LMFDB - Embedded newform 216.3.j.a.125.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(125,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("216.125");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.j (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.88557371018$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			125.7
Character	$\chi$	$=$	216.125
Dual form			216.3.j.a.197.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.16946 - 1.62246i) q^{2} +(-1.26474 + 3.79479i) q^{4} +(2.90774 - 5.03636i) q^{5} +(-0.363382 - 0.629396i) q^{7} +(7.63595 - 2.38585i) q^{8} +O(q^{10})$	\(q+(-1.16946 - 1.62246i) q^{2} +(-1.26474 + 3.79479i) q^{4} +(2.90774 - 5.03636i) q^{5} +(-0.363382 - 0.629396i) q^{7} +(7.63595 - 2.38585i) q^{8} +(-11.5718 + 1.17211i) q^{10} +(-2.03117 - 3.51809i) q^{11} +(13.3457 + 7.70516i) q^{13} +(-0.596210 + 1.32562i) q^{14} +(-12.8008 - 9.59887i) q^{16} -11.6011i q^{17} -35.6847i q^{19} +(15.4344 + 17.4040i) q^{20} +(-3.33259 + 7.40973i) q^{22} +(-26.0887 - 15.0623i) q^{23} +(-4.40992 - 7.63821i) q^{25} +(-3.10595 - 30.6638i) q^{26} +(2.84801 - 0.582934i) q^{28} +(-16.7164 - 28.9536i) q^{29} +(-17.8105 + 30.8487i) q^{31} +(-0.603728 + 31.9943i) q^{32} +(-18.8223 + 13.5669i) q^{34} -4.22648 q^{35} -24.7119i q^{37} +(-57.8969 + 41.7317i) q^{38} +(10.1874 - 45.3948i) q^{40} +(49.7376 + 28.7160i) q^{41} +(-6.79446 + 3.92278i) q^{43} +(15.9193 - 3.25838i) q^{44} +(6.07162 + 59.9427i) q^{46} +(4.39286 - 2.53622i) q^{47} +(24.2359 - 41.9778i) q^{49} +(-7.23546 + 16.0875i) q^{50} +(-46.1184 + 40.8992i) q^{52} -28.1114 q^{53} -23.6244 q^{55} +(-4.27641 - 3.93906i) q^{56} +(-27.4270 + 60.9816i) q^{58} +(19.8481 - 34.3780i) q^{59} +(33.9886 - 19.6234i) q^{61} +(70.8793 - 7.17940i) q^{62} +(52.6155 - 36.4364i) q^{64} +(77.6119 - 44.8092i) q^{65} +(63.9208 + 36.9047i) q^{67} +(44.0236 + 14.6724i) q^{68} +(4.94269 + 6.85730i) q^{70} +88.5602i q^{71} +105.069 q^{73} +(-40.0941 + 28.8995i) q^{74} +(135.416 + 45.1320i) q^{76} +(-1.47618 + 2.55682i) q^{77} +(35.5251 + 61.5313i) q^{79} +(-85.5649 + 36.5586i) q^{80} +(-11.5754 - 114.279i) q^{82} +(-18.1858 - 31.4988i) q^{83} +(-58.4271 - 33.7329i) q^{85} +(14.3104 + 6.43621i) q^{86} +(-23.9035 - 22.0179i) q^{88} +121.817i q^{89} -11.1997i q^{91} +(90.1540 - 79.9513i) q^{92} +(-9.25217 - 4.16124i) q^{94} +(-179.721 - 103.762i) q^{95} +(-25.3236 - 43.8618i) q^{97} +(-96.4501 + 9.76948i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7	$ 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) $ 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.16946	−	1.62246i	−0.584728	−	0.811229i
$2$	−1.16946	−	1.62246i	−0.584728	−	0.811229i
$3$		0			0
$3$		0			0
$4$	−1.26474	+	3.79479i	−0.316186	+	0.948697i
$5$	2.90774	−	5.03636i	0.581548	−	1.00727i	−0.413748	−	0.910392i	$-0.635780\pi$
$5$	2.90774	−	5.03636i	0.581548	−	1.00727i	0.995296	−	0.0968796i	$-0.0308862\pi$
$6$		0			0
$7$	−0.363382	−	0.629396i	−0.0519117	−	0.0899137i	0.838902	−	0.544283i	$-0.183198\pi$
$7$	−0.363382	−	0.629396i	−0.0519117	−	0.0899137i	−0.890814	+	0.454369i	$0.849865\pi$
$8$	7.63595	−	2.38585i	0.954494	−	0.298231i
$9$		0			0
$10$	−11.5718	+	1.17211i	−1.15718	+	0.117211i
$11$	−2.03117	−	3.51809i	−0.184652	−	0.319826i	0.758807	−	0.651315i	$-0.225782\pi$
$11$	−2.03117	−	3.51809i	−0.184652	−	0.319826i	−0.943459	+	0.331489i	$0.892449\pi$
$12$		0			0
$13$	13.3457	+	7.70516i	1.02659	+	0.592705i	0.916007	−	0.401161i	$-0.131393\pi$
$13$	13.3457	+	7.70516i	1.02659	+	0.592705i	0.110588	+	0.993866i	$0.464727\pi$
$14$	−0.596210	+	1.32562i	−0.0425864	+	0.0946874i
$15$		0			0
$16$	−12.8008	−	9.59887i	−0.800053	−	0.599929i
$17$		−	11.6011i		−	0.682416i	−0.939988	−	0.341208i	$-0.889164\pi$
$17$		−	11.6011i		−	0.682416i	0.939988	−	0.341208i	$-0.110836\pi$
$18$		0			0
$19$		−	35.6847i		−	1.87814i	−0.343724	−	0.939071i	$-0.611688\pi$
$19$		−	35.6847i		−	1.87814i	0.343724	−	0.939071i	$-0.388312\pi$
$20$	15.4344	+	17.4040i	0.771718	+	0.870198i
$21$		0			0
$22$	−3.33259	+	7.40973i	−0.151481	+	0.336806i
$23$	−26.0887	−	15.0623i	−1.13429	−	0.654884i	−0.189282	−	0.981923i	$-0.560616\pi$
$23$	−26.0887	−	15.0623i	−1.13429	−	0.654884i	−0.945011	+	0.327038i	$0.893949\pi$
$24$		0			0
$25$	−4.40992	−	7.63821i	−0.176397	−	0.305528i
$26$	−3.10595	−	30.6638i	−0.119460	−	1.17938i
$27$		0			0
$28$	2.84801	−	0.582934i	0.101715	−	0.0208191i
$29$	−16.7164	−	28.9536i	−0.576427	−	0.998400i	−0.995885	−	0.0906257i	$-0.971113\pi$
$29$	−16.7164	−	28.9536i	−0.576427	−	0.998400i	0.419458	−	0.907775i	$-0.362220\pi$
$30$		0			0
$31$	−17.8105	+	30.8487i	−0.574532	+	0.995118i	0.421561	+	0.906800i	$0.361482\pi$
$31$	−17.8105	+	30.8487i	−0.574532	+	0.995118i	−0.996092	+	0.0883179i	$0.971851\pi$
$32$	−0.603728	+	31.9943i	−0.0188665	+	0.999822i
$33$		0			0
$34$	−18.8223	+	13.5669i	−0.553596	+	0.399028i
$35$	−4.22648			−0.120757
$36$		0			0
$37$		−	24.7119i		−	0.667890i	−0.942593	−	0.333945i	$-0.891620\pi$
$37$		−	24.7119i		−	0.667890i	0.942593	−	0.333945i	$-0.108380\pi$
$38$	−57.8969	+	41.7317i	−1.52360	+	1.09820i
$39$		0			0
$40$	10.1874	−	45.3948i	0.254685	−	1.13487i
$41$	49.7376	+	28.7160i	1.21311	+	0.700390i	0.963436	−	0.267939i	$-0.0863426\pi$
$41$	49.7376	+	28.7160i	1.21311	+	0.700390i	0.249676	+	0.968330i	$0.419676\pi$
$42$		0			0
$43$	−6.79446	+	3.92278i	−0.158011	+	0.0912276i	−0.576920	−	0.816800i	$-0.695746\pi$
$43$	−6.79446	+	3.92278i	−0.158011	+	0.0912276i	0.418910	+	0.908028i	$0.362412\pi$
$44$	15.9193	−	3.25838i	0.361802	−	0.0740541i
$45$		0			0
$46$	6.07162	+	59.9427i	0.131992	+	1.30310i
$47$	4.39286	−	2.53622i	0.0934651	−	0.0539621i	−0.452539	−	0.891745i	$-0.649482\pi$
$47$	4.39286	−	2.53622i	0.0934651	−	0.0539621i	0.546004	+	0.837783i	$0.316148\pi$
$48$		0			0
$49$	24.2359	−	41.9778i	0.494610	−	0.856690i
$50$	−7.23546	+	16.0875i	−0.144709	+	0.321749i
$51$		0			0
$52$	−46.1184	+	40.8992i	−0.886892	+	0.786523i
$53$	−28.1114			−0.530405			−0.265202	−	0.964193i	$-0.585439\pi$
$53$	−28.1114			−0.530405			−0.265202	+	0.964193i	$0.585439\pi$
$54$		0			0
$55$	−23.6244			−0.429535
$56$	−4.27641	−	3.93906i	−0.0763645	−	0.0703404i
$57$		0			0
$58$	−27.4270	+	60.9816i	−0.472879	+	1.05141i
$59$	19.8481	−	34.3780i	0.336409	−	0.582678i	−0.647345	−	0.762197i	$-0.724121\pi$
$59$	19.8481	−	34.3780i	0.336409	−	0.582678i	0.983755	+	0.179519i	$0.0574541\pi$
$60$		0			0
$61$	33.9886	−	19.6234i	0.557191	−	0.321694i	−0.194826	−	0.980838i	$-0.562414\pi$
$61$	33.9886	−	19.6234i	0.557191	−	0.321694i	0.752017	+	0.659143i	$0.229081\pi$
$62$	70.8793	−	7.17940i	1.14321	−	0.115797i
$63$		0			0
$64$	52.6155	−	36.4364i	0.822117	−	0.569319i
$65$	77.6119	−	44.8092i	1.19403	−	0.689373i
$66$		0			0
$67$	63.9208	+	36.9047i	0.954041	+	0.550816i	0.894334	−	0.447400i	$-0.147650\pi$
$67$	63.9208	+	36.9047i	0.954041	+	0.550816i	0.0597072	+	0.998216i	$0.480983\pi$
$68$	44.0236	+	14.6724i	0.647406	+	0.215770i
$69$		0			0
$70$	4.94269	+	6.85730i	0.0706098	+	0.0979614i
$71$			88.5602i			1.24733i	0.781693	+	0.623664i	$0.214357\pi$
$71$			88.5602i			1.24733i	−0.781693	+	0.623664i	$0.785643\pi$
$72$		0			0
$73$	105.069			1.43930			0.719650	−	0.694337i	$-0.244302\pi$
$73$	105.069			1.43930			0.719650	+	0.694337i	$0.244302\pi$
$74$	−40.0941	+	28.8995i	−0.541812	+	0.390534i
$75$		0			0
$76$	135.416	+	45.1320i	1.78179	+	0.593842i
$77$	−1.47618	+	2.55682i	−0.0191712	+	0.0332054i
$78$		0			0
$79$	35.5251	+	61.5313i	0.449685	+	0.778877i	0.998365	−	0.0571551i	$-0.0182030\pi$
$79$	35.5251	+	61.5313i	0.449685	+	0.778877i	−0.548680	+	0.836032i	$0.684870\pi$
$80$	−85.5649	+	36.5586i	−1.06956	+	0.456983i
