LMFDB - Embedded newform 1470.2.b.b.881.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(881,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1470.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.b (of order $2$, degree $1$, 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:	$11.7380090971$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 11 x^{10} - 32 x^{9} + 64 x^{8} - 120 x^{7} + 237 x^{6} - 360 x^{5} + 576 x^{4} + \cdots + 729 $ x^12 - 4x^11 + 11x^10 - 32x^9 + 64x^8 - 120x^7 + 237x^6 - 360x^5 + 576x^4 - 864x^3 + 891x^2 - 972*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			881.4
Root			$-0.111613 + 1.72845i$ of defining polynomial
Character	$\chi$	$=$	1470.881
Dual form			1470.2.b.b.881.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.767566 + 1.55269i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.55269 - 0.767566i) q^{6} +1.00000i q^{8} +(-1.82168 + 2.38358i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.767566 + 1.55269i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.55269 - 0.767566i) q^{6} +1.00000i q^{8} +(-1.82168 + 2.38358i) q^{9} +1.00000i q^{10} +2.30680i q^{11} +(-0.767566 - 1.55269i) q^{12} -5.00084i q^{13} +(-0.767566 - 1.55269i) q^{15} +1.00000 q^{16} -6.30230 q^{17} +(2.38358 + 1.82168i) q^{18} +7.55717i q^{19} +1.00000 q^{20} +2.30680 q^{22} -6.37256i q^{23} +(-1.55269 + 0.767566i) q^{24} +1.00000 q^{25} -5.00084 q^{26} +(-5.09922 - 0.998953i) q^{27} -3.83533i q^{29} +(-1.55269 + 0.767566i) q^{30} +4.38153i q^{31} -1.00000i q^{32} +(-3.58174 + 1.77062i) q^{33} +6.30230i q^{34} +(1.82168 - 2.38358i) q^{36} -6.90930 q^{37} +7.55717 q^{38} +(7.76475 - 3.83848i) q^{39} -1.00000i q^{40} -9.79371 q^{41} +2.55278 q^{43} -2.30680i q^{44} +(1.82168 - 2.38358i) q^{45} -6.37256 q^{46} -1.65683 q^{47} +(0.767566 + 1.55269i) q^{48} -1.00000i q^{50} +(-4.83743 - 9.78550i) q^{51} +5.00084i q^{52} -3.25278i q^{53} +(-0.998953 + 5.09922i) q^{54} -2.30680i q^{55} +(-11.7339 + 5.80063i) q^{57} -3.83533 q^{58} -9.93145 q^{59} +(0.767566 + 1.55269i) q^{60} -5.98368i q^{61} +4.38153 q^{62} -1.00000 q^{64} +5.00084i q^{65} +(1.77062 + 3.58174i) q^{66} -2.76716 q^{67} +6.30230 q^{68} +(9.89460 - 4.89136i) q^{69} +2.85910i q^{71} +(-2.38358 - 1.82168i) q^{72} +3.68177i q^{73} +6.90930i q^{74} +(0.767566 + 1.55269i) q^{75} -7.55717i q^{76} +(-3.83848 - 7.76475i) q^{78} +2.55889 q^{79} -1.00000 q^{80} +(-2.36293 - 8.68427i) q^{81} +9.79371i q^{82} +1.83743 q^{83} +6.30230 q^{85} -2.55278i q^{86} +(5.95508 - 2.94387i) q^{87} -2.30680 q^{88} -5.88774 q^{89} +(-2.38358 - 1.82168i) q^{90} +6.37256i q^{92} +(-6.80316 + 3.36311i) q^{93} +1.65683i q^{94} -7.55717i q^{95} +(1.55269 - 0.767566i) q^{96} +4.61723i q^{97} +(-5.49845 - 4.20226i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	$ 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.767566	+	1.55269i	0.443154	+	0.896445i
$3$	0.767566	+	1.55269i	0.443154	+	0.896445i
$4$	−1.00000			−0.500000
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.55269	−	0.767566i	0.633883	−	0.313358i
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.82168	+	2.38358i	−0.607228	+	0.794527i
$10$			1.00000i			0.316228i
$11$			2.30680i			0.695527i	0.937582	+	0.347763i	$0.113059\pi$
$11$			2.30680i			0.695527i	−0.937582	+	0.347763i	$0.886941\pi$
$12$	−0.767566	−	1.55269i	−0.221577	−	0.448223i
$13$		−	5.00084i		−	1.38698i	−0.720464	−	0.693492i	$-0.756071\pi$
$13$		−	5.00084i		−	1.38698i	0.720464	−	0.693492i	$-0.243929\pi$
$14$		0			0
$15$	−0.767566	−	1.55269i	−0.198185	−	0.400903i
$16$	1.00000			0.250000
$17$	−6.30230			−1.52853			−0.764266	−	0.644901i	$-0.776898\pi$
$17$	−6.30230			−1.52853			−0.764266	+	0.644901i	$0.776898\pi$
$18$	2.38358	+	1.82168i	0.561816	+	0.429375i
$19$			7.55717i			1.73373i	0.498539	+	0.866867i	$0.333870\pi$
$19$			7.55717i			1.73373i	−0.498539	+	0.866867i	$0.666130\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	2.30680			0.491812
$23$		−	6.37256i		−	1.32877i	−0.747390	−	0.664385i	$-0.768693\pi$
$23$		−	6.37256i		−	1.32877i	0.747390	−	0.664385i	$-0.231307\pi$
$24$	−1.55269	+	0.767566i	−0.316941	+	0.156679i
$25$	1.00000			0.200000
$26$	−5.00084			−0.980746
$27$	−5.09922	−	0.998953i	−0.981346	−	0.192249i
$28$		0			0
$29$		−	3.83533i		−	0.712204i	−0.934447	−	0.356102i	$-0.884106\pi$
$29$		−	3.83533i		−	0.712204i	0.934447	−	0.356102i	$-0.115894\pi$
$30$	−1.55269	+	0.767566i	−0.283481	+	0.140138i
$31$			4.38153i			0.786946i	0.919336	+	0.393473i	$0.128727\pi$
$31$			4.38153i			0.786946i	−0.919336	+	0.393473i	$0.871273\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.58174	+	1.77062i	−0.623501	+	0.308226i
$34$			6.30230i			1.08083i
$35$		0			0
$36$	1.82168	−	2.38358i	0.303614	−	0.397264i
$37$	−6.90930			−1.13588			−0.567941	−	0.823069i	$-0.692260\pi$
$37$	−6.90930			−1.13588			−0.567941	+	0.823069i	$0.692260\pi$
$38$	7.55717			1.22594
$39$	7.76475	−	3.83848i	1.24335	−	0.614648i
$40$		−	1.00000i		−	0.158114i
$41$	−9.79371			−1.52952			−0.764760	−	0.644315i	$-0.777143\pi$
$41$	−9.79371			−1.52952			−0.764760	+	0.644315i	$0.777143\pi$
$42$		0			0
$43$	2.55278			0.389296			0.194648	−	0.980873i	$-0.437644\pi$
$43$	2.55278			0.389296			0.194648	+	0.980873i	$0.437644\pi$
$44$		−	2.30680i		−	0.347763i
$45$	1.82168	−	2.38358i	0.271561	−	0.355323i
$46$	−6.37256			−0.939583
$47$	−1.65683			−0.241674			−0.120837	−	0.992672i	$-0.538558\pi$
$47$	−1.65683			−0.241674			−0.120837	+	0.992672i	$0.538558\pi$
$48$	0.767566	+	1.55269i	0.110789	+	0.224111i
$49$		0			0
$50$		−	1.00000i		−	0.141421i
$51$	−4.83743	−	9.78550i	−0.677375	−	1.37024i
$52$			5.00084i			0.693492i
$53$		−	3.25278i		−	0.446804i	−0.974726	−	0.223402i	$-0.928284\pi$
$53$		−	3.25278i		−	0.446804i	0.974726	−	0.223402i	$-0.0717163\pi$
$54$	−0.998953	+	5.09922i	−0.135940	+	0.693917i
$55$		−	2.30680i		−	0.311049i
$56$		0			0
$57$	−11.7339	+	5.80063i	−1.55420	+	0.768312i
$58$	−3.83533			−0.503604
$59$	−9.93145			−1.29297			−0.646483	−	0.762929i	$-0.723761\pi$
$59$	−9.93145			−1.29297			−0.646483	+	0.762929i	$0.723761\pi$
$60$	0.767566	+	1.55269i	0.0990923	+	0.200451i
$61$		−	5.98368i		−	0.766131i	−0.923721	−	0.383066i	$-0.874868\pi$
$61$		−	5.98368i		−	0.766131i	0.923721	−	0.383066i	$-0.125132\pi$
$62$	4.38153			0.556455
$63$		0			0
$64$	−1.00000			−0.125000
$65$			5.00084i			0.620278i
$66$	1.77062	+	3.58174i	0.217948	+	0.440882i
$67$	−2.76716			−0.338063			−0.169031	−	0.985611i	$-0.554064\pi$
$67$	−2.76716			−0.338063			−0.169031	+	0.985611i	$0.554064\pi$
$68$	6.30230			0.764266
$69$	9.89460	−	4.89136i	1.19117	−	0.588851i
$70$		0			0
$71$			2.85910i			0.339312i	0.985503	+	0.169656i	$0.0542657\pi$
$71$			2.85910i			0.339312i	−0.985503	+	0.169656i	$0.945734\pi$
$72$	−2.38358	−	1.82168i	−0.280908	−	0.214688i
$73$			3.68177i			0.430919i	0.976513	+	0.215459i	$0.0691249\pi$
$73$			3.68177i			0.430919i	−0.976513	+	0.215459i	$0.930875\pi$
$74$			6.90930i			0.803190i
$75$	0.767566	+	1.55269i	0.0886309	+	0.179289i
$76$		−	7.55717i		−	0.866867i
$77$		0			0
$78$	−3.83848	−	7.76475i	−0.434622	−	0.879185i
