LMFDB - Embedded newform 333.2.s.b.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [333,2,Mod(64,333)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(333, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("333.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 333 = 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	333.s (of order $6$, 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:	$2.65901838731$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 37)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	333.307
Dual form			333.2.s.b.64.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.232051 - 0.133975i) q^{5} +(-1.73205 + 3.00000i) q^{7} +3.00000i q^{8} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.232051 - 0.133975i) q^{5} +(-1.73205 + 3.00000i) q^{7} +3.00000i q^{8} -0.267949 q^{10} +4.73205 q^{11} +(3.00000 + 1.73205i) q^{13} +3.46410i q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.23205 + 1.86603i) q^{17} +(1.09808 + 0.633975i) q^{19} +(0.232051 - 0.133975i) q^{20} +(4.09808 - 2.36603i) q^{22} +0.732051i q^{23} +(-2.46410 - 4.26795i) q^{25} +3.46410 q^{26} +(-1.73205 - 3.00000i) q^{28} -0.267949i q^{29} -8.19615i q^{31} +(-4.33013 - 2.50000i) q^{32} +(-1.86603 + 3.23205i) q^{34} +(0.803848 - 0.464102i) q^{35} +(0.500000 + 6.06218i) q^{37} +1.26795 q^{38} +(0.401924 - 0.696152i) q^{40} +(1.50000 - 2.59808i) q^{41} +3.46410i q^{43} +(-2.36603 + 4.09808i) q^{44} +(0.366025 + 0.633975i) q^{46} +2.19615 q^{47} +(-2.50000 - 4.33013i) q^{49} +(-4.26795 - 2.46410i) q^{50} +(-3.00000 + 1.73205i) q^{52} +(-1.26795 - 2.19615i) q^{53} +(-1.09808 - 0.633975i) q^{55} +(-9.00000 - 5.19615i) q^{56} +(-0.133975 - 0.232051i) q^{58} +(11.6603 - 6.73205i) q^{59} +(3.69615 + 2.13397i) q^{61} +(-4.09808 - 7.09808i) q^{62} -7.00000 q^{64} +(-0.464102 - 0.803848i) q^{65} +(3.63397 - 6.29423i) q^{67} -3.73205i q^{68} +(0.464102 - 0.803848i) q^{70} +(3.00000 - 5.19615i) q^{71} +(3.46410 + 5.00000i) q^{74} +(-1.09808 + 0.633975i) q^{76} +(-8.19615 + 14.1962i) q^{77} +(3.29423 + 1.90192i) q^{79} -0.267949i q^{80} -3.00000i q^{82} +(-4.09808 - 7.09808i) q^{83} +1.00000 q^{85} +(1.73205 + 3.00000i) q^{86} +14.1962i q^{88} +(-7.96410 + 4.59808i) q^{89} +(-10.3923 + 6.00000i) q^{91} +(-0.633975 - 0.366025i) q^{92} +(1.90192 - 1.09808i) q^{94} +(-0.169873 - 0.294229i) q^{95} -4.26795i q^{97} +(-4.33013 - 2.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 4 * q - 2 * q^4 + 6 * q^5	$ 4 q - 2 q^{4} + 6 q^{5} - 8 q^{10} + 12 q^{11} + 12 q^{13} + 2 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{20} + 6 q^{22} + 4 q^{25} - 4 q^{34} + 24 q^{35} + 2 q^{37} + 12 q^{38} + 12 q^{40} + 6 q^{41} - 6 q^{44} - 2 q^{46} - 12 q^{47} - 10 q^{49} - 24 q^{50} - 12 q^{52} - 12 q^{53} + 6 q^{55} - 36 q^{56} - 4 q^{58} + 12 q^{59} - 6 q^{61} - 6 q^{62} - 28 q^{64} + 12 q^{65} + 18 q^{67} - 12 q^{70} + 12 q^{71} + 6 q^{76} - 12 q^{77} - 18 q^{79} - 6 q^{83} + 4 q^{85} - 18 q^{89} - 6 q^{92} + 18 q^{94} - 18 q^{95}+O(q^{100}) $ 4 * q - 2 * q^4 + 6 * q^5 - 8 * q^10 + 12 * q^11 + 12 * q^13 + 2 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^20 + 6 * q^22 + 4 * q^25 - 4 * q^34 + 24 * q^35 + 2 * q^37 + 12 * q^38 + 12 * q^40 + 6 * q^41 - 6 * q^44 - 2 * q^46 - 12 * q^47 - 10 * q^49 - 24 * q^50 - 12 * q^52 - 12 * q^53 + 6 * q^55 - 36 * q^56 - 4 * q^58 + 12 * q^59 - 6 * q^61 - 6 * q^62 - 28 * q^64 + 12 * q^65 + 18 * q^67 - 12 * q^70 + 12 * q^71 + 6 * q^76 - 12 * q^77 - 18 * q^79 - 6 * q^83 + 4 * q^85 - 18 * q^89 - 6 * q^92 + 18 * q^94 - 18 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/333\mathbb{Z}\right)^\times$.

$n$	$38$	$298$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.232051	−	0.133975i	−0.103776	−	0.0599153i	0.447214	−	0.894427i	$-0.352416\pi$
$5$	−0.232051	−	0.133975i	−0.103776	−	0.0599153i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	0.327327	+	0.944911i	$0.393852\pi$
$7$	−1.73205	+	3.00000i	−0.654654	+	1.13389i	−0.981981	+	0.188982i	$0.939481\pi$
$8$			3.00000i			1.06066i
$9$		0			0
$10$	−0.267949			−0.0847330
$11$	4.73205			1.42677			0.713384	−	0.700774i	$-0.247162\pi$
$11$	4.73205			1.42677			0.713384	+	0.700774i	$0.247162\pi$
$12$		0			0
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	0.854554	−	0.519362i	$-0.173830\pi$
$13$	3.00000	+	1.73205i	0.832050	+	0.480384i	−0.0225039	+	0.999747i	$0.507164\pi$
$14$			3.46410i			0.925820i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.23205	+	1.86603i	−0.783887	+	0.452578i	−0.837806	−	0.545968i	$-0.816162\pi$
$17$	−3.23205	+	1.86603i	−0.783887	+	0.452578i	0.0539188	+	0.998545i	$0.482829\pi$
$18$		0			0
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	0.620641	−	0.784095i	$-0.286872\pi$
$19$	1.09808	+	0.633975i	0.251916	+	0.145444i	−0.368725	+	0.929538i	$0.620206\pi$
$20$	0.232051	−	0.133975i	0.0518881	−	0.0299576i
$21$		0			0
$22$	4.09808	−	2.36603i	0.873713	−	0.504438i
$23$			0.732051i			0.152643i	0.997083	+	0.0763216i	$0.0243176\pi$
$23$			0.732051i			0.152643i	−0.997083	+	0.0763216i	$0.975682\pi$
$24$		0			0
$25$	−2.46410	−	4.26795i	−0.492820	−	0.853590i
$26$	3.46410			0.679366
$27$		0			0
$28$	−1.73205	−	3.00000i	−0.327327	−	0.566947i
$29$		−	0.267949i		−	0.0497569i	−0.999690	−	0.0248785i	$-0.992080\pi$
$29$		−	0.267949i		−	0.0497569i	0.999690	−	0.0248785i	$-0.00791988\pi$
$30$		0			0
$31$		−	8.19615i		−	1.47207i	−0.676942	−	0.736036i	$-0.736695\pi$
$31$		−	8.19615i		−	1.47207i	0.676942	−	0.736036i	$-0.263305\pi$
$32$	−4.33013	−	2.50000i	−0.765466	−	0.441942i
$33$		0			0
$34$	−1.86603	+	3.23205i	−0.320021	+	0.554292i
$35$	0.803848	−	0.464102i	0.135875	−	0.0784475i
$36$		0			0
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$37$	0.500000	+	6.06218i	0.0821995	+	0.996616i
$38$	1.26795			0.205689
$39$		0			0
$40$	0.401924	−	0.696152i	0.0635497	−	0.110071i
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$		0			0
$43$			3.46410i			0.528271i	0.964486	+	0.264135i	$0.0850865\pi$
$43$			3.46410i			0.528271i	−0.964486	+	0.264135i	$0.914913\pi$
$44$	−2.36603	+	4.09808i	−0.356692	+	0.617808i
$45$		0			0
$46$	0.366025	+	0.633975i	0.0539675	+	0.0934745i
$47$	2.19615			0.320342			0.160171	−	0.987089i	$-0.448795\pi$
$47$	2.19615			0.320342			0.160171	+	0.987089i	$0.448795\pi$
$48$		0			0
$49$	−2.50000	−	4.33013i	−0.357143	−	0.618590i
$50$	−4.26795	−	2.46410i	−0.603579	−	0.348477i
$51$		0			0
$52$	−3.00000	+	1.73205i	−0.416025	+	0.240192i
$53$	−1.26795	−	2.19615i	−0.174166	−	0.301665i	0.765706	−	0.643191i	$-0.222390\pi$
$53$	−1.26795	−	2.19615i	−0.174166	−	0.301665i	−0.939872	+	0.341526i	$0.889056\pi$
$54$		0			0
$55$	−1.09808	−	0.633975i	−0.148065	−	0.0854851i
$56$	−9.00000	−	5.19615i	−1.20268	−	0.694365i
$57$		0			0
$58$	−0.133975	−	0.232051i	−0.0175917	−	0.0304698i
$59$	11.6603	−	6.73205i	1.51804	−	0.876438i	0.518261	−	0.855223i	$-0.326580\pi$
$59$	11.6603	−	6.73205i	1.51804	−	0.876438i	0.999775	−	0.0212158i	$-0.00675370\pi$
$60$		0			0
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	0.717597	−	0.696459i	$-0.245242\pi$
$61$	3.69615	+	2.13397i	0.473244	+	0.273227i	−0.244353	+	0.969686i	$0.578576\pi$
$62$	−4.09808	−	7.09808i	−0.520456	−	0.901457i
$63$		0			0
$64$	−7.00000			−0.875000
$65$	−0.464102	−	0.803848i	−0.0575647	−	0.0997050i
$66$		0			0
$67$	3.63397	−	6.29423i	0.443961	−	0.768962i	−0.554019	−	0.832504i	$-0.686906\pi$
