LMFDB - Embedded newform 1340.1.bl.a.859.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1340,1,Mod(19,1340)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1340, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([33, 33, 10]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("1340.19");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1340 = 2^{2} \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1340.bl (of order $66$, degree $20$, 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:	$0.668747116928$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\Q(\zeta_{33})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 $ x^20 - x^19 + x^17 - x^16 + x^14 - x^13 + x^11 - x^10 + x^9 - x^7 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{33}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{33} - \cdots)$

Embedding invariants

Embedding label			859.1
Root			$0.981929 - 0.189251i$ of defining polynomial
Character	$\chi$	$=$	1340.859
Dual form			1340.1.bl.a.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.928368 - 0.371662i) q^{2} +(0.947890 - 1.09392i) q^{3} +(0.723734 + 0.690079i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-1.28656 + 0.663268i) q^{6} +(-0.514186 + 0.404360i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.155858 - 1.08402i) q^{9} +O(q^{10})$	\(q+(-0.928368 - 0.371662i) q^{2} +(0.947890 - 1.09392i) q^{3} +(0.723734 + 0.690079i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-1.28656 + 0.663268i) q^{6} +(-0.514186 + 0.404360i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.155858 - 1.08402i) q^{9} +(-0.981929 + 0.189251i) q^{10} +(1.44091 - 0.137591i) q^{12} +(0.627639 - 0.184291i) q^{14} +(0.205996 - 1.43273i) q^{15} +(0.0475819 + 0.998867i) q^{16} +(-0.258195 + 1.06429i) q^{18} +(0.981929 + 0.189251i) q^{20} +(-0.0450525 + 0.945768i) q^{21} +(-0.327068 - 0.945001i) q^{23} +(-1.38884 - 0.407799i) q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.115880 - 0.0744714i) q^{27} +(-0.651174 - 0.0621796i) q^{28} +(-0.981929 - 1.70075i) q^{29} +(-0.723734 + 1.25354i) q^{30} +(0.327068 - 0.945001i) q^{32} +(-0.213947 + 0.618159i) q^{35} +(0.635257 - 0.892094i) q^{36} +(-0.841254 - 0.540641i) q^{40} +(0.273507 + 1.12741i) q^{41} +(0.393332 - 0.861277i) q^{42} +(0.452418 + 0.132842i) q^{43} +(-0.717180 - 0.827670i) q^{45} +(-0.0475819 + 0.998867i) q^{46} +(1.95496 + 0.376789i) q^{47} +(1.13779 + 0.894765i) q^{48} +(-0.134879 + 0.555979i) q^{49} +(-0.723734 + 0.690079i) q^{50} +(0.0799009 + 0.112205i) q^{54} +(0.581419 + 0.299742i) q^{56} +(0.279486 + 1.94387i) q^{58} +(1.13779 - 0.894765i) q^{60} +(-1.49547 + 0.770969i) q^{61} +(0.518473 + 0.494363i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.235759 + 0.971812i) q^{67} +(-1.34378 - 0.537970i) q^{69} +(0.428368 - 0.494363i) q^{70} +(-0.921310 + 0.592090i) q^{72} +(-0.601300 - 1.31666i) q^{75} +(0.580057 + 0.814576i) q^{80} +(0.859495 - 0.252370i) q^{81} +(0.165101 - 1.14831i) q^{82} +(0.0748038 + 1.57033i) q^{83} +(-0.685261 + 0.653395i) q^{84} +(-0.370638 - 0.291473i) q^{86} +(-2.79125 - 0.537970i) q^{87} +(0.186393 + 0.215109i) q^{89} +(0.358193 + 1.03493i) q^{90} +(0.415415 - 0.909632i) q^{92} +(-1.67489 - 1.07639i) q^{94} +(-0.723734 - 1.25354i) q^{96} +(0.331854 - 0.466024i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8	$ 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{10} + q^{12} + 2 q^{14} - 2 q^{15} + q^{16} + q^{20} - 10 q^{21} + q^{23} - 9 q^{24} - 2 q^{25} + 2 q^{27} + q^{28} - q^{29} - q^{30} - q^{32} - 21 q^{35} + 2 q^{40} - q^{41} - 20 q^{42} + 9 q^{43} - q^{46} + q^{47} + q^{48} - q^{50} + q^{54} - q^{56} - 2 q^{58} + q^{60} - 9 q^{61} + 11 q^{63} - 2 q^{64} - q^{67} + q^{69} - 9 q^{70} + 11 q^{72} - 2 q^{75} + q^{80} + 2 q^{81} - 2 q^{82} + q^{83} + q^{84} - q^{86} - q^{87} - 4 q^{89} - 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) $ 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8 - q^10 + q^12 + 2 * q^14 - 2 * q^15 + q^16 + q^20 - 10 * q^21 + q^23 - 9 * q^24 - 2 * q^25 + 2 * q^27 + q^28 - q^29 - q^30 - q^32 - 21 * q^35 + 2 * q^40 - q^41 - 20 * q^42 + 9 * q^43 - q^46 + q^47 + q^48 - q^50 + q^54 - q^56 - 2 * q^58 + q^60 - 9 * q^61 + 11 * q^63 - 2 * q^64 - q^67 + q^69 - 9 * q^70 + 11 * q^72 - 2 * q^75 + q^80 + 2 * q^81 - 2 * q^82 + q^83 + q^84 - q^86 - q^87 - 4 * q^89 - 2 * q^92 + 2 * q^94 - q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1340\mathbb{Z}\right)^\times$.

$n$	$537$	$671$	$1141$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{4}{33}\right)$

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 $

$2$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$2$	−0.928368	−	0.371662i	−0.928368	−	0.371662i
$3$	0.947890	−	1.09392i	0.947890	−	1.09392i	−0.0475819	−	0.998867i	$-0.515152\pi$
$3$	0.947890	−	1.09392i	0.947890	−	1.09392i	0.995472	−	0.0950560i	$-0.0303030\pi$
$4$	0.723734	+	0.690079i	0.723734	+	0.690079i
$5$	0.841254	−	0.540641i	0.841254	−	0.540641i
$5$	0.841254	−	0.540641i	0.841254	−	0.540641i
$6$	−1.28656	+	0.663268i	−1.28656	+	0.663268i
$7$	−0.514186	+	0.404360i	−0.514186	+	0.404360i	−0.841254	−	0.540641i	$-0.818182\pi$
$7$	−0.514186	+	0.404360i	−0.514186	+	0.404360i	0.327068	+	0.945001i	$0.393939\pi$
$8$	−0.415415	−	0.909632i	−0.415415	−	0.909632i
$9$	−0.155858	−	1.08402i	−0.155858	−	1.08402i
$10$	−0.981929	+	0.189251i	−0.981929	+	0.189251i
$11$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$11$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$12$	1.44091	−	0.137591i	1.44091	−	0.137591i
$13$		0			0		−0.580057	−	0.814576i	$-0.696970\pi$
$13$		0			0		0.580057	+	0.814576i	$0.303030\pi$
$14$	0.627639	−	0.184291i	0.627639	−	0.184291i
$15$	0.205996	−	1.43273i	0.205996	−	1.43273i
$16$	0.0475819	+	0.998867i	0.0475819	+	0.998867i
$17$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$17$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$18$	−0.258195	+	1.06429i	−0.258195	+	1.06429i
$19$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$19$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$20$	0.981929	+	0.189251i	0.981929	+	0.189251i
$21$	−0.0450525	+	0.945768i	−0.0450525	+	0.945768i
$22$		0			0
$23$	−0.327068	−	0.945001i	−0.327068	−	0.945001i	−0.981929	−	0.189251i	$-0.939394\pi$
$23$	−0.327068	−	0.945001i	−0.327068	−	0.945001i	0.654861	−	0.755750i	$-0.272727\pi$
$24$	−1.38884	−	0.407799i	−1.38884	−	0.407799i
$25$	0.415415	−	0.909632i	0.415415	−	0.909632i
$26$		0			0
$27$	−0.115880	−	0.0744714i	−0.115880	−	0.0744714i
$28$	−0.651174	−	0.0621796i	−0.651174	−	0.0621796i
$29$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.654861	−	0.755750i	$-0.727273\pi$
$29$	−0.981929	−	1.70075i	−0.981929	−	1.70075i	−0.327068	−	0.945001i	$-0.606061\pi$
$30$	−0.723734	+	1.25354i	−0.723734	+	1.25354i
$31$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$31$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$32$	0.327068	−	0.945001i	0.327068	−	0.945001i
