LMFDB - Embedded newform 162.3.d.c.53.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,3,Mod(53,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("162.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	162.d (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:	$4.41418028264$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			53.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	162.53
Dual form			162.3.d.c.107.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.01910 + 2.89778i) q^{5} +(4.19615 + 7.26795i) q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.01910 + 2.89778i) q^{5} +(4.19615 + 7.26795i) q^{7} -2.82843i q^{8} +8.19615 q^{10} +(-12.7279 + 7.34847i) q^{11} +(10.5981 - 18.3564i) q^{13} +(10.2784 + 5.93426i) q^{14} +(-2.00000 - 3.46410i) q^{16} -7.76457i q^{17} +24.3923 q^{19} +(10.0382 - 5.79555i) q^{20} +(-10.3923 + 18.0000i) q^{22} +(-12.7279 - 7.34847i) q^{23} +(4.29423 + 7.43782i) q^{25} -29.9759i q^{26} +16.7846 q^{28} +(-30.7387 + 17.7470i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-5.49038 - 9.50962i) q^{34} +48.6381i q^{35} -60.5692 q^{37} +(29.8744 - 17.2480i) q^{38} +(8.19615 - 14.1962i) q^{40} +(-29.1301 - 16.8183i) q^{41} +(-4.58846 - 7.94744i) q^{43} +29.3939i q^{44} -20.7846 q^{46} +(14.6969 - 8.48528i) q^{47} +(-10.7154 + 18.5596i) q^{49} +(10.5187 + 6.07296i) q^{50} +(-21.1962 - 36.7128i) q^{52} -25.7605i q^{53} -85.1769 q^{55} +(20.5569 - 11.8685i) q^{56} +(-25.0981 + 43.4711i) q^{58} +(53.4083 + 30.8353i) q^{59} +(6.50000 + 11.2583i) q^{61} +11.3137i q^{62} -8.00000 q^{64} +(106.386 - 61.4217i) q^{65} +(-10.5885 + 18.3397i) q^{67} +(-13.4486 - 7.76457i) q^{68} +(34.3923 + 59.5692i) q^{70} +101.214i q^{71} +40.4115 q^{73} +(-74.1818 + 42.8289i) q^{74} +(24.3923 - 42.2487i) q^{76} +(-106.817 - 61.6706i) q^{77} +(-49.3731 - 85.5167i) q^{79} -23.1822i q^{80} -47.5692 q^{82} +(-89.6231 + 51.7439i) q^{83} +(22.5000 - 38.9711i) q^{85} +(-11.2394 - 6.48906i) q^{86} +(20.7846 + 36.0000i) q^{88} -134.130i q^{89} +177.885 q^{91} +(-25.4558 + 14.6969i) q^{92} +(12.0000 - 20.7846i) q^{94} +(122.427 + 70.6835i) q^{95} +(37.5692 + 65.0718i) q^{97} +30.3077i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4} - 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^4 - 8 * q^7	$ 8 q + 8 q^{4} - 8 q^{7} + 24 q^{10} + 64 q^{13} - 16 q^{16} + 112 q^{19} - 28 q^{25} - 32 q^{28} - 32 q^{31} + 60 q^{34} - 152 q^{37} + 24 q^{40} + 88 q^{43} - 252 q^{49} - 128 q^{52} - 432 q^{55} - 180 q^{58} + 52 q^{61} - 64 q^{64} + 40 q^{67} + 192 q^{70} + 448 q^{73} + 112 q^{76} - 104 q^{79} - 48 q^{82} + 180 q^{85} + 176 q^{91} + 96 q^{94} - 32 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^7 + 24 * q^10 + 64 * q^13 - 16 * q^16 + 112 * q^19 - 28 * q^25 - 32 * q^28 - 32 * q^31 + 60 * q^34 - 152 * q^37 + 24 * q^40 + 88 * q^43 - 252 * q^49 - 128 * q^52 - 432 * q^55 - 180 * q^58 + 52 * q^61 - 64 * q^64 + 40 * q^67 + 192 * q^70 + 448 * q^73 + 112 * q^76 - 104 * q^79 - 48 * q^82 + 180 * q^85 + 176 * q^91 + 96 * q^94 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	5.01910	+	2.89778i	1.00382	+	0.579555i	0.909376	−	0.415975i	$-0.136560\pi$
$5$	5.01910	+	2.89778i	1.00382	+	0.579555i	0.0944434	+	0.995530i	$0.469893\pi$
$6$		0			0
$7$	4.19615	+	7.26795i	0.599450	+	1.03828i	0.992902	+	0.118933i	$0.0379475\pi$
$7$	4.19615	+	7.26795i	0.599450	+	1.03828i	−0.393452	+	0.919345i	$0.628719\pi$
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	8.19615			0.819615
$11$	−12.7279	+	7.34847i	−1.15708	+	0.668043i	−0.950603	−	0.310408i	$-0.899534\pi$
$11$	−12.7279	+	7.34847i	−1.15708	+	0.668043i	−0.206480	+	0.978451i	$0.566201\pi$
$12$		0			0
$13$	10.5981	−	18.3564i	0.815237	−	1.41203i	−0.0939212	−	0.995580i	$-0.529940\pi$
$13$	10.5981	−	18.3564i	0.815237	−	1.41203i	0.909158	−	0.416452i	$-0.136726\pi$
$14$	10.2784	+	5.93426i	0.734174	+	0.423875i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$		−	7.76457i		−	0.456739i	−0.973574	−	0.228370i	$-0.926660\pi$
$17$		−	7.76457i		−	0.456739i	0.973574	−	0.228370i	$-0.0733395\pi$
$18$		0			0
$19$	24.3923			1.28381			0.641903	−	0.766786i	$-0.278145\pi$
$19$	24.3923			1.28381			0.641903	+	0.766786i	$0.278145\pi$
$20$	10.0382	−	5.79555i	0.501910	−	0.289778i
$21$		0			0
$22$	−10.3923	+	18.0000i	−0.472377	+	0.818182i
$23$	−12.7279	−	7.34847i	−0.553388	−	0.319499i	0.197099	−	0.980384i	$-0.436848\pi$
$23$	−12.7279	−	7.34847i	−0.553388	−	0.319499i	−0.750487	+	0.660885i	$0.770181\pi$
$24$		0			0
$25$	4.29423	+	7.43782i	0.171769	+	0.297513i
$26$		−	29.9759i		−	1.15292i
$27$		0			0
$28$	16.7846			0.599450
$29$	−30.7387	+	17.7470i	−1.05996	+	0.611966i	−0.925420	−	0.378942i	$-0.876288\pi$
$29$	−30.7387	+	17.7470i	−1.05996	+	0.611966i	−0.134536	+	0.990909i	$0.542954\pi$
$30$		0			0
$31$	−4.00000	+	6.92820i	−0.129032	+	0.223490i	−0.923302	−	0.384075i	$-0.874520\pi$
$31$	−4.00000	+	6.92820i	−0.129032	+	0.223490i	0.794270	+	0.607565i	$0.207854\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−5.49038	−	9.50962i	−0.161482	−	0.279695i
$35$			48.6381i			1.38966i
$36$		0			0
$37$	−60.5692			−1.63701			−0.818503	−	0.574502i	$-0.805196\pi$
$37$	−60.5692			−1.63701			−0.818503	+	0.574502i	$0.805196\pi$
$38$	29.8744	−	17.2480i	0.786167	−	0.453894i
$39$		0			0
$40$	8.19615	−	14.1962i	0.204904	−	0.354904i
$41$	−29.1301	−	16.8183i	−0.710490	−	0.410201i	0.100753	−	0.994912i	$-0.467875\pi$
$41$	−29.1301	−	16.8183i	−0.710490	−	0.410201i	−0.811242	+	0.584710i	$0.801208\pi$
$42$		0			0
$43$	−4.58846	−	7.94744i	−0.106708	−	0.184824i	0.807727	−	0.589557i	$-0.200698\pi$
$43$	−4.58846	−	7.94744i	−0.106708	−	0.184824i	−0.914435	+	0.404733i	$0.867364\pi$
$44$			29.3939i			0.668043i
$45$		0			0
$46$	−20.7846			−0.451839
$47$	14.6969	−	8.48528i	0.312701	−	0.180538i	−0.335434	−	0.942064i	$-0.608883\pi$
$47$	14.6969	−	8.48528i	0.312701	−	0.180538i	0.648134	+	0.761526i	$0.275549\pi$
$48$		0			0
$49$	−10.7154	+	18.5596i	−0.218681	+	0.378767i
$50$	10.5187	+	6.07296i	0.210373	+	0.121459i
$51$		0			0
$52$	−21.1962	−	36.7128i	−0.407618	−	0.706016i
$53$		−	25.7605i		−	0.486046i	−0.970020	−	0.243023i	$-0.921861\pi$
$53$		−	25.7605i		−	0.486046i	0.970020	−	0.243023i	$-0.0781391\pi$
$54$		0			0
$55$	−85.1769			−1.54867
$56$	20.5569	−	11.8685i	0.367087	−	0.211938i
$57$		0			0
$58$	−25.0981	+	43.4711i	−0.432725	+	0.749502i
$59$	53.4083	+	30.8353i	0.905225	+	0.522632i	0.878892	−	0.477021i	$-0.158283\pi$
$59$	53.4083	+	30.8353i	0.905225	+	0.522632i	0.0263336	+	0.999653i	$0.491617\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.106557	+	0.184563i	0.914373	−	0.404872i	$-0.132684\pi$
$61$	6.50000	+	11.2583i	0.106557	+	0.184563i	−0.807816	+	0.589435i	$0.799351\pi$
$62$			11.3137i			0.182479i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	106.386	−	61.4217i	1.63670	−	0.944950i
$66$		0			0
$67$	−10.5885	+	18.3397i	−0.158037	+	0.273728i	−0.934161	−	0.356853i	$-0.883850\pi$
$67$	−10.5885	+	18.3397i	−0.158037	+	0.273728i	0.776124	+	0.630580i	$0.217183\pi$
$68$	−13.4486	−	7.76457i	−0.197774	−	0.114185i
$69$		0			0
$70$	34.3923	+	59.5692i	0.491319	+	0.850989i
$71$			101.214i			1.42555i	0.701392	+	0.712776i	$0.252562\pi$