$81$		0			0
$82$	−11.5754	−	114.279i	−0.141163	−	1.39365i
$83$	−18.1858	−	31.4988i	−0.219106	−	0.379504i	0.735429	−	0.677602i	$-0.236981\pi$
$83$	−18.1858	−	31.4988i	−0.219106	−	0.379504i	−0.954535	+	0.298099i	$0.903648\pi$
$84$		0			0
$85$	−58.4271	−	33.7329i	−0.687378	−	0.396858i
$86$	14.3104	+	6.43621i	0.166400	+	0.0748396i
$87$		0			0
$88$	−23.9035	−	22.0179i	−0.271631	−	0.250203i
$89$			121.817i			1.36873i	0.729141	+	0.684363i	$0.239920\pi$
$89$			121.817i			1.36873i	−0.729141	+	0.684363i	$0.760080\pi$
$90$		0			0
$91$		−	11.1997i		−	0.123073i
$92$	90.1540	−	79.9513i	0.979934	−	0.869036i
$93$		0			0
$94$	−9.25217	−	4.16124i	−0.0984273	−	0.0442685i
$95$	−179.721	−	103.762i	−1.89180	−	1.09223i
$96$		0			0
$97$	−25.3236	−	43.8618i	−0.261068	−	0.452183i	0.705458	−	0.708752i	$-0.250741\pi$
$97$	−25.3236	−	43.8618i	−0.261068	−	0.452183i	−0.966526	+	0.256568i	$0.917408\pi$
$98$	−96.4501	+	9.76948i	−0.984185	+	0.0996886i
$99$		0			0
$100$	34.5628	−	7.07435i	0.345628	−	0.0707435i
$101$	80.5694	+	139.550i	0.797717	+	1.38169i	0.921100	+	0.389327i	$0.127292\pi$
$101$	80.5694	+	139.550i	0.797717	+	1.38169i	−0.123383	+	0.992359i	$0.539374\pi$
$102$		0			0
$103$	−47.4976	+	82.2682i	−0.461142	+	0.798721i	−0.999018	−	0.0443030i	$-0.985893\pi$
$103$	−47.4976	+	82.2682i	−0.461142	+	0.798721i	0.537877	+	0.843024i	$0.319227\pi$
$104$	120.291	+	26.9954i	1.15664	+	0.259571i
$105$		0			0
$106$	32.8751	+	45.6096i	0.310142	+	0.430280i
$107$	−59.6104			−0.557106			−0.278553	−	0.960421i	$-0.589855\pi$
$107$	−59.6104			−0.557106			−0.278553	+	0.960421i	$0.589855\pi$
$108$		0			0
$109$			119.342i			1.09488i	0.836846	+	0.547438i	$0.184397\pi$
$109$			119.342i			1.09488i	−0.836846	+	0.547438i	$0.815603\pi$
$110$	27.6278	+	38.3297i	0.251161	+	0.348452i
$111$		0			0
$112$	−1.38989	+	11.5449i	−0.0124097	+	0.103079i
$113$	−86.6058	−	50.0019i	−0.766423	−	0.442495i	0.0651741	−	0.997874i	$-0.479240\pi$
$113$	−86.6058	−	50.0019i	−0.766423	−	0.442495i	−0.831597	+	0.555379i	$0.812573\pi$
$114$		0			0
$115$	−151.719	+	87.5948i	−1.31929	+	0.761694i
$116$	131.015	−	26.8162i	1.12944	−	0.231174i
$117$		0			0
$118$	−78.9884	+	8.00078i	−0.669393	+	0.0678032i
$119$	−7.30167	+	4.21562i	−0.0613586	+	0.0354254i
$120$		0			0
$121$	52.2487	−	90.4974i	0.431808	−	0.747913i
$122$	−71.5863	−	32.1965i	−0.586773	−	0.263906i
$123$		0			0
$124$	−94.5385	−	106.603i	−0.762407	−	0.859699i
$125$	94.0954			0.752764
$126$		0			0
$127$	−34.1686			−0.269044			−0.134522	−	0.990911i	$-0.542950\pi$
$127$	−34.1686			−0.269044			−0.134522	+	0.990911i	$0.542950\pi$
$128$	−120.648	−	42.7556i	−0.942563	−	0.334028i
$129$		0			0
$130$	−163.465	−	73.5196i	−1.25742	−	0.565535i
$131$	−24.7155	+	42.8085i	−0.188668	+	0.326783i	−0.944806	−	0.327629i	$-0.893750\pi$
$131$	−24.7155	+	42.8085i	−0.188668	+	0.326783i	0.756138	+	0.654412i	$0.227084\pi$
$132$		0			0
$133$	−22.4598	+	12.9672i	−0.168871	+	0.0974976i
$134$	−14.8763	−	146.867i	−0.111017	−	1.09602i
$135$		0			0
$136$	−27.6784	−	88.5852i	−0.203518	−	0.651362i
$137$	143.254	−	82.7079i	1.04565	−	0.603707i	0.124223	−	0.992254i	$-0.460356\pi$
$137$	143.254	−	82.7079i	1.04565	−	0.603707i	0.921429	+	0.388547i	$0.127023\pi$
$138$		0			0
$139$	18.0427	+	10.4170i	0.129804	+	0.0749421i	0.563496	−	0.826119i	$-0.309456\pi$
$139$	18.0427	+	10.4170i	0.129804	+	0.0749421i	−0.433692	+	0.901061i	$0.642789\pi$
$140$	5.34542	−	16.0386i	0.0381816	−	0.114562i
$141$		0			0
$142$	143.685	−	103.567i	1.01187	−	0.729348i
$143$		−	62.6019i		−	0.437776i
$144$		0			0
$145$	−194.428			−1.34088
$146$	−122.873	−	170.470i	−0.841599	−	1.16760i
$147$		0			0
$148$	93.7765	+	31.2542i	0.633625	+	0.211177i
$149$	−26.6261	+	46.1178i	−0.178699	+	0.309515i	−0.941435	−	0.337194i	$-0.890522\pi$
$149$	−26.6261	+	46.1178i	−0.178699	+	0.309515i	0.762736	+	0.646710i	$0.223855\pi$
$150$		0			0
$151$	−101.373	−	175.584i	−0.671347	−	1.16281i	−0.977522	−	0.210832i	$-0.932383\pi$
$151$	−101.373	−	175.584i	−0.671347	−	1.16281i	0.306175	−	0.951975i	$-0.400951\pi$
$152$	−85.1382	−	272.487i	−0.560120	−	1.79267i
$153$		0			0
$154$	5.87466	−	0.595047i	0.0381471	−	0.00386394i
$155$	103.577	+	179.400i	0.668236	+	1.15742i
$156$		0			0
$157$	−72.8570	−	42.0640i	−0.464057	−	0.267924i	0.249691	−	0.968325i	$-0.419671\pi$
$157$	−72.8570	−	42.0640i	−0.464057	−	0.267924i	−0.713749	+	0.700402i	$0.753004\pi$
$158$	58.2869	−	129.596i	0.368904	−	0.820229i
$159$		0			0
$160$	159.379	+	96.0718i	0.996120	+	0.600448i
$161$			21.8935i			0.135985i
$162$		0			0
$163$		−	107.182i		−	0.657559i	−0.944407	−	0.328780i	$-0.893363\pi$
$163$		−	107.182i		−	0.657559i	0.944407	−	0.328780i	$-0.106637\pi$
$164$	−171.876	+	152.425i	−1.04803	+	0.929422i
$165$		0			0
$166$	−29.8379	+	66.3422i	−0.179747	+	0.399652i
$167$	132.530	+	76.5161i	0.793592	+	0.458180i	0.841226	−	0.540684i	$-0.181835\pi$
$167$	132.530	+	76.5161i	0.793592	+	0.458180i	−0.0476337	+	0.998865i	$0.515168\pi$
$168$		0			0
$169$	34.2391	+	59.3038i	0.202598	+	0.350910i
$170$	13.5977	+	134.245i	0.0799866	+	0.789675i
$171$		0			0
$172$	−6.29289	−	30.7449i	−0.0365866	−	0.178749i
$173$	−28.0520	−	48.5876i	−0.162151	−	0.280853i	0.773489	−	0.633810i	$-0.218510\pi$
$173$	−28.0520	−	48.5876i	−0.162151	−	0.280853i	−0.935640	+	0.352957i	$0.885176\pi$
$174$		0			0
$175$	−3.20497	+	5.55117i	−0.0183141	+	0.0317210i
$176$	−7.76896	+	64.5314i	−0.0441418	+	0.366656i
$177$		0			0
$178$	197.642	−	142.459i	1.11035	−	0.800333i
$179$	184.408			1.03021			0.515106	−	0.857127i	$-0.327753\pi$
$179$	184.408			1.03021			0.515106	+	0.857127i	$0.327753\pi$
$180$		0			0
$181$			249.415i			1.37798i	0.724769	+	0.688992i	$0.241946\pi$
$181$			249.415i			1.37798i	−0.724769	+	0.688992i	$0.758054\pi$
$182$	−18.1710	+	13.0975i	−0.0998407	+	0.0719645i
$183$		0			0
$184$	−235.149	−	52.7715i	−1.27798	−	0.286802i
$185$	−124.458	−	71.8559i	−0.672746	−	0.388410i
$186$		0			0
$187$	−40.8136	+	23.5637i	−0.218254	+	0.126009i
$188$	4.06858	+	19.8776i	0.0216414	+	0.105732i
$189$		0			0
$190$	41.8264	+	412.935i	0.220139	+	2.17334i
$191$	33.2377	−	19.1898i	0.174019	−	0.100470i	−0.410460	−	0.911878i	$-0.634632\pi$
$191$	33.2377	−	19.1898i	0.174019	−	0.100470i	0.584480	+	0.811408i	$0.301299\pi$
$192$		0			0
$193$	−83.3709	+	144.403i	−0.431974	+	0.748200i	−0.997043	−	0.0768429i	$-0.975516\pi$
$193$	−83.3709	+	144.403i	−0.431974	+	0.748200i	0.565069	+	0.825043i	$0.308849\pi$
$194$	−41.5491	+	92.3810i	−0.214170	+	0.476191i
$195$		0			0
$196$	128.645	+	145.061i	0.656351	+	0.740109i
$197$	−188.581			−0.957264			−0.478632	−	0.878016i	$-0.658867\pi$
$197$	−188.581			−0.957264			−0.478632	+	0.878016i	$0.658867\pi$
$198$		0			0
$199$	−9.63131			−0.0483986			−0.0241993	−	0.999707i	$-0.507704\pi$
$199$	−9.63131			−0.0483986			−0.0241993	+	0.999707i	$0.507704\pi$
$200$	−51.8975	−	47.8036i	−0.259488	−	0.239018i
$201$		0			0
$202$	132.192	−	293.919i	0.654417	−	1.45504i
$203$	−12.1489	+	21.0424i	−0.0598466	+	0.103657i
$204$		0			0
$205$	289.248	−	166.997i	1.41097	−	0.814622i
$206$	189.023	−	19.1463i	0.917588	−	0.0929430i
$207$		0			0
$208$	−96.8759	−	226.737i	−0.465750	−	1.09008i
$209$	−125.542	+	72.4816i	−0.600678	+	0.346802i
$210$		0			0
$211$	108.883	+	62.8637i	0.516034	+	0.297932i	0.735310	−	0.677730i	$-0.237036\pi$
$211$	108.883	+	62.8637i	0.516034	+	0.297932i	−0.219277	+	0.975663i	$0.570370\pi$
$212$	35.5538	−	106.677i	0.167706	−	0.503193i
$213$		0			0
$214$	69.7117	+	96.7154i	0.325756	+	0.451941i
$215$			45.6258i			0.212213i
$216$		0			0
$217$	25.8880			0.119300
$218$	193.627	−	139.565i	0.888196	−	0.640205i
$219$		0			0