$33$		0			0
$34$		0			0
$35$	−0.213947	+	0.618159i	−0.213947	+	0.618159i
$36$	0.635257	−	0.892094i	0.635257	−	0.892094i
$37$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$37$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$38$		0			0
$39$		0			0
$40$	−0.841254	−	0.540641i	−0.841254	−	0.540641i
$41$	0.273507	+	1.12741i	0.273507	+	1.12741i	0.928368	+	0.371662i	$0.121212\pi$
$41$	0.273507	+	1.12741i	0.273507	+	1.12741i	−0.654861	+	0.755750i	$0.727273\pi$
$42$	0.393332	−	0.861277i	0.393332	−	0.861277i
$43$	0.452418	+	0.132842i	0.452418	+	0.132842i	0.500000	−	0.866025i	$-0.333333\pi$
$43$	0.452418	+	0.132842i	0.452418	+	0.132842i	−0.0475819	+	0.998867i	$0.515152\pi$
$44$		0			0
$45$	−0.717180	−	0.827670i	−0.717180	−	0.827670i
$46$	−0.0475819	+	0.998867i	−0.0475819	+	0.998867i
$47$	1.95496	+	0.376789i	1.95496	+	0.376789i	0.995472	+	0.0950560i	$0.0303030\pi$
$47$	1.95496	+	0.376789i	1.95496	+	0.376789i	0.959493	+	0.281733i	$0.0909091\pi$
$48$	1.13779	+	0.894765i	1.13779	+	0.894765i
$49$	−0.134879	+	0.555979i	−0.134879	+	0.555979i
$50$	−0.723734	+	0.690079i	−0.723734	+	0.690079i
$51$		0			0
$52$		0			0
$53$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$53$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$54$	0.0799009	+	0.112205i	0.0799009	+	0.112205i
$55$		0			0
$56$	0.581419	+	0.299742i	0.581419	+	0.299742i
$57$		0			0
$58$	0.279486	+	1.94387i	0.279486	+	1.94387i
$59$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$59$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$60$	1.13779	−	0.894765i	1.13779	−	0.894765i
$61$	−1.49547	+	0.770969i	−1.49547	+	0.770969i	−0.995472	−	0.0950560i	$-0.969697\pi$
$61$	−1.49547	+	0.770969i	−1.49547	+	0.770969i	−0.500000	+	0.866025i	$0.666667\pi$
$62$		0			0
$63$	0.518473	+	0.494363i	0.518473	+	0.494363i
$64$	−0.654861	+	0.755750i	−0.654861	+	0.755750i
$65$		0			0
$66$		0			0
$67$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$67$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$68$		0			0
$69$	−1.34378	−	0.537970i	−1.34378	−	0.537970i
$70$	0.428368	−	0.494363i	0.428368	−	0.494363i
$71$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$71$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$72$	−0.921310	+	0.592090i	−0.921310	+	0.592090i
$73$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$73$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$74$		0			0
$75$	−0.601300	−	1.31666i	−0.601300	−	1.31666i
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$79$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$80$	0.580057	+	0.814576i	0.580057	+	0.814576i
$81$	0.859495	−	0.252370i	0.859495	−	0.252370i
$82$	0.165101	−	1.14831i	0.165101	−	1.14831i
$83$	0.0748038	+	1.57033i	0.0748038	+	1.57033i	0.654861	+	0.755750i	$0.272727\pi$
$83$	0.0748038	+	1.57033i	0.0748038	+	1.57033i	−0.580057	+	0.814576i	$0.696970\pi$
$84$	−0.685261	+	0.653395i	−0.685261	+	0.653395i
$85$		0			0
$86$	−0.370638	−	0.291473i	−0.370638	−	0.291473i
$87$	−2.79125	−	0.537970i	−2.79125	−	0.537970i
$88$		0			0
$89$	0.186393	+	0.215109i	0.186393	+	0.215109i	0.841254	−	0.540641i	$-0.181818\pi$
$89$	0.186393	+	0.215109i	0.186393	+	0.215109i	−0.654861	+	0.755750i	$0.727273\pi$
$90$	0.358193	+	1.03493i	0.358193	+	1.03493i
$91$		0			0
$92$	0.415415	−	0.909632i	0.415415	−	0.909632i
$93$		0			0
$94$	−1.67489	−	1.07639i	−1.67489	−	1.07639i
$95$		0			0
$96$	−0.723734	−	1.25354i	−0.723734	−	1.25354i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	0.331854	−	0.466024i	0.331854	−	0.466024i
$99$		0			0
$100$	0.928368	−	0.371662i	0.928368	−	0.371662i
$101$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	−0.500000	−	0.866025i	$-0.666667\pi$
$101$	−0.264241	+	0.105786i	−0.264241	+	0.105786i	0.235759	+	0.971812i	$0.424242\pi$
$102$		0			0
$103$	−1.07701	+	1.51245i	−1.07701	+	1.51245i	−0.235759	+	0.971812i	$0.575758\pi$
$103$	−1.07701	+	1.51245i	−1.07701	+	1.51245i	−0.841254	+	0.540641i	$0.818182\pi$
$104$		0			0
$105$	0.473420	+	0.819988i	0.473420	+	0.819988i
$106$		0			0
$107$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	0.142315	−	0.989821i	$-0.454545\pi$
$107$	−0.698939	−	0.449181i	−0.698939	−	0.449181i	−0.841254	+	0.540641i	$0.818182\pi$
$108$	−0.0324750	−	0.133864i	−0.0324750	−	0.133864i
$109$	0.771316	−	1.68895i	0.771316	−	1.68895i	0.0475819	−	0.998867i	$-0.484848\pi$
$109$	0.771316	−	1.68895i	0.771316	−	1.68895i	0.723734	−	0.690079i	$-0.242424\pi$
$110$		0			0
$111$		0			0
$112$	−0.428368	−	0.494363i	−0.428368	−	0.494363i
$113$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$113$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$114$		0			0
$115$	−0.786053	−	0.618159i	−0.786053	−	0.618159i
$116$	0.462997	−	1.90850i	0.462997	−	1.90850i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	−1.38884	+	0.407799i	−1.38884	+	0.407799i
$121$	0.580057	+	0.814576i	0.580057	+	0.814576i
$122$	1.67489	−	0.159932i	1.67489	−	0.159932i
$123$	1.49256	+	0.769467i	1.49256	+	0.769467i
$124$		0			0
$125$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$126$	−0.297598	−	0.651648i	−0.297598	−	0.651648i
$127$	−1.39734	+	1.09888i	−1.39734	+	1.09888i	−0.415415	+	0.909632i	$0.636364\pi$
$127$	−1.39734	+	1.09888i	−1.39734	+	1.09888i	−0.981929	+	0.189251i	$0.939394\pi$
$128$	0.888835	−	0.458227i	0.888835	−	0.458227i
$129$	0.574161	−	0.368991i	0.574161	−	0.368991i
$130$		0			0
$131$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$131$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$132$		0			0
$133$		0			0
$134$	0.580057	−	0.814576i	0.580057	−	0.814576i
$135$	−0.137747			−0.137747
$136$		0			0
$137$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$137$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$138$	1.04758	+	0.998867i	1.04758	+	0.998867i
$139$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$139$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$140$	−0.581419	+	0.299742i	−0.581419	+	0.299742i
$141$	2.26527	−	1.78143i	2.26527	−	1.78143i
$142$		0			0
$143$		0			0
$144$	1.07537	−	0.207261i	1.07537	−	0.207261i
$145$	−1.74555	−	0.899892i	−1.74555	−	0.899892i
$146$		0			0
$147$	0.480348	+	0.674555i	0.480348	+	0.674555i
$148$		0			0
$149$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	0.723734	+	0.690079i	$0.242424\pi$
$149$	−0.165101	+	1.14831i	−0.165101	+	1.14831i	−0.888835	+	0.458227i	$0.848485\pi$
$150$	0.0688733	+	1.44583i	0.0688733	+	1.44583i
$151$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$151$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$157$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$158$		0			0
$159$		0			0
$160$	−0.235759	−	0.971812i	−0.235759	−	0.971812i
$161$	0.550294	+	0.353653i	0.550294	+	0.353653i
$162$	−0.891724	−	0.0851493i	−0.891724	−	0.0851493i
$163$	−0.959493	−	1.66189i	−0.959493	−	1.66189i	−0.723734	−	0.690079i	$-0.757576\pi$
$163$	−0.959493	−	1.66189i	−0.959493	−	1.66189i	−0.235759	−	0.971812i	$-0.575758\pi$
