LMFDB - Embedded newform 544.2.o.h.353.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [544,2,Mod(225,544)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("544.225"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(544, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 544 = 2^{5} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	544.o (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,6,0,0,0,0,0,12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$4.34386186996$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	6.0.419904.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 6x^{4} + 9x^{2} + 1 $ x^6 + 6x^4 + 9x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			353.1
Root			$-1.87939i$ of defining polynomial
Character	$\chi$	$=$	544.353
Dual form			544.2.o.h.225.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87939 - 1.87939i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-1.18479 + 1.18479i) q^{7} +4.06418i q^{9} +(3.87939 - 3.87939i) q^{11} +3.06418 q^{13} -3.75877i q^{15} +(-1.69459 - 3.75877i) q^{17} -3.75877i q^{19} +4.45336 q^{21} +(-3.18479 + 3.18479i) q^{23} -3.00000i q^{25} +(2.00000 - 2.00000i) q^{27} +(-4.06418 - 4.06418i) q^{29} +(-2.94356 - 2.94356i) q^{31} -14.5817 q^{33} -2.36959 q^{35} +(2.38919 + 2.38919i) q^{37} +(-5.75877 - 5.75877i) q^{39} +(-0.389185 + 0.389185i) q^{41} -1.63041i q^{43} +(-4.06418 + 4.06418i) q^{45} +10.1284 q^{47} +4.19253i q^{49} +(-3.87939 + 10.2490i) q^{51} -13.6459i q^{53} +7.75877 q^{55} +(-7.06418 + 7.06418i) q^{57} -9.88713i q^{59} +(7.12836 - 7.12836i) q^{61} +(-4.81521 - 4.81521i) q^{63} +(3.06418 + 3.06418i) q^{65} -4.00000 q^{67} +11.9709 q^{69} +(2.57398 + 2.57398i) q^{71} +(-6.51754 - 6.51754i) q^{73} +(-5.63816 + 5.63816i) q^{75} +9.19253i q^{77} +(3.42602 - 3.42602i) q^{79} +4.67499 q^{81} +13.1480i q^{83} +(2.06418 - 5.45336i) q^{85} +15.2763i q^{87} +15.9709 q^{89} +(-3.63041 + 3.63041i) q^{91} +11.0642i q^{93} +(3.75877 - 3.75877i) q^{95} +(-1.45336 - 1.45336i) q^{97} +(15.7665 + 15.7665i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{5} + 12 q^{11} - 6 q^{17} - 12 q^{23} + 12 q^{27} - 6 q^{29} + 12 q^{31} - 24 q^{33} + 6 q^{37} - 12 q^{39} + 6 q^{41} - 6 q^{45} + 24 q^{47} - 12 q^{51} + 24 q^{55} - 24 q^{57} + 6 q^{61} - 36 q^{63}+ \cdots + 24 q^{99}+O(q^{100}) $ 6 * q + 6 * q^5 + 12 * q^11 - 6 * q^17 - 12 * q^23 + 12 * q^27 - 6 * q^29 + 12 * q^31 - 24 * q^33 + 6 * q^37 - 12 * q^39 + 6 * q^41 - 6 * q^45 + 24 * q^47 - 12 * q^51 + 24 * q^55 - 24 * q^57 + 6 * q^61 - 36 * q^63 - 24 * q^67 + 6 * q^73 + 36 * q^79 + 18 * q^81 - 6 * q^85 + 24 * q^89 - 36 * q^91 + 18 * q^97 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/544\mathbb{Z}\right)^\times$.

$n$	$69$	$511$	$513$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.87939	−	1.87939i	−1.08506	−	1.08506i	−0.996028	−	0.0890351i	$-0.971622\pi$
$3$	−1.87939	−	1.87939i	−1.08506	−	1.08506i	−0.0890351	−	0.996028i	$-0.528378\pi$
$4$		0			0
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	0.894427	−	0.447214i	$-0.147584\pi$
$5$	1.00000	+	1.00000i	0.447214	+	0.447214i	−0.447214	+	0.894427i	$0.647584\pi$
$6$		0			0
$7$	−1.18479	+	1.18479i	−0.447809	+	0.447809i	−0.894626	−	0.446816i	$-0.852558\pi$
$7$	−1.18479	+	1.18479i	−0.447809	+	0.447809i	0.446816	+	0.894626i	$0.352558\pi$
$8$		0			0
$9$			4.06418i			1.35473i
$10$		0			0
$11$	3.87939	−	3.87939i	1.16968	−	1.16968i	0.187394	−	0.982285i	$-0.439996\pi$
$11$	3.87939	−	3.87939i	1.16968	−	1.16968i	0.982285	−	0.187394i	$-0.0600040\pi$
$12$		0			0
$13$	3.06418			0.849850			0.424925	−	0.905229i	$-0.360300\pi$
$13$	3.06418			0.849850			0.424925	+	0.905229i	$0.360300\pi$
$14$		0			0
$15$		−	3.75877i		−	0.970510i
$16$		0			0
$17$	−1.69459	−	3.75877i	−0.410999	−	0.911636i
$17$	−1.69459	−	3.75877i	−0.410999	−	0.911636i
$18$		0			0
$19$		−	3.75877i		−	0.862321i	−0.902275	−	0.431161i	$-0.858104\pi$
$19$		−	3.75877i		−	0.862321i	0.902275	−	0.431161i	$-0.141896\pi$
$20$		0			0
$21$	4.45336			0.971804
$22$		0			0
$23$	−3.18479	+	3.18479i	−0.664075	+	0.664075i	−0.956338	−	0.292263i	$-0.905592\pi$
$23$	−3.18479	+	3.18479i	−0.664075	+	0.664075i	0.292263	+	0.956338i	$0.405592\pi$
$24$		0			0
$25$		−	3.00000i		−	0.600000i
$26$		0			0
$27$	2.00000	−	2.00000i	0.384900	−	0.384900i
$28$		0			0
$29$	−4.06418	−	4.06418i	−0.754699	−	0.754699i	0.220653	−	0.975352i	$-0.429181\pi$
$29$	−4.06418	−	4.06418i	−0.754699	−	0.754699i	−0.975352	+	0.220653i	$0.929181\pi$
$30$		0			0
$31$	−2.94356	−	2.94356i	−0.528680	−	0.528680i	0.391499	−	0.920179i	$-0.371957\pi$
$31$	−2.94356	−	2.94356i	−0.528680	−	0.528680i	−0.920179	+	0.391499i	$0.871957\pi$
$32$		0			0
$33$	−14.5817			−2.53835
$34$		0			0
$35$	−2.36959			−0.400533
$36$		0			0
$37$	2.38919	+	2.38919i	0.392780	+	0.392780i	0.875677	−	0.482897i	$-0.160416\pi$
$37$	2.38919	+	2.38919i	0.392780	+	0.392780i	−0.482897	+	0.875677i	$0.660416\pi$
$38$		0			0
$39$	−5.75877	−	5.75877i	−0.922141	−	0.922141i
$40$		0			0
$41$	−0.389185	+	0.389185i	−0.0607806	+	0.0607806i	−0.736844	−	0.676063i	$-0.763685\pi$
$41$	−0.389185	+	0.389185i	−0.0607806	+	0.0607806i	0.676063	+	0.736844i	$0.263685\pi$
$42$		0			0
$43$		−	1.63041i		−	0.248636i	−0.992242	−	0.124318i	$-0.960326\pi$
$43$		−	1.63041i		−	0.248636i	0.992242	−	0.124318i	$-0.0396743\pi$
$44$		0			0
$45$	−4.06418	+	4.06418i	−0.605852	+	0.605852i
$46$		0			0
$47$	10.1284			1.47737			0.738686	−	0.674049i	$-0.235447\pi$
$47$	10.1284			1.47737			0.738686	+	0.674049i	$0.235447\pi$
$48$		0			0
$49$			4.19253i			0.598933i
$50$		0			0
$51$	−3.87939	+	10.2490i	−0.543223	+	1.43514i
$52$		0			0
$53$		−	13.6459i		−	1.87441i	−0.348782	−	0.937204i	$-0.613405\pi$
$53$		−	13.6459i		−	1.87441i	0.348782	−	0.937204i	$-0.386595\pi$
$54$		0			0
$55$	7.75877			1.04619
$56$		0			0
$57$	−7.06418	+	7.06418i	−0.935673	+	0.935673i
$58$		0			0
$59$		−	9.88713i		−	1.28719i	−0.765364	−	0.643597i	$-0.777441\pi$
$59$		−	9.88713i		−	1.28719i	0.765364	−	0.643597i	$-0.222559\pi$
$60$		0			0
$61$	7.12836	−	7.12836i	0.912692	−	0.912692i	−0.0837910	−	0.996483i	$-0.526703\pi$
$61$	7.12836	−	7.12836i	0.912692	−	0.912692i	0.996483	+	0.0837910i	$0.0267028\pi$
$62$		0			0
$63$	−4.81521	−	4.81521i	−0.606659	−	0.606659i
