LMFDB - Embedded newform 168.2.u.a.89.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(17,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))

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

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

chi := DirichletCharacter("168.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.u (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + \cdots + 6561 $ x^16 - 6x^15 + 19x^14 - 42x^13 + 65x^12 - 48x^11 - 94x^10 + 444x^9 - 962x^8 + 1332x^7 - 846x^6 - 1296x^5 + 5265x^4 - 10206x^3 + 13851x^2 - 13122*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.4
Root			$0.934861 - 1.45809i$ of defining polynomial
Character	$\chi$	$=$	168.89
Dual form			168.2.u.a.17.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0805675 + 1.73018i) q^{3} +(1.90017 - 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(-2.98702 + 0.278792i) q^{9} +(0.309539 - 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 + 3.02246i) q^{15} +(0.0519689 + 0.0900129i) q^{17} +(-2.12615 - 1.22753i) q^{19} +(-2.26983 + 3.98094i) q^{21} +(-1.15188 - 0.665037i) q^{23} +(-4.72127 - 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(-6.83007 + 3.94335i) q^{31} +(0.334142 + 0.521158i) q^{33} +(8.90704 - 4.66504i) q^{35} +(5.45622 - 9.45046i) q^{37} +(-6.99976 + 0.325951i) q^{39} -6.15464 q^{41} +0.502751 q^{43} +(-4.75828 + 10.3606i) q^{45} +(-5.72578 + 9.91734i) q^{47} +(2.99000 + 6.32929i) q^{49} +(-0.151551 + 0.0971675i) q^{51} +(-5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 - 6.53614i) q^{59} +(8.20485 + 4.73707i) q^{61} +(-7.07060 - 3.60647i) q^{63} +(13.3151 + 7.68750i) q^{65} +(-1.34375 - 2.32744i) q^{67} +(1.05783 - 2.04653i) q^{69} -5.78975i q^{71} +(-0.203925 + 0.117736i) q^{73} +(13.7681 - 8.82748i) q^{75} +(0.944856 + 0.0388878i) q^{77} +(-1.61247 + 2.79289i) q^{79} +(8.84455 - 1.66551i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(8.60356 - 0.400634i) q^{87} +(-3.41213 + 5.90999i) q^{89} +(-5.72862 + 9.04192i) q^{91} +(-7.37296 - 11.4995i) q^{93} +(-8.08008 + 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 + 0.620114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) $ 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.0805675	+	1.73018i	0.0465156	+	0.998918i
$3$	0.0805675	+	1.73018i	0.0465156	+	0.998918i
$4$		0			0
$5$	1.90017	−	3.29119i	0.849781	−	1.47186i	−0.0316229	−	0.999500i	$-0.510068\pi$
$5$	1.90017	−	3.29119i	0.849781	−	1.47186i	0.881404	−	0.472364i	$-0.156599\pi$
$6$		0			0
$7$	2.23495	+	1.41598i	0.844732	+	0.535190i
$7$	2.23495	+	1.41598i	0.844732	+	0.535190i
$8$		0			0
$9$	−2.98702	+	0.278792i	−0.995673	+	0.0929306i
$10$		0			0
$11$	0.309539	−	0.178712i	0.0933294	−	0.0538838i	−0.452609	−	0.891709i	$-0.649507\pi$
$11$	0.309539	−	0.178712i	0.0933294	−	0.0538838i	0.545938	+	0.837825i	$0.316173\pi$
$12$		0			0
$13$			4.04570i			1.12207i	0.827791	+	0.561037i	$0.189597\pi$
$13$			4.04570i			1.12207i	−0.827791	+	0.561037i	$0.810403\pi$
$14$		0			0
$15$	5.84742	+	3.02246i	1.50980	+	0.780396i
$16$		0			0
$17$	0.0519689	+	0.0900129i	0.0126043	+	0.0218313i	0.872259	−	0.489045i	$-0.162654\pi$
$17$	0.0519689	+	0.0900129i	0.0126043	+	0.0218313i	−0.859654	+	0.510876i	$0.829321\pi$
$18$		0			0
$19$	−2.12615	−	1.22753i	−0.487772	−	0.281615i	0.235878	−	0.971783i	$-0.424204\pi$
$19$	−2.12615	−	1.22753i	−0.487772	−	0.281615i	−0.723650	+	0.690167i	$0.757537\pi$
$20$		0			0
$21$	−2.26983	+	3.98094i	−0.495318	+	0.868712i
$22$		0			0
$23$	−1.15188	−	0.665037i	−0.240183	−	0.138670i	0.375078	−	0.926993i	$-0.377616\pi$
$23$	−1.15188	−	0.665037i	−0.240183	−	0.138670i	−0.615261	+	0.788323i	$0.710949\pi$
$24$		0			0
$25$	−4.72127	−	8.17749i	−0.944255	−	1.63550i
$26$		0			0
$27$	−0.723015	−	5.14560i	−0.139144	−	0.990272i
$28$		0			0
$29$		−	4.97265i		−	0.923398i	−0.887037	−	0.461699i	$-0.847240\pi$
$29$		−	4.97265i		−	0.923398i	0.887037	−	0.461699i	$-0.152760\pi$
$30$		0			0
$31$	−6.83007	+	3.94335i	−1.22672	+	0.708246i	−0.966342	−	0.257262i	$-0.917180\pi$
$31$	−6.83007	+	3.94335i	−1.22672	+	0.708246i	−0.260376	+	0.965507i	$0.583846\pi$
$32$		0			0
$33$	0.334142	+	0.521158i	0.0581667	+	0.0907220i
$34$		0			0
$35$	8.90704	−	4.66504i	1.50556	−	0.788535i
$36$		0			0
$37$	5.45622	−	9.45046i	0.896998	−	1.55365i	0.0656853	−	0.997840i	$-0.479077\pi$
$37$	5.45622	−	9.45046i	0.896998	−	1.55365i	0.831312	−	0.555805i	$-0.187590\pi$
$38$		0			0
$39$	−6.99976	+	0.325951i	−1.12086	+	0.0521940i
$40$		0			0
$41$	−6.15464			−0.961193			−0.480597	−	0.876942i	$-0.659580\pi$
$41$	−6.15464			−0.961193			−0.480597	+	0.876942i	$0.659580\pi$
$42$		0			0
$43$	0.502751			0.0766688			0.0383344	−	0.999265i	$-0.487795\pi$
$43$	0.502751			0.0766688			0.0383344	+	0.999265i	$0.487795\pi$
$44$		0			0
$45$	−4.75828	+	10.3606i	−0.709322	+	1.54446i
$46$		0			0
$47$	−5.72578	+	9.91734i	−0.835190	+	1.44659i	0.0586849	+	0.998277i	$0.481309\pi$
$47$	−5.72578	+	9.91734i	−0.835190	+	1.44659i	−0.893875	+	0.448316i	$0.852024\pi$
$48$		0			0
$49$	2.99000	+	6.32929i	0.427143	+	0.904184i
$50$		0			0
$51$	−0.151551	+	0.0971675i	−0.0212214	+	0.0136062i
$52$		0			0
$53$	−5.08143	+	2.93376i	−0.697988	+	0.402983i	−0.806597	−	0.591101i	$-0.798693\pi$
$53$	−5.08143	+	2.93376i	−0.697988	+	0.402983i	0.108610	+	0.994084i	$0.465360\pi$
$54$		0			0
$55$		−	1.35833i		−	0.183158i
$56$		0			0
$57$	1.95255	−	3.77751i	0.258622	−	0.500344i
$58$		0			0
$59$	−3.77364	−	6.53614i	−0.491286	−	0.850933i	0.508664	−	0.860965i	$-0.330140\pi$
$59$	−3.77364	−	6.53614i	−0.491286	−	0.850933i	−0.999950	+	0.0100329i	$0.996806\pi$
$60$		0			0
$61$	8.20485	+	4.73707i	1.05052	+	0.606520i	0.922796	−	0.385289i	$-0.125898\pi$
$61$	8.20485	+	4.73707i	1.05052	+	0.606520i	0.127727	+	0.991809i	$0.459232\pi$
$62$		0			0
$63$	−7.07060	−	3.60647i	−0.890812	−	0.454373i
$64$		0			0
$65$	13.3151	+	7.68750i	1.65154	+	0.953517i
$66$		0			0
$67$	−1.34375	−	2.32744i	−0.164165	−	0.284342i	0.772193	−	0.635388i	$-0.219160\pi$
$67$	−1.34375	−	2.32744i	−0.164165	−	0.284342i	−0.936358	+	0.351045i	$0.885826\pi$
$68$		0			0
$69$	1.05783	−	2.04653i	0.127348	−	0.246374i
$70$		0			0
$71$		−	5.78975i		−	0.687117i	−0.939131	−	0.343558i	$-0.888368\pi$
$71$		−	5.78975i		−	0.687117i	0.939131	−	0.343558i	$-0.111632\pi$
$72$		0			0
$73$	−0.203925	+	0.117736i	−0.0238676	+	0.0137800i	−0.511886	−	0.859053i	$-0.671053\pi$
$73$	−0.203925	+	0.117736i	−0.0238676	+	0.0137800i	0.488019	+	0.872833i	$0.337720\pi$
$74$		0			0
$75$	13.7681	−	8.82748i	1.58980	−	1.01931i
$76$		0			0
$77$	0.944856	+	0.0388878i	0.107676	+	0.00443168i
$78$		0			0
$79$	−1.61247	+	2.79289i	−0.181418	+	0.314224i	−0.942364	−	0.334591i	$-0.891402\pi$
