LMFDB - Embedded newform 1176.2.u.b.521.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(521,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, 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("1176.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.u (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.39040727770$
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:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.5
Root			$0.934861 + 1.45809i$ of defining polynomial
Character	$\chi$	$=$	1176.521
Dual form			1176.2.u.b.1097.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0805675 + 1.73018i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.98702 - 0.278792i) q^{9} +O(q^{10})$	\(q+(-0.0805675 + 1.73018i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.98702 - 0.278792i) q^{9} +(0.309539 + 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 - 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(2.12615 - 1.22753i) q^{19} +(-1.15188 + 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(0.723015 - 5.14560i) q^{27} +4.97265i q^{29} +(6.83007 + 3.94335i) q^{31} +(-0.334142 + 0.521158i) q^{33} +(5.45622 + 9.45046i) q^{37} +(-6.99976 - 0.325951i) q^{39} +6.15464 q^{41} +0.502751 q^{43} +(4.75828 + 10.3606i) q^{45} +(5.72578 + 9.91734i) q^{47} +(-0.151551 - 0.0971675i) q^{51} +(-5.08143 - 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 + 3.77751i) q^{57} +(3.77364 - 6.53614i) q^{59} +(-8.20485 + 4.73707i) q^{61} +(13.3151 - 7.68750i) q^{65} +(-1.34375 + 2.32744i) q^{67} +(-1.05783 - 2.04653i) q^{69} +5.78975i q^{71} +(0.203925 + 0.117736i) q^{73} +(-13.7681 - 8.82748i) q^{75} +(-1.61247 - 2.79289i) q^{79} +(8.84455 + 1.66551i) q^{81} -9.07747 q^{83} +0.394999 q^{85} +(-8.60356 - 0.400634i) q^{87} +(3.41213 + 5.90999i) q^{89} +(-7.37296 + 11.4995i) q^{93} +(-8.08008 - 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 - 0.620114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{9}+O(q^{10}) $ 16 * q + 2 * q^9	$ 16 q + 2 q^{9} + 8 q^{15} + 6 q^{19} - 18 q^{25} + 48 q^{31} + 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} + 42 q^{45} + 6 q^{51} - 8 q^{57} - 36 q^{61} + 14 q^{67} - 30 q^{73} - 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} + 16 q^{93} + 20 q^{99}+O(q^{100}) $ 16 * q + 2 * q^9 + 8 * q^15 + 6 * q^19 - 18 * q^25 + 48 * q^31 + 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 + 42 * q^45 + 6 * q^51 - 8 * q^57 - 36 * q^61 + 14 * q^67 - 30 * q^73 - 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 + 16 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			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	−0.881404	−	0.472364i	$-0.843401\pi$
$5$	−1.90017	−	3.29119i	−0.849781	−	1.47186i	0.0316229	−	0.999500i	$-0.489932\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2.98702	−	0.278792i	−0.995673	−	0.0929306i
$10$		0			0
$11$	0.309539	+	0.178712i	0.0933294	+	0.0538838i	0.545938	−	0.837825i	$-0.316173\pi$
$11$	0.309539	+	0.178712i	0.0933294	+	0.0538838i	−0.452609	+	0.891709i	$0.649507\pi$
$12$		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	$-0.837346\pi$
$17$	−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	−0.235878	−	0.971783i	$-0.575796\pi$
$19$	2.12615	−	1.22753i	0.487772	−	0.281615i	0.723650	+	0.690167i	$0.242463\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.15188	+	0.665037i	−0.240183	+	0.138670i	−0.615261	−	0.788323i	$-0.710949\pi$
$23$	−1.15188	+	0.665037i	−0.240183	+	0.138670i	0.375078	+	0.926993i	$0.377616\pi$
$24$		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	$0.152760\pi$
$29$			4.97265i			0.923398i	−0.887037	+	0.461699i	$0.847240\pi$
