LMFDB - Embedded newform 630.3.v.b.451.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,3,Mod(271,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("630.271");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	630.v (of order $6$, degree $2$, 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:	$17.1662566547$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.3317760000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 7x^{4} - 36x^{2} + 81 $ x^8 - 4x^6 + 7x^4 - 36*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			451.4
Root			$1.01575 - 1.40294i$ of defining polynomial
Character	$\chi$	$=$	630.451
Dual form			630.3.v.b.271.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-9.03504 + 15.6491i) q^{11} -18.6604i q^{13} +(2.26139 - 9.63774i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.33462 - 0.770543i) q^{17} +(29.4836 - 17.0224i) q^{19} +4.47214i q^{20} -25.5549 q^{22} +(-13.4938 - 23.3720i) q^{23} +(2.50000 - 4.33013i) q^{25} +(22.8542 - 13.1949i) q^{26} +(13.4028 - 4.04529i) q^{28} +16.4662 q^{29} +(-24.1988 - 13.9712i) q^{31} +(2.82843 - 4.89898i) q^{32} -2.17942i q^{34} +(-15.2386 - 3.57557i) q^{35} +(-25.8353 - 44.7480i) q^{37} +(41.6961 + 24.0733i) q^{38} +(-5.47723 + 3.16228i) q^{40} -37.4818i q^{41} -63.6947 q^{43} +(-18.0701 - 31.2983i) q^{44} +(19.0831 - 33.0529i) q^{46} +(24.4572 - 14.1204i) q^{47} +(3.06832 + 48.9038i) q^{49} +7.07107 q^{50} +(32.3208 + 18.6604i) q^{52} +(0.221841 - 0.384239i) q^{53} +40.4059i q^{55} +(14.4317 + 13.5546i) q^{56} +(11.6434 + 20.1669i) q^{58} +(-64.2260 - 37.0809i) q^{59} +(91.0443 - 52.5645i) q^{61} -39.5164i q^{62} +8.00000 q^{64} +(-20.8630 - 36.1357i) q^{65} +(6.35442 - 11.0062i) q^{67} +(2.66924 - 1.54109i) q^{68} +(-6.39617 - 21.1917i) q^{70} +45.7647 q^{71} +(31.5463 + 18.2133i) q^{73} +(36.5366 - 63.2833i) q^{74} +68.0895i q^{76} +(121.095 - 36.5494i) q^{77} +(66.5990 + 115.353i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(45.9057 - 26.5037i) q^{82} +49.9265i q^{83} -3.44597 q^{85} +(-45.0389 - 78.0097i) q^{86} +(25.5549 - 44.2625i) q^{88} +(-85.9133 + 49.6020i) q^{89} +(-89.4257 + 95.2123i) q^{91} +53.9752 q^{92} +(34.5878 + 19.9693i) q^{94} +(38.0632 - 65.9274i) q^{95} -150.376i q^{97} +(-57.7251 + 38.3381i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) $ 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$2$	0.707107	+	1.22474i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$5$	1.93649	−	1.11803i	0.387298	−	0.223607i
$6$		0			0
$7$	−5.10237	−	4.79227i	−0.728910	−	0.684610i
$7$	−5.10237	−	4.79227i	−0.728910	−	0.684610i
$8$	−2.82843			−0.353553
$9$		0			0
$10$	2.73861	+	1.58114i	0.273861	+	0.158114i
$11$	−9.03504	+	15.6491i	−0.821367	+	1.42265i	0.0832974	+	0.996525i	$0.473455\pi$
$11$	−9.03504	+	15.6491i	−0.821367	+	1.42265i	−0.904664	+	0.426125i	$0.859878\pi$
$12$		0			0
$13$		−	18.6604i		−	1.43542i	−0.696344	−	0.717708i	$-0.745191\pi$
$13$		−	18.6604i		−	1.43542i	0.696344	−	0.717708i	$-0.254809\pi$
$14$	2.26139	−	9.63774i	0.161528	−	0.688410i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−1.33462	−	0.770543i	−0.0785070	−	0.0453261i	0.460233	−	0.887798i	$-0.347766\pi$
$17$	−1.33462	−	0.770543i	−0.0785070	−	0.0453261i	−0.538740	+	0.842472i	$0.681099\pi$
$18$		0			0
$19$	29.4836	−	17.0224i	1.55177	−	0.895914i	0.553771	−	0.832669i	$-0.313188\pi$
$19$	29.4836	−	17.0224i	1.55177	−	0.895914i	0.997998	−	0.0632454i	$-0.0201451\pi$
$20$			4.47214i			0.223607i
$21$		0			0
$22$	−25.5549			−1.16159
$23$	−13.4938	−	23.3720i	−0.586687	−	1.01617i	−0.994663	−	0.103179i	$-0.967098\pi$
$23$	−13.4938	−	23.3720i	−0.586687	−	1.01617i	0.407975	−	0.912993i	$-0.366235\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.100000	−	0.173205i
$26$	22.8542	−	13.1949i	0.879009	−	0.507496i
$27$		0			0
$28$	13.4028	−	4.04529i	0.478672	−	0.144475i
$29$	16.4662			0.567802			0.283901	−	0.958854i	$-0.408371\pi$
$29$	16.4662			0.567802			0.283901	+	0.958854i	$0.408371\pi$
$30$		0			0
$31$	−24.1988	−	13.9712i	−0.780605	−	0.450683i	0.0560395	−	0.998429i	$-0.482153\pi$
$31$	−24.1988	−	13.9712i	−0.780605	−	0.450683i	−0.836645	+	0.547746i	$0.815486\pi$
$32$	2.82843	−	4.89898i	0.0883883	−	0.153093i
$33$		0			0
$34$		−	2.17942i		−	0.0641007i
$35$	−15.2386	−	3.57557i	−0.435389	−	0.102159i
$36$		0			0
$37$	−25.8353	−	44.7480i	−0.698251	−	1.20941i	−0.969072	−	0.246777i	$-0.920629\pi$
$37$	−25.8353	−	44.7480i	−0.698251	−	1.20941i	0.270821	−	0.962630i	$-0.412705\pi$
$38$	41.6961	+	24.0733i	1.09727	+	0.633507i
$39$		0			0
$40$	−5.47723	+	3.16228i	−0.136931	+	0.0790569i
$41$		−	37.4818i		−	0.914191i	−0.889418	−	0.457095i	$-0.848890\pi$
$41$		−	37.4818i		−	0.914191i	0.889418	−	0.457095i	$-0.151110\pi$
$42$		0			0
$43$	−63.6947			−1.48127			−0.740636	−	0.671907i	$-0.765476\pi$
$43$	−63.6947			−1.48127			−0.740636	+	0.671907i	$0.765476\pi$
$44$	−18.0701	−	31.2983i	−0.410684	−	0.711325i
$45$		0			0
$46$	19.0831	−	33.0529i	0.414851	−	0.718542i
$47$	24.4572	−	14.1204i	0.520367	−	0.300434i	−0.216718	−	0.976234i	$-0.569535\pi$
$47$	24.4572	−	14.1204i	0.520367	−	0.300434i	0.737085	+	0.675800i	$0.236202\pi$
$48$		0			0
$49$	3.06832	+	48.9038i	0.0626188	+	0.998038i
$50$	7.07107			0.141421
$51$		0			0
$52$	32.3208	+	18.6604i	0.621553	+	0.358854i
$53$	0.221841	−	0.384239i	0.00418567	−	0.00724980i	−0.863925	−	0.503621i	$-0.832001\pi$
$53$	0.221841	−	0.384239i	0.00418567	−	0.00724980i	0.868111	+	0.496371i	$0.165334\pi$
$54$		0			0
$55$			40.4059i			0.734653i
$56$	14.4317	+	13.5546i	0.257709	+	0.242046i
$57$		0			0
$58$	11.6434	+	20.1669i	0.200748	+	0.347706i
$59$	−64.2260	−	37.0809i	−1.08858	−	0.628490i	−0.155379	−	0.987855i	$-0.549660\pi$
$59$	−64.2260	−	37.0809i	−1.08858	−	0.628490i	−0.933197	+	0.359365i	$0.882993\pi$
$60$		0			0
$61$	91.0443	−	52.5645i	1.49253	−	0.861712i	0.492566	−	0.870275i	$-0.336059\pi$
$61$	91.0443	−	52.5645i	1.49253	−	0.861712i	0.999963	+	0.00856246i	$0.00272555\pi$
$62$		−	39.5164i		−	0.637361i
$63$		0			0
$64$	8.00000			0.125000
$65$	−20.8630	−	36.1357i	−0.320969	−	0.555934i
$66$		0			0
$67$	6.35442	−	11.0062i	0.0948420	−	0.164271i	−0.814701	−	0.579882i	$-0.803099\pi$
$67$	6.35442	−	11.0062i	0.0948420	−	0.164271i	0.909543	+	0.415611i	$0.136432\pi$
$68$	2.66924	−	1.54109i	0.0392535	−	0.0226630i
$69$		0			0
$70$	−6.39617	−	21.1917i	−0.0913738	−	0.302739i
$71$	45.7647			0.644573			0.322286	−	0.946642i	$-0.395549\pi$
$71$	45.7647			0.644573			0.322286	+	0.946642i	$0.395549\pi$
$72$		0			0
$73$	31.5463	+	18.2133i	0.432141	+	0.249497i	0.700258	−	0.713889i	$-0.253068\pi$
$73$	31.5463	+	18.2133i	0.432141	+	0.249497i	−0.268117	+	0.963386i	$0.586401\pi$
$74$	36.5366	−	63.2833i	0.493738	−	0.855179i
$75$		0			0
$76$			68.0895i			0.895914i
$77$	121.095	−	36.5494i	1.57266	−	0.474667i
$78$		0			0
$79$	66.5990	+	115.353i	0.843025	+	1.46016i	0.887325	+	0.461145i	$0.152561\pi$
$79$	66.5990	+	115.353i	0.843025	+	1.46016i	−0.0442994	+	0.999018i	$0.514106\pi$
$80$	−7.74597	−	4.47214i	−0.0968246	−	0.0559017i
$81$		0			0
$82$	45.9057	−	26.5037i	0.559825	−	0.323215i
$83$			49.9265i			0.601524i	0.953699	+	0.300762i	$0.0972409\pi$
$83$			49.9265i			0.601524i	−0.953699	+	0.300762i	$0.902759\pi$
$84$		0			0
