LMFDB - Embedded newform 1026.3.l.a.37.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1026,3,Mod(37,1026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1026, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1026.37");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1026 = 2 \cdot 3^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1026.l (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:	$27.9564751234$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 342)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.6
Character	$\chi$	$=$	1026.37
Dual form			1026.3.l.a.721.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.69486 + 8.13173i) q^{5} +(5.67137 + 9.82311i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.69486 + 8.13173i) q^{5} +(5.67137 + 9.82311i) q^{7} +2.82843i q^{8} -13.2791i q^{10} +(-3.82304 - 6.62171i) q^{11} +(-15.6637 - 9.04345i) q^{13} +(-13.8920 - 8.02053i) q^{14} +(-2.00000 - 3.46410i) q^{16} -21.1249 q^{17} +(-0.118426 - 18.9996i) q^{19} +(9.38971 + 16.2635i) q^{20} +(9.36451 + 5.40660i) q^{22} +(8.37354 - 14.5034i) q^{23} +(-31.5834 - 54.7040i) q^{25} +25.5787 q^{26} +22.6855 q^{28} +(12.3614 - 7.13685i) q^{29} +(15.1408 + 8.74155i) q^{31} +(4.89898 + 2.82843i) q^{32} +(25.8726 - 14.9376i) q^{34} -106.505 q^{35} -10.6584i q^{37} +(13.5798 + 23.1860i) q^{38} +(-23.0000 - 13.2791i) q^{40} +(1.55194 + 0.896012i) q^{41} +(16.7356 + 28.9869i) q^{43} -15.2922 q^{44} +23.6839i q^{46} +(10.3261 + 17.8853i) q^{47} +(-39.8290 + 68.9858i) q^{49} +(77.3631 + 44.6656i) q^{50} +(-31.3274 + 18.0869i) q^{52} -7.82643i q^{53} +71.7946 q^{55} +(-27.7839 + 16.0411i) q^{56} +(-10.0930 + 17.4816i) q^{58} +(66.1193 + 38.1740i) q^{59} +(-17.7883 - 30.8102i) q^{61} -24.7248 q^{62} -8.00000 q^{64} +(147.078 - 84.9154i) q^{65} +(96.1425 + 55.5079i) q^{67} +(-21.1249 + 36.5894i) q^{68} +(130.442 - 75.3105i) q^{70} -54.5417i q^{71} -117.096 q^{73} +(7.53666 + 13.0539i) q^{74} +(-33.0268 - 18.7945i) q^{76} +(43.3638 - 75.1084i) q^{77} +(-14.5702 + 8.41210i) q^{79} +37.5589 q^{80} -2.53430 q^{82} +(68.7574 + 119.091i) q^{83} +(99.1783 - 171.782i) q^{85} +(-40.9936 - 23.6677i) q^{86} +(18.7290 - 10.8132i) q^{88} -7.70345i q^{89} -205.155i q^{91} +(-16.7471 - 29.0068i) q^{92} +(-25.2936 - 14.6033i) q^{94} +(155.056 + 88.2375i) q^{95} +(-101.184 + 58.4186i) q^{97} -112.653i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 80 q^{4} - 4 q^{7}+O(q^{10}) $ 80 * q + 80 * q^4 - 4 * q^7	$ 80 q + 80 q^{4} - 4 q^{7} - 12 q^{11} - 160 q^{16} - 96 q^{17} + 40 q^{19} + 48 q^{23} - 200 q^{25} - 16 q^{28} - 432 q^{35} - 24 q^{38} + 28 q^{43} - 48 q^{44} - 240 q^{47} - 228 q^{49} - 28 q^{61} + 144 q^{62} - 640 q^{64} - 96 q^{68} - 368 q^{73} + 24 q^{74} + 40 q^{76} + 456 q^{77} - 192 q^{82} + 84 q^{83} - 96 q^{92} + 324 q^{95}+O(q^{100}) $ 80 * q + 80 * q^4 - 4 * q^7 - 12 * q^11 - 160 * q^16 - 96 * q^17 + 40 * q^19 + 48 * q^23 - 200 * q^25 - 16 * q^28 - 432 * q^35 - 24 * q^38 + 28 * q^43 - 48 * q^44 - 240 * q^47 - 228 * q^49 - 28 * q^61 + 144 * q^62 - 640 * q^64 - 96 * q^68 - 368 * q^73 + 24 * q^74 + 40 * q^76 + 456 * q^77 - 192 * q^82 + 84 * q^83 - 96 * q^92 + 324 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1026\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.22474	+	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
$5$	−4.69486	+	8.13173i	−0.938971	+	1.62635i	−0.171577	+	0.985171i	$0.554886\pi$
$5$	−4.69486	+	8.13173i	−0.938971	+	1.62635i	−0.767395	+	0.641175i	$0.778447\pi$
$6$		0			0
$7$	5.67137	+	9.82311i	0.810196	+	1.40330i	0.912726	+	0.408571i	$0.133973\pi$
$7$	5.67137	+	9.82311i	0.810196	+	1.40330i	−0.102530	+	0.994730i	$0.532694\pi$
$8$			2.82843i			0.353553i
$9$		0			0
$10$		−	13.2791i		−	1.32791i
$11$	−3.82304	−	6.62171i	−0.347549	−	0.601973i	0.638264	−	0.769817i	$-0.279653\pi$
$11$	−3.82304	−	6.62171i	−0.347549	−	0.601973i	−0.985814	+	0.167844i	$0.946319\pi$
$12$		0			0
$13$	−15.6637	−	9.04345i	−1.20490	−	0.695650i	−0.243260	−	0.969961i	$-0.578217\pi$
$13$	−15.6637	−	9.04345i	−1.20490	−	0.695650i	−0.961641	+	0.274311i	$0.911550\pi$
$14$	−13.8920	−	8.02053i	−0.992284	−	0.572895i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−21.1249			−1.24264			−0.621320	−	0.783557i	$-0.713403\pi$
$17$	−21.1249			−1.24264			−0.621320	+	0.783557i	$0.713403\pi$
$18$		0			0
$19$	−0.118426	−	18.9996i	−0.00623296	−	0.999981i
$19$	−0.118426	−	18.9996i	−0.00623296	−	0.999981i
$20$	9.38971	+	16.2635i	0.469486	+	0.813173i
$21$		0			0
$22$	9.36451	+	5.40660i	0.425659	+	0.245755i
$23$	8.37354	−	14.5034i	0.364067	−	0.630582i	−0.624559	−	0.780978i	$-0.714721\pi$
$23$	8.37354	−	14.5034i	0.364067	−	0.630582i	0.988626	+	0.150395i	$0.0480546\pi$
$24$		0			0
$25$	−31.5834	−	54.7040i	−1.26333	−	2.18816i
$26$	25.5787			0.983798
$27$		0			0
$28$	22.6855			0.810196
$29$	12.3614	−	7.13685i	0.426255	−	0.246098i	−0.271495	−	0.962440i	$-0.587518\pi$
$29$	12.3614	−	7.13685i	0.426255	−	0.246098i	0.697750	+	0.716341i	$0.254185\pi$
$30$		0			0
$31$	15.1408	+	8.74155i	0.488413	+	0.281986i	0.723916	−	0.689888i	$-0.242340\pi$
$31$	15.1408	+	8.74155i	0.488413	+	0.281986i	−0.235503	+	0.971874i	$0.575674\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$		0			0
$34$	25.8726	−	14.9376i	0.760959	−	0.439340i
$35$	−106.505			−3.04300
$36$		0			0
$37$		−	10.6584i		−	0.288066i	−0.989573	−	0.144033i	$-0.953993\pi$
$37$		−	10.6584i		−	0.288066i	0.989573	−	0.144033i	$-0.0460071\pi$
$38$	13.5798	+	23.1860i	0.357363	+	0.610157i
$39$		0			0
$40$	−23.0000	−	13.2791i	−0.575000	−	0.331976i
$41$	1.55194	+	0.896012i	0.0378521	+	0.0218539i	0.518807	−	0.854892i	$-0.326376\pi$
$41$	1.55194	+	0.896012i	0.0378521	+	0.0218539i	−0.480955	+	0.876746i	$0.659710\pi$
$42$		0			0
$43$	16.7356	+	28.9869i	0.389200	+	0.674113i	0.992342	−	0.123520i	$-0.0394183\pi$
$43$	16.7356	+	28.9869i	0.389200	+	0.674113i	−0.603143	+	0.797633i	$0.706085\pi$
$44$	−15.2922			−0.347549
$45$		0			0
$46$			23.6839i			0.514868i
$47$	10.3261	+	17.8853i	0.219704	+	0.380538i	0.954717	−	0.297514i	$-0.0961576\pi$
$47$	10.3261	+	17.8853i	0.219704	+	0.380538i	−0.735014	+	0.678052i	$0.762824\pi$
$48$		0			0
$49$	−39.8290	+	68.9858i	−0.812836	+	1.40787i
$50$	77.3631	+	44.6656i	1.54726	+	0.893312i
$51$		0			0
$52$	−31.3274	+	18.0869i	−0.602451	+	0.347825i
$53$		−	7.82643i		−	0.147669i	−0.997271	−	0.0738343i	$-0.976476\pi$
$53$		−	7.82643i		−	0.147669i	0.997271	−	0.0738343i	$-0.0235236\pi$
$54$		0			0
$55$	71.7946			1.30536
$56$	−27.7839	+	16.0411i	−0.496142	+	0.286448i
$57$		0			0
$58$	−10.0930	+	17.4816i	−0.174018	+	0.301408i
$59$	66.1193	+	38.1740i	1.12067	+	0.647017i	0.941571	−	0.336815i	$-0.109350\pi$
$59$	66.1193	+	38.1740i	1.12067	+	0.647017i	0.179095	+	0.983832i	$0.442683\pi$
$60$		0			0
$61$	−17.7883	−	30.8102i	−0.291612	−	0.505086i	0.682579	−	0.730811i	$-0.260858\pi$
$61$	−17.7883	−	30.8102i	−0.291612	−	0.505086i	−0.974191	+	0.225725i	$0.927525\pi$
$62$	−24.7248			−0.398788
$63$		0			0
$64$	−8.00000			−0.125000
$65$	147.078	−	84.9154i	2.26274	−	1.30639i
$66$		0			0
$67$	96.1425	+	55.5079i	1.43496	+	0.828476i	0.997494	−	0.0707571i	$-0.0225415\pi$
$67$	96.1425	+	55.5079i	1.43496	+	0.828476i	0.437469	+	0.899233i	$0.355875\pi$
