	−765.794	+	442.131i	−1.19469	+	0.689753i	−0.959366	−	0.282165i	$-0.908947\pi$
$641$	−765.794	+	442.131i	−1.19469	+	0.689753i	−0.235321	+	0.971918i	$0.575614\pi$
$642$		0			0
$643$	884.408	+	510.613i	1.37544	+	0.794111i	0.991607	−	0.129291i	$-0.0412702\pi$
$643$	884.408	+	510.613i	1.37544	+	0.794111i	0.383834	+	0.923402i	$0.374604\pi$
$644$	−747.534	−	431.589i	−1.16077	−	0.670169i
$645$		0			0
$646$	2.15385	+	3.73057i	0.00333413	+	0.00577488i
$647$	−488.043			−0.754317			−0.377159	−	0.926149i	$-0.623099\pi$
$647$	−488.043			−0.754317			−0.377159	+	0.926149i	$0.623099\pi$
$648$		0			0
$649$	−27.0226			−0.0416373
$650$	1331.65	+	36.4454i	2.04869	+	0.0560699i
$651$		0			0
$652$	852.005	+	491.905i	1.30676	+	0.754456i
$653$	−305.648	+	529.397i	−0.468067	+	0.810716i	−0.999334	−	0.0364887i	$-0.988383\pi$
$653$	−305.648	+	529.397i	−0.468067	+	0.810716i	0.531267	+	0.847204i	$0.321716\pi$
$654$		0			0
$655$	885.927	−	224.439i	1.35256	−	0.342656i
$656$			600.240i			0.915001i
$657$		0			0
$658$		−	1370.46i		−	2.08276i
$659$	−125.687	+	72.5657i	−0.190724	+	0.110115i	−0.592322	−	0.805702i	$-0.701789\pi$
$659$	−125.687	+	72.5657i	−0.190724	+	0.110115i	0.401597	+	0.915816i	$0.368455\pi$
$660$		0			0
$661$	−415.128	+	719.023i	−0.628030	+	1.08778i	0.359916	+	0.932985i	$0.382805\pi$
$661$	−415.128	+	719.023i	−0.628030	+	1.08778i	−0.987947	+	0.154796i	$0.950528\pi$
$662$	337.650	−	584.827i	0.510045	−	0.883424i
$663$		0			0
$664$	8.13214	+	14.0853i	0.0122472	+	0.0212128i
$665$	7.02063	−	24.8371i	0.0105573	−	0.0373490i
$666$		0			0
$667$		−	529.550i		−	0.793929i
$668$	271.330	+	469.957i	0.406182	+	0.703529i
$669$		0			0
$670$	322.454	+	331.400i	0.481275	+	0.494627i
$671$	−8.22230	−	4.74715i	−0.0122538	−	0.00707473i
$672$		0			0
$673$	−235.054	+	135.708i	−0.349262	+	0.201647i	−0.664360	−	0.747412i	$-0.731296\pi$
$673$	−235.054	+	135.708i	−0.349262	+	0.201647i	0.315098	+	0.949059i	$0.397963\pi$
$674$		−	801.438i		−	1.18908i
$675$		0			0
$676$	−744.199			−1.10089
$677$	−447.970	−	775.906i	−0.661698	−	1.14609i	−0.980169	−	0.198162i	$-0.936503\pi$
$677$	−447.970	−	775.906i	−0.661698	−	1.14609i	0.318471	−	0.947933i	$-0.396831\pi$
$678$		0			0
$679$	−111.838	+	193.709i	−0.164710	+	0.285286i
$680$	2.17652	−	2.11777i	0.00320077	−	0.00311437i
$681$		0			0
$682$	−13.3489	+	7.70700i	−0.0195732	+	0.0113006i
$683$	255.548			0.374155			0.187078	−	0.982345i	$-0.440098\pi$
$683$	255.548			0.374155			0.187078	+	0.982345i	$0.440098\pi$
$684$		0			0
$685$	26.7706	+	7.56719i	0.0390812	+	0.0110470i
$686$	79.9938	−	46.1844i	0.116609	−	0.0673242i
$687$		0			0
$688$	−785.182	−	453.325i	−1.14125	−	0.658902i
$689$	−724.085	−	418.051i	−1.05092	−	0.606750i
$690$		0			0