$85$	−3.44597			−0.0405409
$86$	−45.0389	−	78.0097i	−0.523709	−	0.907090i
$87$		0			0
$88$	25.5549	−	44.2625i	0.290397	−	0.502983i
$89$	−85.9133	+	49.6020i	−0.965318	+	0.557326i	−0.897806	−	0.440392i	$-0.854839\pi$
$89$	−85.9133	+	49.6020i	−0.965318	+	0.557326i	−0.0675121	+	0.997718i	$0.521506\pi$
$90$		0			0
$91$	−89.4257	+	95.2123i	−0.982700	+	1.04629i
$92$	53.9752			0.586687
$93$		0			0
$94$	34.5878	+	19.9693i	0.367955	+	0.212439i
$95$	38.0632	−	65.9274i	0.400665	−	0.693972i
$96$		0			0
$97$		−	150.376i		−	1.55027i	−0.631796	−	0.775134i	$-0.717682\pi$
$97$		−	150.376i		−	1.55027i	0.631796	−	0.775134i	$-0.282318\pi$
$98$	−57.7251	+	38.3381i	−0.589032	+	0.391206i
$99$		0			0
$100$	5.00000	+	8.66025i	0.0500000	+	0.0866025i
$101$	−40.7726	−	23.5401i	−0.403689	−	0.233070i	0.284386	−	0.958710i	$-0.408210\pi$
$101$	−40.7726	−	23.5401i	−0.403689	−	0.233070i	−0.688074	+	0.725640i	$0.741544\pi$
$102$		0			0
$103$	−65.7708	+	37.9728i	−0.638552	+	0.368668i	−0.784056	−	0.620690i	$-0.786853\pi$
$103$	−65.7708	+	37.9728i	−0.638552	+	0.368668i	0.145505	+	0.989358i	$0.453519\pi$
$104$			52.7796i			0.507496i
$105$		0			0
$106$	0.627460			0.00591944
$107$	−53.6125	−	92.8597i	−0.501052	−	0.867847i	−0.999999	−	0.00121497i	$-0.999613\pi$
$107$	−53.6125	−	92.8597i	−0.501052	−	0.867847i	0.498947	−	0.866632i	$-0.333720\pi$
$108$		0			0
$109$	−40.4452	+	70.0532i	−0.371057	+	0.642690i	−0.989728	−	0.142960i	$-0.954338\pi$
$109$	−40.4452	+	70.0532i	−0.371057	+	0.642690i	0.618671	+	0.785650i	$0.287671\pi$
$110$	−49.4869	+	28.5713i	−0.449881	+	0.259739i
$111$		0			0
$112$	−6.39617	+	27.2597i	−0.0571087	+	0.243390i
$113$	79.9061			0.707134			0.353567	−	0.935409i	$-0.384969\pi$
$113$	79.9061			0.707134			0.353567	+	0.935409i	$0.384969\pi$
$114$		0			0
$115$	−52.2613	−	30.1731i	−0.454446	−	0.262375i
$116$	−16.4662	+	28.5204i	−0.141950	+	0.245865i
$117$		0			0
$118$		−	104.881i		−	0.888819i
$119$	3.11707	+	10.3275i	0.0261939	+	0.0867853i
$120$		0			0
$121$	−102.764	−	177.992i	−0.849288	−	1.47101i
$122$	128.756	+	74.3374i	1.05538	+	0.609323i
$123$		0			0
$124$	48.3975	−	27.9423i	0.390303	−	0.225341i
$125$		−	11.1803i		−	0.0894427i
$126$		0			0
$127$	99.1937			0.781053			0.390526	−	0.920592i	$-0.372293\pi$
$127$	99.1937			0.781053			0.390526	+	0.920592i	$0.372293\pi$
$128$	5.65685	+	9.79796i	0.0441942	+	0.0765466i
$129$		0			0
$130$	29.5047	−	51.1036i	0.226959	−	0.393105i
$131$	−144.309	+	83.3170i	−1.10160	+	0.636008i	−0.936640	−	0.350293i	$-0.886082\pi$
$131$	−144.309	+	83.3170i	−1.10160	+	0.636008i	−0.164958	+	0.986301i	$0.552749\pi$
$132$		0			0
$133$	−232.012	−	54.4390i	−1.74445	−	0.409316i
$134$	17.9730			0.134127
$135$		0			0
$136$	3.77487	+	2.17942i	0.0277564	+	0.0160252i
$137$	−75.7587	+	131.218i	−0.552983	+	0.957795i	0.445074	+	0.895494i	$0.353177\pi$
$137$	−75.7587	+	131.218i	−0.552983	+	0.957795i	−0.998057	+	0.0623012i	$0.980156\pi$
$138$		0			0
$139$			151.816i			1.09220i	0.837719	+	0.546101i	$0.183889\pi$
$139$			151.816i			1.09220i	−0.837719	+	0.546101i	$0.816111\pi$
$140$	21.4317	−	22.8185i	0.153083	−	0.162989i
$141$		0			0
$142$	32.3605	+	56.0500i	0.227891	+	0.394719i
$143$	292.019	+	168.597i	2.04209	+	1.17900i
$144$		0			0
$145$	31.8867	−	18.4098i	0.219909	−	0.126964i
$146$			51.5149i			0.352842i
$147$		0			0
$148$	103.341			0.698251
$149$	16.5970	+	28.7468i	0.111389	+	0.192931i	0.916331	−	0.400423i	$-0.131137\pi$
$149$	16.5970	+	28.7468i	0.111389	+	0.192931i	−0.804941	+	0.593354i	$0.797803\pi$
$150$		0			0
$151$	4.65158	−	8.05678i	0.0308052	−	0.0533562i	−0.850212	−	0.526441i	$-0.823526\pi$
$151$	4.65158	−	8.05678i	0.0308052	−	0.0533562i	0.881017	+	0.473085i	$0.156860\pi$
$152$	−83.3923	+	48.1465i	−0.548633	+	0.316754i
$153$		0			0
$154$	130.391	+	122.466i	0.846693	+	0.795235i
$155$	−62.4809			−0.403103
$156$		0			0
$157$	−20.7746	−	11.9942i	−0.132322	−	0.0763963i	0.432378	−	0.901693i	$-0.357675\pi$
$157$	−20.7746	−	11.9942i	−0.132322	−	0.0763963i	−0.564700	+	0.825296i	$0.691008\pi$
$158$	−94.1852	+	163.134i	−0.596109	+	1.03249i
$159$		0			0
$160$		−	12.6491i		−	0.0790569i
$161$	−43.1543	+	183.918i	−0.268039	+	1.14235i
$162$		0			0
$163$	126.564	+	219.215i	0.776464	+	1.34488i	0.933968	+	0.357357i	$0.116322\pi$
$163$	126.564	+	219.215i	0.776464	+	1.34488i	−0.157504	+	0.987518i	$0.550345\pi$
$164$	64.9204	+	37.4818i	0.395856	+	0.228548i
$165$		0			0
$166$	−61.1472	+	35.3033i	−0.368357	+	0.212671i
$167$			85.7259i			0.513329i	0.966501	+	0.256664i	$0.0826235\pi$
$167$			85.7259i			0.513329i	−0.966501	+	0.256664i	$0.917376\pi$
$168$		0			0
$169$	−179.211			−1.06042
$170$	−2.43667	−	4.22044i	−0.0143334	−	0.0248261i
$171$		0			0
$172$	63.6947	−	110.322i	0.370318	−	0.641409i
$173$	16.8672	−	9.73826i	0.0974980	−	0.0562905i	−0.450458	−	0.892798i	$-0.648739\pi$
$173$	16.8672	−	9.73826i	0.0974980	−	0.0562905i	0.547956	+	0.836507i	$0.315406\pi$
$174$		0			0
$175$	−33.5071	+	10.1132i	−0.191469	+	0.0577899i
$176$	72.2803			0.410684
$177$		0			0
$178$	−121.500	−	70.1479i	−0.682583	−	0.394089i
$179$	126.417	−	218.961i	0.706241	−	1.22324i	−0.260001	−	0.965608i	$-0.583723\pi$
$179$	126.417	−	218.961i	0.706241	−	1.22324i	0.966242	−	0.257637i	$-0.0829437\pi$
$180$		0			0
$181$		−	144.224i		−	0.796820i	−0.917207	−	0.398410i	$-0.869562\pi$
$181$		−	144.224i		−	0.796820i	0.917207	−	0.398410i	$-0.130438\pi$
$182$	−179.844	−	42.1984i	−0.988155	−	0.231859i
$183$		0			0
$184$	38.1663	+	66.1059i	0.207425	+	0.359271i
$185$	−100.060	−	57.7695i	−0.540863	−	0.312267i
$186$		0			0
$187$	24.1167	−	13.9238i	0.128966	−	0.0744587i
$188$			56.4816i			0.300434i
$189$		0			0
$190$	107.659			0.566626
$191$	−157.049	−	272.017i	−0.822246	−	1.42417i	−0.904006	−	0.427520i	$-0.859387\pi$
$191$	−157.049	−	272.017i	−0.822246	−	1.42417i	0.0817601	−	0.996652i	$-0.473946\pi$
$192$		0			0
$193$	−26.4142	+	45.7507i	−0.136861	+	0.237050i	−0.926307	−	0.376770i	$-0.877035\pi$
$193$	−26.4142	+	45.7507i	−0.136861	+	0.237050i	0.789446	+	0.613820i	$0.210368\pi$
$194$	184.172	−	106.332i	0.949342	−	0.548103i
$195$		0			0
$196$	−87.7723	−	43.5893i	−0.447818	−	0.222395i
$197$	−54.2005			−0.275129			−0.137565	−	0.990493i	$-0.543927\pi$
$197$	−54.2005			−0.275129			−0.137565	+	0.990493i	$0.543927\pi$
$198$		0			0
$199$	19.8934	+	11.4855i	0.0999670	+	0.0577160i	0.549150	−	0.835724i	$-0.314952\pi$
$199$	19.8934	+	11.4855i	0.0999670	+	0.0577160i	−0.449183	+	0.893440i	$0.648285\pi$
$200$	−7.07107	+	12.2474i	−0.0353553	+	0.0612372i
$201$		0			0
$202$		−	66.5813i		−	0.329611i
$203$	−84.0168	−	78.9107i	−0.413876	−	0.388722i
$204$		0			0
$205$	−41.9060	−	72.5832i	−0.204419	−	0.354065i
$206$	−93.0140	−	53.7017i	−0.451524	−	0.260688i
$207$		0			0
$208$	−64.6415	+	37.3208i	−0.310777	+	0.179427i
$209$			615.191i			2.94350i
$210$		0			0
$211$	−292.203			−1.38485			−0.692425	−	0.721490i	$-0.743457\pi$
$211$	−292.203			−1.38485			−0.692425	+	0.721490i	$0.743457\pi$
$212$	0.443681	+	0.768479i	0.00209284	+	0.00362490i
$213$		0			0
$214$	75.8196	−	131.323i	0.354297	−	0.613661i
$215$	−123.344	+	71.2128i	−0.573694	+	0.331222i
$216$		0			0
$217$	56.5174	+	187.253i	0.260449	+	0.862917i
$218$	−114.396			−0.524754
$219$		0			0
$220$	−69.9851	−	40.4059i	−0.318114	−	0.183663i