$68$	−21.1249	+	36.5894i	−0.310660	+	0.538079i
$69$		0			0
$70$	130.442	−	75.3105i	1.86345	−	1.07586i
$71$		−	54.5417i		−	0.768192i	−0.923293	−	0.384096i	$-0.874513\pi$
$71$		−	54.5417i		−	0.768192i	0.923293	−	0.384096i	$-0.125487\pi$
$72$		0			0
$73$	−117.096			−1.60405			−0.802026	−	0.597289i	$-0.796245\pi$
$73$	−117.096			−1.60405			−0.802026	+	0.597289i	$0.796245\pi$
$74$	7.53666	+	13.0539i	0.101847	+	0.176404i
$75$		0			0
$76$	−33.0268	−	18.7945i	−0.434563	−	0.247296i
$77$	43.3638	−	75.1084i	0.563167	−	0.975433i
$78$		0			0
$79$	−14.5702	+	8.41210i	−0.184433	+	0.106482i	−0.589374	−	0.807861i	$-0.700625\pi$
$79$	−14.5702	+	8.41210i	−0.184433	+	0.106482i	0.404941	+	0.914343i	$0.367292\pi$
$80$	37.5589			0.469486
$81$		0			0
$82$	−2.53430			−0.0309062
$83$	68.7574	+	119.091i	0.828402	+	1.43483i	0.899291	+	0.437350i	$0.144083\pi$
$83$	68.7574	+	119.091i	0.828402	+	1.43483i	−0.0708894	+	0.997484i	$0.522584\pi$
$84$		0			0
$85$	99.1783	−	171.782i	1.16680	−	2.02096i
$86$	−40.9936	−	23.6677i	−0.476670	−	0.275206i
$87$		0			0
$88$	18.7290	−	10.8132i	0.212830	−	0.122877i
$89$		−	7.70345i		−	0.0865556i	−0.999063	−	0.0432778i	$-0.986220\pi$
$89$		−	7.70345i		−	0.0865556i	0.999063	−	0.0432778i	$-0.0137801\pi$
$90$		0			0
$91$		−	205.155i		−	2.25445i
$92$	−16.7471	−	29.0068i	−0.182033	−	0.315291i
$93$		0			0
$94$	−25.2936	−	14.6033i	−0.269081	−	0.155354i
$95$	155.056	+	88.2375i	1.63217	+	0.928816i
$96$		0			0
$97$	−101.184	+	58.4186i	−1.04313	+	0.602253i	−0.920719	−	0.390226i	$-0.872397\pi$
$97$	−101.184	+	58.4186i	−1.04313	+	0.602253i	−0.122414	+	0.992479i	$0.539064\pi$
$98$		−	112.653i		−	1.14952i
$99$		0			0
$100$	−126.333			−1.26333
$101$	−2.91211	−	5.04392i	−0.0288328	−	0.0499398i	0.851249	−	0.524762i	$-0.175846\pi$
$101$	−2.91211	−	5.04392i	−0.0288328	−	0.0499398i	−0.880082	+	0.474822i	$0.842512\pi$
$102$		0			0
$103$	−148.585	−	85.7857i	−1.44257	−	0.832871i	−0.444554	−	0.895752i	$-0.646638\pi$
$103$	−148.585	−	85.7857i	−1.44257	−	0.832871i	−0.998021	+	0.0628810i	$0.979971\pi$
$104$	25.5787	−	44.3037i	0.245949	−	0.425997i
$105$		0			0
$106$	5.53412	+	9.58538i	0.0522087	+	0.0904281i
$107$		−	123.595i		−	1.15509i	−0.816358	−	0.577546i	$-0.804011\pi$
$107$		−	123.595i		−	1.15509i	0.816358	−	0.577546i	$-0.195989\pi$
$108$		0			0
$109$		−	59.7721i		−	0.548368i	−0.961677	−	0.274184i	$-0.911592\pi$
$109$		−	59.7721i		−	0.548368i	0.961677	−	0.274184i	$-0.0884077\pi$
$110$	−87.9300	+	50.7664i	−0.799364	+	0.461513i
$111$		0			0
$112$	22.6855	−	39.2924i	0.202549	−	0.350825i
$113$	−127.793	−	73.7816i	−1.13092	−	0.652934i	−0.186750	−	0.982407i	$-0.559796\pi$
$113$	−127.793	−	73.7816i	−1.13092	−	0.652934i	−0.944165	+	0.329473i	$0.893129\pi$
$114$		0			0
$115$	78.6251	+	136.183i	0.683697	+	1.18420i
$116$		−	28.5474i		−	0.246098i
$117$		0			0
$118$	−107.972			−0.915020
$119$	−119.807	−	207.512i	−1.00678	−	1.74380i
$120$		0			0
$121$	31.2687	−	54.1589i	0.258419	−	0.447594i
$122$	43.5723	+	25.1565i	0.357150	+	0.206200i
$123$		0			0
$124$	30.2816	−	17.4831i	0.244207	−	0.140993i
$125$	358.374			2.86699
$126$		0			0
$127$		−	2.73827i		−	0.0215612i	−0.999942	−	0.0107806i	$-0.996568\pi$
$127$		−	2.73827i		−	0.0215612i	0.999942	−	0.0107806i	$-0.00343164\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$		0			0
$130$	−120.089	+	207.999i	−0.923758	+	1.60000i
$131$	63.4682	−	109.930i	0.484490	−	0.839161i	−0.515351	−	0.856979i	$-0.672339\pi$
$131$	63.4682	−	109.930i	0.484490	−	0.839161i	0.999841	+	0.0178179i	$0.00567192\pi$
$132$		0			0
$133$	185.964	−	108.917i	1.39822	−	0.818927i
$134$	−157.000			−1.17164
$135$		0			0
$136$		−	59.7502i		−	0.439340i
$137$	−24.8292	−	43.0054i	−0.181235	−	0.313908i	0.761066	−	0.648674i	$-0.224676\pi$
$137$	−24.8292	−	43.0054i	−0.181235	−	0.313908i	−0.942301	+	0.334766i	$0.891343\pi$
$138$		0			0
$139$	−88.0079	+	152.434i	−0.633151	+	1.09665i	0.353753	+	0.935339i	$0.384905\pi$
$139$	−88.0079	+	152.434i	−0.633151	+	1.09665i	−0.986904	+	0.161310i	$0.948428\pi$
$140$	−106.505	+	184.472i	−0.760751	+	1.31766i
$141$		0			0
$142$	38.5668	+	66.7996i	0.271597	+	0.470420i
$143$			138.294i			0.967091i
$144$		0			0
$145$			134.026i			0.924317i
$146$	143.413	−	82.7993i	0.982278	−	0.567118i
$147$		0			0
$148$	−18.4610	−	10.6584i	−0.124736	−	0.0720165i
$149$	−28.8271	+	49.9300i	−0.193471	+	0.335101i	−0.946398	−	0.323003i	$-0.895308\pi$
$149$	−28.8271	+	49.9300i	−0.193471	+	0.335101i	0.752928	+	0.658103i	$0.228641\pi$
$150$		0			0
$151$	28.5137	−	16.4624i	0.188832	−	0.109022i	−0.402603	−	0.915375i	$-0.631895\pi$
$151$	28.5137	−	16.4624i	0.188832	−	0.109022i	0.591436	+	0.806352i	$0.298561\pi$
$152$	53.7391	−	0.334960i	0.353547	−	0.00220368i
$153$		0			0
$154$			122.651i			0.796438i
$155$	−142.168	+	82.0807i	−0.917212	+	0.529553i
$156$		0			0
$157$	85.3745	−	147.873i	0.543786	−	0.941866i	−0.454896	−	0.890545i	$-0.650324\pi$
$157$	85.3745	−	147.873i	0.543786	−	0.941866i	0.998682	−	0.0513209i	$-0.0163431\pi$
$158$	11.8965	−	20.6054i	0.0752944	−	0.130414i
$159$		0			0
$160$	−46.0000	+	26.5581i	−0.287500	+	0.165988i
$161$	189.958			1.17986
$162$		0			0
$163$	59.4491			0.364718			0.182359	−	0.983232i	$-0.441627\pi$
$163$	59.4491			0.364718			0.182359	+	0.983232i	$0.441627\pi$
$164$	3.10388	−	1.79202i	0.0189261	−	0.0109270i
$165$		0			0
$166$	−168.420	−	97.2376i	−1.01458	−	0.585769i
$167$	29.9680	+	17.3020i	0.179449	+	0.103605i	0.587034	−	0.809562i	$-0.300296\pi$
$167$	29.9680	+	17.3020i	0.179449	+	0.103605i	−0.407585	+	0.913167i	$0.633629\pi$
$168$		0			0
$169$	79.0680	+	136.950i	0.467858	+	0.810354i
$170$			280.519i			1.65011i
$171$		0			0
$172$	66.9423			0.389200
$173$	−161.923	+	93.4862i	−0.935971	+	0.540383i	−0.888695	−	0.458499i	$-0.848387\pi$
$173$	−161.923	+	93.4862i	−0.935971	+	0.540383i	−0.0472756	+	0.998882i	$0.515054\pi$
$174$		0			0
$175$	358.242	−	620.493i	2.04710	−	3.54568i
$176$	−15.2922	+	26.4868i	−0.0868874	+	0.150493i
$177$		0			0
$178$	5.44716	+	9.43476i	0.0306020	+	0.0530043i
$179$		−	169.146i		−	0.944948i	−0.881345	−	0.472474i	$-0.843361\pi$
$179$		−	169.146i		−	0.944948i	0.881345	−	0.472474i	$-0.156639\pi$
$180$		0			0
$181$		−	275.892i		−	1.52426i	−0.647421	−	0.762132i	$-0.724153\pi$
$181$		−	275.892i		−	1.52426i	0.647421	−	0.762132i	$-0.275847\pi$
$182$	145.067	+	251.263i	0.797069	+	1.38056i
$183$		0			0
$184$	41.0218	+	23.6839i	0.222945	+	0.128717i
$185$	86.6716	+	50.0398i	0.468495	+	0.270486i
$186$		0			0
$187$	80.7614	+	139.883i	0.431879	+	0.748037i
$188$	41.3043			0.219704
$189$		0			0
$190$	−252.297	+	1.57259i	−1.32788	+	0.00827678i
$191$	−109.421	−	189.522i	−0.572883	−	0.992263i	−0.996268	−	0.0863132i	$-0.972491\pi$
$191$	−109.421	−	189.522i	−0.572883	−	0.992263i	0.423385	−	0.905950i	$-0.360842\pi$
$192$		0			0
$193$	319.126	+	184.247i	1.65350	+	0.954649i	0.975617	+	0.219480i	$0.0704362\pi$
$193$	319.126	+	184.247i	1.65350	+	0.954649i	0.677884	+	0.735169i	$0.262897\pi$
$194$	82.6163	−	143.096i	0.425857	−	0.737607i
$195$		0			0
$196$	79.6579	+	137.972i	0.406418	+	0.703937i
$197$	−246.260			−1.25005			−0.625025	−	0.780605i	$-0.714911\pi$
$197$	−246.260			−1.25005			−0.625025	+	0.780605i	$0.714911\pi$
$198$		0			0
$199$	−9.55232			−0.0480016			−0.0240008	−	0.999712i	$-0.507640\pi$
