LMFDB - Embedded newform 891.2.f.e.487.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(82,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("891.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.f (of order $5$, degree $4$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			487.8
Character	$\chi$	$=$	891.487
Dual form			891.2.f.e.730.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25085 - 0.908796i) q^{2} +(0.120683 - 0.371424i) q^{4} +(0.478964 + 0.347988i) q^{5} +(0.223095 - 0.686616i) q^{7} +(0.768973 + 2.36665i) q^{8} +0.915362 q^{10} +(0.539627 - 3.27243i) q^{11} +(1.27417 - 0.925741i) q^{13} +(-0.344935 - 1.06160i) q^{14} +(3.74458 + 2.72060i) q^{16} +(3.71501 + 2.69911i) q^{17} +(0.775200 + 2.38582i) q^{19} +(0.187054 - 0.135902i) q^{20} +(-2.29898 - 4.58373i) q^{22} +4.45200 q^{23} +(-1.43677 - 4.42194i) q^{25} +(0.752490 - 2.31593i) q^{26} +(-0.228102 - 0.165726i) q^{28} +(-2.15651 + 6.63706i) q^{29} +(7.38490 - 5.36545i) q^{31} +2.17948 q^{32} +7.09986 q^{34} +(0.345788 - 0.251230i) q^{35} +(0.893583 - 2.75017i) q^{37} +(3.13788 + 2.27981i) q^{38} +(-0.455256 + 1.40114i) q^{40} +(0.356643 + 1.09763i) q^{41} -4.21448 q^{43} +(-1.15033 - 0.595357i) q^{44} +(5.56879 - 4.04596i) q^{46} +(0.0703185 + 0.216418i) q^{47} +(5.24145 + 3.80814i) q^{49} +(-5.81583 - 4.22545i) q^{50} +(-0.190071 - 0.584979i) q^{52} +(-4.61430 + 3.35249i) q^{53} +(1.39723 - 1.37959i) q^{55} +1.79654 q^{56} +(3.33426 + 10.2618i) q^{58} +(-2.20439 + 6.78441i) q^{59} +(-3.68827 - 2.67969i) q^{61} +(4.36131 - 13.4227i) q^{62} +(-4.76295 + 3.46049i) q^{64} +0.932429 q^{65} -8.09142 q^{67} +(1.45085 - 1.05411i) q^{68} +(0.204213 - 0.628502i) q^{70} +(-9.95852 - 7.23528i) q^{71} +(4.78461 - 14.7255i) q^{73} +(-1.38160 - 4.25213i) q^{74} +0.979704 q^{76} +(-2.12651 - 1.10058i) q^{77} +(11.8275 - 8.59316i) q^{79} +(0.846785 + 2.60614i) q^{80} +(1.44363 + 1.04886i) q^{82} +(-5.62510 - 4.08687i) q^{83} +(0.840097 + 2.58555i) q^{85} +(-5.27169 + 3.83010i) q^{86} +(8.15967 - 1.23930i) q^{88} -12.4803 q^{89} +(-0.351367 - 1.08140i) q^{91} +(0.537280 - 1.65358i) q^{92} +(0.284638 + 0.206802i) q^{94} +(-0.458943 + 1.41248i) q^{95} +(-11.4722 + 8.33507i) q^{97} +10.0171 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) $ 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	1.25085	−	0.908796i	0.884485	−	0.642616i	−0.0499492	−	0.998752i	$-0.515906\pi$
$2$	1.25085	−	0.908796i	0.884485	−	0.642616i	0.934434	+	0.356136i	$0.115906\pi$
$3$		0			0
$3$		0			0
$4$	0.120683	−	0.371424i	0.0603415	−	0.185712i
$5$	0.478964	+	0.347988i	0.214199	+	0.155625i	0.689712	−	0.724084i	$-0.257737\pi$
$5$	0.478964	+	0.347988i	0.214199	+	0.155625i	−0.475512	+	0.879709i	$0.657737\pi$
$6$		0			0
$7$	0.223095	−	0.686616i	0.0843220	−	0.259516i	−0.900002	−	0.435886i	$-0.856435\pi$
$7$	0.223095	−	0.686616i	0.0843220	−	0.259516i	0.984324	+	0.176369i	$0.0564353\pi$
$8$	0.768973	+	2.36665i	0.271873	+	0.836739i
$9$		0			0
$10$	0.915362			0.289463
$11$	0.539627	−	3.27243i	0.162704	−	0.986675i
$11$	0.539627	−	3.27243i	0.162704	−	0.986675i
$12$		0			0
$13$	1.27417	−	0.925741i	0.353392	−	0.256754i	−0.396899	−	0.917862i	$-0.629914\pi$
$13$	1.27417	−	0.925741i	0.353392	−	0.256754i	0.750291	+	0.661108i	$0.229914\pi$
$14$	−0.344935	−	1.06160i	−0.0921878	−	0.283725i
$15$		0			0
$16$	3.74458	+	2.72060i	0.936145	+	0.680149i
$17$	3.71501	+	2.69911i	0.901022	+	0.654631i	0.938728	−	0.344658i	$-0.112005\pi$
$17$	3.71501	+	2.69911i	0.901022	+	0.654631i	−0.0377065	+	0.999289i	$0.512005\pi$
$18$		0			0
$19$	0.775200	+	2.38582i	0.177843	+	0.547345i	0.999752	−	0.0222743i	$-0.00709072\pi$
$19$	0.775200	+	2.38582i	0.177843	+	0.547345i	−0.821909	+	0.569619i	$0.807091\pi$
$20$	0.187054	−	0.135902i	0.0418265	−	0.0303887i
$21$		0			0
$22$	−2.29898	−	4.58373i	−0.490144	−	0.977255i
$23$	4.45200			0.928306			0.464153	−	0.885755i	$-0.346359\pi$
$23$	4.45200			0.928306			0.464153	+	0.885755i	$0.346359\pi$
$24$		0			0
$25$	−1.43677	−	4.42194i	−0.287355	−	0.884387i
$26$	0.752490	−	2.31593i	0.147576	−	0.454191i
$27$		0			0
$28$	−0.228102	−	0.165726i	−0.0431072	−	0.0313192i
$29$	−2.15651	+	6.63706i	−0.400454	+	1.23247i	0.524177	+	0.851609i	$0.324373\pi$
$29$	−2.15651	+	6.63706i	−0.400454	+	1.23247i	−0.924632	+	0.380863i	$0.875627\pi$
$30$		0			0
$31$	7.38490	−	5.36545i	1.32637	−	0.963662i	0.326538	−	0.945184i	$-0.394118\pi$
$31$	7.38490	−	5.36545i	1.32637	−	0.963662i	0.999829	−	0.0184785i	$-0.00588222\pi$
$32$	2.17948			0.385282
$33$		0			0
$34$	7.09986			1.21762
$35$	0.345788	−	0.251230i	0.0584489	−	0.0424656i
$36$		0			0
$37$	0.893583	−	2.75017i	0.146904	−	0.452125i	−0.850347	−	0.526223i	$-0.823608\pi$
$37$	0.893583	−	2.75017i	0.146904	−	0.452125i	0.997251	+	0.0740981i	$0.0236078\pi$
$38$	3.13788	+	2.27981i	0.509032	+	0.369833i
$39$		0			0
$40$	−0.455256	+	1.40114i	−0.0719824	+	0.221539i
$41$	0.356643	+	1.09763i	0.0556982	+	0.171421i	0.975036	−	0.222049i	$-0.0712744\pi$
$41$	0.356643	+	1.09763i	0.0556982	+	0.171421i	−0.919337	+	0.393470i	$0.871274\pi$
$42$		0			0
$43$	−4.21448			−0.642702			−0.321351	−	0.946960i	$-0.604137\pi$
$43$	−4.21448			−0.642702			−0.321351	+	0.946960i	$0.604137\pi$
$44$	−1.15033	−	0.595357i	−0.173419	−	0.0897534i
$45$		0			0
$46$	5.56879	−	4.04596i	0.821073	−	0.596544i
$47$	0.0703185	+	0.216418i	0.0102570	+	0.0315678i	0.956054	−	0.293191i	$-0.0947170\pi$
$47$	0.0703185	+	0.216418i	0.0102570	+	0.0315678i	−0.945797	+	0.324758i	$0.894717\pi$
$48$		0			0
$49$	5.24145	+	3.80814i	0.748778	+	0.544019i
$50$	−5.81583	−	4.22545i	−0.822482	−	0.597568i
$51$		0			0
$52$	−0.190071	−	0.584979i	−0.0263581	−	0.0811220i
$53$	−4.61430	+	3.35249i	−0.633823	+	0.460500i	−0.857723	−	0.514113i	$-0.828121\pi$
$53$	−4.61430	+	3.35249i	−0.633823	+	0.460500i	0.223899	+	0.974612i	$0.428121\pi$
$54$		0			0
$55$	1.39723	−	1.37959i	0.188402	−	0.186024i
$56$	1.79654			0.240072
$57$		0			0
$58$	3.33426	+	10.2618i	0.437810	+	1.34744i
$59$	−2.20439	+	6.78441i	−0.286987	+	0.883255i	0.698809	+	0.715308i	$0.253714\pi$
$59$	−2.20439	+	6.78441i	−0.286987	+	0.883255i	−0.985796	+	0.167947i	$0.946286\pi$
$60$		0			0
$61$	−3.68827	−	2.67969i	−0.472235	−	0.343099i	0.326077	−	0.945343i	$-0.394273\pi$
$61$	−3.68827	−	2.67969i	−0.472235	−	0.343099i	−0.798312	+	0.602244i	$0.794273\pi$
$62$	4.36131	−	13.4227i	0.553887	−	1.70469i
$63$		0			0
$64$	−4.76295	+	3.46049i	−0.595369	+	0.432561i
$65$	0.932429			0.115654
$66$		0			0
$67$	−8.09142			−0.988524			−0.494262	−	0.869313i	$-0.664562\pi$
$67$	−8.09142			−0.988524			−0.494262	+	0.869313i	$0.664562\pi$
$68$	1.45085	−	1.05411i	0.175942	−	0.127829i
$69$		0			0
$70$	0.204213	−	0.628502i	0.0244081	−	0.0751204i
$71$	−9.95852	−	7.23528i	−1.18186	−	0.858670i	−0.189478	−	0.981885i	$-0.560680\pi$
$71$	−9.95852	−	7.23528i	−1.18186	−	0.858670i	−0.992380	+	0.123215i	$0.960680\pi$
$72$		0			0
$73$	4.78461	−	14.7255i	0.559996	−	1.72349i	−0.122373	−	0.992484i	$-0.539050\pi$
$73$	4.78461	−	14.7255i	0.559996	−	1.72349i	0.682370	−	0.731007i	$-0.260950\pi$
$74$	−1.38160	−	4.25213i	−0.160608	−	0.494300i
$75$		0			0
$76$	0.979704			0.112380
$77$	−2.12651	−	1.10058i	−0.242339	−	0.125423i
$78$		0			0
$79$	11.8275	−	8.59316i	1.33069	−	0.966806i	0.330962	−	0.943644i	$-0.392627\pi$
$79$	11.8275	−	8.59316i	1.33069	−	0.966806i	0.999732	−	0.0231619i	$-0.00737332\pi$
$80$	0.846785	+	2.60614i	0.0946734	+	0.291375i
$81$		0			0
$82$	1.44363	+	1.04886i	0.159422	+	0.115827i
$83$	−5.62510	−	4.08687i	−0.617435	−	0.448593i	0.234590	−	0.972094i	$-0.424625\pi$
