LMFDB - Embedded newform 168.2.u.a.17.2

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			17.2
Root			$1.73018 + 0.0805675i$ of defining polynomial
Character	$\chi$	$=$	168.17
Dual form			168.2.u.a.89.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45809 + 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(2.23495 - 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +O(q^{10})$	\(q+(-1.45809 + 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(2.23495 - 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +(-0.309539 - 0.178712i) q^{11} -4.04570i q^{13} +(5.84742 + 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(-2.12615 + 1.22753i) q^{19} +(-1.93502 + 4.15400i) q^{21} +(1.15188 - 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(0.723015 + 5.14560i) q^{27} -4.97265i q^{29} +(-6.83007 - 3.94335i) q^{31} +(0.618407 - 0.0287968i) q^{33} +(-8.90704 - 4.66504i) q^{35} +(5.45622 + 9.45046i) q^{37} +(3.78216 + 5.89900i) q^{39} +6.15464 q^{41} +0.502751 q^{43} +(-11.3517 + 1.05950i) q^{45} +(5.72578 + 9.91734i) q^{47} +(2.99000 - 6.32929i) q^{49} +(-0.00837401 - 0.179831i) q^{51} +(5.08143 + 2.93376i) q^{53} +1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(3.77364 - 6.53614i) q^{59} +(8.20485 - 4.73707i) q^{61} +(-1.06198 - 7.86589i) q^{63} +(-13.3151 + 7.68750i) q^{65} +(-1.34375 + 2.32744i) q^{67} +(-1.05783 + 2.04653i) q^{69} -5.78975i q^{71} +(-0.203925 - 0.117736i) q^{73} +(-0.760762 - 16.3373i) q^{75} +(-0.944856 + 0.0388878i) q^{77} +(-1.61247 - 2.79289i) q^{79} +(-5.86465 - 6.82685i) q^{81} -9.07747 q^{83} +0.394999 q^{85} +(4.64874 + 7.25058i) q^{87} +(3.41213 + 5.90999i) q^{89} +(-5.72862 - 9.04192i) q^{91} +(13.6454 - 0.635411i) q^{93} +(8.08008 + 4.66504i) q^{95} +5.14243i q^{97} +(-0.874774 + 0.620114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{7} + 2 q^{9}+O(q^{10}) $ 16 * q + 4 * q^7 + 2 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−1.45809	+	0.934861i	−0.841830	+	0.539743i
$3$	−1.45809	+	0.934861i	−0.841830	+	0.539743i
$4$		0			0
$5$	−1.90017	−	3.29119i	−0.849781	−	1.47186i	−0.881404	−	0.472364i	$-0.843401\pi$
$5$	−1.90017	−	3.29119i	−0.849781	−	1.47186i	0.0316229	−	0.999500i	$-0.489932\pi$
$6$		0			0
$7$	2.23495	−	1.41598i	0.844732	−	0.535190i
$7$	2.23495	−	1.41598i	0.844732	−	0.535190i
$8$		0			0
$9$	1.25207	−	2.72623i	0.417356	−	0.908743i
$10$		0			0
$11$	−0.309539	−	0.178712i	−0.0933294	−	0.0538838i	0.452609	−	0.891709i	$-0.350493\pi$
$11$	−0.309539	−	0.178712i	−0.0933294	−	0.0538838i	−0.545938	+	0.837825i	$0.683827\pi$
$12$		0			0
$13$		−	4.04570i		−	1.12207i	−0.827791	−	0.561037i	$-0.810403\pi$
$13$		−	4.04570i		−	1.12207i	0.827791	−	0.561037i	$-0.189597\pi$
$14$		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	$-0.837346\pi$
$17$	−0.0519689	+	0.0900129i	−0.0126043	+	0.0218313i	0.859654	+	0.510876i	$0.170679\pi$
$18$		0			0
$19$	−2.12615	+	1.22753i	−0.487772	+	0.281615i	−0.723650	−	0.690167i	$-0.757537\pi$
$19$	−2.12615	+	1.22753i	−0.487772	+	0.281615i	0.235878	+	0.971783i	$0.424204\pi$
$20$		0			0
$21$	−1.93502	+	4.15400i	−0.422256	+	0.906477i
$22$		0			0
$23$	1.15188	−	0.665037i	0.240183	−	0.138670i	−0.375078	−	0.926993i	$-0.622384\pi$
$23$	1.15188	−	0.665037i	0.240183	−	0.138670i	0.615261	+	0.788323i	$0.289051\pi$
$24$		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	−0.260376	−	0.965507i	$-0.583846\pi$
$31$	−6.83007	−	3.94335i	−1.22672	−	0.708246i	−0.966342	+	0.257262i	$0.917180\pi$
$32$		0			0
$33$	0.618407	−	0.0287968i	0.107651	−	0.00501288i
$34$		0			0
$35$	−8.90704	−	4.66504i	−1.50556	−	0.788535i
$36$		0			0
$37$	5.45622	+	9.45046i	0.896998	+	1.55365i	0.831312	+	0.555805i	$0.187590\pi$
$37$	5.45622	+	9.45046i	0.896998	+	1.55365i	0.0656853	+	0.997840i	$0.479077\pi$
$38$		0			0
$39$	3.78216	+	5.89900i	0.605631	+	0.944596i
$40$		0			0
$41$	6.15464			0.961193			0.480597	−	0.876942i	$-0.340420\pi$
$41$	6.15464			0.961193			0.480597	+	0.876942i	$0.340420\pi$
$42$		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
$45$	−11.3517	+	1.05950i	−1.69221	+	0.157941i
$46$		0			0
$47$	5.72578	+	9.91734i	0.835190	+	1.44659i	0.893875	+	0.448316i	$0.147976\pi$
$47$	5.72578	+	9.91734i	0.835190	+	1.44659i	−0.0586849	+	0.998277i	$0.518691\pi$
$48$		0			0
$49$	2.99000	−	6.32929i	0.427143	−	0.904184i
$50$		0			0
$51$	−0.00837401	−	0.179831i	−0.00117260	−	0.0251814i
$52$		0			0
$53$	5.08143	+	2.93376i	0.697988	+	0.402983i	0.806597	−	0.591101i	$-0.201307\pi$
$53$	5.08143	+	2.93376i	0.697988	+	0.402983i	−0.108610	+	0.994084i	$0.534640\pi$
$54$		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	$-0.669860\pi$
$59$	3.77364	−	6.53614i	0.491286	−	0.850933i	0.999950	+	0.0100329i	$0.00319361\pi$
$60$		0			0
$61$	8.20485	−	4.73707i	1.05052	−	0.606520i	0.127727	−	0.991809i	$-0.459232\pi$
$61$	8.20485	−	4.73707i	1.05052	−	0.606520i	0.922796	+	0.385289i	$0.125898\pi$
$62$		0			0
$63$	−1.06198	−	7.86589i	−0.133797	−	0.991009i
$64$		0			0
$65$	−13.3151	+	7.68750i	−1.65154	+	0.953517i
$66$		0			0
$67$	−1.34375	+	2.32744i	−0.164165	+	0.284342i	−0.936358	−	0.351045i	$-0.885826\pi$
$67$	−1.34375	+	2.32744i	−0.164165	+	0.284342i	0.772193	+	0.635388i	$0.219160\pi$
$68$		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	0.488019	−	0.872833i	$-0.337720\pi$