$220$	29.8788	−	89.6498i	0.135813	−	0.407499i
$221$	89.3881	−	154.825i	0.404471	−	0.700565i
$222$		0			0
$223$	137.654	+	238.424i	0.617282	+	1.06916i	0.989980	+	0.141211i	$0.0450996\pi$
$223$	137.654	+	238.424i	0.617282	+	1.06916i	−0.372697	+	0.927953i	$0.621567\pi$
$224$	20.3565	−	11.2462i	0.0908771	−	0.0502061i
$225$		0			0
$226$	20.1557	+	198.989i	0.0891847	+	0.880484i
$227$	−17.7375	−	30.7223i	−0.0781388	−	0.135340i	0.824308	−	0.566141i	$-0.191564\pi$
$227$	−17.7375	−	30.7223i	−0.0781388	−	0.135340i	−0.902447	+	0.430801i	$0.858231\pi$
$228$		0			0
$229$	−250.235	−	144.473i	−1.09273	−	0.630888i	−0.158429	−	0.987370i	$-0.550643\pi$
$229$	−250.235	−	144.473i	−1.09273	−	0.630888i	−0.934302	+	0.356482i	$0.883976\pi$
$230$	319.547	+	143.719i	1.38934	+	0.624865i
$231$		0			0
$232$	−196.724	−	181.206i	−0.847949	−	0.781059i
$233$			53.5754i			0.229937i	0.993369	+	0.114969i	$0.0366768\pi$
$233$			53.5754i			0.229937i	−0.993369	+	0.114969i	$0.963323\pi$
$234$		0			0
$235$		−	29.4987i		−	0.125526i
$236$	105.354	+	118.799i	0.446417	+	0.503385i
$237$		0			0
$238$	15.3787	+	6.91667i	0.0646162	+	0.0290616i
$239$	155.039	+	89.5120i	0.648700	+	0.374527i	0.787958	−	0.615729i	$-0.211138\pi$
$239$	155.039	+	89.5120i	0.648700	+	0.374527i	−0.139258	+	0.990256i	$0.544472\pi$
$240$		0			0
$241$	31.3738	+	54.3410i	0.130182	+	0.225481i	0.923747	−	0.383004i	$-0.125111\pi$
$241$	31.3738	+	54.3410i	0.130182	+	0.225481i	−0.793565	+	0.608486i	$0.791777\pi$
$242$	−207.931	+	21.0614i	−0.859219	+	0.0870307i
$243$		0			0
$244$	31.4796	+	153.798i	0.129015	+	0.630321i
$245$	−140.943	−	244.121i	−0.575280	−	0.996413i
$246$		0			0
$247$	274.956	−	476.238i	1.11318	−	1.92809i
$248$	−62.3998	+	278.052i	−0.251612	+	1.12118i
$249$		0			0
$250$	−110.041	−	152.666i	−0.440162	−	0.610664i
$251$	−84.9454			−0.338428			−0.169214	−	0.985579i	$-0.554123\pi$
$251$	−84.9454			−0.338428			−0.169214	+	0.985579i	$0.554123\pi$
$252$		0			0
$253$			122.377i			0.483702i
$254$	39.9586	+	55.4371i	0.157317	+	0.218256i
$255$		0			0
$256$	71.7235	+	245.747i	0.280170	+	0.959950i
$257$	−27.9325	−	16.1268i	−0.108687	−	0.0627503i	0.444671	−	0.895694i	$-0.353321\pi$
$257$	−27.9325	−	16.1268i	−0.108687	−	0.0627503i	−0.553358	+	0.832944i	$0.686654\pi$
$258$		0			0
$259$	−15.5536	+	8.97987i	−0.0600525	+	0.0346713i
$260$	71.8825	+	351.193i	0.276471	+	1.35074i
$261$		0			0
$262$	98.3587	−	9.96281i	0.375415	−	0.0380260i
$263$	45.9346	−	26.5204i	0.174656	−	0.100838i	−0.410123	−	0.912030i	$-0.634514\pi$
$263$	45.9346	−	26.5204i	0.174656	−	0.100838i	0.584780	+	0.811192i	$0.301181\pi$
$264$		0			0
$265$	−81.7408	+	141.579i	−0.308456	+	0.534261i
$266$	47.3045	+	21.2756i	0.177836	+	0.0799833i
$267$		0			0
$268$	−220.889	+	195.891i	−0.824212	+	0.730936i
$269$	86.8402			0.322826			0.161413	−	0.986887i	$-0.448395\pi$
$269$	86.8402			0.322826			0.161413	+	0.986887i	$0.448395\pi$
$270$		0			0
$271$	412.202			1.52104			0.760520	−	0.649314i	$-0.224944\pi$
$271$	412.202			1.52104			0.760520	+	0.649314i	$0.224944\pi$
$272$	−111.357	+	148.504i	−0.409401	+	0.545969i
$273$		0			0
$274$	−301.720	−	135.701i	−1.10117	−	0.495258i
$275$	−17.9146	+	31.0290i	−0.0651439	+	0.112833i
$276$		0			0
$277$	99.4029	−	57.3903i	0.358855	−	0.207185i	−0.309723	−	0.950827i	$-0.600236\pi$
$277$	99.4029	−	57.3903i	0.358855	−	0.207185i	0.668578	+	0.743642i	$0.266903\pi$
$278$	−4.19907	−	41.4557i	−0.0151046	−	0.149121i
$279$		0			0
$280$	−32.2732	+	10.0837i	−0.115262	+	0.0360134i
$281$	−317.161	+	183.113i	−1.12869	+	0.651647i	−0.943604	−	0.331076i	$-0.892588\pi$
$281$	−317.161	+	183.113i	−1.12869	+	0.651647i	−0.185082	+	0.982723i	$0.559255\pi$
$282$		0			0
$283$	−16.7891	−	9.69318i	−0.0593253	−	0.0342515i	0.470044	−	0.882643i	$-0.344238\pi$
$283$	−16.7891	−	9.69318i	−0.0593253	−	0.0342515i	−0.529369	+	0.848392i	$0.677571\pi$
$284$	−336.067	−	112.006i	−1.18334	−	0.394387i
$285$		0			0
$286$	−101.569	+	73.2102i	−0.355136	+	0.255980i
$287$		−	41.7395i		−	0.145434i
$288$		0			0
$289$	154.415			0.534309
$290$	227.375	+	315.451i	0.784050	+	1.08776i
$291$		0			0
$292$	−132.885	+	398.714i	−0.455086	+	1.36546i
$293$	−120.913	+	209.427i	−0.412672	+	0.714769i	−0.995181	−	0.0980553i	$-0.968738\pi$
$293$	−120.913	+	209.427i	−0.412672	+	0.714769i	0.582509	+	0.812824i	$0.302071\pi$
$294$		0			0
$295$	−115.427	−	199.925i	−0.391276	−	0.677711i
$296$	−58.9589	−	188.699i	−0.199185	−	0.637497i
$297$		0			0
$298$	105.962	−	10.7330i	0.355578	−	0.0360167i
$299$	−232.116	−	402.036i	−0.776306	−	1.34460i
$300$		0			0
$301$	4.93797	+	2.85094i	0.0164052	+	0.00947156i
$302$	−166.326	+	369.812i	−0.550748	+	1.22454i
$303$		0			0
$304$	−342.533	+	456.794i	−1.12675	+	1.50261i
$305$		−	228.239i		−	0.748323i
$306$		0			0
$307$		−	383.998i		−	1.25081i	−0.780301	−	0.625404i	$-0.784934\pi$
$307$		−	383.998i		−	1.25081i	0.780301	−	0.625404i	$-0.215066\pi$
$308$	−7.83560	−	8.83551i	−0.0254403	−	0.0286867i
$309$		0			0
$310$	169.941	−	377.849i	0.548195	−	1.21887i
$311$	409.820	+	236.610i	1.31775	+	0.760803i	0.983366	−	0.181635i	$-0.0581388\pi$
$311$	409.820	+	236.610i	1.31775	+	0.760803i	0.334383	+	0.942437i	$0.391472\pi$
$312$		0			0
$313$	140.084	+	242.632i	0.447552	+	0.775182i	0.998226	−	0.0595379i	$-0.0189627\pi$
$313$	140.084	+	242.632i	0.447552	+	0.775182i	−0.550674	+	0.834720i	$0.685629\pi$
$314$	16.9560	+	167.399i	0.0539999	+	0.533119i
$315$		0			0
$316$	−278.428	+	56.9890i	−0.881102	+	0.180345i
$317$	89.4931	+	155.007i	0.282313	+	0.488980i	0.971954	−	0.235171i	$-0.0755651\pi$
$317$	89.4931	+	155.007i	0.282313	+	0.488980i	−0.689641	+	0.724151i	$0.742232\pi$
$318$		0			0
$319$	−67.9075	+	117.619i	−0.212876	+	0.368712i
$320$	−30.5146	−	370.938i	−0.0953582	−	1.15918i
$321$		0			0
$322$	35.5214	−	25.6035i	0.110315	−	0.0795141i
$323$	−413.981			−1.28167
$324$		0			0
$325$		−	135.917i		−	0.418205i
$326$	−173.899	+	125.345i	−0.533431	+	0.384494i
$327$		0			0
$328$	448.306	+	100.608i	1.36679	+	0.306731i
$329$	−3.19257	−	1.84323i	−0.00970387	−	0.00560253i
$330$		0			0
$331$	213.367	−	123.187i	0.644613	−	0.372167i	−0.141776	−	0.989899i	$-0.545281\pi$
$331$	213.367	−	123.187i	0.644613	−	0.372167i	0.786389	+	0.617731i	$0.211948\pi$
$332$	142.532	−	29.1735i	0.429312	−	0.0878721i
$333$		0			0
$334$	−30.8436	−	304.506i	−0.0923462	−	0.911696i
$335$	371.730	−	214.618i	1.10964	−	0.640652i
$336$		0			0
$337$	−35.3726	+	61.2672i	−0.104963	+	0.181802i	−0.913723	−	0.406337i	$-0.866806\pi$
$337$	−35.3726	+	61.2672i	−0.104963	+	0.181802i	0.808760	+	0.588139i	$0.200139\pi$
$338$	56.1769	−	124.905i	0.166204	−	0.369541i
$339$		0			0
$340$	201.905	−	179.055i	0.593837	−	0.526633i
$341$	144.704			0.424353
$342$		0			0
$343$	−70.8390			−0.206528
$344$	−42.5230	+	46.1647i	−0.123613	+	0.134200i
$345$		0			0
$346$	−46.0257	+	102.334i	−0.133022	+	0.295764i
$347$	142.174	−	246.252i	0.409723	−	0.709661i	−0.585136	−	0.810935i	$-0.698959\pi$
$347$	142.174	−	246.252i	0.409723	−	0.709661i	0.994859	+	0.101275i	$0.0322920\pi$
$348$		0			0
$349$	441.835	−	255.093i	1.26600	−	0.730927i	0.291773	−	0.956488i	$-0.405755\pi$
$349$	441.835	−	255.093i	1.26600	−	0.730927i	0.974229	+	0.225561i	$0.0724214\pi$
$350$	12.7546	−	1.29192i	0.0364418	−	0.00369121i
$351$		0			0
$352$	113.785	−	62.8618i	0.323253	−	0.178585i
$353$	−183.443	+	105.911i	−0.519669	+	0.300031i	−0.736799	−	0.676112i	$-0.763664\pi$
$353$	−183.443	+	105.911i	−0.519669	+	0.300031i	0.217130	+	0.976143i	$0.430330\pi$
$354$		0			0
$355$	446.021	+	257.510i	1.25640	+	0.725381i
$356$	−462.268	−	154.067i	−1.29851	−	0.432772i
$357$		0			0
$358$	−215.657	−	299.194i	−0.602394	−	0.835738i