$164$	−0.580057	+	1.00469i	−0.580057	+	1.00469i
$165$		0			0
$166$	0.514186	−	1.48564i	0.514186	−	1.48564i
$167$	1.21590	−	0.486774i	1.21590	−	0.486774i	0.327068	−	0.945001i	$-0.393939\pi$
$167$	1.21590	−	0.486774i	1.21590	−	0.486774i	0.888835	+	0.458227i	$0.151515\pi$
$168$	0.879017	−	0.351905i	0.879017	−	0.351905i
$169$	−0.327068	+	0.945001i	−0.327068	+	0.945001i
$170$		0			0
$171$		0			0
$172$	0.235759	+	0.408346i	0.235759	+	0.408346i
$173$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$173$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$174$	2.39136	+	1.53684i	2.39136	+	1.53684i
$175$	0.154218	+	0.635697i	0.154218	+	0.635697i
$176$		0			0
$177$		0			0
$178$	−0.0930932	−	0.268975i	−0.0930932	−	0.268975i
$179$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$179$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$180$	0.0521100	−	1.09392i	0.0521100	−	1.09392i
$181$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.888835	−	0.458227i	$-0.848485\pi$
$181$	−1.88431	−	0.363170i	−1.88431	−	0.363170i	−0.995472	+	0.0950560i	$0.969697\pi$
$182$		0			0
$183$	−0.574161	+	2.36673i	−0.574161	+	2.36673i
$184$	−0.723734	+	0.690079i	−0.723734	+	0.690079i
$185$		0			0
$186$		0			0
$187$		0			0
$188$	1.15486	+	1.62177i	1.15486	+	1.62177i
$189$	0.0896970	−	0.00856503i	0.0896970	−	0.00856503i
$190$		0			0
$191$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$191$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$192$	0.205996	+	1.43273i	0.205996	+	1.43273i
$193$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$193$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$194$		0			0
$195$		0			0
$196$	−0.481286	+	0.309304i	−0.481286	+	0.309304i
$197$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$197$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$198$		0			0
$199$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$199$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$200$	−1.00000			−1.00000
$201$	0.839614	+	1.17907i	0.839614	+	1.17907i
$202$	0.284630			0.284630
$203$	1.19261	+	0.477449i	1.19261	+	0.477449i
$204$		0			0
$205$	0.839614	+	0.800570i	0.839614	+	0.800570i
$206$	1.56199	−	1.00383i	1.56199	−	1.00383i
$207$	−0.973420	+	0.501833i	−0.973420	+	0.501833i
$208$		0			0
$209$		0			0
$210$	−0.134750	−	0.937203i	−0.134750	−	0.937203i
$211$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$211$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$212$		0			0
$213$		0			0
$214$	0.481929	+	0.676774i	0.481929	+	0.676774i
$215$	0.452418	−	0.132842i	0.452418	−	0.132842i
$216$	−0.0196034	+	0.136345i	−0.0196034	+	0.136345i
$217$		0			0
$218$	−1.34378	+	1.28129i	−1.34378	+	1.28129i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.959493	+	0.281733i	$0.0909091\pi$
$223$	1.10181	+	1.27155i	1.10181	+	1.27155i	0.142315	+	0.989821i	$0.454545\pi$
$224$	0.213947	+	0.618159i	0.213947	+	0.618159i
$225$	−1.05080	−	0.308543i	−1.05080	−	0.308543i
$226$		0			0
$227$	0.0671040	+	0.276606i	0.0671040	+	0.276606i	0.995472	−	0.0950560i	$-0.0303030\pi$
$227$	0.0671040	+	0.276606i	0.0671040	+	0.276606i	−0.928368	+	0.371662i	$0.878788\pi$
$228$		0			0
$229$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.928368	−	0.371662i	$-0.121212\pi$
$229$	1.76962	+	0.168978i	1.76962	+	0.168978i	0.841254	+	0.540641i	$0.181818\pi$
$230$	0.500000	+	0.866025i	0.500000	+	0.866025i
$231$		0			0
$232$	−1.13915	+	1.59971i	−1.13915	+	1.59971i
$233$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$233$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$234$		0			0
$235$	1.84833	−	0.739959i	1.84833	−	0.739959i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$239$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$240$	1.44091	+	0.137591i	1.44091	+	0.137591i
$241$	1.56199	+	1.00383i	1.56199	+	1.00383i	0.981929	+	0.189251i	$0.0606061\pi$
$241$	1.56199	+	1.00383i	1.56199	+	1.00383i	0.580057	+	0.814576i	$0.303030\pi$
$242$	−0.235759	−	0.971812i	−0.235759	−	0.971812i
$243$	0.595855	−	1.30474i	0.595855	−	1.30474i
$244$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$245$	0.187118	+	0.540641i	0.187118	+	0.540641i
$246$	−1.09966	−	1.26908i	−1.09966	−	1.26908i
$247$		0			0
$248$		0			0
$249$	1.78872	+	1.40667i	1.78872	+	1.40667i
$250$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$251$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$251$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$252$	0.0340870	+	0.715575i	0.0340870	+	0.715575i
$253$		0			0
$254$	1.70566	−	0.500828i	1.70566	−	0.500828i
$255$		0			0
$256$	−0.995472	+	0.0950560i	−0.995472	+	0.0950560i
$257$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$257$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$258$	−0.670173	+	0.129165i	−0.670173	+	0.129165i
$259$		0			0
$260$		0			0
$261$	−1.69060	+	1.32950i	−1.69060	+	1.32950i
$262$		0			0
$263$	−0.0800569	+	0.0514495i	−0.0800569	+	0.0514495i	−0.580057	−	0.814576i	$-0.696970\pi$
$263$	−0.0800569	+	0.0514495i	−0.0800569	+	0.0514495i	0.500000	+	0.866025i	$0.333333\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.411992			0.411992
$268$	−0.841254	+	0.540641i	−0.841254	+	0.540641i
$269$	−1.91899			−1.91899			−0.959493	−	0.281733i	$-0.909091\pi$
$269$	−1.91899			−1.91899			−0.959493	+	0.281733i	$0.909091\pi$
$270$	0.127880	+	0.0511952i	0.127880	+	0.0511952i
$271$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$271$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$	−0.601300	−	1.31666i	−0.601300	−	1.31666i
$277$		0			0		−0.142315	−	0.989821i	$-0.545455\pi$
$277$		0			0		0.142315	+	0.989821i	$0.454545\pi$
$278$		0			0
$279$		0			0
$280$	0.651174	−	0.0621796i	0.651174	−	0.0621796i
$281$	−1.15486	−	1.62177i	−1.15486	−	1.62177i	−0.654861	−	0.755750i	$-0.727273\pi$
$281$	−1.15486	−	1.62177i	−1.15486	−	1.62177i	−0.500000	−	0.866025i	$-0.666667\pi$
$282$	−2.76509	+	0.811905i	−2.76509	+	0.811905i
$283$	0.0135432	−	0.0941952i	0.0135432	−	0.0941952i	−0.981929	−	0.189251i	$-0.939394\pi$
$283$	0.0135432	−	0.0941952i	0.0135432	−	0.0941952i	0.995472	+	0.0950560i	$0.0303030\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.596514	−	0.469104i	−0.596514	−	0.469104i
$288$	−1.07537	−	0.207261i	−1.07537	−	0.207261i
$289$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$290$	1.28605	+	1.48418i	1.28605	+	1.48418i
$291$		0			0
$292$		0			0
$293$		0			0		0.415415	−	0.909632i	$-0.363636\pi$
$293$		0			0		−0.415415	+	0.909632i	$0.636364\pi$
$294$	−0.195233	−	0.804762i	−0.195233	−	0.804762i
$295$		0			0
$296$		0			0
$297$		0			0
$298$	0.580057	−	1.00469i	0.580057	−	1.00469i
$299$		0			0
$300$	0.473420	−	1.36786i	0.473420	−	1.36786i
$301$	−0.286343	+	0.114634i	−0.286343	+	0.114634i
$302$		0			0
$303$	−0.134750	+	0.389333i	−0.134750	+	0.389333i
$304$		0			0
$305$	−0.841254	+	1.45709i	−0.841254	+	1.45709i
$306$		0			0
$307$	0.827068	+	0.0789754i	0.827068	+	0.0789754i	0.500000	−	0.866025i	$-0.333333\pi$