$83$	−5.62510	−	4.08687i	−0.617435	−	0.448593i	−0.852024	+	0.523502i	$0.824625\pi$
$84$		0			0
$85$	0.840097	+	2.58555i	0.0911214	+	0.280443i
$86$	−5.27169	+	3.83010i	−0.568461	+	0.413011i
$87$		0			0
$88$	8.15967	−	1.23930i	0.869824	−	0.132110i
$89$	−12.4803			−1.32291			−0.661453	−	0.749986i	$-0.730060\pi$
$89$	−12.4803			−1.32291			−0.661453	+	0.749986i	$0.730060\pi$
$90$		0			0
$91$	−0.351367	−	1.08140i	−0.0368332	−	0.113361i
$92$	0.537280	−	1.65358i	0.0560153	−	0.172397i
$93$		0			0
$94$	0.284638	+	0.206802i	0.0293582	+	0.0213300i
$95$	−0.458943	+	1.41248i	−0.0470866	+	0.144918i
$96$		0			0
$97$	−11.4722	+	8.33507i	−1.16483	+	0.846298i	−0.990381	−	0.138368i	$-0.955814\pi$
$97$	−11.4722	+	8.33507i	−1.16483	+	0.846298i	−0.174449	+	0.984666i	$0.555814\pi$
$98$	10.0171			1.01188
$99$		0			0
$100$	−1.81581			−0.181581
$101$	−11.6244	+	8.44561i	−1.15667	+	0.840370i	−0.989353	−	0.145533i	$-0.953510\pi$
$101$	−11.6244	+	8.44561i	−1.15667	+	0.840370i	−0.167317	+	0.985903i	$0.553510\pi$
$102$		0			0
$103$	−1.36859	+	4.21209i	−0.134851	+	0.415029i	−0.995567	−	0.0940566i	$-0.970017\pi$
$103$	−1.36859	+	4.21209i	−0.134851	+	0.415029i	0.860716	+	0.509086i	$0.170017\pi$
$104$	3.17071	+	2.30366i	0.310914	+	0.225892i
$105$		0			0
$106$	−2.72508	+	8.38693i	−0.264683	+	0.814610i
$107$	4.86529	+	14.9738i	0.470345	+	1.44757i	0.852134	+	0.523324i	$0.175308\pi$
$107$	4.86529	+	14.9738i	0.470345	+	1.44757i	−0.381788	+	0.924250i	$0.624692\pi$
$108$		0			0
$109$	−13.6970			−1.31194			−0.655969	−	0.754788i	$-0.727740\pi$
$109$	−13.6970			−1.31194			−0.655969	+	0.754788i	$0.727740\pi$
$110$	0.493954	−	2.99546i	0.0470967	−	0.285606i
$111$		0			0
$112$	2.70340	−	1.96414i	0.255447	−	0.185593i
$113$	−2.48145	−	7.63711i	−0.233435	−	0.718439i	−0.997325	−	0.0730926i	$-0.976713\pi$
$113$	−2.48145	−	7.63711i	−0.233435	−	0.718439i	0.763890	−	0.645346i	$-0.223287\pi$
$114$		0			0
$115$	2.13235	+	1.54924i	0.198842	+	0.144467i
$116$	2.20491	+	1.60196i	0.204721	+	0.148738i
$117$		0			0
$118$	3.40829	+	10.4896i	0.313758	+	0.965648i
$119$	2.68205	−	1.94862i	0.245863	−	0.178630i
$120$		0			0
$121$	−10.4176	−	3.53178i	−0.947055	−	0.321071i
$122$	−7.04877			−0.638166
$123$		0			0
$124$	−1.10162	−	3.39045i	−0.0989286	−	0.304471i
$125$	1.76536	−	5.43321i	0.157898	−	0.485961i
$126$		0			0
$127$	9.70522	+	7.05126i	0.861199	+	0.625698i	0.928211	−	0.372054i	$-0.121347\pi$
$127$	9.70522	+	7.05126i	0.861199	+	0.625698i	−0.0670118	+	0.997752i	$0.521347\pi$
$128$	−4.15986	+	12.8027i	−0.367683	+	1.13161i
$129$		0			0
$130$	1.16633	−	0.847388i	0.102294	−	0.0743209i
$131$	6.89109			0.602077			0.301039	−	0.953612i	$-0.402667\pi$
$131$	6.89109			0.602077			0.301039	+	0.953612i	$0.402667\pi$
$132$		0			0
$133$	1.81109			0.157041
$134$	−10.1212	+	7.35345i	−0.874335	+	0.635242i
$135$		0			0
$136$	−3.53112	+	10.8677i	−0.302791	+	0.931896i
$137$	7.48062	+	5.43499i	0.639112	+	0.464342i	0.859545	−	0.511060i	$-0.170747\pi$
$137$	7.48062	+	5.43499i	0.639112	+	0.464342i	−0.220433	+	0.975402i	$0.570747\pi$
$138$		0			0
$139$	6.67826	−	20.5536i	0.566442	−	1.74333i	−0.0971841	−	0.995266i	$-0.530984\pi$
$139$	6.67826	−	20.5536i	0.566442	−	1.74333i	0.663627	−	0.748064i	$-0.269016\pi$
$140$	−0.0515820	−	0.158753i	−0.00435948	−	0.0134171i
$141$		0			0
$142$	−19.0320			−1.59713
$143$	−2.34184	−	4.66920i	−0.195835	−	0.390458i
$144$		0			0
$145$	−3.34251	+	2.42847i	−0.277580	+	0.201674i
$146$	−7.39766	−	22.7677i	−0.612235	−	1.88426i
$147$		0			0
$148$	−0.913637	−	0.663796i	−0.0751005	−	0.0545637i
$149$	−0.927483	−	0.673856i	−0.0759824	−	0.0552044i	0.549146	−	0.835727i	$-0.314953\pi$
$149$	−0.927483	−	0.673856i	−0.0759824	−	0.0552044i	−0.625128	+	0.780522i	$0.714953\pi$
$150$		0			0
$151$	0.272133	+	0.837539i	0.0221459	+	0.0681579i	0.961519	−	0.274740i	$-0.0885916\pi$
$151$	0.272133	+	0.837539i	0.0221459	+	0.0681579i	−0.939373	+	0.342898i	$0.888592\pi$
$152$	−5.05031	+	3.66926i	−0.409634	+	0.297616i
$153$		0			0
$154$	−3.66015	+	0.555908i	−0.294944	+	0.0447963i
$155$	5.40421			0.434077
$156$		0			0
$157$	−3.02411	−	9.30724i	−0.241350	−	0.742799i	−0.996215	−	0.0869191i	$-0.972298\pi$
$157$	−3.02411	−	9.30724i	−0.241350	−	0.742799i	0.754865	−	0.655880i	$-0.227702\pi$
$158$	6.98497	−	21.4975i	0.555694	−	1.71025i
$159$		0			0
$160$	1.04389	+	0.758434i	0.0825271	+	0.0599594i
$161$	0.993219	−	3.05681i	0.0782766	−	0.240911i
$162$		0			0
$163$	−3.74555	+	2.72130i	−0.293374	+	0.213149i	−0.724730	−	0.689033i	$-0.758035\pi$
$163$	−3.74555	+	2.72130i	−0.293374	+	0.213149i	0.431355	+	0.902182i	$0.358035\pi$
$164$	0.450728			0.0351959
$165$		0			0
$166$	−10.7503			−0.834384
$167$	−13.7431	+	9.98493i	−1.06347	+	0.772657i	−0.974727	−	0.223397i	$-0.928285\pi$
$167$	−13.7431	+	9.98493i	−1.06347	+	0.772657i	−0.0887440	+	0.996054i	$0.528285\pi$
$168$		0			0
$169$	−3.25070	+	10.0046i	−0.250054	+	0.769587i
$170$	3.40058	+	2.47066i	0.260812	+	0.189491i
$171$		0			0
$172$	−0.508616	+	1.56536i	−0.0387816	+	0.119357i
$173$	0.182646	+	0.562127i	0.0138863	+	0.0427378i	0.957760	−	0.287570i	$-0.0928474\pi$
$173$	0.182646	+	0.562127i	0.0138863	+	0.0427378i	−0.943873	+	0.330308i	$0.892847\pi$
$174$		0			0
$175$	−3.35671			−0.253743
$176$	10.9236	−	10.7858i	0.823401	−	0.813008i
$177$		0			0
$178$	−15.6110	+	11.3420i	−1.17009	+	0.850121i
$179$	2.97921	+	9.16907i	0.222677	+	0.685328i	0.998519	+	0.0544017i	$0.0173251\pi$
$179$	2.97921	+	9.16907i	0.222677	+	0.685328i	−0.775842	+	0.630927i	$0.782675\pi$
$180$		0			0
$181$	3.85243	+	2.79896i	0.286349	+	0.208045i	0.721682	−	0.692225i	$-0.243369\pi$
$181$	3.85243	+	2.79896i	0.286349	+	0.208045i	−0.435333	+	0.900270i	$0.643369\pi$
$182$	−1.42228	−	1.03334i	−0.105426	−	0.0765965i
$183$		0			0
$184$	3.42347	+	10.5363i	0.252381	+	0.776750i
$185$	1.38502	−	1.00627i	0.101829	−	0.0739828i
$186$		0			0
$187$	10.8374	−	10.7006i	0.792507	−	0.782505i
$188$	0.0888691			0.00648144
$189$		0			0
$190$	0.709589	+	2.18389i	0.0514790	+	0.158436i
$191$	1.60628	−	4.94362i	0.116226	−	0.357707i	−0.875975	−	0.482357i	$-0.839781\pi$
$191$	1.60628	−	4.94362i	0.116226	−	0.357707i	0.992201	+	0.124650i	$0.0397807\pi$
$192$		0			0
$193$	−2.64390	−	1.92091i	−0.190312	−	0.138270i	0.488549	−	0.872536i	$-0.337526\pi$
$193$	−2.64390	−	1.92091i	−0.190312	−	0.138270i	−0.678861	+	0.734266i	$0.737526\pi$
$194$	−6.77518	+	20.8519i	−0.486430	+	1.49708i
$195$		0			0
$196$	2.04699	−	1.48722i	0.146213	−	0.106230i
$197$	22.4626			1.60039			0.800197	−	0.599737i	$-0.204728\pi$
$197$	22.4626			1.60039			0.800197	+	0.599737i	$0.204728\pi$
$198$		0			0
$199$	−20.8291			−1.47654			−0.738269	−	0.674507i	$-0.764356\pi$
$199$	−20.8291			−1.47654			−0.738269	+	0.674507i	$0.764356\pi$
$200$	9.36035	−	6.80070i	0.661877	−	0.480882i
$201$		0			0
$202$	−6.86504	+	21.1284i	−0.483022	+	1.48659i
$203$	4.07600	+	2.96139i	0.286079	+	0.207849i
$204$		0			0
$205$	−0.211144	+	0.649834i	−0.0147469	+	0.0453864i
$206$	2.11603	+	6.51246i	0.147431	+	0.453745i
$207$		0			0
$208$	7.28981			0.505457
$209$	8.22575	−	1.24934i	0.568987	−	0.0864183i
$210$		0			0
$211$	−2.74420	+	1.99378i	−0.188919	+	0.137258i	−0.678224	−	0.734855i	$-0.737250\pi$
$211$	−2.74420	+	1.99378i	−0.188919	+	0.137258i	0.489306	+	0.872112i	$0.337250\pi$
$212$	0.688326	+	2.11845i	0.0472744	+	0.145496i
$213$		0			0
$214$	19.6939	+	14.3085i	1.34625	+	0.978106i
$215$	−2.01858	−	1.46659i	−0.137666	−	0.100020i
$216$		0			0
$217$	−2.03646	−	6.26759i	−0.138244	−	0.425472i