$79$	−1.61247	+	2.79289i	−0.181418	+	0.314224i	0.760946	+	0.648815i	$0.224735\pi$
$80$		0			0
$81$	8.84455	−	1.66551i	0.982728	−	0.185057i
$82$		0			0
$83$	9.07747			0.996382			0.498191	−	0.867067i	$-0.333998\pi$
$83$	9.07747			0.996382			0.498191	+	0.867067i	$0.333998\pi$
$84$		0			0
$85$	0.394999			0.0428436
$86$		0			0
$87$	8.60356	−	0.400634i	0.922398	−	0.0429525i
$88$		0			0
$89$	−3.41213	+	5.90999i	−0.361685	+	0.626457i	−0.988238	−	0.152921i	$-0.951132\pi$
$89$	−3.41213	+	5.90999i	−0.361685	+	0.626457i	0.626553	+	0.779379i	$0.284465\pi$
$90$		0			0
$91$	−5.72862	+	9.04192i	−0.600523	+	0.947851i
$92$		0			0
$93$	−7.37296	−	11.4995i	−0.764541	−	1.19245i
$94$		0			0
$95$	−8.08008	+	4.66504i	−0.828999	+	0.478623i
$96$		0			0
$97$		−	5.14243i		−	0.522134i	−0.965321	−	0.261067i	$-0.915926\pi$
$97$		−	5.14243i		−	0.522134i	0.965321	−	0.261067i	$-0.0840744\pi$
$98$		0			0
$99$	−0.874774	+	0.620114i	−0.0879181	+	0.0623238i
$100$		0			0
$101$	6.43891	+	11.1525i	0.640695	+	1.10972i	0.985278	+	0.170960i	$0.0546870\pi$
$101$	6.43891	+	11.1525i	0.640695	+	1.10972i	−0.344583	+	0.938756i	$0.611980\pi$
$102$		0			0
$103$	4.88120	+	2.81816i	0.480959	+	0.277682i	0.720816	−	0.693126i	$-0.243767\pi$
$103$	4.88120	+	2.81816i	0.480959	+	0.277682i	−0.239857	+	0.970808i	$0.577101\pi$
$104$		0			0
$105$	8.78895	+	15.0349i	0.857714	+	1.46725i
$106$		0			0
$107$	−7.62737	−	4.40366i	−0.737365	−	0.425718i	0.0837453	−	0.996487i	$-0.473312\pi$
$107$	−7.62737	−	4.40366i	−0.737365	−	0.425718i	−0.821111	+	0.570769i	$0.806645\pi$
$108$		0			0
$109$	2.23862	+	3.87741i	0.214421	+	0.371389i	0.953093	−	0.302676i	$-0.0978801\pi$
$109$	2.23862	+	3.87741i	0.214421	+	0.371389i	−0.738672	+	0.674065i	$0.764547\pi$
$110$		0			0
$111$	16.7905	+	8.67883i	1.59369	+	0.823758i
$112$		0			0
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$		0			0
$115$	−4.37753	+	2.52737i	−0.408206	+	0.235678i
$116$		0			0
$117$	−1.12791	−	12.0846i	−0.104275	−	1.11722i
$118$		0			0
$119$	−0.0113084	+	0.274761i	−0.00103664	+	0.0251873i
$120$		0			0
$121$	−5.43612	+	9.41564i	−0.494193	+	0.855968i
$122$		0			0
$123$	−0.495864	−	10.6486i	−0.0447105	−	0.960153i
$124$		0			0
$125$	−16.8832			−1.51008
$126$		0			0
$127$	12.9198			1.14645			0.573223	−	0.819399i	$-0.305693\pi$
$127$	12.9198			1.14645			0.573223	+	0.819399i	$0.305693\pi$
$128$		0			0
$129$	0.0405054	+	0.869848i	0.00356630	+	0.0765858i
$130$		0			0
$131$	−2.66384	+	4.61391i	−0.232741	+	0.403119i	−0.958614	−	0.284710i	$-0.908103\pi$
$131$	−2.66384	+	4.61391i	−0.232741	+	0.403119i	0.725873	+	0.687829i	$0.241436\pi$
$132$		0			0
$133$	−3.01367	−	5.75406i	−0.261319	−	0.498940i
$134$		0			0
$135$	−18.3090	−	7.39793i	−1.57579	−	0.636713i
$136$		0			0
$137$	4.37380	−	2.52521i	0.373679	−	0.215744i	−0.301386	−	0.953502i	$-0.597449\pi$
$137$	4.37380	−	2.52521i	0.373679	−	0.215744i	0.675064	+	0.737759i	$0.264116\pi$
$138$		0			0
$139$		−	21.2651i		−	1.80368i	−0.432067	−	0.901841i	$-0.642216\pi$
$139$		−	21.2651i		−	1.80368i	0.432067	−	0.901841i	$-0.357784\pi$
$140$		0			0
$141$	−17.6200	−	9.10759i	−1.48388	−	0.766997i
$142$		0			0
$143$	0.723015	+	1.25230i	0.0604616	+	0.104723i
$144$		0			0
$145$	−16.3659	−	9.44887i	−1.35912	−	0.784686i
$146$		0			0
$147$	−10.7099	+	5.68316i	−0.883337	+	0.468739i
$148$		0			0
$149$	10.5482	+	6.09001i	0.864143	+	0.498913i	0.865398	−	0.501086i	$-0.167066\pi$
$149$	10.5482	+	6.09001i	0.864143	+	0.498913i	−0.00125437	+	0.999999i	$0.500399\pi$
$150$		0			0
$151$	4.10880	+	7.11665i	0.334369	+	0.579145i	0.983363	−	0.181649i	$-0.0581434\pi$
$151$	4.10880	+	7.11665i	0.334369	+	0.579145i	−0.648994	+	0.760793i	$0.724810\pi$
$152$		0			0
$153$	−0.180327	−	0.254381i	−0.0145786	−	0.0205655i
$154$		0			0
$155$			29.9721i			2.40741i
$156$		0			0
$157$	11.2104	−	6.47230i	0.894683	−	0.516546i	0.0192119	−	0.999815i	$-0.493884\pi$
$157$	11.2104	−	6.47230i	0.894683	−	0.516546i	0.875472	+	0.483270i	$0.160551\pi$
$158$		0			0
$159$	−5.48532	−	8.55539i	−0.435014	−	0.678487i
$160$		0			0
$161$	−1.63271	−	3.11736i	−0.128676	−	0.245683i
$162$		0			0
$163$	1.09237	−	1.89205i	0.0855613	−	0.148197i	−0.820069	−	0.572265i	$-0.806065\pi$
$163$	1.09237	−	1.89205i	0.0855613	−	0.148197i	0.905630	+	0.424068i	$0.139398\pi$
$164$		0			0
$165$	2.35016	−	0.109437i	0.182959	−	0.00851969i
$166$		0			0
$167$	−0.464592			−0.0359512			−0.0179756	−	0.999838i	$-0.505722\pi$
$167$	−0.464592			−0.0359512			−0.0179756	+	0.999838i	$0.505722\pi$
$168$		0			0
$169$	−3.36765			−0.259050
$170$		0			0
$171$	6.69307	+	3.07391i	0.511832	+	0.235068i
$172$		0			0
$173$	−4.62587	+	8.01224i	−0.351698	+	0.609159i	−0.986547	−	0.163477i	$-0.947729\pi$
$173$	−4.62587	+	8.01224i	−0.351698	+	0.609159i	0.634849	+	0.772636i	$0.281062\pi$
$174$		0			0
$175$	1.02735	−	24.9615i	0.0776603	−	1.88691i
$176$		0			0
$177$	11.0046	−	7.05566i	0.827159	−	0.530336i
$178$		0			0
$179$	−1.77096	+	1.02246i	−0.132367	+	0.0764224i	−0.564722	−	0.825282i	$-0.691016\pi$
$179$	−1.77096	+	1.02246i	−0.132367	+	0.0764224i	0.432354	+	0.901704i	$0.357683\pi$
$180$		0			0
$181$			17.6193i			1.30963i	0.755790	+	0.654815i	$0.227253\pi$
$181$			17.6193i			1.30963i	−0.755790	+	0.654815i	$0.772747\pi$
$182$		0			0
$183$	−7.53492	+	14.5775i	−0.556998	+	1.07760i
$184$		0			0
$185$	−20.7355	−	35.9149i	−1.52450	−	2.64052i
$186$		0			0
$187$	0.0321728	+	0.0185750i	0.00235271	+	0.00135834i
$188$		0			0
$189$	5.67017	−	12.5239i	0.412444	−	0.910983i
$190$		0			0
$191$	19.4811	+	11.2474i	1.40960	+	0.813834i	0.995350	−	0.0963279i	$-0.0307097\pi$
$191$	19.4811	+	11.2474i	1.40960	+	0.813834i	0.414252	+	0.910162i	$0.364043\pi$
$192$		0			0
$193$	−4.81985	−	8.34823i	−0.346940	−	0.600918i	0.638764	−	0.769403i	$-0.279446\pi$
$193$	−4.81985	−	8.34823i	−0.346940	−	0.600918i	−0.985704	+	0.168484i	$0.946113\pi$
$194$		0			0
$195$	−12.2280	+	23.6569i	−0.875662	+	1.69411i
$196$		0			0
$197$		−	15.3750i		−	1.09542i	−0.836667	−	0.547712i	$-0.815499\pi$
$197$		−	15.3750i		−	1.09542i	0.836667	−	0.547712i	$-0.184501\pi$
$198$		0			0
$199$	−3.96967	+	2.29189i	−0.281403	+	0.162468i	−0.634058	−	0.773285i	$-0.718612\pi$
$199$	−3.96967	+	2.29189i	−0.281403	+	0.162468i	0.352656	+	0.935753i	$0.385279\pi$
$200$		0			0
$201$	3.91862	−	2.51244i	0.276398	−	0.177214i
$202$		0			0
$203$	7.04117	−	11.1136i	0.494194	−	0.780023i
$204$		0			0
$205$	−11.6948	+	20.2561i	−0.816804	+	1.41475i
$206$		0			0
$207$	3.62609	+	1.66534i	0.252031	+	0.115749i
$208$		0			0
$209$	−0.877501			−0.0606980
$210$		0			0
$211$	−0.870400			−0.0599208			−0.0299604	−	0.999551i	$-0.509538\pi$
$211$	−0.870400			−0.0599208			−0.0299604	+	0.999551i	$0.509538\pi$
$212$		0			0
$213$	10.0173	−	0.466465i	0.686373	−	0.0319617i
$214$		0			0
