LMFDB - Embedded newform 465.2.i.b.346.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [465,2,Mod(211,465)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(465, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("465.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{97})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 25x^{2} + 24x + 576 $ x^4 - x^3 + 25x^2 + 24x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			346.1
Root			$-2.21221 - 3.83167i$ of defining polynomial
Character	$\chi$	$=$	465.346
Dual form			465.2.i.b.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.21221 - 3.83167i) q^{11} +(-1.00000 + 1.73205i) q^{12} +(-2.71221 - 4.69769i) q^{13} +1.00000 q^{15} +4.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.712214 + 1.23359i) q^{19} +(-1.00000 - 1.73205i) q^{20} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -6.42443 q^{29} +(0.212214 - 5.56372i) q^{31} -4.42443 q^{33} +(1.00000 + 1.73205i) q^{36} +(0.712214 - 1.23359i) q^{37} -5.42443 q^{39} +(-4.21221 - 7.29577i) q^{41} +(1.71221 - 2.96564i) q^{43} +(4.42443 + 7.66334i) q^{44} +(0.500000 - 0.866025i) q^{45} -10.8489 q^{47} +(2.00000 - 3.46410i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(5.42443 + 9.39539i) q^{52} +(4.42443 + 7.66334i) q^{53} +(2.21221 - 3.83167i) q^{55} +(0.712214 + 1.23359i) q^{57} +(-2.21221 + 3.83167i) q^{59} -2.00000 q^{60} +14.4244 q^{61} -8.00000 q^{64} +(2.71221 - 4.69769i) q^{65} +(6.42443 + 11.1274i) q^{67} +(-4.00000 + 6.92820i) q^{68} +(1.00000 - 1.73205i) q^{69} +(-1.21221 - 2.09962i) q^{71} +(5.71221 + 9.89385i) q^{73} +(0.500000 + 0.866025i) q^{75} +(1.42443 - 2.46718i) q^{76} +(8.63664 - 14.9591i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{83} +4.00000 q^{85} +(-3.21221 + 5.56372i) q^{87} -3.57557 q^{89} -4.00000 q^{92} +(-4.71221 - 2.96564i) q^{93} -1.42443 q^{95} -2.57557 q^{97} +(-2.21221 + 3.83167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9	$ 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9} + q^{11} - 4 q^{12} - q^{13} + 4 q^{15} + 16 q^{16} + 8 q^{17} + 7 q^{19} - 4 q^{20} + 8 q^{23} - 2 q^{25} - 4 q^{27} - 6 q^{29} - 9 q^{31} + 2 q^{33} + 4 q^{36} - 7 q^{37} - 2 q^{39} - 7 q^{41} - 3 q^{43} - 2 q^{44} + 2 q^{45} - 4 q^{47} + 8 q^{48} + 14 q^{49} - 8 q^{51} + 2 q^{52} - 2 q^{53} - q^{55} - 7 q^{57} + q^{59} - 8 q^{60} + 38 q^{61} - 32 q^{64} + q^{65} + 6 q^{67} - 16 q^{68} + 4 q^{69} + 5 q^{71} + 13 q^{73} + 2 q^{75} - 14 q^{76} + 5 q^{79} + 8 q^{80} - 2 q^{81} - 12 q^{83} + 16 q^{85} - 3 q^{87} - 34 q^{89} - 16 q^{92} - 9 q^{93} + 14 q^{95} - 30 q^{97} + q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9 + q^11 - 4 * q^12 - q^13 + 4 * q^15 + 16 * q^16 + 8 * q^17 + 7 * q^19 - 4 * q^20 + 8 * q^23 - 2 * q^25 - 4 * q^27 - 6 * q^29 - 9 * q^31 + 2 * q^33 + 4 * q^36 - 7 * q^37 - 2 * q^39 - 7 * q^41 - 3 * q^43 - 2 * q^44 + 2 * q^45 - 4 * q^47 + 8 * q^48 + 14 * q^49 - 8 * q^51 + 2 * q^52 - 2 * q^53 - q^55 - 7 * q^57 + q^59 - 8 * q^60 + 38 * q^61 - 32 * q^64 + q^65 + 6 * q^67 - 16 * q^68 + 4 * q^69 + 5 * q^71 + 13 * q^73 + 2 * q^75 - 14 * q^76 + 5 * q^79 + 8 * q^80 - 2 * q^81 - 12 * q^83 + 16 * q^85 - 3 * q^87 - 34 * q^89 - 16 * q^92 - 9 * q^93 + 14 * q^95 - 30 * q^97 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			−	1.00000i	$-0.5\pi$
$2$		0			0				1.00000i	$0.5\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.00000			−1.00000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.21221	−	3.83167i	−0.667008	−	1.15529i	−0.978737	−	0.205120i	$-0.934241\pi$
$11$	−2.21221	−	3.83167i	−0.667008	−	1.15529i	0.311729	−	0.950171i	$-0.399092\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−2.71221	−	4.69769i	−0.752233	−	1.30291i	−0.946738	−	0.322004i	$-0.895643\pi$
$13$	−2.71221	−	4.69769i	−0.752233	−	1.30291i	0.194505	−	0.980901i	$-0.437690\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	4.00000			1.00000
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	−0.712214	+	1.23359i	−0.163393	+	0.283005i	−0.936084	−	0.351778i	$-0.885577\pi$
$19$	−0.712214	+	1.23359i	−0.163393	+	0.283005i	0.772690	+	0.634783i	$0.218911\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$		0			0
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−6.42443			−1.19299			−0.596493	−	0.802618i	$-0.703440\pi$
$29$	−6.42443			−1.19299			−0.596493	+	0.802618i	$0.703440\pi$
$30$		0			0
$31$	0.212214	−	5.56372i	0.0381148	−	0.999273i
$31$	0.212214	−	5.56372i	0.0381148	−	0.999273i
$32$		0			0
$33$	−4.42443			−0.770194
$34$		0			0
$35$		0			0
$36$	1.00000	+	1.73205i	0.166667	+	0.288675i
$37$	0.712214	−	1.23359i	0.117087	−	0.202801i	−0.801525	−	0.597961i	$-0.795978\pi$
$37$	0.712214	−	1.23359i	0.117087	−	0.202801i	0.918612	+	0.395160i	$0.129311\pi$
$38$		0			0
$39$	−5.42443			−0.868604
$40$		0			0
$41$	−4.21221	−	7.29577i	−0.657837	−	1.13941i	−0.981174	−	0.193124i	$-0.938138\pi$
$41$	−4.21221	−	7.29577i	−0.657837	−	1.13941i	0.323337	−	0.946284i	$-0.395195\pi$
$42$		0			0
$43$	1.71221	−	2.96564i	0.261110	−	0.452256i	−0.705427	−	0.708783i	$-0.749245\pi$
$43$	1.71221	−	2.96564i	0.261110	−	0.452256i	0.966537	+	0.256526i	$0.0825781\pi$
$44$	4.42443	+	7.66334i	0.667008	+	1.15529i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$		0			0
$47$	−10.8489			−1.58247			−0.791234	−	0.611513i	$-0.790561\pi$
$47$	−10.8489			−1.58247			−0.791234	+	0.611513i	$0.790561\pi$
$48$	2.00000	−	3.46410i	0.288675	−	0.500000i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	5.42443	+	9.39539i	0.752233	+	1.30291i
$53$	4.42443	+	7.66334i	0.607742	+	1.05264i	0.991612	+	0.129253i	$0.0412579\pi$
$53$	4.42443	+	7.66334i	0.607742	+	1.05264i	−0.383870	+	0.923387i	$0.625409\pi$
$54$		0			0
$55$	2.21221	−	3.83167i	0.298295	−	0.516662i
$56$		0			0
$57$	0.712214	+	1.23359i	0.0943351	+	0.163393i
$58$		0			0
$59$	−2.21221	+	3.83167i	−0.288006	+	0.498841i	−0.973334	−	0.229394i	$-0.926326\pi$
$59$	−2.21221	+	3.83167i	−0.288006	+	0.498841i	0.685328	+	0.728235i	$0.259659\pi$
$60$	−2.00000			−0.258199
$61$	14.4244			1.84686			0.923429	−	0.383768i	$-0.125374\pi$
$61$	14.4244			1.84686			0.923429	+	0.383768i	$0.125374\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.71221	−	4.69769i	0.336409	−	0.582677i
$66$		0			0
$67$	6.42443	+	11.1274i	0.784869	+	1.35943i	0.929077	+	0.369885i	$0.120603\pi$
$67$	6.42443	+	11.1274i	0.784869	+	1.35943i	−0.144208	+	0.989547i	$0.546064\pi$
$68$	−4.00000	+	6.92820i	−0.485071	+	0.840168i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$		0			0
$71$	−1.21221	−	2.09962i	−0.143863	−	0.249179i	0.785085	−	0.619388i	$-0.212619\pi$
$71$	−1.21221	−	2.09962i	−0.143863	−	0.249179i	−0.928948	+	0.370209i	$0.879286\pi$