$30$		0			0
$31$	6.83007	+	3.94335i	1.22672	+	0.708246i	0.966342	−	0.257262i	$-0.0828202\pi$
$31$	6.83007	+	3.94335i	1.22672	+	0.708246i	0.260376	+	0.965507i	$0.416154\pi$
$32$		0			0
$33$	−0.334142	+	0.521158i	−0.0581667	+	0.0907220i
$34$		0			0
$35$		0			0
$36$		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
$39$	−6.99976	−	0.325951i	−1.12086	−	0.0521940i
$40$		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
$45$	4.75828	+	10.3606i	0.709322	+	1.54446i
$46$		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
$49$		0			0
$50$		0			0
$51$	−0.151551	−	0.0971675i	−0.0212214	−	0.0136062i
$52$		0			0
$53$	−5.08143	−	2.93376i	−0.697988	−	0.402983i	0.108610	−	0.994084i	$-0.465360\pi$
$53$	−5.08143	−	2.93376i	−0.697988	−	0.402983i	−0.806597	+	0.591101i	$0.798693\pi$
$54$		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	−0.922796	−	0.385289i	$-0.874102\pi$
$61$	−8.20485	+	4.73707i	−1.05052	+	0.606520i	−0.127727	+	0.991809i	$0.540768\pi$
$62$		0			0
$63$		0			0
$64$		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	$0.111632\pi$
$71$			5.78975i			0.687117i	−0.939131	+	0.343558i	$0.888368\pi$
$72$		0			0
$73$	0.203925	+	0.117736i	0.0238676	+	0.0137800i	0.511886	−	0.859053i	$-0.328947\pi$
$73$	0.203925	+	0.117736i	0.0238676	+	0.0137800i	−0.488019	+	0.872833i	$0.662280\pi$
$74$		0			0
$75$	−13.7681	−	8.82748i	−1.58980	−	1.01931i
$76$		0			0
$77$		0			0
$78$		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
$81$	8.84455	+	1.66551i	0.982728	+	0.185057i
$82$		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
$87$	−8.60356	−	0.400634i	−0.922398	−	0.0429525i
$88$		0			0
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	0.988238	−	0.152921i	$-0.0488681\pi$
$89$	3.41213	+	5.90999i	0.361685	+	0.626457i	−0.626553	+	0.779379i	$0.715535\pi$
$90$		0			0
$91$		0			0
$92$		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	0.344583	+	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	−0.720816	−	0.693126i	$-0.756233\pi$
$103$	−4.88120	+	2.81816i	−0.480959	+	0.277682i	0.239857	+	0.970808i	$0.422899\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.62737	+	4.40366i	−0.737365	+	0.425718i	−0.821111	−	0.570769i	$-0.806645\pi$
$107$	−7.62737	+	4.40366i	−0.737365	+	0.425718i	0.0837453	+	0.996487i	$0.473312\pi$
$108$		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	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		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			0
$120$		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	$-0.0918972\pi$
$131$	2.66384	+	4.61391i	0.232741	+	0.403119i	−0.725873	+	0.687829i	$0.758564\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−18.3090	+	7.39793i	−1.57579	+	0.636713i
$136$		0			0
$137$	4.37380	+	2.52521i	0.373679	+	0.215744i	0.675064	−	0.737759i	$-0.264116\pi$
$137$	4.37380	+	2.52521i	0.373679	+	0.215744i	−0.301386	+	0.953502i	$0.597449\pi$
$138$		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
$147$		0			0
$148$		0			0
$149$	10.5482	−	6.09001i	0.864143	−	0.498913i	−0.00125437	−	0.999999i	$-0.500399\pi$
$149$	10.5482	−	6.09001i	0.864143	−	0.498913i	0.865398	+	0.501086i	$0.167066\pi$
$150$		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	−0.0192119	−	0.999815i	$-0.506116\pi$
$157$	−11.2104	−	6.47230i	−0.894683	−	0.516546i	−0.875472	+	0.483270i	$0.839449\pi$
$158$		0			0
$159$	5.48532	−	8.55539i	0.435014	−	0.678487i
$160$		0			0
$161$		0			0
$162$		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
$165$	2.35016	+	0.109437i	0.182959	+	0.00851969i
$166$		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
$171$	−6.69307	+	3.07391i	−0.511832	+	0.235068i