$221$	−14.3786	+	24.9045i	−0.0650617	+	0.112690i
$222$		0			0
$223$			271.305i			1.21661i	0.793702	+	0.608306i	$0.208151\pi$
$223$			271.305i			1.21661i	−0.793702	+	0.608306i	$0.791849\pi$
$224$	−37.9089	+	11.4418i	−0.169236	+	0.0510795i
$225$		0			0
$226$	56.5021	+	97.8646i	0.250009	+	0.433029i
$227$	−128.699	−	74.3044i	−0.566956	−	0.327332i	0.188977	−	0.981982i	$-0.439483\pi$
$227$	−128.699	−	74.3044i	−0.566956	−	0.327332i	−0.755933	+	0.654649i	$0.772816\pi$
$228$		0			0
$229$	21.9394	−	12.6667i	0.0958053	−	0.0553132i	−0.451332	−	0.892356i	$-0.649051\pi$
$229$	21.9394	−	12.6667i	0.0958053	−	0.0553132i	0.547137	+	0.837043i	$0.315718\pi$
$230$		−	85.3423i		−	0.371054i
$231$		0			0
$232$	−46.5736			−0.200748
$233$	−204.443	−	354.106i	−0.877438	−	1.51977i	−0.854143	−	0.520038i	$-0.825918\pi$
$233$	−204.443	−	354.106i	−0.877438	−	1.51977i	−0.0232943	−	0.999729i	$-0.507415\pi$
$234$		0			0
$235$	31.5742	−	54.6881i	0.134358	−	0.232715i
$236$	128.452	−	74.1618i	0.544288	−	0.314245i
$237$		0			0
$238$	−10.4444	+	11.1202i	−0.0438840	+	0.0467236i
$239$	−67.0352			−0.280482			−0.140241	−	0.990117i	$-0.544788\pi$
$239$	−67.0352			−0.280482			−0.140241	+	0.990117i	$0.544788\pi$
$240$		0			0
$241$	205.143	+	118.440i	0.851217	+	0.491451i	0.861061	−	0.508501i	$-0.169800\pi$
$241$	205.143	+	118.440i	0.851217	+	0.491451i	−0.00984406	+	0.999952i	$0.503134\pi$
$242$	145.330	−	251.719i	0.600537	−	1.04016i
$243$		0			0
$244$			210.258i			0.861712i
$245$	60.6179	+	91.2714i	0.247420	+	0.372536i
$246$		0			0
$247$	−317.644	−	550.176i	−1.28601	−	2.22743i
$248$	68.4444	+	39.5164i	0.275986	+	0.159340i
$249$		0			0
$250$	13.6931	−	7.90569i	0.0547723	−	0.0316228i
$251$			483.382i			1.92582i	0.269815	+	0.962912i	$0.413037\pi$
$251$			483.382i			1.92582i	−0.269815	+	0.962912i	$0.586963\pi$
$252$		0			0
$253$	487.668			1.92754
$254$	70.1406	+	121.487i	0.276144	+	0.478295i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	281.097	−	162.291i	1.09376	−	0.631484i	0.159187	−	0.987248i	$-0.449113\pi$
$257$	281.097	−	162.291i	1.09376	−	0.631484i	0.934576	+	0.355764i	$0.115779\pi$
$258$		0			0
$259$	−82.6234	+	352.131i	−0.319009	+	1.35958i
$260$	83.4519			0.320969
$261$		0			0
$262$	−204.084	−	117.828i	−0.778948	−	0.449726i
$263$	153.686	−	266.192i	0.584358	−	1.01214i	−0.410598	−	0.911817i	$-0.634680\pi$
$263$	153.686	−	266.192i	0.584358	−	1.01214i	0.994955	−	0.100320i	$-0.0319868\pi$
$264$		0			0
$265$		−	0.992102i		−	0.00374378i
$266$	−97.3834	−	322.650i	−0.366103	−	1.21297i
$267$		0			0
$268$	12.7088	+	22.0123i	0.0474210	+	0.0821356i
$269$	65.6866	+	37.9242i	0.244188	+	0.140982i	0.617100	−	0.786885i	$-0.288307\pi$
$269$	65.6866	+	37.9242i	0.244188	+	0.140982i	−0.372912	+	0.927867i	$0.621641\pi$
$270$		0			0
$271$	−18.8151	+	10.8629i	−0.0694283	+	0.0400844i	−0.534312	−	0.845287i	$-0.679429\pi$
$271$	−18.8151	+	10.8629i	−0.0694283	+	0.0400844i	0.464884	+	0.885372i	$0.346096\pi$
$272$			6.16434i			0.0226630i
$273$		0			0
$274$	−214.278			−0.782036
$275$	45.1752	+	78.2457i	0.164273	+	0.284530i
$276$		0			0
$277$	55.8659	−	96.7627i	0.201682	−	0.349324i	−0.747388	−	0.664387i	$-0.768693\pi$
$277$	55.8659	−	96.7627i	0.201682	−	0.349324i	0.949071	+	0.315064i	$0.102026\pi$
$278$	−185.936	+	107.350i	−0.668835	+	0.386152i
$279$		0			0
$280$	43.1013	+	10.1132i	0.153933	+	0.0361187i
$281$	188.298			0.670101			0.335051	−	0.942200i	$-0.391247\pi$
$281$	188.298			0.670101			0.335051	+	0.942200i	$0.391247\pi$
$282$		0			0
$283$	187.769	+	108.408i	0.663495	+	0.383069i	0.793607	−	0.608430i	$-0.208201\pi$
$283$	187.769	+	108.408i	0.663495	+	0.383069i	−0.130113	+	0.991499i	$0.541534\pi$
$284$	−45.7647	+	79.2667i	−0.161143	+	0.279108i
$285$		0			0
$286$			476.866i			1.66736i
$287$	−179.623	+	191.246i	−0.625864	+	0.666363i
$288$		0			0
$289$	−143.313	−	248.225i	−0.495891	−	0.858909i
$290$	45.0947	+	26.0354i	0.155499	+	0.0897773i
$291$		0			0
$292$	−63.0926	+	36.4265i	−0.216071	+	0.124748i
$293$			57.3776i			0.195828i	0.995195	+	0.0979140i	$0.0312170\pi$
$293$			57.3776i			0.195828i	−0.995195	+	0.0979140i	$0.968783\pi$
$294$		0			0
$295$	−165.831			−0.562138
$296$	73.0732	+	126.567i	0.246869	+	0.427590i
$297$		0			0
$298$	−23.4717	+	40.6541i	−0.0787640	+	0.136423i
$299$	−436.130	+	251.800i	−1.45863	+	0.842140i
$300$		0			0
$301$	324.994	+	305.242i	1.07971	+	1.01409i
$302$	13.1567			0.0435651
$303$		0			0
$304$	−117.934	−	68.0895i	−0.387942	−	0.223979i
$305$	117.538	−	203.581i	0.385370	−	0.667480i
$306$		0			0
$307$		−	291.273i		−	0.948773i	−0.880317	−	0.474386i	$-0.842670\pi$
$307$		−	291.273i		−	0.948773i	0.880317	−	0.474386i	$-0.157330\pi$
$308$	−57.7896	+	246.292i	−0.187629	+	0.799650i
$309$		0			0
$310$	−44.1807	−	76.5232i	−0.142518	−	0.246849i
$311$	−216.368	−	124.920i	−0.695717	−	0.401673i	0.110033	−	0.993928i	$-0.464904\pi$
$311$	−216.368	−	124.920i	−0.695717	−	0.401673i	−0.805750	+	0.592255i	$0.798238\pi$
$312$		0			0
$313$	−3.27832	+	1.89274i	−0.0104739	+	0.00604709i	−0.505228	−	0.862986i	$-0.668592\pi$
$313$	−3.27832	+	1.89274i	−0.0104739	+	0.00604709i	0.494754	+	0.869033i	$0.335258\pi$
$314$		−	33.9248i		−	0.108041i
$315$		0			0
$316$	−266.396			−0.843025
$317$	−35.6805	−	61.8004i	−0.112557	−	0.194954i	0.804244	−	0.594300i	$-0.202571\pi$
$317$	−35.6805	−	61.8004i	−0.112557	−	0.194954i	−0.916800	+	0.399346i	$0.869237\pi$
$318$		0			0
$319$	−148.773	+	257.683i	−0.466373	+	0.807783i
$320$	15.4919	−	8.94427i	0.0484123	−	0.0279508i
$321$		0			0
$322$	−255.768	+	77.1968i	−0.794310	+	0.239742i
$323$	−52.4659			−0.162433
$324$		0			0
$325$	−80.8019	−	46.6510i	−0.248621	−	0.143542i
$326$	−178.988	+	310.016i	−0.549043	+	0.950970i
$327$		0			0
$328$			106.015i			0.323215i
$329$	−192.459	−	45.1582i	−0.584981	−	0.137259i
$330$		0			0
$331$	170.983	+	296.152i	0.516566	+	0.894718i	0.999815	+	0.0192351i	$0.00612311\pi$
$331$	170.983	+	296.152i	0.516566	+	0.894718i	−0.483249	+	0.875483i	$0.660544\pi$
$332$	−86.4752	−	49.9265i	−0.260467	−	0.150381i
$333$		0			0
$334$	−104.992	+	60.6174i	−0.314349	+	0.181489i
$335$		−	28.4178i		−	0.0848293i
$336$		0			0
$337$	246.396			0.731145			0.365573	−	0.930783i	$-0.380873\pi$
$337$	246.396			0.731145			0.365573	+	0.930783i	$0.380873\pi$
$338$	−126.721	−	219.487i	−0.374915	−	0.649371i
$339$		0			0
$340$	3.44597	−	5.96860i	0.0101352	−	0.0175547i
$341$	437.273	−	252.460i	1.28233	−	0.740352i
$342$		0			0
$343$	218.705	−	264.230i	0.637623	−	0.770349i
$344$	180.156			0.523709
$345$		0			0
$346$	23.8538	+	13.7720i	0.0689415	+	0.0398034i
$347$	69.1758	−	119.816i	0.199354	−	0.345291i	−0.748965	−	0.662609i	$-0.769449\pi$
$347$	69.1758	−	119.816i	0.199354	−	0.345291i	0.948319	+	0.317318i	$0.102782\pi$
$348$		0			0
$349$		−	115.858i		−	0.331971i	−0.986128	−	0.165986i	$-0.946919\pi$
$349$		−	115.858i		−	0.331971i	0.986128	−	0.165986i	$-0.0530805\pi$
$350$	−36.0792	−	33.8865i	−0.103083	−	0.0968184i
$351$		0			0
$352$	51.1099	+	88.5249i	0.145199	+	0.251491i
$353$	−162.136	−	93.6093i	−0.459309	−	0.265182i	0.252445	−	0.967611i	$-0.418765\pi$
$353$	−162.136	−	93.6093i	−0.459309	−	0.265182i	−0.711754	+	0.702429i	$0.752099\pi$
$354$		0			0
$355$	88.6229	−	51.1664i	0.249642	−	0.144131i
$356$		−	198.408i		−	0.557326i
$357$		0			0
