LMFDB - Embedded newform 1014.3.f.a.775.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			775.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.a.577.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-0.732051 + 0.732051i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +2.53590i q^{10} +(1.73205 - 1.73205i) q^{11} +3.46410i q^{12} +1.46410 q^{14} +(-2.19615 - 2.19615i) q^{15} -4.00000 q^{16} +5.32051i q^{17} +(-3.00000 - 3.00000i) q^{18} +(14.7321 + 14.7321i) q^{19} +(2.53590 - 2.53590i) q^{20} +(-1.26795 + 1.26795i) q^{21} -3.46410 q^{22} +5.32051i q^{23} +(3.46410 - 3.46410i) q^{24} -21.7846i q^{25} +5.19615 q^{27} +(-1.46410 - 1.46410i) q^{28} +4.14359 q^{29} +4.39230i q^{30} +(24.9808 + 24.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(3.00000 - 3.00000i) q^{33} +(5.32051 - 5.32051i) q^{34} +1.85641 q^{35} +6.00000i q^{36} +(3.14359 - 3.14359i) q^{37} -29.4641i q^{38} -5.07180 q^{40} +(-44.4449 - 44.4449i) q^{41} +2.53590 q^{42} +37.1769i q^{43} +(3.46410 + 3.46410i) q^{44} +(-3.80385 - 3.80385i) q^{45} +(5.32051 - 5.32051i) q^{46} +(30.8038 - 30.8038i) q^{47} -6.92820 q^{48} +47.9282i q^{49} +(-21.7846 + 21.7846i) q^{50} +9.21539i q^{51} +57.7128 q^{53} +(-5.19615 - 5.19615i) q^{54} -4.39230 q^{55} +2.92820i q^{56} +(25.5167 + 25.5167i) q^{57} +(-4.14359 - 4.14359i) q^{58} +(66.6218 - 66.6218i) q^{59} +(4.39230 - 4.39230i) q^{60} +103.426 q^{61} -49.9615i q^{62} +(-2.19615 + 2.19615i) q^{63} -8.00000i q^{64} -6.00000 q^{66} +(-46.6936 - 46.6936i) q^{67} -10.6410 q^{68} +9.21539i q^{69} +(-1.85641 - 1.85641i) q^{70} +(26.9090 + 26.9090i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-5.67949 + 5.67949i) q^{73} -6.28719 q^{74} -37.7321i q^{75} +(-29.4641 + 29.4641i) q^{76} +2.53590i q^{77} +4.21024 q^{79} +(5.07180 + 5.07180i) q^{80} +9.00000 q^{81} +88.8897i q^{82} +(109.799 + 109.799i) q^{83} +(-2.53590 - 2.53590i) q^{84} +(6.74613 - 6.74613i) q^{85} +(37.1769 - 37.1769i) q^{86} +7.17691 q^{87} -6.92820i q^{88} +(19.5167 - 19.5167i) q^{89} +7.60770i q^{90} -10.6410 q^{92} +(43.2679 + 43.2679i) q^{93} -61.6077 q^{94} -37.3590i q^{95} +(6.92820 + 6.92820i) q^{96} +(-4.03332 - 4.03332i) q^{97} +(47.9282 - 47.9282i) q^{98} +(5.19615 - 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} + 4 q^{7} + 8 q^{8} + 12 q^{9} - 8 q^{14} + 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} + 24 q^{20} - 12 q^{21} + 8 q^{28} + 72 q^{29} - 4 q^{31} + 16 q^{32} + 12 q^{33} - 48 q^{34}+ \cdots + 164 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 + 4 * q^7 + 8 * q^8 + 12 * q^9 - 8 * q^14 + 12 * q^15 - 16 * q^16 - 12 * q^18 + 52 * q^19 + 24 * q^20 - 12 * q^21 + 8 * q^28 + 72 * q^29 - 4 * q^31 + 16 * q^32 + 12 * q^33 - 48 * q^34 - 48 * q^35 + 68 * q^37 - 48 * q^40 - 60 * q^41 + 24 * q^42 - 36 * q^45 - 48 * q^46 + 144 * q^47 - 4 * q^50 + 120 * q^53 + 24 * q^55 + 12 * q^57 - 72 * q^58 + 24 * q^59 - 24 * q^60 + 192 * q^61 + 12 * q^63 - 24 * q^66 + 28 * q^67 + 96 * q^68 + 48 * q^70 - 24 * q^71 + 24 * q^72 - 92 * q^73 - 136 * q^74 - 104 * q^76 - 288 * q^79 + 48 * q^80 + 36 * q^81 + 72 * q^83 - 24 * q^84 - 264 * q^85 + 24 * q^86 - 96 * q^87 - 12 * q^89 + 96 * q^92 + 180 * q^93 - 288 * q^94 + 164 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	1.73205			0.577350
$3$	1.73205			0.577350
$4$			2.00000i			0.500000i
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	0.568851	−	0.822441i	$-0.307388\pi$
$5$	−1.26795	−	1.26795i	−0.253590	−	0.253590i	−0.822441	+	0.568851i	$0.807388\pi$
$6$	−1.73205	−	1.73205i	−0.288675	−	0.288675i
$7$	−0.732051	+	0.732051i	−0.104579	+	0.104579i	−0.757460	−	0.652881i	$-0.773560\pi$
$7$	−0.732051	+	0.732051i	−0.104579	+	0.104579i	0.652881	+	0.757460i	$0.273560\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$			2.53590i			0.253590i
$11$	1.73205	−	1.73205i	0.157459	−	0.157459i	−0.623981	−	0.781440i	$-0.714486\pi$
$11$	1.73205	−	1.73205i	0.157459	−	0.157459i	0.781440	+	0.623981i	$0.214486\pi$
$12$			3.46410i			0.288675i
$13$		0			0
$13$		0			0
$14$	1.46410			0.104579
$15$	−2.19615	−	2.19615i	−0.146410	−	0.146410i
$16$	−4.00000			−0.250000
$17$			5.32051i			0.312971i	0.987680	+	0.156486i	$0.0500165\pi$
$17$			5.32051i			0.312971i	−0.987680	+	0.156486i	$0.949984\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	14.7321	+	14.7321i	0.775371	+	0.775371i	0.979040	−	0.203669i	$-0.0652866\pi$
$19$	14.7321	+	14.7321i	0.775371	+	0.775371i	−0.203669	+	0.979040i	$0.565287\pi$
$20$	2.53590	−	2.53590i	0.126795	−	0.126795i
$21$	−1.26795	+	1.26795i	−0.0603785	+	0.0603785i
$22$	−3.46410			−0.157459
$23$			5.32051i			0.231326i	0.993288	+	0.115663i	$0.0368993\pi$
$23$			5.32051i			0.231326i	−0.993288	+	0.115663i	$0.963101\pi$
$24$	3.46410	−	3.46410i	0.144338	−	0.144338i
$25$		−	21.7846i		−	0.871384i
$26$		0			0
$27$	5.19615			0.192450
$28$	−1.46410	−	1.46410i	−0.0522893	−	0.0522893i
$29$	4.14359			0.142883			0.0714413	−	0.997445i	$-0.477240\pi$
$29$	4.14359			0.142883			0.0714413	+	0.997445i	$0.477240\pi$
$30$			4.39230i			0.146410i
$31$	24.9808	+	24.9808i	0.805831	+	0.805831i	0.984000	−	0.178169i	$-0.0570173\pi$
$31$	24.9808	+	24.9808i	0.805831	+	0.805831i	−0.178169	+	0.984000i	$0.557017\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	3.00000	−	3.00000i	0.0909091	−	0.0909091i
$34$	5.32051	−	5.32051i	0.156486	−	0.156486i
$35$	1.85641			0.0530402
$36$			6.00000i			0.166667i
$37$	3.14359	−	3.14359i	0.0849620	−	0.0849620i	−0.663349	−	0.748311i	$-0.730865\pi$
$37$	3.14359	−	3.14359i	0.0849620	−	0.0849620i	0.748311	+	0.663349i	$0.230865\pi$
$38$		−	29.4641i		−	0.775371i
$39$		0			0
$40$	−5.07180			−0.126795
$41$	−44.4449	−	44.4449i	−1.08402	−	1.08402i	−0.996130	−	0.0878910i	$-0.971987\pi$
$41$	−44.4449	−	44.4449i	−1.08402	−	1.08402i	−0.0878910	−	0.996130i	$-0.528013\pi$
$42$	2.53590			0.0603785
$43$			37.1769i			0.864579i	0.901735	+	0.432290i	$0.142294\pi$
$43$			37.1769i			0.864579i	−0.901735	+	0.432290i	$0.857706\pi$
$44$	3.46410	+	3.46410i	0.0787296	+	0.0787296i
$45$	−3.80385	−	3.80385i	−0.0845299	−	0.0845299i
$46$	5.32051	−	5.32051i	0.115663	−	0.115663i
$47$	30.8038	−	30.8038i	0.655401	−	0.655401i	−0.298887	−	0.954288i	$-0.596615\pi$
$47$	30.8038	−	30.8038i	0.655401	−	0.655401i	0.954288	+	0.298887i	$0.0966155\pi$
$48$	−6.92820			−0.144338
$49$			47.9282i			0.978127i
$50$	−21.7846	+	21.7846i	−0.435692	+	0.435692i
$51$			9.21539i			0.180694i
$52$		0			0
$53$	57.7128			1.08892			0.544460	−	0.838786i	$-0.316734\pi$
$53$	57.7128			1.08892			0.544460	+	0.838786i	$0.316734\pi$
$54$	−5.19615	−	5.19615i	−0.0962250	−	0.0962250i
$55$	−4.39230			−0.0798601
$56$			2.92820i			0.0522893i
$57$	25.5167	+	25.5167i	0.447661	+	0.447661i
$58$	−4.14359	−	4.14359i	−0.0714413	−	0.0714413i
$59$	66.6218	−	66.6218i	1.12918	−	1.12918i	0.138872	−	0.990310i	$-0.455652\pi$
$59$	66.6218	−	66.6218i	1.12918	−	1.12918i	0.990310	−	0.138872i	$-0.0443478\pi$
$60$	4.39230	−	4.39230i	0.0732051	−	0.0732051i
$61$	103.426			1.69550			0.847751	−	0.530394i	$-0.177956\pi$
$61$	103.426			1.69550			0.847751	+	0.530394i	$0.177956\pi$
$62$		−	49.9615i		−	0.805831i
$63$	−2.19615	+	2.19615i	−0.0348596	+	0.0348596i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−6.00000			−0.0909091
$67$	−46.6936	−	46.6936i	−0.696919	−	0.696919i	0.266826	−	0.963745i	$-0.414025\pi$
$67$	−46.6936	−	46.6936i	−0.696919	−	0.696919i	−0.963745	+	0.266826i	$0.914025\pi$
$68$	−10.6410			−0.156486
$69$			9.21539i			0.133556i
$70$	−1.85641	−	1.85641i	−0.0265201	−	0.0265201i
$71$	26.9090	+	26.9090i	0.379000	+	0.379000i	0.870741	−	0.491742i	$-0.163640\pi$
$71$	26.9090	+	26.9090i	0.379000	+	0.379000i	−0.491742	+	0.870741i	$0.663640\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−5.67949	+	5.67949i	−0.0778013	+	0.0778013i	−0.744937	−	0.667135i	$-0.767520\pi$