$172$		0			0
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	0.986547	−	0.163477i	$-0.0522710\pi$
$173$	4.62587	+	8.01224i	0.351698	+	0.609159i	−0.634849	+	0.772636i	$0.718938\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	11.0046	+	7.05566i	0.827159	+	0.530336i
$178$		0			0
$179$	−1.77096	−	1.02246i	−0.132367	−	0.0764224i	0.432354	−	0.901704i	$-0.357683\pi$
$179$	−1.77096	−	1.02246i	−0.132367	−	0.0764224i	−0.564722	+	0.825282i	$0.691016\pi$
$180$		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
$189$		0			0
$190$		0			0
$191$	19.4811	−	11.2474i	1.40960	−	0.813834i	0.414252	−	0.910162i	$-0.364043\pi$
$191$	19.4811	−	11.2474i	1.40960	−	0.813834i	0.995350	+	0.0963279i	$0.0307097\pi$
$192$		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	$0.184501\pi$
$197$			15.3750i			1.09542i	−0.836667	+	0.547712i	$0.815499\pi$
$198$		0			0
$199$	3.96967	+	2.29189i	0.281403	+	0.162468i	0.634058	−	0.773285i	$-0.281388\pi$
$199$	3.96967	+	2.29189i	0.281403	+	0.162468i	−0.352656	+	0.935753i	$0.614721\pi$
$200$		0			0
$201$	−3.91862	−	2.51244i	−0.276398	−	0.177214i
$202$		0			0
$203$		0			0
$204$		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
$217$		0			0
$218$		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	$-0.687304\pi$
$227$	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	−0.782609	−	0.622514i	$-0.786111\pi$
$229$	−9.60627	+	5.54618i	−0.634800	+	0.366502i	0.147808	+	0.989016i	$0.452778\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.08411	−	4.09001i	0.464095	−	0.267946i	−0.249669	−	0.968331i	$-0.580322\pi$
$233$	7.08411	−	4.09001i	0.464095	−	0.267946i	0.713765	+	0.700386i	$0.246989\pi$
$234$		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	$0.260833\pi$
$239$			22.5944i			1.46151i	−0.682638	+	0.730757i	$0.739167\pi$
$240$		0			0
$241$	−4.24127	−	2.44870i	−0.273205	−	0.157735i	0.357138	−	0.934051i	$-0.383752\pi$
$241$	−4.24127	−	2.44870i	−0.273205	−	0.157735i	−0.630343	+	0.776317i	$0.717086\pi$
$242$		0			0
$243$	−3.59421	+	15.1684i	−0.230569	+	0.973056i
$244$		0			0
$245$		0			0
$246$		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	$-0.406453\pi$
$251$	9.17857			0.579346			0.289673	+	0.957126i	$0.406453\pi$
$252$		0			0
$253$	−0.475401			−0.0298882
$254$		0			0
$255$	−0.0318241	+	0.683418i	−0.00199290	+	0.0427973i
$256$		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
$259$		0			0
$260$		0			0
$261$	1.38633	−	14.8534i	0.0858119	−	0.919402i
$262$		0			0
$263$	25.2489	+	14.5775i	1.55692	+	0.898886i	0.997549	+	0.0699665i	$0.0222892\pi$
$263$	25.2489	+	14.5775i	1.55692	+	0.898886i	0.559367	+	0.828920i	$0.311044\pi$
$264$		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	0.00982495	−	0.999952i	$-0.496873\pi$
$271$	14.4985	−	8.37071i	0.880721	−	0.508485i	0.870896	+	0.491467i	$0.163539\pi$
$272$		0			0
$273$		0			0
$274$		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	$-0.863448\pi$
$281$		−	13.9453i		−	0.831907i	0.909386	−	0.415953i	$-0.136552\pi$
$282$		0			0
$283$	−14.0386	−	8.10519i	−0.834508	−	0.481803i	0.0208856	−	0.999782i	$-0.493351\pi$
$283$	−14.0386	−	8.10519i	−0.834508	−	0.481803i	−0.855394	+	0.517978i	$0.826685\pi$
$284$		0			0
$285$	8.72233	−	13.6041i	0.516666	−	0.805838i
$286$		0			0
$287$		0			0
$288$		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	$-0.689596\pi$
$293$	−19.2067			−1.12207			−0.561034	+	0.827793i	$0.689596\pi$
$294$		0			0
$295$	−28.6822			−1.66994
$296$		0			0
$297$	1.14338	−	1.46355i	0.0663459	−	0.0849239i
$298$		0			0
$299$	−2.69054	−	4.66015i	−0.155598	−	0.269503i
$300$		0			0
$301$		0			0
$302$		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	$-0.748089\pi$