$72$		0			0
$73$	5.71221	+	9.89385i	0.668564	+	1.15799i	0.978306	+	0.207166i	$0.0664241\pi$
$73$	5.71221	+	9.89385i	0.668564	+	1.15799i	−0.309742	+	0.950821i	$0.600243\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	1.42443	−	2.46718i	0.163393	−	0.283005i
$77$		0			0
$78$		0			0
$79$	8.63664	−	14.9591i	0.971698	−	1.68303i	0.281272	−	0.959628i	$-0.409244\pi$
$79$	8.63664	−	14.9591i	0.971698	−	1.68303i	0.690426	−	0.723403i	$-0.257423\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$		0			0
$87$	−3.21221	+	5.56372i	−0.344386	+	0.596493i
$88$		0			0
$89$	−3.57557			−0.379010			−0.189505	−	0.981880i	$-0.560688\pi$
$89$	−3.57557			−0.379010			−0.189505	+	0.981880i	$0.560688\pi$
$90$		0			0
$91$		0			0
$92$	−4.00000			−0.417029
$93$	−4.71221	−	2.96564i	−0.488634	−	0.307523i
$94$		0			0
$95$	−1.42443			−0.146143
$96$		0			0
$97$	−2.57557			−0.261510			−0.130755	−	0.991415i	$-0.541740\pi$
$97$	−2.57557			−0.261510			−0.130755	+	0.991415i	$0.541740\pi$
$98$		0			0
$99$	−2.21221	+	3.83167i	−0.222336	+	0.385097i
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		0			0
$103$	−1.28779	−	2.23051i	−0.126889	−	0.219779i	0.795581	−	0.605848i	$-0.207166\pi$
$103$	−1.28779	−	2.23051i	−0.126889	−	0.219779i	−0.922470	+	0.386069i	$0.873833\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−7.42443	+	12.8595i	−0.717747	+	1.24317i	0.244144	+	0.969739i	$0.421493\pi$
$107$	−7.42443	+	12.8595i	−0.717747	+	1.24317i	−0.961891	+	0.273435i	$0.911840\pi$
$108$	2.00000			0.192450
$109$	13.8489			1.32648			0.663240	−	0.748407i	$-0.269181\pi$
$109$	13.8489			1.32648			0.663240	+	0.748407i	$0.269181\pi$
$110$		0			0
$111$	−0.712214	−	1.23359i	−0.0676004	−	0.117087i
$112$		0			0
$113$	1.42443	+	2.46718i	0.133999	+	0.232093i	0.925215	−	0.379444i	$-0.123885\pi$
$113$	1.42443	+	2.46718i	0.133999	+	0.232093i	−0.791216	+	0.611537i	$0.790551\pi$
$114$		0			0
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	12.8489			1.19299
$117$	−2.71221	+	4.69769i	−0.250744	+	0.434302i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.28779	+	7.42666i	−0.389799	+	0.675151i
$122$		0			0
$123$	−8.42443			−0.759605
$124$	−0.424429	+	11.1274i	−0.0381148	+	0.999273i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−1.71221	+	2.96564i	−0.151934	+	0.263158i	−0.931939	−	0.362616i	$-0.881884\pi$
$127$	−1.71221	+	2.96564i	−0.151934	+	0.263158i	0.780004	+	0.625774i	$0.215217\pi$
$128$		0			0
$129$	−1.71221	−	2.96564i	−0.150752	−	0.261110i
$130$		0			0
$131$	3.78779	−	6.56064i	0.330940	−	0.573206i	−0.651756	−	0.758429i	$-0.725967\pi$
$131$	3.78779	−	6.56064i	0.330940	−	0.573206i	0.982697	+	0.185223i	$0.0593008\pi$
$132$	8.84886			0.770194
$133$		0			0
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	−11.4244	−	19.7877i	−0.976055	−	1.69058i	−0.676409	−	0.736526i	$-0.736465\pi$
$137$	−11.4244	−	19.7877i	−0.976055	−	1.69058i	−0.299646	−	0.954051i	$-0.596868\pi$
$138$		0			0
$139$	−0.424429			−0.0359996			−0.0179998	−	0.999838i	$-0.505730\pi$
$139$	−0.424429			−0.0359996			−0.0179998	+	0.999838i	$0.505730\pi$
$140$		0			0
$141$	−5.42443	+	9.39539i	−0.456819	+	0.791234i
$142$		0			0
$143$	−12.0000	+	20.7846i	−1.00349	+	1.73810i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$	−3.21221	−	5.56372i	−0.266760	−	0.462042i
$146$		0			0
$147$	7.00000			0.577350
$148$	−1.42443	+	2.46718i	−0.117087	+	0.202801i
$149$	7.63664	−	13.2271i	0.625618	−	1.08360i	−0.362803	−	0.931866i	$-0.618180\pi$
$149$	7.63664	−	13.2271i	0.625618	−	1.08360i	0.988421	−	0.151737i	$-0.0484865\pi$
$150$		0			0
$151$	−13.4244			−1.09246			−0.546232	−	0.837634i	$-0.683938\pi$
$151$	−13.4244			−1.09246			−0.546232	+	0.837634i	$0.683938\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$		0			0
$155$	4.92443	−	2.59808i	0.395540	−	0.208683i
$156$	10.8489			0.868604
$157$	−12.5756			−1.00364			−0.501820	−	0.864972i	$-0.667336\pi$
$157$	−12.5756			−1.00364			−0.501820	+	0.864972i	$0.667336\pi$
$158$		0			0
$159$	8.84886			0.701760
$160$		0			0
$161$		0			0
$162$		0			0
$163$	6.57557			0.515038			0.257519	−	0.966273i	$-0.417095\pi$
$163$	6.57557			0.515038			0.257519	+	0.966273i	$0.417095\pi$
$164$	8.42443	+	14.5915i	0.657837	+	1.13941i
$165$	−2.21221	−	3.83167i	−0.172221	−	0.298295i
$166$		0			0
$167$	0.575571	−	0.996918i	0.0445390	−	0.0771439i	−0.842896	−	0.538076i	$-0.819151\pi$
$167$	0.575571	−	0.996918i	0.0445390	−	0.0771439i	0.887436	+	0.460932i	$0.152485\pi$
$168$		0			0
$169$	−8.21221	+	14.2240i	−0.631709	+	1.09415i
$170$		0			0
$171$	1.42443			0.108929
$172$	−3.42443	+	5.93128i	−0.261110	+	0.452256i
$173$	9.42443	+	16.3236i	0.716526	+	1.24106i	0.962368	+	0.271750i	$0.0876023\pi$
$173$	9.42443	+	16.3236i	0.716526	+	1.24106i	−0.245842	+	0.969310i	$0.579064\pi$
$174$		0			0
$175$		0			0
$176$	−8.84886	−	15.3267i	−0.667008	−	1.15529i
$177$	2.21221	+	3.83167i	0.166280	+	0.288006i
$178$		0			0
$179$	−2.78779	+	4.82859i	−0.208369	+	0.360905i	−0.951201	−	0.308572i	$-0.900149\pi$
$179$	−2.78779	+	4.82859i	−0.208369	+	0.360905i	0.742832	+	0.669478i	$0.233482\pi$
$180$	−1.00000	+	1.73205i	−0.0745356	+	0.129099i
$181$	5.71221	+	9.89385i	0.424586	+	0.735404i	0.996382	−	0.0849920i	$-0.0270865\pi$
$181$	5.71221	+	9.89385i	0.424586	+	0.735404i	−0.571796	+	0.820396i	$0.693753\pi$
$182$		0			0
$183$	7.21221	−	12.4919i	0.533142	−	0.923429i
$184$		0			0
$185$	1.42443			0.104726
$186$		0			0
$187$	−17.6977			−1.29419
$188$	21.6977			1.58247
$189$		0			0
$190$		0			0
$191$	−8.63664	−	14.9591i	−0.624926	−	1.08240i	−0.988555	−	0.150859i	$-0.951796\pi$
$191$	−8.63664	−	14.9591i	−0.624926	−	1.08240i	0.363630	−	0.931544i	$-0.381537\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	2.28779	−	3.96256i	0.164678	−	0.285231i	−0.771863	−	0.635789i	$-0.780675\pi$
$193$	2.28779	−	3.96256i	0.164678	−	0.285231i	0.936541	+	0.350558i	$0.114008\pi$
$194$		0			0
$195$	−2.71221	−	4.69769i	−0.194226	−	0.336409i
$196$	−7.00000	−	12.1244i	−0.500000	−	0.866025i
$197$	10.4244	+	18.0556i	0.742710	+	1.28641i	0.951257	+	0.308399i	$0.0997931\pi$
$197$	10.4244	+	18.0556i	0.742710	+	1.28641i	−0.208547	+	0.978012i	$0.566874\pi$
$198$		0			0
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$		0			0
$201$	12.8489			0.906289
$202$		0			0
$203$		0			0
$204$	4.00000	+	6.92820i	0.280056	+	0.485071i
$205$	4.21221	−	7.29577i	0.294194	−	0.509559i
$206$		0			0
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−10.8489	−	18.7908i	−0.752233	−	1.30291i
$209$	6.30228			0.435938
$210$		0			0
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	−0.328135	−	0.944631i	$-0.606420\pi$