$199$	−9.55232			−0.0480016			−0.0240008	+	0.999712i	$0.507640\pi$
$200$	154.726	−	89.3312i	0.773631	−	0.446656i
$201$		0			0
$202$	7.13318	+	4.11835i	0.0353128	+	0.0203879i
$203$	140.212	+	80.9515i	0.690700	+	0.398776i
$204$		0			0
$205$	−14.5723	+	8.41329i	−0.0710842	+	0.0410405i
$206$	242.639			1.17786
$207$		0			0
$208$			72.3476i			0.347825i
$209$	−125.357	+	73.4206i	−0.599795	+	0.351295i
$210$		0			0
$211$	−120.321	−	69.4672i	−0.570241	−	0.329229i	0.187005	−	0.982359i	$-0.440122\pi$
$211$	−120.321	−	69.4672i	−0.570241	−	0.329229i	−0.757245	+	0.653130i	$0.773455\pi$
$212$	−13.5558	−	7.82643i	−0.0639423	−	0.0369171i
$213$		0			0
$214$	87.3947	+	151.372i	0.408386	+	0.707346i
$215$	−314.285			−1.46179
$216$		0			0
$217$			198.306i			0.913855i
$218$	42.2652	+	73.2055i	0.193877	+	0.335805i
$219$		0			0
$220$	71.7946	−	124.352i	0.326339	−	0.565236i
$221$	330.894	+	191.042i	1.49726	+	0.864443i
$222$		0			0
$223$	75.1582	−	43.3926i	0.337032	−	0.194586i	−0.321927	−	0.946765i	$-0.604330\pi$
$223$	75.1582	−	43.3926i	0.337032	−	0.194586i	0.658959	+	0.752179i	$0.270997\pi$
$224$			64.1643i			0.286448i
$225$		0			0
$226$	208.686			0.923388
$227$	−76.1650	+	43.9739i	−0.335529	+	0.193717i	−0.658293	−	0.752762i	$-0.728721\pi$
$227$	−76.1650	+	43.9739i	−0.335529	+	0.193717i	0.322764	+	0.946479i	$0.395388\pi$
$228$		0			0
$229$	100.571	−	174.195i	0.439177	−	0.760676i	−0.558450	−	0.829538i	$-0.688604\pi$
$229$	100.571	−	174.195i	0.439177	−	0.760676i	0.997626	+	0.0688623i	$0.0219369\pi$
$230$	−192.591	−	111.193i	−0.837354	−	0.483447i
$231$		0			0
$232$	20.1861	+	34.9633i	0.0870089	+	0.150704i
$233$	−123.948			−0.531966			−0.265983	−	0.963978i	$-0.585697\pi$
$233$	−123.948			−0.531966			−0.265983	+	0.963978i	$0.585697\pi$
$234$		0			0
$235$	−193.918			−0.825182
$236$	132.239	−	76.3480i	0.560333	−	0.323508i
$237$		0			0
$238$	293.466	+	169.433i	1.23305	+	0.711903i
$239$	20.1831	−	34.9582i	0.0844482	−	0.146269i	−0.820708	−	0.571348i	$-0.806421\pi$
$239$	20.1831	−	34.9582i	0.0844482	−	0.146269i	0.905156	+	0.425080i	$0.139754\pi$
$240$		0			0
$241$	−145.375	+	83.9323i	−0.603216	+	0.348267i	−0.770306	−	0.637675i	$-0.779896\pi$
$241$	−145.375	+	83.9323i	−0.603216	+	0.348267i	0.167090	+	0.985942i	$0.446563\pi$
$242$			88.4411i			0.365459i
$243$		0			0
$244$	−71.1532			−0.291612
$245$	−373.983	−	647.757i	−1.52646	−	2.64391i
$246$		0			0
$247$	−169.967	+	298.676i	−0.688126	+	1.20921i
$248$	−24.7248	+	42.8247i	−0.0996970	+	0.172680i
$249$		0			0
$250$	−438.917	+	253.409i	−1.75567	+	1.01364i
$251$	81.5710			0.324984			0.162492	−	0.986710i	$-0.448047\pi$
$251$	81.5710			0.324984			0.162492	+	0.986710i	$0.448047\pi$
$252$		0			0
$253$	−128.050			−0.506125
$254$	1.93625	+	3.35369i	0.00762304	+	0.0132035i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−280.685	−	162.054i	−1.09216	−	0.630559i	−0.158009	−	0.987438i	$-0.550507\pi$
$257$	−280.685	−	162.054i	−1.09216	−	0.630559i	−0.934151	+	0.356879i	$0.883841\pi$
$258$		0			0
$259$	104.699	−	60.4480i	0.404243	−	0.233390i
$260$		−	339.662i		−	1.30639i
$261$		0			0
$262$			179.515i			0.685172i
$263$	145.409	+	251.855i	0.552885	+	0.957625i	0.998065	+	0.0621839i	$0.0198065\pi$
$263$	145.409	+	251.855i	0.552885	+	0.957625i	−0.445179	+	0.895441i	$0.646860\pi$
$264$		0			0
$265$	63.6424	+	36.7440i	0.240160	+	0.138657i
$266$	−150.742	+	264.892i	−0.566699	+	0.995835i
$267$		0			0
$268$	192.285	−	111.016i	0.717481	−	0.414238i
$269$		−	412.277i		−	1.53263i	−0.642465	−	0.766315i	$-0.722088\pi$
$269$		−	412.277i		−	1.53263i	0.642465	−	0.766315i	$-0.277912\pi$
$270$		0			0
$271$	80.0609			0.295428			0.147714	−	0.989030i	$-0.452809\pi$
$271$	80.0609			0.295428			0.147714	+	0.989030i	$0.452809\pi$
$272$	42.2498	+	73.1788i	0.155330	+	0.269040i
$273$		0			0
$274$	60.8189	+	35.1138i	0.221967	+	0.128153i
$275$	−241.489	+	418.271i	−0.878142	+	1.52099i
$276$		0			0
$277$	−29.3529	−	50.8407i	−0.105967	−	0.183540i	0.808166	−	0.588955i	$-0.200461\pi$
$277$	−29.3529	−	50.8407i	−0.105967	−	0.183540i	−0.914133	+	0.405415i	$0.867127\pi$
$278$		−	248.924i		−	0.895410i
$279$		0			0
$280$		−	301.242i		−	1.07586i
$281$	438.013	−	252.887i	1.55877	−	0.899953i	0.561390	−	0.827552i	$-0.310267\pi$
$281$	438.013	−	252.887i	1.55877	−	0.899953i	0.997376	−	0.0724018i	$-0.0230664\pi$
$282$		0			0
$283$	208.876	−	361.784i	0.738078	−	1.27839i	−0.215281	−	0.976552i	$-0.569067\pi$
$283$	208.876	−	361.784i	0.738078	−	1.27839i	0.953359	−	0.301837i	$-0.0975999\pi$
$284$	−94.4689	−	54.5417i	−0.332637	−	0.192048i
$285$		0			0
$286$	−97.7887	−	169.375i	−0.341918	−	0.592220i
$287$			20.3265i			0.0708240i
$288$		0			0
$289$	157.261			0.544156
$290$	−94.7707	−	164.148i	−0.326795	−	0.566026i
$291$		0			0
$292$	−117.096	+	202.816i	−0.401013	+	0.694575i
$293$	−281.151	−	162.323i	−0.959559	−	0.554002i	−0.0635219	−	0.997980i	$-0.520233\pi$
$293$	−281.151	−	162.323i	−0.959559	−	0.554002i	−0.896037	+	0.443979i	$0.853567\pi$
$294$		0			0
$295$	−620.841	+	358.443i	−2.10455	+	1.21506i
$296$	30.1466			0.101847
$297$		0			0
$298$		−	81.5354i		−	0.273609i
$299$	−262.321	+	151.451i	−0.877329	+	0.506526i
$300$		0			0
$301$	−189.827	+	328.791i	−0.630656	+	1.09233i
$302$	−23.2813	+	40.3245i	−0.0770905	+	0.133525i
$303$		0			0
$304$	−65.5798	+	38.4095i	−0.215723	+	0.126347i
$305$	334.054			1.09526
$306$		0			0
$307$			50.8776i			0.165725i	0.996561	+	0.0828625i	$0.0264062\pi$
$307$			50.8776i			0.165725i	−0.996561	+	0.0828625i	$0.973594\pi$
$308$	−86.7277	−	150.217i	−0.281583	−	0.487717i
$309$		0			0
$310$	116.080	−	201.056i	0.374450	−	0.648567i
$311$	−81.1604	+	140.574i	−0.260966	+	0.452006i	−0.966499	−	0.256671i	$-0.917374\pi$
$311$	−81.1604	+	140.574i	−0.260966	+	0.452006i	0.705533	+	0.708677i	$0.250708\pi$
$312$		0			0
$313$	11.8965	+	20.6054i	0.0380081	+	0.0658320i	0.884404	−	0.466723i	$-0.154565\pi$
$313$	11.8965	+	20.6054i	0.0380081	+	0.0658320i	−0.846396	+	0.532555i	$0.821232\pi$
$314$			241.475i			0.769030i
$315$		0			0
$316$			33.6484i			0.106482i
$317$	−395.572	+	228.384i	−1.24786	+	0.720453i	−0.970683	−	0.240365i	$-0.922733\pi$
$317$	−395.572	+	228.384i	−1.24786	+	0.720453i	−0.277179	+	0.960818i	$0.589400\pi$
$318$		0			0
$319$	−94.5163	−	54.5690i	−0.296289	−	0.171063i
$320$	37.5589	−	65.0538i	0.117371	−	0.203293i
$321$		0			0
$322$	−232.650	+	134.321i	−0.722515	+	0.417144i
$323$	2.50174	+	401.365i	0.00774532	+	1.24262i
$324$		0			0
$325$			1142.49i			3.51535i
$326$	−72.8099	+	42.0368i	−0.223343	+	0.128947i
$327$		0			0
$328$	−2.53430	+	4.38954i	−0.00772654	+	0.0133828i
$329$	−117.126	+	202.868i	−0.356006	+	0.616621i
$330$		0			0
$331$	398.307	−	229.963i	1.20334	−	0.694752i	0.242048	−	0.970264i	$-0.422181\pi$
$331$	398.307	−	229.963i	1.20334	−	0.694752i	0.961297	+	0.275513i	$0.0888477\pi$
$332$	275.029			0.828402
$333$		0			0
$334$	−48.9376			−0.146520
$335$	−902.751	+	521.203i	−2.69478	+	1.55583i
$336$		0			0
$337$	−111.183	−	64.1915i	−0.329920	−	0.190479i	0.325886	−	0.945409i	$-0.394338\pi$
$337$	−111.183	−	64.1915i	−0.329920	−	0.190479i	−0.655805	+	0.754930i	$0.727671\pi$
$338$	−193.676	−	111.819i	−0.573007	−	0.330825i
$339$		0			0
$340$	−198.357	−	343.564i	−0.583402	−	1.01048i
$341$		−	133.677i		−	0.392016i
$342$		0			0
