LMFDB - Embedded newform 1386.2.k.d.793.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			793.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1386.793
Dual form			1386.2.k.d.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{11} -4.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(2.50000 + 4.33013i) q^{25} +(2.00000 - 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +9.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +6.00000 q^{41} +11.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-2.00000 - 1.73205i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(4.50000 + 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.00000 q^{71} +(2.00000 + 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(8.00000 - 13.8564i) q^{79} +(-3.00000 + 5.19615i) q^{82} +(-5.50000 + 9.52628i) q^{86} +(0.500000 + 0.866025i) q^{88} +(8.00000 + 6.92820i) q^{91} +3.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + q^{11} - 8 q^{13} + 5 q^{14} - q^{16} + 3 q^{17} + q^{19} - 2 q^{22} - 3 q^{23} + 5 q^{25} + 4 q^{26} - q^{28} + 18 q^{29} - 2 q^{31} - q^{32} - 6 q^{34} + 7 q^{37} + q^{38} + 12 q^{41} + 22 q^{43} + q^{44} - 3 q^{46} - 3 q^{47} + 2 q^{49} - 10 q^{50} + 4 q^{52} - 4 q^{56} - 9 q^{58} + 9 q^{59} + 10 q^{61} + 4 q^{62} + 2 q^{64} + 4 q^{67} + 3 q^{68} - 6 q^{71} + 4 q^{73} + 7 q^{74} - 2 q^{76} + q^{77} + 16 q^{79} - 6 q^{82} - 11 q^{86} + q^{88} + 16 q^{91} + 6 q^{92} - 3 q^{94} - 2 q^{97} - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + q^11 - 8 * q^13 + 5 * q^14 - q^16 + 3 * q^17 + q^19 - 2 * q^22 - 3 * q^23 + 5 * q^25 + 4 * q^26 - q^28 + 18 * q^29 - 2 * q^31 - q^32 - 6 * q^34 + 7 * q^37 + q^38 + 12 * q^41 + 22 * q^43 + q^44 - 3 * q^46 - 3 * q^47 + 2 * q^49 - 10 * q^50 + 4 * q^52 - 4 * q^56 - 9 * q^58 + 9 * q^59 + 10 * q^61 + 4 * q^62 + 2 * q^64 + 4 * q^67 + 3 * q^68 - 6 * q^71 + 4 * q^73 + 7 * q^74 - 2 * q^76 + q^77 + 16 * q^79 - 6 * q^82 - 11 * q^86 + q^88 + 16 * q^91 + 6 * q^92 - 3 * q^94 - 2 * q^97 - 13 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$		0			0
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$		0			0
$22$	−1.00000			−0.213201
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$		0			0
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$		0			0
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$		0			0
$36$		0			0
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$		0			0
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	11.0000			1.67748			0.838742	−	0.544529i	$-0.183292\pi$
$43$	11.0000			1.67748			0.838742	+	0.544529i	$0.183292\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−5.00000			−0.707107
$51$		0			0
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$53$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	−	1.73205i	−0.267261	−	0.231455i
$57$		0			0
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		0			0
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	−0.345207	−	0.938527i	$-0.612191\pi$
$61$	5.00000	−	8.66025i	0.640184	−	1.10883i	0.985391	−	0.170305i	$-0.0544754\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		0			0
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	0.959006	−	0.283387i	$-0.0914581\pi$
$73$	2.00000	+	3.46410i	0.234082	+	0.405442i	−0.724923	+	0.688830i	$0.758125\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000			−0.114708
$77$	0.500000	−	2.59808i	0.0569803	−	0.296078i
$78$		0			0
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$		0			0
$81$		0			0
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$		0			0
$85$		0			0
$86$	−5.50000	+	9.52628i	−0.593080	+	1.02725i
$87$		0			0
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	8.00000	+	6.92820i	0.838628	+	0.726273i
$92$	3.00000			0.312772
$93$		0			0
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$		0			0
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	0.949595	+	0.313478i	$0.101494\pi$
$101$	7.50000	+	12.9904i	0.746278	+	1.29259i	−0.203317	+	0.979113i	$0.565172\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$		0			0
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$		0			0
$111$		0			0
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$		0			0
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$	−9.00000			−0.828517
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	−19.0000			−1.61156			−0.805779	−	0.592216i	$-0.798253\pi$
$139$	−19.0000			−1.61156			−0.805779	+	0.592216i	$0.798253\pi$
$140$		0			0
$141$		0			0
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$		0			0
$145$		0			0
$146$	−4.00000			−0.331042
$147$		0			0
$148$	−7.00000			−0.575396
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	−0.620701	−	0.784047i	$-0.713152\pi$
