LMFDB - Embedded newform 1014.2.g.e.437.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(239,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("1014.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			437.4
Character	$\chi$	$=$	1014.437
Dual form			1014.2.g.e.239.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.58955 - 0.688001i) q^{3} -1.00000i q^{4} +(-0.822256 + 0.822256i) q^{5} +(-0.637488 + 1.61047i) q^{6} +(-1.88206 + 1.88206i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.05331 - 2.18722i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.58955 - 0.688001i) q^{3} -1.00000i q^{4} +(-0.822256 + 0.822256i) q^{5} +(-0.637488 + 1.61047i) q^{6} +(-1.88206 + 1.88206i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.05331 - 2.18722i) q^{9} -1.16285i q^{10} +(-3.44793 - 3.44793i) q^{11} +(-0.688001 - 1.58955i) q^{12} -2.66164i q^{14} +(-0.741300 + 1.87273i) q^{15} -1.00000 q^{16} -2.82264 q^{17} +(0.0946882 + 2.99851i) q^{18} +(-3.54655 - 3.54655i) q^{19} +(0.822256 + 0.822256i) q^{20} +(-1.69676 + 4.28648i) q^{21} +4.87612 q^{22} -9.31907 q^{23} +(1.61047 + 0.637488i) q^{24} +3.64779i q^{25} +(1.75902 - 4.88936i) q^{27} +(1.88206 + 1.88206i) q^{28} +3.13597i q^{29} +(-0.800039 - 1.84840i) q^{30} +(-0.709487 - 0.709487i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.85283 - 3.10846i) q^{33} +(1.99591 - 1.99591i) q^{34} -3.09507i q^{35} +(-2.18722 - 2.05331i) q^{36} +(2.63940 - 2.63940i) q^{37} +5.01558 q^{38} -1.16285 q^{40} +(3.75468 - 3.75468i) q^{41} +(-1.83121 - 4.23079i) q^{42} -11.4077i q^{43} +(-3.44793 + 3.44793i) q^{44} +(0.110108 + 3.48680i) q^{45} +(6.58958 - 6.58958i) q^{46} +(8.45064 + 8.45064i) q^{47} +(-1.58955 + 0.688001i) q^{48} -0.0843165i q^{49} +(-2.57938 - 2.57938i) q^{50} +(-4.48671 + 1.94198i) q^{51} -1.57037i q^{53} +(2.21349 + 4.70111i) q^{54} +5.67017 q^{55} -2.66164 q^{56} +(-8.07744 - 3.19738i) q^{57} +(-2.21746 - 2.21746i) q^{58} +(-3.86562 - 3.86562i) q^{59} +(1.87273 + 0.741300i) q^{60} -9.76025 q^{61} +1.00337 q^{62} +(0.252026 + 7.98094i) q^{63} +1.00000i q^{64} +(7.75081 - 3.35477i) q^{66} +(-7.61273 - 7.61273i) q^{67} +2.82264i q^{68} +(-14.8131 + 6.41153i) q^{69} +(2.18855 + 2.18855i) q^{70} +(-0.592330 + 0.592330i) q^{71} +(2.99851 - 0.0946882i) q^{72} +(-6.42392 + 6.42392i) q^{73} +3.73268i q^{74} +(2.50968 + 5.79833i) q^{75} +(-3.54655 + 3.54655i) q^{76} +12.9785 q^{77} -5.98452 q^{79} +(0.822256 - 0.822256i) q^{80} +(-0.567846 - 8.98207i) q^{81} +5.30992i q^{82} +(-1.75308 + 1.75308i) q^{83} +(4.28648 + 1.69676i) q^{84} +(2.32093 - 2.32093i) q^{85} +(8.06650 + 8.06650i) q^{86} +(2.15755 + 4.98476i) q^{87} -4.87612i q^{88} +(-4.76763 - 4.76763i) q^{89} +(-2.54340 - 2.38768i) q^{90} +9.31907i q^{92} +(-1.61589 - 0.639634i) q^{93} -11.9510 q^{94} +5.83235 q^{95} +(0.637488 - 1.61047i) q^{96} +(7.52524 + 7.52524i) q^{97} +(0.0596207 + 0.0596207i) q^{98} +(-14.6211 + 0.461711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 + 20 * q^9	$ 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) $ 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	1.58955	−	0.688001i	0.917724	−	0.397218i
$3$	1.58955	−	0.688001i	0.917724	−	0.397218i
$4$		−	1.00000i		−	0.500000i
$5$	−0.822256	+	0.822256i	−0.367724	+	0.367724i	−0.866647	−	0.498922i	$-0.833729\pi$
$5$	−0.822256	+	0.822256i	−0.367724	+	0.367724i	0.498922	+	0.866647i	$0.333729\pi$
$6$	−0.637488	+	1.61047i	−0.260253	+	0.657471i
$7$	−1.88206	+	1.88206i	−0.711353	+	0.711353i	−0.966818	−	0.255466i	$-0.917771\pi$
$7$	−1.88206	+	1.88206i	−0.711353	+	0.711353i	0.255466	+	0.966818i	$0.417771\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.05331	−	2.18722i	0.684436	−	0.729073i
$10$		−	1.16285i		−	0.367724i
$11$	−3.44793	−	3.44793i	−1.03959	−	1.03959i	−0.999183	−	0.0404080i	$-0.987134\pi$
$11$	−3.44793	−	3.44793i	−1.03959	−	1.03959i	−0.0404080	−	0.999183i	$-0.512866\pi$
$12$	−0.688001	−	1.58955i	−0.198609	−	0.458862i
$13$		0			0
$13$		0			0
$14$		−	2.66164i		−	0.711353i
$15$	−0.741300	+	1.87273i	−0.191403	+	0.483536i
$16$	−1.00000			−0.250000
$17$	−2.82264			−0.684590			−0.342295	−	0.939592i	$-0.611204\pi$
$17$	−2.82264			−0.684590			−0.342295	+	0.939592i	$0.611204\pi$
$18$	0.0946882	+	2.99851i	0.0223182	+	0.706754i
$19$	−3.54655	−	3.54655i	−0.813635	−	0.813635i	0.171542	−	0.985177i	$-0.445125\pi$
$19$	−3.54655	−	3.54655i	−0.813635	−	0.813635i	−0.985177	+	0.171542i	$0.945125\pi$
$20$	0.822256	+	0.822256i	0.183862	+	0.183862i
$21$	−1.69676	+	4.28648i	−0.370264	+	0.935388i
$22$	4.87612			1.03959
$23$	−9.31907			−1.94316			−0.971580	−	0.236712i	$-0.923930\pi$
$23$	−9.31907			−1.94316			−0.971580	+	0.236712i	$0.923930\pi$
$24$	1.61047	+	0.637488i	0.328736	+	0.130127i
$25$			3.64779i			0.729558i
$26$		0			0
$27$	1.75902	−	4.88936i	0.338523	−	0.940958i
$28$	1.88206	+	1.88206i	0.355676	+	0.355676i
$29$			3.13597i			0.582334i	0.956672	+	0.291167i	$0.0940436\pi$
$29$			3.13597i			0.582334i	−0.956672	+	0.291167i	$0.905956\pi$
$30$	−0.800039	−	1.84840i	−0.146067	−	0.337469i
$31$	−0.709487	−	0.709487i	−0.127428	−	0.127428i	0.640517	−	0.767944i	$-0.278720\pi$
$31$	−0.709487	−	0.709487i	−0.127428	−	0.127428i	−0.767944	+	0.640517i	$0.778720\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−7.85283	−	3.10846i	−1.36700	−	0.541114i
$34$	1.99591	−	1.99591i	0.342295	−	0.342295i
$35$		−	3.09507i		−	0.523163i
$36$	−2.18722	−	2.05331i	−0.364536	−	0.342218i
$37$	2.63940	−	2.63940i	0.433915	−	0.433915i	−0.456043	−	0.889958i	$-0.650734\pi$
$37$	2.63940	−	2.63940i	0.433915	−	0.433915i	0.889958	+	0.456043i	$0.150734\pi$
$38$	5.01558			0.813635
$39$		0			0
$40$	−1.16285			−0.183862
$41$	3.75468	−	3.75468i	0.586382	−	0.586382i	−0.350268	−	0.936650i	$-0.613909\pi$
$41$	3.75468	−	3.75468i	0.586382	−	0.586382i	0.936650	+	0.350268i	$0.113909\pi$
$42$	−1.83121	−	4.23079i	−0.282562	−	0.652826i
$43$		−	11.4077i		−	1.73967i	−0.493347	−	0.869833i	$-0.664227\pi$
$43$		−	11.4077i		−	1.73967i	0.493347	−	0.869833i	$-0.335773\pi$
$44$	−3.44793	+	3.44793i	−0.519796	+	0.519796i
$45$	0.110108	+	3.48680i	0.0164139	+	0.519781i
$46$	6.58958	−	6.58958i	0.971580	−	0.971580i
$47$	8.45064	+	8.45064i	1.23265	+	1.23265i	0.962941	+	0.269711i	$0.0869281\pi$
$47$	8.45064	+	8.45064i	1.23265	+	1.23265i	0.269711	+	0.962941i	$0.413072\pi$
$48$	−1.58955	+	0.688001i	−0.229431	+	0.0993044i
$49$		−	0.0843165i		−	0.0120452i
$50$	−2.57938	−	2.57938i	−0.364779	−	0.364779i
$51$	−4.48671	+	1.94198i	−0.628265	+	0.271931i
$52$		0			0
$53$		−	1.57037i		−	0.215707i	−0.994167	−	0.107853i	$-0.965602\pi$
$53$		−	1.57037i		−	0.215707i	0.994167	−	0.107853i	$-0.0343977\pi$
$54$	2.21349	+	4.70111i	0.301217	+	0.639741i
$55$	5.67017			0.764566
$56$	−2.66164			−0.355676
$57$	−8.07744	−	3.19738i	−1.06988	−	0.423503i
$58$	−2.21746	−	2.21746i	−0.291167	−	0.291167i
$59$	−3.86562	−	3.86562i	−0.503261	−	0.503261i	0.409189	−	0.912450i	$-0.365812\pi$
$59$	−3.86562	−	3.86562i	−0.503261	−	0.503261i	−0.912450	+	0.409189i	$0.865812\pi$
$60$	1.87273	+	0.741300i	0.241768	+	0.0957014i
$61$	−9.76025			−1.24967			−0.624836	−	0.780756i	$-0.714834\pi$
$61$	−9.76025			−1.24967			−0.624836	+	0.780756i	$0.714834\pi$
$62$	1.00337			0.127428
$63$	0.252026	+	7.98094i	0.0317523	+	1.00550i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	7.75081	−	3.35477i	0.954058	−	0.412944i
$67$	−7.61273	−	7.61273i	−0.930043	−	0.930043i	0.0676653	−	0.997708i	$-0.478445\pi$
$67$	−7.61273	−	7.61273i	−0.930043	−	0.930043i	−0.997708	+	0.0676653i	$0.978445\pi$
$68$			2.82264i			0.342295i
$69$	−14.8131	+	6.41153i	−1.78329	+	0.771857i
$70$	2.18855	+	2.18855i	0.261582	+	0.261582i
$71$	−0.592330	+	0.592330i	−0.0702966	+	0.0702966i	−0.741381	−	0.671084i	$-0.765829\pi$
$71$	−0.592330	+	0.592330i	−0.0702966	+	0.0702966i	0.671084	+	0.741381i	$0.265829\pi$
$72$	2.99851	−	0.0946882i	0.353377	−	0.0111591i
$73$	−6.42392	+	6.42392i	−0.751863	+	0.751863i	−0.974827	−	0.222964i	$-0.928427\pi$
$73$	−6.42392	+	6.42392i	−0.751863	+	0.751863i	0.222964	+	0.974827i	$0.428427\pi$
$74$			3.73268i			0.433915i
$75$	2.50968	+	5.79833i	0.289793	+	0.669533i
$76$	−3.54655	+	3.54655i	−0.406818	+	0.406818i