$359$		−	9.46105i		−	0.0263539i	−0.999913	−	0.0131769i	$-0.995806\pi$
$359$		−	9.46105i		−	0.0263539i	0.999913	−	0.0131769i	$-0.00419447\pi$
$360$		0			0
$361$	−912.397			−2.52742
$362$	404.665	−	291.680i	1.11786	−	0.805746i
$363$		0			0
$364$	42.5004	+	14.1647i	0.116759	+	0.0389140i
$365$	305.513	−	529.164i	0.837022	−	1.44977i
$366$		0			0
$367$	−219.921	−	380.915i	−0.599241	−	1.03792i	−0.992933	−	0.118673i	$-0.962136\pi$
$367$	−219.921	−	380.915i	−0.599241	−	1.03792i	0.393693	−	0.919242i	$-0.371197\pi$
$368$	189.377	+	443.233i	0.514610	+	1.20444i
$369$		0			0
$370$	28.9651	+	285.960i	0.0782840	+	0.772866i
$371$	10.2152	+	17.6932i	0.0275342	+	0.0476907i
$372$		0			0
$373$	−420.468	−	242.757i	−1.12726	−	0.650823i	−0.184015	−	0.982923i	$-0.558909\pi$
$373$	−420.468	−	242.757i	−1.12726	−	0.650823i	−0.943244	+	0.332100i	$0.892243\pi$
$374$	85.9608	+	38.6616i	0.229842	+	0.103373i
$375$		0			0
$376$	27.4926	−	29.8471i	0.0731187	−	0.0793807i
$377$		−	515.210i		−	1.36660i
$378$		0			0
$379$			189.622i			0.500321i	0.968204	+	0.250161i	$0.0804834\pi$
$379$			189.622i			0.500321i	−0.968204	+	0.250161i	$0.919517\pi$
$380$	621.055	−	550.770i	1.63436	−	1.44940i
$381$		0			0
$382$	−70.0047	−	31.4852i	−0.183258	−	0.0824219i
$383$	−406.033	−	234.423i	−1.06014	−	0.612071i	−0.134668	−	0.990891i	$-0.542997\pi$
$383$	−406.033	−	234.423i	−1.06014	−	0.612071i	−0.925471	+	0.378819i	$0.876330\pi$
$384$		0			0
$385$	8.58470	+	14.8691i	0.0222979	+	0.0386211i
$386$	331.786	−	33.6068i	0.859549	−	0.0870642i
$387$		0			0
$388$	198.474	−	40.6239i	0.511531	−	0.104701i
$389$	34.1349	+	59.1233i	0.0877503	+	0.151988i	0.906560	−	0.422077i	$-0.138699\pi$
$389$	34.1349	+	59.1233i	0.0877503	+	0.151988i	−0.818810	+	0.574065i	$0.805366\pi$
$390$		0			0
$391$	−174.739	+	302.657i	−0.446904	+	0.774060i
$392$	84.9115	−	378.364i	0.216611	−	0.965214i
$393$		0			0
$394$	220.537	+	305.965i	0.559739	+	0.776560i
$395$	413.191			1.04605
$396$		0			0
$397$		−	170.825i		−	0.430289i	−0.976582	−	0.215144i	$-0.930978\pi$
$397$		−	170.825i		−	0.430289i	0.976582	−	0.215144i	$-0.0690222\pi$
$398$	11.2634	+	15.6264i	0.0283000	+	0.0392623i
$399$		0			0
$400$	−16.8674	+	140.106i	−0.0421685	+	0.350264i
$401$	268.522	+	155.031i	0.669631	+	0.386612i	0.795937	−	0.605380i	$-0.206979\pi$
$401$	268.522	+	155.031i	0.669631	+	0.386612i	−0.126306	+	0.991991i	$0.540312\pi$
$402$		0			0
$403$	−475.388	+	274.465i	−1.17962	+	0.681056i
$404$	−631.464	+	129.249i	−1.56303	+	0.319922i
$405$		0			0
$406$	48.3481	−	4.89720i	0.119084	−	0.0120621i
$407$	−86.9387	+	50.1941i	−0.213609	+	0.123327i
$408$		0			0
$409$	−63.7657	+	110.445i	−0.155906	+	0.270038i	−0.933389	−	0.358867i	$-0.883163\pi$
$409$	−63.7657	+	110.445i	−0.155906	+	0.270038i	0.777482	+	0.628905i	$0.216496\pi$
$410$	−609.209	−	273.997i	−1.48588	−	0.668285i
$411$		0			0
$412$	−252.118	−	284.291i	−0.611938	−	0.690028i
$413$	−28.8498			−0.0698543
$414$		0			0
$415$	−211.519			−0.509684
$416$	−254.579	+	422.336i	−0.611968	+	1.01523i
$417$		0			0
$418$	264.414	+	118.922i	0.632569	+	0.284503i
$419$	38.1531	−	66.0831i	0.0910575	−	0.157716i	−0.816899	−	0.576781i	$-0.804309\pi$
$419$	38.1531	−	66.0831i	0.0910575	−	0.157716i	0.907956	+	0.419065i	$0.137642\pi$
$420$		0			0
$421$	−591.625	+	341.575i	−1.40528	+	0.811341i	−0.994929	−	0.100584i	$-0.967929\pi$
$421$	−591.625	+	341.575i	−1.40528	+	0.811341i	−0.410356	+	0.911925i	$0.634596\pi$
$422$	−25.3403	−	250.175i	−0.0600482	−	0.592831i
$423$		0			0
$424$	−214.658	+	67.0696i	−0.506268	+	0.158183i
$425$	−88.6114	+	51.1598i	−0.208497	+	0.120376i
$426$		0			0
$427$	−24.7017	−	14.2615i	−0.0578495	−	0.0333994i
$428$	75.3918	−	226.209i	0.176149	−	0.528525i
$429$		0			0
$430$	74.0259	−	53.3574i	0.172153	−	0.124087i
$431$		−	16.3619i		−	0.0379627i	−0.999820	−	0.0189814i	$-0.993958\pi$
$431$		−	16.3619i		−	0.0379627i	0.999820	−	0.0189814i	$-0.00604231\pi$
$432$		0			0
$433$	618.066			1.42740			0.713702	−	0.700449i	$-0.247017\pi$
$433$	618.066			1.42740			0.713702	+	0.700449i	$0.247017\pi$
$434$	−30.2749	−	42.0023i	−0.0697579	−	0.0967794i
$435$		0			0
$436$	−452.876	−	150.936i	−1.03871	−	0.346184i
$437$	−537.495	+	930.969i	−1.22997	+	2.13036i
$438$		0			0
$439$	279.199	+	483.587i	0.635989	+	1.10157i	0.986305	+	0.164934i	$0.0527411\pi$
$439$	279.199	+	483.587i	0.635989	+	1.10157i	−0.350315	+	0.936632i	$0.613926\pi$
$440$	−180.395	+	56.3643i	−0.409989	+	0.128101i
$441$		0			0
$442$	−355.732	+	36.0323i	−0.804824	+	0.0815211i
$443$	215.042	+	372.464i	0.485422	+	0.840775i	0.999860	−	0.0167523i	$-0.00533266\pi$
$443$	215.042	+	372.464i	0.485422	+	0.840775i	−0.514438	+	0.857528i	$0.671999\pi$
$444$		0			0
$445$	613.512	+	354.211i	1.37868	+	0.795980i
$446$	225.852	−	502.164i	0.506395	−	1.12593i
$447$		0			0
$448$	−42.0525	−	19.8756i	−0.0938671	−	0.0443652i
$449$			229.455i			0.511035i	0.966804	+	0.255517i	$0.0822458\pi$
$449$			229.455i			0.511035i	−0.966804	+	0.255517i	$0.917754\pi$
$450$		0			0
$451$		−	233.308i		−	0.517313i
$452$	299.281	−	265.411i	0.662125	−	0.587193i
$453$		0			0
$454$	−29.1024	+	64.7067i	−0.0641021	+	0.142526i
$455$	−56.4055	−	32.5658i	−0.123968	−	0.0715731i
$456$		0			0
$457$	−393.037	−	680.760i	−0.860037	−	1.48963i	−0.871892	−	0.489698i	$-0.837107\pi$
$457$	−393.037	−	680.760i	−0.860037	−	1.48963i	0.0118556	−	0.999930i	$-0.496226\pi$
$458$	58.2372	+	574.952i	0.127155	+	1.25535i
$459$		0			0
$460$	−140.519	−	686.525i	−0.305475	−	1.49245i
$461$	−219.475	−	380.142i	−0.476084	−	0.824602i	0.523540	−	0.852001i	$-0.324611\pi$
$461$	−219.475	−	380.142i	−0.476084	−	0.824602i	−0.999625	+	0.0273986i	$0.991278\pi$
$462$		0			0
$463$	194.665	−	337.170i	0.420443	−	0.728229i	−0.575539	−	0.817774i	$-0.695208\pi$
$463$	194.665	−	337.170i	0.420443	−	0.728229i	0.995983	+	0.0895448i	$0.0285412\pi$
$464$	−63.9381	+	531.089i	−0.137798	+	1.14459i
$465$		0			0
$466$	86.9239	−	62.6541i	0.186532	−	0.134451i
$467$	310.283			0.664417			0.332209	−	0.943206i	$-0.392206\pi$
$467$	310.283			0.664417			0.332209	+	0.943206i	$0.392206\pi$
$468$		0			0
$469$		−	53.6420i		−	0.114375i
$470$	−47.8604	+	34.4974i	−0.101831	+	0.0733988i
$471$		0			0
$472$	69.5388	−	309.863i	0.147328	−	0.656490i
$473$	27.6014	+	15.9357i	0.0583539	+	0.0336906i
$474$		0			0
$475$	−272.567	+	157.367i	−0.573825	+	0.331298i
$476$	−6.76266	−	33.0400i	−0.0142073	−	0.0694117i
$477$		0			0
$478$	−36.0823	−	356.225i	−0.0754859	−	0.745241i
$479$	−534.788	+	308.760i	−1.11647	+	0.644593i	−0.940497	−	0.339802i	$-0.889640\pi$
$479$	−534.788	+	308.760i	−1.11647	+	0.644593i	−0.175971	+	0.984395i	$0.556306\pi$
$480$		0			0
$481$	190.409	−	329.799i	0.395862	−	0.685652i
$482$	51.4758	−	114.452i	0.106796	−	0.237453i
$483$		0			0
$484$	277.337	+	312.729i	0.573011	+	0.646134i
$485$	−294.538			−0.607295
$486$		0			0
$487$	52.9743			0.108777			0.0543884	−	0.998520i	$-0.482679\pi$
$487$	52.9743			0.108777			0.0543884	+	0.998520i	$0.482679\pi$
$488$	212.717	−	230.935i	0.435896	−	0.473227i
$489$		0			0
$490$	−231.249	+	514.164i	−0.471938	+	1.04931i
$491$	−455.131	+	788.310i	−0.926947	+	1.60552i	−0.138548	+	0.990356i	$0.544244\pi$
$491$	−455.131	+	788.310i	−0.926947	+	1.60552i	−0.788399	+	0.615164i	$0.789090\pi$
$492$		0			0
$493$	−335.893	+	193.928i	−0.681324	+	0.393363i
$494$	−1094.23	+	110.835i	−2.21503	+	0.224362i
$495$		0			0
$496$	524.102	−	223.929i	1.05666	−	0.451469i
$497$	55.7395	−	32.1812i	0.112152	−	0.0647509i
$498$		0			0
$499$	92.0144	+	53.1245i	0.184398	+	0.106462i	0.589357	−	0.807873i	$-0.299381\pi$
$499$	92.0144	+	53.1245i	0.184398	+	0.106462i	−0.404960	+	0.914335i	$0.632714\pi$