$358$	357.562			0.998775
$359$	318.748	+	552.087i	0.887876	+	1.53785i	0.842381	+	0.538883i	$0.181153\pi$
$359$	318.748	+	552.087i	0.887876	+	1.53785i	0.0454957	+	0.998965i	$0.485513\pi$
$360$		0			0
$361$	399.022	−	691.127i	1.10532	−	1.91448i
$362$	176.638	−	101.982i	0.487951	−	0.281718i
$363$		0			0
$364$	−75.4868	−	250.102i	−0.207381	−	0.687094i
$365$	81.4522			0.223157
$366$		0			0
$367$	47.6750	+	27.5252i	0.129905	+	0.0750005i	0.563544	−	0.826086i	$-0.309437\pi$
$367$	47.6750	+	27.5252i	0.129905	+	0.0750005i	−0.433639	+	0.901087i	$0.642771\pi$
$368$	−53.9752	+	93.4878i	−0.146672	+	0.254043i
$369$		0			0
$370$		−	163.397i		−	0.441613i
$371$	−2.97329	+	0.897411i	−0.00801426	+	0.00241890i
$372$		0			0
$373$	−134.578	−	233.097i	−0.360800	−	0.624924i	0.627293	−	0.778784i	$-0.284163\pi$
$373$	−134.578	−	233.097i	−0.360800	−	0.624924i	−0.988093	+	0.153859i	$0.950830\pi$
$374$	34.1061	+	19.6912i	0.0911929	+	0.0526502i
$375$		0			0
$376$	−69.1755	+	39.9385i	−0.183978	+	0.106219i
$377$		−	307.267i		−	0.815031i
$378$		0			0
$379$	469.785			1.23954			0.619769	−	0.784784i	$-0.287226\pi$
$379$	469.785			1.23954			0.619769	+	0.784784i	$0.287226\pi$
$380$	76.1264	+	131.855i	0.200333	+	0.346986i
$381$		0			0
$382$	222.101	−	384.690i	0.581416	−	1.00704i
$383$	348.324	−	201.105i	0.909462	−	0.525078i	0.0292039	−	0.999573i	$-0.490703\pi$
$383$	348.324	−	201.105i	0.909462	−	0.525078i	0.880258	+	0.474495i	$0.157369\pi$
$384$		0			0
$385$	193.636	−	206.166i	0.502951	−	0.535496i
$386$	−74.7107			−0.193551
$387$		0			0
$388$	260.459	+	150.376i	0.671286	+	0.387567i
$389$	−55.3803	+	95.9215i	−0.142366	+	0.246585i	−0.928387	−	0.371615i	$-0.878804\pi$
$389$	−55.3803	+	95.9215i	−0.142366	+	0.246585i	0.786021	+	0.618200i	$0.212138\pi$
$390$		0			0
$391$			41.5902i			0.106369i
$392$	−8.67853	−	138.321i	−0.0221391	−	0.352860i
$393$		0			0
$394$	−38.3255	−	66.3817i	−0.0972729	−	0.168482i
$395$	257.937	+	148.920i	0.653005	+	0.377012i
$396$		0			0
$397$	363.569	−	209.907i	0.915792	−	0.528733i	0.0335018	−	0.999439i	$-0.489334\pi$
$397$	363.569	−	209.907i	0.915792	−	0.528733i	0.882290	+	0.470706i	$0.156001\pi$
$398$			32.4858i			0.0816227i
$399$		0			0
$400$	−20.0000			−0.0500000
$401$	157.034	+	271.990i	0.391605	+	0.678280i	0.992661	−	0.120927i	$-0.0385866\pi$
$401$	157.034	+	271.990i	0.391605	+	0.678280i	−0.601056	+	0.799207i	$0.705253\pi$
$402$		0			0
$403$	−260.708	+	451.559i	−0.646917	+	1.12049i
$404$	81.5451	−	47.0801i	0.201844	−	0.116535i
$405$		0			0
$406$	37.2366	−	158.697i	0.0917156	−	0.390880i
$407$	933.691			2.29408
$408$		0			0
$409$	105.506	+	60.9140i	0.257961	+	0.148934i	0.623404	−	0.781900i	$-0.285749\pi$
$409$	105.506	+	60.9140i	0.257961	+	0.148934i	−0.365443	+	0.930834i	$0.619082\pi$
$410$	59.2640	−	102.648i	0.144546	−	0.250361i
$411$		0			0
$412$		−	151.891i		−	0.368668i
$413$	150.003	+	496.989i	0.363203	+	1.20336i
$414$		0			0
$415$	55.8195	+	96.6822i	0.134505	+	0.232969i
$416$	−91.4169	−	52.7796i	−0.219752	−	0.126874i
$417$		0			0
$418$	−753.452	+	435.006i	−1.80252	+	1.04068i
$419$			43.0872i			0.102833i	0.998677	+	0.0514167i	$0.0163737\pi$
$419$			43.0872i			0.102833i	−0.998677	+	0.0514167i	$0.983626\pi$
$420$		0			0
$421$	135.571			0.322022			0.161011	−	0.986953i	$-0.448525\pi$
$421$	135.571			0.322022			0.161011	+	0.986953i	$0.448525\pi$
$422$	−206.619	−	357.874i	−0.489618	−	0.848043i
$423$		0			0
$424$	−0.627460	+	1.08679i	−0.00147986	+	0.00256319i
$425$	−6.67310	+	3.85272i	−0.0157014	+	0.00906521i
$426$		0			0
$427$	−716.445	−	168.106i	−1.67786	−	0.393690i
$428$	214.450			0.501052
$429$		0			0
$430$	−174.435	−	100.710i	−0.405663	−	0.234210i
$431$	95.6132	−	165.607i	0.221840	−	0.384239i	−0.733527	−	0.679661i	$-0.762127\pi$
$431$	95.6132	−	165.607i	0.221840	−	0.384239i	0.955367	+	0.295422i	$0.0954603\pi$
$432$		0			0
$433$			339.825i			0.784815i	0.919791	+	0.392408i	$0.128358\pi$
$433$			339.825i			0.784815i	−0.919791	+	0.392408i	$0.871642\pi$
$434$	−189.373	+	201.627i	−0.436344	+	0.464579i
$435$		0			0
$436$	−80.8905	−	140.106i	−0.185529	−	0.321345i
$437$	−795.692	−	459.393i	−1.82081	−	1.05124i
$438$		0			0
$439$	286.015	−	165.131i	0.651515	−	0.376153i	−0.137521	−	0.990499i	$-0.543914\pi$
$439$	286.015	−	165.131i	0.651515	−	0.376153i	0.789037	+	0.614346i	$0.210580\pi$
$440$		−	114.285i		−	0.259739i
$441$		0			0
$442$	−40.6690			−0.0920112
$443$	−280.831	−	486.414i	−0.633931	−	1.09800i	−0.986741	−	0.162305i	$-0.948107\pi$
$443$	−280.831	−	486.414i	−0.633931	−	1.09800i	0.352810	−	0.935695i	$-0.385226\pi$
$444$		0			0
$445$	−110.914	+	192.108i	−0.249244	+	0.431703i
$446$	−332.279	+	191.841i	−0.745020	+	0.430138i
$447$		0			0
$448$	−40.8189	−	38.3381i	−0.0911137	−	0.0855762i
$449$	386.250			0.860244			0.430122	−	0.902771i	$-0.358471\pi$
$449$	386.250			0.860244			0.430122	+	0.902771i	$0.358471\pi$
$450$		0			0
$451$	586.558	+	338.650i	1.30057	+	0.750886i
$452$	−79.9061	+	138.401i	−0.176783	+	0.306198i
$453$		0			0
$454$		−	210.165i		−	0.462918i
$455$	−66.7215	+	284.359i	−0.146641	+	0.624964i
$456$		0			0
$457$	−249.533	−	432.203i	−0.546024	−	0.945741i	−0.998542	−	0.0539854i	$-0.982808\pi$
$457$	−249.533	−	432.203i	−0.546024	−	0.945741i	0.452518	−	0.891755i	$-0.350526\pi$
$458$	31.0270	+	17.9135i	0.0677446	+	0.0391124i
$459$		0			0
$460$	104.523	−	60.3461i	0.227223	−	0.131187i
$461$		−	618.290i		−	1.34119i	−0.741823	−	0.670596i	$-0.766038\pi$
$461$		−	618.290i		−	1.34119i	0.741823	−	0.670596i	$-0.233962\pi$
$462$		0			0
$463$	−194.433			−0.419941			−0.209971	−	0.977708i	$-0.567337\pi$
$463$	−194.433			−0.419941			−0.209971	+	0.977708i	$0.567337\pi$
$464$	−32.9325	−	57.0407i	−0.0709752	−	0.122933i
$465$		0			0
$466$	289.126	−	500.781i	0.620442	−	1.07464i
$467$	−131.449	+	75.8923i	−0.281476	+	0.162510i	−0.634091	−	0.773258i	$-0.718626\pi$
$467$	−131.449	+	75.8923i	−0.281476	+	0.162510i	0.352615	+	0.935768i	$0.385292\pi$
$468$		0			0
$469$	−85.1671	+	25.7055i	−0.181593	+	0.0548091i
$470$	89.3052			0.190011
$471$		0			0
$472$	181.659	+	104.881i	0.384870	+	0.222205i
$473$	575.484	−	996.767i	1.21667	−	2.10733i
$474$		0			0
$475$		−	170.224i		−	0.358366i
$476$	−21.0047	−	4.92852i	−0.0441276	−	0.0103540i
$477$		0			0
$478$	−47.4010	−	82.1010i	−0.0991653	−	0.171759i
$479$	−194.656	−	112.385i	−0.406381	−	0.234624i	0.282853	−	0.959163i	$-0.408719\pi$
$479$	−194.656	−	112.385i	−0.406381	−	0.234624i	−0.689233	+	0.724539i	$0.742053\pi$
$480$		0			0
$481$	−835.016	+	482.097i	−1.73600	+	1.00228i
$482$			334.998i			0.695016i
$483$		0			0
$484$	411.055			0.849288
$485$	−168.126	−	291.202i	−0.346651	−	0.600417i
$486$		0			0
$487$	−34.7814	+	60.2432i	−0.0714198	+	0.123703i	−0.899524	−	0.436872i	$-0.856086\pi$
$487$	−34.7814	+	60.2432i	−0.0714198	+	0.123703i	0.828104	+	0.560575i	$0.189420\pi$
$488$	−257.512	+	148.675i	−0.527689	+	0.304661i
$489$		0			0
$490$	−68.9208	+	138.780i	−0.140655	+	0.283225i
$491$	750.454			1.52842			0.764210	−	0.644967i	$-0.223129\pi$
$491$	750.454			1.52842			0.764210	+	0.644967i	$0.223129\pi$
$492$		0			0
$493$	−21.9762	−	12.6880i	−0.0445764	−	0.0257362i
$494$	449.217	−	778.067i	0.909346	−	1.57503i
$495$		0			0
$496$			111.769i			0.225341i
$497$	−233.508	−	219.317i	−0.469835	−	0.441281i