$73$	−0.203925	−	0.117736i	−0.0238676	−	0.0137800i	−0.511886	+	0.859053i	$0.671053\pi$
$74$		0			0
$75$	−0.760762	−	16.3373i	−0.0878453	−	1.88647i
$76$		0			0
$77$	−0.944856	+	0.0388878i	−0.107676	+	0.00443168i
$78$		0			0
$79$	−1.61247	−	2.79289i	−0.181418	−	0.314224i	0.760946	−	0.648815i	$-0.224735\pi$
$79$	−1.61247	−	2.79289i	−0.181418	−	0.314224i	−0.942364	+	0.334591i	$0.891402\pi$
$80$		0			0
$81$	−5.86465	−	6.82685i	−0.651628	−	0.758539i
$82$		0			0
$83$	−9.07747			−0.996382			−0.498191	−	0.867067i	$-0.666002\pi$
$83$	−9.07747			−0.996382			−0.498191	+	0.867067i	$0.666002\pi$
$84$		0			0
$85$	0.394999			0.0428436
$86$		0			0
$87$	4.64874	+	7.25058i	0.498397	+	0.777344i
$88$		0			0
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	0.988238	−	0.152921i	$-0.0488681\pi$
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	−0.626553	+	0.779379i	$0.715535\pi$
$90$		0			0
$91$	−5.72862	−	9.04192i	−0.600523	−	0.947851i
$92$		0			0
$93$	13.6454	−	0.635411i	1.41496	−	0.0658890i
$94$		0			0
$95$	8.08008	+	4.66504i	0.828999	+	0.478623i
$96$		0			0
$97$			5.14243i			0.522134i	0.965321	+	0.261067i	$0.0840744\pi$
$97$			5.14243i			0.522134i	−0.965321	+	0.261067i	$0.915926\pi$
$98$		0			0
$99$	−0.874774	+	0.620114i	−0.0879181	+	0.0623238i
$100$		0			0
$101$	−6.43891	+	11.1525i	−0.640695	+	1.10972i	0.344583	+	0.938756i	$0.388020\pi$
$101$	−6.43891	+	11.1525i	−0.640695	+	1.10972i	−0.985278	+	0.170960i	$0.945313\pi$
$102$		0			0
$103$	4.88120	−	2.81816i	0.480959	−	0.277682i	−0.239857	−	0.970808i	$-0.577101\pi$
$103$	4.88120	−	2.81816i	0.480959	−	0.277682i	0.720816	+	0.693126i	$0.243767\pi$
$104$		0			0
$105$	17.3484	−	1.52479i	1.69303	−	0.148804i
$106$		0			0
$107$	7.62737	−	4.40366i	0.737365	−	0.425718i	−0.0837453	−	0.996487i	$-0.526688\pi$
$107$	7.62737	−	4.40366i	0.737365	−	0.425718i	0.821111	+	0.570769i	$0.193355\pi$
$108$		0			0
$109$	2.23862	−	3.87741i	0.214421	−	0.371389i	−0.738672	−	0.674065i	$-0.764547\pi$
$109$	2.23862	−	3.87741i	0.214421	−	0.371389i	0.953093	+	0.302676i	$0.0978801\pi$
$110$		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
$117$	−11.0295	−	5.06549i	−1.01968	−	0.468304i
$118$		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
$123$	−8.97404	+	5.75374i	−0.809162	+	0.518797i
$124$		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
$129$	−0.733058	+	0.470003i	−0.0645421	+	0.0413814i
$130$		0			0
$131$	2.66384	+	4.61391i	0.232741	+	0.403119i	0.958614	−	0.284710i	$-0.0918972\pi$
$131$	2.66384	+	4.61391i	0.232741	+	0.403119i	−0.725873	+	0.687829i	$0.758564\pi$
$132$		0			0
$133$	−3.01367	+	5.75406i	−0.261319	+	0.498940i
$134$		0			0
$135$	15.5613	−	12.1571i	1.33930	−	1.04632i
$136$		0			0
$137$	−4.37380	−	2.52521i	−0.373679	−	0.215744i	0.301386	−	0.953502i	$-0.402551\pi$
$137$	−4.37380	−	2.52521i	−0.373679	−	0.215744i	−0.675064	+	0.737759i	$0.735884\pi$
$138$		0			0
$139$			21.2651i			1.80368i	0.432067	+	0.901841i	$0.357784\pi$
$139$			21.2651i			1.80368i	−0.432067	+	0.901841i	$0.642216\pi$
$140$		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
$147$	1.55731	+	12.0239i	0.128445	+	0.991717i
$148$		0			0
$149$	−10.5482	+	6.09001i	−0.864143	+	0.498913i	−0.865398	−	0.501086i	$-0.832934\pi$
$149$	−10.5482	+	6.09001i	−0.864143	+	0.498913i	0.00125437	+	0.999999i	$0.499601\pi$
$150$		0			0
$151$	4.10880	−	7.11665i	0.334369	−	0.579145i	−0.648994	−	0.760793i	$-0.724810\pi$
$151$	4.10880	−	7.11665i	0.334369	−	0.579145i	0.983363	+	0.181649i	$0.0581434\pi$
$152$		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	0.875472	−	0.483270i	$-0.160551\pi$
$157$	11.2104	+	6.47230i	0.894683	+	0.516546i	0.0192119	+	0.999815i	$0.493884\pi$
$158$		0			0
$159$	−10.1519	+	0.472732i	−0.805094	+	0.0374901i
$160$		0			0
$161$	1.63271	−	3.11736i	0.128676	−	0.245683i
$162$		0			0
$163$	1.09237	+	1.89205i	0.0855613	+	0.148197i	0.905630	−	0.424068i	$-0.139398\pi$
$163$	1.09237	+	1.89205i	0.0855613	+	0.148197i	−0.820069	+	0.572265i	$0.806065\pi$
$164$		0			0
$165$	−1.26985	−	1.98058i	−0.0988579	−	0.154188i
$166$		0			0
$167$	0.464592			0.0359512			0.0179756	−	0.999838i	$-0.494278\pi$
$167$	0.464592			0.0359512			0.0179756	+	0.999838i	$0.494278\pi$
$168$		0			0
$169$	−3.36765			−0.259050
$170$		0			0
$171$	0.684452	+	7.33333i	0.0523414	+	0.560793i
$172$		0			0
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	0.986547	−	0.163477i	$-0.0522710\pi$
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	−0.634849	+	0.772636i	$0.718938\pi$
$174$		0			0
$175$	1.02735	+	24.9615i	0.0776603	+	1.88691i
$176$		0			0
$177$	0.608065	+	13.0581i	0.0457050	+	0.981509i
$178$		0			0
$179$	1.77096	+	1.02246i	0.132367	+	0.0764224i	0.564722	−	0.825282i	$-0.308984\pi$
$179$	1.77096	+	1.02246i	0.132367	+	0.0764224i	−0.432354	+	0.901704i	$0.642317\pi$
$180$		0			0
$181$		−	17.6193i		−	1.30963i	−0.755790	−	0.654815i	$-0.772747\pi$
$181$		−	17.6193i		−	1.30963i	0.755790	−	0.654815i	$-0.227253\pi$
$182$		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
$189$	8.90198	+	10.4764i	0.647524	+	0.762045i
$190$		0			0
$191$	−19.4811	+	11.2474i	−1.40960	+	0.813834i	−0.995350	−	0.0963279i	$-0.969290\pi$
$191$	−19.4811	+	11.2474i	−1.40960	+	0.813834i	−0.414252	+	0.910162i	$0.635957\pi$