$218$	−17.1329	+	12.4478i	−1.16039	+	0.843072i
$219$		0			0
$220$	−0.343792	−	0.685457i	−0.0231785	−	0.0462135i
$221$	7.23224			0.486493
$222$		0			0
$223$	−3.40734	−	10.4867i	−0.228172	−	0.702243i	−0.997954	−	0.0639353i	$-0.979635\pi$
$223$	−3.40734	−	10.4867i	−0.228172	−	0.702243i	0.769782	−	0.638307i	$-0.220365\pi$
$224$	0.486232	−	1.49647i	0.0324877	−	0.0999870i
$225$		0			0
$226$	−10.0445	−	7.29775i	−0.668150	−	0.485439i
$227$	1.84387	−	5.67485i	0.122382	−	0.376653i	−0.871033	−	0.491224i	$-0.836549\pi$
$227$	1.84387	−	5.67485i	0.122382	−	0.376653i	0.993415	+	0.114571i	$0.0365495\pi$
$228$		0			0
$229$	−20.0237	+	14.5481i	−1.32320	+	0.961364i	−0.323318	+	0.946290i	$0.604798\pi$
$229$	−20.0237	+	14.5481i	−1.32320	+	0.961364i	−0.999886	+	0.0150739i	$0.995202\pi$
$230$	4.07519			0.268710
$231$		0			0
$232$	−17.3659			−1.14013
$233$	3.38850	−	2.46189i	0.221988	−	0.161284i	−0.471233	−	0.882009i	$-0.656191\pi$
$233$	3.38850	−	2.46189i	0.221988	−	0.161284i	0.693221	+	0.720725i	$0.256191\pi$
$234$		0			0
$235$	−0.0416308	+	0.128126i	−0.00271569	+	0.00835805i
$236$	2.25386	+	1.63753i	0.146714	+	0.106594i
$237$		0			0
$238$	1.58394	−	4.87488i	0.102672	−	0.315991i
$239$	2.27833	+	7.01199i	0.147373	+	0.453568i	0.997309	−	0.0733190i	$-0.0233591\pi$
$239$	2.27833	+	7.01199i	0.147373	+	0.453568i	−0.849935	+	0.526887i	$0.823359\pi$
$240$		0			0
$241$	−8.82924			−0.568741			−0.284371	−	0.958714i	$-0.591785\pi$
$241$	−8.82924			−0.568741			−0.284371	+	0.958714i	$0.591785\pi$
$242$	−16.2405	+	5.04975i	−1.04398	+	0.324610i
$243$		0			0
$244$	−1.44041	+	1.04652i	−0.0922129	+	0.0669966i
$245$	1.18528	+	3.64792i	0.0757248	+	0.233057i
$246$		0			0
$247$	3.19639	+	2.32231i	0.203381	+	0.147765i
$248$	18.3769	+	13.3516i	1.16694	+	0.847829i
$249$		0			0
$250$	−2.72948	−	8.40048i	−0.172628	−	0.531293i
$251$	16.6439	−	12.0925i	1.05056	−	0.763274i	0.0782385	−	0.996935i	$-0.475070\pi$
$251$	16.6439	−	12.0925i	1.05056	−	0.763274i	0.972318	+	0.233661i	$0.0750704\pi$
$252$		0			0
$253$	2.40242	−	14.5689i	0.151039	−	0.915936i
$254$	18.5479			1.16380
$255$		0			0
$256$	2.79314	+	8.59640i	0.174571	+	0.537275i
$257$	1.04521	−	3.21684i	0.0651987	−	0.200661i	−0.913150	−	0.407623i	$-0.866358\pi$
$257$	1.04521	−	3.21684i	0.0651987	−	0.200661i	0.978349	+	0.206962i	$0.0663577\pi$
$258$		0			0
$259$	−1.68895	−	1.22710i	−0.104946	−	0.0762481i
$260$	0.112528	−	0.346326i	0.00697871	−	0.0214783i
$261$		0			0
$262$	8.61973	−	6.26260i	0.532528	−	0.386905i
$263$	14.2822			0.880681			0.440341	−	0.897831i	$-0.354858\pi$
$263$	14.2822			0.880681			0.440341	+	0.897831i	$0.354858\pi$
$264$		0			0
$265$	−3.37671			−0.207430
$266$	2.26540	−	1.64591i	0.138900	−	0.100917i
$267$		0			0
$268$	−0.976496	+	3.00535i	−0.0596490	+	0.183581i
$269$	5.43693	+	3.95016i	0.331495	+	0.240845i	0.741065	−	0.671433i	$-0.234321\pi$
$269$	5.43693	+	3.95016i	0.331495	+	0.240845i	−0.409570	+	0.912279i	$0.634321\pi$
$270$		0			0
$271$	−1.23000	+	3.78554i	−0.0747170	+	0.229955i	−0.981439	−	0.191773i	$-0.938576\pi$
$271$	−1.23000	+	3.78554i	−0.0747170	+	0.229955i	0.906722	+	0.421728i	$0.138576\pi$
$272$	6.56795	+	20.2141i	0.398241	+	1.22566i
$273$		0			0
$274$	14.2964			0.863679
$275$	−15.2458	+	2.31555i	−0.919356	+	0.139633i
$276$		0			0
$277$	10.6240	−	7.71880i	0.638335	−	0.463778i	−0.220943	−	0.975287i	$-0.570913\pi$
$277$	10.6240	−	7.71880i	0.638335	−	0.463778i	0.859278	+	0.511509i	$0.170913\pi$
$278$	−10.3255	−	31.7786i	−0.619282	−	1.90595i
$279$		0			0
$280$	0.860476	+	0.625172i	0.0514233	+	0.0373612i
$281$	−2.40106	−	1.74447i	−0.143235	−	0.104066i	0.513860	−	0.857874i	$-0.328215\pi$
$281$	−2.40106	−	1.74447i	−0.143235	−	0.104066i	−0.657095	+	0.753808i	$0.728215\pi$
$282$		0			0
$283$	2.50081	+	7.69669i	0.148657	+	0.457521i	0.997463	−	0.0711843i	$-0.0226778\pi$
$283$	2.50081	+	7.69669i	0.148657	+	0.457521i	−0.848806	+	0.528705i	$0.822678\pi$
$284$	−3.88918	+	2.82565i	−0.230780	+	0.167672i
$285$		0			0
$286$	−7.17265	−	3.71221i	−0.424128	−	0.219508i
$287$	0.833217			0.0491833
$288$		0			0
$289$	1.26279	+	3.88648i	0.0742820	+	0.228616i
$290$	−1.97399	+	6.07532i	−0.115917	+	0.356755i
$291$		0			0
$292$	−4.89199	−	3.55424i	−0.286282	−	0.207996i
$293$	4.85638	−	14.9464i	0.283713	−	0.873178i	−0.703069	−	0.711122i	$-0.748187\pi$
$293$	4.85638	−	14.9464i	0.283713	−	0.873178i	0.986782	−	0.162056i	$-0.0518126\pi$
$294$		0			0
$295$	−3.41671	+	2.48239i	−0.198929	+	0.144530i
$296$	7.19584			0.418249
$297$		0			0
$298$	−1.77254			−0.102681
$299$	5.67262	−	4.12140i	0.328056	−	0.238347i
$300$		0			0
$301$	−0.940229	+	2.89373i	−0.0541939	+	0.166792i
$302$	1.10155	+	0.800323i	0.0633871	+	0.0460534i
$303$		0			0
$304$	−3.58806	+	11.0429i	−0.205789	+	0.633354i
$305$	−0.834052	−	2.56695i	−0.0477577	−	0.146983i
$306$		0			0
$307$	−3.51315			−0.200506			−0.100253	−	0.994962i	$-0.531965\pi$
$307$	−3.51315			−0.200506			−0.100253	+	0.994962i	$0.531965\pi$
$308$	−0.665415	+	0.657017i	−0.0379156	+	0.0374370i
$309$		0			0
$310$	6.75986	−	4.91133i	0.383934	−	0.278945i
$311$	−8.13778	−	25.0455i	−0.461451	−	1.42020i	−0.863391	−	0.504535i	$-0.831664\pi$
$311$	−8.13778	−	25.0455i	−0.461451	−	1.42020i	0.401940	−	0.915666i	$-0.368336\pi$
$312$		0			0
$313$	1.99111	+	1.44662i	0.112544	+	0.0817679i	0.642634	−	0.766174i	$-0.277842\pi$
$313$	1.99111	+	1.44662i	0.112544	+	0.0817679i	−0.530090	+	0.847942i	$0.677842\pi$
$314$	−12.2411	−	8.89367i	−0.690805	−	0.501899i
$315$		0			0
$316$	−1.76433	−	5.43005i	−0.0992513	−	0.305464i
$317$	−21.4447	+	15.5805i	−1.20446	+	0.875089i	−0.994716	−	0.102669i	$-0.967262\pi$
$317$	−21.4447	+	15.5805i	−1.20446	+	0.875089i	−0.209740	+	0.977757i	$0.567262\pi$
$318$		0			0
$319$	20.5556	+	10.6386i	1.15089	+	0.595646i
$320$	−3.48549			−0.194845
$321$		0			0
$322$	−1.53565	−	4.72625i	−0.0855785	−	0.263384i
$323$	−3.55972	+	10.9557i	−0.198068	+	0.609591i
$324$		0			0
$325$	−5.92427	−	4.30423i	−0.328619	−	0.238756i
$326$	−2.21202	+	6.80789i	−0.122512	+	0.377054i
$327$		0			0
$328$	−2.32347	+	1.68810i	−0.128292	+	0.0932097i
$329$	0.164284			0.00905726
$330$		0			0
$331$	8.10397			0.445434			0.222717	−	0.974883i	$-0.428507\pi$
$331$	8.10397			0.445434			0.222717	+	0.974883i	$0.428507\pi$
$332$	−2.19681	+	1.59608i	−0.120566	+	0.0875962i
$333$		0			0
$334$	−8.11627	+	24.9793i	−0.444103	+	1.36681i
$335$	−3.87550	−	2.81571i	−0.211741	−	0.153839i
$336$		0			0
$337$	7.63910	−	23.5107i	0.416128	−	1.28071i	−0.495110	−	0.868830i	$-0.664872\pi$
$337$	7.63910	−	23.5107i	0.416128	−	1.28071i	0.911238	−	0.411880i	$-0.135128\pi$
$338$	5.02603	+	15.4685i	0.273380	+	0.841376i
$339$		0			0
$340$	1.06172			0.0575799
$341$	−13.5730	−	27.0619i	−0.735017	−	1.46549i
$342$		0			0
$343$	7.87256	−	5.71975i	0.425078	−	0.308837i
$344$	−3.24082	−	9.97422i	−0.174733	−	0.537774i
$345$		0			0
$346$	0.739322	+	0.537149i	0.0397462	+	0.0288773i
$347$	−1.67438	−	1.21651i	−0.0898853	−	0.0653055i	0.541935	−	0.840420i	$-0.317692\pi$
$347$	−1.67438	−	1.21651i	−0.0898853	−	0.0653055i	−0.631820	+	0.775115i	$0.717692\pi$
$348$		0			0
$349$	−1.61130	−	4.95906i	−0.0862507	−	0.265452i	0.898624	−	0.438719i	$-0.144568\pi$
$349$	−1.61130	−	4.95906i	−0.0862507	−	0.265452i	−0.984875	+	0.173267i	$0.944568\pi$
$350$	−4.19874	+	3.05056i	−0.224432	+	0.163059i
$351$		0			0
$352$	1.17611	−	7.13221i	0.0626868	−	0.380148i
$353$	−21.6725			−1.15351			−0.576756	−	0.816917i	$-0.695681\pi$
$353$	−21.6725			−1.15351			−0.576756	+	0.816917i	$0.695681\pi$
$354$		0			0
$355$	−2.25198	−	6.93088i	−0.119523	−	0.367853i