$343$	−347.745			−1.01383
$344$	−81.9873	+	47.3354i	−0.238335	+	0.137603i
$345$		0			0
$346$	132.209	−	228.994i	0.382108	−	0.661831i
$347$	128.415	−	222.420i	0.370071	−	0.640981i	−0.619505	−	0.784992i	$-0.712667\pi$
$347$	128.415	−	222.420i	0.370071	−	0.640981i	0.989576	+	0.144011i	$0.0460001\pi$
$348$		0			0
$349$	229.402	+	397.336i	0.657312	+	1.13850i	0.981309	+	0.192439i	$0.0616399\pi$
$349$	229.402	+	397.336i	0.657312	+	1.13850i	−0.323997	+	0.946058i	$0.605027\pi$
$350$			1013.26i			2.89503i
$351$		0			0
$352$		−	43.2528i		−	0.122877i
$353$	226.280	+	391.928i	0.641020	+	1.11028i	0.985206	+	0.171377i	$0.0548216\pi$
$353$	226.280	+	391.928i	0.641020	+	1.11028i	−0.344186	+	0.938901i	$0.611845\pi$
$354$		0			0
$355$	443.518	+	256.065i	1.24935	+	0.721310i
$356$	−13.3428	−	7.70345i	−0.0374797	−	0.0216389i
$357$		0			0
$358$	119.604	+	207.160i	0.334090	+	0.578660i
$359$	−459.016			−1.27860			−0.639299	−	0.768959i	$-0.720775\pi$
$359$	−459.016			−1.27860			−0.639299	+	0.768959i	$0.720775\pi$
$360$		0			0
$361$	−360.972	+	4.50011i	−0.999922	+	0.0124657i
$362$	195.085	+	337.897i	0.538909	+	0.933418i
$363$		0			0
$364$	−355.339	−	205.155i	−0.976206	−	0.563613i
$365$	549.748	−	952.192i	1.50616	−	2.60874i
$366$		0			0
$367$	−349.240	−	604.902i	−0.951608	−	1.64823i	−0.741946	−	0.670460i	$-0.766097\pi$
$367$	−349.240	−	604.902i	−0.951608	−	1.64823i	−0.209662	−	0.977774i	$-0.567236\pi$
$368$	−66.9883			−0.182033
$369$		0			0
$370$	−141.534			−0.382524
$371$	76.8799	−	44.3866i	0.207223	−	0.119640i
$372$		0			0
$373$	−461.435	−	266.409i	−1.23709	−	0.714234i	−0.268592	−	0.963254i	$-0.586558\pi$
$373$	−461.435	−	266.409i	−1.23709	−	0.714234i	−0.968498	+	0.249020i	$0.919892\pi$
$374$	−197.824	−	114.214i	−0.528942	−	0.305385i
$375$		0			0
$376$	−50.5873	+	29.2066i	−0.134541	+	0.0776770i
$377$	−258.167			−0.684793
$378$		0			0
$379$		−	182.927i		−	0.482657i	−0.970443	−	0.241329i	$-0.922417\pi$
$379$		−	182.927i		−	0.482657i	0.970443	−	0.241329i	$-0.0775832\pi$
$380$	307.888	−	180.327i	0.810231	−	0.474545i
$381$		0			0
$382$	268.025	+	154.744i	0.701636	+	0.405090i
$383$	−376.937	−	217.625i	−0.984170	−	0.568211i	−0.0806435	−	0.996743i	$-0.525698\pi$
$383$	−376.937	−	217.625i	−0.984170	−	0.568211i	−0.903527	+	0.428532i	$0.859031\pi$
$384$		0			0
$385$	407.174	+	705.246i	1.05759	+	1.83181i
$386$	−521.130			−1.35008
$387$		0			0
$388$			233.674i			0.602253i
$389$	158.195	+	274.002i	0.406672	+	0.704376i	0.994514	−	0.104599i	$-0.0333559\pi$
$389$	158.195	+	274.002i	0.406672	+	0.704376i	−0.587843	+	0.808975i	$0.700023\pi$
$390$		0			0
$391$	−176.890	+	306.383i	−0.452404	+	0.783587i
$392$	−195.121	−	112.653i	−0.497758	−	0.287381i
$393$		0			0
$394$	301.606	−	174.132i	0.765496	−	0.441960i
$395$		−	157.974i		−	0.399935i
$396$		0			0
$397$	555.614			1.39953			0.699766	−	0.714372i	$-0.253288\pi$
$397$	555.614			1.39953			0.699766	+	0.714372i	$0.253288\pi$
$398$	11.6992	−	6.75451i	0.0293949	−	0.0169711i
$399$		0			0
$400$	−126.333	+	218.816i	−0.315834	+	0.547040i
$401$	−237.374	−	137.048i	−0.591954	−	0.341765i	0.173916	−	0.984761i	$-0.444358\pi$
$401$	−237.374	−	137.048i	−0.591954	−	0.341765i	−0.765870	+	0.642996i	$0.777691\pi$
$402$		0			0
$403$	−158.108	−	273.850i	−0.392327	−	0.679530i
$404$	−11.6484			−0.0288328
$405$		0			0
$406$	−228.965			−0.563954
$407$	−70.5771	+	40.7477i	−0.173408	+	0.100117i
$408$		0			0
$409$	−638.552	−	368.668i	−1.56125	−	0.901389i	−0.997131	−	0.0756974i	$-0.975882\pi$
$409$	−638.552	−	368.668i	−1.56125	−	0.901389i	−0.564121	−	0.825692i	$-0.690785\pi$
$410$	11.8982	−	20.6083i	0.0290200	−	0.0502641i
$411$		0			0
$412$	−297.170	+	171.571i	−0.721287	+	0.416436i
$413$			865.996i			2.09684i
$414$		0			0
$415$	−1291.22			−3.11138
$416$	−51.1575	−	88.6074i	−0.122975	−	0.212998i
$417$		0			0
$418$	101.614	−	178.562i	0.243097	−	0.427183i
$419$	−38.7513	+	67.1193i	−0.0924852	+	0.160189i	−0.908556	−	0.417762i	$-0.862814\pi$
$419$	−38.7513	+	67.1193i	−0.0924852	+	0.160189i	0.816071	+	0.577952i	$0.196148\pi$
$420$		0			0
$421$	370.966	−	214.177i	0.881153	−	0.508734i	0.0101148	−	0.999949i	$-0.496780\pi$
$421$	370.966	−	214.177i	0.881153	−	0.508734i	0.871038	+	0.491215i	$0.163447\pi$
$422$	196.483			0.465600
$423$		0			0
$424$	22.1365			0.0522087
$425$	667.195	+	1155.62i	1.56987	+	2.71909i
$426$		0			0
$427$	201.768	−	349.473i	0.472525	−	0.818438i
$428$	−214.072	−	123.595i	−0.500169	−	0.288773i
$429$		0			0
$430$	384.918	−	222.233i	0.895159	−	0.516820i
$431$		−	725.938i		−	1.68431i	−0.539236	−	0.842155i	$-0.681287\pi$
$431$		−	725.938i		−	1.68431i	0.539236	−	0.842155i	$-0.318713\pi$
$432$		0			0
$433$		−	315.242i		−	0.728043i	−0.931391	−	0.364021i	$-0.881404\pi$
$433$		−	315.242i		−	0.728043i	0.931391	−	0.364021i	$-0.118596\pi$
$434$	−140.224	−	242.875i	−0.323096	−	0.559619i
$435$		0			0
$436$	−103.528	−	59.7721i	−0.237450	−	0.137092i
$437$	−276.551	−	157.377i	−0.632839	−	0.360129i
$438$		0			0
$439$	243.573	−	140.627i	0.554837	−	0.320335i	−0.196234	−	0.980557i	$-0.562871\pi$
$439$	243.573	−	140.627i	0.554837	−	0.320335i	0.751071	+	0.660222i	$0.229538\pi$
$440$			203.066i			0.461513i
$441$		0			0
$442$	−540.348			−1.22251
$443$	−83.3663	−	144.395i	−0.188186	−	0.325948i	0.756460	−	0.654040i	$-0.226927\pi$
$443$	−83.3663	−	144.395i	−0.188186	−	0.325948i	−0.944645	+	0.328093i	$0.893594\pi$
$444$		0			0
$445$	62.6424	+	36.1666i	0.140769	+	0.0812732i
$446$	−61.3664	+	106.290i	−0.137593	+	0.238318i
$447$		0			0
$448$	−45.3710	−	78.5849i	−0.101275	−	0.175413i
$449$			294.066i			0.654936i	0.944862	+	0.327468i	$0.106195\pi$
$449$			294.066i			0.654936i	−0.944862	+	0.327468i	$0.893805\pi$
$450$		0			0
$451$		−	13.7020i		−	0.0303813i
$452$	−255.587	+	147.563i	−0.565458	+	0.326467i
$453$		0			0
$454$	62.1884	−	107.714i	0.136979	−	0.237254i
$455$	1668.27	+	963.174i	3.66652	+	2.11687i
$456$		0			0
$457$	334.386	+	579.173i	0.731697	+	1.26734i	0.956157	+	0.292853i	$0.0946047\pi$
$457$	334.386	+	579.173i	0.731697	+	1.26734i	−0.224460	+	0.974483i	$0.572062\pi$
$458$			284.459i			0.621089i
$459$		0			0
$460$	314.500			0.683697
$461$	−76.9781	−	133.330i	−0.166981	−	0.289219i	0.770376	−	0.637590i	$-0.220068\pi$
$461$	−76.9781	−	133.330i	−0.166981	−	0.289219i	−0.937357	+	0.348370i	$0.886735\pi$
$462$		0			0
$463$	72.5534	−	125.666i	0.156703	−	0.271417i	−0.776975	−	0.629532i	$-0.783247\pi$
$463$	72.5534	−	125.666i	0.156703	−	0.271417i	0.933678	+	0.358114i	$0.116580\pi$
$464$	−49.4456	−	28.5474i	−0.106564	−	0.0615246i
$465$		0			0
$466$	151.805	−	87.6446i	0.325762	−	0.188078i
$467$	−147.528			−0.315906			−0.157953	−	0.987447i	$-0.550489\pi$
$467$	−147.528			−0.315906			−0.157953	+	0.987447i	$0.550489\pi$
$468$		0			0
$469$			1259.22i			2.68491i
$470$	237.500	−	137.121i	0.505319	−	0.291746i
$471$		0			0
$472$	−107.972	+	187.014i	−0.228755	+	0.396215i
$473$	127.962	−	221.636i	0.270532	−	0.468575i
$474$		0			0
$475$	−1035.61	+	606.550i	−2.18024	+	1.27695i
$476$	−479.229			−1.00678
$477$		0			0
$478$			57.0865i			0.119428i
$479$	−249.268	−	431.745i	−0.520392	−	0.901346i	−0.999719	−	0.0237093i	$-0.992452\pi$
$479$	−249.268	−	431.745i	−0.520392	−	0.901346i	0.479327	−	0.877637i	$-0.340881\pi$
$480$		0			0
$481$	−96.3891	+	166.951i	−0.200393	+	0.347091i