$67$	3.63397	−	6.29423i	0.443961	−	0.768962i	0.997979	+	0.0635419i	$0.0202397\pi$
$68$		−	3.73205i		−	0.452578i
$69$		0			0
$70$	0.464102	−	0.803848i	0.0554708	−	0.0960782i
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$		0			0
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	3.46410	+	5.00000i	0.402694	+	0.581238i
$75$		0			0
$76$	−1.09808	+	0.633975i	−0.125958	+	0.0727219i
$77$	−8.19615	+	14.1962i	−0.934038	+	1.61780i
$78$		0			0
$79$	3.29423	+	1.90192i	0.370630	+	0.213983i	0.673734	−	0.738974i	$-0.264690\pi$
$79$	3.29423	+	1.90192i	0.370630	+	0.213983i	−0.303104	+	0.952958i	$0.598023\pi$
$80$		−	0.267949i		−	0.0299576i
$81$		0			0
$82$		−	3.00000i		−	0.331295i
$83$	−4.09808	−	7.09808i	−0.449822	−	0.779115i	0.548552	−	0.836117i	$-0.315179\pi$
$83$	−4.09808	−	7.09808i	−0.449822	−	0.779115i	−0.998374	+	0.0570015i	$0.981846\pi$
$84$		0			0
$85$	1.00000			0.108465
$86$	1.73205	+	3.00000i	0.186772	+	0.323498i
$87$		0			0
$88$			14.1962i			1.51331i
$89$	−7.96410	+	4.59808i	−0.844193	+	0.487395i	−0.858687	−	0.512500i	$-0.828720\pi$
$89$	−7.96410	+	4.59808i	−0.844193	+	0.487395i	0.0144942	+	0.999895i	$0.495386\pi$
$90$		0			0
$91$	−10.3923	+	6.00000i	−1.08941	+	0.628971i
$92$	−0.633975	−	0.366025i	−0.0660964	−	0.0381608i
$93$		0			0
$94$	1.90192	−	1.09808i	0.196168	−	0.113258i
$95$	−0.169873	−	0.294229i	−0.0174286	−	0.0301872i
$96$		0			0
$97$		−	4.26795i		−	0.433345i	−0.976244	−	0.216672i	$-0.930480\pi$
$97$		−	4.26795i		−	0.433345i	0.976244	−	0.216672i	$-0.0695203\pi$
$98$	−4.33013	−	2.50000i	−0.437409	−	0.252538i
$99$		0			0
$100$	4.92820			0.492820
$101$	9.00000			0.895533			0.447767	−	0.894150i	$-0.352219\pi$
$101$	9.00000			0.895533			0.447767	+	0.894150i	$0.352219\pi$
$102$		0			0
$103$		−	12.9282i		−	1.27385i	−0.770924	−	0.636927i	$-0.780205\pi$
$103$		−	12.9282i		−	1.27385i	0.770924	−	0.636927i	$-0.219795\pi$
$104$	−5.19615	+	9.00000i	−0.509525	+	0.882523i
$105$		0			0
$106$	−2.19615	−	1.26795i	−0.213309	−	0.123154i
$107$	−6.46410	+	11.1962i	−0.624908	+	1.08237i	0.363650	+	0.931536i	$0.381530\pi$
$107$	−6.46410	+	11.1962i	−0.624908	+	1.08237i	−0.988559	+	0.150837i	$0.951803\pi$
$108$		0			0
$109$	−5.89230	+	3.40192i	−0.564380	+	0.325845i	−0.754902	−	0.655838i	$-0.772315\pi$
$109$	−5.89230	+	3.40192i	−0.564380	+	0.325845i	0.190521	+	0.981683i	$0.438982\pi$
$110$	−1.26795			−0.120894
$111$		0			0
$112$	−3.46410			−0.327327
$113$	3.92820	−	2.26795i	0.369534	−	0.213351i	−0.303721	−	0.952761i	$-0.598229\pi$
$113$	3.92820	−	2.26795i	0.369534	−	0.213351i	0.673255	+	0.739410i	$0.264896\pi$
$114$		0			0
$115$	0.0980762	−	0.169873i	0.00914565	−	0.0158407i
$116$	0.232051	+	0.133975i	0.0215454	+	0.0124392i
$117$		0			0
$118$	6.73205	−	11.6603i	0.619736	−	1.07341i
$119$		−	12.9282i		−	1.18513i
$120$		0			0
$121$	11.3923			1.03566
$122$	4.26795			0.386402
$123$		0			0
$124$	7.09808	+	4.09808i	0.637426	+	0.368018i
$125$			2.66025i			0.237940i
$126$		0			0
$127$	6.09808	+	10.5622i	0.541117	+	0.937242i	0.998840	+	0.0481471i	$0.0153316\pi$
$127$	6.09808	+	10.5622i	0.541117	+	0.937242i	−0.457723	+	0.889095i	$0.651335\pi$
$128$	2.59808	−	1.50000i	0.229640	−	0.132583i
$129$		0			0
$130$	−0.803848	−	0.464102i	−0.0705021	−	0.0407044i
$131$	9.16987	−	5.29423i	0.801176	−	0.462559i	−0.0427065	−	0.999088i	$-0.513598\pi$
$131$	9.16987	−	5.29423i	0.801176	−	0.462559i	0.843882	+	0.536529i	$0.180265\pi$
$132$		0			0
$133$	−3.80385	+	2.19615i	−0.329835	+	0.190431i
$134$		−	7.26795i		−	0.627855i
$135$		0			0
$136$	−5.59808	−	9.69615i	−0.480031	−	0.831438i
$137$	6.46410			0.552265			0.276133	−	0.961120i	$-0.410947\pi$
$137$	6.46410			0.552265			0.276133	+	0.961120i	$0.410947\pi$
$138$		0			0
$139$	−6.29423	−	10.9019i	−0.533870	−	0.924689i	−0.999217	−	0.0395611i	$-0.987404\pi$
$139$	−6.29423	−	10.9019i	−0.533870	−	0.924689i	0.465348	−	0.885128i	$-0.345929\pi$
$140$			0.928203i			0.0784475i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$	14.1962	+	8.19615i	1.18714	+	0.685397i
$144$		0			0
$145$	−0.0358984	+	0.0621778i	−0.00298120	+	0.00516359i
$146$		0			0
$147$		0			0
$148$	−5.50000	−	2.59808i	−0.452097	−	0.213561i
$149$	−5.53590			−0.453518			−0.226759	−	0.973951i	$-0.572813\pi$
$149$	−5.53590			−0.453518			−0.226759	+	0.973951i	$0.572813\pi$
$150$		0			0
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	0.301502	+	0.953466i	$0.402512\pi$
$151$	−8.29423	+	14.3660i	−0.674975	+	1.16909i	−0.976476	+	0.215625i	$0.930821\pi$
$152$	−1.90192	+	3.29423i	−0.154266	+	0.267197i
$153$		0			0
$154$			16.3923i			1.32093i
$155$	−1.09808	+	1.90192i	−0.0881996	+	0.152766i
$156$		0			0
$157$	7.16025	+	12.4019i	0.571450	+	0.989781i	0.996417	+	0.0845724i	$0.0269524\pi$
$157$	7.16025	+	12.4019i	0.571450	+	0.989781i	−0.424967	+	0.905209i	$0.639714\pi$
$158$	3.80385			0.302618
$159$		0			0
$160$	0.669873	+	1.16025i	0.0529581	+	0.0917261i
$161$	−2.19615	−	1.26795i	−0.173081	−	0.0999284i
$162$		0			0
$163$	19.3923	−	11.1962i	1.51892	−	0.876950i	0.519171	−	0.854671i	$-0.326241\pi$
$163$	19.3923	−	11.1962i	1.51892	−	0.876950i	0.999752	−	0.0222798i	$-0.00709247\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−7.09808	−	4.09808i	−0.550918	−	0.318072i
$167$	−9.46410	−	5.46410i	−0.732354	−	0.422825i	0.0869286	−	0.996215i	$-0.472295\pi$
$167$	−9.46410	−	5.46410i	−0.732354	−	0.422825i	−0.819283	+	0.573390i	$0.805628\pi$
$168$		0			0
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.866025	−	0.500000i	0.0664211	−	0.0383482i
$171$		0			0
$172$	−3.00000	−	1.73205i	−0.228748	−	0.132068i
$173$	4.96410	+	8.59808i	0.377414	+	0.653700i	0.990685	−	0.136173i	$-0.0434802\pi$
$173$	4.96410	+	8.59808i	0.377414	+	0.653700i	−0.613271	+	0.789872i	$0.710147\pi$
$174$		0			0
$175$	17.0718			1.29051
$176$	2.36603	+	4.09808i	0.178346	+	0.308904i
$177$		0			0
$178$	−4.59808	+	7.96410i	−0.344640	+	0.596935i
$179$		−	1.46410i		−	0.109432i	−0.998502	−	0.0547160i	$-0.982575\pi$
$179$		−	1.46410i		−	0.109432i	0.998502	−	0.0547160i	$-0.0174254\pi$
$180$		0			0
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	−0.989406	−	0.145174i	$-0.953626\pi$
$181$	−4.96410	+	8.59808i	−0.368979	+	0.639090i	0.620427	+	0.784264i	$0.286959\pi$
$182$	−6.00000	+	10.3923i	−0.444750	+	0.770329i
$183$		0			0
$184$	−2.19615			−0.161903
$185$	0.696152	−	1.47372i	0.0511821	−	0.108350i
$186$		0			0
$187$	−15.2942	+	8.83013i	−1.11842	+	0.645723i
$188$	−1.09808	+	1.90192i	−0.0800854	+	0.138712i
$189$		0			0
$190$	−0.294229	−	0.169873i	−0.0213456	−	0.0123239i
$191$			6.19615i			0.448338i	0.974550	+	0.224169i	$0.0719667\pi$
$191$			6.19615i			0.448338i	−0.974550	+	0.224169i	$0.928033\pi$
$192$		0			0
$193$		−	14.6603i		−	1.05527i	−0.849472	−	0.527634i	$-0.823079\pi$
$193$		−	14.6603i		−	1.05527i	0.849472	−	0.527634i	$-0.176921\pi$
$194$	−2.13397	−	3.69615i	−0.153210	−	0.265368i
$195$		0			0
$196$	5.00000			0.357143
$197$	13.9641	+	24.1865i	0.994901	+	1.72322i	0.584794	+	0.811182i	$0.301175\pi$
$197$	13.9641	+	24.1865i	0.994901	+	1.72322i	0.410107	+	0.912038i	$0.365491\pi$
$198$		0			0
$199$		−	11.0718i		−	0.784859i	−0.919782	−	0.392429i	$-0.871635\pi$
$199$		−	11.0718i		−	0.784859i	0.919782	−	0.392429i	$-0.128365\pi$
$200$	12.8038	−	7.39230i	0.905369	−	0.522715i
$201$		0			0
$202$	7.79423	−	4.50000i	0.548400	−	0.316619i
