LMFDB - Embedded newform 1170.2.cu.e.1151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1170,2,Mod(71,1170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1170, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("1170.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.cu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
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} - 12x^{14} + 103x^{12} - 396x^{10} + 1089x^{8} - 1584x^{6} + 1648x^{4} - 768x^{2} + 256 $ x^16 - 12x^14 + 103x^12 - 396x^10 + 1089x^8 - 1584x^6 + 1648x^4 - 768*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1151.2
Root			$-1.02094 + 0.589442i$ of defining polynomial
Character	$\chi$	$=$	1170.1151
Dual form			1170.2.cu.e.431.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(3.33834 + 0.894504i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(3.33834 + 0.894504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(-2.57631 + 0.690320i) q^{11} +(3.53796 + 0.694883i) q^{13} -3.45610i q^{14} +(0.500000 - 0.866025i) q^{16} +(0.620970 + 1.07555i) q^{17} +(0.739470 - 2.75974i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(1.33360 + 2.30986i) q^{22} +(-1.51509 + 2.62422i) q^{23} -1.00000i q^{25} +(-0.244486 - 3.59725i) q^{26} +(-3.33834 + 0.894504i) q^{28} +(5.00588 + 2.89015i) q^{29} +(3.35523 + 3.35523i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.878184 - 0.878184i) q^{34} +(2.99307 - 1.72805i) q^{35} +(2.57781 + 9.62050i) q^{37} -2.85709 q^{38} +1.00000 q^{40} +(-1.17888 - 4.39965i) q^{41} +(2.83834 - 1.63871i) q^{43} +(1.88599 - 1.88599i) q^{44} +(2.92693 + 0.784269i) q^{46} +(-1.47839 - 1.47839i) q^{47} +(4.28217 + 2.47231i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(-3.41140 + 1.16719i) q^{52} -3.92676i q^{53} +(-1.33360 + 2.30986i) q^{55} +(1.72805 + 2.99307i) q^{56} +(1.49605 - 5.58333i) q^{58} +(1.64150 - 6.12618i) q^{59} +(1.47705 + 2.55832i) q^{61} +(2.37251 - 4.10930i) q^{62} +1.00000i q^{64} +(2.99307 - 2.01036i) q^{65} +(0.654245 - 0.175304i) q^{67} +(-1.07555 - 0.620970i) q^{68} +(-2.44383 - 2.44383i) q^{70} +(-3.19576 - 0.856300i) q^{71} +(1.27743 - 1.27743i) q^{73} +(8.62551 - 4.97994i) q^{74} +(0.739470 + 2.75974i) q^{76} -9.21808 q^{77} -2.18667 q^{79} +(-0.258819 - 0.965926i) q^{80} +(-3.94462 + 2.27743i) q^{82} +(9.26996 - 9.26996i) q^{83} +(1.19962 + 0.321438i) q^{85} +(-2.31749 - 2.31749i) q^{86} +(-2.30986 - 1.33360i) q^{88} +(13.4419 - 3.60175i) q^{89} +(11.1893 + 5.48447i) q^{91} -3.03018i q^{92} +(-1.04538 + 1.81064i) q^{94} +(-1.42855 - 2.47432i) q^{95} +(3.69941 - 13.8064i) q^{97} +(1.27976 - 4.77614i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{7}+O(q^{10}) $ 16 * q + 8 * q^7	$ 16 q + 8 q^{7} - 12 q^{13} + 8 q^{16} + 36 q^{19} + 12 q^{22} - 8 q^{28} - 12 q^{31} + 16 q^{34} + 20 q^{37} + 16 q^{40} + 32 q^{46} - 12 q^{49} - 24 q^{52} - 12 q^{55} + 32 q^{58} - 44 q^{61} + 4 q^{67} - 4 q^{70} - 24 q^{73} + 36 q^{76} - 24 q^{79} - 4 q^{85} + 12 q^{88} + 36 q^{91} + 56 q^{97}+O(q^{100}) $ 16 * q + 8 * q^7 - 12 * q^13 + 8 * q^16 + 36 * q^19 + 12 * q^22 - 8 * q^28 - 12 * q^31 + 16 * q^34 + 20 * q^37 + 16 * q^40 + 32 * q^46 - 12 * q^49 - 24 * q^52 - 12 * q^55 + 32 * q^58 - 44 * q^61 + 4 * q^67 - 4 * q^70 - 24 * q^73 + 36 * q^76 - 24 * q^79 - 4 * q^85 + 12 * q^88 + 36 * q^91 + 56 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$	3.33834	+	0.894504i	1.26177	+	0.338091i	0.826873	−	0.562388i	$-0.190117\pi$
$7$	3.33834	+	0.894504i	1.26177	+	0.338091i	0.434899	+	0.900479i	$0.356784\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	−0.866025	−	0.500000i	−0.273861	−	0.158114i
$11$	−2.57631	+	0.690320i	−0.776787	+	0.208139i	−0.625368	−	0.780330i	$-0.715051\pi$
$11$	−2.57631	+	0.690320i	−0.776787	+	0.208139i	−0.151419	+	0.988470i	$0.548384\pi$
$12$		0			0
$13$	3.53796	+	0.694883i	0.981253	+	0.192726i
$13$	3.53796	+	0.694883i	0.981253	+	0.192726i
$14$		−	3.45610i		−	0.923681i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.620970	+	1.07555i	0.150607	+	0.260860i	0.931451	−	0.363867i	$-0.118544\pi$
$17$	0.620970	+	1.07555i	0.150607	+	0.260860i	−0.780844	+	0.624727i	$0.785210\pi$
$18$		0			0
$19$	0.739470	−	2.75974i	0.169646	−	0.633128i	−0.827756	−	0.561089i	$-0.810383\pi$
$19$	0.739470	−	2.75974i	0.169646	−	0.633128i	0.997402	−	0.0720393i	$-0.0229507\pi$
$20$	−0.258819	+	0.965926i	−0.0578737	+	0.215988i
$21$		0			0
$22$	1.33360	+	2.30986i	0.284324	+	0.492463i
$23$	−1.51509	+	2.62422i	−0.315919	+	0.547187i	−0.979632	−	0.200800i	$-0.935646\pi$
$23$	−1.51509	+	2.62422i	−0.315919	+	0.547187i	0.663714	+	0.747987i	$0.268979\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−0.244486	−	3.59725i	−0.0479476	−	0.705479i
$27$		0			0
$28$	−3.33834	+	0.894504i	−0.630886	+	0.169045i
$29$	5.00588	+	2.89015i	0.929568	+	0.536687i	0.886675	−	0.462393i	$-0.153009\pi$
$29$	5.00588	+	2.89015i	0.929568	+	0.536687i	0.0428934	+	0.999080i	$0.486342\pi$
$30$		0			0
$31$	3.35523	+	3.35523i	0.602618	+	0.602618i	0.941006	−	0.338389i	$-0.109882\pi$
$31$	3.35523	+	3.35523i	0.602618	+	0.602618i	−0.338389	+	0.941006i	$0.609882\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$		0			0
$34$	0.878184	−	0.878184i	0.150607	−	0.150607i
$35$	2.99307	−	1.72805i	0.505921	−	0.292094i
$36$		0			0
$37$	2.57781	+	9.62050i	0.423789	+	1.58160i	0.766554	+	0.642180i	$0.221970\pi$
$37$	2.57781	+	9.62050i	0.423789	+	1.58160i	−0.342766	+	0.939421i	$0.611364\pi$
$38$	−2.85709			−0.463482
$39$		0			0
$40$	1.00000			0.158114
$41$	−1.17888	−	4.39965i	−0.184111	−	0.687110i	−0.994819	−	0.101660i	$-0.967585\pi$
$41$	−1.17888	−	4.39965i	−0.184111	−	0.687110i	0.810709	−	0.585450i	$-0.199082\pi$
$42$		0			0
$43$	2.83834	−	1.63871i	0.432842	−	0.249901i	−0.267715	−	0.963498i	$-0.586268\pi$
$43$	2.83834	−	1.63871i	0.432842	−	0.249901i	0.700557	+	0.713597i	$0.252935\pi$
$44$	1.88599	−	1.88599i	0.284324	−	0.284324i
$45$		0			0
$46$	2.92693	+	0.784269i	0.431553	+	0.115634i
$47$	−1.47839	−	1.47839i	−0.215645	−	0.215645i	0.591016	−	0.806660i	$-0.298727\pi$
$47$	−1.47839	−	1.47839i	−0.215645	−	0.215645i	−0.806660	+	0.591016i	$0.798727\pi$
$48$		0			0
$49$	4.28217	+	2.47231i	0.611738	+	0.353187i
$50$	−0.965926	+	0.258819i	−0.136603	+	0.0366025i
$51$		0			0
$52$	−3.41140	+	1.16719i	−0.473076	+	0.161860i
$53$		−	3.92676i		−	0.539382i	−0.962947	−	0.269691i	$-0.913078\pi$
$53$		−	3.92676i		−	0.539382i	0.962947	−	0.269691i	$-0.0869216\pi$
$54$		0			0
$55$	−1.33360	+	2.30986i	−0.179822	+	0.311461i
$56$	1.72805	+	2.99307i	0.230920	+	0.399966i
$57$		0			0
$58$	1.49605	−	5.58333i	0.196441	−	0.733128i
$59$	1.64150	−	6.12618i	0.213706	−	0.797560i	−0.772913	−	0.634513i	$-0.781201\pi$
$59$	1.64150	−	6.12618i	0.213706	−	0.797560i	0.986618	−	0.163048i	$-0.0521325\pi$
$60$		0			0
$61$	1.47705	+	2.55832i	0.189117	+	0.327560i	0.944956	−	0.327197i	$-0.106104\pi$
$61$	1.47705	+	2.55832i	0.189117	+	0.327560i	−0.755839	+	0.654757i	$0.772771\pi$
$62$	2.37251	−	4.10930i	0.301309	−	0.521882i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	2.99307	−	2.01036i	0.371245	−	0.249354i
$66$		0			0
$67$	0.654245	−	0.175304i	0.0799288	−	0.0214169i	−0.218633	−	0.975807i	$-0.570160\pi$
$67$	0.654245	−	0.175304i	0.0799288	−	0.0214169i	0.298562	+	0.954390i	$0.403493\pi$
$68$	−1.07555	−	0.620970i	−0.130430	−	0.0753037i
$69$		0			0
$70$	−2.44383	−	2.44383i	−0.292094	−	0.292094i
$71$	−3.19576	−	0.856300i	−0.379267	−	0.101624i	0.0641490	−	0.997940i	$-0.479567\pi$
$71$	−3.19576	−	0.856300i	−0.379267	−	0.101624i	−0.443416	+	0.896316i	$0.646233\pi$