$215$	0.955311	−	1.65465i	0.0651517	−	0.112846i
$216$		0			0
$217$	−20.8486	−	0.858072i	−1.41529	−	0.0582497i
$218$		0			0
$219$	−0.220134	−	0.343341i	−0.0148753	−	0.0232008i
$220$		0			0
$221$	−0.364165	+	0.210251i	−0.0244964	+	0.0141430i
$222$		0			0
$223$			1.21373i			0.0812777i	0.999174	+	0.0406388i	$0.0129393\pi$
$223$			1.21373i			0.0812777i	−0.999174	+	0.0406388i	$0.987061\pi$
$224$		0			0
$225$	16.3823	+	23.1100i	1.09216	+	1.54067i
$226$		0			0
$227$	−6.67205	−	11.5563i	−0.442840	−	0.767021i	0.555059	−	0.831811i	$-0.312696\pi$
$227$	−6.67205	−	11.5563i	−0.442840	−	0.767021i	−0.997899	+	0.0647898i	$0.979362\pi$
$228$		0			0
$229$	9.60627	+	5.54618i	0.634800	+	0.366502i	0.782609	−	0.622514i	$-0.213889\pi$
$229$	9.60627	+	5.54618i	0.634800	+	0.366502i	−0.147808	+	0.989016i	$0.547222\pi$
$230$		0			0
$231$	0.00884196	+	1.63790i	0.000581758	+	0.107766i
$232$		0			0
$233$	7.08411	+	4.09001i	0.464095	+	0.267946i	0.713765	−	0.700386i	$-0.246989\pi$
$233$	7.08411	+	4.09001i	0.464095	+	0.267946i	−0.249669	+	0.968331i	$0.580322\pi$
$234$		0			0
$235$	21.7599	+	37.6892i	1.41946	+	2.45857i
$236$		0			0
$237$	−4.96210	−	2.56485i	−0.322323	−	0.166605i
$238$		0			0
$239$		−	22.5944i		−	1.46151i	−0.682638	−	0.730757i	$-0.739167\pi$
$239$		−	22.5944i		−	1.46151i	0.682638	−	0.730757i	$-0.260833\pi$
$240$		0			0
$241$	4.24127	−	2.44870i	0.273205	−	0.157735i	−0.357138	−	0.934051i	$-0.616248\pi$
$241$	4.24127	−	2.44870i	0.273205	−	0.157735i	0.630343	+	0.776317i	$0.282914\pi$
$242$		0			0
$243$	3.59421	+	15.1684i	0.230569	+	0.973056i
$244$		0			0
$245$	26.5124	+	2.18606i	1.69381	+	0.139662i
$246$		0			0
$247$	4.96622	−	8.60175i	0.315993	−	0.547316i
$248$		0			0
$249$	0.731349	+	15.7056i	0.0463474	+	0.995304i
$250$		0			0
$251$	−9.17857			−0.579346			−0.289673	−	0.957126i	$-0.593547\pi$
$251$	−9.17857			−0.579346			−0.289673	+	0.957126i	$0.593547\pi$
$252$		0			0
$253$	−0.475401			−0.0298882
$254$		0			0
$255$	0.0318241	+	0.683418i	0.00199290	+	0.0427973i
$256$		0			0
$257$	−6.31055	+	10.9302i	−0.393641	+	0.681806i	−0.992927	−	0.118729i	$-0.962118\pi$
$257$	−6.31055	+	10.9302i	−0.393641	+	0.681806i	0.599286	+	0.800535i	$0.295451\pi$
$258$		0			0
$259$	25.5760	−	13.3954i	1.58922	−	0.832349i
$260$		0			0
$261$	1.38633	+	14.8534i	0.0858119	+	0.919402i
$262$		0			0
$263$	25.2489	−	14.5775i	1.55692	−	0.898886i	0.559367	−	0.828920i	$-0.311044\pi$
$263$	25.2489	−	14.5775i	1.55692	−	0.898886i	0.997549	−	0.0699665i	$-0.0222892\pi$
$264$		0			0
$265$			22.2986i			1.36979i
$266$		0			0
$267$	−10.5002	−	5.42744i	−0.642603	−	0.332154i
$268$		0			0
$269$	−2.23640	−	3.87356i	−0.136356	−	0.236175i	0.789759	−	0.613418i	$-0.210206\pi$
$269$	−2.23640	−	3.87356i	−0.136356	−	0.236175i	−0.926115	+	0.377242i	$0.876872\pi$
$270$		0			0
$271$	−14.4985	−	8.37071i	−0.880721	−	0.508485i	−0.00982495	−	0.999952i	$-0.503127\pi$
$271$	−14.4985	−	8.37071i	−0.880721	−	0.508485i	−0.870896	+	0.491467i	$0.836461\pi$
$272$		0			0
$273$	−16.1057	−	9.18304i	−0.974759	−	0.555783i
$274$		0			0
$275$	−2.92283	−	1.68750i	−0.176254	−	0.101760i
$276$		0			0
$277$	−0.510924	−	0.884946i	−0.0306984	−	0.0531713i	0.850268	−	0.526350i	$-0.176440\pi$
$277$	−0.510924	−	0.884946i	−0.0306984	−	0.0531713i	−0.880966	+	0.473179i	$0.843106\pi$
$278$		0			0
$279$	19.3022	−	13.6830i	1.15559	−	0.819181i
$280$		0			0
$281$			13.9453i			0.831907i	0.909386	+	0.415953i	$0.136552\pi$
$281$			13.9453i			0.831907i	−0.909386	+	0.415953i	$0.863448\pi$
$282$		0			0
$283$	14.0386	−	8.10519i	0.834508	−	0.481803i	−0.0208856	−	0.999782i	$-0.506649\pi$
$283$	14.0386	−	8.10519i	0.834508	−	0.481803i	0.855394	+	0.517978i	$0.173315\pi$
$284$		0			0
$285$	−8.72233	−	13.6041i	−0.516666	−	0.805838i
$286$		0			0
$287$	−13.7553	−	8.71485i	−0.811950	−	0.514421i
$288$		0			0
$289$	8.49460	−	14.7131i	0.499682	−	0.865475i
$290$		0			0
$291$	8.89731	−	0.414312i	0.521569	−	0.0242874i
$292$		0			0
$293$	19.2067			1.12207			0.561034	−	0.827793i	$-0.310404\pi$
$293$	19.2067			1.12207			0.561034	+	0.827793i	$0.310404\pi$
$294$		0			0
$295$	−28.6822			−1.66994
$296$		0			0
$297$	−1.14338	−	1.46355i	−0.0663459	−	0.0849239i
$298$		0			0
$299$	2.69054	−	4.66015i	0.155598	−	0.269503i
$300$		0			0
$301$	1.12362	+	0.711886i	0.0647646	+	0.0410324i
$302$		0			0
$303$	−18.7770	+	12.0390i	−1.07871	+	0.691621i
$304$		0			0
$305$	31.1812	−	18.0025i	1.78543	−	1.03082i
$306$		0			0
$307$			0.480498i			0.0274235i	0.999906	+	0.0137117i	$0.00436472\pi$
$307$			0.480498i			0.0274235i	−0.999906	+	0.0137117i	$0.995635\pi$
$308$		0			0
$309$	−4.48265	+	8.67239i	−0.255009	+	0.493355i
$310$		0			0
$311$	−4.66653	−	8.08266i	−0.264615	−	0.458326i	0.702848	−	0.711340i	$-0.251911\pi$
$311$	−4.66653	−	8.08266i	−0.264615	−	0.458326i	−0.967463	+	0.253014i	$0.918578\pi$
$312$		0			0
$313$	15.5147	+	8.95742i	0.876943	+	0.506303i	0.869649	−	0.493670i	$-0.164345\pi$
$313$	15.5147	+	8.95742i	0.876943	+	0.506303i	0.00729351	+	0.999973i	$0.497678\pi$
$314$		0			0
$315$	−25.3049	+	16.4178i	−1.42577	+	0.925036i
$316$		0			0
$317$	−19.3275	−	11.1587i	−1.08554	−	0.626736i	−0.153153	−	0.988202i	$-0.548943\pi$
$317$	−19.3275	−	11.1587i	−1.08554	−	0.626736i	−0.932385	+	0.361467i	$0.882276\pi$
$318$		0			0
$319$	−0.888674	−	1.53923i	−0.0497562	−	0.0861802i
$320$		0			0
$321$	7.00459	−	13.5515i	0.390958	−	0.756370i
$322$		0			0
$323$		−	0.255174i		−	0.0141983i
$324$		0			0
$325$	33.0836	−	19.1008i	1.83515	−	1.05952i
$326$		0			0
$327$	−6.52824	+	4.18561i	−0.361013	+	0.231465i
$328$		0			0
$329$	−26.8396	+	14.0572i	−1.47971	+	0.774996i
$330$		0			0
$331$	−7.05860	+	12.2259i	−0.387976	+	0.671994i	−0.992177	−	0.124838i	$-0.960159\pi$
$331$	−7.05860	+	12.2259i	−0.387976	+	0.671994i	0.604201	+	0.796832i	$0.293492\pi$
$332$		0			0
$333$	−13.6631	+	29.7498i	−0.748735	+	1.63028i
$334$		0			0
$335$	−10.2134			−0.558018
$336$		0			0
$337$	−18.4042			−1.00254			−0.501270	−	0.865291i	$-0.667134\pi$
$337$	−18.4042			−1.00254			−0.501270	+	0.865291i	$0.667134\pi$
$338$		0			0
$339$	6.92070	−	0.322270i	0.375881	−	0.0175033i
$340$		0			0
$341$	−1.40945	+	2.44124i	−0.0763259	+	0.132200i
$342$		0			0
$343$	−2.27965	+	18.3794i	−0.123089	+	0.992396i
$344$		0			0
$345$	−4.72547	−	7.37027i	−0.254411	−	0.396802i
$346$		0			0
$347$	−27.6474	+	15.9623i	−1.48419	+	0.856899i	−0.999838	−	0.0179729i	$-0.994279\pi$
$347$	−27.6474	+	15.9623i	−1.48419	+	0.856899i	−0.484354	+	0.874872i	$0.660945\pi$
$348$		0			0
$349$		−	14.7367i		−	0.788840i	−0.918930	−	0.394420i	$-0.870945\pi$
$349$		−	14.7367i		−	0.788840i	0.918930	−	0.394420i	$-0.129055\pi$
$350$		0			0
$351$	20.8175	−	2.92510i	1.11116	−	0.156130i
$352$		0			0
$353$	13.5686	+	23.5016i	0.722185	+	1.25086i	0.960122	+	0.279581i	$0.0901956\pi$