$500$	−119.007	+	357.072i	−0.238013	+	0.714145i
$501$		0			0
$502$	99.3400	+	137.820i	0.197888	+	0.274543i
$503$		−	452.514i		−	0.899630i	−0.893122	−	0.449815i	$-0.851490\pi$
$503$		−	452.514i		−	0.899630i	0.893122	−	0.449815i	$-0.148510\pi$
$504$		0			0
$505$	937.100			1.85564
$506$	198.551	−	143.114i	0.392393	−	0.282834i
$507$		0			0
$508$	43.2144	−	129.662i	0.0850678	−	0.255241i
$509$	282.090	−	488.595i	0.554205	−	0.959911i	−0.443760	−	0.896146i	$-0.646356\pi$
$509$	282.090	−	488.595i	0.554205	−	0.959911i	0.997965	−	0.0637653i	$-0.0203109\pi$
$510$		0			0
$511$	−38.1801	−	66.1300i	−0.0747165	−	0.129413i
$512$	314.837	−	403.759i	0.614917	−	0.788592i
$513$		0			0
$514$	6.50072	+	64.1789i	0.0126473	+	0.124862i
$515$	276.221	+	478.429i	0.536352	+	0.928989i
$516$		0			0
$517$	−17.8453	−	10.3030i	−0.0345170	−	0.0199284i
$518$	32.7587	+	14.7335i	0.0632408	+	0.0284430i
$519$		0			0
$520$	485.732	−	527.331i	0.934101	−	1.01410i
$521$		−	246.265i		−	0.472678i	−0.971671	−	0.236339i	$-0.924052\pi$
$521$		−	246.265i		−	0.472678i	0.971671	−	0.236339i	$-0.0759475\pi$
$522$		0			0
$523$		−	19.4969i		−	0.0372789i	−0.999826	−	0.0186394i	$-0.994067\pi$
$523$		−	19.4969i		−	0.0372789i	0.999826	−	0.0186394i	$-0.00593346\pi$
$524$	−131.191	−	147.932i	−0.250364	−	0.282313i
$525$		0			0
$526$	−96.7467	−	43.5126i	−0.183929	−	0.0827236i
$527$	357.878	+	206.621i	0.679084	+	0.392070i
$528$		0			0
$529$	189.248	+	327.788i	0.357747	+	0.619636i
$530$	325.299	−	32.9497i	0.613771	−	0.0621692i
$531$		0			0
$532$	−20.8018	−	101.630i	−0.0391012	−	0.191035i
$533$	442.523	+	766.472i	0.830249	+	1.43803i
$534$		0			0
$535$	−173.332	+	300.219i	−0.323984	+	0.561157i
$536$	576.145	+	129.297i	1.07490	+	0.241226i
$537$		0			0
$538$	−101.556	−	140.895i	−0.188766	−	0.261886i
$539$	−196.909			−0.365322
$540$		0			0
$541$			673.728i			1.24534i	0.782485	+	0.622669i	$0.213952\pi$
$541$			673.728i			1.24534i	−0.782485	+	0.622669i	$0.786048\pi$
$542$	−482.052	−	668.780i	−0.889395	−	1.23391i
$543$		0			0
$544$	371.168	+	7.00389i	0.682294	+	0.0128748i
$545$	601.047	+	347.014i	1.10284	+	0.636724i
$546$		0			0
$547$	−445.583	+	257.257i	−0.814594	+	0.470306i	−0.848549	−	0.529117i	$-0.822523\pi$
$547$	−445.583	+	257.257i	−0.814594	+	0.470306i	0.0339545	+	0.999423i	$0.489190\pi$
$548$	132.679	+	648.224i	0.242115	+	1.18289i
$549$		0			0
$550$	71.2935	−	7.22136i	0.129625	−	0.0131297i
$551$	−1033.20	+	596.519i	−1.87514	+	1.08261i
$552$		0			0
$553$	25.8184	−	44.7187i	0.0466878	−	0.0808657i
$554$	−209.361	−	94.1616i	−0.377907	−	0.169967i
$555$		0			0
$556$	−62.3495	+	55.2935i	−0.112139	+	0.0994487i
$557$	612.943			1.10044			0.550218	−	0.835021i	$-0.314545\pi$
$557$	612.943			1.10044			0.550218	+	0.835021i	$0.314545\pi$
$558$		0			0
$559$	−120.903			−0.216284
$560$	54.1026	+	40.5695i	0.0966118	+	0.0724455i
$561$		0			0
$562$	667.999	+	300.438i	1.18861	+	0.534587i
$563$	178.694	−	309.507i	0.317396	−	0.549746i	−0.662548	−	0.749020i	$-0.730525\pi$
$563$	178.694	−	309.507i	0.317396	−	0.549746i	0.979944	+	0.199274i	$0.0638582\pi$
$564$		0			0
$565$	−503.655	+	290.785i	−0.891424	+	0.514664i
$566$	3.90731	+	38.5753i	0.00690338	+	0.0681543i
$567$		0			0
$568$	211.291	+	676.242i	0.371992	+	1.19057i
$569$	227.670	−	131.445i	0.400123	−	0.231011i	−0.286414	−	0.958106i	$-0.592463\pi$
$569$	227.670	−	131.445i	0.400123	−	0.231011i	0.686537	+	0.727095i	$0.259130\pi$
$570$		0			0
$571$	−558.493	−	322.446i	−0.978095	−	0.564704i	−0.0764009	−	0.997077i	$-0.524343\pi$
$571$	−558.493	−	322.446i	−0.978095	−	0.564704i	−0.901695	+	0.432374i	$0.857676\pi$
$572$	237.561	+	79.1753i	0.415317	+	0.138418i
$573$		0			0
$574$	−67.7206	+	48.8126i	−0.117980	+	0.0850393i
$575$			265.695i			0.462078i
$576$		0			0
$577$	−497.297			−0.861867			−0.430933	−	0.902384i	$-0.641816\pi$
$577$	−497.297			−0.861867			−0.430933	+	0.902384i	$0.641816\pi$
$578$	−180.582	−	250.532i	−0.312425	−	0.433447i
$579$		0			0
$580$	245.901	−	737.812i	0.423967	−	1.27209i
$581$	−13.2168	+	22.8922i	−0.0227484	+	0.0394014i
$582$		0			0
$583$	57.0990	+	98.8984i	0.0979400	+	0.169637i
$584$	802.301	−	250.678i	1.37380	−	0.429244i
$585$		0			0
$586$	481.190	−	48.7399i	0.821143	−	0.0831740i
$587$	−272.120	−	471.326i	−0.463578	−	0.802940i	0.535559	−	0.844498i	$-0.320101\pi$
$587$	−272.120	−	471.326i	−0.463578	−	0.802940i	−0.999136	+	0.0415583i	$0.986768\pi$
$588$		0			0
$589$	1100.82	+	635.562i	1.86897	+	1.07905i
$590$	−189.383	+	421.078i	−0.320988	+	0.713692i
$591$		0			0
$592$	−237.206	+	316.334i	−0.400687	+	0.534347i
$593$			629.312i			1.06123i	0.847612	+	0.530617i	$0.178040\pi$
$593$			629.312i			1.06123i	−0.847612	+	0.530617i	$0.821960\pi$
$594$		0			0
$595$			49.0317i			0.0824063i
$596$	−141.332	−	159.368i	−0.237134	−	0.267395i
$597$		0			0
$598$	−380.838	+	846.762i	−0.636852	+	1.41599i
$599$	−82.1059	−	47.4039i	−0.137072	−	0.0791384i	0.429896	−	0.902878i	$-0.358550\pi$
$599$	−82.1059	−	47.4039i	−0.137072	−	0.0791384i	−0.566968	+	0.823740i	$0.691884\pi$
$600$		0			0
$601$	−10.1162	−	17.5218i	−0.0168323	−	0.0291544i	0.857487	−	0.514506i	$-0.172025\pi$
$601$	−10.1162	−	17.5218i	−0.0168323	−	0.0291544i	−0.874319	+	0.485352i	$0.838691\pi$
$602$	−1.14921	−	11.3457i	−0.00190899	−	0.0188467i
$603$		0			0
$604$	794.516	−	162.622i	1.31542	−	0.269242i
$605$	−303.852	−	526.286i	−0.502234	−	0.869895i
$606$		0			0
$607$	−544.261	+	942.688i	−0.896641	+	1.55303i	−0.0648813	+	0.997893i	$0.520667\pi$
$607$	−544.261	+	942.688i	−0.896641	+	1.55303i	−0.831760	+	0.555135i	$0.812666\pi$
$608$	1141.71	+	21.5438i	1.87781	+	0.0354339i
$609$		0			0
$610$	−370.308	+	266.915i	−0.607062	+	0.437566i
$611$	78.1679			0.127934
$612$		0			0
$613$			8.79521i			0.0143478i	0.999974	+	0.00717391i	$0.00228355\pi$
$613$			8.79521i			0.0143478i	−0.999974	+	0.00717391i	$0.997716\pi$
$614$	−623.020	+	449.069i	−1.01469	+	0.731382i
$615$		0			0
$616$	−5.17186	+	23.0457i	−0.00839587	+	0.0374118i
$617$	437.202	+	252.419i	0.708593	+	0.409106i	0.810540	−	0.585684i	$-0.199174\pi$
$617$	437.202	+	252.419i	0.708593	+	0.409106i	−0.101947	+	0.994790i	$0.532507\pi$
$618$		0			0
$619$	951.318	−	549.244i	1.53686	−	0.887308i	0.537843	−	0.843045i	$-0.319239\pi$
$619$	951.318	−	549.244i	1.53686	−	0.887308i	0.999020	−	0.0442628i	$-0.0140939\pi$
$620$	−811.782	+	166.156i	−1.30933	+	0.267994i
$621$		0			0
$622$	−95.3772	−	941.620i	−0.153340	−	1.51386i
$623$	76.6709	−	44.2660i	0.123067	−	0.0710529i
$624$		0			0
$625$	383.853	−	664.853i	0.614165	−	1.06377i
$626$	229.839	−	511.028i	0.367154	−	0.816338i
$627$		0			0
$628$	251.769	−	223.277i	0.400907	−	0.355536i
$629$	−286.685			−0.455779
$630$		0			0
$631$	−131.984			−0.209167			−0.104584	−	0.994516i	$-0.533351\pi$
$631$	−131.984			−0.209167			−0.104584	+	0.994516i	$0.533351\pi$
$632$	418.072	+	385.092i	0.661507	+	0.609323i
$633$		0			0
$634$	146.834	−	326.472i	0.231599	−	0.514941i
$635$	−99.3533	+	172.085i	−0.156462	+	0.271000i
$636$		0			0
$637$	646.892	−	373.483i	1.01553	−	0.586316i
$638$	270.247	−	27.3735i	0.423585	−	0.0429051i
$639$		0			0
$640$	−566.146	+	483.304i	−0.884603	+	0.755163i
$641$	564.096	−	325.681i	0.880025	−	0.508083i	0.00935827	−	0.999956i	$-0.497021\pi$
$641$	564.096	−	325.681i	0.880025	−	0.508083i	0.870667	+	0.491874i	$0.163688\pi$
$642$		0			0
$643$	−523.947	−	302.501i	−0.814847	−	0.470452i	0.0337893	−	0.999429i	$-0.489242\pi$
$643$	−523.947	−	302.501i	−0.814847	−	0.470452i	−0.848636	+	0.528977i	$0.822576\pi$
$644$	−83.0814	−	27.6897i	−0.129008	−	0.0429964i
$645$		0			0
$646$	484.132	+	671.666i	0.749431	+	1.03973i
$647$		−	1266.46i		−	1.95743i	−0.205226	−	0.978715i	$-0.565793\pi$