$64$		0			0
$65$	3.06418	+	3.06418i	0.380064	+	0.380064i
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	11.9709			1.44113
$70$		0			0
$71$	2.57398	+	2.57398i	0.305475	+	0.305475i	0.843151	−	0.537676i	$-0.180698\pi$
$71$	2.57398	+	2.57398i	0.305475	+	0.305475i	−0.537676	+	0.843151i	$0.680698\pi$
$72$		0			0
$73$	−6.51754	−	6.51754i	−0.762820	−	0.762820i	0.214011	−	0.976831i	$-0.431347\pi$
$73$	−6.51754	−	6.51754i	−0.762820	−	0.762820i	−0.976831	+	0.214011i	$0.931347\pi$
$74$		0			0
$75$	−5.63816	+	5.63816i	−0.651038	+	0.651038i
$76$		0			0
$77$			9.19253i			1.04759i
$78$		0			0
$79$	3.42602	−	3.42602i	0.385458	−	0.385458i	−0.487606	−	0.873064i	$-0.662130\pi$
$79$	3.42602	−	3.42602i	0.385458	−	0.385458i	0.873064	+	0.487606i	$0.162130\pi$
$80$		0			0
$81$	4.67499			0.519444
$82$		0			0
$83$			13.1480i			1.44318i	0.692323	+	0.721588i	$0.256587\pi$
$83$			13.1480i			1.44318i	−0.692323	+	0.721588i	$0.743413\pi$
$84$		0			0
$85$	2.06418	−	5.45336i	0.223892	−	0.591500i
$86$		0			0
$87$			15.2763i			1.63779i
$88$		0			0
$89$	15.9709			1.69291			0.846456	−	0.532458i	$-0.178732\pi$
$89$	15.9709			1.69291			0.846456	+	0.532458i	$0.178732\pi$
$90$		0			0
$91$	−3.63041	+	3.63041i	−0.380571	+	0.380571i
$92$		0			0
$93$			11.0642i			1.14730i
$94$		0			0
$95$	3.75877	−	3.75877i	0.385642	−	0.385642i
$96$		0			0
$97$	−1.45336	−	1.45336i	−0.147567	−	0.147567i	0.629463	−	0.777030i	$-0.283275\pi$
$97$	−1.45336	−	1.45336i	−0.147567	−	0.147567i	−0.777030	+	0.629463i	$0.783275\pi$
$98$		0			0
$99$	15.7665	+	15.7665i	1.58459	+	1.58459i
$100$		0			0
$101$	11.0642			1.10093			0.550463	−	0.834859i	$-0.314451\pi$
$101$	11.0642			1.10093			0.550463	+	0.834859i	$0.314451\pi$
$102$		0			0
$103$	−6.77837			−0.667893			−0.333946	−	0.942592i	$-0.608380\pi$
$103$	−6.77837			−0.667893			−0.333946	+	0.942592i	$0.608380\pi$
$104$		0			0
$105$	4.45336	+	4.45336i	0.434604	+	0.434604i
$106$		0			0
$107$	7.02734	+	7.02734i	0.679359	+	0.679359i	0.959855	−	0.280496i	$-0.0904991\pi$
$107$	7.02734	+	7.02734i	0.679359	+	0.679359i	−0.280496	+	0.959855i	$0.590499\pi$
$108$		0			0
$109$	−14.0351	+	14.0351i	−1.34432	+	1.34432i	−0.452607	+	0.891710i	$0.649506\pi$
$109$	−14.0351	+	14.0351i	−1.34432	+	1.34432i	−0.891710	+	0.452607i	$0.850494\pi$
$110$		0			0
$111$		−	8.98040i		−	0.852382i
$112$		0			0
$113$	−11.5817	+	11.5817i	−1.08952	+	1.08952i	−0.0939384	+	0.995578i	$0.529946\pi$
$113$	−11.5817	+	11.5817i	−1.08952	+	1.08952i	−0.995578	+	0.0939384i	$0.970054\pi$
$114$		0			0
$115$	−6.36959			−0.593967
$116$		0			0
$117$			12.4534i			1.15131i
$118$		0			0
$119$	6.46110	+	2.44562i	0.592288	+	0.224190i
$120$		0			0
$121$		−	19.0993i		−	1.73630i
$122$		0			0
$123$	1.46286			0.131902
$124$		0			0
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$		0			0
$127$			21.4047i			1.89936i	0.313226	+	0.949679i	$0.398590\pi$
$127$			21.4047i			1.89936i	−0.313226	+	0.949679i	$0.601410\pi$
$128$		0			0
$129$	−3.06418	+	3.06418i	−0.269786	+	0.269786i
$130$		0			0
$131$	−2.36184	−	2.36184i	−0.206355	−	0.206355i	0.596361	−	0.802716i	$-0.296613\pi$
$131$	−2.36184	−	2.36184i	−0.206355	−	0.206355i	−0.802716	+	0.596361i	$0.796613\pi$
$132$		0			0
$133$	4.45336	+	4.45336i	0.386156	+	0.386156i
$134$		0			0
$135$	4.00000			0.344265
$136$		0			0
$137$	7.97090			0.681000			0.340500	−	0.940244i	$-0.389404\pi$
$137$	7.97090			0.681000			0.340500	+	0.940244i	$0.389404\pi$
$138$		0			0
$139$	−1.75103	−	1.75103i	−0.148520	−	0.148520i	0.628936	−	0.777457i	$-0.283491\pi$
$139$	−1.75103	−	1.75103i	−0.148520	−	0.148520i	−0.777457	+	0.628936i	$0.783491\pi$
$140$		0			0
$141$	−19.0351	−	19.0351i	−1.60304	−	1.60304i
$142$		0			0
$143$	11.8871	−	11.8871i	0.994051	−	0.994051i
$144$		0			0
$145$		−	8.12836i		−	0.675023i
$146$		0			0
$147$	7.87939	−	7.87939i	0.649881	−	0.649881i
$148$		0			0
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$		0			0
$151$			10.3696i			0.843865i	0.906627	+	0.421932i	$0.138648\pi$
$151$			10.3696i			0.843865i	−0.906627	+	0.421932i	$0.861352\pi$
$152$		0			0
$153$	15.2763	−	6.88713i	1.23502	−	0.556791i
$154$		0			0
$155$		−	5.88713i		−	0.472865i
$156$		0			0
$157$	−2.48246			−0.198122			−0.0990609	−	0.995081i	$-0.531584\pi$
$157$	−2.48246			−0.198122			−0.0990609	+	0.995081i	$0.531584\pi$
$158$		0			0
$159$	−25.6459	+	25.6459i	−2.03385	+	2.03385i
$160$		0			0
$161$		−	7.54664i		−	0.594758i
$162$		0			0
$163$	−7.15570	+	7.15570i	−0.560477	+	0.560477i	−0.929443	−	0.368966i	$-0.879712\pi$
$163$	−7.15570	+	7.15570i	−0.560477	+	0.560477i	0.368966	+	0.929443i	$0.379712\pi$
$164$		0			0
$165$	−14.5817	−	14.5817i	−1.13519	−	1.13519i
$166$		0			0
$167$	3.05644	+	3.05644i	0.236514	+	0.236514i	0.815405	−	0.578891i	$-0.196514\pi$
$167$	3.05644	+	3.05644i	0.236514	+	0.236514i	−0.578891	+	0.815405i	$0.696514\pi$
$168$		0			0
$169$	−3.61081			−0.277755
$170$		0			0
$171$	15.2763			1.16821
$172$		0			0
$173$	−3.32501	−	3.32501i	−0.252796	−	0.252796i	0.569320	−	0.822116i	$-0.307206\pi$
$173$	−3.32501	−	3.32501i	−0.252796	−	0.252796i	−0.822116	+	0.569320i	$0.807206\pi$
$174$		0			0
$175$	3.55438	+	3.55438i	0.268686	+	0.268686i
$176$		0			0
$177$	−18.5817	+	18.5817i	−1.39669	+	1.39669i
$178$		0			0
$179$		−	7.75877i		−	0.579918i	−0.957039	−	0.289959i	$-0.906358\pi$
$179$		−	7.75877i		−	0.579918i	0.957039	−	0.289959i	$-0.0936416\pi$
$180$		0			0
$181$	3.61081	−	3.61081i	0.268390	−	0.268390i	−0.560061	−	0.828451i	$-0.689222\pi$
$181$	3.61081	−	3.61081i	0.268390	−	0.268390i	0.828451	+	0.560061i	$0.189222\pi$
$182$		0			0
$183$	−26.7939			−1.98066
$184$		0			0
$185$			4.77837i			0.351313i
$186$		0			0
$187$	−21.1557	−	8.00774i	−1.54706	−	0.585584i
$188$		0			0
$189$			4.73917i			0.344724i
$190$		0			0
$191$	19.6851			1.42436			0.712182	−	0.701995i	$-0.247707\pi$
$191$	19.6851			1.42436			0.712182	+	0.701995i	$0.247707\pi$
$192$		0			0
$193$	3.12836	−	3.12836i	0.225184	−	0.225184i	−0.585493	−	0.810677i	$-0.699099\pi$
$193$	3.12836	−	3.12836i	0.225184	−	0.225184i	0.810677	+	0.585493i	$0.199099\pi$
$194$		0			0
$195$		−	11.5175i		−	0.824788i
$196$		0			0
$197$	−6.67499	+	6.67499i	−0.475574	+	0.475574i	−0.903713	−	0.428139i	$-0.859169\pi$
$197$	−6.67499	+	6.67499i	−0.475574	+	0.475574i	0.428139	+	0.903713i	$0.359169\pi$