$482$	118.698	−	205.591i	0.246262	−	0.426538i
$483$		0			0
$484$	−62.5373	−	108.318i	−0.129209	−	0.223797i
$485$		−	1097.07i		−	2.26199i
$486$		0			0
$487$		−	439.949i		−	0.903386i	−0.892173	−	0.451693i	$-0.850820\pi$
$487$		−	439.949i		−	0.903386i	0.892173	−	0.451693i	$-0.149180\pi$
$488$	87.1445	−	50.3129i	0.178575	−	0.103100i
$489$		0			0
$490$	916.066	+	528.891i	1.86952	+	1.07937i
$491$	104.929	−	181.742i	0.213704	−	0.370146i	−0.739167	−	0.673522i	$-0.764781\pi$
$491$	104.929	−	181.742i	0.213704	−	0.370146i	0.952871	+	0.303376i	$0.0981139\pi$
$492$		0			0
$493$	−261.133	+	150.765i	−0.529682	+	0.305812i
$494$	−3.02919	−	485.987i	−0.00613197	−	0.983779i
$495$		0			0
$496$		−	69.9324i		−	0.140993i
$497$	535.769	−	309.326i	1.07801	−	0.622387i
$498$		0			0
$499$	208.841	−	361.723i	0.418519	−	0.724897i	−0.577272	−	0.816552i	$-0.695883\pi$
$499$	208.841	−	361.723i	0.418519	−	0.724897i	0.995791	+	0.0916557i	$0.0292159\pi$
$500$	358.374	−	620.723i	0.716749	−	1.24145i
$501$		0			0
$502$	−99.9037	+	57.6794i	−0.199011	+	0.114899i
$503$	422.202			0.839367			0.419684	−	0.907671i	$-0.362141\pi$
$503$	422.202			0.839367			0.419684	+	0.907671i	$0.362141\pi$
$504$		0			0
$505$	54.6878			0.108293
$506$	156.828	−	90.5448i	0.309937	−	0.178942i
$507$		0			0
$508$	−4.74283	−	2.73827i	−0.00933628	−	0.00539030i
$509$	−145.016	−	83.7250i	−0.284904	−	0.164489i	0.350738	−	0.936474i	$-0.385931\pi$
$509$	−145.016	−	83.7250i	−0.284904	−	0.164489i	−0.635641	+	0.771985i	$0.719264\pi$
$510$		0			0
$511$	−664.094	−	1150.25i	−1.29960	−	2.25097i
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	458.357			0.891745
$515$	1395.17	−	805.503i	2.70907	−	1.56408i
$516$		0			0
$517$	78.9541	−	136.753i	0.152716	−	0.264512i
$518$	−85.4864	+	148.067i	−0.165032	+	0.285843i
$519$		0			0
$520$	240.177	+	415.999i	0.461879	+	0.799998i
$521$			293.382i			0.563113i	0.959545	+	0.281556i	$0.0908506\pi$
$521$			293.382i			0.563113i	−0.959545	+	0.281556i	$0.909149\pi$
$522$		0			0
$523$			138.278i			0.264394i	0.991223	+	0.132197i	$0.0422032\pi$
$523$			138.278i			0.264394i	−0.991223	+	0.132197i	$0.957797\pi$
$524$	−126.936	−	219.860i	−0.242245	−	0.419581i
$525$		0			0
$526$	−356.177	−	205.639i	−0.677143	−	0.390949i
$527$	−319.848	−	184.664i	−0.606922	−	0.350407i
$528$		0			0
$529$	124.268	+	215.238i	0.234911	+	0.406877i
$530$	−103.928			−0.196090
$531$		0			0
$532$	−2.68656	−	431.016i	−0.00504992	−	0.810181i
$533$	−16.2061	−	28.0698i	−0.0304054	−	0.0526637i
$534$		0			0
$535$	1005.04	+	580.260i	1.87858	+	1.08460i
$536$	−157.000	+	271.932i	−0.292911	+	0.507336i
$537$		0			0
$538$	291.524	+	504.935i	0.541867	+	0.938540i
$539$	609.072			1.13000
$540$		0			0
$541$	680.631			1.25810			0.629049	−	0.777366i	$-0.283444\pi$
$541$	680.631			1.25810			0.629049	+	0.777366i	$0.283444\pi$
$542$	−98.0541	+	56.6116i	−0.180912	+	0.104449i
$543$		0			0
$544$	−103.490	−	59.7502i	−0.190240	−	0.109835i
$545$	486.050	+	280.621i	0.891835	+	0.514901i
$546$		0			0
$547$	−452.278	+	261.123i	−0.826833	+	0.477372i	−0.852767	−	0.522291i	$-0.825077\pi$
$547$	−452.278	+	261.123i	−0.826833	+	0.477372i	0.0259341	+	0.999664i	$0.491744\pi$
$548$	−99.3168			−0.181235
$549$		0			0
$550$		−	683.034i		−	1.24188i
$551$	−137.061	−	234.017i	−0.248750	−	0.424713i
$552$		0			0
$553$	−165.266	−	95.4164i	−0.298854	−	0.172543i
$554$	71.8996	+	41.5113i	0.129783	+	0.0749301i
$555$		0			0
$556$	176.016	+	304.868i	0.316575	+	0.548324i
$557$	740.279			1.32905			0.664523	−	0.747268i	$-0.268635\pi$
$557$	740.279			1.32905			0.664523	+	0.747268i	$0.268635\pi$
$558$		0			0
$559$		−	605.389i		−	1.08299i
$560$	213.010	+	368.945i	0.380376	+	0.658830i
$561$		0			0
$562$	−357.636	+	619.444i	−0.636363	+	1.10221i
$563$	−127.632	−	73.6883i	−0.226699	−	0.130885i	0.382349	−	0.924018i	$-0.375115\pi$
$563$	−127.632	−	73.6883i	−0.226699	−	0.130885i	−0.609049	+	0.793133i	$0.708449\pi$
$564$		0			0
$565$	1199.94	−	692.788i	2.12379	−	1.22617i
$566$			590.791i			1.04380i
$567$		0			0
$568$	154.267			0.271597
$569$	−290.015	+	167.440i	−0.509693	+	0.294271i	−0.732707	−	0.680544i	$-0.761744\pi$
$569$	−290.015	+	167.440i	−0.509693	+	0.294271i	0.223015	+	0.974815i	$0.428410\pi$
$570$		0			0
$571$	372.211	−	644.689i	0.651859	−	1.12905i	−0.330812	−	0.943697i	$-0.607323\pi$
$571$	372.211	−	644.689i	0.651859	−	1.12905i	0.982671	−	0.185356i	$-0.0593439\pi$
$572$	239.532	+	138.294i	0.418763	+	0.241773i
$573$		0			0
$574$	−14.3730	−	24.8947i	−0.0250400	−	0.0433706i
$575$	−1057.86			−1.83975
$576$		0			0
$577$	−558.799			−0.968455			−0.484228	−	0.874942i	$-0.660899\pi$
$577$	−558.799			−0.968455			−0.484228	+	0.874942i	$0.660899\pi$
$578$	−192.605	+	111.200i	−0.333226	+	0.192388i
$579$		0			0
$580$	232.140	+	134.026i	0.400241	+	0.231079i
$581$	−779.897	+	1350.82i	−1.34234	+	2.32499i
$582$		0			0
$583$	−51.8243	+	29.9208i	−0.0888925	+	0.0513221i
$584$		−	331.197i		−	0.567118i
$585$		0			0
$586$	459.117			0.783477
$587$	173.031	+	299.699i	0.294772	+	0.510560i	0.974932	−	0.222504i	$-0.0714230\pi$
$587$	173.031	+	299.699i	0.294772	+	0.510560i	−0.680160	+	0.733064i	$0.738090\pi$
$588$		0			0
$589$	164.293	−	288.705i	0.278936	−	0.490162i
$590$	506.915	−	878.002i	0.859178	−	1.48814i
$591$		0			0
$592$	−36.9219	+	21.3169i	−0.0623681	+	0.0360082i
$593$	−187.654			−0.316449			−0.158225	−	0.987403i	$-0.550577\pi$
$593$	−187.654			−0.316449			−0.158225	+	0.987403i	$0.550577\pi$
$594$		0			0
$595$	2249.91			3.78136
$596$	57.6542	+	99.8600i	0.0967353	+	0.167550i
$597$		0			0
$598$	214.185	−	370.979i	0.358168	−	0.620365i
$599$	−590.699	−	341.040i	−0.986143	−	0.569350i	−0.0820236	−	0.996630i	$-0.526138\pi$
$599$	−590.699	−	341.040i	−0.986143	−	0.569350i	−0.904119	+	0.427281i	$0.859472\pi$
$600$		0			0
$601$	−6.79494	+	3.92306i	−0.0113061	+	0.00652755i	−0.505642	−	0.862743i	$-0.668744\pi$
$601$	−6.79494	+	3.92306i	−0.0113061	+	0.00652755i	0.494336	+	0.869271i	$0.335411\pi$
$602$		−	536.913i		−	0.891882i
$603$		0			0
$604$		−	65.8496i		−	0.109022i
$605$	293.604	+	508.537i	0.485296	+	0.840556i
$606$		0			0
$607$	781.844	+	451.398i	1.28805	+	0.743653i	0.978305	−	0.207168i	$-0.0664246\pi$
$607$	781.844	+	451.398i	1.28805	+	0.743653i	0.309740	+	0.950821i	$0.399758\pi$
$608$	53.1589	−	93.4138i	0.0874324	−	0.153641i
$609$		0			0
$610$	−409.131	+	236.212i	−0.670707	+	0.387233i
$611$		−	373.534i		−	0.611348i
$612$		0			0
$613$	−481.589			−0.785627			−0.392814	−	0.919618i	$-0.628498\pi$
$613$	−481.589			−0.785627			−0.392814	+	0.919618i	$0.628498\pi$
$614$	−35.9759	−	62.3120i	−0.0585926	−	0.101485i
$615$		0			0
$616$	212.439	+	122.651i	0.344868	+	0.199109i
$617$	−120.361	+	208.471i	−0.195075	+	0.337879i	−0.946925	−	0.321455i	$-0.895828\pi$
$617$	−120.361	+	208.471i	−0.195075	+	0.337879i	0.751850	+	0.659334i	$0.229162\pi$
$618$		0			0
$619$	539.689	+	934.768i	0.871872	+	1.51013i	0.860058	+	0.510197i	$0.170427\pi$
$619$	539.689	+	934.768i	0.871872	+	1.51013i	0.0118142	+	0.999930i	$0.496239\pi$
$620$			328.323i			0.529553i
$621$		0			0
$622$		−	229.556i		−	0.369062i
$623$	75.6718	−	43.6891i	0.121464	−	0.0701270i
$624$		0			0
$625$	−892.932	+	1546.60i	−1.42869	+	2.47457i
$626$	−29.1404	−	16.8242i	−0.0465502	−	0.0268758i