$307$	0.827068	+	0.0789754i	0.827068	+	0.0789754i	0.327068	+	0.945001i	$0.393939\pi$
$308$		0			0
$309$	0.633618	+	2.61181i	0.633618	+	2.61181i
$310$		0			0
$311$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$311$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$312$		0			0
$313$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$313$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$314$		0			0
$315$	0.703440	+	0.135577i	0.703440	+	0.135577i
$316$		0			0
$317$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$317$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$318$		0			0
$319$		0			0
$320$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$321$	−1.15389	+	0.338812i	−1.15389	+	0.338812i
$322$	−0.379436	−	0.532843i	−0.379436	−	0.532843i
$323$		0			0
$324$	0.796201	+	0.410470i	0.796201	+	0.410470i
$325$		0			0
$326$	0.273100	+	1.89945i	0.273100	+	1.89945i
$327$	−1.11646	−	2.44470i	−1.11646	−	2.44470i
$328$	0.911911	−	0.717135i	0.911911	−	0.717135i
$329$	−1.15757	+	0.596770i	−1.15757	+	0.596770i
$330$		0			0
$331$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$331$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$332$	−1.02951	+	1.18812i	−1.02951	+	1.18812i
$333$		0			0
$334$	−1.30972			−1.30972
$335$	0.327068	+	0.945001i	0.327068	+	0.945001i
$336$	−0.946841			−0.946841
$337$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$337$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$338$	0.654861	−	0.755750i	0.654861	−	0.755750i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.427201	−	0.935439i	−0.427201	−	0.935439i
$344$	−0.0671040	−	0.466718i	−0.0671040	−	0.466718i
$345$	−1.42131	+	0.273935i	−1.42131	+	0.273935i
$346$		0			0
$347$	1.67489	−	0.159932i	1.67489	−	0.159932i	0.786053	−	0.618159i	$-0.212121\pi$
$347$	1.67489	−	0.159932i	1.67489	−	0.159932i	0.888835	+	0.458227i	$0.151515\pi$
$348$	−1.64888	−	2.31553i	−1.64888	−	2.31553i
$349$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	−0.500000	−	0.866025i	$-0.666667\pi$
$349$	−0.452418	+	0.132842i	−0.452418	+	0.132842i	0.0475819	+	0.998867i	$0.484848\pi$
$350$	0.0930932	−	0.647478i	0.0930932	−	0.647478i
$351$		0			0
$352$		0			0
$353$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$353$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$354$		0			0
$355$		0			0
$356$	−0.0135432	+	0.284307i	−0.0135432	+	0.284307i
$357$		0			0
$358$		0			0
$359$		0			0		−0.959493	−	0.281733i	$-0.909091\pi$
$359$		0			0		0.959493	+	0.281733i	$0.0909091\pi$
$360$	−0.454947	+	0.996196i	−0.454947	+	0.996196i
$361$	0.235759	+	0.971812i	0.235759	+	0.971812i
$362$	1.61435	+	1.03748i	1.61435	+	1.03748i
$363$	1.44091	+	0.137591i	1.44091	+	0.137591i
$364$		0			0
$365$		0			0
$366$	1.41266	−	1.98380i	1.41266	−	1.98380i
$367$	0.607279	−	1.75462i	0.607279	−	1.75462i	−0.0475819	−	0.998867i	$-0.515152\pi$
$367$	0.607279	−	1.75462i	0.607279	−	1.75462i	0.654861	−	0.755750i	$-0.272727\pi$
$368$	0.928368	−	0.371662i	0.928368	−	0.371662i
$369$	1.17951	−	0.472203i	1.17951	−	0.472203i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−1.21769	−	0.782560i	−1.21769	−	0.782560i
$376$	−0.469383	−	1.93482i	−0.469383	−	1.93482i
$377$		0			0
$378$	−0.0864551	−	0.0253855i	−0.0864551	−	0.0253855i
$379$		0			0		−0.327068	−	0.945001i	$-0.606061\pi$
$379$		0			0		0.327068	+	0.945001i	$0.393939\pi$
$380$		0			0
$381$	−0.122434	+	2.57021i	−0.122434	+	2.57021i
$382$		0			0
$383$	−1.56499	−	1.23072i	−1.56499	−	1.23072i	−0.841254	−	0.540641i	$-0.818182\pi$
$383$	−1.56499	−	1.23072i	−1.56499	−	1.23072i	−0.723734	−	0.690079i	$-0.757576\pi$
$384$	0.341254	−	1.40667i	0.341254	−	1.40667i
$385$		0			0
$386$		0			0
$387$	0.0734899	−	0.511133i	0.0734899	−	0.511133i
$388$		0			0
$389$	1.07701	+	1.51245i	1.07701	+	1.51245i	0.841254	+	0.540641i	$0.181818\pi$
$389$	1.07701	+	1.51245i	1.07701	+	1.51245i	0.235759	+	0.971812i	$0.424242\pi$
$390$		0			0
$391$		0			0
$392$	0.561767	−	0.108272i	0.561767	−	0.108272i
$393$		0			0
$394$		0			0
$395$		0			0
$396$		0			0
$397$		0			0		0.841254	−	0.540641i	$-0.181818\pi$
$397$		0			0		−0.841254	+	0.540641i	$0.818182\pi$
$398$		0			0
$399$		0			0
$400$	0.928368	+	0.371662i	0.928368	+	0.371662i
$401$	−0.654136			−0.654136			−0.327068	−	0.945001i	$-0.606061\pi$
$401$	−0.654136			−0.654136			−0.327068	+	0.945001i	$0.606061\pi$
$402$	−0.341254	−	1.40667i	−0.341254	−	1.40667i
$403$		0			0
$404$	−0.264241	−	0.105786i	−0.264241	−	0.105786i
$405$	0.586611	−	0.676985i	0.586611	−	0.676985i
$406$	−0.929730	−	0.886496i	−0.929730	−	0.886496i
$407$		0			0
$408$		0			0
$409$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.580057	−	0.814576i	$-0.303030\pi$
$409$	1.50842	−	1.18624i	1.50842	−	1.18624i	0.928368	−	0.371662i	$-0.121212\pi$
$410$	−0.481929	−	1.05528i	−0.481929	−	1.05528i
$411$		0			0
$412$	−1.82318	+	0.351390i	−1.82318	+	0.351390i
$413$		0			0
$414$	1.09020	−	0.104102i	1.09020	−	0.104102i
$415$	0.911911	+	1.28060i	0.911911	+	1.28060i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$419$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$420$	−0.223226	+	0.920151i	−0.223226	+	0.920151i
$421$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.981929	−	0.189251i	$-0.0606061\pi$
$421$	1.02951	+	0.809616i	1.02951	+	0.809616i	0.0475819	+	0.998867i	$0.484848\pi$
$422$		0			0
$423$	0.103748	−	2.17794i	0.103748	−	2.17794i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.457201	−	1.00113i	0.457201	−	1.00113i
$428$	−0.195876	−	0.807410i	−0.195876	−	0.807410i
$429$		0			0
$430$	−0.469383	−	0.0448206i	−0.469383	−	0.0448206i
$431$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$431$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$432$	0.0688733	−	0.119292i	0.0688733	−	0.119292i
$433$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$433$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$434$		0			0
$435$	−2.63900	+	1.05650i	−2.63900	+	1.05650i
$436$	1.72373	−	0.690079i	1.72373	−	0.690079i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	0.623713	+	0.0595574i	0.623713	+	0.0595574i
$442$		0			0
$443$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.415415	−	0.909632i	$-0.636364\pi$
$443$	−0.462997	−	1.90850i	−0.462997	−	1.90850i	−0.0475819	−	0.998867i	$-0.515152\pi$
$444$		0			0
$445$	0.273100	+	0.0801894i	0.273100	+	0.0801894i
$446$	−0.550294	−	1.58997i	−0.550294	−	1.58997i
$447$	1.09966	+	1.26908i	1.09966	+	1.26908i
$448$	0.0311250	−	0.653395i	0.0311250	−	0.653395i
$449$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.995472	−	0.0950560i	$-0.969697\pi$
$449$	−1.95496	−	0.376789i	−1.95496	−	0.376789i	−0.959493	−	0.281733i	$-0.909091\pi$
$450$	0.860857	+	0.676985i	0.860857	+	0.676985i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.0405070	−	0.281733i	0.0405070	−	0.281733i
$455$		0			0
$456$		0			0