$198$		0			0
$199$	−14.9436	−	14.9436i	−1.05932	−	1.05932i	−0.998126	−	0.0611953i	$-0.980509\pi$
$199$	−14.9436	−	14.9436i	−1.05932	−	1.05932i	−0.0611953	−	0.998126i	$-0.519491\pi$
$200$		0			0
$201$	7.51754	+	7.51754i	0.530246	+	0.530246i
$202$		0			0
$203$	9.63041			0.675923
$204$		0			0
$205$	−0.778371			−0.0543638
$206$		0			0
$207$	−12.9436	−	12.9436i	−0.899640	−	0.899640i
$208$		0			0
$209$	−14.5817	−	14.5817i	−1.00864	−	1.00864i
$210$		0			0
$211$	10.6186	−	10.6186i	0.731011	−	0.731011i	−0.239809	−	0.970820i	$-0.577085\pi$
$211$	10.6186	−	10.6186i	0.731011	−	0.731011i	0.970820	+	0.239809i	$0.0770847\pi$
$212$		0			0
$213$		−	9.67499i		−	0.662920i
$214$		0			0
$215$	1.63041	−	1.63041i	0.111193	−	0.111193i
$216$		0			0
$217$	6.97502			0.473495
$218$		0			0
$219$			24.4979i			1.65542i
$220$		0			0
$221$	−5.19253	−	11.5175i	−0.349288	−	0.774754i
$222$		0			0
$223$			20.4979i			1.37264i	0.727298	+	0.686322i	$0.240776\pi$
$223$			20.4979i			1.37264i	−0.727298	+	0.686322i	$0.759224\pi$
$224$		0			0
$225$	12.1925			0.812836
$226$		0			0
$227$	17.0428	−	17.0428i	1.13117	−	1.13117i	0.141189	−	0.989983i	$-0.454907\pi$
$227$	17.0428	−	17.0428i	1.13117	−	1.13117i	0.989983	−	0.141189i	$-0.0450926\pi$
$228$		0			0
$229$			29.9709i			1.98053i	0.139184	+	0.990267i	$0.455552\pi$
$229$			29.9709i			1.98053i	−0.139184	+	0.990267i	$0.544448\pi$
$230$		0			0
$231$	17.2763	−	17.2763i	1.13670	−	1.13670i
$232$		0			0
$233$	11.4534	+	11.4534i	0.750335	+	0.750335i	0.974542	−	0.224207i	$-0.0719791\pi$
$233$	11.4534	+	11.4534i	0.750335	+	0.750335i	−0.224207	+	0.974542i	$0.571979\pi$
$234$		0			0
$235$	10.1284	+	10.1284i	0.660701	+	0.660701i
$236$		0			0
$237$	−12.8776			−0.836492
$238$		0			0
$239$	16.9067			1.09361			0.546803	−	0.837262i	$-0.315845\pi$
$239$	16.9067			1.09361			0.546803	+	0.837262i	$0.315845\pi$
$240$		0			0
$241$	7.12836	+	7.12836i	0.459178	+	0.459178i	0.898386	−	0.439208i	$-0.144741\pi$
$241$	7.12836	+	7.12836i	0.459178	+	0.459178i	−0.439208	+	0.898386i	$0.644741\pi$
$242$		0			0
$243$	−14.7861	−	14.7861i	−0.948530	−	0.948530i
$244$		0			0
$245$	−4.19253	+	4.19253i	−0.267851	+	0.267851i
$246$		0			0
$247$		−	11.5175i		−	0.732844i
$248$		0			0
$249$	24.7101	−	24.7101i	1.56594	−	1.56594i
$250$		0			0
$251$	17.8135			1.12438			0.562188	−	0.827010i	$-0.309960\pi$
$251$	17.8135			1.12438			0.562188	+	0.827010i	$0.309960\pi$
$252$		0			0
$253$			24.7101i			1.55351i
$254$		0			0
$255$	−14.1284	+	6.36959i	−0.884752	+	0.398879i
$256$		0			0
$257$			6.28581i			0.392098i	0.980594	+	0.196049i	$0.0628111\pi$
$257$			6.28581i			0.392098i	−0.980594	+	0.196049i	$0.937189\pi$
$258$		0			0
$259$	−5.66138			−0.351781
$260$		0			0
$261$	16.5175	−	16.5175i	1.02241	−	1.02241i
$262$		0			0
$263$			1.40467i			0.0866155i	0.999062	+	0.0433077i	$0.0137896\pi$
$263$			1.40467i			0.0866155i	−0.999062	+	0.0433077i	$0.986210\pi$
$264$		0			0
$265$	13.6459	−	13.6459i	0.838261	−	0.838261i
$266$		0			0
$267$	−30.0155	−	30.0155i	−1.83692	−	1.83692i
$268$		0			0
$269$	−6.51754	−	6.51754i	−0.397381	−	0.397381i	0.479927	−	0.877308i	$-0.340663\pi$
$269$	−6.51754	−	6.51754i	−0.397381	−	0.397381i	−0.877308	+	0.479927i	$0.840663\pi$
$270$		0			0
$271$	−0.906726			−0.0550797			−0.0275399	−	0.999621i	$-0.508767\pi$
$271$	−0.906726			−0.0550797			−0.0275399	+	0.999621i	$0.508767\pi$
$272$		0			0
$273$	13.6459			0.825887
$274$		0			0
$275$	−11.6382	−	11.6382i	−0.701807	−	0.701807i
$276$		0			0
$277$	12.1925	+	12.1925i	0.732578	+	0.732578i	0.971130	−	0.238552i	$-0.0766726\pi$
$277$	12.1925	+	12.1925i	0.732578	+	0.732578i	−0.238552	+	0.971130i	$0.576673\pi$
$278$		0			0
$279$	11.9632	−	11.9632i	0.716216	−	0.716216i
$280$		0			0
$281$			18.7784i			1.12022i	0.828417	+	0.560112i	$0.189242\pi$
$281$			18.7784i			1.12022i	−0.828417	+	0.560112i	$0.810758\pi$
$282$		0			0
$283$	−8.37733	+	8.37733i	−0.497980	+	0.497980i	−0.910809	−	0.412828i	$-0.864541\pi$
$283$	−8.37733	+	8.37733i	−0.497980	+	0.497980i	0.412828	+	0.910809i	$0.364541\pi$
$284$		0			0
$285$	−14.1284			−0.836892
$286$		0			0
$287$		−	0.922208i		−	0.0544362i
$288$		0			0
$289$	−11.2567	+	12.7392i	−0.662159	+	0.749363i
$290$		0			0
$291$			5.46286i			0.320238i
$292$		0			0
$293$	20.3851			1.19091			0.595454	−	0.803389i	$-0.296972\pi$
$293$	20.3851			1.19091			0.595454	+	0.803389i	$0.296972\pi$
$294$		0			0
$295$	9.88713	−	9.88713i	0.575651	−	0.575651i
$296$		0			0
$297$		−	15.5175i		−	0.900419i
$298$		0			0
$299$	−9.75877	+	9.75877i	−0.564364	+	0.564364i
$300$		0			0
$301$	1.93170	+	1.93170i	0.111342	+	0.111342i
$302$		0			0
$303$	−20.7939	−	20.7939i	−1.19458	−	1.19458i
$304$		0			0
$305$	14.2567			0.816337
$306$		0			0
$307$	−14.1284			−0.806348			−0.403174	−	0.915123i	$-0.632093\pi$
$307$	−14.1284			−0.806348			−0.403174	+	0.915123i	$0.632093\pi$
$308$		0			0
$309$	12.7392	+	12.7392i	0.724706	+	0.724706i
$310$		0			0
$311$	−7.07192	−	7.07192i	−0.401012	−	0.401012i	0.477578	−	0.878589i	$-0.341515\pi$
$311$	−7.07192	−	7.07192i	−0.401012	−	0.401012i	−0.878589	+	0.477578i	$0.841515\pi$
$312$		0			0
$313$	−6.34998	+	6.34998i	−0.358922	+	0.358922i	−0.863416	−	0.504493i	$-0.831679\pi$
$313$	−6.34998	+	6.34998i	−0.358922	+	0.358922i	0.504493	+	0.863416i	$0.331679\pi$
$314$		0			0
$315$		−	9.63041i		−	0.542612i
$316$		0			0
$317$	−21.4534	+	21.4534i	−1.20494	+	1.20494i	−0.232296	+	0.972645i	$0.574624\pi$
$317$	−21.4534	+	21.4534i	−1.20494	+	1.20494i	−0.972645	+	0.232296i	$0.925376\pi$
$318$		0			0
$319$	−31.5330			−1.76551
$320$		0			0
$321$		−	26.4142i		−	1.47429i
$322$		0			0
$323$	−14.1284	+	6.36959i	−0.786123	+	0.354413i
$324$		0			0
$325$		−	9.19253i		−	0.509910i
$326$		0			0
$327$	52.7547			2.91734
$328$		0			0
$329$	−12.0000	+	12.0000i	−0.661581	+	0.661581i
$330$		0			0
$331$		−	19.4439i		−	1.06873i	−0.845253	−	0.534366i	$-0.820550\pi$
$331$		−	19.4439i		−	1.06873i	0.845253	−	0.534366i	$-0.179450\pi$
$332$		0			0
$333$	−9.71007	+	9.71007i	−0.532109	+	0.532109i
$334$		0			0
$335$	−4.00000	−	4.00000i	−0.218543	−	0.218543i
$336$		0			0
$337$	−15.2567	−	15.2567i	−0.831086	−	0.831086i	0.156579	−	0.987665i	$-0.449953\pi$
$337$	−15.2567	−	15.2567i	−0.831086	−	0.831086i	−0.987665	+	0.156579i	$0.949953\pi$