$203$	0.803848	+	0.464102i	0.0564190	+	0.0325735i
$204$		0			0
$205$	−0.696152	+	0.401924i	−0.0486214	+	0.0280716i
$206$	−6.46410	−	11.1962i	−0.450375	−	0.780073i
$207$		0			0
$208$			3.46410i			0.240192i
$209$	5.19615	+	3.00000i	0.359425	+	0.207514i
$210$		0			0
$211$	−10.0000			−0.688428			−0.344214	−	0.938891i	$-0.611855\pi$
$211$	−10.0000			−0.688428			−0.344214	+	0.938891i	$0.611855\pi$
$212$	2.53590			0.174166
$213$		0			0
$214$			12.9282i			0.883754i
$215$	0.464102	−	0.803848i	0.0316515	−	0.0548219i
$216$		0			0
$217$	24.5885	+	14.1962i	1.66917	+	0.963698i
$218$	−3.40192	+	5.89230i	−0.230407	+	0.399077i
$219$		0			0
$220$	1.09808	−	0.633975i	0.0740323	−	0.0427426i
$221$	−12.9282			−0.869645
$222$		0			0
$223$	4.58846			0.307266			0.153633	−	0.988128i	$-0.450903\pi$
$223$	4.58846			0.307266			0.153633	+	0.988128i	$0.450903\pi$
$224$	15.0000	−	8.66025i	1.00223	−	0.578638i
$225$		0			0
$226$	2.26795	−	3.92820i	0.150862	−	0.261300i
$227$	−20.0263	−	11.5622i	−1.32919	−	0.767409i	−0.344016	−	0.938964i	$-0.611788\pi$
$227$	−20.0263	−	11.5622i	−1.32919	−	0.767409i	−0.985175	+	0.171555i	$0.945121\pi$
$228$		0			0
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−3.50000	+	6.06218i	−0.231287	+	0.400600i	0.726900	+	0.686743i	$0.240960\pi$
$230$		−	0.196152i		−	0.0129339i
$231$		0			0
$232$	0.803848			0.0527752
$233$	10.8564			0.711227			0.355613	−	0.934633i	$-0.384272\pi$
$233$	10.8564			0.711227			0.355613	+	0.934633i	$0.384272\pi$
$234$		0			0
$235$	−0.509619	−	0.294229i	−0.0332439	−	0.0191934i
$236$			13.4641i			0.876438i
$237$		0			0
$238$	−6.46410	−	11.1962i	−0.419005	−	0.725739i
$239$	−14.6603	+	8.46410i	−0.948293	+	0.547497i	−0.892550	−	0.450948i	$-0.851086\pi$
$239$	−14.6603	+	8.46410i	−0.948293	+	0.547497i	−0.0557428	+	0.998445i	$0.517753\pi$
$240$		0			0
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	0.00223270	−	0.999998i	$-0.499289\pi$
$241$	−13.3923	−	7.73205i	−0.862674	−	0.498065i	−0.864907	+	0.501932i	$0.832623\pi$
$242$	9.86603	−	5.69615i	0.634212	−	0.366163i
$243$		0			0
$244$	−3.69615	+	2.13397i	−0.236622	+	0.136614i
$245$			1.33975i			0.0855932i
$246$		0			0
$247$	2.19615	+	3.80385i	0.139738	+	0.242033i
$248$	24.5885			1.56137
$249$		0			0
$250$	1.33013	+	2.30385i	0.0841246	+	0.145708i
$251$		−	25.7128i		−	1.62298i	−0.584367	−	0.811489i	$-0.698657\pi$
$251$		−	25.7128i		−	1.62298i	0.584367	−	0.811489i	$-0.301343\pi$
$252$		0			0
$253$			3.46410i			0.217786i
$254$	10.5622	+	6.09808i	0.662730	+	0.382627i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−16.9641	+	9.79423i	−1.05819	+	0.610947i	−0.924931	−	0.380134i	$-0.875878\pi$
$257$	−16.9641	+	9.79423i	−1.05819	+	0.610947i	−0.133260	+	0.991081i	$0.542545\pi$
$258$		0			0
$259$	−19.0526	−	9.00000i	−1.18387	−	0.559233i
$260$	0.928203			0.0575647
$261$		0			0
$262$	5.29423	−	9.16987i	0.327079	−	0.566517i
$263$	−3.80385	+	6.58846i	−0.234555	+	0.406262i	−0.959143	−	0.282921i	$-0.908697\pi$
$263$	−3.80385	+	6.58846i	−0.234555	+	0.406262i	0.724588	+	0.689182i	$0.242030\pi$
$264$		0			0
$265$			0.679492i			0.0417409i
$266$	−2.19615	+	3.80385i	−0.134655	+	0.233229i
$267$		0			0
$268$	3.63397	+	6.29423i	0.221980	+	0.384481i
$269$	−14.5359			−0.886269			−0.443135	−	0.896455i	$-0.646134\pi$
$269$	−14.5359			−0.886269			−0.443135	+	0.896455i	$0.646134\pi$
$270$		0			0
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	0.986973	−	0.160886i	$-0.0514352\pi$
$271$	5.83013	+	10.0981i	0.354155	+	0.613414i	−0.632818	+	0.774301i	$0.718102\pi$
$272$	−3.23205	−	1.86603i	−0.195972	−	0.113144i
$273$		0			0
$274$	5.59808	−	3.23205i	0.338192	−	0.195255i
$275$	−11.6603	−	20.1962i	−0.703140	−	1.21787i
$276$		0			0
$277$	−8.89230	−	5.13397i	−0.534287	−	0.308471i	0.208474	−	0.978028i	$-0.433150\pi$
$277$	−8.89230	−	5.13397i	−0.534287	−	0.308471i	−0.742760	+	0.669557i	$0.766484\pi$
$278$	−10.9019	−	6.29423i	−0.653854	−	0.377503i
$279$		0			0
$280$	1.39230	+	2.41154i	0.0832061	+	0.144117i
$281$	−28.7487	+	16.5981i	−1.71500	+	0.990158i	−0.787526	+	0.616282i	$0.788638\pi$
$281$	−28.7487	+	16.5981i	−1.71500	+	0.990158i	−0.927478	+	0.373877i	$0.878028\pi$
$282$		0			0
$283$	9.00000	+	5.19615i	0.534994	+	0.308879i	0.743048	−	0.669238i	$-0.233379\pi$
$283$	9.00000	+	5.19615i	0.534994	+	0.308879i	−0.208053	+	0.978117i	$0.566713\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	16.3923			0.969297
$287$	5.19615	+	9.00000i	0.306719	+	0.531253i
$288$		0			0
$289$	−1.53590	+	2.66025i	−0.0903470	+	0.156486i
$290$			0.0717968i			0.00421605i
$291$		0			0
$292$		0			0
$293$	14.4282	−	24.9904i	0.842905	−	1.45995i	−0.0445239	−	0.999008i	$-0.514177\pi$
$293$	14.4282	−	24.9904i	0.842905	−	1.45995i	0.887429	−	0.460945i	$-0.152490\pi$
$294$		0			0
$295$	−3.60770			−0.210048
$296$	−18.1865	+	1.50000i	−1.05707	+	0.0871857i
$297$		0			0
$298$	−4.79423	+	2.76795i	−0.277722	+	0.160343i
$299$	−1.26795	+	2.19615i	−0.0733274	+	0.127007i
$300$		0			0
$301$	−10.3923	−	6.00000i	−0.599002	−	0.345834i
$302$			16.5885i			0.954558i
$303$		0			0
$304$			1.26795i			0.0727219i
$305$	−0.571797	−	0.990381i	−0.0327410	−	0.0567091i
$306$		0			0
$307$	−14.3923			−0.821412			−0.410706	−	0.911768i	$-0.634718\pi$
$307$	−14.3923			−0.821412			−0.410706	+	0.911768i	$0.634718\pi$
$308$	−8.19615	−	14.1962i	−0.467019	−	0.808901i
$309$		0			0
$310$			2.19615i			0.124733i
$311$	26.3205	−	15.1962i	1.49250	−	0.861695i	0.492536	−	0.870292i	$-0.336070\pi$
$311$	26.3205	−	15.1962i	1.49250	−	0.861695i	0.999963	+	0.00859730i	$0.00273664\pi$
$312$		0			0
$313$	−13.5000	+	7.79423i	−0.763065	+	0.440556i	−0.830395	−	0.557175i	$-0.811885\pi$
$313$	−13.5000	+	7.79423i	−0.763065	+	0.440556i	0.0673300	+	0.997731i	$0.478552\pi$
$314$	12.4019	+	7.16025i	0.699881	+	0.404077i
$315$		0			0
$316$	−3.29423	+	1.90192i	−0.185315	+	0.106992i
$317$	−7.96410	−	13.7942i	−0.447309	−	0.774761i	0.550901	−	0.834570i	$-0.314284\pi$
$317$	−7.96410	−	13.7942i	−0.447309	−	0.774761i	−0.998210	+	0.0598093i	$0.980951\pi$
$318$		0			0
$319$		−	1.26795i		−	0.0709915i
$320$	1.62436	+	0.937822i	0.0908042	+	0.0524259i
$321$		0			0
$322$	−2.53590			−0.141320
$323$	−4.73205			−0.263298
$324$		0			0
$325$		−	17.0718i		−	0.946973i
$326$	11.1962	−	19.3923i	0.620098	−	1.07404i
$327$		0			0
$328$	7.79423	+	4.50000i	0.430364	+	0.248471i
$329$	−3.80385	+	6.58846i	−0.209713	+	0.363233i
$330$		0			0
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.563384	−	0.826195i	$-0.309499\pi$
$331$	28.3923	−	16.3923i	1.56058	−	0.901003i	0.997198	−	0.0748075i	$-0.0238342\pi$
$332$	8.19615			0.449822
$333$		0			0
$334$	−10.9282			−0.597965
$335$	−1.68653	+	0.973721i	−0.0921452	+	0.0532000i
$336$		0			0
$337$	−14.6962	+	25.4545i	−0.800550	+	1.38659i	0.118704	+	0.992930i	$0.462126\pi$
$337$	−14.6962	+	25.4545i	−0.800550	+	1.38659i	−0.919254	+	0.393664i	$0.871207\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$		0			0
$340$	−0.500000	+	0.866025i	−0.0271163	+	0.0469668i
$341$		−	38.7846i		−	2.10030i
$342$		0			0
$343$	−6.92820			−0.374088
$344$	−10.3923			−0.560316
$345$		0			0
$346$	8.59808	+	4.96410i	0.462235	+	0.266872i
$347$		−	12.7321i		−	0.683492i	−0.939792	−	0.341746i	$-0.888982\pi$
$347$		−	12.7321i		−	0.683492i	0.939792	−	0.341746i	$-0.111018\pi$
$348$		0			0
$349$	−4.03590	−	6.99038i	−0.216037	−	0.374187i	0.737556	−	0.675286i	$-0.235980\pi$