$73$	−5.67949	+	5.67949i	−0.0778013	+	0.0778013i	0.667135	+	0.744937i	$0.267520\pi$
$74$	−6.28719			−0.0849620
$75$		−	37.7321i		−	0.503094i
$76$	−29.4641	+	29.4641i	−0.387686	+	0.387686i
$77$			2.53590i			0.0329337i
$78$		0			0
$79$	4.21024			0.0532941			0.0266471	−	0.999645i	$-0.491517\pi$
$79$	4.21024			0.0532941			0.0266471	+	0.999645i	$0.491517\pi$
$80$	5.07180	+	5.07180i	0.0633975	+	0.0633975i
$81$	9.00000			0.111111
$82$			88.8897i			1.08402i
$83$	109.799	+	109.799i	1.32288	+	1.32288i	0.911438	+	0.411438i	$0.134973\pi$
$83$	109.799	+	109.799i	1.32288	+	1.32288i	0.411438	+	0.911438i	$0.365027\pi$
$84$	−2.53590	−	2.53590i	−0.0301893	−	0.0301893i
$85$	6.74613	−	6.74613i	0.0793663	−	0.0793663i
$86$	37.1769	−	37.1769i	0.432290	−	0.432290i
$87$	7.17691			0.0824933
$88$		−	6.92820i		−	0.0787296i
$89$	19.5167	−	19.5167i	0.219288	−	0.219288i	−0.588910	−	0.808198i	$-0.700443\pi$
$89$	19.5167	−	19.5167i	0.219288	−	0.219288i	0.808198	+	0.588910i	$0.200443\pi$
$90$			7.60770i			0.0845299i
$91$		0			0
$92$	−10.6410			−0.115663
$93$	43.2679	+	43.2679i	0.465247	+	0.465247i
$94$	−61.6077			−0.655401
$95$		−	37.3590i		−	0.393252i
$96$	6.92820	+	6.92820i	0.0721688	+	0.0721688i
$97$	−4.03332	−	4.03332i	−0.0415806	−	0.0415806i	0.686011	−	0.727591i	$-0.259360\pi$
$97$	−4.03332	−	4.03332i	−0.0415806	−	0.0415806i	−0.727591	+	0.686011i	$0.759360\pi$
$98$	47.9282	−	47.9282i	0.489063	−	0.489063i
$99$	5.19615	−	5.19615i	0.0524864	−	0.0524864i
$100$	43.5692			0.435692
$101$		−	111.464i		−	1.10360i	−0.833975	−	0.551802i	$-0.813940\pi$
$101$		−	111.464i		−	1.10360i	0.833975	−	0.551802i	$-0.186060\pi$
$102$	9.21539	−	9.21539i	0.0903470	−	0.0903470i
$103$		−	71.3205i		−	0.692432i	−0.938155	−	0.346216i	$-0.887466\pi$
$103$		−	71.3205i		−	0.692432i	0.938155	−	0.346216i	$-0.112534\pi$
$104$		0			0
$105$	3.21539			0.0306228
$106$	−57.7128	−	57.7128i	−0.544460	−	0.544460i
$107$	−116.536			−1.08912			−0.544560	−	0.838722i	$-0.683303\pi$
$107$	−116.536			−1.08912			−0.544560	+	0.838722i	$0.683303\pi$
$108$			10.3923i			0.0962250i
$109$	109.315	+	109.315i	1.00289	+	1.00289i	0.999996	+	0.00289735i	$0.000922255\pi$
$109$	109.315	+	109.315i	1.00289	+	1.00289i	0.00289735	+	0.999996i	$0.499078\pi$
$110$	4.39230	+	4.39230i	0.0399300	+	0.0399300i
$111$	5.44486	−	5.44486i	0.0490528	−	0.0490528i
$112$	2.92820	−	2.92820i	0.0261447	−	0.0261447i
$113$	148.277			1.31218			0.656092	−	0.754681i	$-0.272208\pi$
$113$	148.277			1.31218			0.656092	+	0.754681i	$0.272208\pi$
$114$		−	51.0333i		−	0.447661i
$115$	6.74613	−	6.74613i	0.0586620	−	0.0586620i
$116$			8.28719i			0.0714413i
$117$		0			0
$118$	−133.244			−1.12918
$119$	−3.89488	−	3.89488i	−0.0327301	−	0.0327301i
$120$	−8.78461			−0.0732051
$121$			115.000i			0.950413i
$122$	−103.426	−	103.426i	−0.847751	−	0.847751i
$123$	−76.9808	−	76.9808i	−0.625860	−	0.625860i
$124$	−49.9615	+	49.9615i	−0.402916	+	0.402916i
$125$	−59.3205	+	59.3205i	−0.474564	+	0.474564i
$126$	4.39230			0.0348596
$127$			70.0385i			0.551484i	0.961232	+	0.275742i	$0.0889236\pi$
$127$			70.0385i			0.551484i	−0.961232	+	0.275742i	$0.911076\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			64.3923i			0.499165i
$130$		0			0
$131$	238.890			1.82359			0.911793	−	0.410650i	$-0.134698\pi$
$131$	238.890			1.82359			0.911793	+	0.410650i	$0.134698\pi$
$132$	6.00000	+	6.00000i	0.0454545	+	0.0454545i
$133$	−21.5692			−0.162175
$134$			93.3872i			0.696919i
$135$	−6.58846	−	6.58846i	−0.0488034	−	0.0488034i
$136$	10.6410	+	10.6410i	0.0782428	+	0.0782428i
$137$	91.9474	−	91.9474i	0.671149	−	0.671149i	−0.286832	−	0.957981i	$-0.592602\pi$
$137$	91.9474	−	91.9474i	0.671149	−	0.671149i	0.957981	+	0.286832i	$0.0926021\pi$
$138$	9.21539	−	9.21539i	0.0667782	−	0.0667782i
$139$	139.138			1.00100			0.500498	−	0.865738i	$-0.333150\pi$
$139$	139.138			1.00100			0.500498	+	0.865738i	$0.333150\pi$
$140$			3.71281i			0.0265201i
$141$	53.3538	−	53.3538i	0.378396	−	0.378396i
$142$		−	53.8179i		−	0.379000i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	−5.25387	−	5.25387i	−0.0362336	−	0.0362336i
$146$	11.3590			0.0778013
$147$			83.0141i			0.564722i
$148$	6.28719	+	6.28719i	0.0424810	+	0.0424810i
$149$	−126.224	−	126.224i	−0.847143	−	0.847143i	0.142633	−	0.989776i	$-0.454443\pi$
$149$	−126.224	−	126.224i	−0.847143	−	0.847143i	−0.989776	+	0.142633i	$0.954443\pi$
$150$	−37.7321	+	37.7321i	−0.251547	+	0.251547i
$151$	−124.406	+	124.406i	−0.823883	+	0.823883i	−0.986663	−	0.162779i	$-0.947954\pi$
$151$	−124.406	+	124.406i	−0.823883	+	0.823883i	0.162779	+	0.986663i	$0.447954\pi$
$152$	58.9282			0.387686
$153$			15.9615i			0.104324i
$154$	2.53590	−	2.53590i	0.0164669	−	0.0164669i
$155$		−	63.3487i		−	0.408701i
$156$		0			0
$157$	−268.785			−1.71200			−0.856002	−	0.516973i	$-0.827059\pi$
$157$	−268.785			−1.71200			−0.856002	+	0.516973i	$0.827059\pi$
$158$	−4.21024	−	4.21024i	−0.0266471	−	0.0266471i
$159$	99.9615			0.628689
$160$		−	10.1436i		−	0.0633975i
$161$	−3.89488	−	3.89488i	−0.0241918	−	0.0241918i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	46.4449	−	46.4449i	0.284938	−	0.284938i	−0.550137	−	0.835075i	$-0.685424\pi$
$163$	46.4449	−	46.4449i	0.284938	−	0.284938i	0.835075	+	0.550137i	$0.185424\pi$
$164$	88.8897	−	88.8897i	0.542011	−	0.542011i
$165$	−7.60770			−0.0461072
$166$		−	219.597i		−	1.32288i
$167$	119.512	−	119.512i	0.715638	−	0.715638i	−0.252071	−	0.967709i	$-0.581112\pi$
$167$	119.512	−	119.512i	0.715638	−	0.715638i	0.967709	+	0.252071i	$0.0811116\pi$
$168$			5.07180i			0.0301893i
$169$		0			0
$170$	−13.4923			−0.0793663
$171$	44.1962	+	44.1962i	0.258457	+	0.258457i
$172$	−74.3538			−0.432290
$173$		−	242.603i		−	1.40233i	−0.713001	−	0.701163i	$-0.752664\pi$
$173$		−	242.603i		−	1.40233i	0.713001	−	0.701163i	$-0.247336\pi$
$174$	−7.17691	−	7.17691i	−0.0412466	−	0.0412466i
$175$	15.9474	+	15.9474i	0.0911282	+	0.0911282i
$176$	−6.92820	+	6.92820i	−0.0393648	+	0.0393648i
$177$	115.392	−	115.392i	0.651934	−	0.651934i
$178$	−39.0333			−0.219288
$179$			26.7180i			0.149262i	0.997211	+	0.0746312i	$0.0237780\pi$
$179$			26.7180i			0.149262i	−0.997211	+	0.0746312i	$0.976222\pi$
$180$	7.60770	−	7.60770i	0.0422650	−	0.0422650i
$181$		−	256.144i		−	1.41516i	−0.706634	−	0.707579i	$-0.749787\pi$
$181$		−	256.144i		−	1.41516i	0.706634	−	0.707579i	$-0.250213\pi$
$182$		0			0
$183$	179.138			0.978899
$184$	10.6410	+	10.6410i	0.0578316	+	0.0578316i
$185$	−7.97183			−0.0430910
$186$		−	86.5359i		−	0.465247i
$187$	9.21539	+	9.21539i	0.0492802	+	0.0492802i
$188$	61.6077	+	61.6077i	0.327701	+	0.327701i
$189$	−3.80385	+	3.80385i	−0.0201262	+	0.0201262i
$190$	−37.3590	+	37.3590i	−0.196626	+	0.196626i
$191$	−129.282			−0.676869			−0.338435	−	0.940990i	$-0.609897\pi$
$191$	−129.282			−0.676869			−0.338435	+	0.940990i	$0.609897\pi$
$192$		−	13.8564i		−	0.0721688i
$193$	160.282	−	160.282i	0.830477	−	0.830477i	−0.157105	−	0.987582i	$-0.550216\pi$
$193$	160.282	−	160.282i	0.830477	−	0.830477i	0.987582	+	0.157105i	$0.0502161\pi$
$194$			8.06664i			0.0415806i
$195$		0			0
$196$	−95.8564			−0.489063
$197$	109.268	+	109.268i	0.554660	+	0.554660i	0.927782	−	0.373122i	$-0.121713\pi$
$197$	109.268	+	109.268i	0.554660	+	0.554660i	−0.373122	+	0.927782i	$0.621713\pi$
$198$	−10.3923			−0.0524864
$199$		−	25.1000i		−	0.126130i	−0.998009	−	0.0630652i	$-0.979912\pi$
$199$		−	25.1000i		−	0.126130i	0.998009	−	0.0630652i	$-0.0200876\pi$
$200$	−43.5692	−	43.5692i	−0.217846	−	0.217846i
$201$	−80.8756	−	80.8756i	−0.402366	−	0.402366i
$202$	−111.464	+	111.464i	−0.551802	+	0.551802i
$203$	−3.03332	+	3.03332i	−0.0149425	+	0.0149425i
$204$	−18.4308			−0.0903470
$205$			112.708i			0.549793i
$206$	−71.3205	+	71.3205i	−0.346216	+	0.346216i
