LMFDB - Embedded newform 1064.2.q.n.457.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 15 x^{14} - 2 x^{13} + 159 x^{12} - 19 x^{11} + 839 x^{10} - 62 x^{9} + 3204 x^{8} + 8 x^{7} + \cdots + 256 $ x^16 + 15x^14 - 2x^13 + 159x^12 - 19x^11 + 839x^10 - 62x^9 + 3204x^8 + 8x^7 + 4560x^6 + 1376x^5 + 4688x^4 + 736x^3 + 1280x^2 - 128x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			457.7
Root			$1.23497 + 2.13902i$ of defining polynomial
Character	$\chi$	$=$	1064.457
Dual form			1064.2.q.n.305.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.23497 + 2.13902i) q^{3} +(2.01936 - 3.49763i) q^{5} +(1.24923 + 2.33226i) q^{7} +(-1.55028 + 2.68516i) q^{9} +O(q^{10})$	\(q+(1.23497 + 2.13902i) q^{3} +(2.01936 - 3.49763i) q^{5} +(1.24923 + 2.33226i) q^{7} +(-1.55028 + 2.68516i) q^{9} +(-0.801044 - 1.38745i) q^{11} +3.15476 q^{13} +9.97534 q^{15} +(-0.326387 - 0.565319i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.44599 + 5.55239i) q^{21} +(-1.45863 + 2.52642i) q^{23} +(-5.65561 - 9.79580i) q^{25} -0.248363 q^{27} +2.12163 q^{29} +(3.51161 + 6.08229i) q^{31} +(1.97852 - 3.42690i) q^{33} +(10.6800 + 0.340302i) q^{35} +(2.65493 - 4.59847i) q^{37} +(3.89602 + 6.74811i) q^{39} -2.00000 q^{41} +7.97365 q^{43} +(6.26113 + 10.8446i) q^{45} +(0.302680 - 0.524258i) q^{47} +(-3.87883 + 5.82706i) q^{49} +(0.806154 - 1.39630i) q^{51} +(-6.24121 - 10.8101i) q^{53} -6.47038 q^{55} -2.46993 q^{57} +(-7.22587 - 12.5156i) q^{59} +(-4.67267 + 8.09330i) q^{61} +(-8.19914 - 0.261253i) q^{63} +(6.37059 - 11.0342i) q^{65} +(1.39269 + 2.41222i) q^{67} -7.20542 q^{69} -9.50073 q^{71} +(8.31389 + 14.4001i) q^{73} +(13.9690 - 24.1949i) q^{75} +(2.23519 - 3.60149i) q^{77} +(-2.42825 + 4.20585i) q^{79} +(4.34411 + 7.52422i) q^{81} -8.73966 q^{83} -2.63637 q^{85} +(2.62014 + 4.53821i) q^{87} +(1.13805 - 1.97116i) q^{89} +(3.94103 + 7.35771i) q^{91} +(-8.67343 + 15.0228i) q^{93} +(2.01936 + 3.49763i) q^{95} +1.24899 q^{97} +4.96736 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9	$ 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) $ 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	1.23497	+	2.13902i	0.713007	+	1.23497i	0.963723	+	0.266904i	$0.0860008\pi$
$3$	1.23497	+	2.13902i	0.713007	+	1.23497i	−0.250716	+	0.968061i	$0.580666\pi$
$4$		0			0
$5$	2.01936	−	3.49763i	0.903084	−	1.56419i	0.0796155	−	0.996826i	$-0.474631\pi$
$5$	2.01936	−	3.49763i	0.903084	−	1.56419i	0.823469	−	0.567362i	$-0.192036\pi$
$6$		0			0
$7$	1.24923	+	2.33226i	0.472166	+	0.881510i
$7$	1.24923	+	2.33226i	0.472166	+	0.881510i
$8$		0			0
$9$	−1.55028	+	2.68516i	−0.516759	+	0.895053i
$10$		0			0
$11$	−0.801044	−	1.38745i	−0.241524	−	0.418332i	0.719625	−	0.694363i	$-0.244314\pi$
$11$	−0.801044	−	1.38745i	−0.241524	−	0.418332i	−0.961149	+	0.276032i	$0.910981\pi$
$12$		0			0
$13$	3.15476			0.874974			0.437487	−	0.899225i	$-0.355869\pi$
$13$	3.15476			0.874974			0.437487	+	0.899225i	$0.355869\pi$
$14$		0			0
$15$	9.97534			2.57562
$16$		0			0
$17$	−0.326387	−	0.565319i	−0.0791605	−	0.137110i	0.823727	−	0.566986i	$-0.191891\pi$
$17$	−0.326387	−	0.565319i	−0.0791605	−	0.137110i	−0.902888	+	0.429876i	$0.858557\pi$
$18$		0			0
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i
$20$		0			0
$21$	−3.44599	+	5.55239i	−0.751976	+	1.21163i
$22$		0			0
$23$	−1.45863	+	2.52642i	−0.304145	+	0.526794i	−0.977071	−	0.212916i	$-0.931704\pi$
$23$	−1.45863	+	2.52642i	−0.304145	+	0.526794i	0.672926	+	0.739710i	$0.265037\pi$
$24$		0			0
$25$	−5.65561	−	9.79580i	−1.13112	−	1.95916i
$26$		0			0
$27$	−0.248363			−0.0477975
$28$		0			0
$29$	2.12163			0.393977			0.196988	−	0.980406i	$-0.436884\pi$
$29$	2.12163			0.393977			0.196988	+	0.980406i	$0.436884\pi$
$30$		0			0
$31$	3.51161	+	6.08229i	0.630704	+	1.09241i	0.987408	+	0.158194i	$0.0505671\pi$
$31$	3.51161	+	6.08229i	0.630704	+	1.09241i	−0.356704	+	0.934217i	$0.616100\pi$
$32$		0			0
$33$	1.97852	−	3.42690i	0.344417	−	0.596547i
$34$		0			0
$35$	10.6800	+	0.340302i	1.80525	+	0.0575216i
$36$		0			0
$37$	2.65493	−	4.59847i	0.436467	−	0.755983i	−0.560947	−	0.827852i	$-0.689563\pi$
$37$	2.65493	−	4.59847i	0.436467	−	0.755983i	0.997414	+	0.0718685i	$0.0228962\pi$
$38$		0			0
$39$	3.89602	+	6.74811i	0.623863	+	1.08056i
$40$		0			0
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	7.97365			1.21597			0.607985	−	0.793948i	$-0.291978\pi$
$43$	7.97365			1.21597			0.607985	+	0.793948i	$0.291978\pi$
$44$		0			0
$45$	6.26113	+	10.8446i	0.933354	+	1.61662i
$46$		0			0
$47$	0.302680	−	0.524258i	0.0441505	−	0.0764708i	−0.843106	−	0.537748i	$-0.819275\pi$
$47$	0.302680	−	0.524258i	0.0441505	−	0.0764708i	0.887256	+	0.461277i	$0.152609\pi$
$48$		0			0
$49$	−3.87883	+	5.82706i	−0.554119	+	0.832438i
$50$		0			0
$51$	0.806154	−	1.39630i	0.112884	−	0.195521i
$52$		0			0
$53$	−6.24121	−	10.8101i	−0.857296	−	1.48488i	−0.874498	−	0.485029i	$-0.838809\pi$
$53$	−6.24121	−	10.8101i	−0.857296	−	1.48488i	0.0172016	−	0.999852i	$-0.494524\pi$
$54$		0			0
$55$	−6.47038			−0.872465
$56$		0			0
$57$	−2.46993			−0.327150
$58$		0			0
$59$	−7.22587	−	12.5156i	−0.940728	−	1.62939i	−0.764088	−	0.645113i	$-0.776810\pi$
$59$	−7.22587	−	12.5156i	−0.940728	−	1.62939i	−0.176640	−	0.984276i	$-0.556523\pi$
$60$		0			0
$61$	−4.67267	+	8.09330i	−0.598274	+	1.03624i	0.394802	+	0.918766i	$0.370813\pi$
$61$	−4.67267	+	8.09330i	−0.598274	+	1.03624i	−0.993076	+	0.117474i	$0.962520\pi$
$62$		0			0
$63$	−8.19914	−	0.261253i	−1.03299	−	0.0329148i
$64$		0			0
$65$	6.37059	−	11.0342i	0.790175	−	1.36862i
$66$		0			0
$67$	1.39269	+	2.41222i	0.170145	+	0.294699i	0.938470	−	0.345360i	$-0.112243\pi$
$67$	1.39269	+	2.41222i	0.170145	+	0.294699i	−0.768326	+	0.640059i	$0.778910\pi$
$68$		0			0
$69$	−7.20542			−0.867430
$70$		0			0
$71$	−9.50073			−1.12753			−0.563764	−	0.825936i	$-0.690647\pi$
$71$	−9.50073			−1.12753			−0.563764	+	0.825936i	$0.690647\pi$
$72$		0			0
$73$	8.31389	+	14.4001i	0.973067	+	1.68540i	0.686172	+	0.727439i	$0.259290\pi$
$73$	8.31389	+	14.4001i	0.973067	+	1.68540i	0.286895	+	0.957962i	$0.407377\pi$
$74$		0			0
$75$	13.9690	−	24.1949i	1.61300	−	2.79379i
$76$		0			0
$77$	2.23519	−	3.60149i	0.254724	−	0.410428i
$78$		0			0
$79$	−2.42825	+	4.20585i	−0.273199	+	0.473195i	−0.969679	−	0.244381i	$-0.921415\pi$
$79$	−2.42825	+	4.20585i	−0.273199	+	0.473195i	0.696480	+	0.717576i	$0.254749\pi$
$80$		0			0
$81$	4.34411	+	7.52422i	0.482679	+	0.836025i
$82$		0			0