$72$		0			0
$73$	1.27743	−	1.27743i	0.149512	−	0.149512i	−0.628388	−	0.777900i	$-0.716285\pi$
$73$	1.27743	−	1.27743i	0.149512	−	0.149512i	0.777900	+	0.628388i	$0.216285\pi$
$74$	8.62551	−	4.97994i	1.00269	−	0.578906i
$75$		0			0
$76$	0.739470	+	2.75974i	0.0848231	+	0.316564i
$77$	−9.21808			−1.05050
$78$		0			0
$79$	−2.18667			−0.246020			−0.123010	−	0.992405i	$-0.539255\pi$
$79$	−2.18667			−0.246020			−0.123010	+	0.992405i	$0.539255\pi$
$80$	−0.258819	−	0.965926i	−0.0289368	−	0.107994i
$81$		0			0
$82$	−3.94462	+	2.27743i	−0.435610	+	0.251500i
$83$	9.26996	−	9.26996i	1.01751	−	1.01751i	0.0176668	−	0.999844i	$-0.494376\pi$
$83$	9.26996	−	9.26996i	1.01751	−	1.01751i	0.999844	−	0.0176668i	$-0.00562381\pi$
$84$		0			0
$85$	1.19962	+	0.321438i	0.130117	+	0.0348648i
$86$	−2.31749	−	2.31749i	−0.249901	−	0.249901i
$87$		0			0
$88$	−2.30986	−	1.33360i	−0.246232	−	0.142162i
$89$	13.4419	−	3.60175i	1.42484	−	0.381785i	0.537642	−	0.843173i	$-0.319315\pi$
$89$	13.4419	−	3.60175i	1.42484	−	0.381785i	0.887198	+	0.461388i	$0.152649\pi$
$90$		0			0
$91$	11.1893	+	5.48447i	1.17296	+	0.574928i
$92$		−	3.03018i		−	0.315919i
$93$		0			0
$94$	−1.04538	+	1.81064i	−0.107822	+	0.186754i
$95$	−1.42855	−	2.47432i	−0.146566	−	0.253859i
$96$		0			0
$97$	3.69941	−	13.8064i	0.375618	−	1.40183i	−0.476821	−	0.879000i	$-0.658211\pi$
$97$	3.69941	−	13.8064i	0.375618	−	1.40183i	0.852439	−	0.522826i	$-0.175122\pi$
$98$	1.27976	−	4.77614i	0.129275	−	0.482463i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−5.71053	+	9.89093i	−0.568219	+	0.984185i	0.428523	+	0.903531i	$0.359034\pi$
$101$	−5.71053	+	9.89093i	−0.568219	+	0.984185i	−0.996742	+	0.0806538i	$0.974299\pi$
$102$		0			0
$103$		−	17.7447i		−	1.74844i	−0.485534	−	0.874218i	$-0.661375\pi$
$103$		−	17.7447i		−	1.74844i	0.485534	−	0.874218i	$-0.338625\pi$
$104$	2.01036	+	2.99307i	0.197132	+	0.293495i
$105$		0			0
$106$	−3.79296	+	1.01632i	−0.368405	+	0.0987137i
$107$	−2.11164	−	1.21916i	−0.204140	−	0.117860i	0.394445	−	0.918920i	$-0.370937\pi$
$107$	−2.11164	−	1.21916i	−0.204140	−	0.117860i	−0.598585	+	0.801059i	$0.704270\pi$
$108$		0			0
$109$	5.48052	+	5.48052i	0.524938	+	0.524938i	0.919059	−	0.394120i	$-0.128951\pi$
$109$	5.48052	+	5.48052i	0.524938	+	0.524938i	−0.394120	+	0.919059i	$0.628951\pi$
$110$	2.57631	+	0.690320i	0.245642	+	0.0658194i
$111$		0			0
$112$	2.44383	−	2.44383i	0.230920	−	0.230920i
$113$	8.93711	−	5.15984i	0.840733	−	0.485397i	−0.0167805	−	0.999859i	$-0.505342\pi$
$113$	8.93711	−	5.15984i	0.840733	−	0.485397i	0.857513	+	0.514462i	$0.172008\pi$
$114$		0			0
$115$	0.784269	+	2.92693i	0.0731335	+	0.272938i
$116$	−5.78029			−0.536687
$117$		0			0
$118$	−6.34229			−0.583855
$119$	1.11092	+	4.14601i	0.101838	+	0.380064i
$120$		0			0
$121$	−3.36545	+	1.94304i	−0.305950	+	0.176640i
$122$	2.08886	−	2.08886i	0.189117	−	0.189117i
$123$		0			0
$124$	−4.58333	−	1.22810i	−0.411595	−	0.110287i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	6.95747	+	4.01690i	0.617376	+	0.356442i	0.775847	−	0.630922i	$-0.217323\pi$
$127$	6.95747	+	4.01690i	0.617376	+	0.356442i	−0.158471	+	0.987364i	$0.550656\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$		0			0
$130$	−2.71652	−	2.37076i	−0.238254	−	0.207930i
$131$			8.46288i			0.739405i	0.929150	+	0.369703i	$0.120540\pi$
$131$			8.46288i			0.739405i	−0.929150	+	0.369703i	$0.879460\pi$
$132$		0			0
$133$	4.93720	−	8.55148i	0.428110	−	0.741507i
$134$	−0.338662	−	0.586580i	−0.0292560	−	0.0506728i
$135$		0			0
$136$	−0.321438	+	1.19962i	−0.0275631	+	0.102867i
$137$	−4.02696	+	15.0288i	−0.344046	+	1.28400i	0.549676	+	0.835378i	$0.314751\pi$
$137$	−4.02696	+	15.0288i	−0.344046	+	1.28400i	−0.893722	+	0.448620i	$0.851916\pi$
$138$		0			0
$139$	−0.175401	−	0.303803i	−0.0148773	−	0.0257682i	0.858491	−	0.512829i	$-0.171402\pi$
$139$	−0.175401	−	0.303803i	−0.0148773	−	0.0257682i	−0.873368	+	0.487061i	$0.838069\pi$
$140$	−1.72805	+	2.99307i	−0.146047	+	0.252961i
$141$		0			0
$142$			3.30849i			0.277642i
$143$	−9.59456	+	0.652090i	−0.802338	+	0.0545305i
$144$		0			0
$145$	5.58333	−	1.49605i	0.463671	−	0.124240i
$146$	−1.56452	−	0.903277i	−0.129481	−	0.0747558i
$147$		0			0
$148$	−7.04270	−	7.04270i	−0.578906	−	0.578906i
$149$	−11.6425	−	3.11959i	−0.953788	−	0.255567i	−0.251819	−	0.967774i	$-0.581029\pi$
$149$	−11.6425	−	3.11959i	−0.953788	−	0.255567i	−0.701969	+	0.712207i	$0.747696\pi$
$150$		0			0
$151$	−5.23689	+	5.23689i	−0.426172	+	0.426172i	−0.887322	−	0.461150i	$-0.847437\pi$
$151$	−5.23689	+	5.23689i	−0.426172	+	0.426172i	0.461150	+	0.887322i	$0.347437\pi$
$152$	2.47432	−	1.42855i	0.200694	−	0.115870i
$153$		0			0
$154$	2.38581	+	8.90398i	0.192254	+	0.717503i
$155$	4.74502			0.381129
$156$		0			0
$157$	−23.5062			−1.87600			−0.938000	−	0.346634i	$-0.887324\pi$
$157$	−23.5062			−1.87600			−0.938000	+	0.346634i	$0.887324\pi$
$158$	0.565953	+	2.11217i	0.0450248	+	0.168035i
$159$		0			0
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	−7.40526	+	7.40526i	−0.583616	+	0.583616i
$162$		0			0
$163$	−21.2695	−	5.69914i	−1.66595	−	0.446391i	−0.701939	−	0.712237i	$-0.747682\pi$
$163$	−21.2695	−	5.69914i	−1.66595	−	0.446391i	−0.964015	+	0.265846i	$0.914349\pi$
$164$	3.22077	+	3.22077i	0.251500	+	0.251500i
$165$		0			0
$166$	−11.3533	−	6.55485i	−0.881190	−	0.508755i
$167$	−6.22969	+	1.66924i	−0.482068	+	0.129170i	−0.491666	−	0.870784i	$-0.663612\pi$
$167$	−6.22969	+	1.66924i	−0.482068	+	0.129170i	0.00959725	+	0.999954i	$0.496945\pi$
$168$		0			0
$169$	12.0343	+	4.91693i	0.925714	+	0.378225i
$170$		−	1.24194i		−	0.0952524i
$171$		0			0
$172$	−1.63871	+	2.83834i	−0.124951	+	0.216421i
$173$	−1.76051	−	3.04929i	−0.133849	−	0.231833i	0.791308	−	0.611417i	$-0.209400\pi$
$173$	−1.76051	−	3.04929i	−0.133849	−	0.231833i	−0.925157	+	0.379584i	$0.876067\pi$
$174$		0			0
$175$	0.894504	−	3.33834i	0.0676182	−	0.252354i
$176$	−0.690320	+	2.57631i	−0.0520348	+	0.194197i
$177$		0			0
$178$	−6.95805	−	12.0517i	−0.521528	−	0.903313i
$179$	−9.52971	+	16.5059i	−0.712284	+	1.23371i	0.251714	+	0.967802i	$0.419006\pi$
$179$	−9.52971	+	16.5059i	−0.712284	+	1.23371i	−0.963998	+	0.265911i	$0.914327\pi$
$180$		0			0
$181$			6.05179i			0.449826i	0.974379	+	0.224913i	$0.0722098\pi$
$181$			6.05179i			0.449826i	−0.974379	+	0.224913i	$0.927790\pi$
$182$	2.40158	−	12.2275i	0.178017	−	0.906365i
$183$		0			0
$184$	−2.92693	+	0.784269i	−0.215776	+	0.0578171i
$185$	8.62551	+	4.97994i	0.634160	+	0.366132i
$186$		0			0
$187$	−2.34229	−	2.34229i	−0.171285	−	0.171285i
$188$	2.01951	+	0.541127i	0.147288	+	0.0394657i
$189$		0			0
$190$	−2.02027	+	2.02027i	−0.146566	+	0.146566i
$191$	18.7606	−	10.8314i	1.35747	−	0.783735i	0.368187	−	0.929752i	$-0.379978\pi$
$191$	18.7606	−	10.8314i	1.35747	−	0.783735i	0.989282	+	0.146016i	$0.0466451\pi$
$192$		0			0
$193$	−5.64750	−	21.0768i	−0.406516	−	1.51714i	−0.801243	−	0.598339i	$-0.795827\pi$
$193$	−5.64750	−	21.0768i	−0.406516	−	1.51714i	0.394727	−	0.918799i	$-0.370839\pi$
$194$	−14.2934			−1.02621
$195$		0			0
$196$	−4.94462			−0.353187
$197$	6.50732	+	24.2856i	0.463627	+	1.73028i	0.661401	+	0.750033i	$0.269962\pi$
$197$	6.50732	+	24.2856i	0.463627	+	1.73028i	−0.197773	+	0.980248i	$0.563371\pi$
$198$		0			0
$199$	−16.9879	+	9.80796i	−1.20424	+	0.695268i	−0.961495	−	0.274822i	$-0.911381\pi$
$199$	−16.9879	+	9.80796i	−1.20424	+	0.695268i	−0.242745	+	0.970090i	$0.578048\pi$
$200$	0.707107	−	0.707107i	0.0500000	−	0.0500000i
$201$		0			0