$207$			15.9615i			0.0771088i
$208$		0			0
$209$	51.0333			0.244179
$210$	−3.21539	−	3.21539i	−0.0153114	−	0.0153114i
$211$	206.718			0.979706			0.489853	−	0.871805i	$-0.337050\pi$
$211$	206.718			0.979706			0.489853	+	0.871805i	$0.337050\pi$
$212$			115.426i			0.544460i
$213$	46.6077	+	46.6077i	0.218815	+	0.218815i
$214$	116.536	+	116.536i	0.544560	+	0.544560i
$215$	47.1384	−	47.1384i	0.219249	−	0.219249i
$216$	10.3923	−	10.3923i	0.0481125	−	0.0481125i
$217$	−36.5744			−0.168546
$218$		−	218.631i		−	1.00289i
$219$	−9.83717	+	9.83717i	−0.0449186	+	0.0449186i
$220$		−	8.78461i		−	0.0399300i
$221$		0			0
$222$	−10.8897			−0.0490528
$223$	−139.412	−	139.412i	−0.625164	−	0.625164i	0.321683	−	0.946847i	$-0.395751\pi$
$223$	−139.412	−	139.412i	−0.625164	−	0.625164i	−0.946847	+	0.321683i	$0.895751\pi$
$224$	−5.85641			−0.0261447
$225$		−	65.3538i		−	0.290461i
$226$	−148.277	−	148.277i	−0.656092	−	0.656092i
$227$	97.3679	+	97.3679i	0.428934	+	0.428934i	0.888265	−	0.459331i	$-0.151911\pi$
$227$	97.3679	+	97.3679i	0.428934	+	0.428934i	−0.459331	+	0.888265i	$0.651911\pi$
$228$	−51.0333	+	51.0333i	−0.223830	+	0.223830i
$229$	−204.177	+	204.177i	−0.891602	+	0.891602i	−0.994674	−	0.103072i	$-0.967133\pi$
$229$	−204.177	+	204.177i	−0.891602	+	0.891602i	0.103072	+	0.994674i	$0.467133\pi$
$230$	−13.4923			−0.0586620
$231$			4.39230i			0.0190143i
$232$	8.28719	−	8.28719i	0.0357206	−	0.0357206i
$233$			231.962i			0.995543i	0.867308	+	0.497772i	$0.165848\pi$
$233$			231.962i			0.995543i	−0.867308	+	0.497772i	$0.834152\pi$
$234$		0			0
$235$	−78.1154			−0.332406
$236$	133.244	+	133.244i	0.564591	+	0.564591i
$237$	7.29234			0.0307694
$238$			7.78976i			0.0327301i
$239$	−139.981	−	139.981i	−0.585694	−	0.585694i	0.350769	−	0.936462i	$-0.385920\pi$
$239$	−139.981	−	139.981i	−0.585694	−	0.585694i	−0.936462	+	0.350769i	$0.885920\pi$
$240$	8.78461	+	8.78461i	0.0366025	+	0.0366025i
$241$	−53.4589	+	53.4589i	−0.221821	+	0.221821i	−0.809265	−	0.587444i	$-0.800134\pi$
$241$	−53.4589	+	53.4589i	−0.221821	+	0.221821i	0.587444	+	0.809265i	$0.300134\pi$
$242$	115.000	−	115.000i	0.475207	−	0.475207i
$243$	15.5885			0.0641500
$244$			206.851i			0.847751i
$245$	60.7705	−	60.7705i	0.248043	−	0.248043i
$246$			153.962i			0.625860i
$247$		0			0
$248$	99.9230			0.402916
$249$	190.177	+	190.177i	0.763763	+	0.763763i
$250$	118.641			0.474564
$251$		−	421.377i		−	1.67879i	−0.543520	−	0.839396i	$-0.682909\pi$
$251$		−	421.377i		−	1.67879i	0.543520	−	0.839396i	$-0.317091\pi$
$252$	−4.39230	−	4.39230i	−0.0174298	−	0.0174298i
$253$	9.21539	+	9.21539i	0.0364245	+	0.0364245i
$254$	70.0385	−	70.0385i	0.275742	−	0.275742i
$255$	11.6846	−	11.6846i	0.0458221	−	0.0458221i
$256$	16.0000			0.0625000
$257$			249.664i			0.971455i	0.874110	+	0.485728i	$0.161445\pi$
$257$			249.664i			0.971455i	−0.874110	+	0.485728i	$0.838555\pi$
$258$	64.3923	−	64.3923i	0.249583	−	0.249583i
$259$			4.60254i			0.0177704i
$260$		0			0
$261$	12.4308			0.0476275
$262$	−238.890	−	238.890i	−0.911793	−	0.911793i
$263$	−94.8897			−0.360797			−0.180399	−	0.983594i	$-0.557739\pi$
$263$	−94.8897			−0.360797			−0.180399	+	0.983594i	$0.557739\pi$
$264$		−	12.0000i		−	0.0454545i
$265$	−73.1769	−	73.1769i	−0.276139	−	0.276139i
$266$	21.5692	+	21.5692i	0.0810873	+	0.0810873i
$267$	33.8038	−	33.8038i	0.126606	−	0.126606i
$268$	93.3872	−	93.3872i	0.348460	−	0.348460i
$269$	−208.774			−0.776113			−0.388056	−	0.921636i	$-0.626853\pi$
$269$	−208.774			−0.776113			−0.388056	+	0.921636i	$0.626853\pi$
$270$			13.1769i			0.0488034i
$271$	−381.047	+	381.047i	−1.40608	+	1.40608i	−0.627307	+	0.778772i	$0.715843\pi$
$271$	−381.047	+	381.047i	−1.40608	+	1.40608i	−0.778772	+	0.627307i	$0.784157\pi$
$272$		−	21.2820i		−	0.0782428i
$273$		0			0
$274$	−183.895			−0.671149
$275$	−37.7321	−	37.7321i	−0.137207	−	0.137207i
$276$	−18.4308			−0.0667782
$277$			68.7846i			0.248320i	0.992262	+	0.124160i	$0.0396236\pi$
$277$			68.7846i			0.248320i	−0.992262	+	0.124160i	$0.960376\pi$
$278$	−139.138	−	139.138i	−0.500498	−	0.500498i
$279$	74.9423	+	74.9423i	0.268610	+	0.268610i
$280$	3.71281	−	3.71281i	0.0132600	−	0.0132600i
$281$	−69.6218	+	69.6218i	−0.247764	+	0.247764i	−0.820053	−	0.572288i	$-0.806056\pi$
$281$	−69.6218	+	69.6218i	−0.247764	+	0.247764i	0.572288	+	0.820053i	$0.306056\pi$
$282$	−106.708			−0.378396
$283$			425.808i			1.50462i	0.658809	+	0.752310i	$0.271061\pi$
$283$			425.808i			1.50462i	−0.658809	+	0.752310i	$0.728939\pi$
$284$	−53.8179	+	53.8179i	−0.189500	+	0.189500i
$285$		−	64.7077i		−	0.227044i
$286$		0			0
$287$	65.0718			0.226731
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	260.692			0.902049
$290$			10.5077i			0.0362336i
$291$	−6.98592	−	6.98592i	−0.0240066	−	0.0240066i
$292$	−11.3590	−	11.3590i	−0.0389006	−	0.0389006i
$293$	−306.042	+	306.042i	−1.04451	+	1.04451i	−0.0455508	+	0.998962i	$0.514504\pi$
$293$	−306.042	+	306.042i	−1.04451	+	1.04451i	−0.998962	+	0.0455508i	$0.985496\pi$
$294$	83.0141	−	83.0141i	0.282361	−	0.282361i
$295$	−168.946			−0.572699
$296$		−	12.5744i		−	0.0424810i
$297$	9.00000	−	9.00000i	0.0303030	−	0.0303030i
$298$			252.449i			0.847143i
$299$		0			0
$300$	75.4641			0.251547
$301$	−27.2154	−	27.2154i	−0.0904166	−	0.0904166i
$302$	248.813			0.823883
$303$		−	193.061i		−	0.637167i
$304$	−58.9282	−	58.9282i	−0.193843	−	0.193843i
$305$	−131.138	−	131.138i	−0.429962	−	0.429962i
$306$	15.9615	−	15.9615i	0.0521618	−	0.0521618i
$307$	−246.512	+	246.512i	−0.802969	+	0.802969i	−0.983559	−	0.180589i	$-0.942199\pi$
$307$	−246.512	+	246.512i	−0.802969	+	0.802969i	0.180589	+	0.983559i	$0.442199\pi$
$308$	−5.07180			−0.0164669
$309$		−	123.531i		−	0.399776i
$310$	−63.3487	+	63.3487i	−0.204351	+	0.204351i
$311$			313.377i			1.00764i	0.863808	+	0.503821i	$0.168073\pi$
$311$			313.377i			1.00764i	−0.863808	+	0.503821i	$0.831927\pi$
$312$		0			0
$313$	−262.841			−0.839747			−0.419874	−	0.907583i	$-0.637926\pi$
$313$	−262.841			−0.839747			−0.419874	+	0.907583i	$0.637926\pi$
$314$	268.785	+	268.785i	0.856002	+	0.856002i
$315$	5.56922			0.0176801
$316$			8.42047i			0.0266471i
$317$	148.981	+	148.981i	0.469971	+	0.469971i	0.901905	−	0.431934i	$-0.142169\pi$
$317$	148.981	+	148.981i	0.469971	+	0.469971i	−0.431934	+	0.901905i	$0.642169\pi$
$318$	−99.9615	−	99.9615i	−0.314344	−	0.314344i
$319$	7.17691	−	7.17691i	0.0224982	−	0.0224982i
$320$	−10.1436	+	10.1436i	−0.0316987	+	0.0316987i
$321$	−201.846			−0.628804
$322$			7.78976i			0.0241918i
$323$	−78.3820	+	78.3820i	−0.242669	+	0.242669i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	−92.8897			−0.284938
$327$	189.340	+	189.340i	0.579021	+	0.579021i
$328$	−177.779			−0.542011
$329$			45.1000i			0.137082i
$330$	7.60770	+	7.60770i	0.0230536	+	0.0230536i
$331$	295.870	+	295.870i	0.893869	+	0.893869i	0.994885	−	0.101016i	$-0.0322094\pi$
$331$	295.870	+	295.870i	0.893869	+	0.893869i	−0.101016	+	0.994885i	$0.532209\pi$
$332$	−219.597	+	219.597i	−0.661438	+	0.661438i
$333$	9.43078	−	9.43078i	0.0283207	−	0.0283207i
$334$	−239.023			−0.715638
$335$			118.410i			0.353463i
$336$	5.07180	−	5.07180i	0.0150946	−	0.0150946i
$337$		−	48.9385i		−	0.145218i	−0.997360	−	0.0726091i	$-0.976867\pi$
$337$		−	48.9385i		−	0.145218i	0.997360	−	0.0726091i	$-0.0231325\pi$
$338$		0			0
$339$	256.823			0.757590
$340$	13.4923	+	13.4923i	0.0396831	+	0.0396831i
$341$	86.5359			0.253771
$342$		−	88.3923i		−	0.258457i
$343$	−70.9564	−	70.9564i	−0.206870	−	0.206870i
$344$	74.3538	+	74.3538i	0.216145	+	0.216145i
$345$	11.6846	−	11.6846i	0.0338685	−	0.0338685i
$346$	−242.603	+	242.603i	−0.701163	+	0.701163i
$347$	−552.133			−1.59116			−0.795581	−	0.605847i	$-0.792834\pi$
$347$	−552.133			−1.59116			−0.795581	+	0.605847i	$0.792834\pi$
$348$			14.3538i			0.0412466i