$353$	13.5686	+	23.5016i	0.722185	+	1.25086i	−0.237937	+	0.971281i	$0.576471\pi$
$354$		0			0
$355$	−19.0551	−	11.0015i	−1.01134	−	0.583899i
$356$		0			0
$357$	−0.476296	+	0.00257121i	−0.0252083	+	0.000136083i
$358$		0			0
$359$	16.9479	+	9.78486i	0.894475	+	0.516425i	0.875404	−	0.483393i	$-0.160596\pi$
$359$	16.9479	+	9.78486i	0.894475	+	0.516425i	0.0190713	+	0.999818i	$0.493929\pi$
$360$		0			0
$361$	−6.48633	−	11.2346i	−0.341386	−	0.591297i
$362$		0			0
$363$	−16.7287	−	8.64686i	−0.878029	−	0.453842i
$364$		0			0
$365$			0.894875i			0.0468399i
$366$		0			0
$367$	−1.16258	+	0.671213i	−0.0606860	+	0.0350371i	−0.530036	−	0.847975i	$-0.677822\pi$
$367$	−1.16258	+	0.671213i	−0.0606860	+	0.0350371i	0.469350	+	0.883012i	$0.344488\pi$
$368$		0			0
$369$	18.3840	−	1.71586i	0.957034	−	0.0893243i
$370$		0			0
$371$	−15.5109	−	0.638387i	−0.805285	−	0.0331434i
$372$		0			0
$373$	−6.52378	+	11.2995i	−0.337788	+	0.585066i	−0.984016	−	0.178078i	$-0.943012\pi$
$373$	−6.52378	+	11.2995i	−0.337788	+	0.585066i	0.646228	+	0.763144i	$0.276345\pi$
$374$		0			0
$375$	−1.36023	−	29.2109i	−0.0702422	−	1.50844i
$376$		0			0
$377$	20.1178			1.03612
$378$		0			0
$379$	−20.0822			−1.03156			−0.515778	−	0.856722i	$-0.672497\pi$
$379$	−20.0822			−1.03156			−0.515778	+	0.856722i	$0.672497\pi$
$380$		0			0
$381$	1.04092	+	22.3535i	0.0533277	+	1.14521i
$382$		0			0
$383$	11.2613	−	19.5052i	0.575428	−	0.996670i	−0.420567	−	0.907261i	$-0.638169\pi$
$383$	11.2613	−	19.5052i	0.575428	−	0.996670i	0.995995	−	0.0894085i	$-0.0284977\pi$
$384$		0			0
$385$	1.92337	−	3.03581i	0.0980242	−	0.154719i
$386$		0			0
$387$	−1.50173	+	0.140163i	−0.0763370	+	0.00712488i
$388$		0			0
$389$	−32.1899	+	18.5848i	−1.63209	+	0.942289i	−0.648645	+	0.761091i	$0.724664\pi$
$389$	−32.1899	+	18.5848i	−1.63209	+	0.942289i	−0.983447	+	0.181197i	$0.942003\pi$
$390$		0			0
$391$		−	0.138245i		−	0.00699136i
$392$		0			0
$393$	−8.19750	−	4.23719i	−0.413509	−	0.213738i
$394$		0			0
$395$	6.12795	+	10.6139i	0.308330	+	0.534044i
$396$		0			0
$397$	−24.0288	−	13.8730i	−1.20597	−	0.696268i	−0.244095	−	0.969751i	$-0.578491\pi$
$397$	−24.0288	−	13.8730i	−1.20597	−	0.696268i	−0.961877	+	0.273483i	$0.911824\pi$
$398$		0			0
$399$	9.71273	−	5.67778i	0.486245	−	0.284244i
$400$		0			0
$401$	−19.7233	−	11.3872i	−0.984933	−	0.568651i	−0.0811773	−	0.996700i	$-0.525868\pi$
$401$	−19.7233	−	11.3872i	−0.984933	−	0.568651i	−0.903756	+	0.428048i	$0.859201\pi$
$402$		0			0
$403$	−15.9536	−	27.6324i	−0.794704	−	1.37647i
$404$		0			0
$405$	11.3246	−	32.2738i	0.562725	−	1.60370i
$406$		0			0
$407$		−	3.90038i		−	0.193334i
$408$		0			0
$409$	−22.6849	+	13.0972i	−1.12170	+	0.647613i	−0.941834	−	0.336078i	$-0.890899\pi$
$409$	−22.6849	+	13.0972i	−1.12170	+	0.647613i	−0.179865	+	0.983691i	$0.557566\pi$
$410$		0			0
$411$	4.72145	+	7.36399i	0.232892	+	0.363239i
$412$		0			0
$413$	0.821144	−	19.9513i	0.0404059	−	0.981741i
$414$		0			0
$415$	17.2487	−	29.8757i	0.846707	−	1.46654i
$416$		0			0
$417$	36.7924	−	1.71328i	1.80173	−	0.0838995i
$418$		0			0
$419$	8.93992			0.436744			0.218372	−	0.975866i	$-0.429925\pi$
$419$	8.93992			0.436744			0.218372	+	0.975866i	$0.429925\pi$
$420$		0			0
$421$	−5.00735			−0.244043			−0.122022	−	0.992527i	$-0.538938\pi$
$421$	−5.00735			−0.244043			−0.122022	+	0.992527i	$0.538938\pi$
$422$		0			0
$423$	14.3381	−	31.2196i	0.697144	−	1.51795i
$424$		0			0
$425$	0.490719	−	0.849951i	0.0238034	−	0.0412287i
$426$		0			0
$427$	11.6298	+	22.2050i	0.562807	+	1.07458i
$428$		0			0
$429$	−2.10845	+	1.35184i	−0.101797	+	0.0652674i
$430$		0			0
$431$	−5.62468	+	3.24741i	−0.270931	+	0.156422i	−0.629311	−	0.777154i	$-0.716663\pi$
$431$	−5.62468	+	3.24741i	−0.270931	+	0.156422i	0.358379	+	0.933576i	$0.383329\pi$
$432$		0			0
$433$		−	1.05254i		−	0.0505818i	−0.999680	−	0.0252909i	$-0.991949\pi$
$433$		−	1.05254i		−	0.0505818i	0.999680	−	0.0252909i	$-0.00805120\pi$
$434$		0			0
$435$	15.0296	−	29.0772i	0.720616	−	1.39414i
$436$		0			0
$437$	1.63271	+	2.82794i	0.0781032	+	0.135279i
$438$		0			0
$439$	25.8990	+	14.9528i	1.23609	+	0.713658i	0.968293	−	0.249817i	$-0.0803705\pi$
$439$	25.8990	+	14.9528i	1.23609	+	0.713658i	0.267799	+	0.963475i	$0.413704\pi$
$440$		0			0
$441$	−10.6957	−	18.0721i	−0.509321	−	0.860577i
$442$		0			0
$443$	26.7104	+	15.4212i	1.26905	+	0.732685i	0.974808	−	0.223047i	$-0.0716002\pi$
$443$	26.7104	+	15.4212i	1.26905	+	0.732685i	0.294240	+	0.955732i	$0.404934\pi$
$444$		0			0
$445$	12.9672	+	22.4599i	0.614707	+	1.06470i
$446$		0			0
$447$	−9.68695	+	18.7409i	−0.458177	+	0.886415i
$448$		0			0
$449$			36.6953i			1.73176i	0.500253	+	0.865879i	$0.333240\pi$
$449$			36.6953i			1.73176i	−0.500253	+	0.865879i	$0.666760\pi$
$450$		0			0
$451$	−1.90510	+	1.09991i	−0.0897076	+	0.0517927i
$452$		0			0
$453$	−11.9820	+	7.68232i	−0.562964	+	0.360947i
$454$		0			0
$455$	18.8733	+	36.0351i	0.884795	+	1.68935i
$456$		0			0
$457$	11.8750	−	20.5681i	0.555489	−	0.962135i	−0.442376	−	0.896830i	$-0.645864\pi$
$457$	11.8750	−	20.5681i	0.555489	−	0.962135i	0.997865	−	0.0653057i	$-0.0208022\pi$
$458$		0			0
$459$	0.425596	−	0.332492i	0.0198651	−	0.0155194i
$460$		0			0
$461$	−10.5938			−0.493404			−0.246702	−	0.969091i	$-0.579347\pi$
$461$	−10.5938			−0.493404			−0.246702	+	0.969091i	$0.579347\pi$
$462$		0			0
$463$	−0.367649			−0.0170861			−0.00854305	−	0.999964i	$-0.502719\pi$
$463$	−0.367649			−0.0170861			−0.00854305	+	0.999964i	$0.502719\pi$
$464$		0			0
$465$	−51.8570	+	2.41477i	−2.40481	+	0.111982i
$466$		0			0
$467$	−15.7847	+	27.3399i	−0.730428	+	1.26514i	0.226272	+	0.974064i	$0.427346\pi$
$467$	−15.7847	+	27.3399i	−0.730428	+	1.26514i	−0.956700	+	0.291075i	$0.905987\pi$
$468$		0			0
$469$	0.292400	−	7.10444i	0.0135018	−	0.328053i
$470$		0			0
$471$	12.1014	+	18.8744i	0.557603	+	0.869688i
$472$		0			0
$473$	0.155621	−	0.0898478i	0.00715546	−	0.00413120i
$474$		0			0
$475$			23.1821i			1.06367i
$476$		0			0
$477$	14.3604	−	10.1799i	0.657518	−	0.466104i
$478$		0			0
$479$	6.01497	+	10.4182i	0.274831	+	0.476022i	0.970093	−	0.242735i	$-0.0780447\pi$
$479$	6.01497	+	10.4182i	0.274831	+	0.476022i	−0.695261	+	0.718757i	$0.744711\pi$
$480$		0			0
$481$	38.2337	+	22.0742i	1.74331	+	1.00650i
$482$		0			0
$483$	5.26204	−	3.07604i	0.239431	−	0.139964i
$484$		0			0
$485$	−16.9247	−	9.77148i	−0.768511	−	0.443700i
$486$		0			0
$487$	9.47737	+	16.4153i	0.429461	+	0.743848i	0.996825	−	0.0796188i	$-0.0253703\pi$
$487$	9.47737	+	16.4153i	0.429461	+	0.743848i	−0.567365	+	0.823467i	$0.692037\pi$
$488$		0			0
$489$	3.36159	+	1.73756i	0.152016	+	0.0785753i
$490$		0			0
$491$		−	15.8373i		−	0.714727i	−0.933965	−	0.357364i	$-0.883676\pi$