$311$	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	−0.869649	−	0.493670i	$-0.835655\pi$
$313$	−15.5147	+	8.95742i	−0.876943	+	0.506303i	−0.00729351	+	0.999973i	$0.502322\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−19.3275	+	11.1587i	−1.08554	+	0.626736i	−0.932385	−	0.361467i	$-0.882276\pi$
$317$	−19.3275	+	11.1587i	−1.08554	+	0.626736i	−0.153153	+	0.988202i	$0.548943\pi$
$318$		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
$329$		0			0
$330$		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
$333$	−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
$343$		0			0
$344$		0			0
$345$	−4.72547	+	7.37027i	−0.254411	+	0.396802i
$346$		0			0
$347$	−27.6474	−	15.9623i	−1.48419	−	0.856899i	−0.484354	−	0.874872i	$-0.660945\pi$
$347$	−27.6474	−	15.9623i	−1.48419	−	0.856899i	−0.999838	+	0.0179729i	$0.994279\pi$
$348$		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	0.237937	+	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			0
$358$		0			0
$359$	16.9479	−	9.78486i	0.894475	−	0.516425i	0.0190713	−	0.999818i	$-0.493929\pi$
$359$	16.9479	−	9.78486i	0.894475	−	0.516425i	0.875404	+	0.483393i	$0.160596\pi$
$360$		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	$-0.322178\pi$
$367$	1.16258	+	0.671213i	0.0606860	+	0.0350371i	−0.469350	+	0.883012i	$0.655512\pi$
$368$		0			0
$369$	−18.3840	−	1.71586i	−0.957034	−	0.0893243i
$370$		0			0
$371$		0			0
$372$		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
$375$	−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	−0.995995	−	0.0894085i	$-0.971502\pi$
$383$	−11.2613	−	19.5052i	−0.575428	−	0.996670i	0.420567	−	0.907261i	$-0.361831\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.50173	−	0.140163i	−0.0763370	−	0.00712488i
$388$		0			0
$389$	−32.1899	−	18.5848i	−1.63209	−	0.942289i	−0.983447	−	0.181197i	$-0.942003\pi$
$389$	−32.1899	−	18.5848i	−1.63209	−	0.942289i	−0.648645	−	0.761091i	$-0.724664\pi$
$390$		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	$-0.421509\pi$
$397$	24.0288	−	13.8730i	1.20597	−	0.696268i	0.961877	+	0.273483i	$0.0881757\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−19.7233	+	11.3872i	−0.984933	+	0.568651i	−0.903756	−	0.428048i	$-0.859201\pi$
$401$	−19.7233	+	11.3872i	−0.984933	+	0.568651i	−0.0811773	+	0.996700i	$0.525868\pi$
$402$		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	$-0.109101\pi$
$409$	22.6849	+	13.0972i	1.12170	+	0.647613i	0.179865	+	0.983691i	$0.442434\pi$
$410$		0			0
$411$	−4.72145	+	7.36399i	−0.232892	+	0.363239i
$412$		0			0
$413$		0			0
$414$		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	$-0.570075\pi$
$419$	−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
$423$	−14.3381	−	31.2196i	−0.697144	−	1.51795i
$424$		0			0
$425$	−0.490719	−	0.849951i	−0.0238034	−	0.0412287i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.10845	−	1.35184i	−0.101797	−	0.0652674i
$430$		0			0
$431$	−5.62468	−	3.24741i	−0.270931	−	0.156422i	0.358379	−	0.933576i	$-0.383329\pi$
$431$	−5.62468	−	3.24741i	−0.270931	−	0.156422i	−0.629311	+	0.777154i	$0.716663\pi$
$432$		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	$-0.919630\pi$
$439$	−25.8990	+	14.9528i	−1.23609	+	0.713658i	−0.267799	+	0.963475i	$0.586296\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	26.7104	−	15.4212i	1.26905	−	0.732685i	0.294240	−	0.955732i	$-0.404934\pi$
$443$	26.7104	−	15.4212i	1.26905	−	0.732685i	0.974808	+	0.223047i	$0.0716002\pi$
$444$		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	$-0.666760\pi$
$449$		−	36.6953i		−	1.73176i	0.500253	−	0.865879i	$-0.333240\pi$
$450$		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