$349$	−189.210	+	189.210i	−0.542150	+	0.542150i	−0.924159	−	0.382009i	$-0.875232\pi$
$349$	−189.210	+	189.210i	−0.542150	+	0.542150i	0.382009	+	0.924159i	$0.375232\pi$
$350$		−	31.8949i		−	0.0911282i
$351$		0			0
$352$	13.8564			0.0393648
$353$	51.8705	+	51.8705i	0.146942	+	0.146942i	0.776750	−	0.629809i	$-0.216867\pi$
$353$	51.8705	+	51.8705i	0.146942	+	0.146942i	−0.629809	+	0.776750i	$0.716867\pi$
$354$	−230.785			−0.651934
$355$		−	68.2384i		−	0.192221i
$356$	39.0333	+	39.0333i	0.109644	+	0.109644i
$357$	−6.74613	−	6.74613i	−0.0188967	−	0.0188967i
$358$	26.7180	−	26.7180i	0.0746312	−	0.0746312i
$359$	205.119	−	205.119i	0.571363	−	0.571363i	−0.361146	−	0.932509i	$-0.617615\pi$
$359$	205.119	−	205.119i	0.571363	−	0.571363i	0.932509	+	0.361146i	$0.117615\pi$
$360$	−15.2154			−0.0422650
$361$			73.0666i			0.202401i
$362$	−256.144	+	256.144i	−0.707579	+	0.707579i
$363$			199.186i			0.548721i
$364$		0			0
$365$	14.4026			0.0394592
$366$	−179.138	−	179.138i	−0.489449	−	0.489449i
$367$	−351.292			−0.957200			−0.478600	−	0.878033i	$-0.658856\pi$
$367$	−351.292			−0.957200			−0.478600	+	0.878033i	$0.658856\pi$
$368$		−	21.2820i		−	0.0578316i
$369$	−133.335	−	133.335i	−0.361340	−	0.361340i
$370$	7.97183	+	7.97183i	0.0215455	+	0.0215455i
$371$	−42.2487	+	42.2487i	−0.113878	+	0.113878i
$372$	−86.5359	+	86.5359i	−0.232623	+	0.232623i
$373$	−131.836			−0.353447			−0.176724	−	0.984261i	$-0.556550\pi$
$373$	−131.836			−0.353447			−0.176724	+	0.984261i	$0.556550\pi$
$374$		−	18.4308i		−	0.0492802i
$375$	−102.746	+	102.746i	−0.273990	+	0.273990i
$376$		−	123.215i		−	0.327701i
$377$		0			0
$378$	7.60770			0.0201262
$379$	24.7987	+	24.7987i	0.0654319	+	0.0654319i	0.739065	−	0.673634i	$-0.235267\pi$
$379$	24.7987	+	24.7987i	0.0654319	+	0.0654319i	−0.673634	+	0.739065i	$0.735267\pi$
$380$	74.7180			0.196626
$381$			121.310i			0.318399i
$382$	129.282	+	129.282i	0.338435	+	0.338435i
$383$	−174.555	−	174.555i	−0.455758	−	0.455758i	0.441502	−	0.897260i	$-0.354446\pi$
$383$	−174.555	−	174.555i	−0.455758	−	0.455758i	−0.897260	+	0.441502i	$0.854446\pi$
$384$	−13.8564	+	13.8564i	−0.0360844	+	0.0360844i
$385$	3.21539	−	3.21539i	0.00835166	−	0.00835166i
$386$	−320.564			−0.830477
$387$			111.531i			0.288193i
$388$	8.06664	−	8.06664i	0.0207903	−	0.0207903i
$389$			644.305i			1.65631i	0.560498	+	0.828156i	$0.310610\pi$
$389$			644.305i			1.65631i	−0.560498	+	0.828156i	$0.689390\pi$
$390$		0			0
$391$	−28.3078			−0.0723985
$392$	95.8564	+	95.8564i	0.244532	+	0.244532i
$393$	413.769			1.05285
$394$		−	218.536i		−	0.554660i
$395$	−5.33836	−	5.33836i	−0.0135148	−	0.0135148i
$396$	10.3923	+	10.3923i	0.0262432	+	0.0262432i
$397$	−432.692	+	432.692i	−1.08990	+	1.08990i	−0.0943673	+	0.995537i	$0.530083\pi$
$397$	−432.692	+	432.692i	−1.08990	+	1.08990i	−0.995537	+	0.0943673i	$0.969917\pi$
$398$	−25.1000	+	25.1000i	−0.0630652	+	0.0630652i
$399$	−37.3590			−0.0936315
$400$			87.1384i			0.217846i
$401$	274.550	−	274.550i	0.684663	−	0.684663i	−0.276384	−	0.961047i	$-0.589136\pi$
$401$	274.550	−	274.550i	0.684663	−	0.684663i	0.961047	+	0.276384i	$0.0891362\pi$
$402$			161.751i			0.402366i
$403$		0			0
$404$	222.928			0.551802
$405$	−11.4115	−	11.4115i	−0.0281766	−	0.0281766i
$406$	6.06664			0.0149425
$407$		−	10.8897i		−	0.0267561i
$408$	18.4308	+	18.4308i	0.0451735	+	0.0451735i
$409$	−76.1872	−	76.1872i	−0.186277	−	0.186277i	0.607808	−	0.794084i	$-0.292049\pi$
$409$	−76.1872	−	76.1872i	−0.186277	−	0.186277i	−0.794084	+	0.607808i	$0.792049\pi$
$410$	112.708	−	112.708i	0.274897	−	0.274897i
$411$	159.258	−	159.258i	0.387488	−	0.387488i
$412$	142.641			0.346216
$413$			97.5411i			0.236177i
$414$	15.9615	−	15.9615i	0.0385544	−	0.0385544i
$415$		−	278.438i		−	0.670936i
$416$		0			0
$417$	240.995			0.577925
$418$	−51.0333	−	51.0333i	−0.122089	−	0.122089i
$419$	76.8231			0.183349			0.0916743	−	0.995789i	$-0.470778\pi$
$419$	76.8231			0.183349			0.0916743	+	0.995789i	$0.470778\pi$
$420$			6.43078i			0.0153114i
$421$	−117.756	−	117.756i	−0.279707	−	0.279707i	0.553285	−	0.832992i	$-0.313374\pi$
$421$	−117.756	−	117.756i	−0.279707	−	0.279707i	−0.832992	+	0.553285i	$0.813374\pi$
$422$	−206.718	−	206.718i	−0.489853	−	0.489853i
$423$	92.4115	−	92.4115i	0.218467	−	0.218467i
$424$	115.426	−	115.426i	0.272230	−	0.272230i
$425$	115.905			0.272718
$426$		−	93.2154i		−	0.218815i
$427$	−75.7128	+	75.7128i	−0.177313	+	0.177313i
$428$		−	233.072i		−	0.544560i
$429$		0			0
$430$	−94.2769			−0.219249
$431$	−362.478	−	362.478i	−0.841017	−	0.841017i	0.147975	−	0.988991i	$-0.452725\pi$
$431$	−362.478	−	362.478i	−0.841017	−	0.841017i	−0.988991	+	0.147975i	$0.952725\pi$
$432$	−20.7846			−0.0481125
$433$			197.292i			0.455641i	0.973703	+	0.227820i	$0.0731599\pi$
$433$			197.292i			0.455641i	−0.973703	+	0.227820i	$0.926840\pi$
$434$	36.5744	+	36.5744i	0.0842728	+	0.0842728i
$435$	−9.09996	−	9.09996i	−0.0209195	−	0.0209195i
$436$	−218.631	+	218.631i	−0.501447	+	0.501447i
$437$	−78.3820	+	78.3820i	−0.179364	+	0.179364i
$438$	19.6743			0.0449186
$439$		−	272.238i		−	0.620133i	−0.950715	−	0.310067i	$-0.899649\pi$
$439$		−	272.238i		−	0.620133i	0.950715	−	0.310067i	$-0.100351\pi$
$440$	−8.78461	+	8.78461i	−0.0199650	+	0.0199650i
$441$			143.785i			0.326042i
$442$		0			0
$443$	74.7358			0.168704			0.0843519	−	0.996436i	$-0.473118\pi$
$443$	74.7358			0.168704			0.0843519	+	0.996436i	$0.473118\pi$
$444$	10.8897	+	10.8897i	0.0245264	+	0.0245264i
$445$	−49.4923			−0.111219
$446$			278.823i			0.625164i
$447$	−218.627	−	218.627i	−0.489098	−	0.489098i
$448$	5.85641	+	5.85641i	0.0130723	+	0.0130723i
$449$	−516.224	+	516.224i	−1.14972	+	1.14972i	−0.163113	+	0.986607i	$0.552153\pi$
$449$	−516.224	+	516.224i	−1.14972	+	1.14972i	−0.986607	+	0.163113i	$0.947847\pi$
$450$	−65.3538	+	65.3538i	−0.145231	+	0.145231i
$451$	−153.962			−0.341378
$452$			296.554i			0.656092i
$453$	−215.478	+	215.478i	−0.475669	+	0.475669i
$454$		−	194.736i		−	0.428934i
$455$		0			0
$456$	102.067			0.223830
$457$	50.9615	+	50.9615i	0.111513	+	0.111513i	0.760662	−	0.649149i	$-0.224875\pi$
$457$	50.9615	+	50.9615i	0.111513	+	0.111513i	−0.649149	+	0.760662i	$0.724875\pi$
$458$	408.354			0.891602
$459$			27.6462i			0.0602313i
$460$	13.4923	+	13.4923i	0.0293310	+	0.0293310i
$461$	−202.550	−	202.550i	−0.439371	−	0.439371i	0.452429	−	0.891800i	$-0.350557\pi$
$461$	−202.550	−	202.550i	−0.439371	−	0.439371i	−0.891800	+	0.452429i	$0.850557\pi$
$462$	4.39230	−	4.39230i	0.00950715	−	0.00950715i
$463$	223.247	−	223.247i	0.482176	−	0.482176i	−0.423650	−	0.905826i	$-0.639251\pi$
$463$	223.247	−	223.247i	0.482176	−	0.482176i	0.905826	+	0.423650i	$0.139251\pi$
$464$	−16.5744			−0.0357206
$465$		−	109.723i		−	0.235964i
$466$	231.962	−	231.962i	0.497772	−	0.497772i
$467$		−	161.818i		−	0.346505i	−0.984877	−	0.173253i	$-0.944572\pi$
$467$		−	161.818i		−	0.346505i	0.984877	−	0.173253i	$-0.0554277\pi$
$468$		0			0
$469$	68.3641			0.145766
$470$	78.1154	+	78.1154i	0.166203	+	0.166203i
$471$	−465.549			−0.988426
$472$		−	266.487i		−	0.564591i
$473$	64.3923	+	64.3923i	0.136136	+	0.136136i
$474$	−7.29234	−	7.29234i	−0.0153847	−	0.0153847i
$475$	320.932	−	320.932i	0.675646	−	0.675646i
$476$	7.78976	−	7.78976i	0.0163651	−	0.0163651i
$477$	173.138			0.362974
$478$			279.962i			0.585694i
$479$	89.1295	−	89.1295i	0.186074	−	0.186074i	−0.607922	−	0.793996i	$-0.707997\pi$
$479$	89.1295	−	89.1295i	0.186074	−	0.186074i	0.793996	+	0.607922i	$0.207997\pi$
$480$		−	17.5692i		−	0.0366025i
$481$		0			0
$482$	106.918			0.221821
$483$	−6.74613	−	6.74613i	−0.0139672	−	0.0139672i
$484$	−230.000			−0.475207
$485$			10.2281i			0.0210888i
$486$	−15.5885	−	15.5885i	−0.0320750	−	0.0320750i
$487$	527.440	+	527.440i	1.08304	+	1.08304i	0.996225	+	0.0868139i	$0.0276685\pi$