$192$		0			0
$193$	−4.81985	+	8.34823i	−0.346940	+	0.600918i	−0.985704	−	0.168484i	$-0.946113\pi$
$193$	−4.81985	+	8.34823i	−0.346940	+	0.600918i	0.638764	+	0.769403i	$0.279446\pi$
$194$		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	0.352656	−	0.935753i	$-0.385279\pi$
$199$	−3.96967	−	2.29189i	−0.281403	−	0.162468i	−0.634058	+	0.773285i	$0.718612\pi$
$200$		0			0
$201$	−0.216525	−	4.64985i	−0.0152725	−	0.327975i
$202$		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
$207$	−0.370814	−	3.97296i	−0.0257734	−	0.276140i
$208$		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
$213$	5.41261	+	8.44199i	0.370866	+	0.578436i
$214$		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
$219$	0.407409	−	0.0189714i	0.0275301	−	0.00128197i
$220$		0			0
$221$	0.364165	+	0.210251i	0.0244964	+	0.0141430i
$222$		0			0
$223$		−	1.21373i		−	0.0812777i	−0.999174	−	0.0406388i	$-0.987061\pi$
$223$		−	1.21373i		−	0.0812777i	0.999174	−	0.0406388i	$-0.0129393\pi$
$224$		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	$-0.687304\pi$
$227$	6.67205	−	11.5563i	0.442840	−	0.767021i	0.997899	+	0.0647898i	$0.0206377\pi$
$228$		0			0
$229$	9.60627	−	5.54618i	0.634800	−	0.366502i	−0.147808	−	0.989016i	$-0.547222\pi$
$229$	9.60627	−	5.54618i	0.634800	−	0.366502i	0.782609	+	0.622514i	$0.213889\pi$
$230$		0			0
$231$	1.34133	−	0.940012i	0.0882533	−	0.0618482i
$232$		0			0
$233$	−7.08411	+	4.09001i	−0.464095	+	0.267946i	−0.713765	−	0.700386i	$-0.753011\pi$
$233$	−7.08411	+	4.09001i	−0.464095	+	0.267946i	0.249669	+	0.968331i	$0.419678\pi$
$234$		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	0.630343	−	0.776317i	$-0.282914\pi$
$241$	4.24127	+	2.44870i	0.273205	+	0.157735i	−0.357138	+	0.934051i	$0.616248\pi$
$242$		0			0
$243$	14.9334	+	4.47154i	0.957976	+	0.286850i
$244$		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
$249$	13.2358	−	8.48618i	0.838785	−	0.537790i
$250$		0			0
$251$	9.17857			0.579346			0.289673	−	0.957126i	$-0.406453\pi$
$251$	9.17857			0.579346			0.289673	+	0.957126i	$0.406453\pi$
$252$		0			0
$253$	−0.475401			−0.0298882
$254$		0			0
$255$	−0.575945	+	0.369269i	−0.0360671	+	0.0231245i
$256$		0			0
$257$	6.31055	+	10.9302i	0.393641	+	0.681806i	0.992927	−	0.118729i	$-0.0378819\pi$
$257$	6.31055	+	10.9302i	0.393641	+	0.681806i	−0.599286	+	0.800535i	$0.704549\pi$
$258$		0			0
$259$	25.5760	+	13.3954i	1.58922	+	0.832349i
$260$		0			0
$261$	−13.5566	−	6.22610i	−0.839132	−	0.385386i
$262$		0			0
$263$	−25.2489	−	14.5775i	−1.55692	−	0.898886i	−0.997549	−	0.0699665i	$-0.977711\pi$
$263$	−25.2489	−	14.5775i	−1.55692	−	0.898886i	−0.559367	−	0.828920i	$-0.688956\pi$
$264$		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	$-0.789794\pi$
$269$	2.23640	−	3.87356i	0.136356	−	0.236175i	0.926115	+	0.377242i	$0.123128\pi$
$270$		0			0
$271$	−14.4985	+	8.37071i	−0.880721	+	0.508485i	−0.870896	−	0.491467i	$-0.836461\pi$
$271$	−14.4985	+	8.37071i	−0.880721	+	0.508485i	−0.00982495	+	0.999952i	$0.503127\pi$
$272$		0			0
$273$	16.8058	+	7.82849i	1.01713	+	0.473802i
$274$		0			0
$275$	2.92283	−	1.68750i	0.176254	−	0.101760i
$276$		0			0
$277$	−0.510924	+	0.884946i	−0.0306984	+	0.0531713i	−0.880966	−	0.473179i	$-0.843106\pi$
$277$	−0.510924	+	0.884946i	−0.0306984	+	0.0531713i	0.850268	+	0.526350i	$0.176440\pi$
$278$		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	0.855394	−	0.517978i	$-0.173315\pi$
$283$	14.0386	+	8.10519i	0.834508	+	0.481803i	−0.0208856	+	0.999782i	$0.506649\pi$
$284$		0			0
$285$	−16.1427	+	0.751701i	−0.956209	+	0.0445269i
$286$		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
$291$	−4.80746	−	7.49814i	−0.281818	−	0.439549i
$292$		0			0
$293$	−19.2067			−1.12207			−0.561034	−	0.827793i	$-0.689596\pi$
$293$	−19.2067			−1.12207			−0.561034	+	0.827793i	$0.689596\pi$
$294$		0			0
$295$	−28.6822			−1.66994
$296$		0			0
$297$	0.695781	−	1.72198i	0.0403733	−	0.0999192i
$298$		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
$303$	−1.03753	−	22.2809i	−0.0596047	−	1.28000i
$304$		0			0
$305$	−31.1812	−	18.0025i	−1.78543	−	1.03082i
$306$		0			0
$307$		−	0.480498i		−	0.0274235i	−0.999906	−	0.0137117i	$-0.995635\pi$
$307$		−	0.480498i		−	0.0274235i	0.999906	−	0.0137117i	$-0.00436472\pi$
$308$		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	$-0.748089\pi$
$311$	4.66653	−	8.08266i	0.264615	−	0.458326i	0.967463	+	0.253014i	$0.0814220\pi$
$312$		0			0
$313$	15.5147	−	8.95742i	0.876943	−	0.506303i	0.00729351	−	0.999973i	$-0.497678\pi$
$313$	15.5147	−	8.95742i	0.876943	−	0.506303i	0.869649	+	0.493670i	$0.164345\pi$
$314$		0			0
$315$	−23.8702	+	18.4417i	−1.34493	+	1.03907i
$316$		0			0
$317$	19.3275	−	11.1587i	1.08554	−	0.626736i	0.153153	−	0.988202i	$-0.451057\pi$
$317$	19.3275	−	11.1587i	1.08554	−	0.626736i	0.932385	+	0.361467i	$0.117724\pi$
$318$		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
$327$	0.360721	+	7.74643i	0.0199479	+	0.428378i
$328$		0			0
$329$	26.8396	+	14.0572i	1.47971	+	0.774996i
$330$		0			0
$331$	−7.05860	−	12.2259i	−0.387976	−	0.671994i	0.604201	−	0.796832i	$-0.293492\pi$
$331$	−7.05860	−	12.2259i	−0.387976	−	0.671994i	−0.992177	+	0.124838i	$0.960159\pi$
$332$		0			0
$333$	32.5957	−	3.04230i	1.78623	−	0.166717i