$211$	9.50000	−	16.4545i	0.654007	−	1.13277i	0.982142	−	0.188142i	$-0.0602466\pi$
$212$	−8.84886	−	15.3267i	−0.607742	−	1.05264i
$213$	−2.42443			−0.166119
$214$		0			0
$215$	3.42443			0.233544
$216$		0			0
$217$		0			0
$218$		0			0
$219$	11.4244			0.771991
$220$	−4.42443	+	7.66334i	−0.298295	+	0.516662i
$221$	−21.6977			−1.45955
$222$		0			0
$223$	0.712214	−	1.23359i	0.0476934	−	0.0826074i	−0.841193	−	0.540735i	$-0.818146\pi$
$223$	0.712214	−	1.23359i	0.0476934	−	0.0826074i	0.888887	+	0.458127i	$0.151480\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−1.57557	−	2.72897i	−0.104574	−	0.181128i	0.808990	−	0.587823i	$-0.200015\pi$
$227$	−1.57557	−	2.72897i	−0.104574	−	0.181128i	−0.913564	+	0.406695i	$0.866681\pi$
$228$	−1.42443	−	2.46718i	−0.0943351	−	0.163393i
$229$	5.50000	−	9.52628i	0.363450	−	0.629514i	−0.625076	−	0.780564i	$-0.714932\pi$
$229$	5.50000	−	9.52628i	0.363450	−	0.629514i	0.988526	+	0.151050i	$0.0482653\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−3.15114			−0.206438			−0.103219	−	0.994659i	$-0.532914\pi$
$233$	−3.15114			−0.206438			−0.103219	+	0.994659i	$0.532914\pi$
$234$		0			0
$235$	−5.42443	−	9.39539i	−0.353851	−	0.612887i
$236$	4.42443	−	7.66334i	0.288006	−	0.498841i
$237$	−8.63664	−	14.9591i	−0.561010	−	0.971698i
$238$		0			0
$239$	−9.63664	−	16.6912i	−0.623343	−	1.07966i	−0.988859	−	0.148856i	$-0.952441\pi$
$239$	−9.63664	−	16.6912i	−0.623343	−	1.07966i	0.365516	−	0.930805i	$-0.380892\pi$
$240$	4.00000			0.258199
$241$	−2.28779	+	3.96256i	−0.147369	+	0.255251i	−0.930254	−	0.366915i	$-0.880414\pi$
$241$	−2.28779	+	3.96256i	−0.147369	+	0.255251i	0.782885	+	0.622166i	$0.213747\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−28.8489			−1.84686
$245$	−3.50000	+	6.06218i	−0.223607	+	0.387298i
$246$		0			0
$247$	7.72671			0.491639
$248$		0			0
$249$	−6.00000			−0.380235
$250$		0			0
$251$	7.42443	−	12.8595i	0.468626	−	0.811684i	−0.530731	−	0.847540i	$-0.678083\pi$
$251$	7.42443	−	12.8595i	0.468626	−	0.811684i	0.999357	+	0.0358565i	$0.0114159\pi$
$252$		0			0
$253$	−4.42443	−	7.66334i	−0.278161	−	0.481790i
$254$		0			0
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	16.0000			1.00000
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	0.997429	−	0.0716680i	$-0.0228322\pi$
$257$	7.00000	+	12.1244i	0.436648	+	0.756297i	−0.560781	+	0.827964i	$0.689499\pi$
$258$		0			0
$259$		0			0
$260$	−5.42443	+	9.39539i	−0.336409	+	0.582677i
$261$	3.21221	+	5.56372i	0.198831	+	0.344386i
$262$		0			0
$263$	18.0000			1.10993			0.554964	−	0.831875i	$-0.312732\pi$
$263$	18.0000			1.10993			0.554964	+	0.831875i	$0.312732\pi$
$264$		0			0
$265$	−4.42443	+	7.66334i	−0.271791	+	0.470755i
$266$		0			0
$267$	−1.78779	+	3.09654i	−0.109411	+	0.189505i
$268$	−12.8489	−	22.2549i	−0.784869	−	1.35943i
$269$	−7.78779	−	13.4888i	−0.474830	−	0.822429i	0.524755	−	0.851253i	$-0.324157\pi$
$269$	−7.78779	−	13.4888i	−0.474830	−	0.822429i	−0.999584	+	0.0288243i	$0.990824\pi$
$270$		0			0
$271$	1.00000			0.0607457			0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000			0.0607457			0.0303728	+	0.999539i	$0.490331\pi$
$272$	8.00000	−	13.8564i	0.485071	−	0.840168i
$273$		0			0
$274$		0			0
$275$	4.42443			0.266803
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	22.2733			1.33827			0.669136	−	0.743140i	$-0.266664\pi$
$277$	22.2733			1.33827			0.669136	+	0.743140i	$0.266664\pi$
$278$		0			0
$279$	−4.92443	+	2.59808i	−0.294818	+	0.155543i
$280$		0			0
$281$	−21.2733			−1.26906			−0.634529	−	0.772899i	$-0.718806\pi$
$281$	−21.2733			−1.26906			−0.634529	+	0.772899i	$0.718806\pi$
$282$		0			0
$283$	−28.2733			−1.68067			−0.840336	−	0.542066i	$-0.817642\pi$
$283$	−28.2733			−1.68067			−0.840336	+	0.542066i	$0.817642\pi$
$284$	2.42443	+	4.19923i	0.143863	+	0.249179i
$285$	−0.712214	+	1.23359i	−0.0421879	+	0.0730717i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	−1.28779	+	2.23051i	−0.0754913	+	0.130755i
$292$	−11.4244	−	19.7877i	−0.668564	−	1.15799i
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$		0			0
$295$	−4.42443			−0.257600
$296$		0			0
$297$	2.21221	+	3.83167i	0.128366	+	0.222336i
$298$		0			0
$299$	−5.42443	−	9.39539i	−0.313703	−	0.543349i
$300$	−1.00000	−	1.73205i	−0.0577350	−	0.100000i
$301$		0			0
$302$		0			0
$303$	7.00000	−	12.1244i	0.402139	−	0.696526i
$304$	−2.84886	+	4.93437i	−0.163393	+	0.283005i
$305$	7.21221	+	12.4919i	0.412970	+	0.715285i
$306$		0			0
$307$	−4.28779	+	7.42666i	−0.244717	+	0.423862i	−0.962052	−	0.272866i	$-0.912028\pi$
$307$	−4.28779	+	7.42666i	−0.244717	+	0.423862i	0.717335	+	0.696728i	$0.245362\pi$
$308$		0			0
$309$	−2.57557			−0.146519
$310$		0			0
$311$	10.4244			0.591115			0.295558	−	0.955325i	$-0.404495\pi$
$311$	10.4244			0.591115			0.295558	+	0.955325i	$0.404495\pi$
$312$		0			0
$313$	−3.71221	+	6.42974i	−0.209827	+	0.363431i	−0.951660	−	0.307154i	$-0.900623\pi$
$313$	−3.71221	+	6.42974i	−0.209827	+	0.363431i	0.741833	+	0.670585i	$0.233957\pi$
$314$		0			0
$315$		0			0
$316$	−17.2733	+	29.9182i	−0.971698	+	1.68303i
$317$	9.84886	−	17.0587i	0.553167	−	0.958113i	−0.444877	−	0.895592i	$-0.646752\pi$
$317$	9.84886	−	17.0587i	0.553167	−	0.958113i	0.998044	−	0.0625214i	$-0.0199142\pi$
$318$		0			0
$319$	14.2122	+	24.6163i	0.795731	+	1.37825i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	7.42443	+	12.8595i	0.414391	+	0.717747i
$322$		0			0
$323$	2.84886	+	4.93437i	0.158515	+	0.274555i
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$	5.42443			0.300893
$326$		0			0
$327$	6.92443	−	11.9935i	0.382922	−	0.663240i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	0.995134	−	0.0985303i	$-0.0314141\pi$
$331$	7.50000	+	12.9904i	0.412237	+	0.714016i	−0.582897	+	0.812546i	$0.698081\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−1.42443			−0.0780582
$334$		0			0
$335$	−6.42443	+	11.1274i	−0.351004	+	0.607957i
$336$		0			0
$337$	−5.15114			−0.280601			−0.140300	−	0.990109i	$-0.544807\pi$
$337$	−5.15114			−0.280601			−0.140300	+	0.990109i	$0.544807\pi$
$338$		0			0
$339$	2.84886			0.154729
$340$	−8.00000			−0.433861
$341$	−21.7878	+	11.4950i	−1.17987	+	0.622489i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.00000			0.107676
$346$		0			0
$347$	6.84886	−	11.8626i	0.367666	−	0.636816i	−0.621534	−	0.783387i	$-0.713490\pi$
$347$	6.84886	−	11.8626i	0.367666	−	0.636816i	0.989200	+	0.146571i	$0.0468237\pi$
$348$	6.42443	−	11.1274i	0.344386	−	0.596493i
$349$	−0.151142			−0.00809046			−0.00404523	−	0.999992i	$-0.501288\pi$
$349$	−0.151142			−0.00809046			−0.00404523	+	0.999992i	$0.501288\pi$
$350$		0			0
$351$	2.71221	+	4.69769i	0.144767	+	0.250744i
$352$		0			0
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$		0			0