$79$	2.55889			0.287898			0.143949	−	0.989585i	$-0.454020\pi$
$79$	2.55889			0.287898			0.143949	+	0.989585i	$0.454020\pi$
$80$	−1.00000			−0.111803
$81$	−2.36293	−	8.68427i	−0.262548	−	0.964919i
$82$			9.79371i			1.08153i
$83$	1.83743			0.201684			0.100842	−	0.994902i	$-0.467846\pi$
$83$	1.83743			0.201684			0.100842	+	0.994902i	$0.467846\pi$
$84$		0			0
$85$	6.30230			0.683580
$86$		−	2.55278i		−	0.275274i
$87$	5.95508	−	2.94387i	0.638452	−	0.315616i
$88$	−2.30680			−0.245906
$89$	−5.88774			−0.624100			−0.312050	−	0.950066i	$-0.601016\pi$
$89$	−5.88774			−0.624100			−0.312050	+	0.950066i	$0.601016\pi$
$90$	−2.38358	−	1.82168i	−0.251252	−	0.192022i
$91$		0			0
$92$			6.37256i			0.664385i
$93$	−6.80316	+	3.36311i	−0.705454	+	0.348739i
$94$			1.65683i			0.170889i
$95$		−	7.55717i		−	0.775350i
$96$	1.55269	−	0.767566i	0.158471	−	0.0783394i
$97$			4.61723i			0.468808i	0.972139	+	0.234404i	$0.0753139\pi$
$97$			4.61723i			0.468808i	−0.972139	+	0.234404i	$0.924686\pi$
$98$		0			0
$99$	−5.49845	−	4.20226i	−0.552615	−	0.422343i
$100$	−1.00000			−0.100000
$101$	−11.3140			−1.12579			−0.562894	−	0.826529i	$-0.690312\pi$
$101$	−11.3140			−1.12579			−0.562894	+	0.826529i	$0.690312\pi$
$102$	−9.78550	+	4.83743i	−0.968909	+	0.478977i
$103$			7.36407i			0.725603i	0.931866	+	0.362802i	$0.118180\pi$
$103$			7.36407i			0.725603i	−0.931866	+	0.362802i	$0.881820\pi$
$104$	5.00084			0.490373
$105$		0			0
$106$	−3.25278			−0.315938
$107$			8.41874i			0.813870i	0.913457	+	0.406935i	$0.133402\pi$
$107$			8.41874i			0.813870i	−0.913457	+	0.406935i	$0.866598\pi$
$108$	5.09922	+	0.998953i	0.490673	+	0.0961243i
$109$	−6.66311			−0.638211			−0.319105	−	0.947719i	$-0.603382\pi$
$109$	−6.66311			−0.638211			−0.319105	+	0.947719i	$0.603382\pi$
$110$	−2.30680			−0.219945
$111$	−5.30334	−	10.7280i	−0.503371	−	1.01826i
$112$		0			0
$113$		−	4.45505i		−	0.419096i	−0.977798	−	0.209548i	$-0.932801\pi$
$113$		−	4.45505i		−	0.419096i	0.977798	−	0.209548i	$-0.0671992\pi$
$114$	5.80063	+	11.7339i	0.543279	+	1.09898i
$115$			6.37256i			0.594244i
$116$			3.83533i			0.356102i
$117$	11.9199	+	9.10996i	1.10200	+	0.842216i
$118$			9.93145i			0.914264i
$119$		0			0
$120$	1.55269	−	0.767566i	0.141740	−	0.0700689i
$121$	5.67867			0.516243
$122$	−5.98368			−0.541737
$123$	−7.51732	−	15.2066i	−0.677814	−	1.37113i
$124$		−	4.38153i		−	0.393473i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.83694			−0.163002			−0.0815011	−	0.996673i	$-0.525971\pi$
$127$	−1.83694			−0.163002			−0.0815011	+	0.996673i	$0.525971\pi$
$128$			1.00000i			0.0883883i
$129$	1.95943	+	3.96368i	0.172518	+	0.348982i
$130$	5.00084			0.438603
$131$	−5.53883			−0.483930			−0.241965	−	0.970285i	$-0.577792\pi$
$131$	−5.53883			−0.483930			−0.241965	+	0.970285i	$0.577792\pi$
$132$	3.58174	−	1.77062i	0.311751	−	0.154113i
$133$		0			0
$134$			2.76716i			0.239047i
$135$	5.09922	+	0.998953i	0.438871	+	0.0859762i
$136$		−	6.30230i		−	0.540417i
$137$			1.24104i			0.106029i	0.998594	+	0.0530146i	$0.0168830\pi$
$137$			1.24104i			0.106029i	−0.998594	+	0.0530146i	$0.983117\pi$
$138$	−4.89136	−	9.89460i	−0.416380	−	0.842285i
$139$			12.5344i			1.06315i	0.847011	+	0.531576i	$0.178400\pi$
$139$			12.5344i			1.06315i	−0.847011	+	0.531576i	$0.821600\pi$
$140$		0			0
$141$	−1.27173	−	2.57255i	−0.107099	−	0.216647i
$142$	2.85910			0.239930
$143$	11.5359			0.964684
$144$	−1.82168	+	2.38358i	−0.151807	+	0.198632i
$145$			3.83533i			0.318507i
$146$	3.68177			0.304706
$147$		0			0
$148$	6.90930			0.567941
$149$		−	15.5951i		−	1.27760i	−0.769371	−	0.638802i	$-0.779430\pi$
$149$		−	15.5951i		−	1.27760i	0.769371	−	0.638802i	$-0.220570\pi$
$150$	1.55269	−	0.767566i	0.126777	−	0.0626715i
$151$	3.03915			0.247323			0.123661	−	0.992324i	$-0.460536\pi$
$151$	3.03915			0.247323			0.123661	+	0.992324i	$0.460536\pi$
$152$	−7.55717			−0.612968
$153$	11.4808	−	15.0220i	0.928168	−	1.21446i
$154$		0			0
$155$		−	4.38153i		−	0.351933i
$156$	−7.76475	+	3.83848i	−0.621677	+	0.307324i
$157$		−	15.8252i		−	1.26299i	−0.775381	−	0.631494i	$-0.782442\pi$
$157$		−	15.8252i		−	1.26299i	0.775381	−	0.631494i	$-0.217558\pi$
$158$		−	2.55889i		−	0.203575i
$159$	5.05056	−	2.49673i	0.400535	−	0.198003i
$160$			1.00000i			0.0790569i
$161$		0			0
$162$	−8.68427	+	2.36293i	−0.682301	+	0.185649i
$163$	−8.61682			−0.674921			−0.337461	−	0.941340i	$-0.609568\pi$
$163$	−8.61682			−0.674921			−0.337461	+	0.941340i	$0.609568\pi$
$164$	9.79371			0.764760
$165$	3.58174	−	1.77062i	0.278838	−	0.137843i
$166$		−	1.83743i		−	0.142612i
$167$	8.64948			0.669317			0.334658	−	0.942339i	$-0.391379\pi$
$167$	8.64948			0.669317			0.334658	+	0.942339i	$0.391379\pi$
$168$		0			0
$169$	−12.0084			−0.923724
$170$		−	6.30230i		−	0.483364i
$171$	−18.0131	−	13.7668i	−1.37750	−	1.05277i
$172$	−2.55278			−0.194648
$173$	17.9315			1.36330			0.681652	−	0.731677i	$-0.261262\pi$
$173$	17.9315			1.36330			0.681652	+	0.731677i	$0.261262\pi$
$174$	−2.94387	−	5.95508i	−0.223174	−	0.451454i
$175$		0			0
$176$			2.30680i			0.173882i
$177$	−7.62305	−	15.4205i	−0.572983	−	1.15907i
$178$			5.88774i			0.441305i
$179$			12.0170i			0.898190i	0.893484	+	0.449095i	$0.148253\pi$
$179$			12.0170i			0.898190i	−0.893484	+	0.449095i	$0.851747\pi$
$180$	−1.82168	+	2.38358i	−0.135780	+	0.177662i
$181$			9.52612i			0.708071i	0.935232	+	0.354036i	$0.115191\pi$
$181$			9.52612i			0.708071i	−0.935232	+	0.354036i	$0.884809\pi$
$182$		0			0
$183$	9.29079	−	4.59287i	0.686795	−	0.339514i
$184$	6.37256			0.469791
$185$	6.90930			0.507982
$186$	3.36311	+	6.80316i	0.246596	+	0.498832i
$187$		−	14.5381i		−	1.06313i
$188$	1.65683			0.120837
$189$		0			0
$190$	−7.55717			−0.548255
$191$		−	4.97173i		−	0.359741i	−0.983690	−	0.179871i	$-0.942432\pi$
$191$		−	4.97173i		−	0.359741i	0.983690	−	0.179871i	$-0.0575679\pi$
$192$	−0.767566	−	1.55269i	−0.0553943	−	0.112056i
$193$	6.03321			0.434280			0.217140	−	0.976140i	$-0.430327\pi$
$193$	6.03321			0.434280			0.217140	+	0.976140i	$0.430327\pi$
$194$	4.61723			0.331498
$195$	−7.76475	+	3.83848i	−0.556045	+	0.274879i
$196$		0			0
$197$			14.2144i			1.01273i	0.862318	+	0.506366i	$0.169012\pi$
$197$			14.2144i			1.01273i	−0.862318	+	0.506366i	$0.830988\pi$
$198$	−4.20226	+	5.49845i	−0.298642	+	0.390758i
$199$		−	2.25088i		−	0.159560i	−0.996812	−	0.0797802i	$-0.974578\pi$
$199$		−	2.25088i		−	0.159560i	0.996812	−	0.0797802i	$-0.0254219\pi$
$200$			1.00000i			0.0707107i
$201$	−2.12398	−	4.29655i	−0.149814	−	0.303055i
$202$			11.3140i			0.796053i
$203$		0			0
$204$	4.83743	+	9.78550i	0.338688	+	0.685122i
$205$	9.79371			0.684022
$206$	7.36407			0.513079
$207$	15.1895	+	11.6088i	1.05574	+	0.806867i
$208$		−	5.00084i		−	0.346746i
$209$	−17.4329			−1.20586
$210$		0			0
$211$	27.6034			1.90029			0.950147	−	0.311804i	$-0.100933\pi$
$211$	27.6034			1.90029			0.950147	+	0.311804i	$0.100933\pi$
$212$			3.25278i			0.223402i
$213$	−4.43929	+	2.19455i	−0.304175	+	0.150368i
$214$	8.41874			0.575493
$215$	−2.55278			−0.174098
$216$	0.998953	−	5.09922i	0.0679701	−	0.346958i
$217$		0			0