$691$	−61.2973	−	106.170i	−0.0887081	−	0.153647i	0.818257	−	0.574852i	$-0.194940\pi$
$691$	−61.2973	−	106.170i	−0.0887081	−	0.153647i	−0.906965	+	0.421205i	$0.861607\pi$
$692$	−273.184			−0.394775
$693$		0			0
$694$	−1250.23			−1.80148
$695$	208.646	+	823.583i	0.300209	+	1.18501i
$696$		0			0
$697$	94.6296	+	54.6344i	0.135767	+	0.0783852i
$698$	−138.185	+	239.344i	−0.197973	+	0.342900i
$699$		0			0
$700$	−990.753	−	27.1156i	−1.41536	−	0.0387366i
$701$		−	595.027i		−	0.848826i	−0.905469	−	0.424413i	$-0.860480\pi$
$701$		−	595.027i		−	0.848826i	0.905469	−	0.424413i	$-0.139520\pi$
$702$		0			0
$703$			7.73968i			0.0110095i
$704$	24.6214	−	14.2152i	0.0349736	−	0.0201920i
$705$		0			0
$706$	139.517	−	241.651i	0.197617	−	0.342282i
$707$	−279.365	+	483.874i	−0.395141	+	0.684404i
$708$		0			0
$709$	−280.492	−	485.826i	−0.395616	−	0.685227i	0.597564	−	0.801822i	$-0.296136\pi$
$709$	−280.492	−	485.826i	−0.395616	−	0.685227i	−0.993180	+	0.116594i	$0.962802\pi$
$710$	−347.399	+	1229.00i	−0.489295	+	1.73099i
$711$		0			0
$712$		−	6.15588i		−	0.00864589i
$713$	−137.857	−	238.775i	−0.193347	−	0.334887i
$714$		0			0
$715$	28.7849	−	28.0079i	0.0402586	−	0.0391719i
$716$	133.961	+	77.3424i	0.187096	+	0.108020i
$717$		0			0
$718$	−1230.63	+	710.502i	−1.71396	+	0.989557i
$719$			1218.37i			1.69453i	0.531168	+	0.847266i	$0.321753\pi$
$719$			1218.37i			1.69453i	−0.531168	+	0.847266i	$0.678247\pi$
$720$		0			0
$721$	−838.570			−1.16307
$722$	−512.513	−	887.698i	−0.709851	−	1.22950i
$723$		0			0
$724$	−566.423	+	981.074i	−0.782353	+	1.35507i
$725$	−289.502	−	534.702i	−0.399313	−	0.737520i
$726$		0			0
$727$	687.921	−	397.172i	0.946247	−	0.546316i	0.0543338	−	0.998523i	$-0.482696\pi$
$727$	687.921	−	397.172i	0.946247	−	0.546316i	0.891913	+	0.452207i	$0.149363\pi$
$728$	38.7825			0.0532727
$729$		0			0
$730$	−557.788	+	1973.30i	−0.764093	+	2.70315i
$731$	−142.936	+	82.5241i	−0.195535	+	0.112892i
$732$		0			0
$733$	−681.408	−	393.411i	−0.929615	−	0.536714i	−0.0429255	−	0.999078i	$-0.513668\pi$
$733$	−681.408	−	393.411i	−0.929615	−	0.536714i	−0.886690	+	0.462365i	$0.847001\pi$
$734$	−841.186	−	485.659i	−1.14603	−	0.661661i
$735$		0			0
$736$	494.785	+	856.992i	0.672262	+	1.16439i
$737$	13.9404			0.0189150
$738$		0			0
$739$	1398.66			1.89264			0.946320	−	0.323231i	$-0.104769\pi$
$739$	1398.66			1.89264			0.946320	+	0.323231i	$0.104769\pi$
$740$	288.105	−	72.9882i	0.389331	−	0.0986327i
$741$		0			0
$742$	1067.56	+	616.355i	1.43876	+	0.830667i
$743$	−274.315	+	475.127i	−0.369199	+	0.639471i	−0.989440	−	0.144940i	$-0.953701\pi$
$743$	−274.315	+	475.127i	−0.369199	+	0.639471i	0.620242	+	0.784411i	$0.287035\pi$
$744$		0			0
$745$	−391.310	+	99.1340i	−0.525248	+	0.133066i
$746$		−	1736.35i		−	2.32755i