$355$	1.21221	−	2.09962i	0.0643377	−	0.111436i
$356$	7.15114			0.379010
$357$		0			0
$358$		0			0
$359$	5.21221	+	9.02782i	0.275090	+	0.476470i	0.970158	−	0.242474i	$-0.0779590\pi$
$359$	5.21221	+	9.02782i	0.275090	+	0.476470i	−0.695068	+	0.718944i	$0.744626\pi$
$360$		0			0
$361$	8.48550	+	14.6973i	0.446605	+	0.773543i
$362$		0			0
$363$	4.28779	+	7.42666i	0.225050	+	0.389799i
$364$		0			0
$365$	−5.71221	+	9.89385i	−0.298991	+	0.517868i
$366$		0			0
$367$	−10.7122	−	18.5541i	−0.559173	−	0.968516i	−0.997566	−	0.0697326i	$-0.977785\pi$
$367$	−10.7122	−	18.5541i	−0.559173	−	0.968516i	0.438393	−	0.898784i	$-0.355548\pi$
$368$	8.00000			0.417029
$369$	−4.21221	+	7.29577i	−0.219279	+	0.379803i
$370$		0			0
$371$		0			0
$372$	9.42443	+	5.93128i	0.488634	+	0.307523i
$373$	25.1221			1.30078			0.650388	−	0.759602i	$-0.274606\pi$
$373$	25.1221			1.30078			0.650388	+	0.759602i	$0.274606\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	17.4244	+	30.1800i	0.897404	+	1.55435i
$378$		0			0
$379$	0.712214	−	1.23359i	0.0365840	−	0.0633653i	−0.847154	−	0.531348i	$-0.821686\pi$
$379$	0.712214	−	1.23359i	0.0365840	−	0.0633653i	0.883738	+	0.467983i	$0.155019\pi$
$380$	2.84886			0.146143
$381$	1.71221	+	2.96564i	0.0877194	+	0.151934i
$382$		0			0
$383$	7.57557	+	13.1213i	0.387094	+	0.670466i	0.992057	−	0.125787i	$-0.0401457\pi$
$383$	7.57557	+	13.1213i	0.387094	+	0.670466i	−0.604964	+	0.796253i	$0.706812\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.42443			−0.174074
$388$	5.15114			0.261510
$389$	−1.21221	+	2.09962i	−0.0614617	+	0.106455i	−0.895119	−	0.445827i	$-0.852910\pi$
$389$	−1.21221	+	2.09962i	−0.0614617	+	0.106455i	0.833657	+	0.552282i	$0.186243\pi$
$390$		0			0
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$		0			0
$393$	−3.78779	−	6.56064i	−0.191069	−	0.330940i
$394$		0			0
$395$	17.2733			0.869113
$396$	4.42443	−	7.66334i	0.222336	−	0.385097i
$397$	15.4244	−	26.7159i	0.774130	−	1.34083i	−0.161152	−	0.986930i	$-0.551521\pi$
$397$	15.4244	−	26.7159i	0.774130	−	1.34083i	0.935282	−	0.353903i	$-0.115146\pi$
$398$		0			0
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	−12.4244			−0.620446			−0.310223	−	0.950664i	$-0.600404\pi$
$401$	−12.4244			−0.620446			−0.310223	+	0.950664i	$0.600404\pi$
$402$		0			0
$403$	−26.7122	+	14.0931i	−1.33063	+	0.702026i
$404$	−28.0000			−1.39305
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	−6.30228			−0.312393
$408$		0			0
$409$	−0.287786	+	0.498459i	−0.0142301	+	0.0246472i	−0.873053	−	0.487626i	$-0.837863\pi$
$409$	−0.287786	+	0.498459i	−0.0142301	+	0.0246472i	0.858823	+	0.512273i	$0.171196\pi$
$410$		0			0
$411$	−22.8489			−1.12705
$412$	2.57557	+	4.46102i	0.126889	+	0.219779i
$413$		0			0
$414$		0			0
$415$	3.00000	−	5.19615i	0.147264	−	0.255069i
$416$		0			0
$417$	−0.212214	+	0.367566i	−0.0103922	+	0.0179998i
$418$		0			0
$419$	4.72671			0.230915			0.115458	−	0.993312i	$-0.463167\pi$
$419$	4.72671			0.230915			0.115458	+	0.993312i	$0.463167\pi$
$420$		0			0
$421$	−0.363357	−	0.629352i	−0.0177089	−	0.0306727i	0.857035	−	0.515258i	$-0.172304\pi$
$421$	−0.363357	−	0.629352i	−0.0177089	−	0.0306727i	−0.874744	+	0.484585i	$0.838971\pi$
$422$		0			0
$423$	5.42443	+	9.39539i	0.263745	+	0.456819i
$424$		0			0
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$		0			0
$428$	14.8489	−	25.7190i	0.717747	−	1.24317i
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$	−1.21221	+	2.09962i	−0.0583903	+	0.101135i	−0.893743	−	0.448579i	$-0.851930\pi$
$431$	−1.21221	+	2.09962i	−0.0583903	+	0.101135i	0.835353	+	0.549714i	$0.185263\pi$
$432$	−4.00000			−0.192450
$433$	36.2733			1.74318			0.871591	−	0.490233i	$-0.163088\pi$
$433$	36.2733			1.74318			0.871591	+	0.490233i	$0.163088\pi$
$434$		0			0
$435$	−6.42443			−0.308028
$436$	−27.6977			−1.32648
$437$	−1.42443	+	2.46718i	−0.0681397	+	0.118021i
$438$		0			0
$439$	3.07557	+	5.32705i	0.146789	+	0.254246i	0.930039	−	0.367461i	$-0.119773\pi$
$439$	3.07557	+	5.32705i	0.146789	+	0.254246i	−0.783250	+	0.621707i	$0.786440\pi$
$440$		0			0
$441$	3.50000	−	6.06218i	0.166667	−	0.288675i
$442$		0			0
$443$	1.42443	+	2.46718i	0.0676767	+	0.117219i	0.897878	−	0.440244i	$-0.145108\pi$
$443$	1.42443	+	2.46718i	0.0676767	+	0.117219i	−0.830202	+	0.557463i	$0.811775\pi$
$444$	1.42443	+	2.46718i	0.0676004	+	0.117087i
$445$	−1.78779	−	3.09654i	−0.0847492	−	0.146790i
$446$		0			0
$447$	−7.63664	−	13.2271i	−0.361201	−	0.625618i
$448$		0			0
$449$	40.8489			1.92778			0.963888	−	0.266307i	$-0.0858033\pi$
$449$	40.8489			1.92778			0.963888	+	0.266307i	$0.0858033\pi$
$450$		0			0
$451$	−18.6366	+	32.2796i	−0.877565	+	1.51999i
$452$	−2.84886	−	4.93437i	−0.133999	−	0.232093i
$453$	−6.71221	+	11.6259i	−0.315367	+	0.546232i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	20.5756			0.962485			0.481242	−	0.876588i	$-0.340186\pi$
$457$	20.5756			0.962485			0.481242	+	0.876588i	$0.340186\pi$
$458$		0			0
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	−2.00000	−	3.46410i	−0.0932505	−	0.161515i
$461$	8.84886			0.412132			0.206066	−	0.978538i	$-0.433934\pi$
$461$	8.84886			0.412132			0.206066	+	0.978538i	$0.433934\pi$
$462$		0			0
$463$	−33.1221			−1.53932			−0.769658	−	0.638456i	$-0.779573\pi$
$463$	−33.1221			−1.53932			−0.769658	+	0.638456i	$0.779573\pi$
$464$	−25.6977			−1.19299
$465$	0.212214	−	5.56372i	0.00984121	−	0.258011i
$466$		0			0
$467$	23.6977			1.09660			0.548300	−	0.836282i	$-0.315275\pi$
$467$	23.6977			1.09660			0.548300	+	0.836282i	$0.315275\pi$
$468$	5.42443	−	9.39539i	0.250744	−	0.434302i
$469$		0			0
$470$		0			0
$471$	−6.28779	+	10.8908i	−0.289726	+	0.501820i
$472$		0			0
$473$	−15.1511			−0.696650
$474$		0			0
$475$	−0.712214	−	1.23359i	−0.0326786	−	0.0566011i
$476$		0			0
$477$	4.42443	−	7.66334i	0.202581	−	0.350880i
$478$		0			0
$479$	15.6366	−	27.0835i	0.714456	−	1.23747i	−0.248712	−	0.968577i	$-0.580007\pi$
$479$	15.6366	−	27.0835i	0.714456	−	1.23747i	0.963169	−	0.268898i	$-0.0866593\pi$
$480$		0			0
$481$	−7.72671			−0.352308
$482$		0			0
$483$		0			0
$484$	8.57557	−	14.8533i	0.389799	−	0.675151i
$485$	−1.28779	−	2.23051i	−0.0584753	−	0.101282i
$486$		0			0
$487$	10.1366	+	17.5572i	0.459335	+	0.795592i	0.998926	−	0.0463356i	$-0.0147544\pi$
$487$	10.1366	+	17.5572i	0.459335	+	0.795592i	−0.539591	+	0.841927i	$0.681421\pi$
$488$		0			0
$489$	3.28779	−	5.69461i	0.148679	−	0.257519i
$490$		0			0
$491$	2.63664	+	4.56680i	0.118990	+	0.206097i	0.919368	−	0.393399i	$-0.128701\pi$
$491$	2.63664	+	4.56680i	0.118990	+	0.206097i	−0.800378	+	0.599496i	$0.795368\pi$
$492$	16.8489			0.759605
$493$	−12.8489	+	22.2549i	−0.578683	+	1.00231i