$83$	−8.73966			−0.959302			−0.479651	−	0.877459i	$-0.659237\pi$
$83$	−8.73966			−0.959302			−0.479651	+	0.877459i	$0.659237\pi$
$84$		0			0
$85$	−2.63637			−0.285954
$86$		0			0
$87$	2.62014	+	4.53821i	0.280908	+	0.486547i
$88$		0			0
$89$	1.13805	−	1.97116i	0.120633	−	0.208943i	−0.799384	−	0.600820i	$-0.794841\pi$
$89$	1.13805	−	1.97116i	0.120633	−	0.208943i	0.920018	+	0.391877i	$0.128174\pi$
$90$		0			0
$91$	3.94103	+	7.35771i	0.413133	+	0.771298i
$92$		0			0
$93$	−8.67343	+	15.0228i	−0.899393	+	1.55779i
$94$		0			0
$95$	2.01936	+	3.49763i	0.207182	+	0.358849i
$96$		0			0
$97$	1.24899			0.126815			0.0634077	−	0.997988i	$-0.479803\pi$
$97$	1.24899			0.126815			0.0634077	+	0.997988i	$0.479803\pi$
$98$		0			0
$99$	4.96736			0.499239
$100$		0			0
$101$	5.62306	+	9.73942i	0.559515	+	0.969109i	0.997537	+	0.0701442i	$0.0223459\pi$
$101$	5.62306	+	9.73942i	0.559515	+	0.969109i	−0.438022	+	0.898964i	$0.644321\pi$
$102$		0			0
$103$	−1.79648	+	3.11160i	−0.177013	+	0.306595i	−0.940856	−	0.338807i	$-0.889977\pi$
$103$	−1.79648	+	3.11160i	−0.177013	+	0.306595i	0.763843	+	0.645402i	$0.223310\pi$
$104$		0			0
$105$	12.4615	+	23.2651i	1.21612	+	2.27044i
$106$		0			0
$107$	0.873161	−	1.51236i	0.0844117	−	0.146205i	−0.820729	−	0.571318i	$-0.806432\pi$
$107$	0.873161	−	1.51236i	0.0844117	−	0.146205i	0.905140	+	0.425113i	$0.139766\pi$
$108$		0			0
$109$	0.959240	+	1.66145i	0.0918786	+	0.159138i	0.908302	−	0.418316i	$-0.137380\pi$
$109$	0.959240	+	1.66145i	0.0918786	+	0.159138i	−0.816423	+	0.577454i	$0.804046\pi$
$110$		0			0
$111$	13.1150			1.24482
$112$		0			0
$113$	−11.8303			−1.11290			−0.556451	−	0.830881i	$-0.687837\pi$
$113$	−11.8303			−1.11290			−0.556451	+	0.830881i	$0.687837\pi$
$114$		0			0
$115$	5.89098	+	10.2035i	0.549337	+	0.951479i
$116$		0			0
$117$	−4.89076	+	8.47104i	−0.452151	+	0.783148i
$118$		0			0
$119$	0.910735	−	1.46743i	0.0834870	−	0.134519i
$120$		0			0
$121$	4.21666	−	7.30346i	0.383332	−	0.663951i
$122$		0			0
$123$	−2.46993	−	4.27804i	−0.222706	−	0.385738i
$124$		0			0
$125$	−25.4892			−2.27982
$126$		0			0
$127$	−15.3583			−1.36283			−0.681416	−	0.731896i	$-0.738636\pi$
$127$	−15.3583			−1.36283			−0.681416	+	0.731896i	$0.738636\pi$
$128$		0			0
$129$	9.84718	+	17.0558i	0.866996	+	1.50168i
$130$		0			0
$131$	6.69141	−	11.5899i	0.584631	−	1.01261i	−0.410290	−	0.911955i	$-0.634573\pi$
$131$	6.69141	−	11.5899i	0.584631	−	1.01261i	0.994921	−	0.100656i	$-0.0320941\pi$
$132$		0			0
$133$	−2.64441	−	0.0842601i	−0.229299	−	0.00730628i
$134$		0			0
$135$	−0.501534	+	0.868682i	−0.0431651	+	0.0747642i
$136$		0			0
$137$	1.58352	+	2.74274i	0.135289	+	0.234328i	0.925708	−	0.378239i	$-0.123470\pi$
$137$	1.58352	+	2.74274i	0.135289	+	0.234328i	−0.790419	+	0.612567i	$0.790137\pi$
$138$		0			0
$139$	−16.3904			−1.39021			−0.695106	−	0.718907i	$-0.744642\pi$
$139$	−16.3904			−1.39021			−0.695106	+	0.718907i	$0.744642\pi$
$140$		0			0
$141$	1.49520			0.125918
$142$		0			0
$143$	−2.52710	−	4.37707i	−0.211327	−	0.366029i
$144$		0			0
$145$	4.28433	−	7.42067i	0.355794	−	0.616253i
$146$		0			0
$147$	−17.2544	−	1.10069i	−1.42312	−	0.0907834i
$148$		0			0
$149$	−7.01102	+	12.1435i	−0.574366	+	0.994830i	0.421745	+	0.906715i	$0.361418\pi$
$149$	−7.01102	+	12.1435i	−0.574366	+	0.994830i	−0.996110	+	0.0881156i	$0.971915\pi$
$150$		0			0
$151$	−9.27307	−	16.0614i	−0.754632	−	1.30706i	−0.945557	−	0.325456i	$-0.894482\pi$
$151$	−9.27307	−	16.0614i	−0.754632	−	1.30706i	0.190926	−	0.981605i	$-0.438851\pi$
$152$		0			0
$153$	2.02396			0.163628
$154$		0			0
$155$	28.3648			2.27831
$156$		0			0
$157$	−11.7756	−	20.3960i	−0.939796	−	1.62778i	−0.765849	−	0.643020i	$-0.777681\pi$
$157$	−11.7756	−	20.3960i	−0.939796	−	1.62778i	−0.173947	−	0.984755i	$-0.555652\pi$
$158$		0			0
$159$	15.4154	−	26.7002i	1.22252	−	2.11746i
$160$		0			0
$161$	−7.71442	−	0.245808i	−0.607981	−	0.0193724i
$162$		0			0
$163$	−4.53565	+	7.85598i	−0.355260	+	0.615328i	−0.987162	−	0.159720i	$-0.948941\pi$
$163$	−4.53565	+	7.85598i	−0.355260	+	0.615328i	0.631903	+	0.775048i	$0.282274\pi$
$164$		0			0
$165$	−7.99069	−	13.8403i	−0.622074	−	1.07746i
$166$		0			0
$167$	−0.191778			−0.0148402			−0.00742011	−	0.999972i	$-0.502362\pi$
$167$	−0.191778			−0.0148402			−0.00742011	+	0.999972i	$0.502362\pi$
$168$		0			0
$169$	−3.04747			−0.234421
$170$		0			0
$171$	−1.55028	−	2.68516i	−0.118553	−	0.205339i
$172$		0			0
$173$	3.49463	−	6.05288i	0.265692	−	0.460192i	−0.702053	−	0.712125i	$-0.747733\pi$
$173$	3.49463	−	6.05288i	0.265692	−	0.460192i	0.967745	+	0.251933i	$0.0810662\pi$
$174$		0			0
$175$	15.7811	−	25.4276i	1.19294	−	1.92214i
$176$		0			0
$177$	17.8474	−	30.9126i	1.34149	−	2.32353i
$178$		0			0
$179$	7.95433	+	13.7773i	0.594534	+	1.02976i	0.993612	+	0.112847i	$0.0359969\pi$
$179$	7.95433	+	13.7773i	0.594534	+	1.02976i	−0.399078	+	0.916917i	$0.630670\pi$
$180$		0			0
$181$	16.6258			1.23579			0.617894	−	0.786261i	$-0.287986\pi$
$181$	16.6258			1.23579			0.617894	+	0.786261i	$0.287986\pi$
$182$		0			0
$183$	−23.0823			−1.70629
$184$		0			0
$185$	−10.7225	−	18.5719i	−0.788333	−	1.36543i
$186$		0			0
$187$	−0.522901	+	0.905691i	−0.0382383	+	0.0662307i
$188$		0			0
$189$	−0.310263	−	0.579246i	−0.0225683	−	0.0421339i
$190$		0			0
$191$	−12.0050	+	20.7933i	−0.868654	+	1.50455i	−0.00528216	+	0.999986i	$0.501681\pi$
$191$	−12.0050	+	20.7933i	−0.868654	+	1.50455i	−0.863372	+	0.504568i	$0.831652\pi$
$192$		0			0
$193$	−0.0549373	−	0.0951541i	−0.00395447	−	0.00684934i	0.864041	−	0.503421i	$-0.167925\pi$
$193$	−0.0549373	−	0.0951541i	−0.00395447	−	0.00684934i	−0.867996	+	0.496571i	$0.834592\pi$
$194$		0			0
$195$	31.4698			2.25360
$196$		0			0
$197$	−10.9282			−0.778601			−0.389301	−	0.921111i	$-0.627283\pi$
$197$	−10.9282			−0.778601			−0.389301	+	0.921111i	$0.627283\pi$
$198$		0			0
$199$	−11.2686	−	19.5178i	−0.798810	−	1.38358i	−0.920392	−	0.390998i	$-0.872130\pi$
$199$	−11.2686	−	19.5178i	−0.798810	−	1.38358i	0.121582	−	0.992581i	$-0.461203\pi$
$200$		0			0
$201$	−3.43986	+	5.95801i	−0.242629	+	0.420245i
$202$		0			0
$203$	2.65041	+	4.94818i	0.186022	+	0.347294i
$204$		0			0
$205$	−4.03871	+	6.99526i	−0.282076	+	0.488570i
$206$		0			0
$207$	−4.52255	−	7.83329i	−0.314339	−	0.544452i
$208$		0			0
$209$	1.60209			0.110819
$210$		0			0
$211$	23.7342			1.63393			0.816966	−	0.576685i	$-0.195654\pi$
$211$	23.7342			1.63393			0.816966	+	0.576685i	$0.195654\pi$
$212$		0			0
$213$	−11.7331	−	20.3223i	−0.803936	−	1.39246i