$457$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$457$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$458$	−1.58006	−	0.814576i	−1.58006	−	0.814576i
$459$		0			0
$460$	−0.142315	−	0.989821i	−0.142315	−	0.989821i
$461$	−0.653077	−	1.43004i	−0.653077	−	1.43004i	−0.888835	−	0.458227i	$-0.848485\pi$
$461$	−0.653077	−	1.43004i	−0.653077	−	1.43004i	0.235759	−	0.971812i	$-0.424242\pi$
$462$		0			0
$463$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.723734	+	0.690079i	$0.757576\pi$
$463$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.981929	+	0.189251i	$0.939394\pi$
$464$	1.65210	−	1.06174i	1.65210	−	1.06174i
$465$		0			0
$466$		0			0
$467$	1.65033	+	0.660694i	1.65033	+	0.660694i	0.995472	−	0.0950560i	$-0.0303030\pi$
$467$	1.65033	+	0.660694i	1.65033	+	0.660694i	0.654861	+	0.755750i	$0.272727\pi$
$468$		0			0
$469$	−0.271738	−	0.595023i	−0.271738	−	0.595023i
$470$	−1.99094			−1.99094
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$479$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$480$	−1.28656	−	0.663268i	−1.28656	−	0.663268i
$481$		0			0
$482$	−1.07701	−	1.51245i	−1.07701	−	1.51245i
$483$	0.908487	−	0.266756i	0.908487	−	0.266756i
$484$	−0.142315	+	0.989821i	−0.142315	+	0.989821i
$485$		0			0
$486$	−1.03809	+	0.989821i	−1.03809	+	0.989821i
$487$	0.370638	−	1.52779i	0.370638	−	1.52779i	−0.415415	−	0.909632i	$-0.636364\pi$
$487$	0.370638	−	1.52779i	0.370638	−	1.52779i	0.786053	−	0.618159i	$-0.212121\pi$
$488$	1.32254	+	1.04006i	1.32254	+	1.04006i
$489$	−2.72747	−	0.525678i	−2.72747	−	0.525678i
$490$	0.0272219	−	0.571458i	0.0272219	−	0.571458i
$491$		0			0		−0.654861	−	0.755750i	$-0.727273\pi$
$491$		0			0		0.654861	+	0.755750i	$0.272727\pi$
$492$	0.549222	+	1.58687i	0.549222	+	1.58687i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.13779	−	1.97070i	−1.13779	−	1.97070i
$499$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$499$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$500$	0.580057	−	0.814576i	0.580057	−	0.814576i
$501$	0.620049	−	1.79151i	0.620049	−	1.79151i
$502$		0			0
$503$	−1.07701	+	0.431171i	−1.07701	+	0.431171i	−0.841254	−	0.540641i	$-0.818182\pi$
$503$	−1.07701	+	0.431171i	−1.07701	+	0.431171i	−0.235759	+	0.971812i	$0.575758\pi$
$504$	0.234307	−	0.676985i	0.234307	−	0.676985i
$505$	−0.165101	+	0.231852i	−0.165101	+	0.231852i
$506$		0			0
$507$	0.723734	+	1.25354i	0.723734	+	1.25354i
$508$	−1.76962	−	0.168978i	−1.76962	−	0.168978i
$509$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.142315	−	0.989821i	$-0.545455\pi$
$509$	−1.10181	−	0.708089i	−1.10181	−	0.708089i	−0.959493	+	0.281733i	$0.909091\pi$
$510$		0			0
$511$		0			0
$512$	0.959493	+	0.281733i	0.959493	+	0.281733i
$513$		0			0
$514$		0			0
$515$	−0.0883470	+	1.85463i	−0.0883470	+	1.85463i
$516$	0.670173	+	0.129165i	0.670173	+	0.129165i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.142315	−	0.989821i	0.142315	−	0.989821i	−0.786053	−	0.618159i	$-0.787879\pi$
$521$	0.142315	−	0.989821i	0.142315	−	0.989821i	0.928368	−	0.371662i	$-0.121212\pi$
$522$	2.06363	−	0.605935i	2.06363	−	0.605935i
$523$	−0.273507	−	0.384087i	−0.273507	−	0.384087i	0.654861	−	0.755750i	$-0.272727\pi$
$523$	−0.273507	−	0.384087i	−0.273507	−	0.384087i	−0.928368	+	0.371662i	$0.878788\pi$
$524$		0			0
$525$	0.841586	+	0.433868i	0.841586	+	0.433868i
$526$	0.0934441	−	0.0180099i	0.0934441	−	0.0180099i
$527$		0			0
$528$		0			0
$529$		0			0
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	−0.382481	−	0.153122i	−0.382481	−	0.153122i
$535$	−0.830830			−0.830830
$536$	0.981929	−	0.189251i	0.981929	−	0.189251i
$537$		0			0
$538$	1.78153	+	0.713215i	1.78153	+	0.713215i
$539$		0			0
$540$	−0.0996919	−	0.0950560i	−0.0996919	−	0.0950560i
$541$	0.396666	−	0.254922i	0.396666	−	0.254922i	−0.327068	−	0.945001i	$-0.606061\pi$
$541$	0.396666	−	0.254922i	0.396666	−	0.254922i	0.723734	+	0.690079i	$0.242424\pi$
$542$		0			0
$543$	−2.18340	+	1.71704i	−2.18340	+	1.71704i
$544$		0			0
$545$	−0.264241	−	1.83784i	−0.264241	−	1.83784i
$546$		0			0
$547$	−1.58006	−	0.814576i	−1.58006	−	0.814576i	−0.580057	−	0.814576i	$-0.696970\pi$
$547$	−1.58006	−	0.814576i	−1.58006	−	0.814576i	−1.00000			$\pi$
$548$		0			0
$549$	1.06882	+	1.50095i	1.06882	+	1.50095i
$550$		0			0
$551$		0			0
$552$	0.0688733	+	1.44583i	0.0688733	+	1.44583i
$553$		0			0
$554$		0			0
$555$		0			0
$556$		0			0
$557$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$557$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$558$		0			0
$559$		0			0
$560$	−0.627639	−	0.184291i	−0.627639	−	0.184291i
$561$		0			0
$562$	0.469383	+	1.93482i	0.469383	+	1.93482i
$563$	−0.396666	−	0.254922i	−0.396666	−	0.254922i	0.327068	−	0.945001i	$-0.393939\pi$
$563$	−0.396666	−	0.254922i	−0.396666	−	0.254922i	−0.723734	+	0.690079i	$0.757576\pi$
$564$	2.86878	+	0.273935i	2.86878	+	0.273935i
$565$		0			0
$566$	−0.0475819	+	0.0824143i	−0.0475819	+	0.0824143i
$567$	−0.339891	+	0.477310i	−0.339891	+	0.477310i
$568$		0			0
$569$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.888835	−	0.458227i	$-0.848485\pi$
$569$	−1.21590	+	0.486774i	−1.21590	+	0.486774i	−0.327068	+	0.945001i	$0.606061\pi$
$570$		0			0
$571$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$571$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$572$		0			0
$573$		0			0
$574$	0.379436	+	0.657203i	0.379436	+	0.657203i
$575$	−0.995472	−	0.0950560i	−0.995472	−	0.0950560i
$576$	0.921310	+	0.592090i	0.921310	+	0.592090i
$577$		0			0		−0.235759	−	0.971812i	$-0.575758\pi$
$577$		0			0		0.235759	+	0.971812i	$0.424242\pi$
$578$	−0.415415	+	0.909632i	−0.415415	+	0.909632i
$579$		0			0
$580$	−0.642315	−	1.85585i	−0.642315	−	1.85585i
$581$	−0.673440	−	0.777191i	−0.673440	−	0.777191i
$582$		0			0
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0395325	−	0.829889i	−0.0395325	−	0.829889i	−0.928368	−	0.371662i	$-0.878788\pi$
$587$	−0.0395325	−	0.829889i	−0.0395325	−	0.829889i	0.888835	−	0.458227i	$-0.151515\pi$
$588$	−0.117852	+	0.819677i	−0.117852	+	0.819677i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$593$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$594$		0			0
$595$		0			0
$596$	−0.911911	+	0.717135i	−0.911911	+	0.717135i
$597$		0			0
$598$		0			0
$599$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$599$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$600$	−0.947890	+	1.09392i	−0.947890	+	1.09392i
$601$	0.437742	+	0.175245i	0.437742	+	0.175245i	0.580057	−	0.814576i	$-0.303030\pi$
$601$	0.437742	+	0.175245i	0.437742	+	0.175245i	−0.142315	+	0.989821i	$0.545455\pi$
$602$	0.308437			0.308437
$603$	1.09020	+	0.104102i	1.09020	+	0.104102i
$604$		0			0
$605$	0.928368	+	0.371662i	0.928368	+	0.371662i
$606$	0.269798	−	0.311363i	0.269798	−	0.311363i
$607$	1.44091	+	1.37391i	1.44091	+	1.37391i	0.786053	+	0.618159i	$0.212121\pi$
$607$	1.44091	+	1.37391i	1.44091	+	1.37391i	0.654861	+	0.755750i	$0.272727\pi$
$608$		0			0
$609$	1.65275	−	0.852054i	1.65275	−	0.852054i
$610$	1.32254	−	1.04006i	1.32254	−	1.04006i