$218$			6.66311i			0.451283i
$219$	−5.71664	+	2.82600i	−0.386295	+	0.190964i
$220$			2.30680i			0.155524i
$221$			31.5168i			2.12005i
$222$	−10.7280	+	5.30334i	−0.720016	+	0.355937i
$223$			23.0777i			1.54539i	0.634775	+	0.772697i	$0.281093\pi$
$223$			23.0777i			1.54539i	−0.634775	+	0.772697i	$0.718907\pi$
$224$		0			0
$225$	−1.82168	+	2.38358i	−0.121446	+	0.158905i
$226$	−4.45505			−0.296345
$227$	−20.0351			−1.32977			−0.664887	−	0.746944i	$-0.731520\pi$
$227$	−20.0351			−1.32977			−0.664887	+	0.746944i	$0.731520\pi$
$228$	11.7339	−	5.80063i	0.777099	−	0.384156i
$229$			28.7648i			1.90083i	0.310979	+	0.950417i	$0.399343\pi$
$229$			28.7648i			1.90083i	−0.310979	+	0.950417i	$0.600657\pi$
$230$	6.37256			0.420194
$231$		0			0
$232$	3.83533			0.251802
$233$			25.7115i			1.68442i	0.539151	+	0.842209i	$0.318745\pi$
$233$			25.7115i			1.68442i	−0.539151	+	0.842209i	$0.681255\pi$
$234$	9.10996	−	11.9199i	0.595536	−	0.779229i
$235$	1.65683			0.108080
$236$	9.93145			0.646483
$237$	1.96412	+	3.97317i	0.127583	+	0.258085i
$238$		0			0
$239$			10.7220i			0.693551i	0.937948	+	0.346776i	$0.112723\pi$
$239$			10.7220i			0.693551i	−0.937948	+	0.346776i	$0.887277\pi$
$240$	−0.767566	−	1.55269i	−0.0495462	−	0.100226i
$241$		−	1.18465i		−	0.0763100i	−0.999272	−	0.0381550i	$-0.987852\pi$
$241$		−	1.18465i		−	0.0763100i	0.999272	−	0.0381550i	$-0.0121481\pi$
$242$		−	5.67867i		−	0.365039i
$243$	11.6703	−	10.3346i	0.748648	−	0.662968i
$244$			5.98368i			0.383066i
$245$		0			0
$246$	−15.2066	+	7.51732i	−0.969536	+	0.479287i
$247$	37.7922			2.40466
$248$	−4.38153			−0.278228
$249$	1.41035	+	2.85295i	0.0893771	+	0.180799i
$250$			1.00000i			0.0632456i
$251$	14.3689			0.906958			0.453479	−	0.891267i	$-0.350183\pi$
$251$	14.3689			0.906958			0.453479	+	0.891267i	$0.350183\pi$
$252$		0			0
$253$	14.7002			0.924195
$254$			1.83694i			0.115260i
$255$	4.83743	+	9.78550i	0.302932	+	0.612792i
$256$	1.00000			0.0625000
$257$	16.5360			1.03149			0.515745	−	0.856742i	$-0.327515\pi$
$257$	16.5360			1.03149			0.515745	+	0.856742i	$0.327515\pi$
$258$	3.96368	−	1.95943i	0.246768	−	0.121989i
$259$		0			0
$260$		−	5.00084i		−	0.310139i
$261$	9.14184	+	6.98677i	0.565865	+	0.432470i
$262$			5.53883i			0.342190i
$263$		−	30.9400i		−	1.90784i	−0.300060	−	0.953920i	$-0.597007\pi$
$263$		−	30.9400i		−	1.90784i	0.300060	−	0.953920i	$-0.402993\pi$
$264$	−1.77062	−	3.58174i	−0.108974	−	0.220441i
$265$			3.25278i			0.199817i
$266$		0			0
$267$	−4.51923	−	9.14184i	−0.276573	−	0.559471i
$268$	2.76716			0.169031
$269$	−4.10422			−0.250239			−0.125119	−	0.992142i	$-0.539931\pi$
$269$	−4.10422			−0.250239			−0.125119	+	0.992142i	$0.539931\pi$
$270$	0.998953	−	5.09922i	0.0607943	−	0.310329i
$271$		−	9.07677i		−	0.551374i	−0.961247	−	0.275687i	$-0.911095\pi$
$271$		−	9.07677i		−	0.551374i	0.961247	−	0.275687i	$-0.0889054\pi$
$272$	−6.30230			−0.382133
$273$		0			0
$274$	1.24104			0.0749740
$275$			2.30680i			0.139105i
$276$	−9.89460	+	4.89136i	−0.595585	+	0.294425i
$277$	0.216476			0.0130068			0.00650338	−	0.999979i	$-0.497930\pi$
$277$	0.216476			0.0130068			0.00650338	+	0.999979i	$0.497930\pi$
$278$	12.5344			0.751761
$279$	−10.4437	−	7.98177i	−0.625250	−	0.477856i
$280$		0			0
$281$			18.8498i			1.12448i	0.826973	+	0.562241i	$0.190061\pi$
$281$			18.8498i			1.12448i	−0.826973	+	0.562241i	$0.809939\pi$
$282$	−2.57255	+	1.27173i	−0.153193	+	0.0757303i
$283$			1.99832i			0.118788i	0.998235	+	0.0593939i	$0.0189168\pi$
$283$			1.99832i			0.118788i	−0.998235	+	0.0593939i	$0.981083\pi$
$284$		−	2.85910i		−	0.169656i
$285$	11.7339	−	5.80063i	0.695059	−	0.343600i
$286$		−	11.5359i		−	0.682135i
$287$		0			0
$288$	2.38358	+	1.82168i	0.140454	+	0.107344i
$289$	22.7189			1.33641
$290$	3.83533			0.225219
$291$	−7.16912	+	3.54403i	−0.420261	+	0.207755i
$292$		−	3.68177i		−	0.215459i
$293$	−9.28117			−0.542212			−0.271106	−	0.962550i	$-0.587389\pi$
$293$	−9.28117			−0.542212			−0.271106	+	0.962550i	$0.587389\pi$
$294$		0			0
$295$	9.93145			0.578232
$296$		−	6.90930i		−	0.401595i
$297$	2.30439	−	11.7629i	0.133714	−	0.682552i
$298$	−15.5951			−0.903403
$299$	−31.8682			−1.84298
$300$	−0.767566	−	1.55269i	−0.0443154	−	0.0896445i
$301$		0			0
$302$		−	3.03915i		−	0.174883i
$303$	−8.68427	−	17.5672i	−0.498898	−	1.00921i
$304$			7.55717i			0.433434i
$305$			5.98368i			0.342624i
$306$	−15.0220	−	11.4808i	−0.858753	−	0.656314i
$307$		−	26.9282i		−	1.53687i	−0.639927	−	0.768436i	$-0.721035\pi$
$307$		−	26.9282i		−	1.53687i	0.639927	−	0.768436i	$-0.278965\pi$
$308$		0			0
$309$	−11.4341	+	5.65241i	−0.650464	+	0.321554i
$310$	−4.38153			−0.248854
$311$	2.82130			0.159981			0.0799905	−	0.996796i	$-0.474511\pi$
$311$	2.82130			0.159981			0.0799905	+	0.996796i	$0.474511\pi$
$312$	3.83848	+	7.76475i	0.217311	+	0.439592i
$313$		−	11.4427i		−	0.646780i	−0.946266	−	0.323390i	$-0.895177\pi$
$313$		−	11.4427i		−	0.646780i	0.946266	−	0.323390i	$-0.104823\pi$
$314$	−15.8252			−0.893068
$315$		0			0
$316$	−2.55889			−0.143949
$317$			9.30982i			0.522891i	0.965218	+	0.261446i	$0.0841992\pi$
$317$			9.30982i			0.522891i	−0.965218	+	0.261446i	$0.915801\pi$
$318$	−2.49673	−	5.05056i	−0.140009	−	0.283221i
$319$	8.84735			0.495357
$320$	1.00000			0.0559017
$321$	−13.0717	+	6.46194i	−0.729590	+	0.360670i
$322$		0			0
$323$		−	47.6275i		−	2.65007i
$324$	2.36293	+	8.68427i	0.131274	+	0.482460i
$325$		−	5.00084i		−	0.277397i
$326$			8.61682i			0.477241i
$327$	−5.11438	−	10.3457i	−0.282826	−	0.572121i
$328$		−	9.79371i		−	0.540767i
$329$		0			0
$330$	−1.77062	−	3.58174i	−0.0974695	−	0.197168i
$331$	18.2960			1.00564			0.502820	−	0.864391i	$-0.332296\pi$
$331$	18.2960			1.00564			0.502820	+	0.864391i	$0.332296\pi$
$332$	−1.83743			−0.100842
$333$	12.5866	−	16.4689i	0.689740	−	0.902489i
$334$		−	8.64948i		−	0.473279i
$335$	2.76716			0.151186
$336$		0			0
$337$	7.84516			0.427353			0.213676	−	0.976904i	$-0.431456\pi$
$337$	7.84516			0.427353			0.213676	+	0.976904i	$0.431456\pi$
$338$			12.0084i			0.653171i
$339$	6.91730	−	3.41954i	0.375696	−	0.185724i
$340$	−6.30230			−0.341790
$341$	−10.1073			−0.547342
$342$	−13.7668	+	18.0131i	−0.744423	+	0.974039i
$343$		0			0
$344$			2.55278i			0.137637i
$345$	−9.89460	+	4.89136i	−0.532708	+	0.263342i
$346$		−	17.9315i		−	0.964001i
$347$		−	0.232294i		−	0.0124702i	−0.999981	−	0.00623509i	$-0.998015\pi$
$347$		−	0.232294i		−	0.0124702i	0.999981	−	0.00623509i	$-0.00198470\pi$
$348$	−5.95508	+	2.94387i	−0.319226	+	0.157808i
$349$		−	11.5685i		−	0.619249i	−0.950859	−	0.309624i	$-0.899797\pi$
$349$		−	11.5685i		−	0.619249i	0.950859	−	0.309624i	$-0.100203\pi$
$350$		0			0
$351$	−4.99561	+	25.5004i	−0.266646	+	1.36111i
$352$	2.30680			0.122953
$353$	34.7075			1.84729			0.923646	−	0.383247i	$-0.125194\pi$
$353$	34.7075			1.84729			0.923646	+	0.383247i	$0.125194\pi$
$354$	−15.4205	+	7.62305i	−0.819588	+	0.405160i
$355$		−	2.85910i		−	0.151745i
$356$	5.88774			0.312050
$357$		0			0
$358$	12.0170			0.635116
$359$		−	17.5322i		−	0.925316i	−0.886537	−	0.462658i	$-0.846896\pi$
$359$		−	17.5322i		−	0.925316i	0.886537	−	0.462658i	$-0.153104\pi$