$71$			101.214i			1.42555i	−0.701392	+	0.712776i	$0.747438\pi$
$72$		0			0
$73$	40.4115			0.553583			0.276791	−	0.960930i	$-0.410729\pi$
$73$	40.4115			0.553583			0.276791	+	0.960930i	$0.410729\pi$
$74$	−74.1818	+	42.8289i	−1.00246	+	0.578769i
$75$		0			0
$76$	24.3923	−	42.2487i	0.320951	−	0.555904i
$77$	−106.817	−	61.6706i	−1.38723	−	0.800917i
$78$		0			0
$79$	−49.3731	−	85.5167i	−0.624976	−	1.08249i	−0.988546	−	0.150923i	$-0.951776\pi$
$79$	−49.3731	−	85.5167i	−0.624976	−	1.08249i	0.363570	−	0.931567i	$-0.381558\pi$
$80$		−	23.1822i		−	0.289778i
$81$		0			0
$82$	−47.5692			−0.580112
$83$	−89.6231	+	51.7439i	−1.07980	+	0.623420i	−0.930841	−	0.365424i	$-0.880924\pi$
$83$	−89.6231	+	51.7439i	−1.07980	+	0.623420i	−0.148954	+	0.988844i	$0.547591\pi$
$84$		0			0
$85$	22.5000	−	38.9711i	0.264706	−	0.458484i
$86$	−11.2394	−	6.48906i	−0.130690	−	0.0754542i
$87$		0			0
$88$	20.7846	+	36.0000i	0.236189	+	0.409091i
$89$		−	134.130i		−	1.50708i	−0.657403	−	0.753539i	$-0.728345\pi$
$89$		−	134.130i		−	1.50708i	0.657403	−	0.753539i	$-0.271655\pi$
$90$		0			0
$91$	177.885			1.95478
$92$	−25.4558	+	14.6969i	−0.276694	+	0.159749i
$93$		0			0
$94$	12.0000	−	20.7846i	0.127660	−	0.221113i
$95$	122.427	+	70.6835i	1.28871	+	0.744037i
$96$		0			0
$97$	37.5692	+	65.0718i	0.387312	+	0.670843i	0.992087	−	0.125553i	$-0.0400705\pi$
$97$	37.5692	+	65.0718i	0.387312	+	0.670843i	−0.604775	+	0.796396i	$0.706737\pi$
$98$			30.3077i			0.309262i
$99$		0			0
$100$	17.1769			0.171769
$101$	25.1920	−	14.5446i	0.249426	−	0.144006i	−0.370075	−	0.929002i	$-0.620668\pi$
$101$	25.1920	−	14.5446i	0.249426	−	0.144006i	0.619501	+	0.784995i	$0.287335\pi$
$102$		0			0
$103$	−48.3538	+	83.7513i	−0.469455	+	0.813119i	−0.999390	−	0.0349186i	$-0.988883\pi$
$103$	−48.3538	+	83.7513i	−0.469455	+	0.813119i	0.529936	+	0.848038i	$0.322216\pi$
$104$	−51.9198	−	29.9759i	−0.499228	−	0.288230i
$105$		0			0
$106$	−18.2154	−	31.5500i	−0.171843	−	0.297641i
$107$		−	177.582i		−	1.65964i	−0.558030	−	0.829821i	$-0.688442\pi$
$107$		−	177.582i		−	1.65964i	0.558030	−	0.829821i	$-0.311558\pi$
$108$		0			0
$109$	61.9423			0.568278			0.284139	−	0.958783i	$-0.408292\pi$
$109$	61.9423			0.568278			0.284139	+	0.958783i	$0.408292\pi$
$110$	−104.320	+	60.2292i	−0.948364	+	0.547538i
$111$		0			0
$112$	16.7846	−	29.0718i	0.149863	−	0.259570i
$113$	95.0991	+	54.9055i	0.841585	+	0.485889i	0.857803	−	0.513979i	$-0.171829\pi$
$113$	95.0991	+	54.9055i	0.841585	+	0.485889i	−0.0162179	+	0.999868i	$0.505163\pi$
$114$		0			0
$115$	−42.5885	−	73.7654i	−0.370334	−	0.641438i
$116$			70.9881i			0.611966i
$117$		0			0
$118$	87.2154			0.739113
$119$	56.4325	−	32.5813i	0.474223	−	0.273793i
$120$		0			0
$121$	47.5000	−	82.2724i	0.392562	−	0.679937i
$122$	15.9217	+	9.19239i	0.130506	+	0.0753474i
$123$		0			0
$124$	8.00000	+	13.8564i	0.0645161	+	0.111745i
$125$		−	95.1140i		−	0.760912i
$126$		0			0
$127$	141.177			1.11163			0.555815	−	0.831306i	$-0.312406\pi$
$127$	141.177			1.11163			0.555815	+	0.831306i	$0.312406\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	86.8634	−	150.452i	0.668180	−	1.15732i
$131$	−46.0598	−	26.5927i	−0.351602	−	0.202997i	0.313789	−	0.949493i	$-0.398402\pi$
$131$	−46.0598	−	26.5927i	−0.351602	−	0.202997i	−0.665391	+	0.746495i	$0.731735\pi$
$132$		0			0
$133$	102.354	+	177.282i	0.769578	+	1.33295i
$134$			29.9487i			0.223498i
$135$		0			0
$136$	−21.9615			−0.161482
$137$	−1.41555	+	0.817267i	−0.0103325	+	0.00596545i	−0.505157	−	0.863027i	$-0.668566\pi$
$137$	−1.41555	+	0.817267i	−0.0103325	+	0.00596545i	0.494825	+	0.868993i	$0.335232\pi$
$138$		0			0
$139$	9.60770	−	16.6410i	0.0691201	−	0.119720i	−0.829394	−	0.558664i	$-0.811314\pi$
$139$	9.60770	−	16.6410i	0.0691201	−	0.119720i	0.898514	+	0.438944i	$0.144647\pi$
$140$	84.2436	+	48.6381i	0.601740	+	0.347415i
$141$		0			0
$142$	71.5692	+	123.962i	0.504009	+	0.872968i
$143$			311.519i			2.17845i
$144$		0			0
$145$	−205.708			−1.41867
$146$	49.4938	−	28.5753i	0.338999	−	0.195721i
$147$		0			0
$148$	−60.5692	+	104.909i	−0.409251	+	0.708844i
$149$	81.6504	+	47.1409i	0.547989	+	0.316382i	0.748311	−	0.663348i	$-0.230865\pi$
$149$	81.6504	+	47.1409i	0.547989	+	0.316382i	−0.200321	+	0.979730i	$0.564199\pi$
$150$		0			0
$151$	−16.0000	−	27.7128i	−0.105960	−	0.183529i	0.808170	−	0.588949i	$-0.200458\pi$
$151$	−16.0000	−	27.7128i	−0.105960	−	0.183529i	−0.914130	+	0.405421i	$0.867125\pi$
$152$		−	68.9919i		−	0.453894i
$153$		0			0
$154$	−174.431			−1.13267
$155$	−40.1528	+	23.1822i	−0.259050	+	0.149563i
$156$		0			0
$157$	−0.146171	+	0.253175i	−0.000931025	+	0.00161258i	−0.866491	−	0.499193i	$-0.833630\pi$
$157$	−0.146171	+	0.253175i	−0.000931025	+	0.00161258i	0.865560	+	0.500806i	$0.166963\pi$
$158$	−120.939	−	69.8241i	−0.765436	−	0.441924i
$159$		0			0
$160$	−16.3923	−	28.3923i	−0.102452	−	0.177452i
$161$		−	123.341i		−	0.766094i
$162$		0			0
$163$	28.7846			0.176593			0.0882963	−	0.996094i	$-0.471858\pi$
$163$	28.7846			0.176593			0.0882963	+	0.996094i	$0.471858\pi$
$164$	−58.2602	+	33.6365i	−0.355245	+	0.205101i
$165$		0			0
$166$	−73.1769	+	126.746i	−0.440825	+	0.763531i
$167$	48.5564	+	28.0341i	0.290757	+	0.167869i	0.638283	−	0.769802i	$-0.279645\pi$
$167$	48.5564	+	28.0341i	0.290757	+	0.167869i	−0.347526	+	0.937670i	$0.612978\pi$
$168$		0			0
$169$	−140.138	−	242.727i	−0.829222	−	1.43625i
$170$		−	63.6396i		−	0.374351i
$171$		0			0
$172$	−18.3538			−0.106708
$173$	191.350	−	110.476i	1.10607	−	0.638589i	0.168260	−	0.985743i	$-0.446185\pi$
$173$	191.350	−	110.476i	1.10607	−	0.638589i	0.937808	+	0.347154i	$0.112852\pi$
$174$		0			0
$175$	−36.0385	+	62.4205i	−0.205934	+	0.356688i
$176$	50.9117	+	29.3939i	0.289271	+	0.167011i
$177$		0			0
$178$	−94.8442	−	164.275i	−0.532833	−	0.922893i
$179$			248.347i			1.38741i	0.720258	+	0.693706i	$0.244023\pi$
$179$			248.347i			1.38741i	−0.720258	+	0.693706i	$0.755977\pi$
$180$		0			0
$181$	−158.277			−0.874458			−0.437229	−	0.899350i	$-0.644040\pi$
$181$	−158.277			−0.874458			−0.437229	+	0.899350i	$0.644040\pi$
$182$	217.863	−	125.783i	1.19705	−	0.691118i
$183$		0			0
$184$	−20.7846	+	36.0000i	−0.112960	+	0.195652i
$185$	−304.003	−	175.516i	−1.64326	−	0.948736i
$186$		0			0
$187$	57.0577	+	98.8269i	0.305121	+	0.528486i
$188$		−	33.9411i		−	0.180538i
$189$		0			0
$190$	199.923			1.05223
$191$	−29.9215	+	17.2752i	−0.156657	+	0.0904459i	−0.576279	−	0.817253i	$-0.695496\pi$
$191$	−29.9215	+	17.2752i	−0.156657	+	0.0904459i	0.419622	+	0.907699i	$0.362163\pi$
$192$		0			0
$193$	27.5000	−	47.6314i	0.142487	−	0.246795i	−0.785946	−	0.618296i	$-0.787823\pi$
$193$	27.5000	−	47.6314i	0.142487	−	0.246795i	0.928433	+	0.371501i	$0.121157\pi$
$194$	92.0254	+	53.1309i	0.474358	+	0.273871i
$195$		0			0
$196$	21.4308	+	37.1192i	0.109341	+	0.189384i
$197$		−	35.7170i		−	0.181305i	−0.995883	−	0.0906524i	$-0.971105\pi$
$197$		−	35.7170i		−	0.181305i	0.995883	−	0.0906524i	$-0.0288952\pi$
$198$		0			0
$199$	−375.138			−1.88512			−0.942559	−	0.334040i	$-0.891588\pi$
$199$	−375.138			−1.88512			−0.942559	+	0.334040i	$0.891588\pi$
$200$	21.0373	−	12.1459i	0.105187	−	0.0607296i
$201$		0			0
$202$	20.5692	−	35.6269i	0.101828	−	0.176371i
$203$	−257.969	−	148.938i	−1.27078	−	0.733687i