$77$	12.9785			1.47903
$78$		0			0
$79$	−5.98452			−0.673311			−0.336655	−	0.941628i	$-0.609296\pi$
$79$	−5.98452			−0.673311			−0.336655	+	0.941628i	$0.609296\pi$
$80$	0.822256	−	0.822256i	0.0919310	−	0.0919310i
$81$	−0.567846	−	8.98207i	−0.0630940	−	0.998008i
$82$			5.30992i			0.586382i
$83$	−1.75308	+	1.75308i	−0.192426	+	0.192426i	−0.796744	−	0.604318i	$-0.793446\pi$
$83$	−1.75308	+	1.75308i	−0.192426	+	0.192426i	0.604318	+	0.796744i	$0.293446\pi$
$84$	4.28648	+	1.69676i	0.467694	+	0.185132i
$85$	2.32093	−	2.32093i	0.251740	−	0.251740i
$86$	8.06650	+	8.06650i	0.869833	+	0.869833i
$87$	2.15755	+	4.98476i	0.231313	+	0.534422i
$88$		−	4.87612i		−	0.519796i
$89$	−4.76763	−	4.76763i	−0.505368	−	0.505368i	0.407733	−	0.913101i	$-0.366319\pi$
$89$	−4.76763	−	4.76763i	−0.505368	−	0.505368i	−0.913101	+	0.407733i	$0.866319\pi$
$90$	−2.54340	−	2.38768i	−0.268098	−	0.251684i
$91$		0			0
$92$			9.31907i			0.971580i
$93$	−1.61589	−	0.639634i	−0.167560	−	0.0663269i
$94$	−11.9510			−1.23265
$95$	5.83235			0.598387
$96$	0.637488	−	1.61047i	0.0650633	−	0.164368i
$97$	7.52524	+	7.52524i	0.764072	+	0.764072i	0.977056	−	0.212984i	$-0.0683182\pi$
$97$	7.52524	+	7.52524i	0.764072	+	0.764072i	−0.212984	+	0.977056i	$0.568318\pi$
$98$	0.0596207	+	0.0596207i	0.00602260	+	0.00602260i
$99$	−14.6211	+	0.461711i	−1.46947	+	0.0464037i
$100$	3.64779			0.364779
$101$	1.54909			0.154140			0.0770700	−	0.997026i	$-0.475444\pi$
$101$	1.54909			0.154140			0.0770700	+	0.997026i	$0.475444\pi$
$102$	1.79940	−	4.54577i	0.178167	−	0.450098i
$103$			8.25369i			0.813260i	0.913593	+	0.406630i	$0.133296\pi$
$103$			8.25369i			0.813260i	−0.913593	+	0.406630i	$0.866704\pi$
$104$		0			0
$105$	−2.12941	−	4.91976i	−0.207810	−	0.480120i
$106$	1.11042	+	1.11042i	0.107853	+	0.107853i
$107$			15.4267i			1.49136i	0.666306	+	0.745678i	$0.267874\pi$
$107$			15.4267i			1.49136i	−0.666306	+	0.745678i	$0.732126\pi$
$108$	−4.88936	−	1.75902i	−0.470479	−	0.169262i
$109$	−4.36899	−	4.36899i	−0.418473	−	0.418473i	0.466204	−	0.884677i	$-0.345621\pi$
$109$	−4.36899	−	4.36899i	−0.418473	−	0.418473i	−0.884677	+	0.466204i	$0.845621\pi$
$110$	−4.00942	+	4.00942i	−0.382283	+	0.382283i
$111$	2.37954	−	6.01136i	0.225856	−	0.570573i
$112$	1.88206	−	1.88206i	0.177838	−	0.177838i
$113$		−	8.13383i		−	0.765166i	−0.923921	−	0.382583i	$-0.875035\pi$
$113$		−	8.13383i		−	0.765166i	0.923921	−	0.382583i	$-0.124965\pi$
$114$	7.97250	−	3.45073i	0.746693	−	0.323190i
$115$	7.66266	−	7.66266i	0.714547	−	0.714547i
$116$	3.13597			0.291167
$117$		0			0
$118$	5.46682			0.503261
$119$	5.31238	−	5.31238i	0.486985	−	0.486985i
$120$	−1.84840	+	0.800039i	−0.168735	+	0.0730333i
$121$			12.7765i			1.16150i
$122$	6.90154	−	6.90154i	0.624836	−	0.624836i
$123$	3.38501	−	8.55145i	0.305216	−	0.771058i
$124$	−0.709487	+	0.709487i	−0.0637138	+	0.0637138i
$125$	−7.11070	−	7.11070i	−0.636000	−	0.636000i
$126$	−5.82158	−	5.46516i	−0.518628	−	0.486876i
$127$		−	3.06842i		−	0.272278i	−0.990690	−	0.136139i	$-0.956531\pi$
$127$		−	3.06842i		−	0.272278i	0.990690	−	0.136139i	$-0.0434694\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	−7.84855	−	18.1331i	−0.691026	−	1.59653i
$130$		0			0
$131$		−	5.37936i		−	0.469997i	−0.971996	−	0.234998i	$-0.924491\pi$
$131$		−	5.37936i		−	0.469997i	0.971996	−	0.234998i	$-0.0755085\pi$
$132$	−3.10846	+	7.85283i	−0.270557	+	0.683501i
$133$	13.3497			1.15756
$134$	10.7660			0.930043
$135$	2.57394	+	5.46667i	0.221530	+	0.470496i
$136$	−1.99591	−	1.99591i	−0.171148	−	0.171148i
$137$	11.7925	+	11.7925i	1.00750	+	1.00750i	0.999972	+	0.00752981i	$0.00239683\pi$
$137$	11.7925	+	11.7925i	1.00750	+	1.00750i	0.00752981	+	0.999972i	$0.497603\pi$
$138$	5.94079	−	15.0081i	0.505714	−	1.27757i
$139$	−7.60785			−0.645289			−0.322645	−	0.946520i	$-0.604572\pi$
$139$	−7.60785			−0.645289			−0.322645	+	0.946520i	$0.604572\pi$
$140$	−3.09507			−0.261582
$141$	19.2467	+	7.61862i	1.62087	+	0.641604i
$142$		−	0.837681i		−	0.0702966i
$143$		0			0
$144$	−2.05331	+	2.18722i	−0.171109	+	0.182268i
$145$	−2.57857	−	2.57857i	−0.214138	−	0.214138i
$146$		−	9.08479i		−	0.751863i
$147$	−0.0580098	−	0.134025i	−0.00478457	−	0.0110542i
$148$	−2.63940	−	2.63940i	−0.216958	−	0.216958i
$149$	−4.37217	+	4.37217i	−0.358182	+	0.358182i	−0.863143	−	0.504960i	$-0.831507\pi$
$149$	−4.37217	+	4.37217i	−0.358182	+	0.358182i	0.504960	+	0.863143i	$0.331507\pi$
$150$	−5.87465	−	2.32542i	−0.479663	−	0.189870i
$151$	14.5041	−	14.5041i	1.18033	−	1.18033i	0.200672	−	0.979659i	$-0.435688\pi$
$151$	14.5041	−	14.5041i	1.18033	−	1.18033i	0.979659	−	0.200672i	$-0.0643125\pi$
$152$		−	5.01558i		−	0.406818i
$153$	−5.79575	+	6.17373i	−0.468558	+	0.499116i
$154$	−9.17715	+	9.17715i	−0.739516	+	0.739516i
$155$	1.16676			0.0937164
$156$		0			0
$157$	3.72776			0.297508			0.148754	−	0.988874i	$-0.452474\pi$
$157$	3.72776			0.297508			0.148754	+	0.988874i	$0.452474\pi$
$158$	4.23169	−	4.23169i	0.336655	−	0.336655i
$159$	−1.08042	−	2.49617i	−0.0856826	−	0.197959i
$160$			1.16285i			0.0919310i
$161$	17.5391	−	17.5391i	1.38227	−	1.38227i
$162$	6.75281	+	5.94975i	0.530551	+	0.467457i
$163$	−7.87765	+	7.87765i	−0.617026	+	0.617026i	−0.944767	−	0.327742i	$-0.893712\pi$
$163$	−7.87765	+	7.87765i	−0.617026	+	0.617026i	0.327742	+	0.944767i	$0.393712\pi$
$164$	−3.75468	−	3.75468i	−0.293191	−	0.293191i
$165$	9.01299	−	3.90108i	0.701660	−	0.303699i
$166$		−	2.47924i		−	0.192426i
$167$	−4.67144	−	4.67144i	−0.361487	−	0.361487i	0.502873	−	0.864360i	$-0.332276\pi$
$167$	−4.67144	−	4.67144i	−0.361487	−	0.361487i	−0.864360	+	0.502873i	$0.832276\pi$
$168$	−4.23079	+	1.83121i	−0.326413	+	0.141281i
$169$		0			0
$170$			3.28229i			0.251740i
$171$	−15.0393	+	0.474917i	−1.15008	+	0.0363178i
$172$	−11.4077			−0.869833
$173$	22.3305			1.69776			0.848879	−	0.528588i	$-0.177278\pi$
$173$	22.3305			1.69776			0.848879	+	0.528588i	$0.177278\pi$
$174$	−5.05037	−	1.99914i	−0.382868	−	0.151554i
$175$	−6.86537	−	6.86537i	−0.518973	−	0.518973i
$176$	3.44793	+	3.44793i	0.259898	+	0.259898i
$177$	−8.80414	−	3.48503i	−0.661759	−	0.261951i
$178$	6.74245			0.505368
$179$	7.10787			0.531267			0.265634	−	0.964074i	$-0.414419\pi$
$179$	7.10787			0.531267			0.265634	+	0.964074i	$0.414419\pi$
$180$	3.48680	−	0.110108i	0.259891	−	0.00820695i
$181$		−	15.6822i		−	1.16565i	−0.812599	−	0.582823i	$-0.801948\pi$
$181$		−	15.6822i		−	1.16565i	0.812599	−	0.582823i	$-0.198052\pi$
$182$		0			0
$183$	−15.5144	+	6.71507i	−1.14686	+	0.496392i
$184$	−6.58958	−	6.58958i	−0.485790	−	0.485790i
$185$			4.34053i			0.319122i
$186$	1.59490	−	0.690317i	0.116943	−	0.0506165i
$187$	9.73227	+	9.73227i	0.711694	+	0.711694i
$188$	8.45064	−	8.45064i	0.616326	−	0.616326i
$189$	5.89150	+	12.5127i	0.428544	+	0.910162i
$190$	−4.12410	+	4.12410i	−0.299193	+	0.299193i
$191$			21.5435i			1.55883i	0.626507	+	0.779416i	$0.284484\pi$
$191$			21.5435i			1.55883i	−0.626507	+	0.779416i	$0.715516\pi$
$192$	0.688001	+	1.58955i	0.0496522	+	0.114716i
$193$	−1.41440	+	1.41440i	−0.101811	+	0.101811i	−0.756178	−	0.654366i	$-0.772935\pi$
$193$	−1.41440	+	1.41440i	−0.101811	+	0.101811i	0.654366	+	0.756178i	$0.272935\pi$
$194$	−10.6423			−0.764072
$195$		0			0
$196$	−0.0843165			−0.00602260
$197$	0.806866	−	0.806866i	0.0574868	−	0.0574868i	−0.677779	−	0.735266i	$-0.737057\pi$
$197$	0.806866	−	0.806866i	0.0574868	−	0.0574868i	0.735266	+	0.677779i	$0.237057\pi$
$198$	10.0122	−	10.6651i	0.711534	−	0.757938i
$199$		−	4.41361i		−	0.312873i	−0.987688	−	0.156436i	$-0.949999\pi$
$199$		−	4.41361i		−	0.312873i	0.987688	−	0.156436i	$-0.0500006\pi$
$200$	−2.57938	+	2.57938i	−0.182389	+	0.182389i
$201$	−17.3383	−	6.86321i	−1.22295	−	0.484094i
$202$	−1.09537	+	1.09537i	−0.0770700	+	0.0770700i
$203$	−5.90208	−	5.90208i	−0.414245	−	0.414245i
$204$	1.94198	+	4.48671i	0.135966	+	0.314133i
$205$			6.17461i			0.431254i
$206$	−5.83624	−	5.83624i	−0.406630	−	0.406630i
$207$	−19.1349	+	20.3828i	−1.32997	+	1.41670i
$208$		0			0
$209$			24.4566i			1.69170i
$210$	4.98452	+	1.97307i	0.343965	+	0.136155i
$211$	5.83278			0.401545			0.200772	−	0.979638i	$-0.435655\pi$
$211$	5.83278			0.401545			0.200772	+	0.979638i	$0.435655\pi$