$338$		0			0
$339$	43.5330			2.36439
$340$		0			0
$341$	−22.8384			−1.23677
$342$		0			0
$343$	−13.2608	−	13.2608i	−0.716018	−	0.716018i
$344$		0			0
$345$	11.9709	+	11.9709i	0.644492	+	0.644492i
$346$		0			0
$347$	−6.98814	+	6.98814i	−0.375143	+	0.375143i	−0.869346	−	0.494203i	$-0.835460\pi$
$347$	−6.98814	+	6.98814i	−0.375143	+	0.375143i	0.494203	+	0.869346i	$0.335460\pi$
$348$		0			0
$349$		−	18.8675i		−	1.00996i	−0.863132	−	0.504978i	$-0.831501\pi$
$349$		−	18.8675i		−	1.00996i	0.863132	−	0.504978i	$-0.168499\pi$
$350$		0			0
$351$	6.12836	−	6.12836i	0.327107	−	0.327107i
$352$		0			0
$353$	12.1284			0.645527			0.322764	−	0.946480i	$-0.395388\pi$
$353$	12.1284			0.645527			0.322764	+	0.946480i	$0.395388\pi$
$354$		0			0
$355$			5.14796i			0.273225i
$356$		0			0
$357$	−7.54664	−	16.7392i	−0.399410	−	0.885931i
$358$		0			0
$359$		−	17.2371i		−	0.909740i	−0.890558	−	0.454870i	$-0.849686\pi$
$359$		−	17.2371i		−	0.909740i	0.890558	−	0.454870i	$-0.150314\pi$
$360$		0			0
$361$	4.87164			0.256402
$362$		0			0
$363$	−35.8949	+	35.8949i	−1.88399	+	1.88399i
$364$		0			0
$365$		−	13.0351i		−	0.682287i
$366$		0			0
$367$	21.8503	−	21.8503i	1.14058	−	1.14058i	0.152231	−	0.988345i	$-0.451354\pi$
$367$	21.8503	−	21.8503i	1.14058	−	1.14058i	0.988345	−	0.152231i	$-0.0486457\pi$
$368$		0			0
$369$	−1.58172	−	1.58172i	−0.0823410	−	0.0823410i
$370$		0			0
$371$	16.1676	+	16.1676i	0.839378	+	0.839378i
$372$		0			0
$373$	−14.4142			−0.746337			−0.373169	−	0.927764i	$-0.621729\pi$
$373$	−14.4142			−0.746337			−0.373169	+	0.927764i	$0.621729\pi$
$374$		0			0
$375$	−30.0702			−1.55282
$376$		0			0
$377$	−12.4534	−	12.4534i	−0.641381	−	0.641381i
$378$		0			0
$379$	24.6732	+	24.6732i	1.26738	+	1.26738i	0.947437	+	0.319942i	$0.103663\pi$
$379$	24.6732	+	24.6732i	1.26738	+	1.26738i	0.319942	+	0.947437i	$0.396337\pi$
$380$		0			0
$381$	40.2276	−	40.2276i	2.06092	−	2.06092i
$382$		0			0
$383$			6.62630i			0.338588i	0.985566	+	0.169294i	$0.0541487\pi$
$383$			6.62630i			0.338588i	−0.985566	+	0.169294i	$0.945851\pi$
$384$		0			0
$385$	−9.19253	+	9.19253i	−0.468495	+	0.468495i
$386$		0			0
$387$	6.62630			0.336834
$388$		0			0
$389$		−	13.3209i		−	0.675396i	−0.941255	−	0.337698i	$-0.890352\pi$
$389$		−	13.3209i		−	0.675396i	0.941255	−	0.337698i	$-0.109648\pi$
$390$		0			0
$391$	17.3678	+	6.57398i	0.878329	+	0.332460i
$392$		0			0
$393$			8.87763i			0.447817i
$394$		0			0
$395$	6.85204			0.344764
$396$		0			0
$397$	−19.4243	+	19.4243i	−0.974876	+	0.974876i	−0.999692	−	0.0248160i	$-0.992100\pi$
$397$	−19.4243	+	19.4243i	−0.974876	+	0.974876i	0.0248160	+	0.999692i	$0.492100\pi$
$398$		0			0
$399$		−	16.7392i		−	0.838007i
$400$		0			0
$401$	−5.12836	+	5.12836i	−0.256098	+	0.256098i	−0.823465	−	0.567367i	$-0.807962\pi$
$401$	−5.12836	+	5.12836i	−0.256098	+	0.256098i	0.567367	+	0.823465i	$0.307962\pi$
$402$		0			0
$403$	−9.01960	−	9.01960i	−0.449298	−	0.449298i
$404$		0			0
$405$	4.67499	+	4.67499i	0.232302	+	0.232302i
$406$		0			0
$407$	18.5371			0.918852
$408$		0			0
$409$	−26.4243			−1.30660			−0.653298	−	0.757101i	$-0.726615\pi$
$409$	−26.4243			−1.30660			−0.653298	+	0.757101i	$0.726615\pi$
$410$		0			0
$411$	−14.9804	−	14.9804i	−0.738929	−	0.738929i
$412$		0			0
$413$	11.7142	+	11.7142i	0.576418	+	0.576418i
$414$		0			0
$415$	−13.1480	+	13.1480i	−0.645408	+	0.645408i
$416$		0			0
$417$			6.58172i			0.322308i
$418$		0			0
$419$	24.2645	−	24.2645i	1.18540	−	1.18540i	0.207070	−	0.978326i	$-0.433607\pi$
$419$	24.2645	−	24.2645i	1.18540	−	1.18540i	0.978326	−	0.207070i	$-0.0663928\pi$
$420$		0			0
$421$	−22.4142			−1.09240			−0.546200	−	0.837655i	$-0.683926\pi$
$421$	−22.4142			−1.09240			−0.546200	+	0.837655i	$0.683926\pi$
$422$		0			0
$423$			41.1634i			2.00143i
$424$		0			0
$425$	−11.2763	+	5.08378i	−0.546981	+	0.246599i
$426$		0			0
$427$			16.8912i			0.817425i
$428$		0			0
$429$	−44.6810			−2.15722
$430$		0			0
$431$	−25.4807	+	25.4807i	−1.22736	+	1.22736i	−0.262404	+	0.964958i	$0.584515\pi$
$431$	−25.4807	+	25.4807i	−1.22736	+	1.22736i	−0.964958	+	0.262404i	$0.915485\pi$
$432$		0			0
$433$		−	14.9358i		−	0.717770i	−0.933382	−	0.358885i	$-0.883157\pi$
$433$		−	14.9358i		−	0.717770i	0.933382	−	0.358885i	$-0.116843\pi$
$434$		0			0
$435$	−15.2763	+	15.2763i	−0.732443	+	0.732443i
$436$		0			0
$437$	11.9709	+	11.9709i	0.572646	+	0.572646i
$438$		0			0
$439$	3.79561	+	3.79561i	0.181154	+	0.181154i	0.791859	−	0.610704i	$-0.209114\pi$
$439$	3.79561	+	3.79561i	0.181154	+	0.181154i	−0.610704	+	0.791859i	$0.709114\pi$
$440$		0			0
$441$	−17.0392			−0.811391
$442$		0			0
$443$	13.4783			0.640375			0.320188	−	0.947354i	$-0.396254\pi$
$443$	13.4783			0.640375			0.320188	+	0.947354i	$0.396254\pi$
$444$		0			0
$445$	15.9709	+	15.9709i	0.757093	+	0.757093i
$446$		0			0
$447$	18.7939	+	18.7939i	0.888919	+	0.888919i
$448$		0			0
$449$	−6.41828	+	6.41828i	−0.302897	+	0.302897i	−0.842146	−	0.539249i	$-0.818708\pi$
$449$	−6.41828	+	6.41828i	−0.302897	+	0.302897i	0.539249	+	0.842146i	$0.318708\pi$
$450$		0			0
$451$			3.01960i			0.142187i
$452$		0			0
$453$	19.4884	−	19.4884i	0.915647	−	0.915647i
$454$		0			0
$455$	−7.26083			−0.340393
$456$		0			0
$457$		−	31.7844i		−	1.48681i	−0.668842	−	0.743405i	$-0.733210\pi$
$457$		−	31.7844i		−	1.48681i	0.668842	−	0.743405i	$-0.266790\pi$
$458$		0			0
$459$	−10.9067	−	4.12836i	−0.509082	−	0.192695i
$460$		0			0
$461$			10.8675i			0.506151i	0.967447	+	0.253076i	$0.0814421\pi$
$461$			10.8675i			0.506151i	−0.967447	+	0.253076i	$0.918558\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$		0			0
$465$	−11.0642	+	11.0642i	−0.513089	+	0.513089i
$466$		0			0
$467$		−	20.9804i		−	0.970857i	−0.874276	−	0.485429i	$-0.838664\pi$
$467$		−	20.9804i		−	0.970857i	0.874276	−	0.485429i	$-0.161336\pi$
$468$		0			0
$469$	4.73917	−	4.73917i	0.218835	−	0.218835i
$470$		0			0
$471$	4.66550	+	4.66550i	0.214975	+	0.214975i
$472$		0			0
$473$	−6.32501	−	6.32501i	−0.290824	−	0.290824i
$474$		0			0
$475$	−11.2763			−0.517393
$476$		0			0
$477$	55.4593			2.53931
$478$		0			0
$479$	1.48070	+	1.48070i	0.0676551	+	0.0676551i	0.740125	−	0.672470i	$-0.234766\pi$
$479$	1.48070	+	1.48070i	0.0676551	+	0.0676551i	−0.672470	+	0.740125i	$0.734766\pi$
$480$		0			0