$214$		0			0
$215$	16.1017	−	27.8889i	1.09812	−	1.90201i
$216$		0			0
$217$	−9.79863	+	15.7882i	−0.665174	+	1.07177i
$218$		0			0
$219$	−20.5347	+	35.5672i	−1.38761	+	2.40341i
$220$		0			0
$221$	−1.02967	−	1.78345i	−0.0692634	−	0.119968i
$222$		0			0
$223$	4.36632			0.292390			0.146195	−	0.989256i	$-0.453297\pi$
$223$	4.36632			0.292390			0.146195	+	0.989256i	$0.453297\pi$
$224$		0			0
$225$	35.0710			2.33807
$226$		0			0
$227$	−10.9957	−	19.0451i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$227$	−10.9957	−	19.0451i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$228$		0			0
$229$	−2.20172	+	3.81349i	−0.145494	+	0.252003i	−0.929557	−	0.368678i	$-0.879810\pi$
$229$	−2.20172	+	3.81349i	−0.145494	+	0.252003i	0.784063	+	0.620681i	$0.213144\pi$
$230$		0			0
$231$	10.4640	+	0.333421i	0.688484	+	0.0219375i
$232$		0			0
$233$	10.0280	−	17.3690i	0.656956	−	1.13788i	−0.324443	−	0.945905i	$-0.605177\pi$
$233$	10.0280	−	17.3690i	0.656956	−	1.13788i	0.981400	−	0.191976i	$-0.0614897\pi$
$234$		0			0
$235$	−1.22244	−	2.11733i	−0.0797431	−	0.138119i
$236$		0			0
$237$	−11.9952			−0.779173
$238$		0			0
$239$	21.7477			1.40674			0.703370	−	0.710824i	$-0.251678\pi$
$239$	21.7477			1.40674			0.703370	+	0.710824i	$0.251678\pi$
$240$		0			0
$241$	−15.4955	−	26.8390i	−0.998152	−	1.72885i	−0.551701	−	0.834042i	$-0.686021\pi$
$241$	−15.4955	−	26.8390i	−0.998152	−	1.72885i	−0.446451	−	0.894808i	$-0.647312\pi$
$242$		0			0
$243$	−11.1022	+	19.2296i	−0.712206	+	1.23358i
$244$		0			0
$245$	12.5482	+	25.3336i	0.801672	+	1.61851i
$246$		0			0
$247$	−1.57738	+	2.73210i	−0.100366	+	0.173840i
$248$		0			0
$249$	−10.7932	−	18.6943i	−0.683989	−	1.18470i
$250$		0			0
$251$	5.24483			0.331051			0.165525	−	0.986206i	$-0.447068\pi$
$251$	5.24483			0.331051			0.165525	+	0.986206i	$0.447068\pi$
$252$		0			0
$253$	4.67370			0.293833
$254$		0			0
$255$	−3.25582	−	5.63925i	−0.203888	−	0.353144i
$256$		0			0
$257$	14.2971	−	24.7633i	0.891828	−	1.54469i	0.0541469	−	0.998533i	$-0.482756\pi$
$257$	14.2971	−	24.7633i	0.891828	−	1.54469i	0.837681	−	0.546159i	$-0.183911\pi$
$258$		0			0
$259$	14.0414	+	0.447409i	0.872492	+	0.0278006i
$260$		0			0
$261$	−3.28911	+	5.69691i	−0.203591	+	0.352630i
$262$		0			0
$263$	−2.76997	−	4.79772i	−0.170803	−	0.295840i	0.767898	−	0.640573i	$-0.221303\pi$
$263$	−2.76997	−	4.79772i	−0.170803	−	0.295840i	−0.938701	+	0.344733i	$0.887970\pi$
$264$		0			0
$265$	−50.4130			−3.09684
$266$		0			0
$267$	5.62181			0.344049
$268$		0			0
$269$	2.14577	+	3.71658i	0.130830	+	0.226604i	0.923997	−	0.382400i	$-0.124903\pi$
$269$	2.14577	+	3.71658i	0.130830	+	0.226604i	−0.793167	+	0.609004i	$0.791569\pi$
$270$		0			0
$271$	0.445334	−	0.771342i	0.0270521	−	0.0468557i	−0.852182	−	0.523245i	$-0.824721\pi$
$271$	0.445334	−	0.771342i	0.0270521	−	0.0468557i	0.879235	+	0.476389i	$0.158055\pi$
$272$		0			0
$273$	−10.8713	+	17.5165i	−0.657959	+	1.06015i
$274$		0			0
$275$	−9.06078	+	15.6937i	−0.546386	+	0.946368i
$276$		0			0
$277$	6.00531	+	10.4015i	0.360824	+	0.624966i	0.988097	−	0.153834i	$-0.0491621\pi$
$277$	6.00531	+	10.4015i	0.360824	+	0.624966i	−0.627273	+	0.778800i	$0.715829\pi$
$278$		0			0
$279$	−21.7759			−1.30369
$280$		0			0
$281$	−17.4819			−1.04288			−0.521442	−	0.853287i	$-0.674606\pi$
$281$	−17.4819			−1.04288			−0.521442	+	0.853287i	$0.674606\pi$
$282$		0			0
$283$	−10.2431	−	17.7416i	−0.608891	−	1.05463i	−0.991424	−	0.130688i	$-0.958281\pi$
$283$	−10.2431	−	17.7416i	−0.608891	−	1.05463i	0.382533	−	0.923942i	$-0.375052\pi$
$284$		0			0
$285$	−4.98767	+	8.63890i	−0.295444	+	0.511724i
$286$		0			0
$287$	−2.49847	−	4.66451i	−0.147480	−	0.275337i
$288$		0			0
$289$	8.28694	−	14.3534i	0.487467	−	0.844318i
$290$		0			0
$291$	1.54246	+	2.67161i	0.0904203	+	0.156613i
$292$		0			0
$293$	−22.9489			−1.34069			−0.670346	−	0.742049i	$-0.733854\pi$
$293$	−22.9489			−1.34069			−0.670346	+	0.742049i	$0.733854\pi$
$294$		0			0
$295$	−58.3664			−3.39822
$296$		0			0
$297$	0.198950	+	0.344591i	0.0115442	+	0.0199952i
$298$		0			0
$299$	−4.60162	+	7.97025i	−0.266119	+	0.460931i
$300$		0			0
$301$	9.96095	+	18.5966i	0.574140	+	1.07189i
$302$		0			0
$303$	−13.8886	+	24.0557i	−0.797877	+	1.38196i
$304$		0			0
$305$	18.8716	+	32.6865i	1.08058	+	1.87162i
$306$		0			0
$307$	14.1287			0.806365			0.403183	−	0.915120i	$-0.367904\pi$
$307$	14.1287			0.806365			0.403183	+	0.915120i	$0.367904\pi$
$308$		0			0
$309$	−8.87437			−0.504846
$310$		0			0
$311$	6.76522	+	11.7177i	0.383620	+	0.664450i	0.991577	−	0.129521i	$-0.0413439\pi$
$311$	6.76522	+	11.7177i	0.383620	+	0.664450i	−0.607957	+	0.793970i	$0.708011\pi$
$312$		0			0
$313$	−13.2244	+	22.9054i	−0.747489	+	1.29469i	0.201534	+	0.979481i	$0.435407\pi$
$313$	−13.2244	+	22.9054i	−0.747489	+	1.29469i	−0.949023	+	0.315207i	$0.897926\pi$
$314$		0			0
$315$	−17.4708	+	28.1500i	−0.984365	+	1.58607i
$316$		0			0
$317$	1.65641	−	2.86899i	0.0930335	−	0.161139i	−0.815753	−	0.578401i	$-0.803677\pi$
$317$	1.65641	−	2.86899i	0.0930335	−	0.161139i	0.908786	+	0.417262i	$0.137010\pi$
$318$		0			0
$319$	−1.69952	−	2.94365i	−0.0951548	−	0.164813i
$320$		0			0
$321$	4.31329			0.240745
$322$		0			0
$323$	0.652775			0.0363213
$324$		0			0
$325$	−17.8421	−	30.9034i	−0.989702	−	1.71421i
$326$		0			0
$327$	−2.36926	+	4.10367i	−0.131020	+	0.226934i
$328$		0			0
$329$	1.60082	+	0.0510077i	0.0882561	+	0.00281215i
$330$		0			0
$331$	−5.89352	+	10.2079i	−0.323937	+	0.561075i	−0.981297	−	0.192502i	$-0.938340\pi$
$331$	−5.89352	+	10.2079i	−0.323937	+	0.561075i	0.657360	+	0.753577i	$0.271673\pi$
$332$		0			0
$333$	8.23174	+	14.2578i	0.451097	+	0.781322i
$334$		0			0
$335$	11.2494			0.614620
$336$		0			0
$337$	11.3688			0.619298			0.309649	−	0.950851i	$-0.399789\pi$
$337$	11.3688			0.619298			0.309649	+	0.950851i	$0.399789\pi$
$338$		0			0
$339$	−14.6100	−	25.3053i	−0.793507	−	1.37439i
$340$		0			0
$341$	5.62591	−	9.74436i	0.304660	−	0.527687i
$342$		0			0
$343$	−18.4358	−	1.76707i	−0.995438	−	0.0954127i
$344$		0			0
$345$	−14.5503	+	25.2019i	−0.783362	+	1.35682i
$346$		0			0
$347$	0.0424765	+	0.0735715i	0.00228026	+	0.00394952i	0.867163	−	0.498024i	$-0.165941\pi$
$347$	0.0424765	+	0.0735715i	0.00228026	+	0.00394952i	−0.864883	+	0.501973i	$0.832608\pi$
$348$		0			0
$349$	10.5549			0.564989			0.282494	−	0.959269i	$-0.408838\pi$
$349$	10.5549			0.564989			0.282494	+	0.959269i	$0.408838\pi$
$350$		0			0
$351$	−0.783526			−0.0418215