$334$		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
$339$	3.73945	+	5.83237i	0.203099	+	0.316771i
$340$		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
$345$	8.74557	−	0.407247i	0.470846	−	0.0219254i
$346$		0			0
$347$	27.6474	+	15.9623i	1.48419	+	0.856899i	0.999838	−	0.0179729i	$-0.00572127\pi$
$347$	27.6474	+	15.9623i	1.48419	+	0.856899i	0.484354	+	0.874872i	$0.339055\pi$
$348$		0			0
$349$			14.7367i			0.788840i	0.918930	+	0.394420i	$0.129055\pi$
$349$			14.7367i			0.788840i	−0.918930	+	0.394420i	$0.870945\pi$
$350$		0			0
$351$	20.8175	−	2.92510i	1.11116	−	0.156130i
$352$		0			0
$353$	−13.5686	+	23.5016i	−0.722185	+	1.25086i	0.237937	+	0.971281i	$0.423529\pi$
$353$	−13.5686	+	23.5016i	−0.722185	+	1.25086i	−0.960122	+	0.279581i	$0.909804\pi$
$354$		0			0
$355$	−19.0551	+	11.0015i	−1.01134	+	0.583899i
$356$		0			0
$357$	−0.273352	−	0.390055i	−0.0144673	−	0.0206439i
$358$		0			0
$359$	−16.9479	+	9.78486i	−0.894475	+	0.516425i	−0.875404	−	0.483393i	$-0.839404\pi$
$359$	−16.9479	+	9.78486i	−0.894475	+	0.516425i	−0.0190713	+	0.999818i	$0.506071\pi$
$360$		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	0.469350	−	0.883012i	$-0.344488\pi$
$367$	−1.16258	−	0.671213i	−0.0606860	−	0.0350371i	−0.530036	+	0.847975i	$0.677822\pi$
$368$		0			0
$369$	7.70603	−	16.7790i	0.401160	−	0.873478i
$370$		0			0
$371$	15.5109	−	0.638387i	0.805285	−	0.0331434i
$372$		0			0
$373$	−6.52378	−	11.2995i	−0.337788	−	0.585066i	0.646228	−	0.763144i	$-0.276345\pi$
$373$	−6.52378	−	11.2995i	−0.337788	−	0.585066i	−0.984016	+	0.178078i	$0.943012\pi$
$374$		0			0
$375$	−24.6172	+	15.7834i	−1.27123	+	0.815053i
$376$		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
$381$	−18.8383	+	12.0782i	−0.965113	+	0.618786i
$382$		0			0
$383$	−11.2613	−	19.5052i	−0.575428	−	0.996670i	−0.995995	−	0.0894085i	$-0.971502\pi$
$383$	−11.2613	−	19.5052i	−0.575428	−	0.996670i	0.420567	−	0.907261i	$-0.361831\pi$
$384$		0			0
$385$	1.92337	+	3.03581i	0.0980242	+	0.154719i
$386$		0			0
$387$	0.629479	−	1.37061i	0.0319982	−	0.0696723i
$388$		0			0
$389$	32.1899	+	18.5848i	1.63209	+	0.942289i	0.983447	+	0.181197i	$0.0579973\pi$
$389$	32.1899	+	18.5848i	1.63209	+	0.942289i	0.648645	+	0.761091i	$0.275336\pi$
$390$		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	−0.961877	−	0.273483i	$-0.911824\pi$
$397$	−24.0288	+	13.8730i	−1.20597	+	0.696268i	−0.244095	+	0.969751i	$0.578491\pi$
$398$		0			0
$399$	−0.985032	−	11.2073i	−0.0493133	−	0.561068i
$400$		0			0
$401$	19.7233	−	11.3872i	0.984933	−	0.568651i	0.0811773	−	0.996700i	$-0.474132\pi$
$401$	19.7233	−	11.3872i	0.984933	−	0.568651i	0.903756	+	0.428048i	$0.140799\pi$
$402$		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	−0.179865	−	0.983691i	$-0.557566\pi$
$409$	−22.6849	−	13.0972i	−1.12170	−	0.647613i	−0.941834	+	0.336078i	$0.890899\pi$
$410$		0			0
$411$	8.73813	−	0.406900i	0.431020	−	0.0200709i
$412$		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
$417$	−19.8799	−	31.0065i	−0.973524	−	1.51839i
$418$		0			0
$419$	−8.93992			−0.436744			−0.218372	−	0.975866i	$-0.570075\pi$
$419$	−8.93992			−0.436744			−0.218372	+	0.975866i	$0.570075\pi$
$420$		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
$423$	34.2060	−	3.19260i	1.66315	−	0.155229i
$424$		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
$429$	−0.116503	−	2.50189i	−0.00562482	−	0.120792i
$430$		0			0
$431$	5.62468	+	3.24741i	0.270931	+	0.156422i	0.629311	−	0.777154i	$-0.283337\pi$
$431$	5.62468	+	3.24741i	0.270931	+	0.156422i	−0.358379	+	0.933576i	$0.616671\pi$
$432$		0			0
$433$			1.05254i			0.0505818i	0.999680	+	0.0252909i	$0.00805120\pi$
$433$			1.05254i			0.0505818i	−0.999680	+	0.0252909i	$0.991949\pi$
$434$		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	0.267799	−	0.963475i	$-0.413704\pi$
$439$	25.8990	−	14.9528i	1.23609	−	0.713658i	0.968293	+	0.249817i	$0.0803705\pi$
$440$		0			0
$441$	−13.5114	−	16.0761i	−0.643400	−	0.765530i
$442$		0			0
$443$	−26.7104	+	15.4212i	−1.26905	+	0.732685i	−0.974808	−	0.223047i	$-0.928400\pi$
$443$	−26.7104	+	15.4212i	−1.26905	+	0.732685i	−0.294240	+	0.955732i	$0.595066\pi$
$444$		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
$453$	0.662071	+	14.2179i	0.0311068	+	0.668015i
$454$		0			0
$455$	−18.8733	+	36.0351i	−0.884795	+	1.68935i
$456$		0			0
$457$	11.8750	+	20.5681i	0.555489	+	0.962135i	0.997865	+	0.0653057i	$0.0208022\pi$
$457$	11.8750	+	20.5681i	0.555489	+	0.962135i	−0.442376	+	0.896830i	$0.645864\pi$
$458$		0			0
$459$	−0.500745	−	0.202331i	−0.0233728	−	0.00944400i
$460$		0			0
$461$	10.5938			0.493404			0.246702	−	0.969091i	$-0.420653\pi$
$461$	10.5938			0.493404			0.246702	+	0.969091i	$0.420653\pi$
$462$		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
$465$	−28.0197	−	43.7021i	−1.29938	−	2.02663i
$466$		0			0
$467$	15.7847	+	27.3399i	0.730428	+	1.26514i	0.956700	+	0.291075i	$0.0940129\pi$
$467$	15.7847	+	27.3399i	0.730428	+	1.26514i	−0.226272	+	0.974064i	$0.572654\pi$
$468$		0			0
$469$	0.292400	+	7.10444i	0.0135018	+	0.328053i
$470$		0			0
$471$	−22.3964	+	1.04291i	−1.03197	+	0.0480549i
$472$		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	$-0.921955\pi$
$479$	−6.01497	+	10.4182i	−0.274831	+	0.476022i	0.695261	+	0.718757i	$0.255289\pi$