$360$	2.38358	+	1.82168i	0.125626	+	0.0960112i
$361$	−38.1109			−2.00584
$362$	9.52612			0.500682
$363$	4.35875	+	8.81721i	0.228775	+	0.462783i
$364$		0			0
$365$		−	3.68177i		−	0.192713i
$366$	−4.59287	−	9.29079i	−0.240073	−	0.485637i
$367$			10.0402i			0.524093i	0.965055	+	0.262047i	$0.0843974\pi$
$367$			10.0402i			0.524093i	−0.965055	+	0.262047i	$0.915603\pi$
$368$		−	6.37256i		−	0.332193i
$369$	17.8411	−	23.3441i	0.928768	−	1.21525i
$370$		−	6.90930i		−	0.359197i
$371$		0			0
$372$	6.80316	−	3.36311i	0.352727	−	0.174369i
$373$	−0.00482067			−0.000249605			−0.000124803	−	1.00000i	$-0.500040\pi$
$373$	−0.00482067			−0.000249605			−0.000124803		1.00000i	$0.500040\pi$
$374$	−14.5381			−0.751749
$375$	−0.767566	−	1.55269i	−0.0396369	−	0.0801805i
$376$		−	1.65683i		−	0.0854446i
$377$	−19.1799			−0.987815
$378$		0			0
$379$	18.6572			0.958356			0.479178	−	0.877718i	$-0.340935\pi$
$379$	18.6572			0.958356			0.479178	+	0.877718i	$0.340935\pi$
$380$			7.55717i			0.387675i
$381$	−1.40997	−	2.85220i	−0.0722352	−	0.146123i
$382$	−4.97173			−0.254376
$383$	−18.8463			−0.963002			−0.481501	−	0.876446i	$-0.659908\pi$
$383$	−18.8463			−0.963002			−0.481501	+	0.876446i	$0.659908\pi$
$384$	−1.55269	+	0.767566i	−0.0792353	+	0.0391697i
$385$		0			0
$386$		−	6.03321i		−	0.307082i
$387$	−4.65037	+	6.08477i	−0.236391	+	0.309306i
$388$		−	4.61723i		−	0.234404i
$389$		−	10.8601i		−	0.550627i	−0.961354	−	0.275314i	$-0.911218\pi$
$389$		−	10.8601i		−	0.550627i	0.961354	−	0.275314i	$-0.0887817\pi$
$390$	3.83848	+	7.76475i	0.194369	+	0.393183i
$391$			40.1618i			2.03107i
$392$		0			0
$393$	−4.25142	−	8.60008i	−0.214456	−	0.433817i
$394$	14.2144			0.716110
$395$	−2.55889			−0.128752
$396$	5.49845	+	4.20226i	0.276307	+	0.211172i
$397$		−	27.0408i		−	1.35714i	−0.734536	−	0.678570i	$-0.762600\pi$
$397$		−	27.0408i		−	1.35714i	0.734536	−	0.678570i	$-0.237400\pi$
$398$	−2.25088			−0.112826
$399$		0			0
$400$	1.00000			0.0500000
$401$			24.5254i			1.22474i	0.790571	+	0.612371i	$0.209784\pi$
$401$			24.5254i			1.22474i	−0.790571	+	0.612371i	$0.790216\pi$
$402$	−4.29655	+	2.12398i	−0.214292	+	0.105935i
$403$	21.9113			1.09148
$404$	11.3140			0.562894
$405$	2.36293	+	8.68427i	0.117415	+	0.431525i
$406$		0			0
$407$		−	15.9384i		−	0.790036i
$408$	9.78550	−	4.83743i	0.484455	−	0.239488i
$409$		−	5.40347i		−	0.267184i	−0.991036	−	0.133592i	$-0.957349\pi$
$409$		−	5.40347i		−	0.267184i	0.991036	−	0.133592i	$-0.0426512\pi$
$410$		−	9.79371i		−	0.483677i
$411$	−1.92695	+	0.952581i	−0.0950494	+	0.0469873i
$412$		−	7.36407i		−	0.362802i
$413$		0			0
$414$	11.6088	−	15.1895i	0.570541	−	0.746524i
$415$	−1.83743			−0.0901958
$416$	−5.00084			−0.245186
$417$	−19.4620	+	9.62095i	−0.953057	+	0.471140i
$418$			17.4329i			0.852671i
$419$	28.2930			1.38220			0.691101	−	0.722758i	$-0.257126\pi$
$419$	28.2930			1.38220			0.691101	+	0.722758i	$0.257126\pi$
$420$		0			0
$421$	−25.1687			−1.22665			−0.613323	−	0.789832i	$-0.710168\pi$
$421$	−25.1687			−1.22665			−0.613323	+	0.789832i	$0.710168\pi$
$422$		−	27.6034i		−	1.34371i
$423$	3.01823	−	3.94920i	0.146751	−	0.192017i
$424$	3.25278			0.157969
$425$	−6.30230			−0.305706
$426$	2.19455	+	4.43929i	0.106326	+	0.215084i
$427$		0			0
$428$		−	8.41874i		−	0.406935i
$429$	8.85460	+	17.9117i	0.427504	+	0.864786i
$430$			2.55278i			0.123106i
$431$		−	11.2182i		−	0.540361i	−0.962810	−	0.270181i	$-0.912917\pi$
$431$		−	11.2182i		−	0.540361i	0.962810	−	0.270181i	$-0.0870834\pi$
$432$	−5.09922	−	0.998953i	−0.245337	−	0.0480622i
$433$			0.639592i			0.0307368i	0.999882	+	0.0153684i	$0.00489211\pi$
$433$			0.639592i			0.0307368i	−0.999882	+	0.0153684i	$0.995108\pi$
$434$		0			0
$435$	−5.95508	+	2.94387i	−0.285524	+	0.141148i
$436$	6.66311			0.319105
$437$	48.1585			2.30374
$438$	2.82600	+	5.71664i	0.135032	+	0.273152i
$439$		−	13.1635i		−	0.628259i	−0.949380	−	0.314129i	$-0.898287\pi$
$439$		−	13.1635i		−	0.628259i	0.949380	−	0.314129i	$-0.101713\pi$
$440$	2.30680			0.109972
$441$		0			0
$442$	31.5168			1.49910
$443$			25.8446i			1.22791i	0.789339	+	0.613957i	$0.210423\pi$
$443$			25.8446i			1.22791i	−0.789339	+	0.613957i	$0.789577\pi$
$444$	5.30334	+	10.7280i	0.251686	+	0.509128i
$445$	5.88774			0.279106
$446$	23.0777			1.09276
$447$	24.2144	−	11.9703i	1.14530	−	0.566176i
$448$		0			0
$449$		−	28.3586i		−	1.33833i	−0.743116	−	0.669163i	$-0.766653\pi$
$449$		−	28.3586i		−	1.33833i	0.743116	−	0.669163i	$-0.233347\pi$
$450$	2.38358	+	1.82168i	0.112363	+	0.0858750i
$451$		−	22.5921i		−	1.06382i
$452$			4.45505i			0.209548i
$453$	2.33275	+	4.71885i	0.109602	+	0.221711i
$454$			20.0351i			0.940293i
$455$		0			0
$456$	−5.80063	−	11.7339i	−0.271639	−	0.549492i
$457$	−29.1905			−1.36547			−0.682737	−	0.730664i	$-0.739211\pi$
$457$	−29.1905			−1.36547			−0.682737	+	0.730664i	$0.739211\pi$
$458$	28.7648			1.34409
$459$	32.1368	+	6.29570i	1.50002	+	0.293858i
$460$		−	6.37256i		−	0.297122i
$461$	−31.0968			−1.44832			−0.724162	−	0.689630i	$-0.757773\pi$
$461$	−31.0968			−1.44832			−0.724162	+	0.689630i	$0.757773\pi$
$462$		0			0
$463$	−33.4915			−1.55648			−0.778240	−	0.627967i	$-0.783887\pi$
$463$	−33.4915			−1.55648			−0.778240	+	0.627967i	$0.783887\pi$
$464$		−	3.83533i		−	0.178051i
$465$	6.80316	−	3.36311i	0.315489	−	0.155961i
$466$	25.7115			1.19106
$467$	−14.8251			−0.686023			−0.343012	−	0.939331i	$-0.611447\pi$
$467$	−14.8251			−0.686023			−0.343012	+	0.939331i	$0.611447\pi$
$468$	−11.9199	−	9.10996i	−0.550998	−	0.421108i
$469$		0			0
$470$		−	1.65683i		−	0.0764240i
$471$	24.5716	−	12.1469i	1.13220	−	0.559699i
$472$		−	9.93145i		−	0.457132i
$473$			5.88876i			0.270765i
$474$	3.97317	−	1.96412i	0.182494	−	0.0902150i
$475$			7.55717i			0.346747i
$476$		0			0
$477$	7.75328	+	5.92555i	0.354998	+	0.271312i
$478$	10.7220			0.490415
$479$	−23.0447			−1.05294			−0.526469	−	0.850194i	$-0.676484\pi$
$479$	−23.0447			−1.05294			−0.526469	+	0.850194i	$0.676484\pi$
$480$	−1.55269	+	0.767566i	−0.0708702	+	0.0350344i
$481$			34.5523i			1.57545i
$482$	−1.18465			−0.0539593
$483$		0			0
$484$	−5.67867			−0.258121
$485$		−	4.61723i		−	0.209658i
$486$	−10.3346	−	11.6703i	−0.468789	−	0.529374i
$487$	−10.6277			−0.481586			−0.240793	−	0.970577i	$-0.577407\pi$
$487$	−10.6277			−0.481586			−0.240793	+	0.970577i	$0.577407\pi$
$488$	5.98368			0.270868
$489$	−6.61397	−	13.3792i	−0.299094	−	0.605030i
$490$		0			0
$491$			22.4687i			1.01400i	0.861947	+	0.506998i	$0.169245\pi$
$491$			22.4687i			1.01400i	−0.861947	+	0.506998i	$0.830755\pi$
$492$	7.51732	+	15.2066i	0.338907	+	0.685566i
$493$			24.1714i			1.08863i
$494$		−	37.7922i		−	1.70035i
$495$	5.49845	+	4.20226i	0.247137	+	0.188878i
$496$			4.38153i			0.196737i
$497$		0			0
$498$	2.85295	−	1.41035i	0.127844	−	0.0631992i
$499$	−39.7588			−1.77985			−0.889925	−	0.456107i	$-0.849243\pi$
$499$	−39.7588			−1.77985			−0.889925	+	0.456107i	$0.849243\pi$
$500$	1.00000			0.0447214
$501$	6.63905	+	13.4300i	0.296611	+	0.600006i
$502$		−	14.3689i		−	0.641316i
$503$	−18.6717			−0.832530			−0.416265	−	0.909243i	$-0.636661\pi$