$349$	−4.03590	−	6.99038i	−0.216037	−	0.374187i	−0.953593	+	0.301099i	$0.902646\pi$
$350$	14.7846	−	8.53590i	0.790271	−	0.456263i
$351$		0			0
$352$	−20.4904	−	11.8301i	−1.09214	−	0.630548i
$353$	−10.6244	+	6.13397i	−0.565477	+	0.326479i	−0.755341	−	0.655332i	$-0.772529\pi$
$353$	−10.6244	+	6.13397i	−0.565477	+	0.326479i	0.189864	+	0.981810i	$0.439195\pi$
$354$		0			0
$355$	−1.39230	+	0.803848i	−0.0738959	+	0.0426638i
$356$		−	9.19615i		−	0.487395i
$357$		0			0
$358$	−0.732051	−	1.26795i	−0.0386901	−	0.0670132i
$359$	−16.3923			−0.865153			−0.432576	−	0.901597i	$-0.642395\pi$
$359$	−16.3923			−0.865153			−0.432576	+	0.901597i	$0.642395\pi$
$360$		0			0
$361$	−8.69615	−	15.0622i	−0.457692	−	0.792746i
$362$			9.92820i			0.521815i
$363$		0			0
$364$		−	12.0000i		−	0.628971i
$365$		0			0
$366$		0			0
$367$	10.1962	−	17.6603i	0.532235	−	0.921858i	−0.467057	−	0.884227i	$-0.654686\pi$
$367$	10.1962	−	17.6603i	0.532235	−	0.921858i	0.999292	−	0.0376305i	$-0.0119810\pi$
$368$	−0.633975	+	0.366025i	−0.0330482	+	0.0190804i
$369$		0			0
$370$	−0.133975	−	1.62436i	−0.00696501	−	0.0844462i
$371$	8.78461			0.456074
$372$		0			0
$373$	−8.76795	+	15.1865i	−0.453987	+	0.786329i	−0.998629	−	0.0523397i	$-0.983332\pi$
$373$	−8.76795	+	15.1865i	−0.453987	+	0.786329i	0.544642	+	0.838669i	$0.316665\pi$
$374$	−8.83013	+	15.2942i	−0.456595	+	0.790846i
$375$		0			0
$376$			6.58846i			0.339774i
$377$	0.464102	−	0.803848i	0.0239024	−	0.0414003i
$378$		0			0
$379$	−4.26795	−	7.39230i	−0.219230	−	0.379717i	0.735343	−	0.677695i	$-0.237021\pi$
$379$	−4.26795	−	7.39230i	−0.219230	−	0.379717i	−0.954573	+	0.297978i	$0.903688\pi$
$380$	0.339746			0.0174286
$381$		0			0
$382$	3.09808	+	5.36603i	0.158511	+	0.274550i
$383$	13.7321	+	7.92820i	0.701675	+	0.405112i	0.807971	−	0.589222i	$-0.200566\pi$
$383$	13.7321	+	7.92820i	0.701675	+	0.405112i	−0.106296	+	0.994335i	$0.533899\pi$
$384$		0			0
$385$	3.80385	−	2.19615i	0.193862	−	0.111926i
$386$	−7.33013	−	12.6962i	−0.373094	−	0.646217i
$387$		0			0
$388$	3.69615	+	2.13397i	0.187644	+	0.108336i
$389$	−27.0167	−	15.5981i	−1.36980	−	0.790854i	−0.378897	−	0.925439i	$-0.623697\pi$
$389$	−27.0167	−	15.5981i	−1.36980	−	0.790854i	−0.990902	+	0.134585i	$0.957030\pi$
$390$		0			0
$391$	−1.36603	−	2.36603i	−0.0690829	−	0.119655i
$392$	12.9904	−	7.50000i	0.656113	−	0.378807i
$393$		0			0
$394$	24.1865	+	13.9641i	1.21850	+	0.703501i
$395$	−0.509619	−	0.882686i	−0.0256417	−	0.0444127i
$396$		0			0
$397$	−21.2487			−1.06644			−0.533221	−	0.845976i	$-0.679019\pi$
$397$	−21.2487			−1.06644			−0.533221	+	0.845976i	$0.679019\pi$
$398$	−5.53590	−	9.58846i	−0.277490	−	0.480626i
$399$		0			0
$400$	2.46410	−	4.26795i	0.123205	−	0.213397i
$401$			5.60770i			0.280035i	0.990149	+	0.140017i	$0.0447159\pi$
$401$			5.60770i			0.280035i	−0.990149	+	0.140017i	$0.955284\pi$
$402$		0			0
$403$	14.1962	−	24.5885i	0.707161	−	1.22484i
$404$	−4.50000	+	7.79423i	−0.223883	+	0.387777i
$405$		0			0
$406$	0.928203			0.0460660
$407$	2.36603	+	28.6865i	0.117280	+	1.42194i
$408$		0			0
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	−0.302979	−	0.952997i	$-0.597981\pi$
$409$	7.50000	−	4.33013i	0.370851	−	0.214111i	0.673830	+	0.738886i	$0.264648\pi$
$410$	−0.401924	+	0.696152i	−0.0198496	+	0.0343805i
$411$		0			0
$412$	11.1962	+	6.46410i	0.551595	+	0.318463i
$413$			46.6410i			2.29505i
$414$		0			0
$415$			2.19615i			0.107805i
$416$	−8.66025	−	15.0000i	−0.424604	−	0.735436i
$417$		0			0
$418$	6.00000			0.293470
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	0.996239	−	0.0866469i	$-0.0276152\pi$
$419$	8.66025	+	15.0000i	0.423081	+	0.732798i	−0.573158	+	0.819445i	$0.694282\pi$
$420$		0			0
$421$			16.2679i			0.792851i	0.918067	+	0.396426i	$0.129750\pi$
$421$			16.2679i			0.792851i	−0.918067	+	0.396426i	$0.870250\pi$
$422$	−8.66025	+	5.00000i	−0.421575	+	0.243396i
$423$		0			0
$424$	6.58846	−	3.80385i	0.319964	−	0.184731i
$425$	15.9282	+	9.19615i	0.772631	+	0.446079i
$426$		0			0
$427$	−12.8038	+	7.39230i	−0.619622	+	0.357739i
$428$	−6.46410	−	11.1962i	−0.312454	−	0.541186i
$429$		0			0
$430$		−	0.928203i		−	0.0447619i
$431$	9.97372	+	5.75833i	0.480417	+	0.277369i	0.720590	−	0.693361i	$-0.243871\pi$
$431$	9.97372	+	5.75833i	0.480417	+	0.277369i	−0.240173	+	0.970730i	$0.577204\pi$
$432$		0			0
$433$	27.0000			1.29754			0.648769	−	0.760986i	$-0.275284\pi$
$433$	27.0000			1.29754			0.648769	+	0.760986i	$0.275284\pi$
$434$	28.3923			1.36287
$435$		0			0
$436$		−	6.80385i		−	0.325845i
$437$	−0.464102	+	0.803848i	−0.0222010	+	0.0384532i
$438$		0			0
$439$	12.5885	+	7.26795i	0.600814	+	0.346880i	0.769362	−	0.638813i	$-0.220574\pi$
$439$	12.5885	+	7.26795i	0.600814	+	0.346880i	−0.168548	+	0.985694i	$0.553908\pi$
$440$	1.90192	−	3.29423i	0.0906707	−	0.157046i
$441$		0			0
$442$	−11.1962	+	6.46410i	−0.532547	+	0.307466i
$443$	−33.4641			−1.58993			−0.794964	−	0.606657i	$-0.792510\pi$
$443$	−33.4641			−1.58993			−0.794964	+	0.606657i	$0.792510\pi$
$444$		0			0
$445$	2.46410			0.116810
$446$	3.97372	−	2.29423i	0.188161	−	0.108635i
$447$		0			0
$448$	12.1244	−	21.0000i	0.572822	−	0.992157i
$449$	27.9282	+	16.1244i	1.31801	+	0.760955i	0.983409	−	0.181403i	$-0.0580639\pi$
$449$	27.9282	+	16.1244i	1.31801	+	0.760955i	0.334605	+	0.942359i	$0.391397\pi$
$450$		0			0
$451$	7.09808	−	12.2942i	0.334235	−	0.578913i
$452$			4.53590i			0.213351i
$453$		0			0
$454$	−23.1244			−1.08528
$455$	3.21539			0.150740
$456$		0			0
$457$	−31.2846	−	18.0622i	−1.46343	−	0.844913i	−0.464264	−	0.885697i	$-0.653681\pi$
$457$	−31.2846	−	18.0622i	−1.46343	−	0.844913i	−0.999168	+	0.0407837i	$0.987015\pi$
$458$			7.00000i			0.327089i
$459$		0			0
$460$	0.0980762	+	0.169873i	0.00457283	+	0.00792037i
$461$	14.3205	−	8.26795i	0.666973	−	0.385077i	−0.127956	−	0.991780i	$-0.540842\pi$
$461$	14.3205	−	8.26795i	0.666973	−	0.385077i	0.794929	+	0.606703i	$0.207508\pi$
$462$		0			0
$463$	−13.3923	−	7.73205i	−0.622393	−	0.359339i	0.155407	−	0.987851i	$-0.450331\pi$
$463$	−13.3923	−	7.73205i	−0.622393	−	0.359339i	−0.777800	+	0.628512i	$0.783664\pi$
$464$	0.232051	−	0.133975i	0.0107727	−	0.00621961i
$465$		0			0
$466$	9.40192	−	5.42820i	0.435536	−	0.251457i
$467$			3.32051i			0.153655i	0.997044	+	0.0768274i	$0.0244790\pi$
$467$			3.32051i			0.153655i	−0.997044	+	0.0768274i	$0.975521\pi$
$468$		0			0
$469$	12.5885	+	21.8038i	0.581281	+	1.00681i
$470$	−0.588457			−0.0271435
$471$		0			0
$472$	20.1962	+	34.9808i	0.929603	+	1.61012i
$473$			16.3923i			0.753719i
$474$		0			0
$475$		−	6.24871i		−	0.286711i
$476$	11.1962	+	6.46410i	0.513175	+	0.296282i
$477$		0			0
$478$	−8.46410	+	14.6603i	−0.387139	+	0.670544i
$479$	34.0526	−	19.6603i	1.55590	−	0.898300i	0.558259	−	0.829667i	$-0.311469\pi$
$479$	34.0526	−	19.6603i	1.55590	−	0.898300i	0.997642	−	0.0686333i	$-0.0218639\pi$
$480$		0			0
$481$	−9.00000	+	19.0526i	−0.410365	+	0.868722i
$482$	−15.4641			−0.704371
$483$		0			0
$484$	−5.69615	+	9.86603i	−0.258916	+	0.448456i
$485$	−0.571797	+	0.990381i	−0.0259640	+	0.0449709i
$486$		0			0
$487$			32.4449i			1.47022i	0.677949	+	0.735109i	$0.262869\pi$
$487$			32.4449i			1.47022i	−0.677949	+	0.735109i	$0.737131\pi$
$488$	−6.40192	+	11.0885i	−0.289801	+	0.501951i
$489$		0			0
$490$	0.669873	+	1.16025i	0.0302618	+	0.0524149i
$491$	−31.2679			−1.41110			−0.705551	−	0.708659i	$-0.749301\pi$