$481$	7.32089	+	7.32089i	0.333804	+	0.333804i
$482$		0			0
$483$	−14.1830	+	14.1830i	−0.645351	+	0.645351i
$484$		0			0
$485$		−	2.90673i		−	0.131988i
$486$		0			0
$487$	−4.70233	+	4.70233i	−0.213083	+	0.213083i	−0.805576	−	0.592493i	$-0.798144\pi$
$487$	−4.70233	+	4.70233i	−0.213083	+	0.213083i	0.592493	+	0.805576i	$0.298144\pi$
$488$		0			0
$489$	26.8966			1.21631
$490$		0			0
$491$		−	0.0154816i		−	0.000698674i	−1.00000		0.000349337i	$-0.999889\pi$
$491$		−	0.0154816i		−	0.000698674i	1.00000		0.000349337i	$-0.000111197\pi$
$492$		0			0
$493$	−8.38919	+	22.1634i	−0.377830	+	0.998191i
$494$		0			0
$495$			31.5330i			1.41730i
$496$		0			0
$497$	−6.09926			−0.273589
$498$		0			0
$499$	−10.8598	+	10.8598i	−0.486151	+	0.486151i	−0.907089	−	0.420938i	$-0.861701\pi$
$499$	−10.8598	+	10.8598i	−0.486151	+	0.486151i	0.420938	+	0.907089i	$0.361701\pi$
$500$		0			0
$501$		−	11.4884i		−	0.513266i
$502$		0			0
$503$	−0.445622	+	0.445622i	−0.0198693	+	0.0198693i	−0.716972	−	0.697102i	$-0.754472\pi$
$503$	−0.445622	+	0.445622i	−0.0198693	+	0.0198693i	0.697102	+	0.716972i	$0.254472\pi$
$504$		0			0
$505$	11.0642	+	11.0642i	0.492349	+	0.492349i
$506$		0			0
$507$	6.78611	+	6.78611i	0.301382	+	0.301382i
$508$		0			0
$509$	40.9769			1.81627			0.908134	−	0.418679i	$-0.137507\pi$
$509$	40.9769			1.81627			0.908134	+	0.418679i	$0.137507\pi$
$510$		0			0
$511$	15.4439			0.683196
$512$		0			0
$513$	−7.51754	−	7.51754i	−0.331908	−	0.331908i
$514$		0			0
$515$	−6.77837	−	6.77837i	−0.298691	−	0.298691i
$516$		0			0
$517$	39.2918	−	39.2918i	1.72805	−	1.72805i
$518$		0			0
$519$			12.4979i			0.548599i
$520$		0			0
$521$	0.0932736	−	0.0932736i	0.00408639	−	0.00408639i	−0.705061	−	0.709147i	$-0.749080\pi$
$521$	0.0932736	−	0.0932736i	0.00408639	−	0.00408639i	0.709147	+	0.705061i	$0.249080\pi$
$522$		0			0
$523$	29.7351			1.30022			0.650112	−	0.759839i	$-0.274722\pi$
$523$	29.7351			1.30022			0.650112	+	0.759839i	$0.274722\pi$
$524$		0			0
$525$		−	13.3601i		−	0.583082i
$526$		0			0
$527$	−6.07604	+	16.0523i	−0.264676	+	0.699250i
$528$		0			0
$529$			2.71419i			0.118008i
$530$		0			0
$531$	40.1830			1.74380
$532$		0			0
$533$	−1.19253	+	1.19253i	−0.0516544	+	0.0516544i
$534$		0			0
$535$			14.0547i			0.607637i
$536$		0			0
$537$	−14.5817	+	14.5817i	−0.629248	+	0.629248i
$538$		0			0
$539$	16.2645	+	16.2645i	0.700560	+	0.700560i
$540$		0			0
$541$	25.9067	+	25.9067i	1.11382	+	1.11382i	0.992630	+	0.121188i	$0.0386702\pi$
$541$	25.9067	+	25.9067i	1.11382	+	1.11382i	0.121188	+	0.992630i	$0.461330\pi$
$542$		0			0
$543$	−13.5722			−0.582440
$544$		0			0
$545$	−28.0702			−1.20239
$546$		0			0
$547$	−18.6186	−	18.6186i	−0.796072	−	0.796072i	0.186402	−	0.982474i	$-0.440317\pi$
$547$	−18.6186	−	18.6186i	−0.796072	−	0.796072i	−0.982474	+	0.186402i	$0.940317\pi$
$548$		0			0
$549$	28.9709	+	28.9709i	1.23645	+	1.23645i
$550$		0			0
$551$	−15.2763	+	15.2763i	−0.650793	+	0.650793i
$552$		0			0
$553$			8.11825i			0.345223i
$554$		0			0
$555$	8.98040	−	8.98040i	0.381197	−	0.381197i
$556$		0			0
$557$	4.54252			0.192473			0.0962363	−	0.995359i	$-0.469320\pi$
$557$	4.54252			0.192473			0.0962363	+	0.995359i	$0.469320\pi$
$558$		0			0
$559$		−	4.99588i		−	0.211303i
$560$		0			0
$561$	24.7101	+	54.8093i	1.04326	+	2.31405i
$562$		0			0
$563$			22.8830i			0.964404i	0.876060	+	0.482202i	$0.160163\pi$
$563$			22.8830i			0.964404i	−0.876060	+	0.482202i	$0.839837\pi$
$564$		0			0
$565$	−23.1634			−0.974493
$566$		0			0
$567$	−5.53890	+	5.53890i	−0.232612	+	0.232612i
$568$		0			0
$569$			3.77425i			0.158225i	0.996866	+	0.0791124i	$0.0252086\pi$
$569$			3.77425i			0.158225i	−0.996866	+	0.0791124i	$0.974791\pi$
$570$		0			0
$571$	16.4902	−	16.4902i	0.690093	−	0.690093i	−0.272159	−	0.962252i	$-0.587738\pi$
$571$	16.4902	−	16.4902i	0.690093	−	0.690093i	0.962252	+	0.272159i	$0.0877376\pi$
$572$		0			0
$573$	−36.9959	−	36.9959i	−1.54553	−	1.54553i
$574$		0			0
$575$	9.55438	+	9.55438i	0.398445	+	0.398445i
$576$		0			0
$577$	11.7142			0.487668			0.243834	−	0.969817i	$-0.421595\pi$
$577$	11.7142			0.487668			0.243834	+	0.969817i	$0.421595\pi$
$578$		0			0
$579$	−11.7588			−0.488678
$580$		0			0
$581$	−15.5776	−	15.5776i	−0.646268	−	0.646268i
$582$		0			0
$583$	−52.9377	−	52.9377i	−2.19246	−	2.19246i
$584$		0			0
$585$	−12.4534	+	12.4534i	−0.514883	+	0.514883i
$586$		0			0
$587$		−	14.4587i		−	0.596776i	−0.954445	−	0.298388i	$-0.903551\pi$
$587$		−	14.4587i		−	0.596776i	0.954445	−	0.298388i	$-0.0964489\pi$
$588$		0			0
$589$	−11.0642	+	11.0642i	−0.455892	+	0.455892i
$590$		0			0
$591$	25.0898			1.03205
$592$		0			0
$593$		−	6.03920i		−	0.248000i	−0.992282	−	0.124000i	$-0.960428\pi$
$593$		−	6.03920i		−	0.248000i	0.992282	−	0.124000i	$-0.0395723\pi$
$594$		0			0
$595$	4.01548	+	8.90673i	0.164619	+	0.365140i
$596$		0			0
$597$			56.1694i			2.29886i
$598$		0			0
$599$	−6.77837			−0.276957			−0.138478	−	0.990365i	$-0.544221\pi$
$599$	−6.77837			−0.276957			−0.138478	+	0.990365i	$0.544221\pi$
$600$		0			0
$601$	5.00000	−	5.00000i	0.203954	−	0.203954i	−0.597738	−	0.801692i	$-0.703934\pi$
$601$	5.00000	−	5.00000i	0.203954	−	0.203954i	0.801692	+	0.597738i	$0.203934\pi$
$602$		0			0
$603$		−	16.2567i		−	0.662024i
$604$		0			0
$605$	19.0993	−	19.0993i	0.776495	−	0.776495i
$606$		0			0
$607$	5.31315	+	5.31315i	0.215654	+	0.215654i	0.806664	−	0.591010i	$-0.201271\pi$
$607$	5.31315	+	5.31315i	0.215654	+	0.215654i	−0.591010	+	0.806664i	$0.701271\pi$
$608$		0			0
$609$	−18.0993	−	18.0993i	−0.733419	−	0.733419i
$610$		0			0
$611$	31.0351			1.25555
$612$		0			0
$613$	0.443258			0.0179030			0.00895152	−	0.999960i	$-0.497151\pi$
$613$	0.443258			0.0179030			0.00895152	+	0.999960i	$0.497151\pi$
$614$		0			0
$615$	1.46286	+	1.46286i	0.0589882	+	0.0589882i
$616$		0			0
$617$	15.2276	+	15.2276i	0.613041	+	0.613041i	0.943737	−	0.330696i	$-0.107284\pi$
$617$	15.2276	+	15.2276i	0.613041	+	0.613041i	−0.330696	+	0.943737i	$0.607284\pi$
$618$		0			0
$619$	10.1753	−	10.1753i	0.408980	−	0.408980i	−0.472403	−	0.881383i	$-0.656613\pi$
$619$	10.1753	−	10.1753i	0.408980	−	0.408980i	0.881383	+	0.472403i	$0.156613\pi$
$620$		0			0
$621$			12.7392i			0.511205i
$622$		0			0