$202$	11.0319	+	2.95599i	0.776202	+	0.207983i
$203$	14.1261	+	14.1261i	0.991455	+	0.991455i
$204$		0			0
$205$	−3.94462	−	2.27743i	−0.275504	−	0.159062i
$206$	−17.1400	+	4.59266i	−1.19420	+	0.319986i
$207$		0			0
$208$	2.37076	−	2.71652i	0.164383	−	0.188357i
$209$			7.62042i			0.527115i
$210$		0			0
$211$	1.06881	−	1.85123i	0.0735798	−	0.127444i	−0.826888	−	0.562367i	$-0.809891\pi$
$211$	1.06881	−	1.85123i	0.0735798	−	0.127444i	0.900468	+	0.434923i	$0.143224\pi$
$212$	1.96338	+	3.40067i	0.134845	+	0.233559i
$213$		0			0
$214$	−0.631083	+	2.35523i	−0.0431399	+	0.161000i
$215$	0.848261	−	3.16575i	0.0578509	−	0.215902i
$216$		0			0
$217$	8.19962	+	14.2022i	0.556627	+	0.964106i
$218$	3.87531	−	6.71224i	0.262469	−	0.454610i
$219$		0			0
$220$		−	2.66719i		−	0.179822i
$221$	1.44958	+	4.23676i	0.0975095	+	0.284995i
$222$		0			0
$223$	−5.05744	+	1.35514i	−0.338671	+	0.0907467i	−0.424146	−	0.905594i	$-0.639426\pi$
$223$	−5.05744	+	1.35514i	−0.338671	+	0.0907467i	0.0854753	+	0.996340i	$0.472759\pi$
$224$	−2.99307	−	1.72805i	−0.199983	−	0.115460i
$225$		0			0
$226$	−7.29712	−	7.29712i	−0.485397	−	0.485397i
$227$	−19.6777	−	5.27263i	−1.30606	−	0.349957i	−0.462319	−	0.886714i	$-0.652983\pi$
$227$	−19.6777	−	5.27263i	−1.30606	−	0.349957i	−0.843737	+	0.536757i	$0.819649\pi$
$228$		0			0
$229$	10.9219	−	10.9219i	0.721738	−	0.721738i	−0.247221	−	0.968959i	$-0.579517\pi$
$229$	10.9219	−	10.9219i	0.721738	−	0.721738i	0.968959	+	0.247221i	$0.0795174\pi$
$230$	2.62422	−	1.51509i	0.173036	−	0.0999022i
$231$		0			0
$232$	1.49605	+	5.58333i	0.0982205	+	0.366564i
$233$	−4.89630			−0.320768			−0.160384	−	0.987055i	$-0.551273\pi$
$233$	−4.89630			−0.320768			−0.160384	+	0.987055i	$0.551273\pi$
$234$		0			0
$235$	−2.09075			−0.136386
$236$	1.64150	+	6.12618i	0.106853	+	0.398780i
$237$		0			0
$238$	3.71721	−	2.14613i	0.240951	−	0.139113i
$239$	−6.07868	+	6.07868i	−0.393197	+	0.393197i	−0.875825	−	0.482628i	$-0.839682\pi$
$239$	−6.07868	+	6.07868i	−0.393197	+	0.393197i	0.482628	+	0.875825i	$0.339682\pi$
$240$		0			0
$241$	23.4472	+	6.28265i	1.51036	+	0.404701i	0.916556	−	0.399906i	$-0.130957\pi$
$241$	23.4472	+	6.28265i	1.51036	+	0.404701i	0.593808	+	0.804607i	$0.297624\pi$
$242$	2.74788	+	2.74788i	0.176640	+	0.176640i
$243$		0			0
$244$	−2.55832	−	1.47705i	−0.163780	−	0.0945584i
$245$	4.77614	−	1.27976i	0.305136	−	0.0817610i
$246$		0			0
$247$	4.53391	−	9.25000i	0.288486	−	0.588563i
$248$			4.74502i			0.301309i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−12.5400	−	21.7199i	−0.791516	−	1.37095i	−0.925028	−	0.379899i	$-0.875959\pi$
$251$	−12.5400	−	21.7199i	−0.791516	−	1.37095i	0.133512	−	0.991047i	$-0.457375\pi$
$252$		0			0
$253$	2.09180	−	7.80669i	0.131510	−	0.490803i
$254$	2.07930	−	7.76005i	0.130467	−	0.486909i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.801284	−	1.38786i	0.0499827	−	0.0865726i	−0.839952	−	0.542661i	$-0.817417\pi$
$257$	0.801284	−	1.38786i	0.0499827	−	0.0865726i	0.889934	+	0.456089i	$0.150750\pi$
$258$		0			0
$259$			34.4223i			2.13890i
$260$	−1.58690	+	3.23755i	−0.0984151	+	0.200785i
$261$		0			0
$262$	8.17452	−	2.19035i	0.505023	−	0.135321i
$263$	0.110442	+	0.0637636i	0.00681014	+	0.00393183i	0.503401	−	0.864053i	$-0.332082\pi$
$263$	0.110442	+	0.0637636i	0.00681014	+	0.00393183i	−0.496591	+	0.867985i	$0.665415\pi$
$264$		0			0
$265$	−2.77664	−	2.77664i	−0.170568	−	0.170568i
$266$	−9.53794	−	2.55568i	−0.584808	−	0.156699i
$267$		0			0
$268$	−0.478941	+	0.478941i	−0.0292560	+	0.0292560i
$269$	4.28069	−	2.47145i	0.260998	−	0.150687i	−0.363792	−	0.931480i	$-0.618518\pi$
$269$	4.28069	−	2.47145i	0.260998	−	0.150687i	0.624790	+	0.780793i	$0.285185\pi$
$270$		0			0
$271$	4.10282	+	15.3119i	0.249228	+	0.930133i	0.971211	+	0.238221i	$0.0765644\pi$
$271$	4.10282	+	15.3119i	0.249228	+	0.930133i	−0.721983	+	0.691911i	$0.756769\pi$
$272$	1.24194			0.0753037
$273$		0			0
$274$	15.5590			0.939952
$275$	0.690320	+	2.57631i	0.0416279	+	0.155357i
$276$		0			0
$277$	1.83975	−	1.06218i	0.110540	−	0.0638201i	−0.443711	−	0.896170i	$-0.646338\pi$
$277$	1.83975	−	1.06218i	0.110540	−	0.0638201i	0.554251	+	0.832350i	$0.313005\pi$
$278$	−0.248054	+	0.248054i	−0.0148773	+	0.0148773i
$279$		0			0
$280$	3.33834	+	0.894504i	0.199504	+	0.0534569i
$281$	13.5238	+	13.5238i	0.806761	+	0.806761i	0.984142	−	0.177381i	$-0.0567626\pi$
$281$	13.5238	+	13.5238i	0.806761	+	0.806761i	−0.177381	+	0.984142i	$0.556763\pi$
$282$		0			0
$283$	−20.3802	−	11.7665i	−1.21148	−	0.699448i	−0.248398	−	0.968658i	$-0.579904\pi$
$283$	−20.3802	−	11.7665i	−1.21148	−	0.699448i	−0.963082	+	0.269210i	$0.913237\pi$
$284$	3.19576	−	0.856300i	0.189633	−	0.0508121i
$285$		0			0
$286$	3.11313	+	9.09886i	0.184083	+	0.538027i
$287$		−	15.7420i		−	0.929222i
$288$		0			0
$289$	7.72879	−	13.3867i	0.454635	−	0.787451i
$290$	−2.89015	−	5.00588i	−0.169715	−	0.293955i
$291$		0			0
$292$	−0.467571	+	1.74500i	−0.0273625	+	0.102118i
$293$	−2.83717	+	10.5885i	−0.165749	+	0.618585i	0.832194	+	0.554485i	$0.187085\pi$
$293$	−2.83717	+	10.5885i	−0.165749	+	0.618585i	−0.997943	+	0.0641008i	$0.979582\pi$
$294$		0			0
$295$	−3.17114	−	5.49258i	−0.184631	−	0.319790i
$296$	−4.97994	+	8.62551i	−0.289453	+	0.501347i
$297$		0			0
$298$			12.0532i			0.698222i
$299$	−7.18385	+	8.23155i	−0.415453	+	0.476043i
$300$		0			0
$301$	10.9412	−	2.93167i	0.630637	−	0.168979i
$302$	6.41385	+	3.70304i	0.369076	+	0.213086i
$303$		0			0
$304$	−2.02027	−	2.02027i	−0.115870	−	0.115870i
$305$	2.85344	+	0.764577i	0.163387	+	0.0437795i
$306$		0			0
$307$	−20.2752	+	20.2752i	−1.15717	+	1.15717i	−0.172086	+	0.985082i	$0.555051\pi$
$307$	−20.2752	+	20.2752i	−1.15717	+	1.15717i	−0.985082	+	0.172086i	$0.944949\pi$
$308$	7.98309	−	4.60904i	0.454879	−	0.262624i
$309$		0			0
$310$	−1.22810	−	4.58333i	−0.0697514	−	0.260316i
$311$	−17.6425			−1.00042			−0.500208	−	0.865905i	$-0.666743\pi$
$311$	−17.6425			−1.00042			−0.500208	+	0.865905i	$0.666743\pi$
$312$		0			0
$313$	−18.2784			−1.03316			−0.516578	−	0.856240i	$-0.672794\pi$
$313$	−18.2784			−1.03316			−0.516578	+	0.856240i	$0.672794\pi$
$314$	6.08386	+	22.7053i	0.343332	+	1.28133i
$315$		0			0
$316$	1.89372	−	1.09334i	0.106530	−	0.0615050i
$317$	−20.1991	+	20.1991i	−1.13450	+	1.13450i	−0.145077	+	0.989420i	$0.546343\pi$
$317$	−20.1991	+	20.1991i	−1.13450	+	1.13450i	−0.989420	+	0.145077i	$0.953657\pi$
$318$		0			0
$319$	−14.8918	−	3.99025i	−0.833782	−	0.223411i
$320$	0.707107	+	0.707107i	0.0395285	+	0.0395285i
$321$		0			0
$322$	9.06955	+	5.23631i	0.505426	+	0.291808i
$323$	3.42743	−	0.918378i	0.190707	−	0.0510999i
$324$		0			0
$325$	0.694883	−	3.53796i	0.0385452	−	0.196251i
$326$			22.0198i			1.21956i
$327$		0			0
$328$	2.27743	−	3.94462i	0.125750	−	0.217805i
$329$	−3.61292	−	6.25777i	−0.199187	−	0.345002i
$330$		0			0
$331$	−6.78076	+	25.3061i	−0.372704	+	1.39095i	0.483967	+	0.875086i	$0.339196\pi$
$331$	−6.78076	+	25.3061i	−0.372704	+	1.39095i	−0.856671	+	0.515864i	$0.827471\pi$
$332$	−3.39304	+	12.6630i	−0.186217	+	0.694973i
$333$		0			0
$334$	3.22473	+	5.58539i	0.176449	+	0.305619i
$335$	0.338662	−	0.586580i	0.0185031	−	0.0320483i
$336$		0			0
$337$		−	30.5858i		−	1.66612i	−0.553185	−	0.833058i	$-0.686588\pi$
$337$		−	30.5858i		−	1.66612i	0.553185	−	0.833058i	$-0.313412\pi$
$338$	1.63469	−	12.8968i	0.0889154	−	0.701494i
$339$		0			0
$340$	−1.19962	+	0.321438i	−0.0650586	+	0.0174324i
$341$	−10.9603	−	6.32793i	−0.593534	−	0.342677i
$342$		0			0
$343$	−5.02300	−	5.02300i	−0.271217	−	0.271217i
$344$	3.16575	+	0.848261i	0.170686	+	0.0457351i