$747$		0			0
$748$		−	4.98710i		−	0.00666725i
$749$	818.078	−	472.318i	1.09223	−	0.630598i
$750$		0			0
$751$	133.681	−	231.542i	0.178003	−	0.308311i	−0.763193	−	0.646170i	$-0.776370\pi$
$751$	133.681	−	231.542i	0.178003	−	0.308311i	0.941197	+	0.337859i	$0.109703\pi$
$752$	−389.005	+	673.777i	−0.517294	+	0.895980i
$753$		0			0
$754$	648.003	+	1122.37i	0.859420	+	1.48856i
$755$	424.730	+	120.057i	0.562556	+	0.159016i
$756$		0			0
$757$		−	471.386i		−	0.622703i	−0.950295	−	0.311351i	$-0.899218\pi$
$757$		−	471.386i		−	0.622703i	0.950295	−	0.311351i	$-0.100782\pi$
$758$	266.311	+	461.265i	0.351334	+	0.608529i
$759$		0			0
$760$	0.404173	−	0.393263i	0.000531806	−	0.000517451i
$761$	−917.999	−	530.007i	−1.20631	−	0.696461i	−0.244356	−	0.969686i	$-0.578576\pi$
$761$	−917.999	−	530.007i	−1.20631	−	0.696461i	−0.961950	+	0.273225i	$0.911910\pi$
$762$		0			0
$763$	−1386.00	+	800.210i	−1.81652	+	1.04877i
$764$		−	237.585i		−	0.310975i
$765$		0			0
$766$	−420.042			−0.548357
$767$	591.478	+	1024.47i	0.771158	+	1.33569i
$768$		0			0
$769$	−216.513	+	375.012i	−0.281551	+	0.487661i	−0.971767	−	0.235942i	$-0.924182\pi$
$769$	−216.513	+	375.012i	−0.281551	+	0.487661i	0.690216	+	0.723604i	$0.257516\pi$
$770$	−42.4391	+	41.2935i	−0.0551158	+	0.0536280i
$771$		0			0
$772$	446.642	−	257.869i	0.578552	−	0.334027i
$773$	1088.28			1.40787			0.703936	−	0.710264i	$-0.251424\pi$
$773$	1088.28			1.40787			0.703936	+	0.710264i	$0.251424\pi$
$774$		0			0
$775$	−269.734	−	165.732i	−0.348044	−	0.213848i
$776$	−4.23232	+	2.44353i	−0.00545402	+	0.00314888i
$777$		0			0
$778$	1130.65	+	652.782i	1.45328	+	0.839052i
$779$	17.5724	+	10.1454i	0.0225576	+	0.0130237i
$780$		0			0
$781$	19.2523	+	33.3460i	0.0246509	+	0.0426965i
$782$	176.773			0.226052
$783$		0			0
$784$	716.626			0.914063
$785$	−304.125	+	77.0466i	−0.387420	+	0.0981485i
$786$		0			0
$787$	279.669	+	161.467i	0.355361	+	0.205168i	0.667044	−	0.745018i	$-0.267559\pi$
$787$	279.669	+	161.467i	0.355361	+	0.205168i	−0.311683	+	0.950186i	$0.600893\pi$
$788$	−683.665	+	1184.14i	−0.867595	+	1.50272i
$789$		0			0
$790$	175.327	+	692.065i	0.221933	+	0.876032i
$791$		−	416.459i		−	0.526497i
$792$		0			0
$793$			415.628i			0.524121i
$794$	−1769.17	+	1021.43i	−2.22817	+	1.28643i
$795$		0			0
$796$	259.078	−	448.736i	0.325474	−	0.563738i
$797$	722.713	−	1251.78i	0.906792	−	1.57061i	0.0882984	−	0.996094i	$-0.471857\pi$
$797$	722.713	−	1251.78i	0.906792	−	1.57061i	0.818494	−	0.574516i	$-0.194810\pi$
$798$		0			0
$799$	70.8152	+	122.656i	0.0886298	+	0.153511i
$800$	968.111	+	594.834i	1.21014	+	0.743542i
$801$		0			0
$802$			215.234i			0.268372i
$803$	30.9117	+	53.5406i	0.0384953	+	0.0666758i
$804$		0			0