$503$	−18.6717			−0.832530			−0.416265	+	0.909243i	$0.636661\pi$
$504$		0			0
$505$	11.3140			0.503468
$506$		−	14.7002i		−	0.653505i
$507$	−9.21725	−	18.6453i	−0.409352	−	0.828068i
$508$	1.83694			0.0815011
$509$	4.03287			0.178754			0.0893768	−	0.995998i	$-0.471512\pi$
$509$	4.03287			0.178754			0.0893768	+	0.995998i	$0.471512\pi$
$510$	9.78550	−	4.83743i	0.433309	−	0.214205i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	7.54926	−	38.5357i	0.333308	−	1.70139i
$514$		−	16.5360i		−	0.729374i
$515$		−	7.36407i		−	0.324500i
$516$	−1.95943	−	3.96368i	−0.0862591	−	0.174491i
$517$		−	3.82198i		−	0.168091i
$518$		0			0
$519$	13.7636	+	27.8420i	0.604154	+	1.22213i
$520$	−5.00084			−0.219301
$521$	−10.5547			−0.462408			−0.231204	−	0.972905i	$-0.574266\pi$
$521$	−10.5547			−0.462408			−0.231204	+	0.972905i	$0.574266\pi$
$522$	6.98677	−	9.14184i	0.305803	−	0.400127i
$523$		−	20.5323i		−	0.897814i	−0.893579	−	0.448907i	$-0.851814\pi$
$523$		−	20.5323i		−	0.897814i	0.893579	−	0.448907i	$-0.148186\pi$
$524$	5.53883			0.241965
$525$		0			0
$526$	−30.9400			−1.34905
$527$		−	27.6137i		−	1.20287i
$528$	−3.58174	+	1.77062i	−0.155875	+	0.0770564i
$529$	−17.6095			−0.765632
$530$	3.25278			0.141292
$531$	18.0920	−	23.6724i	0.785125	−	1.02730i
$532$		0			0
$533$			48.9768i			2.12142i
$534$	−9.14184	+	4.51923i	−0.395606	+	0.195566i
$535$		−	8.41874i		−	0.363974i
$536$		−	2.76716i		−	0.119523i
$537$	−18.6586	+	9.22381i	−0.805178	+	0.398037i
$538$			4.10422i			0.176946i
$539$		0			0
$540$	−5.09922	−	0.998953i	−0.219436	−	0.0429881i
$541$	−9.18511			−0.394899			−0.197449	−	0.980313i	$-0.563266\pi$
$541$	−9.18511			−0.394899			−0.197449	+	0.980313i	$0.563266\pi$
$542$	−9.07677			−0.389880
$543$	−14.7911	+	7.31193i	−0.634747	+	0.313785i
$544$			6.30230i			0.270209i
$545$	6.66311			0.285416
$546$		0			0
$547$	−5.21319			−0.222900			−0.111450	−	0.993770i	$-0.535550\pi$
$547$	−5.21319			−0.222900			−0.111450	+	0.993770i	$0.535550\pi$
$548$		−	1.24104i		−	0.0530146i
$549$	14.2626	+	10.9004i	0.608712	+	0.465217i
$550$	2.30680			0.0983623
$551$	28.9843			1.23477
$552$	4.89136	+	9.89460i	0.208190	+	0.421142i
$553$		0			0
$554$		−	0.216476i		−	0.00919717i
$555$	5.30334	+	10.7280i	0.225114	+	0.455378i
$556$		−	12.5344i		−	0.531576i
$557$			25.8133i			1.09374i	0.837216	+	0.546872i	$0.184182\pi$
$557$			25.8133i			1.09374i	−0.837216	+	0.546872i	$0.815818\pi$
$558$	−7.98177	+	10.4437i	−0.337895	+	0.442119i
$559$		−	12.7661i		−	0.539947i
$560$		0			0
$561$	22.5732	−	11.1590i	0.953042	−	0.471133i
$562$	18.8498			0.795129
$563$	37.4936			1.58017			0.790084	−	0.612999i	$-0.210037\pi$
$563$	37.4936			1.58017			0.790084	+	0.612999i	$0.210037\pi$
$564$	1.27173	+	2.57255i	0.0535494	+	0.108324i
$565$			4.45505i			0.187425i
$566$	1.99832			0.0839956
$567$		0			0
$568$	−2.85910			−0.119965
$569$			40.4552i			1.69597i	0.530020	+	0.847985i	$0.322185\pi$
$569$			40.4552i			1.69597i	−0.530020	+	0.847985i	$0.677815\pi$
$570$	−5.80063	−	11.7339i	−0.242962	−	0.491481i
$571$	−29.1102			−1.21822			−0.609111	−	0.793085i	$-0.708474\pi$
$571$	−29.1102			−1.21822			−0.609111	+	0.793085i	$0.708474\pi$
$572$	−11.5359			−0.482342
$573$	7.71954	−	3.81613i	0.322488	−	0.159421i
$574$		0			0
$575$		−	6.37256i		−	0.265754i
$576$	1.82168	−	2.38358i	0.0759035	−	0.0993159i
$577$			15.1754i			0.631759i	0.948799	+	0.315880i	$0.102300\pi$
$577$			15.1754i			0.631759i	−0.948799	+	0.315880i	$0.897700\pi$
$578$		−	22.7189i		−	0.944983i
$579$	4.63088	+	9.36769i	0.192453	+	0.389308i
$580$		−	3.83533i		−	0.159254i
$581$		0			0
$582$	3.54403	+	7.16912i	0.146905	+	0.297169i
$583$	7.50352			0.310764
$584$	−3.68177			−0.152353
$585$	−11.9199	−	9.10996i	−0.492828	−	0.376650i
$586$			9.28117i			0.383402i
$587$	3.22807			0.133237			0.0666183	−	0.997779i	$-0.478779\pi$
$587$	3.22807			0.133237			0.0666183	+	0.997779i	$0.478779\pi$
$588$		0			0
$589$	−33.1120			−1.36436
$590$		−	9.93145i		−	0.408872i
$591$	−22.0705	+	10.9105i	−0.907859	+	0.448797i
$592$	−6.90930			−0.283970
$593$	43.7305			1.79580			0.897899	−	0.440202i	$-0.145093\pi$
$593$	43.7305			1.79580			0.897899	+	0.440202i	$0.145093\pi$
$594$	−11.7629	−	2.30439i	−0.482637	−	0.0945501i
$595$		0			0
$596$			15.5951i			0.638802i
$597$	3.49491	−	1.72770i	0.143037	−	0.0707099i
$598$			31.8682i			1.30319i
$599$			8.04569i			0.328738i	0.986399	+	0.164369i	$0.0525588\pi$
$599$			8.04569i			0.328738i	−0.986399	+	0.164369i	$0.947441\pi$
$600$	−1.55269	+	0.767566i	−0.0633883	+	0.0313358i
$601$		−	8.38546i		−	0.342050i	−0.985267	−	0.171025i	$-0.945292\pi$
$601$		−	8.38546i		−	0.342050i	0.985267	−	0.171025i	$-0.0547079\pi$
$602$		0			0
$603$	5.04090	−	6.59576i	0.205281	−	0.268600i
$604$	−3.03915			−0.123661
$605$	−5.67867			−0.230871
$606$	−17.5672	+	8.68427i	−0.713618	+	0.352774i
$607$			16.9336i			0.687315i	0.939095	+	0.343658i	$0.111666\pi$
$607$			16.9336i			0.687315i	−0.939095	+	0.343658i	$0.888334\pi$
$608$	7.55717			0.306484
$609$		0			0
$610$	5.98368			0.242272
$611$			8.28556i			0.335198i
$612$	−11.4808	+	15.0220i	−0.464084	+	0.607230i
$613$	33.8863			1.36866			0.684328	−	0.729174i	$-0.260096\pi$
$613$	33.8863			1.36866			0.684328	+	0.729174i	$0.260096\pi$
$614$	−26.9282			−1.08673
$615$	7.51732	+	15.2066i	0.303128	+	0.613189i
$616$		0			0
$617$		−	37.5359i		−	1.51114i	−0.655068	−	0.755570i	$-0.727360\pi$
$617$		−	37.5359i		−	1.51114i	0.655068	−	0.755570i	$-0.272640\pi$
$618$	5.65241	+	11.4341i	0.227373	+	0.459947i
$619$		−	16.9160i		−	0.679913i	−0.940441	−	0.339957i	$-0.889588\pi$
$619$		−	16.9160i		−	0.679913i	0.940441	−	0.339957i	$-0.110412\pi$
$620$			4.38153i			0.175967i
$621$	−6.36589	+	32.4951i	−0.255454	+	1.30398i
$622$		−	2.82130i		−	0.113124i
$623$		0			0
$624$	7.76475	−	3.83848i	0.310839	−	0.153662i
$625$	1.00000			0.0400000
$626$	−11.4427			−0.457342
$627$	−13.3809	−	27.0679i	−0.534381	−	1.08099i
$628$			15.8252i			0.631494i
$629$	43.5445			1.73623
$630$		0			0
$631$	−29.1879			−1.16195			−0.580977	−	0.813920i	$-0.697329\pi$
$631$	−29.1879			−1.16195			−0.580977	+	0.813920i	$0.697329\pi$
$632$			2.55889i			0.101787i
$633$	21.1874	+	42.8594i	0.842123	+	1.70351i
$634$	9.30982			0.369740
$635$	1.83694			0.0728968
$636$	−5.05056	+	2.49673i	−0.200268	+	0.0990016i
$637$		0			0
$638$		−	8.84735i		−	0.350270i
$639$	−6.81489	−	5.20837i	−0.269593	−	0.206040i
$640$		−	1.00000i		−	0.0395285i
$641$		−	4.57113i		−	0.180549i	−0.995917	−	0.0902743i	$-0.971226\pi$
$641$		−	4.57113i		−	0.180549i	0.995917	−	0.0902743i	$-0.0287744\pi$
$642$	6.46194	+	13.0717i	0.255032	+	0.515898i
$643$		−	24.0758i		−	0.949457i	−0.880132	−	0.474728i	$-0.842546\pi$
$643$		−	24.0758i		−	0.949457i	0.880132	−	0.474728i	$-0.157454\pi$
$644$		0			0
$645$	−1.95943	−	3.96368i	−0.0771524	−	0.156070i
$646$	−47.6275			−1.87388
$647$	−17.4241			−0.685012			−0.342506	−	0.939516i	$-0.611276\pi$
$647$	−17.4241			−0.685012			−0.342506	+	0.939516i	$0.611276\pi$
$648$	8.68427	−	2.36293i	0.341150	−	0.0928246i
$649$		−	22.9099i		−	0.899292i
$650$	−5.00084			−0.196149
$651$		0			0
$652$	8.61682			0.337461