$491$	−31.2679			−1.41110			−0.705551	+	0.708659i	$0.749301\pi$
$492$		0			0
$493$	0.500000	+	0.866025i	0.0225189	+	0.0390038i
$494$	3.80385	+	2.19615i	0.171143	+	0.0988096i
$495$		0			0
$496$	7.09808	−	4.09808i	0.318713	−	0.184009i
$497$	10.3923	+	18.0000i	0.466159	+	0.807410i
$498$		0			0
$499$	10.9019	+	6.29423i	0.488037	+	0.281768i	0.723760	−	0.690052i	$-0.242412\pi$
$499$	10.9019	+	6.29423i	0.488037	+	0.281768i	−0.235723	+	0.971820i	$0.575746\pi$
$500$	−2.30385	−	1.33013i	−0.103031	−	0.0594851i
$501$		0			0
$502$	−12.8564	−	22.2679i	−0.573810	−	0.993867i
$503$	7.77757	−	4.49038i	0.346785	−	0.200216i	−0.316484	−	0.948598i	$-0.602502\pi$
$503$	7.77757	−	4.49038i	0.346785	−	0.200216i	0.663268	+	0.748382i	$0.269169\pi$
$504$		0			0
$505$	−2.08846	−	1.20577i	−0.0929351	−	0.0536561i
$506$	1.73205	+	3.00000i	0.0769991	+	0.133366i
$507$		0			0
$508$	−12.1962			−0.541117
$509$	−2.89230	−	5.00962i	−0.128199	−	0.222047i	0.794780	−	0.606898i	$-0.207586\pi$
$509$	−2.89230	−	5.00962i	−0.128199	−	0.222047i	−0.922979	+	0.384850i	$0.874253\pi$
$510$		0			0
$511$		0			0
$512$		−	11.0000i		−	0.486136i
$513$		0			0
$514$	−9.79423	+	16.9641i	−0.432005	+	0.748254i
$515$	−1.73205	+	3.00000i	−0.0763233	+	0.132196i
$516$		0			0
$517$	10.3923			0.457053
$518$	−21.0000	+	1.73205i	−0.922687	+	0.0761019i
$519$		0			0
$520$	2.41154	−	1.39230i	0.105753	−	0.0610566i
$521$	3.46410	−	6.00000i	0.151765	−	0.262865i	−0.780111	−	0.625641i	$-0.784838\pi$
$521$	3.46410	−	6.00000i	0.151765	−	0.262865i	0.931876	+	0.362776i	$0.118171\pi$
$522$		0			0
$523$	13.9019	+	8.02628i	0.607889	+	0.350965i	0.772139	−	0.635454i	$-0.219187\pi$
$523$	13.9019	+	8.02628i	0.607889	+	0.350965i	−0.164250	+	0.986419i	$0.552520\pi$
$524$			10.5885i			0.462559i
$525$		0			0
$526$			7.60770i			0.331711i
$527$	15.2942	+	26.4904i	0.666227	+	1.15394i
$528$		0			0
$529$	22.4641			0.976700
$530$	0.339746	+	0.588457i	0.0147576	+	0.0255610i
$531$		0			0
$532$		−	4.39230i		−	0.190431i
$533$	9.00000	−	5.19615i	0.389833	−	0.225070i
$534$		0			0
$535$	3.00000	−	1.73205i	0.129701	−	0.0748831i
$536$	18.8827	+	10.9019i	0.815608	+	0.470891i
$537$		0			0
$538$	−12.5885	+	7.26795i	−0.542727	+	0.313344i
$539$	−11.8301	−	20.4904i	−0.509560	−	0.882583i
$540$		0			0
$541$		−	4.26795i		−	0.183493i	−0.995782	−	0.0917467i	$-0.970755\pi$
$541$		−	4.26795i		−	0.183493i	0.995782	−	0.0917467i	$-0.0292450\pi$
$542$	10.0981	+	5.83013i	0.433750	+	0.250425i
$543$		0			0
$544$	18.6603			0.800052
$545$	1.82309			0.0780924
$546$		0			0
$547$			3.80385i			0.162641i	0.996688	+	0.0813204i	$0.0259137\pi$
$547$			3.80385i			0.162641i	−0.996688	+	0.0813204i	$0.974086\pi$
$548$	−3.23205	+	5.59808i	−0.138066	+	0.239138i
$549$		0			0
$550$	−20.1962	−	11.6603i	−0.861167	−	0.497195i
$551$	0.169873	−	0.294229i	0.00723683	−	0.0125346i
$552$		0			0
$553$	−11.4115	+	6.58846i	−0.485268	+	0.280170i
$554$	−10.2679			−0.436243
$555$		0			0
$556$	12.5885			0.533870
$557$	15.3564	−	8.86603i	0.650672	−	0.375666i	−0.138042	−	0.990426i	$-0.544081\pi$
$557$	15.3564	−	8.86603i	0.650672	−	0.375666i	0.788714	+	0.614761i	$0.210747\pi$
$558$		0			0
$559$	−6.00000	+	10.3923i	−0.253773	+	0.439548i
$560$	0.803848	+	0.464102i	0.0339688	+	0.0196119i
$561$		0			0
$562$	−16.5981	+	28.7487i	−0.700148	+	1.21269i
$563$		−	34.5885i		−	1.45773i	−0.684658	−	0.728865i	$-0.740048\pi$
$563$		−	34.5885i		−	1.45773i	0.684658	−	0.728865i	$-0.259952\pi$
$564$		0			0
$565$	−1.21539			−0.0511319
$566$	10.3923			0.436821
$567$		0			0
$568$	15.5885	+	9.00000i	0.654077	+	0.377632i
$569$			36.5167i			1.53086i	0.643520	+	0.765429i	$0.277473\pi$
$569$			36.5167i			1.53086i	−0.643520	+	0.765429i	$0.722527\pi$
$570$		0			0
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	0.980754	+	0.195247i	$0.0625507\pi$
$571$	15.7583	+	27.2942i	0.659466	+	1.14223i	−0.321289	+	0.946981i	$0.604116\pi$
$572$	−14.1962	+	8.19615i	−0.593571	+	0.342698i
$573$		0			0
$574$	9.00000	+	5.19615i	0.375653	+	0.216883i
$575$	3.12436	−	1.80385i	0.130295	−	0.0752256i
$576$		0			0
$577$	11.1962	−	6.46410i	0.466102	−	0.269104i	−0.248505	−	0.968631i	$-0.579939\pi$
$577$	11.1962	−	6.46410i	0.466102	−	0.269104i	0.714607	+	0.699527i	$0.246606\pi$
$578$			3.07180i			0.127770i
$579$		0			0
$580$	−0.0358984	−	0.0621778i	−0.00149060	−	0.00258179i
$581$	28.3923			1.17791
$582$		0			0
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$		0			0
$585$		0			0
$586$		−	28.8564i		−	1.19205i
$587$	14.1506	+	8.16987i	0.584059	+	0.337207i	0.762745	−	0.646699i	$-0.223851\pi$
$587$	14.1506	+	8.16987i	0.584059	+	0.337207i	−0.178686	+	0.983906i	$0.557185\pi$
$588$		0			0
$589$	5.19615	−	9.00000i	0.214104	−	0.370839i
$590$	−3.12436	+	1.80385i	−0.128628	+	0.0742632i
$591$		0			0
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	−17.7846			−0.730326			−0.365163	−	0.930944i	$-0.618987\pi$
$593$	−17.7846			−0.730326			−0.365163	+	0.930944i	$0.618987\pi$
$594$		0			0
$595$	−1.73205	+	3.00000i	−0.0710072	+	0.122988i
$596$	2.76795	−	4.79423i	0.113380	−	0.196379i
$597$		0			0
$598$			2.53590i			0.103701i
$599$	3.97372	−	6.88269i	0.162362	−	0.281219i	−0.773353	−	0.633975i	$-0.781422\pi$
$599$	3.97372	−	6.88269i	0.162362	−	0.281219i	0.935715	+	0.352756i	$0.114755\pi$
$600$		0			0
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	−0.985375	−	0.170402i	$-0.945494\pi$
$601$	−15.6962	−	27.1865i	−0.640259	−	1.10896i	0.345115	−	0.938560i	$-0.387840\pi$
$602$	−12.0000			−0.489083
$603$		0			0
$604$	−8.29423	−	14.3660i	−0.337487	−	0.584545i
$605$	−2.64359	−	1.52628i	−0.107477	−	0.0620521i
$606$		0			0
$607$	4.90192	−	2.83013i	0.198963	−	0.114871i	−0.397209	−	0.917728i	$-0.630021\pi$
$607$	4.90192	−	2.83013i	0.198963	−	0.114871i	0.596172	+	0.802857i	$0.296688\pi$
$608$	−3.16987	−	5.49038i	−0.128555	−	0.222664i
$609$		0			0
$610$	−0.990381	−	0.571797i	−0.0400994	−	0.0231514i
$611$	6.58846	+	3.80385i	0.266540	+	0.153887i
$612$		0			0
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	0.829737	−	0.558154i	$-0.188490\pi$
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	−0.898244	+	0.439497i	$0.855157\pi$
$614$	−12.4641	+	7.19615i	−0.503010	+	0.290413i
$615$		0			0
$616$	−42.5885	−	24.5885i	−1.71594	−	0.990697i
$617$	−12.5885	−	21.8038i	−0.506792	−	0.877790i	−0.999969	−	0.00786080i	$-0.997498\pi$
$617$	−12.5885	−	21.8038i	−0.506792	−	0.877790i	0.493177	−	0.869929i	$-0.335836\pi$
$618$		0			0
$619$	6.78461			0.272696			0.136348	−	0.990661i	$-0.456463\pi$
$619$	6.78461			0.272696			0.136348	+	0.990661i	$0.456463\pi$
$620$	−1.09808	−	1.90192i	−0.0440998	−	0.0763831i
$621$		0			0
$622$	15.1962	−	26.3205i	0.609310	−	1.05536i
$623$		−	31.8564i		−	1.27630i
$624$		0			0
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	−7.79423	+	13.5000i	−0.311520	+	0.539569i
$627$		0			0
$628$	−14.3205			−0.571450
$629$	−12.9282	−	18.6603i	−0.515481	−	0.744033i
$630$		0			0
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	−0.129626	−	0.991563i	$-0.541378\pi$
$631$	16.6865	−	9.63397i	0.664280	−	0.383522i	0.793906	+	0.608041i	$0.208044\pi$
$632$	−5.70577	+	9.88269i	−0.226963	+	0.393112i
$633$		0			0
$634$	−13.7942	−	7.96410i	−0.547839	−	0.316295i
$635$		−	3.26795i		−	0.129685i
$636$		0			0
$637$		−	17.3205i		−	0.686264i
$638$	−0.633975	−	1.09808i	−0.0250993	−	0.0434733i
$639$		0			0
$640$	−0.803848			−0.0317749