$149$	4.50000	−	7.79423i	0.368654	−	0.638528i	0.989355	+	0.145519i	$0.0464853\pi$
$150$		0			0
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	0.935857	+	0.352381i	$0.114628\pi$
$151$	9.50000	+	16.4545i	0.773099	+	1.33905i	−0.162758	+	0.986666i	$0.552039\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$		0			0
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$		0			0
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$		0			0
$160$		0			0
$161$	7.50000	−	2.59808i	0.591083	−	0.204757i
$162$		0			0
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$		0			0
$172$	−5.50000	−	9.52628i	−0.419371	−	0.726372i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	2.50000	−	12.9904i	0.188982	−	0.981981i
$176$	−1.00000			−0.0753778
$177$		0			0
$178$		0			0
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	−0.997446	−	0.0714220i	$-0.977246\pi$
$179$	−7.50000	−	12.9904i	−0.560576	−	0.970947i	0.436870	−	0.899525i	$-0.356087\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−10.0000	+	3.46410i	−0.741249	+	0.256776i
$183$		0			0
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$		0			0
$186$		0			0
$187$	−1.50000	+	2.59808i	−0.109691	+	0.189990i
$188$	3.00000			0.218797
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$	0.500000	−	0.866025i	0.0358979	−	0.0621770i
$195$		0			0
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	21.0000			1.49619			0.748094	−	0.663593i	$-0.230969\pi$
$197$	21.0000			1.49619			0.748094	+	0.663593i	$0.230969\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$		0			0
$202$	−15.0000			−1.05540
$203$	−18.0000	−	15.5885i	−1.26335	−	1.09410i
$204$		0			0
$205$		0			0
$206$	2.00000	+	3.46410i	0.139347	+	0.241355i
$207$		0			0
$208$	2.00000	−	3.46410i	0.138675	−	0.240192i
$209$	1.00000			0.0691714
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$	−9.00000	−	15.5885i	−0.615227	−	1.06561i
$215$		0			0
$216$		0			0
$217$	−1.00000	+	5.19615i	−0.0678844	+	0.352738i
$218$	−10.0000			−0.677285
$219$		0			0
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$		0			0
$226$	6.00000	−	10.3923i	0.399114	−	0.691286i
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	0.993210	+	0.116331i	$0.0371134\pi$
$227$	9.00000	+	15.5885i	0.597351	+	1.03464i	−0.395860	+	0.918311i	$0.629553\pi$
$228$		0			0
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	0.0137585	+	0.999905i	$0.495620\pi$
$229$	−13.0000	+	22.5167i	−0.859064	+	1.48794i	−0.872823	+	0.488037i	$0.837713\pi$
$230$		0			0
$231$		0			0
$232$	9.00000			0.590879
$233$	4.50000	−	7.79423i	0.294805	−	0.510617i	−0.680135	−	0.733087i	$-0.738079\pi$
$233$	4.50000	−	7.79423i	0.294805	−	0.510617i	0.974939	+	0.222470i	$0.0714120\pi$
$234$		0			0
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$		0			0
$238$	6.00000	+	5.19615i	0.388922	+	0.336817i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		0			0
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.825131	+	0.564942i	$0.191101\pi$
$241$	14.0000	+	24.2487i	0.901819	+	1.56200i	0.0766885	+	0.997055i	$0.475565\pi$
$242$	−0.500000	−	0.866025i	−0.0321412	−	0.0556702i
$243$		0			0
$244$	−10.0000			−0.640184
$245$		0			0
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$		0			0
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$	0.500000	−	0.866025i	0.0313728	−	0.0543393i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	−0.615948	−	0.787787i	$-0.711227\pi$
$257$	6.00000	−	10.3923i	0.374270	−	0.648254i	0.990217	+	0.139533i	$0.0445601\pi$
$258$		0			0
$259$	−17.5000	+	6.06218i	−1.08740	+	0.376685i
$260$		0			0
$261$		0			0
$262$	9.00000	+	15.5885i	0.556022	+	0.963058i
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$		0			0
$266$	0.500000	−	2.59808i	0.0306570	−	0.159298i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	0.942871	−	0.333157i	$-0.108114\pi$
$269$	3.00000	+	5.19615i	0.182913	+	0.316815i	−0.759958	+	0.649972i	$0.774781\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	−12.0000			−0.724947
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$		0			0
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.719125	−	0.694881i	$-0.755457\pi$
$277$	−16.0000	−	27.7128i	−0.961347	−	1.66510i	−0.242222	−	0.970221i	$-0.577876\pi$
$278$	9.50000	−	16.4545i	0.569772	−	0.986874i
$279$		0			0
$280$		0			0
$281$	15.0000			0.894825			0.447412	−	0.894328i	$-0.352346\pi$
$281$	15.0000			0.894825			0.447412	+	0.894328i	$0.352346\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$		0			0
$286$	4.00000			0.236525
$287$	−12.0000	−	10.3923i	−0.708338	−	0.613438i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$		0			0
$291$		0			0