$204$		0			0
$205$	−97.4711	−	168.825i	−0.475469	−	0.823536i
$206$			136.765i			0.663909i
$207$		0			0
$208$	−84.7846			−0.407618
$209$	−310.463	+	179.246i	−1.48547	+	0.857637i
$210$		0			0
$211$	−153.727	+	266.263i	−0.728563	+	1.26191i	0.228927	+	0.973444i	$0.426478\pi$
$211$	−153.727	+	266.263i	−0.728563	+	1.26191i	−0.957490	+	0.288465i	$0.906855\pi$
$212$	−44.6184	−	25.7605i	−0.210464	−	0.121512i
$213$		0			0
$214$	−125.569	−	217.492i	−0.586772	−	1.01632i
$215$		−	53.1853i		−	0.247374i
$216$		0			0
$217$	−67.1384			−0.309394
$218$	75.8635	−	43.7998i	0.347998	−	0.200917i
$219$		0			0
$220$	−85.1769	+	147.531i	−0.387168	+	0.670594i
$221$	−142.530	−	82.2895i	−0.644930	−	0.372351i
$222$		0			0
$223$	169.296	+	293.229i	0.759175	+	1.31493i	0.943272	+	0.332022i	$0.107731\pi$
$223$	169.296	+	293.229i	0.759175	+	1.31493i	−0.184096	+	0.982908i	$0.558936\pi$
$224$		−	47.4740i		−	0.211938i
$225$		0			0
$226$	155.296			0.687151
$227$	−107.344	+	61.9752i	−0.472882	+	0.273019i	−0.717445	−	0.696615i	$-0.754689\pi$
$227$	−107.344	+	61.9752i	−0.472882	+	0.273019i	0.244563	+	0.969633i	$0.421355\pi$
$228$		0			0
$229$	−37.0289	+	64.1359i	−0.161698	+	0.280069i	−0.935478	−	0.353386i	$-0.885030\pi$
$229$	−37.0289	+	64.1359i	−0.161698	+	0.280069i	0.773780	+	0.633455i	$0.218364\pi$
$230$	−104.320	−	60.2292i	−0.453565	−	0.261866i
$231$		0			0
$232$	50.1962	+	86.9423i	0.216363	+	0.374751i
$233$			273.223i			1.17263i	0.810082	+	0.586316i	$0.199422\pi$
$233$			273.223i			1.17263i	−0.810082	+	0.586316i	$0.800578\pi$
$234$		0			0
$235$	98.3538			0.418527
$236$	106.817	−	61.6706i	0.452613	−	0.261316i
$237$		0			0
$238$	46.0770	−	79.8076i	0.193601	−	0.335326i
$239$	392.210	+	226.443i	1.64105	+	0.947459i	0.980462	+	0.196708i	$0.0630252\pi$
$239$	392.210	+	226.443i	1.64105	+	0.947459i	0.660585	+	0.750751i	$0.270308\pi$
$240$		0			0
$241$	191.344	+	331.418i	0.793959	+	1.37518i	0.923498	+	0.383604i	$0.125317\pi$
$241$	191.344	+	331.418i	0.793959	+	1.37518i	−0.129538	+	0.991574i	$0.541350\pi$
$242$		−	134.350i		−	0.555166i
$243$		0			0
$244$	26.0000			0.106557
$245$	−107.563	+	62.1016i	−0.439033	+	0.253476i
$246$		0			0
$247$	258.512	−	447.755i	1.04661	−	1.81277i
$248$	19.5959	+	11.3137i	0.0790158	+	0.0456198i
$249$		0			0
$250$	−67.2558	−	116.490i	−0.269023	−	0.465962i
$251$		−	73.9307i		−	0.294544i	−0.989096	−	0.147272i	$-0.952951\pi$
$251$		−	73.9307i		−	0.294544i	0.989096	−	0.147272i	$-0.0470493\pi$
$252$		0			0
$253$	216.000			0.853755
$254$	172.906	−	99.8272i	0.680731	−	0.393020i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	138.398	+	79.9044i	0.538515	+	0.310912i	0.744477	−	0.667648i	$-0.232699\pi$
$257$	138.398	+	79.9044i	0.538515	+	0.310912i	−0.205962	+	0.978560i	$0.566032\pi$
$258$		0			0
$259$	−254.158	−	440.214i	−0.981304	−	1.69967i
$260$		−	245.687i		−	0.944950i
$261$		0			0
$262$	−75.2154			−0.287082
$263$	224.392	−	129.553i	0.853202	−	0.492596i	−0.00852798	−	0.999964i	$-0.502715\pi$
$263$	224.392	−	129.553i	0.853202	−	0.492596i	0.861730	+	0.507367i	$0.169381\pi$
$264$		0			0
$265$	74.6481	−	129.294i	0.281691	−	0.487903i
$266$	250.715	+	144.750i	0.942536	+	0.544174i
$267$		0			0
$268$	21.1769	+	36.6795i	0.0790183	+	0.136864i
$269$			24.8168i			0.0922556i	0.998936	+	0.0461278i	$0.0146881\pi$
$269$			24.8168i			0.0922556i	−0.998936	+	0.0461278i	$0.985312\pi$
$270$		0			0
$271$	98.1154			0.362050			0.181025	−	0.983479i	$-0.442059\pi$
$271$	98.1154			0.362050			0.181025	+	0.983479i	$0.442059\pi$
$272$	−26.8973	+	15.5291i	−0.0988870	+	0.0570924i
$273$		0			0
$274$	−1.15579	+	2.00189i	−0.00421821	+	0.00730616i
$275$	−109.313	−	63.1120i	−0.397503	−	0.229498i
$276$		0			0
$277$	0.707658	+	1.22570i	0.00255472	+	0.00442491i	0.867300	−	0.497786i	$-0.165853\pi$
$277$	0.707658	+	1.22570i	0.00255472	+	0.00442491i	−0.864745	+	0.502211i	$0.832520\pi$
$278$		−	27.1747i		−	0.0977506i
$279$		0			0
$280$	137.569			0.491319
$281$	−87.2230	+	50.3582i	−0.310402	+	0.179211i	−0.647106	−	0.762400i	$-0.724021\pi$
$281$	−87.2230	+	50.3582i	−0.310402	+	0.179211i	0.336704	+	0.941610i	$0.390688\pi$
$282$		0			0
$283$	23.6462	−	40.9564i	0.0835554	−	0.144722i	−0.821219	−	0.570613i	$-0.806706\pi$
$283$	23.6462	−	40.9564i	0.0835554	−	0.144722i	0.904775	+	0.425890i	$0.140039\pi$
$284$	175.308	+	101.214i	0.617282	+	0.356388i
$285$		0			0
$286$	220.277	+	381.531i	0.770199	+	1.33402i
$287$		−	282.288i		−	0.983582i
$288$		0			0
$289$	228.711			0.791389
$290$	−251.939	+	145.457i	−0.868757	+	0.501577i
$291$		0			0
$292$	40.4115	−	69.9948i	0.138396	−	0.239708i
$293$	288.920	+	166.808i	0.986074	+	0.569310i	0.904098	−	0.427324i	$-0.140544\pi$
$293$	288.920	+	166.808i	0.986074	+	0.569310i	0.0819755	+	0.996634i	$0.473877\pi$
$294$		0			0
$295$	178.708	+	309.531i	0.605789	+	1.04926i
$296$			171.316i			0.578769i
$297$		0			0
$298$	133.335			0.447432
$299$	−269.783	+	155.759i	−0.902284	+	0.520934i
$300$		0			0
$301$	38.5077	−	66.6973i	0.127933	−	0.221586i
$302$	−39.1918	−	22.6274i	−0.129774	−	0.0749252i
$303$		0			0
$304$	−48.7846	−	84.4974i	−0.160476	−	0.277952i
$305$			75.3422i			0.247024i
$306$		0			0
$307$	10.3538			0.0337258			0.0168629	−	0.999858i	$-0.494632\pi$
$307$	10.3538			0.0337258			0.0168629	+	0.999858i	$0.494632\pi$
$308$	−213.633	+	123.341i	−0.693614	+	0.400458i
$309$		0			0
$310$	−32.7846	+	56.7846i	−0.105757	+	0.183176i
$311$	8.26229	+	4.77024i	0.0265669	+	0.0153384i	0.513225	−	0.858254i	$-0.328451\pi$
$311$	8.26229	+	4.77024i	0.0265669	+	0.0153384i	−0.486658	+	0.873593i	$0.661784\pi$
$312$		0			0
$313$	239.638	+	415.066i	0.765618	+	1.32609i	0.939919	+	0.341397i	$0.110900\pi$
$313$	239.638	+	415.066i	0.765618	+	1.32609i	−0.174301	+	0.984692i	$0.555767\pi$
$314$			0.413434i			0.00131667i
$315$		0			0
$316$	−197.492			−0.624976
$317$	155.592	−	89.8311i	0.490827	−	0.283379i	−0.234091	−	0.972215i	$-0.575211\pi$
$317$	155.592	−	89.8311i	0.490827	−	0.283379i	0.724917	+	0.688836i	$0.241878\pi$
$318$		0			0
$319$	260.827	−	451.765i	0.817639	−	1.41619i
$320$	−40.1528	−	23.1822i	−0.125477	−	0.0724444i
$321$		0			0
$322$	−87.2154	−	151.061i	−0.270855	−	0.469135i
$323$		−	189.396i		−	0.586365i
$324$		0			0
$325$	182.042			0.560130
$326$	35.2538	−	20.3538i	0.108141	−	0.0624349i
$327$		0			0
$328$	−47.5692	+	82.3923i	−0.145028	+	0.251196i
$329$	123.341	+	71.2111i	0.374897	+	0.216447i
$330$		0			0
$331$	−147.727	−	255.870i	−0.446305	−	0.773023i	0.551837	−	0.833952i	$-0.313927\pi$
$331$	−147.727	−	255.870i	−0.446305	−	0.773023i	−0.998142	+	0.0609292i	$0.980594\pi$
$332$			206.976i			0.623420i
$333$		0			0
$334$	79.2923			0.237402
$335$	−106.289	+	61.3660i	−0.317281	+	0.183182i
$336$		0			0
$337$	−244.631	+	423.713i	−0.725907	+	1.25731i	0.232692	+	0.972550i	$0.425246\pi$
$337$	−244.631	+	423.713i	−0.725907	+	1.25731i	−0.958600	+	0.284758i	$0.908087\pi$
$338$	−343.268	−	198.186i	−1.01558	−	0.586348i
$339$		0			0
$340$	−45.0000	−	77.9423i	−0.132353	−	0.229242i
$341$		−	117.576i		−	0.344796i
$342$		0			0
$343$	231.369			0.674546
$344$	−22.4788	+	12.9781i	−0.0653452	+	0.0377271i
$345$		0			0
$346$	156.237	−	270.610i	0.451551	−	0.782109i
$347$	−577.363	−	333.341i	−1.66387	−	0.960637i	−0.970840	−	0.239730i	$-0.922941\pi$