$491$		−	15.8373i		−	0.714727i	0.933965	−	0.357364i	$-0.116324\pi$
$492$		0			0
$493$	0.447602	−	0.258423i	0.0201590	−	0.0116388i
$494$		0			0
$495$	0.378692	+	4.05736i	0.0170209	+	0.182365i
$496$		0			0
$497$	8.19817	−	12.9398i	0.367738	−	0.580429i
$498$		0			0
$499$	−10.0988	+	17.4916i	−0.452084	+	0.783033i	−0.998515	−	0.0544710i	$-0.982653\pi$
$499$	−10.0988	+	17.4916i	−0.452084	+	0.783033i	0.546431	+	0.837504i	$0.315986\pi$
$500$		0			0
$501$	−0.0374310	−	0.803826i	−0.00167229	−	0.0359123i
$502$		0			0
$503$	−36.8663			−1.64379			−0.821893	−	0.569641i	$-0.807082\pi$
$503$	−36.8663			−1.64379			−0.821893	+	0.569641i	$0.807082\pi$
$504$		0			0
$505$	48.9400			2.17780
$506$		0			0
$507$	−0.271323	−	5.82663i	−0.0120499	−	0.258770i
$508$		0			0
$509$	5.13197	−	8.88884i	0.227471	−	0.393991i	−0.729587	−	0.683888i	$-0.760288\pi$
$509$	5.13197	−	8.88884i	0.227471	−	0.393991i	0.957058	+	0.289897i	$0.0936211\pi$
$510$		0			0
$511$	−0.622475	−	0.0256194i	−0.0275367	−	0.00113334i
$512$		0			0
$513$	−4.77916	+	11.8279i	−0.211005	+	0.522212i
$514$		0			0
$515$	18.5502	−	10.7100i	0.817419	−	0.471937i
$516$		0			0
$517$			4.09307i			0.180013i
$518$		0			0
$519$	−14.2353	−	7.35804i	−0.624859	−	0.322982i
$520$		0			0
$521$	−7.98887	−	13.8371i	−0.349999	−	0.606216i	0.636250	−	0.771483i	$-0.280485\pi$
$521$	−7.98887	−	13.8371i	−0.349999	−	0.606216i	−0.986249	+	0.165267i	$0.947151\pi$
$522$		0			0
$523$	0.676700	+	0.390693i	0.0295900	+	0.0170838i	0.514722	−	0.857357i	$-0.327895\pi$
$523$	0.676700	+	0.390693i	0.0295900	+	0.0170838i	−0.485132	+	0.874441i	$0.661228\pi$
$524$		0			0
$525$	43.2706	−	0.233590i	1.88848	−	0.0101947i
$526$		0			0
$527$	−0.709904	−	0.409863i	−0.0309239	−	0.0178539i
$528$		0			0
$529$	−10.6155	−	18.3865i	−0.461541	−	0.799413i
$530$		0			0
$531$	13.0942	+	18.4715i	0.568238	+	0.801595i
$532$		0			0
$533$		−	24.8998i		−	1.07853i
$534$		0			0
$535$	−28.9865	+	16.7354i	−1.25320	+	0.723534i
$536$		0			0
$537$	−1.91172	−	2.98169i	−0.0824968	−	0.128669i
$538$		0			0
$539$	2.05664	+	1.42481i	0.0885859	+	0.0613709i
$540$		0			0
$541$	3.63362	−	6.29362i	0.156222	−	0.270584i	−0.777282	−	0.629153i	$-0.783402\pi$
$541$	3.63362	−	6.29362i	0.156222	−	0.270584i	0.933503	+	0.358569i	$0.116735\pi$
$542$		0			0
$543$	−30.4844	+	1.41954i	−1.30821	+	0.0609182i
$544$		0			0
$545$	17.0150			0.728845
$546$		0			0
$547$	41.2546			1.76392			0.881960	−	0.471325i	$-0.156224\pi$
$547$	41.2546			1.76392			0.881960	+	0.471325i	$0.156224\pi$
$548$		0			0
$549$	−25.8287	−	11.8623i	−1.10234	−	0.506269i
$550$		0			0
$551$	−6.10409	+	10.5726i	−0.260043	+	0.450408i
$552$		0			0
$553$	−7.55847	+	3.95873i	−0.321419	+	0.168342i
$554$		0			0
$555$	60.4685	−	38.7696i	2.56675	−	1.64568i
$556$		0			0
$557$	5.48798	−	3.16849i	0.232533	−	0.134253i	−0.379207	−	0.925312i	$-0.623803\pi$
$557$	5.48798	−	3.16849i	0.232533	−	0.134253i	0.611740	+	0.791059i	$0.290470\pi$
$558$		0			0
$559$			2.03398i			0.0860281i
$560$		0			0
$561$	−0.0295459	+	0.0571611i	−0.00124743	+	0.00241335i
$562$		0			0
$563$	7.73130	+	13.3910i	0.325836	+	0.564364i	0.981681	−	0.190531i	$-0.0610211\pi$
$563$	7.73130	+	13.3910i	0.325836	+	0.564364i	−0.655846	+	0.754895i	$0.727688\pi$
$564$		0			0
$565$	−13.1647	−	7.60067i	−0.553845	−	0.319763i
$566$		0			0
$567$	22.1255	+	8.80137i	0.929182	+	0.369623i
$568$		0			0
$569$	−10.2364	−	5.90999i	−0.429132	−	0.247760i	0.269845	−	0.962904i	$-0.413028\pi$
$569$	−10.2364	−	5.90999i	−0.429132	−	0.247760i	−0.698977	+	0.715144i	$0.746361\pi$
$570$		0			0
$571$	−18.0386	−	31.2438i	−0.754892	−	1.30751i	−0.945428	−	0.325831i	$-0.894356\pi$
$571$	−18.0386	−	31.2438i	−0.754892	−	1.30751i	0.190536	−	0.981680i	$-0.438977\pi$
$572$		0			0
$573$	−17.8905	+	34.6119i	−0.747385	+	1.44593i
$574$		0			0
$575$			12.5593i			0.523759i
$576$		0			0
$577$	−20.4253	+	11.7926i	−0.850316	+	0.490930i	−0.860758	−	0.509015i	$-0.830010\pi$
$577$	−20.4253	+	11.7926i	−0.850316	+	0.490930i	0.0104412	+	0.999945i	$0.496676\pi$
$578$		0			0
$579$	14.0556	−	9.01178i	0.584130	−	0.374517i
$580$		0			0
$581$	20.2877	+	12.8535i	0.841676	+	0.533254i
$582$		0			0
$583$	−1.04860	+	1.81623i	−0.0434285	+	0.0752204i
$584$		0			0
$585$	−41.9158	−	19.2505i	−1.73300	−	0.795912i
$586$		0			0
$587$	−0.287490			−0.0118660			−0.00593298	−	0.999982i	$-0.501889\pi$
$587$	−0.287490			−0.0118660			−0.00593298	+	0.999982i	$0.501889\pi$
$588$		0			0
$589$	19.3623			0.797812
$590$		0			0
$591$	26.6015	−	1.23872i	1.09424	−	0.0509543i
$592$		0			0
$593$	5.71589	−	9.90021i	0.234723	−	0.406553i	−0.724469	−	0.689308i	$-0.757915\pi$
$593$	5.71589	−	9.90021i	0.234723	−	0.406553i	0.959192	+	0.282755i	$0.0912482\pi$
$594$		0			0
$595$	0.882803	+	0.559311i	0.0361914	+	0.0229295i
$596$		0			0
$597$	−4.28520	−	6.68358i	−0.175382	−	0.273541i
$598$		0			0
$599$	−18.7842	+	10.8451i	−0.767502	+	0.443117i	−0.831983	−	0.554802i	$-0.812794\pi$
$599$	−18.7842	+	10.8451i	−0.767502	+	0.443117i	0.0644810	+	0.997919i	$0.479461\pi$
$600$		0			0
$601$		−	23.7036i		−	0.966889i	−0.875375	−	0.483445i	$-0.839385\pi$
$601$		−	23.7036i		−	0.966889i	0.875375	−	0.483445i	$-0.160615\pi$
$602$		0			0
$603$	4.66268	+	6.57749i	0.189879	+	0.267856i
$604$		0			0
$605$	20.6591	+	35.7826i	0.839912	+	1.45477i
$606$		0			0
$607$	−18.5031	−	10.6828i	−0.751017	−	0.433600i	0.0750445	−	0.997180i	$-0.476090\pi$
$607$	−18.5031	−	10.6828i	−0.751017	−	0.433600i	−0.826061	+	0.563580i	$0.809423\pi$
$608$		0			0
$609$	19.7958	+	11.2871i	0.802167	+	0.457375i
$610$		0			0
$611$	−40.1225	−	23.1647i	−1.62318	−	0.937145i
$612$		0			0
$613$	−19.8248	−	34.3376i	−0.800716	−	1.38688i	−0.919145	−	0.393918i	$-0.871119\pi$
$613$	−19.8248	−	34.3376i	−0.800716	−	1.38688i	0.118429	−	0.992962i	$-0.462214\pi$
$614$		0			0
$615$	−35.9888	−	18.6022i	−1.45121	−	0.750112i
$616$		0			0
$617$			28.6296i			1.15258i	0.817244	+	0.576292i	$0.195501\pi$
$617$			28.6296i			1.15258i	−0.817244	+	0.576292i	$0.804499\pi$
$618$		0			0
$619$	−32.9529	+	19.0254i	−1.32449	+	0.764694i	−0.984441	−	0.175714i	$-0.943776\pi$
$619$	−32.9529	+	19.0254i	−1.32449	+	0.764694i	−0.340047	+	0.940408i	$0.610443\pi$
$620$		0			0
$621$	−2.58919	+	6.40794i	−0.103901	+	0.257142i
$622$		0			0
$623$	−15.9944	+	8.37701i	−0.640801	+	0.335618i
$624$		0			0
$625$	−8.47450	+	14.6783i	−0.338980	+	0.587130i
$626$		0			0
$627$	−0.0706980	−	1.51823i	−0.00282341	−	0.0606323i
$628$		0			0
$629$	1.13422			0.0452242
$630$		0			0
$631$	−3.65235			−0.145398			−0.0726989	−	0.997354i	$-0.523161\pi$
$631$	−3.65235			−0.145398			−0.0726989	+	0.997354i	$0.523161\pi$
$632$		0			0
$633$	−0.0701259	−	1.50595i	−0.00278726	−	0.0598560i
$634$		0			0
$635$	24.5498	−	42.5215i	0.974228	−	1.68741i