$212$	−1.57037			−0.107853
$213$	−0.534012	+	1.34906i	−0.0365899	+	0.0924360i
$214$	−10.9083	−	10.9083i	−0.745678	−	0.745678i
$215$	9.38009	+	9.38009i	0.639717	+	0.639717i
$216$	4.70111	−	2.21349i	0.319870	−	0.150609i
$217$	2.67060			0.181292
$218$	6.17868			0.418473
$219$	−5.79145	+	14.6308i	−0.391350	+	0.988656i
$220$		−	5.67017i		−	0.382283i
$221$		0			0
$222$	2.56809	+	5.93326i	0.172359	+	0.398214i
$223$	14.0220	+	14.0220i	0.938985	+	0.938985i	0.998243	−	0.0592580i	$-0.0188735\pi$
$223$	14.0220	+	14.0220i	0.938985	+	0.938985i	−0.0592580	+	0.998243i	$0.518873\pi$
$224$			2.66164i			0.177838i
$225$	7.97851	+	7.49004i	0.531901	+	0.499336i
$226$	5.75149	+	5.75149i	0.382583	+	0.382583i
$227$	7.06921	−	7.06921i	0.469200	−	0.469200i	−0.432455	−	0.901655i	$-0.642353\pi$
$227$	7.06921	−	7.06921i	0.469200	−	0.469200i	0.901655	+	0.432455i	$0.142353\pi$
$228$	−3.19738	+	8.07744i	−0.211751	+	0.534942i
$229$	0.591631	−	0.591631i	0.0390961	−	0.0390961i	−0.687288	−	0.726385i	$-0.741199\pi$
$229$	0.591631	−	0.591631i	0.0390961	−	0.0390961i	0.726385	+	0.687288i	$0.241199\pi$
$230$			10.8366i			0.714547i
$231$	20.6298	−	8.92919i	1.35734	−	0.587498i
$232$	−2.21746	+	2.21746i	−0.145584	+	0.145584i
$233$	5.78203			0.378793			0.189397	−	0.981901i	$-0.439347\pi$
$233$	5.78203			0.378793			0.189397	+	0.981901i	$0.439347\pi$
$234$		0			0
$235$	−13.8972			−0.906552
$236$	−3.86562	+	3.86562i	−0.251631	+	0.251631i
$237$	−9.51266	+	4.11736i	−0.617914	+	0.267451i
$238$			7.51284i			0.486985i
$239$	−8.54771	+	8.54771i	−0.552906	+	0.552906i	−0.927278	−	0.374373i	$-0.877858\pi$
$239$	−8.54771	+	8.54771i	−0.552906	+	0.552906i	0.374373	+	0.927278i	$0.377858\pi$
$240$	0.741300	−	1.87273i	0.0478507	−	0.120884i
$241$	−8.48784	+	8.48784i	−0.546750	+	0.546750i	−0.925499	−	0.378749i	$-0.876354\pi$
$241$	−8.48784	+	8.48784i	−0.546750	+	0.546750i	0.378749	+	0.925499i	$0.376354\pi$
$242$	−9.03435	−	9.03435i	−0.580750	−	0.580750i
$243$	−7.08229	−	13.8867i	−0.454329	−	0.890834i
$244$			9.76025i			0.624836i
$245$	0.0693297	+	0.0693297i	0.00442931	+	0.00442931i
$246$	3.65323	+	8.44035i	0.232921	+	0.538137i
$247$		0			0
$248$		−	1.00337i		−	0.0637138i
$249$	−1.58048	+	3.99273i	−0.100159	+	0.253029i
$250$	10.0560			0.636000
$251$	24.8857			1.57077			0.785385	−	0.619008i	$-0.212465\pi$
$251$	24.8857			1.57077			0.785385	+	0.619008i	$0.212465\pi$
$252$	7.98094	−	0.252026i	0.502752	−	0.0158761i
$253$	32.1315	+	32.1315i	2.02009	+	2.02009i
$254$	2.16970	+	2.16970i	0.136139	+	0.136139i
$255$	2.09242	−	5.28603i	0.131033	−	0.331024i
$256$	1.00000			0.0625000
$257$	−2.69028			−0.167815			−0.0839074	−	0.996474i	$-0.526740\pi$
$257$	−2.69028			−0.167815			−0.0839074	+	0.996474i	$0.526740\pi$
$258$	18.3718	+	7.27230i	1.14378	+	0.452754i
$259$			9.93504i			0.617333i
$260$		0			0
$261$	6.85904	+	6.43911i	0.424564	+	0.398571i
$262$	3.80378	+	3.80378i	0.234998	+	0.234998i
$263$		−	9.02425i		−	0.556459i	−0.960515	−	0.278230i	$-0.910252\pi$
$263$		−	9.02425i		−	0.556459i	0.960515	−	0.278230i	$-0.0897476\pi$
$264$	−3.35477	−	7.75081i	−0.206472	−	0.477029i
$265$	1.29125	+	1.29125i	0.0793206	+	0.0793206i
$266$	−9.43964	+	9.43964i	−0.578782	+	0.578782i
$267$	−10.8585	−	4.29823i	−0.664530	−	0.263048i
$268$	−7.61273	+	7.61273i	−0.465021	+	0.465021i
$269$			16.0804i			0.980439i	0.871599	+	0.490220i	$0.163083\pi$
$269$			16.0804i			0.980439i	−0.871599	+	0.490220i	$0.836917\pi$
$270$	−5.68557	−	2.04547i	−0.346013	−	0.124483i
$271$	6.94216	−	6.94216i	0.421706	−	0.421706i	−0.464085	−	0.885791i	$-0.653617\pi$
$271$	6.94216	−	6.94216i	0.421706	−	0.421706i	0.885791	+	0.464085i	$0.153617\pi$
$272$	2.82264			0.171148
$273$		0			0
$274$	−16.6771			−1.00750
$275$	12.5773	−	12.5773i	0.758442	−	0.758442i
$276$	6.41153	+	14.8131i	0.385929	+	0.891643i
$277$		−	14.1165i		−	0.848181i	−0.905620	−	0.424090i	$-0.860594\pi$
$277$		−	14.1165i		−	0.848181i	0.905620	−	0.424090i	$-0.139406\pi$
$278$	5.37956	−	5.37956i	0.322645	−	0.322645i
$279$	−3.00860	+	0.0950070i	−0.180120	+	0.00568792i
$280$	2.18855	−	2.18855i	0.130791	−	0.130791i
$281$	−2.66164	−	2.66164i	−0.158780	−	0.158780i	0.623246	−	0.782026i	$-0.285814\pi$
$281$	−2.66164	−	2.66164i	−0.158780	−	0.158780i	−0.782026	+	0.623246i	$0.785814\pi$
$282$	−18.9967	+	8.22231i	−1.13123	+	0.489631i
$283$			6.41512i			0.381339i	0.981654	+	0.190670i	$0.0610659\pi$
$283$			6.41512i			0.381339i	−0.981654	+	0.190670i	$0.938934\pi$
$284$	0.592330	+	0.592330i	0.0351483	+	0.0351483i
$285$	9.27079	−	4.01266i	0.549154	−	0.237690i
$286$		0			0
$287$			14.1331i			0.834249i
$288$	−0.0946882	−	2.99851i	−0.00557956	−	0.176689i
$289$	−9.03271			−0.531336
$290$	3.64664			0.214138
$291$	17.1391	+	6.78433i	1.00471	+	0.397705i
$292$	6.42392	+	6.42392i	0.375931	+	0.375931i
$293$	−17.1258	−	17.1258i	−1.00050	−	1.00050i	−1.00000		0.000502152i	$-0.999840\pi$
$293$	−17.1258	−	17.1258i	−1.00050	−	1.00050i	−0.000502152	−	1.00000i	$-0.500160\pi$
$294$	0.135789	+	0.0537507i	0.00791938	+	0.00313481i
$295$	6.35706			0.370123
$296$	3.73268			0.216958
$297$	−22.9232	+	10.7932i	−1.33014	+	0.626286i
$298$		−	6.18318i		−	0.358182i
$299$		0			0
$300$	5.79833	−	2.50968i	0.334767	−	0.144897i
$301$	21.4701	+	21.4701i	1.23752	+	1.23752i
$302$			20.5120i			1.18033i
$303$	2.46235	−	1.06577i	0.141458	−	0.0612271i
$304$	3.54655	+	3.54655i	0.203409	+	0.203409i
$305$	8.02543	−	8.02543i	0.459535	−	0.459535i
$306$	−0.267271	−	8.46370i	−0.0152788	−	0.483837i
$307$	7.63473	−	7.63473i	0.435737	−	0.435737i	−0.454837	−	0.890574i	$-0.650303\pi$
$307$	7.63473	−	7.63473i	0.435737	−	0.435737i	0.890574	+	0.454837i	$0.150303\pi$
$308$		−	12.9785i		−	0.739516i
$309$	5.67855	+	13.1196i	0.323041	+	0.746349i
$310$	−0.825024	+	0.825024i	−0.0468582	+	0.0468582i
$311$	−7.03599			−0.398974			−0.199487	−	0.979900i	$-0.563928\pi$
$311$	−7.03599			−0.398974			−0.199487	+	0.979900i	$0.563928\pi$
$312$		0			0
$313$	26.0455			1.47218			0.736089	−	0.676885i	$-0.236670\pi$
$313$	26.0455			1.47218			0.736089	+	0.676885i	$0.236670\pi$
$314$	−2.63593	+	2.63593i	−0.148754	+	0.148754i
$315$	−6.76960	−	6.35514i	−0.381424	−	0.358072i
$316$			5.98452i			0.336655i
$317$	4.59387	−	4.59387i	0.258018	−	0.258018i	−0.566230	−	0.824247i	$-0.691599\pi$
$317$	4.59387	−	4.59387i	0.258018	−	0.258018i	0.824247	+	0.566230i	$0.191599\pi$
$318$	2.52903	+	1.00109i	0.141821	+	0.0561384i
$319$	10.8126	−	10.8126i	0.605390	−	0.605390i
$320$	−0.822256	−	0.822256i	−0.0459655	−	0.0459655i
$321$	10.6136	+	24.5215i	0.592393	+	1.36865i
$322$			24.8040i			1.38227i
$323$	10.0106	+	10.0106i	0.557007	+	0.557007i
$324$	−8.98207	+	0.567846i	−0.499004	+	0.0315470i
$325$		0			0
$326$		−	11.1407i		−	0.617026i
$327$	−9.95057	−	3.93884i	−0.550268	−	0.217818i
$328$	5.30992			0.293191
$329$	−31.8093			−1.75370
$330$	−3.61467	+	9.13163i	−0.198981	+	0.502680i
$331$	−15.0240	−	15.0240i	−0.825791	−	0.825791i	0.161140	−	0.986932i	$-0.448483\pi$
$331$	−15.0240	−	15.0240i	−0.825791	−	0.825791i	−0.986932	+	0.161140i	$0.948483\pi$
$332$	1.75308	+	1.75308i	0.0962130	+	0.0962130i
$333$	−0.353441	−	11.1925i	−0.0193684	−	0.613343i
$334$	6.60642			0.361487
$335$	12.5192			0.683998
$336$	1.69676	−	4.28648i	0.0925660	−	0.233847i
$337$		−	17.1577i		−	0.934640i	−0.884088	−	0.467320i	$-0.845220\pi$
$337$		−	17.1577i		−	0.934640i	0.884088	−	0.467320i	$-0.154780\pi$
$338$		0			0
$339$	−5.59608	−	12.9291i	−0.303938	−	0.702212i
$340$	−2.32093	−	2.32093i	−0.125870	−	0.125870i
$341$			4.89253i			0.264945i
$342$	10.2985	−	10.9702i	0.556881	−	0.593199i
$343$	−13.0157	−	13.0157i	−0.702784	−	0.702784i
$344$	8.06650	−	8.06650i	0.434916	−	0.434916i
$345$	6.90823	−	17.4521i	0.371926	−	0.939588i
$346$	−15.7901	+	15.7901i	−0.848879	+	0.848879i
$347$		−	15.3476i		−	0.823903i	−0.911206	−	0.411951i	$-0.864847\pi$
$347$		−	15.3476i		−	0.823903i	0.911206	−	0.411951i	$-0.135153\pi$
$348$	4.98476	−	2.15755i	0.267211	−	0.115657i
$349$	−15.5574	+	15.5574i	−0.832768	+	0.832768i	−0.987895	−	0.155127i	$-0.950421\pi$
$349$	−15.5574	+	15.5574i	−0.832768	+	0.832768i	0.155127	+	0.987895i	$0.450421\pi$
$350$	9.70910			0.518973
$351$		0			0
$352$	−4.87612			−0.259898