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$		0			0
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$		0			0
$298$	4.50000	+	7.79423i	0.260678	+	0.451508i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	−22.0000	−	19.0526i	−1.26806	−	1.09817i
$302$	−19.0000			−1.09333
$303$		0			0
$304$	0.500000	+	0.866025i	0.0286770	+	0.0496700i
$305$		0			0
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	−2.50000	+	0.866025i	−0.142451	+	0.0493464i
$309$		0			0
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$		0			0
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	−0.851549	−	0.524276i	$-0.824336\pi$
$313$	0.500000	−	0.866025i	0.0282617	−	0.0489506i	0.879810	+	0.475325i	$0.157669\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$		0			0
$322$	−1.50000	+	7.79423i	−0.0835917	+	0.434355i
$323$	3.00000			0.166924
$324$		0			0
$325$	−10.0000	−	17.3205i	−0.554700	−	0.960769i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$		0			0
$328$	6.00000			0.331295
$329$	7.50000	−	2.59808i	0.413488	−	0.143237i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$		0			0
$333$		0			0
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$		0			0
$337$	−10.0000			−0.544735			−0.272367	−	0.962193i	$-0.587807\pi$
$337$	−10.0000			−0.544735			−0.272367	+	0.962193i	$0.587807\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$		0			0
$340$		0			0
$341$	1.00000	−	1.73205i	0.0541530	−	0.0937958i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	11.0000			0.593080
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	8.00000			0.428230			0.214115	−	0.976808i	$-0.431313\pi$
$349$	8.00000			0.428230			0.214115	+	0.976808i	$0.431313\pi$
$350$	10.0000	+	8.66025i	0.534522	+	0.462910i
$351$		0			0
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	−0.985719	−	0.168397i	$-0.946141\pi$
$353$	−12.0000	−	20.7846i	−0.638696	−	1.10625i	0.347024	−	0.937856i	$-0.387192\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	15.0000			0.792775
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	−0.999590	−	0.0286287i	$-0.990886\pi$
$359$	−9.00000	+	15.5885i	−0.475002	+	0.822727i	0.524588	+	0.851356i	$0.324219\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$		0			0
$364$	2.00000	−	10.3923i	0.104828	−	0.544705i
$365$		0			0
$366$		0			0
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	2.00000	+	3.46410i	0.104399	+	0.180825i	−0.809093	+	0.587680i	$0.800041\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	−0.427051	−	0.904227i	$-0.640448\pi$
$373$	11.0000	−	19.0526i	0.569558	−	0.986504i	0.996610	−	0.0822766i	$-0.0262191\pi$
$374$	−1.50000	−	2.59808i	−0.0775632	−	0.134343i
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$	−36.0000			−1.85409
$378$		0			0
$379$	14.0000			0.719132			0.359566	−	0.933120i	$-0.382925\pi$
$379$	14.0000			0.719132			0.359566	+	0.933120i	$0.382925\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$		0			0
$386$	−10.0000			−0.508987
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	−10.5000	+	18.1865i	−0.528982	+	0.916224i
$395$		0			0
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$	20.0000			1.00251
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	−0.931158	−	0.364615i	$-0.881200\pi$
$401$	−3.00000	+	5.19615i	−0.149813	+	0.259483i	0.781345	+	0.624099i	$0.214534\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	7.50000	−	12.9904i	0.373139	−	0.646296i
$405$		0			0
$406$	22.5000	−	7.79423i	1.11666	−	0.386821i
$407$	7.00000			0.346977
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$		0			0
$412$	−4.00000			−0.197066
$413$	4.50000	−	23.3827i	0.221431	−	1.15059i
$414$		0			0
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$		0			0
$418$	−0.500000	+	0.866025i	−0.0244558	+	0.0423587i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$		0			0
$424$		0			0
$425$	−7.50000	+	12.9904i	−0.363803	+	0.630126i
$426$		0			0
$427$	−25.0000	+	8.66025i	−1.20983	+	0.419099i
$428$	18.0000			0.870063
$429$		0			0
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$		0			0
$433$	29.0000			1.39365			0.696826	−	0.717241i	$-0.254595\pi$
$433$	29.0000			1.39365			0.696826	+	0.717241i	$0.254595\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	1.50000	+	2.59808i	0.0717547	+	0.124283i
$438$		0			0
$439$	18.5000	−	32.0429i	0.882957	−	1.52933i	0.0349192	−	0.999390i	$-0.488883\pi$
$439$	18.5000	−	32.0429i	0.882957	−	1.52933i	0.848038	−	0.529936i	$-0.177784\pi$
$440$		0			0
$441$		0			0
$442$	12.0000			0.570782
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	−0.828190	−	0.560448i	$-0.810629\pi$
$443$	1.50000	−	2.59808i	0.0712672	−	0.123438i	0.899457	+	0.437009i	$0.143962\pi$