$347$	−577.363	−	333.341i	−1.66387	−	0.960637i	−0.693032	−	0.720907i	$-0.743726\pi$
$348$		0			0
$349$	−255.985	−	443.378i	−0.733480	−	1.27042i	−0.955387	−	0.295357i	$-0.904561\pi$
$349$	−255.985	−	443.378i	−0.733480	−	1.27042i	0.221907	−	0.975068i	$-0.428772\pi$
$350$			101.932i			0.291235i
$351$		0			0
$352$	83.1384			0.236189
$353$	508.081	−	293.340i	1.43932	−	0.830993i	0.441519	−	0.897252i	$-0.354440\pi$
$353$	508.081	−	293.340i	1.43932	−	0.830993i	0.997802	+	0.0662588i	$0.0211063\pi$
$354$		0			0
$355$	−293.296	+	508.004i	−0.826186	+	1.43100i
$356$	−232.320	−	134.130i	−0.652584	−	0.376770i
$357$		0			0
$358$	175.608	+	304.161i	0.490524	+	0.849613i
$359$		−	534.573i		−	1.48906i	−0.667589	−	0.744530i	$-0.732674\pi$
$359$		−	534.573i		−	1.48906i	0.667589	−	0.744530i	$-0.267326\pi$
$360$		0			0
$361$	233.985			0.648157
$362$	−193.849	+	111.919i	−0.535494	+	0.309168i
$363$		0			0
$364$	177.885	−	308.105i	0.488694	−	0.846443i
$365$	202.829	+	117.104i	0.555697	+	0.320832i
$366$		0			0
$367$	−7.64617	−	13.2436i	−0.0208343	−	0.0360860i	0.855420	−	0.517934i	$-0.173299\pi$
$367$	−7.64617	−	13.2436i	−0.0208343	−	0.0360860i	−0.876255	+	0.481848i	$0.839966\pi$
$368$			58.7878i			0.159749i
$369$		0			0
$370$	−496.435			−1.34172
$371$	187.226	−	108.095i	0.504651	−	0.291361i
$372$		0			0
$373$	−326.492	+	565.501i	−0.875314	+	1.51609i	−0.0188869	+	0.999822i	$0.506012\pi$
$373$	−326.492	+	565.501i	−0.875314	+	1.51609i	−0.856427	+	0.516267i	$0.827321\pi$
$374$	139.762	+	80.6918i	0.373696	+	0.215753i
$375$		0			0
$376$	−24.0000	−	41.5692i	−0.0638298	−	0.110556i
$377$			752.337i			1.99559i
$378$		0			0
$379$	−655.215			−1.72880			−0.864400	−	0.502804i	$-0.832302\pi$
$379$	−655.215			−1.72880			−0.864400	+	0.502804i	$0.832302\pi$
$380$	244.855	−	141.367i	0.644355	−	0.372018i
$381$		0			0
$382$	−24.4308	+	42.3154i	−0.0639549	+	0.110773i
$383$	259.410	+	149.771i	0.677311	+	0.391046i	0.798841	−	0.601542i	$-0.205447\pi$
$383$	259.410	+	149.771i	0.677311	+	0.391046i	−0.121530	+	0.992588i	$0.538780\pi$
$384$		0			0
$385$	−357.415	−	619.061i	−0.928351	−	1.60795i
$386$		−	77.7817i		−	0.201507i
$387$		0			0
$388$	150.277			0.387312
$389$	−402.319	+	232.279i	−1.03424	+	0.597119i	−0.918196	−	0.396126i	$-0.870354\pi$
$389$	−402.319	+	232.279i	−1.03424	+	0.597119i	−0.116043	+	0.993244i	$0.537021\pi$
$390$		0			0
$391$	−57.0577	+	98.8269i	−0.145928	+	0.252754i
$392$	52.4945	+	30.3077i	0.133914	+	0.0773156i
$393$		0			0
$394$	−25.2558	−	43.7442i	−0.0641009	−	0.111026i
$395$		−	572.289i		−	1.44883i
$396$		0			0
$397$	−185.708			−0.467777			−0.233889	−	0.972263i	$-0.575145\pi$
$397$	−185.708			−0.467777			−0.233889	+	0.972263i	$0.575145\pi$
$398$	−459.449	+	265.263i	−1.15439	+	0.666490i
$399$		0			0
$400$	17.1769	−	29.7513i	0.0429423	−	0.0743782i
$401$	54.4376	+	31.4296i	0.135755	+	0.0783780i	0.566339	−	0.824172i	$-0.308359\pi$
$401$	54.4376	+	31.4296i	0.135755	+	0.0783780i	−0.430585	+	0.902550i	$0.641693\pi$
$402$		0			0
$403$	84.7846	+	146.851i	0.210384	+	0.364395i
$404$		−	58.1785i		−	0.144006i
$405$		0			0
$406$	−421.261			−1.03759
$407$	770.920	−	445.091i	1.89415	−	1.09359i
$408$		0			0
$409$	163.640	−	283.433i	0.400099	−	0.692991i	−0.593639	−	0.804732i	$-0.702309\pi$
$409$	163.640	−	283.433i	0.400099	−	0.692991i	0.993737	+	0.111741i	$0.0356425\pi$
$410$	−238.755	−	137.845i	−0.582328	−	0.336207i
$411$		0			0
$412$	96.7077	+	167.503i	0.234727	+	0.406560i
$413$			517.558i			1.25317i
$414$		0			0
$415$	−599.769			−1.44523
$416$	−103.840	+	59.9518i	−0.249614	+	0.144115i
$417$		0			0
$418$	−253.492	+	439.061i	−0.606441	+	1.05039i
$419$	−562.808	−	324.937i	−1.34322	−	0.775507i	−0.355939	−	0.934509i	$-0.615839\pi$
$419$	−562.808	−	324.937i	−1.34322	−	0.775507i	−0.987278	+	0.159003i	$0.949172\pi$
$420$		0			0
$421$	−1.65956	−	2.87445i	−0.00394196	−	0.00682767i	0.864048	−	0.503410i	$-0.167921\pi$
$421$	−1.65956	−	2.87445i	−0.00394196	−	0.00682767i	−0.867990	+	0.496582i	$0.834588\pi$
$422$			434.805i			1.03034i
$423$		0			0
$424$	−72.8616			−0.171843
$425$	57.7515	−	33.3428i	0.135886	−	0.0784538i
$426$		0			0
$427$	−54.5500	+	94.4833i	−0.127752	+	0.221272i
$428$	−307.581	−	177.582i	−0.718646	−	0.414910i
$429$		0			0
$430$	−37.6077	−	65.1384i	−0.0874598	−	0.151485i
$431$			803.502i			1.86427i	0.362107	+	0.932136i	$0.382057\pi$
$431$			803.502i			1.86427i	−0.362107	+	0.932136i	$0.617943\pi$
$432$		0			0
$433$	−93.1230			−0.215065			−0.107532	−	0.994202i	$-0.534295\pi$
$433$	−93.1230			−0.215065			−0.107532	+	0.994202i	$0.534295\pi$
$434$	−82.2275	+	47.4740i	−0.189464	+	0.109387i
$435$		0			0
$436$	61.9423	−	107.287i	0.142069	−	0.246072i
$437$	−310.463	−	179.246i	−0.710442	−	0.410174i
$438$		0			0
$439$	236.000	+	408.764i	0.537585	+	0.931125i	0.999033	+	0.0439580i	$0.0139968\pi$
$439$	236.000	+	408.764i	0.537585	+	0.931125i	−0.461448	+	0.887167i	$0.652670\pi$
$440$			240.917i			0.547538i
$441$		0			0
$442$	−232.750			−0.526584
$443$	493.365	−	284.844i	1.11369	−	0.642989i	0.173908	−	0.984762i	$-0.444361\pi$
$443$	493.365	−	284.844i	1.11369	−	0.642989i	0.939783	+	0.341773i	$0.111027\pi$
$444$		0			0
$445$	388.679	−	673.211i	0.873436	−	1.51283i
$446$	414.689	+	239.421i	0.929796	+	0.536818i
$447$		0			0
$448$	−33.5692	−	58.1436i	−0.0749313	−	0.129785i
$449$		−	559.115i		−	1.24524i	−0.782523	−	0.622622i	$-0.786067\pi$
$449$		−	559.115i		−	1.24524i	0.782523	−	0.622622i	$-0.213933\pi$
$450$		0			0
$451$	494.354			1.09613
$452$	190.198	−	109.811i	0.420792	−	0.242945i
$453$		0			0
$454$	−87.6462	+	151.808i	−0.193053	+	0.334378i
$455$	892.820	+	515.470i	1.96224	+	1.13290i
$456$		0			0
$457$	−302.148	−	523.336i	−0.661155	−	1.14515i	−0.980312	−	0.197453i	$-0.936733\pi$
$457$	−302.148	−	523.336i	−0.661155	−	1.14515i	0.319157	−	0.947702i	$-0.396600\pi$
$458$			104.733i			0.228676i
$459$		0			0
$460$	−170.354			−0.370334
$461$	−4.44669	+	2.56730i	−0.00964575	+	0.00556897i	−0.504815	−	0.863227i	$-0.668439\pi$
$461$	−4.44669	+	2.56730i	−0.00964575	+	0.00556897i	0.495169	+	0.868796i	$0.335106\pi$
$462$		0			0
$463$	80.7461	−	139.856i	0.174398	−	0.302066i	−0.765555	−	0.643370i	$-0.777536\pi$
$463$	80.7461	−	139.856i	0.174398	−	0.302066i	0.939953	+	0.341305i	$0.110869\pi$
$464$	122.955	+	70.9881i	0.264989	+	0.152992i
$465$		0			0
$466$	193.198	+	334.629i	0.414588	+	0.718088i
$467$		−	503.025i		−	1.07714i	−0.842581	−	0.538570i	$-0.818965\pi$
$467$		−	503.025i		−	1.07714i	0.842581	−	0.538570i	$-0.181035\pi$
$468$		0			0
$469$	−177.723			−0.378941
$470$	120.458	−	69.5467i	0.256294	−	0.147972i
$471$		0			0
$472$	87.2154	−	151.061i	0.184778	−	0.320046i
$473$	116.803	+	67.4363i	0.246941	+	0.142571i
$474$		0			0
$475$	104.746	+	181.426i	0.220518	+	0.381949i
$476$		−	130.325i		−	0.273793i
$477$		0			0
$478$	640.477			1.33991
$479$	185.153	−	106.898i	0.386541	−	0.223170i	−0.294119	−	0.955769i	$-0.595026\pi$
$479$	185.153	−	106.898i	0.386541	−	0.223170i	0.680660	+	0.732599i	$0.261693\pi$
$480$		0			0
$481$	−641.917	+	1111.83i	−1.33455	+	2.31150i
$482$	468.696	+	270.602i	0.972398	+	0.561414i
$483$		0			0
$484$	−95.0000	−	164.545i	−0.196281	−	0.339969i
$485$			435.469i			0.897874i