$345$		0			0
$346$	−2.48973	+	2.48973i	−0.133849	+	0.133849i
$347$	−2.91061	+	1.68044i	−0.156250	+	0.0902108i	−0.576086	−	0.817389i	$-0.695421\pi$
$347$	−2.91061	+	1.68044i	−0.156250	+	0.0902108i	0.419836	+	0.907600i	$0.362087\pi$
$348$		0			0
$349$	2.75036	+	10.2645i	0.147223	+	0.549445i	0.999646	+	0.0265923i	$0.00846558\pi$
$349$	2.75036	+	10.2645i	0.147223	+	0.549445i	−0.852423	+	0.522853i	$0.824868\pi$
$350$	−3.45610			−0.184736
$351$		0			0
$352$	2.66719			0.142162
$353$	7.80796	+	29.1397i	0.415576	+	1.55095i	0.783680	+	0.621165i	$0.213340\pi$
$353$	7.80796	+	29.1397i	0.415576	+	1.55095i	−0.368104	+	0.929784i	$0.619993\pi$
$354$		0			0
$355$	−2.86524	+	1.65425i	−0.152071	+	0.0877982i
$356$	−9.84017	+	9.84017i	−0.521528	+	0.521528i
$357$		0			0
$358$	18.4100	+	4.93294i	0.972998	+	0.260714i
$359$	14.7851	+	14.7851i	0.780326	+	0.780326i	0.979886	−	0.199560i	$-0.0639511\pi$
$359$	14.7851	+	14.7851i	0.780326	+	0.780326i	−0.199560	+	0.979886i	$0.563951\pi$
$360$		0			0
$361$	9.38513	+	5.41851i	0.493954	+	0.285185i
$362$	5.84558	−	1.56632i	0.307237	−	0.0823239i
$363$		0			0
$364$	−12.4325	+	0.844966i	−0.651638	+	0.0442883i
$365$		−	1.80655i		−	0.0945594i
$366$		0			0
$367$	1.23184	−	2.13361i	0.0643015	−	0.111373i	−0.832082	−	0.554652i	$-0.812851\pi$
$367$	1.23184	−	2.13361i	0.0643015	−	0.111373i	0.896384	+	0.443279i	$0.146185\pi$
$368$	1.51509	+	2.62422i	0.0789796	+	0.136797i
$369$		0			0
$370$	2.57781	−	9.62050i	0.134014	−	0.500146i
$371$	3.51250	−	13.1088i	0.182360	−	0.680577i
$372$		0			0
$373$	−2.45805	−	4.25746i	−0.127273	−	0.220443i	0.795346	−	0.606155i	$-0.207289\pi$
$373$	−2.45805	−	4.25746i	−0.127273	−	0.220443i	−0.922619	+	0.385712i	$0.873956\pi$
$374$	−1.65625	+	2.86870i	−0.0856424	+	0.148337i
$375$		0			0
$376$		−	2.09075i		−	0.107822i
$377$	15.7023	+	13.7037i	0.808708	+	0.705777i
$378$		0			0
$379$	−29.2560	+	7.83912i	−1.50278	+	0.402669i	−0.914030	−	0.405646i	$-0.867046\pi$
$379$	−29.2560	+	7.83912i	−1.50278	+	0.402669i	−0.588750	+	0.808315i	$0.700380\pi$
$380$	2.47432	+	1.42855i	0.126930	+	0.0732829i
$381$		0			0
$382$	−15.3180	−	15.3180i	−0.783735	−	0.783735i
$383$	−13.4429	−	3.60202i	−0.686902	−	0.184055i	−0.101545	−	0.994831i	$-0.532379\pi$
$383$	−13.4429	−	3.60202i	−0.686902	−	0.184055i	−0.585356	+	0.810776i	$0.699045\pi$
$384$		0			0
$385$	−6.51817	+	6.51817i	−0.332197	+	0.332197i
$386$	−18.8969	+	10.9101i	−0.961827	+	0.555311i
$387$		0			0
$388$	3.69941	+	13.8064i	0.187809	+	0.700913i
$389$	1.27960			0.0648784			0.0324392	−	0.999474i	$-0.489672\pi$
$389$	1.27960			0.0648784			0.0324392	+	0.999474i	$0.489672\pi$
$390$		0			0
$391$	−3.76331			−0.190319
$392$	1.27976	+	4.77614i	0.0646377	+	0.241231i
$393$		0			0
$394$	21.7739	−	12.5712i	1.09695	−	0.633327i
$395$	−1.54621	+	1.54621i	−0.0777984	+	0.0777984i
$396$		0			0
$397$	−6.35444	−	1.70267i	−0.318920	−	0.0854545i	0.0958077	−	0.995400i	$-0.469457\pi$
$397$	−6.35444	−	1.70267i	−0.318920	−	0.0854545i	−0.414728	+	0.909945i	$0.636123\pi$
$398$	13.8706	+	13.8706i	0.695268	+	0.695268i
$399$		0			0
$400$	−0.866025	−	0.500000i	−0.0433013	−	0.0250000i
$401$	−5.48842	+	1.47062i	−0.274079	+	0.0734392i	−0.393240	−	0.919436i	$-0.628646\pi$
$401$	−5.48842	+	1.47062i	−0.274079	+	0.0734392i	0.119162	+	0.992875i	$0.461979\pi$
$402$		0			0
$403$	9.53918	+	14.2022i	0.475180	+	0.707460i
$404$		−	11.4211i		−	0.568219i
$405$		0			0
$406$	9.98863	−	17.3008i	0.495727	−	0.858625i
$407$	−13.2825	−	23.0059i	−0.658387	−	1.14036i
$408$		0			0
$409$	8.87423	−	33.1191i	0.438803	−	1.63763i	−0.292997	−	0.956113i	$-0.594653\pi$
$409$	8.87423	−	33.1191i	0.438803	−	1.63763i	0.731799	−	0.681520i	$-0.238681\pi$
$410$	−1.17888	+	4.39965i	−0.0582209	+	0.217283i
$411$		0			0
$412$	8.87234	+	15.3673i	0.437109	+	0.757095i
$413$	10.9598	−	18.9829i	0.539296	−	0.934087i
$414$		0			0
$415$		−	13.1097i		−	0.643530i
$416$	−3.23755	−	1.58690i	−0.158734	−	0.0778040i
$417$		0			0
$418$	7.36076	−	1.97231i	0.360027	−	0.0964688i
$419$	−26.8532	−	15.5037i	−1.31187	−	0.757406i	−0.329461	−	0.944169i	$-0.606867\pi$
$419$	−26.8532	−	15.5037i	−1.31187	−	0.757406i	−0.982405	+	0.186763i	$0.940200\pi$
$420$		0			0
$421$	8.30059	+	8.30059i	0.404546	+	0.404546i	0.879832	−	0.475286i	$-0.157655\pi$
$421$	8.30059	+	8.30059i	0.404546	+	0.404546i	−0.475286	+	0.879832i	$0.657655\pi$
$422$	−2.06478	−	0.553256i	−0.100512	−	0.0269321i
$423$		0			0
$424$	2.77664	−	2.77664i	0.134845	−	0.134845i
$425$	1.07555	−	0.620970i	0.0521719	−	0.0301215i
$426$		0			0
$427$	2.64245	+	9.86177i	0.127877	+	0.477244i
$428$	2.43832			0.117860
$429$		0			0
$430$	−3.27743			−0.158052
$431$	6.15171	+	22.9585i	0.296317	+	1.10587i	0.940165	+	0.340718i	$0.110670\pi$
$431$	6.15171	+	22.9585i	0.296317	+	1.10587i	−0.643848	+	0.765153i	$0.722663\pi$
$432$		0			0
$433$	16.1917	−	9.34829i	0.778124	−	0.449250i	−0.0576407	−	0.998337i	$-0.518358\pi$
$433$	16.1917	−	9.34829i	0.778124	−	0.449250i	0.835765	+	0.549087i	$0.185024\pi$
$434$	11.5960	−	11.5960i	0.556627	−	0.556627i
$435$		0			0
$436$	−7.48653	−	2.00601i	−0.358540	−	0.0960704i
$437$	6.12179	+	6.12179i	0.292845	+	0.292845i
$438$		0			0
$439$	−31.2991	−	18.0706i	−1.49383	−	0.862460i	−0.493850	−	0.869547i	$-0.664411\pi$
$439$	−31.2991	−	18.0706i	−1.49383	−	0.862460i	−0.999975	+	0.00708650i	$0.997744\pi$
$440$	−2.57631	+	0.690320i	−0.122821	+	0.0329097i
$441$		0			0
$442$	3.71721	−	2.49674i	0.176810	−	0.118758i
$443$		−	16.4292i		−	0.780573i	−0.920693	−	0.390287i	$-0.872376\pi$
$443$		−	16.4292i		−	0.780573i	0.920693	−	0.390287i	$-0.127624\pi$
$444$		0			0
$445$	6.95805	−	12.0517i	0.329843	−	0.571305i
$446$	2.61792	+	4.53438i	0.123962	+	0.214709i
$447$		0			0
$448$	−0.894504	+	3.33834i	−0.0422614	+	0.157722i
$449$	10.7090	−	39.9665i	0.505389	−	1.88614i	0.0438079	−	0.999040i	$-0.486051\pi$
$449$	10.7090	−	39.9665i	0.505389	−	1.88614i	0.461581	−	0.887098i	$-0.347282\pi$
$450$		0			0
$451$	6.07434	+	10.5211i	0.286029	+	0.495417i
$452$	−5.15984	+	8.93711i	−0.242699	+	0.420366i
$453$		0			0
$454$			20.3719i			0.956099i
$455$	11.7901	−	4.03393i	0.552730	−	0.189114i
$456$		0			0
$457$	13.4225	−	3.59655i	0.627878	−	0.168240i	0.0691717	−	0.997605i	$-0.477964\pi$
$457$	13.4225	−	3.59655i	0.627878	−	0.168240i	0.558707	+	0.829365i	$0.311298\pi$
$458$	−13.3765	−	7.72294i	−0.625044	−	0.360869i
$459$		0			0
$460$	−2.14266	−	2.14266i	−0.0999022	−	0.0999022i
$461$	10.7422	+	2.87837i	0.500316	+	0.134059i	0.500147	−	0.865941i	$-0.333279\pi$
$461$	10.7422	+	2.87837i	0.500316	+	0.134059i	0.000169374		1.00000i	$0.499946\pi$
$462$		0			0
$463$	0.815865	−	0.815865i	0.0379165	−	0.0379165i	−0.687894	−	0.725811i	$-0.741465\pi$
$463$	0.815865	−	0.815865i	0.0379165	−	0.0379165i	0.725811	+	0.687894i	$0.241465\pi$
$464$	5.00588	−	2.89015i	0.232392	−	0.134172i
$465$		0			0
$466$	1.26726	+	4.72947i	0.0587045	+	0.219088i
$467$	32.2712			1.49333			0.746667	−	0.665198i	$-0.231653\pi$
$467$	32.2712			1.49333			0.746667	+	0.665198i	$0.231653\pi$
$468$		0			0
$469$	2.34090			0.108093
$470$	0.541127	+	2.01951i	0.0249603	+	0.0931531i
$471$		0			0
$472$	5.49258	−	3.17114i	0.252817	−	0.145964i
$473$	−6.18119	+	6.18119i	−0.284212	+	0.284212i
$474$		0			0
$475$	−2.75974	−	0.739470i	−0.126626	−	0.0339292i
$476$	−3.03509	−	3.03509i	−0.139113	−	0.139113i
$477$		0			0
$478$	7.44483	+	4.29828i	0.340519	+	0.196599i
$479$	−5.03098	+	1.34805i	−0.229871	+	0.0615938i	−0.371916	−	0.928266i	$-0.621299\pi$
$479$	−5.03098	+	1.34805i	−0.229871	+	0.0615938i	0.142045	+	0.989860i	$0.454632\pi$