$494$		0			0
$495$	−4.42443			−0.198863
$496$	0.848858	−	22.2549i	0.0381148	−	0.999273i
$497$		0			0
$498$		0			0
$499$	16.6366	−	28.8155i	0.744758	−	1.28996i	−0.205549	−	0.978647i	$-0.565898\pi$
$499$	16.6366	−	28.8155i	0.744758	−	1.28996i	0.950308	−	0.311313i	$-0.100769\pi$
$500$	2.00000			0.0894427
$501$	−0.575571	−	0.996918i	−0.0257146	−	0.0445390i
$502$		0			0
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	−0.630705	−	0.776022i	$-0.717234\pi$
$503$	8.00000	−	13.8564i	0.356702	−	0.617827i	0.987408	+	0.158196i	$0.0505677\pi$
$504$		0			0
$505$	7.00000	+	12.1244i	0.311496	+	0.539527i
$506$		0			0
$507$	8.21221	+	14.2240i	0.364717	+	0.631709i
$508$	3.42443	−	5.93128i	0.151934	−	0.263158i
$509$	−9.63664	−	16.6912i	−0.427137	−	0.739822i	0.569481	−	0.822005i	$-0.307144\pi$
$509$	−9.63664	−	16.6912i	−0.427137	−	0.739822i	−0.996617	+	0.0821823i	$0.973811\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	0.712214	−	1.23359i	0.0314450	−	0.0544644i
$514$		0			0
$515$	1.28779	−	2.23051i	0.0567466	−	0.0982880i
$516$	3.42443	+	5.93128i	0.150752	+	0.261110i
$517$	24.0000	+	41.5692i	1.05552	+	1.82821i
$518$		0			0
$519$	18.8489			0.827373
$520$		0			0
$521$	−8.06107	+	13.9622i	−0.353162	+	0.611695i	−0.986802	−	0.161934i	$-0.948227\pi$
$521$	−8.06107	+	13.9622i	−0.353162	+	0.611695i	0.633640	+	0.773628i	$0.281560\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−7.57557	+	13.1213i	−0.330940	+	0.573206i
$525$		0			0
$526$		0			0
$527$	−18.8489	−	11.8626i	−0.821069	−	0.516742i
$528$	−17.6977			−0.770194
$529$	−19.0000			−0.826087
$530$		0			0
$531$	4.42443			0.192004
$532$		0			0
$533$	−22.8489	+	39.5754i	−0.989694	+	1.71420i
$534$		0			0
$535$	−14.8489			−0.641972
$536$		0			0
$537$	2.78779	+	4.82859i	0.120302	+	0.208369i
$538$		0			0
$539$	15.4855	−	26.8217i	0.667008	−	1.15529i
$540$	1.00000	+	1.73205i	0.0430331	+	0.0745356i
$541$	−16.9244	+	29.3140i	−0.727638	+	1.26031i	0.230241	+	0.973134i	$0.426049\pi$
$541$	−16.9244	+	29.3140i	−0.727638	+	1.26031i	−0.957879	+	0.287172i	$0.907285\pi$
$542$		0			0
$543$	11.4244			0.490269
$544$		0			0
$545$	6.92443	+	11.9935i	0.296610	+	0.513743i
$546$		0			0
$547$	−10.1366	−	17.5572i	−0.433412	−	0.750691i	0.563753	−	0.825943i	$-0.309357\pi$
$547$	−10.1366	−	17.5572i	−0.433412	−	0.750691i	−0.997165	+	0.0752526i	$0.976024\pi$
$548$	22.8489	+	39.5754i	0.976055	+	1.69058i
$549$	−7.21221	−	12.4919i	−0.307810	−	0.533142i
$550$		0			0
$551$	4.57557	−	7.92512i	0.194926	−	0.337622i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	0.712214	−	1.23359i	0.0302318	−	0.0523630i
$556$	0.848858			0.0359996
$557$	−1.15114			−0.0487755			−0.0243877	−	0.999703i	$-0.507764\pi$
$557$	−1.15114			−0.0487755			−0.0243877	+	0.999703i	$0.507764\pi$
$558$		0			0
$559$	−18.5756			−0.785663
$560$		0			0
$561$	−8.84886	+	15.3267i	−0.373599	+	0.647093i
$562$		0			0
$563$	−1.15114	−	1.99384i	−0.0485149	−	0.0840302i	0.840748	−	0.541426i	$-0.182115\pi$
$563$	−1.15114	−	1.99384i	−0.0485149	−	0.0840302i	−0.889263	+	0.457396i	$0.848782\pi$
$564$	10.8489	−	18.7908i	0.456819	−	0.791234i
$565$	−1.42443	+	2.46718i	−0.0599262	+	0.103795i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.21221	−	2.09962i	−0.0508187	−	0.0880205i	0.839497	−	0.543364i	$-0.182850\pi$
$569$	−1.21221	−	2.09962i	−0.0508187	−	0.0880205i	−0.890316	+	0.455344i	$0.849516\pi$
$570$		0			0
$571$	18.7733	+	32.5163i	0.785638	+	1.36076i	0.928617	+	0.371039i	$0.120998\pi$
$571$	18.7733	+	32.5163i	0.785638	+	1.36076i	−0.142980	+	0.989726i	$0.545668\pi$
$572$	24.0000	−	41.5692i	1.00349	−	1.73810i
$573$	−17.2733			−0.721602
$574$		0			0
$575$	−1.00000	+	1.73205i	−0.0417029	+	0.0722315i
$576$	4.00000	+	6.92820i	0.166667	+	0.288675i
$577$	5.42443	−	9.39539i	0.225822	−	0.391135i	−0.730744	−	0.682652i	$-0.760827\pi$
$577$	5.42443	−	9.39539i	0.225822	−	0.391135i	0.956566	+	0.291517i	$0.0941599\pi$
$578$		0			0
$579$	−2.28779	−	3.96256i	−0.0950771	−	0.164678i
$580$	6.42443	+	11.1274i	0.266760	+	0.462042i
$581$		0			0
$582$		0			0
$583$	19.5756	−	33.9059i	0.810737	−	1.40424i
$584$		0			0
$585$	−5.42443			−0.224273
$586$		0			0
$587$	−6.84886			−0.282683			−0.141341	−	0.989961i	$-0.545141\pi$
$587$	−6.84886			−0.282683			−0.141341	+	0.989961i	$0.545141\pi$
$588$	−14.0000			−0.577350
$589$	6.71221	+	4.22435i	0.276572	+	0.174061i
$590$		0			0
$591$	20.8489			0.857607
$592$	2.84886	−	4.93437i	0.117087	−	0.202801i
$593$	−11.1511			−0.457923			−0.228961	−	0.973436i	$-0.573533\pi$
$593$	−11.1511			−0.457923			−0.228961	+	0.973436i	$0.573533\pi$
$594$		0			0
$595$		0			0
$596$	−15.2733	+	26.4541i	−0.625618	+	1.08360i
$597$	−16.0000			−0.654836
$598$		0			0
$599$	6.78779	+	11.7568i	0.277341	+	0.480369i	0.970723	−	0.240201i	$-0.0772134\pi$
$599$	6.78779	+	11.7568i	0.277341	+	0.480369i	−0.693382	+	0.720570i	$0.743880\pi$
$600$		0			0
$601$	−14.0611	+	24.3545i	−0.573563	+	0.993440i	0.422633	+	0.906301i	$0.361106\pi$
$601$	−14.0611	+	24.3545i	−0.573563	+	0.993440i	−0.996196	+	0.0871395i	$0.972227\pi$
$602$		0			0
$603$	6.42443	−	11.1274i	0.261623	−	0.453144i
$604$	26.8489			1.09246
$605$	−8.57557			−0.348647
$606$		0			0
$607$	−12.2878	−	21.2831i	−0.498746	−	0.863853i	0.501253	−	0.865301i	$-0.332873\pi$
$607$	−12.2878	−	21.2831i	−0.498746	−	0.863853i	−0.999999	+	0.00144759i	$0.999539\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	29.4244	+	50.9646i	1.19038	+	2.06181i
$612$	8.00000			0.323381
$613$	17.5611	−	30.4167i	0.709285	−	1.22852i	−0.255838	−	0.966720i	$-0.582351\pi$
$613$	17.5611	−	30.4167i	0.709285	−	1.22852i	0.965123	−	0.261798i	$-0.0843154\pi$
$614$		0			0
$615$	−4.21221	−	7.29577i	−0.169853	−	0.294194i
$616$		0			0
$617$	−4.42443	+	7.66334i	−0.178121	+	0.308514i	−0.941237	−	0.337747i	$-0.890335\pi$
$617$	−4.42443	+	7.66334i	−0.178121	+	0.308514i	0.763116	+	0.646261i	$0.223668\pi$
$618$		0			0
$619$	21.8489			0.878180			0.439090	−	0.898443i	$-0.355301\pi$
$619$	21.8489			0.878180			0.439090	+	0.898443i	$0.355301\pi$
$620$	−9.84886	+	5.19615i	−0.395540	+	0.208683i
$621$	−2.00000			−0.0802572
$622$		0			0
$623$		0			0
$624$	−21.6977			−0.868604
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	3.15114	−	5.45794i	0.125844	−	0.217969i
$628$	25.1511			1.00364
$629$	−2.84886	−	4.93437i	−0.113591	−	0.196746i
$630$		0			0
$631$	−10.6366	−	18.4232i	−0.423438	−	0.733416i	0.572835	−	0.819671i	$-0.305844\pi$
$631$	−10.6366	−	18.4232i	−0.423438	−	0.733416i	−0.996273	+	0.0862544i	$0.972510\pi$
$632$		0			0
$633$	−9.50000	−	16.4545i	−0.377591	−	0.654007i
$634$		0			0
$635$	−3.42443			−0.135894
$636$	−17.6977			−0.701760
$637$	18.9855	−	32.8839i	0.752233	−	1.30291i