$353$	−13.6277	+	13.6277i	−0.725331	+	0.725331i	−0.969686	−	0.244355i	$-0.921424\pi$
$353$	−13.6277	+	13.6277i	−0.725331	+	0.725331i	0.244355	+	0.969686i	$0.421424\pi$
$354$	8.68975	−	3.76118i	0.461855	−	0.199904i
$355$		−	0.974094i		−	0.0516995i
$356$	−4.76763	+	4.76763i	−0.252684	+	0.252684i
$357$	4.78935	−	12.0992i	0.253479	−	0.640357i
$358$	−5.02602	+	5.02602i	−0.265634	+	0.265634i
$359$	4.32758	+	4.32758i	0.228401	+	0.228401i	0.812024	−	0.583624i	$-0.198366\pi$
$359$	4.32758	+	4.32758i	0.228401	+	0.228401i	−0.583624	+	0.812024i	$0.698366\pi$
$360$	−2.38768	+	2.54340i	−0.125842	+	0.134049i
$361$			6.15609i			0.324005i
$362$	11.0890	+	11.0890i	0.582823	+	0.582823i
$363$	8.79025	+	20.3088i	0.461368	+	1.06594i
$364$		0			0
$365$		−	10.5642i		−	0.552956i
$366$	6.22205	−	15.7186i	0.325232	−	0.821624i
$367$	−29.4161			−1.53551			−0.767754	−	0.640745i	$-0.778626\pi$
$367$	−29.4161			−1.53551			−0.767754	+	0.640745i	$0.778626\pi$
$368$	9.31907			0.485790
$369$	−0.502787	−	15.9218i	−0.0261740	−	0.828856i
$370$	−3.06922	−	3.06922i	−0.159561	−	0.159561i
$371$	2.95553	+	2.95553i	0.153444	+	0.153444i
$372$	−0.639634	+	1.61589i	−0.0331635	+	0.0837800i
$373$	−22.5803			−1.16916			−0.584581	−	0.811335i	$-0.698741\pi$
$373$	−22.5803			−1.16916			−0.584581	+	0.811335i	$0.698741\pi$
$374$	−13.7635			−0.711694
$375$	−16.1949	−	6.41061i	−0.836303	−	0.331042i
$376$			11.9510i			0.616326i
$377$		0			0
$378$	−13.0137	−	4.68187i	−0.669353	−	0.240809i
$379$	−9.81124	−	9.81124i	−0.503969	−	0.503969i	0.408700	−	0.912669i	$-0.365982\pi$
$379$	−9.81124	−	9.81124i	−0.503969	−	0.503969i	−0.912669	+	0.408700i	$0.865982\pi$
$380$		−	5.83235i		−	0.299193i
$381$	−2.11108	−	4.87739i	−0.108154	−	0.249876i
$382$	−15.2335	−	15.2335i	−0.779416	−	0.779416i
$383$	4.63172	−	4.63172i	0.236670	−	0.236670i	−0.578800	−	0.815470i	$-0.696479\pi$
$383$	4.63172	−	4.63172i	0.236670	−	0.236670i	0.815470	+	0.578800i	$0.196479\pi$
$384$	−1.61047	−	0.637488i	−0.0821839	−	0.0325317i
$385$	−10.6716	+	10.6716i	−0.543876	+	0.543876i
$386$		−	2.00027i		−	0.101811i
$387$	−24.9512	−	23.4236i	−1.26834	−	1.19069i
$388$	7.52524	−	7.52524i	0.382036	−	0.382036i
$389$	−1.58518			−0.0803720			−0.0401860	−	0.999192i	$-0.512795\pi$
$389$	−1.58518			−0.0803720			−0.0401860	+	0.999192i	$0.512795\pi$
$390$		0			0
$391$	26.3044			1.33027
$392$	0.0596207	−	0.0596207i	0.00301130	−	0.00301130i
$393$	−3.70101	−	8.55074i	−0.186691	−	0.431328i
$394$			1.14108i			0.0574868i
$395$	4.92081	−	4.92081i	0.247593	−	0.247593i
$396$	0.461711	+	14.6211i	0.0232018	+	0.734736i
$397$	−8.72316	+	8.72316i	−0.437803	+	0.437803i	−0.891272	−	0.453469i	$-0.850186\pi$
$397$	−8.72316	+	8.72316i	−0.437803	+	0.437803i	0.453469	+	0.891272i	$0.350186\pi$
$398$	3.12089	+	3.12089i	0.156436	+	0.156436i
$399$	21.2199	−	9.18459i	1.06232	−	0.459805i
$400$		−	3.64779i		−	0.182389i
$401$	−5.25469	−	5.25469i	−0.262407	−	0.262407i	0.563624	−	0.826031i	$-0.309407\pi$
$401$	−5.25469	−	5.25469i	−0.262407	−	0.262407i	−0.826031	+	0.563624i	$0.809407\pi$
$402$	17.1131	−	7.40704i	0.853523	−	0.369429i
$403$		0			0
$404$		−	1.54909i		−	0.0770700i
$405$	7.85248	+	6.91865i	0.390193	+	0.343790i
$406$	8.34681			0.414245
$407$	−18.2010			−0.902188
$408$	−4.54577	−	1.79940i	−0.225049	−	0.0890835i
$409$	6.39911	+	6.39911i	0.316416	+	0.316416i	0.847389	−	0.530973i	$-0.178173\pi$
$409$	6.39911	+	6.39911i	0.316416	+	0.316416i	−0.530973	+	0.847389i	$0.678173\pi$
$410$	−4.36611	−	4.36611i	−0.215627	−	0.215627i
$411$	26.8580	+	10.6315i	1.32481	+	0.524411i
$412$	8.25369			0.406630
$413$	14.5507			0.715993
$414$	−0.882406	−	27.9433i	−0.0433679	−	1.37334i
$415$		−	2.88297i		−	0.141519i
$416$		0			0
$417$	−12.0930	+	5.23421i	−0.592198	+	0.256320i
$418$	−17.2934	−	17.2934i	−0.845848	−	0.845848i
$419$		−	15.2904i		−	0.746984i	−0.927633	−	0.373492i	$-0.878160\pi$
$419$		−	15.2904i		−	0.746984i	0.927633	−	0.373492i	$-0.121840\pi$
$420$	−4.91976	+	2.12941i	−0.240060	+	0.103905i
$421$	10.9253	+	10.9253i	0.532468	+	0.532468i	0.921306	−	0.388838i	$-0.127123\pi$
$421$	10.9253	+	10.9253i	0.532468	+	0.532468i	−0.388838	+	0.921306i	$0.627123\pi$
$422$	−4.12440	+	4.12440i	−0.200772	+	0.200772i
$423$	35.8352	−	1.13162i	1.74236	−	0.0550212i
$424$	1.11042	−	1.11042i	0.0539267	−	0.0539267i
$425$		−	10.2964i		−	0.499448i
$426$	−0.576326	−	1.33153i	−0.0279231	−	0.0645129i
$427$	18.3694	−	18.3694i	0.888958	−	0.888958i
$428$	15.4267			0.745678
$429$		0			0
$430$	−13.2655			−0.639717
$431$	−16.5565	+	16.5565i	−0.797497	+	0.797497i	−0.982700	−	0.185203i	$-0.940706\pi$
$431$	−16.5565	+	16.5565i	−0.797497	+	0.797497i	0.185203	+	0.982700i	$0.440706\pi$
$432$	−1.75902	+	4.88936i	−0.0846308	+	0.235240i
$433$			24.3537i			1.17036i	0.810902	+	0.585182i	$0.198977\pi$
$433$			24.3537i			1.17036i	−0.810902	+	0.585182i	$0.801023\pi$
$434$	−1.88840	+	1.88840i	−0.0906460	+	0.0906460i
$435$	−5.87281	−	2.32469i	−0.281580	−	0.111460i
$436$	−4.36899	+	4.36899i	−0.209237	+	0.209237i
$437$	33.0506	+	33.0506i	1.58102	+	1.58102i
$438$	−6.25035	−	14.4407i	−0.298653	−	0.690003i
$439$		−	19.7742i		−	0.943773i	−0.881659	−	0.471886i	$-0.843573\pi$
$439$		−	19.7742i		−	0.943773i	0.881659	−	0.471886i	$-0.156427\pi$
$440$	4.00942	+	4.00942i	0.191141	+	0.191141i
$441$	−0.184418	−	0.173128i	−0.00878183	−	0.00824418i
$442$		0			0
$443$			2.27483i			0.108080i	0.998539	+	0.0540402i	$0.0172099\pi$
$443$			2.27483i			0.108080i	−0.998539	+	0.0540402i	$0.982790\pi$
$444$	−6.01136	−	2.37954i	−0.285287	−	0.112928i
$445$	7.84043			0.371672
$446$	−19.8301			−0.938985
$447$	−3.94170	+	9.95782i	−0.186436	+	0.470989i
$448$	−1.88206	−	1.88206i	−0.0889191	−	0.0889191i
$449$	−0.624373	−	0.624373i	−0.0294660	−	0.0294660i	0.692220	−	0.721686i	$-0.256633\pi$
$449$	−0.624373	−	0.624373i	−0.0294660	−	0.0294660i	−0.721686	+	0.692220i	$0.756633\pi$
$450$	−10.9379	+	0.345403i	−0.515618	+	0.0162824i
$451$	−25.8918			−1.21920
$452$	−8.13383			−0.382583
$453$	13.0761	−	33.0339i	0.614370	−	1.55207i
$454$			9.99738i			0.469200i
$455$		0			0
$456$	−3.45073	−	7.97250i	−0.161595	−	0.373346i
$457$	8.45732	+	8.45732i	0.395617	+	0.395617i	0.876684	−	0.481067i	$-0.159751\pi$
$457$	8.45732	+	8.45732i	0.395617	+	0.395617i	−0.481067	+	0.876684i	$0.659751\pi$
$458$			0.836693i			0.0390961i
$459$	−4.96507	+	13.8009i	−0.231750	+	0.644171i
$460$	−7.66266	−	7.66266i	−0.357273	−	0.357273i
$461$	−25.0468	+	25.0468i	−1.16655	+	1.16655i	−0.183534	+	0.983013i	$0.558754\pi$
$461$	−25.0468	+	25.0468i	−1.16655	+	1.16655i	−0.983013	+	0.183534i	$0.941246\pi$
$462$	−8.27361	+	20.9014i	−0.384923	+	0.972421i
$463$	27.9427	−	27.9427i	1.29861	−	1.29861i	0.369296	−	0.929312i	$-0.379599\pi$
$463$	27.9427	−	27.9427i	1.29861	−	1.29861i	0.929312	−	0.369296i	$-0.120401\pi$
$464$		−	3.13597i		−	0.145584i
$465$	1.85462	−	0.802732i	0.0860059	−	0.0372258i
$466$	−4.08851	+	4.08851i	−0.189397	+	0.189397i
$467$	−21.7798			−1.00785			−0.503925	−	0.863748i	$-0.668111\pi$
$467$	−21.7798			−1.00785			−0.503925	+	0.863748i	$0.668111\pi$
$468$		0			0
$469$	28.6553			1.32318
$470$	9.82679	−	9.82679i	0.453276	−	0.453276i
$471$	5.92545	−	2.56471i	0.273030	−	0.118175i
$472$		−	5.46682i		−	0.251631i
$473$	−39.3332	+	39.3332i	−1.80854	+	1.80854i
$474$	3.81506	−	9.63788i	0.175231	−	0.442682i
$475$	12.9371	−	12.9371i	0.593594	−	0.593594i
$476$	−5.31238	−	5.31238i	−0.243493	−	0.243493i
$477$	−3.43474	−	3.22445i	−0.157266	−	0.147638i
$478$		−	12.0883i		−	0.552906i
$479$	3.95994	+	3.95994i	0.180934	+	0.180934i	0.791763	−	0.610829i	$-0.209164\pi$
$479$	3.95994	+	3.95994i	0.180934	+	0.180934i	−0.610829	+	0.791763i	$0.709164\pi$
$480$	0.800039	+	1.84840i	0.0365166	+	0.0843674i
$481$		0			0
$482$		−	12.0036i		−	0.546750i
$483$	15.8122	−	39.9460i	0.719482	−	1.81761i
$484$	12.7765			0.580750
$485$	−12.3753			−0.561935
$486$	14.8273	+	4.81146i	0.672582	+	0.218252i
$487$	−2.92644	−	2.92644i	−0.132610	−	0.132610i	0.637686	−	0.770296i	$-0.279892\pi$
$487$	−2.92644	−	2.92644i	−0.132610	−	0.132610i	−0.770296	+	0.637686i	$0.779892\pi$
$488$	−6.90154	−	6.90154i	−0.312418	−	0.312418i
$489$	−7.10205	+	17.9417i	−0.321166	+	0.811353i
