LMFDB - Embedded newform 1088.2.o.v.897.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1088,2,Mod(769,1088)] 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("1088.769"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1088, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1088 = 2^{6} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1088.o (of order $4$, degree $2$, not 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:	$8.68772373992$
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:	no (minimal twist has level 544)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			897.1
Root			$-1.87939i$ of defining polynomial
Character	$\chi$	$=$	1088.897
Dual form			1088.2.o.v.769.1

$q$-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 $\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times$.

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

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	0.447214	−	0.894427i	$-0.352416\pi$
$5$	−1.00000	−	1.00000i	−0.447214	−	0.447214i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	1.18479	−	1.18479i	0.447809	−	0.447809i	−0.446816	−	0.894626i	$-0.647442\pi$
$7$	1.18479	−	1.18479i	0.447809	−	0.447809i	0.894626	+	0.446816i	$0.147442\pi$
$8$		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	$-0.639700\pi$
$13$	−3.06418			−0.849850			−0.424925	+	0.905229i	$0.639700\pi$
$14$		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	−0.292263	−	0.956338i	$-0.594408\pi$
$23$	3.18479	−	3.18479i	0.664075	−	0.664075i	0.956338	+	0.292263i	$0.0944082\pi$
$24$		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	0.975352	−	0.220653i	$-0.0708190\pi$
$29$	4.06418	+	4.06418i	0.754699	+	0.754699i	−0.220653	+	0.975352i	$0.570819\pi$
$30$		0			0
$31$	2.94356	+	2.94356i	0.528680	+	0.528680i	0.920179	−	0.391499i	$-0.128043\pi$
$31$	2.94356	+	2.94356i	0.528680	+	0.528680i	−0.391499	+	0.920179i	$0.628043\pi$
$32$		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	0.482897	−	0.875677i	$-0.339584\pi$
$37$	−2.38919	−	2.38919i	−0.392780	−	0.392780i	−0.875677	+	0.482897i	$0.839584\pi$
$38$		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	$-0.764553\pi$
$47$	−10.1284			−1.47737			−0.738686	+	0.674049i	$0.764553\pi$
$48$		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	$0.386595\pi$
$53$			13.6459i			1.87441i	−0.348782	+	0.937204i	$0.613405\pi$
$54$		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	−0.996483	−	0.0837910i	$-0.973297\pi$
$61$	−7.12836	+	7.12836i	−0.912692	+	0.912692i	0.0837910	+	0.996483i	$0.473297\pi$
$62$		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	0.537676	−	0.843151i	$-0.319302\pi$
$71$	−2.57398	−	2.57398i	−0.305475	−	0.305475i	−0.843151	+	0.537676i	$0.819302\pi$
$72$		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	−0.873064	−	0.487606i	$-0.837870\pi$
$79$	−3.42602	+	3.42602i	−0.385458	+	0.385458i	0.487606	+	0.873064i	$0.337870\pi$
$80$		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	$-0.685549\pi$
$101$	−11.0642			−1.10093			−0.550463	+	0.834859i	$0.685549\pi$
$102$		0			0
$103$	6.77837			0.667893			0.333946	−	0.942592i	$-0.391620\pi$
$103$	6.77837			0.667893			0.333946	+	0.942592i	$0.391620\pi$
$104$		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	$-0.350494\pi$
$109$	14.0351	−	14.0351i	1.34432	−	1.34432i	0.891710	−	0.452607i	$-0.149506\pi$
$110$		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	$-0.601410\pi$
$127$		−	21.4047i		−	1.89936i	0.313226	−	0.949679i	$-0.398590\pi$
$128$		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	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$		0			0
$151$		−	10.3696i		−	0.843865i	−0.906627	−	0.421932i	$-0.861352\pi$
$151$		−	10.3696i		−	0.843865i	0.906627	−	0.421932i	$-0.138648\pi$
$152$		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	$-0.468416\pi$
$157$	2.48246			0.198122			0.0990609	+	0.995081i	$0.468416\pi$