$641$	−8.89230	−	15.4019i	−0.351225	−	0.608339i	0.635239	−	0.772315i	$-0.280901\pi$
$641$	−8.89230	−	15.4019i	−0.351225	−	0.608339i	−0.986464	+	0.163976i	$0.947568\pi$
$642$		0			0
$643$			5.66025i			0.223219i	0.993752	+	0.111609i	$0.0356005\pi$
$643$			5.66025i			0.223219i	−0.993752	+	0.111609i	$0.964399\pi$
$644$	2.19615	−	1.26795i	0.0865405	−	0.0499642i
$645$		0			0
$646$	−4.09808	+	2.36603i	−0.161237	+	0.0930900i
$647$	−37.6410	−	21.7321i	−1.47982	−	0.854375i	−0.480082	−	0.877224i	$-0.659393\pi$
$647$	−37.6410	−	21.7321i	−1.47982	−	0.854375i	−0.999739	+	0.0228485i	$0.992726\pi$
$648$		0			0
$649$	55.1769	−	31.8564i	2.16588	−	1.25047i
$650$	−8.53590	−	14.7846i	−0.334805	−	0.579900i
$651$		0			0
$652$			22.3923i			0.876950i
$653$	2.42820	+	1.40192i	0.0950229	+	0.0548615i	0.546758	−	0.837290i	$-0.315862\pi$
$653$	2.42820	+	1.40192i	0.0950229	+	0.0548615i	−0.451736	+	0.892152i	$0.649195\pi$
$654$		0			0
$655$	−2.83717			−0.110857
$656$	3.00000			0.117130
$657$		0			0
$658$			7.60770i			0.296579i
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	−0.759018	−	0.651070i	$-0.774320\pi$
$659$	4.73205	−	8.19615i	0.184335	−	0.319277i	0.943352	+	0.331793i	$0.107654\pi$
$660$		0			0
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	0.268605	−	0.963250i	$-0.413437\pi$
$661$	−11.0885	−	6.40192i	−0.431291	−	0.249006i	−0.699896	+	0.714244i	$0.746771\pi$
$662$	16.3923	−	28.3923i	0.637105	−	1.10350i
$663$		0			0
$664$	21.2942	−	12.2942i	0.826376	−	0.477109i
$665$	1.17691			0.0456388
$666$		0			0
$667$	0.196152			0.00759505
$668$	9.46410	−	5.46410i	0.366177	−	0.211412i
$669$		0			0
$670$	−0.973721	+	1.68653i	−0.0376181	+	0.0651565i
$671$	17.4904	+	10.0981i	0.675209	+	0.389832i
$672$		0			0
$673$	−7.85641	+	13.6077i	−0.302842	+	0.524538i	−0.976779	−	0.214251i	$-0.931269\pi$
$673$	−7.85641	+	13.6077i	−0.302842	+	0.524538i	0.673936	+	0.738789i	$0.264602\pi$
$674$			29.3923i			1.13215i
$675$		0			0
$676$	1.00000			0.0384615
$677$	44.3205			1.70338			0.851688	−	0.524050i	$-0.175579\pi$
$677$	44.3205			1.70338			0.851688	+	0.524050i	$0.175579\pi$
$678$		0			0
$679$	12.8038	+	7.39230i	0.491367	+	0.283691i
$680$			3.00000i			0.115045i
$681$		0			0
$682$	−19.3923	−	33.5885i	−0.742570	−	1.28617i
$683$	−26.9090	+	15.5359i	−1.02964	+	0.594465i	−0.916882	−	0.399158i	$-0.869303\pi$
$683$	−26.9090	+	15.5359i	−1.02964	+	0.594465i	−0.112761	+	0.993622i	$0.535969\pi$
$684$		0			0
$685$	−1.50000	−	0.866025i	−0.0573121	−	0.0330891i
$686$	−6.00000	+	3.46410i	−0.229081	+	0.132260i
$687$		0			0
$688$	−3.00000	+	1.73205i	−0.114374	+	0.0660338i
$689$		−	8.78461i		−	0.334667i
$690$		0			0
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	0.672002	−	0.740550i	$-0.265435\pi$
$691$	−8.02628	−	13.9019i	−0.305334	−	0.528854i	−0.977336	+	0.211696i	$0.932101\pi$
$692$	−9.92820			−0.377414
$693$		0			0
$694$	−6.36603	−	11.0263i	−0.241651	−	0.418552i
$695$			3.37307i			0.127948i
$696$		0			0
$697$			11.1962i			0.424085i
$698$	−6.99038	−	4.03590i	−0.264590	−	0.152761i
$699$		0			0
$700$	−8.53590	+	14.7846i	−0.322627	+	0.558806i
$701$	5.07180	−	2.92820i	0.191559	−	0.110597i	−0.401153	−	0.916011i	$-0.631390\pi$
$701$	5.07180	−	2.92820i	0.191559	−	0.110597i	0.592712	+	0.805414i	$0.298057\pi$
$702$		0			0
$703$	−3.29423	+	6.97372i	−0.124244	+	0.263019i
$704$	−33.1244			−1.24842
$705$		0			0
$706$	−6.13397	+	10.6244i	−0.230855	+	0.399853i
$707$	−15.5885	+	27.0000i	−0.586264	+	1.01544i
$708$		0			0
$709$		−	30.0000i		−	1.12667i	−0.826227	−	0.563337i	$-0.809517\pi$
$709$		−	30.0000i		−	1.12667i	0.826227	−	0.563337i	$-0.190483\pi$
$710$	−0.803848	+	1.39230i	−0.0301679	+	0.0522523i
$711$		0			0
$712$	−13.7942	−	23.8923i	−0.516961	−	0.895402i
$713$	6.00000			0.224702
$714$		0			0
$715$	−2.19615	−	3.80385i	−0.0821314	−	0.142256i
$716$	1.26795	+	0.732051i	0.0473855	+	0.0273580i
$717$		0			0
$718$	−14.1962	+	8.19615i	−0.529796	+	0.305878i
$719$	13.2224	+	22.9019i	0.493114	+	0.854098i	0.999969	−	0.00793367i	$-0.00252539\pi$
$719$	13.2224	+	22.9019i	0.493114	+	0.854098i	−0.506855	+	0.862031i	$0.669192\pi$
$720$		0			0
$721$	38.7846	+	22.3923i	1.44441	+	0.833933i
$722$	−15.0622	−	8.69615i	−0.560556	−	0.323637i
$723$		0			0
$724$	−4.96410	−	8.59808i	−0.184489	−	0.319545i
$725$	−1.14359	+	0.660254i	−0.0424720	+	0.0245212i
$726$		0			0
$727$	−1.60770	−	0.928203i	−0.0596261	−	0.0344252i	0.469891	−	0.882725i	$-0.344293\pi$
$727$	−1.60770	−	0.928203i	−0.0596261	−	0.0344252i	−0.529517	+	0.848300i	$0.677627\pi$
$728$	−18.0000	−	31.1769i	−0.667124	−	1.15549i
$729$		0			0
$730$		0			0
$731$	−6.46410	−	11.1962i	−0.239083	−	0.414105i
$732$		0			0
$733$	−14.3923	+	24.9282i	−0.531592	+	0.920744i	0.467728	+	0.883872i	$0.345073\pi$
$733$	−14.3923	+	24.9282i	−0.531592	+	0.920744i	−0.999320	+	0.0368718i	$0.988261\pi$
$734$		−	20.3923i		−	0.752694i
$735$		0			0
$736$	1.83013	−	3.16987i	0.0674594	−	0.116843i
$737$	17.1962	−	29.7846i	0.633428	−	1.09713i
$738$		0			0
$739$	−23.8038			−0.875639			−0.437819	−	0.899063i	$-0.644249\pi$
$739$	−23.8038			−0.875639			−0.437819	+	0.899063i	$0.644249\pi$
$740$	0.928203	+	1.33975i	0.0341214	+	0.0492500i
$741$		0			0
$742$	7.60770	−	4.39230i	0.279287	−	0.161247i
$743$	−21.6340	+	37.4711i	−0.793674	+	1.37468i	0.130004	+	0.991513i	$0.458501\pi$
$743$	−21.6340	+	37.4711i	−0.793674	+	1.37468i	−0.923678	+	0.383170i	$0.874833\pi$
$744$		0			0
$745$	1.28461	+	0.741670i	0.0470645	+	0.0271727i
$746$			17.5359i			0.642035i
$747$		0			0
$748$		−	17.6603i		−	0.645723i
$749$	−22.3923	−	38.7846i	−0.818197	−	1.41716i
$750$		0			0
$751$	−9.21539			−0.336274			−0.168137	−	0.985764i	$-0.553775\pi$
$751$	−9.21539			−0.336274			−0.168137	+	0.985764i	$0.553775\pi$
$752$	1.09808	+	1.90192i	0.0400427	+	0.0693560i
$753$		0			0
$754$		−	0.928203i		−	0.0338032i
$755$	3.84936	−	2.22243i	0.140093	−	0.0808826i
$756$		0			0
$757$	36.6962	−	21.1865i	1.33374	−	0.770038i	0.347873	−	0.937542i	$-0.386904\pi$
$757$	36.6962	−	21.1865i	1.33374	−	0.770038i	0.985871	+	0.167504i	$0.0535707\pi$
$758$	−7.39230	−	4.26795i	−0.268501	−	0.155019i
$759$		0			0
$760$	0.882686	−	0.509619i	0.0320184	−	0.0184858i
$761$	−1.83975	−	3.18653i	−0.0666907	−	0.115512i	0.830752	−	0.556643i	$-0.187911\pi$
$761$	−1.83975	−	3.18653i	−0.0666907	−	0.115512i	−0.897443	+	0.441131i	$0.854577\pi$
$762$		0			0
$763$		−	23.5692i		−	0.853263i
$764$	−5.36603	−	3.09808i	−0.194136	−	0.112084i
$765$		0			0
$766$	15.8564			0.572915
$767$	46.6410			1.68411
$768$		0			0
$769$			20.5359i			0.740543i	0.928923	+	0.370272i	$0.120735\pi$
$769$			20.5359i			0.740543i	−0.928923	+	0.370272i	$0.879265\pi$
$770$	2.19615	−	3.80385i	0.0791438	−	0.137081i
$771$		0			0
$772$	12.6962	+	7.33013i	0.456945	+	0.263817i
$773$	−24.0167	+	41.5981i	−0.863819	+	1.49618i	0.00439560	+	0.999990i	$0.498601\pi$
$773$	−24.0167	+	41.5981i	−0.863819	+	1.49618i	−0.868215	+	0.496188i	$0.834733\pi$
$774$		0			0
$775$	−34.9808	+	20.1962i	−1.25655	+	0.725467i
$776$	12.8038			0.459631
$777$		0			0
$778$	−31.1962			−1.11844
$779$	3.29423	−	1.90192i	0.118028	−	0.0681435i
$780$		0			0
$781$	14.1962	−	24.5885i	0.507978	−	0.879844i
$782$	−2.36603	−	1.36603i	−0.0846089	−	0.0488490i
$783$		0			0
$784$	2.50000	−	4.33013i	0.0892857	−	0.154647i
$785$		−	3.83717i		−	0.136954i
$786$		0			0
$787$	0.392305			0.0139842			0.00699208	−	0.999976i	$-0.497774\pi$