$490$	−0.0980470			−0.00442931
$491$	−28.0245			−1.26473			−0.632365	−	0.774671i	$-0.717916\pi$
$491$	−28.0245			−1.26473			−0.632365	+	0.774671i	$0.717916\pi$
$492$	−8.55145	−	3.38501i	−0.385529	−	0.152608i
$493$		−	8.85170i		−	0.398660i
$494$		0			0
$495$	11.6426	−	12.4019i	0.523296	−	0.557424i
$496$	0.709487	+	0.709487i	0.0318569	+	0.0318569i
$497$		−	2.22960i		−	0.100011i
$498$	−1.70572	−	3.94086i	−0.0764350	−	0.176594i
$499$	−11.8491	−	11.8491i	−0.530440	−	0.530440i	0.390264	−	0.920703i	$-0.372384\pi$
$499$	−11.8491	−	11.8491i	−0.530440	−	0.530440i	−0.920703	+	0.390264i	$0.872384\pi$
$500$	−7.11070	+	7.11070i	−0.318000	+	0.318000i
$501$	−10.6394	−	4.21151i	−0.475334	−	0.188156i
$502$	−17.5968	+	17.5968i	−0.785385	+	0.785385i
$503$		−	31.0113i		−	1.38272i	−0.722509	−	0.691362i	$-0.757011\pi$
$503$		−	31.0113i		−	1.38272i	0.722509	−	0.691362i	$-0.242989\pi$
$504$	−5.46516	+	5.82158i	−0.243438	+	0.259314i
$505$	−1.27375	+	1.27375i	−0.0566810	+	0.0566810i
$506$	−45.4408			−2.02009
$507$		0			0
$508$	−3.06842			−0.136139
$509$	−17.5920	+	17.5920i	−0.779753	+	0.779753i	−0.979789	−	0.200036i	$-0.935894\pi$
$509$	−17.5920	+	17.5920i	−0.779753	+	0.779753i	0.200036	+	0.979789i	$0.435894\pi$
$510$	2.25822	+	5.21735i	0.0999957	+	0.231028i
$511$		−	24.1804i		−	1.06968i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−23.5788	+	11.1019i	−1.04103	+	0.490162i
$514$	1.90231	−	1.90231i	0.0839074	−	0.0839074i
$515$	−6.78664	−	6.78664i	−0.299055	−	0.299055i
$516$	−18.1331	+	7.84855i	−0.798267	+	0.345513i
$517$		−	58.2745i		−	2.56291i
$518$	−7.02513	−	7.02513i	−0.308667	−	0.308667i
$519$	35.4954	−	15.3634i	1.55807	−	0.674379i
$520$		0			0
$521$		−	33.1902i		−	1.45409i	−0.686590	−	0.727045i	$-0.740893\pi$
$521$		−	33.1902i		−	1.45409i	0.686590	−	0.727045i	$-0.259107\pi$
$522$	−9.40321	+	0.296939i	−0.411567	+	0.0129967i
$523$	4.73448			0.207024			0.103512	−	0.994628i	$-0.466992\pi$
$523$	4.73448			0.207024			0.103512	+	0.994628i	$0.466992\pi$
$524$	−5.37936			−0.234998
$525$	−15.6362	−	6.18943i	−0.682419	−	0.270129i
$526$	6.38111	+	6.38111i	0.278230	+	0.278230i
$527$	2.00263	+	2.00263i	0.0872357	+	0.0872357i
$528$	7.85283	+	3.10846i	0.341751	+	0.135279i
$529$	63.8450			2.77587
$530$	−1.82610			−0.0793206
$531$	−16.3923	+	0.517643i	−0.711364	+	0.0224638i
$532$		−	13.3497i		−	0.578782i
$533$		0			0
$534$	10.7174	−	4.63881i	0.463789	−	0.200741i
$535$	−12.6847	−	12.6847i	−0.548408	−	0.548408i
$536$		−	10.7660i		−	0.465021i
$537$	11.2983	−	4.89022i	0.487557	−	0.211029i
$538$	−11.3706	−	11.3706i	−0.490220	−	0.490220i
$539$	−0.290718	+	0.290718i	−0.0125221	+	0.0125221i
$540$	5.46667	−	2.57394i	0.235248	−	0.110765i
$541$	−10.9865	+	10.9865i	−0.472346	+	0.472346i	−0.902673	−	0.430327i	$-0.858398\pi$
$541$	−10.9865	+	10.9865i	−0.472346	+	0.472346i	0.430327	+	0.902673i	$0.358398\pi$
$542$			9.81770i			0.421706i
$543$	−10.7894	−	24.9275i	−0.463015	−	1.06974i
$544$	−1.99591	+	1.99591i	−0.0855738	+	0.0855738i
$545$	7.18485			0.307765
$546$		0			0
$547$	−30.4422			−1.30161			−0.650807	−	0.759243i	$-0.725569\pi$
$547$	−30.4422			−1.30161			−0.650807	+	0.759243i	$0.725569\pi$
$548$	11.7925	−	11.7925i	0.503751	−	0.503751i
$549$	−20.0408	+	21.3478i	−0.855321	+	0.911102i
$550$			17.7870i			0.758442i
$551$	11.1219	−	11.1219i	0.473808	−	0.473808i
$552$	−15.0081	−	5.94079i	−0.638786	−	0.252857i
$553$	11.2632	−	11.2632i	0.478962	−	0.478962i
$554$	9.98190	+	9.98190i	0.424090	+	0.424090i
$555$	2.98629	+	6.89947i	0.126761	+	0.292866i
$556$			7.60785i			0.322645i
$557$	4.46211	+	4.46211i	0.189066	+	0.189066i	0.795292	−	0.606226i	$-0.207317\pi$
$557$	4.46211	+	4.46211i	0.189066	+	0.189066i	−0.606226	+	0.795292i	$0.707317\pi$
$558$	2.06022	−	2.19458i	0.0872161	−	0.0929040i
$559$		0			0
$560$			3.09507i			0.130791i
$561$	22.1657	+	8.77407i	0.935837	+	0.370442i
$562$	3.76413			0.158780
$563$	−44.0716			−1.85740			−0.928699	−	0.370834i	$-0.879072\pi$
$563$	−44.0716			−1.85740			−0.928699	+	0.370834i	$0.879072\pi$
$564$	7.61862	−	19.2467i	0.320802	−	0.810433i
$565$	6.68809	+	6.68809i	0.281370	+	0.281370i
$566$	−4.53617	−	4.53617i	−0.190670	−	0.190670i
$567$	17.9735	+	15.8361i	0.754817	+	0.665053i
$568$	−0.837681			−0.0351483
$569$	−40.1848			−1.68463			−0.842317	−	0.538983i	$-0.818809\pi$
$569$	−40.1848			−1.68463			−0.842317	+	0.538983i	$0.818809\pi$
$570$	−3.71805	+	9.39282i	−0.155732	+	0.393422i
$571$		−	19.2449i		−	0.805374i	−0.915338	−	0.402687i	$-0.868076\pi$
$571$		−	19.2449i		−	0.805374i	0.915338	−	0.402687i	$-0.131924\pi$
$572$		0			0
$573$	14.8219	+	34.2443i	0.619195	+	1.43058i
$574$	−9.99359	−	9.99359i	−0.417124	−	0.417124i
$575$		−	33.9940i		−	1.41765i
$576$	2.18722	+	2.05331i	0.0911341	+	0.0855545i
$577$	19.2851	+	19.2851i	0.802851	+	0.802851i	0.983540	−	0.180689i	$-0.0578328\pi$
$577$	19.2851	+	19.2851i	0.802851	+	0.802851i	−0.180689	+	0.983540i	$0.557833\pi$
$578$	6.38709	−	6.38709i	0.265668	−	0.265668i
$579$	−1.27515	+	3.22137i	−0.0529934	+	0.133876i
$580$	−2.57857	+	2.57857i	−0.107069	+	0.107069i
$581$		−	6.59883i		−	0.273766i
$582$	−16.9164	+	7.32191i	−0.701207	+	0.303503i
$583$	−5.41453	+	5.41453i	−0.224247	+	0.224247i
$584$	−9.08479			−0.375931
$585$		0			0
$586$	24.2196			1.00050
$587$	17.4789	−	17.4789i	0.721433	−	0.721433i	−0.247464	−	0.968897i	$-0.579597\pi$
$587$	17.4789	−	17.4789i	0.721433	−	0.721433i	0.968897	+	0.247464i	$0.0795973\pi$
$588$	−0.134025	+	0.0580098i	−0.00552709	+	0.00239228i
$589$			5.03247i			0.207359i
$590$	−4.49512	+	4.49512i	−0.185061	+	0.185061i
$591$	0.727426	−	1.83768i	0.0299223	−	0.0755919i
$592$	−2.63940	+	2.63940i	−0.108479	+	0.108479i
$593$	−29.4094	−	29.4094i	−1.20770	−	1.20770i	−0.971770	−	0.235929i	$-0.924187\pi$
$593$	−29.4094	−	29.4094i	−1.20770	−	1.20770i	−0.235929	−	0.971770i	$-0.575813\pi$
$594$	8.57718	−	23.8411i	0.351926	−	0.978212i
$595$			8.73628i			0.358152i
$596$	4.37217	+	4.37217i	0.179091	+	0.179091i
$597$	−3.03657	−	7.01563i	−0.124278	−	0.287131i
$598$		0			0
$599$		−	43.2194i		−	1.76590i	−0.469469	−	0.882949i	$-0.655555\pi$
$599$		−	43.2194i		−	1.76590i	0.469469	−	0.882949i	$-0.344445\pi$
$600$	−2.32542	+	5.87465i	−0.0949350	+	0.239832i
$601$	−8.21097			−0.334932			−0.167466	−	0.985878i	$-0.553559\pi$
$601$	−8.21097			−0.334932			−0.167466	+	0.985878i	$0.553559\pi$
$602$	−30.3633			−1.23752
$603$	−32.2820	+	1.01942i	−1.31462	+	0.0415138i
$604$	−14.5041	−	14.5041i	−0.590165	−	0.590165i
$605$	−10.5056	−	10.5056i	−0.427112	−	0.427112i
$606$	−0.987525	+	2.49476i	−0.0401155	+	0.101343i
$607$	−11.2076			−0.454901			−0.227451	−	0.973790i	$-0.573039\pi$
$607$	−11.2076			−0.454901			−0.227451	+	0.973790i	$0.573039\pi$
$608$	−5.01558			−0.203409
$609$	−13.4423	−	5.32099i	−0.544708	−	0.215617i
$610$			11.3497i			0.459535i
$611$		0			0
$612$	6.17373	+	5.79575i	0.249558	+	0.234279i
$613$	13.8009	+	13.8009i	0.557414	+	0.557414i	0.928570	−	0.371156i	$-0.121039\pi$
$613$	13.8009	+	13.8009i	0.557414	+	0.557414i	−0.371156	+	0.928570i	$0.621039\pi$
$614$			10.7971i			0.435737i
$615$	4.24814	+	9.81483i	0.171302	+	0.395772i
$616$	9.17715	+	9.17715i	0.369758	+	0.369758i
$617$	0.661069	−	0.661069i	0.0266136	−	0.0266136i	−0.693675	−	0.720288i	$-0.744009\pi$
$617$	0.661069	−	0.661069i	0.0266136	−	0.0266136i	0.720288	+	0.693675i	$0.244009\pi$
$618$	−13.2923	−	5.26163i	−0.534695	−	0.211654i
$619$	−7.75816	+	7.75816i	−0.311827	+	0.311827i	−0.845617	−	0.533790i	$-0.820767\pi$
$619$	−7.75816	+	7.75816i	−0.311827	+	0.311827i	0.533790	+	0.845617i	$0.320767\pi$
$620$		−	1.16676i		−	0.0468582i
$621$	−16.3924	+	45.5643i	−0.657805	+	1.82843i
$622$	4.97519	−	4.97519i	0.199487	−	0.199487i
$623$	17.9460			0.718990
$624$		0			0
$625$	−6.54532			−0.261813
$626$	−18.4169	+	18.4169i	−0.736089	+	0.736089i
$627$	16.8261	+	38.8748i	0.671972	+	1.55251i
$628$		−	3.72776i		−	0.148754i
$629$	−7.45008	+	7.45008i	−0.297054	+	0.297054i
$630$	9.28060	−	0.293067i	0.369748	−	0.0116761i
$631$	18.6131	−	18.6131i	0.740977	−	0.740977i	−0.231789	−	0.972766i	$-0.574458\pi$
$631$	18.6131	−	18.6131i	0.740977	−	0.740977i	0.972766	+	0.231789i	$0.0744580\pi$
$632$	−4.23169	−	4.23169i	−0.168328	−	0.168328i