$647$		−	1266.46i		−	1.95743i	0.205226	−	0.978715i	$-0.434207\pi$
$648$		0			0
$649$	−161.260			−0.248474
$650$	−220.519	+	158.949i	−0.339260	+	0.244536i
$651$		0			0
$652$	406.734	+	135.558i	0.623825	+	0.207911i
$653$	−132.030	+	228.682i	−0.202189	+	0.350202i	−0.949234	−	0.314572i	$-0.898139\pi$
$653$	−132.030	+	228.682i	−0.202189	+	0.350202i	0.747044	+	0.664774i	$0.231472\pi$
$654$		0			0
$655$	143.733	+	248.952i	0.219439	+	0.380080i
$656$	−361.042	−	845.014i	−0.550369	−	1.28813i
$657$		0			0
$658$	0.743006	+	7.33540i	0.00112919	+	0.0111480i
$659$	−246.804	−	427.478i	−0.374513	−	0.648676i	0.615741	−	0.787949i	$-0.288857\pi$
$659$	−246.804	−	427.478i	−0.374513	−	0.648676i	−0.990254	+	0.139273i	$0.955524\pi$
$660$		0			0
$661$	−1071.29	−	618.508i	−1.62071	−	0.935716i	−0.986731	−	0.162364i	$-0.948088\pi$
$661$	−1071.29	−	618.508i	−1.62071	−	0.935716i	−0.633977	−	0.773352i	$-0.718578\pi$
$662$	−449.390	−	202.117i	−0.678837	−	0.305312i
$663$		0			0
$664$	−214.017	−	197.135i	−0.322315	−	0.296889i
$665$			150.821i			0.226798i
$666$		0			0
$667$			1007.15i			1.50997i
$668$	−457.979	+	406.150i	−0.685597	+	0.608008i
$669$		0			0
$670$	−782.932	−	352.130i	−1.16855	−	0.525567i
$671$	−138.073	−	79.7166i	−0.205772	−	0.118803i
$672$		0			0
$673$	−263.390	−	456.205i	−0.391367	−	0.677868i	0.601263	−	0.799051i	$-0.294664\pi$
$673$	−263.390	−	456.205i	−0.391367	−	0.677868i	−0.992630	+	0.121184i	$0.961331\pi$
$674$	140.770	−	14.2587i	0.208858	−	0.0211553i
$675$		0			0
$676$	−268.349	+	54.9260i	−0.396966	+	0.0812515i
$677$	179.206	+	310.394i	0.264706	+	0.458485i	0.967487	−	0.252922i	$-0.0813917\pi$
$677$	179.206	+	310.394i	0.264706	+	0.458485i	−0.702780	+	0.711407i	$0.748058\pi$
$678$		0			0
$679$	−18.4043	+	31.8772i	−0.0271050	+	0.0469472i
$680$	−526.628	−	118.185i	−0.774453	−	0.173801i
$681$		0			0
$682$	−169.225	−	234.777i	−0.248131	−	0.344247i
$683$	237.803			0.348175			0.174087	−	0.984730i	$-0.444303\pi$
$683$	237.803			0.348175			0.174087	+	0.984730i	$0.444303\pi$
$684$		0			0
$685$		−	961.972i		−	1.40434i
$686$	82.8431	+	114.933i	0.120763	+	0.167541i
$687$		0			0
$688$	124.629	+	15.0042i	0.181147	+	0.0218084i
$689$	−375.168	−	216.603i	−0.544511	−	0.314373i
$690$		0			0
$691$	1107.04	−	639.151i	1.60209	−	0.924966i	0.611018	−	0.791616i	$-0.290760\pi$
$691$	1107.04	−	639.151i	1.60209	−	0.924966i	0.991069	−	0.133349i	$-0.0425732\pi$
$692$	219.858	−	45.0008i	0.317714	−	0.0650301i
$693$		0			0
$694$	−565.800	+	57.3102i	−0.815274	+	0.0825796i
$695$	104.927	−	60.5796i	0.150974	−	0.0871649i
$696$		0			0
$697$	333.136	−	577.009i	0.477957	−	0.827847i
$698$	−930.585	−	418.538i	−1.33322	−	0.599625i
$699$		0			0
$700$	−17.0121	−	19.1830i	−0.0243030	−	0.0274043i
$701$	448.586			0.639923			0.319962	−	0.947430i	$-0.396330\pi$
$701$	448.586			0.639923			0.319962	+	0.947430i	$0.396330\pi$
$702$		0			0
$703$	−881.837			−1.25439
$704$	−235.057	−	111.097i	−0.333888	−	0.157809i
$705$		0			0
$706$	386.365	+	173.771i	0.547259	+	0.246134i
$707$	58.5550	−	101.420i	0.0828217	−	0.143451i
$708$		0			0
$709$	27.4595	−	15.8537i	0.0387298	−	0.0223607i	−0.480510	−	0.876989i	$-0.659548\pi$
$709$	27.4595	−	15.8537i	0.0387298	−	0.0223607i	0.519240	+	0.854629i	$0.326215\pi$
$710$	−103.802	−	1024.80i	−0.146200	−	1.44338i
$711$		0			0
$712$	290.636	+	930.186i	0.408197	+	1.30644i
$713$	929.306	−	536.535i	1.30337	−	0.752504i
$714$		0			0
$715$	−315.286	−	182.030i	−0.440959	−	0.254588i
$716$	−233.229	+	699.789i	−0.325738	+	0.977359i
$717$		0			0
$718$	−15.3502	+	11.0643i	−0.0213790	+	0.0154099i
$719$			1090.16i			1.51622i	0.652127	+	0.758110i	$0.273877\pi$
$719$			1090.16i			1.51622i	−0.652127	+	0.758110i	$0.726123\pi$
$720$		0			0
$721$	69.0391			0.0957546
$722$	1067.01	+	1480.33i	1.47785	+	2.05031i
$723$		0			0
$724$	−946.477	−	315.446i	−1.30729	−	0.435699i
$725$	−147.436	+	255.366i	−0.203360	+	0.352229i
$726$		0			0
$727$	−34.1890	−	59.2171i	−0.0470275	−	0.0814540i	0.841553	−	0.540174i	$-0.181642\pi$
$727$	−34.1890	−	59.2171i	−0.0470275	−	0.0814540i	−0.888581	+	0.458720i	$0.848308\pi$
$728$	−26.7207	−	85.5201i	−0.0367043	−	0.117473i
$729$		0			0
$730$	−1215.83	+	123.152i	−1.66552	+	0.168702i
$731$	45.5085	+	78.8230i	0.0622551	+	0.107829i
$732$		0			0
$733$	−212.805	−	122.863i	−0.290321	−	0.167617i	0.347766	−	0.937582i	$-0.386941\pi$
$733$	−212.805	−	122.863i	−0.290321	−	0.167617i	−0.638087	+	0.769965i	$0.720274\pi$
$734$	−360.830	+	802.276i	−0.491594	+	1.09302i
$735$		0			0
$736$	497.660	−	825.598i	0.676168	−	1.12174i
$737$		−	299.838i		−	0.406836i
$738$		0			0
$739$			1019.01i			1.37890i	0.724331	+	0.689452i	$0.242149\pi$
$739$			1019.01i			1.37890i	−0.724331	+	0.689452i	$0.757851\pi$
$740$	430.085	−	381.413i	0.581197	−	0.515423i
$741$		0			0
$742$	16.7603	−	37.2652i	0.0225880	−	0.0502226i
$743$	−890.910	−	514.367i	−1.19907	−	0.692284i	−0.238723	−	0.971088i	$-0.576729\pi$
$743$	−890.910	−	514.367i	−1.19907	−	0.692284i	−0.960348	+	0.278803i	$0.910062\pi$
$744$		0			0
$745$	154.844	+	268.197i	0.207844	+	0.359996i
$746$	97.8553	+	966.085i	0.131173	+	1.29502i
$747$		0			0
$748$	−37.8007	−	184.681i	−0.0505357	−	0.246900i
$749$	21.6613	+	37.5185i	0.0289204	+	0.0500915i
$750$		0			0
$751$	582.388	−	1008.73i	0.775483	−	1.34318i	−0.159039	−	0.987272i	$-0.550840\pi$
$751$	582.388	−	1008.73i	0.775483	−	1.34318i	0.934522	−	0.355904i	$-0.115827\pi$
$752$	−80.5772	−	9.70072i	−0.107150	−	0.0128999i
$753$		0			0
$754$	−835.906	+	602.515i	−1.10863	+	0.799092i
$755$	−1179.07			−1.56168
$756$		0			0
$757$		−	962.868i		−	1.27195i	−0.771709	−	0.635976i	$-0.780598\pi$
$757$		−	962.868i		−	1.27195i	0.771709	−	0.635976i	$-0.219402\pi$
$758$	307.653	−	221.754i	0.405875	−	0.292552i
$759$		0			0
$760$	−1619.90	−	363.534i	−2.13145	−	0.478334i
$761$	−1027.09	−	592.990i	−1.34966	−	0.779225i	−0.361457	−	0.932389i	$-0.617720\pi$
$761$	−1027.09	−	592.990i	−1.34966	−	0.779225i	−0.988201	+	0.153164i	$0.951054\pi$
$762$		0			0
$763$	75.1131	−	43.3666i	0.0984445	−	0.0568369i
$764$	30.7841	+	150.400i	0.0402933	+	0.196859i
$765$		0			0
$766$	94.4959	+	932.920i	0.123363	+	1.21791i
$767$	529.776	−	305.866i	0.690712	−	0.398783i
$768$		0			0
$769$	−540.055	+	935.403i	−0.702282	+	1.21639i	0.265381	+	0.964144i	$0.414502\pi$
$769$	−540.055	+	935.403i	−0.702282	+	1.21639i	−0.967663	+	0.252245i	$0.918831\pi$
$770$	14.0851	−	31.3171i	0.0182924	−	0.0406716i
$771$		0			0
$772$	−442.535	−	499.007i	−0.573232	−	0.646383i
$773$	−1304.13			−1.68711			−0.843553	−	0.537046i	$-0.819540\pi$
$773$	−1304.13			−1.68711			−0.843553	+	0.537046i	$0.819540\pi$
$774$		0			0
$775$	314.171			0.405382
$776$	−298.017	−	274.508i	−0.384043	−	0.353748i
$777$		0			0
$778$	56.0059	−	124.525i	0.0719870	−	0.160057i
$779$	1024.72	−	1774.87i	1.31543	−	2.27840i
$780$		0			0
$781$	311.563	−	179.881i	0.398928	−	0.230321i
$782$	695.399	−	70.4373i	0.889257	−	0.0900733i
$783$		0			0
$784$	−713.180	+	304.715i	−0.909668	+	0.388666i
$785$	−423.699	+	244.622i	−0.539743	+	0.311621i
$786$		0			0
$787$	76.4534	+	44.1404i	0.0971453	+	0.0560869i	0.547786	−	0.836619i	$-0.315471\pi$
$787$	76.4534	+	44.1404i	0.0971453	+	0.0560869i	−0.450640	+	0.892706i	$0.648804\pi$
$788$	238.506	−	715.625i	0.302673	−	0.908154i
$789$		0			0
$790$	−483.209	−	670.386i	−0.611657	−	0.848589i
$791$			72.6791i			0.0918826i
$792$		0			0
$793$	604.805			0.762679
$794$	−277.156	+	199.772i	−0.349063	+	0.251602i
$795$		0			0
$796$	12.1811	−	36.5488i	0.0153029	−	0.0459156i
$797$	527.678	−	913.965i	0.662080	−	1.14676i	−0.317988	−	0.948095i	$-0.603007\pi$