$352$		0			0
$353$	0.308623	+	0.534551i	0.0164263	+	0.0284513i	0.874122	−	0.485707i	$-0.161438\pi$
$353$	0.308623	+	0.534551i	0.0164263	+	0.0284513i	−0.857695	+	0.514158i	$0.828104\pi$
$354$		0			0
$355$	−19.1854	+	33.2300i	−1.01825	+	1.76367i
$356$		0			0
$357$	4.26360	+	0.135853i	0.225654	+	0.00719011i
$358$		0			0
$359$	1.79624	−	3.11118i	0.0948020	−	0.164202i	−0.814724	−	0.579849i	$-0.803112\pi$
$359$	1.79624	−	3.11118i	0.0948020	−	0.164202i	0.909526	+	0.415647i	$0.136445\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.0263158	−	0.0455803i
$362$		0			0
$363$	20.8297			1.09328
$364$		0			0
$365$	67.1548			3.51505
$366$		0			0
$367$	3.09379	+	5.35860i	0.161494	+	0.279717i	0.935405	−	0.353579i	$-0.115035\pi$
$367$	3.09379	+	5.35860i	0.161494	+	0.279717i	−0.773910	+	0.633295i	$0.781702\pi$
$368$		0			0
$369$	3.10055	−	5.37032i	0.161408	−	0.279568i
$370$		0			0
$371$	17.4152	−	28.0604i	0.904151	−	1.45683i
$372$		0			0
$373$	−9.10610	+	15.7722i	−0.471496	+	0.816655i	−0.999468	−	0.0326067i	$-0.989619\pi$
$373$	−9.10610	+	15.7722i	−0.471496	+	0.816655i	0.527972	+	0.849262i	$0.322952\pi$
$374$		0			0
$375$	−31.4783	−	54.5220i	−1.62553	−	2.81550i
$376$		0			0
$377$	6.69324			0.344719
$378$		0			0
$379$	0.847819			0.0435495			0.0217748	−	0.999763i	$-0.493068\pi$
$379$	0.847819			0.0435495			0.0217748	+	0.999763i	$0.493068\pi$
$380$		0			0
$381$	−18.9670	−	32.8518i	−0.971709	−	1.68305i
$382$		0			0
$383$	−16.6278	+	28.8001i	−0.849639	+	1.47162i	0.0318917	+	0.999491i	$0.489847\pi$
$383$	−16.6278	+	28.8001i	−0.849639	+	1.47162i	−0.881531	+	0.472127i	$0.843487\pi$
$384$		0			0
$385$	−8.08301	−	15.0906i	−0.411948	−	0.769087i
$386$		0			0
$387$	−12.3614	+	21.4105i	−0.628364	+	1.08836i
$388$		0			0
$389$	8.87246	+	15.3676i	0.449852	+	0.779166i	0.998376	−	0.0569686i	$-0.0181435\pi$
$389$	8.87246	+	15.3676i	0.449852	+	0.779166i	−0.548524	+	0.836135i	$0.684810\pi$
$390$		0			0
$391$	1.90431			0.0963051
$392$		0			0
$393$	33.0546			1.66739
$394$		0			0
$395$	9.80701	+	16.9862i	0.493444	+	0.854670i
$396$		0			0
$397$	3.80762	−	6.59499i	0.191099	−	0.330993i	−0.754516	−	0.656282i	$-0.772128\pi$
$397$	3.80762	−	6.59499i	0.191099	−	0.330993i	0.945615	+	0.325289i	$0.105462\pi$
$398$		0			0
$399$	−3.08552	−	5.76051i	−0.154469	−	0.288386i
$400$		0			0
$401$	17.4287	−	30.1873i	0.870345	−	1.50748i	0.00870576	−	0.999962i	$-0.497229\pi$
$401$	17.4287	−	30.1873i	0.870345	−	1.50748i	0.861640	−	0.507520i	$-0.169438\pi$
$402$		0			0
$403$	11.0783	+	19.1882i	0.551849	+	0.955831i
$404$		0			0
$405$	35.0893			1.74360
$406$		0			0
$407$	−8.50685			−0.421669
$408$		0			0
$409$	1.60509	+	2.78010i	0.0793668	+	0.137467i	0.902977	−	0.429689i	$-0.141377\pi$
$409$	1.60509	+	2.78010i	0.0793668	+	0.137467i	−0.823610	+	0.567156i	$0.808044\pi$
$410$		0			0
$411$	−3.91118	+	6.77437i	−0.192924	+	0.334155i
$412$		0			0
$413$	20.1627	−	32.4874i	0.992142	−	1.59860i
$414$		0			0
$415$	−17.6485	+	30.5681i	−0.866330	+	1.50053i
$416$		0			0
$417$	−20.2415	−	35.0593i	−0.991231	−	1.71686i
$418$		0			0
$419$	−16.7962			−0.820550			−0.410275	−	0.911962i	$-0.634567\pi$
$419$	−16.7962			−0.820550			−0.410275	+	0.911962i	$0.634567\pi$
$420$		0			0
$421$	−20.3496			−0.991780			−0.495890	−	0.868385i	$-0.665158\pi$
$421$	−20.3496			−0.991780			−0.495890	+	0.868385i	$0.665158\pi$
$422$		0			0
$423$	0.938477	+	1.62549i	0.0456303	+	0.0790340i
$424$		0			0
$425$	−3.69184	+	6.39445i	−0.179080	+	0.310176i
$426$		0			0
$427$	−24.7129	−	0.787439i	−1.19594	−	0.0381068i
$428$		0			0
$429$	6.24177	−	10.8111i	0.301356	−	0.521963i
$430$		0			0
$431$	16.2629	+	28.1682i	0.783358	+	1.35682i	0.929975	+	0.367622i	$0.119828\pi$
$431$	16.2629	+	28.1682i	0.783358	+	1.35682i	−0.146618	+	0.989193i	$0.546839\pi$
$432$		0			0
$433$	40.2853			1.93599			0.967994	−	0.250975i	$-0.0807512\pi$
$433$	40.2853			1.93599			0.967994	+	0.250975i	$0.0807512\pi$
$434$		0			0
$435$	21.1640			1.01474
$436$		0			0
$437$	−1.45863	−	2.52642i	−0.0697756	−	0.120855i
$438$		0			0
$439$	−3.14194	+	5.44199i	−0.149956	+	0.259732i	−0.931211	−	0.364480i	$-0.881247\pi$
$439$	−3.14194	+	5.44199i	−0.149956	+	0.259732i	0.781255	+	0.624212i	$0.214580\pi$
$440$		0			0
$441$	−9.63332	−	19.4488i	−0.458730	−	0.926135i
$442$		0			0
$443$	−12.8205	+	22.2057i	−0.609118	+	1.05502i	0.382268	+	0.924052i	$0.375143\pi$
$443$	−12.8205	+	22.2057i	−0.609118	+	1.05502i	−0.991386	+	0.130972i	$0.958190\pi$
$444$		0			0
$445$	−4.59626	−	7.96096i	−0.217884	−	0.377386i
$446$		0			0
$447$	−34.6335			−1.63811
$448$		0			0
$449$	−28.7456			−1.35659			−0.678294	−	0.734791i	$-0.737280\pi$
$449$	−28.7456			−1.35659			−0.678294	+	0.734791i	$0.737280\pi$
$450$		0			0
$451$	1.60209	+	2.77490i	0.0754394	+	0.130665i
$452$		0			0
$453$	22.9038	−	39.6706i	1.07612	−	1.86389i
$454$		0			0
$455$	33.6929	+	1.07357i	1.57955	+	0.0503299i
$456$		0			0
$457$	−13.9695	+	24.1959i	−0.653467	+	1.13184i	0.328809	+	0.944396i	$0.393353\pi$
$457$	−13.9695	+	24.1959i	−0.653467	+	1.13184i	−0.982276	+	0.187441i	$0.939981\pi$
$458$		0			0
$459$	0.0810625	+	0.140404i	0.00378367	+	0.00655351i
$460$		0			0
$461$	4.95920			0.230973			0.115486	−	0.993309i	$-0.463157\pi$
$461$	4.95920			0.230973			0.115486	+	0.993309i	$0.463157\pi$
$462$		0			0
$463$	13.4715			0.626072			0.313036	−	0.949741i	$-0.398654\pi$
$463$	13.4715			0.626072			0.313036	+	0.949741i	$0.398654\pi$
$464$		0			0
$465$	35.0295	+	60.6729i	1.62446	+	2.81364i
$466$		0			0
$467$	−15.4633	+	26.7833i	−0.715558	+	1.23938i	0.247186	+	0.968968i	$0.420494\pi$
$467$	−15.4633	+	26.7833i	−0.715558	+	1.23938i	−0.962744	+	0.270415i	$0.912839\pi$
$468$		0			0
$469$	−3.88611	+	6.26154i	−0.179444	+	0.289131i
$470$		0			0
$471$	29.0849	−	50.3766i	1.34016	−	2.32123i
$472$		0			0
$473$	−6.38725	−	11.0630i	−0.293686	−	0.508679i
$474$		0			0
$475$	11.3112			0.518994
$476$		0			0
$477$	38.7024			1.77206
$478$		0			0
$479$	−11.9976	−	20.7804i	−0.548183	−	0.949482i	−0.998399	−	0.0565617i	$-0.981986\pi$
$479$	−11.9976	−	20.7804i	−0.548183	−	0.949482i	0.450216	−	0.892920i	$-0.351347\pi$
$480$		0			0
$481$	8.37566	−	14.5071i	0.381897	−	0.661466i
$482$		0			0
$483$	−9.00125	−	16.8049i	−0.409571	−	0.764648i
$484$		0			0
$485$	2.52215	−	4.36849i	0.114525	−	0.198363i
$486$		0			0
$487$	−19.6381	−	34.0142i	−0.889887	−	1.54133i	−0.840008	−	0.542574i	$-0.817450\pi$
$487$	−19.6381	−	34.0142i	−0.889887	−	1.54133i	−0.0498789	−	0.998755i	$-0.515884\pi$
$488$		0			0