$653$			37.8911i			1.48279i	0.671068	+	0.741396i	$0.265836\pi$
$653$			37.8911i			1.48279i	−0.671068	+	0.741396i	$0.734164\pi$
$654$	−10.3457	+	5.11438i	−0.404551	+	0.199988i
$655$	5.53883			0.216420
$656$	−9.79371			−0.382380
$657$	−8.77580	−	6.70703i	−0.342377	−	0.261666i
$658$		0			0
$659$		−	24.7262i		−	0.963197i	−0.876392	−	0.481599i	$-0.840056\pi$
$659$		−	24.7262i		−	0.963197i	0.876392	−	0.481599i	$-0.159944\pi$
$660$	−3.58174	+	1.77062i	−0.139419	+	0.0689214i
$661$			43.6879i			1.69926i	0.527378	+	0.849631i	$0.323175\pi$
$661$			43.6879i			1.69926i	−0.527378	+	0.849631i	$0.676825\pi$
$662$		−	18.2960i		−	0.711095i
$663$	−48.9358	+	24.1912i	−1.90051	+	0.939509i
$664$			1.83743i			0.0713060i
$665$		0			0
$666$	−16.4689	−	12.5866i	−0.638156	−	0.487720i
$667$	−24.4409			−0.946355
$668$	−8.64948			−0.334658
$669$	−35.8324	+	17.7136i	−1.38536	+	0.684849i
$670$		−	2.76716i		−	0.106905i
$671$	13.8031			0.532865
$672$		0			0
$673$	34.1588			1.31673			0.658363	−	0.752701i	$-0.271249\pi$
$673$	34.1588			1.31673			0.658363	+	0.752701i	$0.271249\pi$
$674$		−	7.84516i		−	0.302184i
$675$	−5.09922	−	0.998953i	−0.196269	−	0.0384497i
$676$	12.0084			0.461862
$677$	−13.1326			−0.504727			−0.252364	−	0.967632i	$-0.581208\pi$
$677$	−13.1326			−0.504727			−0.252364	+	0.967632i	$0.581208\pi$
$678$	−3.41954	−	6.91730i	−0.131327	−	0.265657i
$679$		0			0
$680$			6.30230i			0.241682i
$681$	−15.3782	−	31.1082i	−0.589296	−	1.19207i
$682$			10.1073i			0.387029i
$683$			45.8823i			1.75564i	0.478994	+	0.877818i	$0.341002\pi$
$683$			45.8823i			1.75564i	−0.478994	+	0.877818i	$0.658998\pi$
$684$	18.0131	+	13.7668i	0.688750	+	0.526386i
$685$		−	1.24104i		−	0.0474177i
$686$		0			0
$687$	−44.6628	+	22.0789i	−1.70399	+	0.842363i
$688$	2.55278			0.0973239
$689$	−16.2667			−0.619710
$690$	4.89136	+	9.89460i	0.186211	+	0.376681i
$691$		−	17.5647i		−	0.668191i	−0.942539	−	0.334096i	$-0.891569\pi$
$691$		−	17.5647i		−	0.668191i	0.942539	−	0.334096i	$-0.108431\pi$
$692$	−17.9315			−0.681652
$693$		0			0
$694$	−0.232294			−0.00881775
$695$		−	12.5344i		−	0.475456i
$696$	2.94387	+	5.95508i	0.111587	+	0.225727i
$697$	61.7229			2.33792
$698$	−11.5685			−0.437875
$699$	−39.9220	+	19.7353i	−1.50999	+	0.746458i
$700$		0			0
$701$			39.2501i			1.48246i	0.671253	+	0.741228i	$0.265756\pi$
$701$			39.2501i			1.48246i	−0.671253	+	0.741228i	$0.734244\pi$
$702$	25.5004	+	4.99561i	0.962451	+	0.188547i
$703$		−	52.2148i		−	1.96932i
$704$		−	2.30680i		−	0.0869408i
$705$	1.27173	+	2.57255i	0.0478961	+	0.0968877i
$706$		−	34.7075i		−	1.30623i
$707$		0			0
$708$	7.62305	+	15.4205i	0.286492	+	0.579536i
$709$	−47.6680			−1.79021			−0.895105	−	0.445854i	$-0.852900\pi$
$709$	−47.6680			−1.79021			−0.895105	+	0.445854i	$0.852900\pi$
$710$	−2.85910			−0.107300
$711$	−4.66150	+	6.09933i	−0.174820	+	0.228743i
$712$		−	5.88774i		−	0.220653i
$713$	27.9216			1.04567
$714$		0			0
$715$	−11.5359			−0.431420
$716$		−	12.0170i		−	0.449095i
$717$	−16.6480	+	8.22987i	−0.621731	+	0.307350i
$718$	−17.5322			−0.654297
$719$	−33.4214			−1.24641			−0.623205	−	0.782059i	$-0.714170\pi$
$719$	−33.4214			−1.24641			−0.623205	+	0.782059i	$0.714170\pi$
$720$	1.82168	−	2.38358i	0.0678902	−	0.0888309i
$721$		0			0
$722$			38.1109i			1.41834i
$723$	1.83939	−	0.909297i	0.0684077	−	0.0338171i
$724$		−	9.52612i		−	0.354036i
$725$		−	3.83533i		−	0.142441i
$726$	8.81721	−	4.35875i	0.327237	−	0.161769i
$727$		−	31.9845i		−	1.18624i	−0.805115	−	0.593119i	$-0.797896\pi$
$727$		−	31.9845i		−	1.18624i	0.805115	−	0.593119i	$-0.202104\pi$
$728$		0			0
$729$	25.0042	+	10.1878i	0.926081	+	0.377325i
$730$	−3.68177			−0.136268
$731$	−16.0884			−0.595051
$732$	−9.29079	+	4.59287i	−0.343397	+	0.169757i
$733$			39.2002i			1.44789i	0.689857	+	0.723945i	$0.257673\pi$
$733$			39.2002i			1.44789i	−0.689857	+	0.723945i	$0.742327\pi$
$734$	10.0402			0.370590
$735$		0			0
$736$	−6.37256			−0.234896
$737$		−	6.38330i		−	0.235132i
$738$	−23.3441	−	17.8411i	−0.859309	−	0.656738i
$739$	−33.7628			−1.24198			−0.620992	−	0.783817i	$-0.713270\pi$
$739$	−33.7628			−1.24198			−0.620992	+	0.783817i	$0.713270\pi$
$740$	−6.90930			−0.253991
$741$	29.0080	+	58.6796i	1.06564	+	2.15565i
$742$		0			0
$743$		−	14.3933i		−	0.528038i	−0.964517	−	0.264019i	$-0.914952\pi$
$743$		−	14.3933i		−	0.528038i	0.964517	−	0.264019i	$-0.0850482\pi$
$744$	−3.36311	−	6.80316i	−0.123298	−	0.249416i
$745$			15.5951i			0.571362i
$746$			0.00482067i			0.000176497i
$747$	−3.34722	+	4.37966i	−0.122468	+	0.160243i
$748$			14.5381i			0.531567i
$749$		0			0
$750$	−1.55269	+	0.767566i	−0.0566962	+	0.0280275i
$751$	17.8408			0.651020			0.325510	−	0.945539i	$-0.394464\pi$
$751$	17.8408			0.651020			0.325510	+	0.945539i	$0.394464\pi$
$752$	−1.65683			−0.0604185
$753$	11.0291	+	22.3104i	0.401922	+	0.813038i
$754$			19.1799i			0.698491i
$755$	−3.03915			−0.110606
$756$		0			0
$757$	−1.90604			−0.0692760			−0.0346380	−	0.999400i	$-0.511028\pi$
$757$	−1.90604			−0.0692760			−0.0346380	+	0.999400i	$0.511028\pi$
$758$		−	18.6572i		−	0.677660i
$759$	11.2834	+	22.8249i	0.409561	+	0.828491i
$760$	7.55717			0.274127
$761$	−28.2729			−1.02489			−0.512445	−	0.858720i	$-0.671260\pi$
$761$	−28.2729			−1.02489			−0.512445	+	0.858720i	$0.671260\pi$
$762$	−2.85220	+	1.40997i	−0.103324	+	0.0510780i
$763$		0			0
$764$			4.97173i			0.179871i
$765$	−11.4808	+	15.0220i	−0.415089	+	0.543123i
$766$			18.8463i			0.680945i
$767$			49.6656i			1.79332i
$768$	0.767566	+	1.55269i	0.0276972	+	0.0560278i
$769$			1.43146i			0.0516197i	0.999667	+	0.0258098i	$0.00821644\pi$
$769$			1.43146i			0.0516197i	−0.999667	+	0.0258098i	$0.991784\pi$
$770$		0			0
$771$	12.6925	+	25.6753i	0.457109	+	0.924675i
$772$	−6.03321			−0.217140
$773$	−34.8175			−1.25230			−0.626149	−	0.779703i	$-0.715370\pi$
$773$	−34.8175			−1.25230			−0.626149	+	0.779703i	$0.715370\pi$
$774$	6.08477	+	4.65037i	0.218712	+	0.167154i
$775$			4.38153i			0.157389i
$776$	−4.61723			−0.165749
$777$		0			0
$778$	−10.8601			−0.389352
$779$		−	74.0128i		−	2.65178i
$780$	7.76475	−	3.83848i	0.278023	−	0.137439i
$781$	−6.59537			−0.236001
$782$	40.1618			1.43618
$783$	−3.83132	+	19.5572i	−0.136920	+	0.698918i
$784$		0			0
$785$			15.8252i			0.564826i
$786$	−8.60008	+	4.25142i	−0.306755	+	0.151643i
$787$			49.7082i			1.77191i	0.463775	+	0.885953i	$0.346495\pi$
$787$			49.7082i			1.77191i	−0.463775	+	0.885953i	$0.653505\pi$
$788$		−	14.2144i		−	0.506366i
$789$	48.0402	−	23.7485i	1.71027	−	0.845468i
$790$			2.55889i			0.0910414i
$791$		0			0
$792$	4.20226	−	5.49845i	0.149321	−	0.195379i
$793$	−29.9234			−1.06261
$794$	−27.0408			−0.959643
$795$	−5.05056	+	2.49673i	−0.179125	+	0.0885497i
$796$			2.25088i			0.0797802i
$797$	−8.43295			−0.298710			−0.149355	−	0.988784i	$-0.547720\pi$
$797$	−8.43295			−0.298710			−0.149355	+	0.988784i	$0.547720\pi$
$798$		0			0
$799$	10.4419			0.369406
$800$		−	1.00000i		−	0.0353553i
$801$	10.7256	−	14.0339i	0.378971	−	0.495864i
$802$	24.5254			0.866023
$803$	−8.49311			−0.299715
$804$	2.12398	+	4.29655i	0.0749070	+	0.151527i
$805$		0			0