$444$		0			0
$445$		0			0
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	−2.00000	−	1.73205i	−0.0944911	−	0.0818317i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$		0			0
$454$	−18.0000			−0.844782
$455$		0			0
$456$		0			0
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	−0.888466	−	0.458942i	$-0.848229\pi$
$457$	−1.00000	+	1.73205i	−0.0467780	+	0.0810219i	0.841688	+	0.539964i	$0.181562\pi$
$458$	−13.0000	−	22.5167i	−0.607450	−	1.05213i
$459$		0			0
$460$		0			0
$461$	−21.0000			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$462$		0			0
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−16.5000	+	28.5788i	−0.763529	+	1.32247i	0.177492	+	0.984122i	$0.443202\pi$
$467$	−16.5000	+	28.5788i	−0.763529	+	1.32247i	−0.941021	+	0.338349i	$0.890132\pi$
$468$		0			0
$469$	2.00000	−	10.3923i	0.0923514	−	0.479872i
$470$		0			0
$471$		0			0
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	5.50000	+	9.52628i	0.252890	+	0.438019i
$474$		0			0
$475$	5.00000			0.229416
$476$	−7.50000	+	2.59808i	−0.343762	+	0.119083i
$477$		0			0
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$		0			0
$481$	−14.0000	+	24.2487i	−0.638345	+	1.10565i
$482$	−28.0000			−1.27537
$483$		0			0
$484$	1.00000			0.0454545
$485$		0			0
$486$		0			0
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	0.907776	−	0.419456i	$-0.137779\pi$
$487$	2.00000	+	3.46410i	0.0906287	+	0.156973i	−0.817147	+	0.576429i	$0.804446\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$		0			0
$490$		0			0
$491$	36.0000			1.62466			0.812329	−	0.583200i	$-0.198200\pi$
$491$	36.0000			1.62466			0.812329	+	0.583200i	$0.198200\pi$
$492$		0			0
$493$	13.5000	+	23.3827i	0.608009	+	1.05310i
$494$	−2.00000	−	3.46410i	−0.0899843	−	0.155857i
$495$		0			0
$496$	2.00000			0.0898027
$497$	6.00000	+	5.19615i	0.269137	+	0.233079i
$498$		0			0
$499$	5.00000	−	8.66025i	0.223831	−	0.387686i	−0.732137	−	0.681157i	$-0.761477\pi$
$499$	5.00000	−	8.66025i	0.223831	−	0.387686i	0.955968	+	0.293471i	$0.0948104\pi$
$500$		0			0
$501$		0			0
$502$	7.50000	−	12.9904i	0.334741	−	0.579789i
$503$	−30.0000			−1.33763			−0.668817	−	0.743427i	$-0.733199\pi$
$503$	−30.0000			−1.33763			−0.668817	+	0.743427i	$0.733199\pi$
$504$		0			0
$505$		0			0
$506$	1.50000	−	2.59808i	0.0666831	−	0.115499i
$507$		0			0
$508$	0.500000	+	0.866025i	0.0221839	+	0.0384237i
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	0.123187	+	0.992384i	$0.460689\pi$
$509$	−18.0000	+	31.1769i	−0.797836	+	1.38189i	−0.921023	+	0.389509i	$0.872645\pi$
$510$		0			0
$511$	2.00000	−	10.3923i	0.0884748	−	0.459728i
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.00000	+	10.3923i	0.264649	+	0.458385i
$515$		0			0
$516$		0			0
$517$	−3.00000			−0.131940
$518$	3.50000	−	18.1865i	0.153781	−	0.799070i
$519$		0			0
$520$		0			0
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	−0.981347	−	0.192244i	$-0.938423\pi$
$521$	−15.0000	−	25.9808i	−0.657162	−	1.13824i	0.324185	−	0.945994i	$-0.394910\pi$
$522$		0			0
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−18.0000			−0.786334
$525$		0			0
$526$	18.0000			0.784837
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$	2.00000	+	1.73205i	0.0867110	+	0.0750939i
$533$	−24.0000			−1.03956
$534$		0			0
$535$		0			0
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−6.00000			−0.258678
$539$	−5.50000	+	4.33013i	−0.236902	+	0.186512i
$540$		0			0
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	−0.996867	−	0.0790969i	$-0.974796\pi$
$541$	−10.0000	+	17.3205i	−0.429934	+	0.744667i	0.566933	+	0.823764i	$0.308130\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$		0			0
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		0			0
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$	6.00000	−	10.3923i	0.256307	−	0.443937i
$549$		0			0
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	4.50000	−	7.79423i	0.191706	−	0.332045i
$552$		0			0
$553$	−40.0000	+	13.8564i	−1.70097	+	0.589234i
$554$	32.0000			1.35955
$555$		0			0
$556$	9.50000	+	16.4545i	0.402890	+	0.697826i
$557$	22.5000	+	38.9711i	0.953356	+	1.65126i	0.738087	+	0.674705i	$0.235729\pi$
$557$	22.5000	+	38.9711i	0.953356	+	1.65126i	0.215268	+	0.976555i	$0.430937\pi$
$558$		0			0
$559$	−44.0000			−1.86100
$560$		0			0
$561$		0			0
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	−0.943560	−	0.331202i	$-0.892546\pi$
$563$	−18.0000	−	31.1769i	−0.758610	−	1.31395i	0.184950	−	0.982748i	$-0.440788\pi$
$564$		0			0
$565$		0			0
$566$	20.0000			0.840663
$567$		0			0
$568$	−3.00000			−0.125877
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	−0.997703	−	0.0677445i	$-0.978420\pi$