$805$	−738.626	−	759.118i	−0.917548	−	0.943003i
$806$	584.370	+	337.386i	0.725024	+	0.418593i
$807$		0			0
$808$	−10.5721	+	6.10380i	−0.0130843	+	0.00755421i
$809$			981.839i			1.21365i	0.794837	+	0.606823i	$0.207556\pi$
$809$			981.839i			1.21365i	−0.794837	+	0.606823i	$0.792444\pi$
$810$		0			0
$811$	−600.049			−0.739888			−0.369944	−	0.929054i	$-0.620623\pi$
$811$	−600.049			−0.739888			−0.369944	+	0.929054i	$0.620623\pi$
$812$	−482.118	−	835.052i	−0.593741	−	1.02839i
$813$		0			0
$814$	8.87812	−	15.3774i	0.0109068	−	0.0188911i
$815$	841.852	+	865.207i	1.03295	+	1.06160i
$816$		0			0
$817$	−26.5427	+	15.3244i	−0.0324880	+	0.0187570i
$818$	−1449.42			−1.77191
$819$		0			0
$820$	211.943	−	749.798i	0.258467	−	0.914388i
$821$	896.354	−	517.510i	1.09178	−	0.630342i	0.157733	−	0.987482i	$-0.449582\pi$
$821$	896.354	−	517.510i	1.09178	−	0.630342i	0.934051	+	0.357140i	$0.116248\pi$
$822$		0			0
$823$	1219.38	+	704.012i	1.48163	+	0.855421i	0.999783	−	0.0208322i	$-0.00663158\pi$
$823$	1219.38	+	704.012i	1.48163	+	0.855421i	0.481850	+	0.876254i	$0.339965\pi$
$824$	−15.8672	−	9.16091i	−0.0192563	−	0.0111176i
$825$		0			0
$826$	−872.048	−	1510.43i	−1.05575	−	1.82861i
$827$	−1535.05			−1.85617			−0.928086	−	0.372367i	$-0.878546\pi$
$827$	−1535.05			−1.85617			−0.928086	+	0.372367i	$0.878546\pi$
$828$		0			0
$829$	−185.325			−0.223552			−0.111776	−	0.993733i	$-0.535654\pi$
$829$	−185.325			−0.223552			−0.111776	+	0.993733i	$0.535654\pi$
$830$	266.965	+	1053.79i	0.321645	+	1.26962i
$831$		0			0
$832$	−1077.84	−	622.292i	−1.29548	−	0.747947i
$833$	65.2280	−	112.978i	0.0783049	−	0.135628i
$834$		0			0
$835$	163.525	+	645.480i	0.195838	+	0.773030i
$836$		−	0.926087i		−	0.00110776i
$837$		0			0
$838$		−	1981.10i		−	2.36408i
$839$	1120.53	−	646.937i	1.33555	−	0.771081i	0.349408	−	0.936971i	$-0.386383\pi$
$839$	1120.53	−	646.937i	1.33555	−	0.771081i	0.986144	+	0.165889i	$0.0530494\pi$
$840$		0			0
$841$	−124.726	+	216.032i	−0.148307	+	0.256875i
$842$	1075.30	−	1862.47i	1.27708	−	2.21196i
$843$		0			0
$844$	−199.087	−	344.829i	−0.235885	−	0.408565i
$845$	−878.739	−	248.391i	−1.03993	−	0.293954i
$846$		0			0
$847$		−	1175.46i		−	1.38779i
$848$	−349.905	−	606.053i	−0.412623	−	0.714685i
$849$		0			0
$850$	178.493	−	96.6406i	0.209991	−	0.113695i
$851$	275.058	+	158.805i	0.323217	+	0.186610i
$852$		0			0
$853$	−335.726	+	193.832i	−0.393583	+	0.227235i	−0.683711	−	0.729752i	$-0.739635\pi$
$853$	−335.726	+	193.832i	−0.393583	+	0.227235i	0.290128	+	0.956988i	$0.406302\pi$
$854$		−	612.782i		−	0.717543i
$855$		0			0
$856$	20.6392			0.0241112
$857$	39.5696	+	68.5365i	0.0461722	+	0.0799726i	0.888188	−	0.459480i	$-0.151964\pi$
$857$	39.5696	+	68.5365i	0.0461722	+	0.0799726i	−0.842016	+	0.539453i	$0.818631\pi$