$356$	−1.50616	+	4.63547i	−0.0798261	+	0.245680i
$357$		0			0
$358$	12.0594	+	8.76164i	0.637357	+	0.463067i
$359$	−2.70478	+	8.32446i	−0.142753	+	0.439348i	−0.996715	−	0.0809868i	$-0.974193\pi$
$359$	−2.70478	+	8.32446i	−0.142753	+	0.439348i	0.853962	+	0.520335i	$0.174193\pi$
$360$		0			0
$361$	10.2801	−	7.46894i	0.541059	−	0.393102i
$362$	7.36250			0.386964
$363$		0			0
$364$	−0.444060			−0.0232751
$365$	7.41595	−	5.38801i	0.388169	−	0.282021i
$366$		0			0
$367$	−2.09088	+	6.43506i	−0.109143	+	0.335908i	−0.990680	−	0.136206i	$-0.956509\pi$
$367$	−2.09088	+	6.43506i	−0.109143	+	0.335908i	0.881537	+	0.472114i	$0.156509\pi$
$368$	16.6709	+	12.1121i	0.869029	+	0.631387i
$369$		0			0
$370$	0.817952	−	2.51740i	0.0425233	−	0.130873i
$371$	1.27244	+	3.91618i	0.0660620	+	0.203318i
$372$		0			0
$373$	−21.8933			−1.13359			−0.566797	−	0.823857i	$-0.691818\pi$
$373$	−21.8933			−1.13359			−0.566797	+	0.823857i	$0.691818\pi$
$374$	3.83128	−	23.2338i	0.198111	−	1.20139i
$375$		0			0
$376$	−0.458114	+	0.332839i	−0.0236254	+	0.0171649i
$377$	3.39643	+	10.4531i	0.174925	+	0.538364i
$378$		0			0
$379$	27.3639	+	19.8810i	1.40559	+	1.02122i	0.993946	+	0.109873i	$0.0350445\pi$
$379$	27.3639	+	19.8810i	1.40559	+	1.02122i	0.411642	+	0.911346i	$0.364955\pi$
$380$	0.469243	+	0.340925i	0.0240716	+	0.0174891i
$381$		0			0
$382$	−2.48353	−	7.64350i	−0.127068	−	0.391076i
$383$	−14.8648	+	10.7999i	−0.759555	+	0.551849i	−0.898774	−	0.438413i	$-0.855541\pi$
$383$	−14.8648	+	10.7999i	−0.759555	+	0.551849i	0.139219	+	0.990262i	$0.455541\pi$
$384$		0			0
$385$	−0.635536	−	1.26714i	−0.0323899	−	0.0645794i
$386$	−5.05284			−0.257183
$387$		0			0
$388$	1.71134	+	5.26696i	0.0868801	+	0.267390i
$389$	9.51975	−	29.2988i	0.482670	−	1.48551i	−0.352657	−	0.935753i	$-0.614722\pi$
$389$	9.51975	−	29.2988i	0.482670	−	1.48551i	0.835327	−	0.549754i	$-0.185278\pi$
$390$		0			0
$391$	16.5392	+	12.0164i	0.836424	+	0.607698i
$392$	−4.98201	+	15.3331i	−0.251630	+	0.774436i
$393$		0			0
$394$	28.0974	−	20.4139i	1.41552	−	1.02844i
$395$	8.65524			0.435493
$396$		0			0
$397$	−8.29578			−0.416353			−0.208177	−	0.978091i	$-0.566753\pi$
$397$	−8.29578			−0.416353			−0.208177	+	0.978091i	$0.566753\pi$
$398$	−26.0541	+	18.9294i	−1.30598	+	0.948847i
$399$		0			0
$400$	6.65019	−	20.4672i	0.332509	−	1.02336i
$401$	−3.18237	−	2.31212i	−0.158920	−	0.115462i	0.505483	−	0.862836i	$-0.331314\pi$
$401$	−3.18237	−	2.31212i	−0.158920	−	0.115462i	−0.664403	+	0.747374i	$0.731314\pi$
$402$		0			0
$403$	4.44263	−	13.6730i	0.221303	−	0.681101i
$404$	1.73404	+	5.33682i	0.0862716	+	0.265517i
$405$		0			0
$406$	7.78977			0.386600
$407$	−8.51753	−	4.40825i	−0.422198	−	0.218509i
$408$		0			0
$409$	2.02598	−	1.47196i	0.100178	−	0.0727839i	−0.536568	−	0.843857i	$-0.680280\pi$
$409$	2.02598	−	1.47196i	0.100178	−	0.0727839i	0.636747	+	0.771073i	$0.280280\pi$
$410$	0.326457	+	1.00473i	0.0161226	+	0.0496202i
$411$		0			0
$412$	1.39930	+	1.01665i	0.0689388	+	0.0500870i
$413$	4.16650	+	3.02714i	0.205020	+	0.148956i
$414$		0			0
$415$	−1.27204	−	3.91493i	−0.0624419	−	0.192176i
$416$	2.77704	−	2.01764i	0.136156	−	0.0989228i
$417$		0			0
$418$	9.15380	−	9.03826i	0.447727	−	0.442076i
$419$	−10.7394			−0.524654			−0.262327	−	0.964979i	$-0.584490\pi$
$419$	−10.7394			−0.524654			−0.262327	+	0.964979i	$0.584490\pi$
$420$		0			0
$421$	6.85630	+	21.1015i	0.334156	+	1.02843i	0.967136	+	0.254258i	$0.0818311\pi$
$421$	6.85630	+	21.1015i	0.334156	+	1.02843i	−0.632981	+	0.774167i	$0.718169\pi$
$422$	−1.62065	+	4.98785i	−0.0788920	+	0.242805i
$423$		0			0
$424$	−11.4825	−	8.34249i	−0.557637	−	0.405147i
$425$	6.59767	−	20.3055i	0.320034	−	0.984963i
$426$		0			0
$427$	−2.66275	+	1.93460i	−0.128860	+	0.0936219i
$428$	6.14879			0.297213
$429$		0			0
$430$	−3.85778			−0.186038
$431$	−14.9330	+	10.8495i	−0.719297	+	0.522600i	−0.886160	−	0.463380i	$-0.846636\pi$
$431$	−14.9330	+	10.8495i	−0.719297	+	0.522600i	0.166862	+	0.985980i	$0.446636\pi$
$432$		0			0
$433$	4.67130	−	14.3768i	0.224488	−	0.690904i	−0.773855	−	0.633363i	$-0.781674\pi$
$433$	4.67130	−	14.3768i	0.224488	−	0.690904i	0.998343	−	0.0575408i	$-0.0183259\pi$
$434$	−8.24328	−	5.98909i	−0.395690	−	0.287486i
$435$		0			0
$436$	−1.65300	+	5.08740i	−0.0791642	+	0.243642i
$437$	3.45119	+	10.6217i	0.165093	+	0.508103i
$438$		0			0
$439$	23.9553			1.14333			0.571663	−	0.820488i	$-0.306298\pi$
$439$	23.9553			1.14333			0.571663	+	0.820488i	$0.306298\pi$
$440$	4.33945	+	2.24589i	0.206875	+	0.107068i
$441$		0			0
$442$	9.04645	−	6.57263i	0.430296	−	0.312628i
$443$	−7.87922	−	24.2498i	−0.374353	−	1.15214i	−0.943914	−	0.330192i	$-0.892887\pi$
$443$	−7.87922	−	24.2498i	−0.374353	−	1.15214i	0.569561	−	0.821949i	$-0.307113\pi$
$444$		0			0
$445$	−5.97760	−	4.34298i	−0.283366	−	0.205877i
$446$	−13.7924	−	10.0207i	−0.653088	−	0.474496i
$447$		0			0
$448$	1.31343	+	4.04234i	0.0620539	+	0.190982i
$449$	−18.1886	+	13.2148i	−0.858375	+	0.623646i	−0.927442	−	0.373966i	$-0.877998\pi$
$449$	−18.1886	+	13.2148i	−0.858375	+	0.623646i	0.0690672	+	0.997612i	$0.477998\pi$
$450$		0			0
$451$	3.78438	−	0.574776i	0.178200	−	0.0270651i
$452$	−3.13607			−0.147508
$453$		0			0
$454$	−2.85087	−	8.77409i	−0.133798	−	0.411788i
$455$	0.208020	−	0.640221i	0.00975214	−	0.0300140i
$456$		0			0
$457$	−17.5472	−	12.7488i	−0.820825	−	0.596364i	0.0961237	−	0.995369i	$-0.469356\pi$
$457$	−17.5472	−	12.7488i	−0.820825	−	0.596364i	−0.916949	+	0.399005i	$0.869356\pi$
$458$	−11.8254	+	36.3950i	−0.552566	+	1.70062i
$459$		0			0
$460$	0.832763	−	0.605037i	0.0388278	−	0.0282100i
$461$	12.1036			0.563722			0.281861	−	0.959455i	$-0.409048\pi$
$461$	12.1036			0.563722			0.281861	+	0.959455i	$0.409048\pi$
$462$		0			0
$463$	20.0308			0.930910			0.465455	−	0.885071i	$-0.345891\pi$
$463$	20.0308			0.930910			0.465455	+	0.885071i	$0.345891\pi$
$464$	−26.1320	+	18.9860i	−1.21315	+	0.881404i
$465$		0			0
$466$	2.00115	−	6.15891i	0.0927015	−	0.285306i
$467$	4.90871	+	3.56639i	0.227148	+	0.165033i	0.695538	−	0.718489i	$-0.255166\pi$
$467$	4.90871	+	3.56639i	0.227148	+	0.165033i	−0.468390	+	0.883522i	$0.655166\pi$
$468$		0			0
$469$	−1.80516	+	5.55570i	−0.0833543	+	0.256538i
$470$	0.0643669	+	0.198101i	0.00296902	+	0.00913772i
$471$		0			0
$472$	−17.7515			−0.817078
$473$	−2.27425	+	13.7916i	−0.104570	+	0.634138i
$474$		0			0
$475$	9.43616	−	6.85577i	0.432961	−	0.314564i
$476$	−0.400088	−	1.23134i	−0.0183380	−	0.0564385i
$477$		0			0
$478$	9.22233	+	6.70041i	0.421819	+	0.306470i
$479$	29.3453	+	21.3206i	1.34082	+	0.974164i	0.999413	+	0.0342489i	$0.0109039\pi$
$479$	29.3453	+	21.3206i	1.34082	+	0.974164i	0.341408	+	0.939915i	$0.389096\pi$
$480$		0			0
$481$	−1.40736	−	4.33141i	−0.0641702	−	0.197496i
$482$	−11.0441	+	8.02398i	−0.503043	+	0.365482i
$483$		0			0
$484$	−2.56902	+	3.44312i	−0.116773	+	0.156505i
$485$	−8.39529			−0.381211
$486$		0			0
$487$	−2.68379	−	8.25986i	−0.121614	−	0.374290i	0.871655	−	0.490120i	$-0.163047\pi$
$487$	−2.68379	−	8.25986i	−0.121614	−	0.374290i	−0.993269	+	0.115830i	$0.963047\pi$
$488$	3.50571	−	10.7895i	0.158696	−	0.488417i
$489$		0			0
$490$	4.79782	+	3.48582i	0.216744	+	0.157473i
$491$	10.2585	−	31.5725i	0.462961	−	1.42485i	−0.398567	−	0.917139i	$-0.630492\pi$
$491$	10.2585	−	31.5725i	0.462961	−	1.42485i	0.861529	−	0.507709i	$-0.169508\pi$
$492$		0			0
$493$	−25.9256	+	18.8361i	−1.16763	+	0.848334i
$494$	6.10872			0.274844
$495$		0			0
$496$	42.2506			1.89711
$497$	−7.18956	+	5.22352i	−0.322496	+	0.234307i