$638$		0			0
$639$	−1.21221	+	2.09962i	−0.0479545	+	0.0830596i
$640$		0			0
$641$	−4.15114	−	7.18999i	−0.163960	−	0.283987i	0.772325	−	0.635227i	$-0.219094\pi$
$641$	−4.15114	−	7.18999i	−0.163960	−	0.283987i	−0.936286	+	0.351240i	$0.885760\pi$
$642$		0			0
$643$	14.2733			0.562883			0.281442	−	0.959578i	$-0.409187\pi$
$643$	14.2733			0.562883			0.281442	+	0.959578i	$0.409187\pi$
$644$		0			0
$645$	1.71221	−	2.96564i	0.0674184	−	0.116772i
$646$		0			0
$647$	−44.5466			−1.75131			−0.875653	−	0.482940i	$-0.839569\pi$
$647$	−44.5466			−1.75131			−0.875653	+	0.482940i	$0.839569\pi$
$648$		0			0
$649$	19.5756			0.768408
$650$		0			0
$651$		0			0
$652$	−13.1511			−0.515038
$653$	−31.3954			−1.22860			−0.614299	−	0.789073i	$-0.710561\pi$
$653$	−31.3954			−1.22860			−0.614299	+	0.789073i	$0.710561\pi$
$654$		0			0
$655$	7.57557			0.296002
$656$	−16.8489	−	29.1831i	−0.657837	−	1.13941i
$657$	5.71221	−	9.89385i	0.222855	−	0.385996i
$658$		0			0
$659$	−45.6977			−1.78013			−0.890065	−	0.455833i	$-0.849341\pi$
$659$	−45.6977			−1.78013			−0.890065	+	0.455833i	$0.849341\pi$
$660$	4.42443	+	7.66334i	0.172221	+	0.298295i
$661$	−8.56107	−	14.8282i	−0.332987	−	0.576751i	0.650109	−	0.759841i	$-0.274723\pi$
$661$	−8.56107	−	14.8282i	−0.332987	−	0.576751i	−0.983096	+	0.183090i	$0.941390\pi$
$662$		0			0
$663$	−10.8489	+	18.7908i	−0.421335	+	0.729773i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−12.8489			−0.497510
$668$	−1.15114	+	1.99384i	−0.0445390	+	0.0771439i
$669$	−0.712214	−	1.23359i	−0.0275358	−	0.0476934i
$670$		0			0
$671$	−31.9099	−	55.2696i	−1.23187	−	2.13366i
$672$		0			0
$673$	22.6977	+	39.3136i	0.874933	+	1.51543i	0.856834	+	0.515592i	$0.172428\pi$
$673$	22.6977	+	39.3136i	0.874933	+	1.51543i	0.0180982	+	0.999836i	$0.494239\pi$
$674$		0			0
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	16.4244	−	28.4479i	0.631709	−	1.09415i
$677$	12.0000	+	20.7846i	0.461197	+	0.798817i	0.999021	−	0.0442400i	$-0.0140866\pi$
$677$	12.0000	+	20.7846i	0.461197	+	0.798817i	−0.537823	+	0.843057i	$0.680753\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−3.15114			−0.120752
$682$		0			0
$683$	−27.6977			−1.05982			−0.529912	−	0.848053i	$-0.677775\pi$
$683$	−27.6977			−1.05982			−0.529912	+	0.848053i	$0.677775\pi$
$684$	−2.84886			−0.108929
$685$	11.4244	−	19.7877i	0.436505	−	0.756049i
$686$		0			0
$687$	−5.50000	−	9.52628i	−0.209838	−	0.363450i
$688$	6.84886	−	11.8626i	0.261110	−	0.452256i
$689$	24.0000	−	41.5692i	0.914327	−	1.58366i
$690$		0			0
$691$	11.7878	+	20.4170i	0.448428	+	0.776701i	0.998284	−	0.0585589i	$-0.0186505\pi$
$691$	11.7878	+	20.4170i	0.448428	+	0.776701i	−0.549855	+	0.835260i	$0.685317\pi$
$692$	−18.8489	−	32.6472i	−0.716526	−	1.24106i
$693$		0			0
$694$		0			0
$695$	−0.212214	−	0.367566i	−0.00804975	−	0.0139426i
$696$		0			0
$697$	−33.6977			−1.27639
$698$		0			0
$699$	−1.57557	+	2.72897i	−0.0595936	+	0.103219i
$700$		0			0
$701$	−17.0611	+	29.5506i	−0.644388	+	1.11611i	0.340055	+	0.940406i	$0.389554\pi$
$701$	−17.0611	+	29.5506i	−0.644388	+	1.11611i	−0.984443	+	0.175707i	$0.943779\pi$
$702$		0			0
$703$	1.01450	+	1.75716i	0.0382625	+	0.0662727i
$704$	17.6977	+	30.6533i	0.667008	+	1.15529i
$705$	−10.8489			−0.408592
$706$		0			0
$707$		0			0
$708$	−4.42443	−	7.66334i	−0.166280	−	0.288006i
$709$	−17.7267			−0.665741			−0.332870	−	0.942973i	$-0.608017\pi$
$709$	−17.7267			−0.665741			−0.332870	+	0.942973i	$0.608017\pi$
$710$		0			0
$711$	−17.2733			−0.647799
$712$		0			0
$713$	0.424429	−	11.1274i	0.0158950	−	0.416726i
$714$		0			0
$715$	−24.0000			−0.897549
$716$	5.57557	−	9.65717i	0.208369	−	0.360905i
$717$	−19.2733			−0.719774
$718$		0			0
$719$	6.57557	−	11.3892i	0.245227	−	0.424746i	−0.716968	−	0.697106i	$-0.754471\pi$
$719$	6.57557	−	11.3892i	0.245227	−	0.424746i	0.962196	+	0.272360i	$0.0878040\pi$
$720$	2.00000	−	3.46410i	0.0745356	−	0.129099i
$721$		0			0
$722$		0			0
$723$	2.28779	+	3.96256i	0.0850837	+	0.147369i
$724$	−11.4244	−	19.7877i	−0.424586	−	0.735404i
$725$	3.21221	−	5.56372i	0.119299	−	0.206631i
$726$		0			0
$727$	15.7122	−	27.2144i	0.582734	−	1.00932i	−0.412420	−	0.910994i	$-0.635316\pi$
$727$	15.7122	−	27.2144i	0.582734	−	1.00932i	0.995154	−	0.0983307i	$-0.0313503\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.84886	−	11.8626i	−0.253314	−	0.438753i
$732$	−14.4244	+	24.9838i	−0.533142	+	0.923429i
$733$	5.28779	+	9.15871i	0.195309	+	0.338285i	0.947002	−	0.321229i	$-0.104096\pi$
$733$	5.28779	+	9.15871i	0.195309	+	0.338285i	−0.751693	+	0.659513i	$0.770762\pi$
$734$		0			0
$735$	3.50000	+	6.06218i	0.129099	+	0.223607i
$736$		0			0
$737$	28.4244	−	49.2326i	1.04703	−	1.81350i
$738$		0			0
$739$	7.07557	+	12.2552i	0.260279	+	0.450817i	0.966316	−	0.257358i	$-0.0828521\pi$
$739$	7.07557	+	12.2552i	0.260279	+	0.450817i	−0.706037	+	0.708175i	$0.749519\pi$
$740$	−2.84886			−0.104726
$741$	3.86336	−	6.69153i	0.141924	−	0.245819i
$742$		0			0
$743$	8.30228			0.304581			0.152291	−	0.988336i	$-0.451335\pi$
$743$	8.30228			0.304581			0.152291	+	0.988336i	$0.451335\pi$
$744$		0			0
$745$	15.2733			0.559570
$746$		0			0
$747$	−3.00000	+	5.19615i	−0.109764	+	0.190117i
$748$	35.3954			1.29419
$749$		0			0
$750$		0			0
$751$	25.5611	−	44.2731i	0.932737	−	1.61555i	0.154116	−	0.988053i	$-0.450747\pi$
$751$	25.5611	−	44.2731i	0.932737	−	1.61555i	0.778621	−	0.627495i	$-0.215920\pi$
$752$	−43.3954			−1.58247
$753$	−7.42443	−	12.8595i	−0.270561	−	0.468626i
$754$		0			0
$755$	−6.71221	−	11.6259i	−0.244282	−	0.423110i
$756$		0			0
$757$	19.8489	+	34.3792i	0.721419	+	1.24953i	0.960431	+	0.278518i	$0.0898431\pi$
$757$	19.8489	+	34.3792i	0.721419	+	1.24953i	−0.239012	+	0.971017i	$0.576824\pi$
$758$		0			0
$759$	−8.84886			−0.321193
$760$		0			0
$761$	−0.151142	+	0.261786i	−0.00547890	+	0.00948973i	−0.868752	−	0.495248i	$-0.835077\pi$
$761$	−0.151142	+	0.261786i	−0.00547890	+	0.00948973i	0.863273	+	0.504737i	$0.168411\pi$
$762$		0			0
$763$		0			0
$764$	17.2733	+	29.9182i	0.624926	+	1.08240i
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$		0			0
$767$	24.0000			0.866590
$768$	8.00000	−	13.8564i	0.288675	−	0.500000i
$769$	24.4855	−	42.4101i	0.882970	−	1.52935i	0.0349467	−	0.999389i	$-0.488874\pi$
$769$	24.4855	−	42.4101i	0.882970	−	1.52935i	0.848023	−	0.529959i	$-0.177793\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	−4.57557	+	7.92512i	−0.164678	+	0.285231i
$773$	28.5466			1.02675			0.513374	−	0.858165i	$-0.328395\pi$
$773$	28.5466			1.02675			0.513374	+	0.858165i	$0.328395\pi$
$774$		0			0
$775$	4.71221	+	2.96564i	0.169268	+	0.106529i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000			0.429945