$636$		0			0
$637$	−25.6064	+	12.0966i	−1.01456	+	0.479286i
$638$		0			0
$639$	1.61413	+	17.2941i	0.0638542	+	0.684143i
$640$		0			0
$641$	−21.2563	+	12.2723i	−0.839574	+	0.484728i	−0.857119	−	0.515118i	$-0.827748\pi$
$641$	−21.2563	+	12.2723i	−0.839574	+	0.484728i	0.0175456	+	0.999846i	$0.494415\pi$
$642$		0			0
$643$		−	27.3936i		−	1.08030i	−0.841569	−	0.540149i	$-0.818368\pi$
$643$		−	27.3936i		−	1.08030i	0.841569	−	0.540149i	$-0.181632\pi$
$644$		0			0
$645$	2.93980	+	1.51955i	0.115754	+	0.0598321i
$646$		0			0
$647$	16.1181	+	27.9173i	0.633667	+	1.09754i	0.986796	+	0.161969i	$0.0517845\pi$
$647$	16.1181	+	27.9173i	0.633667	+	1.09754i	−0.353129	+	0.935575i	$0.614882\pi$
$648$		0			0
$649$	−2.33618	−	1.34879i	−0.0917029	−	0.0529447i
$650$		0			0
$651$	−0.195101	−	36.1408i	−0.00764660	−	1.41647i
$652$		0			0
$653$	13.5027	+	7.79579i	0.528401	+	0.305073i	0.740365	−	0.672205i	$-0.234653\pi$
$653$	13.5027	+	7.79579i	0.528401	+	0.305073i	−0.211964	+	0.977278i	$0.567986\pi$
$654$		0			0
$655$	10.1235	+	17.5344i	0.395558	+	0.685126i
$656$		0			0
$657$	0.576304	−	0.408533i	0.0224838	−	0.0159384i
$658$		0			0
$659$		−	35.1100i		−	1.36769i	−0.729626	−	0.683847i	$-0.760306\pi$
$659$		−	35.1100i		−	1.36769i	0.729626	−	0.683847i	$-0.239694\pi$
$660$		0			0
$661$	6.96082	−	4.01883i	0.270745	−	0.156314i	−0.358481	−	0.933537i	$-0.616705\pi$
$661$	6.96082	−	4.01883i	0.270745	−	0.156314i	0.629226	+	0.777222i	$0.283372\pi$
$662$		0			0
$663$	−0.393110	−	0.613129i	−0.0152671	−	0.0238120i
$664$		0			0
$665$	−24.6642	−	1.01511i	−0.956436	−	0.0393644i
$666$		0			0
$667$	−3.30700	+	5.72789i	−0.128047	+	0.221785i
$668$		0			0
$669$	−2.09997	+	0.0977875i	−0.0811897	+	0.00378068i
$670$		0			0
$671$	3.38629			0.130726
$672$		0			0
$673$	28.1744			1.08604			0.543022	−	0.839719i	$-0.317280\pi$
$673$	28.1744			1.08604			0.543022	+	0.839719i	$0.317280\pi$
$674$		0			0
$675$	−38.6646	+	30.2063i	−1.48820	+	1.16264i
$676$		0			0
$677$	17.3844	−	30.1106i	0.668135	−	1.15724i	−0.310290	−	0.950642i	$-0.600426\pi$
$677$	17.3844	−	30.1106i	0.668135	−	1.15724i	0.978425	−	0.206602i	$-0.0662405\pi$
$678$		0			0
$679$	7.28158	−	11.4931i	0.279441	−	0.441063i
$680$		0			0
$681$	19.4569	−	12.4749i	0.745592	−	0.478039i
$682$		0			0
$683$	40.7393	−	23.5209i	1.55885	−	0.900001i	0.561479	−	0.827491i	$-0.310232\pi$
$683$	40.7393	−	23.5209i	1.55885	−	0.900001i	0.997368	−	0.0725098i	$-0.0231009\pi$
$684$		0			0
$685$		−	19.1933i		−	0.733339i
$686$		0			0
$687$	−8.82192	+	17.0674i	−0.336577	+	0.651161i
$688$		0			0
$689$	−11.8691	−	20.5579i	−0.452177	−	0.783194i
$690$		0			0
$691$	−27.1758	−	15.6900i	−1.03382	−	0.596874i	−0.115740	−	0.993279i	$-0.536924\pi$
$691$	−27.1758	−	15.6900i	−1.03382	−	0.596874i	−0.918076	+	0.396406i	$0.870257\pi$
$692$		0			0
$693$	−2.83314	+	0.147260i	−0.107622	+	0.00559393i
$694$		0			0
$695$	−69.9874	−	40.4073i	−2.65478	−	1.53274i
$696$		0			0
$697$	−0.319850	−	0.553997i	−0.0121152	−	0.0209841i
$698$		0			0
$699$	−6.50569	+	12.5863i	−0.246068	+	0.476057i
$700$		0			0
$701$			29.9818i			1.13240i	0.824268	+	0.566199i	$0.191587\pi$
$701$			29.9818i			1.13240i	−0.824268	+	0.566199i	$0.808413\pi$
$702$		0			0
$703$	−23.2015	+	13.3954i	−0.875061	+	0.505217i
$704$		0			0
$705$	−63.4558	+	40.6849i	−2.38988	+	1.53228i
$706$		0			0
$707$	−1.40111	+	34.0427i	−0.0526940	+	1.28031i
$708$		0			0
$709$	−11.5451	+	19.9968i	−0.433587	+	0.750995i	−0.997179	−	0.0750583i	$-0.976086\pi$
$709$	−11.5451	+	19.9968i	−0.433587	+	0.750995i	0.563592	+	0.826053i	$0.309419\pi$
$710$		0			0
$711$	4.03786	−	8.79195i	0.151431	−	0.329724i
$712$		0			0
$713$	10.4899			0.392849
$714$		0			0
$715$	5.49540			0.205516
$716$		0			0
$717$	39.0924	−	1.82038i	1.45993	−	0.0679832i
$718$		0			0
$719$	22.5340	−	39.0300i	0.840376	−	1.45557i	−0.0492012	−	0.998789i	$-0.515668\pi$
$719$	22.5340	−	39.0300i	0.840376	−	1.45557i	0.889577	−	0.456785i	$-0.150999\pi$
$720$		0			0
$721$	6.91877	+	13.2101i	0.257669	+	0.491971i
$722$		0			0
$723$	4.57839	+	7.14087i	0.170272	+	0.265572i
$724$		0			0
$725$	−40.6638	+	23.4772i	−1.51022	+	0.871923i
$726$		0			0
$727$		−	3.14662i		−	0.116702i	−0.998296	−	0.0583508i	$-0.981416\pi$
$727$		−	3.14662i		−	0.116702i	0.998296	−	0.0583508i	$-0.0185842\pi$
$728$		0			0
$729$	−25.9545	+	7.44070i	−0.961278	+	0.275582i
$730$		0			0
$731$	0.0261274	+	0.0452541i	0.000966358	+	0.00167378i
$732$		0			0
$733$	14.9590	+	8.63657i	0.552522	+	0.318999i	0.750139	−	0.661281i	$-0.229987\pi$
$733$	14.9590	+	8.63657i	0.552522	+	0.318999i	−0.197616	+	0.980279i	$0.563320\pi$
$734$		0			0
$735$	−1.64624	+	46.0472i	−0.0607224	+	1.69848i
$736$		0			0
$737$	−0.831885	−	0.480289i	−0.0306429	−	0.0176917i
$738$		0			0
$739$	−0.996550	−	1.72607i	−0.0366587	−	0.0634947i	0.847114	−	0.531411i	$-0.178338\pi$
$739$	−0.996550	−	1.72607i	−0.0366587	−	0.0634947i	−0.883773	+	0.467917i	$0.845005\pi$
$740$		0			0
$741$	15.2827	+	7.89942i	0.561423	+	0.290192i
$742$		0			0
$743$			5.54435i			0.203402i	0.994815	+	0.101701i	$0.0324286\pi$
$743$			5.54435i			0.203402i	−0.994815	+	0.101701i	$0.967571\pi$
$744$		0			0
$745$	40.0867	−	23.1441i	1.46866	−	0.847934i
$746$		0			0
$747$	−27.1146	+	2.53073i	−0.992071	+	0.0925944i
$748$		0			0
$749$	−10.8113	−	20.6422i	−0.395036	−	0.754248i
$750$		0			0
$751$	22.0897	−	38.2605i	0.806065	−	1.39615i	−0.109504	−	0.993986i	$-0.534926\pi$
$751$	22.0897	−	38.2605i	0.806065	−	1.39615i	0.915569	−	0.402160i	$-0.131740\pi$
$752$		0			0
$753$	−0.739494	−	15.8805i	−0.0269487	−	0.578719i
$754$		0			0
$755$	31.2296			1.13656
$756$		0			0
$757$	10.6250			0.386172			0.193086	−	0.981182i	$-0.438150\pi$
$757$	10.6250			0.386172			0.193086	+	0.981182i	$0.438150\pi$
$758$		0			0
$759$	−0.0383019	−	0.822528i	−0.00139027	−	0.0298559i
$760$		0			0
$761$	13.9084	−	24.0900i	0.504178	−	0.873262i	−0.495810	−	0.868431i	$-0.665129\pi$
$761$	13.9084	−	24.0900i	0.504178	−	0.873262i	0.999988	−	0.00483132i	$-0.00153786\pi$
$762$		0			0
$763$	−0.487125	+	11.8357i	−0.0176351	+	0.428480i
$764$		0			0
$765$	−1.17987	+	0.110122i	−0.0426582	+	0.00398149i
$766$		0			0
$767$	26.4432	−	15.2670i	0.954809	−	0.551259i
$768$		0			0
$769$		−	10.2707i		−	0.370369i	−0.982704	−	0.185185i	$-0.940712\pi$
$769$		−	10.2707i		−	0.370369i	0.982704	−	0.185185i	$-0.0592883\pi$
$770$		0			0
$771$	−19.4196	−	10.0377i	−0.699379	−	0.361500i
$772$		0			0
$773$	20.2953	+	35.1525i	0.729972	+	1.26435i	0.956895	+	0.290435i	$0.0938001\pi$
$773$	20.2953	+	35.1525i	0.729972	+	1.26435i	−0.226923	+	0.973913i	$0.572867\pi$
$774$		0			0
$775$	64.4933	+	37.2352i	2.31667	+	1.33753i
$776$		0			0
$777$	25.2370	+	43.1718i	0.905372	+	1.54878i
$778$		0			0
$779$	13.0857	+	7.55502i	0.468843	+	0.270687i