$480$		0			0
$481$	2.43505	+	35.8282i	0.111029	+	1.63362i
$482$		−	24.2743i		−	1.10566i
$483$		0			0
$484$	1.94304	−	3.36545i	0.0883201	−	0.152975i
$485$	−7.14671	−	12.3785i	−0.324515	−	0.562077i
$486$		0			0
$487$	2.17787	−	8.12792i	0.0986887	−	0.368311i	−0.898864	−	0.438227i	$-0.855606\pi$
$487$	2.17787	−	8.12792i	0.0986887	−	0.368311i	0.997553	+	0.0699161i	$0.0222732\pi$
$488$	−0.764577	+	2.85344i	−0.0346108	+	0.129169i
$489$		0			0
$490$	−2.47231	−	4.28217i	−0.111688	−	0.193449i
$491$	16.9786	−	29.4077i	0.766232	−	1.32715i	−0.173361	−	0.984858i	$-0.555463\pi$
$491$	16.9786	−	29.4077i	0.766232	−	1.32715i	0.939593	−	0.342294i	$-0.111204\pi$
$492$		0			0
$493$			7.17877i			0.323316i
$494$	−10.1083	−	1.98535i	−0.454793	−	0.0893249i
$495$		0			0
$496$	4.58333	−	1.22810i	0.205798	−	0.0551433i
$497$	−9.90254	−	5.71724i	−0.444190	−	0.256453i
$498$		0			0
$499$	−28.7083	−	28.7083i	−1.28516	−	1.28516i	−0.937693	−	0.347465i	$-0.887042\pi$
$499$	−28.7083	−	28.7083i	−1.28516	−	1.28516i	−0.347465	−	0.937693i	$-0.612958\pi$
$500$	0.965926	+	0.258819i	0.0431975	+	0.0115747i
$501$		0			0
$502$	−17.7342	+	17.7342i	−0.791516	+	0.791516i
$503$	17.7767	−	10.2634i	0.792622	−	0.457620i	−0.0482630	−	0.998835i	$-0.515369\pi$
$503$	17.7767	−	10.2634i	0.792622	−	0.457620i	0.840885	+	0.541214i	$0.182035\pi$
$504$		0			0
$505$	2.95599	+	11.0319i	0.131540	+	0.490913i
$506$	−8.08208			−0.359292
$507$		0			0
$508$	−8.03380			−0.356442
$509$	−3.08482	−	11.5127i	−0.136732	−	0.510292i	−0.999985	−	0.00551934i	$-0.998243\pi$
$509$	−3.08482	−	11.5127i	−0.136732	−	0.510292i	0.863253	−	0.504772i	$-0.168424\pi$
$510$		0			0
$511$	5.40714	−	3.12182i	0.239198	−	0.138101i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$	−1.54796	−	0.414775i	−0.0682776	−	0.0182949i
$515$	−12.5474	−	12.5474i	−0.552904	−	0.552904i
$516$		0			0
$517$	4.82934	+	2.78822i	0.212394	+	0.122626i
$518$	33.2494	−	8.90915i	1.46089	−	0.391446i
$519$		0			0
$520$	3.53796	+	0.694883i	0.155150	+	0.0304726i
$521$		−	24.8907i		−	1.09048i	−0.838279	−	0.545241i	$-0.816438\pi$
$521$		−	24.8907i		−	1.09048i	0.838279	−	0.545241i	$-0.183562\pi$
$522$		0			0
$523$	7.15029	−	12.3847i	0.312661	−	0.541544i	−0.666277	−	0.745704i	$-0.732113\pi$
$523$	7.15029	−	12.3847i	0.312661	−	0.541544i	0.978937	+	0.204160i	$0.0654464\pi$
$524$	−4.23144	−	7.32907i	−0.184851	−	0.320172i
$525$		0			0
$526$	0.0330065	−	0.123182i	0.00143915	−	0.00537099i
$527$	−1.52523	+	5.69222i	−0.0664399	+	0.247957i
$528$		0			0
$529$	6.90899	+	11.9667i	0.300391	+	0.520292i
$530$	−1.96338	+	3.40067i	−0.0852838	+	0.147716i
$531$		0			0
$532$			9.87440i			0.428110i
$533$	−1.11360	−	16.3850i	−0.0482352	−	0.709711i
$534$		0			0
$535$	−2.35523	+	0.631083i	−0.101826	+	0.0272841i
$536$	0.586580	+	0.338662i	0.0253364	+	0.0146280i
$537$		0			0
$538$	−3.49516	−	3.49516i	−0.150687	−	0.150687i
$539$	−12.7389	−	3.41337i	−0.548702	−	0.147024i
$540$		0			0
$541$	−11.2452	+	11.2452i	−0.483469	+	0.483469i	−0.906238	−	0.422768i	$-0.861058\pi$
$541$	−11.2452	+	11.2452i	−0.483469	+	0.483469i	0.422768	+	0.906238i	$0.361058\pi$
$542$	13.7283	−	7.92603i	0.589680	−	0.340452i
$543$		0			0
$544$	−0.321438	−	1.19962i	−0.0137815	−	0.0514334i
$545$	7.75062			0.332000
$546$		0			0
$547$	−19.8132			−0.847153			−0.423576	−	0.905860i	$-0.639225\pi$
$547$	−19.8132			−0.847153			−0.423576	+	0.905860i	$0.639225\pi$
$548$	−4.02696	−	15.0288i	−0.172023	−	0.641999i
$549$		0			0
$550$	2.30986	−	1.33360i	0.0984926	−	0.0568647i
$551$	11.6778	−	11.6778i	0.497489	−	0.497489i
$552$		0			0
$553$	−7.29985	−	1.95599i	−0.310421	−	0.0831771i
$554$	−1.50215	−	1.50215i	−0.0638201	−	0.0638201i
$555$		0			0
$556$	0.303803	+	0.175401i	0.0128841	+	0.00743864i
$557$	−8.34856	+	2.23699i	−0.353740	+	0.0947843i	−0.431313	−	0.902202i	$-0.641950\pi$
$557$	−8.34856	+	2.23699i	−0.353740	+	0.0947843i	0.0775731	+	0.996987i	$0.475283\pi$
$558$		0			0
$559$	11.1806	−	3.82539i	0.472890	−	0.161797i
$560$		−	3.45610i		−	0.146047i
$561$		0			0
$562$	9.56276	−	16.5632i	0.403380	−	0.698675i
$563$	−21.5626	−	37.3475i	−0.908755	−	1.57401i	−0.815796	−	0.578340i	$-0.803701\pi$
$563$	−21.5626	−	37.3475i	−0.908755	−	1.57401i	−0.0929591	−	0.995670i	$-0.529633\pi$
$564$		0			0
$565$	2.67093	−	9.96805i	0.112367	−	0.419359i
$566$	−6.09081	+	22.7312i	−0.256016	+	0.955464i
$567$		0			0
$568$	−1.65425	−	2.86524i	−0.0694106	−	0.120223i
$569$	−13.0827	+	22.6599i	−0.548456	+	0.949953i	0.449925	+	0.893066i	$0.351451\pi$
$569$	−13.0827	+	22.6599i	−0.548456	+	0.949953i	−0.998381	+	0.0568870i	$0.981883\pi$
$570$		0			0
$571$		−	6.55466i		−	0.274304i	−0.990550	−	0.137152i	$-0.956205\pi$
$571$		−	6.55466i		−	0.274304i	0.990550	−	0.137152i	$-0.0437949\pi$
$572$	7.98309	−	5.36201i	0.333790	−	0.224197i
$573$		0			0
$574$	−15.2056	+	4.07434i	−0.634671	+	0.170060i
$575$	2.62422	+	1.51509i	0.109437	+	0.0631837i
$576$		0			0
$577$	−15.2230	−	15.2230i	−0.633742	−	0.633742i	0.315262	−	0.949005i	$-0.397907\pi$
$577$	−15.2230	−	15.2230i	−0.633742	−	0.633742i	−0.949005	+	0.315262i	$0.897907\pi$
$578$	−14.9309	−	4.00072i	−0.621043	−	0.166408i
$579$		0			0
$580$	−4.08728	+	4.08728i	−0.169715	+	0.169715i
$581$	39.2383	−	22.6542i	1.62788	−	0.939856i
$582$		0			0
$583$	2.71072	+	10.1166i	0.112267	+	0.418985i
$584$	1.80655			0.0747558
$585$		0			0
$586$	10.9620			0.452836
$587$	−3.28285	−	12.2517i	−0.135498	−	0.505684i	−0.999995	−	0.00304713i	$-0.999030\pi$
$587$	−3.28285	−	12.2517i	−0.135498	−	0.505684i	0.864498	−	0.502637i	$-0.167637\pi$
$588$		0			0
$589$	11.7407	−	6.77848i	0.483766	−	0.279302i
$590$	−4.48467	+	4.48467i	−0.184631	+	0.184631i
$591$		0			0
$592$	9.62050	+	2.57781i	0.395400	+	0.105947i
$593$	25.8713	+	25.8713i	1.06241	+	1.06241i	0.997918	+	0.0644902i	$0.0205421\pi$
$593$	25.8713	+	25.8713i	1.06241	+	1.06241i	0.0644902	+	0.997918i	$0.479458\pi$
$594$		0			0
$595$	3.71721	+	2.14613i	0.152391	+	0.0879829i
$596$	11.6425	−	3.11959i	0.476894	−	0.127783i
$597$		0			0
$598$	9.81039	+	4.80859i	0.401177	+	0.196638i
$599$			35.7513i			1.46076i	0.683042	+	0.730379i	$0.260656\pi$
$599$			35.7513i			1.46076i	−0.683042	+	0.730379i	$0.739344\pi$
$600$		0			0
$601$	−8.32438	+	14.4183i	−0.339559	+	0.588133i	−0.984350	−	0.176226i	$-0.943611\pi$
$601$	−8.32438	+	14.4183i	−0.339559	+	0.588133i	0.644791	+	0.764359i	$0.276944\pi$
$602$	−5.66356	−	9.80957i	−0.230829	−	0.399808i
$603$		0			0
$604$	1.91683	−	7.15372i	0.0779948	−	0.291081i
$605$	−1.00579	+	3.75367i	−0.0408913	+	0.152608i
$606$		0			0
$607$	15.0634	+	26.0907i	0.611406	+	1.05899i	0.991004	+	0.133835i	$0.0427293\pi$
$607$	15.0634	+	26.0907i	0.611406	+	1.05899i	−0.379597	+	0.925152i	$0.623937\pi$
$608$	−1.42855	+	2.47432i	−0.0579352	+	0.100347i
$609$		0			0
$610$		−	2.95410i		−	0.119608i
$611$	−4.20316	−	6.25777i	−0.170042	−	0.253162i
$612$		0			0
$613$	−17.1605	+	4.59815i	−0.693107	+	0.185717i	−0.588141	−	0.808758i	$-0.700140\pi$
$613$	−17.1605	+	4.59815i	−0.693107	+	0.185717i	−0.104966	+	0.994476i	$0.533473\pi$
$614$	24.8320	+	14.3367i	1.00214	+	0.578584i
$615$		0			0
$616$	−6.51817	−	6.51817i	−0.262624	−	0.262624i
$617$	−10.7895	−	2.89103i	−0.434367	−	0.116388i	0.0350083	−	0.999387i	$-0.488854\pi$
$617$	−10.7895	−	2.89103i	−0.434367	−	0.116388i	−0.469375	+	0.882999i	$0.655521\pi$
$618$		0			0
$619$	23.9690	−	23.9690i	0.963396	−	0.963396i	−0.0359576	−	0.999353i	$-0.511448\pi$
$619$	23.9690	−	23.9690i	0.963396	−	0.963396i	0.999353	+	0.0359576i	$0.0114481\pi$
$620$	−4.10930	+	2.37251i	−0.165034	+	0.0952822i