$489$	−22.4055			−1.01321
$490$		0			0
$491$	28.1575			1.27073			0.635365	−	0.772212i	$-0.280849\pi$
$491$	28.1575			1.27073			0.635365	+	0.772212i	$0.280849\pi$
$492$		0			0
$493$	−0.692473	−	1.19940i	−0.0311874	−	0.0540182i
$494$		0			0
$495$	10.0309	−	17.3740i	0.450854	−	0.780903i
$496$		0			0
$497$	−11.8686	−	22.1581i	−0.532381	−	0.993928i
$498$		0			0
$499$	16.1525	−	27.9770i	0.723087	−	1.25242i	−0.236669	−	0.971590i	$-0.576056\pi$
$499$	16.1525	−	27.9770i	0.723087	−	1.25242i	0.959757	−	0.280833i	$-0.0906109\pi$
$500$		0			0
$501$	−0.236839	−	0.410217i	−0.0105812	−	0.0183272i
$502$		0			0
$503$	22.4333			1.00025			0.500125	−	0.865953i	$-0.333287\pi$
$503$	22.4333			1.00025			0.500125	+	0.865953i	$0.333287\pi$
$504$		0			0
$505$	45.4198			2.02116
$506$		0			0
$507$	−3.76352	−	6.51861i	−0.167144	−	0.289501i
$508$		0			0
$509$	1.28370	−	2.22343i	0.0568988	−	0.0985517i	−0.836173	−	0.548466i	$-0.815212\pi$
$509$	1.28370	−	2.22343i	0.0568988	−	0.0985517i	0.893072	+	0.449914i	$0.148545\pi$
$510$		0			0
$511$	−23.1987	+	37.3792i	−1.02625	+	1.65356i
$512$		0			0
$513$	0.124181	−	0.215089i	0.00548275	−	0.00949639i
$514$		0			0
$515$	7.25548	+	12.5669i	0.319715	+	0.553762i
$516$		0			0
$517$	−0.969841			−0.0426536
$518$		0			0
$519$	17.2630			0.757762
$520$		0			0
$521$	14.1294	+	24.4728i	0.619020	+	1.07217i	0.989665	+	0.143399i	$0.0458032\pi$
$521$	14.1294	+	24.4728i	0.619020	+	1.07217i	−0.370645	+	0.928774i	$0.620863\pi$
$522$		0			0
$523$	6.20116	−	10.7407i	0.271158	−	0.469659i	−0.698001	−	0.716097i	$-0.745927\pi$
$523$	6.20116	−	10.7407i	0.271158	−	0.469659i	0.969159	+	0.246438i	$0.0792601\pi$
$524$		0			0
$525$	73.8793	+	2.35405i	3.22436	+	0.102739i
$526$		0			0
$527$	2.29229	−	3.97036i	0.0998537	−	0.172952i
$528$		0			0
$529$	7.24481	+	12.5484i	0.314992	+	0.545582i
$530$		0			0
$531$	44.8084			1.94452
$532$		0			0
$533$	−6.30953			−0.273296
$534$		0			0
$535$	−3.52645	−	6.10799i	−0.152462	−	0.264071i
$536$		0			0
$537$	−19.6466	+	34.0290i	−0.847815	+	1.46846i
$538$		0			0
$539$	11.1919	+	0.713949i	0.482068	+	0.0307519i
$540$		0			0
$541$	−0.594948	+	1.03048i	−0.0255788	+	0.0443038i	−0.878531	−	0.477685i	$-0.841476\pi$
$541$	−0.594948	+	1.03048i	−0.0255788	+	0.0443038i	0.852953	+	0.521988i	$0.174810\pi$
$542$		0			0
$543$	20.5323	+	35.5630i	0.881126	+	1.52616i
$544$		0			0
$545$	7.74820			0.331896
$546$		0			0
$547$	−15.1927			−0.649593			−0.324797	−	0.945784i	$-0.605296\pi$
$547$	−15.1927			−0.649593			−0.324797	+	0.945784i	$0.605296\pi$
$548$		0			0
$549$	−14.4879	−	25.0937i	−0.618327	−	1.07097i
$550$		0			0
$551$	−1.06081	+	1.83738i	−0.0451922	+	0.0782752i
$552$		0			0
$553$	−12.8426	−	0.409209i	−0.546122	−	0.0174013i
$554$		0			0
$555$	26.4838	−	45.8713i	1.12417	−	1.94713i
$556$		0			0
$557$	12.2937	+	21.2933i	0.520902	+	0.902228i	0.999705	+	0.0243056i	$0.00773747\pi$
$557$	12.2937	+	21.2933i	0.520902	+	0.902228i	−0.478803	+	0.877922i	$0.658929\pi$
$558$		0			0
$559$	25.1550			1.06394
$560$		0			0
$561$	−2.58306			−0.109057
$562$		0			0
$563$	16.9142	+	29.2962i	0.712847	+	1.23469i	0.963784	+	0.266684i	$0.0859280\pi$
$563$	16.9142	+	29.2962i	0.712847	+	1.23469i	−0.250937	+	0.968003i	$0.580739\pi$
$564$		0			0
$565$	−23.8896	+	41.3780i	−1.00504	+	1.74079i
$566$		0			0
$567$	−12.1216	+	19.5311i	−0.509059	+	0.820229i
$568$		0			0
$569$	−4.42916	+	7.67152i	−0.185680	+	0.321607i	−0.943805	−	0.330502i	$-0.892782\pi$
$569$	−4.42916	+	7.67152i	−0.185680	+	0.321607i	0.758126	+	0.652109i	$0.226115\pi$
$570$		0			0
$571$	18.2288	+	31.5733i	0.762854	+	1.32130i	0.941374	+	0.337365i	$0.109536\pi$
$571$	18.2288	+	31.5733i	0.762854	+	1.32130i	−0.178520	+	0.983936i	$0.557131\pi$
$572$		0			0
$573$	−59.3032			−2.47743
$574$		0			0
$575$	32.9977			1.37610
$576$		0			0
$577$	−21.1094	−	36.5625i	−0.878795	−	1.52212i	−0.852664	−	0.522459i	$-0.825015\pi$
$577$	−21.1094	−	36.5625i	−0.878795	−	1.52212i	−0.0261308	−	0.999659i	$-0.508319\pi$
$578$		0			0
$579$	0.135691	−	0.235024i	0.00563913	−	0.00976726i
$580$		0			0
$581$	−10.9179	−	20.3831i	−0.452950	−	0.845634i
$582$		0			0
$583$	−9.99897	+	17.3187i	−0.414115	+	0.717268i
$584$		0			0
$585$	19.7524	+	34.2121i	0.816660	+	1.41450i
$586$		0			0
$587$	−24.3851			−1.00648			−0.503240	−	0.864146i	$-0.667859\pi$
$587$	−24.3851			−1.00648			−0.503240	+	0.864146i	$0.667859\pi$
$588$		0			0
$589$	−7.02322			−0.289387
$590$		0			0
$591$	−13.4959	−	23.3756i	−0.555149	−	0.961545i
$592$		0			0
$593$	8.61782	−	14.9265i	0.353892	−	0.612958i	−0.633036	−	0.774122i	$-0.718192\pi$
$593$	8.61782	−	14.9265i	0.353892	−	0.612958i	0.986928	+	0.161164i	$0.0515248\pi$
$594$		0			0
$595$	−3.29344	−	6.14869i	−0.135018	−	0.252072i
$596$		0			0
$597$	27.8326	−	48.2076i	1.13911	−	1.97300i
$598$		0			0
$599$	2.94345	+	5.09821i	0.120266	+	0.208307i	0.919873	−	0.392217i	$-0.128292\pi$
$599$	2.94345	+	5.09821i	0.120266	+	0.208307i	−0.799606	+	0.600524i	$0.794959\pi$
$600$		0			0
$601$	−13.6088			−0.555114			−0.277557	−	0.960709i	$-0.589525\pi$
$601$	−13.6088			−0.555114			−0.277557	+	0.960709i	$0.589525\pi$
$602$		0			0
$603$	−8.63625			−0.351695
$604$		0			0
$605$	−17.0299	−	29.4966i	−0.692363	−	1.19921i
$606$		0			0
$607$	6.80103	−	11.7797i	0.276045	−	0.478124i	−0.694353	−	0.719635i	$-0.744309\pi$
$607$	6.80103	−	11.7797i	0.276045	−	0.478124i	0.970398	+	0.241510i	$0.0776427\pi$
$608$		0			0
$609$	−7.31111	+	11.7801i	−0.296261	+	0.477354i
$610$		0			0
$611$	0.954884	−	1.65391i	0.0386305	−	0.0669100i
$612$		0			0
$613$	16.4693	+	28.5256i	0.665188	+	1.15214i	0.979234	+	0.202732i	$0.0649819\pi$
$613$	16.4693	+	28.5256i	0.665188	+	1.15214i	−0.314047	+	0.949408i	$0.601685\pi$
$614$		0			0
$615$	−19.9507			−0.804489
$616$		0			0
$617$	39.2585			1.58049			0.790244	−	0.612792i	$-0.209954\pi$
$617$	39.2585			1.58049			0.790244	+	0.612792i	$0.209954\pi$
$618$		0			0
$619$	3.90959	+	6.77161i	0.157140	+	0.272174i	0.933836	−	0.357701i	$-0.116439\pi$
$619$	3.90959	+	6.77161i	0.157140	+	0.272174i	−0.776696	+	0.629875i	$0.783106\pi$
$620$		0			0
$621$	0.362269	−	0.627468i	0.0145374	−	0.0251794i
$622$		0			0
$623$	6.01894	+	0.191785i	0.241144	+	0.00768368i
$624$		0			0
$625$	−23.1938	+	40.1728i	−0.927751	+	1.60691i
$626$		0			0
$627$	1.97852	+	3.42690i	0.0790146	+	0.136857i
$628$		0			0
$629$	−3.46614			−0.138204
$630$		0			0
$631$	−15.0926			−0.600828			−0.300414	−	0.953809i	$-0.597125\pi$
$631$	−15.0926			−0.600828			−0.300414	+	0.953809i	$0.597125\pi$