$787$	0.392305			0.0139842			0.00699208	+	0.999976i	$0.497774\pi$
$788$	−27.9282			−0.994901
$789$		0			0
$790$	−0.882686	−	0.509619i	−0.0314046	−	0.0181314i
$791$			15.7128i			0.558683i
$792$		0			0
$793$	7.39230	+	12.8038i	0.262508	+	0.454678i
$794$	−18.4019	+	10.6244i	−0.653060	+	0.377044i
$795$		0			0
$796$	9.58846	+	5.53590i	0.339854	+	0.196215i
$797$	6.92820	−	4.00000i	0.245410	−	0.141687i	−0.372251	−	0.928132i	$-0.621414\pi$
$797$	6.92820	−	4.00000i	0.245410	−	0.141687i	0.617661	+	0.786445i	$0.288081\pi$
$798$		0			0
$799$	−7.09808	+	4.09808i	−0.251112	+	0.144980i
$800$			24.6410i			0.871191i
$801$		0			0
$802$	2.80385	+	4.85641i	0.0990073	+	0.171486i
$803$		0			0
$804$		0			0
$805$	0.339746	+	0.588457i	0.0119745	+	0.0207404i
$806$		−	28.3923i		−	1.00008i
$807$		0			0
$808$			27.0000i			0.949857i
$809$	−29.3205	−	16.9282i	−1.03085	−	0.595164i	−0.113625	−	0.993524i	$-0.536246\pi$
$809$	−29.3205	−	16.9282i	−1.03085	−	0.595164i	−0.917229	+	0.398360i	$0.869580\pi$
$810$		0			0
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	−0.980570	−	0.196167i	$-0.937150\pi$
$811$	−9.12436	+	15.8038i	−0.320399	+	0.554948i	0.660171	+	0.751115i	$0.270484\pi$
$812$	−0.803848	+	0.464102i	−0.0282095	+	0.0162868i
$813$		0			0
$814$	16.3923	+	23.6603i	0.574550	+	0.829291i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	−2.19615	+	3.80385i	−0.0768336	+	0.133080i
$818$	4.33013	−	7.50000i	0.151399	−	0.262231i
$819$		0			0
$820$		−	0.803848i		−	0.0280716i
$821$	24.5885	−	42.5885i	0.858143	−	1.48635i	−0.0155551	−	0.999879i	$-0.504952\pi$
$821$	24.5885	−	42.5885i	0.858143	−	1.48635i	0.873698	−	0.486468i	$-0.161715\pi$
$822$		0			0
$823$	1.50962	+	2.61474i	0.0526220	+	0.0911440i	0.891137	−	0.453735i	$-0.149909\pi$
$823$	1.50962	+	2.61474i	0.0526220	+	0.0911440i	−0.838515	+	0.544879i	$0.816575\pi$
$824$	38.7846			1.35113
$825$		0			0
$826$	23.3205	+	40.3923i	0.811424	+	1.40543i
$827$	19.8564	+	11.4641i	0.690475	+	0.398646i	0.803790	−	0.594913i	$-0.202814\pi$
$827$	19.8564	+	11.4641i	0.690475	+	0.398646i	−0.113315	+	0.993559i	$0.536147\pi$
$828$		0			0
$829$	−38.5692	+	22.2679i	−1.33956	+	0.773398i	−0.986743	−	0.162293i	$-0.948111\pi$
$829$	−38.5692	+	22.2679i	−1.33956	+	0.773398i	−0.352822	+	0.935691i	$0.614778\pi$
$830$	1.09808	+	1.90192i	0.0381148	+	0.0660167i
$831$		0			0
$832$	−21.0000	−	12.1244i	−0.728044	−	0.420336i
$833$	16.1603	+	9.33013i	0.559920	+	0.323270i
$834$		0			0
$835$	1.46410	+	2.53590i	0.0506673	+	0.0877584i
$836$	−5.19615	+	3.00000i	−0.179713	+	0.103757i
$837$		0			0
$838$	15.0000	+	8.66025i	0.518166	+	0.299164i
$839$	−14.8301	−	25.6865i	−0.511993	−	0.886798i	−0.999903	−	0.0139040i	$-0.995574\pi$
$839$	−14.8301	−	25.6865i	−0.511993	−	0.886798i	0.487910	−	0.872894i	$-0.337759\pi$
$840$		0			0
$841$	28.9282			0.997524
$842$	8.13397	+	14.0885i	0.280315	+	0.485520i
$843$		0			0
$844$	5.00000	−	8.66025i	0.172107	−	0.298098i
$845$			0.267949i			0.00921773i
$846$		0			0
$847$	−19.7321	+	34.1769i	−0.678001	+	1.17433i
$848$	1.26795	−	2.19615i	0.0435416	−	0.0754162i
$849$		0			0
$850$	18.3923			0.630851
$851$	−4.43782	+	0.366025i	−0.152127	+	0.0125472i
$852$		0			0
$853$	36.4808	−	21.0622i	1.24908	−	0.721155i	0.278152	−	0.960537i	$-0.410278\pi$
$853$	36.4808	−	21.0622i	1.24908	−	0.721155i	0.970926	+	0.239382i	$0.0769448\pi$
$854$	−7.39230	+	12.8038i	−0.252959	+	0.438139i
$855$		0			0
$856$	−33.5885	−	19.3923i	−1.14803	−	0.662815i
$857$		−	23.7321i		−	0.810671i	−0.914168	−	0.405336i	$-0.867155\pi$
$857$		−	23.7321i		−	0.810671i	0.914168	−	0.405336i	$-0.132845\pi$
$858$		0			0
$859$		−	8.53590i		−	0.291241i	−0.989341	−	0.145621i	$-0.953482\pi$
$859$		−	8.53590i		−	0.291241i	0.989341	−	0.145621i	$-0.0465179\pi$
$860$	0.464102	+	0.803848i	0.0158257	+	0.0274110i
$861$		0			0
$862$	11.5167			0.392259
$863$	19.2679	+	33.3731i	0.655889	+	1.13603i	0.981670	+	0.190587i	$0.0610392\pi$
$863$	19.2679	+	33.3731i	0.655889	+	1.13603i	−0.325782	+	0.945445i	$0.605627\pi$
$864$		0			0
$865$		−	2.66025i		−	0.0904514i
$866$	23.3827	−	13.5000i	0.794576	−	0.458749i
$867$		0			0
$868$	−24.5885	+	14.1962i	−0.834587	+	0.481849i
$869$	15.5885	+	9.00000i	0.528802	+	0.305304i
$870$		0			0
$871$	21.8038	−	12.5885i	0.738795	−	0.426544i
$872$	−10.2058	−	17.6769i	−0.345611	−	0.598616i
$873$		0			0
$874$			0.928203i			0.0313969i
$875$	−7.98076	−	4.60770i	−0.269799	−	0.155769i
$876$		0			0
$877$	5.78461			0.195332			0.0976662	−	0.995219i	$-0.468862\pi$
$877$	5.78461			0.195332			0.0976662	+	0.995219i	$0.468862\pi$
$878$	14.5359			0.490563
$879$		0			0
$880$		−	1.26795i		−	0.0427426i
$881$	16.1603	−	27.9904i	0.544453	−	0.943020i	−0.454188	−	0.890906i	$-0.650071\pi$
$881$	16.1603	−	27.9904i	0.544453	−	0.943020i	0.998641	−	0.0521142i	$-0.0165960\pi$
$882$		0			0
$883$	−30.8827	−	17.8301i	−1.03929	−	0.600032i	−0.119654	−	0.992816i	$-0.538179\pi$
$883$	−30.8827	−	17.8301i	−1.03929	−	0.600032i	−0.919631	+	0.392784i	$0.871512\pi$
$884$	6.46410	−	11.1962i	0.217411	−	0.376567i
$885$		0			0
$886$	−28.9808	+	16.7321i	−0.973628	+	0.562124i
$887$	−28.9808			−0.973079			−0.486539	−	0.873659i	$-0.661741\pi$
$887$	−28.9808			−0.973079			−0.486539	+	0.873659i	$0.661741\pi$
$888$		0			0
$889$	−42.2487			−1.41698
$890$	2.13397	−	1.23205i	0.0715310	−	0.0412984i
$891$		0			0
$892$	−2.29423	+	3.97372i	−0.0768165	+	0.133050i
$893$	2.41154	+	1.39230i	0.0806992	+	0.0465917i
$894$		0			0
$895$	−0.196152	+	0.339746i	−0.00655665	+	0.0113565i
$896$			10.3923i			0.347183i
$897$		0			0
$898$	32.2487			1.07615
$899$	−2.19615			−0.0732458
$900$		0			0
$901$	8.19615	+	4.73205i	0.273053	+	0.157647i
$902$		−	14.1962i		−	0.472680i
$903$		0			0
$904$	6.80385	+	11.7846i	0.226293	+	0.391950i
$905$	2.30385	−	1.33013i	0.0765825	−	0.0442149i
$906$		0			0
$907$	1.09808	+	0.633975i	0.0364610	+	0.0210508i	0.518120	−	0.855308i	$-0.326632\pi$
$907$	1.09808	+	0.633975i	0.0364610	+	0.0210508i	−0.481659	+	0.876359i	$0.659965\pi$
$908$	20.0263	−	11.5622i	0.664595	−	0.383704i
$909$		0			0
$910$	2.78461	−	1.60770i	0.0923089	−	0.0532946i
$911$			53.5167i			1.77309i	0.462646	+	0.886543i	$0.346900\pi$
$911$			53.5167i			1.77309i	−0.462646	+	0.886543i	$0.653100\pi$
$912$		0			0
$913$	−19.3923	−	33.5885i	−0.641792	−	1.11162i
$914$	−36.1244			−1.19489
$915$		0			0
$916$	−3.50000	−	6.06218i	−0.115643	−	0.200300i
$917$			36.6795i			1.21126i
$918$		0			0
$919$			4.05256i			0.133682i	0.997764	+	0.0668408i	$0.0212920\pi$
$919$			4.05256i			0.133682i	−0.997764	+	0.0668408i	$0.978708\pi$
$920$	0.509619	+	0.294229i	0.0168016	+	0.00970043i
$921$		0			0
$922$	8.26795	−	14.3205i	0.272290	−	0.471621i
$923$	18.0000	−	10.3923i	0.592477	−	0.342067i
$924$		0			0
$925$	24.6410	−	17.0718i	0.810192	−	0.561317i
$926$	−15.4641			−0.508182
$927$		0			0
$928$	−0.669873	+	1.16025i	−0.0219897	+	0.0380872i
$929$	−15.2321	+	26.3827i	−0.499747	+	0.865588i	−1.00000		0.000291680i	$-0.999907\pi$
$929$	−15.2321	+	26.3827i	−0.499747	+	0.865588i	0.500253	+	0.865880i	$0.333240\pi$
$930$		0			0
$931$		−	6.33975i		−	0.207777i
$932$	−5.42820	+	9.40192i	−0.177807	+	0.307970i
$933$		0			0
$934$	1.66025	+	2.87564i	0.0543252	+	0.0940940i
$935$	4.73205			0.154755
$936$		0			0
$937$	6.30385	+	10.9186i	0.205938	+	0.356695i	0.950431	−	0.310935i	$-0.100642\pi$
$937$	6.30385	+	10.9186i	0.205938	+	0.356695i	−0.744493	+	0.667630i	$0.767309\pi$