$611$		0			0
$612$		0			0
$613$		0			0		0.981929	−	0.189251i	$-0.0606061\pi$
$613$		0			0		−0.981929	+	0.189251i	$0.939394\pi$
$614$	−0.738471	−	0.380708i	−0.738471	−	0.380708i
$615$	1.67162	−	0.159621i	1.67162	−	0.159621i
$616$		0			0
$617$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$617$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$618$	0.382481	−	2.66021i	0.382481	−	2.66021i
$619$		0			0		−0.0475819	−	0.998867i	$-0.515152\pi$
$619$		0			0		0.0475819	+	0.998867i	$0.484848\pi$
$620$		0			0
$621$	−0.0324750	+	0.133864i	−0.0324750	+	0.133864i
$622$		0			0
$623$	−0.182822	−	0.0352360i	−0.182822	−	0.0352360i
$624$		0			0
$625$	−0.654861	−	0.755750i	−0.654861	−	0.755750i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−0.602662	−	0.387308i	−0.602662	−	0.387308i
$631$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$631$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.581419	+	1.67990i	−0.581419	+	1.67990i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	0.500000	−	0.866025i	0.500000	−	0.866025i
$641$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	0.841254	−	0.540641i	$-0.181818\pi$
$641$	−0.0475819	−	0.0824143i	−0.0475819	−	0.0824143i	−0.888835	+	0.458227i	$0.848485\pi$
$642$	1.19715	+	0.114314i	1.19715	+	0.114314i
$643$	−1.65210	−	1.06174i	−1.65210	−	1.06174i	−0.928368	−	0.371662i	$-0.878788\pi$
$643$	−1.65210	−	1.06174i	−1.65210	−	1.06174i	−0.723734	−	0.690079i	$-0.757576\pi$
$644$	0.154218	+	0.635697i	0.154218	+	0.635697i
$645$	0.283524	−	0.620830i	0.283524	−	0.620830i
$646$		0			0
$647$	−0.651174	−	1.88144i	−0.651174	−	1.88144i	−0.415415	−	0.909632i	$-0.636364\pi$
$647$	−0.651174	−	1.88144i	−0.651174	−	1.88144i	−0.235759	−	0.971812i	$-0.575758\pi$
$648$	−0.586611	−	0.676985i	−0.586611	−	0.676985i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	0.452418	−	1.86489i	0.452418	−	1.86489i
$653$		0			0		0.723734	−	0.690079i	$-0.242424\pi$
$653$		0			0		−0.723734	+	0.690079i	$0.757576\pi$
$654$	0.127880	+	2.68452i	0.127880	+	2.68452i
$655$		0			0
$656$	−1.11312	+	0.326842i	−1.11312	+	0.326842i
$657$		0			0
$658$	1.29645	−	0.123796i	1.29645	−	0.123796i
$659$		0			0		−0.888835	−	0.458227i	$-0.848485\pi$
$659$		0			0		0.888835	+	0.458227i	$0.151515\pi$
$660$		0			0
$661$	0.186393	+	1.29639i	0.186393	+	1.29639i	0.841254	+	0.540641i	$0.181818\pi$
$661$	0.186393	+	1.29639i	0.186393	+	1.29639i	−0.654861	+	0.755750i	$0.727273\pi$
$662$		0			0
$663$		0			0
$664$	1.39734	−	0.720381i	1.39734	−	0.720381i
$665$		0			0
$666$		0			0
$667$	−1.28605	+	1.48418i	−1.28605	+	1.48418i
$668$	1.21590	+	0.486774i	1.21590	+	0.486774i
$669$	2.43538			2.43538
$670$	0.0475819	−	0.998867i	0.0475819	−	0.998867i
$671$		0			0
$672$	0.879017	+	0.351905i	0.879017	+	0.351905i
$673$		0			0		0.654861	−	0.755750i	$-0.272727\pi$
$673$		0			0		−0.654861	+	0.755750i	$0.727273\pi$
$674$		0			0
$675$	−0.115880	+	0.0744714i	−0.115880	+	0.0744714i
$676$	−0.888835	+	0.458227i	−0.888835	+	0.458227i
$677$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$677$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.366193	+	0.188786i	0.366193	+	0.188786i
$682$		0			0
$683$	−0.481929	−	0.676774i	−0.481929	−	0.676774i	0.500000	−	0.866025i	$-0.333333\pi$
$683$	−0.481929	−	0.676774i	−0.481929	−	0.676774i	−0.981929	+	0.189251i	$0.939394\pi$
$684$		0			0
$685$		0			0
$686$	0.0489319	+	1.02721i	0.0489319	+	1.02721i
$687$	1.86226	−	1.77566i	1.86226	−	1.77566i
$688$	−0.111165	+	0.458227i	−0.111165	+	0.458227i
$689$		0			0
$690$	1.42131	+	0.273935i	1.42131	+	0.273935i
$691$		0			0		0.0475819	−	0.998867i	$-0.484848\pi$
$691$		0			0		−0.0475819	+	0.998867i	$0.515152\pi$
$692$		0			0
$693$		0			0
$694$	−1.61435	−	0.474017i	−1.61435	−	0.474017i
$695$		0			0
$696$	0.670173	+	2.76249i	0.670173	+	2.76249i
$697$		0			0
$698$	0.469383	+	0.0448206i	0.469383	+	0.0448206i
$699$		0			0
$700$	−0.327068	+	0.566498i	−0.327068	+	0.566498i
$701$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	−0.995472	−	0.0950560i	$-0.969697\pi$
$701$	−0.580057	+	0.814576i	−0.580057	+	0.814576i	0.415415	+	0.909632i	$0.363636\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$	0.942554	−	2.72333i	0.942554	−	2.72333i
$706$		0			0
$707$	0.0930932	−	0.161242i	0.0930932	−	0.161242i
$708$		0			0
$709$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.580057	−	0.814576i	$-0.303030\pi$
$709$	0.995472	+	0.0950560i	0.995472	+	0.0950560i	0.415415	+	0.909632i	$0.363636\pi$
$710$		0			0
$711$		0			0
$712$	0.118239	−	0.258908i	0.118239	−	0.258908i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$719$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$720$	0.792607	−	0.755750i	0.792607	−	0.755750i
$721$	−0.0577910	−	1.21318i	−0.0577910	−	1.21318i
$722$	0.142315	−	0.989821i	0.142315	−	0.989821i
$723$	2.57870	−	0.757175i	2.57870	−	0.757175i
$724$	−1.11312	−	1.56316i	−1.11312	−	1.56316i
$725$	−1.95496	+	0.186677i	−1.95496	+	0.186677i
$726$	−1.28656	−	0.663268i	−1.28656	−	0.663268i
$727$	−1.13915	+	0.219553i	−1.13915	+	0.219553i	−0.723734	−	0.690079i	$-0.757576\pi$
$727$	−1.13915	+	0.219553i	−1.13915	+	0.219553i	−0.415415	+	0.909632i	$0.636364\pi$
$728$		0			0
$729$	−0.490360	−	1.07374i	−0.490360	−	1.07374i
$730$		0			0
$731$		0			0
$732$	−2.04877	+	1.31666i	−2.04877	+	1.31666i
$733$		0			0		−0.723734	−	0.690079i	$-0.757576\pi$
$733$		0			0		0.723734	+	0.690079i	$0.242424\pi$
$734$	−1.21590	+	1.40323i	−1.21590	+	1.40323i
$735$	0.768787	+	0.307776i	0.768787	+	0.307776i
$736$	−1.00000			−1.00000
$737$		0			0
$738$	−1.27051			−1.27051
$739$		0			0		−0.928368	−	0.371662i	$-0.878788\pi$
$739$		0			0		0.928368	+	0.371662i	$0.121212\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.723734	+	0.690079i	$0.757576\pi$
$743$	−1.70566	+	0.879330i	−1.70566	+	0.879330i	−0.981929	+	0.189251i	$0.939394\pi$
$744$		0			0
$745$	0.481929	+	1.05528i	0.481929	+	1.05528i
$746$		0			0
$747$	1.69060	−	0.325836i	1.69060	−	0.325836i
$748$		0			0
$749$	0.541015	−	0.0516607i	0.541015	−	0.0516607i
$750$	0.839614	+	1.17907i	0.839614	+	1.17907i
$751$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$751$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$752$	−0.283341	+	1.97068i	−0.283341	+	1.97068i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	0.0708273	+	0.0556992i	0.0708273	+	0.0556992i
$757$		0			0		−0.981929	−	0.189251i	$-0.939394\pi$
$757$		0			0		0.981929	+	0.189251i	$0.0606061\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.84125	+	0.540641i	1.84125	+	0.540641i	1.00000			$0$
$761$	1.84125	+	0.540641i	1.84125	+	0.540641i	0.841254	+	0.540641i	$0.181818\pi$
$762$	1.06891	−	2.34059i	1.06891	−	2.34059i
$763$	0.286343	+	1.18032i	0.286343	+	1.18032i
$764$		0			0
$765$		0			0
$766$	0.995472	+	1.72421i	0.995472	+	1.72421i
$767$		0			0
$768$	−0.839614	+	1.17907i	−0.839614	+	1.17907i
$769$	−0.473420	+	1.36786i	−0.473420	+	1.36786i	0.415415	+	0.909632i	$0.363636\pi$