$498$		0			0
$499$	−80.0848	−	138.711i	−0.160491	−	0.277978i	0.774554	−	0.632508i	$-0.217974\pi$
$499$	−80.0848	−	138.711i	−0.160491	−	0.277978i	−0.935045	+	0.354530i	$0.884641\pi$
$500$	19.3649	+	11.1803i	0.0387298	+	0.0223607i
$501$		0			0
$502$	−592.019	+	341.803i	−1.17932	+	0.680882i
$503$			724.412i			1.44018i	0.693879	+	0.720092i	$0.255900\pi$
$503$			724.412i			1.44018i	−0.693879	+	0.720092i	$0.744100\pi$
$504$		0			0
$505$	−105.274			−0.208464
$506$	344.834	+	597.269i	0.681489	+	1.18037i
$507$		0			0
$508$	−99.1937	+	171.809i	−0.195263	+	0.338206i
$509$	711.944	−	411.041i	1.39871	−	0.807547i	0.404454	−	0.914558i	$-0.367462\pi$
$509$	711.944	−	411.041i	1.39871	−	0.807547i	0.994258	+	0.107012i	$0.0341283\pi$
$510$		0			0
$511$	−73.6780	−	244.109i	−0.144184	−	0.477709i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	397.531	+	229.515i	0.773407	+	0.446527i
$515$	−84.9098	+	147.068i	−0.164873	+	0.285569i
$516$		0			0
$517$			510.313i			0.987066i
$518$	−489.694	+	147.801i	−0.945355	+	0.285331i
$519$		0			0
$520$	59.0094	+	102.207i	0.113480	+	0.196552i
$521$	−392.147	−	226.406i	−0.752681	−	0.434561i	0.0739805	−	0.997260i	$-0.476430\pi$
$521$	−392.147	−	226.406i	−0.752681	−	0.434561i	−0.826662	+	0.562699i	$0.809763\pi$
$522$		0			0
$523$	843.597	−	487.051i	1.61300	−	0.931264i	0.624326	−	0.781164i	$-0.285374\pi$
$523$	843.597	−	487.051i	1.61300	−	0.931264i	0.988671	−	0.150100i	$-0.0479597\pi$
$524$		−	333.268i		−	0.636008i
$525$		0			0
$526$	434.690			0.826406
$527$	21.5308	+	37.2924i	0.0408553	+	0.0707635i
$528$		0			0
$529$	−99.6657	+	172.626i	−0.188404	+	0.326325i
$530$	1.21507	−	0.701522i	0.00229259	−	0.00132363i
$531$		0			0
$532$	326.303	−	347.418i	0.613352	−	0.653041i
$533$	−699.426			−1.31224
$534$		0			0
$535$	−207.640	−	119.881i	−0.388113	−	0.224077i
$536$	−17.9730	+	31.1302i	−0.0335317	+	0.0580786i
$537$		0			0
$538$			107.266i			0.199379i
$539$	−793.026	−	393.831i	−1.47129	−	0.730670i
$540$		0			0
$541$	−138.078	−	239.158i	−0.255228	−	0.442067i	0.709730	−	0.704474i	$-0.248817\pi$
$541$	−138.078	−	239.158i	−0.255228	−	0.442067i	−0.964957	+	0.262407i	$0.915484\pi$
$542$	−26.6085	−	15.3624i	−0.0490932	−	0.0283440i
$543$		0			0
$544$	−7.54975	+	4.35885i	−0.0138782	+	0.00801259i
$545$			180.877i			0.331884i
$546$		0			0
$547$	426.436			0.779591			0.389795	−	0.920901i	$-0.372546\pi$
$547$	426.436			0.779591			0.389795	+	0.920901i	$0.372546\pi$
$548$	−151.517	−	262.436i	−0.276492	−	0.478897i
$549$		0			0
$550$	−63.8874	+	110.656i	−0.116159	+	0.201193i
$551$	485.484	−	280.295i	0.881097	−	0.508702i
$552$		0			0
$553$	212.989	−	907.733i	0.385152	−	1.64147i
$554$	158.013			0.285222
$555$		0			0
$556$	−262.953	−	151.816i	−0.472938	−	0.273051i
$557$	−60.9782	+	105.617i	−0.109476	+	0.189618i	−0.915558	−	0.402186i	$-0.868251\pi$
$557$	−60.9782	+	105.617i	−0.109476	+	0.189618i	0.806082	+	0.591804i	$0.201584\pi$
$558$		0			0
$559$			1188.57i			2.12624i
$560$	18.0911	+	59.9392i	0.0323055	+	0.107034i
$561$		0			0
$562$	133.147	+	230.618i	0.236917	+	0.410351i
$563$	376.532	+	217.391i	0.668796	+	0.386130i	0.795620	−	0.605796i	$-0.207145\pi$
$563$	376.532	+	217.391i	0.668796	+	0.386130i	−0.126824	+	0.991925i	$0.540478\pi$
$564$		0			0
$565$	154.737	−	89.3377i	0.273872	−	0.158120i
$566$			306.625i			0.541741i
$567$		0			0
$568$	−129.442			−0.227891
$569$	−148.138	−	256.583i	−0.260349	−	0.450937i	0.705986	−	0.708226i	$-0.250504\pi$
$569$	−148.138	−	256.583i	−0.260349	−	0.450937i	−0.966335	+	0.257289i	$0.917171\pi$
$570$		0			0
$571$	−29.9578	+	51.8885i	−0.0524655	+	0.0908730i	−0.891065	−	0.453875i	$-0.850041\pi$
$571$	−29.9578	+	51.8885i	−0.0524655	+	0.0908730i	0.838600	+	0.544748i	$0.183375\pi$
$572$	−584.039	+	337.195i	−1.02105	+	0.589502i
$573$		0			0
$574$	−361.240	−	84.7609i	−0.629338	−	0.147667i
$575$	−134.938			−0.234675
$576$		0			0
$577$	288.128	+	166.351i	0.499355	+	0.288303i	0.728447	−	0.685102i	$-0.240242\pi$
$577$	288.128	+	166.351i	0.499355	+	0.288303i	−0.229092	+	0.973405i	$0.573576\pi$
$578$	202.675	−	351.043i	0.350648	−	0.607340i
$579$		0			0
$580$			73.6393i			0.126964i
$581$	239.261	−	254.743i	0.411809	−	0.438456i
$582$		0			0
$583$	4.00868	+	6.94323i	0.00687595	+	0.0119095i
$584$	−89.2264	−	51.5149i	−0.152785	−	0.0882104i
$585$		0			0
$586$	−70.2729	+	40.5721i	−0.119920	+	0.0692356i
$587$		−	656.221i		−	1.11792i	−0.829194	−	0.558961i	$-0.811200\pi$
$587$		−	656.221i		−	1.11792i	0.829194	−	0.558961i	$-0.188800\pi$
$588$		0			0
$589$	−951.289			−1.61509
$590$	−117.260	−	203.100i	−0.198746	−	0.344238i
$591$		0			0
$592$	−103.341	+	178.992i	−0.174563	+	0.302352i
$593$	353.808	−	204.271i	0.596640	−	0.344471i	−0.171078	−	0.985257i	$-0.554725\pi$
$593$	353.808	−	204.271i	0.596640	−	0.344471i	0.767719	+	0.640787i	$0.221392\pi$
$594$		0			0
$595$	17.5826	+	16.5140i	0.0295506	+	0.0277547i
$596$	−66.3879			−0.111389
$597$		0			0
$598$	−616.781	−	356.099i	−1.03141	−	0.595483i
$599$	−588.643	+	1019.56i	−0.982709	+	1.70210i	−0.331003	+	0.943630i	$0.607387\pi$
$599$	−588.643	+	1019.56i	−0.982709	+	1.70210i	−0.651705	+	0.758472i	$0.725946\pi$
$600$		0			0
$601$		−	162.592i		−	0.270536i	−0.990809	−	0.135268i	$-0.956810\pi$
$601$		−	162.592i		−	0.270536i	0.990809	−	0.135268i	$-0.0431896\pi$
$602$	−144.038	+	613.873i	−0.239266	+	1.01972i
$603$		0			0
$604$	9.30317	+	16.1136i	0.0154026	+	0.0266781i
$605$	−398.003	−	229.787i	−0.657855	−	0.379813i
$606$		0			0
$607$	−318.116	+	183.664i	−0.524079	+	0.302577i	−0.738602	−	0.674142i	$-0.764514\pi$
$607$	−318.116	+	183.664i	−0.524079	+	0.302577i	0.214523	+	0.976719i	$0.431180\pi$
$608$		−	192.586i		−	0.316754i
$609$		0			0
$610$	332.447			0.544995
$611$	−263.492	−	456.382i	−0.431248	−	0.746943i
$612$		0			0
$613$	−182.636	+	316.335i	−0.297938	+	0.516044i	−0.975664	−	0.219270i	$-0.929632\pi$
$613$	−182.636	+	316.335i	−0.297938	+	0.516044i	0.677726	+	0.735315i	$0.262966\pi$
$614$	356.735	−	205.961i	0.581002	−	0.335442i
$615$		0			0
$616$	−342.508	+	103.377i	−0.556020	+	0.167820i
$617$	64.2245			0.104092			0.0520458	−	0.998645i	$-0.483426\pi$
$617$	64.2245			0.104092			0.0520458	+	0.998645i	$0.483426\pi$
$618$		0			0
$619$	−990.646	−	571.949i	−1.60040	−	0.923989i	−0.991407	−	0.130811i	$-0.958242\pi$
$619$	−990.646	−	571.949i	−1.60040	−	0.923989i	−0.608989	−	0.793178i	$-0.708425\pi$
$620$	62.4809	−	108.220i	0.100776	−	0.174549i
$621$		0			0
$622$		−	353.328i		−	0.568051i
$623$	676.067	+	158.632i	1.08518	+	0.254625i
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.0200000	−	0.0346410i
$626$	−4.63624	−	2.67674i	−0.00740614	−	0.00427594i
$627$		0			0
$628$	41.5492	−	23.9884i	0.0661611	−	0.0381982i
$629$			79.6288i			0.126596i
$630$		0			0
$631$	257.367			0.407872			0.203936	−	0.978984i	$-0.434627\pi$
$631$	257.367			0.407872			0.203936	+	0.978984i	$0.434627\pi$
$632$	−188.370	−	326.267i	−0.298055	−	0.516246i
$633$		0			0
$634$	50.4598	−	87.3990i	0.0795897	−	0.137853i
$635$	192.088	−	110.902i	0.302501	−	0.174649i
$636$		0			0
$637$	912.565	−	57.2562i	1.43260	−	0.0898841i
$638$	−420.794			−0.659552
$639$		0			0
$640$	21.9089	+	12.6491i	0.0342327	+	0.0197642i
$641$	99.4860	−	172.315i	0.155204	−	0.268822i	−0.777929	−	0.628352i	$-0.783730\pi$