$627$		0			0
$628$	−170.749	−	295.746i	−0.271893	−	0.470933i
$629$			225.158i			0.357962i
$630$		0			0
$631$	−1069.71			−1.69526			−0.847628	−	0.530591i	$-0.821970\pi$
$631$	−1069.71			−1.69526			−0.847628	+	0.530591i	$0.821970\pi$
$632$	−23.7930	−	41.2107i	−0.0376472	−	0.0652068i
$633$		0			0
$634$	322.983	−	559.424i	0.509438	−	0.882372i
$635$	22.2669	+	12.8558i	0.0350660	+	0.0202454i
$636$		0			0
$637$	1247.74	−	720.383i	1.95877	−	1.13090i
$638$	154.344			0.241919
$639$		0			0
$640$			106.232i			0.165988i
$641$	134.017	−	77.3747i	0.209075	−	0.120709i	−0.391807	−	0.920048i	$-0.628150\pi$
$641$	134.017	−	77.3747i	0.209075	−	0.120709i	0.600881	+	0.799338i	$0.294816\pi$
$642$		0			0
$643$	−254.826	+	441.371i	−0.396307	+	0.686425i	−0.993267	−	0.115847i	$-0.963042\pi$
$643$	−254.826	+	441.371i	−0.396307	+	0.686425i	0.596960	+	0.802271i	$0.296375\pi$
$644$	189.958	−	329.017i	0.294966	−	0.510896i
$645$		0			0
$646$	−286.872	−	489.801i	−0.444074	−	0.758206i
$647$	215.440			0.332983			0.166492	−	0.986043i	$-0.446756\pi$
$647$	215.440			0.332983			0.166492	+	0.986043i	$0.446756\pi$
$648$		0			0
$649$		−	583.764i		−	0.899482i
$650$	−807.862	−	1399.26i	−1.24287	−	2.15271i
$651$		0			0
$652$	59.4491	−	102.969i	0.0911796	−	0.157928i
$653$	−92.8163	+	160.763i	−0.142138	+	0.246191i	−0.928302	−	0.371828i	$-0.878731\pi$
$653$	−92.8163	+	160.763i	−0.142138	+	0.246191i	0.786163	+	0.618019i	$0.212064\pi$
$654$		0			0
$655$	595.948	+	1032.21i	0.909844	+	1.57590i
$656$		−	7.16810i		−	0.0109270i
$657$		0			0
$658$		−	331.283i		−	0.503469i
$659$	−1072.33	+	619.112i	−1.62721	+	0.939472i	−0.642294	+	0.766459i	$0.722017\pi$
$659$	−1072.33	+	619.112i	−1.62721	+	0.939472i	−0.984919	+	0.173013i	$0.944650\pi$
$660$		0			0
$661$	−694.069	−	400.721i	−1.05003	−	0.606234i	−0.127371	−	0.991855i	$-0.540654\pi$
$661$	−694.069	−	400.721i	−1.05003	−	0.606234i	−0.922657	+	0.385621i	$0.873987\pi$
$662$	−325.216	+	563.291i	−0.491264	+	0.850893i
$663$		0			0
$664$	−336.841	+	194.475i	−0.507290	+	0.292884i
$665$	12.6130	+	2023.56i	0.0189669	+	3.04295i
$666$		0			0
$667$		−	239.043i		−	0.358385i
$668$	59.9361	−	34.6041i	0.0897246	−	0.0518025i
$669$		0			0
$670$	737.093	−	1276.68i	1.10014	−	1.90550i
$671$	−136.011	+	235.578i	−0.202699	+	0.351085i
$672$		0			0
$673$	−721.063	+	416.306i	−1.07142	+	0.618582i	−0.928568	−	0.371162i	$-0.878959\pi$
$673$	−721.063	+	416.306i	−1.07142	+	0.618582i	−0.142848	+	0.989745i	$0.545626\pi$
$674$	181.561			0.269378
$675$		0			0
$676$	316.272			0.467858
$677$	35.8927	−	20.7226i	0.0530173	−	0.0306095i	−0.473257	−	0.880924i	$-0.656922\pi$
$677$	35.8927	−	20.7226i	0.0530173	−	0.0306095i	0.526274	+	0.850315i	$0.323588\pi$
$678$		0			0
$679$	−1147.70	−	662.627i	−1.69029	−	0.975887i
$680$	485.873	+	280.519i	0.714518	+	0.412527i
$681$		0			0
$682$	94.5242	+	163.721i	0.138599	+	0.240060i
$683$		−	519.839i		−	0.761111i	−0.924758	−	0.380556i	$-0.875733\pi$
$683$		−	519.839i		−	0.761111i	0.924758	−	0.380556i	$-0.124267\pi$
$684$		0			0
$685$	466.278			0.680698
$686$	425.899	−	245.893i	0.620844	−	0.358445i
$687$		0			0
$688$	66.9423	−	115.947i	0.0972999	−	0.168528i
$689$	−70.7779	+	122.591i	−0.102726	+	0.177926i
$690$		0			0
$691$	−482.416	−	835.570i	−0.698142	−	1.20922i	−0.969110	−	0.246630i	$-0.920677\pi$
$691$	−482.416	−	835.570i	−0.698142	−	1.20922i	0.270967	−	0.962589i	$-0.412656\pi$
$692$			373.945i			0.540383i
$693$		0			0
$694$			363.211i			0.523359i
$695$	−826.369	−	1431.31i	−1.18902	−	2.05944i
$696$		0			0
$697$	−32.7845	−	18.9282i	−0.0470366	−	0.0271566i
$698$	−561.917	−	324.423i	−0.805039	−	0.464790i
$699$		0			0
$700$	−716.484	−	1240.99i	−1.02355	−	1.77284i
$701$	903.971			1.28955			0.644773	−	0.764374i	$-0.276952\pi$
$701$	903.971			1.28955			0.644773	+	0.764374i	$0.276952\pi$
$702$		0			0
$703$	−202.506	+	1.26224i	−0.288060	+	0.00179550i
$704$	30.5844	+	52.9737i	0.0434437	+	0.0752467i
$705$		0			0
$706$	−554.270	−	320.008i	−0.785085	−	0.453269i
$707$	33.0313	−	57.2120i	0.0467204	−	0.0809221i
$708$		0			0
$709$	122.373	+	211.957i	0.172600	+	0.298952i	0.939328	−	0.343020i	$-0.111450\pi$
$709$	122.373	+	211.957i	0.172600	+	0.298952i	−0.766728	+	0.641972i	$0.778117\pi$
$710$	−724.262			−1.02009
$711$		0			0
$712$	21.7886			0.0306020
$713$	253.564	−	146.395i	0.355630	−	0.205323i
$714$		0			0
$715$	−1124.57	−	649.271i	−1.57282	−	0.908071i
$716$	−292.969	−	169.146i	−0.409174	−	0.236237i
$717$		0			0
$718$	562.178	−	324.574i	0.782978	−	0.452052i
$719$	385.608			0.536311			0.268155	−	0.963376i	$-0.413586\pi$
$719$	385.608			0.536311			0.268155	+	0.963376i	$0.413586\pi$
$720$		0			0
$721$		−	1946.09i		−	2.69916i
$722$	438.916	−	260.757i	0.607918	−	0.361160i
$723$		0			0
$724$	−477.859	−	275.892i	−0.660026	−	0.381066i
$725$	−780.828	−	450.811i	−1.07700	−	0.621809i
$726$		0			0
$727$	−239.797	−	415.340i	−0.329844	−	0.571307i	0.652637	−	0.757671i	$-0.273663\pi$
$727$	−239.797	−	415.340i	−0.329844	−	0.571307i	−0.982481	+	0.186364i	$0.940329\pi$
$728$	580.266			0.797069
$729$		0			0
$730$			1554.92i			2.13003i
$731$	−353.537	−	612.344i	−0.483635	−	0.837681i
$732$		0			0
$733$	−193.320	+	334.839i	−0.263737	+	0.456807i	−0.967232	−	0.253894i	$-0.918289\pi$
$733$	−193.320	+	334.839i	−0.263737	+	0.456807i	0.703495	+	0.710701i	$0.251622\pi$
$734$	855.460	+	493.900i	1.16548	+	0.672889i
$735$		0			0
$736$	82.0436	−	47.3679i	0.111472	−	0.0643585i
$737$		−	848.837i		−	1.15175i
$738$		0			0
$739$	−210.976			−0.285489			−0.142744	−	0.989760i	$-0.545593\pi$
$739$	−210.976			−0.285489			−0.142744	+	0.989760i	$0.545593\pi$
$740$	173.343	−	100.080i	0.234247	−	0.135243i
$741$		0			0
$742$	−62.7722	+	108.725i	−0.0845986	+	0.146529i
$743$	886.789	+	511.988i	1.19352	+	0.689082i	0.959104	−	0.283054i	$-0.0913475\pi$
$743$	886.789	+	511.988i	1.19352	+	0.689082i	0.234420	+	0.972135i	$0.424681\pi$
$744$		0			0
$745$	−270.678	−	468.829i	−0.363327	−	0.629300i
$746$	753.520			1.01008
$747$		0			0
$748$	323.046			0.431879
$749$	1214.08	−	700.952i	1.62094	−	0.935851i
$750$		0			0
$751$	582.160	+	336.110i	0.775180	+	0.447550i	0.834719	−	0.550676i	$-0.185630\pi$
$751$	582.160	+	336.110i	0.775180	+	0.447550i	−0.0595396	+	0.998226i	$0.518963\pi$
$752$	41.3043	−	71.5412i	0.0549260	−	0.0951345i
$753$		0			0
$754$	316.189	−	182.552i	0.419349	−	0.242111i
$755$			309.154i			0.409476i
$756$		0			0
$757$	208.644			0.275620			0.137810	−	0.990459i	$-0.455994\pi$
$757$	208.644			0.275620			0.137810	+	0.990459i	$0.455994\pi$
$758$	129.349	+	224.039i	0.170645	+	0.295566i
$759$		0			0
$760$	−249.573	+	438.564i	−0.328386	+	0.577058i
$761$	−323.299	+	559.971i	−0.424835	+	0.735835i	−0.996405	−	0.0847178i	$-0.973001\pi$
$761$	−323.299	+	559.971i	−0.424835	+	0.735835i	0.571570	+	0.820553i	$0.306334\pi$
$762$		0			0
$763$	587.147	−	338.990i	0.769525	−	0.444285i
$764$	−437.683			−0.572883
$765$		0			0
$766$	615.536			0.803571
$767$	−690.449	−	1195.89i	−0.900195	−	1.55918i
$768$		0			0
$769$	−643.423	+	1114.44i	−0.836701	+	1.44921i	0.0559376	+	0.998434i	$0.482185\pi$
$769$	−643.423	+	1114.44i	−0.836701	+	1.44921i	−0.892638	+	0.450774i	$0.851148\pi$
$770$	−997.368	−	575.831i	−1.29528	−	0.747832i
$771$		0			0
$772$	638.251	−	368.495i	0.826750	−	0.477325i