$769$	−0.473420	+	1.36786i	−0.473420	+	1.36786i	−0.888835	+	0.458227i	$0.848485\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.580057	−	0.814576i	$-0.303030\pi$
$773$		0			0		−0.580057	+	0.814576i	$0.696970\pi$
$774$	−0.258195	+	0.447206i	−0.258195	+	0.447206i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−0.437742	−	1.80440i	−0.437742	−	1.80440i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.0128716	+	0.270208i	−0.0128716	+	0.270208i
$784$	−0.561767	−	0.108272i	−0.561767	−	0.108272i
$785$		0			0
$786$		0			0
$787$	1.28656	−	1.22673i	1.28656	−	1.22673i	0.327068	−	0.945001i	$-0.393939\pi$
$787$	1.28656	−	1.22673i	1.28656	−	1.22673i	0.959493	−	0.281733i	$-0.0909091\pi$
$788$		0			0
$789$	−0.0196034	+	0.136345i	−0.0196034	+	0.136345i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$797$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$798$		0			0
$799$		0			0
$800$	−0.723734	−	0.690079i	−0.723734	−	0.690079i
$801$	0.204131	−	0.235579i	0.204131	−	0.235579i
$802$	0.607279	+	0.243118i	0.607279	+	0.243118i
$803$		0			0
$804$	−0.205996	+	1.43273i	−0.205996	+	1.43273i
$805$	0.654136			0.654136
$806$		0			0
$807$	−1.81899	+	2.09922i	−1.81899	+	2.09922i
$808$	0.205996	+	0.196417i	0.205996	+	0.196417i
$809$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.500000	+	0.866025i	$0.666667\pi$
$809$	−1.49547	+	0.961081i	−1.49547	+	0.961081i	−0.995472	+	0.0950560i	$0.969697\pi$
$810$	−0.796201	+	0.410470i	−0.796201	+	0.410470i
$811$		0			0		0.786053	−	0.618159i	$-0.212121\pi$
$811$		0			0		−0.786053	+	0.618159i	$0.787879\pi$
$812$	0.533654	+	1.16854i	0.533654	+	1.16854i
$813$		0			0
$814$		0			0
$815$	−1.70566	−	0.879330i	−1.70566	−	0.879330i
$816$		0			0
$817$		0			0
$818$	−1.84125	+	0.540641i	−1.84125	+	0.540641i
$819$		0			0
$820$	0.0552004	+	1.15880i	0.0552004	+	1.15880i
$821$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.235759	−	0.971812i	$-0.424242\pi$
$821$	1.21769	−	1.16106i	1.21769	−	1.16106i	0.981929	−	0.189251i	$-0.0606061\pi$
$822$		0			0
$823$	1.54370	+	1.21398i	1.54370	+	1.21398i	0.888835	+	0.458227i	$0.151515\pi$
$823$	1.54370	+	1.21398i	1.54370	+	1.21398i	0.654861	+	0.755750i	$0.272727\pi$
$824$	1.82318	+	0.351390i	1.82318	+	0.351390i
$825$		0			0
$826$		0			0
$827$	0.379436	+	1.09631i	0.379436	+	1.09631i	0.959493	+	0.281733i	$0.0909091\pi$
$827$	0.379436	+	1.09631i	0.379436	+	1.09631i	−0.580057	+	0.814576i	$0.696970\pi$
$828$	−1.05080	−	0.308543i	−1.05080	−	0.308543i
$829$	0.698939	−	1.53046i	0.698939	−	1.53046i	−0.142315	−	0.989821i	$-0.545455\pi$
$829$	0.698939	−	1.53046i	0.698939	−	1.53046i	0.841254	−	0.540641i	$-0.181818\pi$
$830$	−0.370638	−	1.52779i	−0.370638	−	1.52779i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.759713	−	1.06687i	0.759713	−	1.06687i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.327068	−	0.945001i	$-0.393939\pi$
$839$		0			0		−0.327068	+	0.945001i	$0.606061\pi$
$840$	0.549222	−	0.771274i	0.549222	−	0.771274i
$841$	−1.42837	+	2.47401i	−1.42837	+	2.47401i
$842$	−0.654861	−	1.13425i	−0.654861	−	1.13425i
$843$	−2.86878	−	0.273935i	−2.86878	−	0.273935i
$844$		0			0
$845$	0.235759	+	0.971812i	0.235759	+	0.971812i
$846$	−0.905775	+	1.98337i	−0.905775	+	1.98337i
$847$	−0.627639	−	0.184291i	−0.627639	−	0.184291i
$848$		0			0
$849$	−0.0902048	−	0.104102i	−0.0902048	−	0.104102i
$850$		0			0
$851$		0			0
$852$		0			0
$853$		0			0		0.235759	−	0.971812i	$-0.424242\pi$
$853$		0			0		−0.235759	+	0.971812i	$0.575758\pi$
$854$	−0.796533	+	0.759493i	−0.796533	+	0.759493i
$855$		0			0
$856$	−0.118239	+	0.822373i	−0.118239	+	0.822373i
$857$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$857$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$858$		0			0
$859$		0			0		0.995472	−	0.0950560i	$-0.0303030\pi$
$859$		0			0		−0.995472	+	0.0950560i	$0.969697\pi$
$860$	0.419102	+	0.216062i	0.419102	+	0.216062i
$861$	−1.07859	+	0.207882i	−1.07859	+	0.207882i
$862$		0			0
$863$	−0.0395325	−	0.0865641i	−0.0395325	−	0.0865641i	0.888835	−	0.458227i	$-0.151515\pi$
$863$	−0.0395325	−	0.0865641i	−0.0395325	−	0.0865641i	−0.928368	+	0.371662i	$0.878788\pi$
$864$	−0.108276	+	0.0851493i	−0.108276	+	0.0851493i
$865$		0			0
$866$		0			0
$867$	−1.04758	−	0.998867i	−1.04758	−	0.998867i
$868$		0			0
$869$		0			0
$870$	2.84262			2.84262
$871$		0			0
$872$	−1.85674			−1.85674
$873$		0			0
$874$		0			0
$875$	0.473420	+	0.451405i	0.473420	+	0.451405i
$876$		0			0
$877$		0			0		0.888835	−	0.458227i	$-0.151515\pi$
$877$		0			0		−0.888835	+	0.458227i	$0.848485\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.654861	−	0.755750i	$-0.727273\pi$
$881$	−0.981929	+	0.189251i	−0.981929	+	0.189251i	−0.327068	+	0.945001i	$0.606061\pi$
$882$	−0.556900	−	0.287102i	−0.556900	−	0.287102i
$883$	0.827068	−	0.0789754i	0.827068	−	0.0789754i	0.327068	−	0.945001i	$-0.393939\pi$
$883$	0.827068	−	0.0789754i	0.827068	−	0.0789754i	0.500000	+	0.866025i	$0.333333\pi$
$884$		0			0
$885$		0			0
$886$	−0.279486	+	1.94387i	−0.279486	+	1.94387i
$887$	−0.0934441	−	1.96163i	−0.0934441	−	1.96163i	−0.235759	−	0.971812i	$-0.575758\pi$
$887$	−0.0934441	−	1.96163i	−0.0934441	−	1.96163i	0.142315	−	0.989821i	$-0.454545\pi$
$888$		0			0
$889$	0.274150	−	1.13006i	0.274150	−	1.13006i
$890$	−0.223734	−	0.175946i	−0.223734	−	0.175946i
$891$		0			0
$892$	−0.0800569	+	1.68060i	−0.0800569	+	1.68060i
$893$		0			0
$894$	−0.549222	−	1.58687i	−0.549222	−	1.58687i
$895$		0			0
$896$	−0.271738	+	0.595023i	−0.271738	+	0.595023i
$897$		0			0
$898$	1.67489	+	1.07639i	1.67489	+	1.07639i
$899$		0			0
$900$	−0.547582	−	0.948440i	−0.547582	−	0.948440i
$901$		0			0
$902$		0			0
$903$	−0.146020	+	0.421898i	−0.146020	+	0.421898i
$904$		0			0
$905$	−1.78153	+	0.713215i	−1.78153	+	0.713215i
$906$		0			0
$907$	−0.975950	+	1.37053i	−0.975950	+	1.37053i	−0.0475819	+	0.998867i	$0.515152\pi$
$907$	−0.975950	+	1.37053i	−0.975950	+	1.37053i	−0.928368	+	0.371662i	$0.878788\pi$
$908$	−0.142315	+	0.246497i	−0.142315	+	0.246497i
$909$	0.155858	+	0.269954i	0.155858	+	0.269954i
$910$		0			0
$911$		0			0		−0.841254	−	0.540641i	$-0.818182\pi$
$911$		0			0		0.841254	+	0.540641i	$0.181818\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$	0.796533	+	2.30143i	0.796533	+	2.30143i
$916$	1.16413	+	1.34347i	1.16413	+	1.34347i
$917$		0			0
$918$		0			0
$919$		0			0		−0.786053	−	0.618159i	$-0.787879\pi$
$919$		0			0		0.786053	+	0.618159i	$0.212121\pi$
$920$	−0.235759	+	0.971812i	−0.235759	+	0.971812i
$921$	0.870363	−	0.829889i	0.870363	−	0.829889i
$922$	0.0748038	+	1.57033i	0.0748038	+	1.57033i
$923$		0			0
$924$		0			0
$925$		0			0
$926$	1.91030	−	0.182411i	1.91030	−	0.182411i
$927$	1.80738	+	0.931772i	1.80738	+	0.931772i
$928$	−1.92837	+	0.371662i	−1.92837	+	0.371662i
$929$	0.223734	+	1.55610i	0.223734	+	1.55610i	0.723734	+	0.690079i	$0.242424\pi$
$929$	0.223734	+	1.55610i	0.223734	+	1.55610i	−0.500000	+	0.866025i	$0.666667\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$	−1.28656	−	1.22673i	−1.28656	−	1.22673i