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	0.557520	+	0.830164i	$0.311753\pi$
$570$		0			0
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	−0.991763	−	0.128085i	$-0.959117\pi$
$571$	−14.5000	−	25.1147i	−0.606806	−	1.05102i	0.384957	−	0.922934i	$-0.374216\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		0			0
$574$	15.0000	−	5.19615i	0.626088	−	0.216883i
$575$	−15.0000			−0.625543
$576$		0			0
$577$	11.0000	+	19.0526i	0.457936	+	0.793168i	0.998852	−	0.0479084i	$-0.0152556\pi$
$577$	11.0000	+	19.0526i	0.457936	+	0.793168i	−0.540916	+	0.841077i	$0.681922\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$	2.00000	+	3.46410i	0.0827606	+	0.143346i
$585$		0			0
$586$	4.50000	−	7.79423i	0.185893	−	0.321977i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	−2.00000			−0.0824086
$590$		0			0
$591$		0			0
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	−0.758714	−	0.651424i	$-0.774172\pi$
$593$	4.50000	−	7.79423i	0.184793	−	0.320071i	0.943507	+	0.331353i	$0.107505\pi$
$594$		0			0
$595$		0			0
$596$	−9.00000			−0.368654
$597$		0			0
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.660006	+	0.751260i	$0.270554\pi$
$599$	24.0000	+	41.5692i	0.980613	+	1.69847i	0.320607	+	0.947212i	$0.396113\pi$
$600$		0			0
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$	27.5000	−	9.52628i	1.12082	−	0.388262i
$603$		0			0
$604$	9.50000	−	16.4545i	0.386550	−	0.669523i
$605$		0			0
$606$		0			0
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−1.00000			−0.0405554
$609$		0			0
$610$		0			0
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$		0			0
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$		0			0
$616$	0.500000	−	2.59808i	0.0201456	−	0.104679i
$617$	−18.0000			−0.724653			−0.362326	−	0.932051i	$-0.618017\pi$
$617$	−18.0000			−0.724653			−0.362326	+	0.932051i	$0.618017\pi$
$618$		0			0
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	0.690365	−	0.723462i	$-0.257450\pi$
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	−0.971718	+	0.236143i	$0.924117\pi$
$620$		0			0
$621$		0			0
$622$	21.0000			0.842023
$623$		0			0
$624$		0			0
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	21.0000			0.837325
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	8.00000	−	13.8564i	0.318223	−	0.551178i
$633$		0			0
$634$	−6.00000	−	10.3923i	−0.238290	−	0.412731i
$635$		0			0
$636$		0			0
$637$	−4.00000	−	27.7128i	−0.158486	−	1.09802i
$638$	−9.00000			−0.356313
$639$		0			0
$640$		0			0
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−46.0000			−1.81406			−0.907031	−	0.421063i	$-0.861657\pi$
$643$	−46.0000			−1.81406			−0.907031	+	0.421063i	$0.861657\pi$
$644$	−6.00000	−	5.19615i	−0.236433	−	0.204757i
$645$		0			0
$646$	−1.50000	+	2.59808i	−0.0590167	+	0.102220i
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.758654	+	0.651494i	$0.225858\pi$
$647$	24.0000	+	41.5692i	0.943537	+	1.63425i	0.184884	+	0.982760i	$0.440809\pi$
$648$		0			0
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	20.0000			0.784465
$651$		0			0
$652$	2.00000			0.0783260
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	−0.529799	−	0.848123i	$-0.677733\pi$
$653$	12.0000	−	20.7846i	0.469596	−	0.813365i	0.999396	+	0.0347583i	$0.0110661\pi$
$654$		0			0
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	−1.50000	+	7.79423i	−0.0584761	+	0.303851i
$659$	18.0000			0.701180			0.350590	−	0.936529i	$-0.385981\pi$
$659$	18.0000			0.701180			0.350590	+	0.936529i	$0.385981\pi$
$660$		0			0
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	−0.974776	−	0.223184i	$-0.928355\pi$
$661$	−17.5000	−	30.3109i	−0.680671	−	1.17896i	0.294105	−	0.955773i	$-0.404978\pi$
$662$	5.00000	+	8.66025i	0.194331	+	0.336590i
$663$		0			0
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−13.5000	+	23.3827i	−0.522722	+	0.905381i
$668$	6.00000	+	10.3923i	0.232147	+	0.402090i
$669$		0			0
$670$		0			0
$671$	10.0000			0.386046
$672$		0			0
$673$	44.0000			1.69608			0.848038	−	0.529936i	$-0.177784\pi$
$673$	44.0000			1.69608			0.848038	+	0.529936i	$0.177784\pi$
$674$	5.00000	−	8.66025i	0.192593	−	0.333581i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	0.352549	+	0.935793i	$0.385315\pi$
$677$	−16.5000	+	28.5788i	−0.634147	+	1.09837i	−0.986695	+	0.162581i	$0.948018\pi$
$678$		0			0
$679$	2.00000	+	1.73205i	0.0767530	+	0.0664700i
$680$		0			0
$681$		0			0
$682$	1.00000	+	1.73205i	0.0382920	+	0.0663237i
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	0.987275	+	0.159022i	$0.0508342\pi$
$683$	16.5000	+	28.5788i	0.631355	+	1.09354i	−0.355920	+	0.934516i	$0.615832\pi$
$684$		0			0
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$		0			0
$690$		0			0