$780$		0			0
$781$	−1.03470	−	1.79215i	−0.0370244	−	0.0641282i
$782$		0			0
$783$	−25.5873	+	3.59530i	−0.914415	+	0.128486i
$784$		0			0
$785$		−	49.1938i		−	1.75580i
$786$		0			0
$787$	22.6225	−	13.0611i	0.806404	−	0.465578i	−0.0393014	−	0.999227i	$-0.512513\pi$
$787$	22.6225	−	13.0611i	0.806404	−	0.465578i	0.845706	+	0.533650i	$0.179180\pi$
$788$		0			0
$789$	27.2559	+	42.5107i	0.970334	+	1.51342i
$790$		0			0
$791$	5.66392	−	8.93980i	0.201386	−	0.317863i
$792$		0			0
$793$	−19.1647	+	33.1943i	−0.680560	+	1.17876i
$794$		0			0
$795$	−38.5804	+	1.79654i	−1.36831	+	0.0637167i
$796$		0			0
$797$	38.0284			1.34704			0.673518	−	0.739171i	$-0.264782\pi$
$797$	38.0284			1.34704			0.673518	+	0.739171i	$0.264782\pi$
$798$		0			0
$799$	−1.19025			−0.0421080
$800$		0			0
$801$	8.54444	−	18.6045i	0.301903	−	0.657358i
$802$		0			0
$803$	−0.0420818	+	0.0728879i	−0.00148504	+	0.00257216i
$804$		0			0
$805$	−13.3622	−	0.549955i	−0.470957	−	0.0193834i
$806$		0			0
$807$	6.52176	−	4.18145i	0.229577	−	0.147194i
$808$		0			0
$809$	25.8553	−	14.9276i	0.909024	−	0.524825i	0.0289068	−	0.999582i	$-0.490797\pi$
$809$	25.8553	−	14.9276i	0.909024	−	0.524825i	0.880117	+	0.474757i	$0.157464\pi$
$810$		0			0
$811$		−	15.4099i		−	0.541114i	−0.962704	−	0.270557i	$-0.912792\pi$
$811$		−	15.4099i		−	0.541114i	0.962704	−	0.270557i	$-0.0872079\pi$
$812$		0			0
$813$	13.3147	−	25.7594i	0.466967	−	0.903420i
$814$		0			0
$815$	−4.15139	−	7.19042i	−0.145417	−	0.251869i
$816$		0			0
$817$	−1.06892	−	0.617144i	−0.0373969	−	0.0215911i
$818$		0			0
$819$	14.5907	−	28.6055i	0.509840	−	0.999557i
$820$		0			0
$821$	−25.0908	−	14.4862i	−0.875674	−	0.505570i	−0.00644422	−	0.999979i	$-0.502051\pi$
$821$	−25.0908	−	14.4862i	−0.875674	−	0.505570i	−0.869230	+	0.494409i	$0.835385\pi$
$822$		0			0
$823$	3.58962	+	6.21741i	0.125126	+	0.216725i	0.921782	−	0.387708i	$-0.126733\pi$
$823$	3.58962	+	6.21741i	0.125126	+	0.216725i	−0.796656	+	0.604433i	$0.793400\pi$
$824$		0			0
$825$	2.68419	−	5.19298i	0.0934513	−	0.180796i
$826$		0			0
$827$		−	37.6512i		−	1.30926i	−0.755949	−	0.654630i	$-0.772824\pi$
$827$		−	37.6512i		−	1.30926i	0.755949	−	0.654630i	$-0.227176\pi$
$828$		0			0
$829$	−43.4385	+	25.0792i	−1.50868	+	0.871038i	−0.508733	+	0.860924i	$0.669886\pi$
$829$	−43.4385	+	25.0792i	−1.50868	+	0.871038i	−0.999949	+	0.0101139i	$0.996781\pi$
$830$		0			0
$831$	1.48995	−	0.955286i	0.0516857	−	0.0331385i
$832$		0			0
$833$	−0.414330	+	0.598065i	−0.0143557	+	0.0207217i
$834$		0			0
$835$	−0.882803	+	1.52906i	−0.0305506	+	0.0529153i
$836$		0			0
$837$	25.2291	+	32.2938i	0.872047	+	1.11624i
$838$		0			0
$839$	10.2849			0.355073			0.177536	−	0.984114i	$-0.443187\pi$
$839$	10.2849			0.355073			0.177536	+	0.984114i	$0.443187\pi$
$840$		0			0
$841$	4.27275			0.147336
$842$		0			0
$843$	−24.1278	+	1.12354i	−0.831006	+	0.0386967i
$844$		0			0
$845$	−6.39910	+	11.0836i	−0.220136	+	0.381286i
$846$		0			0
$847$	−25.4818	+	13.3460i	−0.875566	+	0.458575i
$848$		0			0
$849$	15.1545	+	23.6362i	0.520100	+	0.811193i
$850$		0			0
$851$	−12.5698	+	7.25719i	−0.430888	+	0.248773i
$852$		0			0
$853$			29.0278i			0.993891i	0.867782	+	0.496946i	$0.165545\pi$
$853$			29.0278i			0.993891i	−0.867782	+	0.496946i	$0.834455\pi$
$854$		0			0
$855$	22.8348	−	16.1872i	0.780933	−	0.553591i
$856$		0			0
$857$	−7.98887	−	13.8371i	−0.272895	−	0.472668i	0.696707	−	0.717356i	$-0.254648\pi$
$857$	−7.98887	−	13.8371i	−0.272895	−	0.472668i	−0.969602	+	0.244688i	$0.921314\pi$
$858$		0			0
$859$	−4.98253	−	2.87666i	−0.170002	−	0.0981505i	0.412585	−	0.910919i	$-0.364626\pi$
$859$	−4.98253	−	2.87666i	−0.170002	−	0.0981505i	−0.582587	+	0.812769i	$0.697959\pi$
$860$		0			0
$861$	13.9700	−	24.5012i	0.476096	−	0.835000i
$862$		0			0
$863$	10.7735	+	6.22006i	0.366733	+	0.211733i	0.672030	−	0.740524i	$-0.265422\pi$
$863$	10.7735	+	6.22006i	0.366733	+	0.211733i	−0.305297	+	0.952257i	$0.598756\pi$
$864$		0			0
$865$	17.5798	+	30.4492i	0.597733	+	1.03530i
$866$		0			0
$867$	26.1406	+	13.5118i	0.887781	+	0.458883i
$868$		0			0
$869$			1.15268i			0.0391019i
$870$		0			0
$871$	9.41612	−	5.43640i	0.319053	−	0.184205i
$872$		0			0
$873$	1.43367	+	15.3605i	0.0485223	+	0.519875i
$874$		0			0
$875$	−37.7331	−	23.9062i	−1.27561	−	0.808179i
$876$		0			0
$877$	21.9672	−	38.0484i	0.741781	−	1.28480i	−0.209902	−	0.977722i	$-0.567315\pi$
$877$	21.9672	−	38.0484i	0.741781	−	1.28480i	0.951684	−	0.307080i	$-0.0993521\pi$
$878$		0			0
$879$	1.54744	+	33.2310i	0.0521937	+	1.12085i
$880$		0			0
$881$	−51.0805			−1.72095			−0.860473	−	0.509496i	$-0.829832\pi$
$881$	−51.0805			−1.72095			−0.860473	+	0.509496i	$0.829832\pi$
$882$		0			0
$883$	−34.3823			−1.15706			−0.578529	−	0.815662i	$-0.696373\pi$
$883$	−34.3823			−1.15706			−0.578529	+	0.815662i	$0.696373\pi$
$884$		0			0
$885$	−2.31085	−	49.6253i	−0.0776784	−	1.66813i
$886$		0			0
$887$	−20.8829	+	36.1703i	−0.701180	+	1.21448i	0.266873	+	0.963732i	$0.414010\pi$
$887$	−20.8829	+	36.1703i	−0.701180	+	1.21448i	−0.968053	+	0.250748i	$0.919324\pi$
$888$		0			0
$889$	28.8751	+	18.2942i	0.968440	+	0.613567i
$890$		0			0
$891$	2.44008	−	2.09617i	0.0817459	−	0.0702243i
$892$		0			0
$893$	24.3477	−	14.0572i	0.814765	−	0.470405i
$894$		0			0
$895$			7.77140i			0.259769i
$896$		0			0
$897$	8.27965	+	4.27965i	0.276449	+	0.142893i
$898$		0			0
$899$	19.6089	+	33.9636i	0.653993	+	1.13275i
$900$		0			0
$901$	−0.528153	−	0.304929i	−0.0175953	−	0.0101587i
$902$		0			0
$903$	−1.14116	+	2.00142i	−0.0379754	+	0.0666031i
$904$		0			0
$905$	57.9883	+	33.4795i	1.92760	+	1.11290i
$906$		0			0
$907$	18.9839	+	32.8811i	0.630350	+	1.09180i	0.987480	+	0.157744i	$0.0504220\pi$
$907$	18.9839	+	32.8811i	0.630350	+	1.09180i	−0.357130	+	0.934055i	$0.616245\pi$
$908$		0			0
$909$	−22.3424	−	31.5176i	−0.741049	−	1.04537i
$910$		0			0
$911$			55.0007i			1.82225i	0.412127	+	0.911126i	$0.364786\pi$
$911$			55.0007i			1.82225i	−0.412127	+	0.911126i	$0.635214\pi$
$912$		0			0
$913$	2.80983	−	1.62226i	0.0929918	−	0.0536888i
$914$		0			0
$915$	33.6596	+	52.4985i	1.11275	+	1.73555i
$916$		0			0
$917$	−12.4868	+	6.53991i	−0.412349	+	0.215967i
$918$		0			0
$919$	−13.5889	+	23.5367i	−0.448256	+	0.776403i	−0.998273	−	0.0587510i	$-0.981288\pi$
$919$	−13.5889	+	23.5367i	−0.448256	+	0.776403i	0.550016	+	0.835154i	$0.314622\pi$
$920$		0			0
$921$	−0.831347	+	0.0387125i	−0.0273938	+	0.00127562i
$922$		0			0
$923$	23.4236			0.770996
$924$		0			0
$925$	−103.041			−3.38798
$926$		0			0
$927$	−15.3659	−	7.05706i	−0.504683	−	0.231784i
$928$		0			0
$929$	0.982860	−	1.70236i	0.0322466	−	0.0558527i	−0.849452	−	0.527666i	$-0.823067\pi$
$929$	0.982860	−	1.70236i	0.0322466	−	0.0558527i	0.881698	+	0.471814i	$0.156400\pi$