$780$	5.42443	+	9.39539i	0.194226	+	0.336409i
$781$	−5.36336	+	9.28961i	−0.191916	+	0.332408i
$782$		0			0
$783$	6.42443			0.229590
$784$	14.0000	+	24.2487i	0.500000	+	0.866025i
$785$	−6.28779	−	10.8908i	−0.224421	−	0.388708i
$786$		0			0
$787$	4.86336	−	8.42358i	0.173360	−	0.300268i	−0.766233	−	0.642563i	$-0.777871\pi$
$787$	4.86336	−	8.42358i	0.173360	−	0.300268i	0.939592	+	0.342295i	$0.111204\pi$
$788$	−20.8489	−	36.1113i	−0.742710	−	1.28641i
$789$	9.00000	−	15.5885i	0.320408	−	0.554964i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−39.1221	−	67.7615i	−1.38927	−	2.40628i
$794$		0			0
$795$	4.42443	+	7.66334i	0.156918	+	0.271791i
$796$	16.0000	+	27.7128i	0.567105	+	0.982255i
$797$	−21.6977	−	37.5815i	−0.768573	−	1.33121i	−0.938337	−	0.345722i	$-0.887634\pi$
$797$	−21.6977	−	37.5815i	−0.768573	−	1.33121i	0.169764	−	0.985485i	$-0.445699\pi$
$798$		0			0
$799$	−21.6977	+	37.5815i	−0.767610	+	1.32954i
$800$		0			0
$801$	1.78779	+	3.09654i	0.0631683	+	0.109411i
$802$		0			0
$803$	25.2733	−	43.7746i	0.891875	−	1.54477i
$804$	−25.6977			−0.906289
$805$		0			0
$806$		0			0
$807$	−15.5756			−0.548286
$808$		0			0
$809$	−23.2733	+	40.3105i	−0.818245	+	1.41724i	0.0887289	+	0.996056i	$0.471720\pi$
$809$	−23.2733	+	40.3105i	−0.818245	+	1.41724i	−0.906974	+	0.421186i	$0.861614\pi$
$810$		0			0
$811$	2.77329	+	4.80347i	0.0973833	+	0.168673i	0.910601	−	0.413287i	$-0.135619\pi$
$811$	2.77329	+	4.80347i	0.0973833	+	0.168673i	−0.813218	+	0.581960i	$0.802286\pi$
$812$		0			0
$813$	0.500000	−	0.866025i	0.0175358	−	0.0303728i
$814$		0			0
$815$	3.28779	+	5.69461i	0.115166	+	0.199474i
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	2.43893	+	4.22435i	0.0853273	+	0.147791i
$818$		0			0
$819$		0			0
$820$	−8.42443	+	14.5915i	−0.294194	+	0.509559i
$821$	5.57557			0.194589			0.0972944	−	0.995256i	$-0.468981\pi$
$821$	5.57557			0.194589			0.0972944	+	0.995256i	$0.468981\pi$
$822$		0			0
$823$	−28.4244	+	49.2326i	−0.990813	+	1.71614i	−0.378288	+	0.925688i	$0.623487\pi$
$823$	−28.4244	+	49.2326i	−0.990813	+	1.71614i	−0.612525	+	0.790451i	$0.709846\pi$
$824$		0			0
$825$	2.21221	−	3.83167i	0.0770194	−	0.133402i
$826$		0			0
$827$	9.42443	+	16.3236i	0.327720	+	0.567627i	0.982059	−	0.188574i	$-0.0603866\pi$
$827$	9.42443	+	16.3236i	0.327720	+	0.567627i	−0.654339	+	0.756201i	$0.727053\pi$
$828$	2.00000	+	3.46410i	0.0695048	+	0.120386i
$829$	21.8489			0.758842			0.379421	−	0.925224i	$-0.376123\pi$
$829$	21.8489			0.758842			0.379421	+	0.925224i	$0.376123\pi$
$830$		0			0
$831$	11.1366	−	19.2892i	0.386326	−	0.669136i
$832$	21.6977	+	37.5815i	0.752233	+	1.30291i
$833$	28.0000			0.970143
$834$		0			0
$835$	1.15114			0.0398369
$836$	−12.6046			−0.435938
$837$	−0.212214	+	5.56372i	−0.00733520	+	0.192310i
$838$		0			0
$839$	22.1221			0.763741			0.381871	−	0.924216i	$-0.375280\pi$
$839$	22.1221			0.763741			0.381871	+	0.924216i	$0.375280\pi$
$840$		0			0
$841$	12.2733			0.423217
$842$		0			0
$843$	−10.6366	+	18.4232i	−0.366345	+	0.634529i
$844$	−19.0000	+	32.9090i	−0.654007	+	1.13277i
$845$	−16.4244			−0.565018
$846$		0			0
$847$		0			0
$848$	17.6977	+	30.6533i	0.607742	+	1.05264i
$849$	−14.1366	+	24.4854i	−0.485168	+	0.840336i
$850$		0			0
$851$	1.42443	−	2.46718i	0.0488288	−	0.0845740i
$852$	4.84886			0.166119
$853$	−18.2733			−0.625665			−0.312833	−	0.949808i	$-0.601278\pi$
$853$	−18.2733			−0.625665			−0.312833	+	0.949808i	$0.601278\pi$
$854$		0			0
$855$	0.712214	+	1.23359i	0.0243572	+	0.0421879i
$856$		0			0
$857$	25.2733	+	43.7746i	0.863319	+	1.49531i	0.868707	+	0.495327i	$0.164952\pi$
$857$	25.2733	+	43.7746i	0.863319	+	1.49531i	−0.00538761	+	0.999985i	$0.501715\pi$
$858$		0			0
$859$	−12.9244	−	22.3858i	−0.440976	−	0.763793i	0.556786	−	0.830656i	$-0.312034\pi$
$859$	−12.9244	−	22.3858i	−0.440976	−	0.763793i	−0.997762	+	0.0668632i	$0.978701\pi$
$860$	−6.84886			−0.233544
$861$		0			0
$862$		0			0
$863$	2.42443	+	4.19923i	0.0825285	+	0.142944i	0.904335	−	0.426823i	$-0.140367\pi$
$863$	2.42443	+	4.19923i	0.0825285	+	0.142944i	−0.821807	+	0.569766i	$0.807034\pi$
$864$		0			0
$865$	−9.42443	+	16.3236i	−0.320440	+	0.555019i
$866$		0			0
$867$	1.00000			0.0339618
$868$		0			0
$869$	−76.4244			−2.59252
$870$		0			0
$871$	34.8489	−	60.3600i	1.18081	−	2.04522i
$872$		0			0
$873$	1.28779	+	2.23051i	0.0435849	+	0.0754913i
$874$		0			0
$875$		0			0
$876$	−22.8489			−0.771991
$877$	15.1366	+	26.2174i	0.511128	+	0.885300i	0.999917	+	0.0128977i	$0.00410557\pi$
$877$	15.1366	+	26.2174i	0.511128	+	0.885300i	−0.488789	+	0.872402i	$0.662561\pi$
$878$		0			0
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$	8.84886	−	15.3267i	0.298295	−	0.516662i
$881$	−24.6977	−	42.7777i	−0.832087	−	1.44122i	−0.896380	−	0.443286i	$-0.853813\pi$
$881$	−24.6977	−	42.7777i	−0.832087	−	1.44122i	0.0642930	−	0.997931i	$-0.479521\pi$
$882$		0			0
$883$	17.9710			0.604772			0.302386	−	0.953185i	$-0.402217\pi$
$883$	17.9710			0.604772			0.302386	+	0.953185i	$0.402217\pi$
$884$	43.3954			1.45955
$885$	−2.21221	+	3.83167i	−0.0743628	+	0.128800i
$886$		0			0
$887$	−14.4244	+	24.9838i	−0.484325	+	0.838875i	−0.999838	−	0.0180064i	$-0.994268\pi$
$887$	−14.4244	+	24.9838i	−0.484325	+	0.838875i	0.515513	+	0.856882i	$0.327601\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	4.42443			0.148224
$892$	−1.42443	+	2.46718i	−0.0476934	+	0.0826074i
$893$	7.72671	−	13.3831i	0.258565	−	0.447847i
$894$		0			0
$895$	−5.57557			−0.186371
$896$		0			0
$897$	−10.8489			−0.362233
$898$		0			0
$899$	−1.36336	+	35.7437i	−0.0454705	+	1.19212i
$900$	−2.00000			−0.0666667
$901$	35.3954			1.17919
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−5.71221	+	9.89385i	−0.189880	+	0.328883i
$906$		0			0
$907$	40.2443			1.33629			0.668145	−	0.744031i	$-0.267089\pi$
$907$	40.2443			1.33629			0.668145	+	0.744031i	$0.267089\pi$
$908$	3.15114	+	5.45794i	0.104574	+	0.181128i
$909$	−7.00000	−	12.1244i	−0.232175	−	0.402139i
$910$		0			0
$911$	−7.78779	+	13.4888i	−0.258021	+	0.446905i	−0.965712	−	0.259617i	$-0.916404\pi$
$911$	−7.78779	+	13.4888i	−0.258021	+	0.446905i	0.707691	+	0.706522i	$0.249737\pi$
$912$	2.84886	+	4.93437i	0.0943351	+	0.163393i
$913$	−13.2733	+	22.9900i	−0.439282	+	0.760858i
$914$		0			0
$915$	14.4244			0.476857
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$		0			0
$918$		0			0
$919$	−3.50000	−	6.06218i	−0.115454	−	0.199973i	0.802507	−	0.596643i	$-0.203499\pi$
$919$	−3.50000	−	6.06218i	−0.115454	−	0.199973i	−0.917961	+	0.396670i	$0.870166\pi$
$920$		0			0
$921$	4.28779	+	7.42666i	0.141287	+	0.244717i
$922$		0			0
$923$	−6.57557	+	11.3892i	−0.216438	+	0.374881i
$924$		0			0