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$		0			0
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	−4.00000	+	6.92820i	−0.151402	+	0.262236i
$699$		0			0
$700$	−12.5000	+	4.33013i	−0.472456	+	0.163663i
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$		0			0
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$		0			0
$706$	24.0000			0.903252
$707$	7.50000	−	38.9711i	0.282067	−	1.46566i
$708$		0			0
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	6.00000			0.224702
$714$		0			0
$715$		0			0
$716$	−7.50000	+	12.9904i	−0.280288	+	0.485473i
$717$		0			0
$718$	−9.00000	−	15.5885i	−0.335877	−	0.581756i
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	−0.769832	−	0.638247i	$-0.779660\pi$
$719$	4.50000	−	7.79423i	0.167822	−	0.290676i	0.937654	+	0.347571i	$0.112993\pi$
$720$		0			0
$721$	−10.0000	+	3.46410i	−0.372419	+	0.129010i
$722$	−18.0000			−0.669891
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	22.5000	+	38.9711i	0.835629	+	1.44735i
$726$		0			0
$727$	−22.0000			−0.815935			−0.407967	−	0.912996i	$-0.633762\pi$
$727$	−22.0000			−0.815935			−0.407967	+	0.912996i	$0.633762\pi$
$728$	8.00000	+	6.92820i	0.296500	+	0.256776i
$729$		0			0
$730$		0			0
$731$	16.5000	+	28.5788i	0.610275	+	1.05703i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	−4.00000			−0.147643
$735$		0			0
$736$	3.00000			0.110581
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$		0			0
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	0.900464	−	0.434930i	$-0.143227\pi$
$739$	2.00000	+	3.46410i	0.0735712	+	0.127429i	−0.826893	+	0.562360i	$0.809894\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.00000			−0.220119			−0.110059	−	0.993925i	$-0.535104\pi$
$743$	−6.00000			−0.220119			−0.110059	+	0.993925i	$0.535104\pi$
$744$		0			0
$745$		0			0
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$		0			0
$748$	3.00000			0.109691
$749$	45.0000	−	15.5885i	1.64426	−	0.569590i
$750$		0			0
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	−0.883694	−	0.468065i	$-0.844951\pi$
$751$	−1.00000	+	1.73205i	−0.0364905	+	0.0632034i	0.847203	+	0.531269i	$0.178285\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$		0			0
$754$	18.0000	−	31.1769i	0.655521	−	1.13540i
$755$		0			0
$756$		0			0
$757$	−7.00000			−0.254419			−0.127210	−	0.991876i	$-0.540602\pi$
$757$	−7.00000			−0.254419			−0.127210	+	0.991876i	$0.540602\pi$
$758$	−7.00000	+	12.1244i	−0.254251	+	0.440376i
$759$		0			0
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	5.00000	−	25.9808i	0.181012	−	0.940567i
$764$		0			0
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$	−18.0000	−	31.1769i	−0.649942	−	1.12573i
$768$		0			0
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$		0			0
$772$	5.00000	−	8.66025i	0.179954	−	0.311689i
$773$	27.0000	+	46.7654i	0.971123	+	1.68203i	0.692179	+	0.721726i	$0.256651\pi$
$773$	27.0000	+	46.7654i	0.971123	+	1.68203i	0.278944	+	0.960307i	$0.410016\pi$
$774$		0			0
$775$	5.00000	−	8.66025i	0.179605	−	0.311086i
$776$	−1.00000			−0.0358979
$777$		0			0
$778$	−12.0000			−0.430221
$779$	3.00000	−	5.19615i	0.107486	−	0.186171i
$780$		0			0
$781$	−1.50000	−	2.59808i	−0.0536742	−	0.0929665i
$782$	4.50000	−	7.79423i	0.160920	−	0.278721i
$783$		0			0
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	0.584951	−	0.811069i	$-0.301114\pi$
$787$	−11.5000	−	19.9186i	−0.409931	−	0.710021i	−0.994882	+	0.101048i	$0.967780\pi$
$788$	−10.5000	−	18.1865i	−0.374047	−	0.647868i
$789$		0			0
$790$		0			0
$791$	24.0000	+	20.7846i	0.853342	+	0.739016i
$792$		0			0
$793$	−20.0000	+	34.6410i	−0.710221	+	1.23014i
$794$	6.50000	+	11.2583i	0.230676	+	0.399543i
$795$		0			0
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	−9.00000			−0.318397
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$		0			0
$802$	−3.00000	−	5.19615i	−0.105934	−	0.183483i
$803$	−2.00000	+	3.46410i	−0.0705785	+	0.122245i
$804$		0			0
$805$		0			0
$806$	−8.00000			−0.281788
$807$		0			0
$808$	7.50000	+	12.9904i	0.263849	+	0.457000i
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−4.50000	+	23.3827i	−0.157919	+	0.820571i
$813$		0			0
$814$	−3.50000	+	6.06218i	−0.122675	+	0.212479i
$815$		0			0
$816$		0			0
$817$	5.50000	−	9.52628i	0.192421	−	0.333282i
$818$	14.0000			0.489499
$819$		0			0
$820$		0			0
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	−0.222731	−	0.974880i	$-0.571497\pi$
$821$	21.0000	−	36.3731i	0.732905	−	1.26943i	0.955636	−	0.294549i	$-0.0951694\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	2.00000	−	3.46410i	0.0696733	−	0.120678i
$825$		0			0
$826$	18.0000	+	15.5885i	0.626300	+	0.542392i