$480$		0			0
$481$	38.2337	−	22.0742i	1.74331	−	1.00650i
$482$		0			0
$483$	0.533658	+	6.07176i	0.0242823	+	0.276275i
$484$		0			0
$485$	16.9247	−	9.77148i	0.768511	−	0.443700i
$486$		0			0
$487$	9.47737	−	16.4153i	0.429461	−	0.743848i	−0.567365	−	0.823467i	$-0.692037\pi$
$487$	9.47737	−	16.4153i	0.429461	−	0.743848i	0.996825	+	0.0796188i	$0.0253703\pi$
$488$		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
$495$	3.70313	+	1.70073i	0.166443	+	0.0764419i
$496$		0			0
$497$	−8.19817	−	12.9398i	−0.367738	−	0.580429i
$498$		0			0
$499$	−10.0988	−	17.4916i	−0.452084	−	0.783033i	0.546431	−	0.837504i	$-0.315986\pi$
$499$	−10.0988	−	17.4916i	−0.452084	−	0.783033i	−0.998515	+	0.0544710i	$0.982653\pi$
$500$		0			0
$501$	−0.677418	+	0.434329i	−0.0302648	+	0.0194044i
$502$		0			0
$503$	36.8663			1.64379			0.821893	−	0.569641i	$-0.192918\pi$
$503$	36.8663			1.64379			0.821893	+	0.569641i	$0.192918\pi$
$504$		0			0
$505$	48.9400			2.17780
$506$		0			0
$507$	4.91034	−	3.14829i	0.218076	−	0.139820i
$508$		0			0
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	0.729587	−	0.683888i	$-0.239712\pi$
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	−0.957058	+	0.289897i	$0.906379\pi$
$510$		0			0
$511$	−0.622475	+	0.0256194i	−0.0275367	+	0.00113334i
$512$		0			0
$513$	−7.85364	−	10.0528i	−0.346747	−	0.443842i
$514$		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	$-0.719515\pi$
$521$	7.98887	−	13.8371i	0.349999	−	0.606216i	0.986249	+	0.165267i	$0.0528486\pi$
$522$		0			0
$523$	0.676700	−	0.390693i	0.0295900	−	0.0170838i	−0.485132	−	0.874441i	$-0.661228\pi$
$523$	0.676700	−	0.390693i	0.0295900	−	0.0170838i	0.514722	+	0.857357i	$0.327895\pi$
$524$		0			0
$525$	−24.8335	−	35.4358i	−1.08382	−	1.54654i
$526$		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
$537$	−3.53808	+	0.164754i	−0.152679	+	0.00710967i
$538$		0			0
$539$	−2.05664	+	1.42481i	−0.0885859	+	0.0613709i
$540$		0			0
$541$	3.63362	+	6.29362i	0.156222	+	0.270584i	0.933503	−	0.358569i	$-0.116735\pi$
$541$	3.63362	+	6.29362i	0.156222	+	0.270584i	−0.777282	+	0.629153i	$0.783402\pi$
$542$		0			0
$543$	16.4716	+	25.6905i	0.706863	+	1.10249i
$544$		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
$549$	−2.64131	−	28.2994i	−0.112729	−	1.20779i
$550$		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
$555$	3.34121	+	71.7521i	0.141826	+	3.04571i
$556$		0			0
$557$	−5.48798	−	3.16849i	−0.232533	−	0.134253i	0.379207	−	0.925312i	$-0.376197\pi$
$557$	−5.48798	−	3.16849i	−0.232533	−	0.134253i	−0.611740	+	0.791059i	$0.709530\pi$
$558$		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	$-0.938979\pi$
$563$	−7.73130	+	13.3910i	−0.325836	+	0.564364i	0.655846	+	0.754895i	$0.272312\pi$
$564$		0			0
$565$	−13.1647	+	7.60067i	−0.553845	+	0.319763i
$566$		0			0
$567$	−22.7739	−	6.95343i	−0.956413	−	0.292017i
$568$		0			0
$569$	10.2364	−	5.90999i	0.429132	−	0.247760i	−0.269845	−	0.962904i	$-0.586972\pi$
$569$	10.2364	−	5.90999i	0.429132	−	0.247760i	0.698977	+	0.715144i	$0.253639\pi$
$570$		0			0
$571$	−18.0386	+	31.2438i	−0.754892	+	1.30751i	0.190536	+	0.981680i	$0.438977\pi$
$571$	−18.0386	+	31.2438i	−0.754892	+	1.30751i	−0.945428	+	0.325831i	$0.894356\pi$
$572$		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	0.0104412	−	0.999945i	$-0.496676\pi$
$577$	−20.4253	−	11.7926i	−0.850316	−	0.490930i	−0.860758	+	0.509015i	$0.830010\pi$
$578$		0			0
$579$	−0.776646	−	16.6784i	−0.0322763	−	0.693130i
$580$		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
$585$	4.28642	+	45.9254i	0.177222	+	1.89878i
$586$		0			0
$587$	0.287490			0.0118660			0.00593298	−	0.999982i	$-0.498111\pi$
$587$	0.287490			0.0118660			0.00593298	+	0.999982i	$0.498111\pi$
$588$		0			0
$589$	19.3623			0.797812
$590$		0			0
$591$	14.3735	+	22.4182i	0.591247	+	0.922160i
$592$		0			0
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	0.724469	−	0.689308i	$-0.242085\pi$
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	−0.959192	+	0.282755i	$0.908752\pi$
$594$		0			0
$595$	0.882803	−	0.559311i	0.0361914	−	0.0229295i
$596$		0			0
$597$	7.93076	−	0.369304i	0.324584	−	0.0151146i
$598$		0			0
$599$	18.7842	+	10.8451i	0.767502	+	0.443117i	0.831983	−	0.554802i	$-0.187206\pi$
$599$	18.7842	+	10.8451i	0.767502	+	0.443117i	−0.0644810	+	0.997919i	$0.520539\pi$
$600$		0			0
$601$			23.7036i			0.966889i	0.875375	+	0.483445i	$0.160615\pi$
$601$			23.7036i			0.966889i	−0.875375	+	0.483445i	$0.839385\pi$
$602$		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	−0.826061	−	0.563580i	$-0.809423\pi$
$607$	−18.5031	+	10.6828i	−0.751017	+	0.433600i	0.0750445	+	0.997180i	$0.476090\pi$
$608$		0			0
$609$	20.6564	+	9.62217i	0.837039	+	0.389910i
$610$		0			0
$611$	40.1225	−	23.1647i	1.62318	−	0.937145i
$612$		0			0
$613$	−19.8248	+	34.3376i	−0.800716	+	1.38688i	0.118429	+	0.992962i	$0.462214\pi$
$613$	−19.8248	+	34.3376i	−0.800716	+	1.38688i	−0.919145	+	0.393918i	$0.871119\pi$
$614$		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	−0.340047	−	0.940408i	$-0.610443\pi$
$619$	−32.9529	−	19.0254i	−1.32449	−	0.764694i	−0.984441	+	0.175714i	$0.943776\pi$
$620$		0			0
$621$	4.25485	+	5.44628i	0.170741	+	0.218552i
$622$		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