$806$		−	21.9113i		−	0.771794i
$807$	−3.15026	−	6.37258i	−0.110894	−	0.224325i
$808$		−	11.3140i		−	0.398026i
$809$		−	38.9747i		−	1.37028i	−0.728413	−	0.685138i	$-0.759742\pi$
$809$		−	38.9747i		−	1.37028i	0.728413	−	0.685138i	$-0.240258\pi$
$810$	8.68427	−	2.36293i	0.305134	−	0.0830248i
$811$			29.5668i			1.03823i	0.854704	+	0.519116i	$0.173739\pi$
$811$			29.5668i			1.03823i	−0.854704	+	0.519116i	$0.826261\pi$
$812$		0			0
$813$	14.0934	−	6.96702i	0.494277	−	0.244344i
$814$	−15.9384			−0.558640
$815$	8.61682			0.301834
$816$	−4.83743	−	9.78550i	−0.169344	−	0.342561i
$817$			19.2918i			0.674935i
$818$	−5.40347			−0.188928
$819$		0			0
$820$	−9.79371			−0.342011
$821$			33.6571i			1.17464i	0.809355	+	0.587320i	$0.199817\pi$
$821$			33.6571i			1.17464i	−0.809355	+	0.587320i	$0.800183\pi$
$822$	0.952581	+	1.92695i	0.0332251	+	0.0672101i
$823$	−12.5405			−0.437134			−0.218567	−	0.975822i	$-0.570138\pi$
$823$	−12.5405			−0.437134			−0.218567	+	0.975822i	$0.570138\pi$
$824$	−7.36407			−0.256540
$825$	−3.58174	+	1.77062i	−0.124700	+	0.0616451i
$826$		0			0
$827$			15.6875i			0.545506i	0.962084	+	0.272753i	$0.0879342\pi$
$827$			15.6875i			0.545506i	−0.962084	+	0.272753i	$0.912066\pi$
$828$	−15.1895	−	11.6088i	−0.527872	−	0.403434i
$829$			5.67186i			0.196992i	0.995137	+	0.0984959i	$0.0314031\pi$
$829$			5.67186i			0.196992i	−0.995137	+	0.0984959i	$0.968597\pi$
$830$			1.83743i			0.0637781i
$831$	0.166159	+	0.336119i	0.00576400	+	0.0116598i
$832$			5.00084i			0.173373i
$833$		0			0
$834$	9.62095	+	19.4620i	0.333146	+	0.673913i
$835$	−8.64948			−0.299328
$836$	17.4329			0.602929
$837$	4.37694	−	22.3424i	0.151289	−	0.772267i
$838$		−	28.2930i		−	0.977364i
$839$	14.5217			0.501346			0.250673	−	0.968072i	$-0.419348\pi$
$839$	14.5217			0.501346			0.250673	+	0.968072i	$0.419348\pi$
$840$		0			0
$841$	14.2902			0.492766
$842$			25.1687i			0.867370i
$843$	−29.2678	+	14.4684i	−1.00804	+	0.498319i
$844$	−27.6034			−0.950147
$845$	12.0084			0.413102
$846$	−3.94920	−	3.01823i	−0.135776	−	0.103769i
$847$		0			0
$848$		−	3.25278i		−	0.111701i
$849$	−3.10277	+	1.53384i	−0.106487	+	0.0526413i
$850$			6.30230i			0.216167i
$851$			44.0299i			1.50933i
$852$	4.43929	−	2.19455i	0.152087	−	0.0751839i
$853$		−	3.66698i		−	0.125555i	−0.998028	−	0.0627775i	$-0.980004\pi$
$853$		−	3.66698i		−	0.125555i	0.998028	−	0.0627775i	$-0.0199958\pi$
$854$		0			0
$855$	18.0131	+	13.7668i	0.616037	+	0.470814i
$856$	−8.41874			−0.287747
$857$	11.5630			0.394984			0.197492	−	0.980305i	$-0.436720\pi$
$857$	11.5630			0.394984			0.197492	+	0.980305i	$0.436720\pi$
$858$	17.9117	−	8.85460i	0.611496	−	0.302291i
$859$		−	14.9665i		−	0.510650i	−0.966855	−	0.255325i	$-0.917818\pi$
$859$		−	14.9665i		−	0.510650i	0.966855	−	0.255325i	$-0.0821825\pi$
$860$	2.55278			0.0870492
$861$		0			0
$862$	−11.2182			−0.382093
$863$		−	9.37277i		−	0.319053i	−0.987194	−	0.159526i	$-0.949003\pi$
$863$		−	9.37277i		−	0.319053i	0.987194	−	0.159526i	$-0.0509967\pi$
$864$	−0.998953	+	5.09922i	−0.0339851	+	0.173479i
$865$	−17.9315			−0.609688
$866$	0.639592			0.0217342
$867$	17.4383	+	35.2754i	0.592235	+	1.19802i
$868$		0			0
$869$			5.90286i			0.200241i
$870$	2.94387	+	5.95508i	0.0998066	+	0.201896i
$871$			13.8381i			0.468888i
$872$		−	6.66311i		−	0.225642i
$873$	−11.0055	−	8.41113i	−0.372481	−	0.284674i
$874$		−	48.1585i		−	1.62899i
$875$		0			0
$876$	5.71664	−	2.82600i	0.193148	−	0.0954818i
$877$	−15.6223			−0.527529			−0.263764	−	0.964587i	$-0.584964\pi$
$877$	−15.6223			−0.527529			−0.263764	+	0.964587i	$0.584964\pi$
$878$	−13.1635			−0.444246
$879$	−7.12391	−	14.4108i	−0.240284	−	0.486063i
$880$		−	2.30680i		−	0.0777622i
$881$	−4.54709			−0.153195			−0.0765977	−	0.997062i	$-0.524406\pi$
$881$	−4.54709			−0.153195			−0.0765977	+	0.997062i	$0.524406\pi$
$882$		0			0
$883$	−48.8190			−1.64289			−0.821445	−	0.570288i	$-0.806831\pi$
$883$	−48.8190			−1.64289			−0.821445	+	0.570288i	$0.806831\pi$
$884$		−	31.5168i		−	1.06002i
$885$	7.62305	+	15.4205i	0.256246	+	0.518353i
$886$	25.8446			0.868267
$887$	7.28336			0.244551			0.122276	−	0.992496i	$-0.460981\pi$
$887$	7.28336			0.244551			0.122276	+	0.992496i	$0.460981\pi$
$888$	10.7280	−	5.30334i	0.360008	−	0.177969i
$889$		0			0
$890$		−	5.88774i		−	0.197358i
$891$	20.0329	−	5.45080i	0.671127	−	0.182609i
$892$		−	23.0777i		−	0.772697i
$893$		−	12.5210i		−	0.418998i
$894$	−11.9703	−	24.2144i	−0.400347	−	0.809851i
$895$		−	12.0170i		−	0.401683i
$896$		0			0
$897$	−24.4609	−	49.4813i	−0.816726	−	1.65213i
$898$	−28.3586			−0.946339
$899$	16.8046			0.560466
$900$	1.82168	−	2.38358i	0.0607228	−	0.0794527i
$901$			20.5000i			0.682954i
$902$	−22.5921			−0.752236
$903$		0			0
$904$	4.45505			0.148173
$905$		−	9.52612i		−	0.316659i
$906$	4.71885	−	2.33275i	0.156773	−	0.0775004i
$907$	−26.8962			−0.893074			−0.446537	−	0.894765i	$-0.647343\pi$
$907$	−26.8962			−0.893074			−0.446537	+	0.894765i	$0.647343\pi$
$908$	20.0351			0.664887
$909$	20.6106	−	26.9679i	0.683611	−	0.894470i
$910$		0			0
$911$		−	46.4059i		−	1.53750i	−0.639552	−	0.768748i	$-0.720880\pi$
$911$		−	46.4059i		−	1.53750i	0.639552	−	0.768748i	$-0.279120\pi$
$912$	−11.7339	+	5.80063i	−0.388550	+	0.192078i
$913$			4.23858i			0.140277i
$914$			29.1905i			0.965536i
$915$	−9.29079	+	4.59287i	−0.307144	+	0.151835i
$916$		−	28.7648i		−	0.950417i
$917$		0			0
$918$	6.29570	−	32.1368i	0.207789	−	1.06067i
$919$	−4.52146			−0.149149			−0.0745746	−	0.997215i	$-0.523760\pi$
$919$	−4.52146			−0.149149			−0.0745746	+	0.997215i	$0.523760\pi$
$920$	−6.37256			−0.210097
$921$	41.8111	−	20.6691i	1.37772	−	0.681071i
$922$			31.0968i			1.02412i
$923$	14.2979			0.470621
$924$		0			0
$925$	−6.90930			−0.227176
$926$			33.4915i			1.10060i
$927$	−17.5529	−	13.4150i	−0.576512	−	0.440607i
$928$	−3.83533			−0.125901
$929$	−16.6094			−0.544938			−0.272469	−	0.962165i	$-0.587840\pi$
$929$	−16.6094			−0.544938			−0.272469	+	0.962165i	$0.587840\pi$
$930$	−3.36311	−	6.80316i	−0.110281	−	0.223084i
$931$		0			0
$932$		−	25.7115i		−	0.842209i
$933$	2.16553	+	4.38059i	0.0708963	+	0.143414i
$934$			14.8251i			0.485092i
$935$			14.5381i			0.475448i
$936$	−9.10996	+	11.9199i	−0.297768	+	0.389615i
$937$		−	20.5347i		−	0.670839i	−0.942069	−	0.335419i	$-0.891122\pi$
$937$		−	20.5347i		−	0.670839i	0.942069	−	0.335419i	$-0.108878\pi$
$938$		0			0
$939$	17.7670	−	8.78303i	0.579803	−	0.286623i
$940$	−1.65683			−0.0540399
$941$	24.3984			0.795364			0.397682	−	0.917523i	$-0.369815\pi$
$941$	24.3984			0.795364			0.397682	+	0.917523i	$0.369815\pi$
$942$	−12.1469	−	24.5716i	−0.395767	−	0.800586i
$943$			62.4110i			2.03238i
$944$	−9.93145			−0.323241
$945$		0			0
$946$	5.88876			0.191460
$947$		−	19.1133i		−	0.621100i	−0.950557	−	0.310550i	$-0.899487\pi$
$947$		−	19.1133i		−	0.621100i	0.950557	−	0.310550i	$-0.100513\pi$
$948$	−1.96412	−	3.97317i	−0.0637917	−	0.129042i
$949$	18.4120			0.597677
$950$	7.55717			0.245187
$951$	−14.4553	+	7.14590i	−0.468744	+	0.231722i
$952$		0			0
$953$			7.20297i			0.233327i	0.993171	+	0.116664i	$0.0372199\pi$