$641$	99.4860	−	172.315i	0.155204	−	0.268822i	0.933133	+	0.359530i	$0.117063\pi$
$642$		0			0
$643$			708.223i			1.10144i	0.834692	+	0.550718i	$0.185646\pi$
$643$			708.223i			1.10144i	−0.834692	+	0.550718i	$0.814354\pi$
$644$	−275.401	−	258.664i	−0.427642	−	0.401652i
$645$		0			0
$646$	−37.0990	−	64.2573i	−0.0574288	−	0.0994695i
$647$	140.794	+	81.2876i	0.217611	+	0.125638i	0.604844	−	0.796344i	$-0.293236\pi$
$647$	140.794	+	81.2876i	0.217611	+	0.125638i	−0.387233	+	0.921982i	$0.626569\pi$
$648$		0			0
$649$	1160.57	−	670.054i	1.78824	−	1.03244i
$650$		−	131.949i		−	0.202998i
$651$		0			0
$652$	−506.255			−0.776464
$653$	497.880	+	862.354i	0.762450	+	1.32060i	0.941584	+	0.336778i	$0.109337\pi$
$653$	497.880	+	862.354i	0.762450	+	1.32060i	−0.179134	+	0.983825i	$0.557329\pi$
$654$		0			0
$655$	−186.303	+	322.686i	−0.284431	+	0.492650i
$656$	−129.841	+	74.9636i	−0.197928	+	0.114274i
$657$		0			0
$658$	−80.7815	−	267.644i	−0.122768	−	0.406754i
$659$	−897.542			−1.36198			−0.680988	−	0.732295i	$-0.738449\pi$
$659$	−897.542			−1.36198			−0.680988	+	0.732295i	$0.738449\pi$
$660$		0			0
$661$	−74.7048	−	43.1308i	−0.113018	−	0.0652508i	0.442426	−	0.896805i	$-0.354118\pi$
$661$	−74.7048	−	43.1308i	−0.113018	−	0.0652508i	−0.555443	+	0.831554i	$0.687451\pi$
$662$	−241.807	+	418.822i	−0.365267	+	0.632661i
$663$		0			0
$664$		−	141.213i		−	0.212671i
$665$	−510.154	+	153.977i	−0.767149	+	0.231544i
$666$		0			0
$667$	−222.192	−	384.848i	−0.333122	−	0.576984i
$668$	−148.482	−	85.7259i	−0.222278	−	0.128332i
$669$		0			0
$670$	34.8046	−	20.0944i	0.0519471	−	0.0299917i
$671$			1899.69i			2.83113i
$672$		0			0
$673$	486.598			0.723028			0.361514	−	0.932367i	$-0.382260\pi$
$673$	486.598			0.723028			0.361514	+	0.932367i	$0.382260\pi$
$674$	174.228	+	301.772i	0.258499	+	0.447733i
$675$		0			0
$676$	179.211	−	310.402i	0.265105	−	0.459175i
$677$	−47.5668	+	27.4627i	−0.0702612	+	0.0405653i	−0.534719	−	0.845030i	$-0.679583\pi$
$677$	−47.5668	+	27.4627i	−0.0702612	+	0.0405653i	0.464458	+	0.885595i	$0.346249\pi$
$678$		0			0
$679$	−720.643	+	767.274i	−1.06133	+	1.13001i
$680$	9.74668			0.0143334
$681$		0			0
$682$	618.398	+	357.032i	0.906742	+	0.523508i
$683$	−477.185	+	826.509i	−0.698661	+	1.21012i	0.270270	+	0.962784i	$0.412887\pi$
$683$	−477.185	+	826.509i	−0.698661	+	1.21012i	−0.968931	+	0.247331i	$0.920446\pi$
$684$		0			0
$685$			338.803i			0.494603i
$686$	478.261	+	81.0188i	0.697174	+	0.118103i
$687$		0			0
$688$	127.389	+	220.645i	0.185159	+	0.320705i
$689$	−7.17006	−	4.13964i	−0.0104065	−	0.00600818i
$690$		0			0
$691$	−22.3860	+	12.9246i	−0.0323966	+	0.0187042i	−0.516111	−	0.856522i	$-0.672621\pi$
$691$	−22.3860	+	12.9246i	−0.0323966	+	0.0187042i	0.483714	+	0.875226i	$0.339287\pi$
$692$			38.9530i			0.0562905i
$693$		0			0
$694$	195.659			0.281929
$695$	169.736	+	293.991i	0.244224	+	0.423008i
$696$		0			0
$697$	−28.8814	+	50.0240i	−0.0414367	+	0.0717704i
$698$	141.896	−	81.9239i	0.203290	−	0.117370i
$699$		0			0
$700$	15.9904	−	68.1491i	0.0228435	−	0.0973559i
$701$	942.060			1.34388			0.671940	−	0.740606i	$-0.265461\pi$
$701$	942.060			1.34388			0.671940	+	0.740606i	$0.265461\pi$
$702$		0			0
$703$	−1523.44	−	879.556i	−2.16705	−	1.25115i
$704$	−72.2803	+	125.193i	−0.102671	+	0.177831i
$705$		0			0
$706$		−	264.767i		−	0.375024i
$707$	95.2264	+	315.503i	0.134691	+	0.446256i
$708$		0			0
$709$	168.282	+	291.473i	0.237351	+	0.411105i	0.959953	−	0.280160i	$-0.0903874\pi$
$709$	168.282	+	291.473i	0.237351	+	0.411105i	−0.722602	+	0.691264i	$0.757054\pi$
$710$	125.332	+	72.3603i	0.176524	+	0.101916i
$711$		0			0
$712$	242.999	−	140.296i	0.341291	−	0.197045i
$713$			754.097i			1.05764i
$714$		0			0
$715$	753.991			1.05453
$716$	252.834	+	437.922i	0.353120	+	0.611622i
$717$		0			0
$718$	−450.777	+	780.769i	−0.627823	+	1.08742i
$719$	111.447	−	64.3438i	0.155002	−	0.0894907i	−0.420493	−	0.907296i	$-0.638143\pi$
$719$	111.447	−	64.3438i	0.155002	−	0.0894907i	0.575495	+	0.817805i	$0.304809\pi$
$720$		0			0
$721$	517.563	+	121.440i	0.717840	+	0.168433i
$722$	1128.61			1.56317
$723$		0			0
$724$	249.804	+	144.224i	0.345033	+	0.199205i
$725$	41.1656	−	71.3009i	0.0567802	−	0.0983461i
$726$		0			0
$727$		−	684.683i		−	0.941792i	−0.882189	−	0.470896i	$-0.843931\pi$
$727$		−	684.683i		−	0.941792i	0.882189	−	0.470896i	$-0.156069\pi$
$728$	252.934	−	269.301i	0.347437	−	0.369919i
$729$		0			0
$730$	57.5954	+	99.7582i	0.0788978	+	0.136655i
$731$	85.0082	+	49.0795i	0.116290	+	0.0671402i
$732$		0			0
$733$	512.533	−	295.911i	0.699227	−	0.403699i	−0.107832	−	0.994169i	$-0.534391\pi$
$733$	512.533	−	295.911i	0.699227	−	0.403699i	0.807059	+	0.590470i	$0.201058\pi$
$734$			77.8530i			0.106067i
$735$		0			0
$736$	−152.665			−0.207425
$737$	114.825	+	198.882i	0.155800	+	0.269854i
$738$		0			0
$739$	−252.105	+	436.659i	−0.341144	+	0.590878i	−0.984645	−	0.174567i	$-0.944148\pi$
$739$	−252.105	+	436.659i	−0.341144	+	0.590878i	0.643502	+	0.765445i	$0.277481\pi$
$740$	200.119	−	115.539i	0.270431	−	0.156134i
$741$		0			0
$742$	−3.20153	−	3.00696i	−0.00431473	−	0.00405250i
$743$	−983.540			−1.32374			−0.661871	−	0.749618i	$-0.730237\pi$
$743$	−983.540			−1.32374			−0.661871	+	0.749618i	$0.730237\pi$
$744$		0			0
$745$	64.2798	+	37.1120i	0.0862816	+	0.0498147i
$746$	190.323	−	329.649i	0.255124	−	0.441888i
$747$		0			0
$748$			55.6951i			0.0744587i
$749$	−171.457	+	730.730i	−0.228915	+	0.975607i
$750$		0			0
$751$	−458.462	−	794.080i	−0.610469	−	1.05736i	−0.991161	−	0.132662i	$-0.957648\pi$
$751$	−458.462	−	794.080i	−0.610469	−	1.05736i	0.380692	−	0.924702i	$-0.375686\pi$
$752$	−97.8290	−	56.4816i	−0.130092	−	0.0751085i
$753$		0			0
$754$	376.323	−	217.270i	0.499103	−	0.288157i
$755$		−	20.8025i		−	0.0275530i
$756$		0			0
$757$	82.2419			0.108642			0.0543209	−	0.998524i	$-0.482701\pi$
$757$	82.2419			0.108642			0.0543209	+	0.998524i	$0.482701\pi$
$758$	332.188	+	575.367i	0.438243	+	0.759059i
$759$		0			0
$760$	−107.659	+	186.471i	−0.141656	+	0.245356i
$761$	−303.297	+	175.108i	−0.398550	+	0.230103i	−0.685858	−	0.727735i	$-0.740573\pi$
$761$	−303.297	+	175.108i	−0.398550	+	0.230103i	0.287308	+	0.957838i	$0.407240\pi$
$762$		0			0
$763$	542.080	−	163.613i	0.710459	−	0.214434i
$764$	628.196			0.822246
$765$		0			0
$766$	492.604	+	284.405i	0.643087	+	0.371286i
$767$	−691.944	+	1198.48i	−0.902144	+	1.56256i
$768$		0			0
$769$		−	319.560i		−	0.415553i	−0.978176	−	0.207777i	$-0.933377\pi$
$769$		−	319.560i		−	0.415553i	0.978176	−	0.207777i	$-0.0666227\pi$
$770$	389.422	+	91.3734i	0.505743	+	0.118667i
$771$		0			0
$772$	−52.8284	−	91.5015i	−0.0684306	−	0.118525i
$773$	866.904	+	500.507i	1.12148	+	0.647487i	0.941778	−	0.336235i	$-0.109153\pi$
$773$	866.904	+	500.507i	1.12148	+	0.647487i	0.179702	+	0.983721i	$0.442487\pi$
$774$		0			0
$775$	−120.994	+	69.8558i	−0.156121	+	0.0901365i
$776$			425.328i			0.548103i
$777$		0			0
$778$	−156.639			−0.201336
$779$	−638.030	−	1105.10i	−0.819037	−	1.41861i
$780$		0			0
$781$	−413.485	+	716.178i	−0.529431	+	0.917001i
$782$	−50.9374	+	29.4087i	−0.0651374	+	0.0376071i
$783$		0			0
$784$	163.271	−	108.437i	0.208254	−	0.138312i
$785$	−53.6398			−0.0683309
$786$		0			0