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$	0.0311250	+	0.653395i	0.0311250	+	0.653395i
$939$		0			0
$940$	1.84833	+	0.739959i	1.84833	+	0.739959i
$941$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	−0.959493	−	0.281733i	$-0.909091\pi$
$941$	−0.544078	+	0.627899i	−0.544078	+	0.627899i	0.415415	+	0.909632i	$0.363636\pi$
$942$		0			0
$943$	0.975950	−	0.627205i	0.975950	−	0.627205i
$944$		0			0
$945$	0.0708273	−	0.0556992i	0.0708273	−	0.0556992i
$946$		0			0
$947$	0.0671040	+	0.466718i	0.0671040	+	0.466718i	0.995472	+	0.0950560i	$0.0303030\pi$
$947$	0.0671040	+	0.466718i	0.0671040	+	0.466718i	−0.928368	+	0.371662i	$0.878788\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$		0			0		0.142315	−	0.989821i	$-0.454545\pi$
$953$		0			0		−0.142315	+	0.989821i	$0.545455\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.947890	+	1.09392i	0.947890	+	1.09392i
$961$	−0.327068	−	0.945001i	−0.327068	−	0.945001i
$962$		0			0
$963$	−0.377984	+	0.827670i	−0.377984	+	0.827670i
$964$	0.437742	+	1.80440i	0.437742	+	1.80440i
$965$		0			0
$966$	−0.942554	−	0.0900029i	−0.942554	−	0.0900029i
$967$	0.415415	+	0.719520i	0.415415	+	0.719520i	0.995472	−	0.0950560i	$-0.0303030\pi$
$967$	0.415415	+	0.719520i	0.415415	+	0.719520i	−0.580057	+	0.814576i	$0.696970\pi$
$968$	0.500000	−	0.866025i	0.500000	−	0.866025i
$969$		0			0
$970$		0			0
$971$		0			0		0.928368	−	0.371662i	$-0.121212\pi$
$971$		0			0		−0.928368	+	0.371662i	$0.878788\pi$
$972$	1.33161	−	0.533098i	1.33161	−	0.533098i
$973$		0			0
$974$	−0.911911	+	1.28060i	−0.911911	+	1.28060i
$975$		0			0
$976$	−0.841254	−	1.45709i	−0.841254	−	1.45709i
$977$		0			0		−0.995472	−	0.0950560i	$-0.969697\pi$
$977$		0			0		0.995472	+	0.0950560i	$0.0303030\pi$
$978$	2.33673	+	1.50172i	2.33673	+	1.50172i
$979$		0			0
$980$	−0.237662	+	0.520406i	−0.237662	+	0.520406i
$981$	−1.95106	−	0.572883i	−1.95106	−	0.572883i
$982$		0			0
$983$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	0.142315	−	0.989821i	$-0.454545\pi$
$983$	−0.857685	−	0.989821i	−0.857685	−	0.989821i	−1.00000			$\pi$
$984$	0.0799009	−	1.67733i	0.0799009	−	1.67733i
$985$		0			0
$986$		0			0
$987$	−0.444431	+	1.83197i	−0.444431	+	1.83197i
$988$		0			0
$989$	−0.0224357	−	0.470984i	−0.0224357	−	0.470984i
$990$		0			0
$991$		0			0		0.959493	−	0.281733i	$-0.0909091\pi$
$991$		0			0		−0.959493	+	0.281733i	$0.909091\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$	0.323848	+	2.25241i	0.323848	+	2.25241i
$997$		0			0		−0.415415	−	0.909632i	$-0.636364\pi$
$997$		0			0		0.415415	+	0.909632i	$0.363636\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1340.1.bl.a.859.1	yes	20
4.3	odd	2		1340.1.bl.b.859.1	yes	20
5.4	even	2		1340.1.bl.b.859.1	yes	20
20.19	odd	2	CM	1340.1.bl.a.859.1	yes	20
67.39	even	33	inner	1340.1.bl.a.39.1	✓	20
268.39	odd	66		1340.1.bl.b.39.1	yes	20
335.39	even	66		1340.1.bl.b.39.1	yes	20
1340.39	odd	66	inner	1340.1.bl.a.39.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1340.1.bl.a.39.1	✓	20	67.39	even	33	inner
1340.1.bl.a.39.1	✓	20	1340.39	odd	66	inner
1340.1.bl.a.859.1	yes	20	1.1	even	1	trivial
1340.1.bl.a.859.1	yes	20	20.19	odd	2	CM
1340.1.bl.b.39.1	yes	20	268.39	odd	66
1340.1.bl.b.39.1	yes	20	335.39	even	66
1340.1.bl.b.859.1	yes	20	4.3	odd	2
1340.1.bl.b.859.1	yes	20	5.4	even	2

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:	\( N \)	\(=\)	\( 1340 = 2^{2} \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1340.bl (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.928368 - 0.371662i) q^{2} +(0.947890 - 1.09392i) q^{3} +(0.723734 + 0.690079i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-1.28656 + 0.663268i) q^{6} +(-0.514186 + 0.404360i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.155858 - 1.08402i) q^{9} +O(q^{10})\)	\(q+(-0.928368 - 0.371662i) q^{2} +(0.947890 - 1.09392i) q^{3} +(0.723734 + 0.690079i) q^{4} +(0.841254 - 0.540641i) q^{5} +(-1.28656 + 0.663268i) q^{6} +(-0.514186 + 0.404360i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.155858 - 1.08402i) q^{9} +(-0.981929 + 0.189251i) q^{10} +(1.44091 - 0.137591i) q^{12} +(0.627639 - 0.184291i) q^{14} +(0.205996 - 1.43273i) q^{15} +(0.0475819 + 0.998867i) q^{16} +(-0.258195 + 1.06429i) q^{18} +(0.981929 + 0.189251i) q^{20} +(-0.0450525 + 0.945768i) q^{21} +(-0.327068 - 0.945001i) q^{23} +(-1.38884 - 0.407799i) q^{24} +(0.415415 - 0.909632i) q^{25} +(-0.115880 - 0.0744714i) q^{27} +(-0.651174 - 0.0621796i) q^{28} +(-0.981929 - 1.70075i) q^{29} +(-0.723734 + 1.25354i) q^{30} +(0.327068 - 0.945001i) q^{32} +(-0.213947 + 0.618159i) q^{35} +(0.635257 - 0.892094i) q^{36} +(-0.841254 - 0.540641i) q^{40} +(0.273507 + 1.12741i) q^{41} +(0.393332 - 0.861277i) q^{42} +(0.452418 + 0.132842i) q^{43} +(-0.717180 - 0.827670i) q^{45} +(-0.0475819 + 0.998867i) q^{46} +(1.95496 + 0.376789i) q^{47} +(1.13779 + 0.894765i) q^{48} +(-0.134879 + 0.555979i) q^{49} +(-0.723734 + 0.690079i) q^{50} +(0.0799009 + 0.112205i) q^{54} +(0.581419 + 0.299742i) q^{56} +(0.279486 + 1.94387i) q^{58} +(1.13779 - 0.894765i) q^{60} +(-1.49547 + 0.770969i) q^{61} +(0.518473 + 0.494363i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-0.235759 + 0.971812i) q^{67} +(-1.34378 - 0.537970i) q^{69} +(0.428368 - 0.494363i) q^{70} +(-0.921310 + 0.592090i) q^{72} +(-0.601300 - 1.31666i) q^{75} +(0.580057 + 0.814576i) q^{80} +(0.859495 - 0.252370i) q^{81} +(0.165101 - 1.14831i) q^{82} +(0.0748038 + 1.57033i) q^{83} +(-0.685261 + 0.653395i) q^{84} +(-0.370638 - 0.291473i) q^{86} +(-2.79125 - 0.537970i) q^{87} +(0.186393 + 0.215109i) q^{89} +(0.358193 + 1.03493i) q^{90} +(0.415415 - 0.909632i) q^{92} +(-1.67489 - 1.07639i) q^{94} +(-0.723734 - 1.25354i) q^{96} +(0.331854 - 0.466024i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8	\( 20 q - q^{2} - 2 q^{3} + q^{4} - 2 q^{5} - q^{6} + q^{7} + 2 q^{8} - q^{10} + q^{12} + 2 q^{14} - 2 q^{15} + q^{16} + q^{20} - 10 q^{21} + q^{23} - 9 q^{24} - 2 q^{25} + 2 q^{27} + q^{28} - q^{29} - q^{30} - q^{32} - 21 q^{35} + 2 q^{40} - q^{41} - 20 q^{42} + 9 q^{43} - q^{46} + q^{47} + q^{48} - q^{50} + q^{54} - q^{56} - 2 q^{58} + q^{60} - 9 q^{61} + 11 q^{63} - 2 q^{64} - q^{67} + q^{69} - 9 q^{70} + 11 q^{72} - 2 q^{75} + q^{80} + 2 q^{81} - 2 q^{82} + q^{83} + q^{84} - q^{86} - q^{87} - 4 q^{89} - 2 q^{92} + 2 q^{94} - q^{96}+O(q^{100}) \) 20 * q - q^2 - 2 * q^3 + q^4 - 2 * q^5 - q^6 + q^7 + 2 * q^8 - q^10 + q^12 + 2 * q^14 - 2 * q^15 + q^16 + q^20 - 10 * q^21 + q^23 - 9 * q^24 - 2 * q^25 + 2 * q^27 + q^28 - q^29 - q^30 - q^32 - 21 * q^35 + 2 * q^40 - q^41 - 20 * q^42 + 9 * q^43 - q^46 + q^47 + q^48 - q^50 + q^54 - q^56 - 2 * q^58 + q^60 - 9 * q^61 + 11 * q^63 - 2 * q^64 - q^67 + q^69 - 9 * q^70 + 11 * q^72 - 2 * q^75 + q^80 + 2 * q^81 - 2 * q^82 + q^83 + q^84 - q^86 - q^87 - 4 * q^89 - 2 * q^92 + 2 * q^94 - q^96

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