$627$	−1.27948	+	0.820342i	−0.0510974	+	0.0327613i
$628$		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
$633$	1.26912	−	0.813704i	0.0504432	−	0.0323418i
$634$		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
$639$	−15.7842	−	7.24916i	−0.624413	−	0.286772i
$640$		0			0
$641$	21.2563	+	12.2723i	0.839574	+	0.484728i	0.857119	−	0.515118i	$-0.172252\pi$
$641$	21.2563	+	12.2723i	0.839574	+	0.484728i	−0.0175456	+	0.999846i	$0.505585\pi$
$642$		0			0
$643$			27.3936i			1.08030i	0.841569	+	0.540149i	$0.181632\pi$
$643$			27.3936i			1.08030i	−0.841569	+	0.540149i	$0.818368\pi$
$644$		0			0
$645$	2.93980	+	1.51955i	0.115754	+	0.0598321i
$646$		0			0
$647$	−16.1181	+	27.9173i	−0.633667	+	1.09754i	0.353129	+	0.935575i	$0.385118\pi$
$647$	−16.1181	+	27.9173i	−0.633667	+	1.09754i	−0.986796	+	0.161969i	$0.948216\pi$
$648$		0			0
$649$	−2.33618	+	1.34879i	−0.0917029	+	0.0529447i
$650$		0			0
$651$	29.5970	−	20.7417i	1.16000	−	0.812930i
$652$		0			0
$653$	−13.5027	+	7.79579i	−0.528401	+	0.305073i	−0.740365	−	0.672205i	$-0.765347\pi$
$653$	−13.5027	+	7.79579i	−0.528401	+	0.305073i	0.211964	+	0.977278i	$0.432014\pi$
$654$		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	0.629226	−	0.777222i	$-0.283372\pi$
$661$	6.96082	+	4.01883i	0.270745	+	0.156314i	−0.358481	+	0.933537i	$0.616705\pi$
$662$		0			0
$663$	−0.727541	+	0.0338787i	−0.0282553	+	0.00131574i
$664$		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
$669$	1.13467	+	1.76974i	0.0438690	+	0.0684220i
$670$		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
$675$	−45.4917	−	18.3814i	−1.75098	−	0.707499i
$676$		0			0
$677$	−17.3844	−	30.1106i	−0.668135	−	1.15724i	−0.978425	−	0.206602i	$-0.933760\pi$
$677$	−17.3844	−	30.1106i	−0.668135	−	1.15724i	0.310290	−	0.950642i	$-0.399574\pi$
$678$		0			0
$679$	7.28158	+	11.4931i	0.279441	+	0.441063i
$680$		0			0
$681$	1.07510	+	23.0877i	0.0411980	+	0.884721i
$682$		0			0
$683$	−40.7393	−	23.5209i	−1.55885	−	0.900001i	−0.997368	−	0.0725098i	$-0.976899\pi$
$683$	−40.7393	−	23.5209i	−1.55885	−	0.900001i	−0.561479	−	0.827491i	$-0.689768\pi$
$684$		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	−0.918076	−	0.396406i	$-0.870257\pi$
$691$	−27.1758	+	15.6900i	−1.03382	+	0.596874i	−0.115740	+	0.993279i	$0.536924\pi$
$692$		0			0
$693$	−1.07701	+	2.62459i	−0.0409121	+	0.0996998i
$694$		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
$705$	3.50628	+	75.2968i	0.132054	+	2.83584i
$706$		0			0
$707$	1.40111	+	34.0427i	0.0526940	+	1.28031i
$708$		0			0
$709$	−11.5451	−	19.9968i	−0.433587	−	0.750995i	0.563592	−	0.826053i	$-0.309419\pi$
$709$	−11.5451	−	19.9968i	−0.433587	−	0.750995i	−0.997179	+	0.0750583i	$0.976086\pi$
$710$		0			0
$711$	−9.63298	+	0.899089i	−0.361265	+	0.0337185i
$712$		0			0
$713$	−10.4899			−0.392849
$714$		0			0
$715$	5.49540			0.205516
$716$		0			0
$717$	21.1227	+	32.9448i	0.788841	+	1.23035i
$718$		0			0
$719$	−22.5340	−	39.0300i	−0.840376	−	1.45557i	−0.889577	−	0.456785i	$-0.849001\pi$
$719$	−22.5340	−	39.0300i	−0.840376	−	1.45557i	0.0492012	−	0.998789i	$-0.484332\pi$
$720$		0			0
$721$	6.91877	−	13.2101i	0.257669	−	0.491971i
$722$		0			0
$723$	−8.47337	+	0.394571i	−0.315128	+	0.0146743i
$724$		0			0
$725$	40.6638	+	23.4772i	1.51022	+	0.871923i
$726$		0			0
$727$			3.14662i			0.116702i	0.998296	+	0.0583508i	$0.0185842\pi$
$727$			3.14662i			0.116702i	−0.998296	+	0.0583508i	$0.981416\pi$
$728$		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	−0.197616	−	0.980279i	$-0.563320\pi$
$733$	14.9590	−	8.63657i	0.552522	−	0.318999i	0.750139	+	0.661281i	$0.229987\pi$
$734$		0			0
$735$	36.6138	−	27.9729i	1.35052	−	1.03180i
$736$		0			0
$737$	0.831885	−	0.480289i	0.0306429	−	0.0176917i
$738$		0			0
$739$	−0.996550	+	1.72607i	−0.0366587	+	0.0634947i	−0.883773	−	0.467917i	$-0.845005\pi$
$739$	−0.996550	+	1.72607i	−0.0366587	+	0.0634947i	0.847114	+	0.531411i	$0.178338\pi$
$740$		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
$747$	−11.3656	+	24.7473i	−0.415846	+	0.905456i
$748$		0			0
$749$	10.8113	−	20.6422i	0.395036	−	0.754248i
$750$		0			0
$751$	22.0897	+	38.2605i	0.806065	+	1.39615i	0.915569	+	0.402160i	$0.131740\pi$
$751$	22.0897	+	38.2605i	0.806065	+	1.39615i	−0.109504	+	0.993986i	$0.534926\pi$
$752$		0			0
$753$	−13.3832	+	8.58069i	−0.487711	+	0.312698i
$754$		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
$759$	0.693179	−	0.444434i	0.0251608	−	0.0161319i
$760$		0			0
$761$	−13.9084	−	24.0900i	−0.504178	−	0.873262i	−0.999988	−	0.00483132i	$-0.998462\pi$
$761$	−13.9084	−	24.0900i	−0.504178	−	0.873262i	0.495810	−	0.868431i	$-0.334871\pi$
$762$		0			0
$763$	−0.487125	−	11.8357i	−0.0176351	−	0.428480i
$764$		0			0
$765$	0.494565	−	1.07686i	0.0178811	−	0.0389339i
$766$		0			0
$767$	−26.4432	−	15.2670i	−0.954809	−	0.551259i
$768$		0			0
$769$			10.2707i			0.370369i	0.982704	+	0.185185i	$0.0592883\pi$
$769$			10.2707i			0.370369i	−0.982704	+	0.185185i	$0.940712\pi$
$770$		0			0
$771$	−19.4196	−	10.0377i	−0.699379	−	0.361500i
$772$		0			0
$773$	−20.2953	+	35.1525i	−0.729972	+	1.26435i	0.226923	+	0.973913i	$0.427133\pi$
$773$	−20.2953	+	35.1525i	−0.729972	+	1.26435i	−0.956895	+	0.290435i	$0.906200\pi$
$774$		0			0
$775$	64.4933	−	37.2352i	2.31667	−	1.33753i