$787$	112.324	+	64.8506i	0.142725	+	0.0824022i	0.569662	−	0.821879i	$-0.307074\pi$
$787$	112.324	+	64.8506i	0.142725	+	0.0824022i	−0.426937	+	0.904281i	$0.640407\pi$
$788$	54.2005	−	93.8780i	0.0687823	−	0.119134i
$789$		0			0
$790$			421.209i			0.533176i
$791$	−407.710	−	382.931i	−0.515437	−	0.484111i
$792$		0			0
$793$	−980.874	−	1698.92i	−1.23692	−	2.14240i
$794$	514.165	+	296.853i	0.647563	+	0.373870i
$795$		0			0
$796$	−39.7869	+	22.9710i	−0.0499835	+	0.0288580i
$797$		−	420.926i		−	0.528138i	−0.964504	−	0.264069i	$-0.914935\pi$
$797$		−	420.926i		−	0.528138i	0.964504	−	0.264069i	$-0.0850647\pi$
$798$		0			0
$799$	−43.5215			−0.0544700
$800$	−14.1421	−	24.4949i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	−222.079	+	384.652i	−0.276907	+	0.479616i
$803$	−570.044	+	329.115i	−0.709893	+	0.409857i
$804$		0			0
$805$	122.059	+	404.404i	0.151626	+	0.502366i
$806$	−737.392			−0.914879
$807$		0			0
$808$	115.322	+	66.5813i	0.142726	+	0.0824026i
$809$	−582.166	+	1008.34i	−0.719612	+	1.24640i	0.241542	+	0.970390i	$0.422347\pi$
$809$	−582.166	+	1008.34i	−0.719612	+	1.24640i	−0.961154	+	0.276014i	$0.910987\pi$
$810$		0			0
$811$			753.691i			0.929335i	0.885485	+	0.464668i	$0.153826\pi$
$811$			753.691i			0.929335i	−0.885485	+	0.464668i	$0.846174\pi$
$812$	220.694	−	66.6108i	0.271791	−	0.0820330i
$813$		0			0
$814$	660.219	+	1143.53i	0.811080	+	1.40483i
$815$	490.179	+	283.005i	0.601447	+	0.347245i
$816$		0			0
$817$	−1877.95	+	1084.23i	−2.29859	+	1.32709i
$818$			172.291i			0.210625i
$819$		0			0
$820$	167.624			0.204419
$821$	−184.398	−	319.387i	−0.224602	−	0.389022i	0.731598	−	0.681736i	$-0.238775\pi$
$821$	−184.398	−	319.387i	−0.224602	−	0.389022i	−0.956200	+	0.292714i	$0.905442\pi$
$822$		0			0
$823$	258.123	−	447.082i	0.313636	−	0.543234i	−0.665510	−	0.746389i	$-0.731786\pi$
$823$	258.123	−	447.082i	0.313636	−	0.543234i	0.979147	+	0.203155i	$0.0651194\pi$
$824$	186.028	−	107.403i	0.225762	−	0.130344i
$825$		0			0
$826$	−502.616	+	535.139i	−0.608494	+	0.647869i
$827$	534.206			0.645957			0.322978	−	0.946406i	$-0.395316\pi$
$827$	534.206			0.645957			0.322978	+	0.946406i	$0.395316\pi$
$828$		0			0
$829$	692.720	+	399.942i	0.835610	+	0.482439i	0.855769	−	0.517357i	$-0.173084\pi$
$829$	692.720	+	399.942i	0.835610	+	0.482439i	−0.0201599	+	0.999797i	$0.506418\pi$
$830$	−78.9407	+	136.729i	−0.0951092	+	0.164734i
$831$		0			0
$832$		−	149.283i		−	0.179427i
$833$	33.5875	−	67.6323i	0.0403211	−	0.0811912i
$834$		0			0
$835$	95.8445	+	166.008i	0.114784	+	0.198811i
$836$	−1065.54	−	615.191i	−1.27457	−	0.735874i
$837$		0			0
$838$	−52.7708	+	30.4673i	−0.0629724	+	0.0363571i
$839$		−	1250.09i		−	1.48998i	−0.667078	−	0.744988i	$-0.732455\pi$
$839$		−	1250.09i		−	1.48998i	0.667078	−	0.744988i	$-0.267545\pi$
$840$		0			0
$841$	−569.863			−0.677601
$842$	95.8634	+	166.040i	0.113852	+	0.197198i
$843$		0			0
$844$	292.203	−	506.111i	0.346212	−	0.599657i
$845$	−347.040	+	200.364i	−0.410698	+	0.237117i
$846$		0			0
$847$	−328.647	+	1400.65i	−0.388013	+	1.65366i
$848$	−1.77473			−0.00209284
$849$		0			0
$850$	−9.43719	−	5.44856i	−0.0111026	−	0.00641007i
$851$	−697.233	+	1207.64i	−0.819310	+	1.41909i
$852$		0			0
$853$			427.261i			0.500893i	0.968130	+	0.250446i	$0.0805774\pi$
$853$			427.261i			0.500893i	−0.968130	+	0.250446i	$0.919423\pi$
$854$	−300.716	−	996.330i	−0.352127	−	1.16666i
$855$		0			0
$856$	151.639	+	262.647i	0.177149	+	0.306830i
$857$	−364.774	−	210.603i	−0.425641	−	0.245744i	0.271847	−	0.962341i	$-0.412366\pi$
$857$	−364.774	−	210.603i	−0.425641	−	0.245744i	−0.697488	+	0.716597i	$0.745699\pi$
$858$		0			0
$859$	666.524	−	384.818i	0.775930	−	0.447983i	−0.0590558	−	0.998255i	$-0.518809\pi$
$859$	666.524	−	384.818i	0.775930	−	0.447983i	0.834986	+	0.550271i	$0.185476\pi$
$860$		−	284.851i		−	0.331222i
$861$		0			0
$862$	270.435			0.313730
$863$	−759.204	−	1314.98i	−0.879726	−	1.52373i	−0.851641	−	0.524125i	$-0.824393\pi$
$863$	−759.204	−	1314.98i	−0.879726	−	1.52373i	−0.0280846	−	0.999606i	$-0.508941\pi$
$864$		0			0
$865$	21.7754	−	37.7161i	0.0251739	−	0.0436024i
$866$	−416.199	+	240.293i	−0.480599	+	0.277474i
$867$		0			0
$868$	−380.849	−	89.3619i	−0.438766	−	0.102952i
$869$	−2406.90			−2.76973
$870$		0			0
$871$	−205.380	−	118.576i	−0.235798	−	0.136138i
$872$	114.396	−	198.140i	0.131189	−	0.227225i
$873$		0			0
$874$		−	1299.36i		−	1.48668i
$875$	−53.5792	+	57.0462i	−0.0612334	+	0.0651957i
$876$		0			0
$877$	802.916	+	1390.69i	0.915525	+	1.58574i	0.806131	+	0.591738i	$0.201558\pi$
$877$	802.916	+	1390.69i	0.915525	+	1.58574i	0.109395	+	0.993998i	$0.465109\pi$
$878$	404.487	+	233.530i	0.460691	+	0.265980i
$879$		0			0
$880$	139.970	−	80.8118i	0.159057	−	0.0918316i
$881$			538.120i			0.610806i	0.952223	+	0.305403i	$0.0987912\pi$
$881$			538.120i			0.610806i	−0.952223	+	0.305403i	$0.901209\pi$
$882$		0			0
$883$	880.262			0.996899			0.498450	−	0.866919i	$-0.333903\pi$
$883$	880.262			0.996899			0.498450	+	0.866919i	$0.333903\pi$
$884$	−28.7573	−	49.8091i	−0.0325309	−	0.0563451i
$885$		0			0
$886$	397.155	−	687.893i	0.448257	−	0.776403i
$887$	−696.988	+	402.406i	−0.785781	+	0.453671i	−0.838475	−	0.544940i	$-0.816552\pi$
$887$	−696.988	+	402.406i	−0.785781	+	0.453671i	0.0526943	+	0.998611i	$0.483219\pi$
$888$		0			0
$889$	−506.123	−	475.363i	−0.569317	−	0.534717i
$890$	−313.711			−0.352484
$891$		0			0
$892$	−469.913	−	271.305i	−0.526809	−	0.304153i
$893$	480.725	−	832.641i	0.538326	−	0.932408i
$894$		0			0
$895$		−	565.354i		−	0.631681i
$896$	18.0911	−	77.1020i	0.0201910	−	0.0860513i
$897$		0			0
$898$	273.120	+	473.057i	0.304142	+	0.526790i
$899$	−398.463	−	230.053i	−0.443229	−	0.255898i
$900$		0			0
$901$	−0.592146	+	0.341876i	−0.000657210	+	0.000379440i
$902$			957.846i			1.06191i
$903$		0			0
$904$	−226.009			−0.250009
$905$	−161.248	−	279.289i	−0.178174	−	0.308607i
$906$		0			0
$907$	−533.167	+	923.473i	−0.587836	+	1.01816i	0.406679	+	0.913571i	$0.366687\pi$
$907$	−533.167	+	923.473i	−0.587836	+	1.01816i	−0.994515	+	0.104591i	$0.966647\pi$
$908$	257.398	−	148.609i	0.283478	−	0.163666i
$909$		0			0
$910$	−395.446	+	119.355i	−0.434556	+	0.131159i
$911$	1052.95			1.15582			0.577911	−	0.816100i	$-0.303868\pi$
$911$	1052.95			1.15582			0.577911	+	0.816100i	$0.303868\pi$
$912$		0			0
$913$	−781.306	−	451.087i	−0.855757	−	0.494072i
$914$	352.893	−	611.228i	0.386097	−	0.668740i
$915$		0			0
$916$			50.6669i			0.0553132i
$917$	1135.60	+	266.455i	1.23838	+	0.290572i
$918$		0			0
$919$	714.350	+	1237.29i	0.777312	+	1.34634i	0.933486	+	0.358614i	$0.116751\pi$
$919$	714.350	+	1237.29i	0.777312	+	1.34634i	−0.156174	+	0.987730i	$0.549916\pi$
$920$	147.817	+	85.3423i	0.160671	+	0.0927634i
$921$		0			0
$922$	757.247	−	437.197i	0.821309	−	0.474183i
$923$		−	853.987i		−	0.925230i
$924$		0			0
$925$	−258.353			−0.279300
$926$	−137.485	−	238.131i	−0.148472	−	0.257160i
$927$		0			0
$928$	46.5736	−	80.6678i	0.0501870	−	0.0869265i
$929$	1523.62	−	879.664i	1.64007	−	0.946893i	0.659260	−	0.751915i	$-0.270870\pi$
$929$	1523.62	−	879.664i	1.64007	−	0.946893i	0.980808	−	0.194978i	$-0.0624635\pi$
$930$		0			0
$931$	922.925	+	1389.63i	0.991326	+	1.49262i
$932$	817.772			0.877438
$933$		0			0
$934$	−185.897	−	107.328i	−0.199034	−	0.114912i