$827$	−42.0000			−1.46048			−0.730242	−	0.683189i	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		0			0
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$		0			0
$831$		0			0
$832$	−4.00000			−0.138675
$833$	−16.5000	+	12.9904i	−0.571691	+	0.450090i
$834$		0			0
$835$		0			0
$836$	−0.500000	−	0.866025i	−0.0172929	−	0.0299521i
$837$		0			0
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$	36.0000			1.24286			0.621429	−	0.783470i	$-0.286552\pi$
$839$	36.0000			1.24286			0.621429	+	0.783470i	$0.286552\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−8.50000	+	14.7224i	−0.292929	+	0.507369i
$843$		0			0
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$		0			0
$846$		0			0
$847$	2.50000	−	0.866025i	0.0859010	−	0.0297570i
$848$		0			0
$849$		0			0
$850$	−7.50000	−	12.9904i	−0.257248	−	0.445566i
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$		0			0
$853$	20.0000			0.684787			0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000			0.684787			0.342393	+	0.939557i	$0.388762\pi$
$854$	5.00000	−	25.9808i	0.171096	−	0.889043i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	−28.5000	−	49.3634i	−0.973541	−	1.68622i	−0.684667	−	0.728856i	$-0.740052\pi$
$857$	−28.5000	−	49.3634i	−0.973541	−	1.68622i	−0.288875	−	0.957367i	$-0.593281\pi$
$858$		0			0
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$		0			0
$861$		0			0
$862$	12.0000			0.408722
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	−0.586235	−	0.810141i	$-0.699391\pi$
$863$	12.0000	−	20.7846i	0.408485	−	0.707516i	0.994720	+	0.102624i	$0.0327240\pi$
$864$		0			0
$865$		0			0
$866$	−14.5000	+	25.1147i	−0.492730	+	0.853433i
$867$		0			0
$868$	5.00000	−	1.73205i	0.169711	−	0.0587896i
$869$	16.0000			0.542763
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$		0			0
$874$	−3.00000			−0.101477
$875$		0			0
$876$		0			0
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	0.458606	+	0.888640i	$0.348349\pi$
$877$	−16.0000	+	27.7128i	−0.540282	+	0.935795i	−0.998888	+	0.0471555i	$0.984984\pi$
$878$	18.5000	+	32.0429i	0.624345	+	1.08140i
$879$		0			0
$880$		0			0
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$		0			0
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	1.50000	+	2.59808i	0.0503935	+	0.0872841i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	2.00000	+	1.73205i	0.0670778	+	0.0580911i
$890$		0			0
$891$		0			0
$892$	−4.00000	−	6.92820i	−0.133930	−	0.231973i
$893$	1.50000	+	2.59808i	0.0501956	+	0.0869413i
$894$		0			0
$895$		0			0
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$		0			0
$898$		0			0
$899$	−9.00000	−	15.5885i	−0.300167	−	0.519904i
$900$		0			0
$901$		0			0
$902$	−6.00000			−0.199778
$903$		0			0
$904$	−12.0000			−0.399114
$905$		0			0
$906$		0			0
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	0.979531	+	0.201291i	$0.0645138\pi$
$907$	20.0000	+	34.6410i	0.664089	+	1.15024i	−0.315442	+	0.948945i	$0.602153\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$		0			0
$910$		0			0
$911$	−9.00000			−0.298183			−0.149092	−	0.988823i	$-0.547635\pi$
$911$	−9.00000			−0.298183			−0.149092	+	0.988823i	$0.547635\pi$
$912$		0			0
$913$		0			0
$914$	−1.00000	−	1.73205i	−0.0330771	−	0.0572911i
$915$		0			0
$916$	26.0000			0.859064
$917$	−45.0000	+	15.5885i	−1.48603	+	0.514776i
$918$		0			0
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$		0			0
$921$		0			0
$922$	10.5000	−	18.1865i	0.345799	−	0.598942i
$923$	12.0000			0.394985
$924$		0			0
$925$	35.0000			1.15079
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$		0			0
$928$	−4.50000	−	7.79423i	−0.147720	−	0.255858i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	6.50000	+	2.59808i	0.213029	+	0.0851485i
$932$	−9.00000			−0.294805
$933$		0			0
$934$	−16.5000	−	28.5788i	−0.539896	−	0.935128i
$935$		0			0
$936$		0			0
$937$	8.00000			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$937$	8.00000			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$938$	8.00000	+	6.92820i	0.261209	+	0.226214i
$939$		0			0
$940$		0			0
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	0.642567	−	0.766229i	$-0.277869\pi$
$941$	−10.5000	−	18.1865i	−0.342290	−	0.592864i	−0.984858	+	0.173365i	$0.944536\pi$
$942$		0			0
$943$	−9.00000	+	15.5885i	−0.293080	+	0.507630i
$944$	−9.00000			−0.292925
$945$		0			0
$946$	−11.0000			−0.357641
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	−0.840624	−	0.541619i	$-0.817812\pi$
$947$	1.50000	−	2.59808i	0.0487435	−	0.0844261i	0.889368	+	0.457193i	$0.151145\pi$
$948$		0			0
$949$	−8.00000	−	13.8564i	−0.259691	−	0.449798i
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$		0			0
$952$	1.50000	−	7.79423i	0.0486153	−	0.252612i