$621$		0			0
$622$	4.56622	+	17.0414i	0.183089	+	0.683297i
$623$	48.0954			1.92690
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	4.73080	+	17.6556i	0.189081	+	0.705658i
$627$		0			0
$628$	20.3570	−	11.7531i	0.812332	−	0.469000i
$629$	−8.74660	+	8.74660i	−0.348750	+	0.348750i
$630$		0			0
$631$	10.2783	+	2.75405i	0.409171	+	0.109637i	0.457533	−	0.889193i	$-0.348733\pi$
$631$	10.2783	+	2.75405i	0.409171	+	0.109637i	−0.0483614	+	0.998830i	$0.515400\pi$
$632$	−1.54621	−	1.54621i	−0.0615050	−	0.0615050i
$633$		0			0
$634$	24.7388	+	14.2830i	0.982503	+	0.567249i
$635$	7.76005	−	2.07930i	0.307948	−	0.0825145i
$636$		0			0
$637$	13.4322	+	11.7225i	0.532201	+	0.464463i
$638$			15.4172i			0.610371i
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−9.48494	−	16.4284i	−0.374633	−	0.648883i	0.615639	−	0.788028i	$-0.288898\pi$
$641$	−9.48494	−	16.4284i	−0.374633	−	0.648883i	−0.990272	+	0.139145i	$0.955564\pi$
$642$		0			0
$643$	−9.46221	+	35.3134i	−0.373153	+	1.39263i	0.482871	+	0.875691i	$0.339594\pi$
$643$	−9.46221	+	35.3134i	−0.373153	+	1.39263i	−0.856025	+	0.516935i	$0.827073\pi$
$644$	2.71051	−	10.1158i	0.106809	−	0.398617i
$645$		0			0
$646$	−1.77417	−	3.07295i	−0.0698038	−	0.120904i
$647$	0.352179	−	0.609993i	0.0138456	−	0.0239813i	−0.859020	−	0.511943i	$-0.828926\pi$
$647$	0.352179	−	0.609993i	0.0138456	−	0.0239813i	0.872865	+	0.487961i	$0.162259\pi$
$648$		0			0
$649$			16.9161i			0.664015i
$650$	−3.59725	+	0.244486i	−0.141096	+	0.00958951i
$651$		0			0
$652$	21.2695	−	5.69914i	0.832977	−	0.223196i
$653$	6.38128	+	3.68423i	0.249719	+	0.144175i	0.619635	−	0.784890i	$-0.287280\pi$
$653$	6.38128	+	3.68423i	0.249719	+	0.144175i	−0.369917	+	0.929065i	$0.620614\pi$
$654$		0			0
$655$	5.98416	+	5.98416i	0.233821	+	0.233821i
$656$	−4.39965	−	1.17888i	−0.171778	−	0.0460276i
$657$		0			0
$658$	−5.10945	+	5.10945i	−0.199187	+	0.199187i
$659$	11.8634	−	6.84936i	0.462134	−	0.266813i	−0.250807	−	0.968037i	$-0.580696\pi$
$659$	11.8634	−	6.84936i	0.462134	−	0.266813i	0.712941	+	0.701224i	$0.247363\pi$
$660$		0			0
$661$	−5.32144	−	19.8599i	−0.206980	−	0.772460i	−0.988837	−	0.149002i	$-0.952394\pi$
$661$	−5.32144	−	19.8599i	−0.206980	−	0.772460i	0.781857	−	0.623458i	$-0.214273\pi$
$662$	26.1988			1.01825
$663$		0			0
$664$	13.1097			0.508755
$665$	−2.55568	−	9.53794i	−0.0991051	−	0.369865i
$666$		0			0
$667$	−15.1687	+	8.75768i	−0.587336	+	0.339099i
$668$	4.56045	−	4.56045i	0.176449	−	0.176449i
$669$		0			0
$670$	−0.654245	−	0.175304i	−0.0252757	−	0.00677260i
$671$	−5.57140	−	5.57140i	−0.215081	−	0.215081i
$672$		0			0
$673$	−28.7999	−	16.6276i	−1.11015	−	0.640947i	−0.171284	−	0.985222i	$-0.554792\pi$
$673$	−28.7999	−	16.6276i	−1.11015	−	0.640947i	−0.938869	+	0.344274i	$0.888125\pi$
$674$	−29.5436	+	7.91619i	−1.13798	+	0.304920i
$675$		0			0
$676$	−12.8805	+	1.75895i	−0.495402	+	0.0676520i
$677$		−	36.5650i		−	1.40531i	−0.711532	−	0.702653i	$-0.751998\pi$
$677$		−	36.5650i		−	1.40531i	0.711532	−	0.702653i	$-0.248002\pi$
$678$		0			0
$679$	24.6997	−	42.7812i	0.947889	−	1.64179i
$680$	0.620970	+	1.07555i	0.0238131	+	0.0412455i
$681$		0			0
$682$	−3.27558	+	12.2246i	−0.125428	+	0.468105i
$683$	10.8739	−	40.5821i	0.416080	−	1.55283i	−0.366583	−	0.930385i	$-0.619472\pi$
$683$	10.8739	−	40.5821i	0.416080	−	1.55283i	0.782663	−	0.622446i	$-0.213861\pi$
$684$		0			0
$685$	7.77949	+	13.4745i	0.297239	+	0.514833i
$686$	−3.55180	+	6.15190i	−0.135608	+	0.234880i
$687$		0			0
$688$		−	3.27743i		−	0.124951i
$689$	2.72864	−	13.8927i	0.103953	−	0.529270i
$690$		0			0
$691$	−35.1418	+	9.41621i	−1.33686	+	0.358210i	−0.855267	−	0.518188i	$-0.826607\pi$
$691$	−35.1418	+	9.41621i	−1.33686	+	0.358210i	−0.481589	+	0.876397i	$0.659940\pi$
$692$	3.04929	+	1.76051i	0.115917	+	0.0669244i
$693$		0			0
$694$	2.37650	+	2.37650i	0.0902108	+	0.0902108i
$695$	−0.338848	−	0.0907940i	−0.0128532	−	0.00344401i
$696$		0			0
$697$	4.00000	−	4.00000i	0.151511	−	0.151511i
$698$	9.20288	−	5.31329i	0.348334	−	0.201111i
$699$		0			0
$700$	0.894504	+	3.33834i	0.0338091	+	0.126177i
$701$	38.6824			1.46101			0.730507	−	0.682905i	$-0.239284\pi$
$701$	38.6824			1.46101			0.730507	+	0.682905i	$0.239284\pi$
$702$		0			0
$703$	28.4563			1.07325
$704$	−0.690320	−	2.57631i	−0.0260174	−	0.0970983i
$705$		0			0
$706$	26.1259	−	15.0838i	0.983262	−	0.567687i
$707$	−27.9112	+	27.9112i	−1.04971	+	1.04971i
$708$		0			0
$709$	−29.0458	−	7.78280i	−1.09084	−	0.292289i	−0.331810	−	0.943346i	$-0.607659\pi$
$709$	−29.0458	−	7.78280i	−1.09084	−	0.292289i	−0.759029	+	0.651057i	$0.774326\pi$
$710$	2.33946	+	2.33946i	0.0877982	+	0.0877982i
$711$		0			0
$712$	12.0517	+	6.95805i	0.451656	+	0.260764i
$713$	−13.8883	+	3.72137i	−0.520123	+	0.139366i
$714$		0			0
$715$	−6.32328	+	7.24548i	−0.236477	+	0.270966i
$716$		−	19.0594i		−	0.712284i
$717$		0			0
$718$	10.4546	−	18.1079i	0.390163	−	0.675782i
$719$	−14.2044	−	24.6027i	−0.529734	−	0.917526i	−0.999398	−	0.0346810i	$-0.988958\pi$
$719$	−14.2044	−	24.6027i	−0.529734	−	0.917526i	0.469665	−	0.882845i	$-0.344375\pi$
$720$		0			0
$721$	15.8727	−	59.2377i	0.591130	−	2.20613i
$722$	2.80483	−	10.4678i	0.104385	−	0.389569i
$723$		0			0
$724$	−3.02589	−	5.24100i	−0.112456	−	0.194780i
$725$	2.89015	−	5.00588i	0.107337	−	0.185914i
$726$		0			0
$727$		−	44.3072i		−	1.64326i	−0.570018	−	0.821632i	$-0.693064\pi$
$727$		−	44.3072i		−	1.64326i	0.570018	−	0.821632i	$-0.306936\pi$
$728$	4.03393	+	11.7901i	0.149507	+	0.436972i
$729$		0			0
$730$	−1.74500	+	0.467571i	−0.0645853	+	0.0173056i
$731$	3.52504	+	2.03518i	0.130378	+	0.0752740i
$732$		0			0
$733$	11.7103	+	11.7103i	0.432530	+	0.432530i	0.889488	−	0.456958i	$-0.151061\pi$
$733$	11.7103	+	11.7103i	0.432530	+	0.432530i	−0.456958	+	0.889488i	$0.651061\pi$
$734$	−2.37973	−	0.637647i	−0.0878375	−	0.0235360i
$735$		0			0
$736$	2.14266	−	2.14266i	0.0789796	−	0.0789796i
$737$	−1.56452	+	0.903277i	−0.0576299	+	0.0332727i
$738$		0			0
$739$	10.3804	+	38.7401i	0.381849	+	1.42508i	0.843075	+	0.537796i	$0.180743\pi$
$739$	10.3804	+	38.7401i	0.381849	+	1.42508i	−0.461227	+	0.887282i	$0.652590\pi$
$740$	−9.95988			−0.366132
$741$		0			0
$742$	−13.5713			−0.498217
$743$	7.41428	+	27.6705i	0.272003	+	1.01513i	0.957823	+	0.287359i	$0.0927773\pi$
$743$	7.41428	+	27.6705i	0.272003	+	1.01513i	−0.685819	+	0.727772i	$0.740556\pi$
$744$		0			0
$745$	−10.4384	+	6.02659i	−0.382432	+	0.220797i
$746$	−3.47620	+	3.47620i	−0.127273	+	0.127273i
$747$		0			0
$748$	3.19962	+	0.857336i	0.116990	+	0.0313473i
$749$	−5.95883	−	5.95883i	−0.217731	−	0.217731i
$750$		0			0
$751$	−24.2691	−	14.0117i	−0.885591	−	0.511296i	−0.0130929	−	0.999914i	$-0.504168\pi$
$751$	−24.2691	−	14.0117i	−0.885591	−	0.511296i	−0.872498	+	0.488618i	$0.837501\pi$
$752$	−2.01951	+	0.541127i	−0.0736440	+	0.0197329i
$753$		0			0
$754$	9.17272	−	18.7140i	0.334051	−	0.681524i
$755$			7.40607i			0.269535i
$756$		0			0
$757$	−24.3146	+	42.1141i	−0.883729	+	1.53066i	−0.0365655	+	0.999331i	$0.511642\pi$
$757$	−24.3146	+	42.1141i	−0.883729	+	1.53066i	−0.847164	+	0.531332i	$0.821692\pi$
$758$	15.1440	+	26.2302i	0.550056	+	0.952724i
$759$		0			0
$760$	0.739470	−	2.75974i	0.0268234	−	0.100106i
$761$	3.98957	−	14.8893i	0.144622	−	0.539736i	−0.855150	−	0.518380i	$-0.826535\pi$
$761$	3.98957	−	14.8893i	0.144622	−	0.539736i	0.999772	−	0.0213553i	$-0.00679813\pi$
$762$		0			0
$763$	13.3935	+	23.1982i	0.484876	+	0.839829i
$764$	−10.8314	+	18.7606i	−0.391868	+	0.678735i
$765$		0			0
$766$			13.9171i			0.502847i