$455$		0			0
$456$		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
$459$	0.425596	+	0.332492i	0.0198651	+	0.0155194i
$460$		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
$465$	51.8570	+	2.41477i	2.40481	+	0.111982i
$466$		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			0
$470$		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	$-0.921955\pi$
$479$	−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			0
$484$		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	$0.116324\pi$
$491$			15.8373i			0.714727i	−0.933965	+	0.357364i	$0.883676\pi$
$492$		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
$497$		0			0
$498$		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
$501$	−0.0374310	+	0.803826i	−0.00167229	+	0.0359123i
$502$		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
$507$	0.271323	−	5.82663i	0.0120499	−	0.258770i
$508$		0			0
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	0.729587	−	0.683888i	$-0.239712\pi$
$509$	−5.13197	−	8.88884i	−0.227471	−	0.393991i	−0.957058	+	0.289897i	$0.906379\pi$
$510$		0			0
$511$		0			0
$512$		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	$-0.719515\pi$
$521$	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	−0.514722	−	0.857357i	$-0.672105\pi$
$523$	−0.676700	+	0.390693i	−0.0295900	+	0.0170838i	0.485132	+	0.874441i	$0.338772\pi$
$524$		0			0
$525$		0			0
$526$		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
$539$		0			0
$540$		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
$543$	−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
$553$		0			0
$554$		0			0
$555$	60.4685	+	38.7696i	2.56675	+	1.64568i
$556$		0			0
$557$	5.48798	+	3.16849i	0.232533	+	0.134253i	0.611740	−	0.791059i	$-0.290470\pi$
$557$	5.48798	+	3.16849i	0.232533	+	0.134253i	−0.379207	+	0.925312i	$0.623803\pi$
$558$		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
$567$		0			0
$568$		0			0
$569$	−10.2364	+	5.90999i	−0.429132	+	0.247760i	−0.698977	−	0.715144i	$-0.746361\pi$
$569$	−10.2364	+	5.90999i	−0.429132	+	0.247760i	0.269845	+	0.962904i	$0.413028\pi$
$570$		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	0.860758	−	0.509015i	$-0.169990\pi$
$577$	20.4253	+	11.7926i	0.850316	+	0.490930i	−0.0104412	+	0.999945i	$0.503324\pi$
$578$		0			0
$579$	−14.0556	−	9.01178i	−0.584130	−	0.374517i
$580$		0			0
$581$		0			0
$582$		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	$-0.498111\pi$
$587$	0.287490			0.0118660			0.00593298	+	0.999982i	$0.498111\pi$
$588$		0			0
$589$	19.3623			0.797812
$590$		0			0
$591$	−26.6015	−	1.23872i	−1.09424	−	0.0509543i
$592$		0			0
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	0.724469	−	0.689308i	$-0.242085\pi$
$593$	−5.71589	−	9.90021i	−0.234723	−	0.406553i	−0.959192	+	0.282755i	$0.908752\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.28520	+	6.68358i	−0.175382	+	0.273541i
$598$		0			0
$599$	−18.7842	−	10.8451i	−0.767502	−	0.443117i	0.0644810	−	0.997919i	$-0.479461\pi$
$599$	−18.7842	−	10.8451i	−0.767502	−	0.443117i	−0.831983	+	0.554802i	$0.812794\pi$
$600$		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	$-0.523910\pi$
$607$	18.5031	−	10.6828i	0.751017	−	0.433600i	0.826061	+	0.563580i	$0.190577\pi$
$608$		0			0
$609$		0			0
$610$		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	$-0.804499\pi$
$617$		−	28.6296i		−	1.15258i	0.817244	−	0.576292i	$-0.195501\pi$
$618$		0			0
$619$	32.9529	+	19.0254i	1.32449	+	0.764694i	0.984441	−	0.175714i	$-0.0562235\pi$
$619$	32.9529	+	19.0254i	1.32449	+	0.764694i	0.340047	+	0.940408i	$0.389557\pi$
$620$		0			0
$621$	2.58919	+	6.40794i	0.103901	+	0.257142i