$633$	9.27146	−	4.01296i	0.368508	−	0.159501i
$634$			6.49671i			0.258018i
$635$	2.52303	+	2.52303i	0.100123	+	0.100123i
$636$	−2.49617	+	1.08042i	−0.0989797	+	0.0428413i
$637$		0			0
$638$			15.2913i			0.605390i
$639$	0.0793186	+	2.51179i	0.00313779	+	0.0993649i
$640$	1.16285			0.0459655
$641$	0.513748			0.0202918			0.0101459	−	0.999949i	$-0.496770\pi$
$641$	0.513748			0.0202918			0.0101459	+	0.999949i	$0.496770\pi$
$642$	−24.8442	−	9.83434i	−0.980524	−	0.388131i
$643$	7.46148	+	7.46148i	0.294252	+	0.294252i	0.838757	−	0.544505i	$-0.183283\pi$
$643$	7.46148	+	7.46148i	0.294252	+	0.294252i	−0.544505	+	0.838757i	$0.683283\pi$
$644$	−17.5391	−	17.5391i	−0.691136	−	0.691136i
$645$	21.3636	+	8.45657i	0.841191	+	0.332977i
$646$	−14.1572			−0.557007
$647$	46.2005			1.81633			0.908164	−	0.418614i	$-0.137484\pi$
$647$	46.2005			1.81633			0.908164	+	0.418614i	$0.137484\pi$
$648$	5.94975	−	6.75281i	0.233728	−	0.265275i
$649$			26.6568i			1.04637i
$650$		0			0
$651$	4.24504	−	1.83737i	0.166376	−	0.0720124i
$652$	7.87765	+	7.87765i	0.308513	+	0.308513i
$653$		−	38.4717i		−	1.50551i	−0.658300	−	0.752756i	$-0.728724\pi$
$653$		−	38.4717i		−	1.50551i	0.658300	−	0.752756i	$-0.271276\pi$
$654$	9.82129	−	4.25094i	0.384043	−	0.166225i
$655$	4.42321	+	4.42321i	0.172829	+	0.172829i
$656$	−3.75468	+	3.75468i	−0.146596	+	0.146596i
$657$	0.860223	+	27.2408i	0.0335605	+	1.06276i
$658$	22.4925	−	22.4925i	0.876850	−	0.876850i
$659$			28.7163i			1.11863i	0.828956	+	0.559314i	$0.188935\pi$
$659$			28.7163i			1.11863i	−0.828956	+	0.559314i	$0.811065\pi$
$660$	−3.90108	−	9.01299i	−0.151849	−	0.350830i
$661$	20.1141	−	20.1141i	0.782347	−	0.782347i	−0.197879	−	0.980226i	$-0.563405\pi$
$661$	20.1141	−	20.1141i	0.782347	−	0.782347i	0.980226	+	0.197879i	$0.0634055\pi$
$662$	21.2471			0.825791
$663$		0			0
$664$	−2.47924			−0.0962130
$665$	−10.9768	+	10.9768i	−0.425664	+	0.425664i
$666$	8.16418	+	7.66434i	0.316356	+	0.296987i
$667$		−	29.2243i		−	1.13157i
$668$	−4.67144	+	4.67144i	−0.180743	+	0.180743i
$669$	31.9358	+	12.6415i	1.23471	+	0.488748i
$670$	−8.85243	+	8.85243i	−0.341999	+	0.341999i
$671$	33.6527	+	33.6527i	1.29915	+	1.29915i
$672$	1.83121	+	4.23079i	0.0706405	+	0.163206i
$673$			8.12255i			0.313101i	0.987670	+	0.156551i	$0.0500374\pi$
$673$			8.12255i			0.313101i	−0.987670	+	0.156551i	$0.949963\pi$
$674$	12.1323	+	12.1323i	0.467320	+	0.467320i
$675$	17.8354	+	6.41653i	0.686483	+	0.246972i
$676$		0			0
$677$		−	10.9368i		−	0.420337i	−0.977665	−	0.210168i	$-0.932599\pi$
$677$		−	10.9368i		−	0.420337i	0.977665	−	0.210168i	$-0.0674012\pi$
$678$	13.0993	+	5.18522i	0.503075	+	0.199137i
$679$	−28.3259			−1.08705
$680$	3.28229			0.125870
$681$	6.37321	−	16.1005i	0.244222	−	0.616971i
$682$	−3.45954	−	3.45954i	−0.132473	−	0.132473i
$683$	−2.58402	−	2.58402i	−0.0988749	−	0.0988749i	0.655939	−	0.754814i	$-0.272273\pi$
$683$	−2.58402	−	2.58402i	−0.0988749	−	0.0988749i	−0.754814	+	0.655939i	$0.772273\pi$
$684$	0.474917	+	15.0393i	0.0181589	+	0.575040i
$685$	−19.3929			−0.740965
$686$	18.4070			0.702784
$687$	0.533382	−	1.34747i	0.0203498	−	0.0514091i
$688$			11.4077i			0.434916i
$689$		0			0
$690$	7.45562	+	17.2253i	0.283831	+	0.655757i
$691$	7.29941	+	7.29941i	0.277683	+	0.277683i	0.832183	−	0.554501i	$-0.187091\pi$
$691$	7.29941	+	7.29941i	0.277683	+	0.277683i	−0.554501	+	0.832183i	$0.687091\pi$
$692$		−	22.3305i		−	0.848879i
$693$	26.6488	−	28.3867i	1.01230	−	1.07832i
$694$	10.8524	+	10.8524i	0.411951	+	0.411951i
$695$	6.25560	−	6.25560i	0.237288	−	0.237288i
$696$	−1.99914	+	5.05037i	−0.0757772	+	0.191434i
$697$	−10.5981	+	10.5981i	−0.401431	+	0.401431i
$698$		−	22.0015i		−	0.832768i
$699$	9.19080	−	3.97804i	0.347628	−	0.150463i
$700$	−6.86537	+	6.86537i	−0.259486	+	0.259486i
$701$	−25.6690			−0.969506			−0.484753	−	0.874651i	$-0.661091\pi$
$701$	−25.6690			−0.969506			−0.484753	+	0.874651i	$0.661091\pi$
$702$		0			0
$703$	−18.7216			−0.706097
$704$	3.44793	−	3.44793i	0.129949	−	0.129949i
$705$	−22.0902	+	9.56127i	−0.831965	+	0.360098i
$706$		−	19.2725i		−	0.725331i
$707$	−2.91548	+	2.91548i	−0.109648	+	0.109648i
$708$	−3.48503	+	8.80414i	−0.130975	+	0.330880i
$709$	−22.7073	+	22.7073i	−0.852790	+	0.852790i	−0.990476	−	0.137686i	$-0.956034\pi$
$709$	−22.7073	+	22.7073i	−0.852790	+	0.852790i	0.137686	+	0.990476i	$0.456034\pi$
$710$	0.688789	+	0.688789i	0.0258498	+	0.0258498i
$711$	−12.2881	+	13.0894i	−0.460838	+	0.490893i
$712$		−	6.74245i		−	0.252684i
$713$	6.61176	+	6.61176i	0.247612	+	0.247612i
$714$	5.16884	+	11.9420i	0.193439	+	0.446918i
$715$		0			0
$716$		−	7.10787i		−	0.265634i
$717$	−7.70614	+	19.4678i	−0.287791	+	0.727039i
$718$	−6.12012			−0.228401
$719$	17.8697			0.666426			0.333213	−	0.942852i	$-0.391867\pi$
$719$	17.8697			0.666426			0.333213	+	0.942852i	$0.391867\pi$
$720$	−0.110108	−	3.48680i	−0.00410348	−	0.129945i
$721$	−15.5340	−	15.5340i	−0.578515	−	0.578515i
$722$	−4.35301	−	4.35301i	−0.162002	−	0.162002i
$723$	−7.65216	+	19.3315i	−0.284587	+	0.718945i
$724$	−15.6822			−0.582823
$725$	−11.4393			−0.424847
$726$	−20.5762	−	8.14487i	−0.763653	−	0.302284i
$727$			33.1082i			1.22791i	0.789340	+	0.613957i	$0.210423\pi$
$727$			33.1082i			1.22791i	−0.789340	+	0.613957i	$0.789577\pi$
$728$		0			0
$729$	−20.8117	−	17.2010i	−0.770804	−	0.637072i
$730$	7.47003	+	7.47003i	0.276478	+	0.276478i
$731$			32.2000i			1.19096i
$732$	6.71507	+	15.5144i	0.248196	+	0.573428i
$733$	9.19382	+	9.19382i	0.339581	+	0.339581i	0.856210	−	0.516628i	$-0.172813\pi$
$733$	9.19382	+	9.19382i	0.339581	+	0.339581i	−0.516628	+	0.856210i	$0.672813\pi$
$734$	20.8003	−	20.8003i	0.767754	−	0.767754i
$735$	0.157902	+	0.0625038i	0.00582429	+	0.00230549i
$736$	−6.58958	+	6.58958i	−0.242895	+	0.242895i
$737$			52.4964i			1.93373i
$738$	11.6139	+	10.9029i	0.427515	+	0.401341i
$739$	−2.73409	+	2.73409i	−0.100575	+	0.100575i	−0.755604	−	0.655029i	$-0.772657\pi$
$739$	−2.73409	+	2.73409i	−0.100575	+	0.100575i	0.655029	+	0.755604i	$0.272657\pi$
$740$	4.34053			0.159561
$741$		0			0
$742$	−4.17976			−0.153444
$743$	−13.2020	+	13.2020i	−0.484333	+	0.484333i	−0.906512	−	0.422179i	$-0.861265\pi$
$743$	−13.2020	+	13.2020i	−0.484333	+	0.484333i	0.422179	+	0.906512i	$0.361265\pi$
$744$	−0.690317	−	1.59490i	−0.0253083	−	0.0584717i
$745$		−	7.19009i		−	0.263424i
$746$	15.9667	−	15.9667i	0.584581	−	0.584581i
$747$	0.234755	+	7.43400i	0.00858922	+	0.271996i
$748$	9.73227	−	9.73227i	0.355847	−	0.355847i
$749$	−29.0340	−	29.0340i	−1.06088	−	1.06088i
$750$	15.9845	−	6.91857i	0.583673	−	0.252631i
$751$			36.7180i			1.33986i	0.742425	+	0.669929i	$0.233675\pi$
$751$			36.7180i			1.33986i	−0.742425	+	0.669929i	$0.766325\pi$
$752$	−8.45064	−	8.45064i	−0.308163	−	0.308163i
$753$	39.5569	−	17.1214i	1.44153	−	0.623938i
$754$		0			0
$755$			23.8522i			0.868072i
$756$	12.5127	−	5.89150i	0.455081	−	0.214272i
$757$	52.9643			1.92502			0.962511	−	0.271243i	$-0.0874348\pi$
$757$	52.9643			1.92502			0.962511	+	0.271243i	$0.0874348\pi$
$758$	13.8752			0.503969
$759$	73.1811	+	28.9680i	2.65630	+	1.05147i
$760$	4.12410	+	4.12410i	0.149597	+	0.149597i
$761$	−10.6637	−	10.6637i	−0.386558	−	0.386558i	0.486900	−	0.873458i	$-0.338128\pi$
$761$	−10.6637	−	10.6637i	−0.386558	−	0.386558i	−0.873458	+	0.486900i	$0.838128\pi$
$762$	4.94159	+	1.95608i	0.179015	+	0.0708613i
$763$	16.4454			0.595364
$764$	21.5435			0.779416
$765$	−0.310795	−	9.84197i	−0.0112368	−	0.355837i
$766$			6.55024i			0.236670i
$767$		0			0
$768$	1.58955	−	0.688001i	0.0573578	−	0.0248261i
$769$	−19.6491	−	19.6491i	−0.708566	−	0.708566i	0.257668	−	0.966234i	$-0.417046\pi$
$769$	−19.6491	−	19.6491i	−0.708566	−	0.708566i	−0.966234	+	0.257668i	$0.917046\pi$
$770$		−	15.0919i		−	0.543876i
$771$	−4.27631	+	1.85091i	−0.154008	+	0.0666590i
$772$	1.41440	+	1.41440i	0.0509055	+	0.0509055i
$773$	9.78140	−	9.78140i	0.351812	−	0.351812i	−0.508971	−	0.860784i	$-0.669974\pi$
$773$	9.78140	−	9.78140i	0.351812	−	0.351812i	0.860784	+	0.508971i	$0.169974\pi$
$774$	34.2062	−	1.08018i	1.22952	−	0.0388263i
$775$	2.58806	−	2.58806i	0.0929658	−	0.0929658i
$776$			10.6423i			0.382036i
$777$	6.83532	+	15.7922i	0.245216	+	0.566542i