$632$		0			0
$633$	29.3110	+	50.7681i	1.16501	+	2.01785i
$634$		0			0
$635$	−31.0140	+	53.7178i	−1.23075	+	2.13173i
$636$		0			0
$637$	−12.2368	+	18.3830i	−0.484840	+	0.728361i
$638$		0			0
$639$	14.7288	−	25.5110i	0.582661	−	1.00920i
$640$		0			0
$641$	11.5259	+	19.9635i	0.455247	+	0.788510i	0.998702	−	0.0509277i	$-0.0162178\pi$
$641$	11.5259	+	19.9635i	0.455247	+	0.788510i	−0.543456	+	0.839438i	$0.682884\pi$
$642$		0			0
$643$	31.5297			1.24341			0.621706	−	0.783251i	$-0.286440\pi$
$643$	31.5297			1.24341			0.621706	+	0.783251i	$0.286440\pi$
$644$		0			0
$645$	79.5399			3.13188
$646$		0			0
$647$	−3.22140	−	5.57963i	−0.126646	−	0.219358i	0.795729	−	0.605653i	$-0.207088\pi$
$647$	−3.22140	−	5.57963i	−0.126646	−	0.219358i	−0.922375	+	0.386295i	$0.873755\pi$
$648$		0			0
$649$	−11.5765	+	20.0510i	−0.454416	+	0.787072i
$650$		0			0
$651$	−45.8722	−	1.46165i	−1.79787	−	0.0572865i
$652$		0			0
$653$	−8.55730	+	14.8217i	−0.334873	+	0.580017i	−0.983460	−	0.181123i	$-0.942027\pi$
$653$	−8.55730	+	14.8217i	−0.334873	+	0.580017i	0.648587	+	0.761140i	$0.275360\pi$
$654$		0			0
$655$	−27.0247	−	46.8081i	−1.05594	−	1.82895i
$656$		0			0
$657$	−51.5553			−2.01136
$658$		0			0
$659$	27.1362			1.05707			0.528537	−	0.848910i	$-0.322741\pi$
$659$	27.1362			1.05707			0.528537	+	0.848910i	$0.322741\pi$
$660$		0			0
$661$	−4.72991	−	8.19245i	−0.183972	−	0.318649i	0.759257	−	0.650790i	$-0.225562\pi$
$661$	−4.72991	−	8.19245i	−0.183972	−	0.318649i	−0.943230	+	0.332141i	$0.892229\pi$
$662$		0			0
$663$	2.54322	−	4.40499i	0.0987706	−	0.171076i
$664$		0			0
$665$	−5.63472	+	9.07901i	−0.218505	+	0.352069i
$666$		0			0
$667$	−3.09467	+	5.36012i	−0.119826	+	0.207545i
$668$		0			0
$669$	5.39225	+	9.33966i	0.208477	+	0.361092i
$670$		0			0
$671$	14.9721			0.577990
$672$		0			0
$673$	−13.6374			−0.525682			−0.262841	−	0.964839i	$-0.584659\pi$
$673$	−13.6374			−0.525682			−0.262841	+	0.964839i	$0.584659\pi$
$674$		0			0
$675$	1.40464	+	2.43291i	0.0540648	+	0.0936429i
$676$		0			0
$677$	1.25258	−	2.16953i	0.0481405	−	0.0833818i	−0.840951	−	0.541111i	$-0.818004\pi$
$677$	1.25258	−	2.16953i	0.0481405	−	0.0833818i	0.889092	+	0.457729i	$0.151337\pi$
$678$		0			0
$679$	1.56028	+	2.91296i	0.0598779	+	0.111789i
$680$		0			0
$681$	27.1586	−	47.0401i	1.04072	−	1.80258i
$682$		0			0
$683$	12.0276	+	20.8325i	0.460224	+	0.797132i	0.998972	−	0.0453352i	$-0.0144356\pi$
$683$	12.0276	+	20.8325i	0.460224	+	0.797132i	−0.538747	+	0.842467i	$0.681102\pi$
$684$		0			0
$685$	12.7908			0.488710
$686$		0			0
$687$	−10.8762			−0.414953
$688$		0			0
$689$	−19.6895	−	34.1033i	−0.750112	−	1.29923i
$690$		0			0
$691$	5.27056	−	9.12887i	0.200501	−	0.347279i	−0.748189	−	0.663486i	$-0.769076\pi$
$691$	5.27056	−	9.12887i	0.200501	−	0.347279i	0.948690	+	0.316207i	$0.102410\pi$
$692$		0			0
$693$	6.20539	+	11.5852i	0.235723	+	0.440084i
$694$		0			0
$695$	−33.0980	+	57.3274i	−1.25548	+	2.17455i
$696$		0			0
$697$	0.652775	+	1.13064i	0.0247256	+	0.0428260i
$698$		0			0
$699$	49.5369			1.87366
$700$		0			0
$701$	−1.75242			−0.0661880			−0.0330940	−	0.999452i	$-0.510536\pi$
$701$	−1.75242			−0.0661880			−0.0330940	+	0.999452i	$0.510536\pi$
$702$		0			0
$703$	2.65493	+	4.59847i	0.100132	+	0.173434i
$704$		0			0
$705$	3.01934	−	5.22965i	0.113715	−	0.196960i
$706$		0			0
$707$	−15.6903	+	25.2812i	−0.590095	+	0.950798i
$708$		0			0
$709$	−0.948339	+	1.64257i	−0.0356156	+	0.0616880i	−0.883284	−	0.468839i	$-0.844673\pi$
$709$	−0.948339	+	1.64257i	−0.0356156	+	0.0616880i	0.847668	+	0.530527i	$0.178006\pi$
$710$		0			0
$711$	−7.52892	−	13.0405i	−0.282357	−	0.489056i
$712$		0			0
$713$	−20.4885			−0.767301
$714$		0			0
$715$	−20.4125			−0.763384
$716$		0			0
$717$	26.8576	+	46.5188i	1.00302	+	1.73727i
$718$		0			0
$719$	−7.16379	+	12.4081i	−0.267164	+	0.462742i	−0.968128	−	0.250454i	$-0.919420\pi$
$719$	−7.16379	+	12.4081i	−0.267164	+	0.462742i	0.700964	+	0.713197i	$0.252753\pi$
$720$		0			0
$721$	−9.50127	−	0.302744i	−0.353846	−	0.0112748i
$722$		0			0
$723$	38.2728	−	66.2904i	1.42338	−	2.46537i
$724$		0			0
$725$	−11.9991	−	20.7831i	−0.445636	−	0.771863i
$726$		0			0
$727$	−42.5021			−1.57632			−0.788158	−	0.615472i	$-0.788965\pi$
$727$	−42.5021			−1.57632			−0.788158	+	0.615472i	$0.788965\pi$
$728$		0			0
$729$	−28.7786			−1.06588
$730$		0			0
$731$	−2.60250	−	4.50766i	−0.0962569	−	0.166722i
$732$		0			0
$733$	−9.59056	+	16.6113i	−0.354235	+	0.613554i	−0.986987	−	0.160801i	$-0.948592\pi$
$733$	−9.59056	+	16.6113i	−0.354235	+	0.613554i	0.632751	+	0.774355i	$0.281926\pi$
$734$		0			0
$735$	−38.6927	+	58.1270i	−1.42720	+	2.14404i
$736$		0			0
$737$	2.23122	−	3.86458i	0.0821880	−	0.142354i
$738$		0			0
$739$	6.13629	+	10.6284i	0.225727	+	0.390971i	0.956537	−	0.291610i	$-0.0941909\pi$
$739$	6.13629	+	10.6284i	0.225727	+	0.390971i	−0.730810	+	0.682581i	$0.760858\pi$
$740$		0			0
$741$	−7.79204			−0.286248
$742$		0			0
$743$	36.7738			1.34910			0.674549	−	0.738230i	$-0.264338\pi$
$743$	36.7738			1.34910			0.674549	+	0.738230i	$0.264338\pi$
$744$		0			0
$745$	28.3155	+	49.0439i	1.03740	+	1.79683i
$746$		0			0
$747$	13.5489	−	23.4674i	0.495728	−	0.858626i
$748$		0			0
$749$	4.61799	+	0.147145i	0.168738	+	0.00537657i
$750$		0			0
$751$	−18.7421	+	32.4622i	−0.683908	+	1.18456i	0.289870	+	0.957066i	$0.406388\pi$
$751$	−18.7421	+	32.4622i	−0.683908	+	1.18456i	−0.973779	+	0.227498i	$0.926945\pi$
$752$		0			0
$753$	6.47718	+	11.2188i	0.236042	+	0.408836i
$754$		0			0
$755$	−74.9026			−2.72598
$756$		0			0
$757$	11.0641			0.402132			0.201066	−	0.979578i	$-0.435559\pi$
$757$	11.0641			0.402132			0.201066	+	0.979578i	$0.435559\pi$
$758$		0			0
$759$	5.77186	+	9.99715i	0.209505	+	0.362873i
$760$		0			0
$761$	25.2596	−	43.7509i	0.915659	−	1.58597i	0.109726	−	0.993962i	$-0.465003\pi$
$761$	25.2596	−	43.7509i	0.915659	−	1.58597i	0.805933	−	0.592007i	$-0.201664\pi$
$762$		0			0
$763$	−2.67662	+	4.31274i	−0.0969001	+	0.156132i
$764$		0			0
$765$	4.08710	−	7.07907i	0.147770	−	0.255944i
$766$		0			0
$767$	−22.7959	−	39.4836i	−0.823112	−	1.42567i
$768$		0			0
$769$	−10.7883			−0.389037			−0.194518	−	0.980899i	$-0.562314\pi$
$769$	−10.7883			−0.389037			−0.194518	+	0.980899i	$0.562314\pi$
$770$		0			0
$771$	70.6257			2.54352
$772$		0			0
$773$	−2.33644	−	4.04683i	−0.0840358	−	0.145554i	0.820944	−	0.571009i	$-0.193448\pi$
$773$	−2.33644	−	4.04683i	−0.0840358	−	0.145554i	−0.904980	+	0.425454i	$0.860114\pi$