$930$		0			0
$931$	1.41222	−	17.1273i	0.0462838	−	0.561326i
$932$		0			0
$933$	13.6085	−	8.72511i	0.445521	−	0.285647i
$934$		0			0
$935$	0.122267	−	0.0705911i	0.00399857	−	0.00230858i
$936$		0			0
$937$			31.0157i			1.01324i	0.862170	+	0.506620i	$0.169105\pi$
$937$			31.0157i			1.01324i	−0.862170	+	0.506620i	$0.830895\pi$
$938$		0			0
$939$	−14.2479	+	27.5648i	−0.464963	+	0.899544i
$940$		0			0
$941$	−16.7914	−	29.0836i	−0.547384	−	0.948097i	−0.998453	−	0.0556078i	$-0.982290\pi$
$941$	−16.7914	−	29.0836i	−0.547384	−	0.948097i	0.451069	−	0.892489i	$-0.351043\pi$
$942$		0			0
$943$	7.08940	+	4.09307i	0.230863	+	0.133289i
$944$		0			0
$945$	−30.4444	−	42.4592i	−0.990355	−	1.38120i
$946$		0			0
$947$	−8.89077	−	5.13309i	−0.288911	−	0.166803i	0.348539	−	0.937294i	$-0.386678\pi$
$947$	−8.89077	−	5.13309i	−0.288911	−	0.166803i	−0.637451	+	0.770491i	$0.720011\pi$
$948$		0			0
$949$	−0.476325	−	0.825019i	−0.0154622	−	0.0267813i
$950$		0			0
$951$	17.7494	−	34.3389i	0.575563	−	1.11352i
$952$		0			0
$953$			1.00920i			0.0326911i	0.999866	+	0.0163455i	$0.00520318\pi$
$953$			1.00920i			0.0326911i	−0.999866	+	0.0163455i	$0.994797\pi$
$954$		0			0
$955$	74.0347	−	42.7439i	2.39571	−	1.38316i
$956$		0			0
$957$	2.59154	−	1.66157i	0.0837725	−	0.0537110i
$958$		0			0
$959$	13.3509	+	0.549486i	0.431122	+	0.0177438i
$960$		0			0
$961$	15.5999	−	27.0199i	0.503224	−	0.871610i
$962$		0			0
$963$	24.0108	+	11.0274i	0.773737	+	0.355352i
$964$		0			0
$965$	−36.6341			−1.17929
$966$		0			0
$967$	1.83020			0.0588552			0.0294276	−	0.999567i	$-0.490632\pi$
$967$	1.83020			0.0588552			0.0294276	+	0.999567i	$0.490632\pi$
$968$		0			0
$969$	0.441497	−	0.0205588i	0.0141829	−	0.000660442i
$970$		0			0
$971$	−7.28478	+	12.6176i	−0.233780	+	0.404918i	−0.958917	−	0.283686i	$-0.908443\pi$
$971$	−7.28478	+	12.6176i	−0.233780	+	0.404918i	0.725138	+	0.688604i	$0.241776\pi$
$972$		0			0
$973$	30.1110	−	47.5264i	0.965313	−	1.52363i
$974$		0			0
$975$	35.7133	+	55.7016i	1.14374	+	1.78388i
$976$		0			0
$977$	−5.93615	+	3.42724i	−0.189914	+	0.109647i	−0.591942	−	0.805980i	$-0.701639\pi$
$977$	−5.93615	+	3.42724i	−0.189914	+	0.109647i	0.402028	+	0.915627i	$0.368305\pi$
$978$		0			0
$979$			2.43916i			0.0779559i
$980$		0			0
$981$	−7.76780	−	10.9578i	−0.248007	−	0.349855i
$982$		0			0
$983$	−29.5934	−	51.2573i	−0.943883	−	1.63485i	−0.757973	−	0.652286i	$-0.773810\pi$
$983$	−29.5934	−	51.2573i	−0.943883	−	1.63485i	−0.185910	−	0.982567i	$-0.559523\pi$
$984$		0			0
$985$	−50.6020	−	29.2151i	−1.61231	−	0.930870i
$986$		0			0
$987$	−26.4838	−	45.3046i	−0.842987	−	1.44206i
$988$		0			0
$989$	−0.579108	−	0.334348i	−0.0184146	−	0.0106317i
$990$		0			0
$991$	−28.2143	−	48.8686i	−0.896256	−	1.55236i	−0.832243	−	0.554412i	$-0.812943\pi$
$991$	−28.2143	−	48.8686i	−0.896256	−	1.55236i	−0.0640132	−	0.997949i	$-0.520390\pi$
$992$		0			0
$993$	−21.7216	−	11.2276i	−0.689313	−	0.356297i
$994$		0			0
$995$			17.4199i			0.552249i
$996$		0			0
$997$	−45.5831	+	26.3174i	−1.44363	+	0.833480i	−0.998090	−	0.0617814i	$-0.980322\pi$
$997$	−45.5831	+	26.3174i	−1.44363	+	0.833480i	−0.445541	+	0.895262i	$0.646988\pi$
$998$		0			0
$999$	−52.5733	−	21.2427i	−1.66334	−	0.672091i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.u.a.89.4	yes	16
3.2	odd	2	inner	168.2.u.a.89.2	yes	16
4.3	odd	2		336.2.bc.f.257.5		16
7.2	even	3		1176.2.k.a.881.1		16
7.3	odd	6	inner	168.2.u.a.17.2	✓	16
7.4	even	3		1176.2.u.b.521.7		16
7.5	odd	6		1176.2.k.a.881.16		16
7.6	odd	2		1176.2.u.b.1097.5		16
12.11	even	2		336.2.bc.f.257.7		16
21.2	odd	6		1176.2.k.a.881.15		16
21.5	even	6		1176.2.k.a.881.2		16
21.11	odd	6		1176.2.u.b.521.5		16
21.17	even	6	inner	168.2.u.a.17.4	yes	16
21.20	even	2		1176.2.u.b.1097.7		16
28.3	even	6		336.2.bc.f.17.7		16
28.19	even	6		2352.2.k.i.881.1		16
28.23	odd	6		2352.2.k.i.881.16		16
84.23	even	6		2352.2.k.i.881.2		16
84.47	odd	6		2352.2.k.i.881.15		16
84.59	odd	6		336.2.bc.f.17.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.2	✓	16	7.3	odd	6	inner
168.2.u.a.17.4	yes	16	21.17	even	6	inner
168.2.u.a.89.2	yes	16	3.2	odd	2	inner
168.2.u.a.89.4	yes	16	1.1	even	1	trivial
336.2.bc.f.17.5		16	84.59	odd	6
336.2.bc.f.17.7		16	28.3	even	6
336.2.bc.f.257.5		16	4.3	odd	2
336.2.bc.f.257.7		16	12.11	even	2
1176.2.k.a.881.1		16	7.2	even	3
1176.2.k.a.881.2		16	21.5	even	6
1176.2.k.a.881.15		16	21.2	odd	6
1176.2.k.a.881.16		16	7.5	odd	6
1176.2.u.b.521.5		16	21.11	odd	6
1176.2.u.b.521.7		16	7.4	even	3
1176.2.u.b.1097.5		16	7.6	odd	2
1176.2.u.b.1097.7		16	21.20	even	2
2352.2.k.i.881.1		16	28.19	even	6
2352.2.k.i.881.2		16	84.23	even	6
2352.2.k.i.881.15		16	84.47	odd	6
2352.2.k.i.881.16		16	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0805675 + 1.73018i) q^{3} +(1.90017 - 3.29119i) q^{5} +(2.23495 + 1.41598i) q^{7} +(-2.98702 + 0.278792i) q^{9} +(0.309539 - 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 + 3.02246i) q^{15} +(0.0519689 + 0.0900129i) q^{17} +(-2.12615 - 1.22753i) q^{19} +(-2.26983 + 3.98094i) q^{21} +(-1.15188 - 0.665037i) q^{23} +(-4.72127 - 8.17749i) q^{25} +(-0.723015 - 5.14560i) q^{27} -4.97265i q^{29} +(-6.83007 + 3.94335i) q^{31} +(0.334142 + 0.521158i) q^{33} +(8.90704 - 4.66504i) q^{35} +(5.45622 - 9.45046i) q^{37} +(-6.99976 + 0.325951i) q^{39} -6.15464 q^{41} +0.502751 q^{43} +(-4.75828 + 10.3606i) q^{45} +(-5.72578 + 9.91734i) q^{47} +(2.99000 + 6.32929i) q^{49} +(-0.151551 + 0.0971675i) q^{51} +(-5.08143 + 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(-3.77364 - 6.53614i) q^{59} +(8.20485 + 4.73707i) q^{61} +(-7.07060 - 3.60647i) q^{63} +(13.3151 + 7.68750i) q^{65} +(-1.34375 - 2.32744i) q^{67} +(1.05783 - 2.04653i) q^{69} -5.78975i q^{71} +(-0.203925 + 0.117736i) q^{73} +(13.7681 - 8.82748i) q^{75} +(0.944856 + 0.0388878i) q^{77} +(-1.61247 + 2.79289i) q^{79} +(8.84455 - 1.66551i) q^{81} +9.07747 q^{83} +0.394999 q^{85} +(8.60356 - 0.400634i) q^{87} +(-3.41213 + 5.90999i) q^{89} +(-5.72862 + 9.04192i) q^{91} +(-7.37296 - 11.4995i) q^{93} +(-8.08008 + 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 + 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67}+ \cdots + 20 q^{99}+O(q^{100}) \) 16 * q + 4 * q^7 + 2 * q^9 + 8 * q^15 - 6 * q^19 + 14 * q^21 - 18 * q^25 - 48 * q^31 - 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 - 42 * q^45 - 28 * q^49 + 6 * q^51 - 8 * q^57 + 36 * q^61 - 32 * q^63 + 14 * q^67 + 30 * q^73 + 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 + 78 * q^87 + 66 * q^91 + 16 * q^93 + 20 * q^99

Introduction

L-functions

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Database

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