$778$	1.12089	−	1.12089i	0.0401860	−	0.0401860i
$779$	−26.6323			−0.954202
$780$		0			0
$781$	4.08463			0.146160
$782$	−18.6000	+	18.6000i	−0.665134	+	0.665134i
$783$	15.3329	+	5.51622i	0.547952	+	0.197134i
$784$			0.0843165i			0.00301130i
$785$	−3.06518	+	3.06518i	−0.109401	+	0.109401i
$786$	8.66329	+	3.42928i	0.309009	+	0.122318i
$787$	19.7528	−	19.7528i	0.704111	−	0.704111i	−0.261180	−	0.965290i	$-0.584111\pi$
$787$	19.7528	−	19.7528i	0.704111	−	0.704111i	0.965290	+	0.261180i	$0.0841115\pi$
$788$	−0.806866	−	0.806866i	−0.0287434	−	0.0287434i
$789$	−6.20869	−	14.3445i	−0.221035	−	0.510676i
$790$			6.95907i			0.247593i
$791$	15.3084	+	15.3084i	0.544303	+	0.544303i
$792$	−10.6651	−	10.0122i	−0.378969	−	0.355767i
$793$		0			0
$794$		−	12.3364i		−	0.437803i
$795$	2.94087	+	1.16412i	0.104302	+	0.0412869i
$796$	−4.41361			−0.156436
$797$	−15.3326			−0.543109			−0.271555	−	0.962423i	$-0.587538\pi$
$797$	−15.3326			−0.543109			−0.271555	+	0.962423i	$0.587538\pi$
$798$	−8.51025	+	21.4992i	−0.301260	+	0.761064i
$799$	−23.8531	−	23.8531i	−0.843862	−	0.843862i
$800$	2.57938	+	2.57938i	0.0911947	+	0.0911947i
$801$	−20.2173	+	0.638431i	−0.714342	+	0.0225578i
$802$	7.43126			0.262407
$803$	44.2985			1.56326
$804$	−6.86321	+	17.3383i	−0.242047	+	0.611476i
$805$			28.8432i			1.01659i
$806$		0			0
$807$	11.0633	+	25.5605i	0.389448	+	0.899773i
$808$	1.09537	+	1.09537i	0.0385350	+	0.0385350i
$809$		−	9.76631i		−	0.343365i	−0.985152	−	0.171683i	$-0.945080\pi$
$809$		−	9.76631i		−	0.343365i	0.985152	−	0.171683i	$-0.0549203\pi$
$810$	−10.4448	+	0.660318i	−0.366991	+	0.0232012i
$811$	−25.7568	−	25.7568i	−0.904443	−	0.904443i	0.0913735	−	0.995817i	$-0.470874\pi$
$811$	−25.7568	−	25.7568i	−0.904443	−	0.904443i	−0.995817	+	0.0913735i	$0.970874\pi$
$812$	−5.90208	+	5.90208i	−0.207122	+	0.207122i
$813$	6.25867	−	15.8111i	0.219501	−	0.554519i
$814$	12.8700	−	12.8700i	0.451094	−	0.451094i
$815$		−	12.9549i		−	0.453790i
$816$	4.48671	−	1.94198i	0.157066	−	0.0679828i
$817$	−40.4582	+	40.4582i	−1.41545	+	1.41545i
$818$	−9.04971			−0.316416
$819$		0			0
$820$	6.17461			0.215627
$821$	7.75765	−	7.75765i	0.270744	−	0.270744i	−0.558656	−	0.829400i	$-0.688683\pi$
$821$	7.75765	−	7.75765i	0.270744	−	0.270744i	0.829400	+	0.558656i	$0.188683\pi$
$822$	−26.5090	+	11.4739i	−0.924609	+	0.400197i
$823$			12.5691i			0.438132i	0.975710	+	0.219066i	$0.0703010\pi$
$823$			12.5691i			0.438132i	−0.975710	+	0.219066i	$0.929699\pi$
$824$	−5.83624	+	5.83624i	−0.203315	+	0.203315i
$825$	11.3390	−	28.6455i	0.394774	−	0.997307i
$826$	−10.2889	+	10.2889i	−0.357996	+	0.357996i
$827$	−33.6033	−	33.6033i	−1.16850	−	1.16850i	−0.982561	−	0.185938i	$-0.940468\pi$
$827$	−33.6033	−	33.6033i	−1.16850	−	1.16850i	−0.185938	−	0.982561i	$-0.559532\pi$
$828$	20.3828	+	19.1349i	0.708352	+	0.664985i
$829$		−	0.273978i		−	0.00951564i	−0.999989	−	0.00475782i	$-0.998486\pi$
$829$		−	0.273978i		−	0.00951564i	0.999989	−	0.00475782i	$-0.00151447\pi$
$830$	2.03857	+	2.03857i	0.0707597	+	0.0707597i
$831$	−9.71220	−	22.4389i	−0.336912	−	0.778396i
$832$		0			0
$833$			0.237995i			0.00824603i
$834$	4.84991	−	12.2522i	0.167939	−	0.424259i
$835$	7.68224			0.265855
$836$	24.4566			0.845848
$837$	−4.71694	+	2.22094i	−0.163041	+	0.0767668i
$838$	10.8119	+	10.8119i	0.373492	+	0.373492i
$839$	−8.42059	−	8.42059i	−0.290711	−	0.290711i	0.546650	−	0.837361i	$-0.315903\pi$
$839$	−8.42059	−	8.42059i	−0.290711	−	0.290711i	−0.837361	+	0.546650i	$0.815903\pi$
$840$	1.97307	−	4.98452i	0.0680775	−	0.171982i
$841$	19.1657			0.660887
$842$	−15.4508			−0.532468
$843$	−6.06201	−	2.39959i	−0.208787	−	0.0826461i
$844$		−	5.83278i		−	0.200772i
$845$		0			0
$846$	−24.5391	+	26.1395i	−0.843672	+	0.898693i
$847$	−24.0462	−	24.0462i	−0.826236	−	0.826236i
$848$			1.57037i			0.0539267i
$849$	4.41361	+	10.1971i	0.151475	+	0.349964i
$850$	7.28065	+	7.28065i	0.249724	+	0.249724i
$851$	−24.5968	+	24.5968i	−0.843166	+	0.843166i
$852$	1.34906	+	0.534012i	0.0462180	+	0.0182949i
$853$	38.8561	−	38.8561i	1.33041	−	1.33041i	0.425403	−	0.905004i	$-0.360132\pi$
$853$	38.8561	−	38.8561i	1.33041	−	1.33041i	0.905004	−	0.425403i	$-0.139868\pi$
$854$			25.9783i			0.888958i
$855$	11.9756	−	12.7566i	0.409558	−	0.436267i
$856$	−10.9083	+	10.9083i	−0.372839	+	0.372839i
$857$	−40.8286			−1.39468			−0.697340	−	0.716741i	$-0.745633\pi$
$857$	−40.8286			−1.39468			−0.697340	+	0.716741i	$0.745633\pi$
$858$		0			0
$859$	−11.1066			−0.378951			−0.189475	−	0.981885i	$-0.560679\pi$
$859$	−11.1066			−0.378951			−0.189475	+	0.981885i	$0.560679\pi$
$860$	9.38009	−	9.38009i	0.319858	−	0.319858i
$861$	9.72357	+	22.4652i	0.331378	+	0.765611i
$862$		−	23.4144i		−	0.797497i
$863$	−9.97222	+	9.97222i	−0.339458	+	0.339458i	−0.856163	−	0.516705i	$-0.827158\pi$
$863$	−9.97222	+	9.97222i	−0.339458	+	0.339458i	0.516705	+	0.856163i	$0.327158\pi$
$864$	−2.21349	−	4.70111i	−0.0753043	−	0.159935i
$865$	−18.3614	+	18.3614i	−0.624306	+	0.624306i
$866$	−17.2207	−	17.2207i	−0.585182	−	0.585182i
$867$	−14.3579	+	6.21452i	−0.487620	+	0.211056i
$868$		−	2.67060i		−	0.0906460i
$869$	20.6342	+	20.6342i	0.699968	+	0.699968i
$870$	5.79651	−	2.50890i	0.196520	−	0.0850595i
$871$		0			0
$872$		−	6.17868i		−	0.209237i
$873$	31.9110	−	1.00770i	1.08002	−	0.0341055i
$874$	−46.7406			−1.58102
$875$	26.7656			0.904841
$876$	14.6308	+	5.79145i	0.494328	+	0.195675i
$877$	2.86137	+	2.86137i	0.0966218	+	0.0966218i	0.753765	−	0.657144i	$-0.228236\pi$
$877$	2.86137	+	2.86137i	0.0966218	+	0.0966218i	−0.657144	+	0.753765i	$0.728236\pi$
$878$	13.9825	+	13.9825i	0.471886	+	0.471886i
$879$	−39.0049	−	15.4397i	−1.31560	−	0.520768i
$880$	−5.67017			−0.191141
$881$	17.3240			0.583662			0.291831	−	0.956470i	$-0.405736\pi$
$881$	17.3240			0.583662			0.291831	+	0.956470i	$0.405736\pi$
$882$	0.252823	−	0.00798378i	0.00851301	−	0.000268828i
$883$			15.0957i			0.508009i	0.967203	+	0.254005i	$0.0817478\pi$
$883$			15.0957i			0.508009i	−0.967203	+	0.254005i	$0.918252\pi$
$884$		0			0
$885$	10.1048	−	4.37367i	0.339671	−	0.147019i
$886$	−1.60855	−	1.60855i	−0.0540402	−	0.0540402i
$887$			11.2026i			0.376145i	0.982155	+	0.188073i	$0.0602241\pi$
$887$			11.2026i			0.376145i	−0.982155	+	0.188073i	$0.939776\pi$
$888$	5.93326	−	2.56809i	0.199107	−	0.0861794i
$889$	5.77496	+	5.77496i	0.193686	+	0.193686i
$890$	−5.54402	+	5.54402i	−0.185836	+	0.185836i
$891$	−29.0117	+	32.9275i	−0.971928	+	1.10311i
$892$	14.0220	−	14.0220i	0.469492	−	0.469492i
$893$		−	59.9413i		−	2.00586i
$894$	−4.25404	−	9.82845i	−0.142276	−	0.328712i
$895$	−5.84449	+	5.84449i	−0.195360	+	0.195360i
$896$	2.66164			0.0889191
$897$		0			0
$898$	0.882997			0.0294660
$899$	2.22493	−	2.22493i	0.0742055	−	0.0742055i
$900$	7.49004	−	7.97851i	0.249668	−	0.265950i
$901$			4.43259i			0.147671i
$902$	18.3082	−	18.3082i	0.609598	−	0.609598i
$903$	48.8991	+	19.3562i	1.62726	+	0.644135i
$904$	5.75149	−	5.75149i	0.191292	−	0.191292i
$905$	12.8948	+	12.8948i	0.428636	+	0.428636i
$906$	14.1122	+	32.6047i	0.468848	+	1.08322i
$907$			33.4774i			1.11160i	0.831316	+	0.555800i	$0.187588\pi$
$907$			33.4774i			1.11160i	−0.831316	+	0.555800i	$0.812412\pi$
$908$	−7.06921	−	7.06921i	−0.234600	−	0.234600i
$909$	3.18076	−	3.38819i	0.105499	−	0.112379i
$910$		0			0
$911$			14.0761i			0.466363i	0.972433	+	0.233181i	$0.0749136\pi$
$911$			14.0761i			0.466363i	−0.972433	+	0.233181i	$0.925086\pi$
$912$	8.07744	+	3.19738i	0.267471	+	0.105876i
$913$	12.0890			0.400089
$914$	−11.9605			−0.395617
$915$	7.23528	−	18.2783i	0.239191	−	0.604262i
$916$	−0.591631	−	0.591631i	−0.0195480	−	0.0195480i
$917$	10.1243	+	10.1243i	0.334334	+	0.334334i
$918$	−6.24787	−	13.2695i	−0.206210	−	0.437960i
$919$	−27.0031			−0.890750			−0.445375	−	0.895344i	$-0.646930\pi$
$919$	−27.0031			−0.890750			−0.445375	+	0.895344i	$0.646930\pi$
$920$	10.8366			0.357273
$921$	6.88305	−	17.3885i	0.226804	−	0.572969i
$922$		−	35.4216i		−	1.16655i
$923$		0			0
$924$	−8.92919	−	20.6298i	−0.293749	−	0.678672i
$925$	9.62798	+	9.62798i	0.316566	+	0.316566i
$926$			39.5170i			1.29861i
$927$	18.0526	+	16.9474i	0.592926	+	0.556625i
$928$	2.21746	+	2.21746i	0.0727918	+	0.0727918i