$774$		0			0
$775$	39.7206	−	68.7981i	1.42681	−	2.47130i
$776$		0			0
$777$	16.3836	+	30.5874i	0.587760	+	1.09732i
$778$		0			0
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	7.61050	+	13.1818i	0.272325	+	0.471681i
$782$		0			0
$783$	−0.526934			−0.0188311
$784$		0			0
$785$	−95.1167			−3.39486
$786$		0			0
$787$	−6.78939	−	11.7596i	−0.242016	−	0.419184i	0.719273	−	0.694728i	$-0.244475\pi$
$787$	−6.78939	−	11.7596i	−0.242016	−	0.419184i	−0.961288	+	0.275544i	$0.911142\pi$
$788$		0			0
$789$	6.84162	−	11.8500i	0.243568	−	0.421872i
$790$		0			0
$791$	−14.7788	−	27.5913i	−0.525474	−	0.981033i
$792$		0			0
$793$	−14.7412	+	25.5324i	−0.523474	+	0.906683i
$794$		0			0
$795$	−62.2582	−	107.834i	−2.20807	−	3.82449i
$796$		0			0
$797$	25.3577			0.898214			0.449107	−	0.893478i	$-0.351742\pi$
$797$	25.3577			0.898214			0.449107	+	0.893478i	$0.351742\pi$
$798$		0			0
$799$	−0.395164			−0.0139799
$800$		0			0
$801$	3.52859	+	6.11170i	0.124677	+	0.215946i
$802$		0			0
$803$	13.3196	−	23.0702i	0.470038	−	0.814129i
$804$		0			0
$805$	−16.4379	+	26.4858i	−0.579360	+	0.933502i
$806$		0			0
$807$	−5.29990	+	9.17970i	−0.186565	+	0.323141i
$808$		0			0
$809$	−0.769360	−	1.33257i	−0.0270493	−	0.0468507i	0.852184	−	0.523242i	$-0.175278\pi$
$809$	−0.769360	−	1.33257i	−0.0270493	−	0.0468507i	−0.879233	+	0.476392i	$0.841944\pi$
$810$		0			0
$811$	37.5288			1.31781			0.658907	−	0.752225i	$-0.271019\pi$
$811$	37.5288			1.31781			0.658907	+	0.752225i	$0.271019\pi$
$812$		0			0
$813$	2.19989			0.0771535
$814$		0			0
$815$	18.3182	+	31.7281i	0.641659	+	1.11139i
$816$		0			0
$817$	−3.98683	+	6.90538i	−0.139481	+	0.241589i
$818$		0			0
$819$	−25.8663	−	0.824191i	−0.903843	−	0.0287996i
$820$		0			0
$821$	4.41743	−	7.65121i	0.154169	−	0.267029i	−0.778587	−	0.627537i	$-0.784063\pi$
$821$	4.41743	−	7.65121i	0.154169	−	0.267029i	0.932756	+	0.360508i	$0.117397\pi$
$822$		0			0
$823$	15.4105	+	26.6918i	0.537177	+	0.930418i	0.999055	+	0.0434741i	$0.0138426\pi$
$823$	15.4105	+	26.6918i	0.537177	+	0.930418i	−0.461878	+	0.886944i	$0.652824\pi$
$824$		0			0
$825$	−44.7590			−1.55831
$826$		0			0
$827$	0.938262			0.0326266			0.0163133	−	0.999867i	$-0.494807\pi$
$827$	0.938262			0.0326266			0.0163133	+	0.999867i	$0.494807\pi$
$828$		0			0
$829$	3.39228	+	5.87561i	0.117819	+	0.204068i	0.918903	−	0.394483i	$-0.129076\pi$
$829$	3.39228	+	5.87561i	0.117819	+	0.204068i	−0.801084	+	0.598552i	$0.795743\pi$
$830$		0			0
$831$	−14.8327	+	25.6910i	−0.514541	+	0.891210i
$832$		0			0
$833$	4.56015	+	0.290900i	0.158000	+	0.0100791i
$834$		0			0
$835$	−0.387268	+	0.670768i	−0.0134020	+	0.0232129i
$836$		0			0
$837$	−0.872154	−	1.51061i	−0.0301460	−	0.0522145i
$838$		0			0
$839$	−11.6858			−0.403437			−0.201718	−	0.979444i	$-0.564653\pi$
$839$	−11.6858			−0.403437			−0.201718	+	0.979444i	$0.564653\pi$
$840$		0			0
$841$	−24.4987			−0.844782
$842$		0			0
$843$	−21.5895	−	37.3942i	−0.743584	−	1.28792i
$844$		0			0
$845$	−6.15393	+	10.6589i	−0.211702	+	0.366678i
$846$		0			0
$847$	22.3011	+	0.710592i	0.766276	+	0.0244162i
$848$		0			0
$849$	25.2998	−	43.8206i	0.868287	−	1.50392i
$850$		0			0
$851$	7.74510	+	13.4149i	0.265499	+	0.459857i
$852$		0			0
$853$	19.5533			0.669493			0.334746	−	0.942308i	$-0.391349\pi$
$853$	19.5533			0.669493			0.334746	+	0.942308i	$0.391349\pi$
$854$		0			0
$855$	−12.5223			−0.428252
$856$		0			0
$857$	−25.7077	−	44.5271i	−0.878159	−	1.52102i	−0.853359	−	0.521323i	$-0.825439\pi$
$857$	−25.7077	−	44.5271i	−0.878159	−	1.52102i	−0.0247994	−	0.999692i	$-0.507895\pi$
$858$		0			0
$859$	13.9478	−	24.1584i	0.475894	−	0.824273i	−0.523724	−	0.851888i	$-0.675458\pi$
$859$	13.9478	−	24.1584i	0.475894	−	0.824273i	0.999619	+	0.0276145i	$0.00879109\pi$
$860$		0			0
$861$	6.89197	−	11.1048i	0.234878	−	0.378450i
$862$		0			0
$863$	−22.6132	+	39.1672i	−0.769763	+	1.33327i	0.167928	+	0.985799i	$0.446292\pi$
$863$	−22.6132	+	39.1672i	−0.769763	+	1.33327i	−0.937691	+	0.347469i	$0.887041\pi$
$864$		0			0
$865$	−14.1138	−	24.4459i	−0.479885	−	0.831185i
$866$		0			0
$867$	40.9363			1.39027
$868$		0			0
$869$	7.78054			0.263937
$870$		0			0
$871$	4.39362	+	7.60997i	0.148872	+	0.257854i
$872$		0			0
$873$	−1.93628	+	3.35373i	−0.0655330	+	0.113507i
$874$		0			0
$875$	−31.8420	−	59.4474i	−1.07646	−	2.00969i
$876$		0			0
$877$	−4.45633	+	7.71858i	−0.150479	+	0.260638i	−0.931404	−	0.363988i	$-0.881415\pi$
$877$	−4.45633	+	7.71858i	−0.150479	+	0.260638i	0.780924	+	0.624626i	$0.214748\pi$
$878$		0			0
$879$	−28.3411	−	49.0883i	−0.955923	−	1.65571i
$880$		0			0
$881$	−45.9579			−1.54836			−0.774180	−	0.632965i	$-0.781837\pi$
$881$	−45.9579			−1.54836			−0.774180	+	0.632965i	$0.781837\pi$
$882$		0			0
$883$	28.6951			0.965666			0.482833	−	0.875712i	$-0.339608\pi$
$883$	28.6951			0.965666			0.482833	+	0.875712i	$0.339608\pi$
$884$		0			0
$885$	−72.0805	−	124.847i	−2.42296	−	4.19669i
$886$		0			0
$887$	12.0529	−	20.8763i	0.404697	−	0.700956i	−0.589589	−	0.807703i	$-0.700710\pi$
$887$	12.0529	−	20.8763i	0.404697	−	0.700956i	0.994286	+	0.106747i	$0.0340436\pi$
$888$		0			0
$889$	−19.1861	−	35.8196i	−0.643483	−	1.20135i
$890$		0			0
$891$	6.95965	−	12.0545i	0.233157	−	0.403840i
$892$		0			0
$893$	0.302680	+	0.524258i	0.0101288	+	0.0175436i
$894$		0			0
$895$	64.2505			2.14766
$896$		0			0
$897$	−22.7314			−0.758979
$898$		0			0
$899$	7.45034	+	12.9044i	0.248483	+	0.430384i
$900$		0			0
$901$	−4.07410	+	7.05656i	−0.135728	+	0.235088i
$902$		0			0
$903$	−27.4771	+	44.2728i	−0.914381	+	1.47331i
$904$		0			0
$905$	33.5735	−	58.1510i	1.11602	−	1.93300i
$906$		0			0
$907$	−17.1624	−	29.7262i	−0.569869	−	0.987043i	−0.996578	−	0.0826538i	$-0.973660\pi$
$907$	−17.1624	−	29.7262i	−0.569869	−	0.987043i	0.426709	−	0.904389i	$-0.359673\pi$
$908$		0			0
$909$	−34.8692			−1.15654
$910$		0			0
$911$	25.9008			0.858133			0.429066	−	0.903273i	$-0.358843\pi$
$911$	25.9008			0.858133			0.429066	+	0.903273i	$0.358843\pi$
$912$		0			0
$913$	7.00085	+	12.1258i	0.231694	+	0.401306i
$914$		0			0
$915$	−46.6115	+	80.7334i	−1.54093	+	2.66896i
$916$		0			0
$917$	35.3896	+	1.12764i	1.16867	+	0.0372379i
$918$		0			0
$919$	−12.1092	+	20.9738i	−0.399447	+	0.691862i	−0.993658	−	0.112447i	$-0.964131\pi$
$919$	−12.1092	+	20.9738i	−0.399447	+	0.691862i	0.594211	+	0.804309i	$0.297464\pi$
$920$		0			0
$921$	17.4484	+	30.2215i	0.574944	+	0.995833i
$922$		0			0
$923$	−29.9725			−0.986558
$924$		0			0
$925$	−60.0609			−1.97479