$622$		0			0
$623$		0			0
$624$		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
$637$		0			0
$638$		0			0
$639$	1.61413	−	17.2941i	0.0638542	−	0.684143i
$640$		0			0
$641$	−21.2563	−	12.2723i	−0.839574	−	0.484728i	0.0175456	−	0.999846i	$-0.494415\pi$
$641$	−21.2563	−	12.2723i	−0.839574	−	0.484728i	−0.857119	+	0.515118i	$0.827748\pi$
$642$		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	0.353129	+	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
$651$		0			0
$652$		0			0
$653$	13.5027	−	7.79579i	0.528401	−	0.305073i	−0.211964	−	0.977278i	$-0.567986\pi$
$653$	13.5027	−	7.79579i	0.528401	−	0.305073i	0.740365	+	0.672205i	$0.234653\pi$
$654$		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	$0.239694\pi$
$659$			35.1100i			1.36769i	−0.729626	+	0.683847i	$0.760306\pi$
$660$		0			0
$661$	−6.96082	−	4.01883i	−0.270745	−	0.156314i	0.358481	−	0.933537i	$-0.383295\pi$
$661$	−6.96082	−	4.01883i	−0.270745	−	0.156314i	−0.629226	+	0.777222i	$0.716628\pi$
$662$		0			0
$663$	0.393110	−	0.613129i	0.0152671	−	0.0238120i
$664$		0			0
$665$		0			0
$666$		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	−0.978425	−	0.206602i	$-0.933760\pi$
$677$	−17.3844	−	30.1106i	−0.668135	−	1.15724i	0.310290	−	0.950642i	$-0.399574\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	19.4569	+	12.4749i	0.745592	+	0.478039i
$682$		0			0
$683$	40.7393	+	23.5209i	1.55885	+	0.900001i	0.997368	+	0.0725098i	$0.0231009\pi$
$683$	40.7393	+	23.5209i	1.55885	+	0.900001i	0.561479	+	0.827491i	$0.310232\pi$
$684$		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	$-0.463076\pi$
$691$	27.1758	−	15.6900i	1.03382	−	0.596874i	0.918076	+	0.396406i	$0.129743\pi$
$692$		0			0
$693$		0			0
$694$		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	$-0.808413\pi$
$701$		−	29.9818i		−	1.13240i	0.824268	−	0.566199i	$-0.191587\pi$
$702$		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
$707$		0			0
$708$		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
$711$	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	−0.889577	−	0.456785i	$-0.849001\pi$
$719$	−22.5340	−	39.0300i	−0.840376	−	1.45557i	0.0492012	−	0.998789i	$-0.484332\pi$
$720$		0			0
$721$		0			0
$722$		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	$-0.770013\pi$
$733$	−14.9590	+	8.63657i	−0.552522	+	0.318999i	0.197616	+	0.980279i	$0.436680\pi$
$734$		0			0
$735$		0			0
$736$		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	$-0.967571\pi$
$743$		−	5.54435i		−	0.203402i	0.994815	−	0.101701i	$-0.0324286\pi$
$744$		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
$749$		0			0
$750$		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
$753$	−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	−0.999988	−	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			0
$764$		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	0.226923	+	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
$777$		0			0
$778$		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	$-0.487487\pi$
$787$	−22.6225	−	13.0611i	−0.806404	−	0.465578i	−0.845706	+	0.533650i	$0.820820\pi$
$788$		0			0
$789$	−27.2559	+	42.5107i	−0.970334	+	1.51342i
$790$		0			0
$791$		0			0
$792$		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	$-0.735218\pi$
$797$	−38.0284			−1.34704			−0.673518	+	0.739171i	$0.735218\pi$
$798$		0			0
$799$	−1.19025			−0.0421080
$800$		0			0
$801$	−8.54444	−	18.6045i	−0.301903	−	0.657358i
$802$		0			0
$803$	0.0420818	+	0.0728879i	0.00148504	+	0.00257216i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.52176	+	4.18145i	0.229577	+	0.147194i
$808$		0			0
$809$	25.8553	+	14.9276i	0.909024	+	0.524825i	0.880117	−	0.474757i	$-0.157464\pi$