$498$		0			0
$499$	6.45131	−	19.8551i	0.288800	−	0.888837i	−0.696433	−	0.717622i	$-0.745231\pi$
$499$	6.45131	−	19.8551i	0.288800	−	0.888837i	0.985234	−	0.171215i	$-0.0547692\pi$
$500$	−1.80497	−	1.31139i	−0.0807209	−	0.0586472i
$501$		0			0
$502$	9.82944	−	30.2519i	0.438710	−	1.35021i
$503$	−7.20593	−	22.1776i	−0.321297	−	0.988850i	−0.973085	−	0.230448i	$-0.925981\pi$
$503$	−7.20593	−	22.1776i	−0.321297	−	0.988850i	0.651788	−	0.758401i	$-0.274019\pi$
$504$		0			0
$505$	−8.50663			−0.378540
$506$	−10.2351	−	20.4068i	−0.455004	−	0.907192i
$507$		0			0
$508$	3.79026	−	2.75378i	0.168166	−	0.122179i
$509$	−2.00280	−	6.16400i	−0.0887728	−	0.273214i	0.896808	−	0.442420i	$-0.145880\pi$
$509$	−2.00280	−	6.16400i	−0.0887728	−	0.273214i	−0.985581	+	0.169205i	$0.945880\pi$
$510$		0			0
$511$	−9.04335	−	6.57038i	−0.400054	−	0.290656i
$512$	−10.4751	−	7.61063i	−0.462940	−	0.336346i
$513$		0			0
$514$	−1.61605	−	4.97368i	−0.0712807	−	0.219379i
$515$	−2.12126	+	1.54119i	−0.0934739	+	0.0679128i
$516$		0			0
$517$	0.746159	−	0.113327i	0.0328160	−	0.00498413i
$518$	−3.22781			−0.141822
$519$		0			0
$520$	0.717013	+	2.20674i	0.0314431	+	0.0967719i
$521$	10.2625	−	31.5848i	0.449610	−	1.38376i	−0.427738	−	0.903903i	$-0.640689\pi$
$521$	10.2625	−	31.5848i	0.449610	−	1.38376i	0.877348	−	0.479855i	$-0.159311\pi$
$522$		0			0
$523$	32.4728	+	23.5929i	1.41994	+	1.03164i	0.991782	+	0.127938i	$0.0408359\pi$
$523$	32.4728	+	23.5929i	1.41994	+	1.03164i	0.428154	+	0.903706i	$0.359164\pi$
$524$	0.831637	−	2.55952i	0.0363302	−	0.111813i
$525$		0			0
$526$	17.8650	−	12.9797i	0.778949	−	0.565940i
$527$	41.9169			1.82593
$528$		0			0
$529$	−3.17970			−0.138248
$530$	−4.22376	+	3.06874i	−0.183468	+	0.133298i
$531$		0			0
$532$	0.218567	−	0.672680i	0.00947608	−	0.0291644i
$533$	1.47055	+	1.06842i	0.0636965	+	0.0462782i
$534$		0			0
$535$	−2.88041	+	8.86498i	−0.124531	+	0.383267i
$536$	−6.22208	−	19.1496i	−0.268753	−	0.827137i
$537$		0			0
$538$	10.3907			0.447974
$539$	15.2903	−	15.0973i	0.658599	−	0.650287i
$540$		0			0
$541$	−19.9410	+	14.4880i	−0.857332	+	0.622888i	−0.927158	−	0.374671i	$-0.877756\pi$
$541$	−19.9410	+	14.4880i	−0.857332	+	0.622888i	0.0698260	+	0.997559i	$0.477756\pi$
$542$	1.90174	+	5.85296i	0.0816868	+	0.251406i
$543$		0			0
$544$	8.09680	+	5.88267i	0.347147	+	0.252217i
$545$	−6.56038	−	4.76640i	−0.281016	−	0.204170i
$546$		0			0
$547$	7.94803	+	24.4615i	0.339833	+	1.04590i	0.964292	+	0.264841i	$0.0853195\pi$
$547$	7.94803	+	24.4615i	0.339833	+	1.04590i	−0.624459	+	0.781058i	$0.714681\pi$
$548$	2.92147	−	2.12257i	0.124799	−	0.0906716i
$549$		0			0
$550$	−16.9659	+	16.7517i	−0.723427	+	0.714296i
$551$	−17.5066			−0.745805
$552$		0			0
$553$	−3.26155	−	10.0380i	−0.138695	−	0.426860i
$554$	6.27424	−	19.3101i	0.266567	−	0.820409i
$555$		0			0
$556$	−6.82813	−	4.96093i	−0.289577	−	0.210390i
$557$	−3.60979	+	11.1098i	−0.152952	+	0.470737i	−0.997948	−	0.0640357i	$-0.979603\pi$
$557$	−3.60979	+	11.1098i	−0.152952	+	0.470737i	0.844996	+	0.534773i	$0.179603\pi$
$558$		0			0
$559$	−5.36998	+	3.90152i	−0.227126	+	0.165017i
$560$	1.97833			0.0835996
$561$		0			0
$562$	−4.58873			−0.193564
$563$	6.57092	−	4.77405i	0.276931	−	0.201202i	−0.440647	−	0.897681i	$-0.645251\pi$
$563$	6.57092	−	4.77405i	0.276931	−	0.201202i	0.717578	+	0.696478i	$0.245251\pi$
$564$		0			0
$565$	1.46910	−	4.52141i	0.0618053	−	0.190217i
$566$	10.1229	+	7.35468i	0.425495	+	0.309140i
$567$		0			0
$568$	9.46559	−	29.1321i	0.397167	−	1.22236i
$569$	5.56435	+	17.1253i	0.233270	+	0.717930i	0.997346	+	0.0728046i	$0.0231950\pi$
$569$	5.56435	+	17.1253i	0.233270	+	0.717930i	−0.764077	+	0.645126i	$0.776805\pi$
$570$		0			0
$571$	−2.60645			−0.109076			−0.0545382	−	0.998512i	$-0.517369\pi$
$571$	−2.60645			−0.109076			−0.0545382	+	0.998512i	$0.517369\pi$
$572$	−2.01687	+	0.306324i	−0.0843296	+	0.0128081i
$573$		0			0
$574$	1.04223	−	0.757225i	0.0435019	−	0.0316059i
$575$	−6.39652	−	19.6865i	−0.266753	−	0.820982i
$576$		0			0
$577$	−28.4684	−	20.6835i	−1.18515	−	0.861064i	−0.192409	−	0.981315i	$-0.561630\pi$
$577$	−28.4684	−	20.6835i	−1.18515	−	0.861064i	−0.992744	+	0.120251i	$0.961630\pi$
$578$	5.11158	+	3.71378i	0.212614	+	0.154473i
$579$		0			0
$580$	0.498609	+	1.53456i	0.0207036	+	0.0637192i
$581$	−4.06104	+	2.95052i	−0.168480	+	0.122408i
$582$		0			0
$583$	8.48078	+	16.9091i	0.351238	+	0.700303i
$584$	38.5294			1.59436
$585$		0			0
$586$	−7.50863	−	23.1092i	−0.310179	−	0.954631i
$587$	−7.27809	+	22.3997i	−0.300399	+	0.924533i	0.680955	+	0.732325i	$0.261565\pi$
$587$	−7.27809	+	22.3997i	−0.300399	+	0.924533i	−0.981354	+	0.192208i	$0.938435\pi$
$588$		0			0
$589$	18.5258	+	13.4598i	0.763341	+	0.554600i
$590$	−2.01781	+	6.21019i	−0.0830721	+	0.255670i
$591$		0			0
$592$	10.8282	−	7.86714i	0.445036	−	0.323337i
$593$	−13.1828			−0.541354			−0.270677	−	0.962670i	$-0.587248\pi$
$593$	−13.1828			−0.541354			−0.270677	+	0.962670i	$0.587248\pi$
$594$		0			0
$595$	1.96270			0.0804630
$596$	−0.362218	+	0.263166i	−0.0148370	+	0.0107797i
$597$		0			0
$598$	3.35009	−	10.3105i	0.136995	−	0.421628i
$599$	27.6817	+	20.1119i	1.13104	+	0.821750i	0.985846	−	0.167653i	$-0.0536188\pi$
$599$	27.6817	+	20.1119i	1.13104	+	0.821750i	0.145196	+	0.989403i	$0.453619\pi$
$600$		0			0
$601$	8.97030	−	27.6077i	0.365906	−	1.12614i	−0.583505	−	0.812109i	$-0.698319\pi$
$601$	8.97030	−	27.6077i	0.365906	−	1.12614i	0.949412	−	0.314034i	$-0.101681\pi$
$602$	1.45372	+	4.47410i	0.0592493	+	0.182351i
$603$		0			0
$604$	0.343924			0.0139941
$605$	−3.76064	−	5.31680i	−0.152892	−	0.216158i
$606$		0			0
$607$	2.55354	−	1.85526i	0.103645	−	0.0753026i	−0.534756	−	0.845007i	$-0.679596\pi$
$607$	2.55354	−	1.85526i	0.103645	−	0.0753026i	0.638401	+	0.769704i	$0.279596\pi$
$608$	1.68954	+	5.19986i	0.0685197	+	0.210882i
$609$		0			0
$610$	−3.37611	−	2.45288i	−0.136695	−	0.0993144i
$611$	0.289945	+	0.210657i	0.0117299	+	0.00852229i
$612$		0			0
$613$	10.4884	+	32.2798i	0.423620	+	1.30377i	0.904309	+	0.426878i	$0.140387\pi$
$613$	10.4884	+	32.2798i	0.423620	+	1.30377i	−0.480689	+	0.876891i	$0.659613\pi$
$614$	−4.39443	+	3.19274i	−0.177345	+	0.128848i
$615$		0			0
$616$	0.969460	−	5.87904i	0.0390606	−	0.236873i
$617$	21.6077			0.869895			0.434948	−	0.900456i	$-0.356767\pi$
$617$	21.6077			0.869895			0.434948	+	0.900456i	$0.356767\pi$
$618$		0			0
$619$	6.33874	+	19.5086i	0.254775	+	0.784118i	0.993874	+	0.110521i	$0.0352519\pi$
$619$	6.33874	+	19.5086i	0.254775	+	0.784118i	−0.739098	+	0.673598i	$0.764748\pi$
$620$	0.652196	−	2.00725i	0.0261928	−	0.0806132i
$621$		0			0
$622$	−32.9404	−	23.9326i	−1.32079	−	0.959611i
$623$	−2.78429	+	8.56915i	−0.111550	+	0.343316i
$624$		0			0
$625$	−16.0714	+	11.6765i	−0.642855	+	0.467062i
$626$	3.80526			0.152089
$627$		0			0
$628$	−3.82189			−0.152510
$629$	10.7427	−	7.80501i	0.428339	−	0.311206i
$630$		0			0
$631$	9.22863	−	28.4028i	0.367386	−	1.13070i	−0.581087	−	0.813841i	$-0.697372\pi$
$631$	9.22863	−	28.4028i	0.367386	−	1.13070i	0.948473	−	0.316857i	$-0.102628\pi$
$632$	29.4320	+	21.3836i	1.17074	+	0.850595i
$633$		0			0
$634$	−12.6646	+	38.9778i	−0.502977	+	1.54801i
$635$	2.19470	+	6.75459i	0.0870940	+	0.268048i
$636$		0			0
$637$	10.2039			0.404292
$638$	35.3803	−	5.37360i	1.40072	−	0.212743i
$639$		0			0
$640$	−6.44762	+	4.68447i	−0.254864	+	0.185170i
$641$	11.7797	+	36.2543i	0.465272	+	1.43196i	0.858640	+	0.512579i	$0.171310\pi$
$641$	11.7797	+	36.2543i	0.465272	+	1.43196i	−0.393368	+	0.919381i	$0.628690\pi$