$858$		0			0
$859$	329.529	−	570.761i	0.383620	−	0.664448i	−0.607957	−	0.793970i	$-0.708011\pi$
$859$	329.529	−	570.761i	0.383620	−	0.664448i	0.991577	+	0.129521i	$0.0413441\pi$
$860$	820.752	+	843.522i	0.954363	+	0.980840i
$861$		0			0
$862$	1225.23	−	707.386i	1.42138	−	0.820633i
$863$	1070.61			1.24057			0.620286	−	0.784375i	$-0.287016\pi$
$863$	1070.61			1.24057			0.620286	+	0.784375i	$0.287016\pi$
$864$		0			0
$865$	−322.572	−	91.1805i	−0.372916	−	0.105411i
$866$	−1037.63	+	599.077i	−1.19819	+	0.691775i
$867$		0			0
$868$	−434.775	−	251.017i	−0.500892	−	0.289190i
$869$	18.6403	+	10.7620i	0.0214503	+	0.0123843i
$870$		0			0
$871$	−305.131	−	528.502i	−0.350322	−	0.606776i
$872$	−34.9674			−0.0401002
$873$		0			0
$874$	32.8261			0.0375585
$875$	−1160.82	−	362.701i	−1.32665	−	0.414515i
$876$		0			0
$877$	928.802	+	536.244i	1.05907	+	0.611452i	0.925174	−	0.379543i	$-0.123919\pi$
$877$	928.802	+	536.244i	1.05907	+	0.611452i	0.133893	+	0.990996i	$0.457252\pi$
$878$	650.002	−	1125.84i	0.740321	−	1.28227i
$879$		0			0
$880$	32.5861	−	8.25531i	0.0370296	−	0.00938104i
$881$		−	1433.62i		−	1.62726i	−0.581381	−	0.813632i	$-0.697487\pi$
$881$		−	1433.62i		−	1.62726i	0.581381	−	0.813632i	$-0.302513\pi$
$882$		0			0
$883$			731.816i			0.828784i	0.910099	+	0.414392i	$0.136006\pi$
$883$			731.816i			0.828784i	−0.910099	+	0.414392i	$0.863994\pi$
$884$	−189.069	+	109.159i	−0.213879	+	0.123483i
$885$		0			0
$886$	−330.013	+	571.600i	−0.372475	+	0.645146i
$887$	−642.482	+	1112.81i	−0.724331	+	1.25458i	0.234918	+	0.972015i	$0.424518\pi$
$887$	−642.482	+	1112.81i	−0.724331	+	1.25458i	−0.959249	+	0.282563i	$0.908815\pi$
$888$		0			0
$889$	−382.956	−	663.299i	−0.430772	−	0.746119i
$890$	111.918	−	395.935i	0.125750	−	0.444871i
$891$		0			0
$892$		−	380.693i		−	0.426786i
$893$	13.1501	+	22.7767i	0.0147258	+	0.0255058i
$894$		0			0
$895$	132.365	+	136.037i	0.147894	+	0.151997i
$896$	57.3054	+	33.0853i	0.0639569	+	0.0369255i
$897$		0			0
$898$	1669.35	−	963.800i	1.85896	−	1.07327i
$899$		−	307.993i		−	0.342595i
$900$		0			0
$901$	−127.395			−0.141392
$902$	−23.2755	−	40.3143i	−0.0258043	−	0.0446944i
$903$		0			0
$904$	4.54958	−	7.88010i	0.00503272	−	0.00871693i
$905$	−996.277	+	969.383i	−1.10086	+	1.07114i
$906$		0			0
$907$	−877.157	+	506.427i	−0.967097	+	0.558353i	−0.898350	−	0.439281i	$-0.855233\pi$
$907$	−877.157	+	506.427i	−0.967097	+	0.558353i	−0.0687467	+	0.997634i	$0.521900\pi$
$908$	−806.770			−0.888514
$909$		0			0
$910$	2494.43	+	705.092i	2.74113	+	0.774827i
$911$	−551.233	+	318.255i	−0.605086	+	0.349347i	−0.771040	−	0.636787i	$-0.780263\pi$
$911$	−551.233	+	318.255i	−0.605086	+	0.349347i	0.165954	+	0.986134i	$0.446930\pi$
$912$		0			0