$623$	−18.9222	+	18.9222i	−0.758102	+	0.758102i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$			54.8093i			2.18887i
$628$		0			0
$629$	4.93170	−	13.0291i	0.196640	−	0.519504i
$630$		0			0
$631$			31.0196i			1.23487i	0.786622	+	0.617435i	$0.211828\pi$
$631$			31.0196i			1.23487i	−0.786622	+	0.617435i	$0.788172\pi$
$632$		0			0
$633$	−39.9127			−1.58639
$634$		0			0
$635$	−21.4047	+	21.4047i	−0.849418	+	0.849418i
$636$		0			0
$637$			12.8467i			0.509003i
$638$		0			0
$639$	−10.4611	+	10.4611i	−0.413835	+	0.413835i
$640$		0			0
$641$	23.8776	+	23.8776i	0.943110	+	0.943110i	0.998467	−	0.0553569i	$-0.0176297\pi$
$641$	23.8776	+	23.8776i	0.943110	+	0.943110i	−0.0553569	+	0.998467i	$0.517630\pi$
$642$		0			0
$643$	−4.00774	−	4.00774i	−0.158050	−	0.158050i	0.623652	−	0.781702i	$-0.285648\pi$
$643$	−4.00774	−	4.00774i	−0.158050	−	0.158050i	−0.781702	+	0.623652i	$0.785648\pi$
$644$		0			0
$645$	−6.12836			−0.241304
$646$		0			0
$647$	−3.34998			−0.131701			−0.0658507	−	0.997829i	$-0.520976\pi$
$647$	−3.34998			−0.131701			−0.0658507	+	0.997829i	$0.520976\pi$
$648$		0			0
$649$	−38.3560	−	38.3560i	−1.50560	−	1.50560i
$650$		0			0
$651$	−13.1088	−	13.1088i	−0.513773	−	0.513773i
$652$		0			0
$653$	22.9709	−	22.9709i	0.898921	−	0.898921i	−0.0964198	−	0.995341i	$-0.530739\pi$
$653$	22.9709	−	22.9709i	0.898921	−	0.898921i	0.995341	+	0.0964198i	$0.0307391\pi$
$654$		0			0
$655$		−	4.72369i		−	0.184570i
$656$		0			0
$657$	26.4884	−	26.4884i	1.03341	−	1.03341i
$658$		0			0
$659$	−37.4201			−1.45768			−0.728841	−	0.684683i	$-0.759941\pi$
$659$	−37.4201			−1.45768			−0.728841	+	0.684683i	$0.759941\pi$
$660$		0			0
$661$		−	3.68510i		−	0.143334i	−0.997429	−	0.0716668i	$-0.977168\pi$
$661$		−	3.68510i		−	0.143334i	0.997429	−	0.0716668i	$-0.0228318\pi$
$662$		0			0
$663$	−11.8871	+	31.4047i	−0.461658	+	1.21966i
$664$		0			0
$665$			8.90673i			0.345388i
$666$		0			0
$667$	25.8871			1.00235
$668$		0			0
$669$	38.5235	−	38.5235i	1.48941	−	1.48941i
$670$		0			0
$671$		−	55.3073i		−	2.13511i
$672$		0			0
$673$	11.5425	−	11.5425i	0.444931	−	0.444931i	−0.448734	−	0.893665i	$-0.648125\pi$
$673$	11.5425	−	11.5425i	0.444931	−	0.444931i	0.893665	+	0.448734i	$0.148125\pi$
$674$		0			0
$675$	−6.00000	−	6.00000i	−0.230940	−	0.230940i
$676$		0			0
$677$	−13.9358	−	13.9358i	−0.535597	−	0.535597i	0.386635	−	0.922233i	$-0.373637\pi$
$677$	−13.9358	−	13.9358i	−0.535597	−	0.535597i	−0.922233	+	0.386635i	$0.873637\pi$
$678$		0			0
$679$	3.44387			0.132164
$680$		0			0
$681$	−64.0601			−2.45479
$682$		0			0
$683$	6.20977	+	6.20977i	0.237610	+	0.237610i	0.815860	−	0.578250i	$-0.196264\pi$
$683$	6.20977	+	6.20977i	0.237610	+	0.237610i	−0.578250	+	0.815860i	$0.696264\pi$
$684$		0			0
$685$	7.97090	+	7.97090i	0.304553	+	0.304553i
$686$		0			0
$687$	56.3269	−	56.3269i	2.14900	−	2.14900i
$688$		0			0
$689$		−	41.8135i		−	1.59297i
$690$		0			0
$691$	6.17530	−	6.17530i	0.234919	−	0.234919i	−0.579823	−	0.814742i	$-0.696878\pi$
$691$	6.17530	−	6.17530i	0.234919	−	0.234919i	0.814742	+	0.579823i	$0.196878\pi$
$692$		0			0
$693$	−37.3601			−1.41919
$694$		0			0
$695$		−	3.50206i		−	0.132841i
$696$		0			0
$697$	2.12237	+	0.803348i	0.0803905	+	0.0304290i
$698$		0			0
$699$		−	43.0506i		−	1.62832i
$700$		0			0
$701$	−26.6709			−1.00734			−0.503672	−	0.863895i	$-0.668018\pi$
$701$	−26.6709			−1.00734			−0.503672	+	0.863895i	$0.668018\pi$
$702$		0			0
$703$	8.98040	−	8.98040i	0.338702	−	0.338702i
$704$		0			0
$705$		−	38.0702i		−	1.43381i
$706$		0			0
$707$	−13.1088	+	13.1088i	−0.493005	+	0.493005i
$708$		0			0
$709$	22.7452	+	22.7452i	0.854212	+	0.854212i	0.990649	−	0.136437i	$-0.0435650\pi$
$709$	22.7452	+	22.7452i	0.854212	+	0.854212i	−0.136437	+	0.990649i	$0.543565\pi$
$710$		0			0
$711$	13.9240	+	13.9240i	0.522189	+	0.522189i
$712$		0			0
$713$	18.7493			0.702166
$714$		0			0
$715$	23.7743			0.889107
$716$		0			0
$717$	−31.7743	−	31.7743i	−1.18663	−	1.18663i
$718$		0			0
$719$	15.3131	+	15.3131i	0.571084	+	0.571084i	0.932431	−	0.361347i	$-0.117683\pi$
$719$	15.3131	+	15.3131i	0.571084	+	0.571084i	−0.361347	+	0.932431i	$0.617683\pi$
$720$		0			0
$721$	8.03096	−	8.03096i	0.299089	−	0.299089i
$722$		0			0
$723$		−	26.7939i		−	0.996474i
$724$		0			0
$725$	−12.1925	+	12.1925i	−0.452819	+	0.452819i
$726$		0			0
$727$	16.6500			0.617515			0.308757	−	0.951141i	$-0.400087\pi$
$727$	16.6500			0.617515			0.308757	+	0.951141i	$0.400087\pi$
$728$		0			0
$729$			41.5526i			1.53899i
$730$		0			0
$731$	−6.12836	+	2.76289i	−0.226665	+	0.102189i
$732$		0			0
$733$			2.20676i			0.0815084i	0.999169	+	0.0407542i	$0.0129761\pi$
$733$			2.20676i			0.0815084i	−0.999169	+	0.0407542i	$0.987024\pi$
$734$		0			0
$735$	15.7588			0.581271
$736$		0			0
$737$	−15.5175	+	15.5175i	−0.571596	+	0.571596i
$738$		0			0
$739$			35.5330i			1.30710i	0.756882	+	0.653552i	$0.226722\pi$
$739$			35.5330i			1.30710i	−0.756882	+	0.653552i	$0.773278\pi$
$740$		0			0
$741$	−21.6459	+	21.6459i	−0.795182	+	0.795182i
$742$		0			0
$743$	−30.4611	−	30.4611i	−1.11751	−	1.11751i	−0.992106	−	0.125404i	$-0.959977\pi$
$743$	−30.4611	−	30.4611i	−1.11751	−	1.11751i	−0.125404	−	0.992106i	$-0.540023\pi$
$744$		0			0
$745$	−10.0000	−	10.0000i	−0.366372	−	0.366372i
$746$		0			0
$747$	−53.4356			−1.95511
$748$		0			0
$749$	−16.6519			−0.608447
$750$		0			0
$751$	−10.8152	−	10.8152i	−0.394653	−	0.394653i	0.481689	−	0.876342i	$-0.340023\pi$
$751$	−10.8152	−	10.8152i	−0.394653	−	0.394653i	−0.876342	+	0.481689i	$0.840023\pi$
$752$		0			0
$753$	−33.4783	−	33.4783i	−1.22002	−	1.22002i
$754$		0			0
$755$	−10.3696	+	10.3696i	−0.377388	+	0.377388i
$756$		0			0
$757$		−	19.8425i		−	0.721190i	−0.932723	−	0.360595i	$-0.882574\pi$
$757$		−	19.8425i		−	0.721190i	0.932723	−	0.360595i	$-0.117426\pi$
$758$		0			0
$759$	46.4397	−	46.4397i	1.68566	−	1.68566i
$760$		0			0
$761$	3.37908			0.122492			0.0612458	−	0.998123i	$-0.480493\pi$
$761$	3.37908			0.122492			0.0612458	+	0.998123i	$0.480493\pi$
$762$		0			0
$763$		−	33.2573i		−	1.20400i
$764$		0			0
$765$	22.1634	+	8.38919i	0.801321	+	0.303312i
$766$		0			0
$767$		−	30.2959i		−	1.09392i
$768$		0			0
$769$	−11.3209			−0.408242			−0.204121	−	0.978946i	$-0.565434\pi$
$769$	−11.3209			−0.408242			−0.204121	+	0.978946i	$0.565434\pi$
$770$		0			0
$771$	11.8135	−	11.8135i	0.425451	−	0.425451i