$642$		0			0
$643$	13.6118	+	9.88957i	0.536798	+	0.390006i	0.822894	−	0.568194i	$-0.192358\pi$
$643$	13.6118	+	9.88957i	0.536798	+	0.390006i	−0.286097	+	0.958201i	$0.592358\pi$
$644$	−1.01551	−	0.737810i	−0.0400166	−	0.0290738i
$645$		0			0
$646$	5.50381	+	16.9390i	0.216545	+	0.666456i
$647$	−16.9687	+	12.3285i	−0.667109	+	0.484683i	−0.869056	−	0.494713i	$-0.835273\pi$
$647$	−16.9687	+	12.3285i	−0.667109	+	0.484683i	0.201947	+	0.979396i	$0.435273\pi$
$648$		0			0
$649$	21.0120	+	10.8748i	0.824792	+	0.426872i
$650$	−11.3220			−0.444087
$651$		0			0
$652$	0.558733	+	1.71960i	0.0218817	+	0.0673449i
$653$	−6.10818	+	18.7990i	−0.239031	+	0.735663i	0.757530	+	0.652801i	$0.226406\pi$
$653$	−6.10818	+	18.7990i	−0.239031	+	0.735663i	−0.996561	+	0.0828623i	$0.973594\pi$
$654$		0			0
$655$	3.30058	+	2.39801i	0.128964	+	0.0936982i
$656$	−1.65074	+	5.08046i	−0.0644506	+	0.198358i
$657$		0			0
$658$	0.205494	−	0.149300i	0.00801101	−	0.00582034i
$659$	11.8055			0.459879			0.229939	−	0.973205i	$-0.426147\pi$
$659$	11.8055			0.459879			0.229939	+	0.973205i	$0.426147\pi$
$660$		0			0
$661$	17.8076			0.692637			0.346318	−	0.938117i	$-0.387432\pi$
$661$	17.8076			0.692637			0.346318	+	0.938117i	$0.387432\pi$
$662$	10.1369	−	7.36485i	0.393980	−	0.286243i
$663$		0			0
$664$	5.34667	−	16.4554i	0.207491	−	0.638592i
$665$	0.867445	+	0.630235i	0.0336381	+	0.0244395i
$666$		0			0
$667$	−9.60079	+	29.5482i	−0.371744	+	1.14411i
$668$	2.05009	+	6.30952i	0.0793202	+	0.244123i
$669$		0			0
$670$	−7.40658			−0.286141
$671$	−10.7594	+	10.6236i	−0.415361	+	0.410119i
$672$		0			0
$673$	−15.9419	+	11.5825i	−0.614515	+	0.446472i	−0.851001	−	0.525163i	$-0.824004\pi$
$673$	−15.9419	+	11.5825i	−0.614515	+	0.446472i	0.236486	+	0.971635i	$0.424004\pi$
$674$	−11.8111	−	36.3508i	−0.454946	−	1.40018i
$675$		0			0
$676$	3.32365	+	2.41477i	0.127833	+	0.0928760i
$677$	−10.0431	−	7.29671i	−0.385986	−	0.280436i	0.377822	−	0.925878i	$-0.376673\pi$
$677$	−10.0431	−	7.29671i	−0.385986	−	0.280436i	−0.763809	+	0.645443i	$0.776673\pi$
$678$		0			0
$679$	3.16359	+	9.73653i	0.121408	+	0.373654i
$680$	−5.47310	+	3.97644i	−0.209884	+	0.152490i
$681$		0			0
$682$	−41.5715	−	21.5154i	−1.59186	−	0.823866i
$683$	−2.02837			−0.0776135			−0.0388068	−	0.999247i	$-0.512356\pi$
$683$	−2.02837			−0.0776135			−0.0388068	+	0.999247i	$0.512356\pi$
$684$		0			0
$685$	1.69164	+	5.20632i	0.0646341	+	0.198923i
$686$	4.64931	−	14.3091i	0.177511	−	0.546324i
$687$		0			0
$688$	−15.7815	−	11.4659i	−0.601663	−	0.437133i
$689$	−2.77589	+	8.54330i	−0.105753	+	0.325474i
$690$		0			0
$691$	−1.89542	+	1.37710i	−0.0721052	+	0.0523875i	−0.623254	−	0.782020i	$-0.714190\pi$
$691$	−1.89542	+	1.37710i	−0.0721052	+	0.0523875i	0.551149	+	0.834407i	$0.314190\pi$
$692$	0.230830			0.00877483
$693$		0			0
$694$	−3.19995			−0.121469
$695$	10.3510	−	7.52046i	0.392637	−	0.285267i
$696$		0			0
$697$	−1.63770	+	5.04033i	−0.0620324	+	0.190916i
$698$	−6.52227	−	4.73871i	−0.246871	−	0.179363i
$699$		0			0
$700$	−0.405097	+	1.24676i	−0.0153112	+	0.0471231i
$701$	1.37008	+	4.21668i	0.0517473	+	0.159262i	0.973591	−	0.228301i	$-0.0733170\pi$
$701$	1.37008	+	4.21668i	0.0517473	+	0.159262i	−0.921843	+	0.387563i	$0.873317\pi$
$702$		0			0
$703$	7.25411			0.273594
$704$	8.75399	+	17.4538i	0.329928	+	0.657815i
$705$		0			0
$706$	−27.1091	+	19.6959i	−1.02026	+	0.741265i
$707$	3.20555	+	9.86566i	0.120557	+	0.371037i
$708$		0			0
$709$	−24.1755	−	17.5645i	−0.907929	−	0.659649i	0.0325612	−	0.999470i	$-0.489634\pi$
$709$	−24.1755	−	17.5645i	−0.907929	−	0.659649i	−0.940490	+	0.339821i	$0.889634\pi$
$710$	−9.11565	−	6.62291i	−0.342104	−	0.248553i
$711$		0			0
$712$	−9.59699	−	29.5365i	−0.359662	−	1.10693i
$713$	32.8776	−	23.8870i	1.23127	−	0.894574i
$714$		0			0
$715$	0.503164	−	3.05131i	0.0188173	−	0.114113i
$716$	3.76515			0.140710
$717$		0			0
$718$	4.18196	+	12.8707i	0.156069	+	0.480332i
$719$	6.68469	−	20.5734i	0.249297	−	0.767257i	−0.745603	−	0.666390i	$-0.767838\pi$
$719$	6.68469	−	20.5734i	0.249297	−	0.767257i	0.994900	−	0.100867i	$-0.0321616\pi$
$720$		0			0
$721$	2.58676	+	1.87939i	0.0963360	+	0.0699922i
$722$	6.07115	−	18.6851i	0.225945	−	0.695386i
$723$		0			0
$724$	1.50452	−	1.09310i	0.0559151	−	0.0406247i
$725$	32.4471			1.20505
$726$		0			0
$727$	−12.4422			−0.461455			−0.230727	−	0.973018i	$-0.574111\pi$
$727$	−12.4422			−0.461455			−0.230727	+	0.973018i	$0.574111\pi$
$728$	2.28910	−	1.66313i	0.0848396	−	0.0616396i
$729$		0			0
$730$	4.37965	−	13.4792i	0.162098	−	0.498887i
$731$	−15.6568	−	11.3754i	−0.579089	−	0.420733i
$732$		0			0
$733$	−16.1777	+	49.7899i	−0.597538	+	1.83903i	−0.0558724	+	0.998438i	$0.517794\pi$
$733$	−16.1777	+	49.7899i	−0.597538	+	1.83903i	−0.541665	+	0.840594i	$0.682206\pi$
$734$	3.23278	+	9.94949i	0.119324	+	0.367242i
$735$		0			0
$736$	9.70306			0.357660
$737$	−4.36635	+	26.4786i	−0.160837	+	0.975352i
$738$		0			0
$739$	37.7617	−	27.4355i	1.38909	−	1.00923i	0.393122	−	0.919486i	$-0.371395\pi$
$739$	37.7617	−	27.4355i	1.38909	−	1.00923i	0.995965	−	0.0897445i	$-0.0286051\pi$
$740$	−0.206606	−	0.635869i	−0.00759500	−	0.0233750i
$741$		0			0
$742$	5.15064	+	3.74216i	0.189086	+	0.137379i
$743$	−17.6947	−	12.8560i	−0.649156	−	0.471640i	0.213827	−	0.976871i	$-0.431407\pi$
$743$	−17.6947	−	12.8560i	−0.649156	−	0.471640i	−0.862984	+	0.505232i	$0.831407\pi$
$744$		0			0
$745$	−0.209737	−	0.645506i	−0.00768419	−	0.0236495i
$746$	−27.3853	+	19.8966i	−1.00265	+	0.728466i
$747$		0			0
$748$	−2.66657	−	5.31664i	−0.0974994	−	0.194395i
$749$	11.3667			0.415330
$750$		0			0
$751$	12.2346	+	37.6543i	0.446448	+	1.37403i	0.880888	+	0.473326i	$0.156947\pi$
$751$	12.2346	+	37.6543i	0.446448	+	1.37403i	−0.434439	+	0.900701i	$0.643053\pi$
$752$	−0.325473	+	1.00170i	−0.0118688	+	0.0365284i
$753$		0			0
$754$	13.7482	+	9.98865i	0.500680	+	0.363765i
$755$	−0.161111	+	0.495850i	−0.00586344	+	0.0180458i
$756$		0			0
$757$	−18.7253	+	13.6047i	−0.680583	+	0.494472i	−0.873551	−	0.486733i	$-0.838189\pi$
$757$	−18.7253	+	13.6047i	−0.680583	+	0.494472i	0.192968	+	0.981205i	$0.438189\pi$
$758$	52.2959			1.89947
$759$		0			0
$760$	−3.69577			−0.134060
$761$	−12.0486	+	8.75381i	−0.436761	+	0.317325i	−0.784346	−	0.620323i	$-0.787002\pi$
$761$	−12.0486	+	8.75381i	−0.436761	+	0.317325i	0.347586	+	0.937648i	$0.387002\pi$
$762$		0			0
$763$	−3.05574	+	9.40460i	−0.110625	+	0.340469i
$764$	−1.64233	−	1.19322i	−0.0594173	−	0.0431692i
$765$		0			0
$766$	−8.77872	+	27.0181i	−0.317188	+	0.976204i
$767$	3.47183	+	10.6852i	0.125361	+	0.385820i
$768$		0			0
$769$	21.6233			0.779757			0.389879	−	0.920866i	$-0.372517\pi$
$769$	21.6233			0.779757			0.389879	+	0.920866i	$0.372517\pi$
$770$	−1.94653	−	1.00743i	−0.0701481	−	0.0363052i
$771$		0			0
$772$	−1.03255	+	0.750188i	−0.0371621	+	0.0269999i
$773$	1.87664	+	5.77569i	0.0674979	+	0.207737i	0.979117	−	0.203300i	$-0.0651666\pi$
$773$	1.87664	+	5.77569i	0.0674979	+	0.207737i	−0.911619	+	0.411037i	$0.865167\pi$
$774$		0			0
$775$	−34.3361	−	24.9466i	−1.23339	−	0.896109i
$776$	−28.5481	−	20.7414i	−1.02482	−	0.744572i
$777$		0			0
$778$	−14.7188	−	45.2999i	−0.527695	−	1.62408i
$779$	−2.34229	+	1.70177i	−0.0839211	+	0.0609722i
$780$		0			0
$781$	−29.0509	+	28.6842i	−1.03952	+	1.02640i
$782$	31.6086			1.13032
$783$		0			0
$784$	9.26663	+	28.5197i	0.330951	+	1.01856i
$785$	1.79037	−	5.51018i	0.0639010	−	0.196667i
$786$		0			0
$787$	−41.3856	−	30.0684i	−1.47524	−	1.07182i	−0.979053	−	0.203604i	$-0.934735\pi$