$935$	31.1345	−	53.9265i	0.0332989	−	0.0576754i
$936$		0			0
$937$			1264.00i			1.34898i	0.738284	+	0.674490i	$0.235637\pi$
$937$			1264.00i			1.34898i	−0.738284	+	0.674490i	$0.764363\pi$
$938$	−91.7049	−	86.1315i	−0.0977664	−	0.0918246i
$939$		0			0
$940$	63.1483	+	109.376i	0.0671791	+	0.116358i
$941$	−228.636	−	132.003i	−0.242971	−	0.140280i	0.373570	−	0.927602i	$-0.378133\pi$
$941$	−228.636	−	132.003i	−0.242971	−	0.140280i	−0.616542	+	0.787322i	$0.711467\pi$
$942$		0			0
$943$	−876.024	+	505.773i	−0.928975	+	0.536344i
$944$			296.647i			0.314245i
$945$		0			0
$946$	1627.71			1.72063
$947$	−34.9924	−	60.6086i	−0.0369508	−	0.0640006i	0.846959	−	0.531659i	$-0.178431\pi$
$947$	−34.9924	−	60.6086i	−0.0369508	−	0.0640006i	−0.883909	+	0.467658i	$0.845098\pi$
$948$		0			0
$949$	339.867	−	588.667i	0.358132	−	0.620302i
$950$	208.481	−	120.366i	0.219453	−	0.126701i
$951$		0			0
$952$	−8.81641	−	29.2104i	−0.00926094	−	0.0306832i
$953$	1410.53			1.48009			0.740047	−	0.672555i	$-0.234803\pi$
$953$	1410.53			1.48009			0.740047	+	0.672555i	$0.234803\pi$
$954$		0			0
$955$	−608.248	−	351.172i	−0.636909	−	0.367720i
$956$	67.0352	−	116.108i	0.0701205	−	0.121452i
$957$		0			0
$958$		−	317.872i		−	0.331808i
$959$	1015.38	−	306.466i	1.05879	−	0.319568i
$960$		0			0
$961$	−90.1133	−	156.081i	−0.0937704	−	0.162415i
$962$	−1180.89	−	681.788i	−1.22754	−	0.708719i
$963$		0			0
$964$	−410.287	+	236.879i	−0.425609	+	0.245725i
$965$			118.128i			0.122412i
$966$		0			0
$967$	−1581.56			−1.63554			−0.817768	−	0.575548i	$-0.804789\pi$
$967$	−1581.56			−1.63554			−0.817768	+	0.575548i	$0.804789\pi$
$968$	290.660	+	503.438i	0.300269	+	0.520080i
$969$		0			0
$970$	237.765	−	411.822i	0.245119	−	0.424559i
$971$	518.308	−	299.245i	0.533788	−	0.308182i	−0.208770	−	0.977965i	$-0.566946\pi$
$971$	518.308	−	299.245i	0.533788	−	0.308182i	0.742557	+	0.669782i	$0.233613\pi$
$972$		0			0
$973$	727.544	−	774.622i	0.747732	−	0.796117i
$974$	−98.3767			−0.101003
$975$		0			0
$976$	−364.177	−	210.258i	−0.373132	−	0.215428i
$977$	−86.3897	+	149.631i	−0.0884235	+	0.153154i	−0.906845	−	0.421465i	$-0.861516\pi$
$977$	−86.3897	+	149.631i	−0.0884235	+	0.153154i	0.818421	+	0.574618i	$0.194850\pi$
$978$		0			0
$979$		−	1792.63i		−	1.83108i
$980$	−218.705	+	13.7220i	−0.223168	+	0.0140020i
$981$		0			0
$982$	530.651	+	919.115i	0.540378	+	0.935962i
$983$	187.419	+	108.206i	0.190660	+	0.110078i	0.592292	−	0.805724i	$-0.298223\pi$
$983$	187.419	+	108.206i	0.190660	+	0.110078i	−0.401631	+	0.915801i	$0.631557\pi$
$984$		0			0
$985$	−104.959	+	60.5980i	−0.106557	+	0.0615208i
$986$		−	35.8869i		−	0.0363965i
$987$		0			0
$988$	1270.58			1.28601
$989$	859.484	+	1488.67i	0.869043	+	1.50523i
$990$		0			0
$991$	160.993	−	278.849i	0.162455	−	0.281381i	−0.773293	−	0.634048i	$-0.781392\pi$
$991$	160.993	−	278.849i	0.162455	−	0.281381i	0.935749	+	0.352667i	$0.114725\pi$
$992$	−136.889	+	79.0328i	−0.137993	+	0.0796702i
$993$		0			0
$994$	103.492	−	441.068i	0.104116	−	0.443731i
$995$	51.3646			0.0516227
$996$		0			0
$997$	−40.5409	−	23.4063i	−0.0406629	−	0.0234767i	0.479531	−	0.877525i	$-0.340807\pi$
$997$	−40.5409	−	23.4063i	−0.0406629	−	0.0234767i	−0.520194	+	0.854048i	$0.674140\pi$
$998$	113.257	−	196.167i	0.113484	−	0.196560i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.3.v.b.451.4		8
3.2	odd	2		210.3.o.a.31.1	✓	8
7.5	odd	6	inner	630.3.v.b.271.4		8
15.2	even	4		1050.3.q.c.199.8		16
15.8	even	4		1050.3.q.c.199.1		16
15.14	odd	2		1050.3.p.b.451.4		8
21.5	even	6		210.3.o.a.61.1	yes	8
21.11	odd	6		1470.3.f.a.391.5		8
21.17	even	6		1470.3.f.a.391.8		8
105.47	odd	12		1050.3.q.c.649.1		16
105.68	odd	12		1050.3.q.c.649.8		16
105.89	even	6		1050.3.p.b.901.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.o.a.31.1	✓	8	3.2	odd	2
210.3.o.a.61.1	yes	8	21.5	even	6
630.3.v.b.271.4		8	7.5	odd	6	inner
630.3.v.b.451.4		8	1.1	even	1	trivial
1050.3.p.b.451.4		8	15.14	odd	2
1050.3.p.b.901.4		8	105.89	even	6
1050.3.q.c.199.1		16	15.8	even	4
1050.3.q.c.199.8		16	15.2	even	4
1050.3.q.c.649.1		16	105.47	odd	12
1050.3.q.c.649.8		16	105.68	odd	12
1470.3.f.a.391.5		8	21.11	odd	6
1470.3.f.a.391.8		8	21.17	even	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	630.v (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +O(q^{10})\)	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(1.93649 - 1.11803i) q^{5} +(-5.10237 - 4.79227i) q^{7} -2.82843 q^{8} +(2.73861 + 1.58114i) q^{10} +(-9.03504 + 15.6491i) q^{11} -18.6604i q^{13} +(2.26139 - 9.63774i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-1.33462 - 0.770543i) q^{17} +(29.4836 - 17.0224i) q^{19} +4.47214i q^{20} -25.5549 q^{22} +(-13.4938 - 23.3720i) q^{23} +(2.50000 - 4.33013i) q^{25} +(22.8542 - 13.1949i) q^{26} +(13.4028 - 4.04529i) q^{28} +16.4662 q^{29} +(-24.1988 - 13.9712i) q^{31} +(2.82843 - 4.89898i) q^{32} -2.17942i q^{34} +(-15.2386 - 3.57557i) q^{35} +(-25.8353 - 44.7480i) q^{37} +(41.6961 + 24.0733i) q^{38} +(-5.47723 + 3.16228i) q^{40} -37.4818i q^{41} -63.6947 q^{43} +(-18.0701 - 31.2983i) q^{44} +(19.0831 - 33.0529i) q^{46} +(24.4572 - 14.1204i) q^{47} +(3.06832 + 48.9038i) q^{49} +7.07107 q^{50} +(32.3208 + 18.6604i) q^{52} +(0.221841 - 0.384239i) q^{53} +40.4059i q^{55} +(14.4317 + 13.5546i) q^{56} +(11.6434 + 20.1669i) q^{58} +(-64.2260 - 37.0809i) q^{59} +(91.0443 - 52.5645i) q^{61} -39.5164i q^{62} +8.00000 q^{64} +(-20.8630 - 36.1357i) q^{65} +(6.35442 - 11.0062i) q^{67} +(2.66924 - 1.54109i) q^{68} +(-6.39617 - 21.1917i) q^{70} +45.7647 q^{71} +(31.5463 + 18.2133i) q^{73} +(36.5366 - 63.2833i) q^{74} +68.0895i q^{76} +(121.095 - 36.5494i) q^{77} +(66.5990 + 115.353i) q^{79} +(-7.74597 - 4.47214i) q^{80} +(45.9057 - 26.5037i) q^{82} +49.9265i q^{83} -3.44597 q^{85} +(-45.0389 - 78.0097i) q^{86} +(25.5549 - 44.2625i) q^{88} +(-85.9133 + 49.6020i) q^{89} +(-89.4257 + 95.2123i) q^{91} +53.9752 q^{92} +(34.5878 + 19.9693i) q^{94} +(38.0632 - 65.9274i) q^{95} -150.376i q^{97} +(-57.7251 + 38.3381i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 4 q^{11} + 40 q^{14} - 16 q^{16} - 84 q^{17} + 108 q^{19} - 48 q^{22} - 12 q^{23} + 20 q^{25} + 96 q^{26} - 72 q^{29} - 132 q^{31} - 100 q^{35} - 96 q^{37} + 168 q^{38} - 112 q^{43} + 8 q^{44} + 8 q^{46} + 24 q^{47} + 156 q^{49} + 48 q^{52} - 32 q^{53} - 16 q^{56} + 104 q^{58} - 132 q^{59} + 96 q^{61} + 64 q^{64} - 20 q^{65} - 120 q^{67} + 168 q^{68} - 8 q^{71} + 24 q^{73} + 16 q^{74} + 216 q^{77} + 12 q^{79} + 24 q^{82} + 120 q^{85} + 40 q^{86} + 48 q^{88} - 492 q^{89} - 308 q^{91} + 48 q^{92} + 480 q^{94} + 40 q^{95}+O(q^{100}) \) 8 * q - 8 * q^4 + 4 * q^11 + 40 * q^14 - 16 * q^16 - 84 * q^17 + 108 * q^19 - 48 * q^22 - 12 * q^23 + 20 * q^25 + 96 * q^26 - 72 * q^29 - 132 * q^31 - 100 * q^35 - 96 * q^37 + 168 * q^38 - 112 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 + 156 * q^49 + 48 * q^52 - 32 * q^53 - 16 * q^56 + 104 * q^58 - 132 * q^59 + 96 * q^61 + 64 * q^64 - 20 * q^65 - 120 * q^67 + 168 * q^68 - 8 * q^71 + 24 * q^73 + 16 * q^74 + 216 * q^77 + 12 * q^79 + 24 * q^82 + 120 * q^85 + 40 * q^86 + 48 * q^88 - 492 * q^89 - 308 * q^91 + 48 * q^92 + 480 * q^94 + 40 * q^95

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