$926$		0			0
$927$	−5.57009	−	9.64768i	−0.182946	−	0.316872i
$928$		0			0
$929$	6.34446	−	10.9889i	0.208155	−	0.360535i	−0.742978	−	0.669316i	$-0.766587\pi$
$929$	6.34446	−	10.9889i	0.208155	−	0.360535i	0.951133	+	0.308780i	$0.0999208\pi$
$930$		0			0
$931$	−3.10697	−	6.27270i	−0.101827	−	0.205579i
$932$		0			0
$933$	−16.7096	+	28.9419i	−0.547048	+	0.947515i
$934$		0			0
$935$	2.11185	+	3.65783i	0.0690648	+	0.119624i
$936$		0			0
$937$	44.2503			1.44559			0.722797	−	0.691060i	$-0.242856\pi$
$937$	44.2503			1.44559			0.722797	+	0.691060i	$0.242856\pi$
$938$		0			0
$939$	−65.3268			−2.13186
$940$		0			0
$941$	6.86248	+	11.8862i	0.223710	+	0.387478i	0.955932	−	0.293589i	$-0.0948497\pi$
$941$	6.86248	+	11.8862i	0.223710	+	0.387478i	−0.732221	+	0.681067i	$0.761516\pi$
$942$		0			0
$943$	2.91726	−	5.05283i	0.0949989	−	0.164543i
$944$		0			0
$945$	−2.65252	−	0.0845185i	−0.0862865	−	0.00274939i
$946$		0			0
$947$	10.3342	−	17.8993i	0.335815	−	0.581648i	−0.647826	−	0.761788i	$-0.724322\pi$
$947$	10.3342	−	17.8993i	0.335815	−	0.581648i	0.983641	+	0.180140i	$0.0576550\pi$
$948$		0			0
$949$	26.2283	+	45.4288i	0.851408	+	1.47468i
$950$		0			0
$951$	8.18246			0.265334
$952$		0			0
$953$	16.3518			0.529686			0.264843	−	0.964292i	$-0.414680\pi$
$953$	16.3518			0.529686			0.264843	+	0.964292i	$0.414680\pi$
$954$		0			0
$955$	48.4849	+	83.9784i	1.56894	+	2.71748i
$956$		0			0
$957$	4.19769	−	7.27061i	0.135692	−	0.235026i
$958$		0			0
$959$	−4.41858	+	7.11949i	−0.142683	+	0.229900i
$960$		0			0
$961$	−9.16282	+	15.8705i	−0.295575	+	0.511951i
$962$		0			0
$963$	2.70728	+	4.68915i	0.0872410	+	0.151106i
$964$		0			0
$965$	−0.443752			−0.0142849
$966$		0			0
$967$	20.6838			0.665145			0.332573	−	0.943078i	$-0.392083\pi$
$967$	20.6838			0.665145			0.332573	+	0.943078i	$0.392083\pi$
$968$		0			0
$969$	0.806154	+	1.39630i	0.0258974	+	0.0448556i
$970$		0			0
$971$	1.02888	−	1.78208i	0.0330184	−	0.0571896i	−0.849044	−	0.528322i	$-0.822821\pi$
$971$	1.02888	−	1.78208i	0.0330184	−	0.0571896i	0.882062	+	0.471133i	$0.156155\pi$
$972$		0			0
$973$	−20.4754	−	38.2265i	−0.656410	−	1.22549i
$974$		0			0
$975$	44.0688	−	76.3293i	1.41133	−	2.44449i
$976$		0			0
$977$	−2.87654	−	4.98231i	−0.0920285	−	0.159398i	0.816336	−	0.577577i	$-0.196002\pi$
$977$	−2.87654	−	4.98231i	−0.0920285	−	0.159398i	−0.908365	+	0.418179i	$0.862668\pi$
$978$		0			0
$979$	−3.64652			−0.116543
$980$		0			0
$981$	−5.94835			−0.189916
$982$		0			0
$983$	13.4690	+	23.3289i	0.429593	+	0.744077i	0.996837	−	0.0794726i	$-0.0253236\pi$
$983$	13.4690	+	23.3289i	0.429593	+	0.744077i	−0.567244	+	0.823550i	$0.691990\pi$
$984$		0			0
$985$	−22.0679	+	38.2228i	−0.703142	+	1.21788i
$986$		0			0
$987$	1.86785	+	3.48718i	0.0594544	+	0.110998i
$988$		0			0
$989$	−11.6306	+	20.1448i	−0.369831	+	0.640566i
$990$		0			0
$991$	−20.9732	−	36.3266i	−0.666235	−	1.15395i	−0.978949	−	0.204106i	$-0.934571\pi$
$991$	−20.9732	−	36.3266i	−0.666235	−	1.15395i	0.312714	−	0.949847i	$-0.398762\pi$
$992$		0			0
$993$	−29.1132			−0.923878
$994$		0			0
$995$	−91.0213			−2.88557
$996$		0			0
$997$	20.9847	+	36.3466i	0.664593	+	1.15111i	0.979395	+	0.201952i	$0.0647285\pi$
$997$	20.9847	+	36.3466i	0.664593	+	1.15111i	−0.314802	+	0.949157i	$0.601938\pi$
$998$		0			0
$999$	−0.659385	+	1.14209i	−0.0208620	+	0.0361341i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.n.457.7	yes	16
7.2	even	3		7448.2.a.bq.1.2		8
7.4	even	3	inner	1064.2.q.n.305.7	✓	16
7.5	odd	6		7448.2.a.br.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.n.305.7	✓	16	7.4	even	3	inner
1064.2.q.n.457.7	yes	16	1.1	even	1	trivial
7448.2.a.bq.1.2		8	7.2	even	3
7448.2.a.br.1.7		8	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.23497 + 2.13902i) q^{3} +(2.01936 - 3.49763i) q^{5} +(1.24923 + 2.33226i) q^{7} +(-1.55028 + 2.68516i) q^{9} +O(q^{10})\)	\(q+(1.23497 + 2.13902i) q^{3} +(2.01936 - 3.49763i) q^{5} +(1.24923 + 2.33226i) q^{7} +(-1.55028 + 2.68516i) q^{9} +(-0.801044 - 1.38745i) q^{11} +3.15476 q^{13} +9.97534 q^{15} +(-0.326387 - 0.565319i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-3.44599 + 5.55239i) q^{21} +(-1.45863 + 2.52642i) q^{23} +(-5.65561 - 9.79580i) q^{25} -0.248363 q^{27} +2.12163 q^{29} +(3.51161 + 6.08229i) q^{31} +(1.97852 - 3.42690i) q^{33} +(10.6800 + 0.340302i) q^{35} +(2.65493 - 4.59847i) q^{37} +(3.89602 + 6.74811i) q^{39} -2.00000 q^{41} +7.97365 q^{43} +(6.26113 + 10.8446i) q^{45} +(0.302680 - 0.524258i) q^{47} +(-3.87883 + 5.82706i) q^{49} +(0.806154 - 1.39630i) q^{51} +(-6.24121 - 10.8101i) q^{53} -6.47038 q^{55} -2.46993 q^{57} +(-7.22587 - 12.5156i) q^{59} +(-4.67267 + 8.09330i) q^{61} +(-8.19914 - 0.261253i) q^{63} +(6.37059 - 11.0342i) q^{65} +(1.39269 + 2.41222i) q^{67} -7.20542 q^{69} -9.50073 q^{71} +(8.31389 + 14.4001i) q^{73} +(13.9690 - 24.1949i) q^{75} +(2.23519 - 3.60149i) q^{77} +(-2.42825 + 4.20585i) q^{79} +(4.34411 + 7.52422i) q^{81} -8.73966 q^{83} -2.63637 q^{85} +(2.62014 + 4.53821i) q^{87} +(1.13805 - 1.97116i) q^{89} +(3.94103 + 7.35771i) q^{91} +(-8.67343 + 15.0228i) q^{93} +(2.01936 + 3.49763i) q^{95} +1.24899 q^{97} +4.96736 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9}+O(q^{10}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9	\( 16 q + q^{5} + 5 q^{7} - 6 q^{9} - 9 q^{11} + 16 q^{15} - 4 q^{17} - 8 q^{19} - 2 q^{21} - 25 q^{23} - 15 q^{25} + 6 q^{27} + 12 q^{29} - 8 q^{33} + 5 q^{35} - 13 q^{37} + 11 q^{39} - 32 q^{41} + 34 q^{43} - 17 q^{45} + 24 q^{47} - 13 q^{49} - 5 q^{51} - 2 q^{53} + 10 q^{55} - 2 q^{59} + 13 q^{61} - 52 q^{63} + 26 q^{65} - 2 q^{67} - 22 q^{69} + 20 q^{71} - 5 q^{73} + 20 q^{75} + 28 q^{77} - 16 q^{79} + 12 q^{81} - 86 q^{83} + 48 q^{85} - 20 q^{87} - 8 q^{89} - 34 q^{91} - 2 q^{93} + q^{95} - 24 q^{97} + 74 q^{99}+O(q^{100}) \) 16 * q + q^5 + 5 * q^7 - 6 * q^9 - 9 * q^11 + 16 * q^15 - 4 * q^17 - 8 * q^19 - 2 * q^21 - 25 * q^23 - 15 * q^25 + 6 * q^27 + 12 * q^29 - 8 * q^33 + 5 * q^35 - 13 * q^37 + 11 * q^39 - 32 * q^41 + 34 * q^43 - 17 * q^45 + 24 * q^47 - 13 * q^49 - 5 * q^51 - 2 * q^53 + 10 * q^55 - 2 * q^59 + 13 * q^61 - 52 * q^63 + 26 * q^65 - 2 * q^67 - 22 * q^69 + 20 * q^71 - 5 * q^73 + 20 * q^75 + 28 * q^77 - 16 * q^79 + 12 * q^81 - 86 * q^83 + 48 * q^85 - 20 * q^87 - 8 * q^89 - 34 * q^91 - 2 * q^93 + q^95 - 24 * q^97 + 74 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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