$486$		0			0
$487$	8.63071			0.0177222			0.00886110	−	0.999961i	$-0.497179\pi$
$487$	8.63071			0.0177222			0.00886110	+	0.999961i	$0.497179\pi$
$488$	31.8434	−	18.3848i	0.0652528	−	0.0376737i
$489$		0			0
$490$	−87.8250	+	152.117i	−0.179235	+	0.310443i
$491$	−798.873	−	461.229i	−1.62703	−	0.939367i	−0.984972	−	0.172713i	$-0.944747\pi$
$491$	−798.873	−	461.229i	−1.62703	−	0.939367i	−0.642060	−	0.766654i	$-0.721920\pi$
$492$		0			0
$493$	137.798	+	238.673i	0.279509	+	0.484124i
$494$		−	731.181i		−	1.48012i
$495$		0			0
$496$	32.0000			0.0645161
$497$	−735.619	+	424.710i	−1.48012	+	0.854547i
$498$		0			0
$499$	217.296	−	376.368i	0.435463	−	0.754244i	−0.561870	−	0.827225i	$-0.689918\pi$
$499$	217.296	−	376.368i	0.435463	−	0.754244i	0.997333	+	0.0729811i	$0.0232513\pi$
$500$	−164.742	−	95.1140i	−0.329485	−	0.190228i
$501$		0			0
$502$	−52.2769	−	90.5462i	−0.104137	−	0.180371i
$503$			144.087i			0.286454i	0.989690	+	0.143227i	$0.0457480\pi$
$503$			144.087i			0.286454i	−0.989690	+	0.143227i	$0.954252\pi$
$504$		0			0
$505$	168.588			0.333839
$506$	264.545	−	152.735i	0.522816	−	0.301848i
$507$		0			0
$508$	141.177	−	244.526i	0.277907	−	0.481350i
$509$	603.856	+	348.636i	1.18636	+	0.684943i	0.957477	−	0.288511i	$-0.0931602\pi$
$509$	603.856	+	348.636i	1.18636	+	0.684943i	0.228880	+	0.973455i	$0.426494\pi$
$510$		0			0
$511$	169.573	+	293.709i	0.331845	+	0.574773i
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	226.004			0.439696
$515$	−485.385	+	280.237i	−0.942496	+	0.544150i
$516$		0			0
$517$	−124.708	+	216.000i	−0.241214	+	0.417795i
$518$	−622.557	−	359.433i	−1.20185	−	0.693887i
$519$		0			0
$520$	−173.727	−	300.904i	−0.334090	−	0.578661i
$521$		−	426.962i		−	0.819504i	−0.912197	−	0.409752i	$-0.865615\pi$
$521$		−	426.962i		−	0.819504i	0.912197	−	0.409752i	$-0.134385\pi$
$522$		0			0
$523$	179.762			0.343712			0.171856	−	0.985122i	$-0.445024\pi$
$523$	179.762			0.343712			0.171856	+	0.985122i	$0.445024\pi$
$524$	−92.1197	+	53.1853i	−0.175801	+	0.101499i
$525$		0			0
$526$	183.215	−	317.338i	0.348318	−	0.603305i
$527$	53.7945	+	31.0583i	0.102077	+	0.0589341i
$528$		0			0
$529$	−156.500	−	271.066i	−0.295841	−	0.512412i
$530$		−	211.137i		−	0.398371i
$531$		0			0
$532$	409.415			0.769578
$533$	−617.446	+	356.482i	−1.15843	+	0.668822i
$534$		0			0
$535$	514.592	−	891.300i	0.961855	−	1.66598i
$536$	51.8726	+	29.9487i	0.0967773	+	0.0558744i
$537$		0			0
$538$	17.5481	+	30.3942i	0.0326173	+	0.0564948i
$539$		−	314.967i		−	0.584354i
$540$		0			0
$541$	708.734			1.31005			0.655023	−	0.755609i	$-0.272659\pi$
$541$	708.734			1.31005			0.655023	+	0.755609i	$0.272659\pi$
$542$	120.166	−	69.3781i	0.221709	−	0.128004i
$543$		0			0
$544$	−21.9615	+	38.0385i	−0.0403704	+	0.0699237i
$545$	310.894	+	179.495i	0.570448	+	0.329349i
$546$		0			0
$547$	98.1154	+	169.941i	0.179370	+	0.310678i	0.941665	−	0.336552i	$-0.109261\pi$
$547$	98.1154	+	169.941i	0.179370	+	0.310678i	−0.762295	+	0.647230i	$0.775927\pi$
$548$			3.26907i			0.00596545i
$549$		0			0
$550$	−178.508			−0.324560
$551$	−749.789	+	432.891i	−1.36078	+	0.785646i
$552$		0			0
$553$	414.354	−	717.682i	0.749284	−	1.29780i
$554$	1.73340	+	1.00078i	0.00312888	+	0.00180646i
$555$		0			0
$556$	−19.2154	−	33.2820i	−0.0345601	−	0.0598598i
$557$			353.610i			0.634848i	0.948284	+	0.317424i	$0.102818\pi$
$557$			353.610i			0.634848i	−0.948284	+	0.317424i	$0.897182\pi$
$558$		0			0
$559$	−194.515			−0.347970
$560$	168.487	−	97.2761i	0.300870	−	0.173707i
$561$		0			0
$562$	−71.2173	+	123.352i	−0.126721	+	0.219487i
$563$	−323.050	−	186.513i	−0.573801	−	0.331284i	0.184865	−	0.982764i	$-0.440815\pi$
$563$	−323.050	−	186.513i	−0.573801	−	0.331284i	−0.758666	+	0.651480i	$0.774149\pi$
$564$		0			0
$565$	318.208	+	551.152i	0.563199	+	0.975490i
$566$		−	66.8815i		−	0.118165i
$567$		0			0
$568$	286.277			0.504009
$569$	52.0634	−	30.0588i	0.0914999	−	0.0528275i	−0.453552	−	0.891230i	$-0.649843\pi$
$569$	52.0634	−	30.0588i	0.0914999	−	0.0528275i	0.545052	+	0.838402i	$0.316510\pi$
$570$		0			0
$571$	−43.1000	+	74.6513i	−0.0754815	+	0.130738i	−0.901296	−	0.433205i	$-0.857383\pi$
$571$	−43.1000	+	74.6513i	−0.0754815	+	0.130738i	0.825814	+	0.563943i	$0.190716\pi$
$572$	539.566	+	311.519i	0.943297	+	0.544613i
$573$		0			0
$574$	−199.608	−	345.731i	−0.347749	−	0.602318i
$575$		−	126.224i		−	0.219520i
$576$		0			0
$577$	709.123			1.22898			0.614491	−	0.788924i	$-0.289361\pi$
$577$	709.123			1.22898			0.614491	+	0.788924i	$0.289361\pi$
$578$	280.113	−	161.723i	0.484625	−	0.279798i
$579$		0			0
$580$	−205.708	+	356.296i	−0.354668	+	0.614304i
$581$	−752.144	−	434.251i	−1.29457	−	0.747419i
$582$		0			0
$583$	189.300	+	327.877i	0.324700	+	0.562396i
$584$		−	114.301i		−	0.195721i
$585$		0			0
$586$	471.804			0.805126
$587$	−833.363	+	481.143i	−1.41970	+	0.819664i	−0.996272	−	0.0862666i	$-0.972506\pi$
$587$	−833.363	+	481.143i	−1.41970	+	0.819664i	−0.423427	+	0.905930i	$0.639173\pi$
$588$		0			0
$589$	−97.5692	+	168.995i	−0.165652	+	0.286918i
$590$	437.743	+	252.731i	0.741937	+	0.428357i
$591$		0			0
$592$	121.138	+	209.818i	0.204626	+	0.354422i
$593$		−	104.350i		−	0.175969i	−0.996122	−	0.0879847i	$-0.971957\pi$
$593$		−	104.350i		−	0.175969i	0.996122	−	0.0879847i	$-0.0280427\pi$
$594$		0			0
$595$	377.654			0.634712
$596$	163.301	−	94.2818i	0.273995	−	0.158191i
$597$		0			0
$598$	−220.277	+	381.531i	−0.368356	+	0.638011i
$599$	−247.738	−	143.031i	−0.413585	−	0.238784i	0.278744	−	0.960366i	$-0.410082\pi$
$599$	−247.738	−	143.031i	−0.413585	−	0.238784i	−0.692329	+	0.721582i	$0.743415\pi$
$600$		0			0
$601$	140.208	+	242.847i	0.233291	+	0.404071i	0.958775	−	0.284168i	$-0.0917173\pi$
$601$	140.208	+	242.847i	0.233291	+	0.404071i	−0.725484	+	0.688239i	$0.758384\pi$
$602$		−	108.916i		−	0.180924i
$603$		0			0
$604$	−64.0000			−0.105960
$605$	476.814	−	275.289i	0.788123	−	0.455023i
$606$		0			0
$607$	−368.865	+	638.894i	−0.607686	+	1.05254i	0.383935	+	0.923360i	$0.374569\pi$
$607$	−368.865	+	638.894i	−0.607686	+	1.05254i	−0.991621	+	0.129183i	$0.958765\pi$
$608$	−119.497	−	68.9919i	−0.196542	−	0.113473i
$609$		0			0
$610$	53.2750	+	92.2750i	0.0873361	+	0.151270i
$611$		−	359.711i		−	0.588724i
$612$		0			0
$613$	−679.415			−1.10834			−0.554172	−	0.832402i	$-0.686965\pi$
$613$	−679.415			−1.10834			−0.554172	+	0.832402i	$0.686965\pi$
$614$	12.6808	−	7.32126i	0.0206528	−	0.0119239i
$615$		0			0
$616$	−174.431	+	302.123i	−0.283167	+	0.490459i
$617$	409.326	+	236.325i	0.663414	+	0.383022i	0.793576	−	0.608471i	$-0.208217\pi$
$617$	409.326	+	236.325i	0.663414	+	0.383022i	−0.130163	+	0.991493i	$0.541550\pi$
$618$		0			0
$619$	−443.177	−	767.605i	−0.715956	−	1.24007i	−0.962590	−	0.270964i	$-0.912658\pi$
$619$	−443.177	−	767.605i	−0.715956	−	1.24007i	0.246633	−	0.969109i	$-0.420676\pi$
$620$			92.7289i			0.149563i
$621$		0			0
$622$	13.4923			0.0216917
$623$	974.850	−	562.830i	1.56477	−	0.903419i
$624$		0			0
$625$	382.975	−	663.332i	0.612760	−	1.06133i
$626$	586.992	+	338.900i	0.937687	+	0.541374i
$627$		0			0
$628$	0.292342	+	0.506351i	0.000465513	+	0.000806291i
$629$			470.294i			0.747685i
$630$		0			0
$631$	−729.108			−1.15548			−0.577740	−	0.816221i	$-0.696065\pi$