$767$	10.0645	−	20.5335i	0.363410	−	0.741422i
$768$		0			0
$769$	−27.5518	+	7.38249i	−0.993544	+	0.266219i	−0.718738	−	0.695281i	$-0.755280\pi$
$769$	−27.5518	+	7.38249i	−0.993544	+	0.266219i	−0.274805	+	0.961500i	$0.588613\pi$
$770$	7.98309	+	4.60904i	0.287691	+	0.166098i
$771$		0			0
$772$	15.4293	+	15.4293i	0.555311	+	0.555311i
$773$	−12.6151	−	3.38021i	−0.453734	−	0.121578i	0.0247123	−	0.999695i	$-0.492133\pi$
$773$	−12.6151	−	3.38021i	−0.453734	−	0.121578i	−0.478446	+	0.878117i	$0.658800\pi$
$774$		0			0
$775$	3.35523	−	3.35523i	0.120524	−	0.120524i
$776$	12.3785	−	7.14671i	0.444361	−	0.256552i
$777$		0			0
$778$	−0.331186	−	1.23600i	−0.0118736	−	0.0443128i
$779$	−13.0136			−0.466262
$780$		0			0
$781$	8.82438			0.315761
$782$	0.974015	+	3.63507i	0.0348307	+	0.129990i
$783$		0			0
$784$	4.28217	−	2.47231i	0.152935	−	0.0882968i
$785$	−16.6214	+	16.6214i	−0.593243	+	0.593243i
$786$		0			0
$787$	14.8632	+	3.98258i	0.529815	+	0.141964i	0.513803	−	0.857908i	$-0.328236\pi$
$787$	14.8632	+	3.98258i	0.529815	+	0.141964i	0.0160122	+	0.999872i	$0.494903\pi$
$788$	−17.7783	−	17.7783i	−0.633327	−	0.633327i
$789$		0			0
$790$	1.89372	+	1.09334i	0.0673754	+	0.0388992i
$791$	34.4506	−	9.23100i	1.22492	−	0.328217i
$792$		0			0
$793$	3.44800	+	10.0776i	0.122442	+	0.357867i
$794$			6.57860i			0.233466i
$795$		0			0
$796$	9.80796	−	16.9879i	0.347634	−	0.602120i
$797$	−2.15446	−	3.73163i	−0.0763148	−	0.132181i	0.825342	−	0.564632i	$-0.190982\pi$
$797$	−2.15446	−	3.73163i	−0.0763148	−	0.132181i	−0.901657	+	0.432451i	$0.857649\pi$
$798$		0			0
$799$	0.672047	−	2.50811i	0.0237753	−	0.0887306i
$800$	−0.258819	+	0.965926i	−0.00915064	+	0.0341506i
$801$		0			0
$802$	2.84102	+	4.92078i	0.100320	+	0.173759i
$803$	−2.40921	+	4.17288i	−0.0850193	+	0.147258i
$804$		0			0
$805$			10.4726i			0.369111i
$806$	11.2493	−	12.8899i	0.396240	−	0.454028i
$807$		0			0
$808$	−11.0319	+	2.95599i	−0.388101	+	0.103991i
$809$	−29.6639	−	17.1265i	−1.04293	−	0.602134i	−0.122266	−	0.992497i	$-0.539016\pi$
$809$	−29.6639	−	17.1265i	−1.04293	−	0.602134i	−0.920661	+	0.390363i	$0.872349\pi$
$810$		0			0
$811$	25.1638	+	25.1638i	0.883620	+	0.883620i	0.993900	−	0.110281i	$-0.0351750\pi$
$811$	25.1638	+	25.1638i	0.883620	+	0.883620i	−0.110281	+	0.993900i	$0.535175\pi$
$812$	−19.2966	−	5.17050i	−0.677176	−	0.181449i
$813$		0			0
$814$	−18.7842	+	18.7842i	−0.658387	+	0.658387i
$815$	−19.0697	+	11.0099i	−0.667982	+	0.385660i
$816$		0			0
$817$	−2.42356	−	9.04485i	−0.0847896	−	0.316439i
$818$	−34.2874			−1.19883
$819$		0			0
$820$	4.55485			0.159062
$821$	12.9519	+	48.3373i	0.452026	+	1.68698i	0.696687	+	0.717375i	$0.254656\pi$
$821$	12.9519	+	48.3373i	0.452026	+	1.68698i	−0.244662	+	0.969609i	$0.578677\pi$
$822$		0			0
$823$	8.32975	−	4.80918i	0.290357	−	0.167638i	−0.347746	−	0.937589i	$-0.613053\pi$
$823$	8.32975	−	4.80918i	0.290357	−	0.167638i	0.638103	+	0.769951i	$0.279719\pi$
$824$	12.5474	−	12.5474i	0.437109	−	0.437109i
$825$		0			0
$826$	−21.1727	−	5.67320i	−0.736692	−	0.197396i
$827$	31.1480	+	31.1480i	1.08312	+	1.08312i	0.996217	+	0.0869057i	$0.0276979\pi$
$827$	31.1480	+	31.1480i	1.08312	+	1.08312i	0.0869057	+	0.996217i	$0.472302\pi$
$828$		0			0
$829$	32.0196	+	18.4865i	1.11209	+	0.642064i	0.939369	−	0.342908i	$-0.111412\pi$
$829$	32.0196	+	18.4865i	1.11209	+	0.642064i	0.172718	+	0.984971i	$0.444745\pi$
$830$	−12.6630	+	3.39304i	−0.439539	+	0.117774i
$831$		0			0
$832$	−0.694883	+	3.53796i	−0.0240907	+	0.122657i
$833$			6.14092i			0.212770i
$834$		0			0
$835$	−3.22473	+	5.58539i	−0.111596	+	0.193290i
$836$	−3.81021	−	6.59948i	−0.131779	−	0.228248i
$837$		0			0
$838$	−8.02532	+	29.9509i	−0.277230	+	1.03464i
$839$	−6.05982	+	22.6156i	−0.209208	+	0.780776i	0.778917	+	0.627127i	$0.215769\pi$
$839$	−6.05982	+	22.6156i	−0.209208	+	0.780776i	−0.988125	+	0.153649i	$0.950897\pi$
$840$		0			0
$841$	2.20589	+	3.82071i	0.0760651	+	0.131749i
$842$	5.86940	−	10.1661i	0.202273	−	0.350347i
$843$		0			0
$844$			2.13762i			0.0735798i
$845$	11.9863	−	5.03272i	0.412342	−	0.173131i
$846$		0			0
$847$	−12.9731	+	3.47612i	−0.445759	+	0.119441i
$848$	−3.40067	−	1.96338i	−0.116780	−	0.0674227i
$849$		0			0
$850$	−0.878184	−	0.878184i	−0.0301215	−	0.0301215i
$851$	−29.1519	−	7.81123i	−0.999314	−	0.267765i
$852$		0			0
$853$	30.0896	−	30.0896i	1.03025	−	1.03025i	0.0307214	−	0.999528i	$-0.490220\pi$
$853$	30.0896	−	30.0896i	1.03025	−	1.03025i	0.999528	−	0.0307214i	$-0.00978045\pi$
$854$	8.84182	−	5.10483i	0.302561	−	0.174684i
$855$		0			0
$856$	−0.631083	−	2.35523i	−0.0215700	−	0.0805002i
$857$	−49.8325			−1.70225			−0.851123	−	0.524966i	$-0.824078\pi$
$857$	−49.8325			−1.70225			−0.851123	+	0.524966i	$0.824078\pi$
$858$		0			0
$859$	10.5712			0.360684			0.180342	−	0.983604i	$-0.442280\pi$
$859$	10.5712			0.360684			0.180342	+	0.983604i	$0.442280\pi$
$860$	0.848261	+	3.16575i	0.0289254	+	0.107951i
$861$		0			0
$862$	20.5840	−	11.8842i	0.701095	−	0.404777i
$863$	9.81856	−	9.81856i	0.334228	−	0.334228i	−0.519962	−	0.854190i	$-0.674054\pi$
$863$	9.81856	−	9.81856i	0.334228	−	0.334228i	0.854190	+	0.519962i	$0.174054\pi$
$864$		0			0
$865$	−3.40104	−	0.911306i	−0.115639	−	0.0309853i
$866$	−13.2205	−	13.2205i	−0.449250	−	0.449250i
$867$		0			0
$868$	−14.2022	−	8.19962i	−0.482053	−	0.278313i
$869$	5.63355	−	1.50951i	0.191105	−	0.0512065i
$870$		0			0
$871$	2.43651	−	0.165596i	0.0825579	−	0.00561101i
$872$			7.75062i			0.262469i
$873$		0			0
$874$	4.32876	−	7.49763i	0.146423	−	0.253611i
$875$	−1.72805	−	2.99307i	−0.0584187	−	0.101184i
$876$		0			0
$877$	10.3752	−	38.7209i	0.350347	−	1.30751i	−0.535893	−	0.844286i	$-0.680025\pi$
$877$	10.3752	−	38.7209i	0.350347	−	1.30751i	0.886240	−	0.463226i	$-0.153308\pi$
$878$	−9.35401	+	34.9096i	−0.315682	+	1.17814i
$879$		0			0
$880$	1.33360	+	2.30986i	0.0449555	+	0.0778652i
$881$	3.10019	−	5.36969i	0.104448	−	0.180909i	−0.809064	−	0.587720i	$-0.800026\pi$
$881$	3.10019	−	5.36969i	0.104448	−	0.180909i	0.913513	+	0.406810i	$0.133359\pi$
$882$		0			0
$883$			15.0887i			0.507776i	0.967234	+	0.253888i	$0.0817095\pi$
$883$			15.0887i			0.507776i	−0.967234	+	0.253888i	$0.918290\pi$
$884$	−3.37375	−	2.94435i	−0.113472	−	0.0990291i
$885$		0			0
$886$	−15.8694	+	4.25218i	−0.533141	+	0.142855i
$887$	15.8345	+	9.14203i	0.531669	+	0.306959i	0.741696	−	0.670736i	$-0.234022\pi$
$887$	15.8345	+	9.14203i	0.531669	+	0.306959i	−0.210027	+	0.977696i	$0.567355\pi$
$888$		0			0
$889$	19.6332	+	19.6332i	0.658478	+	0.658478i
$890$	−13.4419	−	3.60175i	−0.450574	−	0.120731i
$891$		0			0
$892$	3.70230	−	3.70230i	0.123962	−	0.123962i
$893$	−5.17318	+	2.98674i	−0.173114	+	0.0999474i
$894$		0			0
$895$	4.93294	+	18.4100i	0.164890	+	0.615378i
$896$	3.45610			0.115460
$897$		0			0
$898$	−41.3764			−1.38075
$899$	7.09878	+	26.4930i	0.236758	+	0.883591i
$900$		0			0
$901$	4.22343	−	2.43840i	0.140703	−	0.0812349i
$902$	8.59041	−	8.59041i	0.286029	−	0.286029i
$903$		0			0
$904$	9.96805	+	2.67093i	0.331532	+	0.0888339i
$905$	4.27926	+	4.27926i	0.142247	+	0.142247i
$906$		0			0
$907$	−30.5379	−	17.6310i	−1.01399	−	0.585429i	−0.101635	−	0.994822i	$-0.532407\pi$
$907$	−30.5379	−	17.6310i	−1.01399	−	0.585429i	−0.912358	+	0.409393i	$0.865741\pi$
$908$	19.6777	−	5.27263i	0.653028	−	0.174978i
$909$		0			0
$910$	−6.94799	−	10.3443i	−0.230324	−	0.342912i
$911$			8.79767i			0.291480i	0.989323	+	0.145740i	$0.0465563\pi$
$911$			8.79767i			0.291480i	−0.989323	+	0.145740i	$0.953444\pi$
$912$		0			0
$913$	−17.4831	+	30.2815i	−0.578605	+	1.00217i