$776$		0			0
$777$	−49.8151	+	4.37834i	−1.78711	+	0.157072i
$778$		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	0.845706	−	0.533650i	$-0.179180\pi$
$787$	22.6225	+	13.0611i	0.806404	+	0.465578i	−0.0393014	+	0.999227i	$0.512513\pi$
$788$		0			0
$789$	50.4432	−	2.34894i	1.79583	−	0.0836246i
$790$		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
$795$	20.8461	+	32.5134i	0.739334	+	1.15313i
$796$		0			0
$797$	−38.0284			−1.34704			−0.673518	−	0.739171i	$-0.735218\pi$
$797$	−38.0284			−1.34704			−0.673518	+	0.739171i	$0.735218\pi$
$798$		0			0
$799$	−1.19025			−0.0421080
$800$		0			0
$801$	20.3842	−	1.90255i	0.720240	−	0.0672233i
$802$		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
$807$	0.360362	+	7.73874i	0.0126854	+	0.272416i
$808$		0			0
$809$	−25.8553	−	14.9276i	−0.909024	−	0.524825i	−0.0289068	−	0.999582i	$-0.509203\pi$
$809$	−25.8553	−	14.9276i	−0.909024	−	0.524825i	−0.880117	+	0.474757i	$0.842536\pi$
$810$		0			0
$811$			15.4099i			0.541114i	0.962704	+	0.270557i	$0.0872079\pi$
$811$			15.4099i			0.541114i	−0.962704	+	0.270557i	$0.912792\pi$
$812$		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
$819$	−31.8230	+	4.29644i	−1.11199	+	0.150130i
$820$		0			0
$821$	25.0908	−	14.4862i	0.875674	−	0.505570i	0.00644422	−	0.999979i	$-0.497949\pi$
$821$	25.0908	−	14.4862i	0.875674	−	0.505570i	0.869230	+	0.494409i	$0.164615\pi$
$822$		0			0
$823$	3.58962	−	6.21741i	0.125126	−	0.216725i	−0.796656	−	0.604433i	$-0.793400\pi$
$823$	3.58962	−	6.21741i	0.125126	−	0.216725i	0.921782	+	0.387708i	$0.126733\pi$
$824$		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	−0.999949	−	0.0101139i	$-0.996781\pi$
$829$	−43.4385	−	25.0792i	−1.50868	−	0.871038i	−0.508733	−	0.860924i	$-0.669886\pi$
$830$		0			0
$831$	−0.0823277	−	1.76798i	−0.00285592	−	0.0613304i
$832$		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
$837$	15.3526	−	37.9960i	0.530665	−	1.31333i
$838$		0			0
$839$	−10.2849			−0.355073			−0.177536	−	0.984114i	$-0.556813\pi$
$839$	−10.2849			−0.355073			−0.177536	+	0.984114i	$0.556813\pi$
$840$		0			0
$841$	4.27275			0.147336
$842$		0			0
$843$	−13.0369	−	20.3335i	−0.449016	−	0.700324i
$844$		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
$849$	−28.0468	+	1.30603i	−0.962564	+	0.0448228i
$850$		0			0
$851$	12.5698	+	7.25719i	0.430888	+	0.248773i
$852$		0			0
$853$		−	29.0278i		−	0.993891i	−0.867782	−	0.496946i	$-0.834455\pi$
$853$		−	29.0278i		−	0.993891i	0.867782	−	0.496946i	$-0.165545\pi$
$854$		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	$-0.745352\pi$
$857$	7.98887	−	13.8371i	0.272895	−	0.472668i	0.969602	+	0.244688i	$0.0786856\pi$
$858$		0			0
$859$	−4.98253	+	2.87666i	−0.170002	+	0.0981505i	−0.582587	−	0.812769i	$-0.697959\pi$
$859$	−4.98253	+	2.87666i	−0.170002	+	0.0981505i	0.412585	+	0.910919i	$0.364626\pi$
$860$		0			0
$861$	−11.9093	+	25.5664i	−0.405869	+	0.871299i
$862$		0			0
$863$	−10.7735	+	6.22006i	−0.366733	+	0.211733i	−0.672030	−	0.740524i	$-0.734578\pi$
$863$	−10.7735	+	6.22006i	−0.366733	+	0.211733i	0.305297	+	0.952257i	$0.401244\pi$
$864$		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
$873$	14.0194	+	6.43867i	0.474486	+	0.217916i
$874$		0			0
$875$	37.7331	−	23.9062i	1.27561	−	0.808179i
$876$		0			0
$877$	21.9672	+	38.0484i	0.741781	+	1.28480i	0.951684	+	0.307080i	$0.0993521\pi$
$877$	21.9672	+	38.0484i	0.741781	+	1.28480i	−0.209902	+	0.977722i	$0.567315\pi$
$878$		0			0
$879$	28.0052	−	17.9556i	0.944591	−	0.605628i
$880$		0			0
$881$	51.0805			1.72095			0.860473	−	0.509496i	$-0.170168\pi$
$881$	51.0805			1.72095			0.860473	+	0.509496i	$0.170168\pi$
$882$		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
$885$	41.8213	−	26.8139i	1.40581	−	0.901339i
$886$		0			0
$887$	20.8829	+	36.1703i	0.701180	+	1.21448i	0.968053	+	0.250748i	$0.0806764\pi$
$887$	20.8829	+	36.1703i	0.701180	+	1.21448i	−0.266873	+	0.963732i	$0.585990\pi$
$888$		0			0
$889$	28.8751	−	18.2942i	0.968440	−	0.613567i
$890$		0			0
$891$	0.595295	+	3.16126i	0.0199431	+	0.105906i
$892$		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
$903$	−0.972832	+	2.08843i	−0.0323738	+	0.0694985i
$904$		0			0
$905$	−57.9883	+	33.4795i	−1.92760	+	1.11290i
$906$		0			0
$907$	18.9839	−	32.8811i	0.630350	−	1.09180i	−0.357130	−	0.934055i	$-0.616245\pi$
$907$	18.9839	−	32.8811i	0.630350	−	1.09180i	0.987480	−	0.157744i	$-0.0504220\pi$
$908$		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
$915$	62.2949	−	2.90083i	2.05940	−	0.0958983i
$916$		0			0
$917$	12.4868	+	6.53991i	0.412349	+	0.215967i
$918$		0			0
$919$	−13.5889	−	23.5367i	−0.448256	−	0.776403i	0.550016	−	0.835154i	$-0.314622\pi$
$919$	−13.5889	−	23.5367i	−0.448256	−	0.776403i	−0.998273	+	0.0587510i	$0.981288\pi$
$920$		0			0
$921$	0.449199	+	0.700611i	0.0148016	+	0.0230859i
$922$		0			0
$923$	−23.4236			−0.770996
$924$		0			0
$925$	−103.041			−3.38798
$926$		0			0
$927$	−1.57136	−	16.8358i	−0.0516103	−	0.552960i
$928$		0			0
$929$	−0.982860	−	1.70236i	−0.0322466	−	0.0558527i	0.849452	−	0.527666i	$-0.176933\pi$
$929$	−0.982860	−	1.70236i	−0.0322466	−	0.0558527i	−0.881698	+	0.471814i	$0.843600\pi$
$930$		0			0
$931$	1.41222	+	17.1273i	0.0462838	+	0.561326i
$932$		0			0
$933$	0.751941	+	16.1478i	0.0246174	+	0.528656i