$158$		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	0.578891	−	0.815405i	$-0.303486\pi$
$167$	−3.05644	−	3.05644i	−0.236514	−	0.236514i	−0.815405	+	0.578891i	$0.803486\pi$
$168$		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	0.822116	−	0.569320i	$-0.192794\pi$
$173$	3.32501	+	3.32501i	0.252796	+	0.252796i	−0.569320	+	0.822116i	$0.692794\pi$
$174$		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	−0.828451	−	0.560061i	$-0.810778\pi$
$181$	−3.61081	+	3.61081i	−0.268390	+	0.268390i	0.560061	+	0.828451i	$0.310778\pi$
$182$		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	$-0.752293\pi$
$191$	−19.6851			−1.42436			−0.712182	+	0.701995i	$0.752293\pi$
$192$		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	−0.428139	−	0.903713i	$-0.640831\pi$
$197$	6.67499	−	6.67499i	0.475574	−	0.475574i	0.903713	+	0.428139i	$0.140831\pi$
$198$		0			0
$199$	14.9436	+	14.9436i	1.05932	+	1.05932i	0.998126	+	0.0611953i	$0.0194912\pi$
$199$	14.9436	+	14.9436i	1.05932	+	1.05932i	0.0611953	+	0.998126i	$0.480509\pi$
$200$		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	$-0.759224\pi$
$223$		−	20.4979i		−	1.37264i	0.727298	−	0.686322i	$-0.240776\pi$
$224$		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	$-0.544448\pi$
$229$		−	29.9709i		−	1.98053i	0.139184	−	0.990267i	$-0.455552\pi$
$230$		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	$-0.684155\pi$
$239$	−16.9067			−1.09361			−0.546803	+	0.837262i	$0.684155\pi$
$240$		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	$-0.986210\pi$
$263$		−	1.40467i		−	0.0866155i	0.999062	−	0.0433077i	$-0.0137896\pi$
$264$		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	0.877308	−	0.479927i	$-0.159337\pi$
$269$	6.51754	+	6.51754i	0.397381	+	0.397381i	−0.479927	+	0.877308i	$0.659337\pi$
$270$		0			0
$271$	0.906726			0.0550797			0.0275399	−	0.999621i	$-0.491233\pi$
$271$	0.906726			0.0550797			0.0275399	+	0.999621i	$0.491233\pi$
$272$		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	0.238552	−	0.971130i	$-0.423327\pi$
$277$	−12.1925	−	12.1925i	−0.732578	−	0.732578i	−0.971130	+	0.238552i	$0.923327\pi$
$278$		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	$-0.703028\pi$
$293$	−20.3851			−1.19091			−0.595454	+	0.803389i	$0.703028\pi$
$294$		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	0.878589	−	0.477578i	$-0.158485\pi$
$311$	7.07192	+	7.07192i	0.401012	+	0.401012i	−0.477578	+	0.878589i	$0.658485\pi$
$312$		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	$-0.425376\pi$
$317$	21.4534	−	21.4534i	1.20494	−	1.20494i	0.972645	−	0.232296i	$-0.0746237\pi$
$318$		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	$0.168499\pi$
$349$			18.8675i			1.00996i	−0.863132	+	0.504978i	$0.831501\pi$
$350$		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	$0.150314\pi$
$359$			17.2371i			0.909740i	−0.890558	+	0.454870i	$0.849686\pi$
$360$		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	$0.548646\pi$
$367$	−21.8503	+	21.8503i	−1.14058	+	1.14058i	−0.988345	+	0.152231i	$0.951354\pi$
$368$		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	$-0.378271\pi$
$373$	14.4142			0.746337			0.373169	+	0.927764i	$0.378271\pi$
$374$		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	$-0.945851\pi$
$383$		−	6.62630i		−	0.338588i	0.985566	−	0.169294i	$-0.0541487\pi$
$384$		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	$0.109648\pi$
$389$			13.3209i			0.675396i	−0.941255	+	0.337698i	$0.890352\pi$
$390$		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	−0.0248160	−	0.999692i	$-0.507900\pi$
$397$	19.4243	−	19.4243i	0.974876	−	0.974876i	0.999692	+	0.0248160i	$0.00789999\pi$
$398$		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	$-0.316074\pi$
$421$	22.4142			1.09240			0.546200	+	0.837655i	$0.316074\pi$
$422$		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	$-0.415485\pi$