$929$	17.1281	−	17.1281i	0.561954	−	0.561954i	−0.367908	−	0.929862i	$-0.619926\pi$
$929$	17.1281	−	17.1281i	0.561954	−	0.561954i	0.929862	+	0.367908i	$0.119926\pi$
$930$	−0.743796	+	1.87903i	−0.0243900	+	0.0616158i
$931$	−0.299033	+	0.299033i	−0.00980041	+	0.00980041i
$932$		−	5.78203i		−	0.189397i
$933$	−11.1840	+	4.84077i	−0.366148	+	0.158480i
$934$	15.4006	−	15.4006i	0.503925	−	0.503925i
$935$	−16.0048			−0.523414
$936$		0			0
$937$	−44.9251			−1.46764			−0.733819	−	0.679345i	$-0.762264\pi$
$937$	−44.9251			−1.46764			−0.733819	+	0.679345i	$0.762264\pi$
$938$	−20.2623	+	20.2623i	−0.661588	+	0.661588i
$939$	41.4005	−	17.9193i	1.35105	−	0.584775i
$940$			13.8972i			0.453276i
$941$	33.4372	−	33.4372i	1.09002	−	1.09002i	0.0944953	−	0.995525i	$-0.469876\pi$
$941$	33.4372	−	33.4372i	1.09002	−	1.09002i	0.995525	−	0.0944953i	$-0.0301237\pi$
$942$	−2.37641	+	6.00345i	−0.0774275	+	0.195603i
$943$	−34.9901	+	34.9901i	−1.13943	+	1.13943i
$944$	3.86562	+	3.86562i	0.125815	+	0.125815i
$945$	−15.1329	−	5.44429i	−0.492274	−	0.177103i
$946$		−	55.6255i		−	1.80854i
$947$	27.6170	+	27.6170i	0.897431	+	0.897431i	0.995208	−	0.0977773i	$-0.0311733\pi$
$947$	27.6170	+	27.6170i	0.897431	+	0.897431i	−0.0977773	+	0.995208i	$0.531173\pi$
$948$	4.11736	+	9.51266i	0.133725	+	0.308957i
$949$		0			0
$950$			18.2958i			0.593594i
$951$	4.14158	−	10.4628i	0.134300	−	0.339278i
$952$	7.51284			0.243493
$953$	52.4195			1.69804			0.849018	−	0.528364i	$-0.177195\pi$
$953$	52.4195			1.69804			0.849018	+	0.528364i	$0.177195\pi$
$954$	4.70876	−	0.148696i	0.152452	−	0.00481420i
$955$	−17.7143	−	17.7143i	−0.573220	−	0.573220i
$956$	8.54771	+	8.54771i	0.276453	+	0.276453i
$957$	9.74804	−	24.6262i	0.315109	−	0.796052i
$958$	−5.60020			−0.180934
$959$	−44.3884			−1.43338
$960$	−1.87273	−	0.741300i	−0.0604420	−	0.0239254i
$961$		−	29.9933i		−	0.967524i
$962$		0			0
$963$	33.7416	+	31.6758i	1.08731	+	1.02074i
$964$	8.48784	+	8.48784i	0.273375	+	0.273375i
$965$		−	2.32601i		−	0.0748768i
$966$	17.0652	+	39.4271i	0.549063	+	1.26854i
$967$	−3.16617	−	3.16617i	−0.101817	−	0.101817i	0.654363	−	0.756180i	$-0.272937\pi$
$967$	−3.16617	−	3.16617i	−0.101817	−	0.101817i	−0.756180	+	0.654363i	$0.772937\pi$
$968$	−9.03435	+	9.03435i	−0.290375	+	0.290375i
$969$	22.7997	+	9.02503i	0.732432	+	0.289926i
$970$	8.75069	−	8.75069i	0.280968	−	0.280968i
$971$			2.21667i			0.0711362i	0.999367	+	0.0355681i	$0.0113241\pi$
$971$			2.21667i			0.0711362i	−0.999367	+	0.0355681i	$0.988676\pi$
$972$	−13.8867	+	7.08229i	−0.445417	+	0.227165i
$973$	14.3184	−	14.3184i	0.459028	−	0.459028i
$974$	4.13861			0.132610
$975$		0			0
$976$	9.76025			0.312418
$977$	4.13265	−	4.13265i	0.132215	−	0.132215i	−0.637902	−	0.770117i	$-0.720198\pi$
$977$	4.13265	−	4.13265i	0.132215	−	0.132215i	0.770117	+	0.637902i	$0.220198\pi$
$978$	−7.66481	−	17.7086i	−0.245093	−	0.566259i
$979$			32.8770i			1.05075i
$980$	0.0693297	−	0.0693297i	0.00221466	−	0.00221466i
$981$	−18.5268	+	0.585049i	−0.591516	+	0.0186792i
$982$	19.8163	−	19.8163i	0.632365	−	0.632365i
$983$	−34.1686	−	34.1686i	−1.08981	−	1.08981i	−0.995547	−	0.0942633i	$-0.969950\pi$
$983$	−34.1686	−	34.1686i	−1.08981	−	1.08981i	−0.0942633	−	0.995547i	$-0.530050\pi$
$984$	8.44035	−	3.65323i	0.269069	−	0.116461i
$985$			1.32690i			0.0422786i
$986$	6.25909	+	6.25909i	0.199330	+	0.199330i
$987$	−50.5622	+	21.8848i	−1.60941	+	0.696601i
$988$		0			0
$989$			106.310i			3.38045i
$990$	0.536898	+	17.0020i	0.0170638	+	0.540360i
$991$	−26.8265			−0.852172			−0.426086	−	0.904683i	$-0.640108\pi$
$991$	−26.8265			−0.852172			−0.426086	+	0.904683i	$0.640108\pi$
$992$	−1.00337			−0.0318569
$993$	−34.2178	−	13.5448i	−1.08587	−	0.429830i
$994$	1.57657	+	1.57657i	0.0500057	+	0.0500057i
$995$	3.62912	+	3.62912i	0.115051	+	0.115051i
$996$	3.99273	+	1.58048i	0.126515	+	0.0500795i
$997$	−32.1094			−1.01691			−0.508457	−	0.861087i	$-0.669784\pi$
$997$	−32.1094			−1.01691			−0.508457	+	0.861087i	$0.669784\pi$
$998$	16.7572			0.530440
$999$	−8.26223	−	17.5477i	−0.261405	−	0.555186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.g.e.437.4	yes	48
3.2	odd	2	inner	1014.2.g.e.437.15	yes	48
13.5	odd	4	inner	1014.2.g.e.239.15	yes	48
13.8	odd	4	inner	1014.2.g.e.239.10	yes	48
13.12	even	2	inner	1014.2.g.e.437.21	yes	48
39.5	even	4	inner	1014.2.g.e.239.4	✓	48
39.8	even	4	inner	1014.2.g.e.239.21	yes	48
39.38	odd	2	inner	1014.2.g.e.437.10	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.g.e.239.4	✓	48	39.5	even	4	inner
1014.2.g.e.239.10	yes	48	13.8	odd	4	inner
1014.2.g.e.239.15	yes	48	13.5	odd	4	inner
1014.2.g.e.239.21	yes	48	39.8	even	4	inner
1014.2.g.e.437.4	yes	48	1.1	even	1	trivial
1014.2.g.e.437.10	yes	48	39.38	odd	2	inner
1014.2.g.e.437.15	yes	48	3.2	odd	2	inner
1014.2.g.e.437.21	yes	48	13.12	even	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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.58955 - 0.688001i) q^{3} -1.00000i q^{4} +(-0.822256 + 0.822256i) q^{5} +(-0.637488 + 1.61047i) q^{6} +(-1.88206 + 1.88206i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.05331 - 2.18722i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.58955 - 0.688001i) q^{3} -1.00000i q^{4} +(-0.822256 + 0.822256i) q^{5} +(-0.637488 + 1.61047i) q^{6} +(-1.88206 + 1.88206i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.05331 - 2.18722i) q^{9} -1.16285i q^{10} +(-3.44793 - 3.44793i) q^{11} +(-0.688001 - 1.58955i) q^{12} -2.66164i q^{14} +(-0.741300 + 1.87273i) q^{15} -1.00000 q^{16} -2.82264 q^{17} +(0.0946882 + 2.99851i) q^{18} +(-3.54655 - 3.54655i) q^{19} +(0.822256 + 0.822256i) q^{20} +(-1.69676 + 4.28648i) q^{21} +4.87612 q^{22} -9.31907 q^{23} +(1.61047 + 0.637488i) q^{24} +3.64779i q^{25} +(1.75902 - 4.88936i) q^{27} +(1.88206 + 1.88206i) q^{28} +3.13597i q^{29} +(-0.800039 - 1.84840i) q^{30} +(-0.709487 - 0.709487i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-7.85283 - 3.10846i) q^{33} +(1.99591 - 1.99591i) q^{34} -3.09507i q^{35} +(-2.18722 - 2.05331i) q^{36} +(2.63940 - 2.63940i) q^{37} +5.01558 q^{38} -1.16285 q^{40} +(3.75468 - 3.75468i) q^{41} +(-1.83121 - 4.23079i) q^{42} -11.4077i q^{43} +(-3.44793 + 3.44793i) q^{44} +(0.110108 + 3.48680i) q^{45} +(6.58958 - 6.58958i) q^{46} +(8.45064 + 8.45064i) q^{47} +(-1.58955 + 0.688001i) q^{48} -0.0843165i q^{49} +(-2.57938 - 2.57938i) q^{50} +(-4.48671 + 1.94198i) q^{51} -1.57037i q^{53} +(2.21349 + 4.70111i) q^{54} +5.67017 q^{55} -2.66164 q^{56} +(-8.07744 - 3.19738i) q^{57} +(-2.21746 - 2.21746i) q^{58} +(-3.86562 - 3.86562i) q^{59} +(1.87273 + 0.741300i) q^{60} -9.76025 q^{61} +1.00337 q^{62} +(0.252026 + 7.98094i) q^{63} +1.00000i q^{64} +(7.75081 - 3.35477i) q^{66} +(-7.61273 - 7.61273i) q^{67} +2.82264i q^{68} +(-14.8131 + 6.41153i) q^{69} +(2.18855 + 2.18855i) q^{70} +(-0.592330 + 0.592330i) q^{71} +(2.99851 - 0.0946882i) q^{72} +(-6.42392 + 6.42392i) q^{73} +3.73268i q^{74} +(2.50968 + 5.79833i) q^{75} +(-3.54655 + 3.54655i) q^{76} +12.9785 q^{77} -5.98452 q^{79} +(0.822256 - 0.822256i) q^{80} +(-0.567846 - 8.98207i) q^{81} +5.30992i q^{82} +(-1.75308 + 1.75308i) q^{83} +(4.28648 + 1.69676i) q^{84} +(2.32093 - 2.32093i) q^{85} +(8.06650 + 8.06650i) q^{86} +(2.15755 + 4.98476i) q^{87} -4.87612i q^{88} +(-4.76763 - 4.76763i) q^{89} +(-2.54340 - 2.38768i) q^{90} +9.31907i q^{92} +(-1.61589 - 0.639634i) q^{93} -11.9510 q^{94} +5.83235 q^{95} +(0.637488 - 1.61047i) q^{96} +(7.52524 + 7.52524i) q^{97} +(0.0596207 + 0.0596207i) q^{98} +(-14.6211 + 0.461711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} + 20 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 + 20 * q^9	\( 48 q - 4 q^{3} + 20 q^{9} - 48 q^{16} - 32 q^{22} + 116 q^{27} + 8 q^{40} - 40 q^{42} + 4 q^{48} - 144 q^{55} - 80 q^{61} + 96 q^{66} - 56 q^{79} + 84 q^{81} + 224 q^{87} - 16 q^{94}+O(q^{100}) \) 48 * q - 4 * q^3 + 20 * q^9 - 48 * q^16 - 32 * q^22 + 116 * q^27 + 8 * q^40 - 40 * q^42 + 4 * q^48 - 144 * q^55 - 80 * q^61 + 96 * q^66 - 56 * q^79 + 84 * q^81 + 224 * q^87 - 16 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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