$938$	21.8038	+	12.5885i	0.711921	+	0.411028i
$939$		0			0
$940$	0.509619	−	0.294229i	0.0166219	−	0.00959668i
$941$	−2.08846	−	3.61731i	−0.0680818	−	0.117921i	0.829975	−	0.557800i	$-0.188355\pi$
$941$	−2.08846	−	3.61731i	−0.0680818	−	0.117921i	−0.898057	+	0.439879i	$0.855021\pi$
$942$		0			0
$943$	1.90192	+	1.09808i	0.0619352	+	0.0357583i
$944$	11.6603	+	6.73205i	0.379509	+	0.219110i
$945$		0			0
$946$	8.19615	+	14.1962i	0.266480	+	0.461557i
$947$	23.9090	−	13.8038i	0.776937	−	0.448565i	−0.0584067	−	0.998293i	$-0.518602\pi$
$947$	23.9090	−	13.8038i	0.776937	−	0.448565i	0.835344	+	0.549728i	$0.185269\pi$
$948$		0			0
$949$		0			0
$950$	−3.12436	−	5.41154i	−0.101367	−	0.175574i
$951$		0			0
$952$	38.7846			1.25702
$953$	−2.07180	−	3.58846i	−0.0671121	−	0.116242i	0.830517	−	0.556993i	$-0.188045\pi$
$953$	−2.07180	−	3.58846i	−0.0671121	−	0.116242i	−0.897629	+	0.440752i	$0.854712\pi$
$954$		0			0
$955$	0.830127	−	1.43782i	0.0268623	−	0.0465268i
$956$		−	16.9282i		−	0.547497i
$957$		0			0
$958$	19.6603	−	34.0526i	0.635194	−	1.10019i
$959$	−11.1962	+	19.3923i	−0.361543	+	0.626210i
$960$		0			0
$961$	−36.1769			−1.16700
$962$	1.73205	+	21.0000i	0.0558436	+	0.677067i
$963$		0			0
$964$	13.3923	−	7.73205i	0.431337	−	0.249033i
$965$	−1.96410	+	3.40192i	−0.0632267	+	0.109512i
$966$		0			0
$967$	28.3923	+	16.3923i	0.913035	+	0.527141i	0.881406	−	0.472359i	$-0.156597\pi$
$967$	28.3923	+	16.3923i	0.913035	+	0.527141i	0.0316286	+	0.999500i	$0.489931\pi$
$968$			34.1769i			1.09849i
$969$		0			0
$970$			1.14359i			0.0367186i
$971$	−4.09808	−	7.09808i	−0.131514	−	0.227788i	0.792747	−	0.609551i	$-0.208650\pi$
$971$	−4.09808	−	7.09808i	−0.131514	−	0.227788i	−0.924260	+	0.381763i	$0.875317\pi$
$972$		0			0
$973$	43.6077			1.39800
$974$	16.2224	+	28.0981i	0.519800	+	0.900320i
$975$		0			0
$976$			4.26795i			0.136614i
$977$	14.0718	−	8.12436i	0.450197	−	0.259921i	−0.257717	−	0.966221i	$-0.582970\pi$
$977$	14.0718	−	8.12436i	0.450197	−	0.259921i	0.707913	+	0.706299i	$0.249637\pi$
$978$		0			0
$979$	−37.6865	+	21.7583i	−1.20447	+	0.695399i
$980$	−1.16025	−	0.669873i	−0.0370630	−	0.0213983i
$981$		0			0
$982$	−27.0788	+	15.6340i	−0.864120	+	0.498900i
$983$	28.5622	+	49.4711i	0.910992	+	1.57788i	0.812666	+	0.582730i	$0.198016\pi$
$983$	28.5622	+	49.4711i	0.910992	+	1.57788i	0.0983263	+	0.995154i	$0.468651\pi$
$984$		0			0
$985$		−	7.48334i		−	0.238439i
$986$	0.866025	+	0.500000i	0.0275799	+	0.0159232i
$987$		0			0
$988$	−4.39230			−0.139738
$989$	−2.53590			−0.0806369
$990$		0			0
$991$		−	46.3923i		−	1.47370i	−0.676056	−	0.736850i	$-0.736312\pi$
$991$		−	46.3923i		−	1.47370i	0.676056	−	0.736850i	$-0.263688\pi$
$992$	−20.4904	+	35.4904i	−0.650570	+	1.12682i
$993$		0			0
$994$	18.0000	+	10.3923i	0.570925	+	0.329624i
$995$	−1.48334	+	2.56922i	−0.0470250	+	0.0814497i
$996$		0			0
$997$	17.7846	−	10.2679i	0.563244	−	0.325189i	−0.191202	−	0.981551i	$-0.561239\pi$
$997$	17.7846	−	10.2679i	0.563244	−	0.325189i	0.754447	+	0.656361i	$0.227905\pi$
$998$	12.5885			0.398481
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	333.2.s.b.307.2		4
3.2	odd	2		37.2.e.a.11.1	✓	4
12.11	even	2		592.2.w.c.529.1		4
15.2	even	4		925.2.m.a.899.1		4
15.8	even	4		925.2.m.b.899.2		4
15.14	odd	2		925.2.n.a.751.2		4
37.27	even	6	inner	333.2.s.b.64.2		4
111.8	even	12		1369.2.a.g.1.2		2
111.11	odd	6		1369.2.b.d.1368.3		4
111.26	odd	6		1369.2.b.d.1368.1		4
111.29	even	12		1369.2.a.h.1.2		2
111.101	odd	6		37.2.e.a.27.1	yes	4
444.323	even	6		592.2.w.c.545.1		4
555.212	even	12		925.2.m.b.249.2		4
555.323	even	12		925.2.m.a.249.1		4
555.434	odd	6		925.2.n.a.101.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.e.a.11.1	✓	4	3.2	odd	2
37.2.e.a.27.1	yes	4	111.101	odd	6
333.2.s.b.64.2		4	37.27	even	6	inner
333.2.s.b.307.2		4	1.1	even	1	trivial
592.2.w.c.529.1		4	12.11	even	2
592.2.w.c.545.1		4	444.323	even	6
925.2.m.a.249.1		4	555.323	even	12
925.2.m.a.899.1		4	15.2	even	4
925.2.m.b.249.2		4	555.212	even	12
925.2.m.b.899.2		4	15.8	even	4
925.2.n.a.101.2		4	555.434	odd	6
925.2.n.a.751.2		4	15.14	odd	2
1369.2.a.g.1.2		2	111.8	even	12
1369.2.a.h.1.2		2	111.29	even	12
1369.2.b.d.1368.1		4	111.26	odd	6
1369.2.b.d.1368.3		4	111.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 333 = 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	333.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.232051 - 0.133975i) q^{5} +(-1.73205 + 3.00000i) q^{7} +3.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.232051 - 0.133975i) q^{5} +(-1.73205 + 3.00000i) q^{7} +3.00000i q^{8} -0.267949 q^{10} +4.73205 q^{11} +(3.00000 + 1.73205i) q^{13} +3.46410i q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.23205 + 1.86603i) q^{17} +(1.09808 + 0.633975i) q^{19} +(0.232051 - 0.133975i) q^{20} +(4.09808 - 2.36603i) q^{22} +0.732051i q^{23} +(-2.46410 - 4.26795i) q^{25} +3.46410 q^{26} +(-1.73205 - 3.00000i) q^{28} -0.267949i q^{29} -8.19615i q^{31} +(-4.33013 - 2.50000i) q^{32} +(-1.86603 + 3.23205i) q^{34} +(0.803848 - 0.464102i) q^{35} +(0.500000 + 6.06218i) q^{37} +1.26795 q^{38} +(0.401924 - 0.696152i) q^{40} +(1.50000 - 2.59808i) q^{41} +3.46410i q^{43} +(-2.36603 + 4.09808i) q^{44} +(0.366025 + 0.633975i) q^{46} +2.19615 q^{47} +(-2.50000 - 4.33013i) q^{49} +(-4.26795 - 2.46410i) q^{50} +(-3.00000 + 1.73205i) q^{52} +(-1.26795 - 2.19615i) q^{53} +(-1.09808 - 0.633975i) q^{55} +(-9.00000 - 5.19615i) q^{56} +(-0.133975 - 0.232051i) q^{58} +(11.6603 - 6.73205i) q^{59} +(3.69615 + 2.13397i) q^{61} +(-4.09808 - 7.09808i) q^{62} -7.00000 q^{64} +(-0.464102 - 0.803848i) q^{65} +(3.63397 - 6.29423i) q^{67} -3.73205i q^{68} +(0.464102 - 0.803848i) q^{70} +(3.00000 - 5.19615i) q^{71} +(3.46410 + 5.00000i) q^{74} +(-1.09808 + 0.633975i) q^{76} +(-8.19615 + 14.1962i) q^{77} +(3.29423 + 1.90192i) q^{79} -0.267949i q^{80} -3.00000i q^{82} +(-4.09808 - 7.09808i) q^{83} +1.00000 q^{85} +(1.73205 + 3.00000i) q^{86} +14.1962i q^{88} +(-7.96410 + 4.59808i) q^{89} +(-10.3923 + 6.00000i) q^{91} +(-0.633975 - 0.366025i) q^{92} +(1.90192 - 1.09808i) q^{94} +(-0.169873 - 0.294229i) q^{95} -4.26795i q^{97} +(-4.33013 - 2.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 4 * q - 2 * q^4 + 6 * q^5	\( 4 q - 2 q^{4} + 6 q^{5} - 8 q^{10} + 12 q^{11} + 12 q^{13} + 2 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{20} + 6 q^{22} + 4 q^{25} - 4 q^{34} + 24 q^{35} + 2 q^{37} + 12 q^{38} + 12 q^{40} + 6 q^{41} - 6 q^{44} - 2 q^{46} - 12 q^{47} - 10 q^{49} - 24 q^{50} - 12 q^{52} - 12 q^{53} + 6 q^{55} - 36 q^{56} - 4 q^{58} + 12 q^{59} - 6 q^{61} - 6 q^{62} - 28 q^{64} + 12 q^{65} + 18 q^{67} - 12 q^{70} + 12 q^{71} + 6 q^{76} - 12 q^{77} - 18 q^{79} - 6 q^{83} + 4 q^{85} - 18 q^{89} - 6 q^{92} + 18 q^{94} - 18 q^{95}+O(q^{100}) \) 4 * q - 2 * q^4 + 6 * q^5 - 8 * q^10 + 12 * q^11 + 12 * q^13 + 2 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^20 + 6 * q^22 + 4 * q^25 - 4 * q^34 + 24 * q^35 + 2 * q^37 + 12 * q^38 + 12 * q^40 + 6 * q^41 - 6 * q^44 - 2 * q^46 - 12 * q^47 - 10 * q^49 - 24 * q^50 - 12 * q^52 - 12 * q^53 + 6 * q^55 - 36 * q^56 - 4 * q^58 + 12 * q^59 - 6 * q^61 - 6 * q^62 - 28 * q^64 + 12 * q^65 + 18 * q^67 - 12 * q^70 + 12 * q^71 + 6 * q^76 - 12 * q^77 - 18 * q^79 - 6 * q^83 + 4 * q^85 - 18 * q^89 - 6 * q^92 + 18 * q^94 - 18 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more