$797$	527.678	−	913.965i	0.662080	−	1.14676i	0.980068	−	0.198662i	$-0.0636596\pi$
$798$		0			0
$799$	−29.4229	−	50.9619i	−0.0368246	−	0.0637821i
$800$	247.041	−	136.481i	0.308802	−	0.170601i
$801$		0			0
$802$	−62.4931	−	616.968i	−0.0779215	−	0.769287i
$803$	−213.412	−	369.641i	−0.265769	−	0.460325i
$804$		0			0
$805$	110.264	+	63.6608i	0.136973	+	0.0790817i
$806$	1001.25	+	450.322i	1.24225	+	0.558712i
$807$		0			0
$808$	948.170	+	873.373i	1.17348	+	1.08091i
$809$			635.537i			0.785583i	0.919628	+	0.392792i	$0.128491\pi$
$809$			635.537i			0.785583i	−0.919628	+	0.392792i	$0.871509\pi$
$810$		0			0
$811$		−	338.192i		−	0.417006i	−0.978022	−	0.208503i	$-0.933141\pi$
$811$		−	338.192i		−	0.417006i	0.978022	−	0.208503i	$-0.0668590\pi$
$812$	−64.4864	−	72.7156i	−0.0794168	−	0.0895513i
$813$		0			0
$814$	183.109	+	82.3546i	0.224949	+	0.101173i
$815$	−539.808	−	311.658i	−0.662341	−	0.382403i
$816$		0			0
$817$	139.983	+	242.458i	0.171338	+	0.296767i
$818$	253.764	−	25.7039i	0.310225	−	0.0314229i
$819$		0			0
$820$	267.896	+	1308.84i	0.326702	+	1.59615i
$821$	−360.772	−	624.876i	−0.439430	−	0.761116i	0.558215	−	0.829696i	$-0.311486\pi$
$821$	−360.772	−	624.876i	−0.439430	−	0.761116i	−0.997646	+	0.0685804i	$0.978153\pi$
$822$		0			0
$823$	−426.201	+	738.203i	−0.517863	+	0.896965i	0.481921	+	0.876214i	$0.339939\pi$
$823$	−426.201	+	738.203i	−0.517863	+	0.896965i	−0.999785	+	0.0207510i	$0.993394\pi$
$824$	−166.410	+	741.518i	−0.201954	+	0.899900i
$825$		0			0
$826$	33.7386	+	46.8077i	0.0408458	+	0.0566679i
$827$	210.452			0.254476			0.127238	−	0.991872i	$-0.459389\pi$
$827$	210.452			0.254476			0.127238	+	0.991872i	$0.459389\pi$
$828$		0			0
$829$		−	471.735i		−	0.569041i	−0.958670	−	0.284521i	$-0.908166\pi$
$829$		−	471.735i		−	0.569041i	0.958670	−	0.284521i	$-0.0918344\pi$
$830$	247.362	+	343.181i	0.298027	+	0.413471i
$831$		0			0
$832$	982.941	−	80.8601i	1.18142	−	0.0971876i
$833$	−486.988	−	281.162i	−0.584619	−	0.337530i
$834$		0			0
$835$	770.725	−	444.978i	0.923024	−	0.532908i
$836$	−116.274	−	568.075i	−0.139084	−	0.679516i
$837$		0			0
$838$	−151.836	+	15.3795i	−0.181188	+	0.0183526i
$839$	594.093	−	343.000i	0.708097	−	0.408820i	−0.102259	−	0.994758i	$-0.532607\pi$
$839$	594.093	−	343.000i	0.708097	−	0.408820i	0.810356	+	0.585938i	$0.199274\pi$
$840$		0			0
$841$	−138.374	+	239.671i	−0.164535	+	0.284984i
$842$	1246.07	+	560.430i	1.47989	+	0.665594i
$843$		0			0
$844$	−376.264	+	333.682i	−0.445810	+	0.395358i
$845$	398.234			0.471282
$846$		0			0
$847$	−75.9450			−0.0896635
$848$	359.850	+	269.838i	0.424352	+	0.318205i
$849$		0			0
$850$	186.632	+	83.9391i	0.219567	+	0.0987519i
$851$	−372.219	+	644.703i	−0.437391	+	0.757583i
$852$		0			0
$853$	−732.848	+	423.110i	−0.859141	+	0.496026i	−0.863725	−	0.503964i	$-0.831874\pi$
$853$	−732.848	+	423.110i	−0.859141	+	0.496026i	0.00458321	+	0.999989i	$0.498541\pi$
$854$	5.74882	+	56.7558i	0.00673164	+	0.0664588i
$855$		0			0
$856$	−455.182	+	142.221i	−0.531755	+	0.166146i
$857$	−860.917	+	497.051i	−1.00457	+	0.579989i	−0.909597	−	0.415491i	$-0.863610\pi$
$857$	−860.917	+	497.051i	−1.00457	+	0.579989i	−0.0949730	+	0.995480i	$0.530276\pi$
$858$		0			0
$859$	413.570	+	238.775i	0.481456	+	0.277968i	0.721023	−	0.692911i	$-0.243672\pi$
$859$	413.570	+	238.775i	0.481456	+	0.277968i	−0.239567	+	0.970880i	$0.577006\pi$
$860$	−173.140	−	57.7049i	−0.201326	−	0.0670987i
$861$		0			0
$862$	−26.5465	+	19.1346i	−0.0307965	+	0.0221979i
$863$			1244.01i			1.44150i	0.693196	+	0.720749i	$0.256202\pi$
$863$			1244.01i			1.44150i	−0.693196	+	0.720749i	$0.743798\pi$
$864$		0			0
$865$	−326.272			−0.377194
$866$	−722.801	−	1002.79i	−0.834644	−	1.15795i
$867$		0			0
$868$	−32.7417	+	98.2397i	−0.0377209	+	0.113179i
$869$	144.315	−	249.961i	0.166070	−	0.287642i
$870$		0			0
$871$	568.713	+	985.040i	0.652943	+	1.13093i
$872$	284.731	+	911.286i	0.326526	+	1.04505i
$873$		0			0
$874$	2139.04	−	216.664i	2.44741	−	0.247899i
$875$	−34.1926	−	59.2233i	−0.0390773	−	0.0676838i
$876$		0			0
$877$	1163.95	+	672.007i	1.32719	+	0.766256i	0.984865	−	0.173324i	$-0.0554507\pi$
$877$	1163.95	+	672.007i	1.32719	+	0.766256i	0.342330	+	0.939580i	$0.388784\pi$
$878$	458.089	−	1018.52i	0.521741	−	1.16005i
$879$		0			0
$880$	302.413	+	226.768i	0.343651	+	0.257691i
$881$		−	814.455i		−	0.924467i	−0.886758	−	0.462233i	$-0.847048\pi$
$881$		−	814.455i		−	0.924467i	0.886758	−	0.462233i	$-0.152952\pi$
$882$		0			0
$883$		−	363.806i		−	0.412011i	−0.978551	−	0.206006i	$-0.933953\pi$
$883$		−	363.806i		−	0.412011i	0.978551	−	0.206006i	$-0.0660465\pi$
$884$	474.474	+	535.023i	0.536736	+	0.605229i
$885$		0			0
$886$	352.824	−	784.476i	0.398222	−	0.885414i
$887$	624.016	+	360.276i	0.703513	+	0.406173i	0.808655	−	0.588284i	$-0.200196\pi$
$887$	624.016	+	360.276i	0.703513	+	0.406173i	−0.105141	+	0.994457i	$0.533530\pi$
$888$		0			0
$889$	12.4162	+	21.5056i	0.0139665	+	0.0241907i
$890$	−142.782	−	1409.63i	−0.160430	−	1.58386i
$891$		0			0
$892$	−1078.86	+	220.823i	−1.20949	+	0.247559i
$893$	−90.5042	−	156.758i	−0.101348	−	0.175541i
$894$		0			0
$895$	536.210	−	928.744i	0.599118	−	1.03770i
$896$	16.9311	+	91.4721i	0.0188964	+	0.102089i
$897$		0			0
$898$	372.281	−	268.337i	0.414567	−	0.298817i
$899$	1190.91			1.32470
$900$		0			0
$901$			326.123i			0.361956i
$902$	−378.533	+	272.844i	−0.419659	+	0.302487i
$903$		0			0
$904$	−780.614	−	175.184i	−0.863511	−	0.193787i
$905$	1256.14	+	725.234i	1.38800	+	0.801364i
$906$		0			0
$907$	−311.241	+	179.695i	−0.343155	+	0.198121i	−0.661666	−	0.749798i	$-0.730150\pi$
$907$	−311.241	+	179.695i	−0.343155	+	0.198121i	0.318511	+	0.947919i	$0.396817\pi$
$908$	139.018	−	28.4543i	0.153103	−	0.0313374i
$909$		0			0
$910$	13.1272	+	129.600i	0.0144255	+	0.142417i
$911$	1431.05	−	826.217i	1.57086	−	0.906934i	0.574792	−	0.818300i	$-0.305083\pi$
$911$	1431.05	−	826.217i	1.57086	−	0.906934i	0.996064	−	0.0886344i	$-0.0282503\pi$
$912$		0			0
$913$	−73.8770	+	127.959i	−0.0809167	+	0.140152i
$914$	−644.865	+	1433.80i	−0.705541	+	1.56871i
$915$		0			0
$916$	864.730	−	766.869i	0.944028	−	0.837193i
$917$	35.9247			0.0391763
$918$		0			0
$919$	1051.67			1.14436			0.572181	−	0.820128i	$-0.306098\pi$
$919$	1051.67			1.14436			0.572181	+	0.820128i	$0.306098\pi$
$920$	−949.528	+	1030.85i	−1.03210	+	1.12049i
$921$		0			0
$922$	−360.098	+	800.648i	−0.390562	+	0.868382i
$923$	−682.371	+	1181.90i	−0.739297	+	1.28050i
$924$		0			0
$925$	−188.755	+	108.978i	−0.204059	+	0.117814i
$926$	−774.697	+	78.4695i	−0.836606	+	0.0847402i
$927$		0			0
$928$	936.443	−	517.349i	1.00910	−	0.557488i
$929$	436.589	−	252.065i	0.469956	−	0.271329i	−0.246265	−	0.969202i	$-0.579203\pi$
$929$	436.589	−	252.065i	0.469956	−	0.271329i	0.716221	+	0.697873i	$0.245870\pi$
$930$		0			0
$931$	−1497.97	−	864.851i	−1.60899	−	0.928948i
$932$	−203.307	−	67.7591i	−0.218141	−	0.0727029i
$933$		0			0
$934$	−362.862	−	503.421i	−0.388503	−	0.538995i
$935$			274.069i			0.293122i
$936$		0			0
$937$	−360.581			−0.384825			−0.192412	−	0.981314i	$-0.561631\pi$
$937$	−360.581			−0.384825			−0.192412	+	0.981314i	$0.561631\pi$
$938$	−87.0319	+	62.7320i	−0.0927845	+	0.0668784i
$939$		0			0
$940$	111.941	+	37.3082i	0.119086	+	0.0396896i
$941$	−116.208	+	201.278i	−0.123494	+	0.213898i	−0.921143	−	0.389224i	$-0.872743\pi$
$941$	−116.208	+	201.278i	−0.123494	+	0.213898i	0.797649	+	0.603122i	$0.206077\pi$
$942$		0			0
$943$	−865.060	−	1498.33i	−0.917349	−	1.58890i
$944$	−584.063	+	249.548i	−0.618711	+	0.264352i
$945$		0			0
$946$	−6.42366	−	63.4182i	−0.00679034	−	0.0670382i
$947$	270.427	+	468.394i	0.285562	+	0.494608i	0.972745	−	0.231876i	$-0.0744863\pi$