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$		0			0
$958$	−6.00000			−0.193851
$959$	6.00000	−	31.1769i	0.193750	−	1.00676i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−14.0000	−	24.2487i	−0.451378	−	0.781810i
$963$		0			0
$964$	14.0000	−	24.2487i	0.450910	−	0.780998i
$965$		0			0
$966$		0			0
$967$	−37.0000			−1.18984			−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000			−1.18984			−0.594920	+	0.803785i	$0.702816\pi$
$968$	−0.500000	+	0.866025i	−0.0160706	+	0.0278351i
$969$		0			0
$970$		0			0
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	38.0000	+	32.9090i	1.21822	+	1.05501i
$974$	−4.00000			−0.128168
$975$		0			0
$976$	5.00000	+	8.66025i	0.160046	+	0.277208i
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	0.753942	−	0.656941i	$-0.228150\pi$
$977$	−6.00000	−	10.3923i	−0.191957	−	0.332479i	−0.945899	+	0.324462i	$0.894817\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	−0.989122	−	0.147100i	$-0.953006\pi$
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	0.367168	−	0.930155i	$-0.380327\pi$
$984$		0			0
$985$		0			0
$986$	−27.0000			−0.859855
$987$		0			0
$988$	4.00000			0.127257
$989$	−16.5000	+	28.5788i	−0.524669	+	0.908754i
$990$		0			0
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	0.795474	−	0.605988i	$-0.207222\pi$
$991$	−4.00000	−	6.92820i	−0.127064	−	0.220082i	−0.922538	+	0.385906i	$0.873889\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$		0			0
$994$	−7.50000	+	2.59808i	−0.237886	+	0.0824060i
$995$		0			0
$996$		0			0
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	0.997938	−	0.0641836i	$-0.0204443\pi$
$997$	14.0000	+	24.2487i	0.443384	+	0.767964i	−0.554554	+	0.832148i	$0.687111\pi$
$998$	5.00000	+	8.66025i	0.158272	+	0.274136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.d.793.1		2
3.2	odd	2		462.2.i.b.331.1	yes	2
7.2	even	3		9702.2.a.bl.1.1		1
7.4	even	3	inner	1386.2.k.d.991.1		2
7.5	odd	6		9702.2.a.bn.1.1		1
21.2	odd	6		3234.2.a.l.1.1		1
21.5	even	6		3234.2.a.f.1.1		1
21.11	odd	6		462.2.i.b.67.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.b.67.1	✓	2	21.11	odd	6
462.2.i.b.331.1	yes	2	3.2	odd	2
1386.2.k.d.793.1		2	1.1	even	1	trivial
1386.2.k.d.991.1		2	7.4	even	3	inner
3234.2.a.f.1.1		1	21.5	even	6
3234.2.a.l.1.1		1	21.2	odd	6
9702.2.a.bl.1.1		1	7.2	even	3
9702.2.a.bn.1.1		1	7.5	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.00000 - 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{11} -4.00000 q^{13} +(2.50000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(0.500000 - 0.866025i) q^{19} -1.00000 q^{22} +(-1.50000 + 2.59808i) q^{23} +(2.50000 + 4.33013i) q^{25} +(2.00000 - 3.46410i) q^{26} +(-0.500000 + 2.59808i) q^{28} +9.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(3.50000 - 6.06218i) q^{37} +(0.500000 + 0.866025i) q^{38} +6.00000 q^{41} +11.0000 q^{43} +(0.500000 - 0.866025i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(2.00000 + 3.46410i) q^{52} +(-2.00000 - 1.73205i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(4.50000 + 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} -3.00000 q^{71} +(2.00000 + 3.46410i) q^{73} +(3.50000 + 6.06218i) q^{74} -1.00000 q^{76} +(0.500000 - 2.59808i) q^{77} +(8.00000 - 13.8564i) q^{79} +(-3.00000 + 5.19615i) q^{82} +(-5.50000 + 9.52628i) q^{86} +(0.500000 + 0.866025i) q^{88} +(8.00000 + 6.92820i) q^{91} +3.00000 q^{92} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{97} +(-6.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 4 q^{7} + 2 q^{8} + q^{11} - 8 q^{13} + 5 q^{14} - q^{16} + 3 q^{17} + q^{19} - 2 q^{22} - 3 q^{23} + 5 q^{25} + 4 q^{26} - q^{28} + 18 q^{29} - 2 q^{31} - q^{32} - 6 q^{34} + 7 q^{37} + q^{38} + 12 q^{41} + 22 q^{43} + q^{44} - 3 q^{46} - 3 q^{47} + 2 q^{49} - 10 q^{50} + 4 q^{52} - 4 q^{56} - 9 q^{58} + 9 q^{59} + 10 q^{61} + 4 q^{62} + 2 q^{64} + 4 q^{67} + 3 q^{68} - 6 q^{71} + 4 q^{73} + 7 q^{74} - 2 q^{76} + q^{77} + 16 q^{79} - 6 q^{82} - 11 q^{86} + q^{88} + 16 q^{91} + 6 q^{92} - 3 q^{94} - 2 q^{97} - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^7 + 2 * q^8 + q^11 - 8 * q^13 + 5 * q^14 - q^16 + 3 * q^17 + q^19 - 2 * q^22 - 3 * q^23 + 5 * q^25 + 4 * q^26 - q^28 + 18 * q^29 - 2 * q^31 - q^32 - 6 * q^34 + 7 * q^37 + q^38 + 12 * q^41 + 22 * q^43 + q^44 - 3 * q^46 - 3 * q^47 + 2 * q^49 - 10 * q^50 + 4 * q^52 - 4 * q^56 - 9 * q^58 + 9 * q^59 + 10 * q^61 + 4 * q^62 + 2 * q^64 + 4 * q^67 + 3 * q^68 - 6 * q^71 + 4 * q^73 + 7 * q^74 - 2 * q^76 + q^77 + 16 * q^79 - 6 * q^82 - 11 * q^86 + q^88 + 16 * q^91 + 6 * q^92 - 3 * q^94 - 2 * q^97 - 13 * q^98

Introduction

L-functions

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