$487$	527.440	+	527.440i	1.08304	+	1.08304i	0.0868139	+	0.996225i	$0.472331\pi$
$488$	206.851	−	206.851i	0.423876	−	0.423876i
$489$	80.4449	−	80.4449i	0.164509	−	0.164509i
$490$	−121.541			−0.248043
$491$		−	700.726i		−	1.42714i	−0.700584	−	0.713570i	$-0.747077\pi$
$491$		−	700.726i		−	1.42714i	0.700584	−	0.713570i	$-0.252923\pi$
$492$	153.962	−	153.962i	0.312930	−	0.312930i
$493$			22.0460i			0.0447181i
$494$		0			0
$495$	−13.1769			−0.0266200
$496$	−99.9230	−	99.9230i	−0.201458	−	0.201458i
$497$	−39.3975			−0.0792705
$498$		−	380.354i		−	0.763763i
$499$	−279.065	−	279.065i	−0.559249	−	0.559249i	0.369845	−	0.929094i	$-0.379411\pi$
$499$	−279.065	−	279.065i	−0.559249	−	0.559249i	−0.929094	+	0.369845i	$0.879411\pi$
$500$	−118.641	−	118.641i	−0.237282	−	0.237282i
$501$	207.000	−	207.000i	0.413174	−	0.413174i
$502$	−421.377	+	421.377i	−0.839396	+	0.839396i
$503$	−23.9821			−0.0476782			−0.0238391	−	0.999716i	$-0.507589\pi$
$503$	−23.9821			−0.0476782			−0.0238391	+	0.999716i	$0.507589\pi$
$504$			8.78461i			0.0174298i
$505$	−141.331	+	141.331i	−0.279863	+	0.279863i
$506$		−	18.4308i		−	0.0364245i
$507$		0			0
$508$	−140.077			−0.275742
$509$	287.678	+	287.678i	0.565183	+	0.565183i	0.930775	−	0.365592i	$-0.119134\pi$
$509$	287.678	+	287.678i	0.565183	+	0.565183i	−0.365592	+	0.930775i	$0.619134\pi$
$510$	−23.3693			−0.0458221
$511$		−	8.31535i		−	0.0162727i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	76.5500	+	76.5500i	0.149220	+	0.149220i
$514$	249.664	−	249.664i	0.485728	−	0.485728i
$515$	−90.4308	+	90.4308i	−0.175594	+	0.175594i
$516$	−128.785			−0.249583
$517$		−	106.708i		−	0.206398i
$518$	4.60254	−	4.60254i	0.00888521	−	0.00888521i
$519$		−	420.200i		−	0.809634i
$520$		0			0
$521$	−921.349			−1.76842			−0.884212	−	0.467086i	$-0.845304\pi$
$521$	−921.349			−1.76842			−0.884212	+	0.467086i	$0.845304\pi$
$522$	−12.4308	−	12.4308i	−0.0238138	−	0.0238138i
$523$	−558.677			−1.06822			−0.534108	−	0.845416i	$-0.679352\pi$
$523$	−558.677			−1.06822			−0.534108	+	0.845416i	$0.679352\pi$
$524$			477.779i			0.911793i
$525$	27.6218	+	27.6218i	0.0526129	+	0.0526129i
$526$	94.8897	+	94.8897i	0.180399	+	0.180399i
$527$	−132.910	+	132.910i	−0.252202	+	0.252202i
$528$	−12.0000	+	12.0000i	−0.0227273	+	0.0227273i
$529$	500.692			0.946488
$530$			146.354i			0.276139i
$531$	199.865	−	199.865i	0.376394	−	0.376394i
$532$		−	43.1384i		−	0.0810873i
$533$		0			0
$534$	−67.6077			−0.126606
$535$	147.762	+	147.762i	0.276190	+	0.276190i
$536$	−186.774			−0.348460
$537$			46.2769i			0.0861767i
$538$	208.774	+	208.774i	0.388056	+	0.388056i
$539$	83.0141	+	83.0141i	0.154015	+	0.154015i
$540$	13.1769	−	13.1769i	0.0244017	−	0.0244017i
$541$	101.756	−	101.756i	0.188090	−	0.188090i	−0.606780	−	0.794870i	$-0.707539\pi$
$541$	101.756	−	101.756i	0.188090	−	0.188090i	0.794870	+	0.606780i	$0.207539\pi$
$542$	762.095			1.40608
$543$		−	443.654i		−	0.817042i
$544$	−21.2820	+	21.2820i	−0.0391214	+	0.0391214i
$545$		−	277.213i		−	0.508647i
$546$		0			0
$547$	301.800			0.551737			0.275868	−	0.961195i	$-0.411035\pi$
$547$	301.800			0.551737			0.275868	+	0.961195i	$0.411035\pi$
$548$	183.895	+	183.895i	0.335575	+	0.335575i
$549$	310.277			0.565167
$550$			75.4641i			0.137207i
$551$	61.0436	+	61.0436i	0.110787	+	0.110787i
$552$	18.4308	+	18.4308i	0.0333891	+	0.0333891i
$553$	−3.08211	+	3.08211i	−0.00557343	+	0.00557343i
$554$	68.7846	−	68.7846i	0.124160	−	0.124160i
$555$	−13.8076			−0.0248786
$556$			278.277i			0.500498i
$557$	285.258	−	285.258i	0.512132	−	0.512132i	−0.403047	−	0.915179i	$-0.632049\pi$
$557$	285.258	−	285.258i	0.512132	−	0.512132i	0.915179	+	0.403047i	$0.132049\pi$
$558$		−	149.885i		−	0.268610i
$559$		0			0
$560$	−7.42563			−0.0132600
$561$	15.9615	+	15.9615i	0.0284519	+	0.0284519i
$562$	139.244			0.247764
$563$		−	863.174i		−	1.53317i	−0.642143	−	0.766585i	$-0.721955\pi$
$563$		−	863.174i		−	1.53317i	0.642143	−	0.766585i	$-0.278045\pi$
$564$	106.708	+	106.708i	0.189198	+	0.189198i
$565$	−188.008	−	188.008i	−0.332757	−	0.332757i
$566$	425.808	−	425.808i	0.752310	−	0.752310i
$567$	−6.58846	+	6.58846i	−0.0116199	+	0.0116199i
$568$	107.636			0.189500
$569$		−	317.223i		−	0.557510i	−0.960362	−	0.278755i	$-0.910078\pi$
$569$		−	317.223i		−	0.557510i	0.960362	−	0.278755i	$-0.0899217\pi$
$570$	−64.7077	+	64.7077i	−0.113522	+	0.113522i
$571$			73.2539i			0.128290i	0.997941	+	0.0641452i	$0.0204321\pi$
$571$			73.2539i			0.128290i	−0.997941	+	0.0641452i	$0.979568\pi$
$572$		0			0
$573$	−223.923			−0.390791
$574$	−65.0718	−	65.0718i	−0.113365	−	0.113365i
$575$	115.905			0.201574
$576$		−	24.0000i		−	0.0416667i
$577$	81.6410	+	81.6410i	0.141492	+	0.141492i	0.774305	−	0.632813i	$-0.218100\pi$
$577$	81.6410	+	81.6410i	0.141492	+	0.141492i	−0.632813	+	0.774305i	$0.718100\pi$
$578$	−260.692	−	260.692i	−0.451025	−	0.451025i
$579$	277.617	−	277.617i	0.479476	−	0.479476i
$580$	10.5077	−	10.5077i	0.0181168	−	0.0181168i
$581$	−160.756			−0.276689
$582$			13.9718i			0.0240066i
$583$	99.9615	−	99.9615i	0.171461	−	0.171461i
$584$			22.7180i			0.0389006i
$585$		0			0
$586$	612.084			1.04451
$587$	−382.219	−	382.219i	−0.651140	−	0.651140i	0.302128	−	0.953268i	$-0.402303\pi$
$587$	−382.219	−	382.219i	−0.651140	−	0.651140i	−0.953268	+	0.302128i	$0.902303\pi$
$588$	−166.028			−0.282361
$589$			736.036i			1.24964i
$590$	168.946	+	168.946i	0.286349	+	0.286349i
$591$	189.258	+	189.258i	0.320233	+	0.320233i
$592$	−12.5744	+	12.5744i	−0.0212405	+	0.0212405i
$593$	−171.355	+	171.355i	−0.288963	+	0.288963i	−0.836670	−	0.547707i	$-0.815501\pi$
$593$	−171.355	+	171.355i	−0.288963	+	0.288963i	0.547707	+	0.836670i	$0.315501\pi$
$594$	−18.0000			−0.0303030
$595$			9.87703i			0.0166000i
$596$	252.449	−	252.449i	0.423572	−	0.423572i
$597$		−	43.4744i		−	0.0728215i
$598$		0			0
$599$	−109.608			−0.182984			−0.0914922	−	0.995806i	$-0.529164\pi$
$599$	−109.608			−0.182984			−0.0914922	+	0.995806i	$0.529164\pi$
$600$	−75.4641	−	75.4641i	−0.125774	−	0.125774i
$601$	779.108			1.29635			0.648176	−	0.761491i	$-0.275532\pi$
$601$	779.108			1.29635			0.648176	+	0.761491i	$0.275532\pi$
$602$			54.4308i			0.0904166i
$603$	−140.081	−	140.081i	−0.232306	−	0.232306i
$604$	−248.813	−	248.813i	−0.411942	−	0.411942i
$605$	145.814	−	145.814i	0.241015	−	0.241015i
$606$	−193.061	+	193.061i	−0.318583	+	0.318583i
$607$	1144.40			1.88534			0.942669	−	0.333730i	$-0.108307\pi$
$607$	1144.40			1.88534			0.942669	+	0.333730i	$0.108307\pi$
$608$			117.856i			0.193843i
$609$	−5.25387	+	5.25387i	−0.00862704	+	0.00862704i
$610$			262.277i			0.429962i
$611$		0			0
$612$	−31.9230			−0.0521618
$613$	−292.349	−	292.349i	−0.476915	−	0.476915i	0.427229	−	0.904144i	$-0.359490\pi$
$613$	−292.349	−	292.349i	−0.476915	−	0.476915i	−0.904144	+	0.427229i	$0.859490\pi$
$614$	493.023			0.802969
$615$			195.215i			0.317423i
$616$	5.07180	+	5.07180i	0.00823344	+	0.00823344i
$617$	369.391	+	369.391i	0.598689	+	0.598689i	0.939964	−	0.341275i	$-0.110859\pi$
$617$	369.391	+	369.391i	0.598689	+	0.598689i	−0.341275	+	0.939964i	$0.610859\pi$
$618$	−123.531	+	123.531i	−0.199888	+	0.199888i
$619$	446.070	−	446.070i	0.720631	−	0.720631i	−0.248103	−	0.968734i	$-0.579807\pi$
$619$	446.070	−	446.070i	0.720631	−	0.720631i	0.968734	+	0.248103i	$0.0798071\pi$
$620$	126.697			0.204351
$621$			27.6462i			0.0445188i
$622$	313.377	−	313.377i	0.503821	−	0.503821i
$623$			28.5744i			0.0458658i
$624$		0			0
$625$	−394.184			−0.630695
$626$	262.841	+	262.841i	0.419874	+	0.419874i
$627$	88.3923			0.140977
$628$		−	537.569i		−	0.856002i
$629$	16.7255	+	16.7255i	0.0265906	+	0.0265906i
$630$	−5.56922	−	5.56922i	−0.00884003	−	0.00884003i
$631$	604.406	−	604.406i	0.957855	−	0.957855i	−0.0412923	−	0.999147i	$-0.513147\pi$