$631$	−729.108			−1.15548			−0.577740	+	0.816221i	$0.696065\pi$
$632$	−241.878	+	139.648i	−0.382718	+	0.220962i
$633$		0			0
$634$	127.040	−	220.040i	0.200379	−	0.347067i
$635$	708.581	+	409.099i	1.11588	+	0.644251i
$636$		0			0
$637$	227.125	+	393.392i	0.356554	+	0.617570i
$638$		−	737.730i		−	1.15632i
$639$		0			0
$640$	−65.5692			−0.102452
$641$	753.611	−	435.098i	1.17568	−	0.678780i	0.220669	−	0.975349i	$-0.429176\pi$
$641$	753.611	−	435.098i	1.17568	−	0.678780i	0.955011	+	0.296569i	$0.0958425\pi$
$642$		0			0
$643$	309.061	−	535.310i	0.480656	−	0.832520i	−0.519098	−	0.854715i	$-0.673732\pi$
$643$	309.061	−	535.310i	0.480656	−	0.832520i	0.999754	+	0.0221949i	$0.00706543\pi$
$644$	−213.633	−	123.341i	−0.331729	−	0.191524i
$645$		0			0
$646$	−133.923	−	231.962i	−0.207311	−	0.359074i
$647$			425.439i			0.657556i	0.944407	+	0.328778i	$0.106637\pi$
$647$			425.439i			0.657556i	−0.944407	+	0.328778i	$0.893363\pi$
$648$		0			0
$649$	−906.369			−1.39656
$650$	222.955	−	128.723i	0.343008	−	0.198036i
$651$		0			0
$652$	28.7846	−	49.8564i	0.0441482	−	0.0764669i
$653$	−163.513	−	94.4042i	−0.250403	−	0.144570i	0.369546	−	0.929212i	$-0.379513\pi$
$653$	−163.513	−	94.4042i	−0.250403	−	0.144570i	−0.619949	+	0.784642i	$0.712847\pi$
$654$		0			0
$655$	−154.119	−	266.942i	−0.235296	−	0.407545i
$656$			134.546i			0.205101i
$657$		0			0
$658$	201.415			0.306102
$659$	−571.984	+	330.235i	−0.867958	+	0.501116i	−0.866669	−	0.498884i	$-0.833744\pi$
$659$	−571.984	+	330.235i	−0.867958	+	0.501116i	−0.00128859	+	0.999999i	$0.500410\pi$
$660$		0			0
$661$	294.915	−	510.808i	0.446165	−	0.772781i	−0.551967	−	0.833866i	$-0.686123\pi$
$661$	294.915	−	510.808i	0.446165	−	0.772781i	0.998133	+	0.0610847i	$0.0194560\pi$
$662$	−361.856	−	208.917i	−0.546610	−	0.315585i
$663$		0			0
$664$	146.354	+	253.492i	0.220412	+	0.381765i
$665$			1186.39i			1.78405i
$666$		0			0
$667$	521.654			0.782090
$668$	97.1129	−	56.0682i	0.145379	−	0.0839344i
$669$		0			0
$670$	−86.7846	+	150.315i	−0.129529	+	0.224351i
$671$	−165.463	−	95.5301i	−0.246592	−	0.142370i
$672$		0			0
$673$	195.715	+	338.989i	0.290810	+	0.503698i	0.974002	−	0.226541i	$-0.0727418\pi$
$673$	195.715	+	338.989i	0.290810	+	0.503698i	−0.683191	+	0.730240i	$0.739408\pi$
$674$			691.920i			1.02659i
$675$		0			0
$676$	−560.554			−0.829222
$677$	−600.728	+	346.830i	−0.887338	+	0.512305i	−0.873071	−	0.487593i	$-0.837875\pi$
$677$	−600.728	+	346.830i	−0.887338	+	0.512305i	−0.0142672	+	0.999898i	$0.504542\pi$
$678$		0			0
$679$	−315.292	+	546.102i	−0.464348	+	0.804274i
$680$	−110.227	−	63.6396i	−0.162099	−	0.0935877i
$681$		0			0
$682$	−83.1384	−	144.000i	−0.121904	−	0.211144i
$683$			678.170i			0.992928i	0.868057	+	0.496464i	$0.165368\pi$
$683$			678.170i			0.992928i	−0.868057	+	0.496464i	$0.834632\pi$
$684$		0			0
$685$	−9.47303			−0.0138292
$686$	283.368	−	163.603i	0.413073	−	0.238488i
$687$		0			0
$688$	−18.3538	+	31.7898i	−0.0266771	+	0.0462061i
$689$	−472.869	−	273.011i	−0.686313	−	0.396243i
$690$		0			0
$691$	−337.888	−	585.240i	−0.488985	−	0.846946i	0.510935	−	0.859619i	$-0.329299\pi$
$691$	−337.888	−	585.240i	−0.488985	−	0.846946i	−0.999920	+	0.0126731i	$0.995966\pi$
$692$		−	441.904i		−	0.638589i
$693$		0			0
$694$	−942.831			−1.35855
$695$	96.4439	−	55.6819i	0.138768	−	0.0801179i
$696$		0			0
$697$	−130.587	+	226.183i	−0.187355	+	0.324509i
$698$	−627.031	−	362.017i	−0.898326	−	0.518649i
$699$		0			0
$700$	72.0770	+	124.841i	0.102967	+	0.178344i
$701$		−	797.260i		−	1.13732i	−0.822573	−	0.568659i	$-0.807462\pi$
$701$		−	797.260i		−	1.13732i	0.822573	−	0.568659i	$-0.192538\pi$
$702$		0			0
$703$	−1477.42			−2.10160
$704$	101.823	−	58.7878i	0.144635	−	0.0835053i
$705$		0			0
$706$	414.846	−	718.535i	0.587601	−	1.01775i
$707$	211.419	+	122.063i	0.299037	+	0.172649i
$708$		0			0
$709$	−86.7520	−	150.259i	−0.122358	−	0.211931i	0.798339	−	0.602208i	$-0.205712\pi$
$709$	−86.7520	−	150.259i	−0.122358	−	0.211931i	−0.920697	+	0.390278i	$0.872379\pi$
$710$			829.567i			1.16840i
$711$		0			0
$712$	−379.377			−0.532833
$713$	101.823	−	58.7878i	0.142810	−	0.0824513i
$714$		0			0
$715$	−902.711	+	1563.54i	−1.26253	+	2.18677i
$716$	430.149	+	248.347i	0.600767	+	0.346853i
$717$		0			0
$718$	−378.000	−	654.715i	−0.526462	−	0.911860i
$719$		−	188.177i		−	0.261721i	−0.991401	−	0.130860i	$-0.958226\pi$
$719$		−	188.177i		−	0.261721i	0.991401	−	0.130860i	$-0.0417740\pi$
$720$		0			0
$721$	−811.600			−1.12566
$722$	286.571	−	165.452i	0.396913	−	0.229158i
$723$		0			0
$724$	−158.277	+	274.144i	−0.218614	+	0.378651i
$725$	−263.998	−	152.420i	−0.364136	−	0.210234i
$726$		0			0
$727$	−355.888	−	616.417i	−0.489530	−	0.847891i	0.510397	−	0.859939i	$-0.329498\pi$
$727$	−355.888	−	616.417i	−0.489530	−	0.847891i	−0.999927	+	0.0120478i	$0.996165\pi$
$728$		−	503.134i		−	0.691118i
$729$		0			0
$730$	331.219			0.453725
$731$	−61.7085	+	35.6274i	−0.0844165	+	0.0487379i
$732$		0			0
$733$	−613.415	+	1062.47i	−0.836856	+	1.44948i	0.0556546	+	0.998450i	$0.482275\pi$
$733$	−613.415	+	1062.47i	−0.836856	+	1.44948i	−0.892510	+	0.451027i	$0.851058\pi$
$734$	−18.7292	−	10.8133i	−0.0255166	−	0.0147320i
$735$		0			0
$736$	41.5692	+	72.0000i	0.0564799	+	0.0978261i
$737$		−	311.236i		−	0.422301i
$738$		0			0
$739$	741.892			1.00391			0.501957	−	0.864893i	$-0.332614\pi$
$739$	741.892			1.00391			0.501957	+	0.864893i	$0.332614\pi$
$740$	−608.006	+	351.032i	−0.821629	+	0.474368i
$741$		0			0
$742$	152.869	−	264.777i	0.206023	−	0.356842i
$743$	677.218	+	390.992i	0.911464	+	0.526234i	0.880902	−	0.473299i	$-0.156937\pi$
$743$	677.218	+	390.992i	0.911464	+	0.526234i	0.0305622	+	0.999533i	$0.490270\pi$
$744$		0			0
$745$	273.208	+	473.210i	0.366722	+	0.635181i
$746$			923.460i			1.23788i
$747$		0			0
$748$	228.231			0.305121
$749$	1290.65	−	745.160i	1.72317	−	0.994873i
$750$		0			0
$751$	516.665	−	894.891i	0.687970	−	1.19160i	−0.284524	−	0.958669i	$-0.591835\pi$
$751$	516.665	−	894.891i	0.687970	−	1.19160i	0.972494	−	0.232930i	$-0.0748312\pi$
$752$	−58.7878	−	33.9411i	−0.0781752	−	0.0451345i
$753$		0			0
$754$	531.983	+	921.421i	0.705547	+	1.22204i
$755$		−	185.458i		−	0.245639i
$756$		0			0
$757$	473.877			0.625993			0.312997	−	0.949754i	$-0.398667\pi$
$757$	473.877			0.625993			0.312997	+	0.949754i	$0.398667\pi$
$758$	−802.472	+	463.307i	−1.05867	+	0.611223i
$759$		0			0
$760$	199.923	−	346.277i	0.263057	−	0.455627i
$761$	−814.458	−	470.227i	−1.07025	−	0.617907i	−0.141998	−	0.989867i	$-0.545353\pi$
$761$	−814.458	−	470.227i	−1.07025	−	0.617907i	−0.928249	+	0.371960i	$0.878686\pi$
$762$		0			0
$763$	259.919	+	450.193i	0.340654	+	0.590031i
$764$			69.1007i			0.0904459i
$765$		0			0
$766$	423.615			0.553023
$767$	1132.05	−	653.590i	1.47595	−	0.852138i
$768$		0			0
$769$	−490.408	+	849.411i	−0.637721	+	1.10457i	0.348210	+	0.937416i	$0.386789\pi$
$769$	−490.408	+	849.411i	−0.637721	+	1.10457i	−0.985932	+	0.167149i	$0.946544\pi$
$770$	−875.485	−	505.462i	−1.13699	−	0.656444i
$771$		0			0
$772$	−55.0000	−	95.2628i	−0.0712435	−	0.123397i
$773$		−	1042.20i		−	1.34825i	−0.738618	−	0.674124i	$-0.764521\pi$
$773$		−	1042.20i		−	1.34825i	0.738618	−	0.674124i	$-0.235479\pi$
$774$		0			0