$772$		0			0
$773$			49.5776i			1.78318i	0.452841	+	0.891591i	$0.350410\pi$
$773$			49.5776i			1.78318i	−0.452841	+	0.891591i	$0.649590\pi$
$774$		0			0
$775$	−8.83069	+	8.83069i	−0.317208	+	0.317208i
$776$		0			0
$777$	10.6399	+	10.6399i	0.381705	+	0.381705i
$778$		0			0
$779$	1.46286	+	1.46286i	0.0524124	+	0.0524124i
$780$		0			0
$781$	19.9709			0.714615
$782$		0			0
$783$	−16.2567			−0.580967
$784$		0			0
$785$	−2.48246	−	2.48246i	−0.0886028	−	0.0886028i
$786$		0			0
$787$	12.8598	+	12.8598i	0.458402	+	0.458402i	0.898131	−	0.439729i	$-0.144925\pi$
$787$	12.8598	+	12.8598i	0.458402	+	0.458402i	−0.439729	+	0.898131i	$0.644925\pi$
$788$		0			0
$789$	2.63991	−	2.63991i	0.0939833	−	0.0939833i
$790$		0			0
$791$		−	27.4439i		−	0.975792i
$792$		0			0
$793$	21.8425	−	21.8425i	0.775652	−	0.775652i
$794$		0			0
$795$	−51.2918			−1.81913
$796$		0			0
$797$		−	18.3851i		−	0.651232i	−0.945502	−	0.325616i	$-0.894428\pi$
$797$		−	18.3851i		−	0.651232i	0.945502	−	0.325616i	$-0.105572\pi$
$798$		0			0
$799$	−17.1634	−	38.0702i	−0.607199	−	1.34683i
$800$		0			0
$801$			64.9086i			2.29343i
$802$		0			0
$803$	−50.5681			−1.78451
$804$		0			0
$805$	7.54664	−	7.54664i	0.265984	−	0.265984i
$806$		0			0
$807$			24.4979i			0.862368i
$808$		0			0
$809$	−17.7101	+	17.7101i	−0.622653	+	0.622653i	−0.946209	−	0.323556i	$-0.895122\pi$
$809$	−17.7101	+	17.7101i	−0.622653	+	0.622653i	0.323556	+	0.946209i	$0.395122\pi$
$810$		0			0
$811$	−5.84018	−	5.84018i	−0.205077	−	0.205077i	0.597094	−	0.802171i	$-0.296322\pi$
$811$	−5.84018	−	5.84018i	−0.205077	−	0.205077i	−0.802171	+	0.597094i	$0.796322\pi$
$812$		0			0
$813$	1.70409	+	1.70409i	0.0597650	+	0.0597650i
$814$		0			0
$815$	−14.3114			−0.501306
$816$		0			0
$817$	−6.12836			−0.214404
$818$		0			0
$819$	−14.7547	−	14.7547i	−0.515569	−	0.515569i
$820$		0			0
$821$	7.28581	+	7.28581i	0.254276	+	0.254276i	0.822721	−	0.568445i	$-0.192455\pi$
$821$	7.28581	+	7.28581i	0.254276	+	0.254276i	−0.568445	+	0.822721i	$0.692455\pi$
$822$		0			0
$823$	−16.3482	+	16.3482i	−0.569863	+	0.569863i	−0.932090	−	0.362227i	$-0.882017\pi$
$823$	−16.3482	+	16.3482i	−0.569863	+	0.569863i	0.362227	+	0.932090i	$0.382017\pi$
$824$		0			0
$825$			43.7452i			1.52301i
$826$		0			0
$827$	−0.505681	+	0.505681i	−0.0175843	+	0.0175843i	−0.715844	−	0.698260i	$-0.753958\pi$
$827$	−0.505681	+	0.505681i	−0.0175843	+	0.0175843i	0.698260	+	0.715844i	$0.253958\pi$
$828$		0			0
$829$	20.5526			0.713822			0.356911	−	0.934138i	$-0.383830\pi$
$829$	20.5526			0.713822			0.356911	+	0.934138i	$0.383830\pi$
$830$		0			0
$831$		−	45.8289i		−	1.58979i
$832$		0			0
$833$	15.7588	−	7.10464i	0.546009	−	0.246161i
$834$		0			0
$835$			6.11287i			0.211545i
$836$		0			0
$837$	−11.7743			−0.406978
$838$		0			0
$839$	−0.278066	+	0.278066i	−0.00959991	+	0.00959991i	−0.711890	−	0.702291i	$-0.752161\pi$
$839$	−0.278066	+	0.278066i	−0.00959991	+	0.00959991i	0.702291	+	0.711890i	$0.252161\pi$
$840$		0			0
$841$			4.03508i			0.139141i
$842$		0			0
$843$	35.2918	−	35.2918i	1.21551	−	1.21551i
$844$		0			0
$845$	−3.61081	−	3.61081i	−0.124216	−	0.124216i
$846$		0			0
$847$	22.6287	+	22.6287i	0.777530	+	0.777530i
$848$		0			0
$849$	31.4884			1.08068
$850$		0			0
$851$	−15.2181			−0.521670
$852$		0			0
$853$	6.70409	+	6.70409i	0.229544	+	0.229544i	0.812502	−	0.582958i	$-0.198105\pi$
$853$	6.70409	+	6.70409i	0.229544	+	0.229544i	−0.582958	+	0.812502i	$0.698105\pi$
$854$		0			0
$855$	15.2763	+	15.2763i	0.522439	+	0.522439i
$856$		0			0
$857$	37.9377	−	37.9377i	1.29593	−	1.29593i	0.364867	−	0.931060i	$-0.381114\pi$
$857$	37.9377	−	37.9377i	1.29593	−	1.29593i	0.931060	−	0.364867i	$-0.118886\pi$
$858$		0			0
$859$			18.8830i			0.644280i	0.946692	+	0.322140i	$0.104402\pi$
$859$			18.8830i			0.644280i	−0.946692	+	0.322140i	$0.895598\pi$
$860$		0			0
$861$	−1.73318	+	1.73318i	−0.0590668	+	0.0590668i
$862$		0			0
$863$	−5.81345			−0.197892			−0.0989461	−	0.995093i	$-0.531547\pi$
$863$	−5.81345			−0.197892			−0.0989461	+	0.995093i	$0.531547\pi$
$864$		0			0
$865$		−	6.65002i		−	0.226107i
$866$		0			0
$867$	45.0975	−	2.78611i	1.53159	−	0.0946213i
$868$		0			0
$869$		−	26.5817i		−	0.901723i
$870$		0			0
$871$	−12.2567			−0.415303
$872$		0			0
$873$	5.90673	−	5.90673i	0.199912	−	0.199912i
$874$		0			0
$875$			18.9567i			0.640853i
$876$		0			0
$877$	14.2216	−	14.2216i	0.480230	−	0.480230i	−0.424975	−	0.905205i	$-0.639717\pi$
$877$	14.2216	−	14.2216i	0.480230	−	0.480230i	0.905205	+	0.424975i	$0.139717\pi$
$878$		0			0
$879$	−38.3114	−	38.3114i	−1.29221	−	1.29221i
$880$		0			0
$881$	36.0351	+	36.0351i	1.21405	+	1.21405i	0.969682	+	0.244371i	$0.0785814\pi$
$881$	36.0351	+	36.0351i	1.21405	+	1.21405i	0.244371	+	0.969682i	$0.421419\pi$
$882$		0			0
$883$	−12.7082			−0.427665			−0.213833	−	0.976870i	$-0.568595\pi$
$883$	−12.7082			−0.427665			−0.213833	+	0.976870i	$0.568595\pi$
$884$		0			0
$885$	−37.1634			−1.24924
$886$		0			0
$887$	−1.07192	−	1.07192i	−0.0359915	−	0.0359915i	0.688882	−	0.724874i	$-0.258102\pi$
$887$	−1.07192	−	1.07192i	−0.0359915	−	0.0359915i	−0.724874	+	0.688882i	$0.758102\pi$
$888$		0			0
$889$	−25.3601	−	25.3601i	−0.850550	−	0.850550i
$890$		0			0
$891$	18.1361	−	18.1361i	0.607582	−	0.607582i
$892$		0			0
$893$		−	38.0702i		−	1.27397i
$894$		0			0
$895$	7.75877	−	7.75877i	0.259347	−	0.259347i
$896$		0			0
$897$	36.6810			1.22474
$898$		0			0
$899$			23.9263i			0.797988i
$900$		0			0
$901$	−51.2918	+	23.1242i	−1.70878	+	0.770380i
$902$		0			0
$903$		−	7.26083i		−	0.241625i
$904$		0			0
$905$	7.22163			0.240055
$906$		0			0
$907$	6.97266	−	6.97266i	0.231523	−	0.231523i	−0.581805	−	0.813328i	$-0.697653\pi$
$907$	6.97266	−	6.97266i	0.231523	−	0.231523i	0.813328	+	0.581805i	$0.197653\pi$
$908$		0			0
$909$			44.9668i			1.49145i
$910$		0			0
$911$	−5.66725	+	5.66725i	−0.187764	+	0.187764i	−0.794729	−	0.606965i	$-0.792387\pi$
$911$	−5.66725	+	5.66725i	−0.187764	+	0.187764i	0.606965	+	0.794729i	$0.292387\pi$
$912$		0			0
$913$	51.0060	+	51.0060i	1.68805	+	1.68805i
$914$		0			0
$915$	−26.7939	−	26.7939i	−0.885777	−	0.885777i
$916$		0			0
$917$	5.59659			0.184816
$918$		0			0
$919$	−16.6500			−0.549233			−0.274617	−	0.961554i	$-0.588551\pi$