$773$		−	63.3904i		−	0.0820057i	−0.999159	−	0.0410028i	$-0.986945\pi$
$773$		−	63.3904i		−	0.0820057i	0.999159	−	0.0410028i	$-0.0130553\pi$
$774$		0			0
$775$		−	1104.35i		−	1.42497i
$776$	−165.233	−	286.191i	−0.212929	−	0.368803i
$777$		0			0
$778$	−387.498	−	223.722i	−0.498069	−	0.287560i
$779$	16.8401	−	29.5924i	0.0216176	−	0.0379876i
$780$		0			0
$781$	−361.159	+	208.515i	−0.462431	+	0.266985i
$782$		−	500.321i		−	0.639796i
$783$		0			0
$784$	318.632			0.406418
$785$	801.642	+	1388.48i	1.02120	+	1.76877i
$786$		0			0
$787$	74.7615	+	43.1636i	0.0949956	+	0.0548457i	0.546745	−	0.837299i	$-0.315867\pi$
$787$	74.7615	+	43.1636i	0.0949956	+	0.0548457i	−0.451750	+	0.892145i	$0.649200\pi$
$788$	−246.260	+	426.535i	−0.312513	+	0.541288i
$789$		0			0
$790$	111.705	+	193.478i	0.141399	+	0.244909i
$791$		−	1673.77i		−	2.11602i
$792$		0			0
$793$			643.471i			0.811438i
$794$	−680.486	+	392.879i	−0.857035	+	0.494809i
$795$		0			0
$796$	−9.55232	+	16.5451i	−0.0120004	+	0.0207853i
$797$	1244.32	+	718.409i	1.56126	+	0.901392i	0.997130	+	0.0757027i	$0.0241200\pi$
$797$	1244.32	+	718.409i	1.56126	+	0.901392i	0.564126	+	0.825689i	$0.309213\pi$
$798$		0			0
$799$	−218.137	−	377.825i	−0.273013	−	0.472872i
$800$		−	357.325i		−	0.446656i
$801$		0			0
$802$	387.629			0.483328
$803$	447.663	+	775.374i	0.557488	+	0.965597i
$804$		0			0
$805$	−891.825	+	1544.69i	−1.10786	+	1.91886i
$806$	387.283	+	223.598i	0.480500	+	0.277417i
$807$		0			0
$808$	14.2664	−	8.23669i	0.0176564	−	0.0101939i
$809$	684.177			0.845707			0.422854	−	0.906198i	$-0.361028\pi$
$809$	684.177			0.845707			0.422854	+	0.906198i	$0.361028\pi$
$810$		0			0
$811$			1024.06i			1.26272i	0.775492	+	0.631358i	$0.217502\pi$
$811$			1024.06i			1.26272i	−0.775492	+	0.631358i	$0.782498\pi$
$812$	280.424	−	161.903i	0.345350	−	0.199388i
$813$		0			0
$814$	57.6259	−	99.8110i	0.0707935	−	0.122618i
$815$	−279.105	+	483.424i	−0.342460	+	0.593158i
$816$		0			0
$817$	548.758	−	321.403i	0.671674	−	0.393394i
$818$	1042.75			1.27476
$819$		0			0
$820$			33.6532i			0.0410405i
$821$	−145.846	−	252.613i	−0.177644	−	0.307689i	0.763429	−	0.645892i	$-0.223514\pi$
$821$	−145.846	−	252.613i	−0.177644	−	0.307689i	−0.941073	+	0.338203i	$0.890181\pi$
$822$		0			0
$823$	78.0236	−	135.141i	0.0948039	−	0.164205i	−0.814723	−	0.579851i	$-0.803111\pi$
$823$	78.0236	−	135.141i	0.0948039	−	0.164205i	0.909527	+	0.415645i	$0.136444\pi$
$824$	242.639	−	420.262i	0.294464	−	0.510027i
$825$		0			0
$826$	−612.352	−	1060.62i	−0.741346	−	1.28405i
$827$			900.483i			1.08886i	0.838808	+	0.544428i	$0.183253\pi$
$827$			900.483i			1.08886i	−0.838808	+	0.544428i	$0.816747\pi$
$828$		0			0
$829$			588.063i			0.709364i	0.934987	+	0.354682i	$0.115411\pi$
$829$			588.063i			0.709364i	−0.934987	+	0.354682i	$0.884589\pi$
$830$	1581.42	−	913.033i	1.90532	−	1.10004i
$831$		0			0
$832$	125.310	+	72.3476i	0.150613	+	0.0869563i
$833$	841.383	−	1457.32i	1.01006	−	1.74948i
$834$		0			0
$835$	−281.391	+	162.461i	−0.336995	+	0.194564i
$836$	1.81099	+	290.546i	0.00216626	+	0.347543i
$837$		0			0
$838$		−	109.605i		−	0.130794i
$839$	−124.060	+	71.6259i	−0.147866	+	0.0853705i	−0.572108	−	0.820179i	$-0.693874\pi$
$839$	−124.060	+	71.6259i	−0.147866	+	0.0853705i	0.424242	+	0.905549i	$0.360541\pi$
$840$		0			0
$841$	−318.631	+	551.885i	−0.378871	+	0.656224i
$842$	−302.892	+	524.624i	−0.359729	+	0.623069i
$843$		0			0
$844$	−240.642	+	138.934i	−0.285120	+	0.164614i
$845$	−1484.85			−1.75722
$846$		0			0
$847$	709.345			0.837480
$848$	−27.1116	+	15.6529i	−0.0319712	+	0.0184586i
$849$		0			0
$850$	−1634.29	−	943.556i	−1.92269	−	1.11007i
$851$	−154.584	−	89.2489i	−0.181649	−	0.104875i
$852$		0			0
$853$	48.9522	+	84.7877i	0.0573883	+	0.0993994i	0.893292	−	0.449476i	$-0.148389\pi$
$853$	48.9522	+	84.7877i	0.0573883	+	0.0993994i	−0.835904	+	0.548876i	$0.815056\pi$
$854$			570.687i			0.668252i
$855$		0			0
$856$	349.579			0.408386
$857$	417.160	−	240.847i	0.486767	−	0.281035i	−0.236465	−	0.971640i	$-0.575989\pi$
$857$	417.160	−	240.847i	0.486767	−	0.281035i	0.723232	+	0.690605i	$0.242656\pi$
$858$		0			0
$859$	−815.301	+	1412.14i	−0.949128	+	1.64394i	−0.201862	+	0.979414i	$0.564699\pi$
$859$	−815.301	+	1412.14i	−0.949128	+	1.64394i	−0.747266	+	0.664525i	$0.768634\pi$
$860$	−314.285	+	544.357i	−0.365447	+	0.632973i
$861$		0			0
$862$	513.315	+	889.088i	0.595493	+	1.03142i
$863$		−	1042.37i		−	1.20784i	−0.797044	−	0.603921i	$-0.793604\pi$
$863$		−	1042.37i		−	1.20784i	0.797044	−	0.603921i	$-0.206396\pi$
$864$		0			0
$865$		−	1755.62i		−	2.02962i
$866$	222.910	+	386.092i	0.257402	+	0.445833i
$867$		0			0
$868$	343.477	+	198.306i	0.395711	+	0.228464i
$869$	111.405	+	64.3197i	0.128199	+	0.0740158i
$870$		0			0
$871$	−1003.97	−	1738.92i	−1.15266	−	1.99646i
$872$	169.061			0.193877
$873$		0			0
$874$	449.986	−	2.80480i	0.514858	−	0.00320915i
$875$	2032.48	+	3520.35i	2.32283	+	4.02326i
$876$		0			0
$877$	375.107	+	216.568i	0.427716	+	0.246942i	0.698373	−	0.715734i	$-0.253908\pi$
$877$	375.107	+	216.568i	0.427716	+	0.246942i	−0.270657	+	0.962676i	$0.587241\pi$
$878$	−198.877	+	344.465i	−0.226511	+	0.392329i
$879$		0			0
$880$	−143.589	−	248.704i	−0.163169	−	0.282618i
$881$	−569.865			−0.646839			−0.323419	−	0.946256i	$-0.604832\pi$
$881$	−569.865			−0.646839			−0.323419	+	0.946256i	$0.604832\pi$
$882$		0			0
$883$	−1130.40			−1.28018			−0.640090	−	0.768300i	$-0.721103\pi$
$883$	−1130.40			−1.28018			−0.640090	+	0.768300i	$0.721103\pi$
$884$	661.789	−	382.084i	0.748630	−	0.432221i
$885$		0			0
$886$	204.205	+	117.898i	0.230480	+	0.133068i
$887$	582.034	+	336.037i	0.656182	+	0.378847i	0.790821	−	0.612048i	$-0.209654\pi$
$887$	582.034	+	336.037i	0.656182	+	0.378847i	−0.134638	+	0.990895i	$0.542987\pi$
$888$		0			0
$889$	26.8984	−	15.5298i	0.0302569	−	0.0174688i
$890$	−102.295			−0.114938
$891$		0			0
$892$		−	173.570i		−	0.194586i
$893$	338.591	−	198.310i	0.379161	−	0.222071i
$894$		0			0
$895$	1375.45	+	794.115i	1.53681	+	0.887279i
$896$	111.136	+	64.1643i	0.124035	+	0.0716119i
$897$		0			0
$898$	−207.936	−	360.156i	−0.231555	−	0.401065i
$899$	249.549			0.277585
$900$		0			0
$901$			165.333i			0.183499i
$902$	9.68876	+	16.7814i	0.0107414	+	0.0186047i
$903$		0			0
$904$	208.686	−	361.454i	0.230847	−	0.399839i
$905$	2243.48	+	1295.27i	2.47898	+	1.43124i
$906$		0			0
$907$	1299.82	−	750.453i	1.43310	−	0.827401i	0.435745	−	0.900070i	$-0.356485\pi$
$907$	1299.82	−	750.453i	1.43310	−	0.827401i	0.997356	+	0.0726693i	$0.0231517\pi$
$908$			175.895i			0.193717i
$909$		0			0
$910$	−2724.27			−2.99370
$911$	−1530.99	+	883.916i	−1.68056	+	0.970270i	−0.719267	+	0.694733i	$0.755522\pi$
$911$	−1530.99	+	883.916i	−1.68056	+	0.970270i	−0.961290	+	0.275537i	$0.911144\pi$
$912$		0			0
$913$	525.725	−	910.582i	0.575821	−	0.997352i
$914$	−819.074	−	472.893i	−0.896142	−	0.517388i
$915$		0			0
$916$	−201.143	−	348.390i	−0.219588	−	0.380338i
$917$	1439.81			1.57013
$918$		0			0
$919$	−423.196			−0.460496			−0.230248	−	0.973132i	$-0.573954\pi$
$919$	−423.196			−0.460496			−0.230248	+	0.973132i	$0.573954\pi$
$920$	−385.183	+	222.385i	−0.418677	+	0.241723i
$921$		0			0
$922$	188.557	+	108.864i	0.204509	+	0.118073i
$923$	−493.245	+	854.325i	−0.534393	+	0.925596i