$631$	604.406	−	604.406i	0.957855	−	0.957855i	0.999147	+	0.0412923i	$0.0131475\pi$
$632$	8.42047	−	8.42047i	0.0133235	−	0.0133235i
$633$	358.046			0.565634
$634$		−	297.962i		−	0.469971i
$635$	88.8052	−	88.8052i	0.139851	−	0.139851i
$636$			199.923i			0.314344i
$637$		0			0
$638$	−14.3538			−0.0224982
$639$	80.7269	+	80.7269i	0.126333	+	0.126333i
$640$	20.2872			0.0316987
$641$			1213.91i			1.89378i	0.321565	+	0.946888i	$0.395791\pi$
$641$			1213.91i			1.89378i	−0.321565	+	0.946888i	$0.604209\pi$
$642$	201.846	+	201.846i	0.314402	+	0.314402i
$643$	−413.804	−	413.804i	−0.643552	−	0.643552i	0.307875	−	0.951427i	$-0.400382\pi$
$643$	−413.804	−	413.804i	−0.643552	−	0.643552i	−0.951427	+	0.307875i	$0.900382\pi$
$644$	7.78976	−	7.78976i	0.0120959	−	0.0120959i
$645$	81.6462	−	81.6462i	0.126583	−	0.126583i
$646$	156.764			0.242669
$647$		−	117.913i		−	0.182245i	−0.995840	−	0.0911227i	$-0.970954\pi$
$647$		−	117.913i		−	0.182245i	0.995840	−	0.0911227i	$-0.0290455\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	230.785i		−	0.355600i
$650$		0			0
$651$	−63.3487			−0.0973098
$652$	92.8897	+	92.8897i	0.142469	+	0.142469i
$653$	−1088.62			−1.66711			−0.833553	−	0.552439i	$-0.813697\pi$
$653$	−1088.62			−1.66711			−0.833553	+	0.552439i	$0.813697\pi$
$654$		−	378.679i		−	0.579021i
$655$	−302.900	−	302.900i	−0.462443	−	0.462443i
$656$	177.779	+	177.779i	0.271005	+	0.271005i
$657$	−17.0385	+	17.0385i	−0.0259338	+	0.0259338i
$658$	45.1000	−	45.1000i	0.0685410	−	0.0685410i
$659$	1222.68			1.85535			0.927676	−	0.373387i	$-0.121804\pi$
$659$	1222.68			1.85535			0.927676	+	0.373387i	$0.121804\pi$
$660$		−	15.2154i		−	0.0230536i
$661$	667.851	−	667.851i	1.01036	−	1.01036i	0.0104193	−	0.999946i	$-0.496683\pi$
$661$	667.851	−	667.851i	1.01036	−	1.01036i	0.999946	−	0.0104193i	$-0.00331661\pi$
$662$		−	591.741i		−	0.893869i
$663$		0			0
$664$	439.195			0.661438
$665$	27.3487	+	27.3487i	0.0411258	+	0.0411258i
$666$	−18.8616			−0.0283207
$667$			22.0460i			0.0330525i
$668$	239.023	+	239.023i	0.357819	+	0.357819i
$669$	−241.468	−	241.468i	−0.360939	−	0.360939i
$670$	118.410	−	118.410i	0.176732	−	0.176732i
$671$	179.138	−	179.138i	0.266972	−	0.266972i
$672$	−10.1436			−0.0150946
$673$		−	411.779i		−	0.611857i	−0.952055	−	0.305928i	$-0.901033\pi$
$673$		−	411.779i		−	0.611857i	0.952055	−	0.305928i	$-0.0989668\pi$
$674$	−48.9385	+	48.9385i	−0.0726091	+	0.0726091i
$675$		−	113.196i		−	0.167698i
$676$		0			0
$677$	−948.600			−1.40118			−0.700591	−	0.713563i	$-0.747080\pi$
$677$	−948.600			−1.40118			−0.700591	+	0.713563i	$0.747080\pi$
$678$	−256.823	−	256.823i	−0.378795	−	0.378795i
$679$	5.90519			0.00869690
$680$		−	26.9845i		−	0.0396831i
$681$	168.646	+	168.646i	0.247645	+	0.247645i
$682$	−86.5359	−	86.5359i	−0.126885	−	0.126885i
$683$	−101.809	+	101.809i	−0.149061	+	0.149061i	−0.777699	−	0.628637i	$-0.783613\pi$
$683$	−101.809	+	101.809i	−0.149061	+	0.149061i	0.628637	+	0.777699i	$0.283613\pi$
$684$	−88.3923	+	88.3923i	−0.129229	+	0.129229i
$685$	−233.169			−0.340393
$686$			141.913i			0.206870i
$687$	−353.645	+	353.645i	−0.514767	+	0.514767i
$688$		−	148.708i		−	0.216145i
$689$		0			0
$690$	−23.3693			−0.0338685
$691$	111.135	+	111.135i	0.160832	+	0.160832i	0.782935	−	0.622103i	$-0.213722\pi$
$691$	111.135	+	111.135i	0.160832	+	0.160832i	−0.622103	+	0.782935i	$0.713722\pi$
$692$	485.205			0.701163
$693$			7.60770i			0.0109779i
$694$	552.133	+	552.133i	0.795581	+	0.795581i
$695$	−176.420	−	176.420i	−0.253842	−	0.253842i
$696$	14.3538	−	14.3538i	0.0206233	−	0.0206233i
$697$	236.469	−	236.469i	0.339267	−	0.339267i
$698$	378.420			0.542150
$699$			401.769i			0.574777i
$700$	−31.8949	+	31.8949i	−0.0455641	+	0.0455641i
$701$			779.520i			1.11201i	0.831178	+	0.556006i	$0.187667\pi$
$701$			779.520i			1.11201i	−0.831178	+	0.556006i	$0.812333\pi$
$702$		0			0
$703$	92.6232			0.131754
$704$	−13.8564	−	13.8564i	−0.0196824	−	0.0196824i
$705$	−135.300			−0.191915
$706$		−	103.741i		−	0.146942i
$707$	81.5974	+	81.5974i	0.115414	+	0.115414i
$708$	230.785	+	230.785i	0.325967	+	0.325967i
$709$	−43.0179	+	43.0179i	−0.0606740	+	0.0606740i	−0.736793	−	0.676119i	$-0.763661\pi$
$709$	−43.0179	+	43.0179i	−0.0606740	+	0.0606740i	0.676119	+	0.736793i	$0.263661\pi$
$710$	−68.2384	+	68.2384i	−0.0961104	+	0.0961104i
$711$	12.6307			0.0177647
$712$		−	78.0666i		−	0.109644i
$713$	−132.910	+	132.910i	−0.186410	+	0.186410i
$714$			13.4923i			0.0188967i
$715$		0			0
$716$	−53.4359			−0.0746312
$717$	−242.454	−	242.454i	−0.338150	−	0.338150i
$718$	−410.238			−0.571363
$719$			335.290i			0.466328i	0.972437	+	0.233164i	$0.0749078\pi$
$719$			335.290i			0.466328i	−0.972437	+	0.233164i	$0.925092\pi$
$720$	15.2154	+	15.2154i	0.0211325	+	0.0211325i
$721$	52.2102	+	52.2102i	0.0724136	+	0.0724136i
$722$	73.0666	−	73.0666i	0.101200	−	0.101200i
$723$	−92.5936	+	92.5936i	−0.128069	+	0.128069i
$724$	512.287			0.707579
$725$		−	90.2666i		−	0.124506i
$726$	199.186	−	199.186i	0.274361	−	0.274361i
$727$		−	537.577i		−	0.739445i	−0.929142	−	0.369723i	$-0.879453\pi$
$727$		−	537.577i		−	0.739445i	0.929142	−	0.369723i	$-0.120547\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−14.4026	−	14.4026i	−0.0197296	−	0.0197296i
$731$	−197.800			−0.270588
$732$			358.277i			0.489449i
$733$	479.946	+	479.946i	0.654770	+	0.654770i	0.954138	−	0.299368i	$-0.0967759\pi$
$733$	479.946	+	479.946i	0.654770	+	0.654770i	−0.299368	+	0.954138i	$0.596776\pi$
$734$	351.292	+	351.292i	0.478600	+	0.478600i
$735$	105.258	−	105.258i	0.143208	−	0.143208i
$736$	−21.2820	+	21.2820i	−0.0289158	+	0.0289158i
$737$	−161.751			−0.219473
$738$			266.669i			0.361340i
$739$	−512.788	+	512.788i	−0.693895	+	0.693895i	−0.963087	−	0.269192i	$-0.913243\pi$
$739$	−512.788	+	512.788i	−0.693895	+	0.693895i	0.269192	+	0.963087i	$0.413243\pi$
$740$		−	15.9437i		−	0.0215455i
$741$		0			0
$742$	84.4974			0.113878
$743$	−801.509	−	801.509i	−1.07875	−	1.07875i	−0.996622	−	0.0821246i	$-0.973829\pi$
$743$	−801.509	−	801.509i	−1.07875	−	1.07875i	−0.0821246	−	0.996622i	$-0.526171\pi$
$744$	173.072			0.232623
$745$			320.092i			0.429654i
$746$	131.836	+	131.836i	0.176724	+	0.176724i
$747$	329.396	+	329.396i	0.440959	+	0.440959i
$748$	−18.4308	+	18.4308i	−0.0246401	+	0.0246401i
$749$	85.3102	−	85.3102i	0.113899	−	0.113899i
$750$	205.492			0.273990
$751$		−	1384.43i		−	1.84345i	−0.387849	−	0.921723i	$-0.626782\pi$
$751$		−	1384.43i		−	1.84345i	0.387849	−	0.921723i	$-0.373218\pi$
$752$	−123.215	+	123.215i	−0.163850	+	0.163850i
$753$		−	729.846i		−	0.969251i
$754$		0			0
$755$	315.482			0.417857
$756$	−7.60770	−	7.60770i	−0.0100631	−	0.0100631i
$757$	−125.836			−0.166230			−0.0831148	−	0.996540i	$-0.526487\pi$
$757$	−125.836			−0.166230			−0.0831148	+	0.996540i	$0.526487\pi$
$758$		−	49.5974i		−	0.0654319i
$759$	15.9615	+	15.9615i	0.0210297	+	0.0210297i
$760$	−74.7180	−	74.7180i	−0.0983131	−	0.0983131i
$761$	3.55514	−	3.55514i	0.00467166	−	0.00467166i	−0.704767	−	0.709439i	$-0.748949\pi$
$761$	3.55514	−	3.55514i	0.00467166	−	0.00467166i	0.709439	+	0.704767i	$0.248949\pi$
$762$	121.310	−	121.310i	0.159200	−	0.159200i
$763$	−160.049			−0.209762
$764$		−	258.564i		−	0.338435i
$765$	20.2384	−	20.2384i	0.0264554	−	0.0264554i
$766$			349.110i			0.455758i
$767$		0			0
$768$	27.7128			0.0360844
$769$	958.405	+	958.405i	1.24630	+	1.24630i	0.957342	+	0.288959i	$0.0933091\pi$
$769$	958.405	+	958.405i	1.24630	+	1.24630i	0.288959	+	0.957342i	$0.406691\pi$
$770$	−6.43078			−0.00835166
$771$			432.431i			0.560870i
$772$	320.564	+	320.564i	0.415238	+	0.415238i
$773$	−76.8165	−	76.8165i	−0.0993746	−	0.0993746i	0.655672	−	0.755046i	$-0.272386\pi$
$773$	−76.8165	−	76.8165i	−0.0993746	−	0.0993746i	−0.755046	+	0.655672i	$0.772386\pi$
$774$	111.531	−	111.531i	0.144097	−	0.144097i