$431$	25.4807	−	25.4807i	1.22736	−	1.22736i	0.964958	−	0.262404i	$-0.0845154\pi$
$432$		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	0.610704	−	0.791859i	$-0.290886\pi$
$439$	−3.79561	−	3.79561i	−0.181154	−	0.181154i	−0.791859	+	0.610704i	$0.790886\pi$
$440$		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	$-0.918558\pi$
$461$		−	10.8675i		−	0.506151i	0.967447	−	0.253076i	$-0.0814421\pi$
$462$		0			0
$463$	−20.0000			−0.929479			−0.464739	−	0.885448i	$-0.653852\pi$
$463$	−20.0000			−0.929479			−0.464739	+	0.885448i	$0.653852\pi$
$464$		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	0.672470	−	0.740125i	$-0.265234\pi$
$479$	−1.48070	−	1.48070i	−0.0676551	−	0.0676551i	−0.740125	+	0.672470i	$0.765234\pi$
$480$		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	−0.592493	−	0.805576i	$-0.701856\pi$
$487$	4.70233	−	4.70233i	0.213083	−	0.213083i	0.805576	+	0.592493i	$0.201856\pi$
$488$		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	−0.697102	−	0.716972i	$-0.745528\pi$
$503$	0.445622	−	0.445622i	0.0198693	−	0.0198693i	0.716972	+	0.697102i	$0.245528\pi$
$504$		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	$-0.862493\pi$
$509$	−40.9769			−1.81627			−0.908134	+	0.418679i	$0.862493\pi$
$510$		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	$-0.961330\pi$
$541$	−25.9067	−	25.9067i	−1.11382	−	1.11382i	−0.121188	−	0.992630i	$-0.538670\pi$
$542$		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	$-0.530680\pi$
$557$	−4.54252			−0.192473			−0.0962363	+	0.995359i	$0.530680\pi$
$558$		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	$-0.455779\pi$
$599$	6.77837			0.276957			0.138478	+	0.990365i	$0.455779\pi$
$600$		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	0.591010	−	0.806664i	$-0.298729\pi$
$607$	−5.31315	−	5.31315i	−0.215654	−	0.215654i	−0.806664	+	0.591010i	$0.798729\pi$
$608$		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	$-0.502849\pi$
$613$	−0.443258			−0.0179030			−0.00895152	+	0.999960i	$0.502849\pi$
$614$		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	$-0.788172\pi$
$631$		−	31.0196i		−	1.23487i	0.786622	−	0.617435i	$-0.211828\pi$
$632$		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	$-0.479024\pi$
$647$	3.34998			0.131701			0.0658507	+	0.997829i	$0.479024\pi$
$648$		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	−0.995341	−	0.0964198i	$-0.969261\pi$
$653$	−22.9709	+	22.9709i	−0.898921	+	0.898921i	0.0964198	+	0.995341i	$0.469261\pi$
$654$		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	$0.0228318\pi$
$661$			3.68510i			0.143334i	−0.997429	+	0.0716668i	$0.977168\pi$
$662$		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	0.922233	−	0.386635i	$-0.126363\pi$
$677$	13.9358	+	13.9358i	0.535597	+	0.535597i	−0.386635	+	0.922233i	$0.626363\pi$
$678$		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	$-0.331982\pi$
$701$	26.6709			1.00734			0.503672	+	0.863895i	$0.331982\pi$
$702$		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	0.136437	−	0.990649i	$-0.456435\pi$
$709$	−22.7452	−	22.7452i	−0.854212	−	0.854212i	−0.990649	+	0.136437i	$0.956435\pi$
$710$		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	0.361347	−	0.932431i	$-0.382317\pi$
$719$	−15.3131	−	15.3131i	−0.571084	−	0.571084i	−0.932431	+	0.361347i	$0.882317\pi$
$720$		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	$-0.599913\pi$
$727$	−16.6500			−0.617515			−0.308757	+	0.951141i	$0.599913\pi$
$728$		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	$-0.987024\pi$
$733$		−	2.20676i		−	0.0815084i	0.999169	−	0.0407542i	$-0.0129761\pi$
$734$		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	$0.0400226\pi$
$743$	30.4611	+	30.4611i	1.11751	+	1.11751i	0.125404	+	0.992106i	$0.459977\pi$
$744$		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	0.876342	−	0.481689i	$-0.159977\pi$