$913$	28.3831	+	16.3870i	0.0310877	+	0.0179485i
$914$	1810.13	+	1045.08i	1.98045	+	1.14342i
$915$		0			0
$916$	−369.258	−	639.573i	−0.403120	−	0.698224i
$917$	1778.35			1.93931
$918$		0			0
$919$	1142.09			1.24275			0.621377	−	0.783511i	$-0.286573\pi$
$919$	1142.09			1.24275			0.621377	+	0.783511i	$0.286573\pi$
$920$	−5.68311	−	22.4328i	−0.00617729	−	0.0243835i
$921$		0			0
$922$	−979.654	−	565.603i	−1.06253	−	0.613453i
$923$	842.801	−	1459.77i	0.913110	−	1.58155i
$924$		0			0
$925$	364.552	+	9.97730i	0.394110	+	0.0107863i
$926$		−	456.338i		−	0.492806i
$927$		0			0
$928$			1105.42i			1.19119i
$929$	681.162	−	393.269i	0.733221	−	0.423325i	−0.0863784	−	0.996262i	$-0.527529\pi$
$929$	681.162	−	393.269i	0.733221	−	0.423325i	0.819599	+	0.572937i	$0.194196\pi$
$930$		0			0
$931$	12.1126	−	20.9796i	0.0130103	−	0.0225345i
$932$	363.728	−	629.995i	0.390266	−	0.675960i
$933$		0			0
$934$	577.787	+	1000.76i	0.618615	+	1.07147i
$935$	1.66454	−	5.88870i	0.00178026	−	0.00629807i
$936$		0			0
$937$			811.089i			0.865623i	0.901484	+	0.432812i	$0.142478\pi$
$937$			811.089i			0.865623i	−0.901484	+	0.432812i	$0.857522\pi$
$938$	449.871	+	779.199i	0.479606	+	0.830702i
$939$		0			0
$940$	723.839	−	704.300i	0.770042	−	0.749255i
$941$	715.505	+	413.097i	0.760367	+	0.438998i	0.829428	−	0.558614i	$-0.188667\pi$
$941$	715.505	+	413.097i	0.760367	+	0.438998i	−0.0690604	+	0.997612i	$0.522000\pi$
$942$		0			0
$943$	721.111	−	416.333i	0.764698	−	0.441499i
$944$			990.124i			1.04886i
$945$		0			0
$946$	70.3142			0.0743279
$947$	−458.725	−	794.535i	−0.484398	−	0.839002i	0.515441	−	0.856925i	$-0.327628\pi$
$947$	−458.725	−	794.535i	−0.484398	−	0.839002i	−0.999839	+	0.0179227i	$0.994295\pi$
$948$		0			0
$949$	1353.21	−	2343.83i	1.42593	−	2.46979i
$950$	33.1455	−	17.9458i	0.0348900	−	0.0188904i
$951$		0			0
$952$	5.11751	−	2.95460i	0.00537554	−	0.00310357i
$953$	−192.772			−0.202279			−0.101140	−	0.994872i	$-0.532249\pi$
$953$	−192.772			−0.202279			−0.101140	+	0.994872i	$0.532249\pi$
$954$		0			0
$955$	79.2986	−	280.537i	0.0830352	−	0.293756i
$956$	53.8513	−	31.0910i	0.0563298	−	0.0325220i
$957$		0			0
$958$	−2078.50	−	1200.03i	−2.16963	−	1.25264i
$959$	46.8805	+	27.0665i	0.0488848	+	0.0282236i
$960$		0			0
$961$	400.321	+	693.376i	0.416567	+	0.721515i
$962$	−777.308			−0.808012
$963$		0			0
$964$	−1300.54			−1.34911
$965$	613.457	−	155.412i	0.635707	−	0.161049i
$966$		0			0
$967$	−742.787	−	428.848i	−0.768136	−	0.443483i	0.0640734	−	0.997945i	$-0.479591\pi$
$967$	−742.787	−	428.848i	−0.768136	−	0.443483i	−0.832209	+	0.554462i	$0.812924\pi$
$968$	12.8412	−	22.2416i	0.0132657	−	0.0229769i
$969$		0			0
$970$	−316.641	+	80.2173i	−0.326434	+	0.0826983i