$919$	−16.6500			−0.549233			−0.274617	+	0.961554i	$0.588551\pi$
$920$		0			0
$921$	26.5526	+	26.5526i	0.874939	+	0.874939i
$922$		0			0
$923$	7.88713	+	7.88713i	0.259608	+	0.259608i
$924$		0			0
$925$	7.16756	−	7.16756i	0.235668	−	0.235668i
$926$		0			0
$927$		−	27.5485i		−	0.904812i
$928$		0			0
$929$	30.1634	−	30.1634i	0.989630	−	0.989630i	−0.0103165	−	0.999947i	$-0.503284\pi$
$929$	30.1634	−	30.1634i	0.989630	−	0.989630i	0.999947	+	0.0103165i	$0.00328390\pi$
$930$		0			0
$931$	15.7588			0.516473
$932$		0			0
$933$			26.5817i			0.870246i
$934$		0			0
$935$	−13.1480	−	29.1634i	−0.429984	−	0.953746i
$936$		0			0
$937$		−	41.3310i		−	1.35022i	−0.737715	−	0.675112i	$-0.764095\pi$
$937$		−	41.3310i		−	1.35022i	0.737715	−	0.675112i	$-0.235905\pi$
$938$		0			0
$939$	23.8681			0.778907
$940$		0			0
$941$	9.32501	−	9.32501i	0.303987	−	0.303987i	−0.538585	−	0.842571i	$-0.681041\pi$
$941$	9.32501	−	9.32501i	0.303987	−	0.303987i	0.842571	+	0.538585i	$0.181041\pi$
$942$		0			0
$943$		−	2.47895i		−	0.0807257i
$944$		0			0
$945$	−4.73917	+	4.73917i	−0.154165	+	0.154165i
$946$		0			0
$947$	−7.39693	−	7.39693i	−0.240368	−	0.240368i	0.576634	−	0.817002i	$-0.304366\pi$
$947$	−7.39693	−	7.39693i	−0.240368	−	0.240368i	−0.817002	+	0.576634i	$0.804366\pi$
$948$		0			0
$949$	−19.9709	−	19.9709i	−0.648283	−	0.648283i
$950$		0			0
$951$	80.6383			2.61488
$952$		0			0
$953$	−20.6209			−0.667977			−0.333989	−	0.942577i	$-0.608395\pi$
$953$	−20.6209			−0.667977			−0.333989	+	0.942577i	$0.608395\pi$
$954$		0			0
$955$	19.6851	+	19.6851i	0.636995	+	0.636995i
$956$		0			0
$957$	59.2627	+	59.2627i	1.91569	+	1.91569i
$958$		0			0
$959$	−9.44387	+	9.44387i	−0.304958	+	0.304958i
$960$		0			0
$961$		−	13.6709i		−	0.440996i
$962$		0			0
$963$	−28.5604	+	28.5604i	−0.920345	+	0.920345i
$964$		0			0
$965$	6.25671			0.201411
$966$		0			0
$967$			52.1248i			1.67622i	0.545500	+	0.838111i	$0.316340\pi$
$967$			52.1248i			1.67622i	−0.545500	+	0.838111i	$0.683660\pi$
$968$		0			0
$969$	38.5235	+	14.5817i	1.23755	+	0.468432i
$970$		0			0
$971$			4.43975i			0.142478i	0.997459	+	0.0712392i	$0.0226954\pi$
$971$			4.43975i			0.142478i	−0.997459	+	0.0712392i	$0.977305\pi$
$972$		0			0
$973$	4.14921			0.133018
$974$		0			0
$975$	−17.2763	+	17.2763i	−0.553285	+	0.553285i
$976$		0			0
$977$		−	19.7743i		−	0.632634i	−0.948653	−	0.316317i	$-0.897554\pi$
$977$		−	19.7743i		−	0.632634i	0.948653	−	0.316317i	$-0.102446\pi$
$978$		0			0
$979$	61.9573	−	61.9573i	1.98016	−	1.98016i
$980$		0			0
$981$	−57.0411	−	57.0411i	−1.82118	−	1.82118i
$982$		0			0
$983$	−1.42602	−	1.42602i	−0.0454830	−	0.0454830i	0.683999	−	0.729483i	$-0.260239\pi$
$983$	−1.42602	−	1.42602i	−0.0454830	−	0.0454830i	−0.729483	+	0.683999i	$0.760239\pi$
$984$		0			0
$985$	−13.3500			−0.425366
$986$		0			0
$987$	45.1052			1.43572
$988$		0			0
$989$	5.19253	+	5.19253i	0.165113	+	0.165113i
$990$		0			0
$991$	10.3482	+	10.3482i	0.328722	+	0.328722i	0.852101	−	0.523378i	$-0.175328\pi$
$991$	10.3482	+	10.3482i	0.328722	+	0.328722i	−0.523378	+	0.852101i	$0.675328\pi$
$992$		0			0
$993$	−36.5425	+	36.5425i	−1.15964	+	1.15964i
$994$		0			0
$995$		−	29.8871i		−	0.947486i
$996$		0			0
$997$	−3.74928	+	3.74928i	−0.118741	+	0.118741i	−0.763980	−	0.645240i	$-0.776758\pi$
$997$	−3.74928	+	3.74928i	−0.118741	+	0.118741i	0.645240	+	0.763980i	$0.276758\pi$
$998$		0			0
$999$	9.55674			0.302362

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	544.2.o.h.353.1	yes	6
4.3	odd	2		544.2.o.g.353.3	yes	6
8.3	odd	2		1088.2.o.v.897.1		6
8.5	even	2		1088.2.o.u.897.3		6
17.2	even	8		9248.2.a.bl.1.1		6
17.4	even	4	inner	544.2.o.h.225.1	yes	6
17.15	even	8		9248.2.a.bl.1.6		6
68.15	odd	8		9248.2.a.bm.1.1		6
68.19	odd	8		9248.2.a.bm.1.6		6
68.55	odd	4		544.2.o.g.225.3	✓	6
136.21	even	4		1088.2.o.u.769.3		6
136.123	odd	4		1088.2.o.v.769.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.o.g.225.3	✓	6	68.55	odd	4
544.2.o.g.353.3	yes	6	4.3	odd	2
544.2.o.h.225.1	yes	6	17.4	even	4	inner
544.2.o.h.353.1	yes	6	1.1	even	1	trivial
1088.2.o.u.769.3		6	136.21	even	4
1088.2.o.u.897.3		6	8.5	even	2
1088.2.o.v.769.1		6	136.123	odd	4
1088.2.o.v.897.1		6	8.3	odd	2
9248.2.a.bl.1.1		6	17.2	even	8
9248.2.a.bl.1.6		6	17.15	even	8
9248.2.a.bm.1.1		6	68.15	odd	8
9248.2.a.bm.1.6		6	68.19	odd	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.o (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87939 - 1.87939i) q^{3} +(1.00000 + 1.00000i) q^{5} +(-1.18479 + 1.18479i) q^{7} +4.06418i q^{9} +(3.87939 - 3.87939i) q^{11} +3.06418 q^{13} -3.75877i q^{15} +(-1.69459 - 3.75877i) q^{17} -3.75877i q^{19} +4.45336 q^{21} +(-3.18479 + 3.18479i) q^{23} -3.00000i q^{25} +(2.00000 - 2.00000i) q^{27} +(-4.06418 - 4.06418i) q^{29} +(-2.94356 - 2.94356i) q^{31} -14.5817 q^{33} -2.36959 q^{35} +(2.38919 + 2.38919i) q^{37} +(-5.75877 - 5.75877i) q^{39} +(-0.389185 + 0.389185i) q^{41} -1.63041i q^{43} +(-4.06418 + 4.06418i) q^{45} +10.1284 q^{47} +4.19253i q^{49} +(-3.87939 + 10.2490i) q^{51} -13.6459i q^{53} +7.75877 q^{55} +(-7.06418 + 7.06418i) q^{57} -9.88713i q^{59} +(7.12836 - 7.12836i) q^{61} +(-4.81521 - 4.81521i) q^{63} +(3.06418 + 3.06418i) q^{65} -4.00000 q^{67} +11.9709 q^{69} +(2.57398 + 2.57398i) q^{71} +(-6.51754 - 6.51754i) q^{73} +(-5.63816 + 5.63816i) q^{75} +9.19253i q^{77} +(3.42602 - 3.42602i) q^{79} +4.67499 q^{81} +13.1480i q^{83} +(2.06418 - 5.45336i) q^{85} +15.2763i q^{87} +15.9709 q^{89} +(-3.63041 + 3.63041i) q^{91} +11.0642i q^{93} +(3.75877 - 3.75877i) q^{95} +(-1.45336 - 1.45336i) q^{97} +(15.7665 + 15.7665i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{5} + 12 q^{11} - 6 q^{17} - 12 q^{23} + 12 q^{27} - 6 q^{29} + 12 q^{31} - 24 q^{33} + 6 q^{37} - 12 q^{39} + 6 q^{41} - 6 q^{45} + 24 q^{47} - 12 q^{51} + 24 q^{55} - 24 q^{57} + 6 q^{61} - 36 q^{63}+ \cdots + 24 q^{99}+O(q^{100}) \) 6 * q + 6 * q^5 + 12 * q^11 - 6 * q^17 - 12 * q^23 + 12 * q^27 - 6 * q^29 + 12 * q^31 - 24 * q^33 + 6 * q^37 - 12 * q^39 + 6 * q^41 - 6 * q^45 + 24 * q^47 - 12 * q^51 + 24 * q^55 - 24 * q^57 + 6 * q^61 - 36 * q^63 - 24 * q^67 + 6 * q^73 + 36 * q^79 + 18 * q^81 - 6 * q^85 + 24 * q^89 - 36 * q^91 + 18 * q^97 + 24 * q^99

Introduction

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