$775$	−68.7077			−0.0886550
$776$	184.051	−	106.262i	0.237179	−	0.136935i
$777$		0			0
$778$	−328.492	+	568.965i	−0.422227	+	0.731318i
$779$	−710.550	−	410.236i	−0.912131	−	0.526619i
$780$		0			0
$781$	−743.769	−	1288.25i	−0.952329	−	1.64948i
$782$			161.384i			0.206373i
$783$		0			0
$784$	85.7231			0.109341
$785$	−1.46729	+	0.847142i	−0.00186916	+	0.00107916i
$786$		0			0
$787$	72.3501	−	125.314i	0.0919315	−	0.159230i	−0.816392	−	0.577498i	$-0.804029\pi$
$787$	72.3501	−	125.314i	0.0919315	−	0.159230i	0.908324	+	0.418268i	$0.137363\pi$
$788$	−61.8637	−	35.7170i	−0.0785072	−	0.0453262i
$789$		0			0
$790$	−404.669	−	700.908i	−0.512239	−	0.887225i
$791$			921.567i			1.16507i
$792$		0			0
$793$	275.550			0.347478
$794$	−227.445	+	131.315i	−0.286454	+	0.165384i
$795$		0			0
$796$	−375.138	+	649.759i	−0.471279	+	0.816280i
$797$	134.866	+	77.8647i	0.169217	+	0.0976972i	0.582216	−	0.813034i	$-0.302186\pi$
$797$	134.866	+	77.8647i	0.169217	+	0.0976972i	−0.413000	+	0.910731i	$0.635519\pi$
$798$		0			0
$799$	−65.8846	−	114.115i	−0.0824588	−	0.142823i
$800$		−	48.5837i		−	0.0607296i
$801$		0			0
$802$	88.8963			0.110843
$803$	−514.355	+	296.963i	−0.640542	+	0.369817i
$804$		0			0
$805$	357.415	−	619.061i	0.443994	−	0.769020i
$806$	207.679	+	119.904i	0.257666	+	0.148764i
$807$		0			0
$808$	−41.1384	−	71.2539i	−0.0509139	−	0.0881855i
$809$		−	1216.92i		−	1.50422i	−0.659035	−	0.752112i	$-0.729035\pi$
$809$		−	1216.92i		−	1.50422i	0.659035	−	0.752112i	$-0.270965\pi$
$810$		0			0
$811$	1243.31			1.53305			0.766527	−	0.642212i	$-0.221983\pi$
$811$	1243.31			1.53305			0.766527	+	0.642212i	$0.221983\pi$
$812$	−515.938	+	297.877i	−0.635391	+	0.366843i
$813$		0			0
$814$	629.454	−	1090.25i	0.773285	−	1.33937i
$815$	144.473	+	83.4114i	0.177267	+	0.102345i
$816$		0			0
$817$	−111.923	−	193.856i	−0.136993	−	0.237278i
$818$		−	462.845i		−	0.565825i
$819$		0			0
$820$	−389.885			−0.475469
$821$	11.5055	−	6.64270i	0.0140140	−	0.00809098i	−0.492977	−	0.870043i	$-0.664091\pi$
$821$	11.5055	−	6.64270i	0.0140140	−	0.00809098i	0.506991	+	0.861952i	$0.330758\pi$
$822$		0			0
$823$	107.100	−	185.503i	0.130134	−	0.225398i	−0.793594	−	0.608447i	$-0.791793\pi$
$823$	107.100	−	185.503i	0.130134	−	0.225398i	0.923728	+	0.383049i	$0.125126\pi$
$824$	236.884	+	136.765i	0.287481	+	0.165977i
$825$		0			0
$826$	365.969	+	633.877i	0.443062	+	0.767406i
$827$			1221.27i			1.47675i	0.674391	+	0.738374i	$0.264406\pi$
$827$			1221.27i			1.47675i	−0.674391	+	0.738374i	$0.735594\pi$
$828$		0			0
$829$	−358.431			−0.432365			−0.216183	−	0.976353i	$-0.569361\pi$
$829$	−358.431			−0.432365			−0.216183	+	0.976353i	$0.569361\pi$
$830$	−734.564	+	424.101i	−0.885017	+	0.510965i
$831$		0			0
$832$	−84.7846	+	146.851i	−0.101905	+	0.176504i
$833$	144.107	+	83.2004i	0.172998	+	0.0998804i
$834$		0			0
$835$	162.473	+	281.412i	0.194578	+	0.337020i
$836$			716.984i			0.857637i
$837$		0			0
$838$	−919.061			−1.09673
$839$	−283.707	+	163.799i	−0.338150	+	0.195231i	−0.659453	−	0.751745i	$-0.729212\pi$
$839$	−283.707	+	163.799i	−0.338150	+	0.195231i	0.321304	+	0.946976i	$0.395879\pi$
$840$		0			0
$841$	209.413	−	362.715i	0.249005	−	0.431290i
$842$	−4.06508	−	2.34698i	−0.00482789	−	0.00278738i
$843$		0			0
$844$	307.454	+	532.526i	0.364282	+	0.630954i
$845$		−	1624.36i		−	1.92232i
$846$		0			0
$847$	797.269			0.941286
$848$	−89.2368	+	51.5209i	−0.105232	+	0.0607558i
$849$		0			0
$850$	47.1539	−	81.6730i	0.0554752	−	0.0960858i
$851$	770.920	+	445.091i	0.905899	+	0.523021i
$852$		0			0
$853$	26.4153	+	45.7527i	0.0309675	+	0.0536374i	0.881094	−	0.472942i	$-0.156808\pi$
$853$	26.4153	+	45.7527i	0.0309675	+	0.0536374i	−0.850126	+	0.526579i	$0.823474\pi$
$854$			154.291i			0.180668i
$855$		0			0
$856$	−502.277			−0.586772
$857$	−1081.16	+	624.211i	−1.26157	+	0.728367i	−0.973378	−	0.229206i	$-0.926387\pi$
$857$	−1081.16	+	624.211i	−1.26157	+	0.728367i	−0.288191	+	0.957573i	$0.593054\pi$
$858$		0			0
$859$	223.369	−	386.887i	0.260034	−	0.450392i	−0.706217	−	0.707996i	$-0.749600\pi$
$859$	223.369	−	386.887i	0.260034	−	0.450392i	0.966251	+	0.257604i	$0.0829329\pi$
$860$	−92.1197	−	53.1853i	−0.107116	−	0.0618434i
$861$		0			0
$862$	568.161	+	984.084i	0.659120	+	1.14163i
$863$			635.297i			0.736150i	0.929796	+	0.368075i	$0.119983\pi$
$863$			635.297i			0.736150i	−0.929796	+	0.368075i	$0.880017\pi$
$864$		0			0
$865$	1280.54			1.48039
$866$	−114.052	+	65.8479i	−0.131700	+	0.0760368i
$867$		0			0
$868$	−67.1384	+	116.287i	−0.0773484	+	0.133971i
$869$	1256.83	+	725.633i	1.44630	+	0.835021i
$870$		0			0
$871$	224.435	+	388.732i	0.257675	+	0.446305i
$872$		−	175.199i		−	0.200917i
$873$		0			0
$874$	−506.985			−0.580074
$875$	691.284	−	399.113i	0.790039	−	0.456129i
$876$		0			0
$877$	394.346	−	683.027i	0.449653	−	0.778823i	−0.548710	−	0.836013i	$-0.684881\pi$
$877$	394.346	−	683.027i	0.449653	−	0.778823i	0.998363	+	0.0571902i	$0.0182141\pi$
$878$	578.080	+	333.754i	0.658405	+	0.380130i
$879$		0			0
$880$	170.354	+	295.061i	0.193584	+	0.335297i
$881$		−	558.506i		−	0.633945i	−0.948435	−	0.316972i	$-0.897334\pi$
$881$		−	558.506i		−	0.633945i	0.948435	−	0.316972i	$-0.102666\pi$
$882$		0			0
$883$	313.338			0.354857			0.177428	−	0.984134i	$-0.443222\pi$
$883$	313.338			0.354857			0.177428	+	0.984134i	$0.443222\pi$
$884$	−285.059	+	164.579i	−0.322465	+	0.186175i
$885$		0			0
$886$	402.831	−	697.723i	0.454662	−	0.787498i
$887$	517.624	+	298.850i	0.583567	+	0.336923i	0.762550	−	0.646930i	$-0.223947\pi$
$887$	517.624	+	298.850i	0.583567	+	0.336923i	−0.178983	+	0.983852i	$0.557281\pi$
$888$		0			0
$889$	592.400	+	1026.07i	0.666367	+	1.15418i
$890$		−	1099.35i		−	1.23522i
$891$		0			0
$892$	677.184			0.759175
$893$	358.492	−	206.976i	0.401447	−	0.231776i
$894$		0			0
$895$	−719.654	+	1246.48i	−0.804082	+	1.39271i
$896$	−82.2275	−	47.4740i	−0.0917717	−	0.0529844i
$897$		0			0
$898$	−395.354	−	684.773i	−0.440260	−	0.762553i
$899$		−	283.952i		−	0.315854i
$900$		0			0
$901$	−200.019			−0.221997
$902$	605.457	−	349.561i	0.671239	−	0.387540i
$903$		0			0
$904$	155.296	−	268.981i	0.171788	−	0.297545i
$905$	−794.407	−	458.651i	−0.877798	−	0.506797i
$906$		0			0
$907$	−543.254	−	940.943i	−0.598957	−	1.03742i	−0.992975	−	0.118321i	$-0.962249\pi$
$907$	−543.254	−	940.943i	−0.598957	−	1.03742i	0.394019	−	0.919103i	$-0.371085\pi$
$908$			247.901i			0.273019i
$909$		0			0
$910$	1457.97			1.60216
$911$	−615.123	+	355.142i	−0.675218	+	0.389837i	−0.798051	−	0.602590i	$-0.794135\pi$
$911$	−615.123	+	355.142i	−0.675218	+	0.389837i	0.122833	+	0.992427i	$0.460802\pi$
$912$		0			0
$913$	760.477	−	1317.18i	0.832943	−	1.44270i
$914$	−740.109	−	427.302i	−0.809747	−	0.467508i
$915$		0			0
$916$	74.0577	+	128.272i	0.0808490	+	0.140035i
$917$		−	446.347i		−	0.486747i
$918$		0			0
$919$	1540.01			1.67574			0.837871	−	0.545868i	$-0.183800\pi$
$919$	1540.01			1.67574			0.837871	+	0.545868i	$0.183800\pi$
$920$	−208.640	+	120.458i	−0.226783	+	0.130933i
$921$		0			0
$922$	−3.63071	+	6.28857i	−0.00393786	+	0.00682057i
$923$	1857.93	+	1072.68i	2.01292	+	1.16216i
$924$		0			0
$925$	−260.098	−	450.503i	−0.281187	−	0.487030i
$926$		−	228.385i		−	0.246636i
$927$		0			0