$934$		0			0
$935$	−0.122267	−	0.0705911i	−0.00399857	−	0.00230858i
$936$		0			0
$937$		−	31.0157i		−	1.01324i	−0.862170	−	0.506620i	$-0.830895\pi$
$937$		−	31.0157i		−	1.01324i	0.862170	−	0.506620i	$-0.169105\pi$
$938$		0			0
$939$	−14.2479	+	27.5648i	−0.464963	+	0.899544i
$940$		0			0
$941$	16.7914	−	29.0836i	0.547384	−	0.948097i	−0.451069	−	0.892489i	$-0.648957\pi$
$941$	16.7914	−	29.0836i	0.547384	−	0.948097i	0.998453	−	0.0556078i	$-0.0177096\pi$
$942$		0			0
$943$	7.08940	−	4.09307i	0.230863	−	0.133289i
$944$		0			0
$945$	17.5645	−	49.2050i	0.571374	−	1.60064i
$946$		0			0
$947$	8.89077	−	5.13309i	0.288911	−	0.166803i	−0.348539	−	0.937294i	$-0.613322\pi$
$947$	8.89077	−	5.13309i	0.288911	−	0.166803i	0.637451	+	0.770491i	$0.279989\pi$
$948$		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
$957$	−0.143196	−	3.07512i	−0.00462888	−	0.0994046i
$958$		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
$963$	−2.45541	−	26.3076i	−0.0791245	−	0.847752i
$964$		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
$969$	0.238553	+	0.372068i	0.00766342	+	0.0119525i
$970$		0			0
$971$	7.28478	+	12.6176i	0.233780	+	0.404918i	0.958917	−	0.283686i	$-0.0915572\pi$
$971$	7.28478	+	12.6176i	0.233780	+	0.404918i	−0.725138	+	0.688604i	$0.758224\pi$
$972$		0			0
$973$	30.1110	+	47.5264i	0.965313	+	1.52363i
$974$		0			0
$975$	−66.0956	+	3.07781i	−2.11675	+	0.0985689i
$976$		0			0
$977$	5.93615	+	3.42724i	0.189914	+	0.109647i	0.591942	−	0.805980i	$-0.298361\pi$
$977$	5.93615	+	3.42724i	0.189914	+	0.109647i	−0.402028	+	0.915627i	$0.631695\pi$
$978$		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	0.185910	−	0.982567i	$-0.440477\pi$
$983$	29.5934	−	51.2573i	0.943883	−	1.63485i	0.757973	−	0.652286i	$-0.226190\pi$
$984$		0			0
$985$	−50.6020	+	29.2151i	−1.61231	+	0.930870i
$986$		0			0
$987$	−52.2761	+	4.59464i	−1.66397	+	0.146249i
$988$		0			0
$989$	0.579108	−	0.334348i	0.0184146	−	0.0106317i
$990$		0			0
$991$	−28.2143	+	48.8686i	−0.896256	+	1.55236i	−0.0640132	+	0.997949i	$0.520390\pi$
$991$	−28.2143	+	48.8686i	−0.896256	+	1.55236i	−0.832243	+	0.554412i	$0.812943\pi$
$992$		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	−0.445541	−	0.895262i	$-0.646988\pi$
$997$	−45.5831	−	26.3174i	−1.44363	−	0.833480i	−0.998090	+	0.0617814i	$0.980322\pi$
$998$		0			0
$999$	−44.6834	+	34.9084i	−1.41372	+	1.10445i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.2	✓	16	1.1	even	1	trivial
168.2.u.a.17.4	yes	16	3.2	odd	2	inner
168.2.u.a.89.2	yes	16	21.5	even	6	inner
168.2.u.a.89.4	yes	16	7.5	odd	6	inner
336.2.bc.f.17.5		16	12.11	even	2
336.2.bc.f.17.7		16	4.3	odd	2
336.2.bc.f.257.5		16	28.19	even	6
336.2.bc.f.257.7		16	84.47	odd	6
1176.2.k.a.881.1		16	7.3	odd	6
1176.2.k.a.881.2		16	21.11	odd	6
1176.2.k.a.881.15		16	21.17	even	6
1176.2.k.a.881.16		16	7.4	even	3
1176.2.u.b.521.5		16	21.20	even	2
1176.2.u.b.521.7		16	7.6	odd	2
1176.2.u.b.1097.5		16	7.2	even	3
1176.2.u.b.1097.7		16	21.2	odd	6
2352.2.k.i.881.1		16	28.11	odd	6
2352.2.k.i.881.2		16	84.59	odd	6
2352.2.k.i.881.15		16	84.11	even	6
2352.2.k.i.881.16		16	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.45809 + 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(2.23495 - 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +O(q^{10})\)	\(q+(-1.45809 + 0.934861i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(2.23495 - 1.41598i) q^{7} +(1.25207 - 2.72623i) q^{9} +(-0.309539 - 0.178712i) q^{11} -4.04570i q^{13} +(5.84742 + 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(-2.12615 + 1.22753i) q^{19} +(-1.93502 + 4.15400i) q^{21} +(1.15188 - 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(0.723015 + 5.14560i) q^{27} -4.97265i q^{29} +(-6.83007 - 3.94335i) q^{31} +(0.618407 - 0.0287968i) q^{33} +(-8.90704 - 4.66504i) q^{35} +(5.45622 + 9.45046i) q^{37} +(3.78216 + 5.89900i) q^{39} +6.15464 q^{41} +0.502751 q^{43} +(-11.3517 + 1.05950i) q^{45} +(5.72578 + 9.91734i) q^{47} +(2.99000 - 6.32929i) q^{49} +(-0.00837401 - 0.179831i) q^{51} +(5.08143 + 2.93376i) q^{53} +1.35833i q^{55} +(1.95255 - 3.77751i) q^{57} +(3.77364 - 6.53614i) q^{59} +(8.20485 - 4.73707i) q^{61} +(-1.06198 - 7.86589i) q^{63} +(-13.3151 + 7.68750i) q^{65} +(-1.34375 + 2.32744i) q^{67} +(-1.05783 + 2.04653i) q^{69} -5.78975i q^{71} +(-0.203925 - 0.117736i) q^{73} +(-0.760762 - 16.3373i) q^{75} +(-0.944856 + 0.0388878i) q^{77} +(-1.61247 - 2.79289i) q^{79} +(-5.86465 - 6.82685i) q^{81} -9.07747 q^{83} +0.394999 q^{85} +(4.64874 + 7.25058i) q^{87} +(3.41213 + 5.90999i) q^{89} +(-5.72862 - 9.04192i) q^{91} +(13.6454 - 0.635411i) q^{93} +(8.08008 + 4.66504i) q^{95} +5.14243i q^{97} +(-0.874774 + 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{7} + 2 q^{9}+O(q^{10}) \) 16 * q + 4 * q^7 + 2 * q^9	\( 16 q + 4 q^{7} + 2 q^{9} + 8 q^{15} - 6 q^{19} + 14 q^{21} - 18 q^{25} - 48 q^{31} - 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} - 42 q^{45} - 28 q^{49} + 6 q^{51} - 8 q^{57} + 36 q^{61} - 32 q^{63} + 14 q^{67} + 30 q^{73} + 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} + 78 q^{87} + 66 q^{91} + 16 q^{93} + 20 q^{99}+O(q^{100}) \) 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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