$751$	10.8152	+	10.8152i	0.394653	+	0.394653i	−0.481689	+	0.876342i	$0.659977\pi$
$752$		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	$0.117426\pi$
$757$			19.8425i			0.721190i	−0.932723	+	0.360595i	$0.882574\pi$
$758$		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	$-0.649590\pi$
$773$		−	49.5776i		−	1.78318i	0.452841	−	0.891591i	$-0.350410\pi$
$774$		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	$0.105572\pi$
$797$			18.3851i			0.651232i	−0.945502	+	0.325616i	$0.894428\pi$
$798$		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	0.568445	−	0.822721i	$-0.307545\pi$
$821$	−7.28581	−	7.28581i	−0.254276	−	0.254276i	−0.822721	+	0.568445i	$0.807545\pi$
$822$		0			0
$823$	16.3482	−	16.3482i	0.569863	−	0.569863i	−0.362227	−	0.932090i	$-0.617983\pi$
$823$	16.3482	−	16.3482i	0.569863	−	0.569863i	0.932090	+	0.362227i	$0.117983\pi$
$824$		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	$-0.616170\pi$
$829$	−20.5526			−0.713822			−0.356911	+	0.934138i	$0.616170\pi$
$830$		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	−0.702291	−	0.711890i	$-0.747839\pi$
$839$	0.278066	−	0.278066i	0.00959991	−	0.00959991i	0.711890	+	0.702291i	$0.247839\pi$
$840$		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	0.582958	−	0.812502i	$-0.301895\pi$
$853$	−6.70409	−	6.70409i	−0.229544	−	0.229544i	−0.812502	+	0.582958i	$0.801895\pi$
$854$		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	$-0.468453\pi$
$863$	5.81345			0.197892			0.0989461	+	0.995093i	$0.468453\pi$
$864$		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	−0.905205	−	0.424975i	$-0.860283\pi$
$877$	−14.2216	+	14.2216i	−0.480230	+	0.480230i	0.424975	+	0.905205i	$0.360283\pi$
$878$		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	0.724874	−	0.688882i	$-0.241898\pi$
$887$	1.07192	+	1.07192i	0.0359915	+	0.0359915i	−0.688882	+	0.724874i	$0.741898\pi$
$888$		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	−0.606965	−	0.794729i	$-0.707613\pi$
$911$	5.66725	−	5.66725i	0.187764	−	0.187764i	0.794729	+	0.606965i	$0.207613\pi$
$912$		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	$-0.411449\pi$
$919$	16.6500			0.549233			0.274617	+	0.961554i	$0.411449\pi$
$920$		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	−0.842571	−	0.538585i	$-0.818959\pi$
$941$	−9.32501	+	9.32501i	−0.303987	+	0.303987i	0.538585	+	0.842571i	$0.318959\pi$
$942$		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	$-0.683660\pi$
$967$		−	52.1248i		−	1.67622i	0.545500	−	0.838111i	$-0.316340\pi$
$968$		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	0.729483	−	0.683999i	$-0.239761\pi$
$983$	1.42602	+	1.42602i	0.0454830	+	0.0454830i	−0.683999	+	0.729483i	$0.739761\pi$
$984$		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	0.523378	−	0.852101i	$-0.324672\pi$
$991$	−10.3482	−	10.3482i	−0.328722	−	0.328722i	−0.852101	+	0.523378i	$0.824672\pi$
$992$		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	−0.645240	−	0.763980i	$-0.723242\pi$
$997$	3.74928	−	3.74928i	0.118741	−	0.118741i	0.763980	+	0.645240i	$0.223242\pi$
$998$		0			0
$999$	−9.55674			−0.302362

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
544.2.o.g.225.3	✓	6	136.21	even	4
544.2.o.g.353.3	yes	6	8.5	even	2
544.2.o.h.225.1	yes	6	136.123	odd	4
544.2.o.h.353.1	yes	6	8.3	odd	2
1088.2.o.u.769.3		6	68.55	odd	4
1088.2.o.u.897.3		6	4.3	odd	2
1088.2.o.v.769.1		6	17.4	even	4	inner
1088.2.o.v.897.1		6	1.1	even	1	trivial
9248.2.a.bl.1.1		6	136.19	odd	8
9248.2.a.bl.1.6		6	136.83	odd	8
9248.2.a.bm.1.1		6	136.117	even	8
9248.2.a.bm.1.6		6	136.53	even	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:	\( N \)	\(=\)	\( 1088 = 2^{6} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1088.o (of order \(4\), degree \(2\), not 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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