$928$	200.785			0.216363
$929$	1370.57	−	791.297i	1.47531	−	0.851773i	0.475702	−	0.879607i	$-0.342194\pi$
$929$	1370.57	−	791.297i	1.47531	−	0.851773i	0.999613	+	0.0278334i	$0.00886078\pi$
$930$		0			0
$931$	−261.373	+	452.711i	−0.280744	+	0.486264i
$932$	473.237	+	273.223i	0.507765	+	0.293158i
$933$		0			0
$934$	−355.692	−	616.077i	−0.380827	−	0.659611i
$935$			661.362i			0.707339i
$936$		0			0
$937$	−1747.40			−1.86489			−0.932444	−	0.361315i	$-0.882328\pi$
$937$	−1747.40			−1.86489			−0.932444	+	0.361315i	$0.882328\pi$
$938$	−217.665	+	125.669i	−0.232053	+	0.133976i
$939$		0			0
$940$	98.3538	−	170.354i	0.104632	−	0.181227i
$941$	−318.332	−	183.789i	−0.338292	−	0.195313i	0.321225	−	0.947003i	$-0.395906\pi$
$941$	−318.332	−	183.789i	−0.338292	−	0.195313i	−0.659516	+	0.751690i	$0.729239\pi$
$942$		0			0
$943$	247.177	+	428.123i	0.262118	+	0.454001i
$944$		−	246.682i		−	0.261316i
$945$		0			0
$946$	190.739			0.201626
$947$	164.691	−	95.0841i	0.173908	−	0.100406i	−0.410519	−	0.911852i	$-0.634653\pi$
$947$	164.691	−	95.0841i	0.173908	−	0.100406i	0.584427	+	0.811446i	$0.301319\pi$
$948$		0			0
$949$	428.285	−	741.811i	0.451301	−	0.781676i
$950$	256.575	+	148.133i	0.270079	+	0.155930i
$951$		0			0
$952$	−92.1539	−	159.615i	−0.0968003	−	0.167663i
$953$			861.754i			0.904254i	0.891954	+	0.452127i	$0.149335\pi$
$953$			861.754i			0.904254i	−0.891954	+	0.452127i	$0.850665\pi$
$954$		0			0
$955$	−200.238			−0.209674
$956$	784.421	−	452.885i	0.820524	−	0.473730i
$957$		0			0
$958$	151.177	−	261.846i	0.157805	−	0.273326i
$959$	−11.8797	−	6.85875i	−0.0123876	−	0.00715198i
$960$		0			0
$961$	448.500	+	776.825i	0.466701	+	0.808350i
$962$			1815.62i			1.88733i
$963$		0			0
$964$	765.377			0.793959
$965$	276.050	−	159.378i	0.286063	−	0.165158i
$966$		0			0
$967$	−637.657	+	1104.46i	−0.659418	+	1.14215i	0.321348	+	0.946961i	$0.395864\pi$
$967$	−637.657	+	1104.46i	−0.659418	+	1.14215i	−0.980766	+	0.195185i	$0.937469\pi$
$968$	−232.702	−	134.350i	−0.240394	−	0.138792i
$969$		0			0
$970$	307.923	+	533.338i	0.317446	+	0.549833i
$971$		−	1238.69i		−	1.27568i	−0.770168	−	0.637841i	$-0.779828\pi$
$971$		−	1238.69i		−	1.27568i	0.770168	−	0.637841i	$-0.220172\pi$
$972$		0			0
$973$	161.261			0.165736
$974$	10.5704	−	6.10283i	0.0108526	−	0.00626574i
$975$		0			0
$976$	26.0000	−	45.0333i	0.0266393	−	0.0461407i
$977$	16.0159	+	9.24680i	0.0163930	+	0.00946448i	0.508174	−	0.861254i	$-0.330321\pi$
$977$	16.0159	+	9.24680i	0.0163930	+	0.00946448i	−0.491781	+	0.870719i	$0.663654\pi$
$978$		0			0
$979$	985.650	+	1707.20i	1.00679	+	1.74382i
$980$			248.407i			0.253476i
$981$		0			0
$982$	−1304.55			−1.32847
$983$	−570.401	+	329.321i	−0.580266	+	0.335017i	−0.761239	−	0.648471i	$-0.775409\pi$
$983$	−570.401	+	329.321i	−0.580266	+	0.335017i	0.180973	+	0.983488i	$0.442075\pi$
$984$		0			0
$985$	103.500	−	179.267i	0.105076	−	0.181997i
$986$	337.535	+	194.876i	0.342327	+	0.197643i
$987$		0			0
$988$	−517.023	−	895.510i	−0.523303	−	0.906387i
$989$			134.873i			0.136373i
$990$		0			0
$991$	608.484			0.614010			0.307005	−	0.951708i	$-0.400673\pi$
$991$	608.484			0.614010			0.307005	+	0.951708i	$0.400673\pi$
$992$	39.1918	−	22.6274i	0.0395079	−	0.0228099i
$993$		0			0
$994$	−600.631	+	1040.32i	−0.604256	+	1.04660i
$995$	−1882.86	−	1087.07i	−1.89232	−	1.09253i
$996$		0			0
$997$	308.623	+	534.551i	0.309552	+	0.536159i	0.978264	−	0.207362i	$-0.0664877\pi$
$997$	308.623	+	534.551i	0.309552	+	0.536159i	−0.668713	+	0.743521i	$0.733154\pi$
$998$		−	614.606i		−	0.615838i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.3.d.c.53.4		8
3.2	odd	2	inner	162.3.d.c.53.1		8
4.3	odd	2		1296.3.q.o.1025.4		8
9.2	odd	6	inner	162.3.d.c.107.4		8
9.4	even	3		162.3.b.b.161.3	yes	4
9.5	odd	6		162.3.b.b.161.2	✓	4
9.7	even	3	inner	162.3.d.c.107.1		8
12.11	even	2		1296.3.q.o.1025.1		8
36.7	odd	6		1296.3.q.o.593.1		8
36.11	even	6		1296.3.q.o.593.4		8
36.23	even	6		1296.3.e.d.161.4		4
36.31	odd	6		1296.3.e.d.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.3.b.b.161.2	✓	4	9.5	odd	6
162.3.b.b.161.3	yes	4	9.4	even	3
162.3.d.c.53.1		8	3.2	odd	2	inner
162.3.d.c.53.4		8	1.1	even	1	trivial
162.3.d.c.107.1		8	9.7	even	3	inner
162.3.d.c.107.4		8	9.2	odd	6	inner
1296.3.e.d.161.1		4	36.31	odd	6
1296.3.e.d.161.4		4	36.23	even	6
1296.3.q.o.593.1		8	36.7	odd	6
1296.3.q.o.593.4		8	36.11	even	6
1296.3.q.o.1025.1		8	12.11	even	2
1296.3.q.o.1025.4		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	162.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.01910 + 2.89778i) q^{5} +(4.19615 + 7.26795i) q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(5.01910 + 2.89778i) q^{5} +(4.19615 + 7.26795i) q^{7} -2.82843i q^{8} +8.19615 q^{10} +(-12.7279 + 7.34847i) q^{11} +(10.5981 - 18.3564i) q^{13} +(10.2784 + 5.93426i) q^{14} +(-2.00000 - 3.46410i) q^{16} -7.76457i q^{17} +24.3923 q^{19} +(10.0382 - 5.79555i) q^{20} +(-10.3923 + 18.0000i) q^{22} +(-12.7279 - 7.34847i) q^{23} +(4.29423 + 7.43782i) q^{25} -29.9759i q^{26} +16.7846 q^{28} +(-30.7387 + 17.7470i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-5.49038 - 9.50962i) q^{34} +48.6381i q^{35} -60.5692 q^{37} +(29.8744 - 17.2480i) q^{38} +(8.19615 - 14.1962i) q^{40} +(-29.1301 - 16.8183i) q^{41} +(-4.58846 - 7.94744i) q^{43} +29.3939i q^{44} -20.7846 q^{46} +(14.6969 - 8.48528i) q^{47} +(-10.7154 + 18.5596i) q^{49} +(10.5187 + 6.07296i) q^{50} +(-21.1962 - 36.7128i) q^{52} -25.7605i q^{53} -85.1769 q^{55} +(20.5569 - 11.8685i) q^{56} +(-25.0981 + 43.4711i) q^{58} +(53.4083 + 30.8353i) q^{59} +(6.50000 + 11.2583i) q^{61} +11.3137i q^{62} -8.00000 q^{64} +(106.386 - 61.4217i) q^{65} +(-10.5885 + 18.3397i) q^{67} +(-13.4486 - 7.76457i) q^{68} +(34.3923 + 59.5692i) q^{70} +101.214i q^{71} +40.4115 q^{73} +(-74.1818 + 42.8289i) q^{74} +(24.3923 - 42.2487i) q^{76} +(-106.817 - 61.6706i) q^{77} +(-49.3731 - 85.5167i) q^{79} -23.1822i q^{80} -47.5692 q^{82} +(-89.6231 + 51.7439i) q^{83} +(22.5000 - 38.9711i) q^{85} +(-11.2394 - 6.48906i) q^{86} +(20.7846 + 36.0000i) q^{88} -134.130i q^{89} +177.885 q^{91} +(-25.4558 + 14.6969i) q^{92} +(12.0000 - 20.7846i) q^{94} +(122.427 + 70.6835i) q^{95} +(37.5692 + 65.0718i) q^{97} +30.3077i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4} - 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^4 - 8 * q^7	\( 8 q + 8 q^{4} - 8 q^{7} + 24 q^{10} + 64 q^{13} - 16 q^{16} + 112 q^{19} - 28 q^{25} - 32 q^{28} - 32 q^{31} + 60 q^{34} - 152 q^{37} + 24 q^{40} + 88 q^{43} - 252 q^{49} - 128 q^{52} - 432 q^{55} - 180 q^{58} + 52 q^{61} - 64 q^{64} + 40 q^{67} + 192 q^{70} + 448 q^{73} + 112 q^{76} - 104 q^{79} - 48 q^{82} + 180 q^{85} + 176 q^{91} + 96 q^{94} - 32 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^7 + 24 * q^10 + 64 * q^13 - 16 * q^16 + 112 * q^19 - 28 * q^25 - 32 * q^28 - 32 * q^31 + 60 * q^34 - 152 * q^37 + 24 * q^40 + 88 * q^43 - 252 * q^49 - 128 * q^52 - 432 * q^55 - 180 * q^58 + 52 * q^61 - 64 * q^64 + 40 * q^67 + 192 * q^70 + 448 * q^73 + 112 * q^76 - 104 * q^79 - 48 * q^82 + 180 * q^85 + 176 * q^91 + 96 * q^94 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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