$914$	−6.94800	−	12.0343i	−0.229819	−	0.398059i
$915$		0			0
$916$	−3.99769	+	14.9196i	−0.132087	+	0.492956i
$917$	−7.57008	+	28.2519i	−0.249986	+	0.932961i
$918$		0			0
$919$	−0.767000	−	1.32848i	−0.0253010	−	0.0438226i	0.853098	−	0.521751i	$-0.174721\pi$
$919$	−0.767000	−	1.32848i	−0.0253010	−	0.0438226i	−0.878399	+	0.477929i	$0.841388\pi$
$920$	−1.51509	+	2.62422i	−0.0499511	+	0.0865179i
$921$		0			0
$922$		−	11.1212i		−	0.366257i
$923$	−10.7114	−	5.25023i	−0.352571	−	0.172813i
$924$		0			0
$925$	9.62050	−	2.57781i	0.316320	−	0.0847577i
$926$	−0.999227	−	0.576904i	−0.0328366	−	0.0189582i
$927$		0			0
$928$	−4.08728	−	4.08728i	−0.134172	−	0.134172i
$929$	39.8495	+	10.6776i	1.30742	+	0.350322i	0.844251	−	0.535948i	$-0.180046\pi$
$929$	39.8495	+	10.6776i	1.30742	+	0.350322i	0.463169	+	0.886270i	$0.346712\pi$
$930$		0			0
$931$	9.98947	−	9.98947i	0.327392	−	0.327392i
$932$	4.24032	−	2.44815i	0.138896	−	0.0801919i
$933$		0			0
$934$	−8.35241	−	31.1716i	−0.273299	−	1.01997i
$935$	−3.31249			−0.108330
$936$		0			0
$937$	15.3479			0.501393			0.250697	−	0.968066i	$-0.419340\pi$
$937$	15.3479			0.501393			0.250697	+	0.968066i	$0.419340\pi$
$938$	−0.605870	−	2.26114i	−0.0197823	−	0.0738287i
$939$		0			0
$940$	1.81064	−	1.04538i	0.0590567	−	0.0340964i
$941$	−24.2863	+	24.2863i	−0.791710	+	0.791710i	−0.981772	−	0.190062i	$-0.939131\pi$
$941$	−24.2863	+	24.2863i	−0.791710	+	0.791710i	0.190062	+	0.981772i	$0.439131\pi$
$942$		0			0
$943$	13.3318	+	3.57223i	0.434142	+	0.116328i
$944$	−4.48467	−	4.48467i	−0.145964	−	0.145964i
$945$		0			0
$946$	7.57039	+	4.37076i	0.246134	+	0.142106i
$947$	−37.6195	+	10.0801i	−1.22247	+	0.327559i	−0.811642	−	0.584155i	$-0.801426\pi$
$947$	−37.6195	+	10.0801i	−1.22247	+	0.327559i	−0.410826	+	0.911714i	$0.634760\pi$
$948$		0			0
$949$	5.40714	−	3.63182i	0.175523	−	0.117894i
$950$			2.85709i			0.0926964i
$951$		0			0
$952$	−2.14613	+	3.71721i	−0.0695566	+	0.120476i
$953$	10.7621	+	18.6406i	0.348620	+	0.603827i	0.986005	−	0.166718i	$-0.0533171\pi$
$953$	10.7621	+	18.6406i	0.348620	+	0.603827i	−0.637385	+	0.770546i	$0.719984\pi$
$954$		0			0
$955$	5.60677	−	20.9247i	0.181431	−	0.677108i
$956$	2.22495	−	8.30363i	0.0719601	−	0.268559i
$957$		0			0
$958$	2.60423	+	4.51065i	0.0841387	+	0.145733i
$959$	−26.8867	+	46.5691i	−0.868216	+	1.50379i
$960$		0			0
$961$		−	8.48483i		−	0.273704i
$962$	33.9771	−	11.6251i	1.09547	−	0.374808i
$963$		0			0
$964$	−23.4472	+	6.28265i	−0.755182	+	0.202350i
$965$	−18.8969	−	10.9101i	−0.608313	−	0.351210i
$966$		0			0
$967$	−28.1259	−	28.1259i	−0.904467	−	0.904467i	0.0913519	−	0.995819i	$-0.470881\pi$
$967$	−28.1259	−	28.1259i	−0.904467	−	0.904467i	−0.995819	+	0.0913519i	$0.970881\pi$
$968$	−3.75367	−	1.00579i	−0.120648	−	0.0323274i
$969$		0			0
$970$	−10.1070	+	10.1070i	−0.324515	+	0.324515i
$971$	22.1392	−	12.7821i	0.710481	−	0.410197i	−0.100758	−	0.994911i	$-0.532127\pi$
$971$	22.1392	−	12.7821i	0.710481	−	0.410197i	0.811239	+	0.584714i	$0.198793\pi$
$972$		0			0
$973$	−0.313793	−	1.17109i	−0.0100597	−	0.0375435i
$974$	−8.41464			−0.269623
$975$		0			0
$976$	2.95410			0.0945584
$977$	6.13609	+	22.9002i	0.196311	+	0.732642i	0.991924	+	0.126837i	$0.0404824\pi$
$977$	6.13609	+	22.9002i	0.196311	+	0.732642i	−0.795613	+	0.605806i	$0.792851\pi$
$978$		0			0
$979$	−32.1442	+	18.5585i	−1.02733	+	0.593131i
$980$	−3.49637	+	3.49637i	−0.111688	+	0.111688i
$981$		0			0
$982$	−32.8001	−	8.78875i	−1.04669	−	0.280460i
$983$	−19.5861	−	19.5861i	−0.624701	−	0.624701i	0.322029	−	0.946730i	$-0.395635\pi$
$983$	−19.5861	−	19.5861i	−0.624701	−	0.624701i	−0.946730	+	0.322029i	$0.895635\pi$
$984$		0			0
$985$	21.7739	+	12.5712i	0.693775	+	0.400551i
$986$	6.93416	−	1.85800i	0.220829	−	0.0591709i
$987$		0			0
$988$	0.698518	+	10.2777i	0.0222228	+	0.326977i
$989$			9.93121i			0.315794i
$990$		0			0
$991$	2.28664	−	3.96057i	0.0726374	−	0.125812i	−0.827419	−	0.561585i	$-0.810192\pi$
$991$	2.28664	−	3.96057i	0.0726374	−	0.125812i	0.900056	+	0.435773i	$0.143525\pi$
$992$	−2.37251	−	4.10930i	−0.0753272	−	0.130471i
$993$		0			0
$994$	−2.95946	+	11.0449i	−0.0938683	+	0.350321i
$995$	−5.07698	+	18.9475i	−0.160951	+	0.600677i
$996$		0			0
$997$	0.597806	+	1.03543i	0.0189327	+	0.0327924i	0.875337	−	0.483514i	$-0.160640\pi$
$997$	0.597806	+	1.03543i	0.0189327	+	0.0327924i	−0.856404	+	0.516307i	$0.827307\pi$
$998$	−20.2998	+	35.1603i	−0.642579	+	1.11298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.cu.e.1151.2	yes	16
3.2	odd	2	inner	1170.2.cu.e.1151.4	yes	16
13.2	odd	12	inner	1170.2.cu.e.431.4	yes	16
39.2	even	12	inner	1170.2.cu.e.431.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.cu.e.431.2	✓	16	39.2	even	12	inner
1170.2.cu.e.431.4	yes	16	13.2	odd	12	inner
1170.2.cu.e.1151.2	yes	16	1.1	even	1	trivial
1170.2.cu.e.1151.4	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(3.33834 + 0.894504i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 + 0.500000i) q^{4} +(0.707107 - 0.707107i) q^{5} +(3.33834 + 0.894504i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 - 0.500000i) q^{10} +(-2.57631 + 0.690320i) q^{11} +(3.53796 + 0.694883i) q^{13} -3.45610i q^{14} +(0.500000 - 0.866025i) q^{16} +(0.620970 + 1.07555i) q^{17} +(0.739470 - 2.75974i) q^{19} +(-0.258819 + 0.965926i) q^{20} +(1.33360 + 2.30986i) q^{22} +(-1.51509 + 2.62422i) q^{23} -1.00000i q^{25} +(-0.244486 - 3.59725i) q^{26} +(-3.33834 + 0.894504i) q^{28} +(5.00588 + 2.89015i) q^{29} +(3.35523 + 3.35523i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(0.878184 - 0.878184i) q^{34} +(2.99307 - 1.72805i) q^{35} +(2.57781 + 9.62050i) q^{37} -2.85709 q^{38} +1.00000 q^{40} +(-1.17888 - 4.39965i) q^{41} +(2.83834 - 1.63871i) q^{43} +(1.88599 - 1.88599i) q^{44} +(2.92693 + 0.784269i) q^{46} +(-1.47839 - 1.47839i) q^{47} +(4.28217 + 2.47231i) q^{49} +(-0.965926 + 0.258819i) q^{50} +(-3.41140 + 1.16719i) q^{52} -3.92676i q^{53} +(-1.33360 + 2.30986i) q^{55} +(1.72805 + 2.99307i) q^{56} +(1.49605 - 5.58333i) q^{58} +(1.64150 - 6.12618i) q^{59} +(1.47705 + 2.55832i) q^{61} +(2.37251 - 4.10930i) q^{62} +1.00000i q^{64} +(2.99307 - 2.01036i) q^{65} +(0.654245 - 0.175304i) q^{67} +(-1.07555 - 0.620970i) q^{68} +(-2.44383 - 2.44383i) q^{70} +(-3.19576 - 0.856300i) q^{71} +(1.27743 - 1.27743i) q^{73} +(8.62551 - 4.97994i) q^{74} +(0.739470 + 2.75974i) q^{76} -9.21808 q^{77} -2.18667 q^{79} +(-0.258819 - 0.965926i) q^{80} +(-3.94462 + 2.27743i) q^{82} +(9.26996 - 9.26996i) q^{83} +(1.19962 + 0.321438i) q^{85} +(-2.31749 - 2.31749i) q^{86} +(-2.30986 - 1.33360i) q^{88} +(13.4419 - 3.60175i) q^{89} +(11.1893 + 5.48447i) q^{91} -3.03018i q^{92} +(-1.04538 + 1.81064i) q^{94} +(-1.42855 - 2.47432i) q^{95} +(3.69941 - 13.8064i) q^{97} +(1.27976 - 4.77614i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7}+O(q^{10}) \) 16 * q + 8 * q^7	\( 16 q + 8 q^{7} - 12 q^{13} + 8 q^{16} + 36 q^{19} + 12 q^{22} - 8 q^{28} - 12 q^{31} + 16 q^{34} + 20 q^{37} + 16 q^{40} + 32 q^{46} - 12 q^{49} - 24 q^{52} - 12 q^{55} + 32 q^{58} - 44 q^{61} + 4 q^{67} - 4 q^{70} - 24 q^{73} + 36 q^{76} - 24 q^{79} - 4 q^{85} + 12 q^{88} + 36 q^{91} + 56 q^{97}+O(q^{100}) \) 16 * q + 8 * q^7 - 12 * q^13 + 8 * q^16 + 36 * q^19 + 12 * q^22 - 8 * q^28 - 12 * q^31 + 16 * q^34 + 20 * q^37 + 16 * q^40 + 32 * q^46 - 12 * q^49 - 24 * q^52 - 12 * q^55 + 32 * q^58 - 44 * q^61 + 4 * q^67 - 4 * q^70 - 24 * q^73 + 36 * q^76 - 24 * q^79 - 4 * q^85 + 12 * q^88 + 36 * q^91 + 56 * q^97

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