$925$	0.712214	+	1.23359i	0.0234175	+	0.0405602i
$926$		0			0
$927$	−1.28779	+	2.23051i	−0.0422964	+	0.0732596i
$928$		0			0
$929$	14.4244			0.473250			0.236625	−	0.971601i	$-0.423959\pi$
$929$	14.4244			0.473250			0.236625	+	0.971601i	$0.423959\pi$
$930$		0			0
$931$	−9.97100			−0.326786
$932$	6.30228			0.206438
$933$	5.21221	−	9.02782i	0.170640	−	0.295558i
$934$		0			0
$935$	−8.84886	−	15.3267i	−0.289389	−	0.501236i
$936$		0			0
$937$	−1.71221	+	2.96564i	−0.0559356	+	0.0968833i	−0.892637	−	0.450776i	$-0.851147\pi$
$937$	−1.71221	+	2.96564i	−0.0559356	+	0.0968833i	0.836702	+	0.547659i	$0.184481\pi$
$938$		0			0
$939$	3.71221	+	6.42974i	0.121144	+	0.209827i
$940$	10.8489	+	18.7908i	0.353851	+	0.612887i
$941$	14.4244	+	24.9838i	0.470223	+	0.814450i	0.999420	−	0.0340488i	$-0.0108402\pi$
$941$	14.4244	+	24.9838i	0.470223	+	0.814450i	−0.529197	+	0.848499i	$0.677507\pi$
$942$		0			0
$943$	−8.42443	−	14.5915i	−0.274337	−	0.475166i
$944$	−8.84886	+	15.3267i	−0.288006	+	0.498841i
$945$		0			0
$946$		0			0
$947$	−26.6977	+	46.2418i	−0.867559	+	1.50266i	−0.00307576	+	0.999995i	$0.500979\pi$
$947$	−26.6977	+	46.2418i	−0.867559	+	1.50266i	−0.864483	+	0.502661i	$0.832354\pi$
$948$	17.2733	+	29.9182i	0.561010	+	0.971698i
$949$	30.9855	−	53.6685i	1.00583	−	1.74215i
$950$		0			0
$951$	−9.84886	−	17.0587i	−0.319371	−	0.553167i
$952$		0			0
$953$	−15.6977			−0.508499			−0.254249	−	0.967139i	$-0.581828\pi$
$953$	−15.6977			−0.508499			−0.254249	+	0.967139i	$0.581828\pi$
$954$		0			0
$955$	8.63664	−	14.9591i	0.279475	−	0.484065i
$956$	19.2733	+	33.3823i	0.623343	+	1.07966i
$957$	28.4244			0.918831
$958$		0			0
$959$		0			0
$960$	−8.00000			−0.258199
$961$	−30.9099	−	2.36140i	−0.997095	−	0.0761743i
$962$		0			0
$963$	14.8489			0.478498
$964$	4.57557	−	7.92512i	0.147369	−	0.255251i
$965$	4.57557			0.147293
$966$		0			0
$967$	−11.6977	+	20.2610i	−0.376173	+	0.651551i	−0.990502	−	0.137499i	$-0.956094\pi$
$967$	−11.6977	+	20.2610i	−0.376173	+	0.651551i	0.614329	+	0.789050i	$0.289427\pi$
$968$		0			0
$969$	5.69772			0.183037
$970$		0			0
$971$	28.2733	+	48.9708i	0.907333	+	1.57155i	0.817755	+	0.575567i	$0.195219\pi$
$971$	28.2733	+	48.9708i	0.907333	+	1.57155i	0.0895783	+	0.995980i	$0.471448\pi$
$972$	−1.00000	−	1.73205i	−0.0320750	−	0.0555556i
$973$		0			0
$974$		0			0
$975$	2.71221	−	4.69769i	0.0868604	−	0.150447i
$976$	57.6977			1.84686
$977$	1.69772			0.0543147			0.0271574	−	0.999631i	$-0.491354\pi$
$977$	1.69772			0.0543147			0.0271574	+	0.999631i	$0.491354\pi$
$978$		0			0
$979$	7.90993	+	13.7004i	0.252802	+	0.437867i
$980$	7.00000	−	12.1244i	0.223607	−	0.387298i
$981$	−6.92443	−	11.9935i	−0.221080	−	0.382922i
$982$		0			0
$983$	−22.6977	−	39.3136i	−0.723945	−	1.25391i	−0.959407	−	0.282025i	$-0.908994\pi$
$983$	−22.6977	−	39.3136i	−0.723945	−	1.25391i	0.235462	−	0.971884i	$-0.424340\pi$
$984$		0			0
$985$	−10.4244	+	18.0556i	−0.332150	+	0.575301i
$986$		0			0
$987$		0			0
$988$	−15.4534			−0.491639
$989$	3.42443	−	5.93128i	0.108891	−	0.188604i
$990$		0			0
$991$	−60.0931			−1.90892			−0.954461	−	0.298336i	$-0.903568\pi$
$991$	−60.0931			−1.90892			−0.954461	+	0.298336i	$0.903568\pi$
$992$		0			0
$993$	15.0000			0.476011
$994$		0			0
$995$	8.00000	−	13.8564i	0.253617	−	0.439278i
$996$	12.0000			0.380235
$997$	−25.1221	−	43.5128i	−0.795626	−	1.37807i	−0.922441	−	0.386139i	$-0.873809\pi$
$997$	−25.1221	−	43.5128i	−0.795626	−	1.37807i	0.126814	−	0.991926i	$-0.459525\pi$
$998$		0			0
$999$	−0.712214	+	1.23359i	−0.0225335	+	0.0390291i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.i.b.346.1	yes	4
31.25	even	3	inner	465.2.i.b.211.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.i.b.211.1	✓	4	31.25	even	3	inner
465.2.i.b.346.1	yes	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} -2.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(-2.21221 - 3.83167i) q^{11} +(-1.00000 + 1.73205i) q^{12} +(-2.71221 - 4.69769i) q^{13} +1.00000 q^{15} +4.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(-0.712214 + 1.23359i) q^{19} +(-1.00000 - 1.73205i) q^{20} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} -6.42443 q^{29} +(0.212214 - 5.56372i) q^{31} -4.42443 q^{33} +(1.00000 + 1.73205i) q^{36} +(0.712214 - 1.23359i) q^{37} -5.42443 q^{39} +(-4.21221 - 7.29577i) q^{41} +(1.71221 - 2.96564i) q^{43} +(4.42443 + 7.66334i) q^{44} +(0.500000 - 0.866025i) q^{45} -10.8489 q^{47} +(2.00000 - 3.46410i) q^{48} +(3.50000 + 6.06218i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(5.42443 + 9.39539i) q^{52} +(4.42443 + 7.66334i) q^{53} +(2.21221 - 3.83167i) q^{55} +(0.712214 + 1.23359i) q^{57} +(-2.21221 + 3.83167i) q^{59} -2.00000 q^{60} +14.4244 q^{61} -8.00000 q^{64} +(2.71221 - 4.69769i) q^{65} +(6.42443 + 11.1274i) q^{67} +(-4.00000 + 6.92820i) q^{68} +(1.00000 - 1.73205i) q^{69} +(-1.21221 - 2.09962i) q^{71} +(5.71221 + 9.89385i) q^{73} +(0.500000 + 0.866025i) q^{75} +(1.42443 - 2.46718i) q^{76} +(8.63664 - 14.9591i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{83} +4.00000 q^{85} +(-3.21221 + 5.56372i) q^{87} -3.57557 q^{89} -4.00000 q^{92} +(-4.71221 - 2.96564i) q^{93} -1.42443 q^{95} -2.57557 q^{97} +(-2.21221 + 3.83167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9	\( 4 q + 2 q^{3} - 8 q^{4} + 2 q^{5} - 2 q^{9} + q^{11} - 4 q^{12} - q^{13} + 4 q^{15} + 16 q^{16} + 8 q^{17} + 7 q^{19} - 4 q^{20} + 8 q^{23} - 2 q^{25} - 4 q^{27} - 6 q^{29} - 9 q^{31} + 2 q^{33} + 4 q^{36} - 7 q^{37} - 2 q^{39} - 7 q^{41} - 3 q^{43} - 2 q^{44} + 2 q^{45} - 4 q^{47} + 8 q^{48} + 14 q^{49} - 8 q^{51} + 2 q^{52} - 2 q^{53} - q^{55} - 7 q^{57} + q^{59} - 8 q^{60} + 38 q^{61} - 32 q^{64} + q^{65} + 6 q^{67} - 16 q^{68} + 4 q^{69} + 5 q^{71} + 13 q^{73} + 2 q^{75} - 14 q^{76} + 5 q^{79} + 8 q^{80} - 2 q^{81} - 12 q^{83} + 16 q^{85} - 3 q^{87} - 34 q^{89} - 16 q^{92} - 9 q^{93} + 14 q^{95} - 30 q^{97} + q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 8 * q^4 + 2 * q^5 - 2 * q^9 + q^11 - 4 * q^12 - q^13 + 4 * q^15 + 16 * q^16 + 8 * q^17 + 7 * q^19 - 4 * q^20 + 8 * q^23 - 2 * q^25 - 4 * q^27 - 6 * q^29 - 9 * q^31 + 2 * q^33 + 4 * q^36 - 7 * q^37 - 2 * q^39 - 7 * q^41 - 3 * q^43 - 2 * q^44 + 2 * q^45 - 4 * q^47 + 8 * q^48 + 14 * q^49 - 8 * q^51 + 2 * q^52 - 2 * q^53 - q^55 - 7 * q^57 + q^59 - 8 * q^60 + 38 * q^61 - 32 * q^64 + q^65 + 6 * q^67 - 16 * q^68 + 4 * q^69 + 5 * q^71 + 13 * q^73 + 2 * q^75 - 14 * q^76 + 5 * q^79 + 8 * q^80 - 2 * q^81 - 12 * q^83 + 16 * q^85 - 3 * q^87 - 34 * q^89 - 16 * q^92 - 9 * q^93 + 14 * q^95 - 30 * q^97 + q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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