$924$		0			0
$925$	−583.059	+	336.629i	−0.630334	+	0.363924i
$926$			205.212i			0.221611i
$927$		0			0
$928$	80.7443			0.0870089
$929$	−630.955	−	1092.85i	−0.679176	−	1.17637i	−0.975229	−	0.221196i	$-0.929004\pi$
$929$	−630.955	−	1092.85i	−0.679176	−	1.17637i	0.296053	−	0.955171i	$-0.404329\pi$
$930$		0			0
$931$	1315.42	+	748.566i	1.41291	+	0.804045i
$932$	−123.948	+	214.684i	−0.132992	+	0.230348i
$933$		0			0
$934$	180.684	−	104.318i	0.193452	−	0.111690i
$935$	−1516.65			−1.62209
$936$		0			0
$937$	−90.0561			−0.0961111			−0.0480555	−	0.998845i	$-0.515302\pi$
$937$	−90.0561			−0.0961111			−0.0480555	+	0.998845i	$0.515302\pi$
$938$	−890.406	−	1542.23i	−0.949260	−	1.64417i
$939$		0			0
$940$	−193.918	+	335.876i	−0.206296	+	0.357314i
$941$	−1039.21	−	599.990i	−1.10437	−	0.637609i	−0.167005	−	0.985956i	$-0.553410\pi$
$941$	−1039.21	−	599.990i	−1.10437	−	0.637609i	−0.937366	+	0.348347i	$0.886743\pi$
$942$		0			0
$943$	25.9904	−	15.0056i	0.0275614	−	0.0159126i
$944$		−	305.392i		−	0.323508i
$945$		0			0
$946$			361.930i			0.382590i
$947$	−681.001	−	1179.53i	−0.719114	−	1.24554i	−0.961351	−	0.275325i	$-0.911214\pi$
$947$	−681.001	−	1179.53i	−0.719114	−	1.24554i	0.242237	−	0.970217i	$-0.422119\pi$
$948$		0			0
$949$	1834.16	+	1058.95i	1.93272	+	1.11586i
$950$	839.468	−	1475.16i	0.883651	−	1.55280i
$951$		0			0
$952$	586.933	−	338.866i	0.616526	−	0.355951i
$953$		−	1125.78i		−	1.18130i	−0.806927	−	0.590651i	$-0.798871\pi$
$953$		−	1125.78i		−	1.18130i	0.806927	−	0.590651i	$-0.201129\pi$
$954$		0			0
$955$	2054.86			2.15168
$956$	−40.3662	−	69.9164i	−0.0422241	−	0.0731343i
$957$		0			0
$958$	610.579	+	352.518i	0.637348	+	0.367973i
$959$	281.631	−	487.800i	0.293672	−	0.508655i
$960$		0			0
$961$	−327.670	−	567.542i	−0.340968	−	0.590574i
$962$		−	272.629i		−	0.283399i
$963$		0			0
$964$			335.729i			0.348267i
$965$	−2996.50	+	1730.03i	−3.10518	+	1.79278i
$966$		0			0
$967$	−17.3355	+	30.0259i	−0.0179270	+	0.0310506i	−0.874850	−	0.484394i	$-0.839040\pi$
$967$	−17.3355	+	30.0259i	−0.0179270	+	0.0310506i	0.856923	+	0.515445i	$0.172373\pi$
$968$	153.185	+	88.4411i	0.158249	+	0.0913648i
$969$		0			0
$970$	775.744	+	1343.63i	0.799736	+	1.38518i
$971$			829.722i			0.854503i	0.904133	+	0.427251i	$0.140518\pi$
$971$			829.722i			0.854503i	−0.904133	+	0.427251i	$0.859482\pi$
$972$		0			0
$973$	−1996.50			−2.05190
$974$	311.091	+	538.826i	0.319395	+	0.553209i
$975$		0			0
$976$	−71.1532	+	123.241i	−0.0729029	+	0.126272i
$977$	320.514	+	185.049i	0.328059	+	0.189405i	0.654979	−	0.755647i	$-0.272677\pi$
$977$	320.514	+	185.049i	0.328059	+	0.189405i	−0.326920	+	0.945052i	$0.606011\pi$
$978$		0			0
$979$	−51.0100	+	29.4506i	−0.0521042	+	0.0300824i
$980$	−1495.93			−1.52646
$981$		0			0
$982$			296.783i			0.302223i
$983$	75.4062	−	43.5358i	0.0767103	−	0.0442887i	−0.461154	−	0.887320i	$-0.652565\pi$
$983$	75.4062	−	43.5358i	0.0767103	−	0.0442887i	0.537865	+	0.843031i	$0.319231\pi$
$984$		0			0
$985$	1156.15	−	2002.52i	1.17376	−	2.03301i
$986$	213.214	−	369.298i	0.216242	−	0.374541i
$987$		0			0
$988$	347.354	+	593.068i	0.351573	+	0.600271i
$989$	560.544			0.566779
$990$		0			0
$991$			615.381i			0.620970i	0.950578	+	0.310485i	$0.100491\pi$
$991$			615.381i			0.620970i	−0.950578	+	0.310485i	$0.899509\pi$
$992$	49.4497	+	85.6494i	0.0498485	+	0.0863401i
$993$		0			0
$994$	−437.453	+	757.691i	−0.440094	+	0.762265i
$995$	44.8468	−	77.6769i	0.0450721	−	0.0780672i
$996$		0			0
$997$	304.693	+	527.744i	0.305610	+	0.529332i	0.977397	−	0.211412i	$-0.0678062\pi$
$997$	304.693	+	527.744i	0.305610	+	0.529332i	−0.671787	+	0.740745i	$0.734473\pi$
$998$			590.692i			0.591876i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1026.3.l.a.37.6		80
3.2	odd	2		342.3.l.a.265.34	yes	80
9.2	odd	6		342.3.l.a.151.7	✓	80
9.7	even	3	inner	1026.3.l.a.721.25		80
19.18	odd	2	inner	1026.3.l.a.37.25		80
57.56	even	2		342.3.l.a.265.7	yes	80
171.56	even	6		342.3.l.a.151.34	yes	80
171.151	odd	6	inner	1026.3.l.a.721.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.3.l.a.151.7	✓	80	9.2	odd	6
342.3.l.a.151.34	yes	80	171.56	even	6
342.3.l.a.265.7	yes	80	57.56	even	2
342.3.l.a.265.34	yes	80	3.2	odd	2
1026.3.l.a.37.6		80	1.1	even	1	trivial
1026.3.l.a.37.25		80	19.18	odd	2	inner
1026.3.l.a.721.6		80	171.151	odd	6	inner
1026.3.l.a.721.25		80	9.7	even	3	inner

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:	\( N \)	\(=\)	\( 1026 = 2 \cdot 3^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1026.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.69486 + 8.13173i) q^{5} +(5.67137 + 9.82311i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 + 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(-4.69486 + 8.13173i) q^{5} +(5.67137 + 9.82311i) q^{7} +2.82843i q^{8} -13.2791i q^{10} +(-3.82304 - 6.62171i) q^{11} +(-15.6637 - 9.04345i) q^{13} +(-13.8920 - 8.02053i) q^{14} +(-2.00000 - 3.46410i) q^{16} -21.1249 q^{17} +(-0.118426 - 18.9996i) q^{19} +(9.38971 + 16.2635i) q^{20} +(9.36451 + 5.40660i) q^{22} +(8.37354 - 14.5034i) q^{23} +(-31.5834 - 54.7040i) q^{25} +25.5787 q^{26} +22.6855 q^{28} +(12.3614 - 7.13685i) q^{29} +(15.1408 + 8.74155i) q^{31} +(4.89898 + 2.82843i) q^{32} +(25.8726 - 14.9376i) q^{34} -106.505 q^{35} -10.6584i q^{37} +(13.5798 + 23.1860i) q^{38} +(-23.0000 - 13.2791i) q^{40} +(1.55194 + 0.896012i) q^{41} +(16.7356 + 28.9869i) q^{43} -15.2922 q^{44} +23.6839i q^{46} +(10.3261 + 17.8853i) q^{47} +(-39.8290 + 68.9858i) q^{49} +(77.3631 + 44.6656i) q^{50} +(-31.3274 + 18.0869i) q^{52} -7.82643i q^{53} +71.7946 q^{55} +(-27.7839 + 16.0411i) q^{56} +(-10.0930 + 17.4816i) q^{58} +(66.1193 + 38.1740i) q^{59} +(-17.7883 - 30.8102i) q^{61} -24.7248 q^{62} -8.00000 q^{64} +(147.078 - 84.9154i) q^{65} +(96.1425 + 55.5079i) q^{67} +(-21.1249 + 36.5894i) q^{68} +(130.442 - 75.3105i) q^{70} -54.5417i q^{71} -117.096 q^{73} +(7.53666 + 13.0539i) q^{74} +(-33.0268 - 18.7945i) q^{76} +(43.3638 - 75.1084i) q^{77} +(-14.5702 + 8.41210i) q^{79} +37.5589 q^{80} -2.53430 q^{82} +(68.7574 + 119.091i) q^{83} +(99.1783 - 171.782i) q^{85} +(-40.9936 - 23.6677i) q^{86} +(18.7290 - 10.8132i) q^{88} -7.70345i q^{89} -205.155i q^{91} +(-16.7471 - 29.0068i) q^{92} +(-25.2936 - 14.6033i) q^{94} +(155.056 + 88.2375i) q^{95} +(-101.184 + 58.4186i) q^{97} -112.653i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 80 q^{4} - 4 q^{7}+O(q^{10}) \) 80 * q + 80 * q^4 - 4 * q^7	\( 80 q + 80 q^{4} - 4 q^{7} - 12 q^{11} - 160 q^{16} - 96 q^{17} + 40 q^{19} + 48 q^{23} - 200 q^{25} - 16 q^{28} - 432 q^{35} - 24 q^{38} + 28 q^{43} - 48 q^{44} - 240 q^{47} - 228 q^{49} - 28 q^{61} + 144 q^{62} - 640 q^{64} - 96 q^{68} - 368 q^{73} + 24 q^{74} + 40 q^{76} + 456 q^{77} - 192 q^{82} + 84 q^{83} - 96 q^{92} + 324 q^{95}+O(q^{100}) \) 80 * q + 80 * q^4 - 4 * q^7 - 12 * q^11 - 160 * q^16 - 96 * q^17 + 40 * q^19 + 48 * q^23 - 200 * q^25 - 16 * q^28 - 432 * q^35 - 24 * q^38 + 28 * q^43 - 48 * q^44 - 240 * q^47 - 228 * q^49 - 28 * q^61 + 144 * q^62 - 640 * q^64 - 96 * q^68 - 368 * q^73 + 24 * q^74 + 40 * q^76 + 456 * q^77 - 192 * q^82 + 84 * q^83 - 96 * q^92 + 324 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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