$947$	270.427	+	468.394i	0.285562	+	0.494608i	−0.687183	+	0.726484i	$0.741153\pi$
$948$		0			0
$949$	1402.22	+	809.573i	1.47758	+	0.853080i
$950$	574.076	+	258.195i	0.604291	+	0.271784i
$951$		0			0
$952$	−45.6974	+	49.6109i	−0.0480014	+	0.0521123i
$953$			1654.49i			1.73609i	0.496488	+	0.868044i	$0.334623\pi$
$953$			1654.49i			1.73609i	−0.496488	+	0.868044i	$0.665377\pi$
$954$		0			0
$955$		−	223.196i		−	0.233713i
$956$	−535.764	+	475.132i	−0.560423	+	0.497000i
$957$		0			0
$958$	1126.36	+	506.590i	1.17574	+	0.528800i
$959$	−104.112	−	60.1091i	−0.108563	−	0.0626790i
$960$		0			0
$961$	−153.927	−	266.609i	−0.160173	−	0.277428i
$962$	−757.760	+	76.7539i	−0.787693	+	0.0797858i
$963$		0			0
$964$	−245.893	+	50.3295i	−0.255075	+	0.0522091i
$965$	484.842	+	839.771i	0.502427	+	0.870229i
$966$		0			0
$967$	564.485	−	977.717i	0.583749	−	1.01108i	−0.411281	−	0.911509i	$-0.634918\pi$
$967$	564.485	−	977.717i	0.583749	−	1.01108i	0.995030	−	0.0995746i	$-0.0317482\pi$
$968$	183.056	−	815.691i	0.189107	−	0.842656i
$969$		0			0
$970$	344.449	+	477.876i	0.355103	+	0.492655i
$971$	−1762.47			−1.81511			−0.907555	−	0.419933i	$-0.862054\pi$
$971$	−1762.47			−1.81511			−0.907555	+	0.419933i	$0.862054\pi$
$972$		0			0
$973$		−	15.1413i		−	0.0155615i
$974$	−61.9512	−	85.9486i	−0.0636049	−	0.0882430i
$975$		0			0
$976$	−623.445	−	75.0569i	−0.638776	−	0.0769026i
$977$	−835.276	−	482.247i	−0.854939	−	0.493599i	0.00737503	−	0.999973i	$-0.497652\pi$
$977$	−835.276	−	482.247i	−0.854939	−	0.493599i	−0.862314	+	0.506373i	$0.830986\pi$
$978$		0			0
$979$	428.561	−	247.430i	0.437754	−	0.252738i
$980$	1104.65	−	226.100i	1.12719	−	0.230714i
$981$		0			0
$982$	1811.26	−	183.463i	1.84446	−	0.186826i
$983$	289.032	−	166.872i	0.294030	−	0.169758i	−0.345728	−	0.938335i	$-0.612368\pi$
$983$	289.032	−	166.872i	0.294030	−	0.169758i	0.639758	+	0.768577i	$0.279035\pi$
$984$		0			0
$985$	−548.345	+	949.761i	−0.556695	+	0.964224i
$986$	707.452	+	318.182i	0.717497	+	0.322700i
$987$		0			0
$988$	1459.48	+	1645.72i	1.47720	+	1.66571i
$989$	236.345			0.238974
$990$		0			0
$991$	1203.94			1.21487			0.607435	−	0.794369i	$-0.292198\pi$
$991$	1203.94			1.21487			0.607435	+	0.794369i	$0.292198\pi$
$992$	−976.229	−	588.458i	−0.984102	−	0.593204i
$993$		0			0
$994$	−117.398	−	52.8005i	−0.118106	−	0.0531192i
$995$	−28.0054	+	48.5067i	−0.0281461	+	0.0487505i
$996$		0			0
$997$	−1018.52	+	588.045i	−1.02159	+	0.589815i	−0.914564	−	0.404442i	$-0.867466\pi$
$997$	−1018.52	+	588.045i	−1.02159	+	0.589815i	−0.107025	+	0.994256i	$0.534132\pi$
$998$	−21.4145	−	211.416i	−0.0214574	−	0.211840i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.j.a.125.7		44
3.2	odd	2		72.3.j.a.5.16	yes	44
4.3	odd	2		864.3.n.a.17.18		44
8.3	odd	2		864.3.n.a.17.5		44
8.5	even	2	inner	216.3.j.a.125.15		44
9.2	odd	6	inner	216.3.j.a.197.15		44
9.4	even	3		648.3.h.a.485.43		44
9.5	odd	6		648.3.h.a.485.2		44
9.7	even	3		72.3.j.a.29.8	yes	44
12.11	even	2		288.3.n.a.113.22		44
24.5	odd	2		72.3.j.a.5.8	✓	44
24.11	even	2		288.3.n.a.113.1		44
36.7	odd	6		288.3.n.a.209.1		44
36.11	even	6		864.3.n.a.305.5		44
36.23	even	6		2592.3.h.a.1457.35		44
36.31	odd	6		2592.3.h.a.1457.10		44
72.5	odd	6		648.3.h.a.485.44		44
72.11	even	6		864.3.n.a.305.18		44
72.13	even	6		648.3.h.a.485.1		44
72.29	odd	6	inner	216.3.j.a.197.7		44
72.43	odd	6		288.3.n.a.209.22		44
72.59	even	6		2592.3.h.a.1457.9		44
72.61	even	6		72.3.j.a.29.16	yes	44
72.67	odd	6		2592.3.h.a.1457.36		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.j.a.5.8	✓	44	24.5	odd	2
72.3.j.a.5.16	yes	44	3.2	odd	2
72.3.j.a.29.8	yes	44	9.7	even	3
72.3.j.a.29.16	yes	44	72.61	even	6
216.3.j.a.125.7		44	1.1	even	1	trivial
216.3.j.a.125.15		44	8.5	even	2	inner
216.3.j.a.197.7		44	72.29	odd	6	inner
216.3.j.a.197.15		44	9.2	odd	6	inner
288.3.n.a.113.1		44	24.11	even	2
288.3.n.a.113.22		44	12.11	even	2
288.3.n.a.209.1		44	36.7	odd	6
288.3.n.a.209.22		44	72.43	odd	6
648.3.h.a.485.1		44	72.13	even	6
648.3.h.a.485.2		44	9.5	odd	6
648.3.h.a.485.43		44	9.4	even	3
648.3.h.a.485.44		44	72.5	odd	6
864.3.n.a.17.5		44	8.3	odd	2
864.3.n.a.17.18		44	4.3	odd	2
864.3.n.a.305.5		44	36.11	even	6
864.3.n.a.305.18		44	72.11	even	6
2592.3.h.a.1457.9		44	72.59	even	6
2592.3.h.a.1457.10		44	36.31	odd	6
2592.3.h.a.1457.35		44	36.23	even	6
2592.3.h.a.1457.36		44	72.67	odd	6

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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.16946 - 1.62246i) q^{2} +(-1.26474 + 3.79479i) q^{4} +(2.90774 - 5.03636i) q^{5} +(-0.363382 - 0.629396i) q^{7} +(7.63595 - 2.38585i) q^{8} +O(q^{10})\)	\(q+(-1.16946 - 1.62246i) q^{2} +(-1.26474 + 3.79479i) q^{4} +(2.90774 - 5.03636i) q^{5} +(-0.363382 - 0.629396i) q^{7} +(7.63595 - 2.38585i) q^{8} +(-11.5718 + 1.17211i) q^{10} +(-2.03117 - 3.51809i) q^{11} +(13.3457 + 7.70516i) q^{13} +(-0.596210 + 1.32562i) q^{14} +(-12.8008 - 9.59887i) q^{16} -11.6011i q^{17} -35.6847i q^{19} +(15.4344 + 17.4040i) q^{20} +(-3.33259 + 7.40973i) q^{22} +(-26.0887 - 15.0623i) q^{23} +(-4.40992 - 7.63821i) q^{25} +(-3.10595 - 30.6638i) q^{26} +(2.84801 - 0.582934i) q^{28} +(-16.7164 - 28.9536i) q^{29} +(-17.8105 + 30.8487i) q^{31} +(-0.603728 + 31.9943i) q^{32} +(-18.8223 + 13.5669i) q^{34} -4.22648 q^{35} -24.7119i q^{37} +(-57.8969 + 41.7317i) q^{38} +(10.1874 - 45.3948i) q^{40} +(49.7376 + 28.7160i) q^{41} +(-6.79446 + 3.92278i) q^{43} +(15.9193 - 3.25838i) q^{44} +(6.07162 + 59.9427i) q^{46} +(4.39286 - 2.53622i) q^{47} +(24.2359 - 41.9778i) q^{49} +(-7.23546 + 16.0875i) q^{50} +(-46.1184 + 40.8992i) q^{52} -28.1114 q^{53} -23.6244 q^{55} +(-4.27641 - 3.93906i) q^{56} +(-27.4270 + 60.9816i) q^{58} +(19.8481 - 34.3780i) q^{59} +(33.9886 - 19.6234i) q^{61} +(70.8793 - 7.17940i) q^{62} +(52.6155 - 36.4364i) q^{64} +(77.6119 - 44.8092i) q^{65} +(63.9208 + 36.9047i) q^{67} +(44.0236 + 14.6724i) q^{68} +(4.94269 + 6.85730i) q^{70} +88.5602i q^{71} +105.069 q^{73} +(-40.0941 + 28.8995i) q^{74} +(135.416 + 45.1320i) q^{76} +(-1.47618 + 2.55682i) q^{77} +(35.5251 + 61.5313i) q^{79} +(-85.5649 + 36.5586i) q^{80} +(-11.5754 - 114.279i) q^{82} +(-18.1858 - 31.4988i) q^{83} +(-58.4271 - 33.7329i) q^{85} +(14.3104 + 6.43621i) q^{86} +(-23.9035 - 22.0179i) q^{88} +121.817i q^{89} -11.1997i q^{91} +(90.1540 - 79.9513i) q^{92} +(-9.25217 - 4.16124i) q^{94} +(-179.721 - 103.762i) q^{95} +(-25.3236 - 43.8618i) q^{97} +(-96.4501 + 9.76948i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7}+O(q^{10}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7	\( 44 q + 3 q^{2} - q^{4} - 2 q^{7} + 4 q^{10} + 48 q^{14} - q^{16} + 66 q^{20} + 7 q^{22} + 6 q^{23} - 72 q^{25} + 28 q^{28} - 2 q^{31} + 93 q^{32} + 9 q^{34} - 99 q^{38} - 56 q^{40} - 66 q^{41} + 72 q^{46} + 6 q^{47} - 72 q^{49} - 189 q^{50} - 42 q^{52} + 92 q^{55} - 270 q^{56} - 38 q^{58} + 2 q^{64} + 6 q^{65} - 387 q^{68} - 4 q^{70} - 8 q^{73} + 432 q^{74} - 63 q^{76} - 2 q^{79} + 186 q^{82} + 615 q^{86} - 77 q^{88} + 624 q^{92} - 186 q^{94} - 144 q^{95} - 2 q^{97}+O(q^{100}) \) 44 * q + 3 * q^2 - q^4 - 2 * q^7 + 4 * q^10 + 48 * q^14 - q^16 + 66 * q^20 + 7 * q^22 + 6 * q^23 - 72 * q^25 + 28 * q^28 - 2 * q^31 + 93 * q^32 + 9 * q^34 - 99 * q^38 - 56 * q^40 - 66 * q^41 + 72 * q^46 + 6 * q^47 - 72 * q^49 - 189 * q^50 - 42 * q^52 + 92 * q^55 - 270 * q^56 - 38 * q^58 + 2 * q^64 + 6 * q^65 - 387 * q^68 - 4 * q^70 - 8 * q^73 + 432 * q^74 - 63 * q^76 - 2 * q^79 + 186 * q^82 + 615 * q^86 - 77 * q^88 + 624 * q^92 - 186 * q^94 - 144 * q^95 - 2 * q^97

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