$787$	−41.3856	−	30.0684i	−1.47524	−	1.07182i	−0.496183	−	0.868218i	$-0.665265\pi$
$788$	2.71085	−	8.34314i	0.0965701	−	0.297212i
$789$		0			0
$790$	10.8264	−	7.86585i	0.385187	−	0.279854i
$791$	−5.79736			−0.206130
$792$		0			0
$793$	−7.18019			−0.254976
$794$	−10.3768	+	7.53917i	−0.368258	+	0.267555i
$795$		0			0
$796$	−2.51372	+	7.73643i	−0.0890964	+	0.274211i
$797$	−20.4368	−	14.8482i	−0.723907	−	0.525949i	0.163723	−	0.986506i	$-0.447650\pi$
$797$	−20.4368	−	14.8482i	−0.723907	−	0.525949i	−0.887630	+	0.460557i	$0.847650\pi$
$798$		0			0
$799$	−0.322903	+	0.993792i	−0.0114235	+	0.0351579i
$800$	−3.13143	−	9.63754i	−0.110713	−	0.340738i
$801$		0			0
$802$	−6.08192			−0.214760
$803$	−45.6063	−	23.6036i	−1.60941	−	0.832953i
$804$		0			0
$805$	1.53945	−	1.11848i	0.0542584	−	0.0394211i
$806$	−6.86891	−	21.1403i	−0.241947	−	0.744637i
$807$		0			0
$808$	−28.9267	−	21.0165i	−1.01764	−	0.739357i
$809$	41.5248	+	30.1696i	1.45994	+	1.06071i	0.983380	+	0.181561i	$0.0581150\pi$
$809$	41.5248	+	30.1696i	1.45994	+	1.06071i	0.476556	+	0.879144i	$0.341885\pi$
$810$		0			0
$811$	1.40476	+	4.32339i	0.0493276	+	0.151815i	0.972686	−	0.232124i	$-0.0745674\pi$
$811$	1.40476	+	4.32339i	0.0493276	+	0.151815i	−0.923359	+	0.383939i	$0.874567\pi$
$812$	1.59184	−	1.15654i	0.0558625	−	0.0405865i
$813$		0			0
$814$	−14.6604	+	2.22663i	−0.513845	+	0.0780433i
$815$	−2.74097			−0.0960119
$816$		0			0
$817$	−3.26707	−	10.0550i	−0.114300	−	0.351780i
$818$	1.19649	−	3.68241i	0.0418342	−	0.128753i
$819$		0			0
$820$	0.215882	+	0.156848i	0.00753894	+	0.00547736i
$821$	−3.36019	+	10.3416i	−0.117271	+	0.360924i	−0.992414	−	0.122941i	$-0.960767\pi$
$821$	−3.36019	+	10.3416i	−0.117271	+	0.360924i	0.875143	+	0.483865i	$0.160767\pi$
$822$		0			0
$823$	19.1059	−	13.8812i	0.665988	−	0.483869i	−0.202692	−	0.979243i	$-0.564969\pi$
$823$	19.1059	−	13.8812i	0.665988	−	0.483869i	0.868680	+	0.495374i	$0.164969\pi$
$824$	−11.0210			−0.383934
$825$		0			0
$826$	7.96271			0.277058
$827$	−22.3321	+	16.2252i	−0.776564	+	0.564207i	−0.903946	−	0.427647i	$-0.859343\pi$
$827$	−22.3321	+	16.2252i	−0.776564	+	0.564207i	0.127382	+	0.991854i	$0.459343\pi$
$828$		0			0
$829$	−4.97546	+	15.3129i	−0.172805	+	0.531839i	−0.999526	−	0.0307727i	$-0.990203\pi$
$829$	−4.97546	+	15.3129i	−0.172805	+	0.531839i	0.826722	+	0.562611i	$0.190203\pi$
$830$	−5.14900	−	3.74097i	−0.178724	−	0.129851i
$831$		0			0
$832$	−2.86531	+	8.81852i	−0.0993368	+	0.305727i
$833$	9.19344	+	28.2945i	0.318534	+	0.980347i
$834$		0			0
$835$	−10.0571			−0.348039
$836$	0.528675	−	3.20601i	0.0182846	−	0.110882i
$837$		0			0
$838$	−13.4334	+	9.75993i	−0.464049	+	0.337151i
$839$	6.00479	+	18.4809i	0.207309	+	0.638030i	0.999611	+	0.0279012i	$0.00888236\pi$
$839$	6.00479	+	18.4809i	0.207309	+	0.638030i	−0.792302	+	0.610129i	$0.791118\pi$
$840$		0			0
$841$	−15.9386	−	11.5800i	−0.549606	−	0.399312i
$842$	27.7532	+	20.1639i	0.956438	+	0.694893i
$843$		0			0
$844$	0.409359	+	1.25988i	0.0140907	+	0.0433668i
$845$	−5.03845	+	3.66065i	−0.173328	+	0.125930i
$846$		0			0
$847$	−4.74909	+	6.36497i	−0.163181	+	0.218703i
$848$	−26.3994			−0.906559
$849$		0			0
$850$	−10.2009	−	31.3951i	−0.349888	−	1.07684i
$851$	3.97823	−	12.2437i	0.136372	−	0.419710i
$852$		0			0
$853$	16.0068	+	11.6296i	0.548063	+	0.398191i	0.827071	−	0.562098i	$-0.190006\pi$
$853$	16.0068	+	11.6296i	0.548063	+	0.398191i	−0.279008	+	0.960289i	$0.590006\pi$
$854$	−1.57255	+	4.83980i	−0.0538114	+	0.165614i
$855$		0			0
$856$	−31.6966	+	23.0289i	−1.08337	+	0.787112i
$857$	4.34065			0.148274			0.0741369	−	0.997248i	$-0.476380\pi$
$857$	4.34065			0.148274			0.0741369	+	0.997248i	$0.476380\pi$
$858$		0			0
$859$	−5.17935			−0.176717			−0.0883586	−	0.996089i	$-0.528162\pi$
$859$	−5.17935			−0.176717			−0.0883586	+	0.996089i	$0.528162\pi$
$860$	−0.788334	+	0.572758i	−0.0268820	+	0.0195309i
$861$		0			0
$862$	−8.81901	+	27.1421i	−0.300377	+	0.924464i
$863$	−2.17943	−	1.58345i	−0.0741886	−	0.0539011i	0.550073	−	0.835117i	$-0.314600\pi$
$863$	−2.17943	−	1.58345i	−0.0741886	−	0.0539011i	−0.624261	+	0.781216i	$0.714600\pi$
$864$		0			0
$865$	−0.108132	+	0.332797i	−0.00367661	+	0.0113155i
$866$	−7.22246	−	22.2285i	−0.245429	−	0.755354i
$867$		0			0
$868$	−2.57370			−0.0873571
$869$	−21.7381	−	43.3417i	−0.737414	−	1.47027i
$870$		0			0
$871$	−10.3099	+	7.49056i	−0.349337	+	0.253808i
$872$	−10.5326	−	32.4161i	−0.356680	−	1.09775i
$873$		0			0
$874$	13.9699	+	10.1497i	0.472538	+	0.343319i
$875$	−3.33668	−	2.42424i	−0.112800	−	0.0819543i
$876$		0			0
$877$	−6.44139	−	19.8246i	−0.217510	−	0.669428i	−0.998966	−	0.0454669i	$-0.985522\pi$
$877$	−6.44139	−	19.8246i	−0.217510	−	0.669428i	0.781456	−	0.623961i	$-0.214478\pi$
$878$	29.9646	−	21.7705i	1.01125	−	0.734720i
$879$		0			0
$880$	8.98535	−	1.36470i	0.302896	−	0.0460041i
$881$	−11.5843			−0.390286			−0.195143	−	0.980775i	$-0.562517\pi$
$881$	−11.5843			−0.390286			−0.195143	+	0.980775i	$0.562517\pi$
$882$		0			0
$883$	4.75801	+	14.6437i	0.160120	+	0.492798i	0.998644	−	0.0520667i	$-0.0165808\pi$
$883$	4.75801	+	14.6437i	0.160120	+	0.492798i	−0.838524	+	0.544865i	$0.816581\pi$
$884$	0.872808	−	2.68623i	0.0293557	−	0.0903476i
$885$		0			0
$886$	−31.8938	−	23.1722i	−1.07149	−	0.778486i
$887$	1.82628	−	5.62070i	0.0613204	−	0.188725i	−0.915703	−	0.401855i	$-0.868366\pi$
$887$	1.82628	−	5.62070i	0.0613204	−	0.188725i	0.977024	+	0.213130i	$0.0683657\pi$
$888$		0			0
$889$	7.00669	−	5.09066i	0.234997	−	0.170735i
$890$	−11.4240			−0.382932
$891$		0			0
$892$	−4.30623			−0.144183
$893$	−0.461824	+	0.335535i	−0.0154543	+	0.0112282i
$894$		0			0
$895$	−1.76379	+	5.42838i	−0.0589569	+	0.181451i
$896$	7.86251	+	5.71245i	0.262668	+	0.190840i
$897$		0			0
$898$	−10.7417	+	33.0595i	−0.358455	+	1.10321i
$899$	19.6852	+	60.5847i	0.656537	+	2.02061i
$900$		0			0
$901$	−26.1909			−0.872546
$902$	4.21134	−	4.15819i	0.140222	−	0.138453i
$903$		0			0
$904$	16.1662	−	11.7455i	0.537681	−	0.390648i
$905$	0.871174	+	2.68120i	0.0289588	+	0.0891260i
$906$		0			0
$907$	5.98132	+	4.34568i	0.198606	+	0.144296i	0.682644	−	0.730751i	$-0.260830\pi$
$907$	5.98132	+	4.34568i	0.198606	+	0.144296i	−0.484037	+	0.875047i	$0.660830\pi$
$908$	−1.88525	−	1.36971i	−0.0625642	−	0.0454556i
$909$		0			0
$910$	−0.321628	−	0.989869i	−0.0106619	−	0.0328138i
$911$	−11.4871	+	8.34585i	−0.380584	+	0.276510i	−0.761586	−	0.648064i	$-0.775579\pi$
$911$	−11.4871	+	8.34585i	−0.380584	+	0.276510i	0.381002	+	0.924574i	$0.375579\pi$
$912$		0			0
$913$	−16.4095	+	16.2024i	−0.543074	+	0.536220i
$914$	−33.5350			−1.10924
$915$		0			0
$916$	2.98698	+	9.19299i	0.0986927	+	0.303745i
$917$	1.53737	−	4.73153i	0.0507684	−	0.156249i
$918$		0			0
$919$	33.6895	+	24.4769i	1.11132	+	0.807418i	0.982870	−	0.184299i	$-0.0590013\pi$
$919$	33.6895	+	24.4769i	1.11132	+	0.807418i	0.128445	+	0.991717i	$0.459001\pi$
$920$	−2.02680	+	6.23785i	−0.0668217	+	0.205656i
$921$		0			0
$922$	15.1398	−	10.9997i	0.498604	−	0.362257i
$923$	−19.3869			−0.638127
$924$		0			0
$925$	−13.4449			−0.442067
$926$	25.0555	−	18.2039i	0.823376	−	0.598218i
$927$		0			0
$928$	−4.70008	+	14.4654i	−0.154288	+	0.474849i
$929$	−27.6140	−	20.0627i	−0.905986	−	0.658237i	0.0340108	−	0.999421i	$-0.489172\pi$
$929$	−27.6140	−	20.0627i	−0.905986	−	0.658237i	−0.939996	+	0.341184i	$0.889172\pi$
$930$		0			0
$931$	−5.02236	+	15.4572i	−0.164601	+	0.506590i
$932$	−0.505470	−	1.55568i	−0.0165572	−	0.0509579i
$933$		0			0
$934$	9.38118			0.306962
$935$	8.91439	−	1.35393i	0.291532	−	0.0442781i