$971$			546.278i			0.562594i	0.959621	+	0.281297i	$0.0907645\pi$
$971$			546.278i			0.562594i	−0.959621	+	0.281297i	$0.909235\pi$
$972$		0			0
$973$			1653.20i			1.69908i
$974$	−554.980	+	320.418i	−0.569795	+	0.328971i
$975$		0			0
$976$	−173.938	+	301.270i	−0.178215	+	0.308678i
$977$	397.664	−	688.774i	0.407025	−	0.704988i	−0.587530	−	0.809203i	$-0.699899\pi$
$977$	397.664	−	688.774i	0.407025	−	0.704988i	0.994555	+	0.104214i	$0.0332328\pi$
$978$		0			0
$979$	−6.20231	−	10.7427i	−0.00633535	−	0.0109732i
$980$	−895.182	−	253.039i	−0.913451	−	0.258203i
$981$		0			0
$982$			2174.27i			2.21412i
$983$	539.710	+	934.805i	0.549044	+	0.950972i	0.998340	+	0.0575890i	$0.0183413\pi$
$983$	539.710	+	934.805i	0.549044	+	0.950972i	−0.449297	+	0.893383i	$0.648325\pi$
$984$		0			0
$985$	−1202.49	+	1170.03i	−1.22080	+	1.18785i
$986$	171.013	+	98.7344i	0.173441	+	0.100136i
$987$		0			0
$988$	−35.1095	+	20.2705i	−0.0355359	+	0.0205167i
$989$			1257.72i			1.27171i
$990$		0			0
$991$	168.017			0.169543			0.0847716	−	0.996400i	$-0.472984\pi$
$991$	168.017			0.169543			0.0847716	+	0.996400i	$0.472984\pi$
$992$	287.773	+	498.437i	0.290093	+	0.502457i
$993$		0			0
$994$	−1242.59	+	2152.22i	−1.25009	+	2.16521i
$995$	455.689	−	443.388i	0.457979	−	0.445616i
$996$		0			0
$997$	−757.109	+	437.117i	−0.759387	+	0.438432i	−0.829076	−	0.559137i	$-0.811133\pi$
$997$	−757.109	+	437.117i	−0.759387	+	0.438432i	0.0696887	+	0.997569i	$0.477799\pi$
$998$	579.829			0.580991
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.3.h.a.44.9		20
3.2	odd	2		45.3.h.a.14.2	✓	20
5.2	odd	4		675.3.j.e.476.2		20
5.3	odd	4		675.3.j.e.476.9		20
5.4	even	2	inner	135.3.h.a.44.2		20
9.2	odd	6	inner	135.3.h.a.89.2		20
9.4	even	3		405.3.d.a.404.4		20
9.5	odd	6		405.3.d.a.404.17		20
9.7	even	3		45.3.h.a.29.9	yes	20
15.2	even	4		225.3.j.e.176.9		20
15.8	even	4		225.3.j.e.176.2		20
15.14	odd	2		45.3.h.a.14.9	yes	20
45.2	even	12		675.3.j.e.251.2		20
45.4	even	6		405.3.d.a.404.18		20
45.7	odd	12		225.3.j.e.101.9		20
45.14	odd	6		405.3.d.a.404.3		20
45.29	odd	6	inner	135.3.h.a.89.9		20
45.34	even	6		45.3.h.a.29.2	yes	20
45.38	even	12		675.3.j.e.251.9		20
45.43	odd	12		225.3.j.e.101.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.3.h.a.14.2	✓	20	3.2	odd	2
45.3.h.a.14.9	yes	20	15.14	odd	2
45.3.h.a.29.2	yes	20	45.34	even	6
45.3.h.a.29.9	yes	20	9.7	even	3
135.3.h.a.44.2		20	5.4	even	2	inner
135.3.h.a.44.9		20	1.1	even	1	trivial
135.3.h.a.89.2		20	9.2	odd	6	inner
135.3.h.a.89.9		20	45.29	odd	6	inner
225.3.j.e.101.2		20	45.43	odd	12
225.3.j.e.101.9		20	45.7	odd	12
225.3.j.e.176.2		20	15.8	even	4
225.3.j.e.176.9		20	15.2	even	4
405.3.d.a.404.3		20	45.14	odd	6
405.3.d.a.404.4		20	9.4	even	3
405.3.d.a.404.17		20	9.5	odd	6