$953$			7.20297i			0.233327i	−0.993171	+	0.116664i	$0.962780\pi$
$954$	5.92555	−	7.75328i	0.191847	−	0.251022i
$955$			4.97173i			0.160881i
$956$		−	10.7220i		−	0.346776i
$957$	6.79093	+	13.7372i	0.219519	+	0.444060i
$958$			23.0447i			0.744540i
$959$		0			0
$960$	0.767566	+	1.55269i	0.0247731	+	0.0501128i
$961$	11.8022			0.380715
$962$	34.5523			1.11401
$963$	−20.0668	−	15.3363i	−0.646642	−	0.494205i
$964$			1.18465i			0.0381550i
$965$	−6.03321			−0.194216
$966$		0			0
$967$	−12.2448			−0.393765			−0.196883	−	0.980427i	$-0.563082\pi$
$967$	−12.2448			−0.393765			−0.196883	+	0.980427i	$0.563082\pi$
$968$			5.67867i			0.182519i
$969$	73.9508	−	36.5573i	2.37564	−	1.17439i
$970$	−4.61723			−0.148250
$971$	−26.8777			−0.862546			−0.431273	−	0.902221i	$-0.641935\pi$
$971$	−26.8777			−0.862546			−0.431273	+	0.902221i	$0.641935\pi$
$972$	−11.6703	+	10.3346i	−0.374324	+	0.331484i
$973$		0			0
$974$			10.6277i			0.340533i
$975$	7.76475	−	3.83848i	0.248671	−	0.122930i
$976$		−	5.98368i		−	0.191533i
$977$		−	36.7539i		−	1.17586i	−0.808911	−	0.587931i	$-0.799943\pi$
$977$		−	36.7539i		−	1.17586i	0.808911	−	0.587931i	$-0.200057\pi$
$978$	−13.3792	+	6.61397i	−0.427821	+	0.211492i
$979$		−	13.5819i		−	0.434078i
$980$		0			0
$981$	12.1381	−	15.8821i	0.387540	−	0.507076i
$982$	22.4687			0.717004
$983$	13.3704			0.426449			0.213224	−	0.977003i	$-0.431603\pi$
$983$	13.3704			0.426449			0.213224	+	0.977003i	$0.431603\pi$
$984$	15.2066	−	7.51732i	0.484768	−	0.239643i
$985$		−	14.2144i		−	0.452908i
$986$	24.1714			0.769775
$987$		0			0
$988$	−37.7922			−1.20233
$989$		−	16.2678i		−	0.517285i
$990$	4.20226	−	5.49845i	0.133557	−	0.174752i
$991$	16.6969			0.530393			0.265197	−	0.964194i	$-0.414563\pi$
$991$	16.6969			0.530393			0.265197	+	0.964194i	$0.414563\pi$
$992$	4.38153			0.139114
$993$	14.0434	+	28.4080i	0.445654	+	0.901501i
$994$		0			0
$995$			2.25088i			0.0713576i
$996$	−1.41035	−	2.85295i	−0.0446886	−	0.0903993i
$997$		−	49.1853i		−	1.55771i	−0.627201	−	0.778857i	$-0.715800\pi$
$997$		−	49.1853i		−	1.55771i	0.627201	−	0.778857i	$-0.284200\pi$
$998$			39.7588i			1.25854i
$999$	35.2321	+	6.90207i	1.11469	+	0.218372i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.b.b.881.4		12
3.2	odd	2		1470.2.b.a.881.9		12
7.2	even	3		210.2.r.a.101.1	✓	12
7.3	odd	6		210.2.r.b.131.4	yes	12
7.6	odd	2		1470.2.b.a.881.3		12
21.2	odd	6		210.2.r.b.101.4	yes	12
21.17	even	6		210.2.r.a.131.1	yes	12
21.20	even	2	inner	1470.2.b.b.881.10		12
35.2	odd	12		1050.2.u.f.899.3		12
35.3	even	12		1050.2.u.h.299.1		12
35.9	even	6		1050.2.s.g.101.6		12
35.17	even	12		1050.2.u.e.299.6		12
35.23	odd	12		1050.2.u.g.899.4		12
35.24	odd	6		1050.2.s.f.551.3		12
105.2	even	12		1050.2.u.h.899.1		12
105.17	odd	12		1050.2.u.g.299.4		12
105.23	even	12		1050.2.u.e.899.6		12
105.38	odd	12		1050.2.u.f.299.3		12
105.44	odd	6		1050.2.s.f.101.3		12
105.59	even	6		1050.2.s.g.551.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.r.a.101.1	✓	12	7.2	even	3
210.2.r.a.131.1	yes	12	21.17	even	6
210.2.r.b.101.4	yes	12	21.2	odd	6
210.2.r.b.131.4	yes	12	7.3	odd	6
1050.2.s.f.101.3		12	105.44	odd	6
1050.2.s.f.551.3		12	35.24	odd	6
1050.2.s.g.101.6		12	35.9	even	6
1050.2.s.g.551.6		12	105.59	even	6
1050.2.u.e.299.6		12	35.17	even	12
1050.2.u.e.899.6		12	105.23	even	12
1050.2.u.f.299.3		12	105.38	odd	12
1050.2.u.f.899.3		12	35.2	odd	12
1050.2.u.g.299.4		12	105.17	odd	12
1050.2.u.g.899.4		12	35.23	odd	12
1050.2.u.h.299.1		12	35.3	even	12
1050.2.u.h.899.1		12	105.2	even	12
1470.2.b.a.881.3		12	7.6	odd	2
1470.2.b.a.881.9		12	3.2	odd	2
1470.2.b.b.881.4		12	1.1	even	1	trivial
1470.2.b.b.881.10		12	21.20	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.767566 + 1.55269i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.55269 - 0.767566i) q^{6} +1.00000i q^{8} +(-1.82168 + 2.38358i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.767566 + 1.55269i) q^{3} -1.00000 q^{4} -1.00000 q^{5} +(1.55269 - 0.767566i) q^{6} +1.00000i q^{8} +(-1.82168 + 2.38358i) q^{9} +1.00000i q^{10} +2.30680i q^{11} +(-0.767566 - 1.55269i) q^{12} -5.00084i q^{13} +(-0.767566 - 1.55269i) q^{15} +1.00000 q^{16} -6.30230 q^{17} +(2.38358 + 1.82168i) q^{18} +7.55717i q^{19} +1.00000 q^{20} +2.30680 q^{22} -6.37256i q^{23} +(-1.55269 + 0.767566i) q^{24} +1.00000 q^{25} -5.00084 q^{26} +(-5.09922 - 0.998953i) q^{27} -3.83533i q^{29} +(-1.55269 + 0.767566i) q^{30} +4.38153i q^{31} -1.00000i q^{32} +(-3.58174 + 1.77062i) q^{33} +6.30230i q^{34} +(1.82168 - 2.38358i) q^{36} -6.90930 q^{37} +7.55717 q^{38} +(7.76475 - 3.83848i) q^{39} -1.00000i q^{40} -9.79371 q^{41} +2.55278 q^{43} -2.30680i q^{44} +(1.82168 - 2.38358i) q^{45} -6.37256 q^{46} -1.65683 q^{47} +(0.767566 + 1.55269i) q^{48} -1.00000i q^{50} +(-4.83743 - 9.78550i) q^{51} +5.00084i q^{52} -3.25278i q^{53} +(-0.998953 + 5.09922i) q^{54} -2.30680i q^{55} +(-11.7339 + 5.80063i) q^{57} -3.83533 q^{58} -9.93145 q^{59} +(0.767566 + 1.55269i) q^{60} -5.98368i q^{61} +4.38153 q^{62} -1.00000 q^{64} +5.00084i q^{65} +(1.77062 + 3.58174i) q^{66} -2.76716 q^{67} +6.30230 q^{68} +(9.89460 - 4.89136i) q^{69} +2.85910i q^{71} +(-2.38358 - 1.82168i) q^{72} +3.68177i q^{73} +6.90930i q^{74} +(0.767566 + 1.55269i) q^{75} -7.55717i q^{76} +(-3.83848 - 7.76475i) q^{78} +2.55889 q^{79} -1.00000 q^{80} +(-2.36293 - 8.68427i) q^{81} +9.79371i q^{82} +1.83743 q^{83} +6.30230 q^{85} -2.55278i q^{86} +(5.95508 - 2.94387i) q^{87} -2.30680 q^{88} -5.88774 q^{89} +(-2.38358 - 1.82168i) q^{90} +6.37256i q^{92} +(-6.80316 + 3.36311i) q^{93} +1.65683i q^{94} -7.55717i q^{95} +(1.55269 - 0.767566i) q^{96} +4.61723i q^{97} +(-5.49845 - 4.20226i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9}+O(q^{10}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9	\( 12 q + 4 q^{3} - 12 q^{4} - 12 q^{5} - 2 q^{6} - 6 q^{9} - 4 q^{12} - 4 q^{15} + 12 q^{16} - 24 q^{17} + 8 q^{18} + 12 q^{20} + 2 q^{24} + 12 q^{25} + 8 q^{26} - 8 q^{27} + 2 q^{30} + 20 q^{33} + 6 q^{36} + 16 q^{37} - 16 q^{38} + 12 q^{39} - 4 q^{41} + 6 q^{45} - 4 q^{46} - 32 q^{47} + 4 q^{48} + 4 q^{51} - 28 q^{54} - 36 q^{57} - 16 q^{58} - 24 q^{59} + 4 q^{60} + 8 q^{62} - 12 q^{64} + 20 q^{66} + 8 q^{67} + 24 q^{68} + 50 q^{69} - 8 q^{72} + 4 q^{75} + 32 q^{78} + 8 q^{79} - 12 q^{80} - 10 q^{81} - 40 q^{83} + 24 q^{85} + 56 q^{87} - 52 q^{89} - 8 q^{90} + 28 q^{93} - 2 q^{96} + 48 q^{99}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 - 12 * q^5 - 2 * q^6 - 6 * q^9 - 4 * q^12 - 4 * q^15 + 12 * q^16 - 24 * q^17 + 8 * q^18 + 12 * q^20 + 2 * q^24 + 12 * q^25 + 8 * q^26 - 8 * q^27 + 2 * q^30 + 20 * q^33 + 6 * q^36 + 16 * q^37 - 16 * q^38 + 12 * q^39 - 4 * q^41 + 6 * q^45 - 4 * q^46 - 32 * q^47 + 4 * q^48 + 4 * q^51 - 28 * q^54 - 36 * q^57 - 16 * q^58 - 24 * q^59 + 4 * q^60 + 8 * q^62 - 12 * q^64 + 20 * q^66 + 8 * q^67 + 24 * q^68 + 50 * q^69 - 8 * q^72 + 4 * q^75 + 32 * q^78 + 8 * q^79 - 12 * q^80 - 10 * q^81 - 40 * q^83 + 24 * q^85 + 56 * q^87 - 52 * q^89 - 8 * q^90 + 28 * q^93 - 2 * q^96 + 48 * q^99

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