$809$	25.8553	+	14.9276i	0.909024	+	0.524825i	0.0289068	+	0.999582i	$0.490797\pi$
$810$		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
$819$		0			0
$820$		0			0
$821$	−25.0908	+	14.4862i	−0.875674	+	0.505570i	−0.869230	−	0.494409i	$-0.835385\pi$
$821$	−25.0908	+	14.4862i	−0.875674	+	0.505570i	−0.00644422	+	0.999979i	$0.502051\pi$
$822$		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	$0.227176\pi$
$827$			37.6512i			1.30926i	−0.755949	+	0.654630i	$0.772824\pi$
$828$		0			0
$829$	43.4385	+	25.0792i	1.50868	+	0.871038i	0.999949	+	0.0101139i	$0.00321942\pi$
$829$	43.4385	+	25.0792i	1.50868	+	0.871038i	0.508733	+	0.860924i	$0.330114\pi$
$830$		0			0
$831$	−1.48995	−	0.955286i	−0.0516857	−	0.0331385i
$832$		0			0
$833$		0			0
$834$		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	$-0.556813\pi$
$839$	−10.2849			−0.355073			−0.177536	+	0.984114i	$0.556813\pi$
$840$		0			0
$841$	4.27275			0.147336
$842$		0			0
$843$	24.1278	+	1.12354i	0.831006	+	0.0386967i
$844$		0			0
$845$	6.39910	+	11.0836i	0.220136	+	0.381286i
$846$		0			0
$847$		0			0
$848$		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	$-0.745352\pi$
$857$	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	−0.412585	−	0.910919i	$-0.635374\pi$
$859$	4.98253	−	2.87666i	0.170002	−	0.0981505i	0.582587	+	0.812769i	$0.302041\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.7735	−	6.22006i	0.366733	−	0.211733i	−0.305297	−	0.952257i	$-0.598756\pi$
$863$	10.7735	−	6.22006i	0.366733	−	0.211733i	0.672030	+	0.740524i	$0.265422\pi$
$864$		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
$875$		0			0
$876$		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
$879$	1.54744	−	33.2310i	0.0521937	−	1.12085i
$880$		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
$885$	2.31085	−	49.6253i	0.0776784	−	1.66813i
$886$		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
$889$		0			0
$890$		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
$903$		0			0
$904$		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	$-0.635214\pi$
$911$		−	55.0007i		−	1.82225i	0.412127	−	0.911126i	$-0.364786\pi$
$912$		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
$917$		0			0
$918$		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
$921$	−0.831347	−	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	$-0.176933\pi$
$929$	−0.982860	−	1.70236i	−0.0322466	−	0.0558527i	−0.881698	+	0.471814i	$0.843600\pi$
$930$		0			0
$931$		0			0
$932$		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	−0.451069	−	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
$945$		0			0
$946$		0			0
$947$	−8.89077	+	5.13309i	−0.288911	+	0.166803i	−0.637451	−	0.770491i	$-0.720011\pi$
$947$	−8.89077	+	5.13309i	−0.288911	+	0.166803i	0.348539	+	0.937294i	$0.386678\pi$
$948$		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	$-0.994797\pi$
$953$		−	1.00920i		−	0.0326911i	0.999866	−	0.0163455i	$-0.00520318\pi$
$954$		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
$959$		0			0
$960$		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	$-0.0915572\pi$
$971$	7.28478	+	12.6176i	0.233780	+	0.404918i	−0.725138	+	0.688604i	$0.758224\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	35.7133	−	55.7016i	1.14374	−	1.78388i
$976$		0			0
$977$	−5.93615	−	3.42724i	−0.189914	−	0.109647i	0.402028	−	0.915627i	$-0.368305\pi$
$977$	−5.93615	−	3.42724i	−0.189914	−	0.109647i	−0.591942	+	0.805980i	$0.701639\pi$
$978$		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
$987$		0			0
$988$		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	0.998090	−	0.0617814i	$-0.0196782\pi$