$775$	544.196	−	544.196i	0.702189	−	0.702189i
$776$	−16.1333			−0.0207903
$777$			7.97183i			0.0102598i
$778$	644.305	−	644.305i	0.828156	−	0.828156i
$779$		−	1309.53i		−	1.68104i
$780$		0			0
$781$	93.2154			0.119354
$782$	28.3078	+	28.3078i	0.0361992	+	0.0361992i
$783$	21.5307			0.0274978
$784$		−	191.713i		−	0.244532i
$785$	340.805	+	340.805i	0.434147	+	0.434147i
$786$	−413.769	−	413.769i	−0.526424	−	0.526424i
$787$	486.883	−	486.883i	0.618657	−	0.618657i	−0.326530	−	0.945187i	$-0.605879\pi$
$787$	486.883	−	486.883i	0.618657	−	0.618657i	0.945187	+	0.326530i	$0.105879\pi$
$788$	−218.536	+	218.536i	−0.277330	+	0.277330i
$789$	−164.354			−0.208307
$790$			10.6767i			0.0135148i
$791$	−108.546	+	108.546i	−0.137227	+	0.137227i
$792$		−	20.7846i		−	0.0262432i
$793$		0			0
$794$	865.384			1.08990
$795$	−126.746	−	126.746i	−0.159429	−	0.159429i
$796$	50.1999			0.0630652
$797$			713.587i			0.895341i	0.894198	+	0.447671i	$0.147746\pi$
$797$			713.587i			0.895341i	−0.894198	+	0.447671i	$0.852254\pi$
$798$	37.3590	+	37.3590i	0.0468158	+	0.0468158i
$799$	163.892	+	163.892i	0.205122	+	0.205122i
$800$	87.1384	−	87.1384i	0.108923	−	0.108923i
$801$	58.5500	−	58.5500i	0.0730961	−	0.0730961i
$802$	−549.100			−0.684663
$803$			19.6743i			0.0245010i
$804$	161.751	−	161.751i	0.201183	−	0.201183i
$805$			9.87703i			0.0122696i
$806$		0			0
$807$	−361.608			−0.448089
$808$	−222.928	−	222.928i	−0.275901	−	0.275901i
$809$	−257.600			−0.318418			−0.159209	−	0.987245i	$-0.550894\pi$
$809$	−257.600			−0.318418			−0.159209	+	0.987245i	$0.550894\pi$
$810$			22.8231i			0.0281766i
$811$	127.258	+	127.258i	0.156914	+	0.156914i	0.781198	−	0.624283i	$-0.214609\pi$
$811$	127.258	+	127.258i	0.156914	+	0.156914i	−0.624283	+	0.781198i	$0.714609\pi$
$812$	−6.06664	−	6.06664i	−0.00747123	−	0.00747123i
$813$	−659.993	+	659.993i	−0.811800	+	0.811800i
$814$	−10.8897	+	10.8897i	−0.0133780	+	0.0133780i
$815$	−117.779			−0.144515
$816$		−	36.8616i		−	0.0451735i
$817$	−547.692	+	547.692i	−0.670370	+	0.670370i
$818$			152.374i			0.186277i
$819$		0			0
$820$	−225.415			−0.274897
$821$	−1116.87	−	1116.87i	−1.36038	−	1.36038i	−0.873428	−	0.486953i	$-0.838108\pi$
$821$	−1116.87	−	1116.87i	−1.36038	−	1.36038i	−0.486953	−	0.873428i	$-0.661892\pi$
$822$	−318.515			−0.387488
$823$		−	617.920i		−	0.750814i	−0.926860	−	0.375407i	$-0.877503\pi$
$823$		−	617.920i		−	0.750814i	0.926860	−	0.375407i	$-0.122497\pi$
$824$	−142.641	−	142.641i	−0.173108	−	0.173108i
$825$	−65.3538	−	65.3538i	−0.0792168	−	0.0792168i
$826$	97.5411	−	97.5411i	0.118088	−	0.118088i
$827$	−349.847	+	349.847i	−0.423032	+	0.423032i	−0.886246	−	0.463214i	$-0.846696\pi$
$827$	−349.847	+	349.847i	−0.423032	+	0.423032i	0.463214	+	0.886246i	$0.346696\pi$
$828$	−31.9230			−0.0385544
$829$			247.646i			0.298729i	0.988782	+	0.149364i	$0.0477227\pi$
$829$			247.646i			0.298729i	−0.988782	+	0.149364i	$0.952277\pi$
$830$	−278.438	+	278.438i	−0.335468	+	0.335468i
$831$			119.138i			0.143368i
$832$		0			0
$833$	−255.002			−0.306125
$834$	−240.995	−	240.995i	−0.288963	−	0.288963i
$835$	−303.069			−0.362957
$836$			102.067i			0.122089i
$837$	129.804	+	129.804i	0.155082	+	0.155082i
$838$	−76.8231	−	76.8231i	−0.0916743	−	0.0916743i
$839$	598.868	−	598.868i	0.713788	−	0.713788i	−0.253538	−	0.967325i	$-0.581594\pi$
$839$	598.868	−	598.868i	0.713788	−	0.713788i	0.967325	+	0.253538i	$0.0815943\pi$
$840$	6.43078	−	6.43078i	0.00765569	−	0.00765569i
$841$	−823.831			−0.979585
$842$			235.513i			0.279707i
$843$	−120.588	+	120.588i	−0.143047	+	0.143047i
$844$			413.436i			0.489853i
$845$		0			0
$846$	−184.823			−0.218467
$847$	−84.1858	−	84.1858i	−0.0993930	−	0.0993930i
$848$	−230.851			−0.272230
$849$			737.520i			0.868693i
$850$	−115.905	−	115.905i	−0.136359	−	0.136359i
$851$	16.7255	+	16.7255i	0.0196540	+	0.0196540i
$852$	−93.2154	+	93.2154i	−0.109408	+	0.109408i
$853$	519.210	−	519.210i	0.608687	−	0.608687i	−0.333916	−	0.942603i	$-0.608370\pi$
$853$	519.210	−	519.210i	0.608687	−	0.608687i	0.942603	+	0.333916i	$0.108370\pi$
$854$	151.426			0.177313
$855$		−	112.077i		−	0.131084i
$856$	−233.072	+	233.072i	−0.272280	+	0.272280i
$857$		−	226.756i		−	0.264593i	−0.991210	−	0.132297i	$-0.957765\pi$
$857$		−	226.756i		−	0.264593i	0.991210	−	0.132297i	$-0.0422351\pi$
$858$		0			0
$859$	950.656			1.10670			0.553350	−	0.832949i	$-0.313349\pi$
$859$	950.656			1.10670			0.553350	+	0.832949i	$0.313349\pi$
$860$	94.2769	+	94.2769i	0.109624	+	0.109624i
$861$	112.708			0.130903
$862$			724.956i			0.841017i
$863$	−773.711	−	773.711i	−0.896537	−	0.896537i	0.0985910	−	0.995128i	$-0.468566\pi$
$863$	−773.711	−	773.711i	−0.896537	−	0.896537i	−0.995128	+	0.0985910i	$0.968566\pi$
$864$	20.7846	+	20.7846i	0.0240563	+	0.0240563i
$865$	−307.608	+	307.608i	−0.355616	+	0.355616i
$866$	197.292	−	197.292i	0.227820	−	0.227820i
$867$	451.532			0.520798
$868$		−	73.1487i		−	0.0842728i
$869$	7.29234	−	7.29234i	0.00839165	−	0.00839165i
$870$			18.1999i			0.0209195i
$871$		0			0
$872$	437.261			0.501447
$873$	−12.1000	−	12.1000i	−0.0138602	−	0.0138602i
$874$	156.764			0.179364
$875$		−	86.8513i		−	0.0992586i
$876$	−19.6743	−	19.6743i	−0.0224593	−	0.0224593i
$877$	−646.713	−	646.713i	−0.737415	−	0.737415i	0.234662	−	0.972077i	$-0.424602\pi$
$877$	−646.713	−	646.713i	−0.737415	−	0.737415i	−0.972077	+	0.234662i	$0.924602\pi$
$878$	−272.238	+	272.238i	−0.310067	+	0.310067i
$879$	−530.081	+	530.081i	−0.603050	+	0.603050i
$880$	17.5692			0.0199650
$881$			783.997i			0.889895i	0.895557	+	0.444947i	$0.146778\pi$
$881$			783.997i			0.889895i	−0.895557	+	0.444947i	$0.853222\pi$
$882$	143.785	−	143.785i	0.163021	−	0.163021i
$883$			1089.81i			1.23421i	0.786881	+	0.617105i	$0.211695\pi$
$883$			1089.81i			1.23421i	−0.786881	+	0.617105i	$0.788305\pi$
$884$		0			0
$885$	−292.623			−0.330648
$886$	−74.7358	−	74.7358i	−0.0843519	−	0.0843519i
$887$	−1057.03			−1.19169			−0.595846	−	0.803099i	$-0.703183\pi$
$887$	−1057.03			−1.19169			−0.595846	+	0.803099i	$0.703183\pi$
$888$		−	21.7795i		−	0.0245264i
$889$	−51.2717	−	51.2717i	−0.0576735	−	0.0576735i
$890$	49.4923	+	49.4923i	0.0556093	+	0.0556093i
$891$	15.5885	−	15.5885i	0.0174955	−	0.0174955i
$892$	278.823	−	278.823i	0.312582	−	0.312582i
$893$	907.608			1.01636
$894$			437.254i			0.489098i
$895$	33.8770	−	33.8770i	0.0378514	−	0.0378514i
$896$		−	11.7128i		−	0.0130723i
$897$		0			0
$898$	1032.45			1.14972
$899$	103.510	+	103.510i	0.115139	+	0.115139i
$900$	130.708			0.145231
$901$			307.061i			0.340801i
$902$	153.962	+	153.962i	0.170689	+	0.170689i
$903$	−47.1384	−	47.1384i	−0.0522020	−	0.0522020i
$904$	296.554	−	296.554i	0.328046	−	0.328046i
$905$	−324.777	+	324.777i	−0.358870	+	0.358870i
$906$	430.956			0.475669
$907$		−	546.669i		−	0.602722i	−0.953510	−	0.301361i	$-0.902559\pi$
$907$		−	546.669i		−	0.602722i	0.953510	−	0.301361i	$-0.0974410\pi$
$908$	−194.736	+	194.736i	−0.214467	+	0.214467i
$909$		−	334.392i		−	0.367868i
$910$		0			0
$911$	724.743			0.795547			0.397774	−	0.917484i	$-0.369783\pi$
$911$	724.743			0.795547			0.397774	+	0.917484i	$0.369783\pi$
$912$	−102.067	−	102.067i	−0.111915	−	0.111915i
$913$	380.354			0.416598
$914$		−	101.923i		−	0.111513i
$915$	−227.138	−	227.138i	−0.248239	−	0.248239i
$916$	−408.354	−	408.354i	−0.445801	−	0.445801i
$917$	−174.879	+	174.879i	−0.190708	+	0.190708i
$918$	27.6462	−	27.6462i	0.0301157	−	0.0301157i
$919$	−941.108			−1.02406			−0.512028	−	0.858969i	$-0.671106\pi$
$919$	−941.108			−1.02406			−0.512028	+	0.858969i	$0.671106\pi$
$920$		−	26.9845i		−	0.0293310i
$921$	−426.970	+	426.970i	−0.463594	+	0.463594i
$922$			405.100i			0.439371i
$923$		0			0
$924$	−8.78461			−0.00950715
$925$	−68.4820	−	68.4820i	−0.0740345	−	0.0740345i
$926$	−446.495			−0.482176