$936$		0			0
$937$	−41.8118	+	30.3780i	−1.36593	+	0.992407i	−0.367889	+	0.929870i	$0.619919\pi$
$937$	−41.8118	+	30.3780i	−1.36593	+	0.992407i	−0.998043	+	0.0625376i	$0.980081\pi$
$938$	2.79102	+	8.58987i	0.0911299	+	0.280469i
$939$		0			0
$940$	0.0425651	+	0.0309253i	0.00138832	+	0.00100867i
$941$	14.5673	+	10.5838i	0.474881	+	0.345021i	0.799340	−	0.600878i	$-0.205182\pi$
$941$	14.5673	+	10.5838i	0.474881	+	0.345021i	−0.324460	+	0.945900i	$0.605182\pi$
$942$		0			0
$943$	1.58777	+	4.88666i	0.0517050	+	0.159132i
$944$	−26.7122	+	19.4075i	−0.869407	+	0.631661i
$945$		0			0
$946$	9.68901	+	19.3181i	0.315017	+	0.628084i
$947$	−28.6303			−0.930360			−0.465180	−	0.885216i	$-0.654010\pi$
$947$	−28.6303			−0.930360			−0.465180	+	0.885216i	$0.654010\pi$
$948$		0			0
$949$	−7.53559	−	23.1922i	−0.244616	−	0.752850i
$950$	5.57273	−	17.1511i	0.180803	−	0.556455i
$951$		0			0
$952$	6.67415	+	4.84905i	0.216310	+	0.157159i
$953$	−5.15728	+	15.8725i	−0.167061	+	0.514160i	−0.999182	−	0.0404331i	$-0.987126\pi$
$953$	−5.15728	+	15.8725i	−0.167061	+	0.514160i	0.832121	+	0.554594i	$0.187126\pi$
$954$		0			0
$955$	2.48967	−	1.80885i	0.0805637	−	0.0585330i
$956$	2.87938			0.0931257
$957$		0			0
$958$	56.0827			1.81195
$959$	5.40063	−	3.92379i	0.174396	−	0.126706i
$960$		0			0
$961$	16.1692	−	49.7638i	0.521589	−	1.60528i
$962$	−5.69677	−	4.13895i	−0.183671	−	0.133445i
$963$		0			0
$964$	−1.06554	+	3.27939i	−0.0343187	+	0.105622i
$965$	−0.597882	−	1.84009i	−0.0192465	−	0.0592347i
$966$		0			0
$967$	24.3193			0.782057			0.391029	−	0.920379i	$-0.372119\pi$
$967$	24.3193			0.782057			0.391029	+	0.920379i	$0.372119\pi$
$968$	0.347660	−	27.3707i	0.0111742	−	0.879728i
$969$		0			0
$970$	−10.5013	+	7.62961i	−0.337175	+	0.244972i
$971$	−2.33367	−	7.18229i	−0.0748910	−	0.230491i	0.906603	−	0.421985i	$-0.138667\pi$
$971$	−2.33367	−	7.18229i	−0.0748910	−	0.230491i	−0.981494	+	0.191495i	$0.938667\pi$
$972$		0			0
$973$	−12.6225	−	9.17079i	−0.404659	−	0.294002i
$974$	−10.8635	−	7.89283i	−0.348091	−	0.252903i
$975$		0			0
$976$	−6.52069	−	20.0686i	−0.208722	−	0.642381i
$977$	1.64415	−	1.19455i	0.0526011	−	0.0382170i	−0.561174	−	0.827698i	$-0.689650\pi$
$977$	1.64415	−	1.19455i	0.0526011	−	0.0382170i	0.613775	+	0.789481i	$0.289650\pi$
$978$		0			0
$979$	−6.73470	+	40.8408i	−0.215242	+	1.30528i
$980$	1.49797			0.0478508
$981$		0			0
$982$	−15.8611	−	48.8154i	−0.506148	−	1.55776i
$983$	−10.3334	+	31.8030i	−0.329584	+	1.01436i	0.639744	+	0.768588i	$0.279040\pi$
$983$	−10.3334	+	31.8030i	−0.329584	+	1.01436i	−0.969329	+	0.245769i	$0.920960\pi$
$984$		0			0
$985$	10.7588	+	7.81671i	0.342803	+	0.249061i
$986$	−15.3109	+	47.1222i	−0.487600	+	1.50068i
$987$		0			0
$988$	1.24831	−	0.906952i	0.0397141	−	0.0288540i
$989$	−18.7629			−0.596624
$990$		0			0
$991$	40.1009			1.27385			0.636923	−	0.770927i	$-0.280207\pi$
$991$	40.1009			1.27385			0.636923	+	0.770927i	$0.280207\pi$
$992$	16.0953	−	11.6939i	0.511026	−	0.371282i
$993$		0			0
$994$	−4.24595	+	13.0677i	−0.134673	+	0.414482i
$995$	−9.97640	−	7.24828i	−0.316273	−	0.229786i
$996$		0			0
$997$	4.98448	−	15.3406i	0.157860	−	0.485843i	−0.840580	−	0.541688i	$-0.817785\pi$
$997$	4.98448	−	15.3406i	0.157860	−	0.485843i	0.998439	+	0.0558453i	$0.0177854\pi$
$998$	−9.97461	−	30.6987i	−0.315741	−	0.971750i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.f.e.487.8		36
3.2	odd	2		891.2.f.f.487.2		36
9.2	odd	6		99.2.m.b.58.8	yes	72
9.4	even	3		297.2.n.b.289.8		72
9.5	odd	6		99.2.m.b.25.2	yes	72
9.7	even	3		297.2.n.b.91.2		72
11.2	odd	10		9801.2.a.cn.1.15		18
11.4	even	5	inner	891.2.f.e.730.8		36
11.9	even	5		9801.2.a.cp.1.4		18
33.2	even	10		9801.2.a.co.1.4		18
33.20	odd	10		9801.2.a.cm.1.15		18
33.26	odd	10		891.2.f.f.730.2		36
99.2	even	30		1089.2.e.o.364.15		36
99.4	even	15		297.2.n.b.235.2		72
99.20	odd	30		1089.2.e.p.364.4		36
99.59	odd	30		99.2.m.b.70.8	yes	72
99.68	even	30		1089.2.e.o.727.15		36
99.70	even	15		297.2.n.b.37.8		72
99.86	odd	30		1089.2.e.p.727.4		36
99.92	odd	30		99.2.m.b.4.2	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.2	✓	72	99.92	odd	30
99.2.m.b.25.2	yes	72	9.5	odd	6
99.2.m.b.58.8	yes	72	9.2	odd	6
99.2.m.b.70.8	yes	72	99.59	odd	30
297.2.n.b.37.8		72	99.70	even	15
297.2.n.b.91.2		72	9.7	even	3
297.2.n.b.235.2		72	99.4	even	15
297.2.n.b.289.8		72	9.4	even	3
891.2.f.e.487.8		36	1.1	even	1	trivial
891.2.f.e.730.8		36	11.4	even	5	inner
891.2.f.f.487.2		36	3.2	odd	2
891.2.f.f.730.2		36	33.26	odd	10
1089.2.e.o.364.15		36	99.2	even	30
1089.2.e.o.727.15		36	99.68	even	30
1089.2.e.p.364.4		36	99.20	odd	30
1089.2.e.p.727.4		36	99.86	odd	30
9801.2.a.cm.1.15		18	33.20	odd	10
9801.2.a.cn.1.15		18	11.2	odd	10
9801.2.a.co.1.4		18	33.2	even	10
9801.2.a.cp.1.4		18	11.9	even	5

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.25085 - 0.908796i) q^{2} +(0.120683 - 0.371424i) q^{4} +(0.478964 + 0.347988i) q^{5} +(0.223095 - 0.686616i) q^{7} +(0.768973 + 2.36665i) q^{8} +0.915362 q^{10} +(0.539627 - 3.27243i) q^{11} +(1.27417 - 0.925741i) q^{13} +(-0.344935 - 1.06160i) q^{14} +(3.74458 + 2.72060i) q^{16} +(3.71501 + 2.69911i) q^{17} +(0.775200 + 2.38582i) q^{19} +(0.187054 - 0.135902i) q^{20} +(-2.29898 - 4.58373i) q^{22} +4.45200 q^{23} +(-1.43677 - 4.42194i) q^{25} +(0.752490 - 2.31593i) q^{26} +(-0.228102 - 0.165726i) q^{28} +(-2.15651 + 6.63706i) q^{29} +(7.38490 - 5.36545i) q^{31} +2.17948 q^{32} +7.09986 q^{34} +(0.345788 - 0.251230i) q^{35} +(0.893583 - 2.75017i) q^{37} +(3.13788 + 2.27981i) q^{38} +(-0.455256 + 1.40114i) q^{40} +(0.356643 + 1.09763i) q^{41} -4.21448 q^{43} +(-1.15033 - 0.595357i) q^{44} +(5.56879 - 4.04596i) q^{46} +(0.0703185 + 0.216418i) q^{47} +(5.24145 + 3.80814i) q^{49} +(-5.81583 - 4.22545i) q^{50} +(-0.190071 - 0.584979i) q^{52} +(-4.61430 + 3.35249i) q^{53} +(1.39723 - 1.37959i) q^{55} +1.79654 q^{56} +(3.33426 + 10.2618i) q^{58} +(-2.20439 + 6.78441i) q^{59} +(-3.68827 - 2.67969i) q^{61} +(4.36131 - 13.4227i) q^{62} +(-4.76295 + 3.46049i) q^{64} +0.932429 q^{65} -8.09142 q^{67} +(1.45085 - 1.05411i) q^{68} +(0.204213 - 0.628502i) q^{70} +(-9.95852 - 7.23528i) q^{71} +(4.78461 - 14.7255i) q^{73} +(-1.38160 - 4.25213i) q^{74} +0.979704 q^{76} +(-2.12651 - 1.10058i) q^{77} +(11.8275 - 8.59316i) q^{79} +(0.846785 + 2.60614i) q^{80} +(1.44363 + 1.04886i) q^{82} +(-5.62510 - 4.08687i) q^{83} +(0.840097 + 2.58555i) q^{85} +(-5.27169 + 3.83010i) q^{86} +(8.15967 - 1.23930i) q^{88} -12.4803 q^{89} +(-0.351367 - 1.08140i) q^{91} +(0.537280 - 1.65358i) q^{92} +(0.284638 + 0.206802i) q^{94} +(-0.458943 + 1.41248i) q^{95} +(-11.4722 + 8.33507i) q^{97} +10.0171 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28}+ \cdots + 164 q^{98}+O(q^{100}) \) 36 * q - q^2 - 11 * q^4 - 8 * q^5 + 2 * q^7 - 3 * q^8 - 4 * q^10 - 2 * q^11 + 11 * q^13 - 10 * q^14 + 9 * q^16 + 10 * q^17 + 4 * q^19 - 45 * q^20 + 16 * q^22 + 20 * q^23 - 11 * q^25 + 6 * q^26 - 27 * q^28 - 23 * q^29 - 3 * q^31 + 18 * q^32 - 8 * q^34 - 9 * q^35 - 21 * q^37 - q^38 + 25 * q^40 + 10 * q^41 + 8 * q^43 - 19 * q^44 - 9 * q^46 - 34 * q^47 - q^49 + 27 * q^52 - 2 * q^53 + 9 * q^55 + 114 * q^56 - q^58 - 16 * q^59 + 3 * q^61 - 92 * q^62 + 13 * q^64 + 84 * q^65 - 10 * q^67 - 23 * q^68 + 46 * q^70 + 24 * q^71 - 20 * q^73 + 68 * q^74 - 16 * q^76 - 26 * q^77 - 19 * q^79 + 28 * q^80 + 47 * q^82 + 7 * q^83 - 25 * q^85 - 77 * q^86 - 18 * q^88 + 28 * q^89 + 10 * q^91 + 50 * q^92 + 63 * q^94 - 77 * q^95 + 33 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more