405.3.d.a.404.18		20	45.4	even	6
675.3.j.e.251.2		20	45.2	even	12
675.3.j.e.251.9		20	45.38	even	12
675.3.j.e.476.2		20	5.2	odd	4
675.3.j.e.476.9		20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	135.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.42081 + 2.46092i) q^{2} +(-2.03740 + 3.52889i) q^{4} +(-3.58357 + 3.48684i) q^{5} +(-8.42581 + 4.86464i) q^{7} -0.212574 q^{8} +(-13.6724 - 3.86473i) q^{10} +(-0.370966 + 0.214177i) q^{11} +(16.2396 + 9.37595i) q^{13} +(-23.9429 - 13.8235i) q^{14} +(7.84759 + 13.5924i) q^{16} +2.85718 q^{17} +0.530568 q^{19} +(-5.00347 - 19.7501i) q^{20} +(-1.05414 - 0.608611i) q^{22} +(10.8863 - 18.8557i) q^{23} +(0.683961 - 24.9906i) q^{25} +53.2858i q^{26} -39.6450i q^{28} +(21.0633 - 12.1609i) q^{29} +(6.33163 - 10.9667i) q^{31} +(-22.7250 + 39.3609i) q^{32} +(4.05951 + 7.03128i) q^{34} +(13.2323 - 46.8122i) q^{35} +14.5875i q^{37} +(0.753837 + 1.30568i) q^{38} +(0.761774 - 0.741210i) q^{40} +(33.1200 + 19.1218i) q^{41} +(-50.0269 + 28.8831i) q^{43} -1.74546i q^{44} +61.8697 q^{46} +(24.7850 + 42.9289i) q^{47} +(22.8295 - 39.5418i) q^{49} +(62.4716 - 33.8238i) q^{50} +(-66.1734 + 38.2052i) q^{52} -44.5876 q^{53} +(0.582582 - 2.06102i) q^{55} +(1.79111 - 1.03410i) q^{56} +(59.8538 + 34.5566i) q^{58} +(54.6329 + 31.5423i) q^{59} +(11.0823 + 19.1951i) q^{61} +35.9842 q^{62} -66.3710 q^{64} +(-90.8883 + 23.0255i) q^{65} +(-28.1839 - 16.2720i) q^{67} +(-5.82123 + 10.0827i) q^{68} +(134.001 - 33.9477i) q^{70} -89.8896i q^{71} -144.328i q^{73} +(-35.8987 + 20.7261i) q^{74} +(-1.08098 + 1.87232i) q^{76} +(2.08379 - 3.60923i) q^{77} +(-25.1240 - 43.5160i) q^{79} +(-75.5169 - 21.3462i) q^{80} +108.674i q^{82} +(-38.2556 - 66.2606i) q^{83} +(-10.2389 + 9.96251i) q^{85} +(-142.158 - 82.0747i) q^{86} +(0.0788577 - 0.0455285i) q^{88} +28.9588i q^{89} -182.443 q^{91} +(44.3598 + 76.8334i) q^{92} +(-70.4296 + 121.988i) q^{94} +(-1.90133 + 1.85000i) q^{95} +(19.9099 - 11.4950i) q^{97} +129.746 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 18 q^{4} + 12 q^{5} + 4 q^{10} + 24 q^{11} - 30 q^{14} - 26 q^{16} - 8 q^{19} - 144 q^{20} + 2 q^{25} + 114 q^{29} + 28 q^{31} - 4 q^{34} - 34 q^{40} - 102 q^{41} + 116 q^{46} - 40 q^{49} + 408 q^{50}+ \cdots + 762 q^{95}+O(q^{100}) \) 20 * q - 18 * q^4 + 12 * q^5 + 4 * q^10 + 24 * q^11 - 30 * q^14 - 26 * q^16 - 8 * q^19 - 144 * q^20 + 2 * q^25 + 114 * q^29 + 28 * q^31 - 4 * q^34 - 34 * q^40 - 102 * q^41 + 116 * q^46 - 40 * q^49 + 408 * q^50 + 36 * q^55 + 618 * q^56 - 120 * q^59 - 50 * q^61 + 140 * q^64 - 492 * q^65 - 54 * q^70 - 504 * q^74 - 96 * q^76 - 128 * q^79 - 74 * q^85 - 1488 * q^86 - 288 * q^91 + 218 * q^94 + 762 * q^95

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