$997$	45.5831	+	26.3174i	1.44363	+	0.833480i	0.445541	+	0.895262i	$0.353012\pi$
$998$		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	1176.2.u.b.521.5		16
3.2	odd	2	inner	1176.2.u.b.521.7		16
7.2	even	3		168.2.u.a.89.2	yes	16
7.3	odd	6		1176.2.k.a.881.2		16
7.4	even	3		1176.2.k.a.881.15		16
7.5	odd	6	inner	1176.2.u.b.1097.7		16
7.6	odd	2		168.2.u.a.17.4	yes	16
21.2	odd	6		168.2.u.a.89.4	yes	16
21.5	even	6	inner	1176.2.u.b.1097.5		16
21.11	odd	6		1176.2.k.a.881.1		16
21.17	even	6		1176.2.k.a.881.16		16
21.20	even	2		168.2.u.a.17.2	✓	16
28.3	even	6		2352.2.k.i.881.15		16
28.11	odd	6		2352.2.k.i.881.2		16
28.23	odd	6		336.2.bc.f.257.7		16
28.27	even	2		336.2.bc.f.17.5		16
84.11	even	6		2352.2.k.i.881.16		16
84.23	even	6		336.2.bc.f.257.5		16
84.59	odd	6		2352.2.k.i.881.1		16
84.83	odd	2		336.2.bc.f.17.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.u.a.17.2	✓	16	21.20	even	2
168.2.u.a.17.4	yes	16	7.6	odd	2
168.2.u.a.89.2	yes	16	7.2	even	3
168.2.u.a.89.4	yes	16	21.2	odd	6
336.2.bc.f.17.5		16	28.27	even	2
336.2.bc.f.17.7		16	84.83	odd	2
336.2.bc.f.257.5		16	84.23	even	6
336.2.bc.f.257.7		16	28.23	odd	6
1176.2.k.a.881.1		16	21.11	odd	6
1176.2.k.a.881.2		16	7.3	odd	6
1176.2.k.a.881.15		16	7.4	even	3
1176.2.k.a.881.16		16	21.17	even	6
1176.2.u.b.521.5		16	1.1	even	1	trivial
1176.2.u.b.521.7		16	3.2	odd	2	inner
1176.2.u.b.1097.5		16	21.5	even	6	inner
1176.2.u.b.1097.7		16	7.5	odd	6	inner
2352.2.k.i.881.1		16	84.59	odd	6
2352.2.k.i.881.2		16	28.11	odd	6
2352.2.k.i.881.15		16	28.3	even	6
2352.2.k.i.881.16		16	84.11	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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0805675 + 1.73018i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.98702 - 0.278792i) q^{9} +O(q^{10})\)	\(q+(-0.0805675 + 1.73018i) q^{3} +(-1.90017 - 3.29119i) q^{5} +(-2.98702 - 0.278792i) q^{9} +(0.309539 + 0.178712i) q^{11} +4.04570i q^{13} +(5.84742 - 3.02246i) q^{15} +(-0.0519689 + 0.0900129i) q^{17} +(2.12615 - 1.22753i) q^{19} +(-1.15188 + 0.665037i) q^{23} +(-4.72127 + 8.17749i) q^{25} +(0.723015 - 5.14560i) q^{27} +4.97265i q^{29} +(6.83007 + 3.94335i) q^{31} +(-0.334142 + 0.521158i) q^{33} +(5.45622 + 9.45046i) q^{37} +(-6.99976 - 0.325951i) q^{39} +6.15464 q^{41} +0.502751 q^{43} +(4.75828 + 10.3606i) q^{45} +(5.72578 + 9.91734i) q^{47} +(-0.151551 - 0.0971675i) q^{51} +(-5.08143 - 2.93376i) q^{53} -1.35833i q^{55} +(1.95255 + 3.77751i) q^{57} +(3.77364 - 6.53614i) q^{59} +(-8.20485 + 4.73707i) q^{61} +(13.3151 - 7.68750i) q^{65} +(-1.34375 + 2.32744i) q^{67} +(-1.05783 - 2.04653i) q^{69} +5.78975i q^{71} +(0.203925 + 0.117736i) q^{73} +(-13.7681 - 8.82748i) q^{75} +(-1.61247 - 2.79289i) q^{79} +(8.84455 + 1.66551i) q^{81} -9.07747 q^{83} +0.394999 q^{85} +(-8.60356 - 0.400634i) q^{87} +(3.41213 + 5.90999i) q^{89} +(-7.37296 + 11.4995i) q^{93} +(-8.08008 - 4.66504i) q^{95} -5.14243i q^{97} +(-0.874774 - 0.620114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{9}+O(q^{10}) \) 16 * q + 2 * q^9	\( 16 q + 2 q^{9} + 8 q^{15} + 6 q^{19} - 18 q^{25} + 48 q^{31} + 12 q^{33} - 2 q^{37} - 22 q^{39} + 20 q^{43} + 42 q^{45} + 6 q^{51} - 8 q^{57} - 36 q^{61} + 14 q^{67} - 30 q^{73} - 54 q^{75} + 28 q^{79} + 30 q^{81} + 16 q^{85} - 78 q^{87} + 16 q^{93} + 20 q^{99}+O(q^{100}) \) 16 * q + 2 * q^9 + 8 * q^15 + 6 * q^19 - 18 * q^25 + 48 * q^31 + 12 * q^33 - 2 * q^37 - 22 * q^39 + 20 * q^43 + 42 * q^45 + 6 * q^51 - 8 * q^57 - 36 * q^61 + 14 * q^67 - 30 * q^73 - 54 * q^75 + 28 * q^79 + 30 * q^81 + 16 * q^85 - 78 * q^87 + 16 * q^93 + 20 * q^99

Introduction

L-functions

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