$927$		−	213.962i		−	0.230811i
$928$	16.5744	+	16.5744i	0.0178603	+	0.0178603i
$929$	260.130	+	260.130i	0.280010	+	0.280010i	0.833113	−	0.553103i	$-0.186556\pi$
$929$	260.130	+	260.130i	0.280010	+	0.280010i	−0.553103	+	0.833113i	$0.686556\pi$
$930$	−109.723	+	109.723i	−0.117982	+	0.117982i
$931$	−706.081	+	706.081i	−0.758411	+	0.758411i
$932$	−463.923			−0.497772
$933$			542.785i			0.581763i
$934$	−161.818	+	161.818i	−0.173253	+	0.173253i
$935$		−	23.3693i		−	0.0249939i
$936$		0			0
$937$	1387.56			1.48085			0.740426	−	0.672138i	$-0.234624\pi$
$937$	1387.56			1.48085			0.740426	+	0.672138i	$0.234624\pi$
$938$	−68.3641	−	68.3641i	−0.0728829	−	0.0728829i
$939$	−455.254			−0.484828
$940$		−	156.231i		−	0.166203i
$941$	61.6012	+	61.6012i	0.0654635	+	0.0654635i	0.739081	−	0.673617i	$-0.235260\pi$
$941$	61.6012	+	61.6012i	0.0654635	+	0.0654635i	−0.673617	+	0.739081i	$0.735260\pi$
$942$	465.549	+	465.549i	0.494213	+	0.494213i
$943$	236.469	−	236.469i	0.250763	−	0.250763i
$944$	−266.487	+	266.487i	−0.282296	+	0.282296i
$945$	9.64617			0.0102076
$946$		−	128.785i		−	0.136136i
$947$	−54.5064	+	54.5064i	−0.0575569	+	0.0575569i	−0.735299	−	0.677742i	$-0.762958\pi$
$947$	−54.5064	+	54.5064i	−0.0575569	+	0.0575569i	0.677742	+	0.735299i	$0.262958\pi$
$948$			14.5847i			0.0153847i
$949$		0			0
$950$	−641.864			−0.675646
$951$	258.042	+	258.042i	0.271338	+	0.271338i
$952$	−15.5795			−0.0163651
$953$		−	1079.56i		−	1.13280i	−0.824131	−	0.566399i	$-0.808336\pi$
$953$		−	1079.56i		−	1.13280i	0.824131	−	0.566399i	$-0.191664\pi$
$954$	−173.138	−	173.138i	−0.181487	−	0.181487i
$955$	163.923	+	163.923i	0.171647	+	0.171647i
$956$	279.962	−	279.962i	0.292847	−	0.292847i
$957$	12.4308	−	12.4308i	0.0129893	−	0.0129893i
$958$	−178.259			−0.186074
$959$			134.620i			0.140376i
$960$	−17.5692	+	17.5692i	−0.0183013	+	0.0183013i
$961$			287.077i			0.298727i
$962$		0			0
$963$	−349.608			−0.363040
$964$	−106.918	−	106.918i	−0.110911	−	0.110911i
$965$	−406.459			−0.421201
$966$			13.4923i			0.0139672i
$967$	−493.745	−	493.745i	−0.510594	−	0.510594i	0.404114	−	0.914709i	$-0.367580\pi$
$967$	−493.745	−	493.745i	−0.510594	−	0.510594i	−0.914709	+	0.404114i	$0.867580\pi$
$968$	230.000	+	230.000i	0.237603	+	0.237603i
$969$	−135.762	+	135.762i	−0.140105	+	0.140105i
$970$	10.2281	−	10.2281i	0.0105444	−	0.0105444i
$971$	−1694.52			−1.74513			−0.872566	−	0.488497i	$-0.837545\pi$
$971$	−1694.52			−1.74513			−0.872566	+	0.488497i	$0.837545\pi$
$972$			31.1769i			0.0320750i
$973$	−101.856	+	101.856i	−0.104683	+	0.104683i
$974$		−	1054.88i		−	1.08304i
$975$		0			0
$976$	−413.703			−0.423876
$977$	390.060	+	390.060i	0.399243	+	0.399243i	0.877966	−	0.478723i	$-0.158900\pi$
$977$	390.060	+	390.060i	0.399243	+	0.399243i	−0.478723	+	0.877966i	$0.658900\pi$
$978$	−160.890			−0.164509
$979$		−	67.6077i		−	0.0690579i
$980$	121.541	+	121.541i	0.124021	+	0.124021i
$981$	327.946	+	327.946i	0.334298	+	0.334298i
$982$	−700.726	+	700.726i	−0.713570	+	0.713570i
$983$	1123.12	−	1123.12i	1.14254	−	1.14254i	0.154559	−	0.987984i	$-0.450604\pi$
$983$	1123.12	−	1123.12i	1.14254	−	1.14254i	0.987984	−	0.154559i	$-0.0493956\pi$
$984$	−307.923			−0.312930
$985$		−	277.092i		−	0.281312i
$986$	22.0460	−	22.0460i	0.0223590	−	0.0223590i
$987$			78.1154i			0.0791443i
$988$		0			0
$989$	−197.800			−0.200000
$990$	13.1769	+	13.1769i	0.0133100	+	0.0133100i
$991$	610.985			0.616533			0.308267	−	0.951300i	$-0.400251\pi$
$991$	610.985			0.616533			0.308267	+	0.951300i	$0.400251\pi$
$992$			199.846i			0.201458i
$993$	512.463	+	512.463i	0.516075	+	0.516075i
$994$	39.3975	+	39.3975i	0.0396353	+	0.0396353i
$995$	−31.8255	+	31.8255i	−0.0319854	+	0.0319854i
$996$	−380.354	+	380.354i	−0.381881	+	0.381881i
$997$	−412.123			−0.413363			−0.206682	−	0.978408i	$-0.566266\pi$
$997$	−412.123			−0.413363			−0.206682	+	0.978408i	$0.566266\pi$
$998$			558.131i			0.559249i
$999$	16.3346	−	16.3346i	0.0163509	−	0.0163509i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.a.775.2		4
13.5	odd	4	inner	1014.3.f.a.577.2		4
13.8	odd	4		78.3.f.a.31.2	✓	4
13.12	even	2		78.3.f.a.73.2	yes	4
39.8	even	4		234.3.i.b.109.2		4
39.38	odd	2		234.3.i.b.73.2		4
52.47	even	4		624.3.ba.a.577.1		4
52.51	odd	2		624.3.ba.a.385.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.2	✓	4	13.8	odd	4
78.3.f.a.73.2	yes	4	13.12	even	2
234.3.i.b.73.2		4	39.38	odd	2
234.3.i.b.109.2		4	39.8	even	4
624.3.ba.a.385.1		4	52.51	odd	2
624.3.ba.a.577.1		4	52.47	even	4
1014.3.f.a.577.2		4	13.5	odd	4	inner
1014.3.f.a.775.2		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +1.73205 q^{3} +2.00000i q^{4} +(-1.26795 - 1.26795i) q^{5} +(-1.73205 - 1.73205i) q^{6} +(-0.732051 + 0.732051i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +2.53590i q^{10} +(1.73205 - 1.73205i) q^{11} +3.46410i q^{12} +1.46410 q^{14} +(-2.19615 - 2.19615i) q^{15} -4.00000 q^{16} +5.32051i q^{17} +(-3.00000 - 3.00000i) q^{18} +(14.7321 + 14.7321i) q^{19} +(2.53590 - 2.53590i) q^{20} +(-1.26795 + 1.26795i) q^{21} -3.46410 q^{22} +5.32051i q^{23} +(3.46410 - 3.46410i) q^{24} -21.7846i q^{25} +5.19615 q^{27} +(-1.46410 - 1.46410i) q^{28} +4.14359 q^{29} +4.39230i q^{30} +(24.9808 + 24.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(3.00000 - 3.00000i) q^{33} +(5.32051 - 5.32051i) q^{34} +1.85641 q^{35} +6.00000i q^{36} +(3.14359 - 3.14359i) q^{37} -29.4641i q^{38} -5.07180 q^{40} +(-44.4449 - 44.4449i) q^{41} +2.53590 q^{42} +37.1769i q^{43} +(3.46410 + 3.46410i) q^{44} +(-3.80385 - 3.80385i) q^{45} +(5.32051 - 5.32051i) q^{46} +(30.8038 - 30.8038i) q^{47} -6.92820 q^{48} +47.9282i q^{49} +(-21.7846 + 21.7846i) q^{50} +9.21539i q^{51} +57.7128 q^{53} +(-5.19615 - 5.19615i) q^{54} -4.39230 q^{55} +2.92820i q^{56} +(25.5167 + 25.5167i) q^{57} +(-4.14359 - 4.14359i) q^{58} +(66.6218 - 66.6218i) q^{59} +(4.39230 - 4.39230i) q^{60} +103.426 q^{61} -49.9615i q^{62} +(-2.19615 + 2.19615i) q^{63} -8.00000i q^{64} -6.00000 q^{66} +(-46.6936 - 46.6936i) q^{67} -10.6410 q^{68} +9.21539i q^{69} +(-1.85641 - 1.85641i) q^{70} +(26.9090 + 26.9090i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-5.67949 + 5.67949i) q^{73} -6.28719 q^{74} -37.7321i q^{75} +(-29.4641 + 29.4641i) q^{76} +2.53590i q^{77} +4.21024 q^{79} +(5.07180 + 5.07180i) q^{80} +9.00000 q^{81} +88.8897i q^{82} +(109.799 + 109.799i) q^{83} +(-2.53590 - 2.53590i) q^{84} +(6.74613 - 6.74613i) q^{85} +(37.1769 - 37.1769i) q^{86} +7.17691 q^{87} -6.92820i q^{88} +(19.5167 - 19.5167i) q^{89} +7.60770i q^{90} -10.6410 q^{92} +(43.2679 + 43.2679i) q^{93} -61.6077 q^{94} -37.3590i q^{95} +(6.92820 + 6.92820i) q^{96} +(-4.03332 - 4.03332i) q^{97} +(47.9282 - 47.9282i) q^{98} +(5.19615 - 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} + 4 q^{7} + 8 q^{8} + 12 q^{9} - 8 q^{14} + 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} + 24 q^{20} - 12 q^{21} + 8 q^{28} + 72 q^{29} - 4 q^{31} + 16 q^{32} + 12 q^{33} - 48 q^{34}+ \cdots + 164 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 + 4 * q^7 + 8 * q^8 + 12 * q^9 - 8 * q^14 + 12 * q^15 - 16 * q^16 - 12 * q^18 + 52 * q^19 + 24 * q^20 - 12 * q^21 + 8 * q^28 + 72 * q^29 - 4 * q^31 + 16 * q^32 + 12 * q^33 - 48 * q^34 - 48 * q^35 + 68 * q^37 - 48 * q^40 - 60 * q^41 + 24 * q^42 - 36 * q^45 - 48 * q^46 + 144 * q^47 - 4 * q^50 + 120 * q^53 + 24 * q^55 + 12 * q^57 - 72 * q^58 + 24 * q^59 - 24 * q^60 + 192 * q^61 + 12 * q^63 - 24 * q^66 + 28 * q^67 + 96 * q^68 + 48 * q^70 - 24 * q^71 + 24 * q^72 - 92 * q^73 - 136 * q^74 - 104 * q^76 - 288 * q^79 + 48 * q^80 + 36 * q^81 + 72 * q^83 - 24 * q^84 - 264 * q^85 + 24 * q^86 - 96 * q^87 - 12 * q^89 + 96 * q^92 + 180 * q^93 - 288 * q^94 + 164 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more